lrslib-073/0000777000175000017500000000000014626240571011355 5ustar avisavislrslib-073/2nash.c0000777000175000017500000000456714625766573012571 0ustar avisavis// 2nash.c v1.0a Jan 15, 2009 // Hack of nlrs.c by Conor Meagher to run lrs simultaneously on n processors for n input files // runs lrsnash on input files A B in both orders simultaneously, terminating when first proc finishes // output goes in third argument if any, else in file: out #include #include #include #include #include int main(int argc, char *argv[]) { pid_t cpid[argc - 1], w; char buffer [250]; int status,l,j; if (argc < 3 || argc > 4) { printf("Usage: 2nash A B [outfile]\n"); return(0); } for(l = 1; l < 3; l++) { cpid[l -1] = fork(); if (cpid[l -1] == -1) { perror("fork"); exit(EXIT_FAILURE); } if(cpid[l-1] == 0) { //forked threads // n= sprintf(buffer, "lrs %s > out%i", argv[l], l); if(l==1) { sprintf(buffer, "lrsnash %s %s > out%i", argv[1], argv[2], l); } else { sprintf(buffer, "lrsnash %s %s > out%i", argv[2], argv[1], l); } system(buffer); _exit(0); } } // main thread w = wait(&status); for(j = 1; j < 3; j++) { if(w == cpid[j-1]) { // this child finished first if(j==1) printf("lrsnash %s %s finished first\n", argv[1], argv[2]); else { printf("lrsnash %s %s finished first\n", argv[2], argv[1]); printf("player numbers will be reversed in output\n"); } if(argc == 4) { printf("output file: %s\n", argv[3]); sprintf(buffer, "/bin/mv -f out%i %s", j, argv[3]); } else { printf("output file: out\n"); sprintf(buffer, "/bin/mv -f out%i out", j); } system(buffer); } else { sprintf(buffer, "/bin/rm -f out%i", j); system(buffer); } } printf("the other process will be "); /*...will be killed */ fflush(stdout); kill(0,9); exit(EXIT_SUCCESS); } lrslib-073/buffer.c0000777000175000017500000000541514625766573013020 0ustar avisavis /* buffer.c Reads standard input and builds a circular buffer of maxbuffer lines */ /* input line should have max length maxline and is printed only if it is not in the buffer */ /* calling arguments: maxline maxbuffer */ /* defaults: 50000 500 */ #include #include #include #define MAXBUFFER 5000 /*max number of lines in buffer */ char *line; int maxline; int Getline(void); void notimpl(char s[]); int main(int argc, char *argv[]) { extern int maxline; extern char *line; int i; int bufsize; int next; int count, counton; char *c; char *buffer [MAXBUFFER]; int maxbuffer=500; void *calloc(); maxline=50000; /* allocate space for buffer */ if (argc >= 2 ) maxline=atoi(argv[1])+2; /* allow for \n and \0 */ if (maxline <= 2 ) notimpl("line length must be greater than zero"); if (argc >= 3 ) maxbuffer=atoi(argv[2]); if (maxbuffer <= 0 ) notimpl("buffer length must be greater than zero"); for(i=0;i 0 ) { i=0; if(strncmp(line,"end",3)==0) counton=0; while ( i <= bufsize && (strcmp(line,buffer[i])) != 0 ) i++; if ( i > bufsize ) /* write out line and put in buffer */ { next++; if ( next > maxbuffer-1 ) next=0; if ( bufsize < maxbuffer-1 ) bufsize++; c=strcpy(buffer[next],line); printf("%s",line); if(counton)count++; } if(strncmp(line,"begin",5)==0) counton=1; } printf("\n*Number of output lines between begin/end = %d",count); if(count > maxbuffer ) printf("\n*Buffer size of %d lines exceeded-some duplicates may remain",maxbuffer); else printf("\n*All duplicates removed"); printf("\n"); return 0; } /* getline from KR P.32 */ int Getline(void) { int c,i; extern int maxline; extern char *line; for (i=0;i #include #include "lrsdriver.h" #include "lrslib.h" #define MAXCOL 1000 /* maximum number of colums */ void makecyclic (lrs_dic *P, lrs_dat *Q); int main (int argc, char *argv[]) { lrs_dic *P; /* structure for holding current dictionary and indices */ lrs_dat *Q; /* structure for holding static problem data */ lrs_mp_vector output; /* one line of output:ray,vertex,facet,linearity */ lrs_mp_matrix Lin; /* holds input linearities if any are found */ long i; long col; /* output column index for dictionary */ /* Global initialization - done once */ if ( !lrs_init ("\n*chdemo:")) return 1; /* compute the convex hull of a set of cyclic polytopes */ /* given by V-representations, dimension 2,...,7 */ for(i=1;i<=6;i++) { /* allocate and init structure for static problem data */ Q = lrs_alloc_dat ("LRS globals"); if (Q == NULL) return 1; /* now flags in lrs_dat can be set */ Q->m=i+3; /* number of input rows = number of vertices */ Q->n=i+2; /* number of input columns (dimension + 1 ) */ Q->hull = TRUE; /* convex hull problem: facet enumeration */ Q->polytope= TRUE; /* input is a polytope */ Q->getvolume= TRUE; /* compute the volume */ output = lrs_alloc_mp_vector (Q->n); P = lrs_alloc_dic (Q); /* allocate and initialize lrs_dic */ if (P == NULL) return 1; /* Build polyhedron: constraints and objective */ printf("\n\n*cyclic polytope: %ld vertices in R^%ld",Q->m,Q->n-1); makecyclic(P,Q); /* code from here is borrowed from lrs_main */ /* Pivot to a starting dictionary */ if (!lrs_getfirstbasis (&P, Q, &Lin, FALSE)) return 1; /* There may have been column redundancy */ /* (although not for this example of cyclic polytopes) */ /* If so the linearity space is obtained and redundant */ /* columns are removed. User can access linearity space */ /* from lrs_mp_matrix Lin dimensions nredundcol x d+1 */ for (col = 0L; col < Q->nredundcol; col++) /* print linearity space */ lrs_printoutput (Q, Lin[col]); /* Array Lin[][] holds the coeffs. */ /* We initiate reverse search from this dictionary */ /* getting new dictionaries until the search is complete */ /* User can access each output line from output which is */ /* vertex/ray/facet from the lrs_mp_vector output */ do { for (col = 0; col <= P->d; col++) if (lrs_getsolution (P, Q, output, col)) lrs_printoutput (Q, output); } while (lrs_getnextbasis (&P, Q, FALSE)); lrs_printtotals (P, Q); /* print final totals */ /* free space : do not change order of next 3 lines! */ lrs_clear_mp_vector (output, Q->n); lrs_free_dic (P,Q); /* deallocate lrs_dic */ lrs_free_dat (Q); /* deallocate lrs_dat */ } /* end of loop for i=3 ... */ lrs_close ("chdemo:"); printf("\n"); return 0; } /* end of main */ void makecyclic (lrs_dic *P, lrs_dat *Q) /* generate vertices of a cyclic polytope */ /* (t, t^2, ..., t^n-1 ), t=1..m */ { long num[MAXCOL]; long den[MAXCOL]; long row, j, t; long m=Q->m; long n=Q->n; for (row=1;row<=m;row++) { t=1; for(j=0;j Copyright (C) 19yy This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA. Also add information on how to contact you by electronic and paper mail. If the program is interactive, make it output a short notice like this when it starts in an interactive mode: Gnomovision version 69, Copyright (C) 19yy name of author Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'. This is free software, and you are welcome to redistribute it under certain conditions; type `show c' for details. The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, the commands you use may be called something other than `show w' and `show c'; they could even be mouse-clicks or menu items--whatever suits your program. You should also get your employer (if you work as a programmer) or your school, if any, to sign a "copyright disclaimer" for the program, if necessary. Here is a sample; alter the names: Yoyodyne, Inc., hereby disclaims all copyright interest in the program `Gnomovision' (which makes passes at compilers) written by James Hacker. , 1 April 1989 Ty Coon, President of Vice This General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Library General Public License instead of this License. lrslib-073/cube.ext0000777000175000017500000000022514625766600013024 0ustar avisaviscube V-representation begin 8 4 integer 1 1 1 1 1 0 1 1 1 1 0 1 1 0 0 1 1 1 1 0 1 0 1 0 1 1 0 0 1 0 0 0 end lrslib-073/cube.ine0000777000175000017500000000017314625766605013006 0ustar avisaviscube H-representation begin 6 4 rational 0 1 0 0 0 0 1 0 0 0 0 1 1 -1 0 0 1 0 -1 0 1 0 0 -1 end lrslib-073/ext/0000777000175000017500000000000014625766576012176 5ustar avisavislrslib-073/ext/metric/0000777000175000017500000000000014625766576013461 5ustar avisavislrslib-073/ext/metric/c6.ext0000777000175000017500000000276414625766576014527 0ustar avisavisc6 V-representation *6 point cut cone begin 31 16 integer 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 1 1 0 0 0 0 1 1 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 1 1 0 1 0 0 1 0 0 1 0 1 0 1 0 1 1 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 0 1 1 1 1 1 1 0 0 0 0 0 1 0 1 1 1 0 1 1 1 0 0 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 1 0 1 0 0 1 1 1 0 1 1 1 0 0 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 1 0 1 0 1 1 0 1 0 1 0 1 1 0 1 0 1 0 1 1 0 1 0 0 1 1 1 0 0 1 1 0 1 1 0 0 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 1 1 1 0 0 0 0 1 1 0 1 1 1 1 0 0 0 0 0 1 1 0 0 1 1 0 1 1 1 1 0 0 0 0 1 0 1 0 1 0 1 1 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 0 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1 0 1 1 1 0 0 1 1 0 0 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 end lrslib-073/ext/metric/c6.ine0000777000175000017500000002422214625766576014473 0ustar avisavisc6 *6 point cut cone H-representation begin 210 16 rational 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 -1 0 1 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 -1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 -1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 -1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 -1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 -1 0 0 -1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 1 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 1 0 -2 2 2 2 2 1 1 1 1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 1 0 0 -1 0 0 1 0 0 0 0 -1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 1 0 0 1 0 0 -1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 -1 0 0 0 0 1 0 0 -1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 1 0 0 1 -1 2 -1 -1 1 -2 1 1 2 -1 -1 2 2 -1 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 1 0 0 0 0 0 0 0 -1 0 1 0 0 0 0 1 0 0 1 1 1 1 -2 -1 -1 -1 2 -1 -1 2 -1 2 2 0 1 0 1 1 -1 0 -1 -1 1 0 0 0 -1 1 1 0 0 0 -1 1 0 0 0 0 0 0 0 0 1 0 0 0 -1 1 0 1 -1 1 0 1 -1 0 -1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 1 0 0 0 0 0 0 0 -1 1 0 0 0 0 1 0 0 0 1 0 1 -1 1 0 -1 1 -1 0 0 0 1 -1 1 0 0 0 0 0 0 0 1 -1 0 0 0 0 1 0 0 0 1 0 -1 1 1 0 1 -1 -1 0 0 0 1 1 -1 0 1 1 1 -2 1 -1 -1 2 -1 -1 2 -1 2 -1 2 0 1 1 -2 1 1 -1 2 -1 -1 2 -1 -1 2 2 -1 0 0 -1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 1 0 0 0 1 1 1 -1 0 0 0 0 -1 -1 1 -1 1 1 0 0 0 0 0 0 -1 0 0 1 0 0 1 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 -1 0 0 0 0 0 0 0 0 0 0 -1 1 0 1 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 -1 1 0 0 0 0 -1 1 -1 1 -1 1 0 1 1 0 1 -1 -1 0 -1 1 0 -1 1 0 0 1 0 0 0 0 0 0 -1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 1 0 0 1 1 0 -1 1 -1 0 1 -1 0 1 -1 0 0 1 0 0 -1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 1 0 0 0 0 1 -1 1 1 0 0 0 0 1 -1 -1 1 1 -1 0 0 0 0 0 0 -1 1 0 0 1 0 0 0 0 0 0 1 1 -1 0 1 -1 1 0 -1 1 0 -1 0 1 0 0 1 1 1 -1 0 -1 -1 1 0 -1 1 0 1 0 0 0 1 1 -1 1 0 -1 1 -1 0 1 -1 0 1 0 0 0 2 2 2 -2 2 -1 -1 1 -1 -1 1 -1 1 -1 1 0 2 2 -2 2 2 -1 1 -1 -1 1 -1 -1 1 1 -1 0 1 1 -1 1 -2 -1 1 -1 2 1 -1 2 1 -2 2 0 1 -1 -1 2 -1 1 1 -2 1 -1 2 -1 2 -1 2 0 1 1 1 0 -1 -1 -1 0 1 -1 0 1 0 1 0 0 2 2 2 2 -2 -1 -1 -1 1 -1 -1 1 -1 1 1 0 1 1 1 -1 -2 -1 -1 1 2 -1 1 2 1 2 -2 0 -1 1 1 0 -1 1 1 0 -1 -1 0 1 0 1 0 0 -1 0 1 -1 1 0 1 -1 1 0 0 0 1 -1 1 0 1 -1 -1 -1 2 1 1 1 -2 -1 -1 2 -1 2 2 0 1 -1 1 1 -2 1 -1 -1 2 1 1 -2 -1 2 2 0 -2 1 1 1 -1 2 2 2 -2 -1 -1 1 -1 1 1 0 -2 2 2 2 -2 1 1 1 -1 -1 -1 1 -1 1 1 0 1 -1 -2 1 1 1 2 -1 -1 -2 1 1 2 2 -1 0 0 -1 1 -1 1 0 0 0 0 1 -1 1 1 -1 1 0 -1 1 1 1 0 1 1 1 0 -1 -1 0 -1 0 0 0 -1 2 1 1 -1 2 1 1 -1 -2 -2 2 -1 1 1 0 0 0 0 0 0 1 1 1 -1 -1 -1 1 -1 1 1 0 2 1 -1 1 -1 -2 2 -2 2 1 -1 1 1 -1 1 0 2 -1 -1 -1 1 2 2 2 -2 -1 -1 1 -1 1 1 0 1 2 -1 -1 -1 -2 1 1 1 2 2 2 -1 -1 -1 0 -1 0 -1 1 1 0 -1 1 1 0 0 0 1 1 -1 0 1 2 -1 1 -1 -2 1 -1 1 2 -2 2 1 -1 1 0 -1 -1 1 0 1 -1 1 0 1 1 0 1 0 -1 0 0 -1 -1 2 -1 1 -1 2 -1 1 2 -1 1 2 -2 1 0 1 -1 1 -2 1 1 -1 2 -1 1 -2 1 2 -1 2 0 -1 -1 1 -1 2 -1 1 -1 2 1 -1 2 1 -2 2 0 0 -1 -1 1 1 0 0 0 0 -1 1 1 1 1 -1 0 0 0 0 0 0 -1 1 -1 1 1 -1 1 1 -1 1 0 1 1 -1 2 -1 -1 1 -2 1 1 -2 1 2 -1 2 0 0 0 0 0 0 1 0 -1 0 0 1 0 0 0 0 0 1 -1 0 1 1 1 0 -1 -1 0 1 1 0 0 -1 0 -1 0 1 1 -1 0 1 1 -1 0 0 0 -1 1 1 0 1 -2 1 1 1 2 -1 -1 -1 2 2 2 -1 -1 -1 0 2 -1 -1 1 1 2 2 -2 -2 -1 1 1 1 1 -1 0 0 0 0 0 0 1 1 0 0 -1 0 0 0 0 0 0 -1 1 1 0 1 1 1 0 1 -1 0 -1 0 -1 0 0 -1 2 1 -1 1 2 1 -1 1 -2 2 -2 1 -1 1 0 2 1 1 -1 -1 -2 -2 2 2 -1 1 1 1 1 -1 0 0 0 0 0 0 1 1 -1 1 -1 1 -1 1 -1 1 0 2 -1 -1 1 -1 2 2 -2 2 -1 1 -1 1 -1 1 0 1 -1 -1 2 1 1 1 -2 -1 -1 2 1 2 1 -2 0 -1 1 2 -1 -1 1 2 -1 -1 -2 1 1 2 2 -1 0 1 -1 -1 1 0 1 1 -1 0 -1 1 0 1 0 0 0 1 2 1 -1 -1 -2 -1 1 1 -2 2 2 1 1 -1 0 0 -1 1 1 -1 0 0 0 0 1 1 -1 -1 1 1 0 2 1 -1 -1 1 -2 2 2 -2 1 1 -1 -1 1 1 0 -1 1 1 -1 0 1 1 -1 0 -1 1 0 1 0 0 0 -1 2 1 -1 -1 2 1 -1 -1 -2 2 2 1 1 -1 0 0 0 0 0 0 1 1 -1 -1 -1 1 1 1 1 -1 0 1 1 -1 -2 1 -1 1 2 -1 1 2 -1 -2 1 2 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 -1 0 0 1 0 -1 0 0 0 0 0 0 1 0 0 0 0 0 -1 1 2 -1 1 1 2 -1 1 -2 1 -1 2 -2 1 0 -1 -1 0 1 1 -1 0 1 1 0 1 1 0 0 -1 0 -1 1 0 -1 1 1 0 -1 1 0 1 -1 0 0 1 0 1 2 -1 -1 1 -2 1 1 -1 2 2 -2 -1 1 1 0 -1 -1 1 1 0 -1 1 1 0 1 1 0 -1 0 0 0 -1 -1 2 1 -1 -1 2 1 -1 2 1 -1 -2 2 1 0 1 -1 -1 0 1 1 1 0 -1 -1 0 1 0 1 0 0 -1 -1 1 2 -1 -1 1 2 -1 1 2 -1 -2 1 2 0 -1 -1 -1 2 1 -1 -1 2 1 -1 2 1 2 1 -2 0 0 0 0 0 0 -1 1 1 -1 1 1 -1 -1 1 1 0 -1 1 2 1 -1 1 2 1 -1 -2 -1 1 -2 2 1 0 -2 1 1 -1 1 2 2 -2 2 -1 1 -1 1 -1 1 0 -2 2 2 -2 2 1 1 -1 1 -1 1 -1 1 -1 1 0 -1 -1 -1 1 2 -1 -1 1 2 -1 1 2 1 2 -2 0 0 0 0 0 0 -1 -1 1 1 -1 1 1 1 1 -1 0 1 1 2 -1 -1 -1 -2 1 1 -2 1 1 2 2 -1 0 0 0 0 0 0 1 0 1 0 0 -1 0 0 0 0 0 -1 1 0 1 1 1 0 1 1 0 -1 -1 0 0 -1 0 -1 2 -1 1 1 2 -1 1 1 2 -2 -2 1 1 -1 0 0 0 0 0 0 1 -1 1 1 1 -1 -1 1 1 -1 0 2 -1 1 -1 -1 2 -2 2 2 1 -1 -1 1 1 -1 0 -1 1 1 1 -2 1 1 1 -2 -1 -1 2 -1 2 2 0 1 -1 -1 1 2 1 1 -1 -2 -1 1 2 1 2 -2 0 0 1 1 -1 -1 0 0 0 0 -1 1 1 1 1 -1 0 0 0 0 0 0 1 -1 0 0 1 0 0 0 0 0 0 1 -1 1 0 1 1 -1 0 -1 1 0 1 0 -1 0 0 -2 1 1 1 1 2 2 2 2 -1 -1 -1 -1 -1 -1 0 2 -1 1 -1 1 2 -2 2 -2 1 -1 1 1 -1 1 0 1 -1 2 -1 1 1 -2 1 -1 2 -1 1 2 -2 1 0 -1 1 -1 2 -1 1 -1 2 -1 1 -2 1 2 -1 2 0 -1 1 1 -2 1 1 1 -2 1 -1 2 -1 2 -1 2 0 -1 1 -1 1 0 1 -1 1 0 1 -1 0 1 0 0 0 -1 2 -1 1 -1 2 -1 1 -1 2 -2 2 1 -1 1 0 0 0 0 0 0 1 -1 1 -1 1 -1 1 1 -1 1 0 1 -1 1 1 0 1 -1 -1 0 1 1 0 -1 0 0 0 2 -2 2 2 2 1 -1 -1 -1 1 1 1 -1 -1 -1 0 2 -1 1 1 -1 2 -2 -2 2 1 1 -1 -1 1 1 0 -2 -2 2 2 2 -1 1 1 1 1 1 1 -1 -1 -1 0 -2 -1 1 1 1 -2 2 2 2 1 1 1 -1 -1 -1 0 -1 1 -1 2 1 1 -1 2 1 1 -2 -1 2 1 -2 0 1 -1 1 -1 0 1 -1 1 0 1 -1 0 1 0 0 0 1 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 -1 0 0 0 0 1 0 0 0 -1 0 0 0 1 0 0 0 0 0 0 0 -1 -2 1 1 1 -2 1 1 1 2 2 2 -1 -1 -1 0 1 -1 2 1 -1 1 -2 -1 1 2 1 -1 -2 2 1 0 -1 1 -1 -1 2 1 -1 -1 2 1 1 -2 -1 2 2 0 -1 1 -1 0 1 1 -1 0 1 1 0 -1 0 1 0 0 -1 2 -1 -1 1 2 -1 -1 1 2 2 -2 -1 1 1 0 0 0 0 0 0 1 -1 -1 1 1 1 -1 -1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 -1 0 0 0 0 -1 1 1 1 0 0 0 0 1 1 1 -1 -1 -1 0 0 1 -1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 -1 0 0 0 1 -1 -1 1 0 0 0 0 1 1 -1 -1 1 1 0 1 1 -1 -1 2 -1 1 1 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0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 -1 0 0 1 0 -1 1 -1 0 1 -1 1 0 0 0 1 -1 1 0 1 1 -1 0 -1 -1 1 0 1 1 0 1 0 -1 0 0 1 1 -2 1 -1 -1 2 -1 1 2 -1 1 2 -2 1 0 2 2 -2 2 -2 -1 1 -1 1 1 -1 1 1 -1 1 0 -1 -1 1 1 2 -1 1 1 2 1 1 2 -1 -2 -2 0 1 0 -1 -1 1 0 1 1 -1 0 0 0 -1 1 1 0 1 1 -2 -1 1 -1 2 1 -1 2 1 -1 -2 2 1 0 2 2 -2 -2 2 -1 1 1 -1 1 1 -1 -1 1 1 0 -1 -1 1 2 1 -1 1 2 1 1 2 1 -2 -1 -2 0 -1 1 1 -1 2 1 1 -1 2 -1 1 -2 1 -2 2 0 -1 1 1 2 -1 1 1 2 -1 -1 -2 1 -2 1 2 0 1 -2 -1 1 1 2 1 -1 -1 -2 2 2 1 1 -1 0 2 -2 -2 2 2 1 1 -1 -1 -1 1 1 1 1 -1 end *Totals: facets=210 bases=42331 lrslib-073/ext/metric/c7.ext0000777000175000017500000000564414625766576014530 0ustar avisavisc7 *Complete Cut cone on 7 vertices V-representation begin 63 22 integer 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 1 1 1 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-1 -1 2 -1 -1 2 0 2 1 0 1 1 0 1 1 0 0 -1 -1 0 1 1 0 -1 -1 0 1 1 -1 1 0 0 2 -1 0 1 1 -1 2 1 -3 -2 2 -1 2 1 -1 2 1 -1 -2 2 1 0 2 -1 2 2 2 -3 1 -1 -1 -1 2 1 1 0 -2 -1 -1 2 -1 2 1 0 2 -1 1 0 1 -1 2 -3 1 -2 2 2 -1 1 -1 2 -2 2 1 -1 1 0 1 1 0 0 1 1 0 -1 -1 0 1 1 1 -1 -2 -1 1 2 1 2 -2 0 0 2 -1 -1 1 1 1 -1 -1 1 2 2 2 -2 -3 -1 1 2 1 2 -2 0 1 -1 -1 1 -1 1 0 1 0 1 -1 -1 1 0 1 0 0 1 1 -1 1 0 -1 2 -1 -1 2 3 2 -1 -1 2 3 2 2 -3 -5 -1 2 3 2 3 -5 0 1 -1 1 1 0 -2 1 0 -1 -1 2 1 1 0 -2 0 1 1 -1 2 1 0 1 0 0 1 1 -1 1 -1 -1 0 2 1 1 -1 -2 -1 1 2 0 2 -1 0 1 -1 1 1 0 -2 1 -1 0 -1 2 1 1 0 -2 0 -1 2 1 1 1 0 1 1 0 1 0 -1 0 -1 -1 1 2 1 0 -1 -1 -1 1 2 1 2 -2 0 1 0 1 0 1 -1 1 -1 -1 0 2 1 1 -1 -2 -1 0 2 1 2 -1 0 1 1 1 0 0 -1 0 -1 -1 1 2 0 1 -1 -1 -1 1 2 1 2 -2 0 1 -1 1 2 -1 -2 1 -1 -1 0 2 1 2 -1 -2 -2 1 2 2 3 -1 0 1 -1 1 2 -1 -2 0 -1 -1 1 2 1 2 -1 -1 -2 1 2 2 3 -2 end verbose eliminate 1 21 *Total number of jobs: 692034, L became empty 64 times, tree depth 42, deepest output depth 37 *Finished with 158 64-bit, 0 128-bit, 0 GMP workers *Totals: facets=38781 bases=247271659 *mplrs:lrslib_v.7.3_2024.4.20(128bit,hybrid arithmetic,gmp v.6.2)160 processes *Elapsed time: 40 seconds. lrslib-073/ext/metric/cp4.ext0000777000175000017500000000030514625766576014672 0ustar avisaviscp4.ext H-representation begin 8 7 integer 1 0 0 0 0 0 0 1 0 1 1 1 1 0 1 0 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 0 1 end startingcobasis 2 3 4 5 6 7 8 lrslib-073/ext/metric/cp5.ext0000777000175000017500000000113314625766576014673 0ustar avisaviscp5.ext V-representation *5 point cut polytope begin 16 11 integer 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 0 1 0 1 0 1 1 1 1 1 0 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 1 0 1 0 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 1 0 1 1 0 1 1 1 1 0 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 0 1 1 1 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 1 0 0 1 1 0 1 1 0 0 0 1 1 1 0 0 0 end lrslib-073/ext/metric/cp6.ext0000777000175000017500000000312514625766576014677 0ustar avisaviscp6.ext V-representation *6 point cut cone begin 32 16 integer 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 1 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 1 1 0 1 0 0 1 0 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 1 0 1 1 1 1 1 1 0 0 0 0 1 0 0 1 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 1 1 1 0 0 1 1 0 1 0 1 1 0 1 1 1 0 1 0 1 0 1 0 1 1 0 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 1 0 0 0 1 1 1 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 0 1 1 1 0 1 1 0 1 0 0 1 1 1 0 0 1 1 1 1 1 0 0 1 0 1 1 0 1 1 0 0 1 1 1 1 1 0 1 0 0 1 0 1 1 0 1 1 0 1 1 1 1 1 0 0 0 0 1 1 0 1 1 1 1 0 1 0 0 0 1 1 0 0 1 1 0 1 1 1 1 0 1 0 0 1 0 1 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 0 0 1 1 0 1 1 0 0 1 1 1 0 1 0 0 1 1 0 0 1 1 1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 0 1 0 1 1 0 1 0 1 0 1 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 0 0 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-1 0 -1 0 0 0 0 0 0 -1 0 0 0 0 0 0 -1 1 -1 1 0 0 0 0 1 -1 1 1 -1 1 0 2 -2 2 -2 2 1 -1 1 -1 1 -1 1 1 -1 1 2 0 0 0 0 0 0 0 0 0 0 -1 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 1 0 0 0 -1 1 0 0 0 0 0 0 1 0 0 0 0 0 end *Totals: facets=368 bases=46751 *Dictionary Cache: dict_limit=400 dict_count=73 misses= 0/46468 Tree Depth= 16 *threads=16 counts: 0 14475 19952 0 0 8281 0 0 0 0 0 0 2289 1753 0 0 *children=16 counts: 0 0 0 0 0 0 14475 0 0 19952 1753 2289 8281 0 0 0 *lrs:lrslib_v.7.3_2024.4.20(64bit,lrslong.h,hybrid_arithmetic) *overflow checking on lrslong arithmetic *0.394u 0.016s 2488Kb 0 flts 0 swaps 0 blks-in 40 blks-out lrslib-073/ext/metric/cp7.ext0000777000175000017500000000577614625766576014716 0ustar avisaviscp7.ext *Complete Cut Polytope on 7 vertices *The number of facets is 116,764. V-representation begin 64 22 integer 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 0 1 1 1 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 1 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 1 1 1 1 1 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 1 1 1 1 0 0 0 1 1 1 0 0 0 1 0 1 1 0 1 1 1 1 0 1 1 0 1 0 0 1 0 0 1 1 0 1 0 1 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 1 0 1 1 0 1 1 1 1 0 1 1 1 1 0 0 0 0 1 0 0 1 0 1 1 1 1 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 0 1 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 1 1 0 1 0 1 0 1 0 1 1 1 0 1 1 1 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 1 1 1 0 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 0 1 1 0 0 1 1 1 1 1 1 0 1 0 0 0 1 0 1 0 1 0 1 1 0 1 1 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0 1 1 0 1 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 1 0 0 1 1 0 0 1 1 1 0 0 1 1 1 0 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 0 1 0 0 1 0 1 0 0 1 0 1 1 0 1 0 1 0 1 0 1 1 0 1 0 1 0 0 1 0 1 0 0 1 0 1 1 1 0 0 1 1 0 1 0 1 1 0 0 0 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 1 0 1 1 1 1 0 0 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 1 0 1 1 1 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 1 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 end lrslib-073/ext/redund/0000777000175000017500000000000014625766576013457 5ustar avisavislrslib-073/ext/redund/cube.ext0000777000175000017500000000037214625766575015123 0ustar avisaviscube V-representation begin 14 4 rational 1 1/10 0 0 1 -1/2 1/2 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 1 1 1 1 1 -1 1 -1 1 -1 1 1 -1 -1 1 -1 -1 -1 1 1 -1 1 1 -1 -1 1 end verbose redund 0 0 lrslib-073/ext/redund/f1000_10.ext0000777000175000017500000005676714625766576015257 0ustar avisavisf1000_10 H-representation begin 1000 12 integer 0 1 3 2 2 0 1 3 3 2 2 4 0 1 1 0 1 2 3 3 1 2 0 0 0 1 1 0 0 4 2 1 4 1 1 4 0 1 0 0 1 3 3 4 0 4 0 0 0 1 3 2 0 0 3 0 3 1 3 0 0 1 2 0 1 3 4 3 4 4 1 2 0 1 1 0 0 4 4 0 1 4 3 3 0 1 2 1 1 1 0 1 1 3 2 2 0 1 3 1 3 4 4 2 1 1 1 1 0 1 0 1 0 0 3 1 2 4 3 0 0 1 0 0 0 0 4 2 0 4 2 3 0 1 0 3 2 2 1 1 3 1 2 2 0 1 3 2 0 1 0 2 1 0 1 3 0 1 1 2 4 4 0 1 4 1 1 1 0 1 4 2 1 1 4 4 4 1 1 1 0 1 0 3 1 3 0 3 3 0 2 2 0 1 0 4 0 3 2 4 3 1 0 4 0 1 1 4 4 0 0 3 3 0 3 4 0 1 4 3 2 1 3 2 2 4 0 4 0 1 3 3 3 2 4 3 0 3 3 3 0 1 4 4 4 1 2 3 3 0 4 3 0 1 1 3 2 2 2 0 0 2 3 1 0 1 3 0 3 3 4 3 2 3 0 0 0 1 4 3 1 2 2 2 0 4 0 1 0 1 3 3 1 1 2 4 1 4 1 3 0 1 4 2 2 1 4 1 2 1 0 4 0 1 2 0 4 1 0 2 2 1 0 4 0 1 3 3 1 2 2 1 2 1 2 1 0 1 4 0 0 0 3 4 1 3 2 0 0 1 3 1 1 0 2 1 0 2 2 3 0 1 0 3 0 4 1 4 1 0 3 1 0 1 3 1 4 2 1 3 1 2 2 4 0 1 3 3 1 3 4 1 4 2 2 3 0 1 1 3 4 2 3 2 3 3 0 1 0 1 1 1 0 3 2 3 2 2 0 4 0 1 0 4 4 4 3 3 1 4 3 0 0 1 3 2 3 3 3 1 0 4 4 2 0 1 1 1 3 4 1 2 2 1 0 1 0 1 1 2 1 3 3 2 1 0 0 1 0 1 3 0 4 0 3 3 4 3 3 2 0 1 4 2 2 2 1 3 2 3 1 4 0 1 2 4 3 1 0 1 0 1 3 3 0 1 2 4 1 0 1 0 2 0 4 3 0 1 4 2 1 1 3 3 1 3 0 2 0 1 1 3 3 0 1 1 1 4 1 1 0 1 2 3 3 4 2 2 3 4 4 2 0 1 2 4 3 1 1 4 2 4 3 1 0 1 1 3 1 4 3 0 4 4 0 1 0 1 1 2 0 4 1 3 2 4 4 2 0 1 2 1 3 1 2 3 2 1 1 2 0 1 4 1 3 0 4 3 0 0 4 4 0 1 1 1 0 2 2 3 3 2 0 3 0 1 3 2 3 3 4 0 2 0 2 3 0 1 1 1 0 1 4 4 1 2 0 3 0 1 4 3 0 0 4 0 1 1 1 4 0 1 3 4 3 1 0 2 2 0 0 1 0 1 3 0 4 0 4 4 2 3 4 4 0 1 3 3 1 1 1 3 2 4 0 2 0 1 4 1 1 0 2 1 3 0 3 3 0 1 4 4 2 2 1 0 1 2 4 3 0 1 0 4 2 0 1 1 3 3 1 1 0 1 2 2 4 2 1 0 1 3 0 3 0 1 0 4 4 1 3 3 0 4 3 3 0 1 1 3 4 2 3 0 4 2 2 4 0 1 4 4 1 2 3 1 4 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1 0 4 3 3 0 3 1 1 2 2 0 1 0 1 4 2 4 3 1 3 0 3 0 1 1 0 1 2 1 1 2 2 0 0 0 1 1 2 3 0 4 1 4 0 2 4 0 1 0 3 1 2 1 3 3 2 2 1 0 1 0 0 4 3 0 4 2 0 4 2 0 1 2 4 3 1 3 0 3 3 0 1 0 1 4 2 3 4 4 4 3 4 3 3 0 1 0 4 2 0 4 3 3 1 4 3 0 1 3 3 4 4 2 0 1 4 4 3 0 1 4 1 1 2 2 2 1 3 3 3 0 1 2 0 0 2 2 4 4 3 2 1 0 1 1 2 4 1 0 3 2 2 1 0 0 1 3 2 3 3 2 4 2 3 2 0 0 1 0 1 1 0 3 4 3 4 4 1 0 1 0 3 4 4 1 2 2 1 2 1 0 1 2 3 3 4 2 0 2 4 2 2 0 1 0 4 0 1 1 1 3 2 0 0 0 1 1 1 0 0 2 2 0 0 1 1 0 1 0 2 1 0 2 0 4 3 4 0 0 1 4 4 0 0 0 4 3 4 2 1 0 1 2 1 0 3 4 4 1 0 4 4 0 1 3 2 1 1 3 3 3 2 1 1 0 1 3 1 1 1 4 3 3 3 2 1 0 1 0 0 3 1 1 4 1 3 1 0 0 1 1 1 2 2 0 2 4 0 4 0 0 1 4 4 0 2 0 0 0 3 1 1 0 1 1 4 3 1 0 0 4 0 4 1 0 1 4 1 0 4 0 2 1 2 4 0 0 1 4 3 0 4 1 0 0 0 2 4 0 1 1 4 2 3 3 1 3 1 3 0 0 1 3 4 2 0 1 4 2 0 1 2 0 1 3 3 1 1 0 1 3 1 1 2 0 1 0 2 0 4 4 4 2 2 4 2 0 1 0 3 0 2 4 4 0 2 1 3 0 1 0 2 1 2 1 0 1 0 2 2 0 1 2 2 2 1 4 2 4 2 2 4 0 1 2 2 3 0 4 1 2 0 1 2 0 1 1 3 2 1 2 2 1 1 3 2 0 1 3 3 2 4 0 2 3 4 1 2 0 1 4 3 2 4 2 2 3 2 0 4 0 1 1 0 2 1 3 3 3 1 3 3 0 1 0 3 4 1 1 3 4 3 4 0 0 1 0 1 1 1 2 2 1 0 2 1 0 1 3 0 3 0 4 2 1 3 0 4 0 1 3 4 3 2 4 2 2 0 3 0 0 1 4 2 3 4 1 0 2 0 4 3 0 1 0 4 2 0 2 3 2 2 1 1 0 1 2 1 1 1 0 0 0 2 4 2 0 1 2 1 0 1 2 2 1 0 4 2 0 1 2 2 1 4 3 2 3 2 1 4 0 1 0 0 1 2 2 1 4 1 3 2 0 1 0 2 1 4 3 2 4 3 0 3 0 1 4 2 3 0 0 4 4 1 4 1 0 1 0 0 2 0 4 4 0 2 3 0 0 1 3 4 2 4 4 4 1 1 1 2 0 1 4 0 1 0 2 4 2 0 4 0 0 1 3 1 4 3 0 1 3 4 0 0 0 1 3 1 3 2 3 2 4 2 0 2 0 1 4 1 1 1 3 4 3 3 0 2 0 1 0 3 0 1 3 4 2 3 3 3 0 1 3 4 0 0 1 3 1 3 2 1 0 1 3 0 1 0 0 4 3 3 3 1 0 1 3 4 2 2 2 3 2 0 1 1 0 1 0 0 1 1 3 2 3 1 0 0 0 1 0 3 3 2 2 1 2 0 1 2 0 1 0 3 1 0 4 3 0 4 4 1 0 1 2 4 3 4 3 1 3 3 0 2 0 1 3 4 4 0 3 3 3 3 1 0 0 1 2 2 4 4 4 3 0 4 4 4 0 1 3 3 1 0 0 1 1 3 1 0 0 1 4 2 2 1 2 4 3 0 0 2 0 1 4 4 3 4 2 2 4 2 3 3 0 1 2 2 4 0 4 2 2 3 1 3 0 1 4 4 4 3 2 2 4 0 2 1 0 1 4 1 3 0 2 1 1 3 4 0 0 1 3 0 3 4 3 3 3 1 3 4 0 1 2 2 4 1 4 2 3 1 4 3 0 1 2 2 0 1 1 4 1 0 0 0 0 1 1 2 2 4 0 0 2 3 0 4 0 1 1 3 4 0 2 2 3 4 3 2 0 1 1 4 0 2 1 3 2 0 0 3 0 1 4 2 1 1 1 2 1 4 1 1 0 1 3 1 3 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1 0 3 3 4 3 3 0 1 1 4 0 1 3 4 3 3 2 4 2 3 0 3 0 1 0 0 1 3 3 1 1 1 3 2 0 1 2 2 1 0 0 1 1 0 0 4 0 1 2 0 0 3 1 4 4 0 1 4 0 1 2 2 1 2 2 1 1 4 0 4 0 1 0 1 1 3 2 2 0 2 3 0 0 1 1 3 3 2 3 4 2 0 3 4 0 1 3 1 2 1 3 0 1 4 4 4 0 1 1 0 1 1 3 2 0 0 1 2 0 1 1 2 0 4 0 0 2 1 4 4 0 1 1 2 0 3 3 1 2 0 3 0 0 1 0 4 1 2 4 0 2 3 4 3 0 1 2 3 2 1 2 2 4 3 0 4 0 1 1 2 2 2 0 0 4 0 0 0 0 1 0 1 4 4 4 1 3 2 4 2 0 1 2 2 1 2 1 1 2 0 1 1 0 1 1 3 0 2 0 2 4 1 0 1 0 1 3 4 0 4 2 1 2 0 4 3 0 1 3 2 2 2 1 1 0 4 4 3 0 1 0 3 3 1 4 1 1 1 0 1 0 1 0 4 3 4 3 2 1 4 3 4 0 1 0 1 2 0 0 0 2 1 0 1 0 1 3 2 4 0 1 3 3 0 0 3 0 1 0 4 2 0 4 0 3 0 3 3 0 1 3 0 1 1 4 2 4 4 1 4 0 1 1 2 4 2 3 4 2 3 2 2 0 1 4 0 4 4 1 3 3 0 2 2 0 1 1 4 4 1 0 1 2 4 2 0 0 1 0 3 0 0 3 1 1 0 3 1 0 1 2 1 0 1 0 4 0 4 0 0 0 1 1 1 1 0 1 2 2 4 3 4 0 1 3 3 1 1 3 3 0 3 3 0 0 1 2 1 3 2 0 0 4 2 4 2 0 1 2 4 1 3 2 1 4 3 3 4 0 1 3 4 2 4 2 4 4 2 2 2 0 1 4 3 1 3 2 2 4 0 1 2 0 1 3 1 0 1 2 4 4 0 3 1 0 1 1 2 1 4 3 4 4 2 0 0 0 1 0 0 2 3 1 4 4 1 4 0 0 1 0 1 1 4 2 0 3 4 2 1 0 1 4 3 1 4 3 4 1 1 0 3 0 1 3 1 3 1 0 0 1 4 4 3 0 1 4 0 1 1 4 4 2 2 4 3 0 1 4 0 2 3 3 4 1 2 3 3 0 1 3 0 4 1 3 3 0 1 2 3 0 1 3 4 4 4 1 1 2 4 0 3 0 1 1 2 4 4 1 2 4 3 3 3 0 1 4 3 3 4 1 0 4 0 4 0 0 1 3 1 2 1 2 3 0 0 4 0 0 1 2 0 4 4 4 3 2 1 4 0 0 1 3 2 4 0 1 3 3 4 1 3 0 1 3 1 0 4 0 4 4 2 3 0 0 1 0 0 1 4 4 0 2 2 1 3 0 1 4 4 1 4 1 3 3 4 4 3 0 1 0 2 0 1 4 2 1 0 3 3 0 1 3 4 1 4 1 0 1 2 1 1 0 1 4 0 4 1 0 0 1 3 3 3 0 1 2 2 3 1 4 4 0 2 2 2 0 1 1 2 2 2 0 3 2 4 1 4 0 1 2 2 4 0 3 0 3 4 2 3 0 1 3 1 1 3 1 1 2 3 1 1 0 1 2 1 0 2 4 1 3 4 0 4 0 1 0 0 3 1 4 1 3 1 2 2 0 1 2 3 1 0 3 0 0 1 0 3 0 1 1 4 2 3 1 4 0 4 1 4 0 1 3 2 0 1 4 3 0 1 2 3 0 1 1 2 2 0 0 4 4 1 1 2 0 1 3 3 1 2 4 3 2 0 4 0 0 1 4 4 2 3 2 2 0 2 1 3 0 1 0 1 0 4 1 4 3 3 1 2 0 1 0 2 1 0 0 3 4 1 4 2 0 1 0 4 4 2 1 4 3 3 2 1 0 1 1 1 2 3 3 4 3 3 0 0 0 1 2 1 3 3 2 3 4 4 2 2 0 1 0 1 1 3 1 3 0 4 4 1 0 1 4 0 4 1 4 3 1 2 4 0 0 1 2 4 2 2 2 0 2 0 3 2 0 1 2 0 2 1 4 3 0 1 2 0 0 1 1 0 1 0 4 4 3 4 2 4 0 1 1 0 1 2 1 1 1 3 4 2 0 1 4 1 2 2 2 1 1 4 0 2 0 1 2 2 1 2 0 4 2 1 2 1 0 1 0 2 2 0 2 3 0 0 4 4 0 1 4 3 4 1 0 3 2 0 1 4 0 1 4 2 3 1 3 3 1 0 0 4 0 1 1 4 2 1 0 0 0 4 3 1 0 1 1 1 2 3 3 0 0 3 0 3 0 1 2 4 2 4 2 2 0 3 2 4 0 1 4 0 0 2 1 0 4 2 1 3 0 1 1 4 1 0 0 4 3 3 0 3 0 1 0 0 0 1 4 3 2 3 0 1 0 1 3 4 4 4 2 0 1 2 4 1 0 1 0 2 2 4 3 2 2 0 2 1 0 1 3 4 0 2 3 4 1 0 2 0 0 1 3 1 3 4 1 2 0 1 2 1 0 1 4 3 2 2 0 2 2 1 1 4 0 1 1 2 3 0 1 1 4 4 0 1 0 1 2 3 4 3 3 2 2 1 1 0 0 1 2 1 0 2 2 2 2 2 1 4 0 1 3 3 1 2 3 2 4 0 0 3 0 1 1 0 4 0 4 4 2 1 2 1 0 1 4 4 1 1 0 0 1 1 1 2 0 1 3 4 2 0 4 2 2 2 0 3 0 1 0 0 2 1 1 3 3 0 3 0 0 1 1 2 3 1 1 1 2 2 0 4 0 1 2 3 4 0 4 2 2 0 2 2 0 1 4 3 2 0 3 0 2 3 4 1 0 1 4 4 2 3 2 0 0 4 1 2 0 1 4 0 2 1 1 1 3 0 3 3 0 1 3 4 2 0 0 3 4 2 3 1 0 1 0 0 2 1 3 4 4 2 4 2 0 1 1 4 0 0 2 4 0 4 3 2 0 1 1 4 2 0 0 1 2 4 3 4 0 1 0 1 4 1 4 0 3 4 4 3 0 1 1 4 4 3 0 2 4 3 3 3 0 1 0 1 0 4 4 3 2 3 1 4 0 1 4 3 2 4 4 4 2 3 3 1 0 1 1 0 1 1 4 0 1 0 3 1 0 1 1 3 3 3 1 3 2 4 1 3 0 1 4 3 2 3 4 0 2 1 0 2 0 1 0 1 2 3 3 3 0 1 2 2 0 1 0 0 1 4 4 0 0 1 4 1 0 1 0 2 2 1 4 0 1 4 3 1 0 1 1 2 3 4 1 4 1 1 3 1 0 1 4 2 4 1 2 1 0 1 2 3 0 1 4 2 4 3 4 3 0 1 1 2 0 1 2 4 4 0 2 4 2 1 4 0 0 1 3 1 0 4 3 3 1 0 4 2 0 1 2 2 2 1 2 2 1 2 0 3 0 1 4 0 1 4 2 3 3 0 2 2 0 1 2 4 3 1 0 2 0 0 0 4 0 1 2 2 2 1 4 4 4 2 2 3 0 1 0 4 1 1 2 4 1 1 4 1 0 1 0 3 2 1 4 0 4 1 4 3 0 1 4 4 0 2 0 1 4 0 2 0 0 1 0 1 2 2 0 0 0 4 0 4 0 1 1 2 2 4 4 3 1 2 0 3 0 1 2 2 0 0 1 2 2 4 0 4 0 1 3 3 2 1 3 0 3 0 0 4 0 1 0 3 2 4 4 4 1 1 4 4 0 1 4 1 3 4 2 2 3 2 4 0 0 1 1 3 4 3 2 4 1 2 4 3 0 1 1 2 0 0 2 1 2 1 0 3 0 1 2 0 2 0 2 4 3 4 3 3 0 1 1 1 1 1 0 4 2 1 2 4 0 1 1 1 0 1 0 3 4 3 4 2 0 1 1 2 3 2 2 0 4 2 0 3 0 1 0 1 1 2 4 4 4 0 1 4 0 1 2 1 1 3 2 2 2 4 0 0 0 1 4 1 3 4 2 1 1 2 1 0 0 1 3 0 1 2 4 4 0 4 4 4 0 1 2 3 0 4 2 1 4 0 4 0 0 1 1 4 1 3 0 2 2 4 4 4 0 1 0 1 2 3 2 2 2 2 3 4 0 1 2 2 2 2 2 4 1 4 1 3 0 1 3 4 3 1 3 1 3 0 4 2 0 1 1 2 1 2 3 2 1 3 2 1 0 1 3 1 3 4 1 2 3 3 0 4 0 1 2 4 4 2 1 1 2 0 3 1 0 1 1 1 4 4 4 3 4 1 0 4 0 1 3 2 3 2 4 2 3 0 1 4 0 1 4 0 3 4 2 2 3 4 2 2 0 1 3 1 2 0 3 1 3 0 1 2 0 1 0 0 2 2 2 1 0 2 0 1 0 1 2 4 4 2 4 0 0 1 3 0 0 1 1 1 4 4 2 2 3 2 1 3 0 1 0 1 0 1 1 2 1 3 3 1 0 1 3 2 2 3 1 4 1 1 2 2 0 1 4 0 3 0 2 0 2 2 1 4 0 1 4 0 2 0 1 0 3 1 3 4 0 1 3 2 4 2 0 0 1 3 3 4 0 1 1 1 4 1 4 4 0 1 2 1 0 1 3 2 3 4 1 2 2 4 1 4 0 1 1 0 2 0 0 0 0 1 1 2 0 1 3 3 4 0 0 0 2 0 2 0 0 1 1 0 4 3 2 3 3 3 0 4 0 1 0 2 1 2 3 3 1 1 2 2 0 1 4 3 4 2 0 1 0 3 0 4 0 1 4 1 4 2 3 0 2 3 4 1 0 1 1 2 4 4 3 0 3 0 2 3 0 1 1 0 4 3 2 2 4 2 0 3 0 1 0 2 3 3 0 2 4 0 2 0 0 1 1 4 1 2 3 1 0 3 3 4 0 1 1 2 4 4 2 0 1 4 1 4 0 1 0 2 1 2 4 3 1 0 4 0 0 1 4 0 3 3 1 4 0 0 1 0 0 1 4 2 3 4 4 3 1 3 4 4 0 1 0 0 1 0 1 4 4 0 4 2 0 1 0 3 0 1 3 3 1 4 3 4 0 1 1 2 4 1 1 1 3 0 4 0 0 1 1 3 4 0 0 1 1 4 2 0 0 1 2 0 0 4 0 1 0 4 0 0 0 1 1 2 4 4 2 4 2 4 1 1 0 1 0 2 3 1 1 2 2 1 3 0 0 1 4 2 1 1 2 2 3 0 0 3 0 1 0 3 4 3 2 1 0 3 3 0 0 1 2 1 0 0 4 1 0 2 1 4 0 1 2 1 2 3 0 3 2 4 1 2 0 1 3 0 4 2 3 4 1 4 3 4 0 1 0 3 0 3 1 3 1 2 3 4 0 1 4 4 1 4 3 2 2 0 2 4 0 1 3 1 1 2 3 1 2 2 0 0 0 1 2 2 2 0 3 2 1 1 3 1 0 1 4 3 1 0 4 3 2 0 3 4 0 1 0 4 2 1 2 2 3 2 3 0 0 1 0 4 3 4 4 0 1 4 3 1 0 1 3 2 4 3 4 2 0 0 4 4 0 1 4 3 2 2 2 0 2 2 4 2 0 1 1 3 3 0 1 1 4 0 4 1 0 1 4 2 0 2 1 1 0 4 4 2 0 1 3 1 3 2 0 0 3 2 2 2 0 1 3 1 1 2 0 0 2 3 2 4 0 1 0 0 4 1 2 1 3 2 0 2 0 1 4 4 3 4 1 2 1 1 1 4 0 1 2 4 2 1 2 2 1 1 2 2 0 1 0 1 4 2 1 2 4 1 3 1 0 1 2 4 2 0 3 2 2 1 0 0 0 1 2 0 0 3 3 2 0 0 4 2 0 1 2 3 0 3 1 4 4 3 1 2 0 1 0 1 1 1 4 1 1 3 4 4 0 1 0 3 3 0 2 4 1 2 0 3 0 1 0 0 0 3 1 2 4 0 1 4 0 1 3 1 4 2 0 4 1 0 2 1 0 1 2 2 1 1 3 3 4 1 2 3 0 1 4 2 1 2 2 4 3 1 4 0 0 1 3 2 4 1 1 3 3 2 2 3 0 1 2 1 0 0 3 3 2 1 2 2 0 1 3 4 3 1 0 3 4 1 3 1 0 1 4 3 2 4 4 1 0 4 3 3 0 1 2 4 4 2 1 1 1 1 0 4 0 1 3 3 1 0 4 4 4 1 2 4 0 1 3 4 4 1 4 1 1 3 0 4 0 1 3 3 0 4 2 3 3 4 4 0 0 1 0 0 3 1 3 3 2 2 2 4 0 1 0 0 3 2 3 2 3 4 2 0 0 1 1 2 3 0 3 3 2 3 4 1 0 1 2 0 0 4 0 4 0 2 2 1 0 1 2 1 3 1 3 1 2 1 0 1 0 1 1 0 1 1 1 1 0 1 0 0 0 1 1 3 4 3 3 0 1 2 0 1 0 1 1 2 4 2 3 0 3 1 0 4 0 1 0 0 0 2 0 0 3 4 1 0 0 1 4 0 4 4 4 0 3 3 3 1 0 1 3 4 3 2 3 3 4 4 2 3 0 1 4 1 1 4 2 3 2 1 3 0 0 1 1 2 3 4 4 3 3 4 1 4 0 1 0 3 4 0 4 3 3 4 0 0 0 1 2 1 3 1 3 3 1 2 4 2 0 1 1 3 1 1 1 1 4 2 0 2 0 1 1 1 0 0 4 4 0 2 0 3 0 1 0 4 2 4 1 4 1 3 2 4 0 1 3 2 4 1 0 1 1 4 2 3 0 1 0 3 1 0 2 1 3 0 1 0 0 1 2 3 3 2 3 4 1 0 0 0 0 1 0 1 1 4 3 0 2 3 0 3 0 1 0 1 0 2 3 4 3 4 0 1 0 1 0 2 1 1 1 2 2 0 0 4 0 1 4 2 2 1 4 2 3 4 0 2 0 1 0 2 0 2 4 0 3 4 4 4 0 1 4 0 2 1 2 2 4 0 4 3 0 1 2 2 4 3 3 4 2 4 0 0 0 1 0 0 3 0 0 1 3 4 0 4 0 1 2 3 1 2 4 1 1 2 3 1 0 1 3 2 2 1 0 4 0 4 0 2 0 1 4 3 0 2 4 3 2 4 2 2 0 1 1 3 1 0 2 3 4 2 3 1 0 1 0 0 3 0 0 3 2 1 3 2 0 1 0 2 2 3 2 3 1 1 3 0 0 1 0 3 4 3 3 2 0 4 3 4 0 1 1 1 4 1 3 2 1 0 0 2 0 1 2 4 3 3 2 3 2 0 4 2 0 1 4 0 3 4 3 0 0 0 4 4 0 1 4 1 3 0 3 4 2 3 3 2 0 1 1 3 4 2 3 0 4 3 4 2 0 1 4 4 3 4 2 0 3 4 3 0 0 1 0 1 1 2 4 0 0 3 4 0 0 1 1 3 2 2 1 1 3 0 0 1 0 1 0 3 1 3 4 2 2 0 0 3 0 1 2 4 3 4 4 0 0 4 1 0 0 1 4 4 4 1 3 2 3 1 4 1 0 1 0 3 2 1 2 4 4 1 1 0 0 1 2 4 3 2 0 4 4 0 3 1 0 1 3 4 2 3 3 1 2 4 2 1 0 1 4 1 0 4 0 2 3 1 1 3 0 1 3 3 4 0 0 3 0 2 1 4 0 1 2 3 0 3 1 1 3 4 3 2 0 1 2 4 1 0 2 4 0 2 2 2 0 1 2 0 4 4 3 0 0 2 2 0 0 1 1 3 2 1 1 4 1 2 2 0 0 1 4 4 4 0 4 4 1 0 1 0 0 1 3 1 4 0 3 1 4 1 1 0 0 1 3 3 4 0 0 2 2 0 1 1 0 1 0 4 4 3 0 0 0 4 2 4 0 1 4 4 1 0 3 0 3 1 0 4 0 1 4 2 2 1 2 4 2 0 2 4 0 1 1 1 4 1 3 2 0 1 2 4 0 1 3 1 1 4 3 1 1 4 0 3 0 1 0 0 2 1 1 0 0 0 0 2 0 1 0 4 4 3 4 0 1 4 4 0 0 1 2 4 4 3 3 2 1 1 4 2 0 1 0 4 4 4 0 2 0 3 3 0 0 1 2 2 1 3 3 2 0 4 2 4 0 1 3 1 0 1 2 0 0 4 3 0 0 1 3 4 2 2 3 2 2 1 1 1 0 1 4 2 1 0 1 3 0 4 4 0 0 1 0 1 1 1 1 2 1 1 3 2 0 1 0 0 3 3 0 4 1 1 1 3 0 1 2 2 4 2 0 1 1 2 0 4 0 1 4 2 0 4 0 4 1 1 4 1 0 1 3 3 0 0 4 3 0 2 0 4 0 1 0 1 4 1 4 1 3 2 1 1 0 1 4 1 4 2 4 1 2 0 4 2 0 1 1 1 3 2 1 3 3 1 3 1 0 1 4 1 2 4 2 2 2 0 1 0 0 1 3 2 0 1 1 4 3 0 1 0 0 1 3 4 2 4 4 4 1 0 0 2 0 1 1 0 1 3 1 1 3 3 4 1 0 1 2 1 4 0 0 1 2 3 2 3 0 1 3 2 0 4 3 0 4 2 4 1 0 1 3 1 0 1 1 3 3 4 1 4 0 1 2 1 0 3 4 2 0 1 2 0 0 1 2 1 2 4 2 0 4 2 3 4 0 1 0 1 3 4 3 2 1 2 4 0 0 1 2 2 1 1 2 0 0 2 2 4 0 1 4 2 3 1 1 1 3 3 3 4 0 1 4 2 0 2 1 0 2 1 2 2 0 1 0 2 1 1 3 4 0 0 1 1 0 1 2 4 1 0 0 2 2 1 2 0 0 1 4 4 0 2 2 4 2 0 0 0 0 1 1 3 4 4 2 0 3 1 1 3 0 1 1 3 4 2 1 1 2 2 1 0 0 1 3 0 3 3 2 4 2 3 0 3 0 1 2 1 2 2 1 0 3 2 3 4 0 1 0 2 0 0 3 3 4 1 2 2 0 1 0 2 0 0 4 2 0 3 3 3 0 1 2 4 3 2 2 3 4 2 3 4 0 1 3 0 1 3 3 3 3 4 0 3 0 1 1 2 0 3 2 1 4 2 1 2 0 1 4 3 0 1 2 0 0 0 3 0 0 1 2 4 3 1 0 3 1 4 1 4 0 1 1 3 0 2 3 0 0 2 3 1 0 1 4 2 0 2 2 4 3 2 3 4 0 1 1 1 3 0 3 4 3 0 2 3 0 1 0 3 4 4 1 2 2 3 3 2 0 1 0 2 0 4 4 1 1 2 0 4 0 1 3 3 0 0 3 0 1 2 1 2 0 1 3 2 0 4 2 1 1 2 1 0 0 1 2 1 2 0 4 3 4 4 0 0 0 1 3 3 2 3 4 4 3 4 4 3 0 1 4 4 2 3 2 0 4 4 4 2 0 1 1 3 2 2 3 2 1 1 0 4 0 1 0 1 4 3 0 3 4 3 3 0 0 1 3 3 3 4 1 2 1 1 0 4 0 1 4 3 1 4 2 0 1 1 4 0 0 1 2 3 1 0 4 4 4 3 2 0 0 1 4 0 0 3 4 0 0 3 4 3 0 1 1 1 3 4 1 4 4 2 1 2 0 1 0 3 3 0 2 2 1 3 2 4 0 1 2 0 4 0 3 3 3 4 4 2 0 1 3 2 2 1 2 3 4 3 3 4 0 1 1 1 4 2 4 1 2 3 4 0 0 1 2 2 0 0 3 4 3 0 3 3 0 1 1 1 2 0 0 3 0 4 2 3 0 1 1 0 0 3 0 4 2 3 4 3 0 1 1 4 0 3 0 1 1 0 2 3 0 1 3 4 2 1 1 0 4 0 3 4 0 1 0 1 3 4 0 2 1 2 2 4 0 1 2 4 0 2 0 1 3 1 0 1 0 1 2 3 1 1 0 2 4 0 0 2 0 1 3 1 0 0 1 1 3 1 1 3 0 1 4 2 3 3 3 1 2 2 3 3 0 1 0 3 1 0 4 3 4 2 3 0 0 1 0 2 2 0 2 4 2 4 0 1 0 1 2 1 2 4 1 4 1 1 3 4 0 1 0 2 2 2 1 3 1 0 3 0 0 1 2 1 0 4 0 3 2 3 3 3 0 1 4 3 1 2 0 2 3 1 4 1 0 1 3 1 1 4 2 2 1 4 0 2 0 1 3 4 3 1 0 2 3 4 3 4 0 1 2 1 2 3 3 4 1 0 4 2 0 1 0 1 3 2 1 4 2 3 1 4 0 1 0 0 2 3 0 2 4 2 0 4 0 1 0 2 4 2 0 0 2 1 4 1 0 1 1 4 0 1 1 3 3 2 0 1 0 1 0 1 2 1 1 3 4 2 2 0 0 1 3 3 3 4 2 1 4 1 0 3 0 1 0 0 4 3 2 2 1 2 1 2 0 1 0 0 2 2 0 2 0 0 4 0 0 1 4 0 4 2 0 0 2 1 3 4 0 1 2 2 3 3 1 4 4 4 2 2 0 1 1 3 4 0 2 3 4 1 4 3 0 1 1 0 4 1 1 2 2 3 3 1 0 1 4 2 2 1 2 1 3 1 3 3 0 1 0 0 0 4 2 1 2 3 4 2 0 1 1 4 0 3 0 2 2 3 2 2 0 1 4 4 2 0 0 1 1 0 3 1 0 1 1 4 3 2 4 3 3 4 1 4 0 1 0 3 2 1 4 2 3 0 0 2 0 1 3 1 3 2 0 0 2 2 0 1 0 1 4 2 0 4 1 2 1 3 1 1 0 1 1 4 0 3 0 1 1 2 3 2 0 1 1 2 0 3 2 3 0 2 0 0 0 1 3 4 3 1 3 0 0 2 1 4 0 1 2 3 1 0 1 1 1 0 2 3 0 1 1 0 0 4 4 1 0 2 3 4 0 1 0 3 3 2 4 1 2 1 2 2 0 1 3 0 2 0 3 2 2 1 3 2 0 1 4 0 0 4 2 2 2 2 4 4 0 1 0 2 2 1 4 1 2 3 2 3 0 1 2 0 1 2 2 0 3 1 3 3 0 1 3 2 3 1 2 2 3 4 4 4 0 1 3 1 2 1 0 3 0 4 4 1 0 1 2 1 4 3 1 3 4 3 0 1 0 1 0 4 1 2 4 1 4 4 1 4 0 1 2 0 4 4 0 3 3 0 4 4 0 1 0 2 0 0 0 4 4 3 3 4 0 1 3 2 3 4 1 3 1 3 4 1 0 1 0 4 3 4 2 1 0 3 3 4 0 1 0 2 3 2 2 3 1 2 4 4 0 1 4 4 1 1 0 1 4 3 4 4 0 1 3 1 0 2 0 4 3 3 2 3 0 1 0 4 2 3 4 4 3 3 0 4 0 1 3 4 2 0 3 0 0 1 4 3 0 1 0 4 3 1 4 2 3 4 3 0 0 1 2 1 0 0 3 3 2 0 0 2 0 1 1 0 4 4 4 3 4 3 2 1 0 1 3 4 3 3 3 0 1 0 3 2 0 1 0 4 3 2 4 4 3 3 1 1 0 1 1 3 2 3 0 0 3 2 3 3 0 1 4 3 0 4 2 2 1 2 0 4 0 1 1 1 0 4 0 4 3 4 0 0 0 1 4 2 3 0 1 3 4 2 1 3 0 1 3 1 0 2 4 4 4 2 0 0 0 1 2 4 2 4 0 3 4 2 3 0 0 1 0 2 4 0 2 0 2 2 4 3 0 1 2 2 1 1 1 2 0 3 1 2 0 1 4 4 3 0 4 1 2 4 0 1 0 1 1 3 0 2 2 4 3 1 2 3 0 1 4 3 1 0 2 4 0 2 2 2 0 1 3 2 2 3 3 3 3 0 1 0 0 1 3 2 3 2 1 1 3 3 3 2 0 1 4 1 1 4 2 3 2 4 3 3 0 1 1 0 1 3 4 3 0 1 1 0 0 1 0 0 2 2 0 0 4 3 4 0 0 1 4 4 0 0 4 2 0 1 0 0 0 1 1 3 4 1 4 3 3 1 1 0 0 1 4 3 3 3 2 0 1 4 4 2 0 1 0 1 4 3 2 2 0 0 4 4 0 1 1 1 1 3 4 3 2 0 3 1 0 1 2 0 1 1 1 3 1 0 3 1 0 1 1 2 0 2 4 0 0 0 2 3 0 1 1 4 4 0 1 1 3 3 0 2 0 1 2 0 1 1 0 2 1 4 2 2 0 1 4 2 2 0 4 3 0 0 0 0 0 1 1 0 4 2 0 0 2 0 3 4 0 1 3 4 0 1 0 4 4 2 3 0 0 1 2 4 2 1 1 0 0 3 4 0 0 1 0 3 1 4 0 2 4 2 4 2 0 1 4 0 3 3 4 2 0 3 4 0 0 1 2 2 3 2 1 1 0 3 3 3 0 1 0 0 1 1 4 3 3 4 4 0 0 1 2 3 3 2 0 3 1 1 3 1 0 1 0 1 0 1 0 2 1 0 4 1 0 1 3 4 4 1 4 3 4 0 4 1 0 1 1 0 4 2 1 0 4 1 1 4 0 1 4 3 3 0 1 2 4 4 1 1 0 1 3 2 4 1 4 1 2 0 3 1 0 1 2 4 2 2 3 1 0 1 3 0 0 1 3 4 1 3 0 0 3 4 2 3 0 1 1 4 4 1 0 3 2 2 0 3 0 1 2 3 2 0 4 2 0 1 3 0 0 1 0 4 0 4 4 3 4 1 0 0 0 1 2 4 1 3 3 2 2 2 4 3 0 1 3 2 0 4 1 3 0 4 0 0 0 1 3 4 2 2 4 4 2 0 3 3 0 1 1 1 0 2 0 3 4 1 2 2 end lrslib-073/ext/redund/f1000_10.extmin.ine.tail0000777000175000017500000000114414625766576017440 0ustar avisavis 2503 -23 -62 252 645 -606 207 -121 -153 8 152 3071 144 -545 576 814 -601 631 -231 -325 136 340 end *Totals: facets=26321306 bases=181991726 *Dictionary Cache: dict_limit=400 dict_count=400 misses= 55363989/181989949 Tree Depth= 74 *threads=8 counts: 55996917 6357006 4089515 56092334 1634081 51333508 4997739 1490625 *children=11 counts: 51333508 1634081 55996917 6357006 4089515 4997739 928410 5 1291632 55163924 198988 *lrs:lrslib_v.7.3_2024.4.17(64bit,lrslong.h,hybrid_arithmetic) *overflow checking on lrslong arithmetic *14862.078u 107.671s 5916Kb 23548 flts 0 swaps 0 blks-in 0 blks-out lrslib-073/ext/redund/r100_5.ext0000777000175000017500000000350514625766575015114 0ustar avisavisrand100_5 V-representation begin 100 6 integer 1 15 2 10 6 4 1 6 1 12 9 2 1 20 13 16 6 14 1 1 10 5 7 17 1 13 9 7 11 19 1 8 12 19 16 3 1 12 9 4 17 3 1 4 10 1 15 18 1 11 14 4 18 9 1 14 10 7 19 5 1 8 17 4 20 6 1 5 2 8 14 18 1 20 14 5 12 6 1 7 9 16 6 20 1 13 11 9 14 12 1 7 16 4 18 6 1 12 11 14 17 13 1 7 13 4 14 3 1 3 8 1 16 6 1 16 12 9 1 3 1 5 7 12 4 16 1 12 5 18 7 4 1 16 18 12 14 7 1 19 11 8 10 6 1 15 18 19 12 16 1 15 12 18 4 8 1 12 10 15 18 11 1 3 13 11 19 8 1 19 5 9 13 1 1 6 19 16 20 7 1 15 13 4 12 2 1 9 10 11 7 20 1 4 15 19 6 16 1 4 20 3 5 13 1 9 18 19 14 13 1 17 3 10 20 16 1 18 17 10 6 2 1 6 17 13 11 9 1 9 17 10 7 16 1 14 9 15 8 12 1 7 15 11 5 10 1 17 10 14 3 20 1 17 18 8 19 12 1 12 10 8 16 11 1 16 11 8 6 1 1 11 6 5 2 18 1 13 7 17 19 11 1 15 2 16 10 6 1 7 20 2 8 9 1 13 19 7 16 17 1 6 3 2 15 14 1 19 17 11 6 15 1 16 1 18 12 17 1 14 12 16 11 3 1 18 11 12 14 2 1 17 12 10 5 13 1 10 15 16 2 11 1 10 14 19 5 11 1 14 16 15 3 12 1 16 5 7 6 19 1 12 16 18 4 6 1 15 16 10 4 2 1 5 12 14 9 10 1 17 6 19 13 20 1 15 9 1 5 6 1 2 1 16 6 17 1 3 8 4 12 6 1 13 17 10 3 15 1 18 6 11 1 7 1 13 19 16 1 2 1 19 4 12 13 20 1 12 4 1 19 8 1 17 8 6 9 5 1 14 2 10 9 15 1 17 14 1 8 9 1 16 13 20 10 19 1 19 3 11 13 18 1 12 17 16 14 5 1 18 4 1 3 20 1 1 13 12 18 15 1 7 17 13 10 6 1 4 18 8 1 2 1 19 18 14 20 17 1 19 9 10 1 4 1 1 19 18 4 2 1 14 19 13 4 9 1 3 6 13 2 10 1 12 2 14 16 8 1 13 10 8 2 3 1 16 15 18 4 9 1 4 8 5 2 11 1 6 13 12 1 5 1 7 14 13 16 8 1 20 8 4 17 14 1 20 6 9 8 10 1 19 15 13 16 7 1 4 17 15 13 2 1 13 6 7 9 2 1 19 18 14 17 4 1 19 1 12 20 9 end verbose *redund 0 0 lrslib-073/ext/redund/r100_5.extmin0000777000175000017500000001126414625766575015621 0ustar avisavis*minrep:lrslib_v.7.3_2024.4.17(64bit,lrslong.h,hybrid_arithmetic) rand100_5 *Unbounded solution *interior point found, no hidden linearities * x_1= 0 x_2= 0 x_3= 0 x_4= 0 x_5= 0 : ray *finding minimum representation *nr 1 15 2 10 6 4 *nr 1 6 1 12 9 2 *nr 1 20 13 16 6 14 *nr 1 1 10 5 7 17 *re 1 13 9 7 11 19 *nr 1 8 12 19 16 3 *nr 1 12 9 4 17 3 *nr 1 4 10 1 15 18 *re 1 11 14 4 18 9 *nr 1 14 10 7 19 5 *nr 1 8 17 4 20 6 *nr 1 5 2 8 14 18 *nr 1 20 14 5 12 6 *nr 1 7 9 16 6 20 *re 1 13 11 9 14 12 *re 1 7 16 4 18 6 *re 1 12 11 14 17 13 *nr 1 7 13 4 14 3 *nr 1 3 8 1 16 6 *nr 1 16 12 9 1 3 *nr 1 5 7 12 4 16 *nr 1 12 5 18 7 4 *re 1 16 18 12 14 7 *re 1 19 11 8 10 6 *nr 1 15 18 19 12 16 *nr 1 15 12 18 4 8 *re 1 12 10 15 18 11 *nr 1 3 13 11 19 8 *nr 1 19 5 9 13 1 *nr 1 6 19 16 20 7 *nr 1 15 13 4 12 2 *nr 1 9 10 11 7 20 *nr 1 4 15 19 6 16 *nr 1 4 20 3 5 13 *nr 1 9 18 19 14 13 *nr 1 17 3 10 20 16 *nr 1 18 17 10 6 2 *re 1 6 17 13 11 9 *nr 1 9 17 10 7 16 *re 1 14 9 15 8 12 *re 1 7 15 11 5 10 *nr 1 17 10 14 3 20 *nr 1 17 18 8 19 12 *re 1 12 10 8 16 11 *nr 1 16 11 8 6 1 *nr 1 11 6 5 2 18 *nr 1 13 7 17 19 11 *nr 1 15 2 16 10 6 *nr 1 7 20 2 8 9 *nr 1 13 19 7 16 17 *nr 1 6 3 2 15 14 *nr 1 19 17 11 6 15 *nr 1 16 1 18 12 17 *nr 1 14 12 16 11 3 *nr 1 18 11 12 14 2 *re 1 17 12 10 5 13 *nr 1 10 15 16 2 11 *nr 1 10 14 19 5 11 *nr 1 14 16 15 3 12 *re 1 16 5 7 6 19 *nr 1 12 16 18 4 6 *nr 1 15 16 10 4 2 *re 1 5 12 14 9 10 *nr 1 17 6 19 13 20 *nr 1 15 9 1 5 6 *nr 1 2 1 16 6 17 *nr 1 3 8 4 12 6 *nr 1 13 17 10 3 15 *nr 1 18 6 11 1 7 *nr 1 13 19 16 1 2 *nr 1 19 4 12 13 20 *nr 1 12 4 1 19 8 *re 1 17 8 6 9 5 *nr 1 14 2 10 9 15 *nr 1 17 14 1 8 9 *nr 1 16 13 20 10 19 *nr 1 19 3 11 13 18 *re 1 12 17 16 14 5 *nr 1 18 4 1 3 20 *nr 1 1 13 12 18 15 *re 1 7 17 13 10 6 *nr 1 4 18 8 1 2 *nr 1 19 18 14 20 17 *nr 1 19 9 10 1 4 *nr 1 1 19 18 4 2 *nr 1 14 19 13 4 9 *nr 1 3 6 13 2 10 *nr 1 12 2 14 16 8 *nr 1 13 10 8 2 3 *nr 1 16 15 18 4 9 *nr 1 4 8 5 2 11 *nr 1 6 13 12 1 5 *re 1 7 14 13 16 8 *nr 1 20 8 4 17 14 *nr 1 20 6 9 8 10 *re 1 19 15 13 16 7 *nr 1 4 17 15 13 2 *nr 1 13 6 7 9 2 *nr 1 19 18 14 17 4 *nr 1 19 1 12 20 9 V-representation begin 80 6 rational 1 15 2 10 6 4 1 6 1 12 9 2 1 20 13 16 6 14 1 1 10 5 7 17 1 8 12 19 16 3 1 12 9 4 17 3 1 4 10 1 15 18 1 14 10 7 19 5 1 8 17 4 20 6 1 5 2 8 14 18 1 20 14 5 12 6 1 7 9 16 6 20 1 7 13 4 14 3 1 3 8 1 16 6 1 16 12 9 1 3 1 5 7 12 4 16 1 12 5 18 7 4 1 15 18 19 12 16 1 15 12 18 4 8 1 3 13 11 19 8 1 19 5 9 13 1 1 6 19 16 20 7 1 15 13 4 12 2 1 9 10 11 7 20 1 4 15 19 6 16 1 4 20 3 5 13 1 9 18 19 14 13 1 17 3 10 20 16 1 18 17 10 6 2 1 9 17 10 7 16 1 17 10 14 3 20 1 17 18 8 19 12 1 16 11 8 6 1 1 11 6 5 2 18 1 13 7 17 19 11 1 15 2 16 10 6 1 7 20 2 8 9 1 13 19 7 16 17 1 6 3 2 15 14 1 19 17 11 6 15 1 16 1 18 12 17 1 14 12 16 11 3 1 18 11 12 14 2 1 10 15 16 2 11 1 10 14 19 5 11 1 14 16 15 3 12 1 12 16 18 4 6 1 15 16 10 4 2 1 17 6 19 13 20 1 15 9 1 5 6 1 2 1 16 6 17 1 3 8 4 12 6 1 13 17 10 3 15 1 18 6 11 1 7 1 13 19 16 1 2 1 19 4 12 13 20 1 12 4 1 19 8 1 14 2 10 9 15 1 17 14 1 8 9 1 16 13 20 10 19 1 19 3 11 13 18 1 18 4 1 3 20 1 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-152 -113 187 -82 18146 -679 -156 -447 965 -84 28964 -1143 -568 -270 1449 -221 21514 -425 -520 -387 643 -280 11466 -122 -383 -159 297 -178 24438 -467 -728 -297 1033 -408 44096 -1845 -1384 243 3609 -656 19284 2341 -1631 -239 8236 -2807 23927 2013 -1905 -86 8743 -2872 -13082 209 273 335 4914 -131 -9153 2 217 473 2192 60 -8711 -2 175 479 2176 52 -15770 -2 175 1022 4348 52 -118 1 3 4 24 2 -1061 2 21 53 288 4 -4934 23 84 227 1512 1 4744 125 -461 -83 5200 -741 15875 73 -1249 74 8723 -1500 1314 -65 -104 63 683 -92 15727 -815 -1637 1214 9799 -1256 15311 -755 -1541 1042 9567 -1228 -1 0 0 0 1 0 -1032 -77 -355 131 8112 -715 1620 -83 -102 51 797 -108 94 -7 -10 5 135 -14 -5 -73 -175 104 3171 -278 3382 -173 -148 55 1583 -224 398 -19 -20 5 205 -28 11590 -557 -628 247 5087 -728 end *Totals: facets=1187 bases=3303 lrslib-073/ext/redund/r100_5.ine.ext0000777000175000017500000000437514625766575015674 0ustar avisavis*mplrs:lrslib_v.7.3_2024.4.17(128bit,hybrid arithmetic,gmp v.6.2)64 processes *Input taken from r100_5.ine *Starting depth of 2 maxcobases=50 maxdepth=0 lmin=3 lmax=3 scale=100 *Phase 1 time: 0 seconds. V-representation begin ***** 6 rational 1 11 6 5 2 18 1 19 9 10 1 4 1 13 19 16 1 2 1 18 6 11 1 7 1 13 10 8 2 3 1 17 10 14 3 20 1 16 12 9 1 3 1 18 4 1 3 20 1 13 17 10 3 15 1 2 1 16 6 17 1 20 13 16 6 14 1 4 8 5 2 11 1 16 15 18 4 9 1 18 17 10 6 2 1 16 13 20 10 19 1 10 15 16 2 11 1 20 6 9 8 10 1 14 16 15 3 12 1 13 6 7 9 2 1 12 5 18 7 4 1 9 17 10 7 16 1 19 17 11 6 15 1 16 11 8 6 1 1 4 18 8 1 2 1 3 6 13 2 10 1 5 7 12 4 16 1 7 9 16 6 20 1 20 14 5 12 6 1 1 19 18 4 2 1 16 1 18 12 17 1 13 19 7 16 17 1 15 2 10 6 4 1 14 10 7 19 5 1 6 13 12 1 5 1 6 1 12 9 2 1 9 18 19 14 13 1 1 13 12 18 15 1 15 18 19 12 16 1 15 12 18 4 8 1 19 18 14 20 17 1 15 16 10 4 2 1 4 17 15 13 2 1 6 19 16 20 7 1 14 12 16 11 3 1 17 14 1 8 9 1 19 5 9 13 1 1 12 16 18 4 6 1 8 12 19 16 3 1 10 14 19 5 11 1 15 2 16 10 6 1 3 13 11 19 8 1 12 9 4 17 3 1 15 13 4 12 2 1 7 13 4 14 3 1 9 10 11 7 20 1 19 4 12 13 20 1 17 6 19 13 20 1 1 10 5 7 17 1 3 8 1 16 6 1 12 2 14 16 8 1 18 11 12 14 2 1 4 10 1 15 18 1 5 2 8 14 18 1 3 8 4 12 6 1 15 9 1 5 6 1 7 20 2 8 9 1 20 8 4 17 14 1 4 15 19 6 16 1 19 18 14 17 4 1 14 19 13 4 9 1 17 18 8 19 12 1 4 20 3 5 13 1 13 7 17 19 11 1 8 17 4 20 6 1 14 2 10 9 15 1 6 3 2 15 14 1 12 4 1 19 8 1 19 1 12 20 9 1 19 3 11 13 18 1 17 3 10 20 16 end *Total number of jobs: 1882, L became empty 204 times, tree depth 91, deepest output depth 71 *Finished with 0 64-bit, 0 128-bit, 62 GMP workers *Totals: vertices=80 rays=0 bases=35036 integer-vertices=80 *mplrs:lrslib_v.7.3_2024.4.17(128bit,hybrid arithmetic,gmp v.6.2)64 processes *Elapsed time: 1 seconds. lrslib-073/ext/redund/r2000_5.ext0000777000175000017500000010530714625766576015201 0ustar avisavisrand2000_5 V-representation begin 2000 7 integer 0 1 4 19 16 15 1 0 1 9 11 19 7 4 0 1 1 11 12 4 16 0 1 5 20 18 6 1 0 1 1 8 11 4 17 0 1 1 7 5 6 11 0 1 16 2 18 6 14 0 1 15 13 16 12 20 0 1 16 2 8 18 5 0 1 6 16 3 7 1 0 1 20 14 15 16 12 0 1 14 11 12 8 13 0 1 1 16 18 14 7 0 1 20 13 11 19 9 0 1 17 1 2 4 5 0 1 7 13 19 12 5 0 1 5 14 18 11 2 0 1 20 7 14 12 2 0 1 18 6 10 16 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3 0 1 10 18 1 16 9 0 1 12 5 11 9 17 0 1 17 20 13 7 14 0 1 5 12 10 20 16 0 1 15 11 13 14 7 0 1 17 3 18 13 6 0 1 18 1 15 20 9 0 1 12 18 11 8 3 0 1 18 12 7 15 1 0 1 7 16 2 10 9 0 1 4 15 13 9 2 0 1 11 2 20 10 4 0 1 1 15 9 2 18 0 1 2 7 11 18 4 0 1 14 5 19 9 2 0 1 16 12 20 8 5 0 1 9 19 6 17 1 0 1 15 19 14 10 7 0 1 17 1 15 10 5 0 1 5 12 20 6 1 0 1 17 13 9 11 6 0 1 6 12 5 15 13 0 1 3 19 1 14 11 0 1 12 7 1 19 15 0 1 19 20 7 12 10 0 1 1 6 12 11 17 0 1 10 19 9 18 17 0 1 5 14 18 13 11 0 1 14 6 12 17 5 0 1 10 2 4 7 8 0 1 10 14 16 19 13 0 1 10 4 12 14 20 0 1 16 15 18 14 1 0 1 9 10 2 1 8 0 1 18 10 19 7 17 0 1 15 8 17 11 1 0 1 5 16 10 3 17 0 1 14 7 5 1 20 0 1 6 4 1 9 19 0 1 20 1 8 12 18 0 1 8 19 7 11 13 0 1 3 17 9 18 8 0 1 8 7 2 18 17 0 1 19 4 13 15 14 0 1 13 20 16 5 3 0 1 8 17 15 2 5 0 1 11 7 18 3 14 0 1 1 16 5 8 10 0 1 9 2 1 3 18 0 1 5 18 10 2 12 0 1 8 5 2 20 12 0 1 12 20 9 19 10 0 1 9 6 15 2 11 0 1 1 18 8 2 9 0 1 13 1 17 12 2 0 1 11 19 12 16 18 0 1 19 6 9 3 8 0 1 8 14 3 18 12 0 1 20 13 10 2 14 0 1 4 19 15 12 6 0 1 5 7 15 19 6 0 1 10 7 2 17 16 0 1 12 15 6 18 20 0 1 12 19 3 5 10 0 1 14 11 19 1 16 0 1 5 14 7 8 20 0 1 8 7 18 5 6 0 1 12 16 4 2 5 0 1 1 3 15 10 19 0 1 11 12 6 9 14 0 1 8 7 6 2 15 0 1 5 13 17 6 18 0 1 18 6 12 1 4 0 1 2 12 15 11 8 0 1 4 1 7 2 17 0 1 17 5 18 2 19 0 1 12 13 3 2 17 0 1 17 9 19 3 20 0 1 14 10 20 13 8 0 1 17 10 18 8 15 0 1 14 3 17 6 10 0 1 11 13 15 10 14 0 1 9 2 14 19 13 0 1 15 20 2 4 18 0 1 14 11 3 1 16 0 1 18 9 11 8 2 0 1 8 20 6 5 14 0 1 5 10 15 8 2 0 1 4 18 7 5 9 0 1 1 9 19 4 5 0 1 18 9 4 2 13 0 1 7 5 20 9 1 0 1 16 5 6 13 18 0 1 19 17 1 18 7 0 1 3 16 12 7 1 0 1 9 4 1 3 11 0 1 11 17 4 12 16 0 1 8 9 20 19 13 0 1 9 20 14 2 3 0 1 4 19 17 2 3 0 1 10 6 4 9 1 0 1 5 8 7 2 20 0 1 14 7 17 15 2 0 1 12 2 13 18 17 0 1 15 1 7 8 18 0 1 1 18 5 11 3 0 1 10 1 11 4 2 0 1 1 6 15 8 14 0 1 10 20 16 9 4 0 1 13 8 16 19 14 0 1 20 9 2 14 3 0 1 13 10 5 18 8 0 1 5 7 2 11 19 0 1 6 2 11 13 7 0 1 17 11 15 3 8 0 1 15 20 9 11 2 0 1 9 14 19 11 3 0 1 5 6 8 20 1 0 1 8 18 17 12 19 0 1 4 1 8 12 16 0 1 20 12 17 11 19 0 1 14 1 9 7 13 0 1 3 15 16 2 6 0 1 10 5 8 9 15 0 1 6 18 5 13 19 0 1 8 2 7 19 9 0 1 19 20 10 15 5 0 1 17 14 18 20 6 0 1 11 19 17 8 20 end lrslib-073/ext/redund/r2000_5.ext1600000777000175000017500000004406114625766575015426 0ustar avisavis*mplrs:lrslib_v.7.3_2024.4.17(128bit,hybrid arithmetic,gmp v.6.2)160 processes *Input taken from r2000_5.ext *rows=60 lastp=10 lastrows=10 j=1 *redund *interior point found, no hidden linearities V-representation begin 523 6 rational 1 4 19 16 15 1 1 5 20 18 6 1 1 6 16 3 7 1 1 17 1 2 4 5 1 2 7 1 9 6 1 6 1 15 20 9 1 16 18 20 6 13 1 19 14 1 9 4 1 1 11 17 19 16 1 1 7 2 19 11 1 6 2 7 10 1 1 2 19 15 13 20 1 15 2 9 19 18 1 16 1 17 8 19 1 16 13 19 18 17 1 18 12 17 9 20 1 20 2 19 13 1 1 18 2 10 13 20 1 18 8 6 20 3 1 15 1 6 2 14 1 4 1 15 19 14 1 2 19 15 20 14 1 18 5 12 20 19 1 2 9 6 20 19 1 20 6 3 1 10 1 15 12 5 18 1 1 20 15 1 19 13 1 6 2 1 8 13 1 19 18 1 14 5 1 17 20 19 10 7 1 8 7 1 20 16 1 20 14 1 12 10 1 5 2 7 1 20 1 17 2 3 18 8 1 10 4 17 20 12 1 18 20 14 11 2 1 19 2 16 1 14 1 11 20 6 14 19 1 20 15 7 16 19 1 3 18 7 1 6 1 11 19 1 5 4 1 12 11 19 16 20 1 6 17 20 2 12 1 13 9 20 3 5 1 1 4 12 2 14 1 18 12 19 5 3 1 13 9 20 16 1 1 20 2 9 5 13 1 20 18 3 15 9 1 16 3 1 17 14 1 11 17 16 2 20 1 5 1 3 12 16 1 6 19 20 2 4 1 16 18 20 10 4 1 19 12 17 1 4 1 2 1 4 7 17 1 19 1 9 3 12 1 3 5 10 15 20 1 13 4 8 20 1 1 14 1 9 20 12 1 19 11 2 14 18 1 8 20 3 4 17 1 5 19 17 20 10 1 6 20 5 14 19 1 7 6 17 20 18 1 19 2 18 4 20 1 20 4 6 9 2 1 10 6 20 16 1 1 3 1 15 9 20 1 16 9 19 1 7 1 20 19 4 1 5 1 11 2 1 5 4 1 1 9 13 2 3 1 7 20 15 19 17 1 7 1 11 2 8 1 5 10 20 12 19 1 4 14 19 2 18 1 19 6 20 3 7 1 16 2 20 11 4 1 19 11 20 18 3 1 20 1 16 15 8 1 9 18 15 19 1 1 13 7 1 2 10 1 18 20 15 19 4 1 11 15 8 20 3 1 20 6 9 17 3 1 4 7 1 2 14 1 1 10 20 6 14 1 15 3 7 1 19 1 1 18 19 2 7 1 15 18 20 6 2 1 20 19 2 4 16 1 1 10 20 6 15 1 15 10 20 19 1 1 1 9 11 7 2 1 3 4 9 20 19 1 3 10 9 2 20 1 11 2 6 19 1 1 14 7 10 1 2 1 14 7 3 5 20 1 1 18 2 17 3 1 1 3 18 4 6 1 19 7 18 20 9 1 16 17 1 13 20 1 1 9 2 17 15 1 10 17 16 1 4 1 4 1 13 3 20 1 2 17 1 18 19 1 2 19 7 20 13 1 15 12 20 3 4 1 19 17 18 11 9 1 20 6 9 19 16 1 1 14 7 20 8 1 3 1 20 10 9 1 17 12 18 3 20 1 6 20 11 1 2 1 18 1 16 5 3 1 18 2 20 17 16 1 8 9 3 18 1 1 14 19 16 7 1 1 6 20 19 13 10 1 19 1 20 2 12 1 1 14 17 15 19 1 5 18 15 1 17 1 19 17 20 2 18 1 16 18 15 20 11 1 20 19 11 9 3 1 20 6 5 1 17 1 3 16 1 19 12 1 1 20 9 5 10 1 4 12 19 1 16 1 19 2 3 8 5 1 3 14 9 20 1 1 6 7 1 4 19 1 9 4 7 5 1 1 6 16 12 20 2 1 3 11 1 20 4 1 18 20 3 11 1 1 16 4 1 13 3 1 7 5 18 17 20 1 1 3 13 15 19 1 13 10 19 3 20 1 1 11 4 18 19 1 2 7 13 16 20 1 5 16 1 3 20 1 20 10 19 8 16 1 15 3 1 9 7 1 5 12 2 1 8 1 1 6 4 16 5 1 12 2 1 18 9 1 8 19 1 10 2 1 19 20 2 13 17 1 10 19 7 20 16 1 20 17 10 1 3 1 12 20 4 17 15 1 20 18 5 17 13 1 1 20 17 16 14 1 16 1 9 18 4 1 13 19 1 3 6 1 5 18 17 16 1 1 18 2 4 16 7 1 7 5 1 4 6 1 20 7 3 17 12 1 15 12 20 6 19 1 4 16 6 17 20 1 13 8 17 18 20 1 14 19 13 11 20 1 12 1 17 2 13 1 20 9 1 7 19 1 8 5 2 18 20 1 18 15 1 4 8 1 16 1 17 5 2 1 11 10 3 20 1 1 11 2 18 9 1 1 1 15 18 20 9 1 16 11 9 20 1 1 2 11 3 1 17 1 3 16 5 13 1 1 20 3 7 19 13 1 1 19 13 20 12 1 20 1 18 8 9 1 15 19 18 1 11 1 13 1 17 5 2 1 3 11 2 1 10 1 8 16 15 1 2 1 10 20 11 1 15 1 3 12 6 4 20 1 9 7 19 6 1 1 9 14 2 8 1 1 2 4 10 5 19 1 1 5 18 19 2 1 12 1 3 20 10 1 7 16 15 1 3 1 16 8 14 2 1 1 9 3 20 7 19 1 19 20 11 10 17 1 14 20 3 15 4 1 20 1 7 13 9 1 2 1 5 17 8 1 1 11 9 20 14 1 17 3 20 18 14 1 13 11 2 5 1 1 3 19 2 17 18 1 10 6 20 17 1 1 8 19 13 17 1 1 5 14 2 17 1 1 9 16 20 11 2 1 17 19 4 20 18 1 8 1 10 13 2 1 4 19 10 3 20 1 12 19 2 4 20 1 12 20 4 15 1 1 15 8 19 3 1 1 14 1 10 3 19 1 1 20 8 10 6 1 3 5 16 20 4 1 8 20 1 11 9 1 18 14 12 16 20 1 2 20 9 18 13 1 20 2 19 14 12 1 15 18 19 3 20 1 6 4 1 3 18 1 4 9 16 1 17 1 2 8 17 1 10 1 18 3 1 4 15 1 4 2 14 18 19 1 6 14 12 3 1 1 17 6 18 14 20 1 16 1 20 19 2 1 2 13 20 18 9 1 12 1 11 18 20 1 20 9 19 12 11 1 19 4 1 2 11 1 10 20 13 9 19 1 1 15 13 17 2 1 2 14 1 17 6 1 3 15 17 9 20 1 5 20 2 7 9 1 16 13 18 10 1 1 20 12 19 1 8 1 1 16 12 2 19 1 19 20 10 3 13 1 5 3 2 11 19 1 3 1 12 20 5 1 1 8 15 2 6 1 3 20 6 1 18 1 15 1 20 19 18 1 18 20 19 3 14 1 16 19 15 20 10 1 1 2 12 4 11 1 2 20 14 1 9 1 7 6 1 19 2 1 18 2 6 15 3 1 20 5 19 9 16 1 13 17 1 2 12 1 6 2 10 20 17 1 4 2 20 8 5 1 9 16 1 19 2 1 19 2 15 20 1 1 20 10 3 7 1 1 20 7 16 10 1 1 1 16 15 20 17 1 1 2 20 5 8 1 16 1 2 10 4 1 2 20 3 8 9 1 17 19 10 1 6 1 2 4 1 10 14 1 19 20 7 12 2 1 19 9 1 4 2 1 3 2 19 6 16 1 19 12 1 20 6 1 2 20 16 14 3 1 14 1 6 11 20 1 20 13 5 16 4 1 11 1 8 2 4 1 2 16 4 20 12 1 19 13 4 1 18 1 15 1 19 3 16 1 9 1 14 18 2 1 3 16 2 4 5 1 2 20 14 17 19 1 2 7 12 10 1 1 16 3 20 1 14 1 6 16 1 15 2 1 5 15 8 18 20 1 14 15 1 2 13 1 20 4 19 7 10 1 1 18 14 2 20 1 2 1 6 17 11 1 16 11 9 20 19 1 3 7 9 1 8 1 2 9 12 3 20 1 20 7 1 9 16 1 19 20 17 3 12 1 1 16 8 6 2 1 13 2 8 1 6 1 15 8 17 18 20 1 20 12 7 1 19 1 18 16 15 14 19 1 20 3 12 4 5 1 4 1 3 15 13 1 18 1 11 3 17 1 20 16 1 9 19 1 19 11 18 20 12 1 18 10 1 17 16 1 2 20 8 1 17 1 1 20 7 4 17 1 4 1 13 7 20 1 1 2 20 10 19 1 17 12 6 1 20 1 1 17 20 13 18 1 11 1 20 9 17 1 3 1 5 16 17 1 6 10 20 1 15 1 1 7 20 15 14 1 1 3 13 15 2 1 20 18 8 16 7 1 4 19 8 10 20 1 8 4 2 10 1 1 8 2 1 17 15 1 4 2 11 1 3 1 1 5 19 15 20 1 20 3 18 19 13 1 20 17 12 19 6 1 7 17 19 20 15 1 1 4 16 18 12 1 17 9 1 3 16 1 20 19 5 8 2 1 15 9 5 2 1 1 14 15 1 2 16 1 3 9 1 17 16 1 18 11 2 20 10 1 1 2 8 11 5 1 4 20 1 8 13 1 13 2 12 8 1 1 4 2 12 13 1 1 20 2 16 8 3 1 10 16 20 19 3 1 12 5 3 1 7 1 2 13 20 6 1 1 13 15 5 1 3 1 15 8 1 2 9 1 4 7 5 1 6 1 6 18 2 15 20 1 6 5 20 17 7 1 1 13 19 5 16 1 6 11 4 3 1 1 17 7 2 20 5 1 20 15 2 7 1 1 1 17 5 2 12 1 15 1 2 17 5 1 6 18 13 4 1 1 20 14 11 4 1 1 5 1 18 11 20 1 4 20 1 11 8 1 3 20 8 17 4 1 8 1 15 6 4 1 17 20 8 5 1 1 13 15 18 1 6 1 20 17 12 18 14 1 13 4 19 1 17 1 7 18 17 4 20 1 15 20 2 6 1 1 17 1 7 19 15 1 1 8 2 10 12 1 2 19 6 8 1 1 19 7 16 18 20 1 16 17 6 20 8 1 9 3 5 1 20 1 18 8 7 2 3 1 18 2 13 8 20 1 20 1 3 10 19 1 8 19 20 18 6 1 17 10 20 16 15 1 2 3 5 8 4 1 1 3 2 9 16 1 10 1 3 4 9 1 4 20 9 18 1 1 15 5 7 4 20 1 20 18 10 15 7 1 19 20 2 6 10 1 15 19 1 11 18 1 1 5 20 3 18 1 8 6 1 17 18 1 17 7 20 6 2 1 6 4 16 7 1 1 20 18 17 1 19 1 4 20 5 8 18 1 15 20 12 16 18 1 16 20 2 12 1 1 16 15 7 19 20 1 11 1 3 14 4 1 19 5 18 1 2 1 6 18 2 20 14 1 1 15 20 10 5 1 18 8 9 19 1 1 20 5 2 1 18 1 20 2 19 12 3 1 11 20 16 17 6 1 5 16 18 1 7 1 4 14 5 7 1 1 12 1 2 19 18 1 15 1 17 2 4 1 5 11 6 1 3 1 1 4 2 3 9 1 20 5 3 12 7 1 2 18 17 20 19 1 15 19 3 5 20 1 3 20 18 2 19 1 3 6 19 16 1 1 20 16 17 12 4 1 8 11 19 1 18 1 20 3 11 15 19 1 17 3 19 2 5 1 7 20 2 19 6 1 14 4 20 1 11 1 6 3 8 19 2 1 5 15 7 20 1 1 4 3 13 2 20 1 3 4 20 11 2 1 12 19 20 15 17 1 20 18 15 12 16 1 12 20 11 1 7 1 3 20 15 16 4 1 18 1 19 14 15 1 1 10 20 15 12 1 18 8 5 6 1 1 2 20 18 13 10 1 6 12 20 15 18 1 10 1 5 18 19 1 13 1 20 7 5 1 16 2 17 15 20 1 15 20 10 6 18 1 6 19 20 9 12 1 11 2 4 20 17 1 17 12 16 15 20 1 11 17 2 1 19 1 7 20 19 9 12 1 15 4 16 1 20 1 16 3 19 10 1 1 1 19 15 18 16 1 20 16 1 13 12 1 9 1 10 8 2 1 17 19 5 2 20 1 8 1 6 17 3 1 13 2 20 5 16 1 3 12 14 1 19 1 14 20 2 3 8 1 5 20 18 15 12 1 18 14 12 16 1 1 1 17 7 2 18 1 20 8 1 11 3 1 1 10 3 16 2 1 19 20 4 8 1 1 14 1 20 18 3 1 3 19 20 15 10 1 15 20 2 6 19 1 2 12 14 16 1 1 13 19 5 1 20 1 3 1 6 2 5 1 16 15 14 19 1 1 13 20 8 2 16 1 1 17 19 3 2 1 20 13 9 14 2 1 20 10 18 15 17 1 1 5 18 19 7 1 17 1 13 15 20 1 17 9 20 15 18 1 11 18 15 16 20 1 1 16 18 19 3 1 12 18 3 1 15 1 2 7 3 19 15 1 2 16 20 4 14 1 16 20 9 19 18 1 4 3 19 20 1 1 5 20 19 11 18 1 20 4 14 2 10 1 7 17 1 15 2 1 11 20 4 2 1 1 19 10 4 11 20 1 7 2 3 1 12 1 17 2 6 12 1 1 11 2 6 20 5 1 5 7 1 18 14 1 13 19 1 18 7 1 19 3 5 1 15 1 2 14 20 17 7 1 20 4 9 16 3 1 18 1 15 20 9 1 1 15 9 2 18 1 9 19 6 17 1 1 5 12 20 6 1 1 3 19 1 14 11 1 16 15 18 14 1 1 9 10 2 1 8 1 14 7 5 1 20 1 6 4 1 9 19 1 20 1 8 12 18 1 13 20 16 5 3 1 9 2 1 3 18 1 8 5 2 20 12 1 1 18 8 2 9 1 14 11 19 1 16 1 1 3 15 10 19 1 18 6 12 1 4 1 4 1 7 2 17 1 17 5 18 2 19 1 17 9 19 3 20 1 15 20 2 4 18 1 7 5 20 9 1 1 19 17 1 18 7 1 9 4 1 3 11 1 8 9 20 19 13 1 9 20 14 2 3 1 4 19 17 2 3 1 1 18 5 11 3 1 10 1 11 4 2 1 20 9 2 14 3 1 5 6 8 20 1 1 20 12 17 11 19 1 19 20 10 15 5 1 17 14 18 20 6 1 11 19 17 8 20 end *input had 2000 rows and 7 columns * 1477 redundant row(s) found 2 3 5 6 7 8 9 11 12 13 14 16 17 18 19 20 21 22 23 24 26 27 28 29 31 32 33 34 35 36 37 38 39 40 41 42 45 46 47 49 50 51 53 54 55 56 57 58 59 61 62 63 64 65 66 67 68 70 72 73 74 75 76 77 79 80 81 82 83 85 88 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 110 111 114 115 118 119 121 123 125 127 129 131 133 134 135 136 138 139 140 141 142 143 144 145 146 149 151 152 153 154 155 156 157 159 160 162 163 167 168 171 172 173 174 175 176 177 179 180 181 182 186 187 188 189 190 191 193 194 195 197 198 199 200 205 207 208 210 211 212 213 215 216 217 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 240 241 242 243 246 250 251 253 255 256 257 258 259 260 261 262 263 264 265 266 270 271 272 274 275 276 277 278 279 280 281 282 285 287 288 289 290 292 294 295 296 298 299 300 301 302 305 308 309 310 312 313 314 315 316 317 320 321 322 323 324 325 326 327 329 330 331 334 335 336 337 338 339 341 342 343 344 345 346 349 351 353 355 356 357 358 359 360 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 391 392 393 394 395 396 398 399 400 402 403 404 406 407 409 410 412 413 414 415 416 417 418 420 422 423 424 425 426 427 428 429 430 431 432 434 435 436 437 439 440 442 443 444 445 447 448 449 452 453 454 455 457 458 460 461 462 463 464 465 466 467 468 469 471 472 474 475 476 477 479 480 481 482 483 484 485 486 488 490 491 492 493 494 495 496 498 500 502 503 504 505 506 507 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 529 530 531 532 533 534 535 537 539 540 541 542 543 544 545 546 547 548 549 551 552 553 554 557 558 560 561 562 563 565 566 567 568 569 571 573 574 576 577 578 579 580 581 584 586 587 588 589 590 593 594 595 596 598 599 600 601 602 603 604 605 607 610 611 612 613 616 617 619 621 623 624 625 626 628 629 630 631 632 634 635 636 637 639 640 641 642 644 645 646 647 648 649 650 652 653 655 656 658 659 661 662 663 664 665 666 668 670 671 672 675 676 678 679 683 685 686 687 688 690 691 692 693 694 696 697 698 699 700 701 702 703 706 707 709 710 711 715 716 718 720 721 722 724 725 728 730 732 733 735 736 737 738 739 740 741 742 743 745 746 751 752 753 754 755 756 757 758 760 761 762 763 765 766 768 771 772 773 774 775 777 778 779 780 782 783 784 785 786 787 788 789 790 793 794 795 796 797 798 799 800 801 802 803 804 807 808 814 815 817 818 820 821 822 823 824 825 826 827 828 829 830 831 832 834 836 839 841 842 843 844 845 846 848 849 850 851 852 853 854 856 857 858 860 861 862 863 864 866 868 869 871 872 873 874 875 879 880 881 887 889 891 892 894 899 900 901 902 903 906 907 908 909 910 911 912 914 915 918 919 920 921 922 924 926 928 929 930 931 933 934 936 937 938 939 940 941 942 943 945 946 948 949 950 951 952 953 954 955 956 957 959 960 961 962 963 964 965 966 968 969 970 972 973 974 975 976 978 979 981 983 984 985 986 987 988 990 991 992 993 994 995 996 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1011 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1027 1029 1030 1031 1032 1034 1035 1036 1037 1038 1040 1041 1042 1044 1046 1048 1050 1051 1052 1053 1054 1055 1056 1057 1058 1060 1061 1064 1065 1066 1067 1069 1070 1071 1073 1075 1076 1078 1079 1080 1081 1082 1084 1085 1086 1087 1088 1089 1090 1092 1093 1095 1096 1098 1102 1103 1104 1106 1107 1108 1109 1111 1112 1113 1116 1117 1118 1120 1121 1123 1124 1125 1126 1127 1128 1130 1132 1133 1134 1135 1136 1137 1139 1140 1141 1142 1143 1144 1145 1146 1149 1152 1153 1155 1156 1157 1158 1159 1160 1161 1162 1163 1167 1168 1169 1170 1172 1174 1176 1177 1180 1182 1183 1184 1186 1187 1189 1191 1192 1193 1194 1196 1198 1199 1200 1201 1202 1203 1204 1205 1207 1208 1212 1217 1218 1219 1220 1221 1222 1224 1226 1229 1230 1231 1232 1233 1234 1235 1237 1238 1239 1240 1241 1242 1243 1244 1246 1247 1248 1249 1250 1253 1254 1256 1257 1258 1259 1260 1261 1262 1263 1265 1266 1267 1271 1272 1273 1274 1275 1277 1278 1279 1280 1285 1286 1287 1288 1289 1291 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1316 1317 1320 1323 1324 1326 1328 1329 1330 1332 1334 1336 1339 1340 1341 1343 1344 1345 1346 1348 1349 1351 1352 1353 1354 1356 1357 1358 1360 1361 1362 1363 1364 1366 1367 1369 1370 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1387 1389 1390 1392 1394 1395 1396 1397 1398 1399 1400 1401 1402 1404 1406 1407 1408 1409 1411 1412 1415 1416 1417 1418 1420 1421 1423 1424 1425 1426 1427 1428 1430 1431 1434 1436 1437 1438 1439 1440 1441 1442 1445 1446 1447 1448 1449 1450 1451 1452 1453 1455 1457 1458 1459 1460 1462 1463 1466 1468 1470 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1487 1488 1491 1492 1494 1495 1496 1498 1500 1501 1502 1503 1504 1505 1506 1508 1509 1511 1513 1514 1515 1516 1517 1518 1519 1520 1522 1523 1524 1525 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1543 1544 1545 1546 1547 1552 1554 1555 1556 1557 1558 1560 1561 1562 1563 1564 1566 1567 1568 1569 1570 1571 1572 1574 1575 1576 1577 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1618 1619 1620 1621 1622 1623 1624 1625 1626 1633 1635 1636 1637 1639 1640 1641 1642 1643 1646 1648 1649 1651 1652 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1668 1670 1672 1673 1676 1677 1679 1680 1681 1683 1684 1685 1686 1687 1689 1690 1691 1692 1693 1694 1695 1696 1697 1699 1703 1704 1705 1706 1707 1708 1709 1710 1712 1713 1714 1715 1716 1717 1718 1720 1721 1723 1724 1725 1727 1728 1729 1730 1733 1734 1735 1738 1739 1740 1743 1744 1747 1748 1749 1750 1751 1754 1756 1758 1759 1760 1761 1762 1765 1767 1769 1771 1772 1773 1774 1775 1776 1777 1778 1779 1783 1784 1785 1787 1788 1789 1790 1791 1792 1795 1796 1798 1799 1800 1801 1802 1803 1804 1805 1808 1810 1811 1812 1814 1815 1817 1818 1820 1822 1824 1825 1826 1827 1829 1830 1831 1835 1836 1839 1840 1842 1845 1846 1847 1848 1852 1854 1855 1857 1858 1859 1860 1862 1863 1864 1865 1866 1868 1869 1872 1873 1874 1875 1876 1877 1879 1880 1881 1882 1883 1885 1886 1887 1889 1890 1892 1893 1895 1896 1897 1898 1899 1900 1901 1902 1903 1906 1907 1908 1912 1913 1914 1915 1917 1918 1919 1921 1923 1924 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1937 1938 1939 1941 1942 1943 1945 1948 1950 1951 1952 1953 1954 1956 1957 1958 1959 1960 1961 1962 1964 1966 1968 1972 1973 1974 1975 1976 1979 1980 1981 1983 1984 1985 1986 1987 1988 1990 1991 1993 1994 1995 1996 1997 *Total number of jobs: 158, L became empty 1 times, tree depth 0, deepest output depth 0 *Finished with 158 64-bit, 0 128-bit, 0 GMP workers *mplrs:lrslib_v.7.3_2024.4.17(128bit,hybrid arithmetic,gmp v.6.2)160 processes *Elapsed time: 2 seconds. lrslib-073/ext/redund/r2000_5.extredc0000777000175000017500000003450714625766575016041 0ustar avisavisinput file r2000_5.ext is open redundant rows: 2 3 5 6 7 8 9 11 12 13 14 16 17 18 19 20 21 22 23 24 25 26 27 28 29 31 32 33 34 35 36 37 38 39 40 41 42 45 46 47 49 50 51 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 70 72 73 74 75 76 77 79 80 81 82 83 85 88 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 110 111 114 115 118 119 121 123 125 127 128 129 131 133 134 135 136 138 139 140 141 142 143 144 145 146 149 151 152 153 154 155 156 157 159 160 162 163 167 168 171 172 173 174 175 176 177 179 180 181 182 186 187 188 189 190 191 193 194 195 197 198 199 200 205 207 208 210 211 212 213 215 216 217 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 240 241 242 243 246 250 251 253 255 256 257 258 259 260 261 262 263 264 265 266 270 271 272 274 275 276 277 278 279 280 281 282 285 287 288 289 290 292 293 294 295 296 297 298 299 300 301 302 304 305 308 309 310 312 313 314 315 316 317 320 321 322 323 324 325 326 327 329 330 331 333 334 335 336 337 338 339 341 342 343 344 345 346 349 350 351 353 355 356 357 358 359 360 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 391 392 393 394 395 396 398 399 400 402 403 404 406 407 408 409 410 412 413 414 415 416 417 418 420 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 439 440 442 443 444 445 447 448 449 452 453 454 455 457 458 460 461 462 463 464 465 466 467 468 469 471 472 474 475 476 477 479 480 481 482 483 484 485 486 488 490 491 492 493 494 495 496 498 500 502 503 504 505 506 507 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 529 530 531 532 533 534 535 537 539 540 541 542 543 544 545 546 547 548 549 551 552 553 554 557 558 560 561 562 563 565 566 567 568 569 571 573 574 576 577 578 579 580 581 584 586 587 588 589 590 593 594 595 596 598 599 600 601 602 603 604 605 607 608 610 611 612 613 616 617 619 621 623 624 625 626 628 629 630 631 632 634 635 636 637 639 640 641 642 644 645 646 647 648 649 650 652 653 654 655 656 658 659 661 662 663 664 665 666 668 670 671 672 675 676 678 679 683 685 686 687 688 690 691 692 693 694 696 697 698 699 700 701 702 703 705 706 707 709 710 711 715 716 718 720 721 722 724 725 728 730 732 733 735 736 737 738 739 740 741 742 743 745 746 751 752 753 754 755 756 757 758 760 761 762 763 765 766 768 771 772 773 774 775 777 778 779 780 782 783 784 785 786 787 788 789 790 793 794 795 796 797 798 799 800 801 802 803 804 805 807 808 811 814 815 817 818 820 821 822 823 824 825 826 827 828 829 830 831 832 834 836 839 840 841 842 843 844 845 846 848 849 850 851 852 853 854 856 857 858 860 861 862 863 864 866 868 869 871 872 873 874 875 876 879 880 881 887 889 891 892 894 899 900 901 902 903 906 907 908 909 910 911 912 914 915 916 918 919 920 921 922 924 926 928 929 930 931 933 934 936 937 938 939 940 941 942 943 945 946 948 949 950 951 952 953 954 955 956 957 959 960 961 962 963 964 965 966 968 969 970 972 973 974 975 976 978 979 981 983 984 985 986 987 988 990 991 992 993 994 995 996 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1011 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1029 1030 1031 1032 1034 1035 1036 1037 1038 1040 1041 1042 1044 1046 1048 1050 1051 1052 1053 1054 1055 1056 1057 1058 1060 1061 1064 1065 1066 1067 1069 1070 1071 1073 1075 1076 1078 1079 1080 1081 1082 1084 1085 1086 1087 1088 1089 1090 1092 1093 1095 1096 1098 1102 1103 1104 1106 1107 1108 1109 1111 1112 1113 1115 1116 1117 1118 1120 1121 1123 1124 1125 1126 1127 1128 1130 1132 1133 1134 1135 1136 1137 1139 1140 1141 1142 1143 1144 1145 1146 1149 1152 1153 1155 1156 1157 1158 1159 1160 1161 1162 1163 1167 1168 1169 1170 1172 1174 1175 1176 1177 1180 1182 1183 1184 1186 1187 1189 1191 1192 1193 1194 1196 1198 1199 1200 1201 1202 1203 1204 1205 1207 1208 1212 1217 1218 1219 1220 1221 1222 1224 1226 1229 1230 1231 1232 1233 1234 1235 1237 1238 1239 1240 1241 1242 1243 1244 1246 1247 1248 1249 1250 1253 1254 1256 1257 1258 1259 1260 1261 1262 1263 1265 1266 1267 1269 1271 1272 1273 1274 1275 1277 1278 1279 1280 1285 1286 1287 1288 1289 1291 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1315 1316 1317 1319 1320 1321 1323 1324 1326 1327 1328 1329 1330 1332 1333 1334 1335 1336 1337 1339 1340 1341 1343 1344 1345 1346 1348 1349 1350 1351 1352 1353 1354 1356 1357 1358 1360 1361 1362 1363 1364 1366 1367 1369 1370 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1387 1389 1390 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1404 1406 1407 1408 1409 1411 1412 1415 1416 1417 1418 1420 1421 1423 1424 1425 1426 1427 1428 1429 1430 1431 1434 1436 1437 1438 1439 1440 1441 1442 1445 1446 1447 1448 1449 1450 1451 1452 1453 1455 1457 1458 1459 1460 1462 1463 1465 1466 1468 1469 1470 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1487 1488 1491 1492 1494 1495 1496 1498 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1511 1513 1514 1515 1516 1517 1518 1519 1520 1522 1523 1524 1525 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1541 1543 1544 1545 1546 1547 1552 1554 1555 1556 1557 1558 1560 1561 1562 1563 1564 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1618 1619 1620 1621 1622 1623 1624 1625 1626 1633 1635 1636 1637 1639 1640 1641 1642 1643 1646 1648 1649 1651 1652 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1668 1670 1672 1673 1676 1677 1679 1680 1681 1683 1684 1685 1686 1687 1689 1690 1691 1692 1693 1694 1695 1696 1697 1699 1703 1704 1705 1706 1707 1708 1709 1710 1712 1713 1714 1715 1716 1717 1718 1720 1721 1723 1724 1725 1727 1728 1729 1730 1733 1734 1735 1738 1739 1740 1741 1743 1744 1747 1748 1749 1750 1751 1754 1756 1758 1759 1760 1761 1762 1765 1767 1769 1771 1772 1773 1774 1775 1776 1777 1778 1779 1783 1784 1785 1787 1788 1789 1790 1791 1792 1793 1795 1796 1798 1799 1800 1801 1802 1803 1804 1805 1808 1810 1811 1812 1814 1815 1817 1818 1820 1822 1824 1825 1826 1827 1829 1830 1831 1835 1836 1839 1840 1842 1845 1846 1847 1848 1850 1852 1854 1855 1857 1858 1859 1860 1862 1863 1864 1865 1866 1868 1869 1872 1873 1874 1875 1876 1877 1879 1880 1881 1882 1883 1885 1886 1887 1889 1890 1892 1893 1895 1896 1897 1898 1899 1900 1901 1902 1903 1905 1906 1907 1908 1912 1913 1914 1915 1917 1918 1919 1921 1923 1924 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1937 1938 1939 1941 1942 1943 1944 1945 1948 1950 1951 1952 1953 1954 1956 1957 1958 1959 1960 1961 1962 1964 1966 1967 1968 1972 1973 1974 1975 1976 1978 1979 1980 1981 1983 1984 1985 1986 1987 1988 1990 1991 1993 1994 1995 1996 1997 *Implicit linearity (after removal of redundant rows): 0 *Nonredundant representation (except for the linearity part): V-representation begin 477 6 rational 1 4 19 16 15 1 1 5 20 18 6 1 1 6 16 3 7 1 1 17 1 2 4 5 1 6 1 15 20 9 1 16 18 20 6 13 1 19 14 1 9 4 1 1 11 17 19 16 1 1 7 2 19 11 1 2 19 15 13 20 1 15 2 9 19 18 1 16 1 17 8 19 1 16 13 19 18 17 1 18 12 17 9 20 1 20 2 19 13 1 1 18 2 10 13 20 1 18 8 6 20 3 1 15 1 6 2 14 1 4 1 15 19 14 1 2 19 15 20 14 1 18 5 12 20 19 1 2 9 6 20 19 1 20 6 3 1 10 1 15 12 5 18 1 1 20 15 1 19 13 1 19 18 1 14 5 1 17 20 19 10 7 1 8 7 1 20 16 1 20 14 1 12 10 1 5 2 7 1 20 1 17 2 3 18 8 1 10 4 17 20 12 1 18 20 14 11 2 1 19 2 16 1 14 1 11 20 6 14 19 1 20 15 7 16 19 1 3 18 7 1 6 1 11 19 1 5 4 1 12 11 19 16 20 1 6 17 20 2 12 1 13 9 20 3 5 1 1 4 12 2 14 1 18 12 19 5 3 1 13 9 20 16 1 1 20 2 9 5 13 1 20 18 3 15 9 1 16 3 1 17 14 1 11 17 16 2 20 1 5 1 3 12 16 1 6 19 20 2 4 1 16 18 20 10 4 1 19 12 17 1 4 1 2 1 4 7 17 1 19 1 9 3 12 1 3 5 10 15 20 1 13 4 8 20 1 1 14 1 9 20 12 1 19 11 2 14 18 1 8 20 3 4 17 1 5 19 17 20 10 1 6 20 5 14 19 1 7 6 17 20 18 1 19 2 18 4 20 1 20 4 6 9 2 1 10 6 20 16 1 1 3 1 15 9 20 1 16 9 19 1 7 1 20 19 4 1 5 1 7 20 15 19 17 1 5 10 20 12 19 1 4 14 19 2 18 1 19 6 20 3 7 1 16 2 20 11 4 1 19 11 20 18 3 1 20 1 16 15 8 1 9 18 15 19 1 1 18 20 15 19 4 1 11 15 8 20 3 1 20 6 9 17 3 1 1 10 20 6 14 1 15 3 7 1 19 1 1 18 19 2 7 1 15 18 20 6 2 1 20 19 2 4 16 1 1 10 20 6 15 1 15 10 20 19 1 1 3 4 9 20 19 1 3 10 9 2 20 1 11 2 6 19 1 1 14 7 3 5 20 1 1 18 2 17 3 1 1 3 18 4 6 1 19 7 18 20 9 1 16 17 1 13 20 1 1 9 2 17 15 1 10 17 16 1 4 1 4 1 13 3 20 1 2 17 1 18 19 1 2 19 7 20 13 1 15 12 20 3 4 1 19 17 18 11 9 1 20 6 9 19 16 1 1 14 7 20 8 1 3 1 20 10 9 1 17 12 18 3 20 1 6 20 11 1 2 1 18 1 16 5 3 1 18 2 20 17 16 1 8 9 3 18 1 1 14 19 16 7 1 1 6 20 19 13 10 1 19 1 20 2 12 1 1 14 17 15 19 1 5 18 15 1 17 1 19 17 20 2 18 1 16 18 15 20 11 1 20 19 11 9 3 1 20 6 5 1 17 1 3 16 1 19 12 1 1 20 9 5 10 1 4 12 19 1 16 1 19 2 3 8 5 1 3 14 9 20 1 1 6 7 1 4 19 1 6 16 12 20 2 1 3 11 1 20 4 1 18 20 3 11 1 1 16 4 1 13 3 1 7 5 18 17 20 1 1 3 13 15 19 1 13 10 19 3 20 1 1 11 4 18 19 1 2 7 13 16 20 1 5 16 1 3 20 1 20 10 19 8 16 1 5 12 2 1 8 1 1 6 4 16 5 1 12 2 1 18 9 1 8 19 1 10 2 1 19 20 2 13 17 1 10 19 7 20 16 1 20 17 10 1 3 1 12 20 4 17 15 1 20 18 5 17 13 1 1 20 17 16 14 1 16 1 9 18 4 1 13 19 1 3 6 1 5 18 17 16 1 1 18 2 4 16 7 1 20 7 3 17 12 1 15 12 20 6 19 1 4 16 6 17 20 1 13 8 17 18 20 1 14 19 13 11 20 1 12 1 17 2 13 1 20 9 1 7 19 1 8 5 2 18 20 1 18 15 1 4 8 1 16 1 17 5 2 1 11 10 3 20 1 1 11 2 18 9 1 1 1 15 18 20 9 1 16 11 9 20 1 1 2 11 3 1 17 1 3 16 5 13 1 1 20 3 7 19 13 1 1 19 13 20 12 1 20 1 18 8 9 1 15 19 18 1 11 1 13 1 17 5 2 1 3 11 2 1 10 1 8 16 15 1 2 1 10 20 11 1 15 1 3 12 6 4 20 1 9 7 19 6 1 1 2 4 10 5 19 1 1 5 18 19 2 1 12 1 3 20 10 1 16 8 14 2 1 1 9 3 20 7 19 1 19 20 11 10 17 1 14 20 3 15 4 1 20 1 7 13 9 1 2 1 5 17 8 1 1 11 9 20 14 1 17 3 20 18 14 1 3 19 2 17 18 1 10 6 20 17 1 1 8 19 13 17 1 1 5 14 2 17 1 1 9 16 20 11 2 1 17 19 4 20 18 1 4 19 10 3 20 1 12 19 2 4 20 1 12 20 4 15 1 1 15 8 19 3 1 1 14 1 10 3 19 1 1 20 8 10 6 1 3 5 16 20 4 1 8 20 1 11 9 1 18 14 12 16 20 1 2 20 9 18 13 1 20 2 19 14 12 1 15 18 19 3 20 1 6 4 1 3 18 1 4 9 16 1 17 1 2 8 17 1 10 1 18 3 1 4 15 1 4 2 14 18 19 1 17 6 18 14 20 1 16 1 20 19 2 1 2 13 20 18 9 1 12 1 11 18 20 1 20 9 19 12 11 1 19 4 1 2 11 1 10 20 13 9 19 1 1 15 13 17 2 1 2 14 1 17 6 1 3 15 17 9 20 1 5 20 2 7 9 1 16 13 18 10 1 1 20 12 19 1 8 1 1 16 12 2 19 1 19 20 10 3 13 1 5 3 2 11 19 1 3 1 12 20 5 1 1 8 15 2 6 1 3 20 6 1 18 1 15 1 20 19 18 1 18 20 19 3 14 1 16 19 15 20 10 1 2 20 14 1 9 1 7 6 1 19 2 1 18 2 6 15 3 1 20 5 19 9 16 1 13 17 1 2 12 1 6 2 10 20 17 1 4 2 20 8 5 1 9 16 1 19 2 1 19 2 15 20 1 1 20 10 3 7 1 1 20 7 16 10 1 1 1 16 15 20 17 1 1 2 20 5 8 1 16 1 2 10 4 1 2 20 3 8 9 1 17 19 10 1 6 1 2 4 1 10 14 1 19 20 7 12 2 1 19 9 1 4 2 1 3 2 19 6 16 1 19 12 1 20 6 1 2 20 16 14 3 1 14 1 6 11 20 1 20 13 5 16 4 1 2 16 4 20 12 1 19 13 4 1 18 1 15 1 19 3 16 1 9 1 14 18 2 1 3 16 2 4 5 1 2 20 14 17 19 1 2 7 12 10 1 1 16 3 20 1 14 1 6 16 1 15 2 1 5 15 8 18 20 1 14 15 1 2 13 1 20 4 19 7 10 1 1 18 14 2 20 1 2 1 6 17 11 1 16 11 9 20 19 1 2 9 12 3 20 1 20 7 1 9 16 1 19 20 17 3 12 1 1 16 8 6 2 1 13 2 8 1 6 1 15 8 17 18 20 1 20 12 7 1 19 1 18 16 15 14 19 1 20 3 12 4 5 1 4 1 3 15 13 1 18 1 11 3 17 1 20 16 1 9 19 1 19 11 18 20 12 1 18 10 1 17 16 1 2 20 8 1 17 1 1 20 7 4 17 1 4 1 13 7 20 1 1 2 20 10 19 1 17 12 6 1 20 1 1 17 20 13 18 1 11 1 20 9 17 1 3 1 5 16 17 1 6 10 20 1 15 1 1 7 20 15 14 1 1 3 13 15 2 1 20 18 8 16 7 1 4 19 8 10 20 1 8 2 1 17 15 1 4 2 11 1 3 1 1 5 19 15 20 1 20 3 18 19 13 1 20 17 12 19 6 1 7 17 19 20 15 1 1 4 16 18 12 1 17 9 1 3 16 1 20 19 5 8 2 1 15 9 5 2 1 1 14 15 1 2 16 1 3 9 1 17 16 1 18 11 2 20 10 1 4 20 1 8 13 1 20 2 16 8 3 1 10 16 20 19 3 1 2 13 20 6 1 1 6 18 2 15 20 1 6 5 20 17 7 1 1 13 19 5 16 1 17 7 2 20 5 1 20 15 2 7 1 1 1 17 5 2 12 1 15 1 2 17 5 1 6 18 13 4 1 1 20 14 11 4 1 1 5 1 18 11 20 1 4 20 1 11 8 1 3 20 8 17 4 1 17 20 8 5 1 1 13 15 18 1 6 1 20 17 12 18 14 1 13 4 19 1 17 1 7 18 17 4 20 1 15 20 2 6 1 1 17 1 7 19 15 1 2 19 6 8 1 1 19 7 16 18 20 1 16 17 6 20 8 1 9 3 5 1 20 1 18 8 7 2 3 1 18 2 13 8 20 1 20 1 3 10 19 1 8 19 20 18 6 1 17 10 20 16 15 1 1 3 2 9 16 1 4 20 9 18 1 1 15 5 7 4 20 1 20 18 10 15 7 1 19 20 2 6 10 1 15 19 1 11 18 1 1 5 20 3 18 1 8 6 1 17 18 1 17 7 20 6 2 1 20 18 17 1 19 1 4 20 5 8 18 1 15 20 12 16 18 1 16 20 2 12 1 1 16 15 7 19 20 1 19 5 18 1 2 1 6 18 2 20 14 1 1 15 20 10 5 1 18 8 9 19 1 1 20 5 2 1 18 1 20 2 19 12 3 1 11 20 16 17 6 1 5 16 18 1 7 1 12 1 2 19 18 1 15 1 17 2 4 1 20 5 3 12 7 1 2 18 17 20 19 1 15 19 3 5 20 1 3 20 18 2 19 1 3 6 19 16 1 1 20 16 17 12 4 1 8 11 19 1 18 1 20 3 11 15 19 1 17 3 19 2 5 1 7 20 2 19 6 1 14 4 20 1 11 1 6 3 8 19 2 1 5 15 7 20 1 1 4 3 13 2 20 1 3 4 20 11 2 1 12 19 20 15 17 1 20 18 15 12 16 1 12 20 11 1 7 1 3 20 15 16 4 1 18 1 19 14 15 1 1 10 20 15 12 1 18 8 5 6 1 1 2 20 18 13 10 1 6 12 20 15 18 1 10 1 5 18 19 1 13 1 20 7 5 1 16 2 17 15 20 1 15 20 10 6 18 1 6 19 20 9 12 1 11 2 4 20 17 1 17 12 16 15 20 1 11 17 2 1 19 1 7 20 19 9 12 1 15 4 16 1 20 1 16 3 19 10 1 1 1 19 15 18 16 1 20 16 1 13 12 1 17 19 5 2 20 1 8 1 6 17 3 1 13 2 20 5 16 1 3 12 14 1 19 1 14 20 2 3 8 1 5 20 18 15 12 1 18 14 12 16 1 1 1 17 7 2 18 1 20 8 1 11 3 1 1 10 3 16 2 1 19 20 4 8 1 1 14 1 20 18 3 1 3 19 20 15 10 1 15 20 2 6 19 1 2 12 14 16 1 1 13 19 5 1 20 1 16 15 14 19 1 1 13 20 8 2 16 1 1 17 19 3 2 1 20 13 9 14 2 1 20 10 18 15 17 1 1 5 18 19 7 1 17 1 13 15 20 1 17 9 20 15 18 1 11 18 15 16 20 1 1 16 18 19 3 1 12 18 3 1 15 1 2 7 3 19 15 1 2 16 20 4 14 1 16 20 9 19 18 1 4 3 19 20 1 1 5 20 19 11 18 1 20 4 14 2 10 1 7 17 1 15 2 1 11 20 4 2 1 1 19 10 4 11 20 1 17 2 6 12 1 1 11 2 6 20 5 1 5 7 1 18 14 1 13 19 1 18 7 1 19 3 5 1 15 1 2 14 20 17 7 1 20 4 9 16 3 1 18 1 15 20 9 1 1 15 9 2 18 1 9 19 6 17 1 1 5 12 20 6 1 1 3 19 1 14 11 1 16 15 18 14 1 1 14 7 5 1 20 1 6 4 1 9 19 1 20 1 8 12 18 1 13 20 16 5 3 1 9 2 1 3 18 1 8 5 2 20 12 1 1 18 8 2 9 1 14 11 19 1 16 1 1 3 15 10 19 1 4 1 7 2 17 1 17 5 18 2 19 1 17 9 19 3 20 1 15 20 2 4 18 1 7 5 20 9 1 1 19 17 1 18 7 1 8 9 20 19 13 1 9 20 14 2 3 1 4 19 17 2 3 1 1 18 5 11 3 1 20 9 2 14 3 1 5 6 8 20 1 1 20 12 17 11 19 1 19 20 10 15 5 1 17 14 18 20 6 1 11 19 17 8 20 end * Computation started at Thu Apr 18 15:45:37 2024 * ended at Thu Apr 18 15:45:41 2024 * Total processor time = 4 seconds * = 0 h 0 m 4 s lrslib-073/ext/redund/r20k_5.ext0000777000175000017500000072467514625766576015233 0ustar avisavisr20k_5 V-representation begin 20000 6 integer 1 1 2 7 1 5 1 9 8 8 1 8 1 3 3 5 5 7 1 3 9 6 1 4 1 2 4 4 2 6 1 2 5 4 7 3 1 9 3 0 4 0 1 1 6 3 9 5 1 3 7 8 6 7 1 7 0 7 6 6 1 3 4 1 8 1 1 0 2 3 0 4 1 7 0 5 2 0 1 3 4 1 0 8 1 2 1 4 5 3 1 5 3 4 6 4 1 9 9 2 4 8 1 1 5 9 7 9 1 1 2 1 5 5 1 7 4 5 0 7 1 8 1 6 0 1 1 5 9 8 7 3 1 6 5 7 4 7 1 7 8 0 2 2 1 4 8 1 8 1 1 1 9 2 1 3 1 6 4 5 7 4 1 8 2 4 5 0 1 5 1 7 0 4 1 2 7 6 8 0 1 0 9 2 3 0 1 7 3 7 6 4 1 9 5 9 6 4 1 8 8 2 8 6 1 2 3 1 0 1 1 1 5 4 1 8 1 9 9 5 6 9 1 5 2 8 9 8 1 5 4 0 8 1 1 6 4 8 1 1 1 0 5 5 9 1 1 9 2 0 1 6 1 4 2 0 1 7 1 9 5 3 8 2 1 6 0 8 9 9 1 3 5 5 5 6 1 4 3 8 2 1 1 4 2 2 6 4 1 5 4 9 3 4 1 2 7 7 2 0 1 4 1 8 0 4 1 1 9 3 2 6 1 2 6 6 0 3 1 9 3 5 1 6 1 7 1 7 3 3 1 7 0 8 0 3 1 2 3 8 4 0 1 7 6 5 7 1 1 3 7 1 6 0 1 5 2 4 7 2 1 7 9 9 4 0 1 5 4 3 5 3 1 8 1 3 6 6 1 8 1 2 0 1 1 1 1 1 1 4 1 7 0 7 6 1 1 0 7 3 3 7 1 9 5 8 6 7 1 3 5 7 4 8 1 5 7 5 2 5 1 7 9 1 0 9 1 7 7 3 0 3 1 8 0 0 6 1 1 1 6 7 8 8 1 5 3 1 8 9 1 6 1 5 0 5 1 6 5 8 1 0 1 1 1 9 7 7 1 0 2 6 8 2 1 9 7 3 5 8 1 2 2 9 0 9 1 7 5 8 9 3 1 1 9 4 8 2 1 2 5 5 0 8 1 2 4 5 7 6 1 1 9 2 3 4 1 3 4 5 5 5 1 5 3 9 7 7 1 5 8 8 4 0 1 0 4 2 8 7 1 2 3 4 5 8 1 8 6 0 1 8 1 9 7 7 7 9 1 8 9 6 3 1 1 8 7 0 8 4 1 4 0 4 5 9 1 8 9 8 3 4 1 8 9 4 4 0 1 5 6 1 3 4 1 2 5 9 3 6 1 2 4 6 8 6 1 5 4 8 3 2 1 0 5 9 0 0 1 6 5 8 5 3 1 3 9 5 5 4 1 5 3 6 6 2 1 6 8 1 0 4 1 5 9 1 9 5 1 8 6 7 1 9 1 8 1 8 0 9 1 1 4 4 3 8 1 4 7 7 9 2 1 6 7 7 1 0 1 3 9 9 0 7 1 0 1 1 7 9 1 6 9 7 6 9 1 0 1 0 8 6 1 2 0 8 6 0 1 0 0 2 8 8 1 2 6 4 2 7 1 9 1 5 7 2 1 5 2 9 8 3 1 7 4 4 0 1 1 8 1 1 6 8 1 4 5 6 3 0 1 9 1 0 9 7 1 2 2 8 8 7 1 2 0 9 9 5 1 5 8 3 6 4 1 4 6 3 6 6 1 9 7 0 6 1 1 7 3 7 3 2 1 0 8 4 7 9 1 2 0 7 9 1 1 4 2 3 2 8 1 3 1 3 4 9 1 9 3 5 4 3 1 6 0 7 0 1 1 5 1 7 5 0 1 2 3 6 4 2 1 1 8 2 2 2 1 7 5 8 5 6 1 7 2 5 3 1 1 5 8 0 2 6 1 0 9 8 2 2 1 0 2 1 4 8 1 5 3 6 8 7 1 9 6 2 3 6 1 3 3 5 5 6 1 9 5 5 0 2 1 1 7 0 5 2 1 1 1 6 9 3 1 0 1 7 5 0 1 9 8 5 8 9 1 6 0 7 7 1 1 0 1 9 7 8 1 5 0 2 5 3 1 3 8 1 2 9 1 8 3 9 6 3 1 6 3 6 6 8 1 5 1 5 0 1 1 5 6 7 1 2 1 5 6 8 0 1 1 8 2 9 5 9 1 0 2 0 2 7 1 9 4 7 2 5 1 6 3 9 1 6 1 5 7 4 0 3 1 9 8 2 7 6 1 6 5 0 5 9 1 2 7 8 1 3 1 2 7 1 8 9 1 7 8 0 5 0 1 1 9 3 0 3 1 6 3 5 4 5 1 6 2 0 2 2 1 9 3 3 3 0 1 8 6 6 9 5 1 9 5 8 2 3 1 5 9 1 4 2 1 2 7 8 6 9 1 5 2 9 6 0 1 9 8 0 1 3 1 0 5 8 2 5 1 8 5 8 6 7 1 6 5 9 0 9 1 5 8 6 9 1 1 8 6 1 5 0 1 4 5 1 9 7 1 0 0 8 7 9 1 1 0 9 7 2 1 0 6 9 4 0 1 2 5 1 4 6 1 7 9 3 7 9 1 4 9 5 5 5 1 3 8 8 0 9 1 4 9 2 3 2 1 2 5 9 9 3 1 5 4 0 4 3 1 8 9 4 5 3 1 7 0 9 9 2 1 5 3 4 2 4 1 7 1 9 1 8 1 1 0 4 0 9 1 2 4 8 1 0 1 5 4 8 3 9 1 7 2 1 6 3 1 9 5 3 1 6 1 3 2 1 7 9 1 9 6 2 3 0 1 0 1 0 4 1 1 9 8 0 9 5 1 6 3 2 3 0 1 6 4 5 1 1 1 5 8 2 8 3 1 3 3 1 0 0 1 5 5 5 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11 19 17 8 20 end verbose redund 0 0 lrslib-073/ext/redund/r40_5.ext0000777000175000017500000000137714625766576015045 0ustar avisavisrand100_5 V-representation begin 40 6 integer 1 12 16 18 4 6 1 15 16 10 4 2 1 5 12 14 9 10 1 17 6 19 13 20 1 15 9 1 5 6 1 2 1 16 6 17 1 3 8 4 12 6 1 13 17 10 3 15 1 18 6 11 1 7 1 13 19 16 1 2 1 19 4 12 13 20 1 12 4 1 19 8 1 17 8 6 9 5 1 14 2 10 9 15 1 17 14 1 8 9 1 16 13 20 10 19 1 19 3 11 13 18 1 12 17 16 14 5 1 18 4 1 3 20 1 1 13 12 18 15 1 7 17 13 10 6 1 4 18 8 1 2 1 19 18 14 20 17 1 19 9 10 1 4 1 1 19 18 4 2 1 14 19 13 4 9 1 3 6 13 2 10 1 12 2 14 16 8 1 13 10 8 2 3 1 16 15 18 4 9 1 4 8 5 2 11 1 6 13 12 1 5 1 7 14 13 16 8 1 20 8 4 17 14 1 20 6 9 8 10 1 19 15 13 16 7 1 4 17 15 13 2 1 13 6 7 9 2 1 19 18 14 17 4 1 19 1 12 20 9 end verbose lrslib-073/ext/redund/r500_5.ext0000777000175000017500000002131514625766575015117 0ustar avisavisrand500_5 V-representation begin 500 6 integer 1 7 19 20 14 2 1 13 5 9 6 2 1 8 19 16 9 13 1 7 19 20 14 2 1 7 11 10 4 14 1 1 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14 12 9 *re 1 14 8 6 12 1 *re 1 12 20 9 16 10 *re 1 17 18 1 9 6 *nr 1 17 7 9 1 16 *nr 1 7 14 17 18 2 *nr 1 2 7 8 5 1 *re 1 9 19 3 11 12 *re 1 8 10 3 16 17 *re 1 18 6 11 7 4 *re 1 14 4 7 8 3 *re 1 16 17 11 8 14 *nr 1 19 20 1 7 6 *nr 1 20 8 14 15 3 *nr 1 16 4 12 1 13 *re 1 17 13 9 7 12 *nr 1 16 20 5 7 4 *nr 1 12 1 3 4 2 *re 1 8 9 17 18 4 *re 1 9 14 5 8 17 *nr 1 15 5 7 1 12 *re 1 7 18 3 4 15 *re 1 9 3 17 15 4 *nr 1 4 14 3 19 17 *re 1 12 17 5 4 10 *nr 1 15 20 9 16 4 *nr 1 5 11 20 3 12 *nr 1 19 3 15 17 13 *re 1 11 15 20 14 8 *nr 1 3 15 10 2 18 *re 1 13 9 3 15 5 *nr 1 17 10 1 11 18 *re 1 15 13 18 6 16 *re 1 12 17 14 11 16 *nr 1 3 10 18 13 2 *re 1 1 11 8 7 13 *nr 1 19 1 7 12 13 *re 1 15 3 13 9 7 *nr 1 15 1 7 16 5 *re 1 19 7 10 14 3 *nr 1 4 7 9 18 1 *re 1 16 7 15 4 12 *nr 1 19 17 1 9 20 *re 1 12 10 18 11 9 *re 1 14 18 10 17 2 *re 1 4 3 13 19 9 *re 1 11 14 6 8 15 *nr 1 2 7 3 20 9 *re 1 11 3 13 4 12 *re 1 3 15 11 8 12 *re 1 3 15 12 6 17 *nr 1 11 8 1 10 3 *re 1 13 6 4 16 12 *re 1 12 3 6 9 17 *nr 1 6 20 2 18 9 *nr 1 1 6 8 15 18 *nr 1 2 8 17 5 20 *re 1 9 17 10 18 7 *nr 1 15 16 11 19 20 *re 1 9 6 17 16 15 *nr 1 1 14 2 8 17 *nr 1 10 15 14 19 1 *re 1 8 11 1 10 6 *nr 1 10 1 11 8 19 *nr 1 20 8 17 16 15 *nr 1 18 2 20 11 13 *nr 1 7 1 5 3 20 *nr 1 1 16 2 17 3 *re 1 11 14 15 12 20 *re 1 5 11 17 6 19 *nr 1 2 4 3 1 18 *re 1 10 17 16 19 8 *nr 1 11 7 17 2 19 *re 1 10 8 9 12 20 *re 1 4 14 7 17 8 *re 1 15 13 7 17 4 *re 1 11 16 14 4 13 *nr 1 5 7 1 3 8 *re 1 16 12 7 17 4 *re 1 16 6 3 8 13 *re 1 7 3 6 16 8 *re 1 2 12 9 18 17 *re 1 8 12 9 18 16 *re 1 19 5 15 6 14 *nr 1 12 1 18 4 16 *re 1 20 17 6 3 8 *nr 1 20 19 10 11 18 *re 1 18 2 10 8 14 *re 1 19 13 12 4 9 *re 1 11 13 18 7 12 *nr 1 1 13 9 18 19 *nr 1 3 1 10 6 7 *nr 1 1 11 7 3 19 *nr 1 1 20 2 15 3 *re 1 13 7 18 11 19 *nr 1 3 5 1 13 9 *nr 1 20 18 3 6 12 *re 1 10 4 19 9 5 *re 1 10 11 6 3 15 *nr 1 12 19 3 17 6 *re 1 11 17 18 6 14 *re 1 3 11 13 15 5 *nr 1 19 11 16 20 5 *re 1 4 19 10 18 13 *re 1 16 20 9 15 8 *re 1 20 13 9 12 14 *re 1 4 8 6 19 11 *re 1 8 3 11 2 12 *re 1 5 12 8 2 14 *re 1 6 8 13 9 16 *nr 1 20 17 5 1 8 *nr 1 18 20 7 15 6 *re 1 4 16 17 9 8 *nr 1 5 17 12 20 7 *nr 1 1 2 3 20 16 *re 1 10 3 11 9 7 *re 1 13 15 8 18 17 *re 1 14 12 18 13 7 *nr 1 17 12 3 2 6 *re 1 6 14 11 7 1 *re 1 13 12 11 9 15 *re 1 19 13 12 8 15 *nr 1 7 1 4 17 5 *re 1 6 8 4 7 10 *re 1 13 20 3 11 9 *nr 1 3 20 16 11 2 *re 1 15 4 9 12 6 *nr 1 15 3 19 20 7 *re 1 4 7 5 2 14 *re 1 11 5 20 4 12 *re 1 7 16 11 14 20 *nr 1 6 12 4 20 16 *re 1 20 4 8 16 2 *re 1 19 4 6 15 2 *nr 1 3 20 2 1 4 *re 1 11 4 20 14 5 *nr 1 2 1 20 8 15 *nr 1 5 16 17 12 1 *nr 1 17 2 18 8 16 *re 1 16 11 9 2 6 *nr 1 3 6 13 14 1 *re 1 14 17 9 18 8 *nr 1 19 15 11 18 4 *nr 1 1 20 11 15 12 *nr 1 4 18 16 7 2 *nr 1 8 17 1 20 9 *nr 1 1 16 14 7 13 *nr 1 5 20 6 11 17 *nr 1 6 1 20 4 2 *re 1 18 7 19 17 6 *nr 1 9 6 16 1 13 *re 1 16 6 13 9 15 *re 1 5 4 7 19 15 *re 1 10 8 6 11 19 *nr 1 8 1 20 15 6 *re 1 8 4 7 9 6 *re 1 6 9 5 3 11 *nr 1 15 1 13 17 4 *re 1 15 16 3 17 8 V-representation begin 241 6 rational 1 7 19 20 14 2 1 1 14 19 9 13 1 17 4 20 18 2 1 4 3 2 17 9 1 11 16 3 1 4 1 20 6 15 10 16 1 10 13 8 1 20 1 11 19 16 1 17 1 12 2 3 5 18 1 19 1 10 18 15 1 20 2 4 19 1 1 7 3 2 19 10 1 10 8 14 4 1 1 9 4 1 6 10 1 19 2 12 17 7 1 11 9 4 1 18 1 16 3 20 8 4 1 2 11 19 5 6 1 5 6 12 20 2 1 3 17 2 8 20 1 20 14 1 6 11 1 8 1 10 6 2 1 1 17 6 7 10 1 1 2 6 12 4 1 6 2 5 17 4 1 16 7 19 2 5 1 1 10 4 2 3 1 3 19 16 11 20 1 6 19 15 20 5 1 1 18 12 11 17 1 14 1 15 8 2 1 11 7 19 1 10 1 19 4 15 6 1 1 9 14 20 7 3 1 3 19 20 18 13 1 7 2 9 16 20 1 2 1 11 17 12 1 4 17 1 15 3 1 15 3 13 7 1 1 10 1 20 16 8 1 9 3 18 19 16 1 16 15 5 20 9 1 3 12 16 4 17 1 20 19 18 1 5 1 3 18 2 1 5 1 20 9 5 3 12 1 1 4 8 2 19 1 9 7 1 18 6 1 5 18 9 1 14 1 7 17 1 2 15 1 12 13 3 18 1 1 20 16 4 3 18 1 9 8 20 1 17 1 7 20 13 19 5 1 17 20 5 14 15 1 18 17 20 10 2 1 5 19 16 20 12 1 17 3 10 16 20 1 3 1 12 19 6 1 3 13 20 10 12 1 12 3 1 10 7 1 20 3 7 16 8 1 1 20 12 7 14 1 12 20 10 1 15 1 5 6 18 20 16 1 7 3 2 10 15 1 13 17 20 10 4 1 15 6 1 5 14 1 19 7 20 15 18 1 3 8 19 15 7 1 11 7 1 9 4 1 7 10 2 17 19 1 3 20 16 8 7 1 7 8 20 15 5 1 12 2 3 18 16 1 9 15 19 20 7 1 1 9 6 17 4 1 1 2 11 19 8 1 1 15 18 13 14 1 6 19 12 13 20 1 14 18 8 20 2 1 12 17 19 10 1 1 17 7 19 2 9 1 1 9 12 4 18 1 10 20 13 19 7 1 10 6 20 15 17 1 18 19 11 15 20 1 7 1 4 9 8 1 17 20 1 2 16 1 19 6 14 13 1 1 9 5 6 2 3 1 17 11 15 2 19 1 17 3 18 7 2 1 20 10 16 6 17 1 13 12 7 9 1 1 10 7 13 1 3 1 20 1 9 6 14 1 18 1 3 4 12 1 6 4 1 16 14 1 1 3 10 2 14 1 8 11 17 20 2 1 9 18 7 10 20 1 2 19 3 9 1 1 16 1 14 18 9 1 18 15 1 5 19 1 3 9 6 10 20 1 17 7 1 12 4 1 9 5 13 18 1 1 12 19 5 2 18 1 3 20 16 13 19 1 20 5 15 9 1 1 17 1 13 2 19 1 14 3 19 11 20 1 16 3 2 18 6 1 17 10 4 2 15 1 19 7 4 12 14 1 3 1 8 6 19 1 15 5 12 2 1 1 8 9 14 6 1 1 20 19 1 18 13 1 4 16 11 19 17 1 3 11 20 8 18 1 14 16 9 20 13 1 8 20 6 15 17 1 14 16 18 8 1 1 12 16 4 10 2 1 6 2 4 10 19 1 17 20 12 14 18 1 16 9 4 20 10 1 2 3 19 5 9 1 20 9 4 11 13 1 11 17 19 8 20 1 13 18 4 1 8 1 14 10 4 9 2 1 12 1 20 2 14 1 14 4 1 7 17 1 10 12 4 19 20 1 16 2 10 17 1 1 19 6 11 20 18 1 18 12 20 9 15 1 14 4 18 2 19 1 8 14 18 20 15 1 6 1 20 2 14 1 14 1 5 2 19 1 18 19 15 10 16 1 2 20 1 15 6 1 16 3 4 19 2 1 17 2 3 18 6 1 3 7 14 1 11 1 11 17 18 2 13 1 18 19 17 10 13 1 1 3 17 9 2 1 6 16 1 19 17 1 1 20 3 15 11 1 1 20 4 17 10 1 15 5 13 1 7 1 1 2 19 20 15 1 8 5 1 9 6 1 12 5 9 20 4 1 14 10 5 20 19 1 11 3 17 20 2 1 13 2 6 1 16 1 17 8 20 6 10 1 10 4 11 18 1 1 1 13 18 8 20 1 11 20 19 2 1 1 5 20 7 19 8 1 3 8 1 4 13 1 10 15 18 1 11 1 12 19 7 20 13 1 6 20 8 7 1 1 17 7 9 1 16 1 7 14 17 18 2 1 2 7 8 5 1 1 19 20 1 7 6 1 20 8 14 15 3 1 16 4 12 1 13 1 16 20 5 7 4 1 12 1 3 4 2 1 15 5 7 1 12 1 4 14 3 19 17 1 15 20 9 16 4 1 5 11 20 3 12 1 19 3 15 17 13 1 3 15 10 2 18 1 17 10 1 11 18 1 3 10 18 13 2 1 19 1 7 12 13 1 15 1 7 16 5 1 4 7 9 18 1 1 19 17 1 9 20 1 2 7 3 20 9 1 11 8 1 10 3 1 6 20 2 18 9 1 1 6 8 15 18 1 2 8 17 5 20 1 15 16 11 19 20 1 1 14 2 8 17 1 10 15 14 19 1 1 10 1 11 8 19 1 20 8 17 16 15 1 18 2 20 11 13 1 7 1 5 3 20 1 1 16 2 17 3 1 2 4 3 1 18 1 11 7 17 2 19 1 5 7 1 3 8 1 12 1 18 4 16 1 20 19 10 11 18 1 1 13 9 18 19 1 3 1 10 6 7 1 1 11 7 3 19 1 1 20 2 15 3 1 3 5 1 13 9 1 20 18 3 6 12 1 12 19 3 17 6 1 19 11 16 20 5 1 20 17 5 1 8 1 18 20 7 15 6 1 5 17 12 20 7 1 1 2 3 20 16 1 17 12 3 2 6 1 7 1 4 17 5 1 3 20 16 11 2 1 15 3 19 20 7 1 6 12 4 20 16 1 3 20 2 1 4 1 2 1 20 8 15 1 5 16 17 12 1 1 17 2 18 8 16 1 3 6 13 14 1 1 19 15 11 18 4 1 1 20 11 15 12 1 4 18 16 7 2 1 8 17 1 20 9 1 1 16 14 7 13 1 5 20 6 11 17 1 6 1 20 4 2 1 9 6 16 1 13 1 8 1 20 15 6 1 15 1 13 17 4 end verbose *input had 500 rows and 7 columns * 259 redundant row(s) found 1 2 3 5 11 14 15 16 18 19 21 22 23 24 29 31 33 35 37 40 41 44 45 48 49 51 53 54 61 63 65 67 70 71 74 75 76 79 82 84 86 87 88 91 92 94 95 98 101 103 106 108 109 115 116 121 122 128 129 131 133 134 135 140 144 145 147 150 152 155 156 160 161 163 166 169 170 171 173 175 176 177 179 183 184 185 186 190 197 198 200 202 203 207 208 209 210 212 213 215 216 219 220 223 225 227 230 231 233 234 235 236 238 241 242 243 244 245 246 247 249 254 255 258 259 260 262 264 265 266 269 272 279 281 286 287 288 289 292 293 294 297 299 301 302 303 304 305 306 308 309 310 312 314 315 319 320 322 323 324 325 326 329 330 331 334 337 338 340 341 342 343 344 345 349 350 351 352 353 357 360 361 363 364 366 370 372 374 375 377 379 381 383 385 386 387 388 390 391 392 394 395 399 401 404 410 411 413 415 416 417 418 420 421 422 423 424 425 427 429 430 431 436 439 440 442 443 445 446 447 448 449 450 451 454 457 458 459 461 462 463 465 466 468 470 471 472 474 475 477 481 483 491 493 494 495 497 498 500 *minrep:lrslib_v.7.3_2024.4.17(64bit,lrslong.h,hybrid_arithmetic) *overflow checking on lrslong arithmetic *0.428u 0.004s 2368Kb 0 flts 0 swaps 0 blks-in 40 blks-out lrslib-073/ext/redund/r500_5.extredc0000777000175000017500000001155314625766575015760 0ustar avisavisinput file r500_5.ext is open redundant rows: 2 3 4 5 11 14 15 16 18 19 21 22 23 24 27 28 29 31 33 35 37 40 41 43 44 45 48 49 51 53 54 61 63 65 67 70 71 73 74 75 76 79 82 84 85 86 87 88 91 92 94 95 98 101 103 106 108 109 115 116 121 122 123 128 129 130 131 133 134 135 140 144 145 147 150 152 155 156 159 160 161 163 165 166 169 170 171 173 175 176 177 179 183 184 185 186 190 197 198 200 202 203 207 208 209 210 212 213 215 216 219 220 222 223 225 227 230 231 233 234 235 236 238 241 242 243 244 245 246 247 249 254 255 258 259 260 262 264 265 266 269 272 279 281 286 287 288 289 292 293 294 297 299 301 302 303 304 305 306 307 308 309 310 312 314 315 319 320 322 323 324 325 326 329 330 331 334 337 338 340 341 342 343 344 345 349 350 351 352 353 357 360 361 363 364 366 370 372 374 375 377 379 381 383 385 386 387 388 390 391 392 393 394 395 399 401 404 410 411 413 415 416 417 418 419 420 421 422 423 424 425 427 429 430 431 433 436 439 440 442 443 445 446 447 448 449 450 451 454 457 458 459 461 462 463 465 466 468 470 471 472 474 475 477 481 483 491 492 493 494 495 497 498 500 *Implicit linearity (after removal of redundant rows): 0 *Nonredundant representation (except for the linearity part): V-representation begin 226 6 rational 1 7 19 20 14 2 1 1 14 19 9 13 1 17 4 20 18 2 1 4 3 2 17 9 1 11 16 3 1 4 1 20 6 15 10 16 1 10 13 8 1 20 1 11 19 16 1 17 1 12 2 3 5 18 1 19 1 10 18 15 1 20 2 4 19 1 1 7 3 2 19 10 1 19 2 12 17 7 1 11 9 4 1 18 1 16 3 20 8 4 1 2 11 19 5 6 1 5 6 12 20 2 1 3 17 2 8 20 1 20 14 1 6 11 1 1 17 6 7 10 1 1 2 6 12 4 1 6 2 5 17 4 1 16 7 19 2 5 1 1 10 4 2 3 1 3 19 16 11 20 1 6 19 15 20 5 1 1 18 12 11 17 1 14 1 15 8 2 1 11 7 19 1 10 1 19 4 15 6 1 1 9 14 20 7 3 1 3 19 20 18 13 1 7 2 9 16 20 1 2 1 11 17 12 1 4 17 1 15 3 1 10 1 20 16 8 1 9 3 18 19 16 1 16 15 5 20 9 1 3 12 16 4 17 1 20 19 18 1 5 1 20 9 5 3 12 1 1 4 8 2 19 1 9 7 1 18 6 1 5 18 9 1 14 1 7 17 1 2 15 1 12 13 3 18 1 1 20 16 4 3 18 1 9 8 20 1 17 1 7 20 13 19 5 1 17 20 5 14 15 1 18 17 20 10 2 1 5 19 16 20 12 1 17 3 10 16 20 1 3 1 12 19 6 1 3 13 20 10 12 1 12 3 1 10 7 1 20 3 7 16 8 1 1 20 12 7 14 1 12 20 10 1 15 1 5 6 18 20 16 1 13 17 20 10 4 1 15 6 1 5 14 1 19 7 20 15 18 1 3 8 19 15 7 1 7 10 2 17 19 1 3 20 16 8 7 1 7 8 20 15 5 1 12 2 3 18 16 1 9 15 19 20 7 1 1 9 6 17 4 1 1 2 11 19 8 1 1 15 18 13 14 1 6 19 12 13 20 1 14 18 8 20 2 1 12 17 19 10 1 1 17 7 19 2 9 1 1 9 12 4 18 1 10 20 13 19 7 1 10 6 20 15 17 1 18 19 11 15 20 1 17 20 1 2 16 1 19 6 14 13 1 1 17 11 15 2 19 1 17 3 18 7 2 1 20 10 16 6 17 1 13 12 7 9 1 1 10 7 13 1 3 1 20 1 9 6 14 1 18 1 3 4 12 1 6 4 1 16 14 1 1 3 10 2 14 1 8 11 17 20 2 1 9 18 7 10 20 1 2 19 3 9 1 1 16 1 14 18 9 1 18 15 1 5 19 1 3 9 6 10 20 1 17 7 1 12 4 1 9 5 13 18 1 1 12 19 5 2 18 1 3 20 16 13 19 1 20 5 15 9 1 1 17 1 13 2 19 1 14 3 19 11 20 1 16 3 2 18 6 1 17 10 4 2 15 1 19 7 4 12 14 1 3 1 8 6 19 1 15 5 12 2 1 1 20 19 1 18 13 1 4 16 11 19 17 1 3 11 20 8 18 1 14 16 9 20 13 1 8 20 6 15 17 1 14 16 18 8 1 1 12 16 4 10 2 1 6 2 4 10 19 1 17 20 12 14 18 1 16 9 4 20 10 1 2 3 19 5 9 1 20 9 4 11 13 1 11 17 19 8 20 1 13 18 4 1 8 1 14 10 4 9 2 1 12 1 20 2 14 1 14 4 1 7 17 1 10 12 4 19 20 1 16 2 10 17 1 1 19 6 11 20 18 1 18 12 20 9 15 1 14 4 18 2 19 1 8 14 18 20 15 1 6 1 20 2 14 1 14 1 5 2 19 1 18 19 15 10 16 1 2 20 1 15 6 1 16 3 4 19 2 1 17 2 3 18 6 1 3 7 14 1 11 1 11 17 18 2 13 1 18 19 17 10 13 1 1 3 17 9 2 1 6 16 1 19 17 1 1 20 3 15 11 1 1 20 4 17 10 1 15 5 13 1 7 1 1 2 19 20 15 1 12 5 9 20 4 1 14 10 5 20 19 1 11 3 17 20 2 1 13 2 6 1 16 1 17 8 20 6 10 1 10 4 11 18 1 1 1 13 18 8 20 1 11 20 19 2 1 1 5 20 7 19 8 1 3 8 1 4 13 1 10 15 18 1 11 1 12 19 7 20 13 1 6 20 8 7 1 1 17 7 9 1 16 1 7 14 17 18 2 1 2 7 8 5 1 1 19 20 1 7 6 1 20 8 14 15 3 1 16 4 12 1 13 1 16 20 5 7 4 1 12 1 3 4 2 1 15 5 7 1 12 1 4 14 3 19 17 1 15 20 9 16 4 1 5 11 20 3 12 1 19 3 15 17 13 1 3 15 10 2 18 1 17 10 1 11 18 1 3 10 18 13 2 1 19 1 7 12 13 1 15 1 7 16 5 1 4 7 9 18 1 1 19 17 1 9 20 1 2 7 3 20 9 1 6 20 2 18 9 1 1 6 8 15 18 1 2 8 17 5 20 1 15 16 11 19 20 1 1 14 2 8 17 1 10 15 14 19 1 1 10 1 11 8 19 1 20 8 17 16 15 1 18 2 20 11 13 1 7 1 5 3 20 1 1 16 2 17 3 1 2 4 3 1 18 1 11 7 17 2 19 1 12 1 18 4 16 1 20 19 10 11 18 1 1 13 9 18 19 1 1 11 7 3 19 1 1 20 2 15 3 1 3 5 1 13 9 1 20 18 3 6 12 1 12 19 3 17 6 1 19 11 16 20 5 1 20 17 5 1 8 1 18 20 7 15 6 1 5 17 12 20 7 1 1 2 3 20 16 1 17 12 3 2 6 1 7 1 4 17 5 1 3 20 16 11 2 1 15 3 19 20 7 1 6 12 4 20 16 1 3 20 2 1 4 1 2 1 20 8 15 1 5 16 17 12 1 1 17 2 18 8 16 1 3 6 13 14 1 1 19 15 11 18 4 1 1 20 11 15 12 1 4 18 16 7 2 1 8 17 1 20 9 1 1 16 14 7 13 1 5 20 6 11 17 1 6 1 20 4 2 1 8 1 20 15 6 1 15 1 13 17 4 end * Computation started at Thu Apr 18 15:57:21 2024 * ended at Thu Apr 18 15:57:21 2024 * Total processor time = 0 seconds * = 0 h 0 m 0 s lrslib-073/ext/redund/r5k_100.ext0000777000175000017500000366467414625766575015316 0ustar avisavisr5k_100 *https://onlinetools.com/math/generate-random-matrix V-representation begin 5000 101 integer 1 7 2 6 6 9 2 0 1 7 5 4 0 5 0 3 5 7 5 7 0 5 6 3 1 4 2 4 7 9 6 1 5 1 1 4 4 9 2 3 4 2 1 7 2 0 2 3 8 2 6 5 1 3 3 7 9 3 8 9 0 3 0 5 9 8 9 5 1 2 6 1 7 2 0 6 2 4 8 8 7 7 2 8 2 7 7 7 0 9 9 5 3 8 7 1 0 7 6 7 8 1 4 6 7 9 8 9 5 5 0 9 3 9 7 4 2 4 7 4 9 2 6 2 6 4 8 3 6 7 8 6 1 5 3 6 5 5 6 9 7 5 9 6 9 1 7 8 9 6 4 8 7 3 3 8 7 5 1 8 6 3 4 8 7 3 9 2 7 6 5 3 2 6 3 5 0 1 1 5 0 9 0 0 4 4 7 2 7 7 9 5 4 2 7 9 2 7 8 0 6 5 1 1 8 4 8 0 8 4 5 2 3 7 6 6 4 2 9 3 6 4 6 9 6 8 6 0 9 4 9 2 4 7 2 5 7 2 7 1 8 3 4 4 0 8 0 8 5 4 6 3 1 8 0 2 0 6 3 2 9 5 1 4 3 8 9 3 9 9 3 0 0 3 2 9 8 3 4 7 4 6 3 4 9 5 9 5 1 3 8 6 5 7 1 9 8 0 6 0 7 4 8 1 3 6 4 9 7 3 6 9 1 7 0 5 1 0 6 6 7 4 1 4 3 9 0 0 7 0 6 1 0 7 6 3 9 6 5 1 6 6 6 4 0 9 9 7 7 9 7 7 4 0 3 2 0 2 2 6 5 8 7 5 5 6 9 8 2 4 7 6 2 9 3 9 2 5 2 8 2 0 4 9 2 3 6 0 8 0 2 0 0 5 9 8 3 5 1 0 5 7 5 5 1 5 9 9 3 1 9 3 5 7 9 2 6 3 6 2 6 3 0 0 3 2 0 3 7 0 7 6 9 9 6 7 5 3 2 4 8 6 1 5 7 6 4 2 2 8 7 6 7 5 5 7 5 8 6 4 8 8 4 9 4 8 1 3 5 8 0 4 9 0 0 2 5 0 8 9 4 6 3 1 0 4 1 1 0 9 2 6 7 2 6 4 9 6 7 6 7 2 0 2 4 1 7 1 7 8 5 8 1 4 4 9 7 9 1 2 4 2 8 8 3 7 3 3 8 5 4 0 1 8 6 6 1 6 7 2 8 8 0 3 7 8 2 6 0 9 3 7 6 6 3 4 2 7 2 1 0 1 7 6 1 1 8 6 1 5 1 1 2 2 0 7 4 7 8 7 6 4 6 1 2 2 4 2 7 0 6 9 8 9 2 7 5 7 0 8 2 0 3 5 2 4 1 4 9 4 4 0 5 1 4 5 8 2 6 0 6 0 3 9 0 3 5 3 4 4 5 3 9 6 6 1 7 9 6 5 8 3 2 4 3 8 0 3 3 0 8 6 4 7 7 0 8 4 7 1 1 5 7 2 8 3 5 5 2 4 3 4 3 7 0 1 0 8 6 8 3 5 0 6 4 4 0 8 1 5 1 4 1 8 7 5 4 8 4 3 2 3 6 8 2 5 5 1 5 5 1 4 4 3 2 1 0 9 1 0 9 8 6 9 3 4 5 4 7 3 0 2 5 7 1 2 1 9 9 9 2 8 9 2 0 0 8 9 7 7 5 8 2 5 5 7 3 9 4 6 4 8 4 3 9 4 5 3 8 0 8 6 2 1 2 5 0 2 0 8 9 7 9 1 3 2 3 5 8 2 3 1 3 3 2 9 8 4 0 8 2 2 2 7 0 7 5 3 1 4 2 3 6 8 8 0 8 5 7 0 3 0 8 2 4 0 3 2 3 5 0 4 5 3 4 7 8 2 3 1 8 2 1 6 3 0 9 4 5 3 0 9 8 0 1 4 0 5 4 7 4 9 8 1 5 5 8 1 4 8 1 1 3 2 5 0 5 2 4 0 8 8 5 8 4 1 4 0 1 9 7 0 1 9 2 9 3 0 5 0 9 3 2 8 9 6 9 4 2 1 4 6 3 0 8 0 6 6 6 5 2 3 7 8 6 8 5 1 8 0 5 7 8 4 7 9 8 7 0 0 8 1 8 1 1 7 9 5 7 1 5 1 2 1 9 4 0 5 3 4 1 0 7 5 0 2 0 0 3 0 0 0 4 3 2 5 5 3 6 1 9 4 3 5 2 7 6 4 3 7 1 6 5 9 3 8 4 2 0 8 4 2 3 2 5 0 0 7 7 9 1 2 6 2 7 7 7 9 6 4 4 5 6 2 7 8 3 9 5 4 0 0 8 7 8 1 1 9 6 3 6 3 2 1 9 1 7 7 6 7 5 9 0 6 4 2 0 6 9 2 1 0 3 9 9 1 2 1 1 3 4 2 5 2 5 8 8 4 7 6 4 5 7 3 7 9 2 7 8 0 9 8 8 3 5 1 7 5 5 6 4 5 3 2 2 5 5 5 8 1 2 1 7 1 6 3 0 2 8 9 0 6 4 5 4 4 7 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0 7 3 6 5 8 8 1 1 5 7 1 4 5 7 1 7 5 1 8 1 2 6 6 4 6 4 9 7 6 8 9 4 6 0 9 2 2 2 0 6 7 2 8 8 6 9 3 1 6 0 9 8 5 2 1 9 5 2 5 0 3 1 0 3 6 3 0 4 2 0 7 0 4 9 5 0 0 4 6 4 4 2 3 4 1 8 1 2 9 7 5 3 8 7 1 5 4 4 1 2 2 3 7 0 0 2 9 6 1 0 5 5 3 3 2 1 4 4 2 5 2 1 4 8 4 9 8 9 5 6 5 8 6 7 3 7 7 3 8 1 9 9 1 9 2 5 2 6 9 2 7 3 9 7 3 5 7 7 6 7 5 5 5 1 3 9 0 8 4 4 8 8 3 8 1 5 0 6 0 6 4 5 9 2 6 9 2 2 3 7 7 6 7 8 3 5 2 5 9 7 8 1 4 1 1 0 0 0 5 5 8 6 5 9 5 9 1 5 2 2 2 7 7 4 0 9 1 0 3 3 5 0 3 2 1 7 5 0 6 6 1 1 8 4 5 0 1 0 3 7 9 8 0 9 7 5 5 8 9 8 2 3 6 5 8 2 2 2 1 4 6 6 0 6 6 4 0 0 5 2 8 5 9 6 7 9 0 0 9 4 5 8 0 3 1 3 2 1 1 2 5 5 2 7 4 3 5 2 1 3 7 2 5 3 3 6 8 1 2 9 9 7 1 1 0 1 1 0 5 0 7 6 0 0 9 2 4 3 9 9 3 3 1 0 2 6 8 2 5 3 2 6 3 6 7 3 6 2 2 3 9 3 6 7 0 2 6 7 2 8 8 3 7 9 8 4 2 3 9 4 6 5 3 0 4 2 7 5 8 1 0 1 5 8 8 9 9 0 5 2 1 4 6 9 9 6 4 2 8 6 3 1 6 9 9 9 5 0 1 5 6 7 1 5 9 9 9 8 4 9 2 7 3 5 6 3 6 0 9 5 9 1 4 5 5 3 6 1 8 6 1 7 5 8 3 6 7 5 4 7 9 9 1 3 0 5 3 1 9 0 4 9 8 4 2 9 6 0 5 9 3 9 3 1 1 8 4 8 2 3 3 8 4 9 0 6 5 5 4 8 4 3 5 7 4 8 7 7 5 8 6 6 8 7 7 4 9 0 4 1 4 6 1 4 8 6 2 8 3 1 1 5 5 6 1 1 3 3 5 2 9 7 1 7 3 8 6 6 2 2 3 0 4 9 4 7 3 0 4 0 6 5 5 0 3 3 0 0 1 8 1 0 6 0 7 1 2 1 7 9 9 8 7 5 2 3 4 1 0 4 3 7 9 6 2 1 5 0 4 9 4 2 7 7 1 8 7 1 3 4 6 7 6 0 6 2 5 2 0 0 1 5 9 4 1 8 7 8 3 4 4 8 8 2 9 0 9 9 5 2 9 7 8 7 8 6 9 6 5 7 2 7 5 0 4 1 0 2 6 9 9 4 0 0 0 7 6 0 5 8 1 8 6 9 7 2 5 2 6 3 7 9 8 4 4 6 8 4 3 2 8 4 5 8 7 9 0 9 4 8 0 5 8 8 0 3 2 3 0 8 2 3 6 0 5 2 2 6 1 5 0 1 1 8 5 5 1 5 0 2 1 8 0 1 1 2 2 4 0 5 9 6 1 4 1 5 7 8 8 5 6 9 9 7 6 1 5 9 3 5 7 5 7 2 3 2 3 7 3 1 2 6 5 0 2 7 9 3 9 7 5 5 2 9 1 2 8 6 0 3 9 2 9 8 9 5 0 0 5 0 6 4 4 0 7 4 6 1 5 6 2 1 2 9 1 8 0 1 1 4 3 4 1 9 5 9 0 0 9 9 0 0 4 9 8 2 9 0 2 4 4 2 8 1 4 9 0 4 3 8 1 3 6 2 9 6 2 1 4 5 9 2 3 1 3 2 7 3 0 2 1 5 4 5 0 7 8 8 1 8 8 7 1 6 4 5 1 1 8 3 7 5 2 7 1 8 9 2 5 9 6 6 0 6 6 4 0 5 5 8 0 1 6 2 0 4 3 3 6 3 1 9 1 1 5 2 8 4 9 9 5 4 8 1 9 7 1 7 9 4 2 1 1 2 6 7 9 3 7 2 1 3 0 8 6 1 6 1 3 5 2 0 7 6 9 7 9 6 3 7 4 0 8 7 8 7 6 5 7 0 5 6 8 0 3 0 5 2 7 8 4 9 9 0 2 3 7 9 5 7 9 6 0 1 1 7 9 7 1 4 4 5 1 7 0 3 9 6 0 7 8 3 5 4 1 1 8 4 7 3 4 8 8 0 1 2 8 0 0 7 6 0 5 8 7 6 7 5 6 2 4 6 0 6 0 1 6 1 7 0 1 8 1 0 5 0 3 8 2 0 5 7 2 4 4 7 1 8 8 0 5 4 5 2 0 0 0 7 9 9 9 9 0 9 8 3 6 6 8 9 3 1 8 2 6 9 3 1 6 4 0 2 8 6 4 9 0 3 1 3 5 0 3 3 4 1 3 5 2 1 4 5 8 9 3 4 3 6 8 3 6 9 6 9 7 2 7 8 0 3 5 9 2 1 6 6 3 0 8 0 0 1 2 5 7 6 3 4 8 9 7 4 8 9 2 8 4 1 7 5 3 0 7 3 4 1 0 0 6 5 7 1 6 2 6 9 6 5 5 2 0 7 7 4 6 0 2 3 3 3 2 3 8 0 3 1 4 9 1 1 6 3 8 5 4 8 1 4 8 2 8 4 5 2 3 1 7 7 3 0 6 6 8 8 6 7 1 7 9 4 2 8 6 7 3 9 6 9 2 8 4 8 0 7 5 3 5 3 1 4 3 1 2 2 2 2 8 3 2 3 5 8 0 1 6 4 0 8 4 4 4 9 3 2 8 6 5 2 1 1 3 0 0 4 3 1 7 2 2 5 3 9 0 8 2 8 1 6 6 8 6 4 9 1 3 2 2 1 1 0 2 1 8 8 2 4 8 5 5 5 7 4 1 4 6 4 0 7 1 1 9 8 8 7 5 8 9 7 1 1 7 3 9 9 2 1 0 5 3 7 8 7 3 7 2 3 0 9 6 2 4 8 3 6 3 9 0 1 5 0 6 9 9 1 0 7 4 6 5 4 3 8 3 5 8 1 2 8 9 0 9 4 8 4 4 1 2 7 3 5 0 5 4 2 9 6 7 2 1 7 0 9 3 3 5 2 5 8 9 2 9 0 3 0 2 6 6 4 6 3 0 8 0 3 5 0 5 8 6 2 7 5 5 8 6 9 0 4 1 8 3 3 1 6 5 4 5 7 9 2 1 2 7 9 3 0 8 6 2 4 4 8 4 4 4 9 5 0 6 4 4 6 5 9 8 0 2 6 3 0 4 2 8 2 3 0 3 3 9 4 8 4 9 5 9 6 3 8 0 1 8 7 2 2 8 0 5 8 1 5 2 4 4 2 5 2 1 5 4 1 3 1 6 6 9 5 7 7 2 3 6 5 6 1 8 9 6 5 8 0 2 0 8 8 3 4 4 0 0 1 7 1 3 9 6 2 7 3 0 3 9 4 5 0 0 3 4 0 6 4 4 0 1 1 0 7 4 7 6 5 8 2 0 1 8 6 7 2 9 3 0 9 0 7 7 1 9 4 9 6 1 8 4 6 5 0 9 7 8 5 0 6 7 1 1 6 6 2 3 7 3 4 8 4 9 4 6 3 0 4 3 8 0 5 9 1 5 6 5 4 4 9 3 7 6 4 2 8 5 8 3 7 9 7 5 5 6 2 6 9 6 8 2 9 8 4 3 5 3 1 7 5 1 4 9 6 8 7 7 7 5 9 3 2 8 3 0 0 7 9 2 3 1 6 7 7 9 9 3 0 7 1 0 5 1 4 8 0 4 1 4 3 9 6 5 3 0 3 5 0 5 2 8 6 4 4 4 7 2 4 1 1 7 8 0 8 7 4 6 9 4 2 4 6 5 1 1 2 3 7 0 4 6 5 3 3 3 3 1 5 0 6 1 9 1 6 4 5 8 4 8 3 6 3 6 5 3 1 3 3 4 7 1 0 8 8 4 6 2 7 1 0 8 3 1 0 7 8 0 4 7 7 1 3 1 1 9 5 9 4 9 6 2 4 8 7 8 7 4 8 3 5 6 4 0 7 7 5 9 6 4 1 2 5 2 1 7 1 9 9 9 9 2 2 4 7 8 4 2 0 7 5 8 1 6 7 7 6 5 7 6 7 6 4 5 3 4 2 0 3 7 7 8 8 3 2 8 1 7 4 0 6 0 5 7 1 3 2 3 3 0 5 2 4 7 6 6 0 5 4 1 6 2 1 0 5 5 9 1 7 3 6 6 7 2 5 7 1 5 3 2 1 8 5 8 3 5 4 2 3 9 7 8 0 2 6 2 4 0 6 3 3 7 1 2 4 7 0 7 6 3 4 1 5 0 4 6 8 0 8 8 2 8 2 4 3 5 1 3 0 8 2 5 9 6 5 9 0 0 4 5 2 4 8 5 4 6 8 2 4 3 3 0 2 8 0 8 9 2 3 5 6 9 4 1 1 2 2 4 4 6 0 9 8 9 0 8 9 6 4 4 6 7 6 6 4 3 5 0 1 8 6 5 8 3 9 2 6 1 3 2 2 1 2 7 2 5 1 1 3 7 9 1 0 5 5 3 3 8 8 9 9 9 9 2 5 5 0 3 7 1 4 2 9 9 1 1 0 9 2 4 9 0 3 2 8 1 8 9 8 6 2 5 6 1 4 2 2 9 3 5 4 6 9 1 1 5 7 5 2 0 5 6 1 9 4 3 8 5 8 4 4 2 6 6 7 2 3 0 4 1 9 1 9 2 1 2 1 8 4 1 9 2 1 0 3 9 5 8 7 6 6 9 8 9 8 5 9 6 5 3 7 1 0 9 7 9 1 5 6 4 5 8 5 8 9 4 7 3 9 4 9 6 0 3 6 8 3 2 7 9 0 3 5 4 0 2 4 4 6 0 1 0 2 2 6 1 0 6 4 5 6 8 9 7 7 7 7 7 5 6 0 3 2 1 5 1 0 8 6 3 2 0 1 3 2 1 8 1 7 8 3 2 1 5 7 9 4 7 0 2 8 8 9 4 7 7 9 3 7 0 5 4 2 1 0 3 9 8 8 7 8 2 2 9 4 1 0 7 7 8 1 2 9 8 4 3 2 9 2 6 2 0 0 6 1 7 3 0 8 8 2 7 9 7 0 0 1 0 0 6 3 4 2 1 1 5 4 9 6 6 8 2 0 7 1 5 0 0 6 6 1 8 4 0 1 3 5 0 1 9 0 0 4 5 9 5 6 0 7 5 4 9 3 1 7 9 0 5 9 5 8 7 3 1 9 7 4 3 0 5 3 7 3 9 3 3 3 3 3 2 1 6 7 0 6 5 9 4 4 2 4 8 4 5 2 5 8 9 2 5 2 1 2 7 3 9 7 1 8 8 2 9 6 6 4 5 2 4 0 2 8 6 9 5 2 4 5 5 1 8 2 7 4 4 3 6 8 3 7 8 3 4 2 8 5 5 4 5 2 9 1 9 1 0 0 0 7 3 5 5 7 9 1 9 9 1 9 3 4 8 9 9 9 6 2 8 0 4 4 3 9 0 1 1 3 9 7 5 9 2 3 3 3 4 0 3 0 3 4 1 0 1 2 0 4 8 1 4 1 5 9 9 5 7 8 8 7 4 3 7 7 6 8 5 3 6 3 1 2 9 8 7 7 6 3 2 3 7 6 8 6 7 9 8 2 1 0 4 5 9 9 0 2 0 2 7 3 1 4 1 9 7 3 1 3 6 2 1 6 3 2 0 5 2 3 8 2 3 9 6 5 6 5 2 6 6 5 1 8 7 1 0 3 4 3 6 1 0 9 1 7 7 1 0 2 3 7 3 8 1 6 1 1 3 7 7 6 0 5 8 9 3 4 5 6 7 6 7 2 4 6 2 3 6 6 0 4 6 3 1 0 4 5 9 7 9 4 7 2 7 8 9 6 8 8 7 4 3 7 8 9 3 5 4 1 5 2 8 0 0 0 2 7 8 8 2 5 2 2 4 9 9 8 2 9 9 7 7 5 6 6 8 2 6 8 8 6 9 7 4 1 1 3 3 0 8 8 1 7 6 1 1 6 0 5 6 6 4 4 0 3 4 5 4 4 2 6 9 7 3 0 6 3 9 7 3 8 4 7 5 7 3 3 5 0 6 5 7 1 7 8 5 0 2 0 5 2 3 4 6 6 0 2 6 3 9 6 4 0 9 9 8 8 2 2 1 8 7 3 2 9 2 8 3 9 2 5 1 6 6 7 6 4 4 7 8 9 5 3 6 6 5 4 8 7 4 7 3 9 3 9 1 3 5 3 8 4 4 9 6 3 7 9 0 4 3 5 9 6 4 9 8 8 6 7 4 2 6 6 4 4 9 2 7 7 7 0 7 8 6 2 9 3 9 3 7 9 9 7 6 2 4 3 5 4 1 6 9 5 2 3 2 2 2 2 2 9 5 5 9 9 0 0 5 7 0 9 6 7 6 8 1 5 0 0 1 5 0 1 9 1 1 0 0 2 2 7 9 8 9 6 1 1 1 8 6 4 1 9 0 7 5 7 0 8 3 3 1 7 5 3 5 0 6 3 2 2 6 8 4 3 1 9 8 9 1 1 5 3 1 4 0 5 8 9 0 4 7 5 3 3 6 5 4 7 7 9 3 7 0 0 3 1 1 1 4 3 9 9 9 8 8 4 1 6 2 2 0 7 8 7 3 8 9 7 1 6 4 8 3 0 7 2 3 4 7 8 3 8 4 0 9 9 1 3 4 4 0 0 7 9 8 8 5 6 6 4 2 9 1 8 8 9 6 1 7 0 2 5 9 7 9 4 2 5 6 4 6 4 5 4 3 5 2 7 3 6 0 5 3 1 6 7 3 1 0 5 9 0 9 4 6 2 0 4 2 9 8 4 8 0 7 9 1 2 3 4 5 1 6 6 5 0 1 8 5 2 8 5 0 7 8 0 3 9 7 4 7 5 6 0 7 3 2 1 5 7 4 8 4 5 0 0 0 4 7 1 1 1 8 6 7 7 1 2 3 8 7 6 2 4 3 7 5 3 0 6 5 4 2 2 7 3 4 0 6 5 2 0 5 1 5 4 4 9 8 4 1 4 0 4 7 9 6 2 4 3 4 2 3 8 1 8 1 2 6 8 3 2 9 6 7 6 9 3 9 5 7 6 8 5 9 4 2 6 0 7 7 9 5 6 9 2 5 1 1 6 5 6 8 4 1 6 1 7 8 7 7 9 6 1 5 1 8 9 3 5 1 2 8 7 9 7 8 3 7 7 5 8 9 1 3 6 5 0 5 2 5 0 1 8 5 9 6 0 7 7 7 3 3 0 4 5 5 2 1 5 6 0 0 1 4 4 3 5 6 2 6 3 8 2 2 1 4 4 6 9 6 2 7 8 3 6 2 3 9 8 5 1 2 2 6 1 6 6 9 1 1 2 1 6 8 2 0 0 7 7 1 1 8 1 6 7 9 9 3 6 0 6 3 6 9 4 4 5 6 6 0 6 9 3 5 8 9 6 5 8 6 3 6 2 5 1 6 1 4 2 4 7 9 8 9 6 3 3 9 7 8 1 1 1 0 9 0 3 5 9 1 3 2 7 5 2 5 5 6 1 4 6 6 5 3 6 9 6 4 5 1 4 0 6 3 6 1 6 6 7 1 8 7 1 4 6 9 7 9 3 4 1 2 3 2 4 2 9 3 7 1 1 9 4 3 8 9 9 6 3 3 7 5 4 7 0 8 2 5 0 9 2 4 2 3 9 0 1 1 8 9 0 9 2 3 3 5 9 2 4 0 6 9 5 3 6 8 8 2 1 0 5 0 5 4 8 9 4 8 6 2 0 2 3 2 9 7 1 8 9 1 2 8 9 5 7 4 2 3 8 8 1 8 4 8 4 1 3 1 4 9 1 1 5 2 8 1 0 4 5 6 4 8 3 6 1 7 3 9 3 5 8 6 9 5 3 3 8 3 3 7 0 9 8 9 4 8 0 1 0 4 0 8 5 6 8 0 8 4 8 5 1 0 0 4 6 1 3 6 9 3 7 9 1 8 8 7 5 9 6 1 6 6 2 5 4 4 8 0 7 2 6 3 3 1 5 0 2 6 0 3 8 1 6 8 0 5 7 8 7 1 9 1 2 0 0 2 8 5 4 8 3 5 6 0 0 5 3 3 4 1 5 6 7 4 0 3 2 0 1 9 5 5 4 8 4 5 3 4 2 1 3 1 8 8 8 0 5 7 2 5 3 2 9 7 6 3 0 6 8 4 5 5 3 9 7 4 9 4 9 4 8 8 7 2 0 8 8 9 9 3 2 7 6 5 1 9 2 5 9 1 9 1 1 3 2 6 4 1 8 6 9 3 4 6 3 1 8 5 7 2 0 3 6 4 6 9 2 5 0 5 0 5 0 7 7 7 6 9 8 1 0 7 3 8 8 4 5 1 8 8 0 3 5 6 9 5 8 6 9 3 1 2 6 1 3 0 1 0 1 3 1 4 3 6 6 5 0 4 0 1 8 1 6 8 2 4 4 4 8 5 4 7 9 2 4 1 8 9 2 4 4 9 8 1 7 2 0 9 6 9 6 9 3 9 5 1 8 9 3 8 9 3 2 9 1 1 7 5 4 0 5 2 1 0 9 5 6 9 8 5 7 3 5 3 2 8 5 5 2 3 1 5 2 2 4 3 1 7 7 2 5 1 1 6 6 0 0 7 5 6 6 6 0 4 5 1 4 7 1 0 1 4 7 5 3 7 9 6 9 8 8 1 3 0 2 7 7 3 4 5 1 6 8 7 1 7 6 0 6 7 7 4 7 2 7 4 2 3 3 1 1 0 2 7 1 5 7 4 7 9 7 8 1 7 3 1 2 9 1 1 7 4 4 5 7 6 3 2 8 8 3 9 4 8 3 2 0 4 2 3 7 5 0 9 8 6 6 5 3 3 5 4 8 7 4 5 1 8 5 5 7 3 0 5 0 7 0 3 2 0 7 1 1 3 0 2 3 2 0 3 7 4 4 0 4 1 9 7 3 7 3 3 2 9 4 5 7 7 7 5 8 7 5 0 9 1 0 5 9 2 3 4 4 5 6 6 4 3 0 0 2 8 1 4 6 4 3 9 6 0 3 7 5 8 9 6 6 7 3 9 8 5 4 4 5 4 5 5 3 9 5 8 7 6 5 8 3 0 3 3 7 9 9 8 0 1 6 1 1 9 8 9 8 1 1 9 2 0 7 4 9 9 3 2 3 2 1 4 7 6 4 4 0 1 5 6 6 5 4 7 2 8 6 9 8 1 7 9 9 8 3 8 4 4 8 9 3 5 9 3 5 1 0 8 2 2 6 5 4 8 7 9 7 0 8 9 5 3 1 9 5 8 8 0 3 6 0 1 9 0 8 7 5 3 7 0 7 0 0 9 0 4 4 4 6 9 7 1 9 1 0 3 7 6 6 0 6 4 5 1 4 3 0 0 6 2 8 1 4 5 5 0 6 3 1 6 5 8 9 1 1 3 2 3 1 7 1 3 4 9 9 8 1 8 7 1 7 2 6 6 8 9 9 0 9 6 3 8 0 4 9 4 9 6 6 6 1 0 5 7 9 8 7 0 8 0 3 3 4 2 7 7 5 9 6 3 5 5 0 3 8 9 0 5 6 3 8 3 6 4 8 7 0 6 9 7 0 0 2 4 8 8 1 6 8 0 9 5 1 2 3 2 2 9 8 6 7 4 1 1 8 8 4 7 1 5 5 6 3 5 3 9 1 9 9 0 8 6 0 8 0 0 4 5 4 2 3 9 7 9 5 4 2 8 0 9 9 6 7 4 0 8 0 9 8 5 7 8 5 4 4 6 0 9 8 7 3 2 4 1 2 1 7 2 4 1 3 4 1 4 0 3 3 3 3 3 3 2 1 6 5 4 0 8 5 2 7 0 9 1 1 1 0 4 9 4 6 5 7 8 4 1 3 5 1 4 2 5 0 7 6 4 1 9 4 5 5 9 5 7 2 1 7 2 1 5 1 7 8 1 3 3 8 7 4 9 3 4 9 0 5 3 4 3 9 2 7 7 3 1 6 1 9 3 9 9 8 4 3 3 0 6 4 1 7 7 8 2 4 2 6 7 8 2 3 0 4 1 1 2 9 9 9 1 9 0 7 1 5 0 1 8 0 6 9 0 1 3 4 5 4 4 6 5 7 9 8 9 6 0 1 7 5 2 0 5 7 4 5 8 8 8 3 8 5 5 4 4 5 9 0 7 1 1 2 3 6 7 3 4 8 0 6 0 2 1 4 9 5 8 0 7 0 0 7 2 9 9 0 4 6 0 2 4 4 9 4 1 1 3 5 6 9 8 8 9 5 8 6 8 6 1 0 0 9 2 2 8 8 9 5 1 6 5 3 8 8 0 0 8 3 6 7 6 0 0 5 1 5 3 7 3 9 9 9 0 7 7 4 2 1 3 3 6 2 3 6 9 9 1 9 6 6 2 6 6 7 9 8 2 0 3 4 8 7 8 3 9 4 3 9 9 6 3 1 5 4 0 3 5 3 2 3 7 5 1 5 2 8 6 5 8 5 3 3 8 7 7 1 8 0 8 0 2 9 3 9 0 7 5 8 6 1 7 7 2 8 6 6 5 4 2 8 2 3 1 7 4 4 8 4 6 3 8 1 8 6 9 1 5 5 3 9 3 0 7 0 4 1 6 6 1 3 6 9 5 0 9 9 4 6 4 8 3 8 7 1 5 6 1 1 6 4 2 5 4 4 5 0 7 8 3 0 9 3 3 8 7 5 7 9 2 7 2 1 8 6 9 7 4 8 3 4 2 7 8 8 3 7 3 4 4 3 1 4 9 7 1 9 3 4 8 9 3 0 5 9 1 8 9 7 7 6 5 8 6 2 9 8 4 5 9 4 1 9 3 8 6 3 4 5 2 3 5 5 3 7 0 8 6 1 9 4 4 8 6 7 5 7 0 7 0 2 0 9 0 4 9 6 3 8 3 1 4 7 3 7 5 5 3 4 2 4 6 4 9 6 2 8 1 5 3 5 6 3 1 5 7 9 2 2 7 0 2 1 7 5 8 5 3 6 5 0 1 4 0 5 0 6 1 8 2 4 4 5 5 0 2 3 8 2 6 2 6 3 8 1 3 3 2 6 6 7 4 2 5 3 5 1 8 5 2 6 5 3 5 2 8 1 5 0 1 4 9 1 9 4 8 2 1 4 4 4 1 7 2 2 6 4 9 7 5 3 9 9 3 2 6 4 7 1 3 4 7 0 7 5 5 9 3 7 5 6 4 1 1 0 7 0 0 3 1 2 7 3 6 3 8 4 2 3 5 8 7 8 5 8 6 9 1 0 1 2 8 2 7 5 9 1 2 8 9 9 7 8 1 6 5 0 2 4 4 3 0 6 7 9 7 3 3 6 6 1 5 3 9 5 1 2 0 0 4 0 2 2 0 7 0 2 0 6 3 2 8 9 1 0 2 6 2 2 4 5 3 1 1 4 1 2 1 1 1 8 3 9 3 1 0 1 3 4 2 9 5 4 0 5 7 4 9 0 9 7 9 2 8 7 5 0 5 6 8 5 7 3 9 3 1 8 8 9 4 8 4 9 7 0 0 4 4 7 3 5 5 2 8 6 1 6 4 9 3 1 9 0 1 3 3 4 9 9 5 1 2 8 7 4 0 9 0 8 3 8 4 2 3 5 6 0 2 3 4 9 3 9 2 6 6 0 5 0 9 1 3 9 7 5 1 8 6 5 7 7 9 8 9 8 9 7 9 9 2 8 2 7 5 4 0 4 6 2 1 5 4 3 5 9 9 9 2 1 9 0 5 9 6 0 7 9 8 4 8 5 2 2 9 5 5 2 9 3 4 4 2 0 9 3 7 2 7 2 5 8 3 6 8 1 8 7 3 9 0 3 3 8 4 2 7 5 7 5 7 7 3 6 1 6 8 6 8 3 9 3 9 3 7 4 5 1 5 0 2 5 4 1 0 7 3 7 8 2 1 1 2 5 2 0 0 9 8 8 2 5 8 8 3 7 3 2 7 0 0 1 5 6 2 7 3 0 9 3 1 8 6 0 1 8 7 5 8 6 6 5 4 1 7 8 6 6 1 9 0 9 8 7 6 9 1 7 9 7 5 9 5 4 0 3 2 5 0 5 5 7 4 7 3 8 2 1 4 4 8 2 3 0 8 6 6 5 1 1 4 6 1 7 3 7 5 5 8 8 6 4 9 8 5 2 7 0 3 4 7 3 0 7 6 0 5 4 0 1 4 2 4 8 8 6 2 5 4 1 2 5 6 4 4 0 8 6 7 6 0 3 5 1 3 6 4 6 6 4 8 2 8 9 8 5 2 0 5 5 8 9 2 1 6 9 8 4 2 6 0 3 4 3 8 2 5 2 2 7 5 6 4 8 9 2 1 2 3 1 2 7 0 1 5 3 9 1 2 7 6 9 1 5 2 6 5 5 0 5 2 7 9 9 3 7 8 6 0 0 7 0 6 3 0 4 2 7 3 7 0 2 8 7 3 5 9 5 0 6 2 7 9 9 3 5 2 1 2 1 9 0 9 9 4 1 5 3 9 8 8 8 2 9 2 7 0 4 1 2 1 6 6 0 4 2 3 1 9 5 2 1 9 8 8 5 7 8 3 2 1 1 3 2 9 4 9 5 8 0 8 4 4 8 9 4 3 9 5 3 4 1 4 9 7 0 5 5 4 9 4 4 2 9 3 6 0 6 2 8 5 8 7 4 2 6 0 2 1 5 4 2 3 3 8 1 4 3 0 7 6 0 8 5 6 8 8 5 9 6 4 2 1 5 5 4 5 2 0 8 0 2 1 5 6 6 8 5 9 5 3 0 3 9 8 2 2 5 8 5 7 1 7 2 3 5 9 9 1 8 1 3 9 6 4 5 5 8 5 3 6 6 1 3 4 5 4 4 4 7 6 9 3 5 5 0 2 9 2 4 1 3 4 5 1 2 0 8 4 4 9 6 9 7 8 9 7 1 5 3 9 6 8 0 3 0 4 0 3 3 5 3 6 2 1 4 3 0 8 9 8 1 9 4 9 5 4 9 6 2 4 2 6 8 6 5 4 2 8 1 0 3 end lrslib-073/ext/redund/r5k_100.ext320000777000175000017500000000030314625766576015426 0ustar avisavis*mplrs:lrslib_v.7.3_2024.4.17(128bit,hybrid arithmetic,gmp v.6.2)32 processes *Input taken from r5k_100.ext *rows=60 lastp=10 lastrows=10 j=1 *redund *interior point found, no hidden linearities lrslib-073/ext/test/0000777000175000017500000000000014625766575013154 5ustar avisavislrslib-073/ext/test/c30-15.ext0000777000175000017500000001117014625766574014510 0ustar avisavisc30-15 *cyclic polytope n=30, d=15 V-representation begin 30 16 integer 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 1 3 9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969 14348907 1 4 16 64 256 1024 4096 16384 65536 262144 1048576 4194304 16777216 67108864 268435456 1073741824 1 5 25 125 625 3125 15625 78125 390625 1953125 9765625 48828125 244140625 1220703125 6103515625 30517578125 1 6 36 216 1296 7776 46656 279936 1679616 10077696 60466176 362797056 2176782336 13060694016 78364164096 470184984576 1 7 49 343 2401 16807 117649 823543 5764801 40353607 282475249 1977326743 13841287201 96889010407 678223072849 4747561509943 1 8 64 512 4096 32768 262144 2097152 16777216 134217728 1073741824 8589934592 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36 37 39 40 I#30 det= 16 in_det= 16 z= 6 1 1 0 0 1 1 1 0 0 1 1 V#15 R#0 B#1589 h=6 facets 8 11 19 23 24 31 32 34 36 40 I#10 det= 48 in_det= 48 z= 10/3 1 2/3 1/3 2/3 2/3 1/3 2/3 2/3 1/3 1/3 2/3 V#16 R#0 B#1666 h=9 facets 4 6 7 10 13 19 23 24 31 33 I#10 det= 48 in_det= 48 z= 16/3 1 1/3 2/3 1/3 1/3 1/3 2/3 2/3 1/3 1/3 2/3 V#17 R#0 B#1845 h=11 facets 3 5 9 12 13 17 21 27 28 32 I#10 det= 48 in_det= 48 z= 6 1 2/3 1/3 1/3 1/3 1/3 1/3 1/3 2/3 2/3 2/3 V#18 R#0 B#2165 h=2 facets 28 30 31 32 33 34 35 37 38 40 I#30 det= 16 in_det= 16 z= 4 1 0 0 1 0 0 1 0 1 0 1 V#19 R#0 B#2238 h=12 facets 1 5 10 15 16 22 25 30 34 38 I#10 det= 48 in_det= 48 z= 16/3 1 2/3 2/3 2/3 1/3 2/3 2/3 1/3 2/3 1/3 1/3 V#20 R#0 B#2497 h=5 facets 27 28 30 31 32 34 35 36 38 40 I#30 det= 16 in_det= 16 z= 6 1 1 0 1 0 1 0 1 1 0 1 V#21 R#0 B#2972 h=10 facets 3 9 11 14 17 23 26 30 32 36 I#10 det= 48 in_det= 48 z= 16/3 1 2/3 1/3 1/3 2/3 1/3 1/3 2/3 2/3 1/3 1/3 V#22 R#0 B#3997 h=12 facets 2 4 9 11 14 16 22 25 30 37 I#10 det= 48 in_det= 48 z= 6 1 1/3 1/3 1/3 2/3 2/3 2/3 1/3 2/3 1/3 1/3 V#23 R#0 B#4410 h=16 facets 2 4 6 9 12 13 16 20 24 28 I#10 det= 48 in_det= 48 z= 20/3 1 1/3 1/3 1/3 1/3 2/3 2/3 2/3 2/3 2/3 2/3 V#24 R#0 B#4621 h=6 facets 22 27 28 29 30 33 35 37 38 39 I#30 det= 16 in_det= 16 z= 10 1 0 1 0 0 1 0 0 1 1 0 V#25 R#0 B#4823 h=11 facets 5 8 12 15 19 21 25 29 32 34 I#10 det= 48 in_det= 48 z= 16/3 1 2/3 1/3 2/3 1/3 1/3 2/3 1/3 1/3 2/3 1/3 V#26 R#0 B#5091 h=9 facets 4 7 14 19 21 25 29 33 37 39 I#10 det= 48 in_det= 48 z= 14/3 1 1/3 2/3 1/3 2/3 1/3 2/3 1/3 1/3 2/3 1/3 V#27 R#0 B#5861 h=13 facets 2 6 8 12 15 18 20 26 29 35 I#10 det= 48 in_det= 48 z= 6 1 1/3 1/3 2/3 1/3 2/3 1/3 2/3 1/3 2/3 1/3 V#28 R#0 B#6307 h=4 facets 13 28 29 30 32 33 34 36 38 39 I#30 det= 16 in_det= 16 z= 8 1 1 1 0 0 0 1 1 1 1 0 V#29 R#0 B#6899 h=9 facets 6 10 15 17 23 26 30 33 35 38 I#10 det= 48 in_det= 48 z= 14/3 1 1/3 2/3 2/3 1/3 1/3 1/3 2/3 2/3 1/3 1/3 V#30 R#0 B#7160 h=7 facets 13 23 24 26 29 30 31 32 34 36 I#30 det= 16 in_det= 16 z= 12 1 1 0 0 0 1 1 1 0 0 0 V#31 R#0 B#8058 h=12 facets 1 3 7 14 18 20 26 29 36 39 I#10 det= 48 in_det= 48 z= 16/3 1 2/3 2/3 1/3 2/3 2/3 1/3 2/3 1/3 2/3 1/3 V#32 R#0 B#8474 h=5 facets 13 26 27 29 30 31 32 33 35 37 I#30 det= 32 in_det= 32 z= 10 1 0 0 0 0 0 0 0 0 0 0 end *Totals: vertices=32 rays=0 bases=9041 integer_vertices=16 max_vertex_depth=16 *Dictionary Cache: max size= 17 misses= 0/9040 Tree Depth= 16 *overflow checking on lrslong arithmetic *lrs:lrslib_v.7.2_2022.2.8(64bit,lrslong.h,hybrid arithmetic) *0.062u 0.000s 3968Kb 1033 flts 0 swaps 0 blks-in 0 blks-out lrslib-073/ext/test/simp15.ext0000777000175000017500000000110114625766574015007 0ustar avisavisV-representation begin 16 16 integer 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 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0 1 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 1 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 1 1 1 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 1 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 0 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 1 end lrslib-073/float2rat.c0000777000175000017500000000457314625766600013440 0ustar avisavis/* * Reads a polyhedron file on stdin with rationals and outputs * an approximation in decimal floating point * * David Bremner. bremner@cs.mcgill.ca * */ /* Hacked by DA, April 20 2006 * * first argument overides stdin * if column 0=0 then column 1 scaled to 1 (otherwise big ugly integers come out) * since lrs does not define m (# of output lines) this is skipped * lines are converted until "end" is read */ static char rcsid[]="$Id: float2rat.c,v 1.1.1.1 2006/04/03 20:42:10 bremner Exp $"; #include #include #include #include FILE *lrs_ifp; /* input file pointer */ #define DOCSTRING "\n\ $Id: float2rat.ds,v 1.2 2006/04/03 21:15:39 bremner Exp $\n\ \n\ Converts floating point coefficent $f$ to rational by the \n\ simple expedient of outputing 10^k*f/10^k for appropriate \n\ $k$. Does no reduction of numbers. In particular this may cause overflow in \n\ old versions of lrs input (and I'm not about cdd).\n\ " int usage(){ fprintf(stderr,"\n%s\n",rcsid);fprintf(stderr,DOCSTRING); exit(1); } #define CHECK_HELP if (argc > 1 && argv[1][0]=='-' && argv[1][1]=='h') usage(); int main(argc,argv) int argc; char **argv; { long int m,n; int i,j; long atol(); char buf[BUFSIZ]; CHECK_HELP; if(argc > 1 ) /* command line argument overides stdin */ { if ((lrs_ifp = fopen (argv[1], "r")) == NULL) { printf ("\nBad input file name\n"); return(1); } } else lrs_ifp=stdin; while ( fgets(buf,BUFSIZ,lrs_ifp) !=NULL ) { fputs(buf,stdout); if (strncmp(buf,"begin",5)==0) break; } if (fscanf(lrs_ifp,"%ld %ld %s",&m,&n,buf)==EOF){ fprintf(stderr,"No begin line"); exit(1); } printf("%ld %ld rational\n",m,n); for (i=0;ipayoff[player][row][col] is a pointer to a payoff string. All payoff strings are stored in the character array game->pstore, whose length is the size of the input file. Removed MAXSTRAT (max number of strategies in games). Game storage is now dynamically allocated and freed. Removed the following three functions to compute field width for pretty printing of games: initFwidth, setFwidth, and updateFwidth. This is now handled by printGame in lrsnashlib.c. lrsnash.c --------- Removed two superfluous warnings: RATWARN and SIZERRROR. Removed function tl_readrat, which converted payoff strings to (num, den) pairs of long integers. All conversion is now handled by the functions in lrsgmp.c Added two functions allocateGameStorage and freeGameStorage to handle storage for game payoffs. lrsnashlib.c ------------ Added the function str2rat (lrs_mp Na, lrs_mp Da, char *str) to convert payoff strings to lrs_mp (Num, Den) pairs. It is based on readrat in lrsgmp.c. Modified the function FillConstraintRows(lrs_dic * P, lrs_dat * Q, const game * g, int p1, int p2, int firstRow). - Replaced the long int data structures for (Num, Den) pairs by lrs_mp - using str2rat to convert payoff strings to (Num, Den) pairs - and using the macros zero and changesign from lrsgmp.h to handle sign changes. The functions FillNonnegativityRows, FillLinearityRow and FillFirstRow are reused because they do not use any information about game payoffs. (Still not sure if FillFirstRow is needed). Rewrote printGame to handle payoff strings and use them to compute field widths. setupnash_v2.c -------------- Introduced variable string length for game payoffs (as in lrsnashlib) TODO: ----- lrsnash should be able to handle two legacy input files, but it produces a segfault at the statement "fclose(lrs_ifp);" at line 828 in lrsnashlib.c. When that statement is commented out, it seems to run without errors. lrslib-073/games/g0000777000175000017500000000014314625766574012642 0ustar avisavis2 2 0 18446744073709551616 18446744073709551616 0 0 -18446744073709551616 -18446744073709551616 0 lrslib-073/games/g10000777000175000017500000000024114625766574012722 0ustar avisavis*g: player 1 H-representation linearity 1 5 begin 5 4 rational 0 1 0 0 0 0 1 0 0 0 18446744073709551616 1 0 18446744073709551616 0 1 -1 1 1 0 end lrslib-073/games/g20000777000175000017500000000024114625766574012723 0ustar avisavis*g: player 2 H-representation linearity 1 5 begin 5 4 rational 0 0 -18446744073709551616 1 0 -18446744073709551616 0 1 0 1 0 0 0 0 1 0 -1 1 1 0 end lrslib-073/games/game0000777000175000017500000000003614625766574013326 0ustar avisavis3 2 0 6 2 5 3 3 1 0 0 2 4 3 lrslib-073/games/game10000777000175000017500000000021714625766574013410 0ustar avisavis*game: player 1 H-representation linearity 1 6 begin 6 5 rational 0 1 0 0 0 0 0 1 0 0 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0 0 0 0 0 0 0 0 0 0 0 4608 *Number of equilibria found: 14 *Player 1: vertices=1394399 bases=1404287 pivots=1404509 *Player 2: vertices=14 bases=1 pivots=1851723 *Overflow checking on lrslong arithmetic *lrsnash:lrslib v.6.3 2018.5.1(128bit,lrslong.h) *445.359u 0.000s 4676Kb 2007 flts 0 swaps 0 blks-in 0 blks-out lrslib-073/games/gamem.gmp0000777000175000017500000001254614625766574014276 0ustar avisavis*lrsnash:lrslib v.6.3 2018.5.1(64bit,lrsgmp.h) gmp v.6.1 2 1/2449 0 0 0 0 144/2449 0 0 2304/2449 2304/2449 1 0 0 144/12245 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1/2449 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12096/12245 2304/2449 2 1/2449 0 0 0 0 144/2449 0 0 2304/2449 2304/2449 1 0 0 144/12245 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1/2449 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4608 *Number of equilibria found: 14 *Player 1: vertices=1394399 bases=1404287 pivots=1404509 *Player 2: vertices=14 bases=1 pivots=1851723 *lrsnash:lrslib v.6.3 2018.5.1(64bit,lrsgmp.h) *934.875u 0.015s 5032Kb 2910 flts 0 swaps 0 blks-in 0 blks-out lrslib-073/games/gamemp0000777000175000017500000000727114625766574013673 0ustar avisavis40 16 0 -1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 2 -1 -1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 -1 0 0 0 0 0 0 0 0 2 -1 0 -1 0 0 0 -1 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 -1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 -1 0 0 0 0 0 0 0 2 -1 0 0 -1 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 -1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 -1 0 0 0 0 0 0 2 -1 0 0 0 -1 0 0 0 -1 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 -1 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8105110306037952534 24315330918113857602 72945992754341572806 109418989131512359209 lrslib-073/games/h0000777000175000017500000000005714625766574012647 0ustar avisavis2 2 0 9551616 9551616 0 0 -9551616 -9551616 0 lrslib-073/games/h10000777000175000017500000000020714625766574012725 0ustar avisavis*h: player 1 H-representation linearity 1 5 begin 5 4 rational 0 1 0 0 0 0 1 0 0 0 9551616 1 0 9551616 0 1 -1 1 1 0 end lrslib-073/games/h20000777000175000017500000000020714625766574012726 0ustar avisavis*h: player 2 H-representation linearity 1 5 begin 5 4 rational 0 0 -9551616 1 0 -9551616 0 1 0 1 0 0 0 0 1 0 -1 1 1 0 end lrslib-073/hvref.c0000777000175000017500000000652114625766573012660 0ustar avisavis#include #include #include /****************************************************************** December 30,2019 Program to make a cross reference list between H and V reps Usage (same for ext file): Add printcobasis and incidence options to cube.ine % lrs cube.ine cube.ext % xref cube.ext Edit the output file cube.ext.x so that the second line contains two integers rows maxindex where rows >= # output lines in cube.ext.x maxindex >= # input lines in cube.ine or just use 0 0 and the program will tell you which values to use % hvref cube.ext.x gives V to H and H to V cross reference tables **********************************************************************/ int main(int argc, char *argv[]) { int i=0, j=0; int first=1; int Hrep=1; int rows=0, maxindex=0; int inrows=0, outrows=0; int rowindex; char s[10000]; int x; int *nrow; int **table; FILE *lrs_ifp; if(argc > 1) { if((lrs_ifp = fopen (argv[1], "r")) == NULL) { printf ("\nBad input file name\n"); return 1; } } else lrs_ifp=stdin; x=fscanf(lrs_ifp,"%s", s); while(first && x != EOF ) { if(strcmp(s,"H-representation") == 0 || strcmp(s,"V-representation") == 0) { if(strcmp(s,"H-representation") == 0) printf("\nH-representation"); else { printf("\nV-representation"); Hrep=0; } first=0; if(fscanf(lrs_ifp,"%d %d",&rows,&maxindex)==EOF) { printf("\n*input file missing data"); return 0; } printf("\n%d %d",rows,maxindex); nrow=(int *)malloc((maxindex+2)*sizeof(int)); table = (int **)malloc((rows+2) * (maxindex+2) * sizeof(int)); for (i=0;i<=maxindex+1;i++) table[i] = (int*)malloc((rows+2) * sizeof(int)); for(i=0;i<=maxindex;i++) { nrow[i]=0; for(j=0;j<=rows;j++) table[i][j]=0; } } if(first) x=fscanf(lrs_ifp,"%s", s); } while(x != EOF) { first=1; x=fscanf(lrs_ifp,"%s", s); while(x != EOF && strcmp(s,"#") !=0) { i=atoi(s); if(first==1) { printf("\n%d:",i); rowindex=i; inrows++; } else { if(i>outrows) outrows=i; if(i <= maxindex && nrow[i] < rows) { nrow[i]++; table[i][ nrow[i]]=rowindex; } printf(" %d",i); } x=fscanf(lrs_ifp,"%s", s); first=0; } } if(inrows <= rows && outrows <= maxindex) { if(Hrep) printf("\n\nV-representation"); else printf("\n\nH-representation"); printf("\n%d %d",outrows,inrows); for(i=1;i<=outrows;i++) { printf("\n%d:",i); for(j=1;j<=nrow[i];j++) printf(" %d",table[i][j]); } } else printf("\n\nInput parameters too small, rerun with:"); printf("\ninput rows=%d maxindex=%d",inrows,outrows); printf("\n"); free(nrow); for (i=0;i<=maxindex+1;i++) free(table[i]); free(table); return 0; } lrslib-073/ine/0000777000175000017500000000000014625766517012144 5ustar avisavislrslib-073/ine/afsa/0000777000175000017500000000000014625766512013051 5ustar avisavislrslib-073/ine/afsa/cp6.ine0000777000175000017500000004330414625766512014245 0ustar avisaviscp6 *cut polytope 6 points H-representation begin 368 16 rational 2 0 1 1 1 1 0 0 0 0 -1 -1 -1 -1 -1 -1 2 1 0 1 1 1 0 -1 -1 -1 0 0 0 -1 -1 -1 2 1 1 0 1 1 -1 0 -1 -1 0 -1 -1 0 0 -1 0 1 0 0 1 0 0 0 -1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 -1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 -1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 -1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 -1 2 2 2 2 2 2 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 2 1 1 1 1 0 -1 -1 -1 0 -1 -1 0 -1 0 0 2 0 0 0 0 0 0 -1 -1 0 0 0 0 -1 0 0 0 0 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0 -4 2 -1 2 -6 -1 0 4 2 -4 2 0 6 4 0 -2 -6 4 2 -2 2 -4 0 -2 -4 0 -4 4 0 -8 4 -4 -2 4 4 2 -2 0 6 8 1 1 2 0 -2 0 0 -2 0 4 -6 -2 4 -4 2 -4 1 -6 0 0 2 2 2 -1 1 -4 0 2 3 -2 2 -6 0 0 10 -4 4 0 2 0 -2 0 -2 0 0 -4 4 -6 -1 -2 -2 3 0 0 -6 4 2 0 2 0 0 6 -2 -4 -2 -2 -6 4 0 2 0 0 0 0 0 0 -4 0 6 0 -4 2 6 0 2 0 1 -3 2 4 2 -4 -4 6 0 -4 -2 -2 0 0 -2 4 -3 -2 4 0 -2 2 2 -1 1 -4 6 0 1 -4 4 -4 0 0 4 0 8 0 -4 -4 0 -8 0 -8 4 4 0 0 1 0 0 -1 2 -4 0 0 0 0 -4 0 0 -4 4 8 4 0 4 -8 0 -4 0 0 0 0 -4 8 0 4 0 4 0 0 0 -2 0 8 -1 1 0 -4 0 0 0 4 0 -8 -4 4 0 0 -4 0 -1 0 4 -6 0 4 0 -1 1 -4 0 -6 3 6 6 6 0 0 -2 -12 12 0 -2 0 -2 0 -2 0 0 12 -12 -6 -1 6 6 3 0 0 -6 -12 6 0 6 0 0 -6 -6 -12 -6 -6 6 12 0 6 0 0 0 0 0 0 12 0 6 0 12 2 6 0 -6 0 1 -3 2 -12 -6 4 4 -6 0 -12 -6 2 0 0 -6 12 -3 6 -12 0 6 -2 6 -1 1 -4 -2 4 1 0 -8 0 4 0 8 0 0 4 0 4 -4 -8 4 -8 4 -4 -8 -4 1 -4 4 -1 -6 4 4 8 -4 0 -8 0 16 0 8 0 -8 4 0 0 -16 8 0 0 0 0 -4 8 -8 -4 -4 -4 8 4 4 6 -4 8 -1 1 -4 4 4 0 0 0 0 0 -8 0 -4 -4 8 0 -1 -4 -4 2 4 0 4 -1 1 -6 0 2 1 10 2 -2 -2 0 -6 0 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0 6 12 -3 -6 -12 0 -6 2 6 -1 end lrslib-073/ine/polybase/0000777000175000017500000000000014625766605013760 5ustar avisavislrslib-073/ine/polybase/dwarfcube.pl0000777000175000017500000000130514625766512016256 0ustar avisavisprint "enter d\n"; $d=; chomp $d; print "dwarfcube",$d,"\n"; print "V-representation\n"; print "begin\n"; print $d*$d+1, " ", $d+1, " rational\n"; for ($i=1; $i<=$d; $i++){ @row=( $d, (-1) x ($i-1), 3*$d-1, (-1) x ($d-$i) ); print join(" ", @row); print "\n"; for($j=$i+1; $j<= $d; $j++){ @row=( $d, (-1) x ($i-1), 3*$d-1, (-1) x ($j-$i-1), 2*$d-1, (-1) x ($d-$j) ); print join(" ", @row); print "\n"; @row=( $d, (-1) x ($i-1), 2*$d-1, (-1) x ($j-$i-1), 3*$d-1, (-1) x ($d-$j) ); print join(" ", @row); print "\n"; } } @row=( $d, (-1) x $d ); print join(" ", @row); print "\n"; print "end\n"; lrslib-073/ine/polybase/metric.pl0000777000175000017500000000172314625766512015603 0ustar avisavisprint "*enter n\n"; $n=; chomp $n; print "metric",$n,"\n"; print "H-representation\n"; 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5sÐÌA3Í4sÐÌA3Í4sÐÌA3Í4sÐÌA3Í4sÐÌA3Í4sÐÌA3Í4sÐÌA3Í4sÐÌA3Í4sÐÌA3Í4sÐÌA3Í4sè ÉÔ}ñ›¼+:uGtzßÜ4ΘbÓ™ÁLf1›9ÌeóYÀB±˜%,eËYÁJV±š5¬eëÙÀF6±™-leÛÙÁNv±›=ìeû9ÀAq˜#å<Îçp!q1—p)—q9Wpœ+9ÁUœäj®áZ®ãznàFnâfn᧹•Û¸;¸“»¸›{¸—û¸Ÿx‡8óx6Ïá¹<çó^Èü($3qÃ*:çpfmôº»ùPôúiŽÞpiôxÇ£÷<ÂÓÑGã¾6~‚OD'NEW•G×<½üb^=ZMß•WGï*z²,ú@`MôáÛ¢§²Ù}z//‰_ž4DóŽñæhþ Æ1Uð¤êH2{çØUƒ]5 †TçñΓIòN²Øæ endstream endobj startxref 141023 %%EOF lrslib-073/ine/polybase/randsphere.c0000777000175000017500000000577614625766512016276 0ustar avisavis/* randsphere.c * * Generates V-representation of random rational points on the unit sphere * using: * Cook. Rational Formulae for the Production of a Spherically Symmetric * Probability Distribution. Mathematics of Computation 11(50):81-82, 1957. * * Usage: randsphere n p * to get n points starting from random rationals of the form r/p between -1,1. */ #include #include #include #include /* should be improved to get 64-bit rands */ long long getrand(void) { return random(); } int main(int argc, char **argv) { long long i, n=0, p=0; long long x0_n, x1_n, x2_n, x3_n; mpq_t x0, x1, x2, x3, x, y, z; mpq_t tmp1, tmp2, tmp3; mpq_t denom; if (argc!=3) { printf("Usage: %s \n", argv[0]); return 0; } n = atoll(argv[1]); p = atoll(argv[2]); if (n<=0 || p<=0) { printf("Usage: %s \n", argv[0]); return 0; } printf("\n*sphere%lld_%lld",n,p); printf("\n*random %lld points on unit sphere\nV-representation\nbegin\n",n); srandom((unsigned int) time(NULL)); mpq_init(x0); mpq_init(x1); mpq_init(x2); mpq_init(x3); mpq_init(x); mpq_init(y); mpq_init(z); mpq_init(tmp1); mpq_init(tmp2); mpq_init(tmp3); mpq_init(denom); printf("%lld 4 rational\n", n); for (i=0; i=0 || /* reject >= 1 */ mpq_cmp_ui(denom, 0, 1)==0 ); /* also reject 0 */ /* construct x */ mpq_mul(tmp1, x1, x3); mpq_mul(tmp2, x0, x2); mpq_add(tmp3, tmp1, tmp2); mpq_add(tmp1, tmp3, tmp3); /* numerator of x */ mpq_div(x, tmp1, denom); /* tmp1 / sum of squares */ /* construct y */ mpq_mul(tmp1, x2, x3); mpq_mul(tmp2, x0, x1); mpq_sub(tmp3, tmp1, tmp2); mpq_add(tmp1, tmp3, tmp3); /* numerator of y */ mpq_div(y, tmp1, denom); /* construct z */ mpq_mul(tmp1, x0, x0); mpq_mul(tmp2, x3, x3); mpq_add(tmp3, tmp1, tmp2); mpq_mul(tmp1, x1, x1); mpq_sub(tmp2, tmp3, tmp1); mpq_mul(tmp3, x2, x2); mpq_sub(tmp1, tmp2, tmp3); /* numerator of z */ mpq_div(z, tmp1, denom); printf(" 1 "); mpq_out_str(stdout, 10, x); printf(" "); mpq_out_str(stdout, 10, y); printf(" "); mpq_out_str(stdout, 10, z); printf("\n"); } mpq_clear(x); mpq_clear(y); mpq_clear(z); mpq_clear(x1); mpq_clear(x2); mpq_clear(x3); mpq_clear(tmp1); mpq_clear(tmp2); mpq_clear(tmp3); mpq_clear(denom); printf("end\n"); } lrslib-073/ine/polybase/README.txt0000777000175000017500000000053314625766605015462 0ustar avisavis2024.5.30 randsphere is Skip Jordan's C code to produce random rational points on the 3-sphere 2024.2.8 These perl scripts were extracted from David Bremner's PolyBase page: https://www.cs.unb.ca/~bremner/research/PolytopeBase/catalog/catmain.html converted to be standalone perl scripts. Corrections: Metric(n) n_facets 2n(n-1)(n-2)/3 lrslib-073/ine/project/0000777000175000017500000000000014625766510013603 5ustar avisavislrslib-073/ine/project/cube.ine0000777000175000017500000000024314625766506015225 0ustar avisaviscube H-representation begin 7 4 rational 1 1 0 0 1 0 1 0 1 0 0 1 1 -1 0 0 1 0 0 -1 1 0 -1 0 -1 -1 0 0 end project 1 2 verbose *debug lrslib-073/ine/project/hec/0000777000175000017500000000000014625766510014342 5ustar avisavislrslib-073/ine/project/hec/h3.ext0000777000175000017500000000033214625766507015405 0ustar avisavish3 V-representation begin 7 8 rational 0 1 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 0 1 0 1 0 1 1 0 0 0 1 0 1 1 1 0 1 1 1 2 2 2 1 end lrslib-073/ine/project/hec/h3.ine0000777000175000017500000000033214625766507015360 0ustar avisavish3 H-representation begin 7 8 rational 0 1 0 0 0 0 -1 1 0 0 1 0 0 -1 0 1 0 0 0 1 -1 0 0 1 0 1 1 0 -1 0 0 0 0 1 0 1 0 -1 0 0 0 0 1 1 0 0 -1 0 0 -1 -1 -1 1 1 1 -1 end lrslib-073/ine/project/hec/h4.ext0000777000175000017500000000211414625766507015406 0ustar avisavish4 V-representation begin 21 16 rational 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 1 0 0 1 0 0 1 0 0 1 1 0 1 1 0 1 1 0 0 0 1 0 0 1 0 1 0 1 1 0 1 1 1 0 0 0 0 1 0 0 1 0 1 1 0 1 1 1 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 1 0 0 1 0 1 0 1 0 1 1 0 1 0 1 0 1 0 0 1 0 0 1 1 1 0 0 1 1 1 0 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 1 0 0 0 0 0 1 1 0 1 1 1 1 0 1 1 0 0 0 0 1 1 1 0 2 2 1 2 1 1 1 2 2 2 1 0 0 1 1 1 1 1 1 2 2 2 2 2 2 1 1 0 1 2 1 1 3 2 2 3 3 2 2 2 3 2 1 0 1 1 0 1 2 1 2 1 2 1 2 1 2 2 1 0 1 1 1 1 2 2 2 2 2 2 3 3 3 3 2 0 1 0 1 1 1 2 2 1 1 2 2 2 1 2 1 0 1 1 1 2 2 2 3 2 3 3 3 2 2 2 1 0 2 1 1 1 3 3 3 2 2 2 2 2 2 3 1 0 1 1 1 1 2 2 2 2 2 2 1 1 1 1 0 0 1 1 2 1 2 3 2 3 2 3 2 3 2 2 1 end *project 7 1 2 3 5 6 8 11 lrslib-073/ine/project/hec/h4.ine0000777000175000017500000000203314625766510015353 0ustar avisavish4 H-representation begin 20 16 rational 0 0 -1 -1 0 0 0 -1 1 0 0 0 1 1 0 -1 0 -1 -1 0 0 1 0 0 0 0 -1 0 0 1 1 -1 0 0 -1 0 -1 0 -1 0 0 1 0 1 0 1 0 -1 0 -1 -1 -1 0 1 1 0 1 0 0 -1 0 0 0 0 0 0 -1 -1 -1 0 0 0 1 1 1 0 0 0 -1 0 0 -1 -1 0 -1 1 0 1 0 1 0 0 -1 0 0 0 0 -1 0 -1 0 0 1 0 0 -1 0 0 1 0 1 -1 0 0 0 -1 -1 -1 0 0 0 0 1 1 1 0 0 -1 0 -1 0 0 -1 0 0 1 -1 0 0 1 0 0 1 -1 0 -1 0 -1 -1 0 1 1 0 0 1 0 0 -1 0 0 0 0 0 0 1 0 0 0 0 0 0 -1 0 0 0 1 0 1 0 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 -1 0 0 0 0 0 0 1 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 end project 7 1 2 3 5 6 8 11 lrslib-073/ine/project/hec/h5.ext0000777000175000017500000065665314625766507015436 0ustar avisavish5 V-representation begin 2267 32 rational 0 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 0 0 1 0 1 0 0 1 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 1 0 1 0 1 0 1 0 1 1 0 1 0 1 0 1 0 1 1 0 1 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 0 0 0 1 1 1 1 0 0 0 1 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 1 0 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 0 1 1 1 1 0 0 0 1 1 0 0 1 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 1 1 1 0 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 1 1 1 0 1 1 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1 1 1 1 0 0 1 1 0 1 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 0 0 0 1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 1 1 0 1 1 1 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0 1 0 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 2 2 2 2 3 2 2 3 2 3 3 3 3 2 3 2 2 3 2 2 2 2 1 1 1 1 0 0 0 1 1 1 0 1 1 1 0 2 2 1 2 1 1 2 2 1 2 1 1 1 2 2 2 1 2 2 2 1 1 0 1 0 1 1 1 1 2 2 2 1 1 1 2 2 2 2 2 2 1 1 1 2 2 2 1 1 1 1 0 1 0 0 0 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 3 2 2 2 4 2 2 4 2 4 4 3 3 3 3 3 3 3 3 3 3 4 2 2 2 2 1 0 1 1 1 3 1 2 2 4 2 2 4 2 4 2 4 3 3 3 3 3 3 3 3 3 3 2 4 2 2 2 1 0 1 1 3 1 1 2 4 2 2 4 2 2 4 4 2 3 3 3 3 3 3 3 3 3 3 2 2 4 2 2 1 0 1 3 1 1 1 4 2 2 2 4 4 4 2 2 2 3 3 3 3 3 3 3 3 3 3 2 2 2 4 2 1 0 3 1 1 1 1 4 4 4 4 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 2 2 2 2 4 1 0 0 2 1 1 1 2 1 1 1 3 3 3 2 2 2 3 3 3 2 2 2 2 2 2 3 2 2 2 3 1 1 0 2 0 1 1 1 2 3 3 3 1 1 1 2 2 2 3 3 3 2 2 2 2 2 2 3 2 2 2 1 3 1 0 1 1 0 1 1 2 1 2 2 1 2 2 1 1 2 2 1 1 2 2 1 2 2 1 2 1 1 0 1 1 0 0 1 1 1 2 1 2 2 3 2 2 3 2 3 2 3 3 2 3 2 3 2 2 3 2 2 1 2 1 1 1 0 0 1 1 1 0 2 2 2 1 3 2 1 3 1 3 2 3 2 2 2 2 3 2 2 3 3 3 1 2 2 2 1 0 1 1 1 2 0 2 2 3 1 2 3 1 3 1 2 3 2 2 2 2 3 2 2 3 3 1 3 2 2 2 1 0 1 1 1 0 1 2 2 1 2 2 1 2 1 2 1 1 2 1 2 1 2 2 1 2 2 1 0 1 1 1 0 0 0 1 1 0 1 1 1 0 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 2 2 1 2 2 1 1 0 0 1 2 1 1 1 2 1 1 3 2 2 3 3 2 3 2 2 3 3 2 2 2 3 2 2 2 3 2 1 1 0 2 1 0 1 1 3 2 3 3 1 2 2 1 1 2 3 2 2 3 3 2 2 2 3 2 2 2 1 2 3 1 0 1 1 0 1 0 2 1 2 1 1 2 1 1 0 1 2 1 2 2 1 2 2 1 2 1 1 2 1 2 2 1 0 1 0 1 1 0 1 2 2 1 1 1 0 2 1 1 2 2 1 1 2 2 2 1 1 2 1 2 2 1 2 1 0 1 1 2 1 1 2 3 2 2 3 2 2 3 3 2 2 3 3 2 2 3 2 2 3 2 1 1 2 1 1 0 0 1 0 0 1 1 1 1 2 2 0 1 1 1 1 2 1 2 2 2 2 1 1 1 2 2 2 2 1 1 2 1 0 1 1 0 0 1 2 1 1 2 1 1 2 0 1 1 2 2 1 1 2 2 1 2 2 1 2 1 1 2 2 1 0 1 2 1 1 1 3 2 2 2 3 3 3 2 2 2 2 2 2 3 3 3 2 2 2 3 1 1 1 2 1 0 0 2 1 1 1 2 3 3 3 4 2 2 3 2 3 3 4 4 3 4 3 3 3 2 4 4 3 2 2 2 3 1 0 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 3 0 1 1 1 1 0 2 2 2 1 2 2 1 2 1 1 3 3 2 3 2 2 3 2 2 2 2 3 3 3 3 2 0 1 1 1 1 0 2 2 2 1 2 2 1 2 1 1 1 1 2 1 2 2 1 2 2 2 0 1 1 1 1 0 0 2 1 1 1 1 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 1 1 1 1 2 0 0 1 0 1 0 1 1 2 1 2 1 0 1 1 2 1 2 1 2 2 1 2 1 2 1 2 2 1 2 1 2 1 0 2 1 2 2 2 3 4 4 4 3 3 3 4 4 4 5 5 5 4 4 4 3 3 5 4 3 3 3 2 3 1 0 3 1 1 2 2 4 4 5 5 2 3 3 3 3 4 5 4 4 4 4 3 4 4 5 5 3 3 2 2 4 1 0 1 2 1 1 2 3 2 2 3 3 3 4 2 3 3 4 4 3 3 4 4 2 3 3 4 3 2 2 3 2 1 0 2 2 1 2 2 4 3 4 4 3 4 4 3 3 4 5 4 4 3 5 4 3 5 4 5 3 3 2 3 3 1 0 2 2 1 2 2 4 3 4 4 3 4 4 3 3 4 5 4 4 5 5 4 3 3 4 5 3 3 2 3 3 1 0 1 1 0 1 2 2 1 2 3 1 2 3 1 2 3 2 3 2 2 3 2 2 3 2 3 3 2 1 2 2 1 0 1 1 2 1 0 2 3 2 1 3 2 1 3 2 1 2 3 2 2 3 2 2 3 2 3 1 2 3 2 2 1 0 2 1 1 2 1 3 3 4 3 2 3 2 3 2 3 4 3 4 3 4 3 2 3 4 4 2 3 2 2 3 1 0 2 2 1 1 2 4 3 3 4 3 3 4 2 3 3 5 5 4 4 5 3 4 3 5 4 4 3 3 4 4 2 0 1 1 0 1 1 2 1 2 2 1 2 2 1 1 2 2 3 3 2 2 3 2 2 3 2 3 3 2 3 3 2 0 1 0 2 1 1 1 3 2 2 2 1 1 3 3 2 3 2 2 2 2 3 3 3 2 2 2 2 3 1 2 1 0 1 2 0 1 1 3 1 2 2 2 3 3 1 1 2 3 2 2 2 2 3 3 3 2 2 2 2 1 3 2 1 0 2 1 2 1 1 3 4 3 3 3 2 2 3 3 2 3 4 4 3 3 4 2 4 3 4 2 2 3 2 3 1 0 1 2 1 1 2 3 2 2 3 3 3 4 2 3 3 4 4 3 3 2 4 4 3 3 4 3 2 2 3 2 1 0 1 1 2 0 1 2 3 1 2 3 1 2 2 3 1 2 2 3 3 2 2 3 2 2 3 2 1 3 2 2 1 0 1 1 0 2 1 2 1 3 2 1 3 2 2 1 3 2 2 3 3 2 2 3 2 2 3 2 3 1 2 2 1 0 1 2 1 1 2 3 2 2 3 3 3 4 2 3 3 4 4 3 3 4 2 4 3 3 4 3 2 2 3 2 1 0 1 2 2 1 1 3 3 2 2 4 3 3 3 3 2 3 4 2 4 4 3 3 3 4 4 2 2 3 3 2 1 0 1 2 2 1 2 3 3 2 3 4 3 4 3 4 3 5 4 3 4 5 4 3 4 5 5 4 3 4 4 3 2 0 1 2 2 2 2 3 3 3 3 4 4 4 4 4 4 5 5 5 5 3 3 4 4 4 4 3 3 3 3 2 1 0 2 2 1 2 2 4 3 4 4 3 4 4 3 3 4 5 4 4 3 3 4 5 5 4 5 3 3 2 3 3 1 0 1 0 1 1 2 1 2 2 3 1 1 2 2 3 3 2 2 3 3 2 2 2 3 3 2 3 2 2 1 2 1 0 1 2 1 1 0 3 2 2 1 3 3 2 2 1 1 2 2 3 3 2 2 2 3 3 2 1 2 2 3 2 1 0 1 2 2 2 1 3 3 3 2 4 4 3 4 3 3 5 3 4 5 4 4 4 3 5 5 3 4 4 4 3 2 0 1 2 2 2 2 3 3 3 3 4 4 4 4 4 4 5 5 3 5 5 3 4 4 4 4 3 3 3 3 2 1 0 1 2 2 2 2 3 3 3 3 4 4 4 4 4 4 5 5 3 5 3 5 4 4 4 4 3 3 3 3 2 1 0 1 2 2 1 3 3 3 2 4 4 3 5 3 5 4 5 4 4 4 4 5 5 3 4 4 4 2 3 3 2 1 0 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 2 3 3 2 2 2 3 3 2 2 2 2 2 1 0 2 3 2 2 3 5 4 4 5 5 5 6 4 5 5 7 7 4 6 7 5 5 6 6 7 5 4 4 5 4 2 0 1 1 2 2 1 2 3 3 2 3 3 2 4 3 3 2 4 3 3 4 4 3 4 4 3 2 3 3 2 2 1 0 2 1 2 2 2 3 4 4 4 3 3 3 4 4 4 3 5 3 4 4 4 5 5 5 4 3 3 3 2 3 1 0 2 2 1 1 1 4 3 3 3 3 3 3 2 2 2 3 3 3 4 4 2 4 4 4 3 2 2 2 3 3 1 0 2 3 2 1 1 5 4 3 3 5 4 4 3 3 2 3 4 4 5 5 4 4 4 5 4 2 2 3 4 3 1 0 2 2 3 2 3 4 5 4 5 5 4 5 5 6 5 7 6 7 5 6 7 7 4 5 6 5 4 5 4 4 2 0 2 2 3 2 3 4 5 4 5 5 4 5 5 6 5 7 4 7 5 6 7 7 6 5 6 5 4 5 4 4 2 0 2 2 1 2 1 4 3 4 3 3 4 3 3 2 3 5 4 5 5 4 3 3 4 5 4 3 4 3 4 4 2 0 1 2 1 2 2 3 2 3 3 3 4 4 3 3 4 4 5 3 4 4 5 3 5 4 5 4 4 3 4 3 2 0 2 2 3 2 3 4 5 4 5 5 4 5 5 6 5 7 6 7 7 6 5 5 4 7 6 5 4 5 4 4 2 0 1 0 1 2 1 1 2 3 2 1 2 1 3 2 3 2 3 2 2 3 2 3 2 3 2 2 3 2 1 2 1 0 1 2 1 0 1 3 2 1 2 3 2 3 1 2 1 2 3 2 2 3 2 3 2 3 2 2 1 2 3 2 1 0 2 1 2 1 2 3 4 3 4 3 2 3 3 4 3 5 4 5 5 4 3 4 3 4 5 4 3 4 3 4 2 0 1 2 1 2 1 3 2 3 2 3 4 3 3 2 3 4 3 4 4 3 2 3 4 3 4 2 3 2 3 2 1 0 1 1 1 0 1 2 2 1 2 2 1 2 1 2 1 3 2 3 2 3 2 2 3 2 2 3 2 3 3 3 2 0 2 2 1 2 2 4 3 4 4 3 4 4 3 3 4 5 4 4 5 3 4 5 3 4 5 3 3 2 3 3 1 0 1 2 1 2 1 3 2 3 2 3 4 3 3 2 3 4 3 4 4 3 4 3 2 3 4 2 3 2 3 2 1 0 2 2 2 2 1 4 4 4 3 4 4 3 4 3 3 4 4 5 4 5 5 4 3 5 3 2 3 3 3 3 1 0 1 2 2 2 2 3 3 3 3 4 4 4 4 4 4 5 5 5 3 3 5 4 4 4 4 3 3 3 3 2 1 0 1 2 2 2 2 3 3 3 3 4 4 4 4 4 4 5 3 5 3 5 5 4 4 4 4 3 3 3 3 2 1 0 2 3 2 2 3 5 4 4 5 5 5 6 4 5 5 7 7 6 6 7 5 5 4 6 7 5 4 4 5 4 2 0 3 2 1 2 1 5 4 5 4 3 4 3 3 2 3 4 3 4 4 5 4 5 4 5 4 2 3 2 3 4 1 0 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 2 3 2 2 2 3 3 2 2 2 2 2 1 0 1 1 2 1 2 2 3 2 3 3 2 3 3 4 3 4 3 4 4 3 2 4 3 4 3 3 2 3 2 2 1 0 2 3 2 2 3 5 4 4 5 5 5 6 4 5 5 7 7 4 6 5 7 5 6 6 7 5 4 4 5 4 2 0 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 2 3 2 3 2 3 2 3 2 2 2 2 2 1 0 2 2 2 2 1 4 4 4 3 4 4 3 4 3 3 4 4 3 4 5 5 4 3 5 5 2 3 3 3 3 1 0 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 3 2 3 3 3 2 3 3 2 2 2 2 2 2 1 0 2 3 3 2 2 5 5 4 4 6 5 5 5 5 4 4 7 5 7 7 6 6 6 7 5 4 4 5 5 4 2 0 2 3 2 3 2 5 4 5 4 5 6 5 5 4 5 7 6 7 7 6 5 4 5 6 7 4 5 4 5 4 2 0 2 2 2 2 1 4 4 4 3 4 4 3 4 3 3 4 4 3 4 5 3 4 5 5 5 2 3 3 3 3 1 0 2 3 2 2 3 5 4 4 5 5 5 6 4 5 5 7 7 6 4 7 5 5 6 6 7 5 4 4 5 4 2 0 1 1 2 2 1 2 3 3 2 3 3 2 4 3 3 4 4 3 3 2 4 3 4 4 3 2 3 3 2 2 1 0 2 2 3 3 2 4 5 5 4 5 5 4 6 5 5 7 7 6 4 7 5 6 5 7 6 4 5 5 4 4 2 0 2 1 1 2 1 3 3 4 3 2 3 2 3 2 3 4 3 2 3 4 3 4 3 4 4 2 3 2 2 3 1 0 2 1 2 3 1 3 4 5 3 3 4 2 5 3 4 5 4 4 3 5 4 4 4 5 4 2 4 3 2 3 1 0 2 2 2 1 2 4 4 3 4 4 3 4 3 4 3 4 3 4 5 4 5 3 4 5 5 3 2 3 3 3 1 0 2 2 1 1 1 4 3 3 3 3 3 3 2 2 2 3 3 3 4 4 4 2 4 4 3 2 2 2 3 3 1 0 2 2 3 2 3 4 5 4 5 5 4 5 5 6 5 7 4 7 7 6 5 5 6 7 6 5 4 5 4 4 2 0 3 2 1 1 2 5 4 4 5 3 3 4 2 3 3 4 4 3 5 4 4 4 5 5 4 3 2 2 3 4 1 0 0 0 1 1 1 0 1 1 1 1 1 1 2 2 2 1 1 1 2 2 2 2 2 2 1 2 2 2 1 1 1 0 2 2 1 2 2 4 3 4 4 3 4 4 3 3 4 3 4 4 3 5 4 5 5 4 5 3 3 2 3 3 1 0 2 3 2 3 2 5 4 5 4 5 6 5 5 4 5 7 6 7 7 4 5 6 5 6 7 4 5 4 5 4 2 0 1 2 2 2 2 3 3 3 3 4 4 4 4 4 4 5 3 5 5 5 3 4 4 4 4 3 3 3 3 2 1 0 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 2 2 2 2 3 3 2 2 2 2 2 1 0 1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 3 5 5 5 3 5 4 4 4 4 3 3 2 0 2 2 3 3 2 4 5 5 4 5 5 4 6 5 5 7 5 6 4 7 7 6 5 7 6 4 5 5 4 4 2 0 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 2 3 2 3 3 3 2 3 2 2 2 2 2 2 1 0 2 2 1 1 2 4 3 3 4 3 3 4 2 3 3 5 5 4 4 5 3 4 5 3 4 4 3 3 4 4 2 0 1 2 1 1 2 3 2 2 3 3 3 4 2 3 3 2 4 3 3 4 4 4 3 3 4 3 2 2 3 2 1 0 2 1 2 2 2 3 4 4 4 3 3 3 4 4 4 5 5 5 4 4 4 5 3 3 4 3 3 3 2 3 1 0 2 1 1 2 1 3 3 4 3 2 3 2 3 2 3 4 3 4 3 4 3 4 3 2 4 2 3 2 2 3 1 0 2 1 1 1 2 3 3 3 4 2 2 3 2 3 3 4 2 3 4 3 3 3 4 4 4 3 2 2 2 3 1 0 2 1 2 1 3 3 4 3 5 3 2 4 3 5 4 5 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1996/05/02 16:14:20 bremner Exp $ Transforms a fukuda/avis .ine file into a .ieq file suitable for porta '; sub usage { print($docstring); exit(1); } &usage if ($ARGV[0] eq "-h"); open(IN,"-"); $_=; while (!/^begin/){ $_=; } $_=; ($m,$n,$type) = m/(\d+)\s+(\d+)\s+(\w+)/; printf "DIM = %d \n",$n-1; #print $m,"\n"; print "INEQUALITIES_SECTION\n"; while (){ last if (m/^end/); ($b,@a)=split(' '); for ($i=0; $i<=$#a; $i++){ if ($a[$i] ne "0"){ $a[$i]= "-".$a[$i] unless ($a[$i] =~ s/^-/\+/); printf "%sx%d",$a[$i],$i+1; } } print "<=$b\n"; } print "END\n" lrslib-073/ine/project/ieq/rc100-4.ieq0000777000175000017500000000367414625766505016070 0ustar avisavisDIM = 4 ELIMINATION_ORDER 0 1 2 3 INEQUALITIES_SECTION -5x1+8x2+4x4<=1 +4x1+9x2-2x3+1x4<=1 -10x1-3x2-6x3+4x4<=1 +9x1+5x3+3x4<=1 -3x1+1x2+3x3-1x4<=1 +2x1-2x2-9x3-6x4<=1 -2x1+1x2+6x3-7x4<=1 +6x1+9x3-5x4<=1 -1x1-4x2+6x3-8x4<=1 -4x1+3x3-9x4<=1 +2x1-7x2+6x3-10x4<=1 +5x1+8x2+2x3-4x4<=1 -10x1-4x2+5x3-2x4<=1 +3x1+1x2-6x3+4x4<=1 -3x1-1x2+1x3-4x4<=1 +3x1-6x2+6x3-8x4<=1 -2x1-1x2-4x3-7x4<=1 +3x1-3x2+6x3-4x4<=1 +7x1+2x2+9x3-6x4<=1 -6x1-2x2+1x3+9x4<=1 +5x1+3x2-2x3+6x4<=1 -2x1+5x2-8x3+3x4<=1 -6x1-8x2-2x3-4x4<=1 -9x1-1x2+2x3<=1 -5x1-8x2-9x3-2x4<=1 -5x1-2x2-8x3+6x4<=1 -2x1-5x3-8x4<=1 +7x1-3x2-1x3-9x4<=1 -9x1+5x2+1x3-3x4<=1 +4x1-9x2-6x3-10x4<=1 -5x1-3x2+6x3-2x4<=1 +1x1-1x3+3x4<=1 +6x1-5x2-9x3+4x4<=1 +6x1-10x2+7x3+5x4<=1 +1x1-8x2-9x3-4x4<=1 -7x1+7x2-10x4<=1 -8x1-7x2+4x4<=1 +4x1-7x2-3x3-1x4<=1 +1x1-7x2+3x4<=1 -4x1+1x2-5x3+2x4<=1 +3x1-5x2-1x3+5x4<=1 -7x1-4x3+7x4<=1 -7x1-8x2+2x3-9x4<=1 -2x1+2x3-6x4<=1 -6x1-1x2+2x3+4x4<=1 -1x1+4x2+5x3+8x4<=1 -3x1+3x2-7x3-9x4<=1 -5x1+8x2-6x3<=1 +3x1-10x2+8x3+2x4<=1 -3x1-9x2+3x3-6x4<=1 +4x1+7x2+8x3-5x4<=1 -9x1-7x2-1x3+4x4<=1 -6x1+9x2-8x3-2x4<=1 -4x1-2x2-6x3-1x4<=1 -8x1-1x2-2x3-4x4<=1 -7x1-2x2+5x4<=1 -5x2-6x3+8x4<=1 -4x2-9x3+5x4<=1 -4x1-6x2-5x3+7x4<=1 -6x1+5x2+3x3+4x4<=1 -2x1-6x2-8x3+6x4<=1 -5x1-6x2+6x4<=1 +5x1-2x2-4x3+1x4<=1 -7x1+4x2-9x3-3x4<=1 -5x1+1x2+9x3+5x4<=1 +8x1+9x2-6x3+4x4<=1 +7x1+2x2+6x3-2x4<=1 -3x1-7x2+7x4<=1 -8x1+4x2-1x3+9x4<=1 -3x1-9x2-6x3+9x4<=1 -9x1+6x2-2x3-3x4<=1 -2x1+6x2+9x3-9x4<=1 -7x1+2x2+4x3+1x4<=1 -4x1+8x2+1x4<=1 -7x1-4x2+9x3+2x4<=1 -6x1-3x2-10x3<=1 -9x1+7x2-1x3-3x4<=1 -2x1-7x2-6x3-4x4<=1 -8x1+6x2+9x3+7x4<=1 +9x1-3x2-2x3-8x4<=1 +3x1-7x2-3x3<=1 +6x1-8x2+2x3+9x4<=1 -9x1-8x2-4x3-10x4<=1 -9x1+1x2+9x4<=1 +9x1-9x2-8x3+6x4<=1 -4x1-9x2-3x3+6x4<=1 +7x1+4x2-3x3+8x4<=1 -2x1+8x2-4x3-6x4<=1 -3x1+2x3+8x4<=1 -6x1-5x2-8x3+6x4<=1 +6x1+2x2+5x3+8x4<=1 +4x1-3x2-2x3+9x4<=1 +3x1-4x2-3x3-6x4<=1 -10x1+2x2+6x3-7x4<=1 -10x1+4x2+1x3+2x4<=1 -9x1-5x2-3x3-6x4<=1 +6x1-7x2-5x3-3x4<=1 -3x1+4x2+3x3+1x4<=1 -9x1-8x2-4x3-7x4<=1 -9x1+9x2-2x3-10x4<=1 END lrslib-073/ine/project/ieq/rc100-5.ieq0000777000175000017500000000452714625766505016067 0ustar avisavisDIM = 5 ELIMINATION_ORDER 0 1 2 3 4 INEQUALITIES_SECTION +8x2+6x3+3x4+2x5<=1 -4x2-6x3-9x4-3x5<=1 +6x2-2x3-4x4-10x5<=1 -6x1-5x2-8x3-4x4+9x5<=1 +1x1+8x3+9x4+2x5<=1 -8x1-9x3+3x4-7x5<=1 -5x1+2x2-7x3-1x4+9x5<=1 +5x1-6x2+7x4-7x5<=1 -4x1+3x2+5x3+9x4-10x5<=1 +4x1+6x2+9x3+1x4-9x5<=1 -10x1+9x2+2x3-2x4-8x5<=1 +2x1-9x2+3x3-1x4-3x5<=1 +7x1-7x2+1x3-8x4+2x5<=1 +2x1+3x2+8x3-8x4-7x5<=1 -9x1+6x2-3x3-5x4-4x5<=1 -3x1-10x2-6x3+5x4+7x5<=1 +2x1-7x2-5x3+8x4+5x5<=1 -1x1+3x2-8x3+7x4-4x5<=1 +9x1-6x2+5x3+2x4<=1 +1x1+8x2+9x3+7x4-8x5<=1 +5x1-8x2+8x4-2x5<=1 +2x1+5x2+8x3-10x4-2x5<=1 -2x1-10x2+1x3-9x4<=1 +1x1+4x2-5x3+8x4-1x5<=1 +9x1-8x2+2x3+8x4+1x5<=1 -3x1+9x2-7x3-2x4+8x5<=1 -1x1-9x2-2x3-6x4-8x5<=1 -9x1+4x2+1x3+7x4+2x5<=1 +2x1-4x2+7x3-8x4-2x5<=1 -10x1-3x2+8x4-4x5<=1 +6x1-9x2-5x3-2x4+4x5<=1 +5x1+3x2-5x3-9x4+4x5<=1 +3x2+8x3-7x4-6x5<=1 -2x1-5x2+4x3-8x4-10x5<=1 -2x1-9x2+7x3+5x4<=1 -4x1-1x2-9x3+9x4-6x5<=1 +5x1-4x2+3x3+2x4-10x5<=1 +2x1+3x2-8x3+5x4+4x5<=1 -2x1-6x2+6x3+8x4+5x5<=1 +9x1+7x2-5x3-9x5<=1 -1x1-2x2+4x3+1x4-4x5<=1 +2x1+3x2+4x3+8x4-5x5<=1 +5x1-3x2-7x3+4x4-8x5<=1 -8x1+4x2-2x3+9x4+6x5<=1 +8x1-2x2-5x3-1x4+2x5<=1 +6x1+9x2+3x3+8x4-7x5<=1 -7x1+5x2-8x3+8x4-9x5<=1 -2x1-3x2+7x3+8x4-7x5<=1 -7x1+1x2-9x3+7x4-10x5<=1 -4x1-10x3-3x4+2x5<=1 -7x1-8x3+2x4-5x5<=1 -4x1+7x2-7x3+4x4<=1 -1x1-3x2-5x3-4x5<=1 +1x1+8x2-4x3-9x4-3x5<=1 -5x1-10x2+8x3+6x4-8x5<=1 -4x1-1x2+7x3+9x4-6x5<=1 -8x1+1x2-1x3+2x4+8x5<=1 +2x1-10x2+4x3+5x4-4x5<=1 +5x1-5x3+2x4+8x5<=1 +6x1-8x2+3x3+5x4+1x5<=1 +9x1+1x2-9x3+6x4+5x5<=1 -8x1+1x2+6x3+8x4-3x5<=1 +3x1+5x2-10x3+1x4+9x5<=1 -6x1+5x2+4x3-3x4-8x5<=1 -9x1-7x2+9x3-8x4+3x5<=1 +7x1-6x2-2x3+3x4+9x5<=1 +1x1+6x2+9x3+7x4-1x5<=1 -1x1-7x2+6x3-2x4-6x5<=1 +2x1+1x2-10x3-9x4-3x5<=1 +1x1-10x2-4x3+8x4+7x5<=1 +6x1-9x2-7x3+8x4+7x5<=1 +4x2+6x3+1x4+9x5<=1 +5x1+2x2+3x3+8x4-10x5<=1 -4x1+3x2-7x3-5x4+8x5<=1 -2x1+8x2-3x3-8x4-7x5<=1 -5x1+9x2+3x3+2x4-8x5<=1 +9x1-8x2+5x3-1x4+7x5<=1 +9x2-1x3+6x4+8x5<=1 +9x1+4x2-5x3+2x4-4x5<=1 -10x2-6x3+1x4+6x5<=1 -3x1+2x2-6x3-9x4-4x5<=1 -10x1+1x2+8x3-4x4+7x5<=1 -3x1+5x3-8x4+2x5<=1 +5x1+3x2+8x3-1x4-9x5<=1 +4x1+8x2-1x3-3x4+3x5<=1 -7x1-1x2-5x3+7x4+2x5<=1 -5x1-10x2+1x3-1x4+8x5<=1 +1x1-4x2-9x3-1x4+7x5<=1 +5x1+4x2+2x3-10x4+9x5<=1 +2x1-8x2-7x3-2x4-9x5<=1 +6x1+9x2+2x3-2x4-6x5<=1 -10x1-2x2-7x3-1x4-9x5<=1 -4x1+9x2+1x3+3x4-3x5<=1 +7x1-5x2-6x3+8x4+4x5<=1 +5x2+2x3+1x4-5x5<=1 +4x1-8x2+5x3-3x4-9x5<=1 +2x1+8x2+3x3-9x4+1x5<=1 -9x1-10x2-5x4+5x5<=1 -7x1-4x2-8x3-10x4+4x5<=1 -1x1-9x2-7x3+2x4-10x5<=1 END lrslib-073/ine/project/ieq/rc20-5.ieq0000777000175000017500000000102014625766505015771 0ustar avisavisDIM = 5 ELIMINATION_ORDER 0 2 1 3 4 INEQUALITIES_SECTION +3x1-9x2-10x3-4x4+8x5<=1 -3x1+5x2+1x3+4x4+8x5<=1 +2x1-9x2-6x3+1x4-3x5<=1 +3x1-9x2-10x3-4x4+8x5<=1 +3x1-1x2+6x4-4x5<=1 +9x1-4x2-9x3+1x4-3x5<=1 -7x1+6x2-10x3-8x4+8x5<=1 +6x1+7x2+8x3-7x4+1x5<=1 -1x1-6x2+7x3+9x4+6x5<=1 -10x1+4x2-5x3-6x5<=1 +3x1+4x2-1x3+8x4-6x5<=1 -3x2+2x3+9x4-10x5<=1 -1x1-9x2-6x3+9x4-7x5<=1 -5x1+8x2+3x3+5x5<=1 +5x1+3x2-7x3-2x4+7x5<=1 -3x1-1x2-4x3+1x4+6x5<=1 -2x1+8x2+7x3+5x4-8x5<=1 +1x2-5x3-4x4-2x5<=1 +5x1-2x2-5x3+1x4-3x5<=1 -2x1+6x2-3x3-5x4+1x5<=1 END lrslib-073/ine/project/ieq/rc250-5.ieq0000777000175000017500000001334514625766505016073 0ustar avisavisDIM = 5 INEQUALITIES_SECTION -3x1-4x2+8x3-6x4+5x5<=1 +7x1-2x2-4x3+9x4-9x5<=1 -4x1-10x2+8x3+7x4+2x5<=1 -2x1-9x2-6x3-4x4+3x5<=1 +5x1-10x2-8x3-5x4-2x5<=1 +1x1-4x2-6x3+3x4+6x5<=1 -8x1-4x2-2x3-6x4+9x5<=1 -2x1+4x2-7x3-6x4+3x5<=1 +9x1-8x2+4x4-1x5<=1 +5x1+1x2-8x3-4x4<=1 -8x1-9x2-3x3-5x4-1x5<=1 -7x1-5x2+2x3+3x4+5x5<=1 +9x1-7x2+3x3+8x4-8x5<=1 -10x1+2x2+9x3-1x4+7x5<=1 -6x1+2x2-8x3-4x4+7x5<=1 +9x1+7x3-6x4+8x5<=1 -3x1+7x2-1x4+3x5<=1 -9x1-10x2+6x3+2x4+9x5<=1 -3x1-6x2+8x3+7x4-7x5<=1 -4x1+9x2-10x3-8x4+7x5<=1 -7x1-10x3+1x4-3x5<=1 +6x1-4x2-5x3-8x4-1x5<=1 -4x1+1x2-10x3-9x4+8x5<=1 -10x1-6x2+2x3+1x4<=1 -4x1-2x2-1x3+5x4-3x5<=1 +3x2+7x3-3x4+5x5<=1 -2x1+7x2+5x3+3x4-4x5<=1 -6x1-9x2-7x3+6x4+3x5<=1 -4x1-1x2+6x3-3x4-10x5<=1 +7x1-9x2-10x3-5x4<=1 -5x1-10x2+8x3+4x4-9x5<=1 +8x1-2x2-4x3-6x4+9x5<=1 -10x1-5x3-8x4-1x5<=1 -3x1-5x2+1x3-10x4-7x5<=1 -2x1-6x3-5x4-9x5<=1 -3x1-9x2+5x3+9x4-10x5<=1 +4x1+7x2-3x3+6x4+1x5<=1 -2x1+2x2-6x3+6x5<=1 -5x1-10x2-8x3+1x5<=1 +6x1-3x2-4x3-6x4+4x5<=1 +1x1-9x2-2x4-6x5<=1 -5x1-3x2+4x3-8x4-1x5<=1 +7x1+9x2+4x3+8x4+5x5<=1 -6x1-5x2-4x3-9x4+9x5<=1 -7x1-2x2+5x3+1x4-1x5<=1 +9x1-4x2+3x3+4x4+5x5<=1 -3x1-10x2+2x3+8x4-6x5<=1 +6x1-7x2-3x3+2x4-6x5<=1 +1x1-3x3-4x4+4x5<=1 -1x1-6x2-3x3+5x4+1x5<=1 -2x1-5x2-1x3+3x4+4x5<=1 +4x1+6x2-2x3+5x4+1x5<=1 -9x1-7x2-1x3+9x4+1x5<=1 -2x1-1x2+7x3-7x4-9x5<=1 -1x1-7x2+6x3-8x4-3x5<=1 +9x1-7x2-9x3+7x4+8x5<=1 -10x1-3x2+1x3-4x4+8x5<=1 +3x1-9x2+5x3+4x4+2x5<=1 -10x1-8x3-5x4-7x5<=1 -5x1-2x2+7x3+5x4-4x5<=1 -5x1-10x2-1x3+5x4+1x5<=1 +8x1-3x2-4x4-2x5<=1 +9x1+5x2-8x3-9x4+3x5<=1 -2x1-3x2-5x3-1x4+7x5<=1 +4x1+1x2+6x3-9x4+8x5<=1 -7x1+9x2-3x3-5x4-10x5<=1 -8x1-7x2+8x3+2x5<=1 +6x1-1x2-2x3-9x5<=1 -7x1+1x2-10x3-5x4-8x5<=1 -2x1+4x2+3x3+6x4<=1 -1x1-8x2-5x3-6x4-10x5<=1 -8x1-6x2+7x3+6x4+2x5<=1 +9x1-6x2-8x3-9x4+7x5<=1 +5x1-8x2-4x3-1x4+6x5<=1 -1x1+3x2+7x4+4x5<=1 -5x1-8x2+8x3-1x4-2x5<=1 +9x1-1x2-3x3-4x4+6x5<=1 -2x1-8x2+7x3+9x4-5x5<=1 -9x1-3x2+7x3-2x4-1x5<=1 -2x1-4x2+7x3-1x4+8x5<=1 +4x1-8x2-6x3-2x4-7x5<=1 +8x1+3x2+7x3-9x4-5x5<=1 +8x1-6x2-10x3+6x4-4x5<=1 -6x1-10x2+1x3-9x4-8x5<=1 -9x2-7x3-5x4-6x5<=1 -3x1-9x2-8x3-6x4-5x5<=1 +6x1+7x2-9x3-10x4+9x5<=1 +5x1-10x2-9x3-1x4-8x5<=1 -1x1-8x2+8x3+2x4-3x5<=1 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0 5 -5 1 7 4 8 10 -4 1 1 9 7 -2 10 end eliminate 1 3 lrslib-073/ine/project/tsp4.ext0000777000175000017500000000015014625766506015223 0ustar avisavistsp4 V-representation begin 3 7 integer 1 1 0 1 1 0 1 1 0 1 1 1 1 0 1 1 1 0 0 1 1 end project 4 1 2 3 4 lrslib-073/ine/project/tsp4.ine0000777000175000017500000000015414625766504015200 0ustar avisavisTsp4 H-representation begin 4 8 integer 0 1 1 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 end lrslib-073/ine/project/tsp5.ext0000777000175000017500000000051414625766506015230 0ustar avisavistsp5 V-representation begin 12 11 integer 1 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 1 1 0 0 1 0 1 0 1 0 1 0 1 1 1 0 0 1 0 1 0 1 1 1 0 0 0 1 1 0 1 1 0 0 1 1 0 1 0 1 0 1 1 0 1 0 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 1 1 0 0 1 1 0 0 1 0 1 1 1 0 1 0 0 0 1 1 1 0 1 1 0 1 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 1 1 1 0 0 0 1 0 0 1 1 end eliminate 5 1 2 3 4 5 lrslib-073/ine/project/tsp5.ine0000777000175000017500000000165414625766504015207 0ustar avisavistsp5 H-representation linearity 5 1 2 3 4 5 begin 25 11 rational -2 1 1 1 1 0 0 0 0 0 0 -2 1 0 0 0 1 1 1 0 0 0 -3 1 1 1 0 1 1 0 1 0 0 1 -1 0 -1 0 0 -1 0 0 1 0 1 -1 -1 0 0 -1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 2 -1 -1 -1 0 0 0 0 0 0 0 2 -1 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 -1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 1 1 0 0 0 0 -1 1 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 -1 1 0 1 0 0 1 0 0 0 0 -1 1 1 1 0 0 0 0 0 0 0 -2 1 1 1 0 1 1 0 0 0 0 2 -1 0 -1 0 0 -1 0 0 0 0 3 -1 -1 -1 0 -1 -1 0 0 0 0 1 0 0 -1 0 0 0 0 0 0 0 2 -1 0 0 0 -1 -1 0 0 0 0 1 0 0 0 0 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 end eliminate 4 1 2 3 4 lrslib-073/ine/project/tsp6.ext0000777000175000017500000000365614625766506015243 0ustar avisavistsp6 V-representation begin 60 16 integer 1 0 0 0 1 1 0 1 0 1 1 1 0 0 0 0 1 0 0 0 1 1 0 1 1 0 1 0 1 0 0 0 1 0 0 0 1 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 0 0 1 1 1 1 0 0 0 0 1 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 0 1 0 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1799 1800 1801 1802 1803 1804 1805 1808 1810 1811 1812 1814 1815 1817 1818 1820 1822 1824 1825 1826 1827 1829 1830 1831 1835 1836 1839 1840 1842 1845 1846 1847 1848 1850 1852 1854 1855 1857 1858 1859 1860 1862 1863 1864 1865 1866 1868 1869 1872 1873 1874 1875 1876 1877 1879 1880 1881 1882 1883 1885 1886 1887 1889 1890 1892 1893 1895 1896 1897 1898 1899 1900 1901 1902 1903 1905 1906 1907 1908 1912 1913 1914 1915 1917 1918 1919 1921 1923 1924 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1937 1938 1939 1941 1942 1943 1944 1945 1948 1950 1951 1952 1953 1954 1956 1957 1958 1959 1960 1961 1962 1964 1966 1967 1968 1972 1973 1974 1975 1976 1978 1979 1980 1981 1983 1984 1985 1986 1987 1988 1990 1991 1993 1994 1995 1996 1997 *no check for hidden linearities *overflow checking on lrslong arithmetic *redund:lrslib_v.7.3_2024.1.10(64bit,lrslong.h,hybrid arithmetic) *9.163u 0.008s 2720Kb 0 flts 0 swaps 0 blks-in 40 blks-out lrslib-073/ine/redund/r2000_5.redundc0000777000175000017500000003435314625766514015772 0ustar avisavisredundant rows: 2 3 5 6 7 8 9 11 12 13 14 16 17 18 19 20 21 22 23 24 25 26 27 28 29 31 32 33 34 35 36 37 38 39 40 41 42 45 46 47 49 50 51 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 70 72 73 74 75 76 77 79 80 81 82 83 85 88 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 110 111 114 115 118 119 121 123 125 127 128 129 131 133 134 135 136 138 139 140 141 142 143 144 145 146 149 151 152 153 154 155 156 157 159 160 162 163 167 168 171 172 173 174 175 176 177 179 180 181 182 186 187 188 189 190 191 193 194 195 197 198 199 200 205 207 208 210 211 212 213 215 216 217 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 240 241 242 243 246 250 251 253 255 256 257 258 259 260 261 262 263 264 265 266 270 271 272 274 275 276 277 278 279 280 281 282 285 287 288 289 290 292 293 294 295 296 297 298 299 300 301 302 304 305 308 309 310 312 313 314 315 316 317 320 321 322 323 324 325 326 327 329 330 331 333 334 335 336 337 338 339 341 342 343 344 345 346 349 350 351 353 355 356 357 358 359 360 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 391 392 393 394 395 396 398 399 400 402 403 404 406 407 408 409 410 412 413 414 415 416 417 418 420 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 439 440 442 443 444 445 447 448 449 452 453 454 455 457 458 460 461 462 463 464 465 466 467 468 469 471 472 474 475 476 477 479 480 481 482 483 484 485 486 488 490 491 492 493 494 495 496 498 500 502 503 504 505 506 507 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 529 530 531 532 533 534 535 537 539 540 541 542 543 544 545 546 547 548 549 551 552 553 554 557 558 560 561 562 563 565 566 567 568 569 571 573 574 576 577 578 579 580 581 584 586 587 588 589 590 593 594 595 596 598 599 600 601 602 603 604 605 607 608 610 611 612 613 616 617 619 621 623 624 625 626 628 629 630 631 632 634 635 636 637 639 640 641 642 644 645 646 647 648 649 650 652 653 654 655 656 658 659 661 662 663 664 665 666 668 670 671 672 675 676 678 679 683 685 686 687 688 690 691 692 693 694 696 697 698 699 700 701 702 703 705 706 707 709 710 711 715 716 718 720 721 722 724 725 728 730 732 733 735 736 737 738 739 740 741 742 743 745 746 751 752 753 754 755 756 757 758 760 761 762 763 765 766 768 771 772 773 774 775 777 778 779 780 782 783 784 785 786 787 788 789 790 793 794 795 796 797 798 799 800 801 802 803 804 805 807 808 811 814 815 817 818 820 821 822 823 824 825 826 827 828 829 830 831 832 834 836 839 840 841 842 843 844 845 846 848 849 850 851 852 853 854 856 857 858 860 861 862 863 864 866 868 869 871 872 873 874 875 876 879 880 881 887 889 891 892 894 899 900 901 902 903 906 907 908 909 910 911 912 914 915 916 918 919 920 921 922 924 926 928 929 930 931 933 934 936 937 938 939 940 941 942 943 945 946 948 949 950 951 952 953 954 955 956 957 959 960 961 962 963 964 965 966 968 969 970 972 973 974 975 976 978 979 981 983 984 985 986 987 988 990 991 992 993 994 995 996 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1011 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1029 1030 1031 1032 1034 1035 1036 1037 1038 1040 1041 1042 1044 1046 1048 1050 1051 1052 1053 1054 1055 1056 1057 1058 1060 1061 1064 1065 1066 1067 1069 1070 1071 1073 1075 1076 1078 1079 1080 1081 1082 1084 1085 1086 1087 1088 1089 1090 1092 1093 1095 1096 1098 1102 1103 1104 1106 1107 1108 1109 1111 1112 1113 1115 1116 1117 1118 1120 1121 1123 1124 1125 1126 1127 1128 1130 1132 1133 1134 1135 1136 1137 1139 1140 1141 1142 1143 1144 1145 1146 1149 1152 1153 1155 1156 1157 1158 1159 1160 1161 1162 1163 1167 1168 1169 1170 1172 1174 1175 1176 1177 1180 1182 1183 1184 1186 1187 1189 1191 1192 1193 1194 1196 1198 1199 1200 1201 1202 1203 1204 1205 1207 1208 1212 1217 1218 1219 1220 1221 1222 1224 1226 1229 1230 1231 1232 1233 1234 1235 1237 1238 1239 1240 1241 1242 1243 1244 1246 1247 1248 1249 1250 1253 1254 1256 1257 1258 1259 1260 1261 1262 1263 1265 1266 1267 1269 1271 1272 1273 1274 1275 1277 1278 1279 1280 1285 1286 1287 1288 1289 1291 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1315 1316 1317 1319 1320 1321 1323 1324 1326 1327 1328 1329 1330 1332 1333 1334 1335 1336 1337 1339 1340 1341 1343 1344 1345 1346 1348 1349 1350 1351 1352 1353 1354 1356 1357 1358 1360 1361 1362 1363 1364 1366 1367 1369 1370 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1387 1389 1390 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1404 1406 1407 1408 1409 1411 1412 1415 1416 1417 1418 1420 1421 1423 1424 1425 1426 1427 1428 1429 1430 1431 1434 1436 1437 1438 1439 1440 1441 1442 1445 1446 1447 1448 1449 1450 1451 1452 1453 1455 1457 1458 1459 1460 1462 1463 1465 1466 1468 1469 1470 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1487 1488 1491 1492 1494 1495 1496 1498 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1511 1513 1514 1515 1516 1517 1518 1519 1520 1522 1523 1524 1525 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1541 1543 1544 1545 1546 1547 1552 1554 1555 1556 1557 1558 1560 1561 1562 1563 1564 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1618 1619 1620 1621 1622 1623 1624 1625 1626 1633 1635 1636 1637 1639 1640 1641 1642 1643 1646 1648 1649 1651 1652 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1668 1670 1672 1673 1676 1677 1679 1680 1681 1683 1684 1685 1686 1687 1689 1690 1691 1692 1693 1694 1695 1696 1697 1699 1703 1704 1705 1706 1707 1708 1709 1710 1712 1713 1714 1715 1716 1717 1718 1720 1721 1723 1724 1725 1727 1728 1729 1730 1733 1734 1735 1738 1739 1740 1741 1743 1744 1747 1748 1749 1750 1751 1754 1756 1758 1759 1760 1761 1762 1765 1767 1769 1771 1772 1773 1774 1775 1776 1777 1778 1779 1783 1784 1785 1787 1788 1789 1790 1791 1792 1793 1795 1796 1798 1799 1800 1801 1802 1803 1804 1805 1808 1810 1811 1812 1814 1815 1817 1818 1820 1822 1824 1825 1826 1827 1829 1830 1831 1835 1836 1839 1840 1842 1845 1846 1847 1848 1850 1852 1854 1855 1857 1858 1859 1860 1862 1863 1864 1865 1866 1868 1869 1872 1873 1874 1875 1876 1877 1879 1880 1881 1882 1883 1885 1886 1887 1889 1890 1892 1893 1895 1896 1897 1898 1899 1900 1901 1902 1903 1905 1906 1907 1908 1912 1913 1914 1915 1917 1918 1919 1921 1923 1924 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1937 1938 1939 1941 1942 1943 1944 1945 1948 1950 1951 1952 1953 1954 1956 1957 1958 1959 1960 1961 1962 1964 1966 1967 1968 1972 1973 1974 1975 1976 1978 1979 1980 1981 1983 1984 1985 1986 1987 1988 1990 1991 1993 1994 1995 1996 1997 Nonredundant representation (except for the linearity part): H-representation begin 477 6 rational 1 4 19 16 15 1 1 5 20 18 6 1 1 6 16 3 7 1 1 17 1 2 4 5 1 6 1 15 20 9 1 16 18 20 6 13 1 19 14 1 9 4 1 1 11 17 19 16 1 1 7 2 19 11 1 2 19 15 13 20 1 15 2 9 19 18 1 16 1 17 8 19 1 16 13 19 18 17 1 18 12 17 9 20 1 20 2 19 13 1 1 18 2 10 13 20 1 18 8 6 20 3 1 15 1 6 2 14 1 4 1 15 19 14 1 2 19 15 20 14 1 18 5 12 20 19 1 2 9 6 20 19 1 20 6 3 1 10 1 15 12 5 18 1 1 20 15 1 19 13 1 19 18 1 14 5 1 17 20 19 10 7 1 8 7 1 20 16 1 20 14 1 12 10 1 5 2 7 1 20 1 17 2 3 18 8 1 10 4 17 20 12 1 18 20 14 11 2 1 19 2 16 1 14 1 11 20 6 14 19 1 20 15 7 16 19 1 3 18 7 1 6 1 11 19 1 5 4 1 12 11 19 16 20 1 6 17 20 2 12 1 13 9 20 3 5 1 1 4 12 2 14 1 18 12 19 5 3 1 13 9 20 16 1 1 20 2 9 5 13 1 20 18 3 15 9 1 16 3 1 17 14 1 11 17 16 2 20 1 5 1 3 12 16 1 6 19 20 2 4 1 16 18 20 10 4 1 19 12 17 1 4 1 2 1 4 7 17 1 19 1 9 3 12 1 3 5 10 15 20 1 13 4 8 20 1 1 14 1 9 20 12 1 19 11 2 14 18 1 8 20 3 4 17 1 5 19 17 20 10 1 6 20 5 14 19 1 7 6 17 20 18 1 19 2 18 4 20 1 20 4 6 9 2 1 10 6 20 16 1 1 3 1 15 9 20 1 16 9 19 1 7 1 20 19 4 1 5 1 7 20 15 19 17 1 5 10 20 12 19 1 4 14 19 2 18 1 19 6 20 3 7 1 16 2 20 11 4 1 19 11 20 18 3 1 20 1 16 15 8 1 9 18 15 19 1 1 18 20 15 19 4 1 11 15 8 20 3 1 20 6 9 17 3 1 1 10 20 6 14 1 15 3 7 1 19 1 1 18 19 2 7 1 15 18 20 6 2 1 20 19 2 4 16 1 1 10 20 6 15 1 15 10 20 19 1 1 3 4 9 20 19 1 3 10 9 2 20 1 11 2 6 19 1 1 14 7 3 5 20 1 1 18 2 17 3 1 1 3 18 4 6 1 19 7 18 20 9 1 16 17 1 13 20 1 1 9 2 17 15 1 10 17 16 1 4 1 4 1 13 3 20 1 2 17 1 18 19 1 2 19 7 20 13 1 15 12 20 3 4 1 19 17 18 11 9 1 20 6 9 19 16 1 1 14 7 20 8 1 3 1 20 10 9 1 17 12 18 3 20 1 6 20 11 1 2 1 18 1 16 5 3 1 18 2 20 17 16 1 8 9 3 18 1 1 14 19 16 7 1 1 6 20 19 13 10 1 19 1 20 2 12 1 1 14 17 15 19 1 5 18 15 1 17 1 19 17 20 2 18 1 16 18 15 20 11 1 20 19 11 9 3 1 20 6 5 1 17 1 3 16 1 19 12 1 1 20 9 5 10 1 4 12 19 1 16 1 19 2 3 8 5 1 3 14 9 20 1 1 6 7 1 4 19 1 6 16 12 20 2 1 3 11 1 20 4 1 18 20 3 11 1 1 16 4 1 13 3 1 7 5 18 17 20 1 1 3 13 15 19 1 13 10 19 3 20 1 1 11 4 18 19 1 2 7 13 16 20 1 5 16 1 3 20 1 20 10 19 8 16 1 5 12 2 1 8 1 1 6 4 16 5 1 12 2 1 18 9 1 8 19 1 10 2 1 19 20 2 13 17 1 10 19 7 20 16 1 20 17 10 1 3 1 12 20 4 17 15 1 20 18 5 17 13 1 1 20 17 16 14 1 16 1 9 18 4 1 13 19 1 3 6 1 5 18 17 16 1 1 18 2 4 16 7 1 20 7 3 17 12 1 15 12 20 6 19 1 4 16 6 17 20 1 13 8 17 18 20 1 14 19 13 11 20 1 12 1 17 2 13 1 20 9 1 7 19 1 8 5 2 18 20 1 18 15 1 4 8 1 16 1 17 5 2 1 11 10 3 20 1 1 11 2 18 9 1 1 1 15 18 20 9 1 16 11 9 20 1 1 2 11 3 1 17 1 3 16 5 13 1 1 20 3 7 19 13 1 1 19 13 20 12 1 20 1 18 8 9 1 15 19 18 1 11 1 13 1 17 5 2 1 3 11 2 1 10 1 8 16 15 1 2 1 10 20 11 1 15 1 3 12 6 4 20 1 9 7 19 6 1 1 2 4 10 5 19 1 1 5 18 19 2 1 12 1 3 20 10 1 16 8 14 2 1 1 9 3 20 7 19 1 19 20 11 10 17 1 14 20 3 15 4 1 20 1 7 13 9 1 2 1 5 17 8 1 1 11 9 20 14 1 17 3 20 18 14 1 3 19 2 17 18 1 10 6 20 17 1 1 8 19 13 17 1 1 5 14 2 17 1 1 9 16 20 11 2 1 17 19 4 20 18 1 4 19 10 3 20 1 12 19 2 4 20 1 12 20 4 15 1 1 15 8 19 3 1 1 14 1 10 3 19 1 1 20 8 10 6 1 3 5 16 20 4 1 8 20 1 11 9 1 18 14 12 16 20 1 2 20 9 18 13 1 20 2 19 14 12 1 15 18 19 3 20 1 6 4 1 3 18 1 4 9 16 1 17 1 2 8 17 1 10 1 18 3 1 4 15 1 4 2 14 18 19 1 17 6 18 14 20 1 16 1 20 19 2 1 2 13 20 18 9 1 12 1 11 18 20 1 20 9 19 12 11 1 19 4 1 2 11 1 10 20 13 9 19 1 1 15 13 17 2 1 2 14 1 17 6 1 3 15 17 9 20 1 5 20 2 7 9 1 16 13 18 10 1 1 20 12 19 1 8 1 1 16 12 2 19 1 19 20 10 3 13 1 5 3 2 11 19 1 3 1 12 20 5 1 1 8 15 2 6 1 3 20 6 1 18 1 15 1 20 19 18 1 18 20 19 3 14 1 16 19 15 20 10 1 2 20 14 1 9 1 7 6 1 19 2 1 18 2 6 15 3 1 20 5 19 9 16 1 13 17 1 2 12 1 6 2 10 20 17 1 4 2 20 8 5 1 9 16 1 19 2 1 19 2 15 20 1 1 20 10 3 7 1 1 20 7 16 10 1 1 1 16 15 20 17 1 1 2 20 5 8 1 16 1 2 10 4 1 2 20 3 8 9 1 17 19 10 1 6 1 2 4 1 10 14 1 19 20 7 12 2 1 19 9 1 4 2 1 3 2 19 6 16 1 19 12 1 20 6 1 2 20 16 14 3 1 14 1 6 11 20 1 20 13 5 16 4 1 2 16 4 20 12 1 19 13 4 1 18 1 15 1 19 3 16 1 9 1 14 18 2 1 3 16 2 4 5 1 2 20 14 17 19 1 2 7 12 10 1 1 16 3 20 1 14 1 6 16 1 15 2 1 5 15 8 18 20 1 14 15 1 2 13 1 20 4 19 7 10 1 1 18 14 2 20 1 2 1 6 17 11 1 16 11 9 20 19 1 2 9 12 3 20 1 20 7 1 9 16 1 19 20 17 3 12 1 1 16 8 6 2 1 13 2 8 1 6 1 15 8 17 18 20 1 20 12 7 1 19 1 18 16 15 14 19 1 20 3 12 4 5 1 4 1 3 15 13 1 18 1 11 3 17 1 20 16 1 9 19 1 19 11 18 20 12 1 18 10 1 17 16 1 2 20 8 1 17 1 1 20 7 4 17 1 4 1 13 7 20 1 1 2 20 10 19 1 17 12 6 1 20 1 1 17 20 13 18 1 11 1 20 9 17 1 3 1 5 16 17 1 6 10 20 1 15 1 1 7 20 15 14 1 1 3 13 15 2 1 20 18 8 16 7 1 4 19 8 10 20 1 8 2 1 17 15 1 4 2 11 1 3 1 1 5 19 15 20 1 20 3 18 19 13 1 20 17 12 19 6 1 7 17 19 20 15 1 1 4 16 18 12 1 17 9 1 3 16 1 20 19 5 8 2 1 15 9 5 2 1 1 14 15 1 2 16 1 3 9 1 17 16 1 18 11 2 20 10 1 4 20 1 8 13 1 20 2 16 8 3 1 10 16 20 19 3 1 2 13 20 6 1 1 6 18 2 15 20 1 6 5 20 17 7 1 1 13 19 5 16 1 17 7 2 20 5 1 20 15 2 7 1 1 1 17 5 2 12 1 15 1 2 17 5 1 6 18 13 4 1 1 20 14 11 4 1 1 5 1 18 11 20 1 4 20 1 11 8 1 3 20 8 17 4 1 17 20 8 5 1 1 13 15 18 1 6 1 20 17 12 18 14 1 13 4 19 1 17 1 7 18 17 4 20 1 15 20 2 6 1 1 17 1 7 19 15 1 2 19 6 8 1 1 19 7 16 18 20 1 16 17 6 20 8 1 9 3 5 1 20 1 18 8 7 2 3 1 18 2 13 8 20 1 20 1 3 10 19 1 8 19 20 18 6 1 17 10 20 16 15 1 1 3 2 9 16 1 4 20 9 18 1 1 15 5 7 4 20 1 20 18 10 15 7 1 19 20 2 6 10 1 15 19 1 11 18 1 1 5 20 3 18 1 8 6 1 17 18 1 17 7 20 6 2 1 20 18 17 1 19 1 4 20 5 8 18 1 15 20 12 16 18 1 16 20 2 12 1 1 16 15 7 19 20 1 19 5 18 1 2 1 6 18 2 20 14 1 1 15 20 10 5 1 18 8 9 19 1 1 20 5 2 1 18 1 20 2 19 12 3 1 11 20 16 17 6 1 5 16 18 1 7 1 12 1 2 19 18 1 15 1 17 2 4 1 20 5 3 12 7 1 2 18 17 20 19 1 15 19 3 5 20 1 3 20 18 2 19 1 3 6 19 16 1 1 20 16 17 12 4 1 8 11 19 1 18 1 20 3 11 15 19 1 17 3 19 2 5 1 7 20 2 19 6 1 14 4 20 1 11 1 6 3 8 19 2 1 5 15 7 20 1 1 4 3 13 2 20 1 3 4 20 11 2 1 12 19 20 15 17 1 20 18 15 12 16 1 12 20 11 1 7 1 3 20 15 16 4 1 18 1 19 14 15 1 1 10 20 15 12 1 18 8 5 6 1 1 2 20 18 13 10 1 6 12 20 15 18 1 10 1 5 18 19 1 13 1 20 7 5 1 16 2 17 15 20 1 15 20 10 6 18 1 6 19 20 9 12 1 11 2 4 20 17 1 17 12 16 15 20 1 11 17 2 1 19 1 7 20 19 9 12 1 15 4 16 1 20 1 16 3 19 10 1 1 1 19 15 18 16 1 20 16 1 13 12 1 17 19 5 2 20 1 8 1 6 17 3 1 13 2 20 5 16 1 3 12 14 1 19 1 14 20 2 3 8 1 5 20 18 15 12 1 18 14 12 16 1 1 1 17 7 2 18 1 20 8 1 11 3 1 1 10 3 16 2 1 19 20 4 8 1 1 14 1 20 18 3 1 3 19 20 15 10 1 15 20 2 6 19 1 2 12 14 16 1 1 13 19 5 1 20 1 16 15 14 19 1 1 13 20 8 2 16 1 1 17 19 3 2 1 20 13 9 14 2 1 20 10 18 15 17 1 1 5 18 19 7 1 17 1 13 15 20 1 17 9 20 15 18 1 11 18 15 16 20 1 1 16 18 19 3 1 12 18 3 1 15 1 2 7 3 19 15 1 2 16 20 4 14 1 16 20 9 19 18 1 4 3 19 20 1 1 5 20 19 11 18 1 20 4 14 2 10 1 7 17 1 15 2 1 11 20 4 2 1 1 19 10 4 11 20 1 17 2 6 12 1 1 11 2 6 20 5 1 5 7 1 18 14 1 13 19 1 18 7 1 19 3 5 1 15 1 2 14 20 17 7 1 20 4 9 16 3 1 18 1 15 20 9 1 1 15 9 2 18 1 9 19 6 17 1 1 5 12 20 6 1 1 3 19 1 14 11 1 16 15 18 14 1 1 14 7 5 1 20 1 6 4 1 9 19 1 20 1 8 12 18 1 13 20 16 5 3 1 9 2 1 3 18 1 8 5 2 20 12 1 1 18 8 2 9 1 14 11 19 1 16 1 1 3 15 10 19 1 4 1 7 2 17 1 17 5 18 2 19 1 17 9 19 3 20 1 15 20 2 4 18 1 7 5 20 9 1 1 19 17 1 18 7 1 8 9 20 19 13 1 9 20 14 2 3 1 4 19 17 2 3 1 1 18 5 11 3 1 20 9 2 14 3 1 5 6 8 20 1 1 20 12 17 11 19 1 19 20 10 15 5 1 17 14 18 20 6 1 11 19 17 8 20 end * Computation started at Sun Apr 14 14:56:27 2024 * ended at Sun Apr 14 14:56:36 2024 * Total processor time = 9 seconds * = 0 h 0 m 9 s lrslib-073/ine/redund/r20_5.ine0000777000175000017500000000063614625766514014756 0ustar avisavisrand20_5 H-representation begin 20 6 integer 1 7 19 20 14 2 1 13 5 9 6 2 1 8 19 16 9 13 1 7 19 20 14 2 1 7 11 10 4 14 1 1 14 19 9 13 1 17 4 20 18 2 1 4 3 2 17 9 1 11 16 3 1 4 1 20 6 15 10 16 1 7 6 11 2 16 1 10 13 8 1 20 1 11 19 16 1 17 1 15 2 7 10 5 1 5 7 17 12 3 1 13 11 14 9 4 1 12 2 3 5 18 1 10 9 15 14 12 1 5 12 15 9 13 1 12 4 13 15 9 end verbose lrslib-073/ine/redund/r35_5.ine0000777000175000017500000002070214625766514014760 0ustar avisavisrand35_5 H-representation begin 35 6 integer 1 13 11 14 9 4 1 12 2 3 5 18 1 10 9 15 14 12 1 5 12 15 9 13 1 19 1 10 18 15 1 10 6 17 7 18 1 7 9 18 19 13 1 9 8 3 6 5 1 17 15 6 7 9 1 20 2 4 19 1 1 7 3 2 19 10 1 10 8 14 4 1 1 9 4 1 6 10 1 8 2 6 13 16 1 19 2 12 17 7 1 15 9 19 12 3 1 11 9 4 1 18 1 14 4 13 17 3 1 16 3 20 8 4 1 6 17 15 11 5 1 2 11 19 5 6 1 4 7 19 13 11 1 5 6 12 20 2 1 3 17 2 8 20 1 17 7 4 18 3 1 5 1 13 11 10 1 20 14 1 6 11 1 8 1 10 6 2 1 17 19 6 9 5 1 3 16 6 17 12 1 1 17 6 7 10 1 1 2 6 12 4 1 18 8 7 15 9 1 13 6 15 4 3 1 6 2 5 17 4 1 4 2 12 6 8 1 16 7 19 2 5 1 3 14 8 18 6 1 15 3 10 19 13 1 1 10 4 2 3 1 3 19 16 11 20 1 6 19 15 20 5 1 1 18 12 11 17 1 14 1 15 8 2 1 11 7 19 1 10 1 6 14 13 9 15 1 19 4 15 6 1 1 20 8 11 9 6 1 9 14 20 7 3 1 3 12 13 10 20 1 3 19 20 18 13 1 18 12 8 17 4 1 7 2 9 16 20 1 2 1 11 17 12 1 6 11 18 17 4 1 5 3 13 4 9 1 4 17 1 15 3 1 15 3 13 7 1 1 17 13 8 15 6 1 8 7 17 19 15 1 11 7 14 4 5 1 10 1 20 16 8 1 9 3 18 19 16 1 17 2 3 12 7 1 16 15 5 20 9 1 3 12 16 4 17 1 12 13 11 10 16 1 20 19 18 1 5 1 11 14 5 20 15 1 3 18 2 1 5 1 5 8 6 18 4 1 10 9 13 1 6 1 7 1 13 6 14 1 20 9 5 3 12 1 1 4 8 2 19 1 11 6 13 19 2 1 16 10 6 8 3 1 9 7 1 18 6 1 12 13 16 4 8 1 16 3 10 2 13 1 5 18 9 1 14 1 7 17 1 2 15 1 10 14 6 5 19 1 12 13 3 18 1 1 20 16 4 3 18 1 6 1 14 5 12 1 9 8 20 1 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7 1 4 17 5 1 6 8 4 7 10 1 13 20 3 11 9 1 3 20 16 11 2 1 15 4 9 12 6 1 15 3 19 20 7 1 4 7 5 2 14 1 11 5 20 4 12 1 7 16 11 14 20 1 6 12 4 20 16 1 20 4 8 16 2 1 19 4 6 15 2 1 3 20 2 1 4 1 11 4 20 14 5 1 2 1 20 8 15 1 5 16 17 12 1 1 17 2 18 8 16 1 16 11 9 2 6 1 3 6 13 14 1 1 14 17 9 18 8 1 19 15 11 18 4 1 1 20 11 15 12 1 4 18 16 7 2 1 8 17 1 20 9 1 1 16 14 7 13 1 5 20 6 11 17 1 6 1 20 4 2 1 18 7 19 17 6 1 9 6 16 1 13 1 16 6 13 9 15 1 5 4 7 19 15 1 10 8 6 11 19 1 8 1 20 15 6 1 8 4 7 9 6 1 6 9 5 3 11 1 15 1 13 17 4 1 15 16 3 17 8 1 12 4 13 15 9 end lrslib-073/ine/test/0000777000175000017500000000000014625766514013120 5ustar avisavislrslib-073/ine/test/cp4.ine0000777000175000017500000000073514625766513014312 0ustar avisaviscp4.ine *redundant projection checking *linearity 3 1 5 6 H-representation begin 16 7 rational 2 0 -1 -1 0 0 -1 2 -1 -1 0 -1 0 0 2 0 0 0 -1 -1 -1 2 -1 0 -1 0 -1 0 0 0 0 0 1 1 -1 0 -1 0 1 0 1 0 0 0 1 1 0 0 -1 0 -1 1 0 1 0 0 0 1 0 -1 0 1 0 0 0 0 0 -1 1 1 0 1 1 0 -1 0 0 0 0 1 -1 0 0 1 0 1 -1 0 1 0 0 0 0 -1 1 0 0 1 0 1 0 1 0 -1 0 0 0 0 0 1 -1 1 end *redund 0 0 eliminate 1 1 lrslib-073/ine/test/cross4.ine0000777000175000017500000000040314625766512015030 0ustar avisaviscross4.ine H-representation begin 16 5 integer 1 1 1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 1 -1 1 1 -1 -1 1 1 1 -1 1 1 1 1 1 -1 1 1 1 1 1 1 1 -1 -1 -1 1 1 -1 -1 1 1 1 -1 1 -1 1 1 -1 1 1 1 1 1 -1 -1 -1 1 1 -1 1 -1 1 1 1 -1 -1 1 -1 -1 -1 -1 end lrslib-073/ine/test/cube.ine0000777000175000017500000000024414625766512014534 0ustar avisaviscube H-representation begin 6 4 rational 1 1 0 0 1 0 1 0 1 0 0 1 1 -1 0 0 1 0 0 -1 1 0 -1 0 end startingcobasis 1 2 6 5 4 3 printcobasis lrslib-073/ine/test/cyclic17_8.ine0000777000175000017500000000210014625766512015454 0ustar avisaviscylic17-8.ine begin 17 9 integer 1 -72 516 -4608 36156 -294912 2349516 -18874368 150850236 1 -63 381 -3087 20901 -151263 1049061 -7411887 51738501 1 -54 264 -1944 10956 -69984 410124 -2519424 14971836 1 -45 165 -1125 4917 -28125 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H-representation begin 17 4 rational 0 1 -1 0 0 0 1 -1 0 1 1 2 1 -2 0 2 691 -1562 -1562 -1562 0 1 0 -1 2/11 0 0 -1 17/142 1/2 1/2 -1 37/142 0 0 0 691/1562 -1 0 0 27/71 -1/2 1/2 0 2/11 1 1 1 4/11 0 1 1 471/1562 1/2 3/2 1 2/11 1 -1 -1 4/11 0 -1 -1 471/1562 1/2 -1/2 -1 end redund 0 0 verbose *debug 0 0 lrslib-073/ine/test/in0.ine0000777000175000017500000000022114625766513014300 0ustar avisavisin0.ine begin 8 6 integer 9 -2 -3 -3 -2 -2 9 -2 0 0 2 0 9 -2 -1 -1 -1 -3 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 end lrslib-073/ine/test/in1.ine0000777000175000017500000000133114625766513014304 0ustar avisavisin1.ine begin 34 5 integer 1 -299 -534 815 807 1 -887 -399 -867 -543 1 683 632 958 -181 1 -756 681 -658 470 1 -99 135 -921 -825 1 -795 -874 -286 732 1 43 -567 588 -143 1 -955 414 -159 -378 1 -235 -695 947 166 1 957 853 -194 -258 1 487 -914 -100 -991 1 -515 -786 -169 200 1 954 -758 -178 985 1 505 -970 400 -211 1 714 997 401 661 1 -475 618 459 775 1 -219 704 -111 -876 1 152 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120443568 3373047308 7 175 5747 169939 4946291 143549035 4163578427 7 182 6160 188216 5665324 170070992 5102815180 7 189 6587 207753 6459971 200375049 6212340947 7 196 7028 228592 7335356 234852016 7516007948 7 203 7483 250775 8296771 273918743 9040090963 7 210 7952 274344 9349676 318018960 10813446092 7 217 8435 299341 10499699 367624117 12867674555 7 224 8932 325808 11752636 423234224 15237291532 -2919394390774395218459333 4379091595292464054287507 36492430237104184038520181 253987324572060483286422939 1691789494531258045567157717 11149182918946980113429731347 73511950112254277868261780941 end lrslib-073/ine/test/kq20_11.ine0000777000175000017500000000153314625766513014677 0ustar avisaviskq20_11.ine H-representation nonnegative begin 10 11 integer 10000 -915 -828 -303 -632 -786 -231 -12 -568 -351 -308 10000 -930 -217 -480 -704 -700 -91 -441 -927 -33 -330 10000 -765 -616 -962 -274 -276 -39 -924 -541 -444 -838 10000 -747 -470 -506 -329 -481 -425 -679 -140 -764 -960 10000 -243 -664 -760 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*metric polytope on 5 points H-representation begin 40 11 integer 0 0 0 1 1 0 0 0 0 0 -1 0 0 1 0 1 0 0 0 0 -1 0 0 0 1 1 0 0 0 0 -1 0 0 0 1 0 0 1 0 0 -1 0 0 0 0 1 0 1 0 0 -1 0 0 0 0 0 1 1 0 0 -1 0 0 0 0 0 0 -1 0 0 1 0 0 1 0 0 0 0 0 0 -1 1 0 0 0 0 0 1 0 0 0 0 0 0 -1 1 0 0 1 0 0 -1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 -1 1 1 0 0 0 0 0 -1 0 1 0 1 0 2 0 0 0 0 -1 -1 0 -1 0 0 0 -1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 1 0 0 0 1 -1 0 0 0 0 0 1 0 0 -1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 -1 1 0 0 0 0 0 -1 1 0 1 0 0 2 -1 -1 0 0 -1 0 0 0 0 0 2 0 0 0 0 -1 0 -1 0 -1 0 0 -1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 1 0 0 0 1 0 -1 0 0 0 0 1 0 2 -1 0 0 -1 0 0 -1 0 0 0 0 0 0 0 0 1 -1 0 1 0 0 0 0 0 0 0 0 0 0 1 1 -1 0 0 1 -1 0 0 0 0 1 0 0 2 -1 0 -1 0 0 -1 0 0 0 0 2 0 0 0 0 0 -1 -1 0 0 -1 0 0 0 0 0 1 1 0 -1 0 0 0 0 0 0 0 1 0 1 0 -1 0 0 1 -1 0 0 1 0 0 0 0 0 0 1 0 0 -1 0 0 1 0 0 0 2 0 -1 0 -1 0 0 0 0 -1 0 0 0 0 0 0 0 1 1 0 0 -1 0 1 0 -1 0 0 1 0 0 0 0 2 0 0 -1 -1 0 0 0 0 0 -1 2 0 -1 -1 0 0 0 0 -1 0 0 2 0 0 0 0 0 0 0 -1 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6864742100 1279634800 -3346341200 0 -1223784100 35749168 -1440369600 930993540 -3004955300 -25679281 0 -935892200 -129544890 1528908700 2954193399 -2958306400 427239050 0 29586836 -16982840 -642790400 1925328000 358894280 -938535540 0 0 0 0 0 0 0 0 990727340 29341662 -1558120400 283839350 961245970 4544466400 end lrslib-073/ine/test/tsp5.ine0000777000175000017500000000163414625766513014516 0ustar avisavistsp5.ine H-representation linearity 5 1 2 3 4 5 begin 25 11 rational -2 1 1 1 1 0 0 0 0 0 0 -2 1 0 0 0 1 1 1 0 0 0 -3 1 1 1 0 1 1 0 1 0 0 1 -1 0 -1 0 0 -1 0 0 1 0 1 -1 -1 0 0 -1 0 0 0 0 1 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 2 -1 -1 0 0 -1 0 0 0 0 0 1 0 0 0 0 -1 0 0 0 0 0 2 -1 0 0 0 -1 -1 0 0 0 0 -1 1 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 -1 1 1 1 0 0 0 0 0 0 0 -2 1 1 1 0 1 1 0 0 0 0 2 -1 -1 -1 0 0 0 0 0 0 0 1 0 0 -1 0 0 0 0 0 0 0 2 -1 0 -1 0 0 -1 0 0 0 0 3 -1 -1 -1 0 -1 -1 0 0 0 0 -1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 -1 1 1 0 0 1 0 0 0 0 0 1 0 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lrslib-073/ine/test-062/porta/0000777000175000017500000000000014625766515014553 5ustar avisavislrslib-073/ine/test-062/porta/bv7.ine.ieq0000777000175000017500000000236514625766515016534 0ustar avisavisDIM = 56 INEQUALITIES_SECTION -7x1-6x8-5x15-4x22-3x29-2x36-1x43+1x50==0 -7x2-6x9-5x16-4x23-3x30-2x37-1x44+1x51==0 -7x3-6x10-5x17-4x24-3x31-2x38-1x45+1x52==0 -7x4-6x11-5x18-4x25-3x32-2x39-1x46+1x53==0 -7x5-6x12-5x19-4x26-3x33-2x40-1x47+1x54==0 -7x6-6x13-5x20-4x27-3x34-2x41-1x48+1x55==0 -7x7-6x14-5x21-4x28-3x35-2x42-1x49+1x56==0 -1x1-1x2-1x3-1x4-1x5-1x6-1x7==-1 -1x8-1x9-1x10-1x11-1x12-1x13-1x14==-1 -1x15-1x16-1x17-1x18-1x19-1x20-1x21==-1 -1x22-1x23-1x24-1x25-1x26-1x27-1x28==-1 -1x29-1x30-1x31-1x32-1x33-1x34-1x35==-1 -1x36-1x37-1x38-1x39-1x40-1x41-1x42==-1 -1x43-1x44-1x45-1x46-1x47-1x48-1x49==-1 -1x1-1x8-1x15-1x22-1x29-1x36-1x43==-1 -1x2-1x9-1x16-1x23-1x30-1x37-1x44==-1 -1x3-1x10-1x17-1x24-1x31-1x38-1x45==-1 -1x4-1x11-1x18-1x25-1x32-1x39-1x46==-1 -1x5-1x12-1x19-1x26-1x33-1x40-1x47==-1 -1x6-1x13-1x20-1x27-1x34-1x41-1x48==-1 -1x1<=0 -1x2<=0 -1x3<=0 -1x4<=0 -1x5<=0 -1x6<=0 -1x7<=0 -1x8<=0 -1x9<=0 -1x10<=0 -1x11<=0 -1x12<=0 -1x13<=0 -1x14<=0 -1x15<=0 -1x16<=0 -1x17<=0 -1x18<=0 -1x19<=0 -1x20<=0 -1x21<=0 -1x22<=0 -1x23<=0 -1x24<=0 -1x25<=0 -1x26<=0 -1x27<=0 -1x28<=0 -1x29<=0 -1x30<=0 -1x31<=0 -1x32<=0 -1x33<=0 -1x34<=0 -1x35<=0 -1x36<=0 -1x37<=0 -1x38<=0 -1x39<=0 -1x40<=0 -1x41<=0 -1x42<=0 -1x43<=0 -1x44<=0 -1x45<=0 -1x46<=0 -1x47<=0 -1x48<=0 -1x49<=0 END lrslib-073/ine/test-062/porta/c30-15.ext.poi0000777000175000017500000001100314625766515016671 0ustar avisavisDIM = 15 CONV_SECTION 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 3 9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969 14348907 4 16 64 256 1024 4096 16384 65536 262144 1048576 4194304 16777216 67108864 268435456 1073741824 5 25 125 625 3125 15625 78125 390625 1953125 9765625 48828125 244140625 1220703125 6103515625 30517578125 6 36 216 1296 7776 46656 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90224199 3518743761 137231006679 5352009260481 208728361158759 8140406085191601 317475837322472439 12381557655576425121 482880748567480579719 18832349194131742609041 734461618571137961752599 28644003124274380508351361 1117116121846700839825703079 43567528752021332753202420081 1699133621328831977374894383159 66266211231824447117620880943201 40 1600 64000 2560000 102400000 4096000000 163840000000 6553600000000 262144000000000 10485760000000000 419430400000000000 16777216000000000000 671088640000000000000 26843545600000000000000 1073741824000000000000000 42949672960000000000000000 1717986918400000000000000000 68719476736000000000000000000 2748779069440000000000000000000 109951162777600000000000000000000 END lrslib-073/ine/test-062/porta/cp6.ine.ieq0000777000175000017500000004601114625766515016522 0ustar avisavisDIM = 15 INEQUALITIES_SECTION -1x2-1x3-1x4-1x5+1x10+1x11+1x12+1x13+1x14+1x15<=2 -1x1-1x3-1x4-1x5+1x7+1x8+1x9+1x13+1x14+1x15<=2 -1x1-1x2-1x4-1x5+1x6+1x8+1x9+1x11+1x12+1x15<=2 -1x1-1x4+1x8<=0 -1x1-1x5+1x9<=0 -1x2-1x4+1x11<=0 -1x2-1x5+1x12<=0 -1x3-1x4+1x13<=0 -1x3-1x5+1x14<=0 -1x4-1x5+1x15<=0 -2x1-2x2-2x3-2x4-2x5+1x6+1x7+1x8+1x9+1x10+1x11+1x12+1x13+1x14+1x15<=2 -1x2-1x3+1x10<=0 +1x1-1x2-1x6<=0 +2x1-2x2-2x3-2x4-2x5-1x6-1x7-1x8-1x9+1x10+1x11+1x12+1x13+1x14+1x15<=0 +2x1-1x2-1x3-1x4-1x5-2x6-2x7-2x8-2x9+1x10+1x11+1x12+1x13+1x14+1x15<=0 -1x1+1x2-2x3+1x4+1x5-1x6+2x7-1x8-1x9-2x10+1x11+1x12-2x13-2x14+1x15<=0 -1x1+1x2+1x3-2x4+1x5-1x6-1x7+2x8-1x9+1x10-2x11+1x12-2x13+1x14-2x15<=0 +2x1-1x2-1x3+1x4+1x5-2x6-2x7+2x8+2x9+1x10-1x11-1x12-1x13-1x14+1x15<=2 +1x1-2x2-1x3+1x4+1x5-2x6-1x7+1x8+1x9+2x10-2x11-2x12-1x13-1x14+1x15<=0 +2x1-1x2+1x3+1x4-1x5-2x6+2x7+2x8-2x9-1x10-1x11+1x12+1x13-1x14-1x15<=2 +1x1-2x2+1x3+1x4-1x5-2x6+1x7+1x8-1x9-2x10-2x11+2x12+1x13-1x14-1x15<=0 +1x1-2x2-1x3-1x4-1x5-2x6-1x7-1x8-1x9+2x10+2x11+2x12+1x13+1x14+1x15<=2 +2x1-1x2+1x3-1x4+1x5-2x6+2x7-2x8+2x9-1x10+1x11-1x12-1x13+1x14-1x15<=2 +1x1-2x2+1x3-1x4+1x5-2x6+1x7-1x8+1x9-2x10+2x11-2x12-1x13+1x14-1x15<=0 -1x1+1x2+1x3+1x4-2x5-1x6-1x7-1x8+2x9+1x10+1x11-2x12+1x13-2x14-2x15<=0 -1x6+1x9-1x12<=0 +1x1-1x2-1x3-1x4-1x6-1x7-1x8+1x10+1x11+1x13<=0 -1x1+2x2+1x3+1x4-1x5-2x6-1x7-1x8+1x9+2x10+2x11-2x12+1x13-1x14-1x15<=2 -2x1+1x2+1x3+1x4-1x5-2x6-2x7-2x8+2x9+1x10+1x11-1x12+1x13-1x14-1x15<=0 -1x2-1x3-1x4+1x5+1x10+1x11-1x12+1x13-1x14-1x15<=0 +1x1-2x2-1x3-1x4+1x5-2x6-1x7-1x8+1x9+2x10+2x11-2x12+1x13-1x14-1x15<=0 -1x6-1x7-1x8+1x9+1x10+1x11-1x12+1x13-1x14-1x15<=0 -1x1-2x2+1x3+1x4+1x5+2x6-1x7-1x8-1x9-2x10-2x11-2x12+1x13+1x14+1x15<=0 +2x1-2x2+2x3-2x4+2x5-1x6+1x7-1x8+1x9-1x10+1x11-1x12-1x13+1x14-1x15<=2 +1x1-1x2+1x3-1x4+2x5-1x6+1x7-1x8+2x9-1x10+1x11-2x12-1x13+2x14-2x15<=2 -1x2+1x5-1x12<=0 +1x1-2x2+1x3+1x4+1x5-2x6+1x7+1x8+1x9-2x10-2x11-2x12+1x13+1x14+1x15<=2 +1x1-1x2+1x3+1x4+2x5-1x6+1x7+1x8+2x9-1x10-1x11-2x12+1x13+2x14+2x15<=6 -1x2+1x3+1x4+1x5-1x10-1x11-1x12+1x13+1x14+1x15<=2 +1x1-1x2+1x3+1x5-1x6+1x7+1x9-1x10-1x12+1x14<=2 +1x1-1x2+1x4+1x5-1x6+1x8+1x9-1x11-1x12+1x15<=2 -1x6+1x7+1x8+1x9-1x10-1x11-1x12+1x13+1x14+1x15<=2 -1x1+1x2-1x3-1x4-2x5-1x6+1x7+1x8+2x9-1x10-1x11-2x12+1x13+2x14+2x15<=2 +2x1-1x2-1x3-1x4+1x5-2x6-2x7-2x8+2x9+1x10+1x11-1x12+1x13-1x14-1x15<=0 +1x1-1x2-1x4+1x5-1x6-1x8+1x9+1x11-1x12-1x15<=0 +1x1-1x2-1x3+1x5-1x6-1x7+1x9+1x10-1x12-1x14<=0 +1x1+1x5+1x9<=2 +1x1-1x3-1x4+1x5-1x7-1x8+1x9+1x13-1x14-1x15<=0 +2x1-2x2-2x3-2x4+2x5-1x6-1x7-1x8+1x9+1x10+1x11-1x12+1x13-1x14-1x15<=0 +2x1+2x2-2x3-2x4+2x5+1x6-1x7-1x8+1x9-1x10-1x11+1x12+1x13-1x14-1x15<=2 +1x1+1x2-1x3-1x4+2x5+1x6-1x7-1x8+2x9-1x10-1x11+2x12+1x13-2x14-2x15<=2 +1x1+1x2+1x3+1x4+2x5+1x6+1x7+1x8+2x9+1x10+1x11+2x12+1x13+2x14+2x15<=12 -1x6+1x8-1x11<=0 +1x1-1x2-1x3-1x5-1x6-1x7-1x9+1x10+1x12+1x14<=0 -1x1+2x2+1x3-1x4+1x5-2x6-1x7+1x8-1x9+2x10-2x11+2x12-1x13+1x14-1x15<=2 -2x1+1x2+1x3-1x4+1x5-2x6-2x7+2x8-2x9+1x10-1x11+1x12-1x13+1x14-1x15<=0 -1x2-1x3+1x4-1x5+1x10-1x11+1x12-1x13+1x14-1x15<=0 +1x1-2x2-1x3+1x4-1x5-2x6-1x7+1x8-1x9+2x10-2x11+2x12-1x13+1x14-1x15<=0 -1x6-1x7+1x8-1x9+1x10-1x11+1x12-1x13+1x14-1x15<=0 -1x6-1x7+1x10<=0 -1x1+1x2-1x4-1x5-1x6+1x8+1x9-1x11-1x12+1x15<=0 -1x1+1x2+2x3-1x4+1x5-1x6-2x7+1x8-1x9+2x10-1x11+1x12-2x13+2x14-1x15<=2 +2x1+1x2-1x3+1x4-1x5+2x6-2x7+2x8-2x9-1x10+1x11-1x12-1x13+1x14-1x15<=2 +1x1+1x2-2x3+1x4-1x5+1x6-2x7+1x8-1x9-2x10+1x11-1x12-2x13+2x14-1x15<=0 +1x1-1x2-2x3-1x4-1x5-1x6-2x7-1x8-1x9+2x10+1x11+1x12+2x13+2x14+1x15<=2 -1x1+1x2-1x3-2x4-1x5-1x6+1x7+2x8+1x9-1x10-2x11-1x12+2x13+1x14+2x15<=2 +1x10-1x11-1x13<=0 -1x1+1x2+1x3-1x4-1x6-1x7+1x8+1x10-1x11-1x13<=0 -1x7+1x8-1x13<=0 -1x1+1x3-1x4-1x5-1x7+1x8+1x9-1x13-1x14+1x15<=0 -2x1+1x2+1x3-1x4-1x5-2x6-2x7+2x8+2x9+1x10-1x11-1x12-1x13-1x14+1x15<=0 -1x1-1x2+1x3-2x4-1x5+1x6-1x7+2x8+1x9-1x10+2x11+1x12-2x13-1x14+2x15<=2 -1x1+1x2+1x3-2x4-1x5-1x6-1x7+2x8+1x9+1x10-2x11-1x12-2x13-1x14+2x15<=0 +1x1-1x2-2x3+1x4+1x5-1x6-2x7+1x8+1x9+2x10-1x11-1x12-2x13-2x14+1x15<=0 +1x1-1x2-1x3+1x4-1x6-1x7+1x8+1x10-1x11-1x13<=0 +1x1-1x2-2x3+1x4-1x5-1x6-2x7+1x8-1x9+2x10-1x11+1x12-2x13+2x14-1x15<=0 -1x6-1x7+1x8+1x9+1x10-1x11-1x12-1x13-1x14+1x15<=0 +2x1+1x2-1x3-1x4+1x5+2x6-2x7-2x8+2x9-1x10-1x11+1x12+1x13-1x14-1x15<=2 +1x1+1x2-2x3-1x4+1x5+1x6-2x7-1x8+1x9-2x10-1x11+1x12+2x13-2x14-1x15<=0 -1x2+1x4-1x11<=0 -1x11-1x12+1x15<=0 +2x1-1x2-1x3+1x4-1x5-2x6-2x7+2x8-2x9+1x10-1x11+1x12-1x13+1x14-1x15<=0 +1x1-1x2+1x4-1x5-1x6+1x8-1x9-1x11+1x12-1x15<=0 +1x10-1x12-1x14<=0 -1x1+2x2+1x3-1x4-1x5-2x6-1x7+1x8+1x9+2x10-2x11-2x12-1x13-1x14+1x15<=0 -1x1+1x2+1x3-1x5-1x6-1x7+1x9+1x10-1x12-1x14<=0 +2x1-2x2+2x3+2x4-2x5-1x6+1x7+1x8-1x9-1x10-1x11+1x12+1x13-1x14-1x15<=2 +1x1-1x2+1x3+2x4-1x5-1x6+1x7+2x8-1x9-1x10-2x11+1x12+2x13-1x14-2x15<=2 -1x1+1x2+2x3+1x4-1x5-1x6-2x7-1x8+1x9+2x10+1x11-1x12+2x13-2x14-1x15<=2 +1x1-1x2+1x3+2x4+1x5-1x6+1x7+2x8+1x9-1x10-2x11-1x12+2x13+1x14+2x15<=6 +1x1-1x2+1x3+1x4-1x6+1x7+1x8-1x10-1x11+1x13<=2 -1x1+1x2+2x3-1x4-1x5-1x6-2x7+1x8+1x9+2x10-1x11-1x12-2x13-2x14+1x15<=0 +1x1-1x2-2x3-1x4+1x5-1x6-2x7-1x8+1x9+2x10+1x11-1x12+2x13-2x14-1x15<=0 +1x1+1x2-1x3+2x4+1x5+1x6-1x7+2x8+1x9-1x10+2x11+1x12-2x13-1x14+2x15<=6 +1x1+1x2-1x3+1x4+1x6-1x7+1x8-1x10+1x11-1x13<=2 +1x1+1x4+1x8<=2 +1x1-1x3+1x4-1x5-1x7+1x8-1x9-1x13+1x14-1x15<=0 +2x1-2x2-2x3+2x4-2x5-1x6-1x7+1x8-1x9+1x10-1x11+1x12-1x13+1x14-1x15<=0 +2x1+2x2-2x3+2x4-2x5+1x6-1x7+1x8-1x9-1x10+1x11-1x12-1x13+1x14-1x15<=2 +1x1+1x2-1x3+2x4-1x5+1x6-1x7+2x8-1x9-1x10+2x11-1x12-2x13+1x14-2x15<=2 +1x1+1x2+1x3+2x4+1x5+1x6+1x7+2x8+1x9+1x10+2x11+1x12+2x13+1x14+2x15<=12 -1x1+1x2+1x3-1x4-2x5-1x6-1x7+1x8+2x9+1x10-1x11-2x12-1x13-2x14+2x15<=0 +1x8+1x9+1x15<=2 -1x7+1x9-1x14<=0 +1x1-1x3-1x7<=0 -1x3+1x5-1x14<=0 +1x1+1x2-2x3+1x4+1x5+1x6-2x7+1x8+1x9-2x10+1x11+1x12-2x13-2x14+1x15<=2 +1x1+1x2-1x3+1x4+2x5+1x6-1x7+1x8+2x9-1x10+1x11+2x12-1x13-2x14+2x15<=6 +1x2-1x3+1x4+1x5-1x10+1x11+1x12-1x13-1x14+1x15<=2 +1x1+1x2-1x3+1x5+1x6-1x7+1x9-1x10+1x12-1x14<=2 +1x1-1x3+1x4+1x5-1x7+1x8+1x9-1x13-1x14+1x15<=2 +1x6-1x7+1x8+1x9-1x10+1x11+1x12-1x13-1x14+1x15<=2 -1x1-1x2+1x3-1x4-2x5+1x6-1x7+1x8+2x9-1x10+1x11+2x12-1x13-2x14+2x15<=2 -1x3+1x4-1x13<=0 -1x13-1x14+1x15<=0 -1x1-1x3+1x7<=0 -1x6+1x7-1x10<=0 +1x1-1x2-1x4-1x5-1x6-1x8-1x9+1x11+1x12+1x15<=0 -1x1+2x2-1x3+1x4+1x5-2x6+1x7-1x8-1x9-2x10+2x11+2x12-1x13-1x14+1x15<=2 -2x1+1x2-1x3+1x4+1x5-2x6+2x7-2x8-2x9-1x10+1x11+1x12-1x13-1x14+1x15<=0 -1x2+1x3-1x4-1x5-1x10+1x11+1x12-1x13-1x14+1x15<=0 +1x1-2x2+1x3-1x4-1x5-2x6+1x7-1x8-1x9-2x10+2x11+2x12-1x13-1x14+1x15<=0 -1x6+1x7-1x8-1x9-1x10+1x11+1x12-1x13-1x14+1x15<=0 -1x6-1x8+1x11<=0 -1x1+1x2-1x3-1x5-1x6+1x7+1x9-1x10-1x12+1x14<=0 -1x1+1x2-1x3+2x4+1x5-1x6+1x7-2x8-1x9-1x10+2x11+1x12-2x13-1x14+2x15<=2 +2x1+1x2+1x3-1x4-1x5+2x6+2x7-2x8-2x9+1x10-1x11-1x12-1x13-1x14+1x15<=2 +1x1+1x2+1x3-2x4-1x5+1x6+1x7-2x8-1x9+1x10-2x11-1x12-2x13-1x14+2x15<=0 +2x1-2x2-2x3+2x4+2x5-1x6-1x7+1x8+1x9+1x10-1x11-1x12-1x13-1x14+1x15<=2 -1x1+1x2-2x3-1x4-1x5-1x6+2x7+1x8+1x9-2x10-1x11-1x12+2x13+2x14+1x15<=2 -1x1-2x2+1x3-1x4-1x5+2x6-1x7+1x8+1x9-2x10+2x11+2x12-1x13-1x14+1x15<=2 +1x1-1x2-1x3-2x4-1x5-1x6-1x7-2x8-1x9+1x10+2x11+1x12+2x13+1x14+2x15<=2 -2x1+2x2+2x3-2x4+2x5-1x6-1x7+1x8-1x9+1x10-1x11+1x12-1x13+1x14-1x15<=2 +1x1-1x2-1x3+1x4+2x5-1x6-1x7+1x8+2x9+1x10-1x11-2x12-1x13-2x14+2x15<=2 -1x1+1x2+1x3-1x4+2x5-1x6-1x7+1x8-2x9+1x10-1x11+2x12-1x13+2x14-2x15<=2 +1x7-1x8-1x13<=0 -1x1-1x3+1x4-1x5+1x7-1x8+1x9-1x13+1x14-1x15<=0 -2x1+1x2-1x3+1x4-1x5-2x6+2x7-2x8+2x9-1x10+1x11-1x12-1x13+1x14-1x15<=0 -1x1-1x2-2x3+1x4-1x5+1x6+2x7-1x8+1x9+2x10-1x11+1x12-2x13+2x14-1x15<=2 -1x1+1x2-2x3+1x4-1x5-1x6+2x7-1x8+1x9-2x10+1x11-1x12-2x13+2x14-1x15<=0 +1x1-1x2+1x3-2x4+1x5-1x6+1x7-2x8+1x9-1x10+2x11-1x12-2x13+1x14-2x15<=0 +1x1-1x2+1x3-1x4-1x6+1x7-1x8-1x10+1x11-1x13<=0 +1x1-1x2+1x3-2x4-1x5-1x6+1x7-2x8-1x9-1x10+2x11+1x12-2x13-1x14+2x15<=0 -1x6+1x7-1x8+1x9-1x10+1x11-1x12-1x13+1x14-1x15<=0 -1x10+1x11-1x13<=0 -1x1+1x2-1x3+1x4-1x6+1x7-1x8-1x10+1x11-1x13<=0 -1x6-1x9+1x12<=0 -1x1+1x2-1x3-1x4-1x6+1x7+1x8-1x10-1x11+1x13<=0 -1x1+1x2-1x6<=0 -2x1+2x2-2x3-2x4-2x5-1x6+1x7+1x8+1x9-1x10-1x11-1x12+1x13+1x14+1x15<=0 -1x1+2x2-1x3-1x4-1x5-2x6+1x7+1x8+1x9-2x10-2x11-2x12+1x13+1x14+1x15<=0 -2x1+1x2-1x3-1x4-1x5-2x6+2x7+2x8+2x9-1x10-1x11-1x12+1x13+1x14+1x15<=2 -1x1+1x5-1x9<=0 -1x1-1x2-1x3-1x4+2x5+1x6+1x7+1x8-2x9+1x10+1x11-2x12+1x13-2x14-2x15<=0 -2x1-2x2-2x3-2x4+2x5+1x6+1x7+1x8-1x9+1x10+1x11-1x12+1x13-1x14-1x15<=0 -2x1-1x2-1x3-1x4+1x5+2x6+2x7+2x8-2x9+1x10+1x11-1x12+1x13-1x14-1x15<=2 -2x1-2x2+2x3+2x4+2x5+1x6-1x7-1x8-1x9-1x10-1x11-1x12+1x13+1x14+1x15<=2 -2x1+1x2+1x3+1x4+1x5-2x6-2x7-2x8-2x9+1x10+1x11+1x12+1x13+1x14+1x15<=2 -1x1+1x2+1x3+1x4+2x5-1x6-1x7-1x8-2x9+1x10+1x11+2x12+1x13+2x14+2x15<=6 -1x1+1x3+1x4+1x5-1x7-1x8-1x9+1x13+1x14+1x15<=2 -1x1-1x2+1x3+1x4+2x5+1x6-1x7-1x8-2x9-1x10-1x11-2x12+1x13+2x14+2x15<=2 -1x1+1x2+1x3+1x5-1x6-1x7-1x9+1x10+1x12+1x14<=2 -1x1+1x2+1x3+2x4+1x5-1x6-1x7-2x8-1x9+1x10+2x11+1x12+2x13+1x14+2x15<=6 -1x1+1x2+1x4+1x5-1x6-1x8-1x9+1x11+1x12+1x15<=2 -2x1+2x2-2x3+2x4+2x5-1x6+1x7-1x8-1x9-1x10+1x11+1x12-1x13-1x14+1x15<=2 -1x1+1x2-1x3+1x4+2x5-1x6+1x7-1x8-2x9-1x10+1x11+2x12-1x13-2x14+2x15<=2 +1x1+2x2-1x3-1x4+1x5+2x6-1x7-1x8+1x9-2x10-2x11+2x12+1x13-1x14-1x15<=2 +1x1-1x2-1x3+2x4+1x5-1x6-1x7+2x8+1x9+1x10-2x11-1x12-2x13-1x14+2x15<=2 +1x1-1x2-1x3-1x4-2x5-1x6-1x7-1x8-2x9+1x10+1x11+2x12+1x13+2x14+2x15<=2 -2x1+2x2+2x3+2x4-2x5-1x6-1x7-1x8+1x9+1x10+1x11-1x12+1x13-1x14-1x15<=2 +1x1-1x2+2x3-1x4+1x5-1x6+2x7-1x8+1x9-2x10+1x11-1x12-2x13+2x14-1x15<=2 -1x1+1x2+1x3+1x4-1x6-1x7-1x8+1x10+1x11+1x13<=2 -1x6-1x7-1x8-1x9+1x10+1x11+1x12+1x13+1x14+1x15<=2 -1x1+2x2-1x3-1x4+1x5-2x6+1x7+1x8-1x9-2x10-2x11+2x12+1x13-1x14-1x15<=0 -1x1+1x2-1x4+1x5-1x6+1x8-1x9-1x11+1x12-1x15<=0 -1x1+1x2-1x3+1x5-1x6+1x7-1x9-1x10+1x12-1x14<=0 +1x2+1x5+1x12<=2 +1x2-1x3-1x4+1x5-1x10-1x11+1x12+1x13-1x14-1x15<=0 -2x1+2x2-2x3-2x4+2x5-1x6+1x7+1x8-1x9-1x10-1x11+1x12+1x13-1x14-1x15<=0 -1x8-1x9+1x15<=0 -1x1-1x2-1x3+1x4+1x6+1x7-1x8+1x10-1x11-1x13<=0 -1x1+1x4-1x8<=0 -2x1-1x2-1x3+1x4-1x5+2x6+2x7-2x8+2x9+1x10-1x11+1x12-1x13+1x14-1x15<=2 -2x1-2x2-2x3+2x4-2x5+1x6+1x7-1x8+1x9+1x10-1x11+1x12-1x13+1x14-1x15<=0 -1x1-1x2-1x3+2x4-1x5+1x6+1x7-2x8+1x9+1x10-2x11+1x12-2x13+1x14-2x15<=0 -1x1-1x2-1x3+2x4+1x5+1x6+1x7-2x8-1x9+1x10-2x11-1x12-2x13-1x14+2x15<=0 -1x1-1x3+1x4+1x5+1x7-1x8-1x9-1x13-1x14+1x15<=0 -1x1-1x2+1x4+1x5+1x6-1x8-1x9-1x11-1x12+1x15<=0 +1x4+1x5+1x15<=2 -1x2-1x3+1x4+1x5+1x10-1x11-1x12-1x13-1x14+1x15<=0 -2x1-2x2-2x3+2x4+2x5+1x6+1x7-1x8-1x9+1x10-1x11-1x12-1x13-1x14+1x15<=0 -1x1-1x2+1x3+2x4+1x5+1x6-1x7-2x8-1x9-1x10-2x11-1x12+2x13+1x14+2x15<=2 +1x7-1x9-1x14<=0 -1x1-1x2-2x3-1x4+1x5+1x6+2x7+1x8-1x9+2x10+1x11-1x12+2x13-2x14-1x15<=2 -1x1-1x3-1x4+1x5+1x7+1x8-1x9+1x13-1x14-1x15<=0 -2x1+1x2-1x3-1x4+1x5-2x6+2x7+2x8-2x9-1x10-1x11+1x12+1x13-1x14-1x15<=0 -1x1+1x2-2x3-1x4+1x5-1x6+2x7+1x8-1x9-2x10-1x11+1x12+2x13-2x14-1x15<=0 +1x1-1x2+1x3+1x4-2x5-1x6+1x7+1x8-2x9-1x10-1x11+2x12+1x13-2x14-2x15<=0 +2x1-1x2+1x3-1x4-1x5-2x6+2x7-2x8-2x9-1x10+1x11+1x12-1x13-1x14+1x15<=0 +1x1-1x2+1x3-1x5-1x6+1x7-1x9-1x10+1x12-1x14<=0 +1x1-1x2+2x3-1x4-1x5-1x6+2x7-1x8-1x9-2x10+1x11+1x12-2x13-2x14+1x15<=0 +1x1-1x2+1x3-1x4-2x5-1x6+1x7-1x8-2x9-1x10+1x11+2x12-1x13-2x14+2x15<=0 -1x6+1x7+1x8-1x9-1x10-1x11+1x12+1x13-1x14-1x15<=0 -1x1+2x2-1x3+1x4-1x5-2x6+1x7-1x8+1x9-2x10+2x11-2x12-1x13+1x14-1x15<=0 -1x1+1x2+1x4-1x5-1x6-1x8+1x9+1x11-1x12-1x15<=0 +1x6+1x7-1x8-1x9+1x10-1x11-1x12-1x13-1x14+1x15<=0 -1x1-1x2-2x3+1x4+1x5+1x6+2x7-1x8-1x9+2x10-1x11-1x12-2x13-2x14+1x15<=0 +1x1+2x2-1x3+1x4-1x5+2x6-1x7+1x8-1x9-2x10+2x11-2x12-1x13+1x14-1x15<=2 +1x1+1x2+1x3-1x4-2x5+1x6+1x7-1x8-2x9+1x10-1x11-2x12-1x13-2x14+2x15<=0 -1x1+1x2+1x3+2x4-1x5-1x6-1x7-2x8+1x9+1x10+2x11-1x12+2x13-1x14-2x15<=2 +1x1-1x2+2x3+1x4-1x5-1x6+2x7+1x8-1x9-2x10-1x11+1x12+2x13-2x14-1x15<=2 +1x2+1x4+1x11<=2 +1x2-1x3+1x4-1x5-1x10+1x11-1x12-1x13+1x14-1x15<=0 -2x1+2x2-2x3+2x4-2x5-1x6+1x7-1x8+1x9-1x10+1x11-1x12-1x13+1x14-1x15<=0 +1x11+1x12+1x15<=2 -1x10+1x12-1x14<=0 +1x2-1x3-1x10<=0 -1x1-1x2+1x6<=0 +1x6-1x7-1x10<=0 +1x1-1x3-1x4-1x5-1x7-1x8-1x9+1x13+1x14+1x15<=0 -1x1-1x2+2x3+1x4+1x5+1x6-2x7-1x8-1x9-2x10-1x11-1x12+2x13+2x14+1x15<=2 -2x1-1x2+1x3+1x4+1x5+2x6-2x7-2x8-2x9-1x10-1x11-1x12+1x13+1x14+1x15<=0 +1x2-1x3-1x4-1x5-1x10-1x11-1x12+1x13+1x14+1x15<=0 +1x1+1x2-2x3-1x4-1x5+1x6-2x7-1x8-1x9-2x10-1x11-1x12+2x13+2x14+1x15<=0 +1x6-1x7-1x8-1x9-1x10-1x11-1x12+1x13+1x14+1x15<=0 -1x7-1x8+1x13<=0 -1x1-1x2+1x3-1x5+1x6-1x7+1x9-1x10+1x12-1x14<=0 -1x10-1x11+1x13<=0 -1x1-1x2+1x3+1x4+1x6-1x7-1x8-1x10-1x11+1x13<=0 -1x7-1x9+1x14<=0 -1x1-1x2+1x3-1x4+1x6-1x7+1x8-1x10+1x11-1x13<=0 -1x1+1x3-1x7<=0 -2x1-1x2+1x3-1x4-1x5+2x6-2x7+2x8+2x9-1x10+1x11+1x12-1x13-1x14+1x15<=2 -2x1-2x2+2x3-2x4-2x5+1x6-1x7+1x8+1x9-1x10+1x11+1x12-1x13-1x14+1x15<=0 -1x1-1x2+2x3-1x4-1x5+1x6-2x7+1x8+1x9-2x10+1x11+1x12-2x13-2x14+1x15<=0 -1x1-1x2+2x3-1x4+1x5+1x6-2x7+1x8-1x9-2x10+1x11-1x12-2x13+2x14-1x15<=0 -1x1+1x3-1x4+1x5-1x7+1x8-1x9-1x13+1x14-1x15<=0 -1x1-1x2+1x3+1x5+1x6-1x7-1x9-1x10-1x12+1x14<=0 +1x3+1x5+1x14<=2 -1x2+1x3-1x4+1x5-1x10+1x11-1x12-1x13+1x14-1x15<=0 -2x1-2x2+2x3-2x4+2x5+1x6-1x7+1x8-1x9-1x10+1x11-1x12-1x13+1x14-1x15<=0 +1x13+1x14+1x15<=2 -1x2+1x3-1x10<=0 -1x10-1x12+1x14<=0 -1x1-1x2-1x3-1x4+1x6+1x7+1x8+1x10+1x11+1x13<=2 +1x7+1x8+1x13<=2 +1x8-1x9-1x15<=0 +1x1-1x5-1x9<=0 +1x4-1x5-1x15<=0 +1x1+1x2+1x3+1x4-2x5+1x6+1x7+1x8-2x9+1x10+1x11-2x12+1x13-2x14-2x15<=2 +1x1+1x2+1x3+2x4-1x5+1x6+1x7+2x8-1x9+1x10+2x11-1x12+2x13-1x14-2x15<=6 +1x2+1x3+1x4-1x5+1x10+1x11-1x12+1x13-1x14-1x15<=2 +1x1+1x2+1x4-1x5+1x6+1x8-1x9+1x11-1x12-1x15<=2 +1x1+1x3+1x4-1x5+1x7+1x8-1x9+1x13-1x14-1x15<=2 +1x6+1x7+1x8-1x9+1x10+1x11-1x12+1x13-1x14-1x15<=2 -1x1-1x2-1x3-2x4+1x5+1x6+1x7+2x8-1x9+1x10+2x11-1x12+2x13-1x14-2x15<=2 +1x13-1x14-1x15<=0 +1x3-1x5-1x14<=0 +1x10+1x11+1x13<=2 +1x11-1x12-1x15<=0 +1x2-1x5-1x12<=0 +1x6-1x9-1x12<=0 -1x1-2x2-1x3-1x4+1x5+2x6+1x7+1x8-1x9+2x10+2x11-2x12+1x13-1x14-1x15<=2 -1x1-1x2-1x4+1x5+1x6+1x8-1x9+1x11-1x12-1x15<=0 -2x1-1x2+1x3-1x4+1x5+2x6-2x7+2x8-2x9-1x10+1x11-1x12-1x13+1x14-1x15<=0 -1x1-2x2+1x3-1x4+1x5+2x6-1x7+1x8-1x9-2x10+2x11-2x12-1x13+1x14-1x15<=0 -1x1-1x2-1x3+1x5+1x6+1x7-1x9+1x10-1x12-1x14<=0 -2x1-1x2-1x3+1x4+1x5+2x6+2x7-2x8-2x9+1x10-1x11-1x12-1x13-1x14+1x15<=0 -1x1-1x2-1x3+1x4+2x5+1x6+1x7-1x8-2x9+1x10-1x11-2x12-1x13-2x14+2x15<=0 -1x1-2x2-1x3+1x4+1x5+2x6+1x7-1x8-1x9+2x10-2x11-2x12-1x13-1x14+1x15<=0 -1x1-1x2+1x3-1x4+2x5+1x6-1x7+1x8-2x9-1x10+1x11-2x12-1x13+2x14-2x15<=0 +2x1+1x2-1x3-1x4-1x5+2x6-2x7-2x8-2x9-1x10-1x11-1x12+1x13+1x14+1x15<=0 +1x1+1x2-1x3-1x5+1x6-1x7-1x9-1x10-1x12+1x14<=0 +1x1+2x2-1x3-1x4-1x5+2x6-1x7-1x8-1x9-2x10-2x11-2x12+1x13+1x14+1x15<=0 +1x1+1x2-1x3-1x4-2x5+1x6-1x7-1x8-2x9-1x10-1x11-2x12+1x13+2x14+2x15<=0 +1x1+1x2-1x3+1x4-2x5+1x6-1x7+1x8-2x9-1x10+1x11-2x12-1x13+2x14-2x15<=0 -1x1-1x2+2x3+1x4-1x5+1x6-2x7-1x8+1x9-2x10-1x11+1x12+2x13-2x14-1x15<=0 -1x1+1x3+1x4-1x5-1x7-1x8+1x9+1x13-1x14-1x15<=0 +1x3+1x4+1x13<=2 -1x2+1x3+1x4-1x5-1x10-1x11+1x12+1x13-1x14-1x15<=0 -2x1-2x2+2x3+2x4-2x5+1x6-1x7-1x8+1x9-1x10-1x11+1x12+1x13-1x14-1x15<=0 +1x6-1x7+1x8-1x9-1x10+1x11-1x12-1x13+1x14-1x15<=0 -1x1-1x2+1x3-2x4+1x5+1x6-1x7+2x8-1x9-1x10+2x11-1x12-2x13+1x14-2x15<=0 -1x1+1x2+2x3+1x4+1x5-1x6-2x7-1x8-1x9+2x10+1x11+1x12+2x13+2x14+1x15<=6 +1x6+1x8+1x11<=2 -1x1-1x2-1x3-2x4-1x5+1x6+1x7+2x8+1x9+1x10+2x11+1x12+2x13+1x14+2x15<=6 -1x1-1x2-1x3-1x5+1x6+1x7+1x9+1x10+1x12+1x14<=2 +1x7+1x9+1x14<=2 -1x8+1x9-1x15<=0 +1x1-1x4-1x8<=0 -1x4+1x5-1x15<=0 +1x1+1x2+1x3-2x4+1x5+1x6+1x7-2x8+1x9+1x10-2x11+1x12-2x13+1x14-2x15<=2 +1x1+1x2+1x3-1x4+2x5+1x6+1x7-1x8+2x9+1x10-1x11+2x12-1x13+2x14-2x15<=6 +1x2+1x3-1x4+1x5+1x10-1x11+1x12-1x13+1x14-1x15<=2 +1x1+1x2-1x4+1x5+1x6-1x8+1x9-1x11+1x12-1x15<=2 +1x1+1x3-1x4+1x5+1x7-1x8+1x9-1x13+1x14-1x15<=2 +1x6+1x7-1x8+1x9+1x10-1x11+1x12-1x13+1x14-1x15<=2 -1x1-1x2-1x3+1x4-2x5+1x6+1x7-1x8+2x9+1x10-1x11+2x12-1x13+2x14-2x15<=2 -1x13+1x14-1x15<=0 +1x3-1x4-1x13<=0 +1x10+1x12+1x14<=2 -1x11+1x12-1x15<=0 +1x2-1x4-1x11<=0 +1x6-1x8-1x11<=0 -1x1-1x2+1x4-1x5+1x6-1x8+1x9-1x11+1x12-1x15<=0 -2x1-1x2+1x3+1x4-1x5+2x6-2x7-2x8+2x9-1x10-1x11+1x12+1x13-1x14-1x15<=0 -1x1-2x2-1x3+1x4-1x5+2x6+1x7-1x8+1x9+2x10-2x11+2x12-1x13+1x14-1x15<=2 -1x1-2x2+1x3+1x4-1x5+2x6-1x7-1x8+1x9-2x10-2x11+2x12+1x13-1x14-1x15<=0 +1x1+1x2-1x3-1x4+1x6-1x7-1x8-1x10-1x11+1x13<=0 +1x1+1x2-1x3-2x4-1x5+1x6-1x7-2x8-1x9-1x10-2x11-1x12+2x13+1x14+2x15<=0 +1x1+1x2-1x3-2x4+1x5+1x6-1x7-2x8+1x9-1x10-2x11+1x12+2x13-1x14-2x15<=0 +1x6-1x7-1x8+1x9-1x10-1x11+1x12+1x13-1x14-1x15<=0 +1x6+1x7+1x10<=2 -1x1-1x2-2x3-1x4-1x5+1x6+2x7+1x8+1x9+2x10+1x11+1x12+2x13+2x14+1x15<=6 -1x1+1x2-1x3-1x4+2x5-1x6+1x7+1x8-2x9-1x10-1x11+2x12+1x13-2x14-2x15<=0 +1x1-1x2-1x3+2x4-1x5-1x6-1x7+2x8-1x9+1x10-2x11+1x12-2x13+1x14-2x15<=0 +1x1+1x2+2x3+1x4-1x5+1x6+2x7+1x8-1x9+2x10+1x11-1x12+2x13-2x14-1x15<=6 +1x1+1x2+1x3-1x5+1x6+1x7-1x9+1x10-1x12-1x14<=2 +1x1-1x2-1x3+1x4-2x5-1x6-1x7+1x8-2x9+1x10-1x11+2x12-1x13+2x14-2x15<=0 -1x1+1x2-1x3-2x4+1x5-1x6+1x7+2x8-1x9-1x10-2x11+1x12+2x13-1x14-2x15<=0 -1x1+1x2-1x3+2x4-1x5-1x6+1x7-2x8+1x9-1x10+2x11-1x12-2x13+1x14-2x15<=0 +1x1-1x2-1x3-1x4+2x5-1x6-1x7-1x8+2x9+1x10+1x11-2x12+1x13-2x14-2x15<=0 +1x1-1x2-1x3-2x4+1x5-1x6-1x7-2x8+1x9+1x10+2x11-1x12+2x13-1x14-2x15<=0 +1x1+1x2+2x3-1x4+1x5+1x6+2x7-1x8+1x9+2x10-1x11+1x12-2x13+2x14-1x15<=6 +1x1+1x2+1x3-1x4+1x6+1x7-1x8+1x10-1x11-1x13<=2 +2x1+2x2+2x3-2x4-2x5+1x6+1x7-1x8-1x9+1x10-1x11-1x12-1x13-1x14+1x15<=2 +2x1-2x2+2x3-2x4-2x5-1x6+1x7-1x8-1x9-1x10+1x11+1x12-1x13-1x14+1x15<=0 +1x1+1x3-1x4-1x5+1x7-1x8-1x9-1x13-1x14+1x15<=0 +1x1+1x2+2x3-1x4-1x5+1x6+2x7-1x8-1x9+2x10-1x11-1x12-2x13-2x14+1x15<=2 +1x1+1x3+1x7<=2 +2x1+2x2+2x3+2x4+2x5+1x6+1x7+1x8+1x9+1x10+1x11+1x12+1x13+1x14+1x15<=12 +1x1+1x2+2x3+1x4+1x5+1x6+2x7+1x8+1x9+2x10+1x11+1x12+2x13+2x14+1x15<=12 +1x1-1x2+2x3+1x4+1x5-1x6+2x7+1x8+1x9-2x10-1x11-1x12+2x13+2x14+1x15<=6 +1x1+1x3+1x4+1x5+1x7+1x8+1x9+1x13+1x14+1x15<=6 +2x1-1x2+1x3+1x4+1x5-2x6+2x7+2x8+2x9-1x10-1x11-1x12+1x13+1x14+1x15<=6 -1x1+1x2-1x3+1x4-2x5-1x6+1x7-1x8+2x9-1x10+1x11-2x12-1x13+2x14-2x15<=0 -2x1+2x2+2x3-2x4-2x5-1x6-1x7+1x8+1x9+1x10-1x11-1x12-1x13-1x14+1x15<=0 +1x2+1x3-1x4-1x5+1x10-1x11-1x12-1x13-1x14+1x15<=0 +1x2+1x3+1x10<=2 -1x1-1x2+1x3+2x4-1x5+1x6-1x7-2x8+1x9-1x10-2x11+1x12+2x13-1x14-2x15<=0 +2x1+2x2-2x3-2x4-2x5+1x6-1x7-1x8-1x9-1x10-1x11-1x12+1x13+1x14+1x15<=0 +1x1+1x2-1x4-1x5+1x6-1x8-1x9-1x11-1x12+1x15<=0 +1x1+2x2+1x3-1x4-1x5+2x6+1x7-1x8-1x9+2x10-2x11-2x12-1x13-1x14+1x15<=2 -1x1-1x2+1x3+1x4-2x5+1x6-1x7-1x8+2x9-1x10-1x11+2x12+1x13-2x14-2x15<=0 -1x1-2x2-1x3-1x4-1x5+2x6+1x7+1x8+1x9+2x10+2x11+2x12+1x13+1x14+1x15<=6 -2x1+2x2+2x3+2x4+2x5-1x6-1x7-1x8-1x9+1x10+1x11+1x12+1x13+1x14+1x15<=6 -2x1-1x2-1x3-1x4-1x5+2x6+2x7+2x8+2x9+1x10+1x11+1x12+1x13+1x14+1x15<=6 +2x1-2x2+2x3+2x4+2x5-1x6+1x7+1x8+1x9-1x10-1x11-1x12+1x13+1x14+1x15<=6 +2x1+2x2-2x3+2x4+2x5+1x6-1x7+1x8+1x9-1x10+1x11+1x12-1x13-1x14+1x15<=6 +1x1+1x2+1x6<=2 +1x1+2x2+1x3+1x4+1x5+2x6+1x7+1x8+1x9+2x10+2x11+2x12+1x13+1x14+1x15<=12 +1x1+2x2-1x3+1x4+1x5+2x6-1x7+1x8+1x9-2x10+2x11+2x12-1x13-1x14+1x15<=6 +1x1+1x2+1x4+1x5+1x6+1x8+1x9+1x11+1x12+1x15<=6 +2x1+1x2-1x3+1x4+1x5+2x6-2x7+2x8+2x9-1x10+1x11+1x12-1x13-1x14+1x15<=6 +1x1+2x2+1x3-1x4+1x5+2x6+1x7-1x8+1x9+2x10-2x11+2x12-1x13+1x14-1x15<=6 +2x1+2x2+2x3-2x4+2x5+1x6+1x7-1x8+1x9+1x10-1x11+1x12-1x13+1x14-1x15<=6 +1x1+1x2+1x3+1x5+1x6+1x7+1x9+1x10+1x12+1x14<=6 +2x1+1x2+1x3-1x4+1x5+2x6+2x7-2x8+2x9+1x10-1x11+1x12-1x13+1x14-1x15<=6 +2x1+1x2+1x3+1x4+1x5+2x6+2x7+2x8+2x9+1x10+1x11+1x12+1x13+1x14+1x15<=12 +1x1+2x2+1x3+1x4-1x5+2x6+1x7+1x8-1x9+2x10+2x11-2x12+1x13-1x14-1x15<=6 +2x1+2x2+2x3+2x4-2x5+1x6+1x7+1x8-1x9+1x10+1x11-1x12+1x13-1x14-1x15<=6 +1x1+1x2+1x3+1x4+1x6+1x7+1x8+1x10+1x11+1x13<=6 +2x1+1x2+1x3+1x4-1x5+2x6+2x7+2x8-2x9+1x10+1x11-1x12+1x13-1x14-1x15<=6 +1x2+1x3+1x4+1x5+1x10+1x11+1x12+1x13+1x14+1x15<=6 -1x1+2x2+1x3+1x4+1x5-2x6-1x7-1x8-1x9+2x10+2x11+2x12+1x13+1x14+1x15<=6 +1x6+1x7+1x8+1x9+1x10+1x11+1x12+1x13+1x14+1x15<=6 +1x6+1x9+1x12<=2 -1x1-1x2-1x3-1x4-2x5+1x6+1x7+1x8+2x9+1x10+1x11+2x12+1x13+2x14+2x15<=6 END lrslib-073/ine/test-062/porta/fq48-19.ine.ieq0000777000175000017500000000131214625766515017036 0ustar avisavisDIM = 18 INEQUALITIES_SECTION +1x1+1x2+1x3<=1 +1x4+1x5+1x6<=1 +1x7+1x8+1x9<=1 +1x10+1x11+1x12<=1 +1x13+1x14+1x16<=1 +1x13+1x15+1x17<=1 +1x14+1x15+1x18<=1 +1x16+1x17+1x18<=1 +1x4+1x7+1x10<=1 +1x1+1x8+1x11<=1 +1x2+1x5+1x12<=1 +1x3+1x6+1x9<=1 +1x2-1x4+1x15<=1 +1x3-1x4+1x17<=1 -1x5+1x7+1x13<=1 -1x5+1x9+1x17<=1 -1x6+1x10+1x13<=1 -1x6+1x12+1x15<=1 +1x1-1x7+1x15<=1 +1x3-1x7+1x18<=1 +1x4-1x8+1x14<=1 +1x6-1x8+1x18<=1 -1x9+1x10+1x14<=1 -1x9+1x11+1x15<=1 +1x1-1x10+1x17<=1 +1x2-1x10+1x18<=1 +1x4-1x11+1x16<=1 +1x5-1x11+1x18<=1 +1x7-1x12+1x16<=1 +1x8-1x12+1x17<=1 -1x1<=0 -1x2<=0 -1x3<=0 -1x4<=0 -1x5<=0 -1x6<=0 -1x7<=0 -1x8<=0 -1x9<=0 -1x10<=0 -1x11<=0 -1x12<=0 -1x13<=0 -1x14<=0 -1x15<=0 -1x16<=0 -1x17<=0 -1x18<=0 END lrslib-073/ine/test-062/porta/m6.ine.ieq0000777000175000017500000000260314625766515016353 0ustar avisavisDIM = 15 INEQUALITIES_SECTION +1x1-1x2-1x6<=0 -1x1+1x2-1x6<=0 -1x1-1x2+1x6<=0 +1x1+1x2+1x6<=2 +1x1-1x3-1x7<=0 -1x1+1x3-1x7<=0 -1x1-1x3+1x7<=0 +1x1+1x3+1x7<=2 +1x1-1x4-1x8<=0 -1x1+1x4-1x8<=0 -1x1-1x4+1x8<=0 +1x1+1x4+1x8<=2 +1x1-1x5-1x9<=0 -1x1+1x5-1x9<=0 -1x1-1x5+1x9<=0 +1x1+1x5+1x9<=2 +1x2-1x3-1x10<=0 -1x2+1x3-1x10<=0 -1x2-1x3+1x10<=0 +1x2+1x3+1x10<=2 +1x2-1x4-1x11<=0 -1x2+1x4-1x11<=0 -1x2-1x4+1x11<=0 +1x2+1x4+1x11<=2 +1x2-1x5-1x12<=0 -1x2+1x5-1x12<=0 -1x2-1x5+1x12<=0 +1x2+1x5+1x12<=2 +1x3-1x4-1x13<=0 -1x3+1x4-1x13<=0 -1x3-1x4+1x13<=0 +1x3+1x4+1x13<=2 +1x3-1x5-1x14<=0 -1x3+1x5-1x14<=0 -1x3-1x5+1x14<=0 +1x3+1x5+1x14<=2 +1x4-1x5-1x15<=0 -1x4+1x5-1x15<=0 -1x4-1x5+1x15<=0 +1x4+1x5+1x15<=2 +1x6-1x7-1x10<=0 -1x6+1x7-1x10<=0 -1x6-1x7+1x10<=0 +1x6+1x7+1x10<=2 +1x6-1x8-1x11<=0 -1x6+1x8-1x11<=0 -1x6-1x8+1x11<=0 +1x6+1x8+1x11<=2 +1x6-1x9-1x12<=0 -1x6+1x9-1x12<=0 -1x6-1x9+1x12<=0 +1x6+1x9+1x12<=2 +1x7-1x8-1x13<=0 -1x7+1x8-1x13<=0 -1x7-1x8+1x13<=0 +1x7+1x8+1x13<=2 +1x7-1x9-1x14<=0 -1x7+1x9-1x14<=0 -1x7-1x9+1x14<=0 +1x7+1x9+1x14<=2 +1x8-1x9-1x15<=0 -1x8+1x9-1x15<=0 -1x8-1x9+1x15<=0 +1x8+1x9+1x15<=2 +1x10-1x11-1x13<=0 -1x10+1x11-1x13<=0 -1x10-1x11+1x13<=0 +1x10+1x11+1x13<=2 +1x10-1x12-1x14<=0 -1x10+1x12-1x14<=0 -1x10-1x12+1x14<=0 +1x10+1x12+1x14<=2 +1x11-1x12-1x15<=0 -1x11+1x12-1x15<=0 -1x11-1x12+1x15<=0 +1x11+1x12+1x15<=2 +1x13-1x14-1x15<=0 -1x13+1x14-1x15<=0 -1x13-1x14+1x15<=0 +1x13+1x14+1x15<=2 END lrslib-073/ine/test-062/porta/mit.ine.ieq0000777000175000017500000006364414625766515016636 0ustar avisavisDIM = 8 INEQUALITIES_SECTION +4x3+4x4+2x5<=72 +2x1+2x2+10x3+12x4+6x5<=216 +4x1+2x2+8x3+8x4+8x5<=192 +12x1-6x2-8x3+16x4+8x5<=288 +4x1-2x2+4x4+4x5<=96 +5x1-1x2+4x3+6x4+6x5<=144 +8x1+2x2+10x3+12x4+12x5<=288 +4x1-2x2+4x3+2x4+4x5<=96 +7x1+1x2+10x3+8x4+10x5<=240 +8x1+2x2+12x3+8x4+12x5<=288 +8x1+2x2+8x3+16x4+8x5<=288 +4x1-2x2+8x3<=96 -6x2+8x3-4x4-8x5<=0 -4x1-6x2+8x3-8x5<=0 -2x1-2x2+4x3+2x4-2x5<=24 +24x1+6x2+40x3+16x4+32x5<=864 +2x3+2x4-2x5<=24 -4x1-10x2+16x3-24x5<=0 -1x1-1x2+4x3-12x5<=0 -6x2+16x3-8x4-40x5<=0 +4x1-2x2+16x3-16x4-32x5<=96 +8x1+2x2+16x3<=288 +4x1-2x2-8x3+8x4-8x5<=96 +8x1+2x2-8x3+24x4-24x5<=288 -2x2+8x3-8x4-24x5<=0 +1x1+1x2+4x3+8x4-8x5<=96 +12x1+6x2+16x3+40x4-16x5<=576 +4x1+2x2+16x4-16x5<=192 +8x1+6x2+24x3+32x4+16x5<=576 +12x1+6x2+20x3+32x4+16x5<=576 +16x1+10x2+40x3+56x4+16x5<=960 +7x3+7x4+6x5+1x6+1x8<=160 +4x1+4x2+21x3+21x4+18x5+1x6+3x8<=480 +4x1+4x2+12x3+4x4+8x5-4x6-2x7+4x8<=192 +16x1+8x2+28x3+28x4+24x5-4x6-2x7+4x8<=640 +8x1+6x2+28x3+28x4+24x5+4x8<=640 +8x1+8x3+8x4+8x5-4x6-2x7<=192 +12x1+4x2+16x3+16x4+16x5-4x6-2x7<=384 +20x1+12x2+42x3+42x4+36x5-4x6-2x7+6x8<=960 +9x1+1x2+11x3+9x4+10x5-3x6-2x7+1x8<=240 -2x1-2x2-4x3+4x6+2x7<=0 +22x1+4x2+24x3+28x4+24x5-8x6-4x7+4x8<=640 +60x1+20x2+76x3+84x4+72x5-20x6-10x7+12x8<=1920 +32x1+22x2+84x3+84x4+72x5-4x6-2x7+12x8<=1920 +28x1+10x2+44x3+36x4+40x5-8x6-4x7+4x8<=960 +36x1+12x2+52x3+44x4+48x5-12x6-6x7+4x8<=1152 +23x1+7x2+33x3+27x4+30x5-7x6-4x7+3x8<=720 +48x1+24x2+88x3+72x4+80x5-12x6-6x7+8x8<=1920 +96x1+40x2+160x3+128x4+144x5-28x6-14x7+16x8<=3456 +15x1+7x2+26x3+20x4+24x5-4x6-2x7+4x8<=576 +12x1+4x2+20x3+12x4+16x5-4x6-2x7<=384 +11x1+3x2+17x3+11x4+14x5-3x6-2x7+1x8<=336 +8x1+12x3+4x4+8x5-4x6-2x7<=192 +4x3-4x4-4x6-2x7<=0 -2x2+8x3-8x4-8x6-4x7+2x8<=0 +12x1-12x2+28x3-12x4+8x5-20x6-10x7+4x8<=192 +12x1-12x2+20x3-4x4+8x5-12x6-6x7+2x8<=192 +48x1+24x2+92x3+60x4+80x5-12x6-6x7+4x8<=1920 +15x1+7x2+28x3+18x4+24x5-4x6-2x7+2x8<=576 +42x1+18x2+76x3+40x4+64x5-12x6-6x7+8x8<=1536 +12x1+4x2+20x3-4x4+16x5-4x6-2x7+4x8<=384 +60x1+20x2+102x3-18x4+76x5-14x6-10x7+18x8<=1920 +60x1+20x2+102x3+46x4+76x5-14x6-10x7+2x8<=1920 +22x1+6x2+37x3+17x4+26x5-5x6-4x7+1x8<=672 +22x1+4x2+36x3+16x4+24x5-4x6-4x7<=640 +40x1+64x3+16x4+32x5-8x6-10x7<=960 +4x1-4x2+8x3-2x7<=64 -8x2+6x3-2x4-4x5+2x6-2x7<=0 -8x1-18x2+8x3-8x5+8x6-2x7<=0 -36x1-60x2+28x3+4x4-24x5+28x6-6x7+4x8<=64 -28x1-36x2+20x3+12x4-8x5+20x6-2x7+4x8<=192 -4x1-4x2+5x3+5x4+2x5+3x6+1x8<=96 -4x1-6x2+4x3+4x4+4x6<=64 +5x3+5x4+2x5+1x6+1x8<=96 +1x3+1x4<=16 +6x1+8x3-12x4+8x5+4x8<=192 +6x1+8x3+4x4+8x5<=192 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-14x1-22x2+44x3-8x4-64x5+12x6-6x7+8x8<=0 -6x1-10x2+18x3-2x4-28x5+6x6-2x7+2x8<=0 -28x1-36x2+52x3+12x4-72x5+36x6-2x7+12x8<=192 -3x1-3x2+8x3+6x4-4x5+4x6+2x8<=96 -1x1-1x2+2x3-4x5<=0 -12x2+10x3-6x4-12x5+6x6-2x7+2x8<=0 +3x3+3x4-2x5+1x6+1x8<=48 -16x1-24x2+44x3+12x4-72x5+28x6-2x7+12x8<=192 -4x1-12x2+14x3-2x4-20x5+8x6-2x7+2x8<=0 -1x1-9x2+11x3-3x4-14x5+5x6-2x7+1x8<=0 -32x1-40x2+68x3+4x4-88x5+36x6-6x7+20x8<=192 -1x1-1x2+3x3+1x4-6x5+1x6+1x8<=16 -4x1-6x2+12x3+4x4-24x5+8x6+4x8<=64 -4x1-12x2+20x3-4x4-40x5+12x6-2x7+4x8<=0 -10x2+16x3-8x4-24x5+8x6-2x7<=0 +12x1-12x2+40x3-16x4-32x5+8x6-6x7<=192 -24x2+34x3-14x4-44x5+14x6-6x7+2x8<=0 +4x1-4x2+16x3-8x4-16x5-2x7<=64 -8x2+20x3-12x4-32x5-2x7<=0 -4x2+14x3-10x4-20x5-2x6-2x7+2x8<=0 -2x2+2x3-2x4-4x5+2x6<=0 -24x2+44x3-20x4-72x5+20x6-6x7+4x8<=0 -24x2+60x3-36x4-104x5+4x6-6x7+4x8<=0 -6x1-10x2+16x3-4x4-24x5+8x6-2x7+4x8<=0 -1x1-1x2+1x3-1x4-2x5+1x6+1x8<=0 -6x1-18x2+16x3-4x4-24x5+12x6-2x7+4x8<=0 +2x2+20x3+20x4+8x5+4x8<=384 +12x1+4x2+12x3+20x4+8x5-4x6-2x7+4x8<=384 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-19x1+1x2+21x3+3x4-18x5-5x6-6x7+3x8<=48 +18x1+14x2+50x3+62x4+20x5-2x6-2x7+10x8<=1152 -2x1+2x2+2x3-2x4-4x5-2x6-2x7+2x8<=0 +4x1+2x2-4x3+12x4-40x5+4x6+8x8<=192 +4x1+2x2-4x3+12x4-24x5+4x6+6x8<=192 +3x1+1x2-2x3+8x4-16x5+2x6+4x8<=128 +4x1-4x2+20x3-20x4-40x5+4x6-2x7+4x8<=64 +12x1-12x2+52x3-36x4-104x5+20x6-6x7+4x8<=192 -6x2+12x3-20x4-40x5+8x6+4x8<=0 +12x1+4x2+24x3-32x4-64x5+8x6-2x7<=384 +6x3-18x4-4x5-2x6-2x7+6x8<=0 +8x3-20x4-8x5-4x6-2x7+6x8<=0 -8x2+24x3-40x4-208x5+32x6-2x7+16x8<=0 -8x2+24x3-40x4-144x5+24x6-2x7+16x8<=0 -8x2+24x3-40x4-112x5+16x6-2x7+16x8<=0 +8x1+20x3-60x4-152x5+20x6-2x7+4x8<=192 +4x1-4x2+20x3-84x4-264x5+36x6-2x7+12x8<=64 +16x1+12x2+26x3+42x4+36x5+6x6-2x7+6x8<=960 +20x1+12x2+34x3+42x4+36x5-2x7+6x8<=960 +20x1+16x2+18x3+42x4+36x5+2x6-6x7+6x8<=960 +8x1+8x2+20x3+36x4-88x5+4x6-2x7+20x8<=576 -132x1+60x2+84x3+12x4-72x5-76x6-58x7+12x8<=192 -20x1+12x2+20x3+12x4-8x5-12x6-10x7+4x8<=192 -3x1+3x2+6x3+6x4-2x6-2x7<=96 -16x1+16x2+48x3+48x4-8x6-10x7<=768 +1x1+1x2+6x4-20x5+4x6+4x8<=96 -3x1-5x2+10x3-8x4-72x5+14x6+8x8<=0 -4x1-12x2+32x3-24x4-176x5+32x6-2x7+16x8<=0 +12x1-12x2+60x3-60x4-152x5+28x6-6x7+4x8<=192 +12x1-12x2+76x3-76x4-184x5+28x6-10x7+12x8<=192 -48x4-2x7+16x8<=0 +12x1+8x2+12x3+36x4-24x5-2x7+12x8<=576 +4x1+4x2+4x3+12x4-8x5-4x6-2x7+4x8<=192 -12x2+32x3-32x4-96x5+16x6-2x7+8x8<=0 -24x1+8x2+24x3-8x4-16x5-16x6-10x7+8x8<=0 -52x1+28x2+64x3-40x4-80x5-48x6-30x7+40x8<=0 +12x1-12x2-20x3-156x4+8x5+28x6-6x7+60x8<=192 +12x1-12x2-20x3-380x4+8x5+28x6-6x7+116x8<=192 -2x2-4x3-40x4+4x6+12x8<=0 -6x2-8x3-24x4+8x6+10x8<=0 -8x2+36x3-28x4-152x5+20x6-6x7+4x8<=0 +2x1-2x2+12x3-8x4-32x5+4x6-2x7<=32 -2x2-4x3-4x4+4x6<=0 -6x2-8x3-8x4+8x6+2x8<=0 -6x2-1x3-5x4-2x5+5x6+1x8<=0 +16x1+12x2+48x3+48x4+32x5-4x6-2x7+8x8<=1024 +23x1+15x2+55x3+57x4+42x5-3x6-2x7+9x8<=1248 +24x1+16x2+58x3+66x4+36x5-2x6-2x7+12x8<=1344 +21x1+13x2+45x3+51x4+30x5-3x6-2x7+9x8<=1056 +20x1+12x2+40x3+48x4+24x5-4x6-2x7+8x8<=960 -8x2+24x3-24x4-112x5+20x6-2x7+8x8<=0 -4x1-12x2+32x3-24x4-144x5+24x6-2x7+16x8<=0 -8x2+24x3-24x4-80x5+12x6-2x7+8x8<=0 -8x1+8x3-24x4-80x5+8x6-2x7+24x8<=0 -6x1+2x2+4x3-16x4-48x5-4x6-2x7+16x8<=0 -14x1+10x2+20x3-16x4-48x5-20x6-10x7+16x8<=0 -20x1+12x2+32x3-24x4-80x5-16x6-14x7+24x8<=0 -14x1+2x2+20x3-8x4-16x5-12x6-6x7+8x8<=0 -12x1+4x2+16x3-8x4-16x5-8x6-6x7+8x8<=0 -2x1-4x4-8x5+4x8<=0 -4x1+4x2+12x3+4x4-88x5-4x6-2x7+20x8<=192 -1x1+3x2+4x3+6x4-36x5-2x7+6x8<=96 -4x1+12x2+4x3+12x4-72x5-12x6-10x7+12x8<=192 +4x1+4x2-22x3+10x4+4x5+6x6-2x7+2x8<=192 +28x1+16x2+54x3+62x4+44x5-2x6-2x7+10x8<=1344 +36x1+28x2+120x3+144x4+32x5+8x6-2x7+32x8<=2688 +8x1+6x2+28x3+36x4+4x6+8x8<=640 +1x1+1x2+5x3+7x4-2x5+1x6+1x8<=112 -2x1-2x2+7x3+3x4-18x5+5x6+3x8<=48 -1x1-1x2+2x3-8x5+2x6<=0 -12x1-20x2+48x3-24x4-240x5+48x6-2x7+24x8<=0 +80x1+56x2+216x3+216x4+176x5-8x6-6x7+32x8<=4864 +32x1+24x2+104x3+104x4+80x5-2x7+16x8<=2304 +24x1+14x2+44x3+60x4+24x5-4x6-2x7+12x8<=1152 +6x1+4x2+12x3+24x4-24x5+4x6+8x8<=384 +28x1+20x2+64x3+104x4-48x5+8x6-2x7+32x8<=1728 +24x1+16x2+36x3+84x4-88x5+12x6-2x7+28x8<=1344 -8x1+8x2+12x3+12x4-8x5-4x6-6x7+4x8<=192 -48x1+32x2+28x3+12x4-72x5-20x6-30x7+12x8<=192 +48x1+24x2+44x3+108x4-8x5-4x6-6x7+28x8<=1920 +20x1+12x2+20x3+60x4-40x5+4x6-2x7+16x8<=960 +28x1+16x2+28x3+84x4-40x5+4x6-2x7+20x8<=1344 +14x1+8x2+20x3+48x4-24x5+4x6+12x8<=768 +32x1+24x2+68x3+132x4-152x5+20x6-2x7+52x8<=2112 +4x1+2x2+3x3+11x4-2x5+1x6+3x8<=192 +12x1+6x2+4x3+36x4-16x5+4x6+8x8<=576 +4x1+2x2-4x3+12x4-16x5+4x6+4x8<=192 +36x1+18x2+59x3+75x4+62x5+3x6+13x8<=1728 -4x1+4x2+12x3+12x4-4x6-2x7<=192 +1x1+1x2+3x3+5x4+2x5+1x6+1x8<=96 +2x2+4x3+12x4+4x6<=192 +36x1+28x2+96x3+152x4-16x5+8x6-2x7+16x8<=2496 +12x1+12x2+36x3+60x4-8x5+4x6-2x7+4x8<=960 +18x1+26x2+76x3+120x4+4x6-6x7<=1920 +42x1+34x2+116x3+144x4+48x5-4x6-6x7+24x8<=2688 +17x1+11x2+37x3+43x4+22x5-3x6-2x7+7x8<=864 +60x1+36x2+118x3+142x4+76x5-10x6-6x7+26x8<=2880 +6x1+10x3-10x4+4x5+2x6+2x8<=192 +6x1+10x3-2x4+4x5+2x6<=192 -2x2+2x3-26x4-4x5+2x6+6x8<=0 +12x1-12x2+40x3-240x4-32x5+8x6-6x7+56x8<=192 +7x1+5x2+12x3+30x4-52x5+8x6+14x8<=480 -4x2+16x3-16x4-80x5+12x6-2x7+4x8<=0 -4x1-6x2+12x3-4x4-48x5+12x6+4x8<=0 +36x1+12x2+60x3+20x4+40x5-4x6-6x7+4x8<=1152 -2x1-8x2+16x3-12x4-56x5+12x6+4x8<=0 -10x1-16x2+32x3-12x4-120x5+28x6+12x8<=0 -9x1+1x2-16x3+6x4-36x5+20x6+6x8<=96 -1x1+1x2+6x4-4x5+4x6+2x8<=96 +10x1+6x2+12x3+24x4-16x5-4x6-2x7+8x8<=416 +4x1+4x2-6x3+10x4+4x5+2x6-2x7+2x8<=192 +4x1+4x2-8x3+12x4+2x6-2x7<=192 -4x1+2x2+3x3-1x4-2x5-3x6-2x7+1x8<=0 +12x1+12x2+44x3+52x4+16x5-4x6-2x7+8x8<=960 +8x1+8x2+28x3+28x4+16x5-4x6-2x7+4x8<=576 -3x1-5x2+9x3-1x4-10x5+1x6-2x7+1x8<=0 -3x1-7x2+9x3-1x4-10x5+3x6-2x7+1x8<=0 +16x1+24x2+88x3+88x4+48x5-8x6-6x7+16x8<=1792 +15x1+11x2+39x3+41x4+26x5-3x6-2x7+7x8<=864 +11x1+9x2+31x3+33x4+18x5-3x6-2x7+5x8<=672 +16x1+12x2+42x3+50x4+20x5-2x6-2x7+8x8<=960 +80x1+40x2+154x3+90x4+132x5-18x6-10x7+6x8<=3200 +48x1+24x2+94x3+46x4+76x5-10x6-6x7+2x8<=1920 +12x1+12x2+50x3+58x4+4x5+2x6-2x7+14x8<=1056 +12x1+12x2+44x3+52x4+8x5-4x6-2x7+12x8<=960 -6x2+20x3-20x4-56x5+8x6-2x7+6x8<=0 -8x1-8x2+24x3+8x4-16x5+8x6-2x7+8x8<=192 -3x1-1x2+2x3-4x4-8x5+2x6+4x8<=0 -11x1-1x2+2x3-20x4-40x5+6x6+20x8<=0 -18x2+3x3-13x4-10x5+13x6+3x8<=0 +6x1+4x2+16x3+20x4+8x5+2x6+4x8<=400 +64x1+40x2+144x3+176x4+96x5+8x6-2x7+32x8<=3648 +8x1+6x2+26x3+34x4+4x5+4x6+8x8<=624 +6x2+28x3+36x4+4x6-2x7<=576 +60x1+52x2+200x3+240x4+96x5+8x6-6x7+48x8<=4608 +18x1+14x2+48x3+60x4+24x5-2x7+12x8<=1152 +34x1+22x2+80x3+92x4+56x5-2x7+16x8<=1920 +36x1+22x2+74x3+82x4+52x5-8x6-4x7+14x8<=1728 +28x1+20x2+40x3+80x4-96x5-8x6-6x7+32x8<=1344 +12x1+8x2+12x3+36x4-56x5-2x7+16x8<=576 +13x1+7x2+16x3+30x4-4x5-4x6-2x7+8x8<=528 +12x1-12x2+48x3-40x4-80x5+16x6-6x7+8x8<=192 +12x1-12x2+48x3-200x4-80x5+16x6-6x7+48x8<=192 -6x2+12x3-52x4-40x5+8x6+12x8<=0 -2x2+3x3-21x4-10x5+3x6+5x8<=0 +8x1+12x3-12x4+8x5+2x6+4x8<=256 +6x1+7x3-13x4+6x5+3x6+5x8<=192 +16x1+24x3+16x5+4x6+2x8<=512 +14x1+6x2+4x3+32x4-2x6-2x7<=512 +16x1+8x2+8x3+40x4-2x6-2x7<=640 +20x1+14x2+20x3+60x4-2x6-4x7<=960 +20x1+12x2+4x3+60x4-72x5+12x6-2x7+20x8<=960 +20x1+12x2+4x3+60x4-104x5+12x6-2x7+28x8<=960 +12x1-12x2-20x3-36x4+8x5+28x6-6x7<=192 -2x2+3x3-5x4-10x5+3x6+1x8<=0 -28x1+4x2+44x3+4x4-24x5-20x6-10x7+12x8<=192 -8x1+12x3+4x4-8x5-4x6-2x7+2x8<=64 -14x1-6x2+36x3+16x4-32x5-4x6-2x7+8x8<=256 -4x1-6x2+10x3+2x4-20x5+8x6+4x8<=48 -2x1-4x2+4x3-8x5+4x6+2x8<=16 -12x1-36x2+28x3-12x4-56x5+28x6-2x7+12x8<=0 -4x1-4x2+8x3-8x5-2x7<=0 -4x1-8x2+12x3+4x4-8x5+4x6-2x7<=64 -12x1-12x2+36x3+28x4-8x5+12x6-2x7+4x8<=448 +10x1+8x2+28x3+48x4-8x5+4x6+4x8<=768 +22x1+16x2+52x3+96x4-56x5+12x6+28x8<=1536 +16x1+16x2+88x3+88x4+48x5-2x7+16x8<=1792 -6x1+10x2+20x3+24x4-4x6-6x7<=384 +12x1+28x2+104x3+144x4+8x6-6x7<=2304 +48x1+40x2+168x3+200x4+80x5+8x6-2x7+40x8<=3840 -8x2+6x3-10x4-4x5+2x6-2x7+4x8<=0 -4x1-8x2+6x3-18x4-4x5+2x6-2x7+10x8<=0 +16x1+10x2+16x3+48x4-24x5+2x6-2x7+12x8<=768 +56x1+32x2+32x3+144x4-96x5-8x6-10x7+48x8<=2304 +48x1+24x2+16x3+112x4-8x6-10x7<=1792 +56x1+32x2+32x3+144x4-8x6-10x7<=2304 +6x1+7x3-5x4+6x5+3x6+3x8<=192 +14x1+19x3-1x4+14x5+5x6+3x8<=448 +18x1+24x3-4x4+16x5+8x6+4x8<=576 +60x1+36x2+96x3+168x4+16x5-8x6-6x7+16x8<=2880 +6x1-10x3+10x4+4x5+2x6+2x8<=192 +8x1-12x3+12x4+8x5+4x6+2x8<=256 +16x1+24x4+16x5+2x6+4x8<=512 +6x1-2x3+10x4+4x5+2x8<=192 +18x1-4x3+24x4+16x5+4x6+8x8<=576 +14x1-1x3+19x4+14x5+3x6+5x8<=448 +18x1+3x3+23x4+22x5+3x6+5x8<=576 +6x1-5x3+7x4+6x5+3x6+3x8<=192 +6x1-13x3+7x4+6x5+5x6+3x8<=192 +4x1-4x2-20x3+4x4-24x5-4x6-2x7+4x8<=64 +56x1+32x2+96x3+96x4+96x5-16x6-10x7<=2304 +30x1+32x3+28x4+32x5-8x6-6x7<=768 -1x1<=0 -1x2<=0 -1x3<=0 -1x4<=0 -1x5<=0 -1x6<=0 -1x7<=0 -1x8<=0 END lrslib-073/ine/test-062/porta/mit71-61.ine.ieq0000777000175000017500000001350114625766515017215 0ustar avisavisDIM = 60 INEQUALITIES_SECTION +384x1-192x3-768x6+512x9+768x13-768x19-192x33+384x39-64x51<=64 -2x9+6x10-6x11+2x12+2x28-6x29+6x30-2x31<=0 -2x9+2x10+2x11-2x12+2x28-2x29-2x30+2x31<=0 -2x9-2x10+2x11+2x12+2x28+2x29-2x30-2x31<=0 -2x9-6x10-6x11-2x12+2x28+6x29+6x30+2x31<=0 -4x6+8x7-4x8+8x9-16x10+8x11-4x28+8x29-4x30<=0 -4x6+4x8+8x9-8x11-4x28+4x30<=0 -4x6-8x7-4x8+8x9+16x10+8x11-4x28-8x29-4x30<=0 -8x1+8x2+24x6-24x7-24x9+24x10+8x28-8x29<=0 -8x1-8x2+24x6+24x7-24x9-24x10+8x28+8x29<=0 +64x1-96x6+64x9-16x28<=16 -1x51+6x52-12x53-3x54+12x55+8x56-3x57-12x58+6x59-1x60<=0 -1x51+4x52-4x53-1x54+1x57+4x58-4x59+1x60<=0 -1x51+2x52+1x54-4x55+1x57+2x59-1x60<=0 -1x51+2x52+4x53-3x54+4x55-8x56-3x57+4x58+2x59-1x60<=0 -1x51+4x53-1x54+1x57-4x58+1x60<=0 -1x51+3x54-3x57+1x60<=0 -1x51-2x52+4x53-3x54-4x55+8x56-3x57+4x58-2x59-1x60<=0 -1x51-2x52+1x54+4x55+1x57-2x59-1x60<=0 -1x51-4x52-4x53-1x54+1x57+4x58+4x59+1x60<=0 -1x51-6x52-12x53-3x54-12x55-8x56-3x57-12x58-6x59-1x60<=0 -2x39+8x40+2x41-8x42-4x43-8x44+4x45+8x46+8x47-8x48-2x49+2x50+2x51-10x52+16x53+4x54-12x55-8x56+2x57+8x58-2x59<=0 -2x39+4x40+2x41-4x42-4x47+4x48+2x49-2x50+2x51-6x52+4x53+4x55-2x57-4x58+2x59<=0 -2x39+8x40-2x41+8x42-4x43-8x44-4x45-8x46+8x47+8x48-2x49-2x50+2x51-6x52+4x54-4x55+8x56+2x57-8x58+2x59<=0 -2x39+4x40-2x41+4x42-4x47-4x48+2x49+2x50+2x51-2x52-4x53+4x55-2x57+4x58-2x59<=0 -2x39+2x41-4x43+8x44+4x45-8x46-2x49+2x50+2x51-2x52-8x53+4x54-4x55+8x56+2x57-2x59<=0 -2x39+2x41+4x43-4x45-2x49+2x50+2x51-2x52-4x54+4x55+2x57-2x59<=0 -2x39-2x41-4x43+8x44-4x45+8x46-2x49-2x50+2x51+2x52-8x53+4x54+4x55-8x56+2x57+2x59<=0 -2x39-2x41+4x43+4x45-2x49-2x50+2x51+2x52-4x54-4x55+2x57+2x59<=0 -2x39-4x40+2x41+4x42+4x47-4x48+2x49-2x50+2x51+2x52-4x53-4x55-2x57+4x58+2x59<=0 -2x39-4x40-2x41-4x42+4x47+4x48+2x49+2x50+2x51+6x52+4x53-4x55-2x57-4x58-2x59<=0 -2x39-8x40+2x41+8x42-4x43-8x44+4x45+8x46-8x47+8x48-2x49+2x50+2x51+6x52+4x54+4x55-8x56+2x57-8x58-2x59<=0 -2x39-8x40-2x41-8x42-4x43-8x44-4x45-8x46-8x47-8x48-2x49-2x50+2x51+10x52+16x53+4x54+12x55+8x56+2x57+8x58+2x59<=0 -4x19+8x20+8x21-4x22-16x23-4x24+8x25+8x26-4x27+8x39-24x40-8x41+24x42+8x43+16x44-8x45-16x46-8x47+8x48-4x51+16x52-20x53-4x54+8x55+8x56-4x58<=0 -4x19+8x21+4x22-4x24-8x25+4x27+8x39-16x40-8x42+8x43+16x46-8x48-4x51+8x52+4x53-4x54-8x56+4x58<=0 -4x19+8x20-4x22+4x24-8x26+4x27+8x39-8x40-8x41+8x42-8x43+8x45+8x47-8x48-4x51+8x52-4x53+4x54-8x55+4x58<=0 -4x19-8x20+8x21-4x22+16x23-4x24+8x25-8x26-4x27+8x39-8x40+8x41-8x42+8x43-16x44+8x45-16x46+8x47+8x48-4x51+12x53-4x54-8x55+8x56-4x58<=0 -4x19+4x22+4x24-4x27+8x39-8x42-8x43+8x48-4x51+4x53+4x54-4x58<=0 -4x19+8x20-8x21-4x22+16x23-4x24-8x25+8x26-4x27+8x39+8x40-8x41-8x42+8x43-16x44-8x45+16x46-8x47+8x48-4x51+12x53-4x54+8x55-8x56-4x58<=0 -4x19-8x20-4x22+4x24+8x26+4x27+8x39+8x40+8x41+8x42-8x43-8x45-8x47-8x48-4x51-8x52-4x53+4x54+8x55+4x58<=0 -4x19-8x21+4x22-4x24+8x25+4x27+8x39+16x40-8x42+8x43-16x46-8x48-4x51-8x52+4x53-4x54+8x56+4x58<=0 -4x19-8x20-8x21-4x22-16x23-4x24-8x25-8x26-4x27+8x39+24x40+8x41+24x42+8x43+16x44+8x45+16x46+8x47+8x48-4x51-16x52-20x53-4x54-8x55-8x56-4x58<=0 -4x33+16x34-8x35-16x36+16x37-4x38+8x39-32x40+16x43+32x44-32x47+8x49-4x51+16x52-16x53-8x54+16x55-4x57<=0 -4x33+8x34-8x37+4x38+8x39-16x40+16x47-8x49-4x51+8x52-8x55+4x57<=0 -4x33-8x35+16x36-4x38+8x39+16x43-32x44+8x49-4x51+16x53-8x54-4x57<=0 -4x33+8x35-4x38+8x39-16x43+8x49-4x51+8x54-4x57<=0 -4x33-8x34+8x37+4x38+8x39+16x40-16x47-8x49-4x51-8x52+8x55+4x57<=0 -4x33-16x34-8x35-16x36-16x37-4x38+8x39+32x40+16x43+32x44+32x47+8x49-4x51-16x52-16x53-8x54-16x55-4x57<=0 -8x13+8x14+16x15-16x16-8x17+8x18+16x19-16x20-32x21+32x23+16x24-16x26+8x33-24x34+8x35+16x36-8x37-24x39+64x40+8x41-16x42-24x43-32x44+8x45+16x47+8x51-24x52+16x53+8x54-8x55<=0 -8x13-8x14+16x15+16x16-8x17-8x18+16x19+16x20-32x21-32x23+16x24+16x26+8x33-8x34+8x35-16x36+8x37-24x39+32x40-8x41+16x42-24x43+32x44-8x45-16x47+8x51-8x52-16x53+8x54+8x55<=0 -8x13+8x14+8x17-8x18+16x19-16x20-16x24+16x26+8x33-8x34-8x35+8x37-24x39+16x40+8x41+24x43-8x45-16x47+8x51-8x52-8x54+8x55<=0 -8x13-8x14+8x17+8x18+16x19+16x20-16x24-16x26+8x33+8x34-8x35-8x37-24x39-16x40-8x41+24x43+8x45+16x47+8x51+8x52-8x54-8x55<=0 -8x13+8x14-16x15+16x16-8x17+8x18+16x19-16x20+32x21-32x23+16x24-16x26+8x33+8x34+8x35-16x36-8x37-24x39-32x40+8x41+16x42-24x43+32x44+8x45+16x47+8x51+8x52-16x53+8x54-8x55<=0 -8x13-8x14-16x15-16x16-8x17-8x18+16x19+16x20+32x21+32x23+16x24+16x26+8x33+24x34+8x35+16x36+8x37-24x39-64x40-8x41-16x42-24x43-32x44-8x45-16x47+8x51+24x52+16x53+8x54+8x55<=0 -8x9+24x10-24x11+8x12+24x19-48x20-24x21+24x22+48x23-24x25-24x39+48x40+24x41-48x42-24x44+24x46+8x51-24x52+24x53-8x56<=0 -8x9+8x10+8x11-8x12+24x19-16x20-8x21-8x22-16x23+24x25-24x39+16x40+8x41+16x42+8x44-24x46+8x51-8x52-8x53+8x56<=0 -8x9-8x10+8x11+8x12+24x19+16x20+8x21-8x22-16x23-24x25-24x39-16x40-8x41+16x42+8x44+24x46+8x51+8x52-8x53-8x56<=0 -8x9-24x10-24x11-8x12+24x19+48x20+24x21+24x22+48x23+24x25-24x39-48x40-24x41-48x42-24x44-24x46+8x51+24x52+24x53+8x56<=0 -16x3+32x4-16x5+64x13-128x15+64x17-64x19+128x21-64x24-32x33+64x34-32x35+64x39-128x40+64x43-16x51+32x52-16x54<=0 -16x3+16x5+64x13-64x17-64x19+64x24-32x33+32x35+64x39-64x43-16x51+16x54<=0 -16x3-32x4-16x5+64x13+128x15+64x17-64x19-128x21-64x24-32x33-64x34-32x35+64x39+128x40+64x43-16x51-32x52-16x54<=0 -16x6+32x7-16x8+32x9-64x10+32x11+32x13-32x14-32x15+32x16-80x19+96x20+64x21-16x22-64x23-16x33+32x34-16x36+64x39-96x40-32x41+32x42+32x44-16x51+32x52-16x53<=0 -16x6+16x8+32x9-32x11+32x13-32x16-80x19+16x22+64x23-16x33+16x36+64x39-32x42-32x44-16x51+16x53<=0 -16x6-32x7-16x8+32x9+64x10+32x11+32x13+32x14+32x15+32x16-80x19-96x20-64x21-16x22-64x23-16x33-32x34-16x36+64x39+96x40+32x41+32x42+32x44-16x51-32x52-16x53<=0 -32x1+32x2+32x3-32x4+128x6-128x7-128x9+128x10-192x13+64x14+128x15+256x19-128x20-128x21+64x33-64x34-160x39+128x40+32x41+32x51-32x52<=0 -32x1-32x2+32x3+32x4+128x6+128x7-128x9-128x10-192x13-64x14-128x15+256x19+128x20+128x21+64x33+64x34-160x39-128x40-32x41+32x51+32x52<=0 -1x28+4x29-6x30+4x31-1x32<=0 -1x28+2x29-2x31+1x32<=0 -1x28+2x30-1x32<=0 -1x28-2x29+2x31+1x32<=0 -1x28-4x29-6x30-4x31-1x32<=0 END lrslib-073/ine/test-062/porta/perm10.ine.ieq0000777000175000017500000006310314625766515017137 0ustar avisavisDIM = 10 VALID 1 2 3 4 5 6 7 8 9 10 INEQUALITIES_SECTION -1x1-1x2-1x3-1x4-1x5-1x6-1x7-1x8-1x9-1x10==-55 +1x1+1x2+1x3+1x4+1x5+1x6+1x7+1x8+1x9<=54 +1x1+1x2+1x3+1x4+1x5+1x6+1x7+1x8+1x10<=54 +1x1+1x2+1x3+1x4+1x5+1x6+1x7+1x9+1x10<=54 +1x1+1x2+1x3+1x4+1x5+1x6+1x8+1x9+1x10<=54 +1x1+1x2+1x3+1x4+1x5+1x7+1x8+1x9+1x10<=54 +1x1+1x2+1x3+1x4+1x6+1x7+1x8+1x9+1x10<=54 +1x1+1x2+1x3+1x5+1x6+1x7+1x8+1x9+1x10<=54 +1x1+1x2+1x4+1x5+1x6+1x7+1x8+1x9+1x10<=54 +1x1+1x3+1x4+1x5+1x6+1x7+1x8+1x9+1x10<=54 +1x2+1x3+1x4+1x5+1x6+1x7+1x8+1x9+1x10<=54 +1x1+1x2+1x3+1x4+1x5+1x6+1x7+1x8<=52 +1x1+1x2+1x3+1x4+1x5+1x6+1x7+1x9<=52 +1x1+1x2+1x3+1x4+1x5+1x6+1x7+1x10<=52 +1x1+1x2+1x3+1x4+1x5+1x6+1x8+1x9<=52 +1x1+1x2+1x3+1x4+1x5+1x6+1x8+1x10<=52 +1x1+1x2+1x3+1x4+1x5+1x6+1x9+1x10<=52 +1x1+1x2+1x3+1x4+1x5+1x7+1x8+1x9<=52 +1x1+1x2+1x3+1x4+1x5+1x7+1x8+1x10<=52 +1x1+1x2+1x3+1x4+1x5+1x7+1x9+1x10<=52 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-1x27<=0 -1x28<=0 -1x29<=0 -1x30<=0 -1x31<=0 -1x32<=0 -1x33<=0 -1x34<=0 -1x35<=0 -1x36<=0 -1x37<=0 END lrslib-073/ine/test-062/zfw91.ine0000777000175000017500000001612314625766516015112 0ustar avisavis*Wang Zengfu's problem: wangzengfu@gmail.com nonnegative H-representation begin 91 38 integer 1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 -1 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 -1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 -1 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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1 -1 1 1 6 -1 -1 -1 -1 0 -1 -1 -1 0 -1 -1 0 -1 0 0 6 -2 -1 -1 -1 1 -2 -2 -2 2 -1 -1 1 -1 1 1 6 0 -1 -1 -1 -1 0 0 0 0 -1 -1 -1 -1 -1 -1 6 1 -2 -1 -1 -1 2 1 1 1 -2 -2 -2 -1 -1 -1 6 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 2 0 0 0 0 0 -1 0 0 -1 0 0 -1 0 0 0 6 1 1 1 1 2 -1 -1 -1 -2 -1 -1 -2 -1 -2 -2 end *printcobasis maxdepth 12 lrslib-073/inedel.c0000777000175000017500000001245514625766517013007 0ustar avisavis/* inedel.c * * Removes an inequality from an H-representation, updating * redund_list and/or linearity lines if present */ #define VERSION "20221021" #include #include #include #ifdef LRSLONG #define ARITH "lrslong.h" /* lrs long integer arithmetic package */ #else #if defined(GMP) || defined(FLINT) #define ARITH "lrsgmp.h" /* lrs wrapper for gmp multiple precsion arithmetic */ #else #define ARITH "lrsmp.h" /* lrs multiple precsion arithmetic */ #endif #endif #include ARITH FILE *lrs_ifp; /* hook to make readrat work */ FILE *lrs_ofp; /* hook to be able to link to lrsgmp/etc */ #define printusage() \ printf("Usage: %s \nDelete inequality i from stdin\n", argv[0]); void eatspace(FILE *f) { int c; while (isspace(c=getc(f))); ungetc(c,f); } void parse_error(const char *str) { fprintf(stderr, "Parse error: %s\n", str); exit(1); } /* str is a redund or redund_list line. * read it and print it out. * note that we must remove ineq if present * note that we remove ineq so any indices>ineq need to decrement * if this is the last, don't print anything */ void handle_redund(char *str, int ineq) { unsigned int nred, cur, offs=0; int hit = 0, ret, j; unsigned long i, jj, *rr; if (!strncmp(str, "redund ", 7)) /* "redund" */ { sscanf(str, "redund %lu %lu", &i, &jj); if (i!=0 && jj!=0 && i>ineq) i--; if (i!=0 && jj!=0 && jj>=ineq) jj--; if ((i==0&&jj==0) || (jj>=i)) printf("redund %lu %lu\n", i, jj); return; } if (strncmp(str, "redund_list ", 12)) parse_error("mixed up on redund call"); ret = sscanf(str, "redund_list %u%n", &nred, &cur); if (ret == 0) parse_error("bad redund_list"); rr = malloc(sizeof(unsigned long) * nred); for (j=0; jhit) /* didn't remove them all */ { printf("redund_list %u ", nred-hit); for (j=0; jineq ? rr[j]-1 : rr[j])); printf("\n"); } free(rr); return; } /* str is a startingcobasis line, remove ineq if it appears * and reindex higher values one lower */ void handle_startingcob(char *str, int ineq) { unsigned cur, offs=0; unsigned long cob; sscanf(str, "startingcobasis %n", &offs); printf("startingcobasis"); while (sscanf(str+offs, "%lu%n", &cob, &cur)>0) { offs+=cur; if (cob==ineq) continue; else if (cobineq */ printf(" %lu", cob-1); } printf("\n"); return; } /* str is a linearity line * read it and print it out * note that we remove ineq, so don't print ineq if present * note that we remove ineq, so any indices>ineq need to decrement */ void handle_linearity(char *str, int ineq) { unsigned int nlin, cur, offs=0; int hit=0, ret, j; unsigned long *lin; ret = sscanf(str, "linearity %u%n", &nlin, &cur); if (ret == 0) parse_error("bad linearity line"); lin = malloc(sizeof(unsigned long) * nlin); for (j=0; jhit) /* didn't remove them all */ { printf("linearity %u ", nlin-hit); for (j=0; jineq? lin[j]-1 : lin[j])); printf("\n"); } free(lin); return; } int main(int argc, char **argv) { char *p, str[4096]={0}; /* lrslib uses 1000 */ FILE *f = stdin; lrs_mp num, den; int ineq; unsigned int i, j, m, n; int ret, begin = 0, end = 0; lrs_ofp = stdout; if (argc!=2 || ((ineq=atoi(argv[1]))<1)) { printusage(); return 0; } /* prior to begin */ while (begin == 0) { p = fgets(str, 4000, f); if (p == NULL) parse_error("file error"); if (!strncmp(str, "begin", 5)) { begin=1; continue; } else if (!strncmp(str, "V-representation", 16)) parse_error("V-representation not supported"); else if (!strncmp(str, "linearity ", 10)) handle_linearity(str, ineq); else printf("%s", str); } /* read a begin */ printf("begin\n"); ret = fscanf(f, "%u %u", &m, &n); if (ret != 2) parse_error("missing or broken dimension"); if (ineq > m) parse_error("can't remove non-existent inequality"); fgets(str, 4000, f); for (i=0; isspace(str[i]); i++); if (strncmp(str+i, "integer", 7)==0) printf("%u %u integer\n", m-1, n); else if (strncmp(str+i, "rational", 8)==0) printf("%u %u rational\n", m-1, n); else parse_error("data type must be integer or rational"); lrs_ifp = f; /* hook to make readrat work */ lrs_alloc_mp(num); lrs_alloc_mp(den); for (i=1; i<=m; i++) { for (j=0; j #include #include "lrsdriver.h" #include "lrslib.h" #define MAXCOL 1000 /* maximum number of colums */ long num[MAXCOL]; long den[MAXCOL]; void makecube (lrs_dic *P, lrs_dat *Q); int main (int argc, char *argv[]) { lrs_dic *P; /* structure for holding current dictionary and indices */ lrs_dat *Q; /* structure for holding static problem data */ lrs_mp_vector output; /* one line of output:ray,vertex,facet,linearity */ long i; long m; /* number of constraints in the problem */ long n; /* number of variables in the problem + 1 */ long col; /* output column index for dictionary */ /* Global initialization - done once */ if ( !lrs_init ("\n*lpdemo:")) return 1; /* generate cubes with dimension d */ for(i=1;i<=2;i++) { n=10; m=18; /* number of rows for cube dimension d */ /* allocate and init structure for static problem data */ Q = lrs_alloc_dat ("LRS globals"); if (Q == NULL) return 1; strcpy(Q->fname,"lpdemo"); Q->m=m; Q->n=n; Q->lponly=TRUE; /* we do not want all vertices generated! */ output = lrs_alloc_mp_vector (Q->n); P = lrs_alloc_dic (Q); /* allocate and initialize lrs_dic */ if (P == NULL) return 1; /* Build polyhedron: constraints and objective */ makecube(P,Q); /* Solve the LP */ if (!lrs_solve_lp(P,Q)) return 1; /* Print output */ prat ("\nObjective value = ", P->objnum, P->objden); for (col = 0; col < Q->n; col++) if (lrs_getsolution (P, Q, output, col)) lrs_printoutput (Q, output); /* free space : do not change order of next lines! */ lrs_clear_mp_vector (output, Q->n); lrs_free_dic (P,Q); /* deallocate lrs_dic */ lrs_free_dat (Q); /* deallocate lrs_dat */ } /* end of loop for i=1 ... */ lrs_close ("lpdemo:"); printf("\n"); return 0; } /* end of main */ /* code to generate unit cube and objective function */ void makecube (lrs_dic *P, lrs_dat *Q) /* generate H-representation of a unit hypercube */ /* with dimension n-1 */ { long num[MAXCOL]; long den[MAXCOL]; long row, j; long m=Q->m; long n=Q->n; for (row=1;row<=m;row++) { /* set up a cube */ for(j=0;j #include #include "lrsdriver.h" #include "lrslib.h" #define MAXCOL 1000 /* maximum number of colums */ long num[MAXCOL]; long den[MAXCOL]; void makecube (lrs_dic *P, lrs_dat *Q); int main (int argc, char *argv[]) { lrs_dic *P; /* structure for holding current dictionary and indices */ lrs_dat *Q; /* structure for holding static problem data */ lrs_mp_vector output; /* one line of output:ray,vertex,facet,linearity */ long col; /* output column index for dictionary */ /* Global initialization - done once */ if ( !lrs_init ("\n*lpdemo1:")) return 1; /* allocate and init structure for static problem data and read input */ Q = lrs_alloc_dat ("LRS globals"); if (Q == NULL) return 1; if (!lrs_read_dat (Q, argc, argv)) /* read first part of problem data to get dimensions */ return 1; /* and problem type: H- or V- input representation */ strcpy(Q->fname,"lpdemo1"); P = lrs_alloc_dic (Q); /* allocate and initialize lrs_dic */ if (P == NULL) return 1; if (!lrs_read_dic (P, Q)) /* read remainder of input to setup P and Q */ return 1; Q->lponly=TRUE; /* we do not want all vertices generated! */ output = lrs_alloc_mp_vector (Q->n); /* Solve the LP */ if (!lrs_solve_lp(P,Q)) return 1; /* Print output */ prat ("\nObjective value = ", P->objnum, P->objden); for (col = 0; col < Q->n; col++) if (lrs_getsolution (P, Q, output, col)) lrs_printoutput (Q, output); /* free space : do not change order of next lines! */ lrs_clear_mp_vector (output, Q->n); lrs_free_dic (P,Q); /* deallocate lrs_dic */ lrs_free_dat (Q); /* deallocate lrs_dat */ lrs_close ("lpdemo1:"); printf("\n"); return 0; } /* end of main */ /* code to generate unit cube and objective function */ void makecube (lrs_dic *P, lrs_dat *Q) /* generate H-representation of a unit hypercube */ /* with dimension n-1 */ { long num[MAXCOL]; long den[MAXCOL]; long row, j; long m=Q->m; long n=Q->n; for (row=1;row<=m;row++) { /* set up a cube */ for(j=0;j #include #include "lrsdriver.h" #include "lrslib.h" #define LE -1L // A constraint type used here. GE and EQ are defined in lrslib.h #define ROW 0 #define COL 1 #define MAXROW 10 // maximum number of rows #define MAXCOL 10 // maximum number of columns typedef struct { long num; long den; } ratnum; // Rational number: "num/den" typedef struct { ratnum a[MAXCOL]; // Coefficients long ctype; // Constraint type (GE, LE, EQ) ratnum rhs; // 'b' } lprow; // A row in the LP problem typedef struct { // C struct to represent an LP problem long dim[2]; // Number of rows and cols lprow row[MAXROW]; // The rows } lpp; /* An LP problem: max z = (3/4)*x1 + x2 - x3 s.t. 2*x1 + (2/3)*x2 - (2/3)*x3 <= 1 x1 + 2*x2 + (1/3)*x3 <= 3/2 x1 + x2 + x3 = 1 x1 >= 0 x2 >= 0 x3 >= 0 Solution: x1 = 11/32, x2 = 9/16, x3 = 3/32, z = 93/128 */ lpp LP = // The LP problem as a C struct with coefficients as rational numbers {num,den} { {7, 3}, // Dimensions { // -------- a --------- ctype rhs // lprow contents { {{3,4}, {1,1}, {-1,1}}, GE, {0,1} }, // Objective function (goes in row 0 with constraint type GE) { {{2,1}, {2,3}, {-2,3}}, LE, {1,1} }, // Inequality constraints { {{1,1}, {2,1}, { 1,3}}, LE, {3,2} }, { {{1,1}, {1,1}, { 1,1}}, EQ, {1,1} }, // Equality constraint { {{1,1}, {0,1}, { 0,1}}, GE, {0,1} }, // Lower bounds { {{0,1}, {1,1}, { 0,1}}, GE, {0,1} }, { {{0,1}, {0,1}, { 1,1}}, GE, {0,1} } } }; //----------------------------------------------------------------------------------------// // Build an lrs representation from the C struct: // - Replace LE constraints with GE by multiplying LE rows by -1 // - Multiply the RHS column by -1 and move it in front of matrix a // - For each row, call lrs_set_row() with the associated (and possibly modified) constraint type void buildLP (lrs_dic *P, lrs_dat *Q, lpp *lp) { long num[MAXCOL]; long den[MAXCOL]; long i, j, sgn; long m = lp->dim[ROW]; long n = lp->dim[COL]; lprow *row; for (i=0; irow + i; sgn = row->ctype == LE ? -1L : 1L; // sgn = 1 for EQ too if(sgn < 0L) // ctype == LE. Multiply row by -1 and change ctype to GE row->ctype = GE; // RHS num[0] = -sgn*row->rhs.num; // Opposite sign in column 0 den[0] = row->rhs.den; // Coef. matrix for(j=0; ja[j].num; // j+1: RHS goes in column 0 den[j+1] = row->a[j].den; } // Specify constraint type and set row lrs_set_row(P,Q,i,num,den,row->ctype); /* { // Uncomment this to print the lrs input representation of the LP problem char out[40]; printf("\n"); for(j=0;jctype == GE ? "GE" : "EQ"); } // end print */ } printf("\n"); } //----------------------------------------------------------------------------------------// // This is a slightly modified version of main() in lpdemo.c int lp_solve (lpp *lp) { lrs_dic *P; /* structure for holding current dictionary and indices */ lrs_dat *Q; /* structure for holding static problem data */ lrs_mp_vector output; /* one line of output:ray,vertex,facet,linearity */ long col; /* output column index for dictionary */ // allocate and init structure for static problem data Q = lrs_alloc_dat ("LRS globals"); if (Q == NULL) return 1; strcpy(Q->fname,"lpdemo2"); Q->m = lp->dim[ROW]-1; // Rows, excluding the objective function Q->n = 1+lp->dim[COL]; // Columns, including RHS which goes in column 0 Q->lponly = TRUE; // we do not want all vertices generated! Q->maximize = TRUE; output = lrs_alloc_mp_vector (Q->n); P = lrs_alloc_dic (Q); // allocate and initialize lrs_dic if (P == NULL) return 1; // Build the LP representation in the format required by lrs buildLP(P,Q,lp); // Solve the LP if (!lrs_solve_lp(P,Q)) return 1; // Print output prat ("\nObjective value = ", P->objnum, P->objden); for (col = 0; col < Q->n; col++) if (lrs_getsolution (P, Q, output, col)) lrs_printoutput (Q, output); /* free space : do not change order of next lines! */ lrs_clear_mp_vector (output, Q->n); lrs_free_dic (P,Q); /* deallocate lrs_dic */ lrs_free_dat (Q); /* deallocate lrs_dat */ return 0; } //----------------------------------------------------------------------------------------// int main(void) { lpp *lp = &LP; /* Global initialization - done once */ if ( !lrs_init ("\n*lpdemo2:")) return 1; lp_solve(lp); lrs_close ("lp:"); printf("\n"); } lrslib-073/lrs.c0000777000175000017500000000562314625766601012340 0ustar avisavis#include #include #include #include #include #include #include "lrsdriver.h" int main (int argc, char *argv[]) { struct timeval start, end; #ifndef MA gettimeofday(&start, NULL); lrs_main(argc,argv); /* legacy lrs */ gettimeofday(&end, NULL); fprintf(stdout,"\n*elapsed time: %ld seconds\n", end.tv_sec - start.tv_sec); return 0; #else /* hybrid arithmetic version of lrs */ lrs_restart_dat *R; lrs_dic *P; lrs_dat *Q; char* tmp; /* when overflow occurs a new input file name is returned */ char** newargv; long overfl=0; /* =0 no overflow =1 restart overwrite =2 restart append */ #ifdef B128 long overfl2=0; /* for B128 */ #endif int lrs_stdin=0; int i; gettimeofday(&start, NULL); P=NULL; Q=NULL; tmp=NULL; R = lrs_alloc_restart(); if (R == NULL) exit(1); if(argc == 1) lrs_stdin=1; tmp = malloc(PATH_MAX * sizeof (char)); overfl=lrs1_main(argc,argv,&P,&Q,0,0,tmp,R); /* set up, read input, no run */ if(overfl==0) overfl=lrs1_main(argc,argv,&P,&Q,overfl,1,tmp,R); /* run main part of code */ lrs1_main(argc,argv,&P,&Q,0,2,tmp,R); /* free memory and close */ if(overfl==0) goto byebye; if (overfl==-1) { printf("\n*unrecoverable input error\n"); exit(1); } /* overflow condition triggered: a temporary file was created for restart */ /* create new argv for the remaining calls */ newargv = makenewargv(&argc,argv,tmp); free(R->redineq); /* reallocated in stage 0 */ #ifdef B128 fprintf(stderr,"\n*lrs:overflow possible: restarting with 128 bit arithmetic\n"); overfl2=lrs2_main(argc,argv,&P,&Q,overfl,0,tmp,R); /* set up, read input, no run */ if(overfl2==0) overfl2=lrs2_main(argc,argv,&P,&Q,overfl,1,tmp,R); /* run main part of code */ lrs2_main(argc,argv,&P,&Q,overfl,2,tmp,R); /* free memory and close */ if(overfl2==0) goto done; overfl=overfl2; free(R->redineq); /* reallocated in stage 0 */ #endif /* if you change tmp file name update newargv[1] */ fprintf(stderr,"\n*lrs:overflow possible: restarting with GMP arithmetic\n"); lrsgmp_main(argc,newargv,&P,&Q,overfl,0,tmp,R); lrsgmp_main(argc,newargv,&P,&Q,overfl,1,tmp,R); lrsgmp_main(argc,newargv,&P,&Q,overfl,2,tmp,R); #ifdef B128 done: #endif for(i = 0; i < argc; ++i) free(newargv[i]); free(newargv); byebye: free(R->redineq); free(R->facet); free(R); if(lrs_stdin==1) /* get rid of temporary file for stdin */ remove(tmp); free(tmp); gettimeofday(&end, NULL); fprintf(stdout,"*Elapsed time: %ld seconds\n", end.tv_sec - start.tv_sec); return 0; #endif /* hybrid version of lrs */ } /* lrs.c */ lrslib-073/lrsarith-011/0000777000175000017500000000000014625766602013513 5ustar avisavislrslib-073/lrsarith-011/coll.c0000777000175000017500000000156114625766601014615 0ustar avisavis/* reverse search of Collatz verification paths 2020.11.25 */ /* versions depending on arithmetic: coll(hybrid),coll1,coll2,collgmp */ /* collmp, collflint */ /* maxn=largest value in Collatz tree, maxcount=max # of nodes */ /* Usage: % coll maxn maxcount */ #include "coll.h" int main () { long k,maxcount; printf("coll: enter maxn maxcount"); printf("\n maxn<0 : print counts only "); printf("\n maxcount=-1 : scale to maxn^8 MAXCOUNT=10^8 "); printf("\n maxcount=0 : no upper bound on tree size\n"); scanf("%ld %ld",&k,&maxcount); #ifdef MA if(run1(k,maxcount)) /* TRUE on 64 bit overflow */ if(run2(k,maxcount)) /* TRUE on 128 bit overflow */ runmp(k,maxcount); #else runmp(k,maxcount); #endif printf("\n"); return 0; } lrslib-073/lrsarith-011/coll.h0000777000175000017500000000061714625766601014623 0ustar avisavis/* 2020.11.13 hybrid.h */ /* contains files and defs that are arithmetic independent */ #include #include FILE *lrs_ifp; /* input file pointer */ FILE *lrs_ofp; /* output file pointer */ int run1(long k,long maxcount); int run2(long k,long maxcount); int rungmp(long k,long maxcount); int runmp(long k,long maxcount); lrslib-073/lrsarith-011/colllib.c0000777000175000017500000000735014625766601015306 0ustar avisavis/* reverse search of Collatz verification paths 2020.11.25 * * versions depending on arithmetic: coll(hybrid),coll1,coll2,collgmp * * collmp, collflint * * Usage: % coll or %coll2 * * Input: n * * integer n prints all integers k for which max(k)<=n^8 * * -n prints count only * * MAXCOUNT = maximum # nodes generated */ #define MAXCOUNT 100000000 #include #include #include #include "lrsarith.h" #define reverse suf(reverse) #define reversesearch suf(reversesearch) static jmp_buf buf1; /* return location when overflowing */ lrs_mp One; lrs_mp u,v,w,x; int reverse(lrs_mp v, long j) { copy(w,v); if (j==2) { copy(w,v); addint(w,w,v); return TRUE; } /* if (((w-1) % 3) || !((w-1) % 6)) return FALSE; w=w/3; */ subint(w,One,w); itomp(3,u); divint(w,u,x); if(!zero(w)) return FALSE; copy(w,v); subint(w,One,w); itomp(6,u); divint(w,u,x); if(zero(w)) return FALSE; itomp(3,u); copy(w,v); divint(w,u,v); return TRUE; } int reversesearch (long n, long maxcount) { lrs_mp maxv,Maxv; /* maxv=current max v, Max=limit on v */ long count=4,j=0,d=3,odd=0; long maxdeg=2,printall=FALSE; lrs_mp_init(60,stdin,stdout); long verbose=TRUE; lrs_alloc_mp(u); lrs_alloc_mp(w); lrs_alloc_mp(x); lrs_alloc_mp(v); lrs_alloc_mp(One); lrs_alloc_mp(maxv); lrs_alloc_mp(Maxv); if (!setjmp(buf1)){ /* overflow test */ printf(" v odd full"); printf("\n depth depth"); printf("\n 1 0 0"); if(n>0) { printall=TRUE; printf("\n 2 1"); printf("\n 4 2"); printf("\n 8 3"); } else n=-n; if(maxcount==-1) /* scale up to Maxv=n^8 maxcount=MAXCOUNT */ { itomp(n,u); mulint(u,u,v); mulint(v,v,x); mulint(x,x,Maxv); maxcount=MAXCOUNT; } else itomp(n,Maxv); /* don't scale up */ if(maxcount==0) /* no limit on number of nodes */ maxcount=MAXD; itomp(8,v); itomp(8,maxv); itomp(1,One); while ( j <= maxdeg && count < maxcount ) { do j++; while (!mp_greater(v,Maxv) && j<= maxdeg && !reverse (v, j)); if (!mp_greater(v,Maxv) && j <= maxdeg) /* forward step */ { if(mp_greater(v,maxv)) copy(maxv,v); d++; itomp(2,u); copy(x,v); divint(x,u,w); if(printall) { if(!zero(x)) { odd++; pmp("\n",v); printf(" %ld %ld",odd,d); } else { pmp("\n",v); printf(" %ld",d); } } count++; j = 0; } else if(d>3) /* backtrack step */ { d--; itomp(2,u); copy(x,v); divint(x,u,w); if(zero(x)) { copy(v,w); j=2; } else { odd--; addint(v,v,w); addint(w,v,w); addint(w,One,v); d++; j=1; } } } printf("\ncount=%ld ",count); pmp("\nMaxv=",Maxv); pmp("\nmaxv=",maxv); printf("\n"); return 0; } printf(" overflow detected:restarting\n"); return 1; } void lrs_overflow(int parm){ longjmp(buf1,1); } #if defined(MA) && defined(LRSLONG) #ifdef B128 int run2(long k, long maxcount){ /* 128 bit */ #else int run1(long k, long maxcount){ /* 64 bit */ #endif #else int runmp(long k, long maxcount){ /* other arithmetic */ #endif return reversesearch(k,maxcount); } lrslib-073/lrsarith-011/COPYING0000777000175000017500000004314614625766602014561 0ustar avisavis GNU GENERAL PUBLIC LICENSE Version 2, June 1991 Copyright (C) 1989, 1991 Free Software Foundation, Inc. 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. Preamble The licenses for most software are designed to take away your freedom to share and change it. By contrast, the GNU General Public License is intended to guarantee your freedom to share and change free software--to make sure the software is free for all its users. This General Public License applies to most of the Free Software Foundation's software and to any other program whose authors commit to using it. (Some other Free Software Foundation software is covered by the GNU Library General Public License instead.) You can apply it to your programs, too. When we speak of free software, we are referring to freedom, not price. Our General Public Licenses are designed to make sure that you have the freedom to distribute copies of free software (and charge for this service if you wish), that you receive source code or can get it if you want it, that you can change the software or use pieces of it in new free programs; and that you know you can do these things. To protect your rights, we need to make restrictions that forbid anyone to deny you these rights or to ask you to surrender the rights. These restrictions translate to certain responsibilities for you if you distribute copies of the software, or if you modify it. For example, if you distribute copies of such a program, whether gratis or for a fee, you must give the recipients all the rights that you have. You must make sure that they, too, receive or can get the source code. And you must show them these terms so they know their rights. We protect your rights with two steps: (1) copyright the software, and (2) offer you this license which gives you legal permission to copy, distribute and/or modify the software. Also, for each author's protection and ours, we want to make certain that everyone understands that there is no warranty for this free software. If the software is modified by someone else and passed on, we want its recipients to know that what they have is not the original, so that any problems introduced by others will not reflect on the original authors' reputations. Finally, any free program is threatened constantly by software patents. We wish to avoid the danger that redistributors of a free program will individually obtain patent licenses, in effect making the program proprietary. To prevent this, we have made it clear that any patent must be licensed for everyone's free use or not licensed at all. The precise terms and conditions for copying, distribution and modification follow. GNU GENERAL PUBLIC LICENSE TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION 0. This License applies to any program or other work which contains a notice placed by the copyright holder saying it may be distributed under the terms of this General Public License. The "Program", below, refers to any such program or work, and a "work based on the Program" means either the Program or any derivative work under copyright law: that is to say, a work containing the Program or a portion of it, either verbatim or with modifications and/or translated into another language. (Hereinafter, translation is included without limitation in the term "modification".) Each licensee is addressed as "you". Activities other than copying, distribution and modification are not covered by this License; they are outside its scope. The act of running the Program is not restricted, and the output from the Program is covered only if its contents constitute a work based on the Program (independent of having been made by running the Program). Whether that is true depends on what the Program does. 1. You may copy and distribute verbatim copies of the Program's source code as you receive it, in any medium, provided that you conspicuously and appropriately publish on each copy an appropriate copyright notice and disclaimer of warranty; keep intact all the notices that refer to this License and to the absence of any warranty; and give any other recipients of the Program a copy of this License along with the Program. You may charge a fee for the physical act of transferring a copy, and you may at your option offer warranty protection in exchange for a fee. 2. You may modify your copy or copies of the Program or any portion of it, thus forming a work based on the Program, and copy and distribute such modifications or work under the terms of Section 1 above, provided that you also meet all of these conditions: a) You must cause the modified files to carry prominent notices stating that you changed the files and the date of any change. b) You must cause any work that you distribute or publish, that in whole or in part contains or is derived from the Program or any part thereof, to be licensed as a whole at no charge to all third parties under the terms of this License. c) If the modified program normally reads commands interactively when run, you must cause it, when started running for such interactive use in the most ordinary way, to print or display an announcement including an appropriate copyright notice and a notice that there is no warranty (or else, saying that you provide a warranty) and that users may redistribute the program under these conditions, and telling the user how to view a copy of this License. (Exception: if the Program itself is interactive but does not normally print such an announcement, your work based on the Program is not required to print an announcement.) These requirements apply to the modified work as a whole. If identifiable sections of that work are not derived from the Program, and can be reasonably considered independent and separate works in themselves, then this License, and its terms, do not apply to those sections when you distribute them as separate works. But when you distribute the same sections as part of a whole which is a work based on the Program, the distribution of the whole must be on the terms of this License, whose permissions for other licensees extend to the entire whole, and thus to each and every part regardless of who wrote it. 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You may copy and distribute the Program (or a work based on it, under Section 2) in object code or executable form under the terms of Sections 1 and 2 above provided that you also do one of the following: a) Accompany it with the complete corresponding machine-readable source code, which must be distributed under the terms of Sections 1 and 2 above on a medium customarily used for software interchange; or, b) Accompany it with a written offer, valid for at least three years, to give any third party, for a charge no more than your cost of physically performing source distribution, a complete machine-readable copy of the corresponding source code, to be distributed under the terms of Sections 1 and 2 above on a medium customarily used for software interchange; or, c) Accompany it with the information you received as to the offer to distribute corresponding source code. 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If the distribution and/or use of the Program is restricted in certain countries either by patents or by copyrighted interfaces, the original copyright holder who places the Program under this License may add an explicit geographical distribution limitation excluding those countries, so that distribution is permitted only in or among countries not thus excluded. In such case, this License incorporates the limitation as if written in the body of this License. 9. The Free Software Foundation may publish revised and/or new versions of the General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. Each version is given a distinguishing version number. If the Program specifies a version number of this License which applies to it and "any later version", you have the option of following the terms and conditions either of that version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of this License, you may choose any version ever published by the Free Software Foundation. 10. If you wish to incorporate parts of the Program into other free programs whose distribution conditions are different, write to the author to ask for permission. For software which is copyrighted by the Free Software Foundation, write to the Free Software Foundation; we sometimes make exceptions for this. Our decision will be guided by the two goals of preserving the free status of all derivatives of our free software and of promoting the sharing and reuse of software generally. NO WARRANTY 11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. END OF TERMS AND CONDITIONS Appendix: How to Apply These Terms to Your New Programs If you develop a new program, and you want it to be of the greatest possible use to the public, the best way to achieve this is to make it free software which everyone can redistribute and change under these terms. To do so, attach the following notices to the program. It is safest to attach them to the start of each source file to most effectively convey the exclusion of warranty; and each file should have at least the "copyright" line and a pointer to where the full notice is found. Copyright (C) 19yy This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA. Also add information on how to contact you by electronic and paper mail. If the program is interactive, make it output a short notice like this when it starts in an interactive mode: Gnomovision version 69, Copyright (C) 19yy name of author Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'. This is free software, and you are welcome to redistribute it under certain conditions; type `show c' for details. The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, the commands you use may be called something other than `show w' and `show c'; they could even be mouse-clicks or menu items--whatever suits your program. You should also get your employer (if you work as a programmer) or your school, if any, to sign a "copyright disclaimer" for the program, if necessary. Here is a sample; alter the names: Yoyodyne, Inc., hereby disclaims all copyright interest in the program `Gnomovision' (which makes passes at compilers) written by James Hacker. , 1 April 1989 Ty Coon, President of Vice This General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Library General Public License instead of this License. lrslib-073/lrsarith-011/fixed.c0000777000175000017500000000117314625766601014762 0ustar avisavis/* 2020.11.12 test code for single arithmetic with overflow checking */ /* reads integer k and ouputs k^2 k^4 .. k^64 */ #include #include #include "lrsarith.h" FILE *lrs_ifp,*lrs_ofp; void lrs_overflow(int parm){ fprintf(lrs_ofp," overflow detected:halting\n"); exit (1); } int main (void){ long i,k; lrs_mp a,b; lrs_mp_init(10,stdin,stdout); lrs_alloc_mp(a); lrs_alloc_mp(b); fscanf(lrs_ifp,"%ld",&k); itomp(k,b); pmp("",b); for(i=1;i<=6;i++) { copy(a,b); mulint(a,a,b); pmp("",b); } lrs_clear_mp(a); lrs_clear_mp(b); fprintf(lrs_ofp,"\n"); return 0; } lrslib-073/lrsarith-011/hybrid.c0000777000175000017500000000032314625766601015140 0ustar avisavis#include "hybrid.h" int main (void) { long k; scanf("%ld",&k); if(run1(k)) /* TRUE on 64 bit overflow */ if(run2(k)) /* TRUE on 128 bit overflow */ runmp(k); printf("\n"); return 0; } lrslib-073/lrsarith-011/hybrid.h0000777000175000017500000000050214625766602015145 0ustar avisavis/* 2020.11.13 hybrid.h */ /* contains files and defs that are arithmetic independent */ #include #include FILE *lrs_ifp; /* input file pointer */ FILE *lrs_ofp; /* output file pointer */ int run1(long k); int run2(long k); int runmp(long k); lrslib-073/lrsarith-011/hybridlib.c0000777000175000017500000000167414625766601015641 0ustar avisavis/* 2020.11.13 hybridlib.c */ /* model routines for lrslib hybrid arithmetic */ #include #include #include #include "lrsarith.h" #define run suf(run) static jmp_buf buf1; /* return location when overflowing */ int run(long k){ long i; lrs_mp a,b; lrs_mp_init(0,stdin,stdout); lrs_alloc_mp(a); lrs_alloc_mp(b); itomp(k,b); pmp("",b); if (!setjmp(buf1)){ /* overflow test */ for(i=1;i<=6;i++){ copy(a,b); mulint(a,a,b); pmp("",b); } lrs_clear_mp(a); lrs_clear_mp(b); return 0; } printf(" overflow detected:restarting\n"); lrs_clear_mp(a); lrs_clear_mp(b); return 1; } void lrs_overflow(int parm){ longjmp(buf1,1); } #if defined(MA) && defined(LRSLONG) #ifdef B128 int run2(long k){ /* 128 bit */ #else int run1(long k){ /* 64 bit */ #endif #else int runmp(long k){ /* other arithmetic */ #endif return(run(k)); } lrslib-073/lrsarith-011/lrsarith.c0000777000175000017500000000024514625766602015513 0ustar avisavis/* lrsarith.c lrs arithmetic library */ #ifdef LRSLONG #include "lrslong.c" #elif defined(GMP) #include "lrsgmp.c" #else #include "lrsmp.c" #endif lrslib-073/lrsarith-011/lrsarith.h0000777000175000017500000000024614625766601015520 0ustar avisavis/* lrsarith.h (lrs arithmetic library */ #ifdef LRSLONG #include "lrslong.h" #elif defined(GMP) #include "lrsgmp.h" #else #include "lrsmp.h" #endif lrslib-073/lrsarith-011/lrsgmp.c0000777000175000017500000003021014625766601015161 0ustar avisavis/* lrsgmp.c library code for lrs extended precision arithmetic */ /* Version 4.1, April 3, 2001 */ /* Copyright: David Avis 2001, avis@cs.mcgill.ca */ /* Version 4.2, January 20, 2018 */ /* modified to use generic wrappers for everything in lrsgmp.c */ /* For gmp package */ /* derived from lrslong.c and lrsmp.c */ #include #include #include #include "lrsgmp.h" long lrs_digits; /* max permitted no. of digits */ long lrs_record_digits; /* this is the biggest acheived so far. */ #define MAXINPUT 1000 /*max length of any input rational */ void lcm (lrs_mp a, lrs_mp b) /* a = least common multiple of a, b; b is preserved */ { lrs_mp temp1,temp2; lrs_alloc_mp(temp1); lrs_alloc_mp(temp2); copy (temp1, a); copy (temp2, b); gcd (temp1,temp2); exactdivint (a, temp1, temp2); /* temp2=a/temp1 there is no remainder */ mulint (temp2, b, a); lrs_clear_mp(temp1); lrs_clear_mp(temp2); } /* end of lcm */ /***************************************************************/ /* */ /* Package of routines for rational arithmetic */ /* (Built on top of package for multiprecision arithmetic */ /* */ /***************************************************************/ void reduce (lrs_mp Na, lrs_mp Da) /* reduces Na/Da by gcd(Na,Da) */ { lrs_mp Nb, Db, Nc, Dc; lrs_alloc_mp(Nb); lrs_alloc_mp(Db); lrs_alloc_mp(Nc); lrs_alloc_mp(Dc); copy (Nb, Na); copy (Db, Da); storesign (Nb, POS); storesign (Db, POS); copy (Nc, Na); copy (Dc, Da); gcd (Nb, Db); /* Nb is the gcd(Na,Da) */ exactdivint (Nc, Nb, Na); exactdivint (Dc, Nb, Da); lrs_clear_mp(Nb); lrs_clear_mp(Db); lrs_clear_mp(Nc); lrs_clear_mp(Dc); } void reduceint (lrs_mp Na, lrs_mp Da) /* divide Na by Da and return */ { lrs_mp temp1; lrs_alloc_mp(temp1); copy (temp1, Na); exactdivint (temp1, Da, Na); lrs_clear_mp(temp1); } long comprod (lrs_mp Na, lrs_mp Nb, lrs_mp Nc, lrs_mp Nd) /* +1 if Na*Nb > Nc*Nd */ /* -1 if Na*Nb < Nc*Nd */ /* 0 if Na*Nb = Nc*Nd */ { long i; lrs_mp temp1,temp2; lrs_alloc_mp(temp1); lrs_alloc_mp(temp2); mulint (Na, Nb, temp1); mulint (Nc, Nd, temp2); //i=mpz_cmp(temp1,temp2); i=mpcmp(temp1,temp2); lrs_clear_mp(temp1); lrs_clear_mp(temp2); if (i > 0) return (ONE); else if (i < 0) return (-ONE); else return (ZERO); } void linrat (lrs_mp Na, lrs_mp Da, long ka, lrs_mp Nb, lrs_mp Db, long kb, lrs_mp Nc, lrs_mp Dc) /* computes Nc/Dc = ka*Na/Da +kb* Nb/Db and reduces answer by gcd(Nc,Dc) */ { lrs_mp temp1; lrs_alloc_mp(temp1); mulint (Na, Db, Nc); mulint (Da, Nb, temp1); linint (Nc, ka, temp1, kb); /* Nc = (ka*Na*Db)+(kb*Da*Nb) */ mulint (Da, Db, Dc); /* Dc = Da*Db */ reduce (Nc, Dc); lrs_clear_mp(temp1); } void divrat (lrs_mp Na, lrs_mp Da, lrs_mp Nb, lrs_mp Db, lrs_mp Nc, lrs_mp Dc) /* computes Nc/Dc = (Na/Da) /( Nb/Db ) and reduce */ { mulint (Na, Db, Nc); mulint (Da, Nb, Dc); reduce (Nc, Dc); } void mulrat (lrs_mp Na, lrs_mp Da, lrs_mp Nb, lrs_mp Db, lrs_mp Nc, lrs_mp Dc) /* computes Nc/Dc=(Na/Da)*(Nb/Db) and reduce */ { mulint (Na, Nb, Nc); mulint (Da, Db, Dc); reduce (Nc, Dc); } /***************************************************************/ /* */ /* Conversion and I/O functions */ /* */ /***************************************************************/ void atomp (const char *s, lrs_mp a) /*convert string to lrs_mp integer */ /* based on atoi KR p.58 */ { long diff, ten, i, sig; lrs_mp mpone; lrs_alloc_mp (mpone); itomp (ONE, mpone); ten = 10L; for (i = 0; s[i] == ' ' || s[i] == '\n' || s[i] == '\t'; i++); /*skip white space */ sig = POS; if (s[i] == '+' || s[i] == '-') /* sign */ sig = (s[i++] == '+') ? POS : NEG; itomp (0L, a); while (s[i] >= '0' && s[i] <= '9') { diff = s[i] - '0'; linint (a, ten, mpone, diff); i++; } storesign (a, sig); if (s[i]) { fprintf (stderr, "\nIllegal character in number: '%s'\n", s + i); exit (1); } lrs_clear_mp (mpone); } /* end of atomp */ void atoaa (const char *in, char *num, char *den) /* convert rational string in to num/den strings */ { long i, j; for (i = 0; in[i] != '\0' && in[i] != '/'; i++) num[i] = in[i]; num[i] = '\0'; den[0] = '\0'; if (in[i] == '/') { for (j = 0; in[j + i + 1] != '\0'; j++) den[j] = in[i + j + 1]; den[j] = '\0'; } } /* end of atoaa */ void rattodouble (lrs_mp a, lrs_mp b, double *x) /* convert lrs_mp rati onal to double */ { double y; //y=mpz_get_d (a); y=mptodouble (a); //(*x)=mpz_get_d (b); (*x)=mptodouble (b); (*x) = y / (*x); } /* read a rational or integer and convert to lrs_mp with base BASE */ /* returns true if denominator is not one */ /* returns 999 if premature end of file */ long plrs_readrat (lrs_mp Na, lrs_mp Da, const char* rat) { char in[MAXINPUT], num[MAXINPUT], den[MAXINPUT]; strcpy(in, rat); atoaa (in, num, den); /*convert rational to num/dem strings */ atomp (num, Na); if (den[0] == '\0') { itomp (1L, Da); return (FALSE); } atomp (den, Da); return (TRUE); } long readrat (lrs_mp Na, lrs_mp Da) /* read a rational or integer and convert to lrs_mp */ /* returns true if denominator is not one */ { char in[MAXINPUT], num[MAXINPUT], den[MAXINPUT]; if((fscanf (lrs_ifp, "%s", in)==EOF) || (strcmp("end",in)==0)) { fprintf (lrs_ofp, "\n**Invalid input: check you have entered enough data!\n"); exit(1); } atoaa (in, num, den); /*convert rational to num/dem strings */ atomp (num, Na); if (den[0] == '\0') { itomp (1L, Da); return (FALSE); } atomp (den, Da); return (TRUE); } char *cprat (const char *name, lrs_mp Nin, lrs_mp Din) { char *num, *den, *ret; unsigned long len; lrs_mp Nt, Dt; lrs_alloc_mp (Nt); lrs_alloc_mp (Dt); copy (Nt, Nin); copy (Dt, Din); reduce (Nt, Dt); num = mpgetstr10(NULL, Nt); den = mpgetstr10(NULL, Dt); len = snprintf(NULL, 0, " %s %s/%s", name, num, den); ret = (char*)malloc(sizeof(char)*(len+1)); if(one(Dt)) { if (sign (Nt) != NEG) sprintf(ret, "%s %s", name, num); else sprintf(ret, "%s%s", name, num); } else { if (sign (Nt) != NEG) sprintf(ret, " %s %s/%s", name, num, den); else sprintf(ret, "%s%s/%s", name, num, den); } free(num); free(den); lrs_clear_mp(Nt); lrs_clear_mp(Dt); return ret; } char *cpmp (const char *name, lrs_mp Nin) { char *num, *ret; unsigned long len; num = mpgetstr10(NULL, Nin); len = snprintf(NULL, 0, "%s %s", name, num); ret = (char*)malloc(sizeof(char)*(len+1)); if (sign (Nin) != NEG) sprintf(ret, "%s %s", name, num); else sprintf(ret, "%s%s", name, num); free(num); return ret; } void pmp (const char *name, lrs_mp Nt) { fprintf (lrs_ofp, "%s", name); if (sign (Nt) != NEG) fprintf (lrs_ofp, " "); //mpz_out_str (lrs_ofp,10,Nt); mpoutstr (lrs_ofp,10,Nt); fprintf (lrs_ofp, " "); } void prat (const char *name, lrs_mp Nin, lrs_mp Din) /*print the long precision rational Nt/Dt */ { lrs_mp temp1, temp2; lrs_alloc_mp(temp1); lrs_alloc_mp(temp2); copy (temp1, Nin); copy (temp2, Din); reduce (temp1, temp2); fprintf (lrs_ofp, "%s", name); if (sign (temp1) != NEG) fprintf (lrs_ofp, " "); mpoutstr (lrs_ofp,10,temp1); if ( !one(temp2)) { fprintf (lrs_ofp, "/"); mpoutstr (lrs_ofp,10,temp2); } fprintf (lrs_ofp, " "); lrs_clear_mp(temp1); lrs_clear_mp(temp2); } /* prat */ void readmp (lrs_mp a) /* read an integer and convert to lrs_mp */ { long in; if(fscanf (lrs_ifp, "%ld", &in)==EOF) { fprintf (lrs_ofp, "\n**Invalid integer input"); exit(1); } itomp (in, a); } /***************************************************************/ /* */ /* Memory allocation functions */ /* */ /***************************************************************/ lrs_mp_vector lrs_alloc_mp_vector (long n) /* allocate lrs_mp_vector for n+1 lrs_mp numbers */ { lrs_mp_vector p; long i; p = (lrs_mp_vector) CALLOC ((n + 1), sizeof (lrs_mp )); for (i = 0; i <= n; i++) lrs_alloc_mp(p[i]); return p; } void lrs_clear_mp_vector (lrs_mp_vector p, long n) /* free space allocated to p */ { long i; for (i=0; i<=n; i++) lrs_clear_mp (p[i] ); free (p); } lrs_mp_matrix lrs_alloc_mp_matrix (long m, long n) /* allocate lrs_mp_matrix for m+1 x n+1 lrs_mp numbers */ { lrs_mp_matrix a; int i, j; a = (lrs_mp_matrix) calloc ((m + 1), sizeof (lrs_mp_vector)); for (i = 0; i < m + 1; i++) { a[i] = (lrs_mp_vector) calloc ((n + 1), sizeof (lrs_mp )); for (j = 0; j < n + 1; j++) lrs_alloc_mp (a[i][j]); } return a; } void lrs_clear_mp_matrix (lrs_mp_matrix p, long m, long n) /* free space allocated to p */ { long i,j; for (i = 0; i < m + 1; i++) { for (j = 0; j < n + 1; j++) lrs_clear_mp (p[i][j]); free (p[i]); } free (p); } void lrs_getdigits (long *a, long *b) { /* send digit information to user */ *a = ZERO; *b = ZERO; return; } void * xcalloc (long n, long s, long l, const char *f) { void *tmp; tmp = calloc (n, s); if (tmp == 0) { char buf[200]; sprintf (buf, "\n\nFatal error on line %ld of %s", l, f); perror (buf); exit (1); } return tmp; } long lrs_mp_init (long dec_digits, FILE * fpin, FILE * fpout) /* max number of decimal digits for the computation */ /* long int version */ { lrs_ifp = fpin; lrs_ofp = fpout; lrs_record_digits = 0; /* not used for gmp arithmetic */ lrs_digits = 0; /* not used for gmp arithmetic */ return TRUE; } void notimpl (const char *s) { fflush (stdout); fprintf (stderr, "\nAbnormal Termination %s\n", s); exit (1); } /***************************************************************/ /* */ /* Misc. functions */ /* */ /***************************************************************/ /* find largest gcd of p[0]..p[n-1] and divide through */ void reducearray (lrs_mp_vector p, long n) { lrs_mp divisor, temp1; long i = 0L; while ((i < n) && zero (p[i])) i++; if (i == n) return; lrs_alloc_mp (divisor); lrs_alloc_mp (temp1); copy (divisor, p[i]); storesign (divisor, POS); i++; while (i < n) { if (!zero (p[i])) { copy (temp1, p[i]); storesign (temp1, POS); gcd (divisor, temp1); } i++; } for (i = 0; i < n; i++) if (!zero (p[i])) reduceint (p[i], divisor); lrs_clear_mp (divisor); lrs_clear_mp (temp1); } /* end of reducearray */ long myrandom (long num, long nrange) /* return a random number in range 0..nrange-1 */ { long i; i = (num * 401 + 673) % nrange; return (i); } void stringcpy (char *s, char *t) /*copy t to s pointer version */ { while (((*s++) = (*t++)) != '\0'); } void linint(lrs_mp a, long ka, lrs_mp b, long kb) /* a=a*ka+b*kb, b unchanged */ { lrs_mp temp1; lrs_alloc_mp (temp1); //mpz_mul_ui (a,a,labs(ka)); mului (a,a,labs(ka)); if (ka < 0) // mpz_neg(a,a); changesign(a); mului (temp1,b,labs(kb)); if (kb < 0) // mpz_neg(temp1,temp1); changesign(temp1); //mpz_add(a,a,temp1); addint(a,temp1,a); lrs_clear_mp (temp1); } void storesign(lrs_mp a, long sa) { if ( (sa)*sign(a) < 0 ) // mpz_neg(a,a); changesign(a); } lrslib-073/lrsarith-011/lrsgmp.h0000777000175000017500000003066214625766601015201 0ustar avisavis/* lrsgmp.h (lrs long integer arithmetic library based on gmp */ /* Copyright: David Avis 2000, avis@cs.mcgill.ca */ /* Version 4.0, April 13, 2000 */ /* Version 4.2, January 20, 2018 */ /* modified to use generic wrappers for everything in lrsgmp.c */ /* This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA. */ /******************************************************************************/ /* See http://cgm.cs.mcgill.ca/~avis/C/lrs.html for lrs usage instructions */ /******************************************************************************/ /* This package contains the extended precision routines used by lrs and some other miscellaneous routines. It is based on gmp and this file is derived from lrsmp.h and lrslong.h */ #ifdef GMP #ifdef MGMP #include "mini-gmp.h" #else #include "gmp.h" #endif #elif defined(FLINT) #include "fmpz.h" #include "flint.h" #endif /***********/ /* defines */ /***********/ /* this is number of longwords. Increasing this won't cost you that much since only variables other than the A matrix are allocated this size. Changing affects running time in small but not very predictable ways. */ #define MAX_DIGITS 255L /* this is in decimal digits, you pay in memory if you increase this, unless you override by a line with digits n before the begin line of your file. */ #define DEFAULT_DIGITS 100L /* 64 bit machines */ #define MAXD 9223372036854775807L #define BASE 1000000000L #define FORMAT "%9.9u" #define BASE_DIG 9 #define INTSIZE 16L #define BIT "64bit" #define MAXINPUT 1000 /*max length of any input rational */ #define POS 1L #define NEG -1L #ifndef TRUE #define TRUE 1L #endif #ifndef FALSE #define FALSE 0L #endif #define ONE 1L #define TWO 2L #define ZERO 0L #ifdef MA #define suf(func) func##_gmp #else #define suf(func) func #endif #define atoaa suf(atoaa) #define atomp suf(atomp) #define comprod suf(comprod) #define divrat suf(divrat) #define lcm suf(lcm) #define linint suf(linint) #define linrat suf(linrat) #define lrs_alloc_mp_matrix suf(lrs_alloc_mp_matrix) #define lrs_alloc_mp_vector suf(lrs_alloc_mp_vector) #define lrs_clear_mp_matrix suf(lrs_clear_mp_matrix) #define lrs_clear_mp_vector suf(lrs_clear_mp_vector) #define lrs_getdigits suf(lrs_getdigits) #define lrs_mp_init suf(lrs_mp_init) #define lrs_overflow suf(lrs_overflow) #define mulrat suf(mulrat) #define myrandom suf(myrandom) #define notimpl suf(notimpl) #define pmp suf(pmp) #define prat suf(prat) #define cprat suf(cprat) #define cpmp suf(cpmp ) #define rattodouble suf(rattodouble) #define readmp suf(readmp) #define readrat suf(readrat) #define plrs_readrat suf(plrs_readrat) #define reduce suf(reduce) #define reducearray suf(reducearray) #define reduceint suf(reduceint) #define storesign suf(storesign) #define stringcpy suf(stringcpy) #define xcalloc suf(xcalloc) /**********************************/ /* MACROS */ /* dependent on mp implementation */ /**********************************/ #ifdef GMP #define addint(a, b, c) mpz_add((c),(a),(b)) #define changesign(a) mpz_neg((a),(a)) #define copy(a, b) mpz_set(a,b) #define decint(a, b) mpz_sub((a),(a),(b)) #define divint(a, b, c) mpz_tdiv_qr((c),(a),(a),(b)) #define exactdivint(a, b, c) mpz_divexact((c),(a),(b)) /*known there is no remainder */ #define getfactorial(a, b) mpz_fac_ui( (a), (b)) #define mpcmp(a,b) mpz_cmp((a),(b)) #define mp_greater(a, b) (mpz_cmp((a),(b))>0 ? ONE : ZERO) #define mp_equal(a, b) (mpz_cmp((a),(b))==0 ? ONE : ZERO) #define gcd(a,b) mpz_gcd((a),(a),(b)) #define itomp(in, a) mpz_set_si( (a) , (in) ) #define mptoi(a) mpz_get_si( (a) ) #define mptodouble(a) mpz_get_d ( (a) ) #define mpgetstr10(a,c) mpgetstr(a,10,c) #define mpgetstr(a,b,c) mpz_get_str((a),(b),(c)) #ifndef PLRS #define mpoutstr(a,b,c) mpz_out_str((a),(b),(c)) #else #define mpoutstr(a,b,c) \ {\ char *tmp = mpz_get_str(NULL,10,c);\ fprintf(lrs_ofp, "%s", tmp);\ free(tmp);\ } #endif #define mulint(a, b, c) mpz_mul((c),(a),(b)) #define mului(a, b, c) mpz_mul_ui((a),(b),(c)) #define one(a) (mpz_cmp_si((a),ONE) == 0 ? ONE : ZERO) #define negative(a) (mpz_sgn(a) < 0 ? ONE : ZERO) #define normalize(a) (void) 0 #define positive(a) (mpz_sgn(a) > 0 ? ONE : ZERO) #define sign(a) (mpz_sgn(a) < 0 ? NEG : POS) #define subint(a, b, c) mpz_sub((c),(a),(b)) #define zero(a) (mpz_sgn(a) == 0 ? ONE : ZERO) #elif defined(FLINT) #define addint(a, b, c) fmpz_add((c),(a),(b)) #define changesign(a) fmpz_neg((a),(a)) #define copy(a, b) fmpz_set(a,b) #define decint(a, b) fmpz_sub((a),(a),(b)) #define divint(a, b, c) fmpz_tdiv_qr((c),(a),(a),(b)) #define exactdivint(a, b, c) fmpz_divexact((c),(a),(b)) /*known there is no remainder */ #define getfactorial(a, b) fmpz_fac_ui( (a), (b)) #define mpcmp(a,b) fmpz_cmp((a),(b)) #define mp_greater(a, b) (fmpz_cmp((a),(b))>0 ? ONE : ZERO) #define gcd(a,b) fmpz_gcd((a),(a),(b)) #define itomp(in, a) fmpz_set_si( (a) , (in) ) #define mptoi(a) fmpz_get_si( (a) ) #define mptodouble(a) fmpz_get_d ( (a) ) #define mpgetstr10(a,c) mpgetstr(a,10,c) #define mpgetstr(a,b,c) fmpz_get_str((a),(b),(c)) #define mpoutstr(a,b,c) fmpz_fprint((a),(c)) /* had a (b) */ #define mulint(a, b, c) fmpz_mul((c),(a),(b)) #define mului(a, b, c) fmpz_mul_ui((a),(b),(c)) #define one(a) (fmpz_cmp_si((a),ONE) == 0 ? ONE : ZERO) #define negative(a) (fmpz_sgn(a) < 0 ? ONE : ZERO) #define normalize(a) (void) 0 #define positive(a) (fmpz_sgn(a) > 0 ? ONE : ZERO) #define sign(a) (fmpz_sgn(a) < 0 ? NEG : POS) #define subint(a, b, c) fmpz_sub((c),(a),(b)) #define zero(a) (fmpz_sgn(a) == 0 ? ONE : ZERO) #endif /* * convert between decimal and machine (longword digits). Notice lovely * implementation of ceiling function :-) */ #define DEC2DIG(d) ( (d) % BASE_DIG ? (d)/BASE_DIG+1 : (d)/BASE_DIG) #define DIG2DEC(d) ((d)*BASE_DIG) #ifndef OMIT_SIGNALS #include #include /* labs */ #include #define errcheck(s,e) if ((long)(e)==-1L){ perror(s);exit(1);} #endif #define CALLOC(n,s) xcalloc(n,s,__LINE__,__FILE__) /*************/ /* typedefs */ /*************/ #ifdef GMP typedef mpz_t lrs_mp; /* type lrs_mp holds one long integer */ typedef mpz_t lrs_mp_t; /* for GMP same as lrs_mp for MP *lrs_mp */ typedef mpz_t *lrs_mp_vector; typedef mpz_t **lrs_mp_matrix; #elif defined(FLINT) typedef fmpz_t lrs_mp; /* type lrs_mp holds one long integer */ typedef fmpz_t lrs_mp_t; /* for GMP same as lrs_mp for MP *lrs_mp */ typedef fmpz_t *lrs_mp_vector; typedef fmpz_t **lrs_mp_matrix; #endif /*********************/ /*global variables */ /*********************/ extern long lrs_digits; /* max permitted no. of digits */ extern long lrs_record_digits; /* this is the biggest acheived so far. */ #include extern FILE *lrs_ifp; /* input file pointer */ extern FILE *lrs_ofp; /* output file pointer */ /*********************************************************/ /* Initialization and allocation procedures - must use! */ /******************************************************* */ long lrs_mp_init (long dec_digits, FILE * lrs_ifp, FILE * lrs_ofp); /* max number of decimal digits, fps */ #ifdef GMP #define lrs_alloc_mp(a) (mpz_init (a) ) #define lrs_clear_mp(a) (mpz_clear (a) ) #elif defined(FLINT) #define lrs_alloc_mp(a) (fmpz_init (a) ) #define lrs_clear_mp(a) (fmpz_clear (a) ) #endif lrs_mp_vector lrs_alloc_mp_vector (long n); /* allocate lrs_mp_vector for n+1 lrs_mp numbers */ lrs_mp_matrix lrs_alloc_mp_matrix (long m, long n); /* allocate lrs_mp_matrix for m+1 x n+1 lrs_mp */ void lrs_clear_mp_vector (lrs_mp_vector p, long n); /* clear lrs_mp_vector for n+1 lrs_mp numbers */ void lrs_clear_mp_matrix (lrs_mp_matrix p, long m, long n); /* clear m by n lrs_mp_matrix */ /*********************************************************/ /* Core library functions - depend on mp implementation */ /******************************************************* */ void atomp (const char s[], lrs_mp a); /* convert string to lrs_mp integer */ long compare (lrs_mp a, lrs_mp b); /* a ? b and returns -1,0,1 for <,=,> */ void linint (lrs_mp a, long ka, lrs_mp b, long kb); /* compute a*ka+b*kb --> a */ #ifdef MPLRS long plrs_readrat (lrs_mp Na, lrs_mp Da, const char * rat); /* take a rational number and convert to lrs_mp */ #endif char *cprat(const char *name, lrs_mp Nt, lrs_mp Dt); /* mp rat to char */ char *cpmp(const char *name, lrs_mp Nt); /* mp int to char */ void pmp (const char *name, lrs_mp a); /* print the long precision integer a */ void prat (const char *name, lrs_mp Nt, lrs_mp Dt); /* reduce and print Nt/Dt */ void readmp (lrs_mp a); /* read an integer and convert to lrs_mp */ long readrat (lrs_mp Na, lrs_mp Da); /* read a rational or int and convert to lrs_mp */ void reduce (lrs_mp Na, lrs_mp Da); /* reduces Na Da by gcd(Na,Da) */ void storesign(lrs_mp Na, long sa); /* change sign of Na to sa=POS/NEG */ /*********************************************************/ /* Standard arithmetic & misc. functions */ /* should be independent of mp implementation */ /******************************************************* */ void atoaa (const char in[], char num[], char den[]); /* convert rational string in to num/den strings */ long atos (char s[]); /* convert s to integer */ long comprod (lrs_mp Na, lrs_mp Nb, lrs_mp Nc, lrs_mp Nd); /* +1 if Na*Nb > Nc*Nd,-1 if Na*Nb > Nc*Nd else 0 */ void divrat (lrs_mp Na, lrs_mp Da, lrs_mp Nb, lrs_mp Db, lrs_mp Nc, lrs_mp Dc); /* computes Nc/Dc = (Na/Da) /( Nb/Db ) and reduce */ void linrat (lrs_mp Na, lrs_mp Da, long ka, lrs_mp Nb, lrs_mp Db, long kb, lrs_mp Nc, lrs_mp Dc); void lcm (lrs_mp a, lrs_mp b); /* a = least common multiple of a, b; b is saved */ void mulrat (lrs_mp Na, lrs_mp Da, lrs_mp Nb, lrs_mp Db, lrs_mp Nc, lrs_mp Dc); /* computes Nc/Dc=(Na/Da)*(Nb/Db) and reduce */ long myrandom (long num, long nrange); /* return a random number in range 0..nrange-1 */ void notimpl (const char *s); /* bail out - help! */ void rattodouble (lrs_mp a, lrs_mp b, double *x); /* convert lrs_mp rational to double */ void reduceint (lrs_mp Na, lrs_mp Da); /* divide Na by Da and return it */ void reducearray (lrs_mp_vector p, long n); /* find gcd of p[0]..p[n-1] and divide through by */ void scalerat (lrs_mp Na, lrs_mp Da, long ka); /* scales rational by ka */ /**********************************/ /* Miscellaneous functions */ /******************************** */ void lrs_getdigits (long *a, long *b); /* send digit information to user */ void stringcpy (char *s, char *t); /* copy t to s pointer version */ #ifndef __STDC__ void *calloc (); void *malloc (); #endif void *xcalloc (long n, long s, long l, const char *f); void lrs_default_digits_overflow (); void lrs_exit(int i); void lrs_overflow(int parm); /* should never be called */ /* end of lrsgmp.h (vertex enumeration using lexicographic reverse search) */ lrslib-073/lrsarith-011/lrslong.c0000777000175000017500000003377414625766601015357 0ustar avisavis/* lrslong.c library code for lrs extended precision arithmetic */ /* Version 4.0, April 13, 2000 */ /* Copyright: David Avis 1999, avis@cs.mcgill.ca */ /* Derived from prs_single.c ( rational arithmetic for lrs and prs) */ /* authored by Ambros Marzetta Revision 1.2 1998/05/27 */ #include #include #include #include #include "lrslong.h" long lrs_digits; /* max permitted no. of digits */ long lrs_record_digits; /* this is the biggest acheived so far. */ #if defined(B128) && !defined(CONS) __int128 MAXDm,MAXDl,MAXDa; #endif #define MAXINPUT 1000 /*max length of any input rational */ /* lrs_overflow routine should user supplied if not using lrslib.c */ /* void lrs_overflow(int parm) { } */ void gcd (lrs_mp u, lrs_mp v) /* Returns u=gcd(u,v) using classic Euclid's algorithm. v is destroyed. Knuth, II, p.320 */ { #ifndef B128 unsigned long long ul, vl, r; ul = llabs (*u); vl = llabs (*v); #else __int128 ul, vl, r; ul = abs128 (*u); vl = abs128 (*v); #endif if (ul == 0) { *u = vl; return; } while (vl != 0) { r= ul % vl; ul = vl; vl = r; } *u = ul; } /* gcd */ void lcm (lrs_mp a, lrs_mp b) /* a = least common multiple of a, b; b is preserved */ { lrs_mp u, v; copy (u, a); copy (v, b); gcd (u, v); exactdivint (a, u, v); /* v=a/u a contains remainder = 0 */ mulint (v, b, a); } /* end of lcm */ /***************************************************************/ /* */ /* Package of routines for rational arithmetic */ /* (Built on top of package for multiprecision arithmetic */ /* */ /***************************************************************/ void reduce (lrs_mp Na, lrs_mp Da) /* reduces Na/Da by gcd(Na,Da) */ { lrs_mp Nb, Db, Nc, Dc; copy (Nb, Na); copy (Db, Da); storesign (Nb, POS); storesign (Db, POS); copy (Nc, Na); copy (Dc, Da); gcd (Nb, Db); /* Nb is the gcd(Na,Da) */ exactdivint (Nc, Nb, Na); exactdivint (Dc, Nb, Da); } void reduceint (lrs_mp Na, lrs_mp Da) /* divide Na by Da and return */ { lrs_mp Temp; copy (Temp, Na); exactdivint (Temp, Da, Na); } long comprod (lrs_mp Na, lrs_mp Nb, lrs_mp Nc, lrs_mp Nd) /* +1 if Na*Nb > Nc*Nd */ /* -1 if Na*Nb < Nc*Nd */ /* 0 if Na*Nb = Nc*Nd */ { lrs_mp mc, md; itomp(ZERO,mc); itomp(ZERO,md); /*just to please some compilers */ mulint (Na, Nb, mc); mulint (Nc, Nd, md); if (mp_greater(mc,md)) return (1); if (mp_greater(md,mc)) return (-1); return (0); } void linrat (lrs_mp Na, lrs_mp Da, long ka, lrs_mp Nb, lrs_mp Db, long kb, lrs_mp Nc, lrs_mp Dc) /* computes Nc/Dc = ka*Na/Da +kb* Nb/Db and reduces answer by gcd(Nc,Dc) */ { lrs_mp c; itomp(ZERO,c); /*just to please some compilers */ mulint (Na, Db, Nc); mulint (Da, Nb, c); linint (Nc, ka, c, kb); /* Nc = (ka*Na*Db)+(kb*Da*Nb) */ mulint (Da, Db, Dc); /* Dc = Da*Db */ reduce (Nc, Dc); } void divrat (lrs_mp Na, lrs_mp Da, lrs_mp Nb, lrs_mp Db, lrs_mp Nc, lrs_mp Dc) /* computes Nc/Dc = (Na/Da) / ( Nb/Db ) and reduces answer by gcd(Nc,Dc) */ { mulint (Na, Db, Nc); mulint (Da, Nb, Dc); reduce (Nc, Dc); } void mulrat (lrs_mp Na, lrs_mp Da, lrs_mp Nb, lrs_mp Db, lrs_mp Nc, lrs_mp Dc) /* computes Nc/Dc = Na/Da * Nb/Db and reduces answer by gcd(Nc,Dc) */ { mulint (Na, Nb, Nc); mulint (Da, Db, Dc); reduce (Nc, Dc); } /***************************************************************/ /* */ /* Conversion and I/O functions */ /* */ /***************************************************************/ void atomp (const char *s, lrs_mp a) /*convert string to lrs_mp integer */ /* based on atoi KR p.58 */ { long diff, ten, i, sig; lrs_mp mpone; itomp (ONE, mpone); ten = 10L; for (i = 0; s[i] == ' ' || s[i] == '\n' || s[i] == '\t'; i++); /*skip white space */ sig = POS; if (s[i] == '+' || s[i] == '-') /* sign */ sig = (s[i++] == '+') ? POS : NEG; itomp (0L, a); while (s[i] >= '0' && s[i] <= '9') { diff = s[i] - '0'; linint (a, ten, mpone, diff); i++; } storesign (a, sig); if (s[i]) { fprintf (stderr, "\nIllegal character in number: '%s'\n", s + i); exit (1); } } /* end of atomp */ void atoaa (const char *in, char *num, char *den) /* convert rational string in to num/den strings */ { long i, j; for (i = 0; in[i] != '\0' && in[i] != '/'; i++) num[i] = in[i]; num[i] = '\0'; den[0] = '\0'; if (in[i] == '/') { for (j = 0; in[j + i + 1] != '\0'; j++) den[j] = in[i + j + 1]; den[j] = '\0'; } } /* end of atoaa */ void mptodouble (lrs_mp a, double *x) /* convert lrs_mp to double */ { (*x) = (*a); } long mptoi (lrs_mp a) /* convert lrs_mp to long */ { return (*a); } /* return char * representation of a in base 10. * use out if non-NULL, otherwise allocate and return. */ char *mpgetstr10(char *out, lrs_mp a) { char *buf=NULL; #ifndef B128 int len=0; len = snprintf(buf, 0, "%lld", *a); if (out != NULL) buf = out; else buf = malloc(sizeof(char)*(len+1)); sprintf(buf, "%lld", *a); return buf; #else __int128 tmp=abs128(*a); int i,j=0; int t[41]; if (out != NULL) buf = out; else buf = calloc(43, sizeof(char)); if (*a>=LLONG_MIN && *a<=LLONG_MAX) { sprintf(buf, "%lld", (long long)*a); return buf; } for (i=0; tmp>0; i++) { t[i] = tmp%10; tmp = tmp / 10; } i--; if (*a<0) buf[j++]='-'; while (i>=0) buf[j++] = '0'+t[i--]; return buf; #endif } void rattodouble (lrs_mp a, lrs_mp b, double *x) /* convert lrs_mp rati onal to double */ { double y; mptodouble (a, &y); mptodouble (b, x); *x = y / (*x); } long readrat (lrs_mp Na, lrs_mp Da) /* read a rational or integer and convert to lrs_mp */ /* returns true if denominator is not one */ { char in[MAXINPUT], num[MAXINPUT], den[MAXINPUT]; if((fscanf (lrs_ifp, "%s", in)==EOF) || (strcmp("end",in)==0)) { fprintf (lrs_ofp, "\n**Invalid input: check you have entered enough data!\n"); exit(1); } if(!strcmp(in,"end")) /*premature end of input file */ { return (999L); } atoaa (in, num, den); /*convert rational to num/dem strings */ atomp (num, Na); if (den[0] == '\0') { itomp (1L, Da); return (FALSE); } atomp (den, Da); return (TRUE); } /* read a rational or integer and convert to lrs_mp with base BASE */ /* returns true if denominator is not one */ long plrs_readrat (lrs_mp Na, lrs_mp Da, const char* rat) { char in[MAXINPUT], num[MAXINPUT], den[MAXINPUT]; strcpy(in, rat); atoaa (in, num, den); /*convert rational to num/dem strings */ atomp (num, Na); if (den[0] == '\0') { itomp (1L, Da); return (FALSE); } atomp (den, Da); return (TRUE); } void readmp (lrs_mp a) /* read an integer and convert to lrs_mp */ { long in; if(fscanf (lrs_ifp, "%ld", &in)==EOF) { fprintf (lrs_ofp, "\n**Invalid integer input"); exit(1); } itomp (in, a); } char *cprat (const char *name, lrs_mp Nin, lrs_mp Din) { char *num, *den, *ret; unsigned long len; lrs_mp Nt, Dt; lrs_alloc_mp (Nt); lrs_alloc_mp (Dt); copy (Nt, Nin); copy (Dt, Din); reduce (Nt, Dt); num = mpgetstr10(NULL, Nt); den = mpgetstr10(NULL, Dt); len = snprintf(NULL, 0, " %s %s/%s", name, num, den); ret = (char*)malloc(sizeof(char)*(len+1)); if(one(Dt)) { if (sign (Nt) != NEG) sprintf(ret, "%s %s", name, num); else sprintf(ret, "%s%s", name, num); } else { if (sign (Nt) != NEG) sprintf(ret, "%s %s/%s", name, num, den); else sprintf(ret, "%s%s/%s", name, num, den); } free(num); free(den); lrs_clear_mp(Nt); lrs_clear_mp(Dt); return ret; } char *cpmp (const char *name, lrs_mp Nin) { char *num, *ret; unsigned long len; num = mpgetstr10(NULL, Nin); len = snprintf(NULL, 0, "%s %s", name, num); ret = (char*)malloc(sizeof(char)*(len+1)); if (sign (Nin) != NEG) sprintf(ret, "%s %s", name, num); else sprintf(ret, "%s%s", name, num); free(num); return ret; } void pmp (const char *name, lrs_mp Nt) { fprintf (lrs_ofp, "%s", name); if (sign (Nt) != NEG) fprintf (lrs_ofp, " "); #ifndef B128 fprintf (lrs_ofp, "%lld", *Nt); #else char buf[41]={0}; __int128 tmp=abs128(*Nt); int c; int i; if (*Nt>=LLONG_MIN && *Nt<=LLONG_MAX) { fprintf (lrs_ofp, "%lld ", (long long)*Nt); return; } if (*Nt<0) putc('-', lrs_ofp); for (i=0; tmp>0; i++) { buf[i] = tmp%10; tmp = tmp / 10; } i--; while (i>=0) { c='0'+buf[i--]; putc(c, lrs_ofp); } #endif putc(' ', lrs_ofp); } void prat (const char *name, lrs_mp Nin, lrs_mp Din) /*print the long precision rational Nt/Dt */ { lrs_mp Nt, Dt; copy (Nt, Nin); copy (Dt, Din); reduce (Nt, Dt); if (sign (Nt) != NEG) fprintf (lrs_ofp, " "); #ifndef B128 fprintf (lrs_ofp, "%s%lld", name, *Nt); if (*Dt != 1) fprintf (lrs_ofp, "/%lld", *Dt); #else { char *Nc, *Dc; Nc = mpgetstr10(NULL, Nt); fprintf(lrs_ofp, "%s%s", name, Nc); free(Nc); if (*Dt != 1) { Dc = mpgetstr10(NULL, Dt); fprintf(lrs_ofp, "/%s", Dc); free(Dc); } } #endif fprintf (lrs_ofp, " "); } /* prat */ /***************************************************************/ /* */ /* Memory allocation functions */ /* */ /***************************************************************/ lrs_mp_t lrs_alloc_mp_t () /* dynamic allocation of lrs_mp number */ { lrs_mp_t p; p=(lrs_mp_t)calloc (1, sizeof (lrs_mp)); return p; } lrs_mp_vector lrs_alloc_mp_vector (long n) /* allocate lrs_mp_vector for n+1 lrs_mp numbers */ { lrs_mp_vector p; long i; p = (lrs_mp_t *) CALLOC ((n + 1), sizeof (lrs_mp_t)); for (i = 0; i <= n; i++) p[i] = (lrs_mp_t) CALLOC (1, sizeof (lrs_mp)); return p; } void lrs_clear_mp_vector (lrs_mp_vector p, long n) /* free space allocated to p */ { long i; for (i = 0; i <= n; i++) free (p[i]); free (p); p=NULL; } lrs_mp_matrix lrs_alloc_mp_matrix (long m, long n) /* allocate lrs_mp_matrix for m+1 x n+1 lrs_mp numbers */ { lrs_mp_matrix a; lrs_mp_t araw; int mp_width, row_width; int i, j; mp_width = lrs_digits + 1; row_width = (n + 1) * mp_width; araw = (lrs_mp_t) calloc ((m + 1) * row_width, sizeof (lrs_mp)); a = (lrs_mp_t **) calloc ((m + 1), sizeof (lrs_mp_vector)); for (i = 0; i < m + 1; i++) { a[i] = (lrs_mp_t *) calloc ((n + 1), sizeof (lrs_mp_t)); for (j = 0; j < n + 1; j++) a[i][j] = (araw + i * row_width + j * mp_width); } return a; } void lrs_clear_mp_matrix (lrs_mp_matrix p, long m, long n) /* free space allocated to lrs_mp_matrix p */ { long i; /* p[0][0] is araw, the actual matrix storage address */ free(p[0][0]); for (i = 0; i < m + 1; i++) free (p[i]); /* 2015.9.9 memory leak fix */ free(p); p=NULL; } void lrs_getdigits (long *a, long *b) { /* send digit information to user */ *a = DIG2DEC (ZERO); *b = DIG2DEC (ZERO); return; } void * xcalloc (long n, long s, long l, const char *f) { void *tmp; tmp = calloc (n, s); if (tmp == 0) { char buf[200]; sprintf (buf, "\n\nFatal error on line %ld of %s", l, f); perror (buf); exit (1); } return tmp; } long lrs_mp_init (long dec_digits, FILE * fpin, FILE * fpout) /* max number of decimal digits for the computation */ /* long int version */ { #ifndef PLRS lrs_ifp = fpin; lrs_ofp = fpout; #endif #ifdef B128 #ifndef CONS MAXDl=9223372036854775807L; /* 2^63 - 1 */ MAXDa=MAXDl*MAXDl; /* should be 2^126 - 1 */ MAXDm=3611622602L; /* sqrt(sqrt( 2^127 -1 )) */ MAXDm=MAXDm*MAXDm+6000000000; /* too big to initialize directly */ #endif #endif lrs_record_digits = 0; lrs_digits = 0; /* max permitted no. of digits */ return TRUE; } void notimpl (const char *s) { fflush (stdout); fprintf (stderr, "\nAbnormal Termination %s\n", s); exit (1); } /***************************************************************/ /* */ /* Misc. functions */ /* */ /***************************************************************/ void reducearray (lrs_mp_vector p, long n) /* find largest gcd of p[0]..p[n-1] and divide through */ { lrs_mp divisor; lrs_mp Temp; long i = 0L; while ((i < n) && zero (p[i])) i++; if (i == n) return; copy (divisor, p[i]); storesign (divisor, POS); i++; while (i < n) { if (!zero (p[i])) { copy (Temp, p[i]); storesign (Temp, POS); gcd (divisor, Temp); } i++; } /* reduce by divisor */ for (i = 0; i < n; i++) if (!zero (p[i])) reduceint (p[i], divisor); } /* end of reducearray */ long myrandom (long num, long nrange) /* return a random number in range 0..nrange-1 */ { long i; i = (num * 401 + 673) % nrange; return (i); } void getfactorial (lrs_mp factorial, long k) /* compute k factorial in lrs_mp */ { lrs_mp temp; long i; itomp (ONE, factorial); for (i = 2; i <= k; i++) { itomp (i, temp); mulint (temp, factorial, factorial); } } /* end of getfactorial */ void stringcpy (char *s, char *t) /*copy t to s pointer version */ { while (((*s++) = (*t++)) != '\0'); } lrslib-073/lrsarith-011/lrslong.h0000777000175000017500000003545614625766601015363 0ustar avisavis/* lrslong.h (lrs long integer arithmetic library */ /* Copyright: David Avis 2000, avis@cs.mcgill.ca */ /* Version 4.0, February 17, 2000 */ /* Version 4.1, November 15, 2020 for bigger mulint range */ /* This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA. */ /******************************************************************************/ /* See http://cgm.cs.mcgill.ca/~avis/C/lrs.html for lrs usage instructions */ /******************************************************************************/ /* This package contains the extended precision routines used by lrs and some other miscellaneous routines. The maximum precision depends on the parameter MAX_DIGITS defined below, with usual default of 255L. This gives a maximum of 1020 decimal digits on 32 bit machines. The procedure lrs_mp_init(dec_digits) may set a smaller number of dec_digits, and this is useful if arrays or matrices will be used. */ /***********/ /* defines */ /***********/ /* this is number of longwords. Increasing this won't cost you that much since only variables other than the A matrix are allocated this size. Changing affects running time in small but not very predictable ways. */ #define MAX_DIGITS 255L /* this is in decimal digits, you pay in memory if you increase this, unless you override by a line with digits n before the begin line of your file. */ #define DEFAULT_DIGITS 100L /**********MACHINE DEPENDENT CONSTANTS***********/ /* MAXD is 2^(k-1)-1 where k is word size */ /* MAXDm is sqrt(2^(k-1)-1) where k is word size*/ /* MAXDl is 2^(k/2-1)-1 where k is word size */ /* MAXDa is 2^(k-2)-1 where k is word size */ /* MAXD must be at least 2*BASE^2 */ /* If BASE is 10^k, use "%k.ku" for FORMAT */ /* INTSIZE is number of bytes for integer */ /* 64/128 bit arithmetic */ /************************************************/ #ifdef B128 /* 128 bit machines */ /* compiler does not accept big constants! */ #ifdef CONS #define MAXDm 9223372036854775807LL /* 2^63 - 1 */ #define MAXDl 9223372036854775807LL /* should be 2^126 -1 but is 2^63 - 1 */ #define MAXDa 9223372036854775807LL /* should be 2^126 -1 but is 2^63 - 1 */ #else extern __int128 MAXDm,MAXDl,MAXDa; /* set correctly in lrs_mp_init in lrslong.c */ #endif /* max power of 10 fitting in signed int64 */ #define P10_INT64 1000000000000000000ULL #define MAXD 9223372036854775807LL /* should be 2^127 -1 but is 2^63 - 1 */ #define BASE 1000000000L #define FORMAT "%9.9u" #define BASE_DIG 9 #define INTSIZE 16L #define BIT "128bit" #else /* 64 bit machines */ #define MAXD 9223372036854775807LL /* 2^63 - 1 */ #define MAXDl 2147483647LL /* 2^31 - 1 */ #define MAXDm 3037000499LL /* sqrt(2^63 - 1) */ #define MAXDa 4611686018427387903LL /* 2^62 - 1 */ #define BASE 1000000000L #define FORMAT "%9.9u" #define BASE_DIG 9 #define INTSIZE 16L #define BIT "64bit" #endif #define MAXINPUT 1000 /*max length of any input rational */ #define POS 1L #define NEG -1L #ifndef TRUE #define TRUE 1L #endif #ifndef FALSE #define FALSE 0L #endif #define ONE 1L #define TWO 2L #define ZERO 0L /**********************************/ /* MACROS */ /* dependent on mp implementation */ /**********************************/ #ifdef SAFE /* lazy but fast overflow checking */ #define mpsafem(a,b) *(a)>MAXDm||*(b)>MAXDm||*(a)<-MAXDm||*(b)<-MAXDm #define mpsafel(a,b) *(a)>MAXDl||*(b)>MAXDl||*(a)<-MAXDl||*(b)<-MAXDl #define mpsafea(a,b) *(a)>MAXDa||*(b)>MAXDa||*(a)<-MAXDa||*(b)<-MAXDa #ifdef DEBUG #define mperrorm(a,b) fprintf(stdout," : max(|a|,|b|) > %ld\n",MAXDm);lrs_overflow(1) #define mperrorl(a,b) fprintf(stdout," : max(|a|,|b|) > %ld\n",MAXDl);lrs_overflow(1) #define mperrora(a,b) fprintf(stdout," : max(|a|,|b|) > %ld\n",MAXDa);lrs_overflow(1) #define linint(a, ka, b, kb) {if( mpsafel(a,b) ) {fprintf(stdout, "\n*linint ");mperrorl(a,b);} else *(a) = *(a) * ka + *(b) * kb;} #define mulint(a, b, c) {if( mpsafem(a,b) ) {fprintf(stdout, "\n*mulint ");mperrorm(a,b);} else *(c) = *(a) * *(b);} #define addint(a, b, c) {if( mpsafea(a,b) ) {fprintf(stdout, "\n*addint ");mperrora(a,b);} else *(c) = *(a) + *(b);} #define subint(a, b, c) {if( mpsafea(a,b) ) {fprintf(stdout, "\n*subint ");mperrora(a,b);} else *(c) = *(a) - *(b);} #define decint(a, b) {if( mpsafea(a,b) ) {fprintf(stdout, "\n*decint ");mperrora(a,b);} else *(a) = *(a) - *(b);} #define qpiv(a,b,c,d,e) {if( mpsafel(a,b)|| mpsafel(c,d)){fprintf(stdout, "\n*qpiv ");mperrorl(a,b); mperrorl(c,d);} ; else *(a) =(*(a) * *(b) - *(c) * *(d))/ (*e);} #else #define qpiv(a,b,c,d,e) {if( mpsafel(a,b)|| mpsafel(c,d)) lrs_overflow(1) ; else *(a) =(*(a) * *(b) - *(c) * *(d))/ (*e);} #define linint(a, ka, b, kb) {if( mpsafel(a,b) ) lrs_overflow(1) ; else *(a) = *(a) * ka + *(b) * kb;} #define mulint(a, b, c) {if( mpsafem(a,b) ) lrs_overflow(1) ; else *(c) = *(a) * *(b);} #define addint(a, b, c) {if( mpsafea(a,b) ) lrs_overflow(1) ; else *(c) = *(a) + *(b);} #define subint(a, b, c) {if( mpsafea(a,b) ) lrs_overflow(1) ; else *(c) = *(a) - *(b);} #define decint(a, b) {if( mpsafea(a,b) ) lrs_overflow(1) ; else *(a) = *(a) - *(b);} #endif #else /* unprotected routines */ #define qpiv(a,b,c,d,e) *(a) =(*(a) * *(b) - *(c) * *(d))/ (*e) #define addint(a, b, c) *(c) = *(a) + *(b) #define subint(a, b, c) *(c) = *(a) - *(b) #define linint(a, ka, b, kb) *(a) = *(a) * ka + *(b) * kb #define mulint(a, b, c) *(c) = *(a) * *(b) #endif // #define unchecked_decint(a, b) *(a) = *(a) - *(b) /* v.7.1 only safe if a,b come from mulint */ #define unchecked_decint(a, b) decint(a, b) /* v 7.2 has larger range for mulint */ #define divint(a, b, c) {*(c) = *(a) / *(b); *(a) = *(a) % *(b);} #define exactdivint(a,b,c) *(c) = *(a) / *(b); #define abs128(a) (a>0? a : -1*a) #define changesign(a) (*(a) = - *(a)) #define copy(a, b) ((a)[0] = (b)[0]) #define mp_greater(a, b) (*(a) > *(b) ) #define mp_equal(a, b) (*(a) == *(b) ) #define itomp(in, a) *(a) = in #define one(a) (*(a) == 1) #define negative(a) (*(a) < 0) #define normalize(a) (void) 0 #define positive(a) (*(a) > 0) #define sign(a) (*(a) < 0 ? NEG : POS) #ifndef B128 #define storesign(a, sa) (*(a) = llabs(*(a)) * sa) #else #define storesign(a, sa) (*(a) = abs128(*(a)) * sa) #endif #define zero(a) (*(a) == 0) /* * convert between decimal and machine (longword digits). Notice lovely * implementation of ceiling function :-) */ #define DEC2DIG(d) ( (d) % BASE_DIG ? (d)/BASE_DIG+1 : (d)/BASE_DIG) #define DIG2DEC(d) ((d)*BASE_DIG) #ifndef OMIT_SIGNALS #include #include /* llabs */ #include #define errcheck(s,e) if ((long)(e)==-1L){ perror(s);exit(1);} #endif #define CALLOC(n,s) xcalloc(n,s,__LINE__,__FILE__) /*************/ /* typedefs */ /*************/ #ifndef B128 typedef long long lrs_mp[1]; /* type lrs_mp holds one long integer */ typedef long long *lrs_mp_t; typedef long long **lrs_mp_vector; typedef long long ***lrs_mp_matrix; #else typedef __int128 lrs_mp[1]; /* type lrs_mp holds one 128-bit integer */ typedef __int128 *lrs_mp_t; typedef __int128 **lrs_mp_vector; typedef __int128 ***lrs_mp_matrix; #endif /*********************/ /*global variables */ /*********************/ extern long lrs_digits; /* max permitted no. of digits */ extern long lrs_record_digits; /* this is the biggest acheived so far. */ extern FILE *lrs_ifp; /* input file pointer */ extern FILE *lrs_ofp; /* output file pointer */ /*********************************************************/ /* Initialization and allocation procedures - must use! */ /******************************************************* */ //void mulint(lrs_mp a, lrs_mp b, lrs_mp c); long lrs_mp_init (long dec_digits, FILE * lrs_ifp, FILE * lrs_ofp); /* max number of decimal digits, fps */ #define lrs_alloc_mp(a) #define lrs_clear_mp(a) lrs_mp_t lrs_alloc_mp_t(); /* dynamic allocation of lrs_mp */ lrs_mp_vector lrs_alloc_mp_vector (long n); /* allocate lrs_mp_vector for n+1 lrs_mp numbers */ lrs_mp_matrix lrs_alloc_mp_matrix (long m, long n); /* allocate lrs_mp_matrix for m+1 x n+1 lrs_mp */ void lrs_clear_mp_vector (lrs_mp_vector a, long n); void lrs_clear_mp_matrix (lrs_mp_matrix a, long m, long n); #ifndef MA #define suf(func) func #endif #ifdef MA #ifdef B128 #define suf(func) func##_2 #else #define suf(func) func##_1 #endif #endif #define atoaa suf(atoaa) #define atomp suf(atomp) #define comprod suf(comprod) #define divrat suf(divrat) #define gcd suf(gcd) #define getfactorial suf(getfactorial) #define lcm suf(lcm) #define linrat suf(linrat) #define lrs_alloc_mp_matrix suf(lrs_alloc_mp_matrix) #define lrs_alloc_mp_t suf(lrs_alloc_mp_t) #define lrs_alloc_mp_vector suf(lrs_alloc_mp_vector) #define lrs_clear_mp_matrix suf(lrs_clear_mp_matrix) #define lrs_clear_mp_vector suf(lrs_clear_mp_vector) #define lrs_digits suf(lrs_digits) #define lrs_getdigits suf(lrs_getdigits) #define lrs_overflow suf(lrs_overflow) #define lrs_mp_init suf(lrs_mp_init) #define lrs_record_digits suf(lrs_record_digits) #define mptodouble suf(mptodouble) #define mptoi suf(mptoi) #define mpgetstr10 suf(mpgetstr10) #define mulrat suf(mulrat) #define myrandom suf(myrandom) #define notimpl suf(notimpl) #define pmp suf(pmp) #define prat suf(prat) #define cprat suf(cprat) #define cpmp suf(cpmp) #define rattodouble suf(rattodouble) #define readmp suf(readmp) #define readrat suf(readrat) #define plrs_readrat suf(plrs_readrat) #define reduce suf(reduce) #define reducearray suf(reducearray) #define reduceint suf(reduceint) #define stringcpy suf(stringcpy) #define xcalloc suf(xcalloc) /*********************************************************/ /* Core library functions - depend on mp implementation */ /******************************************************* */ void atomp (const char s[], lrs_mp a); /* convert string to lrs_mp integer */ long compare (lrs_mp a, lrs_mp b); /* a ? b and returns -1,0,1 for <,=,> */ void gcd (lrs_mp u, lrs_mp v); /* returns u=gcd(u,v) destroying v */ void mptodouble (lrs_mp a, double *x); /* convert lrs_mp to double */ long mptoi (lrs_mp a); /* convert lrs_mp to long integer */ char *mpgetstr10(char *, lrs_mp); /* convert lrs_mp to string */ #ifdef MPLRS long plrs_readrat (lrs_mp Na, lrs_mp Da, const char * rat); /* take a rational number and convert to lrs_mp */ #endif char *cprat(const char *name, lrs_mp Nt, lrs_mp Dt); /* mp rat to char */ char *cpmp(const char *name, lrs_mp Nt); /* mp int to char */ void pmp (const char *name, lrs_mp a); /* print the long precision integer a */ void prat (const char *name, lrs_mp Nt, lrs_mp Dt); /* reduce and print Nt/Dt */ void readmp (lrs_mp a); /* read an integer and convert to lrs_mp */ long readrat (lrs_mp Na, lrs_mp Da); /* read a rational or int and convert to lrs_mp */ void reduce (lrs_mp Na, lrs_mp Da); /* reduces Na Da by gcd(Na,Da) */ /*********************************************************/ /* Standard arithmetic & misc. functions */ /* should be independent of mp implementation */ /******************************************************* */ void atoaa (const char in[], char num[], char den[]); /* convert rational string in to num/den strings */ long atos (char s[]); /* convert s to integer */ long comprod (lrs_mp Na, lrs_mp Nb, lrs_mp Nc, lrs_mp Nd); /* +1 if Na*Nb > Nc*Nd,-1 if Na*Nb > Nc*Nd else 0 */ void divrat (lrs_mp Na, lrs_mp Da, lrs_mp Nb, lrs_mp Db, lrs_mp Nc, lrs_mp Dc); /* computes Nc/Dc = (Na/Da) /( Nb/Db ) and reduce */ void getfactorial (lrs_mp factorial, long k); /* compute k factorial in lrs_mp */ void linrat (lrs_mp Na, lrs_mp Da, long ka, lrs_mp Nb, lrs_mp Db, long kb, lrs_mp Nc, lrs_mp Dc); void lcm (lrs_mp a, lrs_mp b); /* a = least common multiple of a, b; b is saved */ void mulrat (lrs_mp Na, lrs_mp Da, lrs_mp Nb, lrs_mp Db, lrs_mp Nc, lrs_mp Dc); /* computes Nc/Dc=(Na/Da)*(Nb/Db) and reduce */ long myrandom (long num, long nrange); /* return a random number in range 0..nrange-1 */ void notimpl (const char *s); /* bail out - help! */ void rattodouble (lrs_mp a, lrs_mp b, double *x); /* convert lrs_mp rational to double */ void reduceint (lrs_mp Na, lrs_mp Da); /* divide Na by Da and return it */ void reducearray (lrs_mp_vector p, long n); /* find gcd of p[0]..p[n-1] and divide through by */ void scalerat (lrs_mp Na, lrs_mp Da, long ka); /* scales rational by ka */ /********************************/ /* Matrix and vector allocation */ /********************************/ void lrs_clear_mp_vector (lrs_mp_vector p, long n); lrs_mp_vector lrs_alloc_mp_vector(long n); void lrs_clear_mp_vector(lrs_mp_vector p, long n); lrs_mp_matrix lrs_alloc_mp_matrix(long m, long n); void lrs_clear_mp_matrix(lrs_mp_matrix p, long m, long n); long lrs_mp_init(long dec_digits, FILE *fpin, FILE *fpout); /* how big are numbers? */ extern long lrs_digits; /* max permitted no. of digits */ extern long lrs_record_digits; /* this is the biggest achieved so far. */ /**********************************/ /* Miscellaneous functions */ /******************************** */ void lrs_getdigits (long *a, long *b); /* send digit information to user */ void stringcpy (char *s, char *t); /* copy t to s pointer version */ #ifndef __STDC__ void *calloc (); void *malloc (); #endif void *xcalloc (long n, long s, long l, const char *f); void lrs_default_digits_overflow (); void lrs_exit(int i); void lrs_overflow(int i); /* end of lrs_long.h (vertex enumeration using lexicographic reverse search) */ lrslib-073/lrsarith-011/lrsmp.c0000777000175000017500000006046314625766601015027 0ustar avisavis/* lrsmp.c library code for lrs extended precision arithmetic */ /* Version 4.0c, August 26, 2009 */ /* minor change to check result of fscanf */ /* Copyright: David Avis 1999, avis@cs.mcgill.ca */ /* This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA. */ #include #include #include #include "lrsmp.h" long lrs_digits=DEC2DIG(DEFAULT_DIGITS); long lrs_record_digits; /* this is the biggest acheived so far. */ /******************************************************************/ /* digit overflow is caught by digits_overflow at the end of this */ /* file, make sure it is either user supplied or uncomment */ /* the define below */ /******************************************************************/ #define digits_overflow() lrs_default_digits_overflow() /*********************************************************/ /* Initialization and allocation procedures - must use! */ /******************************************************* */ long lrs_mp_init (long dec_digits, FILE * fpin, FILE * fpout) /* max number of decimal digits for the computation */ { /* global variables lrs_ifp and lrs_ofp are file pointers for input and output */ lrs_ifp = fpin; lrs_ofp = fpout; lrs_record_digits = 0; if (dec_digits <= 0) dec_digits = DEFAULT_DIGITS; lrs_digits = DEC2DIG (dec_digits); /* max permitted no. of digits */ printf("\ndec_digits=%ld lrs_digits=%ld\n",dec_digits,lrs_digits); if (lrs_digits > MAX_DIGITS) { lrs_digits = MAX_DIGITS; return FALSE; } return TRUE; } lrs_mp_t lrs_alloc_mp_t () /* dynamic allocation of lrs_mp number */ { lrs_mp_t p; p=(long long *)calloc (lrs_digits+1, sizeof (long long)); return p; } lrs_mp_vector lrs_alloc_mp_vector (long n) /* allocate lrs_mp_vector for n+1 lrs_mp numbers */ { lrs_mp_vector p; long i; p = (lrs_mp_vector) CALLOC ((n + 1), sizeof (lrs_mp *)); for (i = 0; i <= n; i++) p[i] = (long long int *)CALLOC (1, sizeof (lrs_mp)); return p; } void lrs_clear_mp_vector (lrs_mp_vector p, long n) /* free space allocated to p */ { long i; for (i=0; i<=n; i++) free (p[i] ); free (p); } lrs_mp_matrix lrs_alloc_mp_matrix (long m, long n) /* allocate lrs_mp_matrix for m+1 x n+1 lrs_mp numbers */ { lrs_mp_matrix a; long long *araw; int mp_width, row_width; int i, j; mp_width = lrs_digits + 1; row_width = (n + 1) * mp_width; araw = (long long int*)calloc ((m + 1) * row_width, sizeof (long long)); a = (lrs_mp_matrix) calloc ((m + 1), sizeof (lrs_mp_vector)); for (i = 0; i < m + 1; i++) { a[i] = (long long int **)calloc ((n + 1), sizeof (lrs_mp *)); for (j = 0; j < n + 1; j++) a[i][j] = (araw + i * row_width + j * mp_width); } return a; } void lrs_clear_mp_matrix (lrs_mp_matrix p, long m, long n) /* free space allocated to lrs_mp_matrix p */ { long i; /* p[0][0] is araw, the actual matrix storage address */ free(p[0][0]); for (i = 0; i < m + 1; i++) free (p[i]); free(p); } /*********************************************************/ /* Core library functions - depend on mp implementation */ /******************************************************* */ void copy (lrs_mp a, lrs_mp b) /* assigns a=b */ { long i; for (i = 0; i <= length (b); i++) a[i] = b[i]; } /********************************************************/ /* Divide two multiple precision integers (c=a/b). */ /* a is destroyed and contains the remainder on return. */ /* From Knuth Vol.2 SemiNumerical Algorithms */ /* coded by J. Quinn */ /********************************************************/ void divint (lrs_mp a, lrs_mp b, lrs_mp c) /* c=a/b, a contains remainder on return */ { long long cy, la, lb, lc, d1, s, t, sig; long long i, j, qh; /* figure out and save sign, do everything with positive numbers */ sig = sign (a) * sign (b); la = length (a); lb = length (b); lc = la - lb + 2; if (la < lb) { storelength (c, TWO); storesign (c, POS); c[1] = 0; normalize (c); return; } for (i = 1; i < lc; i++) c[i] = 0; storelength (c, lc); storesign (c, (sign (a) == sign (b)) ? POS : NEG); /******************************/ /* division by a single word: */ /* do it directly */ /******************************/ if (lb == 2) { cy = 0; t = b[1]; for (i = la - 1; i > 0; i--) { cy = cy * BASE + a[i]; a[i] = 0; cy -= (c[i] = cy / t) * t; } a[1] = cy; storesign (a, (cy == 0) ? POS : sign (a)); storelength (a, TWO); /* set sign of c to sig (**mod**) */ storesign (c, sig); normalize (c); return; } else { /* mp's are actually DIGITS+1 in length, so if length of a or b = */ /* DIGITS, there will still be room after normalization. */ /****************************************************/ /* Step D1 - normalize numbers so b > floor(BASE/2) */ d1 = BASE / (b[lb - 1] + 1); if (d1 > 1) { cy = 0; for (i = 1; i < la; i++) { cy = (a[i] = a[i] * d1 + cy) / BASE; a[i] %= BASE; } a[i] = cy; cy = 0; for (i = 1; i < lb; i++) { cy = (b[i] = b[i] * d1 + cy) / BASE; b[i] %= BASE; } b[i] = cy; } else { a[la] = 0; /* if la or lb = DIGITS this won't work */ b[lb] = 0; } /*********************************************/ /* Steps D2 & D7 - start and end of the loop */ for (j = 0; j <= la - lb; j++) { /*************************************/ /* Step D3 - determine trial divisor */ if (a[la - j] == b[lb - 1]) qh = BASE - 1; else { s = (a[la - j] * BASE + a[la - j - 1]); qh = s / b[lb - 1]; while (qh * b[lb - 2] > (s - qh * b[lb - 1]) * BASE + a[la - j - 2]) qh--; } /*******************************************************/ /* Step D4 - divide through using qh as quotient digit */ cy = 0; for (i = 1; i <= lb; i++) { s = qh * b[i] + cy; a[la - j - lb + i] -= s % BASE; cy = s / BASE; if (a[la - j - lb + i] < 0) { a[la - j - lb + i] += BASE; cy++; } } /*****************************************************/ /* Step D6 - adjust previous step if qh is 1 too big */ if (cy) { qh--; cy = 0; for (i = 1; i <= lb; i++) /* add a back in */ { a[la - j - lb + i] += b[i] + cy; cy = a[la - j - lb + i] / BASE; a[la - j - lb + i] %= BASE; } } /***********************************************************************/ /* Step D5 - write final value of qh. Saves calculating array indices */ /* to do it here instead of before D6 */ c[la - lb - j + 1] = qh; } /**********************************************************************/ /* Step D8 - unnormalize a and b to get correct remainder and divisor */ for (i = lc; c[i - 1] == 0 && i > 2; i--); /* strip excess 0's from quotient */ storelength (c, i); if (i == 2 && c[1] == 0) storesign (c, POS); cy = 0; for (i = lb - 1; i >= 1; i--) { cy = (a[i] += cy * BASE) % d1; a[i] /= d1; } for (i = la; a[i - 1] == 0 && i > 2; i--); /* strip excess 0's from quotient */ storelength (a, i); if (i == 2 && a[1] == 0) storesign (a, POS); if (cy){ fprintf (stdout, "divide error"); exit(1); } for (i = lb - 1; i >= 1; i--) { cy = (b[i] += cy * BASE) % d1; b[i] /= d1; } } } /* end of divint */ void gcd (lrs_mp u, lrs_mp v) /*returns u=gcd(u,v) destroying v */ /*Euclid's algorithm. Knuth, II, p.320 modified to avoid copies r=u,u=v,v=r Switches to single precision when possible for greater speed */ { lrs_mp r; unsigned long long ul, vl; long i; static unsigned long long maxspval = MAXD; /* Max value for the last digit to guarantee */ /* fitting into a single long integer. */ static long maxsplen; /* Maximum digits for a number that will fit */ /* into a single long integer. */ static long firstime = TRUE; if (firstime) /* initialize constants */ { for (maxsplen = 2; maxspval >= BASE; maxsplen++) maxspval /= BASE; firstime = FALSE; } if (mp_greater (v, u)) goto bigv; bigu: if (zero (v)) return; if ((i = length (u)) < maxsplen || (i == maxsplen && u[maxsplen - 1] < maxspval)) goto quickfinish; divint (u, v, r); normalize (u); bigv: if (zero (u)) { copy (u, v); return; } if ((i = length (v)) < maxsplen || (i == maxsplen && v[maxsplen - 1] < maxspval)) goto quickfinish; divint (v, u, r); normalize (v); goto bigu; /* Base 10000 only at the moment */ /* when u and v are small enough, transfer to single precision integers */ /* and finish with euclid's algorithm, then transfer back to lrs_mp */ quickfinish: ul = vl = 0; for (i = length (u) - 1; i > 0; i--) ul = BASE * ul + u[i]; for (i = length (v) - 1; i > 0; i--) vl = BASE * vl + v[i]; if (ul > vl) goto qv; qu: if (!vl) { for (i = 1; ul; i++) { u[i] = ul % BASE; ul = ul / BASE; } storelength (u, i); return; } ul %= vl; qv: if (!ul) { for (i = 1; vl; i++) { u[i] = vl % BASE; vl = vl / BASE; } storelength (u, i); return; } vl %= ul; goto qu; } long compare (lrs_mp a, lrs_mp b) /* a ? b and returns -1,0,1 for <,=,> */ { long i; if (a[0] > b[0]) return 1L; if (a[0] < b[0]) return -1L; for (i = length (a) - 1; i >= 1; i--) { if (a[i] < b[i]) { if (sign (a) == POS) return -1L; else return 1L; } if (a[i] > b[i]) { if (sign (a) == NEG) return -1L; else return 1L; } } return 0L; } long mp_greater (lrs_mp a, lrs_mp b) /* tests if a > b and returns (TRUE=POS) */ { long i; if (a[0] > b[0]) return (TRUE); if (a[0] < b[0]) return (FALSE); for (i = length (a) - 1; i >= 1; i--) { if (a[i] < b[i]) { if (sign (a) == POS) return (0); else return (1); } if (a[i] > b[i]) { if (sign (a) == NEG) return (0); else return (1); } } return (0); } void itomp (long in, lrs_mp a) /* convert integer i to multiple precision with base BASE */ { long i; a[0] = 2; /* initialize to zero */ for (i = 1; i < lrs_digits; i++) a[i] = 0; if (in < 0) { storesign (a, NEG); in = in * (-1); } i = 0; while (in != 0) { i++; a[i] = in - BASE * (in / BASE); in = in / BASE; storelength (a, i + 1); } } /* end of itomp */ void linint (lrs_mp a, long ka, lrs_mp b, long kb) /*compute a*ka+b*kb --> a */ /***Handbook of Algorithms and Data Structures P.239 ***/ { long i, la, lb; la = length (a); lb = length (b); for (i = 1; i < la; i++) a[i] *= ka; if (sign (a) != sign (b)) kb = (-kb); if (lb > la) { storelength (a, lb); for (i = la; i < lb; i++) a[i] = 0; } for (i = 1; i < lb; i++) a[i] += kb * b[i]; normalize (a); } /***end of linint***/ void mptodouble (lrs_mp a, double *x) /* convert lrs_mp to double */ { long i, la; double y = 1.0; (*x) = 0; la = length (a); for (i = 1; i < la; i++) { (*x) = (*x) + y * a[i]; y = y * BASE; } if (negative (a)) (*x)= -(*x); } void mulint (lrs_mp a, lrs_mp b, lrs_mp c) /* multiply two integers a*b --> c */ /***Handbook of Algorithms and Data Structures, p239 ***/ { long nlength, i, j, la, lb; /*** b and c may coincide ***/ la = length (a); lb = length (b); nlength = la + lb - 2; if (nlength > lrs_digits) digits_overflow (); for (i = 0; i < la - 2; i++) c[lb + i] = 0; for (i = lb - 1; i > 0; i--) { for (j = 2; j < la; j++) if ((c[i + j - 1] += b[i] * a[j]) > MAXD - (BASE - 1) * (BASE - 1) - MAXD / BASE) { c[i + j - 1] -= (MAXD / BASE) * BASE; c[i + j] += MAXD / BASE; } c[i] = b[i] * a[1]; } storelength (c, nlength); storesign (c, sign (a) == sign (b) ? POS : NEG); normalize (c); } /***end of mulint ***/ void normalize (lrs_mp a) { long long cy, i, la; la = length (a); start: cy = 0; for (i = 1; i < la; i++) { cy = (a[i] += cy) / BASE; a[i] -= cy * BASE; if (a[i] < 0) { a[i] += BASE; cy--; } } while (cy > 0) { a[i++] = cy % BASE; cy /= BASE; } if (cy < 0) { a[la - 1] += cy * BASE; for (i = 1; i < la; i++) a[i] = (-a[i]); storesign (a, sign (a) == POS ? NEG : POS); goto start; } while (a[i - 1] == 0 && i > 2) i--; if (i > lrs_record_digits) { if ((lrs_record_digits = i) > lrs_digits) digits_overflow (); }; storelength (a, i); if (i == 2 && a[1] == 0) storesign (a, POS); } /* end of normalize */ long length (lrs_mp a) { /* formerly a macro but conflicts with string length */ return ((a[0] > 0) ? a[0] : -a[0]); } long mptoi (lrs_mp a) /* convert lrs_mp to long integer */ { long len = length (a); if (len == 2) return sign (a) * a[1]; if (len == 3) return sign (a) * (a[1] + BASE * a[2]); notimpl ("mp to large for conversion to long"); return 0; /* never executed */ } /* untested */ char *mpgetstr10(char *out, lrs_mp a) { int len = 0; char *buf = NULL; int i; if (sign (a) == NEG) len++; len += snprintf(buf, 0, "%llu", a[length (a) -1]); for (i = length (a) - 2; i >= 1; i--) len +=snprintf(buf, 0, FORMAT, a[i]); if (out != NULL) buf = out; else buf = (char *)malloc(sizeof(char)*(len + 1)); len = 0; if (sign (a) == NEG) len++,sprintf(buf, "-"); len += sprintf(buf+len, "%llu", a[length (a) -1]); for (i = length (a) - 2; i >= 1; i--) len += sprintf(buf+len, FORMAT, a[i]); return buf; } char *cprat (const char *name, lrs_mp Nin, lrs_mp Din) { char *num, *den, *ret; unsigned long len; lrs_mp Nt, Dt; lrs_alloc_mp (Nt); lrs_alloc_mp (Dt); copy (Nt, Nin); copy (Dt, Din); reduce (Nt, Dt); num = mpgetstr10(NULL, Nt); den = mpgetstr10(NULL, Dt); len = snprintf(NULL, 0, " %s %s/%s", name, num, den); ret = (char*)malloc(sizeof(char)*(len+1)); if(one(Dt)) { if (sign (Nt) != NEG) sprintf(ret, "%s %s", name, num); else sprintf(ret, "%s%s", name, num); } else { if (sign (Nt) != NEG) sprintf(ret, " %s %s/%s", name, num, den); else sprintf(ret, "%s%s/%s", name, num, den); } free(num); free(den); lrs_clear_mp(Nt); lrs_clear_mp(Dt); return ret; } char *cpmp (const char *name, lrs_mp Nin) { char *num, *ret; unsigned long len; num = mpgetstr10(NULL, Nin); len = snprintf(NULL, 0, "%s %s", name, num); ret = (char*)malloc(sizeof(char)*(len+1)); if (sign (Nin) != NEG) sprintf(ret, "%s %s", name, num); else sprintf(ret, "%s%s", name, num); free(num); return ret; } /* char *cprat (const char *name, lrs_mp Nin, lrs_mp Din) { char *num, *den, *ret; unsigned long len; num = mpgetstr10(NULL, Nin); den = mpgetstr10(NULL, Din); len = snprintf(NULL, 0, "%s%s/%s", name, num, den); ret = (char*)malloc(sizeof(char)*(len+1)); sprintf(ret, "%s%s/%s", name, num, den); free(num); free(den); return ret; } */ void prat (const char *name, lrs_mp Nin, lrs_mp Din) /*reduce and print Nin/Din */ { lrs_mp Nt, Dt; long i; fprintf (lrs_ofp, "%s", name); /* reduce fraction */ copy (Nt, Nin); copy (Dt, Din); reduce (Nt, Dt); /* print out */ if (sign (Nin) * sign (Din) == NEG) fprintf (lrs_ofp, "-"); else fprintf (lrs_ofp, " "); fprintf (lrs_ofp, "%llu", Nt[length (Nt) - 1]); for (i = length (Nt) - 2; i >= 1; i--) fprintf (lrs_ofp, FORMAT, Nt[i]); if (!(Dt[0] == 2 && Dt[1] == 1)) /* rational */ { fprintf (lrs_ofp, "/"); fprintf (lrs_ofp, "%llu", Dt[length (Dt) - 1]); for (i = length (Dt) - 2; i >= 1; i--) fprintf (lrs_ofp, FORMAT, Dt[i]); } fprintf (lrs_ofp, " "); } void pmp (const char *name, lrs_mp a) /*print the long precision integer a */ { long i; fprintf (lrs_ofp, "%s", name); if (sign (a) == NEG) fprintf (lrs_ofp, "-"); else fprintf (lrs_ofp, " "); fprintf (lrs_ofp, "%llu", a[length (a) - 1]); for (i = length (a) - 2; i >= 1; i--) fprintf (lrs_ofp, FORMAT, a[i]); fprintf (lrs_ofp, " "); } long readrat (lrs_mp Na, lrs_mp Da) /* read a rational or integer and convert to lrs_mp with base BASE */ /* returns true if denominator is not one */ /* returns 999 if premature end of file */ { char in[MAXINPUT], num[MAXINPUT], den[MAXINPUT]; if((fscanf (lrs_ifp, "%s", in)==EOF) || (strcmp("end",in)==0)) { fprintf (lrs_ofp, "\n**Invalid input: check you have entered enough data!\n"); exit(1); } atoaa (in, num, den); /*convert rational to num/dem strings */ atomp (num, Na); if (den[0] == '\0') { itomp (1L, Da); return (FALSE); } atomp (den, Da); return (TRUE); } void readmp (lrs_mp a) /* read an integer and convert to lrs_mp */ { char in[MAXINPUT]; if(fscanf (lrs_ifp, "%s", in)==EOF) { fprintf (lrs_ofp, "\n**Invalid integer input"); exit(1); } atomp (in, a); } void addint (lrs_mp a, lrs_mp b, lrs_mp c) /* compute c=a+b; b,c different vars */ { copy (c, a); linint (c, 1, b, 1); } void atomp (char s[], lrs_mp a) /*convert string to lrs_mp integer */ { lrs_mp mpone; long diff, ten, i, sig; itomp (1L, mpone); ten = 10L; for (i = 0; s[i] == ' ' || s[i] == '\n' || s[i] == '\t'; i++); /*skip white space */ sig = POS; if (s[i] == '+' || s[i] == '-') /* sign */ sig = (s[i++] == '+') ? POS : NEG; itomp (0L, a); while (s[i] >= '0' && s[i] <= '9') { diff = s[i] - '0'; linint (a, ten, mpone, diff); i++; } storesign (a, sig); if (s[i]) { fprintf (stderr, "\nIllegal character in number: '%s'\n", s + i); exit (1); } } /* end of atomp */ void subint (lrs_mp a, lrs_mp b, lrs_mp c) /* compute c=a-b */ { copy (c, a); linint (a, 1, b, -1); } void decint (lrs_mp a, lrs_mp b) /* compute a=a-b */ { linint (a, 1, b, -1); } long myrandom (long num, long nrange) /* return a random number in range 0..nrange-1 */ { long i; i = (num * 401 + 673) % nrange; return (i); } long atos (char s[]) /* convert s to integer */ { long i, j; j = 0; for (i = 0; s[i] >= '0' && s[i] <= '9'; ++i) j = 10 * j + s[i] - '0'; return (j); } void stringcpy (char *s, char *t) /*copy t to s pointer version */ { while (((*s++) = (*t++)) != '\0'); } void rattodouble (lrs_mp a, lrs_mp b, double *x) /* convert lrs_mp rational to double */ { double y; mptodouble (a, &y); mptodouble (b, x); *x = y / (*x); } void atoaa (char in[], char num[], char den[]) /* convert rational string in to num/den strings */ { long i, j; for (i = 0; in[i] != '\0' && in[i] != '/'; i++) num[i] = in[i]; num[i] = '\0'; den[0] = '\0'; if (in[i] == '/') { for (j = 0; in[j + i + 1] != '\0'; j++) den[j] = in[i + j + 1]; den[j] = '\0'; } } /* end of atoaa */ void lcm (lrs_mp a, lrs_mp b) /* a = least common multiple of a, b; b is preserved */ { lrs_mp u, v; copy (u, a); copy (v, b); gcd (u, v); exactdivint (a, u, v); /* v=a/u no remainder*/ mulint (v, b, a); } /* end of lcm */ void reducearray (lrs_mp_vector p, long n) /* find largest gcd of p[0]..p[n-1] and divide through */ { lrs_mp divisor; lrs_mp Temp; long i = 0L; while ((i < n) && zero (p[i])) i++; if (i == n) return; copy (divisor, p[i]); storesign (divisor, POS); i++; while (i < n) { if (!zero (p[i])) { copy (Temp, p[i]); storesign (Temp, POS); gcd (divisor, Temp); } i++; } /* reduce by divisor */ for (i = 0; i < n; i++) if (!zero (p[i])) reduceint (p[i], divisor); } /* end of reducearray */ void reduceint (lrs_mp Na, lrs_mp Da) /* divide Na by Da and return */ { lrs_mp Temp; copy (Temp, Na); exactdivint (Temp, Da, Na); } void reduce (lrs_mp Na, lrs_mp Da) /* reduces Na Da by gcd(Na,Da) */ { lrs_mp Nb, Db, Nc, Dc; copy (Nb, Na); copy (Db, Da); storesign (Nb, POS); storesign (Db, POS); copy (Nc, Na); copy (Dc, Da); gcd (Nb, Db); /* Nb is the gcd(Na,Da) */ exactdivint (Nc, Nb, Na); exactdivint (Dc, Nb, Da); } long comprod (lrs_mp Na, lrs_mp Nb, lrs_mp Nc, lrs_mp Nd) /* +1 if Na*Nb > Nc*Nd */ /* -1 if Na*Nb < Nc*Nd */ /* 0 if Na*Nb = Nc*Nd */ { lrs_mp mc, md; mulint (Na, Nb, mc); mulint (Nc, Nd, md); linint (mc, ONE, md, -ONE); if (positive (mc)) return (1); if (negative (mc)) return (-1); return (0); } void notimpl (const char *s) { fflush (stdout); fprintf (stderr, "\nAbnormal Termination %s\n", s); exit (1); } void getfactorial (lrs_mp factorial, long k) /* compute k factorial in lrs_mp */ { lrs_mp temp; long i; itomp (ONE, factorial); for (i = 2; i <= k; i++) { itomp (i, temp); mulint (temp, factorial, factorial); } } /* end of getfactorial */ /***************************************************************/ /* Package of routines for rational arithmetic */ /***************************************************************/ void scalerat (lrs_mp Na, lrs_mp Da, long ka) /* scales rational by ka */ { lrs_mp Nt; copy (Nt, Na); itomp (ZERO, Na); linint (Na, ZERO, Nt, ka); reduce (Na, Da); } void linrat (lrs_mp Na, lrs_mp Da, long ka, lrs_mp Nb, lrs_mp Db, long kb, lrs_mp Nc, lrs_mp Dc) /* computes Nc/Dc = ka*Na/Da +kb* Nb/Db and reduces answer by gcd(Nc,Dc) */ { lrs_mp c; mulint (Na, Db, Nc); mulint (Da, Nb, c); linint (Nc, ka, c, kb); /* Nc = (ka*Na*Db)+(kb*Da*Nb) */ mulint (Da, Db, Dc); /* Dc = Da*Db */ reduce (Nc, Dc); } void divrat (lrs_mp Na, lrs_mp Da, lrs_mp Nb, lrs_mp Db, lrs_mp Nc, lrs_mp Dc) /* computes Nc/Dc = (Na/Da) / ( Nb/Db ) and reduces answer by gcd(Nc,Dc) */ { mulint (Na, Db, Nc); mulint (Da, Nb, Dc); reduce (Nc, Dc); } void mulrat (lrs_mp Na, lrs_mp Da, lrs_mp Nb, lrs_mp Db, lrs_mp Nc, lrs_mp Dc) /* computes Nc/Dc = Na/Da * Nb/Db and reduces by gcd(Nc,Dc) */ { mulint (Na, Nb, Nc); mulint (Da, Db, Dc); reduce (Nc, Dc); } /* End package of routines for rational arithmetic */ /***************************************************************/ /* */ /* End of package for multiple precision arithmetic */ /* */ /***************************************************************/ void * xcalloc (long n, long s, long l, const char *f) { void *tmp; tmp = calloc (n, s); if (tmp == 0) { char buf[200]; sprintf (buf, "\n\nFatal error on line %ld of %s", l, f); perror (buf); exit (1); } return tmp; } void lrs_getdigits (long *a, long *b) { /* send digit information to user */ *a = DIG2DEC (lrs_digits); *b = DIG2DEC (lrs_record_digits); return; } void lrs_default_digits_overflow () { lrs_overflow (1); } /* read a rational or integer and convert to lrs_mp with base BASE */ /* returns true if denominator is not one */ /* returns 999 if premature end of file */ long plrs_readrat (lrs_mp Na, lrs_mp Da, const char* rat) { char in[MAXINPUT], num[MAXINPUT], den[MAXINPUT]; strcpy(in, rat); atoaa (in, num, den); /*convert rational to num/dem strings */ atomp (num, Na); if (den[0] == '\0') { itomp (1L, Da); return (FALSE); } atomp (den, Da); return (TRUE); } /* end of lrsmp.c */ lrslib-073/lrsarith-011/lrsmp.h0000777000175000017500000002376614625766601015041 0ustar avisavis/* lrsmp.h (lrs extended precision arithmetic library) */ /* Copyright: David Avis 2000, avis@cs.mcgill.ca */ /* Version 4.1, February 17, 2000 */ /* This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA. */ /******************************************************************************/ /* See http://cgm.cs.mcgill.ca/~avis/C/lrs.html for lrs usage instructions */ /******************************************************************************/ /* This package contains the extended precision routines used by lrs and some other miscellaneous routines. The maximum precision depends on the parameter MAX_DIGITS defined below, with usual default of 255L. This gives a maximum of 1020 decimal digits on 32 bit machines. The procedure lrs_mp_init(dec_digits) may set a smaller number of dec_digits, and this is useful if arrays or matrices will be used. */ /***********/ /* defines */ /***********/ #define suf(func) func /* this is number of longwords. Increasing this won't cost you that much since only variables other than the A matrix are allocated this size. Changing affects running time in small but not very predictable ways. */ #define MAX_DIGITS 255L /* this is in decimal digits, you pay in memory if you increase this, unless you overide it in lrs_mp_init() or (lrs only)unless you override by a line with digits n before the begin line of your file. */ #define DEFAULT_DIGITS 1000L /**********MACHINE DEPENDENT CONSTANTS***********/ /* MAXD is 2^(k-1)-1 where k is word size */ /* MAXD must be at least 2*BASE^2 */ /* If BASE is 10^k, use "%k.ku" for FORMAT */ /* INTSIZE is number of bytes for integer */ /***********************************************/ /* 64 bit machines */ #define MAXD 9223372036854775807LL #define BASE 1000000000LL #define FORMAT "%9.9llu" #define BASE_DIG 9 #define INTSIZE 16L #define BIT "64bit" #define MAXINPUT 1000 /*max length of any input rational */ #define POS 1L #define NEG -1L #ifndef TRUE #define TRUE 1L #endif #ifndef FALSE #define FALSE 0L #endif #define ONE 1L #define TWO 2L #define ZERO 0L /**********************************/ /* MACROS */ /* dependent on mp implementation */ /**********************************/ #define exactdivint(a,b,c) divint((a),(b),(c)) /*should use special code here */ #define positive(a) (((a)[0] < 2 || ((a)[0]==2 && (a)[1]==0))?FALSE:TRUE) #define negative(a) (((a)[0] > -2 || ((a)[0]==-2 && (a)[1]==0))?FALSE:TRUE) #define zero(a) ((((a)[0]==2 || (a)[0]==-2) && (a)[1]==0)?TRUE:FALSE) #define one(a) (((a)[0]==2 && (a)[1]==1)?TRUE:FALSE) //#define length(a) (((a)[0] > 0) ? (a)[0] : -(a)[0]) #define sign(a) (((a)[0] < 0) ? NEG : POS) #define storesign(a,sa) a[0]=((a)[0] > 0) ? (sa)*((a)[0]) : -(sa)*((a)[0]) #define changesign(a) a[0]= -(a)[0] #define storelength(a,la) a[0]=((a)[0] > 0) ? (la) : -(la) /* * convert between decimal and machine (longword digits). Notice lovely * implementation of ceiling function :-) */ #define DEC2DIG(d) ( (d) % BASE_DIG ? (d)/BASE_DIG+1 : (d)/BASE_DIG) #define DIG2DEC(d) ((d)*BASE_DIG) #include #ifdef SIGNALS #include #include #define errcheck(s,e) if ((long)(e)==-1L){ perror(s);exit(1);} #endif #define CALLOC(n,s) xcalloc(n,s,__LINE__,__FILE__) extern long lrs_digits; /* max permitted no. of digits */ extern long lrs_record_digits; /* this is the biggest acheived so far. */ extern FILE* lrs_ifp; /* input file pointer */ extern FILE* lrs_ofp; /* output file pointer */ /*************/ /* typedefs */ /*************/ typedef long long lrs_mp[MAX_DIGITS + 1]; /* type lrs_mp holds one multi-precision integer */ typedef long long *lrs_mp_t; typedef long long **lrs_mp_vector; typedef long long ***lrs_mp_matrix; /*********************************************************/ /* Initialization and allocation procedures - must use! */ /******************************************************* */ /* next two functions are not used by lrsmp, but are for lrsgmp compatability */ #define lrs_alloc_mp(a) #define lrs_clear_mp(a) lrs_mp_t lrs_alloc_mp_t(); /* dynamic allocation of lrs_mp */ lrs_mp_vector lrs_alloc_mp_vector (long n); /* allocate lrs_mp_vector for n+1 lrs_mp numbers */ lrs_mp_matrix lrs_alloc_mp_matrix (long m, long n); /* allocate lrs_mp_matrix for m+1 x n+1 lrs_mp */ long lrs_mp_init (long dec_digits, FILE * lrs_ifp, FILE * lrs_ofp); /* max number of decimal digits, fps */ void lrs_clear_mp_vector (lrs_mp_vector a, long n); void lrs_clear_mp_matrix (lrs_mp_matrix a, long m, long n); /*********************************************************/ /* Core library functions - depend on mp implementation */ /******************************************************* */ long length (lrs_mp a); /* return length of lrs_mp integer */ void atomp (char s[], lrs_mp a); /* convert string to lrs_mp integer */ long compare (lrs_mp a, lrs_mp b); /* a ? b and returns -1,0,1 for <,=,> */ void copy (lrs_mp a, lrs_mp b); /* assigns a=b */ void divint (lrs_mp a, lrs_mp b, lrs_mp c); /* c=a/b, a contains remainder on return */ void gcd (lrs_mp u, lrs_mp v); /* returns u=gcd(u,v) destroying v */ long mp_greater (lrs_mp a, lrs_mp b); /* tests if a > b and returns (TRUE=POS) */ #define mp_equal(a,b) (compare((a),(b)) == 0 ? ONE : ZERO ) void itomp (long in, lrs_mp a); /* convert integer i to lrs_mp */ void linint (lrs_mp a, long ka, lrs_mp b, long kb); /* compute a*ka+b*kb --> a */ #ifdef MPLRS long plrs_readrat (lrs_mp Na, lrs_mp Da, const char * rat); /* take a rational number and convert to lrs_mp */ #endif void mptodouble (lrs_mp a, double *x); /* convert lrs_mp to double */ long mptoi (lrs_mp a); /* convert lrs_mp to long integer */ char *mpgetstr10 (char *, lrs_mp); /* convert lrs_mp to char array */ void mulint (lrs_mp a, lrs_mp b, lrs_mp c); /* multiply two integers a*b --> c */ void normalize (lrs_mp a); /* normalize lrs_mp after computation */ void pmp (const char *name, lrs_mp a); /* print the long precision integer a */ void prat (const char *name, lrs_mp Nt, lrs_mp Dt); /* reduce and print Nt/Dt */ char *cpmp(const char *name, lrs_mp Nt); /* mp int to char */ char *cprat(const char *name, lrs_mp Nt, lrs_mp Dt); /* C version of prat */ void readmp (lrs_mp Na); /* read an int and convert to lrs_mp */ long readrat (lrs_mp Na, lrs_mp Da); /* read a rational or int and convert to lrs_mp */ void reduce (lrs_mp Na, lrs_mp Da); /* reduces Na Da by gcd(Na,Da) */ /*********************************************************/ /* Standard arithmetic & misc. functions */ /* should be independent of mp implementation */ /******************************************************* */ void atoaa (char in[], char num[], char den[]); /* convert rational string in to num/den strings */ void addint (lrs_mp a, lrs_mp b, lrs_mp c); /* compute c=a+b */ long atos (char s[]); /* convert s to integer */ long comprod (lrs_mp Na, lrs_mp Nb, lrs_mp Nc, lrs_mp Nd); /* +1 if Na*Nb > Nc*Nd,-1 if Na*Nb > Nc*Nd else 0 */ void decint (lrs_mp a, lrs_mp b); /* compute a=a-b */ void divrat (lrs_mp Na, lrs_mp Da, lrs_mp Nb, lrs_mp Db, lrs_mp Nc, lrs_mp Dc); /* computes Nc/Dc = (Na/Da) /( Nb/Db ) and reduce */ void getfactorial (lrs_mp factorial, long k); /* compute k factorial in lrs_mp */ /* NC/DC = ka*Na/Da + kb*Nb/Db */ void linrat (lrs_mp Na, lrs_mp Da, long ka, lrs_mp Nb, lrs_mp Db, long kb, lrs_mp Nc, lrs_mp Dc); void lcm (lrs_mp a, lrs_mp b); /* a = least common multiple of a, b; b is saved */ void mulrat (lrs_mp Na, lrs_mp Da, lrs_mp Nb, lrs_mp Db, lrs_mp Nc, lrs_mp Dc); /* computes Nc/Dc=(Na/Da)*(Nb/Db) and reduce */ long myrandom (long num, long nrange); /* return a random number in range 0..nrange-1 */ void notimpl (const char *s); /* bail out - help! */ void rattodouble (lrs_mp a, lrs_mp b, double *x); /* convert lrs_mp rational to double */ void reduceint (lrs_mp Na, lrs_mp Da); /* divide Na by Da and return it */ void reducearray (lrs_mp_vector p, long n); /* find gcd of p[0]..p[n-1] and divide through by */ void scalerat (lrs_mp Na, lrs_mp Da, long ka); /* scales rational by ka */ void subint (lrs_mp a, lrs_mp b, lrs_mp c); /* compute c=a-b */ /**********************************/ /* Miscellaneous functions */ /******************************** */ void free (void *); void lrs_getdigits (long *a, long *b); /* send digit information to user */ void stringcpy (char *s, char *t); /* copy t to s pointer version */ void *xcalloc (long n, long s, long l, const char *f); void lrs_default_digits_overflow (); void digits_overflow (); void lrs_exit(int i); void lrs_overflow(int i); /* end of lrsmp.h (vertex enumeration using lexicographic reverse search) */ lrslib-073/lrsarith-011/makefile0000777000175000017500000000630014625766601015214 0ustar avisavis# 2020-11-13 makefile for model programs of hybrid/fixed arithmetic with lrslib #CC=gcc HOBJ=lrslong1.o hybridlib1.o lrslong2.o lrsgmp.o hybridlib2.o hybridlibgmp.o hybrid: hybrid.c lrslong.c lrslong.h lrsgmp.c lrsgmp.h hybridlib.c hybrid.h lrsarith.c $(CC) -DMA -DSAFE -DLRSLONG -c -o lrslong1.o lrsarith.c $(CC) -DMA -DB128 -DSAFE -DLRSLONG -c -o lrslong2.o lrsarith.c $(CC) -DMA -DGMP -c -o lrsgmp.o lrsarith.c $(CC) -DMA -DSAFE -DLRSLONG -c -o hybridlib1.o hybridlib.c $(CC) -DMA -DB128 -DSAFE -DLRSLONG -c -o hybridlib2.o hybridlib.c $(CC) -DMA -DGMP -c -o hybridlibgmp.o hybridlib.c $(CC) -DMA -DLRSLONG -DSAFE -o hybrid ${HOBJ} hybrid.c -lgmp rm -f *.o fixed: fixed.c lrsarith.c lrsarith.h lrslong.c lrslong.h lrsgmp.c lrsgmp.h lrsmp.c lrsmp.h $(CC) -DLRSLONG -DSAFE -o fixed1 lrsarith.c fixed.c $(CC) -DLRSLONG -DB128 -DSAFE -o fixed2 lrsarith.c fixed.c $(CC) -DLRSLONG -o fixed1n lrsarith.c fixed.c $(CC) -DLRSLONG -DB128 -o fixed2n lrsarith.c fixed.c $(CC) -DMP -o fixedmp lrsarith.c fixed.c $(CC) -DGMP -o fixedgmp lrsarith.c fixed.c -lgmp HOBJmp=lrslong1.o hybridlib1.o lrslong2.o lrsmp.o hybridlib2.o hybridlibmp.o mp: hybrid.c lrslong.c lrslong.h lrsmp.c lrsmp.h hybridlib.c hybrid.h $(CC) -DMA -DSAFE -DLRSLONG -c -o lrslong1.o lrsarith.c $(CC) -DMA -DMP -c -o lrsmp.o lrsarith.c $(CC) -DMA -DB128 -DSAFE -DLRSLONG -c -o lrslong2.o lrsarith.c $(CC) -DMA -DSAFE -DLRSLONG -c -o hybridlib1.o hybridlib.c $(CC) -DMA -DB128 -DSAFE -DLRSLONG -c -o hybridlib2.o hybridlib.c $(CC) -DMA -DMP -c -o hybridlibmp.o hybridlib.c $(CC) -DMA -DLRSLONG -DSAFE -o hybridmp ${HOBJmp} hybrid.c rm -f *.o test: $(CC) -DLRSLONG -DSAFE -o test1 lrsarith.c test.c $(CC) -DLRSLONG -o test1n lrsarith.c test.c $(CC) -DLRSLONG -DB128 -DSAFE -o test2 lrsarith.c test.c $(CC) -DLRSLONG -DB128 -o test2n lrsarith.c test.c # $(CC) -DGMP -o testgmp lrsarith.c test.c -lgmp test1; test2; flint: lrsarith.c coll.c colllib.c $(CC) -O3 -DFLINT -I/usr/local/include/flint lrsarith.c colllib.c coll.c -L/usr/local/lib -Wl,-rpath=/usr/local/lib -lflint -o collflint -lgmp HOBJ3=lrslong1.o lrslong2.o lrsgmp.o coll1.o coll2.o collgmp.o coll: lrslong.c lrslong.h lrsgmp.c lrsgmp.h hybrid.c hybrid.h coll.c lrsarith.c $(CC) -O3 -DLRSLONG -DSAFE -o coll1 lrsarith.c coll.c colllib.c $(CC) -O3 -DLRSLONG -DSAFE -DB128 -o coll2 lrsarith.c coll.c colllib.c $(CC) -O3 -DLRSLONG -o coll1n lrsarith.c coll.c colllib.c $(CC) -O3 -DLRSLONG -DB128 -o coll2n lrsarith.c coll.c colllib.c $(CC) -O3 -DGMP -o collgmp lrsarith.c coll.c colllib.c -lgmp $(CC) -O3 -DMP -o collmp lrsarith.c coll.c colllib.c $(CC) -DMA -O3 -DSAFE -DLRSLONG -c -o lrslong1.o lrsarith.c $(CC) -DMA -O3 -DB128 -DSAFE -DLRSLONG -c -o lrslong2.o lrsarith.c $(CC) -DMA -O3 -DGMP -c -o lrsgmp.o lrsarith.c $(CC) -DMA -O3 -DSAFE -DLRSLONG -c -o coll1.o colllib.c $(CC) -DMA -O3 -DB128 -DSAFE -DLRSLONG -c -o coll2.o colllib.c $(CC) -DMA -O3 -DGMP -c -o collgmp.o colllib.c $(CC) -DMA -O3 -DLRSLONG -DSAFE -o coll ${HOBJ3} coll.c -lgmp rm -f *.o all: fixed hybrid mp coll test clean: rm -f *.o fixed1 fixed1n fixed2 fixed2n fixedmp fixedgmp hybrid hybridmp rm -f *.o coll collgmp collflint coll1 coll2 coll1n coll2n collmp test1 test1n test2 test2n testgmp lrslib-073/lrsarith-011/man/0000777000175000017500000000000014625766601014265 5ustar avisavislrslib-073/lrsarith-011/man/man5/0000777000175000017500000000000014625766601015125 5ustar avisavislrslib-073/lrsarith-011/man/man5/lrsarith.50000777000175000017500000001216214625766601017050 0ustar avisavis.TH "LRSARITH" "5" "2020.12.07" "December 2020" "lrsarith 1\&.0" .\" ----------------------------------------------------------------- .\" * Define some portability stuff .\" ----------------------------------------------------------------- .\" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .\" http://bugs.debian.org/507673 .\" http://lists.gnu.org/archive/html/groff/2009-02/msg00013.html .\" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .ie \n(.g .ds Aq \(aq .el .ds Aq ' .\" ----------------------------------------------------------------- .\" * set default formatting .\" ----------------------------------------------------------------- .\" disable hyphenation .nh .\" disable justification (adjust text to left margin only) .ad l .\" ----------------------------------------------------------------- .\" * MAIN CONTENT STARTS HERE * .\" ----------------------------------------------------------------- .SH "NAME" lrsarith: library routines for exact precision integer and rational arithmetic from lrslib with sample programs. 64bit integer, 128bit integer, GMP, lrslib MP, and FLINT arithmetic packages are supported. as well as hybrid arithmetic. Overflow checking is done for 64bit and 128bit arithmetic. .SH "SYNOPSIS" .HP \w'\fBlrslong.h lrslong.c\fR\ [64bit and 128bit arithmetic with overflow handling]\ \fBlrslong.h lrslong.c\fR\ \fI[64bit and 128bit arithmetic]\fR .HP \w'\fBlrsgmp.h lrsgmp.c\fR\ [GMP and FLINT arithmetic]\ \fBlrsgmp.h lrsgmp.c\fR\ \fI[GMP and FLINT arithmetic]\fR (requires external library) .HP \w'\fBlrsmp.h lrsmp.c\fR\ [lrslib MP arithmetic]\ \fBlrsmp.h lrsmp.c\fR\ \fI[lrslib MP arithmetic]\fR .SH "DESCRIPTION" .PP This package was extracted from version 7.1 of lrslib which uses hybrid arithmetic with overflow checking, starting in 64bit integers, moving to 128bit (if available) and then GMP. Overflow checking is conservative to improve performance: eg. with 64 bit arithmetic, a*b triggers overflow if either a or b is at least 2^31, and a+b triggers an overflow if either a or b is at least 2^62. Typically problems that can be solved in 64bits run 3-4 times faster than with GMP and inputs solvable in 128bits run twice as fast as GMP. A rational number is represented by a pair of integers, however the user must keep track of the numerator and denominators manually. Operations for rational arithmetic are included. Various test programs are available and can be built from the makefile: .PP \fI% make fixed\fR Build the programs fixed1, fixed1n, fixed2, fixed2n, fixedmp, fixedgmp that read an integer k and repeatedly square it 6 times. .PP \fI% make hybrid\fR\ (% make mp use internal MP arithmetic instead of GMP) Build the program hybrid (and fixed1, fixed2, fixedgmp) that runs through the three arithmetic packages as needed. .PP \fI% make coll\fR\ (% make flint make FLINT arithmetic version) Reverse search code for building a Collatz tree with largest value maxn in all arithmetic versions. .PP \fI% make test\fR\ Test the arithmetic constants used in overflow checking. .SH "INTIALIZATION" lrs_mp_init(digits,fpin,fpout); digits: maximum number of decimal digits in MP arithmetic else set digits=0 fpin, fpout: input and output file pointers, eg, stdin, stdout .SH "TYPES" Fixed arithmetic is handled by defining a generic integer type and a set of generic operations. A generic integer a, integer vector v and integer matrix A are defined lrs_mp a; lrs_mp_vector v; lrs_mp_matrix A; allocated lrs_alloc_mp(a); v=lrs_alloc_mp_vector(n); A=lrs_alloc_mp_matrix(m,n); and freed lrs_clear_mp(a); lrs_clear_mp_vector(n); lrs_clear_mp_matrix(m,n); where m and n are the dimensions. .SH "OPERATIONS" Operations using lrs_mp integers are written generically. The most basic ones are below and a complete list is included in lrslong.h. Operations may be implemented as macros which may evaluate their arguments more than once. Arguments should not be expressions with potential side effects. Here, a,b,c,d,e are lrs_mp integers, i is a long long int and the equivalent C code is given in parenthesis. addint(a,b,c) (c=a+b) /* a and b should be different */ changesign(a) (a = -a) compare(a,b) (a ? b and returns -1,0,1 for <,=,>) copy(a,b) (a=b) decint(a,b) (a=a-b) divint(a,b,c) (c=a/b a=a%b) exactdivint(a,b,c) (c=a/b) itomp(i,a); (a=i) linint(a, ka, b, kb) (a=a*ka+b*kb for ka, kb long long integers) mp_greater(a, b) (a>b) mulint(a,b,c) (c=a*b) /* b and c may be the same */ negative(a) (a<0) one(a) (a == 1) pmp("string",a) (print "string" followed by a to lrs_ofp) positive(a) (a>0) qpiv(a,b,c,d,e) (a=(a*b-c*d)/e where the division is exact ) sign(a) (a < 0 ? NEG : POS) storesign(a, i) (a = labs(a) * i) subint(a,b,c) (c=a-b) zero(a) (a == 0) .SH "NOTES" .PP User's guide for lrslib .RS 4 \%http://cgm.cs.mcgill.ca/~avis/C/lrslib/USERGUIDE.html .RE .SH AUTHOR David Avis .SH "SEE ALSO" .BR lrslib (5), lrslib-073/lrsarith-011/mini-gmp.c0000777000175000017500000025713014625766601015406 0ustar avisavis/* mini-gmp, a minimalistic implementation of a GNU GMP subset. Contributed to the GNU project by Niels Möller Copyright 1991-1997, 1999-2019 Free Software Foundation, Inc. This file is part of the GNU MP Library. The GNU MP Library is free software; you can redistribute it and/or modify it under the terms of either: * the GNU Lesser General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version. or * the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. or both in parallel, as here. The GNU MP Library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received copies of the GNU General Public License and the GNU Lesser General Public License along with the GNU MP Library. If not, see https://www.gnu.org/licenses/. */ /* NOTE: All functions in this file which are not declared in mini-gmp.h are internal, and are not intended to be compatible with GMP or with future versions of mini-gmp. */ /* Much of the material copied from GMP files, including: gmp-impl.h, longlong.h, mpn/generic/add_n.c, mpn/generic/addmul_1.c, mpn/generic/lshift.c, mpn/generic/mul_1.c, mpn/generic/mul_basecase.c, mpn/generic/rshift.c, mpn/generic/sbpi1_div_qr.c, mpn/generic/sub_n.c, mpn/generic/submul_1.c. */ #include #include #include #include #include #include #include "mini-gmp.h" #if !defined(MINI_GMP_DONT_USE_FLOAT_H) #include #endif /* Macros */ #define GMP_LIMB_BITS (sizeof(mp_limb_t) * CHAR_BIT) #define GMP_LIMB_MAX ((mp_limb_t) ~ (mp_limb_t) 0) #define GMP_LIMB_HIGHBIT ((mp_limb_t) 1 << (GMP_LIMB_BITS - 1)) #define GMP_HLIMB_BIT ((mp_limb_t) 1 << (GMP_LIMB_BITS / 2)) #define GMP_LLIMB_MASK (GMP_HLIMB_BIT - 1) #define GMP_ULONG_BITS (sizeof(unsigned long) * CHAR_BIT) #define GMP_ULONG_HIGHBIT ((unsigned long) 1 << (GMP_ULONG_BITS - 1)) #define GMP_ABS(x) ((x) >= 0 ? (x) : -(x)) #define GMP_NEG_CAST(T,x) (-((T)((x) + 1) - 1)) #define GMP_MIN(a, b) ((a) < (b) ? (a) : (b)) #define GMP_MAX(a, b) ((a) > (b) ? (a) : (b)) #define GMP_CMP(a,b) (((a) > (b)) - ((a) < (b))) #if defined(DBL_MANT_DIG) && FLT_RADIX == 2 #define GMP_DBL_MANT_BITS DBL_MANT_DIG #else #define GMP_DBL_MANT_BITS (53) #endif /* Return non-zero if xp,xsize and yp,ysize overlap. If xp+xsize<=yp there's no overlap, or if yp+ysize<=xp there's no overlap. If both these are false, there's an overlap. */ #define GMP_MPN_OVERLAP_P(xp, xsize, yp, ysize) \ ((xp) + (xsize) > (yp) && (yp) + (ysize) > (xp)) #define gmp_assert_nocarry(x) do { \ mp_limb_t __cy = (x); \ assert (__cy == 0); \ } while (0) #define gmp_clz(count, x) do { \ mp_limb_t __clz_x = (x); \ unsigned __clz_c = 0; \ int LOCAL_SHIFT_BITS = 8; \ if (GMP_LIMB_BITS > LOCAL_SHIFT_BITS) \ for (; \ (__clz_x & ((mp_limb_t) 0xff << (GMP_LIMB_BITS - 8))) == 0; \ __clz_c += 8) \ { __clz_x <<= LOCAL_SHIFT_BITS; } \ for (; (__clz_x & GMP_LIMB_HIGHBIT) == 0; __clz_c++) \ __clz_x <<= 1; \ (count) = __clz_c; \ } while (0) #define gmp_ctz(count, x) do { \ mp_limb_t __ctz_x = (x); \ unsigned __ctz_c = 0; \ gmp_clz (__ctz_c, __ctz_x & - __ctz_x); \ (count) = GMP_LIMB_BITS - 1 - __ctz_c; \ } while (0) #define gmp_add_ssaaaa(sh, sl, ah, al, bh, bl) \ do { \ mp_limb_t __x; \ __x = (al) + (bl); \ (sh) = (ah) + (bh) + (__x < (al)); \ (sl) = __x; \ } while (0) #define gmp_sub_ddmmss(sh, sl, ah, al, bh, bl) \ do { \ mp_limb_t __x; \ __x = (al) - (bl); \ (sh) = (ah) - (bh) - ((al) < (bl)); \ (sl) = __x; \ } while (0) #define gmp_umul_ppmm(w1, w0, u, v) \ do { \ int LOCAL_GMP_LIMB_BITS = GMP_LIMB_BITS; \ if (sizeof(unsigned int) * CHAR_BIT >= 2 * GMP_LIMB_BITS) \ { \ unsigned int __ww = (unsigned int) (u) * (v); \ w0 = (mp_limb_t) __ww; \ w1 = (mp_limb_t) (__ww >> LOCAL_GMP_LIMB_BITS); \ } \ else if (GMP_ULONG_BITS >= 2 * GMP_LIMB_BITS) \ { \ unsigned long int __ww = (unsigned long int) (u) * (v); \ w0 = (mp_limb_t) __ww; \ w1 = (mp_limb_t) (__ww >> LOCAL_GMP_LIMB_BITS); \ } \ else { \ mp_limb_t __x0, __x1, __x2, __x3; \ unsigned __ul, __vl, __uh, __vh; \ mp_limb_t __u = (u), __v = (v); \ \ __ul = __u & GMP_LLIMB_MASK; \ __uh = __u >> (GMP_LIMB_BITS / 2); \ __vl = __v & GMP_LLIMB_MASK; \ __vh = __v >> (GMP_LIMB_BITS / 2); \ \ __x0 = (mp_limb_t) __ul * __vl; \ __x1 = (mp_limb_t) __ul * __vh; \ __x2 = (mp_limb_t) __uh * __vl; \ __x3 = (mp_limb_t) __uh * __vh; \ \ __x1 += __x0 >> (GMP_LIMB_BITS / 2);/* this can't give carry */ \ __x1 += __x2; /* but this indeed can */ \ if (__x1 < __x2) /* did we get it? */ \ __x3 += GMP_HLIMB_BIT; /* yes, add it in the proper pos. */ \ \ (w1) = __x3 + (__x1 >> (GMP_LIMB_BITS / 2)); \ (w0) = (__x1 << (GMP_LIMB_BITS / 2)) + (__x0 & GMP_LLIMB_MASK); \ } \ } while (0) #define gmp_udiv_qrnnd_preinv(q, r, nh, nl, d, di) \ do { \ mp_limb_t _qh, _ql, _r, _mask; \ gmp_umul_ppmm (_qh, _ql, (nh), (di)); \ gmp_add_ssaaaa (_qh, _ql, _qh, _ql, (nh) + 1, (nl)); \ _r = (nl) - _qh * (d); \ _mask = -(mp_limb_t) (_r > _ql); /* both > and >= are OK */ \ _qh += _mask; \ _r += _mask & (d); \ if (_r >= (d)) \ { \ _r -= (d); \ _qh++; \ } \ \ (r) = _r; \ (q) = _qh; \ } while (0) #define gmp_udiv_qr_3by2(q, r1, r0, n2, n1, n0, d1, d0, dinv) \ do { \ mp_limb_t _q0, _t1, _t0, _mask; \ gmp_umul_ppmm ((q), _q0, (n2), (dinv)); \ gmp_add_ssaaaa ((q), _q0, (q), _q0, (n2), (n1)); \ \ /* Compute the two most significant limbs of n - q'd */ \ (r1) = (n1) - (d1) * (q); \ gmp_sub_ddmmss ((r1), (r0), (r1), (n0), (d1), (d0)); \ gmp_umul_ppmm (_t1, _t0, (d0), (q)); \ gmp_sub_ddmmss ((r1), (r0), (r1), (r0), _t1, _t0); \ (q)++; \ \ /* Conditionally adjust q and the remainders */ \ _mask = - (mp_limb_t) ((r1) >= _q0); \ (q) += _mask; \ gmp_add_ssaaaa ((r1), (r0), (r1), (r0), _mask & (d1), _mask & (d0)); \ if ((r1) >= (d1)) \ { \ if ((r1) > (d1) || (r0) >= (d0)) \ { \ (q)++; \ gmp_sub_ddmmss ((r1), (r0), (r1), (r0), (d1), (d0)); \ } \ } \ } while (0) /* Swap macros. */ #define MP_LIMB_T_SWAP(x, y) \ do { \ mp_limb_t __mp_limb_t_swap__tmp = (x); \ (x) = (y); \ (y) = __mp_limb_t_swap__tmp; \ } while (0) #define MP_SIZE_T_SWAP(x, y) \ do { \ mp_size_t __mp_size_t_swap__tmp = (x); \ (x) = (y); \ (y) = __mp_size_t_swap__tmp; \ } while (0) #define MP_BITCNT_T_SWAP(x,y) \ do { \ mp_bitcnt_t __mp_bitcnt_t_swap__tmp = (x); \ (x) = (y); \ (y) = __mp_bitcnt_t_swap__tmp; \ } while (0) #define MP_PTR_SWAP(x, y) \ do { \ mp_ptr __mp_ptr_swap__tmp = (x); \ (x) = (y); \ (y) = __mp_ptr_swap__tmp; \ } while (0) #define MP_SRCPTR_SWAP(x, y) \ do { \ mp_srcptr __mp_srcptr_swap__tmp = (x); \ (x) = (y); \ (y) = __mp_srcptr_swap__tmp; \ } while (0) #define MPN_PTR_SWAP(xp,xs, yp,ys) \ do { \ MP_PTR_SWAP (xp, yp); \ MP_SIZE_T_SWAP (xs, ys); \ } while(0) #define MPN_SRCPTR_SWAP(xp,xs, yp,ys) \ do { \ MP_SRCPTR_SWAP (xp, yp); \ MP_SIZE_T_SWAP (xs, ys); \ } while(0) #define MPZ_PTR_SWAP(x, y) \ do { \ mpz_ptr __mpz_ptr_swap__tmp = (x); \ (x) = (y); \ (y) = __mpz_ptr_swap__tmp; \ } while (0) #define MPZ_SRCPTR_SWAP(x, y) \ do { \ mpz_srcptr __mpz_srcptr_swap__tmp = (x); \ (x) = (y); \ (y) = __mpz_srcptr_swap__tmp; \ } while (0) const int mp_bits_per_limb = GMP_LIMB_BITS; /* Memory allocation and other helper functions. */ static void gmp_die (const char *msg) { fprintf (stderr, "%s\n", msg); abort(); } static void * gmp_default_alloc (size_t size) { void *p; assert (size > 0); p = malloc (size); if (!p) gmp_die("gmp_default_alloc: Virtual memory exhausted."); return p; } static void * gmp_default_realloc (void *old, size_t unused_old_size, size_t new_size) { void * p; p = realloc (old, new_size); if (!p) gmp_die("gmp_default_realloc: Virtual memory exhausted."); return p; } static void gmp_default_free (void *p, size_t unused_size) { free (p); } static void * (*gmp_allocate_func) (size_t) = gmp_default_alloc; static void * (*gmp_reallocate_func) (void *, size_t, size_t) = gmp_default_realloc; static void (*gmp_free_func) (void *, size_t) = gmp_default_free; void mp_get_memory_functions (void *(**alloc_func) (size_t), void *(**realloc_func) (void *, size_t, size_t), void (**free_func) (void *, size_t)) { if (alloc_func) *alloc_func = gmp_allocate_func; if (realloc_func) *realloc_func = gmp_reallocate_func; if (free_func) *free_func = gmp_free_func; } void mp_set_memory_functions (void *(*alloc_func) (size_t), void *(*realloc_func) (void *, size_t, size_t), void (*free_func) (void *, size_t)) { if (!alloc_func) alloc_func = gmp_default_alloc; if (!realloc_func) realloc_func = gmp_default_realloc; if (!free_func) free_func = gmp_default_free; gmp_allocate_func = alloc_func; gmp_reallocate_func = realloc_func; gmp_free_func = free_func; } #define gmp_xalloc(size) ((*gmp_allocate_func)((size))) #define gmp_free(p) ((*gmp_free_func) ((p), 0)) static mp_ptr gmp_xalloc_limbs (mp_size_t size) { return (mp_ptr) gmp_xalloc (size * sizeof (mp_limb_t)); } static mp_ptr gmp_xrealloc_limbs (mp_ptr old, mp_size_t size) { assert (size > 0); return (mp_ptr) (*gmp_reallocate_func) (old, 0, size * sizeof (mp_limb_t)); } /* MPN interface */ void mpn_copyi (mp_ptr d, mp_srcptr s, mp_size_t n) { mp_size_t i; for (i = 0; i < n; i++) d[i] = s[i]; } void mpn_copyd (mp_ptr d, mp_srcptr s, mp_size_t n) { while (--n >= 0) d[n] = s[n]; } int mpn_cmp (mp_srcptr ap, mp_srcptr bp, mp_size_t n) { while (--n >= 0) { if (ap[n] != bp[n]) return ap[n] > bp[n] ? 1 : -1; } return 0; } static int mpn_cmp4 (mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn) { if (an != bn) return an < bn ? -1 : 1; else return mpn_cmp (ap, bp, an); } static mp_size_t mpn_normalized_size (mp_srcptr xp, mp_size_t n) { while (n > 0 && xp[n-1] == 0) --n; return n; } int mpn_zero_p(mp_srcptr rp, mp_size_t n) { return mpn_normalized_size (rp, n) == 0; } void mpn_zero (mp_ptr rp, mp_size_t n) { while (--n >= 0) rp[n] = 0; } mp_limb_t mpn_add_1 (mp_ptr rp, mp_srcptr ap, mp_size_t n, mp_limb_t b) { mp_size_t i; assert (n > 0); i = 0; do { mp_limb_t r = ap[i] + b; /* Carry out */ b = (r < b); rp[i] = r; } while (++i < n); return b; } mp_limb_t mpn_add_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n) { mp_size_t i; mp_limb_t cy; for (i = 0, cy = 0; i < n; i++) { mp_limb_t a, b, r; a = ap[i]; b = bp[i]; r = a + cy; cy = (r < cy); r += b; cy += (r < b); rp[i] = r; } return cy; } mp_limb_t mpn_add (mp_ptr rp, mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn) { mp_limb_t cy; assert (an >= bn); cy = mpn_add_n (rp, ap, bp, bn); if (an > bn) cy = mpn_add_1 (rp + bn, ap + bn, an - bn, cy); return cy; } mp_limb_t mpn_sub_1 (mp_ptr rp, mp_srcptr ap, mp_size_t n, mp_limb_t b) { mp_size_t i; assert (n > 0); i = 0; do { mp_limb_t a = ap[i]; /* Carry out */ mp_limb_t cy = a < b; rp[i] = a - b; b = cy; } while (++i < n); return b; } mp_limb_t mpn_sub_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n) { mp_size_t i; mp_limb_t cy; for (i = 0, cy = 0; i < n; i++) { mp_limb_t a, b; a = ap[i]; b = bp[i]; b += cy; cy = (b < cy); cy += (a < b); rp[i] = a - b; } return cy; } mp_limb_t mpn_sub (mp_ptr rp, mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn) { mp_limb_t cy; assert (an >= bn); cy = mpn_sub_n (rp, ap, bp, bn); if (an > bn) cy = mpn_sub_1 (rp + bn, ap + bn, an - bn, cy); return cy; } mp_limb_t mpn_mul_1 (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_limb_t vl) { mp_limb_t ul, cl, hpl, lpl; assert (n >= 1); cl = 0; do { ul = *up++; gmp_umul_ppmm (hpl, lpl, ul, vl); lpl += cl; cl = (lpl < cl) + hpl; *rp++ = lpl; } while (--n != 0); return cl; } mp_limb_t mpn_addmul_1 (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_limb_t vl) { mp_limb_t ul, cl, hpl, lpl, rl; assert (n >= 1); cl = 0; do { ul = *up++; gmp_umul_ppmm (hpl, lpl, ul, vl); lpl += cl; cl = (lpl < cl) + hpl; rl = *rp; lpl = rl + lpl; cl += lpl < rl; *rp++ = lpl; } while (--n != 0); return cl; } mp_limb_t mpn_submul_1 (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_limb_t vl) { mp_limb_t ul, cl, hpl, lpl, rl; assert (n >= 1); cl = 0; do { ul = *up++; gmp_umul_ppmm (hpl, lpl, ul, vl); lpl += cl; cl = (lpl < cl) + hpl; rl = *rp; lpl = rl - lpl; cl += lpl > rl; *rp++ = lpl; } while (--n != 0); return cl; } mp_limb_t mpn_mul (mp_ptr rp, mp_srcptr up, mp_size_t un, mp_srcptr vp, mp_size_t vn) { assert (un >= vn); assert (vn >= 1); assert (!GMP_MPN_OVERLAP_P(rp, un + vn, up, un)); assert (!GMP_MPN_OVERLAP_P(rp, un + vn, vp, vn)); /* We first multiply by the low order limb. This result can be stored, not added, to rp. We also avoid a loop for zeroing this way. */ rp[un] = mpn_mul_1 (rp, up, un, vp[0]); /* Now accumulate the product of up[] and the next higher limb from vp[]. */ while (--vn >= 1) { rp += 1, vp += 1; rp[un] = mpn_addmul_1 (rp, up, un, vp[0]); } return rp[un]; } void mpn_mul_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n) { mpn_mul (rp, ap, n, bp, n); } void mpn_sqr (mp_ptr rp, mp_srcptr ap, mp_size_t n) { mpn_mul (rp, ap, n, ap, n); } mp_limb_t mpn_lshift (mp_ptr rp, mp_srcptr up, mp_size_t n, unsigned int cnt) { mp_limb_t high_limb, low_limb; unsigned int tnc; mp_limb_t retval; assert (n >= 1); assert (cnt >= 1); assert (cnt < GMP_LIMB_BITS); up += n; rp += n; tnc = GMP_LIMB_BITS - cnt; low_limb = *--up; retval = low_limb >> tnc; high_limb = (low_limb << cnt); while (--n != 0) { low_limb = *--up; *--rp = high_limb | (low_limb >> tnc); high_limb = (low_limb << cnt); } *--rp = high_limb; return retval; } mp_limb_t mpn_rshift (mp_ptr rp, mp_srcptr up, mp_size_t n, unsigned int cnt) { mp_limb_t high_limb, low_limb; unsigned int tnc; mp_limb_t retval; assert (n >= 1); assert (cnt >= 1); assert (cnt < GMP_LIMB_BITS); tnc = GMP_LIMB_BITS - cnt; high_limb = *up++; retval = (high_limb << tnc); low_limb = high_limb >> cnt; while (--n != 0) { high_limb = *up++; *rp++ = low_limb | (high_limb << tnc); low_limb = high_limb >> cnt; } *rp = low_limb; return retval; } static mp_bitcnt_t mpn_common_scan (mp_limb_t limb, mp_size_t i, mp_srcptr up, mp_size_t un, mp_limb_t ux) { unsigned cnt; assert (ux == 0 || ux == GMP_LIMB_MAX); assert (0 <= i && i <= un ); while (limb == 0) { i++; if (i == un) return (ux == 0 ? ~(mp_bitcnt_t) 0 : un * GMP_LIMB_BITS); limb = ux ^ up[i]; } gmp_ctz (cnt, limb); return (mp_bitcnt_t) i * GMP_LIMB_BITS + cnt; } mp_bitcnt_t mpn_scan1 (mp_srcptr ptr, mp_bitcnt_t bit) { mp_size_t i; i = bit / GMP_LIMB_BITS; return mpn_common_scan ( ptr[i] & (GMP_LIMB_MAX << (bit % GMP_LIMB_BITS)), i, ptr, i, 0); } mp_bitcnt_t mpn_scan0 (mp_srcptr ptr, mp_bitcnt_t bit) { mp_size_t i; i = bit / GMP_LIMB_BITS; return mpn_common_scan (~ptr[i] & (GMP_LIMB_MAX << (bit % GMP_LIMB_BITS)), i, ptr, i, GMP_LIMB_MAX); } void mpn_com (mp_ptr rp, mp_srcptr up, mp_size_t n) { while (--n >= 0) *rp++ = ~ *up++; } mp_limb_t mpn_neg (mp_ptr rp, mp_srcptr up, mp_size_t n) { while (*up == 0) { *rp = 0; if (!--n) return 0; ++up; ++rp; } *rp = - *up; mpn_com (++rp, ++up, --n); return 1; } /* MPN division interface. */ /* The 3/2 inverse is defined as m = floor( (B^3-1) / (B u1 + u0)) - B */ mp_limb_t mpn_invert_3by2 (mp_limb_t u1, mp_limb_t u0) { mp_limb_t r, m; { mp_limb_t p, ql; unsigned ul, uh, qh; /* For notation, let b denote the half-limb base, so that B = b^2. Split u1 = b uh + ul. */ ul = u1 & GMP_LLIMB_MASK; uh = u1 >> (GMP_LIMB_BITS / 2); /* Approximation of the high half of quotient. Differs from the 2/1 inverse of the half limb uh, since we have already subtracted u0. */ qh = (u1 ^ GMP_LIMB_MAX) / uh; /* Adjust to get a half-limb 3/2 inverse, i.e., we want qh' = floor( (b^3 - 1) / u) - b = floor ((b^3 - b u - 1) / u = floor( (b (~u) + b-1) / u), and the remainder r = b (~u) + b-1 - qh (b uh + ul) = b (~u - qh uh) + b-1 - qh ul Subtraction of qh ul may underflow, which implies adjustments. But by normalization, 2 u >= B > qh ul, so we need to adjust by at most 2. */ r = ((~u1 - (mp_limb_t) qh * uh) << (GMP_LIMB_BITS / 2)) | GMP_LLIMB_MASK; p = (mp_limb_t) qh * ul; /* Adjustment steps taken from udiv_qrnnd_c */ if (r < p) { qh--; r += u1; if (r >= u1) /* i.e. we didn't get carry when adding to r */ if (r < p) { qh--; r += u1; } } r -= p; /* Low half of the quotient is ql = floor ( (b r + b-1) / u1). This is a 3/2 division (on half-limbs), for which qh is a suitable inverse. */ p = (r >> (GMP_LIMB_BITS / 2)) * qh + r; /* Unlike full-limb 3/2, we can add 1 without overflow. For this to work, it is essential that ql is a full mp_limb_t. */ ql = (p >> (GMP_LIMB_BITS / 2)) + 1; /* By the 3/2 trick, we don't need the high half limb. */ r = (r << (GMP_LIMB_BITS / 2)) + GMP_LLIMB_MASK - ql * u1; if (r >= (GMP_LIMB_MAX & (p << (GMP_LIMB_BITS / 2)))) { ql--; r += u1; } m = ((mp_limb_t) qh << (GMP_LIMB_BITS / 2)) + ql; if (r >= u1) { m++; r -= u1; } } /* Now m is the 2/1 inverse of u1. If u0 > 0, adjust it to become a 3/2 inverse. */ if (u0 > 0) { mp_limb_t th, tl; r = ~r; r += u0; if (r < u0) { m--; if (r >= u1) { m--; r -= u1; } r -= u1; } gmp_umul_ppmm (th, tl, u0, m); r += th; if (r < th) { m--; m -= ((r > u1) | ((r == u1) & (tl > u0))); } } return m; } struct gmp_div_inverse { /* Normalization shift count. */ unsigned shift; /* Normalized divisor (d0 unused for mpn_div_qr_1) */ mp_limb_t d1, d0; /* Inverse, for 2/1 or 3/2. */ mp_limb_t di; }; static void mpn_div_qr_1_invert (struct gmp_div_inverse *inv, mp_limb_t d) { unsigned shift; assert (d > 0); gmp_clz (shift, d); inv->shift = shift; inv->d1 = d << shift; inv->di = mpn_invert_limb (inv->d1); } static void mpn_div_qr_2_invert (struct gmp_div_inverse *inv, mp_limb_t d1, mp_limb_t d0) { unsigned shift; assert (d1 > 0); gmp_clz (shift, d1); inv->shift = shift; if (shift > 0) { d1 = (d1 << shift) | (d0 >> (GMP_LIMB_BITS - shift)); d0 <<= shift; } inv->d1 = d1; inv->d0 = d0; inv->di = mpn_invert_3by2 (d1, d0); } static void mpn_div_qr_invert (struct gmp_div_inverse *inv, mp_srcptr dp, mp_size_t dn) { assert (dn > 0); if (dn == 1) mpn_div_qr_1_invert (inv, dp[0]); else if (dn == 2) mpn_div_qr_2_invert (inv, dp[1], dp[0]); else { unsigned shift; mp_limb_t d1, d0; d1 = dp[dn-1]; d0 = dp[dn-2]; assert (d1 > 0); gmp_clz (shift, d1); inv->shift = shift; if (shift > 0) { d1 = (d1 << shift) | (d0 >> (GMP_LIMB_BITS - shift)); d0 = (d0 << shift) | (dp[dn-3] >> (GMP_LIMB_BITS - shift)); } inv->d1 = d1; inv->d0 = d0; inv->di = mpn_invert_3by2 (d1, d0); } } /* Not matching current public gmp interface, rather corresponding to the sbpi1_div_* functions. */ static mp_limb_t mpn_div_qr_1_preinv (mp_ptr qp, mp_srcptr np, mp_size_t nn, const struct gmp_div_inverse *inv) { mp_limb_t d, di; mp_limb_t r; mp_ptr tp = NULL; if (inv->shift > 0) { /* Shift, reusing qp area if possible. In-place shift if qp == np. */ tp = qp ? qp : gmp_xalloc_limbs (nn); r = mpn_lshift (tp, np, nn, inv->shift); np = tp; } else r = 0; d = inv->d1; di = inv->di; while (--nn >= 0) { mp_limb_t q; gmp_udiv_qrnnd_preinv (q, r, r, np[nn], d, di); if (qp) qp[nn] = q; } if ((inv->shift > 0) && (tp != qp)) gmp_free (tp); return r >> inv->shift; } static void mpn_div_qr_2_preinv (mp_ptr qp, mp_ptr np, mp_size_t nn, const struct gmp_div_inverse *inv) { unsigned shift; mp_size_t i; mp_limb_t d1, d0, di, r1, r0; assert (nn >= 2); shift = inv->shift; d1 = inv->d1; d0 = inv->d0; di = inv->di; if (shift > 0) r1 = mpn_lshift (np, np, nn, shift); else r1 = 0; r0 = np[nn - 1]; i = nn - 2; do { mp_limb_t n0, q; n0 = np[i]; gmp_udiv_qr_3by2 (q, r1, r0, r1, r0, n0, d1, d0, di); if (qp) qp[i] = q; } while (--i >= 0); if (shift > 0) { assert ((r0 & (GMP_LIMB_MAX >> (GMP_LIMB_BITS - shift))) == 0); r0 = (r0 >> shift) | (r1 << (GMP_LIMB_BITS - shift)); r1 >>= shift; } np[1] = r1; np[0] = r0; } static void mpn_div_qr_pi1 (mp_ptr qp, mp_ptr np, mp_size_t nn, mp_limb_t n1, mp_srcptr dp, mp_size_t dn, mp_limb_t dinv) { mp_size_t i; mp_limb_t d1, d0; mp_limb_t cy, cy1; mp_limb_t q; assert (dn > 2); assert (nn >= dn); d1 = dp[dn - 1]; d0 = dp[dn - 2]; assert ((d1 & GMP_LIMB_HIGHBIT) != 0); /* Iteration variable is the index of the q limb. * * We divide * by */ i = nn - dn; do { mp_limb_t n0 = np[dn-1+i]; if (n1 == d1 && n0 == d0) { q = GMP_LIMB_MAX; mpn_submul_1 (np+i, dp, dn, q); n1 = np[dn-1+i]; /* update n1, last loop's value will now be invalid */ } else { gmp_udiv_qr_3by2 (q, n1, n0, n1, n0, np[dn-2+i], d1, d0, dinv); cy = mpn_submul_1 (np + i, dp, dn-2, q); cy1 = n0 < cy; n0 = n0 - cy; cy = n1 < cy1; n1 = n1 - cy1; np[dn-2+i] = n0; if (cy != 0) { n1 += d1 + mpn_add_n (np + i, np + i, dp, dn - 1); q--; } } if (qp) qp[i] = q; } while (--i >= 0); np[dn - 1] = n1; } static void mpn_div_qr_preinv (mp_ptr qp, mp_ptr np, mp_size_t nn, mp_srcptr dp, mp_size_t dn, const struct gmp_div_inverse *inv) { assert (dn > 0); assert (nn >= dn); if (dn == 1) np[0] = mpn_div_qr_1_preinv (qp, np, nn, inv); else if (dn == 2) mpn_div_qr_2_preinv (qp, np, nn, inv); else { mp_limb_t nh; unsigned shift; assert (inv->d1 == dp[dn-1]); assert (inv->d0 == dp[dn-2]); assert ((inv->d1 & GMP_LIMB_HIGHBIT) != 0); shift = inv->shift; if (shift > 0) nh = mpn_lshift (np, np, nn, shift); else nh = 0; mpn_div_qr_pi1 (qp, np, nn, nh, dp, dn, inv->di); if (shift > 0) gmp_assert_nocarry (mpn_rshift (np, np, dn, shift)); } } static void mpn_div_qr (mp_ptr qp, mp_ptr np, mp_size_t nn, mp_srcptr dp, mp_size_t dn) { struct gmp_div_inverse inv; mp_ptr tp = NULL; assert (dn > 0); assert (nn >= dn); mpn_div_qr_invert (&inv, dp, dn); if (dn > 2 && inv.shift > 0) { tp = gmp_xalloc_limbs (dn); gmp_assert_nocarry (mpn_lshift (tp, dp, dn, inv.shift)); dp = tp; } mpn_div_qr_preinv (qp, np, nn, dp, dn, &inv); if (tp) gmp_free (tp); } /* MPN base conversion. */ static unsigned mpn_base_power_of_two_p (unsigned b) { switch (b) { case 2: return 1; case 4: return 2; case 8: return 3; case 16: return 4; case 32: return 5; case 64: return 6; case 128: return 7; case 256: return 8; default: return 0; } } struct mpn_base_info { /* bb is the largest power of the base which fits in one limb, and exp is the corresponding exponent. */ unsigned exp; mp_limb_t bb; }; static void mpn_get_base_info (struct mpn_base_info *info, mp_limb_t b) { mp_limb_t m; mp_limb_t p; unsigned exp; m = GMP_LIMB_MAX / b; for (exp = 1, p = b; p <= m; exp++) p *= b; info->exp = exp; info->bb = p; } static mp_bitcnt_t mpn_limb_size_in_base_2 (mp_limb_t u) { unsigned shift; assert (u > 0); gmp_clz (shift, u); return GMP_LIMB_BITS - shift; } static size_t mpn_get_str_bits (unsigned char *sp, unsigned bits, mp_srcptr up, mp_size_t un) { unsigned char mask; size_t sn, j; mp_size_t i; unsigned shift; sn = ((un - 1) * GMP_LIMB_BITS + mpn_limb_size_in_base_2 (up[un-1]) + bits - 1) / bits; mask = (1U << bits) - 1; for (i = 0, j = sn, shift = 0; j-- > 0;) { unsigned char digit = up[i] >> shift; shift += bits; if (shift >= GMP_LIMB_BITS && ++i < un) { shift -= GMP_LIMB_BITS; digit |= up[i] << (bits - shift); } sp[j] = digit & mask; } return sn; } /* We generate digits from the least significant end, and reverse at the end. */ static size_t mpn_limb_get_str (unsigned char *sp, mp_limb_t w, const struct gmp_div_inverse *binv) { mp_size_t i; for (i = 0; w > 0; i++) { mp_limb_t h, l, r; h = w >> (GMP_LIMB_BITS - binv->shift); l = w << binv->shift; gmp_udiv_qrnnd_preinv (w, r, h, l, binv->d1, binv->di); assert ((r & (GMP_LIMB_MAX >> (GMP_LIMB_BITS - binv->shift))) == 0); r >>= binv->shift; sp[i] = r; } return i; } static size_t mpn_get_str_other (unsigned char *sp, int base, const struct mpn_base_info *info, mp_ptr up, mp_size_t un) { struct gmp_div_inverse binv; size_t sn; size_t i; mpn_div_qr_1_invert (&binv, base); sn = 0; if (un > 1) { struct gmp_div_inverse bbinv; mpn_div_qr_1_invert (&bbinv, info->bb); do { mp_limb_t w; size_t done; w = mpn_div_qr_1_preinv (up, up, un, &bbinv); un -= (up[un-1] == 0); done = mpn_limb_get_str (sp + sn, w, &binv); for (sn += done; done < info->exp; done++) sp[sn++] = 0; } while (un > 1); } sn += mpn_limb_get_str (sp + sn, up[0], &binv); /* Reverse order */ for (i = 0; 2*i + 1 < sn; i++) { unsigned char t = sp[i]; sp[i] = sp[sn - i - 1]; sp[sn - i - 1] = t; } return sn; } size_t mpn_get_str (unsigned char *sp, int base, mp_ptr up, mp_size_t un) { unsigned bits; assert (un > 0); assert (up[un-1] > 0); bits = mpn_base_power_of_two_p (base); if (bits) return mpn_get_str_bits (sp, bits, up, un); else { struct mpn_base_info info; mpn_get_base_info (&info, base); return mpn_get_str_other (sp, base, &info, up, un); } } static mp_size_t mpn_set_str_bits (mp_ptr rp, const unsigned char *sp, size_t sn, unsigned bits) { mp_size_t rn; size_t j; unsigned shift; for (j = sn, rn = 0, shift = 0; j-- > 0; ) { if (shift == 0) { rp[rn++] = sp[j]; shift += bits; } else { rp[rn-1] |= (mp_limb_t) sp[j] << shift; shift += bits; if (shift >= GMP_LIMB_BITS) { shift -= GMP_LIMB_BITS; if (shift > 0) rp[rn++] = (mp_limb_t) sp[j] >> (bits - shift); } } } rn = mpn_normalized_size (rp, rn); return rn; } /* Result is usually normalized, except for all-zero input, in which case a single zero limb is written at *RP, and 1 is returned. */ static mp_size_t mpn_set_str_other (mp_ptr rp, const unsigned char *sp, size_t sn, mp_limb_t b, const struct mpn_base_info *info) { mp_size_t rn; mp_limb_t w; unsigned k; size_t j; assert (sn > 0); k = 1 + (sn - 1) % info->exp; j = 0; w = sp[j++]; while (--k != 0) w = w * b + sp[j++]; rp[0] = w; for (rn = 1; j < sn;) { mp_limb_t cy; w = sp[j++]; for (k = 1; k < info->exp; k++) w = w * b + sp[j++]; cy = mpn_mul_1 (rp, rp, rn, info->bb); cy += mpn_add_1 (rp, rp, rn, w); if (cy > 0) rp[rn++] = cy; } assert (j == sn); return rn; } mp_size_t mpn_set_str (mp_ptr rp, const unsigned char *sp, size_t sn, int base) { unsigned bits; if (sn == 0) return 0; bits = mpn_base_power_of_two_p (base); if (bits) return mpn_set_str_bits (rp, sp, sn, bits); else { struct mpn_base_info info; mpn_get_base_info (&info, base); return mpn_set_str_other (rp, sp, sn, base, &info); } } /* MPZ interface */ void mpz_init (mpz_t r) { static const mp_limb_t dummy_limb = GMP_LIMB_MAX & 0xc1a0; r->_mp_alloc = 0; r->_mp_size = 0; r->_mp_d = (mp_ptr) &dummy_limb; } /* The utility of this function is a bit limited, since many functions assigns the result variable using mpz_swap. */ void mpz_init2 (mpz_t r, mp_bitcnt_t bits) { mp_size_t rn; bits -= (bits != 0); /* Round down, except if 0 */ rn = 1 + bits / GMP_LIMB_BITS; r->_mp_alloc = rn; r->_mp_size = 0; r->_mp_d = gmp_xalloc_limbs (rn); } void mpz_clear (mpz_t r) { if (r->_mp_alloc) gmp_free (r->_mp_d); } static mp_ptr mpz_realloc (mpz_t r, mp_size_t size) { size = GMP_MAX (size, 1); if (r->_mp_alloc) r->_mp_d = gmp_xrealloc_limbs (r->_mp_d, size); else r->_mp_d = gmp_xalloc_limbs (size); r->_mp_alloc = size; if (GMP_ABS (r->_mp_size) > size) r->_mp_size = 0; return r->_mp_d; } /* Realloc for an mpz_t WHAT if it has less than NEEDED limbs. */ #define MPZ_REALLOC(z,n) ((n) > (z)->_mp_alloc \ ? mpz_realloc(z,n) \ : (z)->_mp_d) /* MPZ assignment and basic conversions. */ void mpz_set_si (mpz_t r, signed long int x) { if (x >= 0) mpz_set_ui (r, x); else /* (x < 0) */ if (GMP_LIMB_BITS < GMP_ULONG_BITS) { mpz_set_ui (r, GMP_NEG_CAST (unsigned long int, x)); mpz_neg (r, r); } else { r->_mp_size = -1; MPZ_REALLOC (r, 1)[0] = GMP_NEG_CAST (unsigned long int, x); } } void mpz_set_ui (mpz_t r, unsigned long int x) { if (x > 0) { r->_mp_size = 1; MPZ_REALLOC (r, 1)[0] = x; if (GMP_LIMB_BITS < GMP_ULONG_BITS) { int LOCAL_GMP_LIMB_BITS = GMP_LIMB_BITS; while (x >>= LOCAL_GMP_LIMB_BITS) { ++ r->_mp_size; MPZ_REALLOC (r, r->_mp_size)[r->_mp_size - 1] = x; } } } else r->_mp_size = 0; } void mpz_set (mpz_t r, const mpz_t x) { /* Allow the NOP r == x */ if (r != x) { mp_size_t n; mp_ptr rp; n = GMP_ABS (x->_mp_size); rp = MPZ_REALLOC (r, n); mpn_copyi (rp, x->_mp_d, n); r->_mp_size = x->_mp_size; } } void mpz_init_set_si (mpz_t r, signed long int x) { mpz_init (r); mpz_set_si (r, x); } void mpz_init_set_ui (mpz_t r, unsigned long int x) { mpz_init (r); mpz_set_ui (r, x); } void mpz_init_set (mpz_t r, const mpz_t x) { mpz_init (r); mpz_set (r, x); } int mpz_fits_slong_p (const mpz_t u) { return (LONG_MAX + LONG_MIN == 0 || mpz_cmp_ui (u, LONG_MAX) <= 0) && mpz_cmpabs_ui (u, GMP_NEG_CAST (unsigned long int, LONG_MIN)) <= 0; } static int mpn_absfits_ulong_p (mp_srcptr up, mp_size_t un) { int ulongsize = GMP_ULONG_BITS / GMP_LIMB_BITS; mp_limb_t ulongrem = 0; if (GMP_ULONG_BITS % GMP_LIMB_BITS != 0) ulongrem = (mp_limb_t) (ULONG_MAX >> GMP_LIMB_BITS * ulongsize) + 1; return un <= ulongsize || (up[ulongsize] < ulongrem && un == ulongsize + 1); } int mpz_fits_ulong_p (const mpz_t u) { mp_size_t us = u->_mp_size; return us >= 0 && mpn_absfits_ulong_p (u->_mp_d, us); } long int mpz_get_si (const mpz_t u) { unsigned long r = mpz_get_ui (u); unsigned long c = -LONG_MAX - LONG_MIN; if (u->_mp_size < 0) /* This expression is necessary to properly handle -LONG_MIN */ return -(long) c - (long) ((r - c) & LONG_MAX); else return (long) (r & LONG_MAX); } unsigned long int mpz_get_ui (const mpz_t u) { if (GMP_LIMB_BITS < GMP_ULONG_BITS) { int LOCAL_GMP_LIMB_BITS = GMP_LIMB_BITS; unsigned long r = 0; mp_size_t n = GMP_ABS (u->_mp_size); n = GMP_MIN (n, 1 + (mp_size_t) (GMP_ULONG_BITS - 1) / GMP_LIMB_BITS); while (--n >= 0) r = (r << LOCAL_GMP_LIMB_BITS) + u->_mp_d[n]; return r; } return u->_mp_size == 0 ? 0 : u->_mp_d[0]; } size_t mpz_size (const mpz_t u) { return GMP_ABS (u->_mp_size); } mp_limb_t mpz_getlimbn (const mpz_t u, mp_size_t n) { if (n >= 0 && n < GMP_ABS (u->_mp_size)) return u->_mp_d[n]; else return 0; } void mpz_realloc2 (mpz_t x, mp_bitcnt_t n) { mpz_realloc (x, 1 + (n - (n != 0)) / GMP_LIMB_BITS); } mp_srcptr mpz_limbs_read (mpz_srcptr x) { return x->_mp_d; } mp_ptr mpz_limbs_modify (mpz_t x, mp_size_t n) { assert (n > 0); return MPZ_REALLOC (x, n); } mp_ptr mpz_limbs_write (mpz_t x, mp_size_t n) { return mpz_limbs_modify (x, n); } void mpz_limbs_finish (mpz_t x, mp_size_t xs) { mp_size_t xn; xn = mpn_normalized_size (x->_mp_d, GMP_ABS (xs)); x->_mp_size = xs < 0 ? -xn : xn; } static mpz_srcptr mpz_roinit_normal_n (mpz_t x, mp_srcptr xp, mp_size_t xs) { x->_mp_alloc = 0; x->_mp_d = (mp_ptr) xp; x->_mp_size = xs; return x; } mpz_srcptr mpz_roinit_n (mpz_t x, mp_srcptr xp, mp_size_t xs) { mpz_roinit_normal_n (x, xp, xs); mpz_limbs_finish (x, xs); return x; } /* Conversions and comparison to double. */ void mpz_set_d (mpz_t r, double x) { int sign; mp_ptr rp; mp_size_t rn, i; double B; double Bi; mp_limb_t f; /* x != x is true when x is a NaN, and x == x * 0.5 is true when x is zero or infinity. */ if (x != x || x == x * 0.5) { r->_mp_size = 0; return; } sign = x < 0.0 ; if (sign) x = - x; if (x < 1.0) { r->_mp_size = 0; return; } B = 4.0 * (double) (GMP_LIMB_HIGHBIT >> 1); Bi = 1.0 / B; for (rn = 1; x >= B; rn++) x *= Bi; rp = MPZ_REALLOC (r, rn); f = (mp_limb_t) x; x -= f; assert (x < 1.0); i = rn-1; rp[i] = f; while (--i >= 0) { x = B * x; f = (mp_limb_t) x; x -= f; assert (x < 1.0); rp[i] = f; } r->_mp_size = sign ? - rn : rn; } void mpz_init_set_d (mpz_t r, double x) { mpz_init (r); mpz_set_d (r, x); } double mpz_get_d (const mpz_t u) { int m; mp_limb_t l; mp_size_t un; double x; double B = 4.0 * (double) (GMP_LIMB_HIGHBIT >> 1); un = GMP_ABS (u->_mp_size); if (un == 0) return 0.0; l = u->_mp_d[--un]; gmp_clz (m, l); m = m + GMP_DBL_MANT_BITS - GMP_LIMB_BITS; if (m < 0) l &= GMP_LIMB_MAX << -m; for (x = l; --un >= 0;) { x = B*x; if (m > 0) { l = u->_mp_d[un]; m -= GMP_LIMB_BITS; if (m < 0) l &= GMP_LIMB_MAX << -m; x += l; } } if (u->_mp_size < 0) x = -x; return x; } int mpz_cmpabs_d (const mpz_t x, double d) { mp_size_t xn; double B, Bi; mp_size_t i; xn = x->_mp_size; d = GMP_ABS (d); if (xn != 0) { xn = GMP_ABS (xn); B = 4.0 * (double) (GMP_LIMB_HIGHBIT >> 1); Bi = 1.0 / B; /* Scale d so it can be compared with the top limb. */ for (i = 1; i < xn; i++) d *= Bi; if (d >= B) return -1; /* Compare floor(d) to top limb, subtract and cancel when equal. */ for (i = xn; i-- > 0;) { mp_limb_t f, xl; f = (mp_limb_t) d; xl = x->_mp_d[i]; if (xl > f) return 1; else if (xl < f) return -1; d = B * (d - f); } } return - (d > 0.0); } int mpz_cmp_d (const mpz_t x, double d) { if (x->_mp_size < 0) { if (d >= 0.0) return -1; else return -mpz_cmpabs_d (x, d); } else { if (d < 0.0) return 1; else return mpz_cmpabs_d (x, d); } } /* MPZ comparisons and the like. */ int mpz_sgn (const mpz_t u) { return GMP_CMP (u->_mp_size, 0); } int mpz_cmp_si (const mpz_t u, long v) { mp_size_t usize = u->_mp_size; if (v >= 0) return mpz_cmp_ui (u, v); else if (usize >= 0) return 1; else return - mpz_cmpabs_ui (u, GMP_NEG_CAST (unsigned long int, v)); } int mpz_cmp_ui (const mpz_t u, unsigned long v) { mp_size_t usize = u->_mp_size; if (usize < 0) return -1; else return mpz_cmpabs_ui (u, v); } int mpz_cmp (const mpz_t a, const mpz_t b) { mp_size_t asize = a->_mp_size; mp_size_t bsize = b->_mp_size; if (asize != bsize) return (asize < bsize) ? -1 : 1; else if (asize >= 0) return mpn_cmp (a->_mp_d, b->_mp_d, asize); else return mpn_cmp (b->_mp_d, a->_mp_d, -asize); } int mpz_cmpabs_ui (const mpz_t u, unsigned long v) { mp_size_t un = GMP_ABS (u->_mp_size); if (! mpn_absfits_ulong_p (u->_mp_d, un)) return 1; else { unsigned long uu = mpz_get_ui (u); return GMP_CMP(uu, v); } } int mpz_cmpabs (const mpz_t u, const mpz_t v) { return mpn_cmp4 (u->_mp_d, GMP_ABS (u->_mp_size), v->_mp_d, GMP_ABS (v->_mp_size)); } void mpz_abs (mpz_t r, const mpz_t u) { mpz_set (r, u); r->_mp_size = GMP_ABS (r->_mp_size); } void mpz_neg (mpz_t r, const mpz_t u) { mpz_set (r, u); r->_mp_size = -r->_mp_size; } void mpz_swap (mpz_t u, mpz_t v) { MP_SIZE_T_SWAP (u->_mp_size, v->_mp_size); MP_SIZE_T_SWAP (u->_mp_alloc, v->_mp_alloc); MP_PTR_SWAP (u->_mp_d, v->_mp_d); } /* MPZ addition and subtraction */ void mpz_add_ui (mpz_t r, const mpz_t a, unsigned long b) { mpz_t bb; mpz_init_set_ui (bb, b); mpz_add (r, a, bb); mpz_clear (bb); } void mpz_sub_ui (mpz_t r, const mpz_t a, unsigned long b) { mpz_ui_sub (r, b, a); mpz_neg (r, r); } void mpz_ui_sub (mpz_t r, unsigned long a, const mpz_t b) { mpz_neg (r, b); mpz_add_ui (r, r, a); } static mp_size_t mpz_abs_add (mpz_t r, const mpz_t a, const mpz_t b) { mp_size_t an = GMP_ABS (a->_mp_size); mp_size_t bn = GMP_ABS (b->_mp_size); mp_ptr rp; mp_limb_t cy; if (an < bn) { MPZ_SRCPTR_SWAP (a, b); MP_SIZE_T_SWAP (an, bn); } rp = MPZ_REALLOC (r, an + 1); cy = mpn_add (rp, a->_mp_d, an, b->_mp_d, bn); rp[an] = cy; return an + cy; } static mp_size_t mpz_abs_sub (mpz_t r, const mpz_t a, const mpz_t b) { mp_size_t an = GMP_ABS (a->_mp_size); mp_size_t bn = GMP_ABS (b->_mp_size); int cmp; mp_ptr rp; cmp = mpn_cmp4 (a->_mp_d, an, b->_mp_d, bn); if (cmp > 0) { rp = MPZ_REALLOC (r, an); gmp_assert_nocarry (mpn_sub (rp, a->_mp_d, an, b->_mp_d, bn)); return mpn_normalized_size (rp, an); } else if (cmp < 0) { rp = MPZ_REALLOC (r, bn); gmp_assert_nocarry (mpn_sub (rp, b->_mp_d, bn, a->_mp_d, an)); return -mpn_normalized_size (rp, bn); } else return 0; } void mpz_add (mpz_t r, const mpz_t a, const mpz_t b) { mp_size_t rn; if ( (a->_mp_size ^ b->_mp_size) >= 0) rn = mpz_abs_add (r, a, b); else rn = mpz_abs_sub (r, a, b); r->_mp_size = a->_mp_size >= 0 ? rn : - rn; } void mpz_sub (mpz_t r, const mpz_t a, const mpz_t b) { mp_size_t rn; if ( (a->_mp_size ^ b->_mp_size) >= 0) rn = mpz_abs_sub (r, a, b); else rn = mpz_abs_add (r, a, b); r->_mp_size = a->_mp_size >= 0 ? rn : - rn; } /* MPZ multiplication */ void mpz_mul_si (mpz_t r, const mpz_t u, long int v) { if (v < 0) { mpz_mul_ui (r, u, GMP_NEG_CAST (unsigned long int, v)); mpz_neg (r, r); } else mpz_mul_ui (r, u, v); } void mpz_mul_ui (mpz_t r, const mpz_t u, unsigned long int v) { mpz_t vv; mpz_init_set_ui (vv, v); mpz_mul (r, u, vv); mpz_clear (vv); return; } void mpz_mul (mpz_t r, const mpz_t u, const mpz_t v) { int sign; mp_size_t un, vn, rn; mpz_t t; mp_ptr tp; un = u->_mp_size; vn = v->_mp_size; if (un == 0 || vn == 0) { r->_mp_size = 0; return; } sign = (un ^ vn) < 0; un = GMP_ABS (un); vn = GMP_ABS (vn); mpz_init2 (t, (un + vn) * GMP_LIMB_BITS); tp = t->_mp_d; if (un >= vn) mpn_mul (tp, u->_mp_d, un, v->_mp_d, vn); else mpn_mul (tp, v->_mp_d, vn, u->_mp_d, un); rn = un + vn; rn -= tp[rn-1] == 0; t->_mp_size = sign ? - rn : rn; mpz_swap (r, t); mpz_clear (t); } void mpz_mul_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t bits) { mp_size_t un, rn; mp_size_t limbs; unsigned shift; mp_ptr rp; un = GMP_ABS (u->_mp_size); if (un == 0) { r->_mp_size = 0; return; } limbs = bits / GMP_LIMB_BITS; shift = bits % GMP_LIMB_BITS; rn = un + limbs + (shift > 0); rp = MPZ_REALLOC (r, rn); if (shift > 0) { mp_limb_t cy = mpn_lshift (rp + limbs, u->_mp_d, un, shift); rp[rn-1] = cy; rn -= (cy == 0); } else mpn_copyd (rp + limbs, u->_mp_d, un); mpn_zero (rp, limbs); r->_mp_size = (u->_mp_size < 0) ? - rn : rn; } void mpz_addmul_ui (mpz_t r, const mpz_t u, unsigned long int v) { mpz_t t; mpz_init_set_ui (t, v); mpz_mul (t, u, t); mpz_add (r, r, t); mpz_clear (t); } void mpz_submul_ui (mpz_t r, const mpz_t u, unsigned long int v) { mpz_t t; mpz_init_set_ui (t, v); mpz_mul (t, u, t); mpz_sub (r, r, t); mpz_clear (t); } void mpz_addmul (mpz_t r, const mpz_t u, const mpz_t v) { mpz_t t; mpz_init (t); mpz_mul (t, u, v); mpz_add (r, r, t); mpz_clear (t); } void mpz_submul (mpz_t r, const mpz_t u, const mpz_t v) { mpz_t t; mpz_init (t); mpz_mul (t, u, v); mpz_sub (r, r, t); mpz_clear (t); } /* MPZ division */ enum mpz_div_round_mode { GMP_DIV_FLOOR, GMP_DIV_CEIL, GMP_DIV_TRUNC }; /* Allows q or r to be zero. Returns 1 iff remainder is non-zero. */ static int mpz_div_qr (mpz_t q, mpz_t r, const mpz_t n, const mpz_t d, enum mpz_div_round_mode mode) { mp_size_t ns, ds, nn, dn, qs; ns = n->_mp_size; ds = d->_mp_size; if (ds == 0) gmp_die("mpz_div_qr: Divide by zero."); if (ns == 0) { if (q) q->_mp_size = 0; if (r) r->_mp_size = 0; return 0; } nn = GMP_ABS (ns); dn = GMP_ABS (ds); qs = ds ^ ns; if (nn < dn) { if (mode == GMP_DIV_CEIL && qs >= 0) { /* q = 1, r = n - d */ if (r) mpz_sub (r, n, d); if (q) mpz_set_ui (q, 1); } else if (mode == GMP_DIV_FLOOR && qs < 0) { /* q = -1, r = n + d */ if (r) mpz_add (r, n, d); if (q) mpz_set_si (q, -1); } else { /* q = 0, r = d */ if (r) mpz_set (r, n); if (q) q->_mp_size = 0; } return 1; } else { mp_ptr np, qp; mp_size_t qn, rn; mpz_t tq, tr; mpz_init_set (tr, n); np = tr->_mp_d; qn = nn - dn + 1; if (q) { mpz_init2 (tq, qn * GMP_LIMB_BITS); qp = tq->_mp_d; } else qp = NULL; mpn_div_qr (qp, np, nn, d->_mp_d, dn); if (qp) { qn -= (qp[qn-1] == 0); tq->_mp_size = qs < 0 ? -qn : qn; } rn = mpn_normalized_size (np, dn); tr->_mp_size = ns < 0 ? - rn : rn; if (mode == GMP_DIV_FLOOR && qs < 0 && rn != 0) { if (q) mpz_sub_ui (tq, tq, 1); if (r) mpz_add (tr, tr, d); } else if (mode == GMP_DIV_CEIL && qs >= 0 && rn != 0) { if (q) mpz_add_ui (tq, tq, 1); if (r) mpz_sub (tr, tr, d); } if (q) { mpz_swap (tq, q); mpz_clear (tq); } if (r) mpz_swap (tr, r); mpz_clear (tr); return rn != 0; } } void mpz_cdiv_qr (mpz_t q, mpz_t r, const mpz_t n, const mpz_t d) { mpz_div_qr (q, r, n, d, GMP_DIV_CEIL); } void mpz_fdiv_qr (mpz_t q, mpz_t r, const mpz_t n, const mpz_t d) { mpz_div_qr (q, r, n, d, GMP_DIV_FLOOR); } void mpz_tdiv_qr (mpz_t q, mpz_t r, const mpz_t n, const mpz_t d) { mpz_div_qr (q, r, n, d, GMP_DIV_TRUNC); } void mpz_cdiv_q (mpz_t q, const mpz_t n, const mpz_t d) { mpz_div_qr (q, NULL, n, d, GMP_DIV_CEIL); } void mpz_fdiv_q (mpz_t q, const mpz_t n, const mpz_t d) { mpz_div_qr (q, NULL, n, d, GMP_DIV_FLOOR); } void mpz_tdiv_q (mpz_t q, const mpz_t n, const mpz_t d) { mpz_div_qr (q, NULL, n, d, GMP_DIV_TRUNC); } void mpz_cdiv_r (mpz_t r, const mpz_t n, const mpz_t d) { mpz_div_qr (NULL, r, n, d, GMP_DIV_CEIL); } void mpz_fdiv_r (mpz_t r, const mpz_t n, const mpz_t d) { mpz_div_qr (NULL, r, n, d, GMP_DIV_FLOOR); } void mpz_tdiv_r (mpz_t r, const mpz_t n, const mpz_t d) { mpz_div_qr (NULL, r, n, d, GMP_DIV_TRUNC); } void mpz_mod (mpz_t r, const mpz_t n, const mpz_t d) { mpz_div_qr (NULL, r, n, d, d->_mp_size >= 0 ? GMP_DIV_FLOOR : GMP_DIV_CEIL); } static void mpz_div_q_2exp (mpz_t q, const mpz_t u, mp_bitcnt_t bit_index, enum mpz_div_round_mode mode) { mp_size_t un, qn; mp_size_t limb_cnt; mp_ptr qp; int adjust; un = u->_mp_size; if (un == 0) { q->_mp_size = 0; return; } limb_cnt = bit_index / GMP_LIMB_BITS; qn = GMP_ABS (un) - limb_cnt; bit_index %= GMP_LIMB_BITS; if (mode == ((un > 0) ? GMP_DIV_CEIL : GMP_DIV_FLOOR)) /* un != 0 here. */ /* Note: Below, the final indexing at limb_cnt is valid because at that point we have qn > 0. */ adjust = (qn <= 0 || !mpn_zero_p (u->_mp_d, limb_cnt) || (u->_mp_d[limb_cnt] & (((mp_limb_t) 1 << bit_index) - 1))); else adjust = 0; if (qn <= 0) qn = 0; else { qp = MPZ_REALLOC (q, qn); if (bit_index != 0) { mpn_rshift (qp, u->_mp_d + limb_cnt, qn, bit_index); qn -= qp[qn - 1] == 0; } else { mpn_copyi (qp, u->_mp_d + limb_cnt, qn); } } q->_mp_size = qn; if (adjust) mpz_add_ui (q, q, 1); if (un < 0) mpz_neg (q, q); } static void mpz_div_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t bit_index, enum mpz_div_round_mode mode) { mp_size_t us, un, rn; mp_ptr rp; mp_limb_t mask; us = u->_mp_size; if (us == 0 || bit_index == 0) { r->_mp_size = 0; return; } rn = (bit_index + GMP_LIMB_BITS - 1) / GMP_LIMB_BITS; assert (rn > 0); rp = MPZ_REALLOC (r, rn); un = GMP_ABS (us); mask = GMP_LIMB_MAX >> (rn * GMP_LIMB_BITS - bit_index); if (rn > un) { /* Quotient (with truncation) is zero, and remainder is non-zero */ if (mode == ((us > 0) ? GMP_DIV_CEIL : GMP_DIV_FLOOR)) /* us != 0 here. */ { /* Have to negate and sign extend. */ mp_size_t i; gmp_assert_nocarry (! mpn_neg (rp, u->_mp_d, un)); for (i = un; i < rn - 1; i++) rp[i] = GMP_LIMB_MAX; rp[rn-1] = mask; us = -us; } else { /* Just copy */ if (r != u) mpn_copyi (rp, u->_mp_d, un); rn = un; } } else { if (r != u) mpn_copyi (rp, u->_mp_d, rn - 1); rp[rn-1] = u->_mp_d[rn-1] & mask; if (mode == ((us > 0) ? GMP_DIV_CEIL : GMP_DIV_FLOOR)) /* us != 0 here. */ { /* If r != 0, compute 2^{bit_count} - r. */ mpn_neg (rp, rp, rn); rp[rn-1] &= mask; /* us is not used for anything else, so we can modify it here to indicate flipped sign. */ us = -us; } } rn = mpn_normalized_size (rp, rn); r->_mp_size = us < 0 ? -rn : rn; } void mpz_cdiv_q_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt) { mpz_div_q_2exp (r, u, cnt, GMP_DIV_CEIL); } void mpz_fdiv_q_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt) { mpz_div_q_2exp (r, u, cnt, GMP_DIV_FLOOR); } void mpz_tdiv_q_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt) { mpz_div_q_2exp (r, u, cnt, GMP_DIV_TRUNC); } void mpz_cdiv_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt) { mpz_div_r_2exp (r, u, cnt, GMP_DIV_CEIL); } void mpz_fdiv_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt) { mpz_div_r_2exp (r, u, cnt, GMP_DIV_FLOOR); } void mpz_tdiv_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt) { mpz_div_r_2exp (r, u, cnt, GMP_DIV_TRUNC); } void mpz_divexact (mpz_t q, const mpz_t n, const mpz_t d) { gmp_assert_nocarry (mpz_div_qr (q, NULL, n, d, GMP_DIV_TRUNC)); } int mpz_divisible_p (const mpz_t n, const mpz_t d) { return mpz_div_qr (NULL, NULL, n, d, GMP_DIV_TRUNC) == 0; } int mpz_congruent_p (const mpz_t a, const mpz_t b, const mpz_t m) { mpz_t t; int res; /* a == b (mod 0) iff a == b */ if (mpz_sgn (m) == 0) return (mpz_cmp (a, b) == 0); mpz_init (t); mpz_sub (t, a, b); res = mpz_divisible_p (t, m); mpz_clear (t); return res; } static unsigned long mpz_div_qr_ui (mpz_t q, mpz_t r, const mpz_t n, unsigned long d, enum mpz_div_round_mode mode) { unsigned long ret; mpz_t rr, dd; mpz_init (rr); mpz_init_set_ui (dd, d); mpz_div_qr (q, rr, n, dd, mode); mpz_clear (dd); ret = mpz_get_ui (rr); if (r) mpz_swap (r, rr); mpz_clear (rr); return ret; } unsigned long mpz_cdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, unsigned long d) { return mpz_div_qr_ui (q, r, n, d, GMP_DIV_CEIL); } unsigned long mpz_fdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, unsigned long d) { return mpz_div_qr_ui (q, r, n, d, GMP_DIV_FLOOR); } unsigned long mpz_tdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, unsigned long d) { return mpz_div_qr_ui (q, r, n, d, GMP_DIV_TRUNC); } unsigned long mpz_cdiv_q_ui (mpz_t q, const mpz_t n, unsigned long d) { return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_CEIL); } unsigned long mpz_fdiv_q_ui (mpz_t q, const mpz_t n, unsigned long d) { return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_FLOOR); } unsigned long mpz_tdiv_q_ui (mpz_t q, const mpz_t n, unsigned long d) { return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_TRUNC); } unsigned long mpz_cdiv_r_ui (mpz_t r, const mpz_t n, unsigned long d) { return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_CEIL); } unsigned long mpz_fdiv_r_ui (mpz_t r, const mpz_t n, unsigned long d) { return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_FLOOR); } unsigned long mpz_tdiv_r_ui (mpz_t r, const mpz_t n, unsigned long d) { return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_TRUNC); } unsigned long mpz_cdiv_ui (const mpz_t n, unsigned long d) { return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_CEIL); } unsigned long mpz_fdiv_ui (const mpz_t n, unsigned long d) { return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_FLOOR); } unsigned long mpz_tdiv_ui (const mpz_t n, unsigned long d) { return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_TRUNC); } unsigned long mpz_mod_ui (mpz_t r, const mpz_t n, unsigned long d) { return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_FLOOR); } void mpz_divexact_ui (mpz_t q, const mpz_t n, unsigned long d) { gmp_assert_nocarry (mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_TRUNC)); } int mpz_divisible_ui_p (const mpz_t n, unsigned long d) { return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_TRUNC) == 0; } /* GCD */ static mp_limb_t mpn_gcd_11 (mp_limb_t u, mp_limb_t v) { unsigned shift; assert ( (u | v) > 0); if (u == 0) return v; else if (v == 0) return u; gmp_ctz (shift, u | v); u >>= shift; v >>= shift; if ( (u & 1) == 0) MP_LIMB_T_SWAP (u, v); while ( (v & 1) == 0) v >>= 1; while (u != v) { if (u > v) { u -= v; do u >>= 1; while ( (u & 1) == 0); } else { v -= u; do v >>= 1; while ( (v & 1) == 0); } } return u << shift; } unsigned long mpz_gcd_ui (mpz_t g, const mpz_t u, unsigned long v) { mpz_t t; mpz_init_set_ui(t, v); mpz_gcd (t, u, t); if (v > 0) v = mpz_get_ui (t); if (g) mpz_swap (t, g); mpz_clear (t); return v; } static mp_bitcnt_t mpz_make_odd (mpz_t r) { mp_bitcnt_t shift; assert (r->_mp_size > 0); /* Count trailing zeros, equivalent to mpn_scan1, because we know that there is a 1 */ shift = mpn_common_scan (r->_mp_d[0], 0, r->_mp_d, 0, 0); mpz_tdiv_q_2exp (r, r, shift); return shift; } void mpz_gcd (mpz_t g, const mpz_t u, const mpz_t v) { mpz_t tu, tv; mp_bitcnt_t uz, vz, gz; if (u->_mp_size == 0) { mpz_abs (g, v); return; } if (v->_mp_size == 0) { mpz_abs (g, u); return; } mpz_init (tu); mpz_init (tv); mpz_abs (tu, u); uz = mpz_make_odd (tu); mpz_abs (tv, v); vz = mpz_make_odd (tv); gz = GMP_MIN (uz, vz); if (tu->_mp_size < tv->_mp_size) mpz_swap (tu, tv); mpz_tdiv_r (tu, tu, tv); if (tu->_mp_size == 0) { mpz_swap (g, tv); } else for (;;) { int c; mpz_make_odd (tu); c = mpz_cmp (tu, tv); if (c == 0) { mpz_swap (g, tu); break; } if (c < 0) mpz_swap (tu, tv); if (tv->_mp_size == 1) { mp_limb_t vl = tv->_mp_d[0]; mp_limb_t ul = mpz_tdiv_ui (tu, vl); mpz_set_ui (g, mpn_gcd_11 (ul, vl)); break; } mpz_sub (tu, tu, tv); } mpz_clear (tu); mpz_clear (tv); mpz_mul_2exp (g, g, gz); } void mpz_gcdext (mpz_t g, mpz_t s, mpz_t t, const mpz_t u, const mpz_t v) { mpz_t tu, tv, s0, s1, t0, t1; mp_bitcnt_t uz, vz, gz; mp_bitcnt_t power; if (u->_mp_size == 0) { /* g = 0 u + sgn(v) v */ signed long sign = mpz_sgn (v); mpz_abs (g, v); if (s) s->_mp_size = 0; if (t) mpz_set_si (t, sign); return; } if (v->_mp_size == 0) { /* g = sgn(u) u + 0 v */ signed long sign = mpz_sgn (u); mpz_abs (g, u); if (s) mpz_set_si (s, sign); if (t) t->_mp_size = 0; return; } mpz_init (tu); mpz_init (tv); mpz_init (s0); mpz_init (s1); mpz_init (t0); mpz_init (t1); mpz_abs (tu, u); uz = mpz_make_odd (tu); mpz_abs (tv, v); vz = mpz_make_odd (tv); gz = GMP_MIN (uz, vz); uz -= gz; vz -= gz; /* Cofactors corresponding to odd gcd. gz handled later. */ if (tu->_mp_size < tv->_mp_size) { mpz_swap (tu, tv); MPZ_SRCPTR_SWAP (u, v); MPZ_PTR_SWAP (s, t); MP_BITCNT_T_SWAP (uz, vz); } /* Maintain * * u = t0 tu + t1 tv * v = s0 tu + s1 tv * * where u and v denote the inputs with common factors of two * eliminated, and det (s0, t0; s1, t1) = 2^p. Then * * 2^p tu = s1 u - t1 v * 2^p tv = -s0 u + t0 v */ /* After initial division, tu = q tv + tu', we have * * u = 2^uz (tu' + q tv) * v = 2^vz tv * * or * * t0 = 2^uz, t1 = 2^uz q * s0 = 0, s1 = 2^vz */ mpz_setbit (t0, uz); mpz_tdiv_qr (t1, tu, tu, tv); mpz_mul_2exp (t1, t1, uz); mpz_setbit (s1, vz); power = uz + vz; if (tu->_mp_size > 0) { mp_bitcnt_t shift; shift = mpz_make_odd (tu); mpz_mul_2exp (t0, t0, shift); mpz_mul_2exp (s0, s0, shift); power += shift; for (;;) { int c; c = mpz_cmp (tu, tv); if (c == 0) break; if (c < 0) { /* tv = tv' + tu * * u = t0 tu + t1 (tv' + tu) = (t0 + t1) tu + t1 tv' * v = s0 tu + s1 (tv' + tu) = (s0 + s1) tu + s1 tv' */ mpz_sub (tv, tv, tu); mpz_add (t0, t0, t1); mpz_add (s0, s0, s1); shift = mpz_make_odd (tv); mpz_mul_2exp (t1, t1, shift); mpz_mul_2exp (s1, s1, shift); } else { mpz_sub (tu, tu, tv); mpz_add (t1, t0, t1); mpz_add (s1, s0, s1); shift = mpz_make_odd (tu); mpz_mul_2exp (t0, t0, shift); mpz_mul_2exp (s0, s0, shift); } power += shift; } } /* Now tv = odd part of gcd, and -s0 and t0 are corresponding cofactors. */ mpz_mul_2exp (tv, tv, gz); mpz_neg (s0, s0); /* 2^p g = s0 u + t0 v. Eliminate one factor of two at a time. To adjust cofactors, we need u / g and v / g */ mpz_divexact (s1, v, tv); mpz_abs (s1, s1); mpz_divexact (t1, u, tv); mpz_abs (t1, t1); while (power-- > 0) { /* s0 u + t0 v = (s0 - v/g) u - (t0 + u/g) v */ if (mpz_odd_p (s0) || mpz_odd_p (t0)) { mpz_sub (s0, s0, s1); mpz_add (t0, t0, t1); } assert (mpz_even_p (t0) && mpz_even_p (s0)); mpz_tdiv_q_2exp (s0, s0, 1); mpz_tdiv_q_2exp (t0, t0, 1); } /* Arrange so that |s| < |u| / 2g */ mpz_add (s1, s0, s1); if (mpz_cmpabs (s0, s1) > 0) { mpz_swap (s0, s1); mpz_sub (t0, t0, t1); } if (u->_mp_size < 0) mpz_neg (s0, s0); if (v->_mp_size < 0) mpz_neg (t0, t0); mpz_swap (g, tv); if (s) mpz_swap (s, s0); if (t) mpz_swap (t, t0); mpz_clear (tu); mpz_clear (tv); mpz_clear (s0); mpz_clear (s1); mpz_clear (t0); mpz_clear (t1); } void mpz_lcm (mpz_t r, const mpz_t u, const mpz_t v) { mpz_t g; if (u->_mp_size == 0 || v->_mp_size == 0) { r->_mp_size = 0; return; } mpz_init (g); mpz_gcd (g, u, v); mpz_divexact (g, u, g); mpz_mul (r, g, v); mpz_clear (g); mpz_abs (r, r); } void mpz_lcm_ui (mpz_t r, const mpz_t u, unsigned long v) { if (v == 0 || u->_mp_size == 0) { r->_mp_size = 0; return; } v /= mpz_gcd_ui (NULL, u, v); mpz_mul_ui (r, u, v); mpz_abs (r, r); } int mpz_invert (mpz_t r, const mpz_t u, const mpz_t m) { mpz_t g, tr; int invertible; if (u->_mp_size == 0 || mpz_cmpabs_ui (m, 1) <= 0) return 0; mpz_init (g); mpz_init (tr); mpz_gcdext (g, tr, NULL, u, m); invertible = (mpz_cmp_ui (g, 1) == 0); if (invertible) { if (tr->_mp_size < 0) { if (m->_mp_size >= 0) mpz_add (tr, tr, m); else mpz_sub (tr, tr, m); } mpz_swap (r, tr); } mpz_clear (g); mpz_clear (tr); return invertible; } /* Higher level operations (sqrt, pow and root) */ void mpz_pow_ui (mpz_t r, const mpz_t b, unsigned long e) { unsigned long bit; mpz_t tr; mpz_init_set_ui (tr, 1); bit = GMP_ULONG_HIGHBIT; do { mpz_mul (tr, tr, tr); if (e & bit) mpz_mul (tr, tr, b); bit >>= 1; } while (bit > 0); mpz_swap (r, tr); mpz_clear (tr); } void mpz_ui_pow_ui (mpz_t r, unsigned long blimb, unsigned long e) { mpz_t b; mpz_init_set_ui (b, blimb); mpz_pow_ui (r, b, e); mpz_clear (b); } void mpz_powm (mpz_t r, const mpz_t b, const mpz_t e, const mpz_t m) { mpz_t tr; mpz_t base; mp_size_t en, mn; mp_srcptr mp; struct gmp_div_inverse minv; unsigned shift; mp_ptr tp = NULL; en = GMP_ABS (e->_mp_size); mn = GMP_ABS (m->_mp_size); if (mn == 0) gmp_die ("mpz_powm: Zero modulo."); if (en == 0) { mpz_set_ui (r, 1); return; } mp = m->_mp_d; mpn_div_qr_invert (&minv, mp, mn); shift = minv.shift; if (shift > 0) { /* To avoid shifts, we do all our reductions, except the final one, using a *normalized* m. */ minv.shift = 0; tp = gmp_xalloc_limbs (mn); gmp_assert_nocarry (mpn_lshift (tp, mp, mn, shift)); mp = tp; } mpz_init (base); if (e->_mp_size < 0) { if (!mpz_invert (base, b, m)) gmp_die ("mpz_powm: Negative exponent and non-invertible base."); } else { mp_size_t bn; mpz_abs (base, b); bn = base->_mp_size; if (bn >= mn) { mpn_div_qr_preinv (NULL, base->_mp_d, base->_mp_size, mp, mn, &minv); bn = mn; } /* We have reduced the absolute value. Now take care of the sign. Note that we get zero represented non-canonically as m. */ if (b->_mp_size < 0) { mp_ptr bp = MPZ_REALLOC (base, mn); gmp_assert_nocarry (mpn_sub (bp, mp, mn, bp, bn)); bn = mn; } base->_mp_size = mpn_normalized_size (base->_mp_d, bn); } mpz_init_set_ui (tr, 1); while (--en >= 0) { mp_limb_t w = e->_mp_d[en]; mp_limb_t bit; bit = GMP_LIMB_HIGHBIT; do { mpz_mul (tr, tr, tr); if (w & bit) mpz_mul (tr, tr, base); if (tr->_mp_size > mn) { mpn_div_qr_preinv (NULL, tr->_mp_d, tr->_mp_size, mp, mn, &minv); tr->_mp_size = mpn_normalized_size (tr->_mp_d, mn); } bit >>= 1; } while (bit > 0); } /* Final reduction */ if (tr->_mp_size >= mn) { minv.shift = shift; mpn_div_qr_preinv (NULL, tr->_mp_d, tr->_mp_size, mp, mn, &minv); tr->_mp_size = mpn_normalized_size (tr->_mp_d, mn); } if (tp) gmp_free (tp); mpz_swap (r, tr); mpz_clear (tr); mpz_clear (base); } void mpz_powm_ui (mpz_t r, const mpz_t b, unsigned long elimb, const mpz_t m) { mpz_t e; mpz_init_set_ui (e, elimb); mpz_powm (r, b, e, m); mpz_clear (e); } /* x=trunc(y^(1/z)), r=y-x^z */ void mpz_rootrem (mpz_t x, mpz_t r, const mpz_t y, unsigned long z) { int sgn; mpz_t t, u; sgn = y->_mp_size < 0; if ((~z & sgn) != 0) gmp_die ("mpz_rootrem: Negative argument, with even root."); if (z == 0) gmp_die ("mpz_rootrem: Zeroth root."); if (mpz_cmpabs_ui (y, 1) <= 0) { if (x) mpz_set (x, y); if (r) r->_mp_size = 0; return; } mpz_init (u); mpz_init (t); mpz_setbit (t, mpz_sizeinbase (y, 2) / z + 1); if (z == 2) /* simplify sqrt loop: z-1 == 1 */ do { mpz_swap (u, t); /* u = x */ mpz_tdiv_q (t, y, u); /* t = y/x */ mpz_add (t, t, u); /* t = y/x + x */ mpz_tdiv_q_2exp (t, t, 1); /* x'= (y/x + x)/2 */ } while (mpz_cmpabs (t, u) < 0); /* |x'| < |x| */ else /* z != 2 */ { mpz_t v; mpz_init (v); if (sgn) mpz_neg (t, t); do { mpz_swap (u, t); /* u = x */ mpz_pow_ui (t, u, z - 1); /* t = x^(z-1) */ mpz_tdiv_q (t, y, t); /* t = y/x^(z-1) */ mpz_mul_ui (v, u, z - 1); /* v = x*(z-1) */ mpz_add (t, t, v); /* t = y/x^(z-1) + x*(z-1) */ mpz_tdiv_q_ui (t, t, z); /* x'=(y/x^(z-1) + x*(z-1))/z */ } while (mpz_cmpabs (t, u) < 0); /* |x'| < |x| */ mpz_clear (v); } if (r) { mpz_pow_ui (t, u, z); mpz_sub (r, y, t); } if (x) mpz_swap (x, u); mpz_clear (u); mpz_clear (t); } int mpz_root (mpz_t x, const mpz_t y, unsigned long z) { int res; mpz_t r; mpz_init (r); mpz_rootrem (x, r, y, z); res = r->_mp_size == 0; mpz_clear (r); return res; } /* Compute s = floor(sqrt(u)) and r = u - s^2. Allows r == NULL */ void mpz_sqrtrem (mpz_t s, mpz_t r, const mpz_t u) { mpz_rootrem (s, r, u, 2); } void mpz_sqrt (mpz_t s, const mpz_t u) { mpz_rootrem (s, NULL, u, 2); } int mpz_perfect_square_p (const mpz_t u) { if (u->_mp_size <= 0) return (u->_mp_size == 0); else return mpz_root (NULL, u, 2); } int mpn_perfect_square_p (mp_srcptr p, mp_size_t n) { mpz_t t; assert (n > 0); assert (p [n-1] != 0); return mpz_root (NULL, mpz_roinit_normal_n (t, p, n), 2); } mp_size_t mpn_sqrtrem (mp_ptr sp, mp_ptr rp, mp_srcptr p, mp_size_t n) { mpz_t s, r, u; mp_size_t res; assert (n > 0); assert (p [n-1] != 0); mpz_init (r); mpz_init (s); mpz_rootrem (s, r, mpz_roinit_normal_n (u, p, n), 2); assert (s->_mp_size == (n+1)/2); mpn_copyd (sp, s->_mp_d, s->_mp_size); mpz_clear (s); res = r->_mp_size; if (rp) mpn_copyd (rp, r->_mp_d, res); mpz_clear (r); return res; } /* Combinatorics */ void mpz_mfac_uiui (mpz_t x, unsigned long n, unsigned long m) { mpz_set_ui (x, n + (n == 0)); if (m + 1 < 2) return; while (n > m + 1) mpz_mul_ui (x, x, n -= m); } void mpz_2fac_ui (mpz_t x, unsigned long n) { mpz_mfac_uiui (x, n, 2); } void mpz_fac_ui (mpz_t x, unsigned long n) { mpz_mfac_uiui (x, n, 1); } void mpz_bin_uiui (mpz_t r, unsigned long n, unsigned long k) { mpz_t t; mpz_set_ui (r, k <= n); if (k > (n >> 1)) k = (k <= n) ? n - k : 0; mpz_init (t); mpz_fac_ui (t, k); for (; k > 0; --k) mpz_mul_ui (r, r, n--); mpz_divexact (r, r, t); mpz_clear (t); } /* Primality testing */ /* Computes Kronecker (a/b) with odd b, a!=0 and GCD(a,b) = 1 */ /* Adapted from JACOBI_BASE_METHOD==4 in mpn/generic/jacbase.c */ static int gmp_jacobi_coprime (mp_limb_t a, mp_limb_t b) { int c, bit = 0; assert (b & 1); assert (a != 0); /* assert (mpn_gcd_11 (a, b) == 1); */ /* Below, we represent a and b shifted right so that the least significant one bit is implicit. */ b >>= 1; gmp_ctz(c, a); a >>= 1; do { a >>= c; /* (2/b) = -1 if b = 3 or 5 mod 8 */ bit ^= c & (b ^ (b >> 1)); if (a < b) { bit ^= a & b; a = b - a; b -= a; } else { a -= b; assert (a != 0); } gmp_ctz(c, a); ++c; } while (b > 0); return bit & 1 ? -1 : 1; } static void gmp_lucas_step_k_2k (mpz_t V, mpz_t Qk, const mpz_t n) { mpz_mod (Qk, Qk, n); /* V_{2k} <- V_k ^ 2 - 2Q^k */ mpz_mul (V, V, V); mpz_submul_ui (V, Qk, 2); mpz_tdiv_r (V, V, n); /* Q^{2k} = (Q^k)^2 */ mpz_mul (Qk, Qk, Qk); } /* Computes V_k, Q^k (mod n) for the Lucas' sequence */ /* with P=1, Q=Q; k = (n>>b0)|1. */ /* Requires an odd n > 4; b0 > 0; -2*Q must not overflow a long */ /* Returns (U_k == 0) and sets V=V_k and Qk=Q^k. */ static int gmp_lucas_mod (mpz_t V, mpz_t Qk, long Q, mp_bitcnt_t b0, const mpz_t n) { mp_bitcnt_t bs; mpz_t U; int res; assert (b0 > 0); assert (Q <= - (LONG_MIN / 2)); assert (Q >= - (LONG_MAX / 2)); assert (mpz_cmp_ui (n, 4) > 0); assert (mpz_odd_p (n)); mpz_init_set_ui (U, 1); /* U1 = 1 */ mpz_set_ui (V, 1); /* V1 = 1 */ mpz_set_si (Qk, Q); for (bs = mpz_sizeinbase (n, 2) - 1; --bs >= b0;) { /* U_{2k} <- U_k * V_k */ mpz_mul (U, U, V); /* V_{2k} <- V_k ^ 2 - 2Q^k */ /* Q^{2k} = (Q^k)^2 */ gmp_lucas_step_k_2k (V, Qk, n); /* A step k->k+1 is performed if the bit in $n$ is 1 */ /* mpz_tstbit(n,bs) or the bit is 0 in $n$ but */ /* should be 1 in $n+1$ (bs == b0) */ if (b0 == bs || mpz_tstbit (n, bs)) { /* Q^{k+1} <- Q^k * Q */ mpz_mul_si (Qk, Qk, Q); /* U_{k+1} <- (U_k + V_k) / 2 */ mpz_swap (U, V); /* Keep in V the old value of U_k */ mpz_add (U, U, V); /* We have to compute U/2, so we need an even value, */ /* equivalent (mod n) */ if (mpz_odd_p (U)) mpz_add (U, U, n); mpz_tdiv_q_2exp (U, U, 1); /* V_{k+1} <-(D*U_k + V_k) / 2 = U_{k+1} + (D-1)/2*U_k = U_{k+1} - 2Q*U_k */ mpz_mul_si (V, V, -2*Q); mpz_add (V, U, V); mpz_tdiv_r (V, V, n); } mpz_tdiv_r (U, U, n); } res = U->_mp_size == 0; mpz_clear (U); return res; } /* Performs strong Lucas' test on x, with parameters suggested */ /* for the BPSW test. Qk is only passed to recycle a variable. */ /* Requires GCD (x,6) = 1.*/ static int gmp_stronglucas (const mpz_t x, mpz_t Qk) { mp_bitcnt_t b0; mpz_t V, n; mp_limb_t maxD, D; /* The absolute value is stored. */ long Q; mp_limb_t tl; /* Test on the absolute value. */ mpz_roinit_normal_n (n, x->_mp_d, GMP_ABS (x->_mp_size)); assert (mpz_odd_p (n)); /* assert (mpz_gcd_ui (NULL, n, 6) == 1); */ if (mpz_root (Qk, n, 2)) return 0; /* A square is composite. */ /* Check Ds up to square root (in case, n is prime) or avoid overflows */ maxD = (Qk->_mp_size == 1) ? Qk->_mp_d [0] - 1 : GMP_LIMB_MAX; D = 3; /* Search a D such that (D/n) = -1 in the sequence 5,-7,9,-11,.. */ /* For those Ds we have (D/n) = (n/|D|) */ do { if (D >= maxD) return 1 + (D != GMP_LIMB_MAX); /* (1 + ! ~ D) */ D += 2; tl = mpz_tdiv_ui (n, D); if (tl == 0) return 0; } while (gmp_jacobi_coprime (tl, D) == 1); mpz_init (V); /* n-(D/n) = n+1 = d*2^{b0}, with d = (n>>b0) | 1 */ b0 = mpz_scan0 (n, 0); /* D= P^2 - 4Q; P = 1; Q = (1-D)/4 */ Q = (D & 2) ? (long) (D >> 2) + 1 : -(long) (D >> 2); if (! gmp_lucas_mod (V, Qk, Q, b0, n)) /* If Ud != 0 */ while (V->_mp_size != 0 && --b0 != 0) /* while Vk != 0 */ /* V <- V ^ 2 - 2Q^k */ /* Q^{2k} = (Q^k)^2 */ gmp_lucas_step_k_2k (V, Qk, n); mpz_clear (V); return (b0 != 0); } static int gmp_millerrabin (const mpz_t n, const mpz_t nm1, mpz_t y, const mpz_t q, mp_bitcnt_t k) { assert (k > 0); /* Caller must initialize y to the base. */ mpz_powm (y, y, q, n); if (mpz_cmp_ui (y, 1) == 0 || mpz_cmp (y, nm1) == 0) return 1; while (--k > 0) { mpz_powm_ui (y, y, 2, n); if (mpz_cmp (y, nm1) == 0) return 1; /* y == 1 means that the previous y was a non-trivial square root of 1 (mod n). y == 0 means that n is a power of the base. In either case, n is not prime. */ if (mpz_cmp_ui (y, 1) <= 0) return 0; } return 0; } /* This product is 0xc0cfd797, and fits in 32 bits. */ #define GMP_PRIME_PRODUCT \ (3UL*5UL*7UL*11UL*13UL*17UL*19UL*23UL*29UL) /* Bit (p+1)/2 is set, for each odd prime <= 61 */ #define GMP_PRIME_MASK 0xc96996dcUL int mpz_probab_prime_p (const mpz_t n, int reps) { mpz_t nm1; mpz_t q; mpz_t y; mp_bitcnt_t k; int is_prime; int j; /* Note that we use the absolute value of n only, for compatibility with the real GMP. */ if (mpz_even_p (n)) return (mpz_cmpabs_ui (n, 2) == 0) ? 2 : 0; /* Above test excludes n == 0 */ assert (n->_mp_size != 0); if (mpz_cmpabs_ui (n, 64) < 0) return (GMP_PRIME_MASK >> (n->_mp_d[0] >> 1)) & 2; if (mpz_gcd_ui (NULL, n, GMP_PRIME_PRODUCT) != 1) return 0; /* All prime factors are >= 31. */ if (mpz_cmpabs_ui (n, 31*31) < 0) return 2; mpz_init (nm1); mpz_init (q); /* Find q and k, where q is odd and n = 1 + 2**k * q. */ mpz_abs (nm1, n); nm1->_mp_d[0] -= 1; k = mpz_scan1 (nm1, 0); mpz_tdiv_q_2exp (q, nm1, k); /* BPSW test */ mpz_init_set_ui (y, 2); is_prime = gmp_millerrabin (n, nm1, y, q, k) && gmp_stronglucas (n, y); reps -= 24; /* skip the first 24 repetitions */ /* Use Miller-Rabin, with a deterministic sequence of bases, a[j] = j^2 + j + 41 using Euler's polynomial. We potentially stop early, if a[j] >= n - 1. Since n >= 31*31, this can happen only if reps > 30 (a[30] == 971 > 31*31 == 961). */ for (j = 0; is_prime & (j < reps); j++) { mpz_set_ui (y, (unsigned long) j*j+j+41); if (mpz_cmp (y, nm1) >= 0) { /* Don't try any further bases. This "early" break does not affect the result for any reasonable reps value (<=5000 was tested) */ assert (j >= 30); break; } is_prime = gmp_millerrabin (n, nm1, y, q, k); } mpz_clear (nm1); mpz_clear (q); mpz_clear (y); return is_prime; } /* Logical operations and bit manipulation. */ /* Numbers are treated as if represented in two's complement (and infinitely sign extended). For a negative values we get the two's complement from -x = ~x + 1, where ~ is bitwise complement. Negation transforms xxxx10...0 into yyyy10...0 where yyyy is the bitwise complement of xxxx. So least significant bits, up to and including the first one bit, are unchanged, and the more significant bits are all complemented. To change a bit from zero to one in a negative number, subtract the corresponding power of two from the absolute value. This can never underflow. To change a bit from one to zero, add the corresponding power of two, and this might overflow. E.g., if x = -001111, the two's complement is 110001. Clearing the least significant bit, we get two's complement 110000, and -010000. */ int mpz_tstbit (const mpz_t d, mp_bitcnt_t bit_index) { mp_size_t limb_index; unsigned shift; mp_size_t ds; mp_size_t dn; mp_limb_t w; int bit; ds = d->_mp_size; dn = GMP_ABS (ds); limb_index = bit_index / GMP_LIMB_BITS; if (limb_index >= dn) return ds < 0; shift = bit_index % GMP_LIMB_BITS; w = d->_mp_d[limb_index]; bit = (w >> shift) & 1; if (ds < 0) { /* d < 0. Check if any of the bits below is set: If so, our bit must be complemented. */ if (shift > 0 && (mp_limb_t) (w << (GMP_LIMB_BITS - shift)) > 0) return bit ^ 1; while (--limb_index >= 0) if (d->_mp_d[limb_index] > 0) return bit ^ 1; } return bit; } static void mpz_abs_add_bit (mpz_t d, mp_bitcnt_t bit_index) { mp_size_t dn, limb_index; mp_limb_t bit; mp_ptr dp; dn = GMP_ABS (d->_mp_size); limb_index = bit_index / GMP_LIMB_BITS; bit = (mp_limb_t) 1 << (bit_index % GMP_LIMB_BITS); if (limb_index >= dn) { mp_size_t i; /* The bit should be set outside of the end of the number. We have to increase the size of the number. */ dp = MPZ_REALLOC (d, limb_index + 1); dp[limb_index] = bit; for (i = dn; i < limb_index; i++) dp[i] = 0; dn = limb_index + 1; } else { mp_limb_t cy; dp = d->_mp_d; cy = mpn_add_1 (dp + limb_index, dp + limb_index, dn - limb_index, bit); if (cy > 0) { dp = MPZ_REALLOC (d, dn + 1); dp[dn++] = cy; } } d->_mp_size = (d->_mp_size < 0) ? - dn : dn; } static void mpz_abs_sub_bit (mpz_t d, mp_bitcnt_t bit_index) { mp_size_t dn, limb_index; mp_ptr dp; mp_limb_t bit; dn = GMP_ABS (d->_mp_size); dp = d->_mp_d; limb_index = bit_index / GMP_LIMB_BITS; bit = (mp_limb_t) 1 << (bit_index % GMP_LIMB_BITS); assert (limb_index < dn); gmp_assert_nocarry (mpn_sub_1 (dp + limb_index, dp + limb_index, dn - limb_index, bit)); dn = mpn_normalized_size (dp, dn); d->_mp_size = (d->_mp_size < 0) ? - dn : dn; } void mpz_setbit (mpz_t d, mp_bitcnt_t bit_index) { if (!mpz_tstbit (d, bit_index)) { if (d->_mp_size >= 0) mpz_abs_add_bit (d, bit_index); else mpz_abs_sub_bit (d, bit_index); } } void mpz_clrbit (mpz_t d, mp_bitcnt_t bit_index) { if (mpz_tstbit (d, bit_index)) { if (d->_mp_size >= 0) mpz_abs_sub_bit (d, bit_index); else mpz_abs_add_bit (d, bit_index); } } void mpz_combit (mpz_t d, mp_bitcnt_t bit_index) { if (mpz_tstbit (d, bit_index) ^ (d->_mp_size < 0)) mpz_abs_sub_bit (d, bit_index); else mpz_abs_add_bit (d, bit_index); } void mpz_com (mpz_t r, const mpz_t u) { mpz_add_ui (r, u, 1); mpz_neg (r, r); } void mpz_and (mpz_t r, const mpz_t u, const mpz_t v) { mp_size_t un, vn, rn, i; mp_ptr up, vp, rp; mp_limb_t ux, vx, rx; mp_limb_t uc, vc, rc; mp_limb_t ul, vl, rl; un = GMP_ABS (u->_mp_size); vn = GMP_ABS (v->_mp_size); if (un < vn) { MPZ_SRCPTR_SWAP (u, v); MP_SIZE_T_SWAP (un, vn); } if (vn == 0) { r->_mp_size = 0; return; } uc = u->_mp_size < 0; vc = v->_mp_size < 0; rc = uc & vc; ux = -uc; vx = -vc; rx = -rc; /* If the smaller input is positive, higher limbs don't matter. */ rn = vx ? un : vn; rp = MPZ_REALLOC (r, rn + (mp_size_t) rc); up = u->_mp_d; vp = v->_mp_d; i = 0; do { ul = (up[i] ^ ux) + uc; uc = ul < uc; vl = (vp[i] ^ vx) + vc; vc = vl < vc; rl = ( (ul & vl) ^ rx) + rc; rc = rl < rc; rp[i] = rl; } while (++i < vn); assert (vc == 0); for (; i < rn; i++) { ul = (up[i] ^ ux) + uc; uc = ul < uc; rl = ( (ul & vx) ^ rx) + rc; rc = rl < rc; rp[i] = rl; } if (rc) rp[rn++] = rc; else rn = mpn_normalized_size (rp, rn); r->_mp_size = rx ? -rn : rn; } void mpz_ior (mpz_t r, const mpz_t u, const mpz_t v) { mp_size_t un, vn, rn, i; mp_ptr up, vp, rp; mp_limb_t ux, vx, rx; mp_limb_t uc, vc, rc; mp_limb_t ul, vl, rl; un = GMP_ABS (u->_mp_size); vn = GMP_ABS (v->_mp_size); if (un < vn) { MPZ_SRCPTR_SWAP (u, v); MP_SIZE_T_SWAP (un, vn); } if (vn == 0) { mpz_set (r, u); return; } uc = u->_mp_size < 0; vc = v->_mp_size < 0; rc = uc | vc; ux = -uc; vx = -vc; rx = -rc; /* If the smaller input is negative, by sign extension higher limbs don't matter. */ rn = vx ? vn : un; rp = MPZ_REALLOC (r, rn + (mp_size_t) rc); up = u->_mp_d; vp = v->_mp_d; i = 0; do { ul = (up[i] ^ ux) + uc; uc = ul < uc; vl = (vp[i] ^ vx) + vc; vc = vl < vc; rl = ( (ul | vl) ^ rx) + rc; rc = rl < rc; rp[i] = rl; } while (++i < vn); assert (vc == 0); for (; i < rn; i++) { ul = (up[i] ^ ux) + uc; uc = ul < uc; rl = ( (ul | vx) ^ rx) + rc; rc = rl < rc; rp[i] = rl; } if (rc) rp[rn++] = rc; else rn = mpn_normalized_size (rp, rn); r->_mp_size = rx ? -rn : rn; } void mpz_xor (mpz_t r, const mpz_t u, const mpz_t v) { mp_size_t un, vn, i; mp_ptr up, vp, rp; mp_limb_t ux, vx, rx; mp_limb_t uc, vc, rc; mp_limb_t ul, vl, rl; un = GMP_ABS (u->_mp_size); vn = GMP_ABS (v->_mp_size); if (un < vn) { MPZ_SRCPTR_SWAP (u, v); MP_SIZE_T_SWAP (un, vn); } if (vn == 0) { mpz_set (r, u); return; } uc = u->_mp_size < 0; vc = v->_mp_size < 0; rc = uc ^ vc; ux = -uc; vx = -vc; rx = -rc; rp = MPZ_REALLOC (r, un + (mp_size_t) rc); up = u->_mp_d; vp = v->_mp_d; i = 0; do { ul = (up[i] ^ ux) + uc; uc = ul < uc; vl = (vp[i] ^ vx) + vc; vc = vl < vc; rl = (ul ^ vl ^ rx) + rc; rc = rl < rc; rp[i] = rl; } while (++i < vn); assert (vc == 0); for (; i < un; i++) { ul = (up[i] ^ ux) + uc; uc = ul < uc; rl = (ul ^ ux) + rc; rc = rl < rc; rp[i] = rl; } if (rc) rp[un++] = rc; else un = mpn_normalized_size (rp, un); r->_mp_size = rx ? -un : un; } static unsigned gmp_popcount_limb (mp_limb_t x) { unsigned c; /* Do 16 bits at a time, to avoid limb-sized constants. */ int LOCAL_SHIFT_BITS = 16; for (c = 0; x > 0;) { unsigned w = x - ((x >> 1) & 0x5555); w = ((w >> 2) & 0x3333) + (w & 0x3333); w = (w >> 4) + w; w = ((w >> 8) & 0x000f) + (w & 0x000f); c += w; if (GMP_LIMB_BITS > LOCAL_SHIFT_BITS) x >>= LOCAL_SHIFT_BITS; else x = 0; } return c; } mp_bitcnt_t mpn_popcount (mp_srcptr p, mp_size_t n) { mp_size_t i; mp_bitcnt_t c; for (c = 0, i = 0; i < n; i++) c += gmp_popcount_limb (p[i]); return c; } mp_bitcnt_t mpz_popcount (const mpz_t u) { mp_size_t un; un = u->_mp_size; if (un < 0) return ~(mp_bitcnt_t) 0; return mpn_popcount (u->_mp_d, un); } mp_bitcnt_t mpz_hamdist (const mpz_t u, const mpz_t v) { mp_size_t un, vn, i; mp_limb_t uc, vc, ul, vl, comp; mp_srcptr up, vp; mp_bitcnt_t c; un = u->_mp_size; vn = v->_mp_size; if ( (un ^ vn) < 0) return ~(mp_bitcnt_t) 0; comp = - (uc = vc = (un < 0)); if (uc) { assert (vn < 0); un = -un; vn = -vn; } up = u->_mp_d; vp = v->_mp_d; if (un < vn) MPN_SRCPTR_SWAP (up, un, vp, vn); for (i = 0, c = 0; i < vn; i++) { ul = (up[i] ^ comp) + uc; uc = ul < uc; vl = (vp[i] ^ comp) + vc; vc = vl < vc; c += gmp_popcount_limb (ul ^ vl); } assert (vc == 0); for (; i < un; i++) { ul = (up[i] ^ comp) + uc; uc = ul < uc; c += gmp_popcount_limb (ul ^ comp); } return c; } mp_bitcnt_t mpz_scan1 (const mpz_t u, mp_bitcnt_t starting_bit) { mp_ptr up; mp_size_t us, un, i; mp_limb_t limb, ux; us = u->_mp_size; un = GMP_ABS (us); i = starting_bit / GMP_LIMB_BITS; /* Past the end there's no 1 bits for u>=0, or an immediate 1 bit for u<0. Notice this test picks up any u==0 too. */ if (i >= un) return (us >= 0 ? ~(mp_bitcnt_t) 0 : starting_bit); up = u->_mp_d; ux = 0; limb = up[i]; if (starting_bit != 0) { if (us < 0) { ux = mpn_zero_p (up, i); limb = ~ limb + ux; ux = - (mp_limb_t) (limb >= ux); } /* Mask to 0 all bits before starting_bit, thus ignoring them. */ limb &= GMP_LIMB_MAX << (starting_bit % GMP_LIMB_BITS); } return mpn_common_scan (limb, i, up, un, ux); } mp_bitcnt_t mpz_scan0 (const mpz_t u, mp_bitcnt_t starting_bit) { mp_ptr up; mp_size_t us, un, i; mp_limb_t limb, ux; us = u->_mp_size; ux = - (mp_limb_t) (us >= 0); un = GMP_ABS (us); i = starting_bit / GMP_LIMB_BITS; /* When past end, there's an immediate 0 bit for u>=0, or no 0 bits for u<0. Notice this test picks up all cases of u==0 too. */ if (i >= un) return (ux ? starting_bit : ~(mp_bitcnt_t) 0); up = u->_mp_d; limb = up[i] ^ ux; if (ux == 0) limb -= mpn_zero_p (up, i); /* limb = ~(~limb + zero_p) */ /* Mask all bits before starting_bit, thus ignoring them. */ limb &= GMP_LIMB_MAX << (starting_bit % GMP_LIMB_BITS); return mpn_common_scan (limb, i, up, un, ux); } /* MPZ base conversion. */ size_t mpz_sizeinbase (const mpz_t u, int base) { mp_size_t un; mp_srcptr up; mp_ptr tp; mp_bitcnt_t bits; struct gmp_div_inverse bi; size_t ndigits; assert (base >= 2); assert (base <= 62); un = GMP_ABS (u->_mp_size); if (un == 0) return 1; up = u->_mp_d; bits = (un - 1) * GMP_LIMB_BITS + mpn_limb_size_in_base_2 (up[un-1]); switch (base) { case 2: return bits; case 4: return (bits + 1) / 2; case 8: return (bits + 2) / 3; case 16: return (bits + 3) / 4; case 32: return (bits + 4) / 5; /* FIXME: Do something more clever for the common case of base 10. */ } tp = gmp_xalloc_limbs (un); mpn_copyi (tp, up, un); mpn_div_qr_1_invert (&bi, base); ndigits = 0; do { ndigits++; mpn_div_qr_1_preinv (tp, tp, un, &bi); un -= (tp[un-1] == 0); } while (un > 0); gmp_free (tp); return ndigits; } char * mpz_get_str (char *sp, int base, const mpz_t u) { unsigned bits; const char *digits; mp_size_t un; size_t i, sn; digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"; if (base > 1) { if (base <= 36) digits = "0123456789abcdefghijklmnopqrstuvwxyz"; else if (base > 62) return NULL; } else if (base >= -1) base = 10; else { base = -base; if (base > 36) return NULL; } sn = 1 + mpz_sizeinbase (u, base); if (!sp) sp = (char *) gmp_xalloc (1 + sn); un = GMP_ABS (u->_mp_size); if (un == 0) { sp[0] = '0'; sp[1] = '\0'; return sp; } i = 0; if (u->_mp_size < 0) sp[i++] = '-'; bits = mpn_base_power_of_two_p (base); if (bits) /* Not modified in this case. */ sn = i + mpn_get_str_bits ((unsigned char *) sp + i, bits, u->_mp_d, un); else { struct mpn_base_info info; mp_ptr tp; mpn_get_base_info (&info, base); tp = gmp_xalloc_limbs (un); mpn_copyi (tp, u->_mp_d, un); sn = i + mpn_get_str_other ((unsigned char *) sp + i, base, &info, tp, un); gmp_free (tp); } for (; i < sn; i++) sp[i] = digits[(unsigned char) sp[i]]; sp[sn] = '\0'; return sp; } int mpz_set_str (mpz_t r, const char *sp, int base) { unsigned bits, value_of_a; mp_size_t rn, alloc; mp_ptr rp; size_t dn; int sign; unsigned char *dp; assert (base == 0 || (base >= 2 && base <= 62)); while (isspace( (unsigned char) *sp)) sp++; sign = (*sp == '-'); sp += sign; if (base == 0) { if (sp[0] == '0') { if (sp[1] == 'x' || sp[1] == 'X') { base = 16; sp += 2; } else if (sp[1] == 'b' || sp[1] == 'B') { base = 2; sp += 2; } else base = 8; } else base = 10; } if (!*sp) { r->_mp_size = 0; return -1; } dp = (unsigned char *) gmp_xalloc (strlen (sp)); value_of_a = (base > 36) ? 36 : 10; for (dn = 0; *sp; sp++) { unsigned digit; if (isspace ((unsigned char) *sp)) continue; else if (*sp >= '0' && *sp <= '9') digit = *sp - '0'; else if (*sp >= 'a' && *sp <= 'z') digit = *sp - 'a' + value_of_a; else if (*sp >= 'A' && *sp <= 'Z') digit = *sp - 'A' + 10; else digit = base; /* fail */ if (digit >= (unsigned) base) { gmp_free (dp); r->_mp_size = 0; return -1; } dp[dn++] = digit; } if (!dn) { gmp_free (dp); r->_mp_size = 0; return -1; } bits = mpn_base_power_of_two_p (base); if (bits > 0) { alloc = (dn * bits + GMP_LIMB_BITS - 1) / GMP_LIMB_BITS; rp = MPZ_REALLOC (r, alloc); rn = mpn_set_str_bits (rp, dp, dn, bits); } else { struct mpn_base_info info; mpn_get_base_info (&info, base); alloc = (dn + info.exp - 1) / info.exp; rp = MPZ_REALLOC (r, alloc); rn = mpn_set_str_other (rp, dp, dn, base, &info); /* Normalization, needed for all-zero input. */ assert (rn > 0); rn -= rp[rn-1] == 0; } assert (rn <= alloc); gmp_free (dp); r->_mp_size = sign ? - rn : rn; return 0; } int mpz_init_set_str (mpz_t r, const char *sp, int base) { mpz_init (r); return mpz_set_str (r, sp, base); } size_t mpz_out_str (FILE *stream, int base, const mpz_t x) { char *str; size_t len; str = mpz_get_str (NULL, base, x); if (!str) return 0; len = strlen (str); len = fwrite (str, 1, len, stream); gmp_free (str); return len; } static int gmp_detect_endian (void) { static const int i = 2; const unsigned char *p = (const unsigned char *) &i; return 1 - *p; } /* Import and export. Does not support nails. */ void mpz_import (mpz_t r, size_t count, int order, size_t size, int endian, size_t nails, const void *src) { const unsigned char *p; ptrdiff_t word_step; mp_ptr rp; mp_size_t rn; /* The current (partial) limb. */ mp_limb_t limb; /* The number of bytes already copied to this limb (starting from the low end). */ size_t bytes; /* The index where the limb should be stored, when completed. */ mp_size_t i; if (nails != 0) gmp_die ("mpz_import: Nails not supported."); assert (order == 1 || order == -1); assert (endian >= -1 && endian <= 1); if (endian == 0) endian = gmp_detect_endian (); p = (unsigned char *) src; word_step = (order != endian) ? 2 * size : 0; /* Process bytes from the least significant end, so point p at the least significant word. */ if (order == 1) { p += size * (count - 1); word_step = - word_step; } /* And at least significant byte of that word. */ if (endian == 1) p += (size - 1); rn = (size * count + sizeof(mp_limb_t) - 1) / sizeof(mp_limb_t); rp = MPZ_REALLOC (r, rn); for (limb = 0, bytes = 0, i = 0; count > 0; count--, p += word_step) { size_t j; for (j = 0; j < size; j++, p -= (ptrdiff_t) endian) { limb |= (mp_limb_t) *p << (bytes++ * CHAR_BIT); if (bytes == sizeof(mp_limb_t)) { rp[i++] = limb; bytes = 0; limb = 0; } } } assert (i + (bytes > 0) == rn); if (limb != 0) rp[i++] = limb; else i = mpn_normalized_size (rp, i); r->_mp_size = i; } void * mpz_export (void *r, size_t *countp, int order, size_t size, int endian, size_t nails, const mpz_t u) { size_t count; mp_size_t un; if (nails != 0) gmp_die ("mpz_import: Nails not supported."); assert (order == 1 || order == -1); assert (endian >= -1 && endian <= 1); assert (size > 0 || u->_mp_size == 0); un = u->_mp_size; count = 0; if (un != 0) { size_t k; unsigned char *p; ptrdiff_t word_step; /* The current (partial) limb. */ mp_limb_t limb; /* The number of bytes left to do in this limb. */ size_t bytes; /* The index where the limb was read. */ mp_size_t i; un = GMP_ABS (un); /* Count bytes in top limb. */ limb = u->_mp_d[un-1]; assert (limb != 0); k = (GMP_LIMB_BITS <= CHAR_BIT); if (!k) { do { int LOCAL_CHAR_BIT = CHAR_BIT; k++; limb >>= LOCAL_CHAR_BIT; } while (limb != 0); } /* else limb = 0; */ count = (k + (un-1) * sizeof (mp_limb_t) + size - 1) / size; if (!r) r = gmp_xalloc (count * size); if (endian == 0) endian = gmp_detect_endian (); p = (unsigned char *) r; word_step = (order != endian) ? 2 * size : 0; /* Process bytes from the least significant end, so point p at the least significant word. */ if (order == 1) { p += size * (count - 1); word_step = - word_step; } /* And at least significant byte of that word. */ if (endian == 1) p += (size - 1); for (bytes = 0, i = 0, k = 0; k < count; k++, p += word_step) { size_t j; for (j = 0; j < size; ++j, p -= (ptrdiff_t) endian) { if (sizeof (mp_limb_t) == 1) { if (i < un) *p = u->_mp_d[i++]; else *p = 0; } else { int LOCAL_CHAR_BIT = CHAR_BIT; if (bytes == 0) { if (i < un) limb = u->_mp_d[i++]; bytes = sizeof (mp_limb_t); } *p = limb; limb >>= LOCAL_CHAR_BIT; bytes--; } } } assert (i == un); assert (k == count); } if (countp) *countp = count; return r; } lrslib-073/lrsarith-011/mini-gmp.h0000777000175000017500000002643414625766601015414 0ustar avisavis/* mini-gmp, a minimalistic implementation of a GNU GMP subset. Copyright 2011-2015, 2017, 2019-2020 Free Software Foundation, Inc. This file is part of the GNU MP Library. The GNU MP Library is free software; you can redistribute it and/or modify it under the terms of either: * the GNU Lesser General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version. or * the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. or both in parallel, as here. The GNU MP Library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received copies of the GNU General Public License and the GNU Lesser General Public License along with the GNU MP Library. If not, see https://www.gnu.org/licenses/. */ /* About mini-gmp: This is a minimal implementation of a subset of the GMP interface. It is intended for inclusion into applications which have modest bignums needs, as a fallback when the real GMP library is not installed. This file defines the public interface. */ #ifndef __MINI_GMP_H__ #define __MINI_GMP_H__ /* For size_t */ #include #if defined (__cplusplus) extern "C" { #endif void mp_set_memory_functions (void *(*) (size_t), void *(*) (void *, size_t, size_t), void (*) (void *, size_t)); void mp_get_memory_functions (void *(**) (size_t), void *(**) (void *, size_t, size_t), void (**) (void *, size_t)); #ifndef MINI_GMP_LIMB_TYPE #define MINI_GMP_LIMB_TYPE long #endif typedef unsigned MINI_GMP_LIMB_TYPE mp_limb_t; typedef long mp_size_t; typedef unsigned long mp_bitcnt_t; typedef mp_limb_t *mp_ptr; typedef const mp_limb_t *mp_srcptr; typedef struct { int _mp_alloc; /* Number of *limbs* allocated and pointed to by the _mp_d field. */ int _mp_size; /* abs(_mp_size) is the number of limbs the last field points to. If _mp_size is negative this is a negative number. */ mp_limb_t *_mp_d; /* Pointer to the limbs. */ } __mpz_struct; typedef __mpz_struct mpz_t[1]; typedef __mpz_struct *mpz_ptr; typedef const __mpz_struct *mpz_srcptr; extern const int mp_bits_per_limb; void mpn_copyi (mp_ptr, mp_srcptr, mp_size_t); void mpn_copyd (mp_ptr, mp_srcptr, mp_size_t); void mpn_zero (mp_ptr, mp_size_t); int mpn_cmp (mp_srcptr, mp_srcptr, mp_size_t); int mpn_zero_p (mp_srcptr, mp_size_t); mp_limb_t mpn_add_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t); mp_limb_t mpn_add_n (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t); mp_limb_t mpn_add (mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t); mp_limb_t mpn_sub_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t); mp_limb_t mpn_sub_n (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t); mp_limb_t mpn_sub (mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t); mp_limb_t mpn_mul_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t); mp_limb_t mpn_addmul_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t); mp_limb_t mpn_submul_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t); mp_limb_t mpn_mul (mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t); void mpn_mul_n (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t); void mpn_sqr (mp_ptr, mp_srcptr, mp_size_t); int mpn_perfect_square_p (mp_srcptr, mp_size_t); mp_size_t mpn_sqrtrem (mp_ptr, mp_ptr, mp_srcptr, mp_size_t); mp_limb_t mpn_lshift (mp_ptr, mp_srcptr, mp_size_t, unsigned int); mp_limb_t mpn_rshift (mp_ptr, mp_srcptr, mp_size_t, unsigned int); mp_bitcnt_t mpn_scan0 (mp_srcptr, mp_bitcnt_t); mp_bitcnt_t mpn_scan1 (mp_srcptr, mp_bitcnt_t); void mpn_com (mp_ptr, mp_srcptr, mp_size_t); mp_limb_t mpn_neg (mp_ptr, mp_srcptr, mp_size_t); mp_bitcnt_t mpn_popcount (mp_srcptr, mp_size_t); mp_limb_t mpn_invert_3by2 (mp_limb_t, mp_limb_t); #define mpn_invert_limb(x) mpn_invert_3by2 ((x), 0) size_t mpn_get_str (unsigned char *, int, mp_ptr, mp_size_t); mp_size_t mpn_set_str (mp_ptr, const unsigned char *, size_t, int); void mpz_init (mpz_t); void mpz_init2 (mpz_t, mp_bitcnt_t); void mpz_clear (mpz_t); #define mpz_odd_p(z) (((z)->_mp_size != 0) & (int) (z)->_mp_d[0]) #define mpz_even_p(z) (! mpz_odd_p (z)) int mpz_sgn (const mpz_t); int mpz_cmp_si (const mpz_t, long); int mpz_cmp_ui (const mpz_t, unsigned long); int mpz_cmp (const mpz_t, const mpz_t); int mpz_cmpabs_ui (const mpz_t, unsigned long); int mpz_cmpabs (const mpz_t, const mpz_t); int mpz_cmp_d (const mpz_t, double); int mpz_cmpabs_d (const mpz_t, double); void mpz_abs (mpz_t, const mpz_t); void mpz_neg (mpz_t, const mpz_t); void mpz_swap (mpz_t, mpz_t); void mpz_add_ui (mpz_t, const mpz_t, unsigned long); void mpz_add (mpz_t, const mpz_t, const mpz_t); void mpz_sub_ui (mpz_t, const mpz_t, unsigned long); void mpz_ui_sub (mpz_t, unsigned long, const mpz_t); void mpz_sub (mpz_t, const mpz_t, const mpz_t); void mpz_mul_si (mpz_t, const mpz_t, long int); void mpz_mul_ui (mpz_t, const mpz_t, unsigned long int); void mpz_mul (mpz_t, const mpz_t, const mpz_t); void mpz_mul_2exp (mpz_t, const mpz_t, mp_bitcnt_t); void mpz_addmul_ui (mpz_t, const mpz_t, unsigned long int); void mpz_addmul (mpz_t, const mpz_t, const mpz_t); void mpz_submul_ui (mpz_t, const mpz_t, unsigned long int); void mpz_submul (mpz_t, const mpz_t, const mpz_t); void mpz_cdiv_qr (mpz_t, mpz_t, const mpz_t, const mpz_t); void mpz_fdiv_qr (mpz_t, mpz_t, const mpz_t, const mpz_t); void mpz_tdiv_qr (mpz_t, mpz_t, const mpz_t, const mpz_t); void mpz_cdiv_q (mpz_t, const mpz_t, const mpz_t); void mpz_fdiv_q (mpz_t, const mpz_t, const mpz_t); void mpz_tdiv_q (mpz_t, const mpz_t, const mpz_t); void mpz_cdiv_r (mpz_t, const mpz_t, const mpz_t); void mpz_fdiv_r (mpz_t, const mpz_t, const mpz_t); void mpz_tdiv_r (mpz_t, const mpz_t, const mpz_t); void mpz_cdiv_q_2exp (mpz_t, const mpz_t, mp_bitcnt_t); void mpz_fdiv_q_2exp (mpz_t, const mpz_t, mp_bitcnt_t); void mpz_tdiv_q_2exp (mpz_t, const mpz_t, mp_bitcnt_t); void mpz_cdiv_r_2exp (mpz_t, const mpz_t, mp_bitcnt_t); void mpz_fdiv_r_2exp (mpz_t, const mpz_t, mp_bitcnt_t); void mpz_tdiv_r_2exp (mpz_t, const mpz_t, mp_bitcnt_t); void mpz_mod (mpz_t, const mpz_t, const mpz_t); void mpz_divexact (mpz_t, const mpz_t, const mpz_t); int mpz_divisible_p (const mpz_t, const mpz_t); int mpz_congruent_p (const mpz_t, const mpz_t, const mpz_t); unsigned long mpz_cdiv_qr_ui (mpz_t, mpz_t, const mpz_t, unsigned long); unsigned long mpz_fdiv_qr_ui (mpz_t, mpz_t, const mpz_t, unsigned long); unsigned long mpz_tdiv_qr_ui (mpz_t, mpz_t, const mpz_t, unsigned long); unsigned long mpz_cdiv_q_ui (mpz_t, const mpz_t, unsigned long); unsigned long mpz_fdiv_q_ui (mpz_t, const mpz_t, unsigned long); unsigned long mpz_tdiv_q_ui (mpz_t, const mpz_t, unsigned long); unsigned long mpz_cdiv_r_ui (mpz_t, const mpz_t, unsigned long); unsigned long mpz_fdiv_r_ui (mpz_t, const mpz_t, unsigned long); unsigned long mpz_tdiv_r_ui (mpz_t, const mpz_t, unsigned long); unsigned long mpz_cdiv_ui (const mpz_t, unsigned long); unsigned long mpz_fdiv_ui (const mpz_t, unsigned long); unsigned long mpz_tdiv_ui (const mpz_t, unsigned long); unsigned long mpz_mod_ui (mpz_t, const mpz_t, unsigned long); void mpz_divexact_ui (mpz_t, const mpz_t, unsigned long); int mpz_divisible_ui_p (const mpz_t, unsigned long); unsigned long mpz_gcd_ui (mpz_t, const mpz_t, unsigned long); void mpz_gcd (mpz_t, const mpz_t, const mpz_t); void mpz_gcdext (mpz_t, mpz_t, mpz_t, const mpz_t, const mpz_t); void mpz_lcm_ui (mpz_t, const mpz_t, unsigned long); void mpz_lcm (mpz_t, const mpz_t, const mpz_t); int mpz_invert (mpz_t, const mpz_t, const mpz_t); void mpz_sqrtrem (mpz_t, mpz_t, const mpz_t); void mpz_sqrt (mpz_t, const mpz_t); int mpz_perfect_square_p (const mpz_t); void mpz_pow_ui (mpz_t, const mpz_t, unsigned long); void mpz_ui_pow_ui (mpz_t, unsigned long, unsigned long); void mpz_powm (mpz_t, const mpz_t, const mpz_t, const mpz_t); void mpz_powm_ui (mpz_t, const mpz_t, unsigned long, const mpz_t); void mpz_rootrem (mpz_t, mpz_t, const mpz_t, unsigned long); int mpz_root (mpz_t, const mpz_t, unsigned long); void mpz_fac_ui (mpz_t, unsigned long); void mpz_2fac_ui (mpz_t, unsigned long); void mpz_mfac_uiui (mpz_t, unsigned long, unsigned long); void mpz_bin_uiui (mpz_t, unsigned long, unsigned long); int mpz_probab_prime_p (const mpz_t, int); int mpz_tstbit (const mpz_t, mp_bitcnt_t); void mpz_setbit (mpz_t, mp_bitcnt_t); void mpz_clrbit (mpz_t, mp_bitcnt_t); void mpz_combit (mpz_t, mp_bitcnt_t); void mpz_com (mpz_t, const mpz_t); void mpz_and (mpz_t, const mpz_t, const mpz_t); void mpz_ior (mpz_t, const mpz_t, const mpz_t); void mpz_xor (mpz_t, const mpz_t, const mpz_t); mp_bitcnt_t mpz_popcount (const mpz_t); mp_bitcnt_t mpz_hamdist (const mpz_t, const mpz_t); mp_bitcnt_t mpz_scan0 (const mpz_t, mp_bitcnt_t); mp_bitcnt_t mpz_scan1 (const mpz_t, mp_bitcnt_t); int mpz_fits_slong_p (const mpz_t); int mpz_fits_ulong_p (const mpz_t); long int mpz_get_si (const mpz_t); unsigned long int mpz_get_ui (const mpz_t); double mpz_get_d (const mpz_t); size_t mpz_size (const mpz_t); mp_limb_t mpz_getlimbn (const mpz_t, mp_size_t); void mpz_realloc2 (mpz_t, mp_bitcnt_t); mp_srcptr mpz_limbs_read (mpz_srcptr); mp_ptr mpz_limbs_modify (mpz_t, mp_size_t); mp_ptr mpz_limbs_write (mpz_t, mp_size_t); void mpz_limbs_finish (mpz_t, mp_size_t); mpz_srcptr mpz_roinit_n (mpz_t, mp_srcptr, mp_size_t); #define MPZ_ROINIT_N(xp, xs) {{0, (xs),(xp) }} void mpz_set_si (mpz_t, signed long int); void mpz_set_ui (mpz_t, unsigned long int); void mpz_set (mpz_t, const mpz_t); void mpz_set_d (mpz_t, double); void mpz_init_set_si (mpz_t, signed long int); void mpz_init_set_ui (mpz_t, unsigned long int); void mpz_init_set (mpz_t, const mpz_t); void mpz_init_set_d (mpz_t, double); size_t mpz_sizeinbase (const mpz_t, int); char *mpz_get_str (char *, int, const mpz_t); int mpz_set_str (mpz_t, const char *, int); int mpz_init_set_str (mpz_t, const char *, int); /* This long list taken from gmp.h. */ /* For reference, "defined(EOF)" cannot be used here. In g++ 2.95.4, defines EOF but not FILE. */ #if defined (FILE) \ || defined (H_STDIO) \ || defined (_H_STDIO) /* AIX */ \ || defined (_STDIO_H) /* glibc, Sun, SCO */ \ || defined (_STDIO_H_) /* BSD, OSF */ \ || defined (__STDIO_H) /* Borland */ \ || defined (__STDIO_H__) /* IRIX */ \ || defined (_STDIO_INCLUDED) /* HPUX */ \ || defined (__dj_include_stdio_h_) /* DJGPP */ \ || defined (_FILE_DEFINED) /* Microsoft */ \ || defined (__STDIO__) /* Apple MPW MrC */ \ || defined (_MSL_STDIO_H) /* Metrowerks */ \ || defined (_STDIO_H_INCLUDED) /* QNX4 */ \ || defined (_ISO_STDIO_ISO_H) /* Sun C++ */ \ || defined (__STDIO_LOADED) /* VMS */ \ || defined (__DEFINED_FILE) /* musl */ size_t mpz_out_str (FILE *, int, const mpz_t); #endif void mpz_import (mpz_t, size_t, int, size_t, int, size_t, const void *); void *mpz_export (void *, size_t *, int, size_t, int, size_t, const mpz_t); #if defined (__cplusplus) } #endif #endif /* __MINI_GMP_H__ */ lrslib-073/lrsarith-011/README0000777000175000017500000000541714625766601014404 0ustar avisavisREADME file for lrsarith : arithmetic package for lrslib ----------------------------------------------------------------------------- Library routines and sample programs for using 64bit, 128bit, GMP (or MP) arithmetic packages, as well as hybrid arithmetic using all three. Overflow checking is done for 64 and 128bit arithmetic. Documentation is currently being maintained at the URL: http://cgm.cs.mcgill.ca/~avis/C/lrs.html ----------------------------------------------------------------------------- Version 1.0 2020.12.18 Note that lrsarith procedures may be implemented as macros that may evaluate arguments more than once. Arguments given to lrsarith procedures should not be expressions with potential side effects. 2020.12.7 % make fixed Build the programs fixed1, fixed1n, fixed2, fixed2n, fixedmp, fixedgmp that read an integer k and repeatedly square it 6 times. % fixed2 5 produces 5 25 625 390625 152587890625 23283064365386962890625 overflow detected:halting % make hybrid (% make mp does same using internal MP arithmetic instead of GMP) Build the program hybrid (and fixed1, fixed2, fixedgmp) that runs through the three arithmetic packages as needed. % hybrid 5 produces 5 25 625 390625 152587890625 overflow detected:restarting 5 25 625 390625 152587890625 23283064365386962890625 overflow detected:restarting 5 25 625 390625 152587890625 23283064365386962890625 542101086242752217003726400434970855712890625 -------------------------------------------------------------------------------------------------------------- % make coll (% make flint make FLINT arithmetic version) Reverse search code for building a Collatz tree with largest value maxn in all arithmetic versions % coll coll: enter maxn maxcount maxn<0 : print counts only maxcount=-1 : scale to maxn^8 MAXCOUNT=10^8 maxcount=0 : no upper bound on tree size 16 0 v odd full depth depth 1 0 0 2 1 4 2 8 3 16 4 5 1 5 10 6 3 2 7 6 8 12 9 count=10 Maxv= 16 maxv= 16 ----------------------------------------------------------------------------------------------------------- % make test Test the arithmetic constants used in overflow checking. Current output: MAXDa 4611686018427387903 MAXDl 2147483647 MAXDm 3037000499 addint 9223372036854775806 mulint 9223372030926249001 linint 9223372028264841218 MAXDa 85070591730234615847396907784232501249 MAXDl 9223372036854775807 MAXDm 13043817825277250404 addint 170141183460469231694793815568465002498 mulint 170141183459020538148444170386518163216 linint 170141183460469231694793815568465002498 lrslib-073/lrsarith-011/test.c0000777000175000017500000000143114625766601014637 0ustar avisavis/* 2020.11.12 test code for single arithmetic with overflow checking */ /* reads and tests constants for overflow checking */ #include #include #include "lrsarith.h" FILE *lrs_ifp,*lrs_ofp; void lrs_overflow(int parm){ fprintf(lrs_ofp," overflow detected\n"); exit (1); } int main (void){ lrs_mp a,b,c,l,m; lrs_alloc_mp(a); lrs_alloc_mp(b); lrs_alloc_mp(c); lrs_alloc_mp(l); lrs_alloc_mp(m); lrs_mp_init(0,stdin,stdout); itomp(MAXDa,a); pmp("MAXDa",a); itomp(MAXDl,l); pmp("MAXDl",l); itomp(MAXDm,m); pmp("MAXDm",m); printf("\naddint "); addint(a,a,b); pmp("",b); printf("\nmulint "); mulint(m,m,b); pmp("",b); printf("\nlinint "); copy(a,l); linint(a,MAXDl,l,MAXDl); pmp("",a); fprintf(lrs_ofp,"\n"); return 0; } lrslib-073/lrsdriver.c0000777000175000017500000000356314625766602013556 0ustar avisavis/* This file contains functions and variables that should not be duplicated per arithmetic */ #include #include #include #include #include #include #include "lrsdriver.h" /* Globals; these need to be here, rather than lrsdriver.h, so they are not multiply defined. */ FILE *lrs_cfp; /* output file for checkpoint information */ FILE *lrs_ifp; /* input file pointer */ FILE *lrs_ofp; /* output file pointer */ char** makenewargv(int *argc,char** argv,char *tmp) { int i; char** newargv; newargv = (char**) malloc((*argc+3) * sizeof *newargv); for(i = 0; i < *argc; ++i) { if (i != 1) { size_t length = strlen(argv[i])+1; newargv[i] = (char *) malloc(length); strcpy(newargv[i], argv[i]); } } /* make tmp the new input file */ size_t length = strlen(tmp)+1; newargv[1] = (char *)malloc(length); strcpy(newargv[1], tmp); if(*argc == 1) /* input was stdin*/ *argc = 2; newargv[*argc] = NULL; return newargv; } lrs_restart_dat* lrs_alloc_restart() { int i; lrs_restart_dat *R; R = (lrs_restart_dat *) malloc (sizeof (lrs_restart_dat)); if (R == NULL) return R; R->overide=0; /* do not overide Q */ R->restart=0; /* do not do a restart */ R->facet=NULL; /* this will be allocated later when we know its size */ R->d=0; R->maxcobases=0; R->maxdepth=-1; /* will be set to MAXD in lrs*_main */ R->mindepth=0; R->maxcobases=0; for(i=0;i<10;i++) R->count[i]=0; R->depth=0; R->lrs=1; R->redund=0; R->messages=0; R->fel=0; R->testlin = 0; R->redundphase = 0; R->redineq = NULL; R->rank = 0; R->size = 0; return R; } char *lrs_basename(char *str) { int i = strlen(str); while (i>=0 && str[i]!='/' && str[i]!='\\') i--; return str+i+1; } lrslib-073/lrsdriver.h0000777000175000017500000000232414625766503013555 0ustar avisavis/* This file contains functions and variables that should not be duplicated per arithmetic */ #ifndef LRS_DRIVER_H #define LRS_DRIVER_H #include #include #include #include #include "lrsrestart.h" struct lrs_dic_struct; typedef struct lrs_dic_struct lrs_dic; struct lrs_dat; typedef struct lrs_dat lrs_dat; long lrs_main (int argc, char *argv[]); /* legacy lrs driver, argv[1]=input file, [argc-1]=output file */ long lrs1_main(int argc, char *argv[],lrs_dic **P,lrs_dat **Q, long overf,long stage,char *tmp,lrs_restart_dat *R)/*__attribute__ ((visibility ("default") ))*/; long lrs2_main(int argc, char *argv[],lrs_dic **P,lrs_dat **Q, long overf,long stage,char *tmp,lrs_restart_dat *R)/*__attribute__ ((visibility ("default") ))*/; long lrsgmp_main(int argc, char *argv[],lrs_dic **P,lrs_dat **Q, long overf,long stage,char *tmp,lrs_restart_dat *R)/*__attribute__ ((visibility ("default") ))*/; char** makenewargv(int *argc,char** argv,char* tmp); lrs_restart_dat* lrs_alloc_restart(); extern FILE *lrs_cfp; /* output file for checkpoint information */ extern FILE *lrs_ifp; /* input file pointer */ extern FILE *lrs_ofp; /* output file pointer */ #endif lrslib-073/lrslib.c0000777000175000017500000071113414625766605013034 0ustar avisavis/* lrslib.c library code for lrs */ /* This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA. */ /*2022.1.22 lrs now has 3 modes controlled by these routines: lrs_run default, V->H or H->V conversion redund_run redundancy removal, redund or redund_list options fel_run Fourier-Motzkin elimination, project or elimiminate options */ /* modified by Gary Roumanis and Skip Jordan for multithread compatability */ /* truncate needs mod to supress last pivot */ /* need to add a test for non-degenerate pivot step in reverse I guess?? */ /* Copyright: David Avis 2005,2022 avis@cs.mcgill.ca */ #include #include #include #include #include #include #include "lrsrestart.h" #include "lrslib.h" #ifdef PLRS #include //#include //static _Atomic long overflow_detected=0; static long overflow_detected=0; /* =0 no overflow =1 overflowed */ #else static long overflow_detected=0; /* =0 no overflow =1 overflowed */ #endif static long overflow=0; /* =0 no overflow =1 restart */ static unsigned long dict_limit=50; static unsigned long dict_count=1, cache_tries=0, cache_misses=0; /* Variables and functions global to this file only */ static long lrs_checkpoint_seconds = 0; static long lrs_Q_count = 0; /* Track how many lrs_dat records are allocated */ static size_t infileLen; /* length of cache of input file */ static char *infile = NULL; /* cache of input for restart */ static char infilename[PATH_MAX]; static char outfilename[PATH_MAX]; static char tmpfilename[PATH_MAX]; static lrs_dat *lrs_Q_list[MAX_LRS_Q + 1]; static lrs_dic *new_lrs_dic (long m, long d, long m_A); static void cache_dict (lrs_dic ** D_p, lrs_dat * Q, long i, long j); static long check_cache (lrs_dic ** D_p, lrs_dat * Q, long *i_p, long *j_p); static void save_basis (lrs_dic * D, lrs_dat * Q); static void pushQ (lrs_dat * Q, long m, long d, long m_A); static int tmpfd; #ifndef TIMES static void ptimes (void); static double get_time(void); #endif char *lrs_basename(char *path); /*******************************/ /* signals handling */ /*******************************/ #ifndef SIGNALS static void checkpoint (); static void die_gracefully (); static void setup_signals (void); static void timecheck (); #endif /*******************************/ /* functions for external use */ /*******************************/ /******************************************************************/ /* lrs_run is the main reverse search part of lrs */ /* should be called by lrsv2_main which does setup and close also */ /******************************************************************/ long lrs_run ( lrs_dic *P, lrs_dat * Q) { lrs_dic *Pin; lrs_mp_matrix Lin; /* holds input linearities if any are found */ long col; /* output column index for dictionary */ long startcol = 0; long prune = FALSE; /* if TRUE, getnextbasis will prune tree and backtrack */ Pin=P; /*********************************************************************************/ /* Step 1: Find a starting cobasis from default of specified order */ /* P is created to hold active dictionary data and may be cached */ /* Lin is created if necessary to hold linearity space */ /* Print linearity space if any, and retrieve output from first dict. */ /*********************************************************************************/ if (lrs_getfirstbasis (&P, Q, &Lin, FALSE)==0 || overflow_detected) { if(Q->verbose && !Q->mplrs && overflow_detected) lrs_warning(Q,"warning","*overflow beginning of step 1"); lrs_free_dic(P,Q); /* note Q is not free here and can be reused */ return 1; } /* Pivot to a starting dictionary */ /* There may have been column redundancy */ /* If so the linearity space is obtained and redundant */ /* columns are removed. User can access linearity space */ /* from lrs_mp_matrix Lin dimensions nredundcol x d+1 */ if (Q->homogeneous && Q->hull) startcol++; /* col zero not treated as redundant */ if(!Q->lponly && !Q->restart && Q->child == 0) /* printed once in multithreading */ for (col = startcol; col < Q->nredundcol; col++) /* print linearity space */ lrs_printoutput (Q, Lin[col]); /* Array Lin[][] holds the coeffs. */ if (Q->child >1) Q->giveoutput=FALSE; if(Q->nredundcol > 0) lrs_clear_mp_matrix(Lin,Q->nredundcol,Q->n); if(Q->plrs && Q->child==0) /* we just wanted initial output */ { lrs_free_dic(P,Q); return 0; } /*********************************************************************************/ /* Step 3: Terminate if lponly option set, otherwise initiate a reverse */ /* search from the starting dictionary. Get output for each new dict. */ /*********************************************************************************/ /* We initiate reverse search from this dictionary */ /* getting new dictionaries until the search is complete */ /* User can access each output line from output which is */ /* vertex/ray/facet from the lrs_mp_vector output */ /* prune is TRUE if tree should be pruned at current node */ do { //2015.6.5 after maxcobases reached, generate subtrees that have not been enumerated //2018.1.19 fix printcobasis bug when maxcobases set //2019.5.8 new givoutput flag to avoid printing restart cobases prune=lrs_checkbound(P,Q); if (!prune && Q->giveoutput) { lrs_open_outputblock(); /* keeps output together when using mplrs */ for (col = 0; col <= P->d; col++) /* print output if any */ if (!Q->testlin && lrs_getsolution (P, Q, Q->output, col)) lrs_printoutput (Q, Q->output); lrs_close_outputblock(); } else Q->giveoutput=TRUE; /* first output supressed for restart */ /*2020.3.9 bounds on objective function check corrected */ /*2023.6.30 do not proceed from high incidence bases */ if(Q->nincidence >= Q->maxincidence && P->depth >= Q->minprunedepth) { if(Q->verbose && !Q->mplrs) fprintf(lrs_ofp,"\n*pruning: incidence=%ld depth=%ld",Q->nincidence,P->depth); prune=TRUE; } if ((Q->maxcobases > 0) && (Q->count[2] >=Q->maxcobases)) { prune=TRUE; if( !lrs_leaf(P,Q)) /* do not return cobases of a leaf */ lrs_return_unexplored(P,Q); } save_basis(P,Q); /*2023.1.9*/ if(overflow_detected) { Q->m=Pin->m; lrs_free_dic(Pin,Q); if(Q->debug) fprintf(lrs_ofp,"\n*Overflow detected"); fflush(lrs_ofp); return 0; } }while ( !Q->lponly && lrs_getnextbasis (&P, Q, prune)); // do ... if (Q->lponly) lrs_lpoutput(P,Q,Q->output); else if(!Q->plrs) lrs_printtotals (P, Q); /* print final totals, including estimates */ Q->m=P->m; lrs_free_dic(P,Q); /* note Q is not free here and can be reused */ return 0; } /*********************************************/ /* end lrs_run */ /*********************************************/ /*******************************************************/ /* redund_run is main loop for redundancy removal */ /*******************************************************/ long redund_run ( lrs_dic *P, lrs_dat * Q) { lrs_mp_matrix Ain; /* holds a copy of the input matrix to output at the end */ long ineq; /* input inequality number of current index */ lrs_mp_matrix Lin; /* holds input linearities if any are found */ long i, j, d, m; long nlinearity; /* number of linearities in input file */ long lastdv; long index; /* basic index for redundancy test */ long min,nin; const char * redlab[] = { "*sr", "*nr","*re","*li"}; long debug = Q->debug; long *redineq = Q->redineq; /*********************************************************************************/ /* if non-negative flag is set, non-negative constraints are not input */ /* explicitly, and are not checked for redundancy */ m = P->m_A; /* number of rows of A matrix */ d = P->d; min=Q->m; nin=Q->n; Q->Ain = lrs_alloc_mp_matrix (Q->m, Q->n); /* make a copy of A matrix for output later */ Ain=Q->Ain; Q->printcobasis=0; for (i = 1; i <= m; i++) { for (j = 0; j <= d; j++) copy (Ain[i][j], P->A[i][j]); } /*********************************************************************************/ /* Step 1: Find a starting cobasis from default of specified order */ /* Lin is created if necessary to hold linearity space */ /*********************************************************************************/ if ( lrs_getfirstbasis (&P, Q, &Lin, TRUE)==0 || overflow_detected) return 1; if(Q->mplrs && Q->redundphase==1 && Q->tid == 1) { for (i = 0; i < Q->nlinearity; i++) redineq[Q->linearity[i]] = 2; goto done; /* consumer rank=1 print only */ } /* Pivot to a starting dictionary */ /* There may have been column redundancy */ /* If so the linearity space is obtained and redundant */ /* columns are removed. User can access linearity space */ /* from lrs_mp_matrix Lin dimensions nredundcol x d+1 */ d=P->d; lastdv=Q->lastdv; if(Q->nredundcol > 0) lrs_clear_mp_matrix(Lin,Q->nredundcol,Q->n); if (Q->testlin) /* we added extra var and column to look for interior point */ { lrs_getsolution(P,Q,Q->output,0); lrs_lpoutput(P,Q,Q->output); if( negative (P->objnum) ) return 1; remove_artificial(P,Q); if(Q->debug) fprintf(lrs_ofp,"\n*Q->fel=%ld Q->tid=%ld Q->hiddenlin=%ld",Q->fel,Q->tid, Q->hiddenlin); } if(Q->mplrs) /* used for workers at which did not do the lp step */ cleanupA(P,Q); if(overflow_detected) return 1; /*********************************************************************************/ /* Step 2: Test rows i where redineq[i]=1 for redundancy */ /*********************************************************************************/ /* note some of these may have been changed in getting initial dictionary */ m = P->m_A; d = P->d; nlinearity = Q->nlinearity; lastdv = Q->lastdv; /* linearities are not considered for redundancy */ for (i = 0; i < nlinearity; i++) redineq[Q->linearity[i]] = 2L; if (Q->debug) { fprintf (lrs_ofp, "\n*Step 2: redundphase=%ld testlin=%ld redineq:\n",Q->redundphase, Q->testlin); for (i = 1; i <= m; i++) fprintf (lrs_ofp, " %ld", redineq[i]); } /* Q->redundphase=1 indicates no hidden linearities */ /* in this case only one lp per row is performed, the redundancy check */ /* otherwise two lps are performed to test for linearity */ /* rows 0..lastdv are cost, decision variables, or linearities */ /* other rows need to be tested */ if(redineq[0] == 0) /* 2020.9.11 patch, this was set to 1 in readredund but got reset somewhere */ redineq[0] = 1; if (debug) fprintf (lrs_ofp, "\nlastdv=%ld, redineq[0]=%ld", lastdv, redineq[0]); /* main loop for checking redundancy of +1 rows in redineq */ /*2023.11.15 lrs can skip looking for linearities but mplrs can't */ if( !Q->testlin && Q->redund && !Q->mplrs) Q->redundphase=1; if(Q->debug) fprintf(lrs_ofp,"\n*testlin=%ld redund=%ld redundphase=%ld",Q->testlin, Q->redund,Q->redundphase); if(!Q->mplrs) { if(Q->fel) fprintf(lrs_ofp,"\n*removing redundant rows"); else if (!Q->testlin) fprintf(lrs_ofp,"\n*checking for redundant rows only"); else if(Q->fullredund) fprintf(lrs_ofp,"\n*finding minimum representation"); } /* redundphase=0 lin+ine tested =1 ine only after hidden linearities removed*/ for (index = lastdv + redineq[0]; index <= m + d; index++) { ineq = Q->inequality[index - lastdv]; /* the input inequality number corr. to this index */ redineq[0] = ineq; /* used for restarting after arithmetic overflow */ if( redineq[ineq]==1 ) { redineq[ineq] = checkindex (P, Q, index,Q->redundphase); if(overflow_detected) return 1; if(Q->debug) fprintf (lrs_ofp, "\ncheck index=%ld, inequality=%ld, redineq=%ld", index, ineq, redineq[ineq]); if(!Q->fel && Q->verbose ) lrs_printrow (redlab[redineq[ineq]+1], Q, Ain[ineq], Q->inputd); fflush(lrs_ofp); } } /* end for index ..... */ done: if(Q->debug) { fprintf(lrs_ofp,"\n*done: rank=%ld redundphase=%ld",Q->tid,Q->redundphase); fprintf (lrs_ofp, "\n*redineq:"); for (i = 1; i <= m; i++) fprintf (lrs_ofp, " %ld", redineq[i]); } /* 2023.6.3 all except boss or consumer go home */ if(Q->mplrs && Q->tid > 1 ) { lrs_clear_mp_matrix(Q->Ain,min,nin); Q->m=P->m; lrs_free_dic(P,Q); return 0; } if(Q->fel && Q->hull) lrs_clear_mp_matrix(Q->Ain,min,nin); else redund_print(P,Q); if(!Q->fel) lrs_clear_mp_matrix(Q->Ain,min,nin); lrs_free_dic(P,Q); return 0; } /***********redund_run************************/ void cleanupA(lrs_dic *P,lrs_dat *Q) { /* remove duplicate rows from the raw A matrix including those */ /* which appear as an identity row x_i=x_j for slacks i and j */ /* no indices updated except to mark linearities in redineq */ /* duplicate and identity rows are simply zeroed out */ lrs_mp_matrix A1; lrs_mp_matrix A = P->A; long i, j, d, m; long k,oneindex,nonzero; long debug = Q->debug; //long verbose = Q->verbose; long lastdv=Q->lastdv; long *redineq = Q->redineq; long *Row=P->Row; long *Col=P->Col; m = P->m_A; /* number of rows of A matrix */ d = P->d; A1=lrs_alloc_mp_matrix(m,d); for(i=1;i<=m;i++) for (j=0;j<=d;j++) copy(A1[i][j],A[i][j]); /* linearities are not considered for duplicates */ for (i = 0; i < Q->nlinearity; i++) redineq[Q->linearity[i]] = 2L; if(debug) { fprintf (lrs_ofp, "\n*cleanupA_start *redineq:"); for (i = 1; i <= m; i++) fprintf (lrs_ofp, " %ld", redineq[i]); } /* clean up A reducing by Gcd and zeroing out duplicate rows */ for(i=lastdv+1;i<=m;i++) if(redineq[Row[i]] != 2) reducearray(A[Row[i]],d+1); /* check non-decision variable rows of the dictionary */ for(i=lastdv+1;i<=m;i++) if(redineq[Row[i]] != 2) { /* first we check for identity rows */ oneindex=-1; nonzero=0; j=0; while(j <= d && nonzero <= 1) { if(!zero(A[Row[i]][Col[j]])) { nonzero++; if(one(A[Row[i]][Col[j]])) oneindex=j; } j++; } if(!nonzero || (nonzero==1 && oneindex >= 0)) /* zero or identity row found*/ { if(Q->debug) fprintf(lrs_ofp,"\n* nonzero=%ld i=%ld m=%ld d=%ld j=%ld oneindex=%ld",nonzero,i,m,d,j,oneindex); if(nonzero) itomp(ZERO, A[Row[i]][Col[oneindex]]); redineq[Row[i]]=-1; for (k=0;k<=d;k++) itomp(ZERO, A[Row[i]][k]); } else /* now we check for duplicate pairs rows */ { for (j=lastdv+1;j d ) /* zero out an equal row */ { if(Q->debug) fprintf(lrs_ofp,"\n*i=%ld j=%ld Row[%ld]=Row[%ld]",i,j,Row[i],Row[j]); redineq[Row[i]]=-1; for (k=0;k<=d;k++) itomp(ZERO, A[Row[i]][k]); break; } } /* for j */ } /* else now we check */ } /* for i */ /* restore non duplicate rows that were reduced */ for(i=1;i<=m;i++) for (j=0;j<=d;j++) if(!zero(A[i][j])) { for (k=0;k<=d;k++) copy(A[i][k],A1[i][k]); break; } lrs_clear_mp_matrix (A1,m,d); if(debug) { fprintf (lrs_ofp, "\n*cleanupA_end *redineq:"); for (i = 1; i <= m; i++) fprintf (lrs_ofp, " %ld", redineq[i]); } if(debug) { printA(P,Q); prawA(P,Q); } debug=FALSE; } /* end of cleanupA() */ void remove_artificial(lrs_dic *P,lrs_dat *Q) { long k,cob; long m=P->m_A; long lastdv=Q->lastdv; long *B = P->B; long debug = Q->debug; if(debug) printA(P,Q); if(P->C[0] != lastdv) /* pivot artificial var to cobasis */ { k=0; while (k <= m && B[k]!=lastdv) k++; if(k>m) { fprintf(lrs_ofp,"\n*artificial variable missing : bye bye\n"); exit(1); } cob=0; while (cob < lastdv-1) { if ( !zero(P->A[P->Row[k]][P->Col[cob]])) break; cob++; } if(cob == lastdv-1) { fprintf(lrs_ofp,"\n*artificial variable cannot leave basis : bye bye\n"); exit(1); } pivot(P,Q,k,cob); update(P,Q,&k,&cob); if(debug) printA(P,Q); } removecobasicindex(P,Q,0); /* lying: we remove the artificial basic variable */ Q->lastdv--; Q->inputd--; if(debug) printA(P,Q); } /* remove_artificial */ void redund_print(lrs_dic *P,lrs_dat *Q) { long i,j,k,cob,index; long nredund; /* number of redundant rows in input file */ long *redineq=Q->redineq; long *inequality = Q->inequality; long m = P->m_A; /* number of rows of A matrix */ long nlinearity = Q->nlinearity; long lastdv=Q->lastdv; long d; lrs_mp_matrix Ain=Q->Ain; long *B = P->B; long *C = P->C; long verbose=Q->verbose; long debug=Q->debug; if (debug) { fprintf (lrs_ofp, "\n*redund_print redineq:"); for (i = 1; i <= m; i++) fprintf (lrs_ofp, " %ld", redineq[i]); fprintf (lrs_ofp, "\n*inequality:"); for (i = 1; i <= m; i++) fprintf (lrs_ofp, " %ld", inequality[i]); } d=P->d; lastdv=Q->lastdv; /* update linearity with newly found linearities if any */ /* 2022.4.21 remove linearly dependent linearities */ nlinearity=0; for (i = 1; i <= m; i++) if(redineq[i]==2) { if(debug) printA(P,Q); j=1; while (j<=m && inequality[j] != i ) j++; k=1; cob=0; if ( j<=m ) /* hidden linearity, look in cobasis */ { index=j+lastdv; /* we are looking for variable index */ while (k<=m && B[k] != index ) k++; while(cobm ) /* index removed or in cobasis */ { if(debug) fprintf(lrs_ofp,"\n*linearity in row=%ld removed or in cobasis, independent",i); Q->linearity[nlinearity++]=i; } else /*index in basis */ { cob=0; while (cob < d) { if(debug) pmp(" A",P->A[P->Row[k]][P->Col[cob]]); if ( !zero(P->A[P->Row[k]][P->Col[cob]])) { if(debug) { fprintf(lrs_ofp,"\n* i=%ld cob=%ld lastdv=%ld ",i,cob,lastdv); fprintf(lrs_ofp,"C[cob]=%ld inequality=%ld ",C[cob],inequality[C[cob]-lastdv]); } /* 2023.11.2*/ if (redineq[inequality[C[cob]-lastdv]] != 2) break; } cob++; } if(cob==d) { if(verbose) fprintf(lrs_ofp,"\n*linearity in row=%ld dependent, made redundant",i); redineq[i]= -1; /* could not remove linearity from basis */ } else /* linearity in cobasis now */ { if(verbose) fprintf(lrs_ofp,"\n*linearity in row=%ld pivoted to cobasis",i); pivot(P,Q,k,cob); update(P,Q,&k,&cob); Q->linearity[nlinearity++]=i; } } /* else index in basis */ } if(debug) { fprintf(lrs_ofp,"\n*redineq:"); for(j=1;j<=m;j++) fprintf(lrs_ofp," %ld",redineq[j]); } if(Q->nonnegative) fprintf (lrs_ofp, "\nnonnegative"); if (!Q->hull) fprintf (lrs_ofp, "\nH-representation"); else fprintf (lrs_ofp, "\nV-representation"); /* linearities will be printed first in output */ if (nlinearity > 0) { fprintf (lrs_ofp, "\nlinearity %ld", nlinearity); for (i = 1; i <= nlinearity; i++) fprintf (lrs_ofp, " %ld", i); } nredund = 0; /* count number of non-redundant inequalities */ for (i = 1; i <= m; i++) if (redineq[i] == 0) nredund++; fprintf (lrs_ofp, "\nbegin"); fprintf (lrs_ofp, "\n%ld %ld rational", nlinearity+nredund, Q->inputd+1-Q->hull); /* print the linearities first */ for (i = 0; i < nlinearity; i++) lrs_printrow ("", Q, Ain[Q->linearity[i]], Q->inputd); for (i = 1; i <= m; i++) { if (redineq[i] == 0) lrs_printrow ("", Q, Ain[i], Q->inputd); /* remove redundant rows */ /* if( redineq[i] != 1 && redineq[i] != -1) { row++; for(j=0; j<= Q->inputd;j++) copy(P->A[row][j],Ain[i][j]); } */ } fprintf (lrs_ofp, "\nend"); if(sizeof(Q->projmess) > 0 ) fprintf (lrs_ofp, "\n%s",Q->projmess); if(verbose) fprintf (lrs_ofp, "\nverbose"); if(debug || Q->redund) { fprintf (lrs_ofp, "\n*input had %ld rows and %ld columns", m, Q->inputd+1); } redineq[0]=m - nredund-nlinearity; /* number of redundant rows */ if( m==nredund || redineq[0]==0) { if(debug || Q->redund) { fprintf (lrs_ofp, "\n*no redundant rows found"); if(!Q->fullredund) fprintf (lrs_ofp, " among those tested"); fprintf (lrs_ofp, "\n"); } } else { j=0; if(debug || Q->redund) { fprintf (lrs_ofp, "\n* %ld redundant row(s) found", redineq[0]); if(!Q->fullredund) fprintf (lrs_ofp, " among those tested"); fprintf (lrs_ofp, "\n"); for (i=1; i<=m; i++) if(redineq[i]==1 || redineq[i]==-1) { j++; if(j>20) { j=1; fprintf (lrs_ofp, "\n %ld",i); } else fprintf (lrs_ofp, " %ld",i); } if(Q->nonnegative) fprintf (lrs_ofp, "\n*implicit nonnegative constraints not tested"); } } if(nlinearity > Q->nlinearity && Q->redund) { if(nlinearity - Q->nlinearity==1) fprintf (lrs_ofp, "\n* %ld hidden linearity found",nlinearity - Q->nlinearity); else fprintf (lrs_ofp, "\n* %ld hidden linearities found",nlinearity - Q->nlinearity); if(!Q->fullredund) fprintf (lrs_ofp, " among those tested"); fprintf (lrs_ofp, "\n"); } if(Q->mplrs) /* always checks for hidden linearities */ Q->testlin=1; if( Q->redund && !Q->hull) { if(!Q->testlin && Q->hiddenlin) fprintf (lrs_ofp, "\n*no check for hidden linearities"); else if(Q->fullredund) fprintf (lrs_ofp, "\n*minimum representation : dimension=%ld", Q->inputd-nlinearity); } Q->nlinearity=nlinearity; fprintf (lrs_ofp, "\n"); return; } /* end of redund_print */ /*******************/ /* lrs_printoutput */ /* one line only */ /*******************/ void lrs_printoutput (lrs_dat * Q, lrs_mp_vector output) { char *sss; char **ss; long i; long len=0; if (Q->countonly) return; ss = (char **)malloc((1+Q->n) * sizeof(char*)); if (Q->hull || zero (output[0])) /*non vertex */ for (i = 0; i < Q->n; i++) { ss[i]=cpmp ("", output[i]); len=len+snprintf(NULL, 0, "%s ", ss[i] ); } else for (i = 1; i < Q->n; i++) { ss[i]=cprat("", output[i], output[0]); len=len+snprintf(NULL, 0, "%s ", ss[i] ); } sss=(char*)malloc((len+5)* sizeof(char*)); len=0; if (Q->hull || zero (output[0])) /*non vertex */ for (i = 0; i < Q->n; i++) { len=len+sprintf(sss+len,"%s ",ss[i]); free(ss[i]); } else { /* vertex */ len=sprintf (sss, " 1 "); for (i = 1; i < Q->n; i++) { len=len+sprintf(sss+len, "%s ", ss[i] ); free(ss[i]); } } if(Q->mplrs) lrs_post_output("vertex",sss); else fprintf (lrs_ofp, "\n%s",sss); free(ss); free(sss); } /**************************/ /* end of lrs_printoutput */ /**************************/ /****************/ /* lrs_lpoutput */ /****************/ void lrs_lpoutput(lrs_dic * P,lrs_dat * Q, lrs_mp_vector output) { if(!Q->testlin && !Q->messages) return; lrs_mp Temp1, Temp2; long i; long messages=Q->messages; Q->messages=TRUE; lrs_getsolution(P,Q,Q->output,0); if(Q->testlin) { if(positive(P->objnum) || Q->unbounded) { if(Q->nlinearity == 0) lrs_warning(Q,"warning","*interior point found, no hidden linearities"); else lrs_warning(Q,"warning","*relative interior point found, no hidden linearities"); Q->redundphase=1; Q->hiddenlin=0; } else { if(zero(P->objnum)) { lrs_warning(Q,"warning","\n*hidden linearities exist"); Q->redundphase=0; Q->hiddenlin=1; } else if(negative(P->objnum)) lrs_warning(Q,"warning", "\n*original problem is infeasible\n"); return; } } if((Q->testlin && !Q->fel) || Q->verbose) { if(!zero(output[0])) { if(!Q->testlin) fprintf (lrs_ofp, "\n\n*Primal: "); else { if(!Q->mplrs) fprintf (lrs_ofp, "\n* "); } char* buf="*"; for (i = 1; i < Q->n-Q->testlin; i++) /* do not print artificial var for testlin*/ { if(Q->mplrs) { char *sss=(char *)malloc(20+sizeof(long)); sprintf(sss,"x_%ld=",i); char *ss=cprat (sss, output[i], output[0]); char *buf1 = malloc((strlen(ss) + strlen(buf) + 10) * sizeof(char)); sprintf(buf1,"%s %s",buf,ss); if(i == Q->n-Q->testlin-1) lrs_warning(Q,"warning",buf1); if(i>1) free(buf); free(ss); free(sss); buf=buf1; } else { fprintf(lrs_ofp,"x_%ld=",i); prat ("", output[i], output[0]); } } /*for i=1 ... */ if(Q->mplrs) free(buf); } if(Q->unbounded && Q->testlin && !Q->hull) if(!Q->mplrs) /* fix the output below */ { lrs_getsolution(P,Q,Q->output,Q->n-1); fprintf(lrs_ofp,"\n* "); for (i = 1; i < Q->n-1; i++) /* do not print artificial var */ { fprintf(lrs_ofp,"x_%ld=",i); itomp(ONE,output[0]); prat ("", output[i], output[0]); } fprintf(lrs_ofp,": ray"); } Q->messages=messages; /* reset to orinal value */ if(Q->unbounded || Q->testlin) return; prat ("\n*Obj=",P->objnum, P->objden); fprintf (lrs_ofp, " pivots=%ld ",Q->count[3]); if(Q->nlinearity > 0) fprintf (lrs_ofp, "\n\n*Linearities in input file - partial dual solution only"); fprintf (lrs_ofp, "\n\n*Dual: "); lrs_alloc_mp (Temp2); for (i = 0; i < P->d; i++) { fprintf(lrs_ofp,"y_%ld=",Q->inequality[P->C[i]-Q->lastdv]); changesign(P->A[0][P->Col[i]]); mulint(Q->Lcm[P->Col[i]],P->A[0][P->Col[i]],Temp1); mulint(Q->Gcd[P->Col[i]],P->det,Temp2); prat("",Temp1,Temp2); changesign(P->A[0][P->Col[i]]); } lrs_clear_mp (Temp1); lrs_clear_mp (Temp2); } /* if verbose */ } /***********************/ /* end of lrs_lpoutput */ /***********************/ void lrs_printrow (const char *name, lrs_dat * Q, lrs_mp_vector output, long rowd) /* print a row of A matrix in output in "original" form */ /* rowd+1 is the dimension of output vector */ /* if input is H-rep. output[0] contains the RHS */ /* if input is V-rep. vertices are scaled by 1/output[1] */ { char *sss; char **ss; long i; long len=0; ss = (char **)malloc((1+Q->n) * sizeof(char*)); /* first compute length */ len=len+snprintf(NULL, 0, "%s", name); if (!Q->hull || zero (output[1])) for (i = Q->hull; i <= rowd; i++) { ss[i]=cpmp ("", output[i]); len=len+snprintf(NULL, 0, "%s ", ss[i] ); } else for (i = 2; i <= rowd; i++) { ss[i]=cprat("", output[i], output[1]); len=len+snprintf(NULL, 0, "%s ", ss[i] ); } /* now build output string */ sss=(char*)malloc((len+5)* sizeof(char*)); len=sprintf(sss, "%s",name); if (!Q->hull || zero (output[1])) for (i = Q->hull; i <= rowd; i++) { len=len+sprintf(sss+len,"%s ",ss[i]); free(ss[i]); } else { /* vertex */ len=len+sprintf(sss+len," 1 "); for (i = 2; i <= rowd; i++) { len=len+sprintf(sss+len,"%s ",ss[i]); free(ss[i]); } } if(Q->mplrs) { if(strcmp(name,"")==0) /* consumer printing output */ fprintf (lrs_ofp, "\n%s",sss); else lrs_post_output("flush",sss); // fprintf (lrs_ofp, "\n%s",sss); } else fprintf (lrs_ofp, "\n%s",sss); free(ss); free(sss); return; } /* end of lrs_printrow */ long lrs_getsolution (lrs_dic * P, lrs_dat * Q, lrs_mp_vector output, long col) /* check if column indexed by col in this dictionary */ /* contains output */ /* col=0 for vertex 1....d for ray/facet */ { long j; /* cobasic index */ lrs_mp_matrix A = P->A; long *Row = P->Row; if (col == ZERO) /* check for lexmin vertex */ { j = lrs_getvertex (P, Q, output); return j; } /* check for rays: negative in row 0 , positive if lponly */ if (Q->lponly) { if (!positive (A[0][col])) return FALSE; } else if (!negative (A[0][col])) return FALSE; /* and non-negative for all basic non decision variables */ j = Q->lastdv + 1; while (j <= P->m && !negative (A[Row[j]][col])) j++; if (j <= P->m) return FALSE; /* 2021.5.21 check for max depth output */ if (lexmin (P, Q, col)) { if(P->depth > Q->count[8]) Q->count[8] = P->depth; return lrs_getray (P, Q, col, Q->n, output); } if (Q->geometric || Q->allbases || Q->lponly) return lrs_getray (P, Q, col, Q->n, output); return FALSE; /* no more output in this dictionary */ } /* end of lrs_getsolution */ void lrs_print_header(const char *name) { if(lrs_ofp == NULL) lrs_ofp=stdout; #ifdef LRS_QUIET return; #endif fprintf (lrs_ofp,"%s:", name); fprintf (lrs_ofp,TITLE); fprintf (lrs_ofp,VERSION); fprintf (lrs_ofp,"("); fprintf (lrs_ofp,BIT); fprintf (lrs_ofp,","); fprintf (lrs_ofp,ARITH); #ifdef MA fprintf (lrs_ofp,",hybrid_arithmetic"); #endif #ifdef LRSLONG #ifndef SAFE fprintf (lrs_ofp,",no_overflow_checking"); #endif #endif #ifdef GMP #ifdef MGMP fprintf(lrs_ofp,",mini-gmp"); #else fprintf(lrs_ofp,",_gmp_v.%d.%d",__GNU_MP_VERSION,__GNU_MP_VERSION_MINOR); #endif #elif defined(FLINT) fprintf(lrs_ofp,"_%dbit_flint_v.%s", FLINT_BITS, FLINT_VERSION); #endif fprintf (lrs_ofp,")"); } long lrs_init (const char *name) /* returns TRUE if successful, else FALSE */ { #ifndef MPLRS #ifndef LRS_QUIET lrs_print_header(name); #endif #endif if (!lrs_mp_init (0, stdin, stdout)) /* initialize arithmetic */ return FALSE; lrs_Q_count = 0; lrs_checkpoint_seconds = 0; #ifndef SIGNALS setup_signals (); #endif return TRUE; } void lrs_close (const char *name) { #ifdef MPLRS return; #endif #ifdef LRS_QUIET fprintf (lrs_ofp, "\n"); if (lrs_ofp != stdout) { fclose (lrs_ofp); lrs_ofp=NULL; } return; #endif fprintf (lrs_ofp, "\n*"); lrs_print_header(name); #ifdef LRSLONG #ifndef SAFE fprintf (lrs_ofp, "\n*caution: no overflow checking on long integer arithemtic"); #endif #endif #ifdef MP fprintf (lrs_ofp, " max decimal digits=%ld/%ld", DIG2DEC (lrs_record_digits), DIG2DEC (lrs_digits)); #endif #ifndef TIMES ptimes (); #endif if (lrs_ofp != stdout) { fclose (lrs_ofp); lrs_ofp=NULL; } } /***********************************/ /* allocate and initialize lrs_dat */ /***********************************/ lrs_dat * lrs_alloc_dat (const char *name) { lrs_dat *Q; long i; if (lrs_Q_count >= MAX_LRS_Q) { fprintf (stderr, "Fatal: Attempt to allocate more than %ld global data blocks\n", MAX_LRS_Q); return NULL; } Q = (lrs_dat *) malloc (sizeof (lrs_dat)); if (Q == NULL) return Q; /* failure to allocate */ lrs_Q_list[lrs_Q_count] = Q; Q->id = lrs_Q_count; lrs_Q_count++; Q->name=(char *) CALLOC ((unsigned) strlen(name)+1, sizeof (char)); strcpy(Q->name,name); /* initialize variables */ Q->mplrs=FALSE; Q->plrs=FALSE; Q->messages=TRUE; #ifdef MPLRS Q->mplrs=TRUE; #endif #ifdef PLRS Q->plrs=TRUE; #endif #ifdef LRS_QUIET Q->messages=FALSE; #endif strcpy(Q->fname,""); /* name of program, filled in later */ Q->m = 0L; Q->n = 0L; Q->inputd = 0L; Q->deepest = 0L; Q->nlinearity = 0L; Q->nredundcol = 0L; Q->runs = 0L; Q->subtreesize=MAXD; Q->seed = 1234L; Q->totalnodes = 0L; for (i = 0; i < 10; i++) { Q->count[i] = 0L; Q->cest[i] = 0.0; if(i < 5) Q->startcount[i] = 0L; } Q->count[2] = 1L; /* basis counter */ Q->startcount[2] = 0L; /* starting basis counter */ /* initialize flags */ Q->allbases = FALSE; Q->bound = FALSE; /* upper/lower bound on objective function given */ Q->countonly = FALSE; /* produce the usual output */ Q->debug = FALSE; Q->frequency = 0L; Q->dualdeg = FALSE; /* TRUE if dual degenerate starting dictionary */ Q->geometric = FALSE; Q->getvolume = FALSE; Q->homogeneous = TRUE; Q->polytope = FALSE; Q->triangulation = FALSE; Q->hull = FALSE; Q->incidence = FALSE; Q->nincidence=0; Q->maxincidence=MAXD; Q->minprunedepth=MAXD; Q->lponly = FALSE; Q->maxdepth = MAXD; Q->mindepth = -MAXD; Q->maxoutput = 0L; Q->maxcobases = 0L; /* after maxcobases have been found unexplored subtrees reported */ Q->redund = FALSE; Q->nash = FALSE; Q->fel = FALSE; Q->nonnegative = FALSE; Q->printcobasis = FALSE; Q->printslack = FALSE; Q->truncate = FALSE; /* truncate tree when moving from opt vertex */ Q->extract=FALSE; Q->verbose=FALSE; Q->voronoi = FALSE; Q->maximize = FALSE; /*flag for LP maximization */ Q->minimize = FALSE; /*flag for LP minimization */ Q->restart = FALSE; /* TRUE if restarting from some cobasis */ Q->givenstart = FALSE; /* TRUE if a starting cobasis is given */ Q->strace = -1L; /* turn on debug at basis # strace */ Q->etrace = -1L; /* turn off debug at basis # etrace */ Q->newstart=FALSE; Q->giveoutput=TRUE; /* set to false for first output after restart */ Q->redundphase=FALSE; /* set to true when mplrs skips verifying output */ Q->hiddenlin=TRUE; /* set to true hidden linearities may exist */ Q->nextineq=15; /* start redundancy testing from this row */ Q->testlin=0; /* redund mode: test for hidden linearities */ Q->fullredund=TRUE; /* minrep/redund mode: test all rows */ Q->facet=NULL; Q->redundcol=NULL; Q->inequality=NULL; Q->linearity=NULL; Q->vars=NULL; Q->startcob=NULL; Q->minratio=NULL; Q->temparray=NULL; Q->redineq=NULL; Q->Ain=NULL; Q->olddic=NULL; Q->tid=0; /* thread index */ Q->child=0; Q->threads=0; Q->saved_flag = 0; /* no cobasis saved initially, db */ lrs_alloc_mp (Q->Nvolume); lrs_alloc_mp (Q->Dvolume); lrs_alloc_mp (Q->sumdet); lrs_alloc_mp (Q->saved_det); lrs_alloc_mp (Q->boundn); lrs_alloc_mp (Q->boundd); itomp (ZERO, Q->Nvolume); itomp (ONE, Q->Dvolume); itomp (ZERO, Q->sumdet); Q->unbounded = FALSE; return Q; } /* end of allocate and initialize lrs_dat */ /*******************************/ /* lrs_read_dat */ /*******************************/ long lrs_read_dat (lrs_dat * Q, int argc, char *argv[]) { char name[1000]; char writemode[2]="w"; long dec_digits = DEFAULT_DIGITS; long infilenum=0; /*input file number to open if any */ long firstline = TRUE; /*flag for picking off name at line 1 */ long i; int c; /* for fgetc */ int messages = Q->messages; /* print output for each option */ *tmpfilename='\0'; strcpy(outfilename, "\0"); if(argc > 1 ) { infilenum=1; if(Q->nash && argc ==2) /* legacy code to open second nash input file */ infilenum=2; if(Q->nash && argc ==4) /* legacy code for nash output file */ strcpy(outfilename,argv[3]); } if (infilenum > 0 && (lrs_ifp = fopen (argv[infilenum], "r")) == NULL) /* command line overides stdin */ { fprintf (stderr,"\n*bad input file name\n"); return (FALSE); } if (infilenum==1) { strcpy(infilename,argv[1]); if(!Q->mplrs && messages && overflow == 0 ) printf ("\n*Input taken from %s", infilename); fflush(stdout); } #ifdef LRSLONG if(infilenum==0) /* stdin gets written to a temporary file */ { strcpy(tmpfilename,"/tmp/lrs_stdinXXXXXX"); if(mkstemp(tmpfilename)==-1) { fprintf (stderr,"\n*could not open temporary file for stdin\n"); return (FALSE); } lrs_stdin_to_file(tmpfilename); lrs_ifp=fopen (tmpfilename, "r"); strcpy(infilename,tmpfilename); } lrs_file_to_cache(lrs_ifp); #endif if(argc > 2) /* lrs has commandline arguments for newstart */ { if (!Q->nash ) { i=2; while (i < argc) /* add command line arguments here */ { if(strcmp(argv[i],"-newstart")==0) /* newstart not currently used ... */ { strcpy(writemode,"a"); Q->newstart=TRUE; } else /* command line argument overides stdout */ strcpy(outfilename,argv[i++]); } } if(strcmp(outfilename,"\0") != 0 ) { if(strcmp(outfilename,"-") == 0 ) lrs_ofp = stdout; else { if ((lrs_ofp = fopen (outfilename, writemode)) == NULL) { fprintf (stderr,"\n*bad output file name %s\n",outfilename); return (FALSE); } else if(overflow == 0) printf ("\n*Output sent to file %s\n", outfilename); } } } /*2020.5.19 new redund handling, thanks to DB */ /* symbolic link from redund to lrs needed */ /* similar links if lrs1, lrs2 or lrsgmp used */ /* any redund option in input will overide */ if(!Q->mplrs && lrs_ofp != stdout) /* headers for the output file also */ { char *name; name=(char *) malloc(strlen(Q->fname)+5); strcpy(name,"*"); strcat(name,Q->fname); lrs_print_header(name); free(name); } /* process input file */ if( fscanf (lrs_ifp, "%s", name) == EOF) { fprintf (stderr, "\n*no begin line"); return (FALSE); } while (strcmp (name, "begin") != 0) /*skip until "begin" found processing options */ { if (strncmp (name, "*", 1) == 0) /* skip any line beginning with * */ { c = name[0]; while (c != EOF && c != '\n') c = fgetc (lrs_ifp); } else if (strcmp (name, "H-representation") == 0) Q->hull = FALSE; else if ((strcmp (name, "hull") == 0) || (strcmp (name, "V-representation") == 0)) { if(Q->mplrs && Q->fel) { lrs_post_output("flush","\n*project/eliminate are not mplrs options for a V-representation"); lrs_post_output("flush","*for large problems use extract option with lrs then 'mplrs -minrep'\n"); return(FALSE); } Q->hull = TRUE; Q->polytope = TRUE; /* will be updated as input read */ } else if (strcmp (name, "digits") == 0) { if (fscanf (lrs_ifp, "%ld", &dec_digits) == EOF) { fprintf (stderr, "\n*no begin line"); return (FALSE); } if (!lrs_set_digits(dec_digits)) return (FALSE); } else if (strcmp (name, "testlin") == 0) { if(Q->fel) { if(!Q->mplrs) lrs_warning(Q,"warning","\n*testlin ignored in fel mode"); } else if (!(Q->mplrs && Q->redund)) { Q->testlin=TRUE; Q->plrs=FALSE; lrs_warning(Q,"warning","\n*testlin"); } } else if (strcmp (name, "linearity") == 0) { if (!readlinearity (Q)) return FALSE; } else if (strcmp (name, "nonnegative") == 0) { if(Q->nash) fprintf (stderr, "\nNash incompatibile with nonnegative option - skipped"); else Q->nonnegative = TRUE; } else if (firstline && !Q->mplrs) /* print firstline of input file */ { lrs_warning(Q,"warning",name); firstline = FALSE; } if (fscanf (lrs_ifp, "%s", name) == EOF) { fprintf (stderr, "\n*no begin line\n"); return (FALSE); } } /* end of while */ if (fscanf (lrs_ifp, "%ld %ld %s", &Q->m, &Q->n, name) == EOF) { fprintf (stderr, "\n*no data in file\n"); return (FALSE); } if(Q->tid==1) /* consumer does not do the artificial LP */ Q->testlin=0; if(Q->debug) fprintf(lrs_ofp,"\n+++Q->rank=%ld Q->testlin=%ld Q->redundphase=%ld",Q->tid,Q->testlin,Q->redundphase); if(Q->testlin && !Q->redundphase) Q->n++; /* col of ones will be appended for rank=0 proc only */ if (strcmp (name, "integer") != 0 && strcmp (name, "rational") != 0) { fprintf (stderr,"\n*data type must be integer or rational\n"); return (FALSE); } if (Q->m == 0) { fprintf (stderr, "\n*no input given\n"); /* program dies ungracefully */ return (FALSE); } /* inputd may be reduced in preprocessing of linearities and redund cols */ return TRUE; } /* end of lrs_read_dat */ /****************************/ /* set up lrs_dic structure */ /****************************/ long lrs_read_dic (lrs_dic * P, lrs_dat * Q) /* read constraint matrix and set up problem and dictionary */ { lrs_mp Temp,Tempn,Tempd, mpone, mptwo; long i, j, m, d;; long allzero=1; char name[100]; char mess[200]; char *ss; int c; /* fgetc actually returns an int. db */ long redundstart, redundend; long dualperturb=FALSE; /* dualperturb=TRUE: objective function perturbed */ /* assign local variables to structures */ lrs_mp_matrix A; lrs_mp_vector Gcd, Lcm; lrs_mp_vector oD=Q->output; /* Denom for obj fun, temp use of output */ long hull = Q->hull; long messages=Q->messages; lrs_alloc_mp(Temp); lrs_alloc_mp(mpone); lrs_alloc_mp(Tempn); lrs_alloc_mp(Tempd); lrs_alloc_mp(mptwo); A = P->A; m = Q->m; d = Q->inputd; Gcd = Q->Gcd; Lcm = Q->Lcm; itomp (ONE, mpone); itomp(2L,mptwo); itomp (ONE, A[0][0]); itomp (ONE, Lcm[0]); itomp (ONE, Gcd[0]); for (i = 1; i <= m; i++) /* read in input matrix row by row */ { itomp (ONE, Lcm[i]); /* Lcm of denominators */ itomp (ZERO, Gcd[i]); /* Gcd of numerators */ for (j = hull; j <= d; j++) /* hull data copied to cols 1..d */ { /*2022.4.25 added column to test for full dimension */ if(j==d && Q->testlin) { itomp(-1, A[i][d]); itomp( 1, A[0][d]); } else if (readrat (A[i][j], A[0][j])) lcm (Lcm[i], A[0][j]); /* update lcm of denominators */ if(overflow_detected) { lrs_warning(Q,"warning","*integer overflow reading input"); goto end_read_dic; } copy (Temp, A[i][j]); gcd (Gcd[i], Temp); /* update gcd of numerators */ } if (hull) { itomp (ZERO, A[i][0]); /*for hull, we have to append an extra column of zeroes */ if (!one (A[i][1]) || !one (A[0][1])) /* all rows must have a one in column one */ Q->polytope = FALSE; } if (!zero (A[i][hull])) /* for H-rep, are zero in column 0 */ Q->homogeneous = FALSE; /* for V-rep, all zero in column 1 */ storesign (Gcd[i], POS); storesign (Lcm[i], POS); if (mp_greater (Gcd[i], mpone) || mp_greater (Lcm[i], mpone)) for (j = 0; j <= d; j++) { exactdivint (A[i][j], Gcd[i], Temp); /*reduce numerators by Gcd */ mulint (Lcm[i], Temp, Temp); /*remove denominators */ exactdivint (Temp, A[0][j], A[i][j]); /*reduce by former denominator */ } } /* end of for i= */ if(Q->testlin && !Q->redundphase) /* setup extra col for hiddenlin test */ { for (i = 1; i <= m; i++) /* zero row treated like linearity */ { allzero=1; for(j=0;jnlinearity;i++) itomp(ZERO,A[Q->linearity[i]][d]); Q->lponly=TRUE; Q->maximize=TRUE; } /* setup extra col ... */ /* 2010.4.26 patch */ if(Q->nonnegative) /* set up Gcd and Lcm for nonexistent nonnegative inequalities */ for (i=m+1;i<=m+d;i++) { itomp (ONE, Lcm[i]); itomp (ONE, Gcd[i]); } if (Q->homogeneous && Q->verbose) { lrs_warning(Q,"warning","*Input is homogeneous, column 1 not treated as redundant"); } /* read in flags */ while (fscanf (lrs_ifp, "%s", name) != EOF) { if (strncmp (name, "*", 1) == 0) /* skip any line beginning with * */ { c = name[0]; while (c != EOF && c != '\n') c = fgetc (lrs_ifp); } if (strcmp (name, "checkpoint") == 0) { long seconds; if(fscanf (lrs_ifp, "%ld", &seconds) == EOF) { fprintf (lrs_ofp, "\nInvalid checkpoint option"); return (FALSE); } #ifndef SIGNALS if (seconds > 0) { lrs_checkpoint_seconds = seconds; errcheck ("signal", signal (SIGALRM, timecheck)); alarm (lrs_checkpoint_seconds); } #endif } if (strcmp (name, "debug") == 0) { Q->etrace =0; if(fscanf (lrs_ifp, "%ld %ld", &Q->strace, &Q->etrace)==EOF) Q->strace =0; if(!Q->mplrs) fprintf (lrs_ofp, "\n*%s from B#%ld to B#%ld", name, Q->strace, Q->etrace); Q->debug=TRUE; if (Q->strace <= 1) Q->debug = TRUE; } if (strcmp (name, "startingcobasis") == 0) { if(Q->nonnegative) lrs_warning(Q,"warning", "*startingcobasis incompatible with nonnegative option:skipped"); else { if(!Q->mplrs && messages) fprintf (lrs_ofp, "\n*startingcobasis"); Q->givenstart = TRUE; if (!readfacets (Q, Q->inequality)) return FALSE; } } if (strcmp (name, "restart")==0 ) { if(Q->mplrs) { fprintf (lrs_ofp, "\n\n*** %s is an lrs option only\n", name); return(FALSE); } Q->restart = TRUE; Q->giveoutput = FALSE; /* first time only */ if(Q->voronoi) { if(fscanf (lrs_ifp, "%ld %ld %ld %ld", &Q->count[1], &Q->count[0], &Q->count[2], &P->depth)==EOF) return FALSE; if(!Q->mplrs && messages) fprintf (lrs_ofp, "\n*%s V#%ld R#%ld B#%ld h=%ld data points", name, Q->count[1], Q->count[0], Q->count[2], P->depth); } else if(hull) { if( fscanf (lrs_ifp, "%ld %ld %ld", &Q->count[0], &Q->count[2], &P->depth)==EOF) return(FALSE); if(!Q->mplrs && messages) fprintf (lrs_ofp, "\n*%s F#%ld B#%ld h=%ld vertices/rays", name, Q->count[0], Q->count[2], P->depth); } else { if(fscanf (lrs_ifp, "%ld %ld %ld %ld", &Q->count[1], &Q->count[0], &Q->count[2], &P->depth)==EOF) return FALSE; if(!Q->mplrs && messages) fprintf (lrs_ofp, "\n*%s V#%ld R#%ld B#%ld h=%ld facets", name, Q->count[1], Q->count[0], Q->count[2], P->depth); } /* store starting counts to calculate totals of plrs/mplrs subjob */ for (i = 0; i<5; i++) Q->startcount[i] = Q->count[i]; if (!readfacets (Q, Q->facet)) return FALSE; } /* end of restart */ /* The next flags request a LP solution only */ if(Q->mplrs) { if (strncmp (name,"lponly",6)== 0) { fprintf (lrs_ofp, "\n\n*** %s is an lrs option only\n", name); return(FALSE); } } else { if (strcmp (name, "lponly") == 0 || strcmp (name, "lponly_d") == 0 ) { if (Q->hull || Q->testlin || Q->redund || Q->fel) fprintf (lrs_ofp, "\n*lponly option not valid -skipped"); else { Q->lponly = 1; /*Dantzig's rule is default */ fprintf (lrs_ofp, "\n*lponly mode: Dantzig's rule"); } } if (strcmp (name, "lponly_r") == 0) { if (Q->hull || Q->testlin || Q->redund || Q->fel) fprintf (lrs_ofp, "\n*lponly option not valid -skipped"); else { Q->lponly = 2; /*random edge rule */ fprintf (lrs_ofp, "\n*lponly mode: random edge rule"); } } if (strcmp (name, "lponly_rd") == 0) { if (Q->hull || Q->testlin || Q->redund || Q->fel) fprintf (lrs_ofp, "\n*lponly option not valid -skipped"); else { Q->lponly = 3; /*random edge/Dantzig hybrid */ fprintf (lrs_ofp, "\n*lponly mode: random edge/Dantzig hybrid"); } } if (strcmp (name, "lponly_b") == 0 ) { if (Q->hull || Q->testlin || Q->redund || Q->fel) fprintf (lrs_ofp, "\n*lponly option not valid -skipped"); else { Q->lponly = 4; /*Bland' rule */ fprintf (lrs_ofp, "\n*lponly mode: Bland's rule"); } } } /* else !Q->mplrs */ /* The LP will be solved after initialization to get starting vertex */ if (strcmp (name, "maximize") == 0 || strcmp (name, "minimize") == 0) { if(!Q->testlin && !Q->fel && !Q->redund ) { if(Q->hull) /*2021.1.18 lrs will find the max/min lines in input file */ { if(Q->mplrs) { fprintf (lrs_ofp, "\n\n*%s for V-representation is an lrs option only\n", name); return(FALSE); } Q->lponly=TRUE; } if (strcmp (name, "maximize") == 0) Q->maximize = TRUE; else Q->minimize = TRUE; lrs_warning(Q,"warning",name); if(dualperturb) /* apply a perturbation to objective function */ { lrs_warning(Q,"warning","*Objective function perturbed"); copy(Temp,mptwo); } for (j = Q->hull; j <= d; j++) { if (readrat (A[0][j], oD[j]) || dualperturb ) { if(dualperturb && j > 0 && j < d-Q->hull ) { linrat(A[0][j], oD[j],ONE,mpone,Temp,ONE,Tempn,Tempd); copy(A[0][j],Tempn); copy(oD[j],Tempd); mulint(mptwo,Temp,Temp); } reduce (A[0][j], oD[j]); lcm (Q->Lcm[0], oD[j]); /* update lcm of denominators */ } } storesign (Q->Lcm[0], POS); if (mp_greater (Q->Lcm[0], mpone)) for (j = Q->hull; j <= d; j++) { mulint (Q->Lcm[0], A[0][j], A[0][j]); /*remove denominators */ copy (Temp, A[0][j]); exactdivint (Temp, oD[j], A[0][j]); } if(messages) for(j = Q->hull; j <= d; j++) pmp("",A[0][j]); for (j = Q->hull; j <= d; j++) if (!Q->maximize) changesign (A[0][j]); if (Q->debug) printA (P, Q); } /* not used for redund, minrep, fel */ } /* end of LP setup */ if (strcmp (name, "volume") == 0) { lrs_warning(Q,"warning", "*volume"); Q->getvolume = TRUE; } if (strcmp (name, "geometric") == 0) { if (hull && !Q->voronoi) lrs_warning(Q,"warning", "*geometric - option for H-representation or voronoi only, skipped"); else { lrs_warning(Q,"warning", "*geometric"); Q->geometric = TRUE; } } if (strcmp (name, "allbases") == 0) { lrs_warning (Q,"warning", "*allbases"); Q->allbases = TRUE; } if (strcmp (name, "countonly") == 0) { lrs_warning (Q,"warning", "*countonly"); Q->countonly = TRUE; } if (strcmp (name, "triangulation") == 0) { if (hull) { lrs_warning (Q,"warning","*triangulation"); Q->triangulation = TRUE; Q->getvolume = TRUE; } else printf ("\n*triangulation only valid for V-representations: skipped"); } if (strcmp (name, "dualperturb") == 0) { dualperturb = TRUE; } if (strcmp (name, "maxincidence") == 0) { if(fscanf (lrs_ifp, "%lld %lld", &Q->maxincidence,&Q->minprunedepth)==EOF) lrs_warning (Q,"warning", "*maxincidence: 2 parameters needed"); else { Q->incidence=TRUE; sprintf(mess,"*%s %lld %lld",name, Q->maxincidence,Q->minprunedepth); lrs_warning(Q,"warning",mess); } } if (strcmp (name, "incidence") == 0) { lrs_warning (Q,"warning", "*incidence"); Q->incidence = TRUE; } if (strcmp (name, "#incidence") == 0) /* number of incident inequalities only */ { Q->printcobasis = TRUE; } if (strcmp (name, "printcobasis") == 0) { if(fscanf (lrs_ifp, "%ld", &Q->frequency)==EOF) /*2010.7.7 set default to zero = print only when outputting vertex/ray/facet */ Q->frequency=0; if (Q->frequency > 0) sprintf(mess,"*%s %ld",name, Q->frequency); else sprintf(mess,"%s",name); lrs_warning(Q,"warning",mess); Q->printcobasis = TRUE; } if (strcmp (name, "integervertices") == 0) /* when restarting reinitialize */ { if(fscanf (lrs_ifp, "%ld", &Q->count[4])==EOF) Q->count[4]=0; } if (strcmp (name, "printslack") == 0) { Q->printslack = TRUE; } if (strcmp (name, "threads") == 0) { if(fscanf (lrs_ifp, "%ld", &Q->threads)==EOF) Q->threads=1; if(Q->threads < 1) Q->threads=1; } if (strcmp (name, "cache") == 0) { if(fscanf (lrs_ifp, "%ld", &dict_limit)==EOF) dict_limit=1; if (dict_limit < 1) dict_limit = 1; sprintf(mess,"*%s %ld",name, dict_limit); lrs_warning(Q,"warning",mess); } if (strcmp (name, "linearity") == 0) { if (!readlinearity (Q)) return FALSE; } if (strcmp (name, "maxdepth") == 0) { Q->maxdepth=MAXD; if(fscanf (lrs_ifp, "%lld", &Q->maxdepth)==EOF) Q->maxdepth=MAXD; /*2021.5.19 implement in mplrs */ sprintf(mess,"*%s %lld",name, Q->maxdepth); lrs_warning(Q,"warning",mess); } if (strcmp (name, "mindepth") == 0) { Q->mindepth=0; if(fscanf (lrs_ifp, "%lld", &Q->mindepth)==EOF) Q->mindepth=0; if(Q->mplrs) /* taken from control line */ lrs_warning(Q,"warning","*mindepth option skipped in mplrs"); else fprintf (lrs_ofp, "\n*%s %lld", name, Q->mindepth); } if (strcmp (name, "maxoutput") == 0) { if(fscanf (lrs_ifp, "%ld", &Q->maxoutput)==EOF) Q->maxoutput = 100; if(Q->mplrs) /* taken from control line */ lrs_warning(Q,"warning","*maxoutput option skipped in mplrs"); else fprintf (lrs_ofp, "\n*%s %ld", name, Q->maxoutput); } if (strcmp (name, "maxcobases") == 0) { if(fscanf (lrs_ifp, "%ld", &Q->maxcobases)==EOF) Q->maxcobases = 1000; if(Q->mplrs) /* taken from control line */ lrs_warning(Q,"warning","*maxcobases option skipped - supplied on control line in mplrs"); else fprintf (lrs_ofp, "\n*%s %ld", name, Q->maxcobases); } /*2019.8.24 bounds for redund */ if (strcmp (name, "redund") == 0 && strcmp("fel",Q->fname)!=0) { if(!Q->redund && messages) lrs_warning (Q,"warning", "*switching to redund mode"); for (i = 1; i <= Q->m; i++) /*reset any previous redund option except =2 values */ if (Q->redineq[i] != 2) Q->redineq[i]=0; Q->redineq[0]=1; if( fscanf (lrs_ifp, "%ld %ld", &redundstart, &redundend)==EOF) { redundstart=1; redundend=m; } if (redundstart <1 || redundstart > redundend ) redundstart=1; if (redundend < 1 || redundend > m ) redundend=Q->m; for (i=redundstart;i<=redundend;i++) Q->redineq[i]=1; if(redundstart > 1 || redundend < m ) Q->fullredund=FALSE; /*not testing all rows */ if(messages) if (!Q->mplrs || !Q->redund) { sprintf (mess, "*%s %ld %ld", name, redundstart, redundend); lrs_warning(Q,"warning",mess); } if(strcmp("fel",Q->fname)==0) Q->redund=FALSE; else { Q->fel=FALSE; Q->redund=TRUE; Q->extract=FALSE; } } if (strcmp (name, "redund_list") == 0) { if(!Q->redund && messages) lrs_warning (Q,"warning", "*switching to redund mode"); readredund(Q); if(!Q->mplrs && (strcmp("fel",Q->fname)==0)) Q->redund=FALSE; else { Q->fel=FALSE; Q->redund=TRUE; Q->extract=FALSE; } } if (strcmp (name, "truncate") == 0) { if (hull) lrs_warning(Q,"warning","*truncate - option for H-representation only, skipped"); else { Q->truncate = TRUE; lrs_warning(Q,"warning","*truncate"); } } if (strcmp (name, "project") == 0 || strcmp (name, "eliminate") == 0) /* fel */ { if(Q->mplrs && Q->hull) { lrs_post_output("flush","\n*project/eliminate are not mplrs options for V-representations"); lrs_post_output("flush","*for large problems use extract option with lrs then 'mplrs -minrep'\n"); return(FALSE); } if( Q->fel || (strncmp("lrs",Q->fname,3)==0 && !Q->testlin) || strcmp("mplrs-internal",Q->fname)==0) { if( messages ) lrs_warning (Q,"warning", "\n*switching to fel mode"); Q->fel=TRUE; Q->redund=FALSE; Q->extract=FALSE; } else { if(messages) lrs_warning (Q,"warning","*project/eliminate option skipped"); } fflush(lrs_ofp); if(!readvars(Q,name)) { free(Q->vars); Q->vars=NULL; return FALSE; } } if (strcmp (name, "extract") == 0 ) /* redundancies are not removed */ { if(Q->mplrs) { fprintf (lrs_ofp, "\n\n*%s is an lrs option only\n", name); return(FALSE); } if(Q->nash) fprintf (lrs_ofp, "\n*%s is an lrs option only - skipped\n", name); else { if(messages) lrs_warning (Q,"warning", "\n*switching to extract mode"); Q->fel=FALSE; Q->redund=FALSE; Q->extract=TRUE; if(!readvars(Q,name)) { free(Q->vars); Q->vars=NULL; return FALSE; } } } if (strcmp (name, "verbose") == 0) Q->verbose = TRUE; if (strcmp (name, "bound") == 0) { readrat(Q->boundn,Q->boundd); Q->bound = TRUE; } if (strcmp (name, "nonnegative") == 0) lrs_warning(Q,"warning","*nonnegative - option must come before begin line - skipped"); if (strcmp (name, "seed") == 0) { if(fscanf (lrs_ifp, "%ld", &Q->seed)==EOF) Q->seed = 3142; sprintf(mess,"*seed=%ld",Q->seed); lrs_warning(Q,"warning",mess); srand(Q->seed); } if (strcmp (name, "estimates") == 0) { if(Q->mplrs) { fprintf (lrs_ofp, "\n\n*** %s is an lrs option only\n", name); return(FALSE); } Q->plrs=FALSE; /* both plrs and mplrs should do estimates! */ if(fscanf (lrs_ifp, "%ld", &Q->runs)==EOF) Q->runs=1; if(messages) fprintf (lrs_ofp, "\n*%s %ld", name, Q->runs); } // 2015.2.9 Estimates will continue until estimate is less than subtree size if (strcmp (name, "subtreesize") == 0) { if(fscanf (lrs_ifp, "%lld", &Q->subtreesize)==EOF) Q->subtreesize=MAXD; if(messages) fprintf (lrs_ofp, "\n*%s %lld", name, Q->subtreesize); if(Q->mplrs) { fprintf (lrs_ofp, "\n\n*** %s is an lrs option only\n", name); return(FALSE); } } if ((strcmp (name, "voronoi") == 0) || (strcmp (name, "Voronoi") == 0)) { if (!hull) lrs_warning(Q,"warning","*voronoi requires V-representation - option skipped"); else { lrs_warning(Q,"warning","*voronoi"); Q->voronoi = TRUE; Q->polytope = FALSE; } } } /* end of while for reading flags */ if(Q->bound) { if(Q->maximize) ss=cprat("*Lower bound on objective function:",Q->boundn,Q->boundd); else ss=cprat("*Upper bound on objective function:",Q->boundn,Q->boundd); lrs_warning(Q,"warning",ss); free(ss); } /* Certain options are incompatible, this is fixed here */ if (Q->restart && Q->maxcobases > 0) //2015.4.3 adjust for restart Q->maxcobases = Q->maxcobases + Q->count[2]; if (Q->incidence) Q->printcobasis = TRUE; if(Q->allbases && Q->printcobasis && Q->frequency == 0) Q->frequency =1; /* otherwise only lexmin are printed */ if (Q->debug) { printA (P, Q); fprintf (lrs_ofp, "\nexiting lrs_read_dic"); } fflush(lrs_ofp); fflush(stdout); if( Q->lponly || Q->mplrs || Q->fel || Q->extract || Q->redund || Q->testlin ) { Q->threads=1; /* multithreading not implemented */ Q->plrs=FALSE; } for(i=0;inlinearity;i++) /* didn't know m when we read these*/ if(Q->linearity[i]<1 || Q->linearity[i]>Q->m) { lrs_warning(Q,"warning","*Linearity indices must be in range 1..m"); return FALSE; } /*removing tmpfiles */ end_read_dic: if(Q->debug) fprintf(lrs_ofp,"\n*end_read_dic: overflow=%ld",overflow); if ( overflow > 0 ) /* we made a temporary file for overflow or stdin */ if(remove(infilename) != 0) lrs_warning(Q,"warning","*Could not delete temporary file"); if (*tmpfilename != '\0' ) /* we made a temporary file for stdin */ if(remove(tmpfilename) != 0) lrs_warning(Q,"warning", "*Could not delete temporary file"); *tmpfilename = '\0'; fclose(lrs_ifp); lrs_ifp=NULL; lrs_clear_mp(Temp); lrs_clear_mp(mpone); lrs_clear_mp(Tempn); lrs_clear_mp(Tempd); lrs_clear_mp(mptwo); return TRUE; } /* lrs_read_dic */ /* In lrs_getfirstbasis and lrs_getnextbasis we use D instead of P */ /* since the dictionary P may change, ie. &P in calling routine */ #define D (*D_p) long lrs_getfirstbasis (lrs_dic ** D_p, lrs_dat * Q, lrs_mp_matrix * Lin, long no_output) /* gets first basis, FALSE if none */ /* P may get changed if lin. space Lin found */ /* no_output is TRUE supresses output headers */ /* 2017.12.22 could use no_output=2 to get early exit for criss-cross method */ { lrs_mp scale, Temp; long i, j, k; /* assign local variables to structures */ lrs_mp_matrix A; long *B, *C, *Col; long *inequality; long *linearity; long hull = Q->hull; long m, d, lastdv, nlinearity, nredundcol; if (Q->lponly || Q->child > 0 ) no_output = TRUE; m = D->m; d = D->d; lastdv = Q->lastdv; nredundcol = 0L; /* will be set after getabasis */ nlinearity = Q->nlinearity; /* may be reset if new linearity read or in getabasis*/ linearity = Q->linearity; A = D->A; B = D->B; C = D->C; Col = D->Col; inequality = Q->inequality; /**2020.6.17 with extract just select columns and quit */ if(Q->extract) if (Q->hull || Q->nlinearity==0) { extractcols(D,Q); return FALSE; } lrs_alloc_mp(Temp); lrs_alloc_mp(scale); if(Q->verbose) { if (Q->nlinearity > 0 && Q->nonnegative) { fprintf (lrs_ofp, "\n*linearity and nonnegative options incompatible"); fprintf (lrs_ofp, " - all linearities are skipped"); fprintf (lrs_ofp, "\n*add nonnegative constraints explicitly and "); fprintf (lrs_ofp, " remove nonnegative option"); } if (Q->nlinearity && Q->voronoi) fprintf (lrs_ofp, "\n*linearity and Voronoi options set - results unpredictable"); if (Q->lponly && !Q->maximize && !Q->minimize) fprintf (lrs_ofp, "\n*LP has no objective function given - assuming all zero"); } if (Q->runs > 0) /* arrays for estimator */ { Q->isave = (long *) CALLOC ((unsigned) (m * d), sizeof (long)); Q->jsave = (long *) CALLOC ((unsigned) (m * d), sizeof (long)); } /* default is to look for starting cobasis using linearies first, then */ /* filling in from last rows of input as necessary */ /* linearity array is assumed sorted here */ /* note if restart/given start inequality indices already in place */ /* from nlinearity..d-1 */ for (i = 0; i < nlinearity; i++) /* put linearities first in the order */ inequality[i] = linearity[i]; k = 0; /* index for linearity array */ if (Q->givenstart) k = d; else k = nlinearity; for (i = m; i >= 1; i--) { j = 0; while (j < k && inequality[j] != i) j++; /* see if i is in inequality */ if (j == k) inequality[k++] = i; } if (Q->debug) { fprintf (lrs_ofp, "\n*Starting cobasis uses input row order"); for (i = 0; i < m; i++) fprintf (lrs_ofp, " %ld", inequality[i]); } /* for voronoi convert to h-description using the transform */ /* a_0 .. a_d-1 -> (a_0^2 + ... a_d-1 ^2)-2a_0x_0-...-2a_d-1x_d-1 + x_d >= 0 */ /* note constant term is stored in column d, and column d-1 is all ones */ /* the other coefficients are multiplied by -2 and shifted one to the right */ if (Q->debug) printA (D, Q); if (Q->voronoi) { Q->hull = FALSE; hull = FALSE; for (i = 1; i <= m; i++) { if (zero (A[i][1])) { printf("\nWith voronoi option column one must be all one\n"); return (FALSE); } copy (scale, A[i][1]); /*adjust for scaling to integers of rationals */ itomp (ZERO, A[i][0]); for (j = 2; j <= d; j++) /* transform each input row */ { copy (Temp, A[i][j]); mulint (A[i][j], Temp, Temp); linint (A[i][0], ONE, Temp, ONE); linint (A[i][j - 1], ZERO, A[i][j], -TWO); mulint (scale, A[i][j - 1], A[i][j - 1]); } /* end of for (j=1;..) */ copy (A[i][d], scale); mulint (scale, A[i][d], A[i][d]); }/* end of for (i=1;..) */ if (Q->debug) printA (D, Q); } /* end of if(voronoi) */ if (!Q->maximize && !Q->minimize) for (j = 0; j <= d; j++) itomp (ZERO, A[0][j]); /* Now we pivot to standard form, and then find a primal feasible basis */ /* Note these steps MUST be done, even if restarting, in order to get */ /* the same index/inequality correspondance we had for the original prob. */ /* The inequality array is used to give the insertion order */ /* and is defaulted to the last d rows when givenstart=FALSE */ if(Q->nonnegative) { /* no need for initial pivots here, labelling already done */ Q->lastdv = d; Q->nredundcol = 0; } else { if (!getabasis (D, Q, inequality)) return FALSE; /* bug fix 2009.12.2 */ nlinearity=Q->nlinearity; /*may have been reset if some lins are redundant*/ } if(overflow_detected) { if(Q->verbose && !Q->mplrs) lrs_warning(Q,"warning","*overflow getfirstbasis"); return 1; } /* 2020.2.2 */ /* extract option asked to remove all linearities and output the reduced A matrix */ /* should be followed by redund to get minimum representation */ if (Q->extract) { linextractcols(D,Q); return FALSE; } if(Q->debug) { fprintf(lrs_ofp,"\nafter getabasis"); printA(D, Q); } nredundcol = Q->nredundcol; lastdv = Q->lastdv; d = D->d; /********************************************************************/ /* now we start printing the output file unless no output requested */ /********************************************************************/ if (Q->count[2]==1 && no_output==0 ) /* don't reprint after newstart */ { int len=0; char *header; header=(char *)malloc((100+20*Q->n)*sizeof(char)); if (Q->voronoi) len=sprintf (header, "*Voronoi Diagram: Voronoi vertices and rays are output"); else { if (hull) len=sprintf (header, "H-representation"); else len=sprintf (header, "V-representation"); } /* Print linearity space */ /* Don't print linearity if first column zero in hull computation */ if (hull && Q->homogeneous) k = 1; /* 0 normally, 1 for homogeneous case */ else k = 0; if (nredundcol > k) { len=len+sprintf (header+len, "\nlinearity %ld ", nredundcol - k); /*adjust nredundcol for homog. */ for (i = 1; i <= nredundcol - k; i++) len=len+sprintf (header+len, " %ld", i); } /* end print of linearity space */ len=len+sprintf (header+len, "\nbegin"); len=len+sprintf (header+len, "\n***** %ld rational", Q->n); if(Q->mplrs) lrs_post_output("header",header); else if(Q->messages) fprintf(lrs_ofp,"\n%s",header); free(header); } /* end of if !no_output ....... */ /* Reset up the inequality array to remember which index is which input inequality */ /* inequality[B[i]-lastdv] is row number of the inequality with index B[i] */ /* inequality[C[i]-lastdv] is row number of the inequality with index C[i] */ for (i = 1; i <= m; i++) inequality[i] = i; if (nlinearity > 0) /* some cobasic indices will be removed */ { for (i = 0; i < nlinearity; i++) /* remove input linearity indices */ inequality[linearity[i]] = 0; k = 1; /* counter for linearities */ for (i = 1; i <= m - nlinearity; i++) { while (k <= m && inequality[k] == 0) k++; /* skip zeroes in corr. to linearity */ inequality[i] = inequality[k++]; } } /* end if linearity */ if (Q->debug) { fprintf (lrs_ofp, "\ninequality array initialization:"); for (i = 1; i <= m - nlinearity; i++) fprintf (lrs_ofp, " %ld", inequality[i]); } if (nredundcol > 0) { const unsigned int Qn = Q->n; *Lin = lrs_alloc_mp_matrix (nredundcol, Qn); for (i = 0; i < nredundcol; i++) { if (!(Q->homogeneous && Q->hull && i == 0)) /* skip redund col 1 for homog. hull */ { lrs_getray (D, Q, Col[0], D->C[0] + i - hull, (*Lin)[i]); /* adjust index for deletions */ } if (!removecobasicindex (D, Q, 0L)) { lrs_clear_mp_matrix (*Lin, nredundcol, Qn); return FALSE; } } } /* end if nredundcol > 0 */ if (Q->lponly || Q->nash ){ if (Q->verbose && !Q->testlin) { fprintf (lrs_ofp, "\nNumber of pivots for starting dictionary: %ld",Q->count[3]); if(Q->lponly && Q->debug) printA (D, Q); } } /*2017.12.22 If you want to do criss-cross now is the time ! */ /* Do dual pivots to get primal feasibility */ if (!primalfeasible (D, Q)) { if (overflow_detected) return FALSE; if(!Q->mplrs) fprintf (lrs_ofp, "\nend"); lrs_warning(Q,"warning", "\nNo feasible solution"); if (Q->nash && Q->verbose ) { fprintf (lrs_ofp, "\nNumber of pivots for feasible solution: %ld",Q->count[3]); fprintf (lrs_ofp, " - No feasible solution"); } return FALSE; } if (Q->lponly || Q->nash ) if (Q->verbose && !Q->testlin) { fprintf (lrs_ofp, "\nNumber of pivots for feasible solution: %ld",Q->count[3]); if(Q->lponly && Q->debug) printA (D, Q); } /* Now solve LP if objective function was given */ if (Q->maximize || Q->minimize) { Q->unbounded = !lrs_solvelp (D, Q, Q->maximize); if (Q->lponly) { if (Q->verbose && !Q->testlin) { fprintf (lrs_ofp, "\nNumber of pivots for optimum solution: %ld",Q->count[3]); if(Q->debug) printA (D, Q); } lrs_clear_mp(Temp); lrs_clear_mp(scale); // if(Q->testlin || Q->mplrs ) /*2024.2.16 what is this for?*/ return TRUE; } else /* check to see if objective is dual degenerate */ { j = 1; while (j <= d && !zero (A[0][j])) j++; if (j <= d) Q->dualdeg = TRUE; } } else /* re-initialize cost row to -det */ { for (j = 1; j <= d; j++) { copy (A[0][j], D->det); storesign (A[0][j], NEG); } itomp (ZERO, A[0][0]); /* zero optimum objective value */ } /* reindex basis to 0..m if necessary */ /* we use the fact that cobases are sorted by index value */ if (Q->debug) printA (D, Q); while (C[0] <= m) { i = C[0]; j = inequality[B[i] - lastdv]; inequality[B[i] - lastdv] = inequality[C[0] - lastdv]; inequality[C[0] - lastdv] = j; C[0] = B[i]; B[i] = i; reorder1 (C, Col, ZERO, d); } if (Q->debug) { fprintf (lrs_ofp, "\n*Inequality numbers for indices %ld .. %ld : ", lastdv + 1, m + d); for (i = 1; i <= m - nlinearity; i++) fprintf (lrs_ofp, " %ld ", inequality[i]); printA (D, Q); } if (Q->restart) { if (Q->debug) fprintf (lrs_ofp, "\nPivoting to restart co-basis"); if (!restartpivots (D, Q)) return FALSE; D->lexflag = lexmin (D, Q, ZERO); /* see if lexmin basis */ if (Q->debug) printA (D, Q); } /* Check to see if necessary to resize */ /* bug fix 2018.6.7 new value of d required below */ if (Q->inputd > D->d) *D_p = resize (D, Q); lrs_clear_mp(Temp); lrs_clear_mp(scale); return TRUE; } /********* end of lrs_getfirstbasis ***************/ /*****************************************/ /* getnextbasis in reverse search order */ /*****************************************/ long lrs_getnextbasis (lrs_dic ** D_p, lrs_dat * Q, long backtrack) /* gets next reverse search tree basis, FALSE if none */ /* switches to estimator if maxdepth set */ /* backtrack TRUE means backtrack from here */ { /* assign local variables to structures */ long i = 0L, j = 0L; long m = D->m; long d = D->d; long saveflag; long cob_est=0; /* estimated number of cobases in subtree from current node */ /* 2022.3.23 multithreading */ if(Q->child > 0 && D->depth == 0 ) j=Q->child-1; /* first time only start at Q-> child */ if (backtrack && D->depth == 0) return FALSE; /* cannot backtrack from root */ if (Q->maxoutput > 0 && Q->count[0]+Q->count[1]-Q->hull >= Q->maxoutput) return FALSE; /* output limit reached */ while ((j < d) || (D->B[m] != m)) /*main while loop for getnextbasis */ { if (D->depth >= Q->maxdepth) { if (Q->runs > 0 && !backtrack ) /*get an estimate of remaining tree */ { //2015.2.9 do iterative estimation backtracking when estimate is small saveflag=Q->printcobasis; Q->printcobasis=FALSE; cob_est=lrs_estimate (D, Q); Q->printcobasis=saveflag; if(cob_est <= Q->subtreesize) /* stop iterative estimation */ { if(Q->verbose && cob_est > 0) /* when zero we are at a leaf */ { lrs_printcobasis(D,Q,ZERO); fprintf(lrs_ofp," cob_est= %ld *subtree",cob_est); } backtrack=TRUE; } } else // either not estimating or we are backtracking if (!backtrack ) if(!lrs_leaf(D,Q)) /* 2015.6.5 cobasis returned if not a leaf */ lrs_return_unexplored(D,Q); backtrack = TRUE; if (Q->maxdepth == 0 && cob_est <= Q->subtreesize) /* root estimate only */ return FALSE; /* no nextbasis */ } // if (D->depth >= Q->maxdepth) if (backtrack) /* go back to prev. dictionary, restore i,j */ { backtrack = FALSE; if (check_cache (D_p, Q, &i, &j)) { if (Q->debug) fprintf (lrs_ofp, "\n Cached Dict. restored to depth %ld\n", D->depth); } else { D->depth--; selectpivot (D, Q, &i, &j); pivot (D, Q, i, j); update (D, Q, &i, &j); /*Update B,C,i,j */ } if (Q->debug) { fprintf (lrs_ofp, "\n Backtrack Pivot: indices i=%ld j=%ld depth=%ld", i, j, D->depth); printA (D, Q); }; j++; /* go to next column */ } /* end of if backtrack */ if (D->depth < Q->mindepth) break; /* try to go down tree */ /* 2022.3.23 */ if(Q->child > 0 && D->depth == 0 ) /* multithread, only check one child at top */ { if (!reverse (D, Q, &i, j) ) break; else Q->mindepth=1; } else while ((j < d) && (!reverse (D, Q, &i, j) || (Q->truncate && Q->minratio[D->m]==1))) j++; if (j == d ) backtrack = TRUE; else /*reverse pivot found */ { cache_dict (D_p, Q, i, j); /* Note that the next two lines must come _after_ the call to cache_dict */ D->depth++; if (D->depth > Q->deepest) Q->deepest++; pivot (D, Q, i, j); update (D, Q, &i, &j); /*Update B,C,i,j */ D->lexflag = lexmin (D, Q, ZERO); /* see if lexmin basis */ Q->count[2]++; Q->totalnodes++; if (Q->strace == Q->count[2]) Q->debug = TRUE; if (Q->etrace == Q->count[2]) Q->debug = FALSE; return TRUE; /*return new dictionary */ } } /* end of main while loop for getnextbasis */ return FALSE; /* done, no more bases */ } /*end of lrs_getnextbasis */ /*************************************/ /* print out one line of output file */ /*************************************/ long lrs_getvertex (lrs_dic * P, lrs_dat * Q, lrs_mp_vector output) /*Print out current vertex if it is lexmin and return it in output */ /* return FALSE if no output generated */ { lrs_mp_matrix A = P->A; long i; long ind; /* output index */ long ired; /* counts number of redundant columns */ /* assign local variables to structures */ long *redundcol = Q->redundcol; long *count = Q->count; long *B = P->B; long *Row = P->Row; long lastdv = Q->lastdv; long hull; long lexflag; hull = Q->hull; lexflag = P->lexflag; if (lexflag || Q->allbases) { ++(Q->count[1]); /* 2021.5.21 check for max depth output */ if(P->depth > Q->count[8]) Q->count[8] = P->depth; } if (Q->debug) printA (P, Q); if (Q->getvolume) { linint (Q->sumdet, 1, P->det, 1); updatevolume (P, Q); } if(Q->triangulation) /* this will print out a triangulation */ lrs_printcobasis(P,Q,ZERO); /*print cobasis if printcobasis=TRUE and count[2] a multiple of frequency */ /* or for lexmin basis, except origin for hull computation - ugly! */ if (Q->printcobasis) if ((lexflag && !hull) || ((Q->frequency > 0) && (count[2] == (count[2] / Q->frequency) * Q->frequency))) lrs_printcobasis(P,Q,ZERO); if (hull) return FALSE; /* skip printing the origin */ if (!lexflag && !Q->allbases && !Q->lponly) /* not lexmin, and not printing forced */ return FALSE; /* copy column 0 to output */ i = 1; ired = 0; copy (output[0], P->det); for (ind = 1; ind < Q->n; ind++) /* extract solution */ if ((ired < Q->nredundcol) && (redundcol[ired] == ind)) /* column was deleted as redundant */ { itomp (ZERO, output[ind]); ired++; } else /* column not deleted as redundant */ { getnextoutput (P, Q, i, ZERO, output[ind]); i++; } reducearray (output, Q->n); if (lexflag && one(output[0])) ++Q->count[4]; /* integer vertex */ /* uncomment to print nonzero basic variables printf("\n nonzero basis: vars"); for(i=1;i<=lastdv; i++) { if ( !zero(A[Row[i]][0]) ) printf(" %ld ",B[i]); } */ /* printslack inequality indices */ if (Q->printslack) { fprintf(lrs_ofp,"\nslack ineq:"); for(i=lastdv+1;i<=P->m; i++) { if (!zero(A[Row[i]][0])) fprintf(lrs_ofp," %ld ", Q->inequality[B[i]-lastdv]); } } return TRUE; } /* end of lrs_getvertex */ long lrs_getray (lrs_dic * P, lrs_dat * Q, long col, long redcol, lrs_mp_vector output) /*Print out solution in col and return it in output */ /*redcol =n for ray/facet 0..n-1 for linearity column */ /*hull=1 implies facets will be recovered */ /* return FALSE if no output generated in column col */ { long i; long ind; /* output index */ long ired; /* counts number of redundant columns */ /* assign local variables to structures */ long *redundcol = Q->redundcol; long *count = Q->count; long hull = Q->hull; long n = Q->n; long *B = P->B; long *Row = P->Row; long lastdv = Q->lastdv; if (Q->debug) { printA (P, Q); for (i = 0; i < Q->nredundcol; i++) fprintf (lrs_ofp, " %ld", redundcol[i]); fflush(lrs_ofp); } if (redcol == n) { ++count[0]; if (Q->printcobasis) lrs_printcobasis(P,Q,col); } i = 1; ired = 0; for (ind = 0; ind < n; ind++) /* print solution */ { if (ind == 0 && !hull) /* must have a ray, set first column to zero */ itomp (ZERO, output[0]); else if ((ired < Q->nredundcol) && (redundcol[ired] == ind)) /* column was deleted as redundant */ { if (redcol == ind) /* true for linearity on this cobasic index */ /* we print reduced determinant instead of zero */ copy (output[ind], P->det); else itomp (ZERO, output[ind]); ired++; } else /* column not deleted as redundant */ { getnextoutput (P, Q, i, col, output[ind]); i++; } } reducearray (output, n); /* printslack for rays: 2006.10.10 */ /* printslack inequality indices */ if (Q->printslack) { fprintf(lrs_ofp,"\nslack ineq:"); for(i=lastdv+1;i<=P->m; i++) { if (!zero(P->A[Row[i]][col])) fprintf(lrs_ofp," %ld ", Q->inequality[B[i]-lastdv]); } } return TRUE; } /* end of lrs_getray */ void getnextoutput (lrs_dic * P, lrs_dat * Q, long i, long col, lrs_mp out) /* get A[B[i][col] and copy to out */ { long row; long m = P->m; long d = P->d; long lastdv = Q->lastdv; lrs_mp_matrix A = P->A; long *B = P->B; long *Row = P->Row; long j; if (i == d && Q->voronoi) return; /* skip last column if voronoi set */ if (i == lastdv && Q->testlin) return; /* skip last column if testlin set */ row = Row[i]; if (Q->nonnegative) /* if m+i basic get correct value from dictionary */ /* the slack for the inequality m-d+i contains decision */ /* variable x_i. We first see if this is in the basis */ /* otherwise the value of x_i is zero, except for a ray */ /* when it is one (det/det) for the actual column it is in */ { for (j = lastdv+ 1; j <= m; j++) { if ( Q->inequality[B[j]-lastdv] == m-d+i ) { copy (out, A[Row[j]][col]); return; } } /* did not find inequality m-d+i in basis */ if ( i == col ) copy(out,P->det); else itomp(ZERO,out); } else copy (out, A[row][col]); } /* end of getnextoutput */ void lrs_printcobasis (lrs_dic * P, lrs_dat * Q, long col) /* col is output column being printed */ { char *ss, *sdet, *sin_det, *sz; long i; long rflag; /* used to find inequality number for ray column */ /* assign local variables to structures */ lrs_mp_matrix A = P->A; lrs_mp Nvol, Dvol; /* hold rescaled det of current basis */ long *B = P->B; long *C = P->C; long *Col = P->Col; long *Row = P->Row; long *inequality = Q->inequality; long *temparray = Q->temparray; long *count = Q->count; long hull = Q->hull; long d = P->d; long lastdv = Q->lastdv; long m=P->m; long firstime=TRUE; long len=0; lrs_alloc_mp(Nvol); lrs_alloc_mp(Dvol); /* convert lrs_mp to char, compute length of string ss and malloc*/ sdet=cpmp(" det=", P->det); rescaledet (P, Q, Nvol, Dvol); /* scales determinant in case input rational */ sin_det=cprat("in_det=", Nvol,Dvol); itomp(ONE,P->objden); itomp(ONE,P->objnum); sz=cprat("z=", P->objnum, P->objden); len = snprintf(NULL, 0, "%s%s%s", sdet,sin_det,sz); ss=(char*)malloc(len+(d+m)*20); /* build the printcobasis string */ len=0; if (hull) len=len+sprintf (ss+len, "F#%ld B#%ld h=%ld vertices/rays ", count[0], count[2], P->depth); else if (Q->voronoi) len=len+sprintf (ss+len, "V#%ld R#%ld B#%ld h=%ld data points ", count[1], count[0], count[2], P->depth); else len=len+sprintf (ss+len, "V#%ld R#%ld B#%ld h=%ld facets ", count[1], count[0], count[2], P->depth); rflag = (-1); for (i = 0; i < d; i++) { temparray[i] = inequality[C[i] - lastdv]; if (Col[i] == col) rflag = temparray[i]; /* look for ray index */ } for (i = 0; i < d; i++) reorder (temparray, d); for (i = 0; i < d; i++) { len=len+sprintf (ss+len, " %ld", temparray[i]); if (!(col == ZERO) && (rflag == temparray[i])) /* missing cobasis element for ray */ len=len+sprintf (ss+len, "*"); } /* get and print incidence information */ if ( col == 0 ) Q->nincidence = d; else Q->nincidence = d-1; for(i=lastdv+1;i<=m;i++) if ( zero (A[Row[i]][0] )) if( ( col == ZERO ) || zero (A[Row[i]] [col]) ) { Q->nincidence++; if( Q->incidence ) { if (firstime) { len=len+sprintf (ss+len," :"); firstime = FALSE; } len=len+sprintf(ss+len," %ld",inequality[B[i] - lastdv ] ); } } len=len+sprintf(ss+len," I#%ld",Q->nincidence); sprintf (ss+len,"%s %s %s ",sdet,sin_det,sz); if(Q->maxincidence == MAXD || Q->verbose) { if(Q->mplrs) lrs_post_output("cobasis", ss); else fprintf(lrs_ofp,"\n%s",ss); } free(ss); free(sdet); free(sin_det); free(sz); lrs_clear_mp(Nvol); lrs_clear_mp(Dvol); } /* end of lrs_printcobasis */ /*********************/ /* print final totals */ /*********************/ void lrs_printtotals (lrs_dic * P, lrs_dat * Q) { static int first_time=1; /* print warnings */ if(first_time) { first_time=0; if (!Q->mplrs) fprintf(lrs_ofp,"\nend"); if (Q->dualdeg) { lrs_warning(Q,"finalwarn","*Warning: Starting dictionary is dual degenerate"); lrs_warning(Q,"finalwarn","*Complete enumeration may not have been produced"); if (Q->maximize) lrs_warning(Q,"finalwarn","*Recommendation: Add dualperturb option before maximize in input file\n"); else lrs_warning(Q,"finalwarn","*Recommendation: Add dualperturb option before minimize in input file\n"); } if (Q->unbounded) { lrs_warning(Q,"finalwarn","*Warning: Starting dictionary contains rays"); lrs_warning(Q,"finalwarn","*Complete enumeration may not have been produced"); if (Q->maximize) lrs_warning(Q,"finalwarn","*Recommendation: Change or remove maximize option or add bounds\n"); else lrs_warning(Q,"finalwarn","*Recommendation: Change or remove minimize option or add bounds\n"); } if (Q->truncate) lrs_warning(Q,"finalwarn","*Tree truncated at each new vertex"); } if(!Q->hull) { if ( Q->allbases ) lrs_warning(Q,"finalwarn","*Note! Duplicate vertices/rays may be present"); else if (Q->count[0] > 1 && !Q->homogeneous) lrs_warning(Q,"finalwarn","*Note! Duplicate rays may be present"); } if(Q->mplrs) { char *vol; if (Q->hull && Q->getvolume) { rescalevolume (P, Q, Q->Nvolume, Q->Dvolume); vol=cprat("",Q->Nvolume, Q->Dvolume); lrs_post_output("volume", vol); free(vol); } return; } if(!Q->messages) return; long i; double x; /* local assignments */ double *cest = Q->cest; long *count = Q->count; long *inequality = Q->inequality; long *linearity = Q->linearity; long *temparray = Q->temparray; long *C = P->C; long hull = Q->hull; long homogeneous = Q->homogeneous; long nlinearity = Q->nlinearity; long nredundcol = Q->nredundcol; long d, lastdv; d = P->d; lastdv = Q->lastdv; if(Q->hull) /* count[1] stores the number of linearities */ Q->count[1]=Q->nredundcol - Q->homogeneous; /* warnings for lrs only */ if (Q->maxdepth < MAXD) fprintf (lrs_ofp, "\n*Tree truncated at depth %lld", Q->maxdepth); if (Q->maxcobases > 0L) fprintf (lrs_ofp, "\n*maxcobases = %ld", Q->maxcobases-Q->startcount[2]); if (Q->maxoutput > 0L) fprintf (lrs_ofp, "\n*Maximum number of output lines = %ld", Q->maxoutput); /* next block with volume rescaling must come before estimates are printed */ if (Q->getvolume && Q->runs == 0) { if( Q->debug) { fprintf (lrs_ofp, "\n*Sum of det(B)="); pmp ("", Q->sumdet); } rescalevolume (P, Q, Q->Nvolume, Q->Dvolume); if (Q->polytope) prat ("\n*Volume=", Q->Nvolume, Q->Dvolume); else prat ("\n*Pseudovolume=", Q->Nvolume, Q->Dvolume); } if (hull) /* output things that are specific to hull computation */ { fprintf (lrs_ofp, "\n*Totals: facets=%ld bases=%ld", count[0], count[2]); if (count[1] > 0 ) { fprintf (lrs_ofp, " linearities=%ld", count[1]); fprintf (lrs_ofp, " facets+linearities=%ld",count[1]+count[0]); } printf (" max_facet_depth=%ld", count[8]); if(lrs_ofp != stdout) { printf ("\n*Totals: facets=%ld bases=%ld", count[0], count[2]); if (count[1] > 0) { printf (" linearities=%ld", count[1]); printf (" facets+linearities=%ld",count[1]+count[0]); } printf (" max_facet_depth=%ld", count[8]); } if(Q->runs > 0) { fprintf (lrs_ofp, "\n*Estimates: facets=%.0f bases=%.0f", count[0] + cest[0], count[2] + cest[2]); if (Q->getvolume) { rescalevolume (P, Q, Q->Nvolume, Q->Dvolume); rattodouble (Q->Nvolume, Q->Dvolume, &x); for (i = 2; i < d; i++) cest[3] = cest[3] / i; /*adjust for dimension */ if(cest[3]==0) prat (" volume=", Q->Nvolume, Q->Dvolume); else fprintf (lrs_ofp, " volume=%g", cest[3] + x); } fprintf (lrs_ofp, "\n*Total number of tree nodes evaluated: %ld", Q->totalnodes); #ifndef TIMES fprintf (lrs_ofp, "\n*Estimated total running time=%.1f secs ",(count[2]+cest[2])/Q->totalnodes*get_time () ); #endif } } else /* output things specific to vertex/ray computation */ { fprintf (lrs_ofp, "\n*Totals: vertices=%ld rays=%ld bases=%ld", count[1], count[0], count[2]); fprintf (lrs_ofp, " integer_vertices=%ld max_vertex_depth=%ld",count[4],count[8]); if (nredundcol > 0) fprintf (lrs_ofp, " linearities=%ld", nredundcol); if ( count[0] + nredundcol > 0 ) { fprintf (lrs_ofp, " vertices+rays"); if ( nredundcol > 0 ) fprintf (lrs_ofp, "+linearities"); fprintf (lrs_ofp, "=%ld",nredundcol+count[0]+count[1]); } if(lrs_ofp != stdout) { printf ("\n*Totals: vertices=%ld rays=%ld bases=%ld", count[1], count[0], count[2]); printf (" integer_vertices=%ld max_vertex_depth=%ld",count[4],count[8]); if (nredundcol > 0) printf (" linearities=%ld", nredundcol); if ( count[0] + nredundcol > 0 ) { printf (" vertices+rays"); if ( nredundcol > 0 ) printf ("+linearities"); printf ("=%ld",nredundcol+count[0]+count[1]); } } /* end lrs_ofp != stdout */ if (Q->runs > 0) { fprintf (lrs_ofp, "\n*Estimates: vertices=%.0f rays=%.0f", count[1]+cest[1], count[0]+cest[0]); fprintf (lrs_ofp, " bases=%.0f integer_vertices=%.0f ",count[2]+cest[2], count[4]+cest[4]); if (Q->getvolume) { rattodouble (Q->Nvolume, Q->Dvolume, &x); for (i = 2; i <= d-homogeneous; i++) cest[3] = cest[3] / i; /*adjust for dimension */ fprintf (lrs_ofp, " pseudovolume=%g", cest[3] + x); } fprintf (lrs_ofp, "\n*Total number of tree nodes evaluated: %ld", Q->totalnodes); #ifndef TIMES fprintf (lrs_ofp, "\n*Estimated total running time=%.1f secs ",(count[2]+cest[2])/Q->totalnodes*get_time () ); #endif } } /* end of output for vertices/rays */ if(Q->verbose) { fprintf (lrs_ofp, "\n*Dictionary Cache: dict_limit=%ld dict_count=%ld misses= %ld/%ld Tree Depth= %ld", dict_limit, dict_count, cache_misses, cache_tries, Q->deepest); if(lrs_ofp != stdout) printf ("\n*Dictionary Cache: max size= %ld misses= %ld/%ld Tree Depth= %ld", dict_count, cache_misses, cache_tries, Q->deepest); } if(Q->maxincidence != MAXD) fprintf(lrs_ofp,"\n*maxincidence %lld %lld used to prune search", Q->maxincidence,Q->minprunedepth); if(Q->debug) { fprintf (lrs_ofp, "\n*Input size m=%ld rows n=%ld columns", P->m, Q->n); if (hull) fprintf (lrs_ofp, " working dimension=%ld", d - 1 + homogeneous); else fprintf (lrs_ofp, " working dimension=%ld", d); fprintf (lrs_ofp, "\n*Starting cobasis defined by input rows"); for (i = 0; i < nlinearity; i++) temparray[i] = linearity[i]; for (i = nlinearity; i < lastdv; i++) temparray[i] = inequality[C[i - nlinearity] - lastdv]; for (i = 0; i < lastdv; i++) reorder (temparray, lastdv); for (i = 0; i < lastdv; i++) fprintf (lrs_ofp, " %ld", temparray[i]); } fprintf(lrs_ofp,"\n"); return; } /* end of lrs_printtotals */ /************************/ /* Estimation function */ /************************/ long lrs_estimate (lrs_dic * P, lrs_dat * Q) /*returns estimate of subtree size (no. cobases) from current node */ /*current node is not counted. */ /*cest[0]rays [1]vertices [2]bases [3]volume */ /* [4] integer vertices */ { lrs_mp_vector output; /* holds one line of output; ray,vertex,facet,linearity */ lrs_mp Nvol, Dvol; /* hold volume of current basis */ long estdepth = 0; /* depth of basis/vertex in subtree for estimate */ long i = 0, j = 0, k, nchild, runcount, col; double prod = 0.0; double cave[] = {0.0, 0.0, 0.0, 0.0, 0.0}; double nvertices, nbases, nrays, nvol, nivertices; long rays = 0; double newvol = 0.0; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *isave = Q->isave; long *jsave = Q->jsave; double *cest = Q->cest; long d = P->d; lrs_alloc_mp(Nvol); lrs_alloc_mp(Dvol); /* Main Loop of Estimator */ output = lrs_alloc_mp_vector (Q->n); /* output holds one line of output from dictionary */ for (runcount = 1; runcount <= Q->runs; runcount++) { /* runcount counts number of random probes */ j = 0; nchild = 1; prod = 1; nvertices = 0.0; nbases = 0.0; nrays = 0.0; nvol = 0.0; nivertices =0.0; while (nchild != 0) /* while not finished yet */ { nchild = 0; while (j < d) { if (reverse (P, Q, &i, j)) { isave[nchild] = i; jsave[nchild] = j; nchild++; } j++; } if (estdepth == 0 && nchild == 0) { cest[0] = cest[0] + rays; /* may be some rays here */ lrs_clear_mp(Nvol); lrs_clear_mp(Dvol); lrs_clear_mp_vector(output, Q->n); return(0L); /*subtree is a leaf */ } prod = prod * nchild; nbases = nbases + prod; if (Q->debug) { fprintf (lrs_ofp, " degree= %ld ", nchild); fprintf (lrs_ofp, "\nPossible reverse pivots: i,j="); for (k = 0; k < nchild; k++) fprintf (lrs_ofp, "%ld,%ld ", isave[k], jsave[k]); } if (nchild > 0) /*reverse pivot found choose random child */ { k = myrandom (Q->seed, nchild); Q->seed = myrandom (Q->seed, 977L); i = isave[k]; j = jsave[k]; if (Q->debug) fprintf (lrs_ofp, " selected pivot k=%ld seed=%ld ", k, Q->seed); estdepth++; Q->totalnodes++; /* calculate total number of nodes evaluated */ pivot (P, Q, i, j); update (P, Q, &i, &j); /*Update B,C,i,j */ if (lexmin (P, Q, ZERO)) /* see if lexmin basis for vertex */ { nvertices = nvertices + prod; /* integer vertex estimate */ if( lrs_getvertex(P,Q,output)) { --Q->count[1]; if (one(output[0] )) { --Q->count[4]; nivertices = nivertices + prod; } } } rays = 0; for (col = 1; col <= d; col++) if (negative (A[0][col]) && (lrs_ratio (P, Q, col) == 0) && lexmin (P, Q, col)) rays++; nrays = nrays + prod * rays; /* update ray info */ if (Q->getvolume) { rescaledet (P, Q, Nvol, Dvol); /* scales determinant in case input rational */ rattodouble (Nvol, Dvol, &newvol); nvol = nvol + newvol * prod; /* adjusts volume for degree */ } j = 0; } } cave[0] = cave[0] + nrays; cave[1] = cave[1] + nvertices; cave[2] = cave[2] + nbases; cave[3] = cave[3] + nvol; cave[4] = cave[4] + nivertices; /* backtrack to root and do it again */ while (estdepth > 0) { estdepth = estdepth - 1; selectpivot (P, Q, &i, &j); pivot (P, Q, i, j); update (P, Q, &i, &j); /*Update B,C,i,j */ if (Q->debug) { fprintf (lrs_ofp, "\n Backtrack Pivot: indices i,j %ld %ld ", i, j); printA (P, Q); } j++; } } /* end of for loop on runcount */ j=(long) cave[2]/Q->runs; //2015.2.9 Do not update totals if we do iterative estimating and subtree is too big if(Q->subtreesize == 0 || j <= Q->subtreesize ) for (i = 0; i < 5; i++) cest[i] = cave[i] / Q->runs + cest[i]; lrs_clear_mp(Nvol); lrs_clear_mp(Dvol); lrs_clear_mp_vector(output, Q->n); return(j); } /* end of lrs_estimate */ /*********************************/ /* Internal functions */ /*********************************/ /* Basic Dictionary functions */ /******************************* */ long reverse (lrs_dic * P, lrs_dat * Q, long *r, long s) /* find reverse indices */ /* TRUE if B[*r] C[s] is a reverse lexicographic pivot */ { long i, j, enter, row, col; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *B = P->B; long *C = P->C; long *Row = P->Row; long *Col = P->Col; long d = P->d; enter = C[s]; col = Col[s]; if (Q->debug) { fprintf (lrs_ofp, "\n+reverse: col index %ld C %ld Col %ld ", s, enter, col); fflush (lrs_ofp); } if (!negative (A[0][col])) { if (Q->debug) fprintf (lrs_ofp, " Pos/Zero Cost Coeff"); Q->minratio[P->m]=0; /* 2011.7.14 */ return (FALSE); } *r = lrs_ratio (P, Q, col); if (*r == 0) /* we have a ray */ { if (Q->debug) fprintf (lrs_ofp, " Pivot col non-negative: ray found"); Q->minratio[P->m]=0; /* 2011.7.14 */ return (FALSE); } row = Row[*r]; /* check cost row after "pivot" for smaller leaving index */ /* ie. j s.t. A[0][j]*A[row][col] < A[0][col]*A[row][j] */ /* note both A[row][col] and A[0][col] are negative */ for (i = 0; i < d && C[i] < B[*r]; i++) if (i != s) { j = Col[i]; if (positive (A[0][j]) || negative (A[row][j])) /*or else sign test fails trivially */ if ((!negative (A[0][j]) && !positive (A[row][j])) || comprod (A[0][j], A[row][col], A[0][col], A[row][j]) == -1) { /*+ve cost found */ if (Q->debug) { fprintf (lrs_ofp, "\nPositive cost found: index %ld C %ld Col %ld", i, C[i], j); fflush(lrs_ofp); } Q->minratio[P->m]=0; /* 2011.7.14 */ return (FALSE); } } if (Q->debug) { fprintf (lrs_ofp, "\n+end of reverse : indices r %ld s %ld \n", *r, s); fflush (stdout); } return (TRUE); } /* end of reverse */ long selectpivot (lrs_dic * P, lrs_dat * Q, long *r, long *s) /* select pivot indices using lexicographic rule */ /* returns TRUE if pivot found else FALSE */ /* pivot variables are B[*r] C[*s] in locations Row[*r] Col[*s] */ { long j, col; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *Col = P->Col; long d = P->d; *r = 0; *s = d; j = 0; /*find positive cost coef */ while ((j < d) && (!positive (A[0][Col[j]]))) j++; if (j < d) /* pivot column found! */ { *s = j; col = Col[j]; /*find min index ratio */ *r = lrs_ratio (P, Q, col); if (*r != 0) return (TRUE); /* unbounded if *r=0 */ } return (FALSE); } /* end of selectpivot */ /******************************************************* */ void pivot (lrs_dic * P, lrs_dat * Q, long bas, long cob) /* Qpivot routine for array A */ /* indices bas, cob are for Basis B and CoBasis C */ /* corresponding to row Row[bas] and column */ /* Col[cob] respectively */ { long r, s; long i, j; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *B = P->B; long *C = P->C; long *Row = P->Row; long *Col = P->Col; long d, m_A; #ifndef LRSLONG lrs_mp Ns, Nt; lrs_alloc_mp(Ns); lrs_alloc_mp(Nt); #endif lrs_mp Ars; lrs_alloc_mp(Ars); d = P->d; m_A = P->m_A; Q->count[3]++; /* count the pivot */ r = Row[bas]; s = Col[cob]; /* Ars=A[r][s] */ if (Q->debug) fprintf (lrs_ofp, "\n pivot B[%ld]=%ld C[%ld]=%ld ", bas, B[bas], cob, C[cob]); copy (Ars, A[r][s]); storesign (P->det, sign (Ars)); /*adjust determinant to new sign */ for (i = 0; i <= m_A; i++) { if (i != r) for (j = 0; j <= d; j++) if (j != s) { /* A[i][j]=(A[i][j]*Ars-A[i][s]*A[r][j])/P->det; */ #ifdef LRSLONG qpiv(A[i][j],Ars,A[i][s],A[r][j],P->det); if(overflow_detected) return; #else mulint (A[i][j], Ars, Nt); mulint (A[i][s], A[r][j], Ns); decint (Nt, Ns); exactdivint (Nt, P->det, A[i][j]); if(overflow_detected) return; #endif } /* end if j .... */ } /*for i */ if (sign (Ars) == POS) { for (j = 0; j <= d; j++) /* no need to change sign if Ars neg */ /* A[r][j]=-A[r][j]; */ if (!zero (A[r][j])) changesign (A[r][j]); } /* watch out for above "if" when removing this "}" ! */ else for (i = 0; i <= m_A; i++) if (!zero (A[i][s])) changesign (A[i][s]); /* A[r][s]=P->det; */ copy (A[r][s], P->det); /* restore old determinant */ copy (P->det, Ars); storesign (P->det, POS); /* always keep positive determinant */ if (Q->debug) { fprintf (lrs_ofp, " depth=%ld ", P->depth); pmp ("det=", P->det); fflush(stdout); } /* set the new rescaled objective function value */ mulint (P->det, Q->Lcm[0], P->objden); mulint (Q->Gcd[0], A[0][0], P->objnum); if (!Q->maximize) changesign (P->objnum); if (zero (P->objnum)) storesign (P->objnum, POS); else reduce (P->objnum,P->objden); #ifndef LRSLONG lrs_clear_mp(Ns); lrs_clear_mp(Nt); #endif lrs_clear_mp(Ars); } /* end of pivot */ long primalfeasible (lrs_dic * P, lrs_dat * Q) /* Do dual pivots to get primal feasibility */ /* Note that cost row is all zero, so no ratio test needed for Dual Bland's rule */ { long primalinfeasible = TRUE; long i, j; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *Row = P->Row; long *Col = P->Col; long m, d, lastdv; m = P->m; d = P->d; lastdv = Q->lastdv; /*temporary: try to get new start after linearity */ while (primalinfeasible) { i=lastdv+1; while (i <= m && !negative (A[Row[i]][0]) ) i++; if (i <= m ) { j = 0; /*find a positive entry for in row */ while (j < d && !positive (A[Row[i]][Col[j]])) j++; if (j >= d) return (FALSE); /* no positive entry */ pivot (P, Q, i, j); update (P, Q, &i, &j); if(overflow_detected) { if(Q->debug) lrs_warning(Q,"warning","*overflow primalfeasible"); return FALSE; } } else primalinfeasible = FALSE; } /* end of while primalinfeasibile */ return (TRUE); } /* end of primalfeasible */ long lrs_solvelp (lrs_dic * P, lrs_dat * Q, long maximize) /* Solve primal feasible lp by Dantzig`s rule and lexicographic ratio test */ /* return TRUE if bounded, FALSE if unbounded */ { long i, j, k=0L; long notdone=TRUE; /* assign local variables to structures */ long d = P->d; /* lponly=1 Dantzig, =2 random, =3 hybrid, =4 Bland */ if(Q->lponly <=1) /* Dantzig's rule */ while (dan_selectpivot (P, Q, &i, &j)) { pivot (P, Q, i, j); update (P, Q, &i, &j); /*Update B,C,i,j */ if(overflow_detected) { if(Q->verbose && !Q->mplrs) lrs_warning(Q,"warning","*overflow lrs_solvelp"); return FALSE; } } if(Q->lponly ==2) /* random edge rule */ while (ran_selectpivot (P, Q, &i, &j)) { pivot (P, Q, i, j); update (P, Q, &i, &j); /*Update B,C,i,j */ } if(Q->lponly ==3) /* alternate Dantzig/randome rules */ while (notdone) { if(k % 2) /* odd for dantzig even for random */ notdone=dan_selectpivot (P, Q, &i, &j); else notdone=ran_selectpivot (P, Q, &i, &j); if(notdone) { pivot (P, Q, i, j); update (P, Q, &i, &j); /*Update B,C,i,j */ } k++; } if(Q->lponly ==4) /* Bland's rule - used for vertex enumeration */ while (selectpivot (P, Q, &i, &j)) { pivot (P, Q, i, j); update (P, Q, &i, &j); /*Update B,C,i,j */ } if (Q->debug) printA (P, Q); if (j < d && i == 0) /* selectpivot gives information on unbounded solution */ { if (Q->lponly && Q->messages) { fprintf (lrs_ofp, "\n*Unbounded solution"); if(Q->debug && Q->testlin) printA(P,Q); } return FALSE; } return TRUE; } /* end of lrs_solvelp */ long getabasis (lrs_dic * P, lrs_dat * Q, long order[]) /* Pivot Ax<=b to standard form */ /*Try to find a starting basis by pivoting in the variables x[1]..x[d] */ /*If there are any input linearities, these appear first in order[] */ /* Steps: (a) Try to pivot out basic variables using order */ /* Stop if some linearity cannot be made to leave basis */ /* (b) Permanently remove the cobasic indices of linearities */ /* (c) If some decision variable cobasic, it is a linearity, */ /* and will be removed. */ { long i, j, k; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *B = P->B; long *C = P->C; long *Row = P->Row; long *Col = P->Col; long *linearity = Q->linearity; long *redundcol = Q->redundcol; long m, d, nlinearity; long nredundcol = 0L; /* will be calculated here */ char mess[100]; m = P->m; d = P->d; nlinearity = Q->nlinearity; if (Q->debug) { fprintf (lrs_ofp, "\ngetabasis from inequalities given in order"); for (i = 0l; i < m; i++) fprintf (lrs_ofp, " %ld", order[i]); } for (j = 0l; j < m; j++) { i = 0l; while (i <= m && B[i] != d + order[j]) i++; /* find leaving basis index i */ if (j < nlinearity && i > m) /* cannot pivot linearity to cobasis */ { if (Q->debug) printA (P, Q); if(Q->messages) fprintf (lrs_ofp, "\nCannot find linearity in the basis"); return FALSE; } if (i <= m) { /* try to do a pivot */ k = 0l; while (C[k] <= d && zero (A[Row[i]][Col[k]])){ k++; } if (C[k] <= d) { pivot (P, Q, i, k); if(overflow_detected) { if(Q->debug) lrs_warning(Q,"warning","*overflow in getabasis\n"); return FALSE; } update (P, Q, &i, &k); } else if (jmessages) { sprintf (mess,"*Input linearity in row %ld is redundant--converted to inequality", order[j]); lrs_warning(Q,"warning",mess); } linearity[j]=0l; Q->redineq[order[j]]=-1; /* check for redundancy if running redund */ } else { if (Q->debug) printA (P, Q); lrs_warning(Q,"warning","*No feasible solution"); return FALSE; } } } } /* update linearity array to get rid of redundancies */ i = 0; k = 0; /* counters for linearities */ while (k < nlinearity) { while (k < nlinearity && linearity[k] == 0) k++; if (k < nlinearity) linearity[i++] = linearity[k++]; } nlinearity = i; /* bug fix, 2009.6.27 */ Q->nlinearity = i; /* column dependencies now can be recorded */ /* redundcol contains input column number 0..n-1 where redundancy is */ /* 2022.4.26 testlin=T adds extra column and basic variable that shoud not be considered */ k = 0; while (k < d && C[k] <= d) { if (C[k] <= d-Q->testlin) /* decision variable still in cobasis */ redundcol[nredundcol++] = C[k] - Q->hull; /* adjust for hull indices */ k++; } /* now we know how many decision variables remain in problem */ Q->nredundcol = nredundcol; Q->lastdv = d - nredundcol; if (Q->debug) { fprintf (lrs_ofp, "\nend of first phase of getabasis: "); fprintf (lrs_ofp, "lastdv=%ld nredundcol=%ld", Q->lastdv, Q->nredundcol); fprintf (lrs_ofp, "\nredundant cobases:"); for (i = 0; i < nredundcol; i++) fprintf (lrs_ofp, " %ld", redundcol[i]); printA (P, Q); } /* Remove linearities from cobasis for rest of computation */ /* This is done in order so indexing is not screwed up */ for (i = 0; i < nlinearity; i++) { /* find cobasic index */ k = 0; while (k < d && C[k] != linearity[i] + d) k++; if (k >= d) { lrs_warning(Q,"warning","\nError removing linearity"); return FALSE; } if (!removecobasicindex (P, Q, k)) return FALSE; d = P->d; } if (Q->debug && nlinearity > 0) printA (P, Q); /* Check feasability */ if (Q->givenstart) { i = Q->lastdv + 1; while (i <= m && !negative (A[Row[i]][0])) i++; if (i <= m) fprintf (lrs_ofp, "\n*Infeasible startingcobasis - will be modified"); } return TRUE; } /* end of getabasis */ long removecobasicindex (lrs_dic * P, lrs_dat * Q, long k) /* remove the variable C[k] from the problem */ /* used after detecting column dependency */ { long i, j, cindex, deloc; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *B = P->B; long *C = P->C; long *Col = P->Col; long m, d; m = P->m; d = P->d; if (Q->debug) fprintf (lrs_ofp, "\nremoving cobasic index k=%ld C[k]=%ld Col[k]=%ld d=%ld m=%ld", k, C[k],Col[k],d,m); cindex = C[k]; /* cobasic index to remove */ deloc = Col[k]; /* matrix column location to remove */ for (i = 1; i <= m; i++) /* reduce basic indices by 1 after index */ if (B[i] > cindex) B[i]--; for (j = k; j < d; j++) /* move down other cobasic variables */ { C[j] = C[j + 1] - 1; /* cobasic index reduced by 1 */ Col[j] = Col[j + 1]; } if (deloc != d) { /* copy col d to deloc */ for (i = 0; i <= m-Q->nonnegative*Q->inputd; i++) /* nonnegative rows do not exist */ copy (A[i][deloc], A[i][d]); /* reassign location for moved column */ j = 0; while (Col[j] != d) j++; Col[j] = deloc; } P->d--; if (Q->debug) printA (P, Q); return TRUE; } /* end of removecobasicindex */ lrs_dic * resize (lrs_dic * P, lrs_dat * Q) /* resize the dictionary after some columns are deleted, ie. inputd>d */ /* a new lrs_dic record is created with reduced size, and items copied over */ { lrs_dic *P1; /* to hold new dictionary in case of resizing */ long i, j; long m, d, m_A; m = P->m; d = P->d; m_A = P->m_A; /* get new dictionary record */ P1 = new_lrs_dic (m, d, m_A); /* copy data from P to P1 */ P1->i = P->i; P1->j = P->j; P1->depth = P->depth; P1->m = P->m; P1->d = P1->d_orig = d; P1->lexflag = P->lexflag; P1->m_A = P->m_A; copy (P1->det, P->det); copy (P1->objnum, P->objnum); copy (P1->objden, P->objden); for (i = 0; i <= m; i++) { P1->B[i] = P->B[i]; P1->Row[i] = P->Row[i]; } for (i = 0; i <= m_A; i++) { for (j = 0; j <= d; j++) copy (P1->A[i][j], P->A[i][j]); } for (j = 0; j <= d; j++) { P1->Col[j] = P->Col[j]; P1->C[j] = P->C[j]; } if (Q->debug) { fprintf (lrs_ofp, "\nDictionary resized from d=%ld to d=%ld", Q->inputd, P->d); printA (P1, Q); } lrs_free_dic (P,Q); /* Reassign cache pointers */ Q->Qhead = P1; Q->Qtail = P1; P1->next = P1; P1->prev = P1; return P1; } /********* resize ***************/ long restartpivots (lrs_dic * P, lrs_dat * Q) /* facet contains a list of the inequalities in the cobasis for the restart */ /* inequality contains the relabelled inequalities after initialization */ { long i, j, k; long *Cobasic; /* when restarting, Cobasic[j]=1 if j is in cobasis */ /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *B = P->B; long *C = P->C; long *Row = P->Row; long *Col = P->Col; long *inequality = Q->inequality; long *facet = Q->facet; long nlinearity = Q->nlinearity; long m, d, lastdv; m = P->m; d = P->d; lastdv = Q->lastdv; Cobasic = (long *) CALLOC ((unsigned) m + d + 2, sizeof (long)); if (Q->debug) fprintf(lrs_ofp,"\nCobasic flags in restartpivots"); /* set Cobasic flags */ for (i = 0; i < m + d + 1; i++) Cobasic[i] = 0; for (i = 0; i < d; i++) /* find index corresponding to facet[i] */ { j = 1; while (facet[i +nlinearity] != inequality[j]) j++; Cobasic[j + lastdv] = 1; if (Q->debug) fprintf(lrs_ofp," %ld %ld;",facet[i+nlinearity],j+lastdv); } /* Note that the order of doing the pivots is important, as */ /* the B and C vectors are reordered after each pivot */ /* Suggested new code from db starts */ i=m; while (i>d){ while(Cobasic[B[i]]){ k = d - 1; while ((k >= 0) && (zero (A[Row[i]][Col[k]]) || Cobasic[C[k]])){ k--; } if (k >= 0) { /*db asks: should i really be modified here? (see old code) */ /*da replies: modifying i only makes is larger, and so */ /*the second while loop will put it back where it was */ /*faster (and safer) as done below */ long ii=i; pivot (P, Q, ii, k); update (P, Q, &ii, &k); if(overflow_detected) { if(Q->verbose && !Q->mplrs) lrs_warning(Q,"warning","*overflow restartpivots"); return FALSE; } } else { lrs_warning(Q,"warning","\nInvalid Co-basis - does not have correct rank"); free(Cobasic); return FALSE; } } i--; } /* Suggested new code from db ends */ /* check restarting from a primal feasible dictionary */ for (i = lastdv + 1; i <= m; i++) if (negative (A[Row[i]][0])) { lrs_warning(Q,"warning","\nTrying to restart from infeasible dictionary"); free(Cobasic); return FALSE; } free(Cobasic); return TRUE; } /* end of restartpivots */ long lrs_ratio (lrs_dic * P, lrs_dat * Q, long col) /*find lex min. ratio */ /* find min index ratio -aig/ais, ais<0 */ /* if multiple, checks successive basis columns */ /* recoded Dec 1997 */ { long i, j, comp, ratiocol, basicindex, start, nstart, cindex, bindex; long firstime; /*For ratio test, true on first pass,else false */ lrs_mp Nmin, Dmin; long degencount, ndegencount; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *B = P->B; long *Row = P->Row; long *Col = P->Col; long *minratio = Q->minratio; long m, d, lastdv; m = P->m; d = P->d; lastdv = Q->lastdv; nstart=0; ndegencount=0; degencount = 0; minratio[P->m]=1; /*2011.7.14 non-degenerate pivot flag */ for (j = lastdv + 1; j <= m; j++) { /* search rows with negative coefficient in dictionary */ /* minratio contains indices of min ratio cols */ if (negative (A[Row[j]][col])) { minratio[degencount++] = j; if(zero (A[Row[j]][0])) minratio[P->m]=0; /*2011.7.14 degenerate pivot flag */ } } /* end of for loop */ if (Q->debug) { fprintf (lrs_ofp, " Min ratios: "); for (i = 0; i < degencount; i++) fprintf (lrs_ofp, " %ld ", B[minratio[i]]); } if (degencount == 0) return (degencount); /* non-negative pivot column */ lrs_alloc_mp(Nmin); lrs_alloc_mp(Dmin); ratiocol = 0; /* column being checked, initially rhs */ start = 0; /* starting location in minratio array */ bindex = d + 1; /* index of next basic variable to consider */ cindex = 0; /* index of next cobasic variable to consider */ basicindex = d; /* index of basis inverse for current ratio test, except d=rhs test */ while (degencount > 1) /*keep going until unique min ratio found */ { if (B[bindex] == basicindex) /* identity col in basis inverse */ { if (minratio[start] == bindex) /* remove this index, all others stay */ { start++; degencount--; } bindex++; } else /* perform ratio test on rhs or column of basis inverse */ { firstime = TRUE; /*get next ratio column and increment cindex */ if (basicindex != d) ratiocol = Col[cindex++]; for (j = start; j < start + degencount; j++) { i = Row[minratio[j]]; /* i is the row location of the next basic variable */ comp = 1; /* 1: lhs>rhs; 0:lhs=rhs; -1: lhsdebug) { fprintf (lrs_ofp, " ratiocol=%ld degencount=%ld ", ratiocol, degencount); fprintf (lrs_ofp, " Min ratios: "); for (i = start; i < start + degencount; i++) fprintf (lrs_ofp, " %ld ", B[minratio[i]]); } } /*end of while loop */ lrs_clear_mp(Nmin); lrs_clear_mp(Dmin); return (minratio[start]); } /* end of ratio */ long lexmin (lrs_dic * P, lrs_dat * Q, long col) /*test if basis is lex-min for vertex or ray, if so TRUE */ /* FALSE if a_r,g=0, a_rs !=0, r > s */ { /*do lexmin test for vertex if col=0, otherwise for ray */ long r, s, i, j; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *B = P->B; long *C = P->C; long *Row = P->Row; long *Col = P->Col; long m = P->m; long d = P->d; for (i = Q->lastdv + 1; i <= m; i++) { r = Row[i]; if (zero (A[r][col])) /* necessary for lexmin to fail */ for (j = 0; j < d; j++) { s = Col[j]; if (B[i] > C[j]) /* possible pivot to reduce basis */ { if (zero (A[r][0])) /* no need for ratio test, any pivot feasible */ { if (!zero (A[r][s])) return (FALSE); } else if (negative (A[r][s]) && ismin (P, Q, r, s)) { return (FALSE); } } /* end of if B[i] ... */ } } if ((col != ZERO) && Q->debug) { fprintf (lrs_ofp, "\n lexmin ray in col=%ld ", col); printA (P, Q); } return (TRUE); } /* end of lexmin */ long ismin (lrs_dic * P, lrs_dat * Q, long r, long s) /*test if A[r][s] is a min ratio for col s */ { long i; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long m_A = P->m_A; for (i = 1; i <= m_A; i++) if ((i != r) && negative (A[i][s]) && comprod (A[i][0], A[r][s], A[i][s], A[r][0])) { return (FALSE); } return (TRUE); } void update (lrs_dic * P, lrs_dat * Q, long *i, long *j) /*update the B,C arrays after a pivot */ /* involving B[bas] and C[cob] */ { long leave, enter; /* assign local variables to structures */ long *B = P->B; long *C = P->C; long *Row = P->Row; long *Col = P->Col; long m = P->m; long d = P->d; leave = B[*i]; enter = C[*j]; B[*i] = enter; reorder1 (B, Row, *i, m + 1); C[*j] = leave; reorder1 (C, Col, *j, d); /* restore i and j to new positions in basis */ for (*i = 1; B[*i] != enter; (*i)++); /*Find basis index */ for (*j = 0; C[*j] != leave; (*j)++); /*Find co-basis index */ if (Q->debug) printA(P,Q); } /* end of update */ long lrs_degenerate (lrs_dic * P, lrs_dat * Q) /* TRUE if the current dictionary is primal degenerate */ /* not thoroughly tested 2000/02/15 */ { long i; long *Row; lrs_mp_matrix A = P->A; long d = P->d; long m = P->m; Row = P->Row; for (i = d + 1; i <= m; i++) if (zero (A[Row[i]][0])) return TRUE; return FALSE; } /*********************************************************/ /* Miscellaneous */ /******************************************************* */ void reorder (long a[], long range) /*reorder array in increasing order with one misplaced element */ { long i, temp; for (i = 0; i < range - 1; i++) if (a[i] > a[i + 1]) { temp = a[i]; a[i] = a[i + 1]; a[i + 1] = temp; } for (i = range - 2; i >= 0; i--) if (a[i] > a[i + 1]) { temp = a[i]; a[i] = a[i + 1]; a[i + 1] = temp; } } /* end of reorder */ void reorder1 (long a[], long b[], long newone, long range) /*reorder array a in increasing order with one misplaced element at index newone */ /*elements of array b are updated to stay aligned with a */ { long temp; while (newone > 0 && a[newone] < a[newone - 1]) { temp = a[newone]; a[newone] = a[newone - 1]; a[newone - 1] = temp; temp = b[newone]; b[newone] = b[newone - 1]; b[--newone] = temp; } while (newone < range - 1 && a[newone] > a[newone + 1]) { temp = a[newone]; a[newone] = a[newone + 1]; a[newone + 1] = temp; temp = b[newone]; b[newone] = b[newone + 1]; b[++newone] = temp; } } /* end of reorder1 */ void rescaledet (lrs_dic * P, lrs_dat * Q, lrs_mp Vnum, lrs_mp Vden) /* rescale determinant to get its volume */ /* Vnum/Vden is volume of current basis */ { lrs_mp gcdprod; /* to hold scale factors */ long i; /* assign local variables to structures */ long *C = P->C; long *B = P->B; long m, d, lastdv; lrs_alloc_mp(gcdprod); m = P->m; d = P->d; lastdv = Q->lastdv; itomp (ONE, gcdprod); itomp (ONE, Vden); for (i = 0; i < d; i++) if (B[i] <= m) { mulint (Q->Gcd[Q->inequality[C[i] - lastdv]], gcdprod, gcdprod); mulint (Q->Lcm[Q->inequality[C[i] - lastdv]], Vden, Vden); } mulint (P->det, gcdprod, Vnum); // reduce (Vnum, Vden); lrs_clear_mp(gcdprod); } /* end rescaledet */ void rescalevolume (lrs_dic * P, lrs_dat * Q, lrs_mp Vnum, lrs_mp Vden) /* adjust volume for dimension */ { lrs_mp temp, dfactorial; /* assign local variables to structures */ long lastdv = Q->lastdv; lrs_alloc_mp(temp); lrs_alloc_mp(dfactorial); /*reduce Vnum by d factorial */ getfactorial (dfactorial, lastdv); mulint (dfactorial, Vden, Vden); if (Q->hull && !Q->homogeneous) { /* For hull option multiply by d to correct for lifting */ itomp (lastdv, temp); mulint (temp, Vnum, Vnum); } reduce (Vnum, Vden); lrs_clear_mp(temp); lrs_clear_mp(dfactorial); } void updatevolume (lrs_dic * P, lrs_dat * Q) /* rescale determinant and update the volume */ { lrs_mp tN, tD, Vnum, Vden; lrs_alloc_mp(tN); lrs_alloc_mp(tD); lrs_alloc_mp(Vnum); lrs_alloc_mp(Vden); rescaledet (P, Q, Vnum, Vden); copy (tN, Q->Nvolume); copy (tD, Q->Dvolume); linrat (tN, tD, ONE, Vnum, Vden, ONE, Q->Nvolume, Q->Dvolume); if (Q->debug) { prat ("\n*Volume=", Q->Nvolume, Q->Dvolume); pmp (" Vnum=", Vnum); pmp (" Vden=", Vden); } lrs_clear_mp(tN); lrs_clear_mp(tD); lrs_clear_mp(Vnum); lrs_clear_mp(Vden); } /* end of updatevolume */ /***************************************************/ /* Routines for redundancy checking */ /***************************************************/ long checkredund (lrs_dic * P, lrs_dat * Q) /* Solve primal feasible lp by least subscript and lex min basis method */ /* to check redundancy of a row in objective function */ /* return 0=nonredundant -1=strict redundant(interior) 1=non-strict redundant 2=unbounded possible linearity */ { lrs_mp Ns, Nt; long i, j; long r, s; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *Row, *Col; long d = P->d; lrs_alloc_mp(Ns); lrs_alloc_mp(Nt); itomp (ONE, Ns); /* unnecessary but avoids compile warning */ itomp (ONE, Nt); Row = P->Row; Col = P->Col; while (selectpivot (P, Q, &i, &j)) { Q->count[2]++; /* sign of new value of A[0][0] */ /* is A[0][s]*A[r][0]-A[0][0]*A[r][s] */ r = Row[i]; s = Col[j]; mulint (A[0][s], A[r][0], Ns); mulint (A[0][0], A[r][s], Nt); if (mp_greater (Ns, Nt)) { lrs_clear_mp(Ns); lrs_clear_mp(Nt); if(Q->debug && !Q->mplrs) fprintf(lrs_ofp,"\n*mp_greater: nonredundant"); return 0; } pivot (P, Q, i, j); update (P, Q, &i, &j); /*Update B,C,i,j */ if(overflow_detected) { if(Q->verbose && !Q->mplrs) lrs_warning(Q,"warning","*overflow checkredund"); return FALSE; } } lrs_clear_mp(Ns); lrs_clear_mp(Nt); if(positive(P->A[0][0])) { if(Q->debug) fprintf(lrs_ofp,"\n*positive objective: nonredundant"); return 0; } if(j < d && i == 0) /* unbounded is also non-redundant */ { if(Q->debug) fprintf(lrs_ofp,"\n*unbounded-non redundant"); return 2; } /* 2020.6.8 check for strict redundancy and return -1 if so */ if(Q->debug ) pmp("\n*obj =",P->A[0][0]); if (negative(P->A[0][0])) return -1; else return 1; } /* end of checkredund */ long checkcobasic (lrs_dic * P, lrs_dat * Q, long index) /* TRUE if index is cobasic and nondegenerate */ /* FALSE if basic, or degen. cobasic, where it will get pivoted out */ { /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *B, *C, *Row, *Col; long d = P->d; long m = P->m; long debug = Q->debug; long i = 0; long j = 0; long s; long start=Q->lastdv+1; if(index < 0) { start = 1; /*replace cobasic by basic variable */ index=-index; } B = P->B; C = P->C; Row = P->Row; Col = P->Col; while ((j < d) && C[j] != index) j++; if (j == d) return FALSE; /* not cobasic index */ /* index is cobasic */ if (debug) fprintf (lrs_ofp, "\nindex=%ld cobasic", index); s = Col[j]; i = start; while ((i <= m) && (zero (A[Row[i]][s]) || !zero (A[Row[i]][0]))) i++; if (i > m) { if (debug) fprintf (lrs_ofp, " is non-degenerate"); return TRUE; } if (debug) fprintf (lrs_ofp, " is degenerate B[i]=%ld C[j]=%ld", B[i],C[j]); pivot (P, Q, i, j); update (P, Q, &i, &j); /*Update B,C,i,j */ return FALSE; /*index is no longer cobasic */ } /* end of checkcobasic */ long checkindex (lrs_dic * P, lrs_dat * Q, long index, long phase) /* phase=0 find hidden linearities phase=1 redundant inequalities only */ /* 0 if index is non-redundant inequality */ /*-1 if index is strict redundant inequality */ /* 1 if index is non-strict redundant ine */ /* 2 if index is input linearity */ /*NOTE: row is returned all zero if redundant!! */ { long i, j,k, res1=0, res2=0; lrs_mp_matrix A = P->A; long *Row = P->Row; long *B = P->B; long d = P->d; long m = P->m; long zeroonly=0; long allzero=1; if(index < 0) /* used to zero out known redundant rows in mplrs */ { zeroonly=1; index=-index; } if (Q->debug) { printA (P, Q); prawA(P,Q); } /* each slack index must be checked for degeneracy */ /* if in cobasis, it is pivoted out if degenerate */ if (checkcobasic (P, Q, index)) { if(Q->debug) fprintf(lrs_ofp,"\n*checkcobasic res1=%ld",res1); return ZERO; } /* index is basic */ j = 1; while ((j <= m) && (B[j] != index)) j++; i = Row[j]; /* copy row i to cost row, and set it to zero */ for (k = 0; k <= d; k++) { if(!zero(A[i][k])) allzero=0; copy (A[0][k], A[i][k]); changesign (A[0][k]); itomp (ZERO, A[i][k]); } if(zeroonly) return 1; /* zero row is strongly redundant */ if(allzero) { if(Q->debug) { prawA(P,Q); printA(P,Q); } if(Q->debug) fprintf(lrs_ofp,"\n*zero row index=%ld j=%ld Row[j]=%ld",index,j,Row[j]); return -1; } /* test for redundant inequalities */ res1=checkredund (P, Q); /* res=0 non-red =-1 strong red =1 weak red =2 LP unbounded */ if (!Q->mplrs ) if(res1 ==1 || res1 == -1 ) return res1; /* redundant */ /* 2022.4.19 res1=2 is unbounded, possible linearity, not used at present */ if(res1==2) res1=0; for (j = 0; j <= d; j++) changesign (A[0][j]); if(Q->debug) fprintf(lrs_ofp,"\n*phase=%ld",phase); /* 2023.3.20 need to verify that this is skipped on mplrs second round */ if( phase==0 ) /* find hidden linearities */ { res2=checkredund (P, Q); if ( res2==1 || res2 == -1 ) /* indicates linearity */ if ( zero (P->A[0][0])) res1=2 ; } /* testlin */ if(res1 == 0 || res1 ==2) for (j = 0; j <= d; j++) /* restore tested row that was zeroed */ copy (A[i][j], A[0][j]); return res1; } /* end of checkindex */ /***************************************************************/ /* */ /* f I/O routines */ /* */ /***************************************************************/ void lprat (const char *name, long Nt, long Dt) /*print the long precision rational Nt/Dt without reducing */ { if ( Nt > 0 ) fprintf (lrs_ofp, " "); fprintf (lrs_ofp, "%s%ld", name, Nt); if (Dt != 1) fprintf (lrs_ofp, "/%ld", Dt); fprintf (lrs_ofp, " "); } /* lprat */ long lreadrat (long *Num, long *Den) /* read a rational string and convert to long */ /* returns true if denominator is not one */ { char in[MAXINPUT], num[MAXINPUT], den[MAXINPUT]; if(fscanf (lrs_ifp, "%s", in) == EOF) return(FALSE); atoaa (in, num, den); /*convert rational to num/dem strings */ *Num = atol (num); if (den[0] == '\0') { *Den = 1L; return (FALSE); } *Den = atol (den); return (TRUE); } void lrs_getinput(lrs_dic *P,lrs_dat *Q,long *num,long *den, long m, long d) /* code for reading data matrix in lrs/cdd format */ { long j,row; printf("\nEnter each row: b_i a_ij j=1..%ld",d); for (row=1;row<=m;row++) { printf("\nEnter row %ld: ",row ); for(j=0;j<=d;j++) { lreadrat(&num[j],&den[j]); lprat(" ",num[j],den[j]); } lrs_set_row(P,Q,row,num,den,GE); } printf("\nEnter objective row c_j j=1..%ld: ",d); num[0]=0; den[0]=1; for(j=1;j<=d;j++) { lreadrat(&num[j],&den[j]); lprat(" ",num[j],den[j]); } lrs_set_obj(P,Q,num,den,MAXIMIZE); } long readlinearity (lrs_dat * Q) /* read in and check linearity list */ { long i, j; long nlinearity; if(fscanf (lrs_ifp, "%ld", &nlinearity)==EOF ) { lrs_warning(Q,"warning","\nLinearity option invalid, no indices "); return (FALSE); } if (nlinearity < 1) { lrs_warning(Q,"warning","\nLinearity option invalid, indices must be positive"); return (FALSE); } Q->linearity = (long int*) CALLOC ((nlinearity + 1), sizeof (long)); for (i = 0; i < nlinearity; i++) { if(fscanf (lrs_ifp, "%ld", &j)==EOF) { lrs_warning(Q,"warning","\nLinearity option invalid, missing indices"); return (FALSE); } Q->linearity[i] = j; } for (i = 1; i < nlinearity; i++) /*sort in order */ reorder (Q->linearity, nlinearity); Q->nlinearity = nlinearity; Q->polytope = FALSE; return TRUE; } /* end readlinearity */ long readredund (lrs_dat * Q) /* read in and check linearity list */ { long i,j,k; char *mess; int len=0; if(fscanf (lrs_ifp, "%ld", &k)==EOF ) { lrs_warning(Q,"warning","\nredund_list option invalid: no indices "); return (FALSE); } if ( k < 0 ) { lrs_warning(Q,"warning","\nredund_list option invalid, first index must be >= 0"); return (FALSE); } if ( k < Q->m) Q->fullredund=FALSE; for (i = 1; i <= Q->m; i++) /*reset any previous redund option except =2 values */ if (Q->redineq[i] != 2) Q->redineq[i]=0; Q->redineq[0]=1; for (i = 0; i < k; i++) { if(fscanf (lrs_ifp, "%ld", &j)==EOF) { lrs_warning(Q,"warning","\nredund_list option invalid: missing indices"); fflush(lrs_ofp); return (FALSE); } if( j< 0 || j > Q->m) { fprintf (lrs_ofp,"\nredund_list option invalid: indices not between 1 and %ld",Q->m); return (FALSE); } Q->redineq[j] = 1; } if( Q->messages ) if (!(Q->mplrs && Q->redund) ) { mess=(char *)malloc(20*Q->m*sizeof(char)); len=sprintf(mess,"*redund_list %ld ",k); for (i=1;i<=Q->m;i++) if(Q->redineq[i] == 1) len=len+sprintf(mess+len," %ld",i); lrs_warning(Q,"warning",mess); free(mess); } return TRUE; } /* end readredund */ long readfacets (lrs_dat * Q, long facet[]) /* read and check facet list for obvious errors during start/restart */ /* this must be done after linearity option is processed!! */ { long i, j; char str[1000000],*p,*e; /* assign local variables to structures */ long m, d; long *linearity = Q->linearity; m = Q->m; d = Q->inputd; /* modified 2018.6.7 to fix bug restarting with less than full dimension input */ /* number of restart indices is not known at this point */ j=Q->nlinearity; /* note we place these after the linearity indices */ if (fgets(str,1000000,lrs_ifp)==NULL) return FALSE; /* pick up indices from the input line */ for (p = str; ; p = e) { facet[j] = strtol(p, &e, 10); if (p == e) break; if(!Q->mplrs) fprintf(lrs_ofp," %ld",facet[j] ); /* 2010.4.26 nonnegative option needs larger range of indices */ if(Q->nonnegative) if (facet[j] < 1 || facet[j] > m+d) { fprintf (lrs_ofp,"\n Start/Restart cobasic indices must be in range 1 .. %ld ", m+d); return FALSE; } if(!Q->nonnegative) if (facet[j] < 1 || facet[j] > m) { fprintf (lrs_ofp, "\n Start/Restart cobasic indices must be in range 1 .. %ld ", m); return FALSE; } for (i = 0; i < Q->nlinearity; i++) if (linearity[i] == facet[j]) { fprintf (lrs_ofp, "\n Start/Restart cobasic indices should not include linearities"); return FALSE; } /* bug fix 2011.8.1 reported by Steven Wu*/ for (i = Q->nlinearity; i < j; i++) /* end bug fix 2011.8.1 */ if (facet[i] == facet[j]) { fprintf (lrs_ofp, "\n Start/Restart cobasic indices must be distinct"); return FALSE; } j++; } return TRUE; } /* end of readfacets */ long readvars (lrs_dat * Q,char *name) { /* read in and check ordered list of vars for extract/project */ /* extract mode: *vars is an ordered list of variables to be kept */ /* fel mode: *vars is an ordered list of variables to be removed */ long i, j, len,nremove; long nvars=0; long k=0; long *vars; long *var; /* binary representation of vars */ long n=Q->n; Q->vars = (long int*) CALLOC ((n + 3), sizeof (long)); var = (long int*) CALLOC ((n + 3), sizeof (long)); vars=Q->vars; for (i=0;i<=n+2;i++) { vars[i]=0; var[i]=0; } if((fscanf (lrs_ifp, "%ld", &nvars)==EOF ) || nvars < 1) { fprintf (lrs_ofp, "\n*%s: incorrect or missing indices\n",name); free(var); return FALSE; } if( nvars > n-1) { nvars = n-1; fprintf (lrs_ofp, "\n*%s: too many indices, first %ld taken",name,n-1); } for (i = 0; i < nvars; i++) { if(fscanf (lrs_ifp, "%ld", &j)==EOF) { fprintf (lrs_ofp, "\n*%s: missing indices\n",name); free(var); return FALSE; } if(j>0 && jmessages ) /* need the leading * for mfel */ if (!(Q->mplrs && Q->fel ) ) { len=sprintf(Q->projmess,"*%s %ld ",name,nvars); for(i=0;iprojmess+len,"%ld ", vars[i]); lrs_warning(Q,"warning",Q->projmess); } /* now we build a new string for output after the end with no * */ len=sprintf(Q->projmess,"%s %ld ",name,nvars); for(i=0;iprojmess+len,"%ld ", vars[i]); if(strcmp (name, "project") == 0) /* convert to project vars to remove vars */ { for(i=0;ifel) return TRUE; /* if nlinearity>0 fill up list with remaining decision variables */ if(!Q->hull && Q->nlinearity > 0) for (i=1;iCol; Row = P->Row; remain=Q->vars; output=Q->temparray; m=P->m; n=Q->n; if(Q->fel) ncols=n-remain[n+1]-1; else ncols=remain[n+1]; for(j=0;jfel) for(j=1;jverbose) { fprintf(lrs_ofp,"\n*output"); for (j=0;jfel) /* fel mode remove redundancy */ { for(i=1;i<=m;i++ ) /* zero out removed cols */ for(j=0;jA[Row[i]][Col[j]]); P1=lrs_getdic (Q); Q->Qhead=P; Q->Qtail=P; copy_dict (Q,P1,P); Q->Qhead=P1; Q->Qtail=P1; Q->olddic=P; /*in case of overflow */ A = P1->A; redund_run(P1,Q); if(overflow_detected) { if(Q->debug) { fprintf(lrs_ofp,"\n*overflow in fel"); return 1; } } redineq=Q->redineq; rows=0; for(i=1;i<=P->m_A; i++) if(redineq[i]==0 || redineq[i]==2 ) rows++; Q->Qhead=P; Q->Qtail=P; } /* end if(Q->fel)... */ else /* initialization for extract mode */ { redineq=Q->redineq; rows=m; for(i=1;i<=m;i++ ) redineq[i] = 0; } A=P->A; m=Q->m; if(Q->hull) fprintf(lrs_ofp,"\nV-representation"); else fprintf(lrs_ofp,"\nH-representation"); if (Q->nlinearity > 0) { fprintf(lrs_ofp, "\nlinearity %ld", Q->nlinearity); for(i=0; inlinearity;i++) fprintf(lrs_ofp, " %ld", Q->linearity[i]); } fprintf(lrs_ofp,"\nbegin\n%ld %ld rational",rows,ncols+1); for(i=1;i<=m;i++ ) { if(redineq[i] != 1 && redineq[i] != -1) /* 2023.10.30 added -1 here */ { reducearray(A[Row[i]],n+Q->hull); /*we already decremented n */ fprintf(lrs_ofp,"\n"); if(Q->hull) { for(j=0;jdebug) printA(P,Q); return 0; } /* extractcols */ long linextractcols (lrs_dic * P, lrs_dat * Q) /* 2020.2.2 */ /* extract option to output the reduced A matrix after linearities are removed */ /* should be followed by redund to get minimum representation */ { long d,i,j,k,m,n; long ii,jj; long nlinearity=Q->nlinearity; lrs_mp_matrix A; long *B, *C, *Col, *Row, *remain; A = P->A; B = P->B; C = P->C; Col = P->Col; Row = P->Row; remain=Q->vars; m=P->m; n=Q->n; d=Q->inputd; fprintf(lrs_ofp,"\n*extract col order: "); for(j=0;jhull) fprintf(lrs_ofp,"\n*columns retained:"); else fprintf(lrs_ofp,"\n*columns retained: 0"); for (j=0;jhull); if(Q->hull) fprintf(lrs_ofp,"\nV-representation\nbegin"); else fprintf(lrs_ofp,"\nH-representation\nbegin"); fprintf(lrs_ofp,"\n%ld %ld rational",m-nlinearity,d-nlinearity+1-Q->hull); for(i=nlinearity+1;i<=m;i++ ) { reducearray(A[Row[i]],n-nlinearity); fprintf(lrs_ofp,"\n"); if(!Q->hull) pmp("",A[Row[i]][0]); for(j=0;jhull) fprintf(lrs_ofp,"\n*columns retained:"); else fprintf(lrs_ofp,"\n*columns retained: 0"); for (j=0;jhull); fprintf(lrs_ofp,"\n"); if(Q->debug) printA(P,Q); return 0; } /* linextractcols */ void printA (lrs_dic * P, lrs_dat * Q) /* print the integer m by n array A with B,C,Row,Col vectors */ { long i, j; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *B = P->B; long *C = P->C; long *Row = P->Row; long *Col = P->Col; long m, d; m = P->m; d = P->d; fprintf (lrs_ofp, "\n Basis "); for (i = 0; i <= m; i++) fprintf (lrs_ofp, "%ld ", B[i]); fprintf (lrs_ofp, " Row "); for (i = 0; i <= m; i++) fprintf (lrs_ofp, "%ld ", Row[i]); fprintf (lrs_ofp, "\n Co-Basis "); for (i = 0; i <= d; i++) fprintf (lrs_ofp, "%ld ", C[i]); fprintf (lrs_ofp, " Column "); for (i = 0; i <= d; i++) fprintf (lrs_ofp, "%ld ", Col[i]); pmp (" det=", P->det); fprintf (lrs_ofp, "\n"); i=0; while ( i<= m ) { for (j = 0; j <= d; j++) pimat (P, i, j, A[Row[i]][Col[j]], "A"); fprintf (lrs_ofp, "\n"); if (i==0 && Q->nonnegative) /* skip basic rows - don't exist! */ i=d; i++; fflush (stdout); } fflush (stdout); } void prawA (lrs_dic * P, lrs_dat * Q) /* raw matrix print */ { long i, j; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long m, d; m = P->m; d = P->d; fprintf (lrs_ofp, "\n Raw A matrix"); fprintf (lrs_ofp, "\n"); i=0; while ( i<= m ) { fprintf (lrs_ofp, "Row[%ld][0]=", i); pmp("",A[i][0]); for (j = 1; j <= d; j++) { fprintf (lrs_ofp, "[%ld]=", j); pmp("",A[i][j]); } fprintf (lrs_ofp, "\n"); if (i==0 && Q->nonnegative) /* skip basic rows - don't exist! */ i=d; i++; fflush (stdout); } } void pimat (lrs_dic * P, long r, long s, lrs_mp Nt, const char *name) /*print the long precision integer in row r col s of matrix A */ { long *B = P->B; long *C = P->C; if (s == 0) fprintf (lrs_ofp, "%s[%ld][%ld]=", name, B[r], C[s]); else fprintf (lrs_ofp, "[%ld]=", C[s]); pmp ("", Nt); } /***************************************************************/ /* */ /* Routines for caching, allocating etc. */ /* */ /***************************************************************/ /* From here mostly Bremner's handiwork */ static void cache_dict (lrs_dic ** D_p, lrs_dat * global, long i, long j) { if (dict_limit > 1) { /* save row, column indicies */ (*D_p)->i = i; (*D_p)->j = j; /* Make a new, blank spot at the end of the queue to copy into */ pushQ (global, (*D_p)->m, (*D_p)->d, (*D_p)->m_A); /*2019.6.7 This ought not to happen but it does */ if( global->Qtail== *D_p) return; copy_dict (global, global->Qtail, *D_p); /* Copy current dictionary */ } *D_p = global->Qtail; } void copy_dict (lrs_dat * global, lrs_dic * dest, lrs_dic * src) { long m = src->m; long m_A = src->m_A; /* number of rows in A */ long d = src->d; long r,s; if( dest == src) { if(global->mplrs) lrs_post_output("warning", "*copy_dict has dest=src -ignoring copy"); else fprintf(stderr,"*copy_dict has dest=src -ignoring copy"); return; } #if defined(GMP) || defined(FLINT) for ( r=0;r<=m_A;r++) for( s=0;s<=d;s++) copy(dest->A[r][s],src->A[r][s]); #else /* fast copy for MP and LRSLONG arithmetic */ /* Note that the "A" pointer trees need not be copied, since they always point to the same places within the corresponding space */ /* I wish I understood the above remark. For the time being, do it the easy way for Nash */ /* Looking at lrs_alloc_mp_matrix for MP and LRSLONG, A[0][0] is the * start of araw, which holds the actual values and so the memcpy below * copies the values. The pointer trees (A, A[i], A[i][j]) already point * to the appropriate places: we don't want to change the pointers, only the * values. lrs_alloc_mp_matrix is different for GMP. */ if(global->nash) { for ( r=0;r<=m_A;r++) for( s=0;s<=d;s++) copy(dest->A[r][s],src->A[r][s]); } else #ifdef B128 memcpy (dest->A[0][0], (global->Qtail->prev)->A[0][0], (d + 1) * (lrs_digits + 1) * (m_A + 1) * sizeof (__int128)); #else memcpy (dest->A[0][0], (global->Qtail->prev)->A[0][0], (d + 1) * (lrs_digits + 1) * (m_A + 1) * sizeof (long long)); #endif #endif dest->i = src->i; dest->j = src->j; dest->m = m; dest->d = d; dest->d_orig = src->d_orig; dest->m_A = src->m_A; dest->depth = src->depth; dest->lexflag = src->lexflag; copy (dest->det, src->det); copy (dest->objnum, src->objnum); copy (dest->objden, src->objden); if (global->debug) fprintf (lrs_ofp, "\nSaving dict at depth %ld\n", src->depth); memcpy (dest->B, src->B, (m + 1) * sizeof (long)); memcpy (dest->C, src->C, (d + 1) * sizeof (long)); memcpy (dest->Row, src->Row, (m + 1) * sizeof (long)); memcpy (dest->Col, src->Col, (d + 1) * sizeof (long)); } /* * pushQ(lrs_dat *globals,m,d): * this routine ensures that Qtail points to a record that * may be copied into. * * It may create a new record, or it may just move the head pointer * forward so that know that the old record has been overwritten. */ #if 0 #define TRACE(s) fprintf(stderr,"\n%s %p %p\n",s,global->Qhead,global->Qtail); #else #define TRACE(s) #endif static void pushQ (lrs_dat * global, long m, long d ,long m_A) { if ((global->Qtail->next) == global->Qhead) { /* the Queue is full */ if (dict_count < dict_limit) { /* but we are allowed to create more */ lrs_dic *p; p = new_lrs_dic (m, d, m_A); if (p) { /* we successfully created another record */ p->next = global->Qtail->next; (global->Qtail->next)->prev = p; (global->Qtail->next) = p; p->prev = global->Qtail; /*2023.1.25*/ dict_count++; global->Qtail = p; TRACE ("Added new record to Q"); } else { /* virtual memory exhausted. bummer */ global->Qhead = global->Qhead->next; global->Qtail = global->Qtail->next; TRACE ("VM exhausted"); } } else { /* * user defined limit reached. start overwriting the * beginning of Q */ global->Qhead = global->Qhead->next; global->Qtail = global->Qtail->next; TRACE ("User limit"); } } else { global->Qtail = global->Qtail->next; TRACE ("Reusing"); } } lrs_dic * lrs_getdic(lrs_dat *Q) /* create another dictionary for Q without copying any values */ /* derived from lrs_alloc_dic, used by nash.c */ { lrs_dic *p; long m; m = Q->m; /* nonnegative flag set means that problem is d rows "bigger" */ /* since nonnegative constraints are not kept explicitly */ if(Q->nonnegative) m = m+Q->inputd; p = new_lrs_dic (m, Q->inputd, Q->m); if (!p) return NULL; p->next = p; p->prev = p; Q->Qhead = p; Q->Qtail = p; return p; } #define NULLRETURN(e) if (!(e)) return NULL; static lrs_dic * new_lrs_dic (long m, long d, long m_A) { lrs_dic *p; NULLRETURN (p = (lrs_dic *) malloc (sizeof (lrs_dic))); NULLRETURN (p->B = (long int*) calloc ((m + 1), sizeof (long))); NULLRETURN (p->Row = (long int*) calloc ((m + 1), sizeof (long))); NULLRETURN (p->C = (long int*) calloc ((d + 1), sizeof (long))); NULLRETURN (p->Col = (long int*) calloc ((d + 1), sizeof (long))); #if defined(GMP) || defined(FLINT) lrs_alloc_mp(p->det); lrs_alloc_mp(p->objnum); lrs_alloc_mp(p->objden); #endif p->d_orig=d; p->A=lrs_alloc_mp_matrix(m_A,d); return p; } void lrs_free_dic (lrs_dic * P, lrs_dat *Q) { /* do the same steps as for allocation, but backwards */ /* gmp variables cannot be cleared using free: use lrs_clear_mp* */ lrs_dic *P1; if (Q == NULL ) { if(Q->mplrs) lrs_post_output("warning","*lrs_free_dic trying to free null Q : skipped"); else fprintf(stderr,"*lrs_free_dic trying to free null Q : skipped"); return; } if (P == NULL ) { if(Q->mplrs) lrs_post_output("warning","*lrs_free_dic trying to free null P : skipped"); else fprintf(stderr,"*lrs_free_dic trying to free null P : skipped"); return; } /* repeat until cache is empty */ do /*2023.1.26 This clears cache only */ { /* I moved these here because I'm not certain the cached dictionaries need to be the same size. Well, it doesn't cost anything to be safe. db */ long d = P->d_orig; long m_A = P->m_A; lrs_clear_mp_matrix (P->A,m_A,d); /* "it is a ghastly error to free something not assigned my malloc" KR167 */ /* so don't try: free (P->det); */ lrs_clear_mp (P->det); lrs_clear_mp (P->objnum); lrs_clear_mp (P->objden); free (P->Row); free (P->Col); free (P->C); free (P->B); /* go to next record in cache if any */ P1 =P->next; free (P); P=P1; }while (Q->Qhead != P ); Q->Qhead=NULL; Q->Qtail=NULL; } void lrs_free_dic2 (lrs_dic * P, lrs_dat *Q) { /* do the same steps as for allocation, but backwards */ /* same as lrs_free_dic except no cache for P */ /* I moved these here because I'm not certain the cached dictionaries need to be the same size. Well, it doesn't cost anything to be safe. db */ long d = P->d_orig; long m_A = P->m_A; lrs_clear_mp_matrix (P->A,m_A,d); /* "it is a ghastly error to free something not assigned my malloc" KR167 */ /* so don't try: free (P->det); */ lrs_clear_mp (P->det); lrs_clear_mp (P->objnum); lrs_clear_mp (P->objden); free (P->Row); free (P->Col); free (P->C); free (P->B); free (P); } void lrs_free_dat ( lrs_dat *Q ) { int i=0; if (Q == NULL) { if(Q->mplrs) lrs_post_output("warning","*lrs_free_dat trying to free null Q : skipped"); else fprintf(stderr,"*lrs_free_dat trying to free null Q : skipped"); return; } /* most of these items were allocated in lrs_alloc_dic */ lrs_clear_mp_vector (Q->Gcd,Q->m); lrs_clear_mp_vector (Q->Lcm,Q->m); lrs_clear_mp_vector (Q->output,Q->n+1); lrs_clear_mp (Q->sumdet); lrs_clear_mp (Q->Nvolume); lrs_clear_mp (Q->Dvolume); lrs_clear_mp (Q->saved_det); lrs_clear_mp (Q->boundd); lrs_clear_mp (Q->boundn); free (Q->facet); free (Q->redundcol); free (Q->inequality); free (Q->linearity); free (Q->vars); free (Q->startcob); free (Q->minratio); free (Q->redineq); free (Q->temparray); free (Q->projmess); free (Q->name); free (Q->saved_C); /*2020.8.1 DA: lrs_Q_list is not a stack but a list, so have to delete Q */ if(dict_limit > 1) { while(iverbose) lrs_warning(Q,"warning","lrs_free_dat(Q) not in global list - skipped"); } else while(iQtail == Q->Qhead) { TRACE ("cache miss"); /* Q has only one element */ cache_misses++; return 0; } else { Q->Qtail = Q->Qtail->prev; *D_p = Q->Qtail; *i_p = Q->Qtail->i; *j_p = Q->Qtail->j; TRACE ("restoring dict"); return 1; } } lrs_dic * lrs_alloc_dic (lrs_dat * Q) /* allocate and initialize lrs_dic */ { lrs_dic *p; long i, j; long m, d, m_A; if (Q->hull) /* d=col dimension of A */ Q->inputd = Q->n; /* extra column for hull */ else Q->inputd = Q->n - 1; m = Q->m; d = Q->inputd; m_A = m; /* number of rows in A */ if(m > MAX_ROWS) { fprintf(lrs_ofp,"\n*trying to allocate dictionary with %ld rows exceding MAX_ROWS=%ld\n",m,MAX_ROWS); return NULL; } /* nonnegative flag set means that problem is d rows "bigger" */ /* since nonnegative constraints are not kept explicitly */ if(Q->nonnegative) m = m+d; p = new_lrs_dic (m, d, m_A); if (!p) return NULL; p->next = p; p->prev = p; Q->Qhead = p; Q->Qtail = p; /* Initializations */ p->d = p->d_orig = d; p->m = m; p->m_A = m_A; p->depth = 0L; p->lexflag = TRUE; itomp (ONE, p->det); itomp (ZERO, p->objnum); itomp (ONE, p->objden); /*m+d+1 is the number of variables, labelled 0,1,2,...,m+d */ /* initialize array to zero */ for (i = 0; i <= m_A; i++) for (j = 0; j <= d; j++) itomp (ZERO, p->A[i][j]); Q->inequality = (long int*) CALLOC ((m + d + 1), sizeof (long)); Q->facet = (long int*) CALLOC ((unsigned) m + d + 1, sizeof (long)); Q->redundcol = (long int*) CALLOC ((m + d + 1), sizeof (long)); Q->minratio = (long int*) CALLOC ((m+d + 1), sizeof (long)); /* 2011.7.14 minratio[m]=0 for degen =1 for nondegen pivot*/ Q->redineq = (long int*) CALLOC ((m + d + 1), sizeof (long)); Q->projmess=(char *)malloc(20+20*Q->n*sizeof(char)); strcpy(Q->projmess,""); Q->temparray = (long int*) CALLOC ((unsigned) m + d + 1, sizeof (long)); if (Q->nlinearity == ZERO) /* linearity may already be allocated */ Q->linearity = (long int*) CALLOC ((m + d + 1), sizeof (long)); else { /* we may add linearities so need to resize it */ for(i=0;inlinearity;i++) Q->temparray[i]=Q->linearity[i]; free(Q->linearity); Q->linearity = (long int*) CALLOC ((m + d + 1), sizeof (long)); for(i=0;inlinearity;i++) Q->linearity[i]=Q->temparray[i]; } Q->inequality[0] = 2L; Q->Gcd = lrs_alloc_mp_vector(m); Q->Lcm = lrs_alloc_mp_vector(m); Q->output = lrs_alloc_mp_vector(Q->n+1); Q->saved_C = (long int*) CALLOC (d + 1, sizeof (long)); Q->lastdv = d; /* last decision variable may be decreased */ /* if there are redundant columns */ for (i = 0; i < m+d+1; i++) { Q->redineq[i]=1; Q->inequality[i]=0; } /*initialize basis and co-basis indices, and row col locations */ /*if nonnegative, we label differently to avoid initial pivots */ /* set basic indices and rows */ if(Q->nonnegative) for (i = 0; i <= m; i++) { p->B[i] = i; if (i <= d ) p->Row[i]=0; /* no row for decision variables */ else p->Row[i]=i-d; } else for (i = 0; i <= m; i++) { if (i == 0 ) p->B[0]=0; else p->B[i] = d + i; p->Row[i] = i; } for (j = 0; j < d; j++) { if(Q->nonnegative) p->C[j] = m+j+1; else p->C[j] = j + 1; p->Col[j] = j + 1; } p->C[d] = m + d + 1; p->Col[d] = 0; return p; } /* end of lrs_alloc_dic */ /* this routine makes a copy of the information needed to restart, so that we can guarantee that if a signal is received, we can guarantee that nobody is messing with it. This as opposed to adding all kinds of critical regions in the main line code. It is also used to make sure that in case of overflow, we have a valid cobasis to restart from. */ static void save_basis (lrs_dic * P, lrs_dat * Q) { int i; /* assign local variables to structures */ long *C = P->C; long d; #ifndef SIGNALS sigset_t oset, blockset; sigemptyset (&blockset); sigaddset (&blockset, SIGTERM); sigaddset (&blockset, SIGHUP); sigaddset (&blockset, SIGUSR1); errcheck ("sigprocmask", sigprocmask (SIG_BLOCK, &blockset, &oset)); #endif d = P->d; Q->saved_flag = 1; for (i = 0; i < 5; i++) Q->saved_count[i] = Q->count[i]; for (i = 0; i < d + 1; i++) Q->saved_C[i] = C[i]; copy (Q->saved_det, P->det); Q->saved_d = P->d; Q->saved_depth = P->depth; #ifndef SIGNALS errcheck ("sigproceask", sigprocmask (SIG_SETMASK, &oset, 0)); #endif } /* print out the saved copy of the basis */ void print_basis (FILE * fp, lrs_dat * Q) { int i; /* assign local variables to structures */ fprintf (fp, "lrs_lib: State #%ld: (%s)\t", Q->id, Q->name); if (Q->saved_flag) { /* legacy output which is not actually correct for V-representations as V# is not used */ /* fprintf (fp, "V#%ld R#%ld B#%ld h=%ld facets ", Q->saved_count[1], Q->saved_count[0], Q->saved_count[2], Q->saved_depth); for (i = 0; i < Q->saved_d; i++) fprintf (fp, "%ld ", Q->inequality[Q->saved_C[i] - Q->lastdv]); pmp (" det=", Q->saved_det); fprintf (fp, "\n"); */ if( Q->hull) fprintf (fp, "\nrestart %ld %ld %ld ", Q->saved_count[0], Q->saved_count[2], Q->saved_depth); else fprintf (fp, "\nrestart %ld %ld %ld %ld ", Q->saved_count[1], Q->saved_count[0], Q->saved_count[2], Q->saved_depth); for (i = 0; i < Q->saved_d; i++) fprintf (fp, "%ld ", Q->inequality[Q->saved_C[i] - Q->lastdv]); if(Q->saved_count[4] >0) fprintf (fp, "\nintegervertices %ld", Q->saved_count[4]); fprintf (fp, "\n"); } else { fprintf (fp, "lrs_lib: Computing initial basis\n"); } fflush (fp); } #ifndef SIGNALS static void lrs_dump_state () { long i; fprintf (lrs_ofp, "\n\nlrs_lib: checkpointing:\n"); #ifdef MP fprintf (stderr, "lrs_lib: Current digits at %ld out of %ld\n", DIG2DEC (lrs_record_digits), DIG2DEC (lrs_digits)); #endif for (i = 0; i < lrs_Q_count; i++) { print_basis (lrs_ofp, lrs_Q_list[i]); } fprintf (lrs_ofp, "lrs_lib: checkpoint finished\n"); } /* If given a signal USR1 print current cobasis and continue TERM print current cobasis and terminate INT (ctrl-C) ditto HUP ditto */ static void setup_signals () { errcheck ("signal", signal (SIGTERM, die_gracefully)); errcheck ("signal", signal (SIGALRM, timecheck)); errcheck ("signal", signal (SIGHUP, die_gracefully)); errcheck ("signal", signal (SIGINT, die_gracefully)); errcheck ("signal", signal (SIGUSR1, checkpoint)); } static void timecheck () { lrs_dump_state (); errcheck ("signal", signal (SIGALRM, timecheck)); alarm (lrs_checkpoint_seconds); } static void checkpoint () { lrs_dump_state (); errcheck ("signal", signal (SIGUSR1, checkpoint)); } static void die_gracefully () { lrs_dump_state (); exit (1); } #endif #ifndef TIMES /* * Not sure about the portability of this yet, * - db */ #include #define double_time(t) ((double)(t.tv_sec)+(double)(t.tv_usec)/1000000) static void ptimes () { struct rusage rusage; getrusage (RUSAGE_SELF, &rusage); fprintf (lrs_ofp, "\n*%0.3fu %0.3fs %ldKb %ld flts %ld swaps %ld blks-in %ld blks-out \n", double_time (rusage.ru_utime), double_time (rusage.ru_stime), rusage.ru_maxrss, rusage.ru_majflt, rusage.ru_nswap, rusage.ru_inblock, rusage.ru_oublock); if(lrs_ofp != stdout) printf ("\n*%0.3fu %0.3fs %ldKb %ld flts %ld swaps %ld blks-in %ld blks-out \n", double_time (rusage.ru_utime), double_time (rusage.ru_stime), rusage.ru_maxrss, rusage.ru_majflt, rusage.ru_nswap, rusage.ru_inblock, rusage.ru_oublock); } static double get_time() { struct rusage rusage; getrusage (RUSAGE_SELF, &rusage); return ( double_time (rusage.ru_utime)); } #endif /* Routines based on lp_solve */ void lrs_set_row(lrs_dic *P, lrs_dat *Q, long row, long num[], long den[], long ineq) /* convert to lrs_mp then call lrs_set_row */ { lrs_mp_vector Num, Den; long d; long j; d = P->d; Num=lrs_alloc_mp_vector(d+1); Den=lrs_alloc_mp_vector(d+1); for (j=0;j<=d;j++) { itomp(num[j],Num[j]); itomp(den[j],Den[j]); } lrs_set_row_mp(P,Q,row,Num,Den,ineq); lrs_clear_mp_vector(Num,d+1); lrs_clear_mp_vector(Den,d+1); } void lrs_set_row_mp(lrs_dic *P, lrs_dat *Q, long row, lrs_mp_vector num, lrs_mp_vector den, long ineq) /* set row of dictionary using num and den arrays for rational input */ /* ineq = 1 (GE) - ordinary row */ /* = 0 (EQ) - linearity */ { lrs_mp Temp, mpone; lrs_mp_vector oD; /* denominator for row */ long i, j; /* assign local variables to structures */ lrs_mp_matrix A; lrs_mp_vector Gcd, Lcm; long hull; long m, d; lrs_alloc_mp(Temp); lrs_alloc_mp(mpone); hull = Q->hull; A = P->A; m = P->m; d = P->d; Gcd = Q->Gcd; Lcm = Q->Lcm; oD = lrs_alloc_mp_vector (d); itomp (ONE, mpone); itomp (ONE, oD[0]); i=row; itomp (ONE, Lcm[i]); /* Lcm of denominators */ itomp (ZERO, Gcd[i]); /* Gcd of numerators */ for (j = hull; j <= d; j++) /* hull data copied to cols 1..d */ { copy( A[i][j],num[j-hull]); copy(oD[j],den[j-hull]); if (!one(oD[j])) lcm (Lcm[i], oD[j]); /* update lcm of denominators */ copy (Temp, A[i][j]); gcd (Gcd[i], Temp); /* update gcd of numerators */ } if (hull) { itomp (ZERO, A[i][0]); /*for hull, we have to append an extra column of zeroes */ if (!one (A[i][1]) || !one (oD[1])) /* all rows must have a one in column one */ Q->polytope = FALSE; } if (!zero (A[i][hull])) /* for H-rep, are zero in column 0 */ Q->homogeneous = FALSE; /* for V-rep, all zero in column 1 */ storesign (Gcd[i], POS); storesign (Lcm[i], POS); if (mp_greater (Gcd[i], mpone) || mp_greater (Lcm[i], mpone)) for (j = 0; j <= d; j++) { exactdivint (A[i][j], Gcd[i], Temp); /*reduce numerators by Gcd */ mulint (Lcm[i], Temp, Temp); /*remove denominators */ exactdivint (Temp, oD[j], A[i][j]); /*reduce by former denominator */ } if ( ineq == EQ ) /* input is linearity */ { Q->linearity[Q->nlinearity]=row; Q->nlinearity++; } /* 2010.4.26 Set Gcd and Lcm for the non-existant rows when nonnegative set */ if(Q->nonnegative && row==m) for(j=1;j<=d;j++) { itomp (ONE, Lcm[m+j]); itomp (ONE, Gcd[m+j]); } lrs_clear_mp_vector (oD,d); lrs_clear_mp(Temp); lrs_clear_mp(mpone); } /* end of lrs_set_row_mp */ void lrs_set_obj(lrs_dic *P, lrs_dat *Q, long num[], long den[], long max) { long i; if (max == MAXIMIZE) Q->maximize=TRUE; else { Q->minimize=TRUE; for(i=0;i<=P->d;i++) num[i]=-num[i]; } lrs_set_row(P,Q,0L,num,den,GE); } void lrs_set_obj_mp(lrs_dic *P, lrs_dat *Q, lrs_mp_vector num, lrs_mp_vector den, long max) { long i; if (max == MAXIMIZE) Q->maximize=TRUE; else { Q->minimize=TRUE; for(i=0;i<=P->d;i++) changesign(num[i]); } lrs_set_row_mp(P,Q,0L,num,den,GE); } long lrs_solve_lp(lrs_dic *P, lrs_dat *Q) /* user callable function to solve lp only */ { lrs_mp_matrix Lin; /* holds input linearities if any are found */ long col; Q->lponly = TRUE; if (!lrs_getfirstbasis (&P, Q, &Lin, FALSE)) return FALSE; if(overflow_detected) return 1; /* There may have been column redundancy */ /* If so the linearity space is obtained and redundant */ /* columns are removed. User can access linearity space */ /* from lrs_mp_matrix Lin dimensions nredundcol x d+1 */ for (col = 0; col < Q->nredundcol; col++) /* print linearity space */ lrs_printoutput (Q, Lin[col]); /* Array Lin[][] holds the coeffs. */ return TRUE; } /* end of lrs_solve_lp */ long dan_selectpivot (lrs_dic * P, lrs_dat * Q, long *r, long *s) /* select pivot indices using dantzig simplex method */ /* largest coefficient with lexicographic rule to avoid cycling */ /* Bohdan Kaluzny's handiwork */ /* returns TRUE if pivot found else FALSE */ /* pivot variables are B[*r] C[*s] in locations Row[*r] Col[*s] */ { long j,k,col; lrs_mp coeff; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *Col = P->Col; long d = P->d; /* printf("\n*dantzig"); */ lrs_alloc_mp (coeff); *r = 0; *s = d; j = 0; k = 0; itomp(0,coeff); /*find positive cost coef */ while (k < d) { if(mp_greater(A[0][Col[k]],coeff)) { j = k; copy(coeff,A[0][Col[j]]); } k++; } if (positive(coeff)) /* pivot column found! */ { *s = j; col = Col[j]; /*find min index ratio */ *r = lrs_ratio (P, Q, col); if (*r != 0) { lrs_clear_mp(coeff); return (TRUE); /* pivot found */ } } lrs_clear_mp(coeff); return (FALSE); } /* end of dan_selectpivot */ long ran_selectpivot (lrs_dic * P, lrs_dat * Q, long *r, long *s) /* select pivot indices using random edge rule */ /* largest coefficient with lexicographic rule to avoid cycling */ /* pivot variables are B[*r] C[*s] in locations Row[*r] Col[*s] */ { long i,j,k,col,t; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *Col = P->Col; long d = P->d; long *perm; perm = (long *) calloc ((d + 1), sizeof (long)); *r = 0; *s = d; k = 0; /* printf("\n*random edge"); */ /* generate random permutation of 0..d-1 */ for (i = 0; i < d; i++) perm[i] = i; for ( i = 0; i < d; i++) { j = rand() % (d-i) + i; t = perm[j]; perm[j] = perm[i]; perm[i] = t; // Swap i and j } if(Q->debug) { printf("\n perm: "); for (i = 0; i < d; i++) printf(" %ld",perm[i]); } /*find first positive cost coef according to perm */ while (k < d && !positive(A[0][Col[perm[k]]])) k++; if ( kA; long *Row = P->Row; long *Col = P->Col; long m, d; lrs_mp b_vector; lrs_alloc_mp (b_vector); m = P->m; d = P->d; i = 0; k = d+1; itomp(0,b_vector); fprintf (lrs_ofp, "\nLP: Phase One: Dual pivot on artificial variable"); /*find most negative b vector */ while (k <= m) { if(mp_greater(b_vector,A[Row[k]][0])) { i = k; copy(b_vector,A[Row[i]][0]); } k++; } if (negative(b_vector)) /* pivot row found! */ { j = 0; /*find a positive entry for in row */ while (j < d && !positive (A[Row[i]][Col[j]])) j++; if (j >= d) { lrs_clear_mp (b_vector); return (FALSE); /* no positive entry */ } pivot (P, Q, i, j); update (P, Q, &i, &j); if(overflow_detected) { if(Q->verbose && !Q->mplrs) lrs_warning(Q,"warning","*overflow phaseone"); return FALSE; } } lrs_clear_mp (b_vector); return (TRUE); } long lrs_set_digits(long dec_digits) { /* convert user specified decimal digits to mp digits */ if (dec_digits > 0) lrs_digits = DEC2DIG (dec_digits); if (lrs_digits > MAX_DIGITS) { fprintf (lrs_ofp, "\nDigits must be at most %ld\nChange MAX_DIGITS and recompile", DIG2DEC (MAX_DIGITS)); fflush(stdout); return (FALSE); } return (TRUE); } long lrs_checkbound(lrs_dic *P, lrs_dat *Q) { /* check bound on objective and return TRUE if exceeded */ if(!Q->bound) return FALSE; if( Q->maximize && comprod(Q->boundn,P->objden,P->objnum,Q->boundd) == 1 ) { if(Q->verbose) { prat(" \nObj value: ",P->objnum,P->objden); fprintf(lrs_ofp," Pruning "); } return TRUE; } if( Q->minimize && comprod(Q->boundn,P->objden,P->objnum,Q->boundd) == -1 ) { if(Q->verbose) { prat(" \nObj value: ",P->objnum,P->objden); fprintf(lrs_ofp," Pruning "); } return TRUE; } return FALSE; } long lrs_leaf(lrs_dic *P, lrs_dat *Q) { /* check if current dictionary is a leaf of reverse search tree */ long col=0; long tmp=0; while (col < P->d && !reverse(P,Q,&tmp,col)) col++; if(col < P->d) return 0; /* dictionary is not a leaf */ else return 1; } /* prevent output flushes in mplrs */ void lrs_open_outputblock(void) { #ifdef MPLRS open_outputblock(); #endif } /* re-enable output flushes in mplrs */ void lrs_close_outputblock(void) { #ifdef MPLRS close_outputblock(); #endif } void lrs_post_output(const char *type, const char *data) { #ifdef MPLRS post_output(type,data); #endif } void lrs_return_unexplored(lrs_dic *P,lrs_dat *Q) /* send cobasis data for unexplored nodes */ { #ifdef MPLRS lrs_restart_dat R; int i; if((Q->mindepth != 0) && (P->depth == Q->maxdepth)) /*2021.5.19 implement maxdepth in mplrs */ return; /*don't send back to job queue! */ for (i = 0; i < P->d; i++) Q->temparray[i] = Q->inequality[P->C[i] - Q->lastdv]; R.facet=Q->temparray; R.d=P->d; R.depth=P->depth; update_R(P,Q,&R); post_R(&R); #else if(Q->debug) { lrs_printcobasis(P,Q,ZERO); fprintf(lrs_ofp," *unexplored"); } #endif } /* replace by user overflow routine if not using lrsv2_main() */ void lrs_overflow(int parm) { #ifdef NASH #ifdef B128 fprintf(lrs_ofp,"\n*arithmetic overflow, suggest lrsnash\n"); #else fprintf(lrs_ofp,"\n*arithmetic overflow, suggest lrsnash2 or lrsnash\n"); #endif lrs_exit(1); #endif overflow_detected=1; } void lrsv2_overflow(char *tmp, lrs_dic *P, lrs_dat *Q) { if(Q->nash) { fprintf(lrs_ofp,"Nash overflow\n"); lrs_exit(1); } #ifdef MPLRS overflow=1; return; /* return to lrsv2_main */ #endif #ifdef MP overflow=1; fprintf (stdout, "\n*lrsmp: overflow at digits=%ld", DIG2DEC (lrs_digits)); fprintf (stdout, "\n*use 'digits n' option with n > %ld\n", DIG2DEC (lrs_digits)); return; #endif int try_restart=FALSE; if (lrs_Q_list[0] == NULL) { fprintf(stderr,"*lrs_overflow has null Q "); lrs_exit(1); } /* db's cunningly hidden locations */ /* now sadly not used */ /* Q = lrs_Q_list[lrs_Q_count-1]; P = Q->Qhead; */ /* lrs, redund,fel restarted at the moment */ #ifdef MA if(!Q->mplrs) try_restart=TRUE; #endif if(lrs_ifp != NULL) fclose(lrs_ifp); if (!try_restart ) /* hard exit */ { fflush(lrs_ofp); fflush(stderr); if (strcmp(BIT,"64bit")==0 ) { fprintf(lrs_ofp,"\n*64bit integer overflow: try running 128bit or gmp versions\n"); if (lrs_ofp != stdout) fprintf(stderr,"\n*64bit integer overflow: try running 128bit or gmp versions\n"); } else { fprintf(stderr,"\n*128bit integer overflow: try running gmp version\n"); if (lrs_ofp != stdout) fprintf(lrs_ofp,"\n*128bit integer overflow: try running gmp version\n"); } return; } /* try to restart */ if(overflow == 0) /* first overflow */ { fflush(lrs_ofp); if (*tmpfilename != '\0' ) /* we made a temporary file for stdin */ { if(remove(tmpfilename) != 0) fprintf (lrs_ofp, "\nCould not delete temporary file"); } #ifdef WIN strncpy(tmpfilename,"lrs_restartXXXXXX",PATH_MAX); #else strncpy(tmpfilename,"/tmp/lrs_restartXXXXXX",PATH_MAX); #endif /* XXX in principle this file descriptor should be used instead of the name */ tmpfd = mkstemp(tmpfilename); } else strcpy(tmpfilename,infilename); overflow=1L; lrs_cache_to_file(tmpfilename," "); if(Q->fel || Q->redund) if(Q->Ain != NULL) lrs_clear_mp_matrix(Q->Ain,Q->m,Q->n); Q->m=P->m; if(tmp != NULL) strcpy(tmp,tmpfilename); if (lrs_ofp != NULL && lrs_ofp != stdout ) { fclose (lrs_ofp); lrs_ofp=NULL; } close(tmpfd); return; } /* lrsv2_overflow */ void lrs_exit(int i) { fflush(stdout); exit(i); } void lrs_free_all_memory(lrs_dic * P, lrs_dat * Q) { if(Q->runs > 0) { free(Q->isave); free(Q->jsave); } if(P != NULL) /* may not have allocated P yet */ { long savem=P->m; /* need this to clear Q*/ lrs_free_dic (P,Q); /* deallocate lrs_dic */ Q->m=savem; } lrs_free_dat (Q); /* deallocate lrs_dat */ #ifdef LRSLONG free(infile); /* we cached input file for possible restart */ #endif return; } long lrs_stdin_to_file(char *filename) { FILE *fptr1, *fptr2; char c; fptr1 = stdin; fptr2 = fopen(filename, "w"); if (fptr2 == NULL) { printf("Cannot open file %s \n", filename); exit(0); } c = fgetc(fptr1); while (c != EOF) { fputc(c, fptr2); c = fgetc(fptr1); } fclose(fptr2); fptr2=NULL; return 0; } long lrs_file_to_cache(FILE *ifp) { long ret; if (ifp != NULL) if (fseek(ifp, 0L, SEEK_END) == 0) { ret = ftell(ifp); if (ret == -1) { fputs("*Error reading file", stderr); return 1; } infileLen = ret; infile = (char *) malloc(sizeof(char) * (infileLen + 1)); if (fseek(ifp, 0L, SEEK_SET) != 0) { fputs("*Error resetting input file", stderr); return 1; } infileLen = fread(infile, sizeof(char), infileLen, ifp); if ( ferror( ifp ) != 0 ) { fputs("*Error reading input file", stderr); return 1; } else infile[infileLen++] = '\0'; /* Just to be safe. */ } rewind(ifp); return 0; } long lrs_cache_to_file(char *name,const char *restart) { FILE *ofp = fopen(name, "wb"); if (ofp == NULL) { printf("*Error opening output file %s",name); return 1; } fwrite(infile, sizeof(char), infileLen, ofp); fclose(ofp); return 0; } void lrs_setup_R(lrs_dic *P, lrs_dat *Q, lrs_restart_dat *R) { int i; R->d = P->d; /* length of R->facets */ R->m = P->m; /* number of input rows*/ Q->startcob = (long int*) CALLOC ((R->d + R->m + 1), sizeof (long)); R->redineq = (long int*) CALLOC ((R->m + 1), sizeof (long)); for(i=0;id;i++) Q->startcob[i]=Q->inequality[i]; for (i=0; i<= R->m; i++) R->redineq[i] = 1; R->redundphase=1; /* will be set =0 if there are linearities */ R->testlin=Q->testlin; if (Q->redund) { R->redund=1; R->lrs=0; for(i=0;inlinearity; i++) Q->redineq[Q->linearity[i]]=2; for (i=0; i<= R->m; i++) R->redineq[i] = Q->redineq[i]; } if (Q->fel) { R->fel=1; R->lrs=0; } if((Q->redund || Q->fel)&& R->rank==1) Q->testlin=1; R->printcobasis=Q->printcobasis; /* mplrs renumbers B# in output */ } /* lrs_setup_R */ lrs_dic *lrs_setup(int argc, char *argv[], lrs_dat **Q, lrs_restart_dat *R) /* allocate lrs_dat Q, lrs_dic P, read in the problem data and make a copy of P */ { lrs_dic *P; /* structure for holding current dictionary and indices */ lrs_ifp = stdin; lrs_ofp = stdout; if ( !lrs_init(lrs_basename(argv[0]))) return NULL; *Q = lrs_alloc_dat ("LRS globals"); /* allocate and init structure for static problem data */ if (*Q == NULL) return NULL; strcpy((*Q)->fname,lrs_basename(argv[0])); if(strcmp("redund",(*Q)->fname)==0) (*Q)->redund=TRUE; if(strcmp("minrep",(*Q)->fname)==0) { (*Q)->redund=TRUE; if(R->rank==0) (*Q)->testlin=TRUE; /* check for hidden linearities performed */ } if(strcmp("fel",(*Q)->fname)==0) (*Q)->fel=TRUE; if((*Q)->mplrs) { /* 2023.11.23 */ if(R->rank == 0 ) { if((*Q)->redund) /* sets up LP for testing hidden linearity */ (*Q)->testlin=1; else /* does a minrep for mplrs/fel */ (*Q)->testlin=R->testlin; } (*Q)->tid=R->rank; (*Q)->messages=R->messages; if((*Q)->redund ) { if(R->rank == 1) (*Q)->redundphase=1; } } if (!lrs_read_dat (*Q, argc, argv)) /* read first part of problem data to get dimensions */ return NULL; /* and problem type: H- or V- input representation */ P = lrs_alloc_dic (*Q); /* allocate and initialize lrs_dic */ if (P == NULL ) return NULL; if (!lrs_read_dic (P, *Q)) /* read remainder of input to setup P and Q */ return NULL; return P; } /* lrs_setup */ lrs_dic *lrs_reset(lrs_dic *P_orig, lrs_dat *Q, lrs_restart_dat *R) { static long long inputmaxd=0; /* hide maxd for restoring when using mplrs */ lrs_dic *P; long i; itomp (ZERO, Q->Nvolume); itomp (ONE, Q->Dvolume); itomp (ZERO, Q->sumdet); if(inputmaxd ==0) inputmaxd=Q->maxdepth; //2023.1.24 if(Q->plrs) P=lrs_alloc_dic (Q); else P=lrs_getdic (Q); Q->Qhead=P_orig; Q->Qtail=P_orig; if( P == P_orig) { if(Q->mplrs) lrs_post_output("warning", "*lrs_reset: copy_dict has dest=src -ignoring copy"); else fprintf(stderr,"*lrs_reset: copy_dict has dest=src -ignoring copy"); } copy_dict (Q,P,P_orig); /* restore original input */ Q->Qhead=P; Q->Qtail=P; /*if overiding, update Q from R */ if (R->lrs && R->overide == 1) { Q->messages=R->messages; /* 2021.5.19 implement maxdepth in mplrs */ /* if(R->maxdepth == -1) Q->maxdepth=MAXD; else */ Q->maxdepth=R->maxdepth; Q->mindepth=R->mindepth; Q->maxcobases=R->maxcobases; if (Q->maxcobases > 0) Q->maxcobases = Q->maxcobases + R->count[2]; if(R->restart==1) { Q->restart=TRUE; if(!Q->lponly) Q->giveoutput=FALSE; /* supress first output */ for(i=0;id;i++) { Q->facet[i+Q->nlinearity]=R->facet[i]; Q->inequality[i]=Q->startcob[i]; } for(i=0;i<5;i++) { Q->count[i]=R->count[i]; Q->startcount[i] = Q->count[i]; /* for mplrs subjob counts */ } } P->depth = R->depth; R->maxdepth=inputmaxd; } Q->tid=R->rank; Q->redundphase=R->redundphase; /* we test for hidden linearities in fel mode */ if(R->redund) { /* this restores original linearities that somehow got lost! */ /* definitely not needed for fel! */ if(!R->fel) for(i=0;inlinearity;i++) { Q->redineq[Q->linearity[i]]=2; R->redineq[Q->linearity[i]]=2; } if(R->rank==1) /* consumer will print output */ { Q->redundphase=1; Q->testlin=0; } /* rebuild linearities after first parallel phase */ if(R->rank > 1 && Q->redundphase) { Q->nlinearity=0; for (i=1; i<= R->m; i++) { if (R->redineq[i] ==2) Q->linearity[Q->nlinearity++]=i; } } } /* if R->redund */ return P; } /* lrs_reset */ void update_R(lrs_dic *P, lrs_dat *Q, lrs_restart_dat *R) { int i; for (i=0;i<=4;i++) R->count[i]=Q->count[i]; R->count[8]=Q->count[8]; R->count[5]=Q->hull; if(Q->hull) R->count[6]=Q->nredundcol-Q->homogeneous; else R->count[6]=Q->nredundcol; R->count[7]=Q->deepest; R->redundphase=Q->redundphase; return; } lrs_dat *copy_Q(lrs_dat *Q) { lrs_dat *Q1; if( (Q1 = lrs_alloc_dat("LRS GLOBALS")) == NULL) { fprintf(lrs_ofp,"\n*Can't allocate memory for Q1"); exit(1); } Q1->m = Q->m; Q1->n = Q->n; Q1->allbases = Q->allbases; Q->bound = Q->bound; Q1->countonly = Q->countonly; Q1->dualdeg = Q->dualdeg; Q1->debug = Q->debug; Q1->deepest = Q->deepest; Q1->fel = Q->fel; Q1->frequency = Q->frequency; Q1->geometric = Q->geometric; Q1->getvolume = Q->getvolume; Q1->homogeneous = Q->homogeneous; Q1->hull = Q->hull; Q1->incidence = Q->incidence; Q1->inputd = Q->inputd; Q1->lponly = Q->lponly; Q1->maxdepth = Q->maxdepth; Q1->maxincidence = Q->maxincidence; Q1->messages = Q->messages; Q1->mindepth = Q->mindepth; Q1->minprunedepth = Q->minprunedepth; Q1->maxoutput = Q->maxoutput; Q1->maxcobases = Q->maxcobases; Q1->mplrs = Q->mplrs; Q1->nredundcol = Q->nredundcol; Q1->nonnegative = Q->nonnegative; Q1->polytope = Q->polytope; Q1->printcobasis = Q->printcobasis; Q1->redund = Q->redund; Q1->runs = Q->runs; Q1->seed = Q->seed; Q1->threads = Q->threads; Q1->triangulation = Q->triangulation; Q1->verbose = Q-> verbose; return Q1; } void copy2_Q(lrs_dat *Q1, lrs_dat *Q) /* fill in the arrays allocated in Q1 from Q */ { int i,m,d; m=Q->m; d=Q->inputd; copy_linearity(Q1,Q); for (i = 0; i <= m; i++) { copy(Q1->Gcd[i],Q->Gcd[i]); copy(Q1->Lcm[i],Q->Lcm[i]); } for(i=0;iinequality[i]=Q->inequality[i]; Q1->facet[i]=Q->facet[i]; Q1->redundcol[i]=Q->redundcol[i]; } } #ifdef LRSLONG #ifdef B128 long lrs2_main(int argc, char *argv[],lrs_dic **P_orig, lrs_dat **Q,long overf,long stage,char *tmp, lrs_restart_dat *R) #else long lrs1_main(int argc, char *argv[],lrs_dic **P_orig, lrs_dat **Q,long overf,long stage,char *tmp, lrs_restart_dat *R) #endif #else long lrsgmp_main(int argc, char *argv[],lrs_dic **P_orig, lrs_dat **Q,long overf,long stage,char *tmp, lrs_restart_dat *R) #endif { return lrsv2_main(argc,argv,P_orig,Q,overf,stage,tmp,R); } long lrs_main(int argc, char *argv[]) /* legacy version, replaced by lrsv2_main but still maintained */ { lrs_dic *P; lrs_dat *Q; lrs_restart_dat *R; char* tmp; /* when overflow occurs a new input file name is returned */ long overfl=0; /* =0 no overflow =1 restart */ /* =2 append restart disabled 2023.12.13 since plrs doesn't use it */ P=NULL; Q=NULL; R=NULL; tmp=NULL; R = lrs_alloc_restart(); if (R == NULL) exit(1); overfl=lrsv2_main(argc,argv,&P,&Q,0,0,tmp,R); /* set up, read input, no run */ if(overfl == -1) /* lrs_setup failed due to bad input file etc. - no cleanup*/ return 0; if(overfl == 0) overfl=lrsv2_main(argc,argv,&P,&Q,0,1,tmp,R); /* standard lrs run - argc, argv, R not used */ lrsv2_main(argc,argv,&P,&Q,0,2,tmp,R); /* free memory and close, does not access argc, argv */ free(R->facet); free(R->redineq); free(R); return 0; } #define Q (*Qin) long lrsv2_main(int argc, char *argv[],lrs_dic **P_orig, lrs_dat **Qin,long overf,long stage,char *tmp, lrs_restart_dat *R) /* compiled independently with all supported arithmetic packages */ /* should be called from one of lrsX_main where X is an arithmetic package */ { lrs_dic *P; long i,n; long verbose; overflow_detected=0; /* reinitialize as per DB suggestion*/ /* initial call: allocate lrs_dat, lrs_dic and set up the problem - no run */ if(stage==0) { /* printf("\n*begin Stage 0 rank=%ld redundphase=%ld testlin=%ld R->redund=%ld R->fel=%ld argv[0]=%s", R->rank,R->redundphase,R->testlin,R->redund,R->fel,argv[0]); */ *P_orig=lrs_setup(argc,argv,&Q,R); if(overflow_detected) goto over; if(*P_orig==NULL) { fprintf(stderr,"\n*lrs_setup failed\n"); return -1; } verbose=Q->verbose; if(Q->debug) fprintf(lrs_ofp,"\n*mid Stage 0 rank=%ld redundphase=%ld testlin=%ld Q->redund=%ld Q->fel=%ld R->redund=%ld R->fel=%ld Q->fname=%s", Q->tid,Q->redundphase,Q->testlin,Q->redund,Q->fel,R->redund,R->fel,Q->fname); lrs_setup_R(*P_orig,Q,R); if(Q->debug) fprintf(lrs_ofp,"\n*end Stage 0 rank=%ld redundphase=%ld testlin=%ld Q->redund=%ld Q->fel=%ld R->redund=%ld R->fel=%ld Q->fname=%s", Q->tid,Q->redundphase,Q->testlin,Q->redund,Q->fel,R->redund,R->fel,Q->fname); return 0; } verbose=Q->verbose; /* main work for lrs/redund/fel runs */ if(stage==1) { if(overflow_detected) goto over; if(R->rank==1 && R->fel==1 && R->redundphase==0) { /*consumer just prints ouput*/ R->fel=0; Q->fel=0; R->redund=1; Q->redund=1; } if(overflow_detected) goto over; if(Q->debug) fprintf(lrs_ofp,"\n*begin Stage 1 rank=%ld Q->redund=%ld Q->fel=%ld R->redund=%ld R->fel=%ld R->redundphase=%ld R->testlin=%ld Q->fname=%s", R->rank,Q->redund,Q->fel,R->redund,R->fel,R->redundphase,R->testlin,Q->fname); if(Q->plrs) P= *P_orig; else P=lrs_reset(*P_orig,Q,R); /* restore P and reset Q from R */ if(Q->mplrs && R->rank==0 && R->fel && Q->testlin) { R->fel=0; R->redund=0; } if(Q->debug) fprintf(lrs_ofp,"\n*Begin Stage 1 rank=%ld Q->redund=%ld Q->fel=%ld R->redund=%ld R->fel=%ld R->redundphase=%ld R->testlin=%ld Q->fname=%s", R->rank,Q->redund,Q->fel,R->redund,R->fel,R->redundphase,R->testlin,Q->fname); n=Q->n; if(overf==2) Q->giveoutput=FALSE; /* suppress first output */ if(R->fel ) { if(Q->debug && Q->mplrs) { fprintf(lrs_ofp,"\n*begin fel Stage=1 R->redund=%ld R->rank=%ld R->redineq:", R->redund, R->rank); for (i=1; i<= R->m; i++) fprintf(lrs_ofp," %ld", R->redineq[i]); } if(Q->vars == NULL) { if(R->rank==0) { Q->messages=TRUE; lrs_warning(Q,"warning","*no project/eliminate option found - removing last column"); } Q->vars = (long int*) CALLOC ((n + 3), sizeof (long)); for (i=0;i<=n+2;i++) Q->vars[i]=1-Q->hull; Q->vars[0]=n-1; Q->vars[n+1]=1; Q->fel=1; } put_linearities_first(Q, P); fel_run(P, Q, R); if(overflow_detected) goto over; if(Q->debug && Q->mplrs) { fprintf(lrs_ofp,"\n*end fel Stage=1 R->redund=%ld R->rank=%ld R->redineq:",R->redund,R->rank); for (i=1; i<= R->m; i++) fprintf(lrs_ofp," %ld", R->redineq[i]); fprintf(lrs_ofp,"\n"); } return 0; } if(R->redund) { for (i=0; i<= R->m; i++) Q->redineq[i] = R->redineq[i]; if(Q->debug) { fprintf(lrs_ofp,"\n*begin Stage 1 redund R->redund=%ld R->rank=%ld Q->redineq:", R->redund, R->rank); for (i=1; i<= R->m; i++) fprintf(lrs_ofp," %ld", Q->redineq[i]); } redund_run(P,Q); if(overflow_detected) goto over; for (i=0; i<= R->m; i++) R->redineq[i] = Q->redineq[i]; /* sometimes we are doing a mplrs/fel run */ R->redundphase=1-Q->hiddenlin; R->testlin=0; if(Q->debug) { fprintf(lrs_ofp,"\n*end Stage 1 redund R->redund=%ld R->rank=%ld R->redundphase=%ld R->redineq:", R->redund, R->rank,R->redundphase); for (i=1; i<= R->m; i++) fprintf(lrs_ofp," %ld", R->redineq[i]); } return 0; } /* if R->redund */ /* we are in lrs mode */ if(Q->debug) fprintf(lrs_ofp,"\n*begin Stage 1 lrs R->redund=%ld R->rank=%ld Q->fname=%s",R->redund,R->rank,Q->fname); if(Q->hull && Q->lponly && !Q->testlin) /*2024.4.20 find optimizing input rows in V-rep */ if(!(Q->mplrs && Q->tid==0)) /* not a mplrs/redund run */ return lrs_check_inequality(P,Q); if(!Q->plrs) /* single thread lrs */ { Q->child=0; lrs_run(P,Q); } else plrs_run(P,Q,R,tmp); if(overflow_detected) goto over; update_R(*P_orig,Q,R); /* update counts for mplrs */ if(Q->testlin) R->count[6]=0; if(Q->debug) fprintf(lrs_ofp,"\n*end Stage 1 lrs R->rank=%ld R->redundphase=%ld \n",R->rank,R->redundphase); return 0; } /* stage 1 */ /* final cleanup */ if(stage == 2 ) { if(!Q->mplrs && verbose && overflow_detected) printf("\n*cleanup after overflow"); Q->Qhead=*P_orig; Q->Qtail=*P_orig; if(overflow==0) lrs_close (Q->fname); lrs_free_all_memory(*P_orig,Q); for(i=0;iQhead != NULL) lrs_free_dic(Q->Qhead,Q); lrs_free_dat(lrs_Q_list[0]); } return overflow; } return 0; over: Q->Qhead=*P_orig; Q->Qtail=*P_orig; lrsv2_overflow(tmp,*P_orig,Q); /* prepare restart */ return 1; } /* lrsv2_main */ #undef Q long plrs_run(lrs_dic *P, lrs_dat *Q, lrs_restart_dat *R, char *tmp) { #ifdef PLRS /*2023.1.9*/ /* multithread plrs but only used for V-H */ lrs_dic *P1; lrs_dat *Q1; long (*c)[10]; /* collect counts from parallel threads */ long i,j,tdeepest=0,fdeepest=0; lrs_mp_vector Nvol,Dvol; long d=Q->inputd; if(Q->threads == 0) Q->threads = (d < omp_get_max_threads()) ? d : omp_get_max_threads(); fprintf(stderr,"\n*starting %ld threads\n",Q->threads); c=calloc(d+1,sizeof(*c)); for(i=1;i<=d;i++) for(j=0;j<=9;j++) c[i][j]=0; Nvol = lrs_alloc_mp_vector(d+1); Dvol = lrs_alloc_mp_vector(d+1); fflush(lrs_ofp); fflush(stdout); Q1=copy_Q(Q); P1=lrs_reset(P,Q1,R); copy2_Q(Q1,Q); Q1->Qhead = P1; Q1->Qtail = P1; Q1->child=0; Q1->plrs=1; /* get children of the root */ i=lrs_run(P1,Q1); lrs_free_dat(Q1); if(i==1) /* failure such as infeasible solution */ return 1; #pragma omp parallel for private(P1,Q1) schedule(dynamic,1) reduction(max:fdeepest,tdeepest) num_threads(Q->threads) for(i=1;i<=d;i++) /* parallel reverse search for each child of root */ { if(!overflow_detected) { int tid = omp_get_thread_num(); #pragma omp critical { Q1=copy_Q(Q); P1=lrs_reset(P,Q1,R); copy2_Q(Q1,Q); } Q1->messages=FALSE; Q1->Qhead = P1; Q1->Qtail = P1; Q1->tid=tid; Q1->child=i; lrs_run(P1,Q1); /* do reverse search */ copy(Nvol[i],Q1->Nvolume); copy(Dvol[i],Q1->Dvolume); for(j=0;j<=7;j++) c[i][j]=Q1->count[j]; c[tid][9]=c[tid][9]+Q1->count[2]-1; /* one extra per child */ fdeepest=Q1->count[8]; tdeepest=Q1->deepest; if(i==1) /* set Q values once only */ { Q->nredundcol=Q1->nredundcol; Q->homogeneous=Q1->homogeneous; } #pragma omp critical { lrs_free_dat(Q1); } } } /* end of parallel for */ if(Q->getvolume) { lrs_mp tN, tD; lrs_alloc_mp(tN); lrs_alloc_mp(tD); itomp(ZERO,Q->Nvolume); itomp(ONE,Q->Dvolume); for(i=1;i<=d;i++) { copy (tN, Q->Nvolume); copy (tD, Q->Dvolume); if(!zero(Dvol[i])) linrat (Nvol[i], Dvol[i], ONE, tN, tD, ONE, Q->Nvolume,Q->Dvolume); } lrs_clear_mp(tN); lrs_clear_mp(tD); } /*2023.1.9*/ if(overflow_detected) { free(c); lrs_clear_mp_vector(Nvol,d+1); lrs_clear_mp_vector(Dvol,d+1); return 0; } for(j=0;j<=7;j++) for(i=1;i<=d;i++) Q->count[j]= Q->count[j] + c[i][j]; Q->count[2]=Q->count[2]-d; /* one basis extra per child */ Q->count[8]=fdeepest; Q->deepest=tdeepest; lrs_clear_mp_vector(Nvol,d+1); lrs_clear_mp_vector(Dvol,d+1); lrs_printtotals(P,Q); if(Q->verbose) { fprintf(lrs_ofp,"*threads=%ld counts:",Q->threads); for(i=0;ithreads;i++) fprintf(lrs_ofp," %ld",c[i][9]); fprintf(lrs_ofp,"\n*children=%ld counts:",d); for(i=1;i<=d;i++) fprintf(lrs_ofp," %ld",c[i][2]-1); if(lrs_ofp != stdout) { printf("\n*threads=%ld counts:",Q->threads); for(i=0;ithreads;i++) printf(" %ld",c[i][9]); printf("\n*children=%ld counts:",d); for(i=1;i<=d;i++) printf(" %ld",c[i][2]-1); printf("\n"); } } free(c); #endif return 0; } /* plrs_run */ void lrs_warning(lrs_dat *Q, char* type, char* ss) { if(Q->messages) { if(Q->mplrs) lrs_post_output(type,ss); else { fprintf (lrs_ofp, "\n%s",ss); if(lrs_ofp != stdout) fprintf (stderr, "\n%s",ss); } } } /*********************************************************************************/ /*2022.1.18 For V-rep with lponly just find optimizing input rows */ /*********************************************************************************/ long lrs_check_inequality(lrs_dic *P, lrs_dat *Q) { lrs_mp_matrix A=P->A; lrs_mp tmp,opt,total; long m, d, i, j, count; lrs_alloc_mp(tmp); lrs_alloc_mp(total); lrs_alloc_mp(opt); itomp(ONE,tmp); /*unnecessary but avoids warning */ fprintf (lrs_ofp, "\n"); m = P->m; d = P->d; itomp(0,opt); if (Q->nonnegative) /* skip basic rows - don't exist! */ m=m-d; for(i=1;i<=m;i++) { itomp(0,total); for (j = 1; j <= d; j++) { mulint(A[0][j],A[i][j],tmp); linint(total,1,tmp,1); if(Q->debug) pmp(" ",A[i][j]); } if(i==1) copy(opt,total); else if(mp_greater(total,opt) ) copy(opt,total); if(Q->debug) { pmp("total",total); pmp("opt",opt); fprintf (lrs_ofp, "\n"); } } fprintf(lrs_ofp,"\n*optimum row(s):"); count=0; for(i=1;i<=m;i++) /* once more to print optima */ { itomp(0,total); for (j = 1; j <= d; j++) { mulint(A[0][j],A[i][j],tmp); linint(total,1,tmp,1); } if(!mp_greater(opt,total) ) { count++; fprintf(lrs_ofp," %ld",i); } } if(Q->minimize) /* lrs only maximizes */ { changesign(opt); prat("\n*min value:",opt,P->det); } else pmp("\n*max value:",opt); fprintf(lrs_ofp," obtained by %ld row(s)",count); fprintf(lrs_ofp,"\n"); lrs_clear_mp(tmp); lrs_clear_mp(opt); return 0; } /************************************************************************************/ /* Tallman Nkgau's functions for Fourier elimination modified by DA */ /************************************************************************************/ void fel_abort(char str[]) { printf("%s\n", str ); fflush(stdout); exit(1); } lrs_dic *makecopy(lrs_dat *Q2,lrs_dic *P, lrs_dat *Q) { lrs_dic *P2; Q2->m = Q->m; Q2->n = Q->n; Q2->nlinearity = 0; if (( P2 = lrs_alloc_dic(Q2)) == NULL) fel_abort("ERROR>Can't allocate dictionary space"); copydicA(P2,P,-1,-1); return P2; } void linear_dep(lrs_dic *P, lrs_dat *Q, long *Dep) { long d; long nlinearity; lrs_mp_matrix A; long i, j, k, row, col,m; d = P->d; nlinearity = Q->nlinearity; A = lrs_alloc_mp_matrix(nlinearity+1, d+2); for(i=0;iA[i][j]); itomp(ZERO, A[i][d+1]); } for(col=1;col<=d;col++) { row = -1; for(i=1;i<=nlinearity;i++) if ((zero(A[i][d+1]))&& !zero(A[i][col])) { row = i; break; } if (row > 0) for(k=1;k<=nlinearity;k++) { if ((zero(A[k][d+1]))&&(!zero(A[k][col])) && (k!=row)) { if (sign(A[k][col])*sign(A[row][col]) < 0) { copy(A[0][0], A[k][col]); copy(A[0][1], A[row][col]); storesign(A[0][0], POS); storesign(A[0][1], POS); for(i=0;i<=d;i++) { mulint(A[0][0], A[row][i], A[0][2]); mulint(A[0][1], A[k][i], A[0][3]); addint(A[0][2], A[0][3], A[k][i]); } } else { copy(A[0][0], A[k][col]); copy(A[0][1], A[row][col]); storesign(A[0][0], NEG); storesign(A[0][1], POS); for(i=0;i<=d;i++) { mulint(A[0][0], A[row][i], A[0][2]); mulint(A[0][1], A[k][i], A[0][3]); addint(A[0][2], A[0][3], A[k][i]); } } itomp(ONE, A[row][d+1]); if(Q->debug) { for(i=1;i<=nlinearity; i++) { for(m=0;m<=d;m++) pmp("", A[i][m]); fprintf(lrs_ofp, "\n"); } fprintf(lrs_ofp, "\n"); } } } } for(row=1,i=0;row<=nlinearity;row++) { for(k=0,i=0;k<=d;k++) if(zero(A[row][k])) i++; if (i==d+1) Dep[row] =1; } lrs_clear_mp_matrix(A,nlinearity+1, d+2); } /********************************************************************************/ /* groups[i] = +1 if A[i][col] > 0, groups[i] = -1 if A[i][col] < 0, */ /* groups[i] = 0 if A[i][col] = 0, groups[m+1] = # of rows with <0 entry */ /* in column 'col', and groups[m+2] = # of rows with > 0 entry in column 'col' */ /********************************************************************************/ void lrs_compute_groups(lrs_dat *Q, lrs_dic *P, long col, long *groups) { long i, row; long m; m = Q->m; for(i=0;i<= m+2; i++) { groups[i] = 0; } for(row = 1; row <= Q->m; row++) { if (sign(P->A[row][col]) < 0) { groups[row] = -1; groups[m+1]++; } else if (zero(P->A[row][col])) { groups[0]++; } else { groups[row] = 1; groups[m+2]++; } } if(Q->debug) printf("\n*signs in col=%ld: - =%ld + =%ld 0 =%ld",col,groups[m+1],groups[m+2],m-groups[m+1]-groups[m+2]); } long lrs_next_col(lrs_dat *Q, lrs_dic *P, long *remove) /* in fel mode determine the next column to eliminate */ /* start with linearities, otherwise min new matrix size*/ { long row,col,plus,minus; long long size=MAXD; long minind=0; long i,j,ind; long n=Q->n; if(Q->debug) { fprintf(lrs_ofp,"\n*in n=%ld nlinearity=%ld remove" ,n,Q->nlinearity); for(i=0;i<=n+1;i++) fprintf(lrs_ofp," %ld",remove[i]); } /* user chose order */ if(remove[n]==0) { ind=0; goto gotcol; } /* try to use linearities */ for(ind=0;indnlinearity && zero(P->A[j][col])) j++; if(j<=Q->nlinearity) goto gotcol; } /* find col minimizing size of new matrix */ for(ind=0;indm; row++) { if (negative(P->A[row][col]) ) minus++; else if (positive(P->A[row][col])) plus++; } if(plus*minus < size) { size=plus*minus; minind=ind; } if(Q->debug) fprintf(lrs_ofp,"\n*col=%ld minind=%ld pm=%ld size=%lld",col,minind,plus*minus,size); } ind=minind; gotcol: col=remove[ind]; for(i=0;i<=remove[n+1];i++) { if(remove[i]>col) remove[i]--; if(i>ind) remove[i-1]=remove[i]; } remove[i]=0; remove[n-1]=remove[n]; /* selection heuristic if any */ remove[n]=remove[n+1]-1; if(Q->debug) { fprintf(lrs_ofp,"\n*out col=%ld n=%ld remove" ,col,n); for(i=0;i<=n;i++) fprintf(lrs_ofp," %ld",remove[i]); fflush(stdout); } return col; } /* lrs_next_col */ /*******************************************************************/ /* Function to copy matrix A from dictionary P to dictionary P1. */ /* The column (variable) with index 'skip' is left out. */ /* Set skip to '-1' if no column is to be left out. */ /* Adapted from function in lrslib.c. */ /*******************************************************************/ void copydicA(lrs_dic *P1, lrs_dic *P, long skip_row, long skip_col) { long i, j; long d, m_A; d = P->d; /* dimension of space of variables */ m_A = P->m_A; if (skip_col > 0) { if (skip_row > 0) { for (i = 0; i < skip_row; i++) { for(j = 0; j < skip_col; j++) copy (P1->A[i][j], P->A[i][j]); for(j = skip_col+1; j <= d; j++) copy (P1->A[i][j-1], P->A[i][j]); } for (i = skip_row+1; i <= m_A; i++) { for(j = 0; j < skip_col; j++) copy (P1->A[i-1][j], P->A[i][j]); for(j = skip_col+1; j <= d; j++) copy (P1->A[i-1][j-1], P->A[i][j]); } } else { for (i = 0; i <= m_A; i++) { for(j = 0; j < skip_col; j++) copy (P1->A[i][j], P->A[i][j]); for(j = skip_col+1; j <= d; j++) copy (P1->A[i][j-1], P->A[i][j]); } } } else /* skip_col <= 0 */ { if (skip_row > 0) { for (i = 0; i < skip_row; i++) for(j = 0; j <= d; j++) copy (P1->A[i][j], P->A[i][j]); for (i = skip_row+1; i <= m_A; i++) for(j = 0; j <= d; j++) copy (P1->A[i-1][j], P->A[i][j]); } else { for (i = 0; i <= m_A; i++) for(j = 0; j <= d; j++) copy (P1->A[i][j], P->A[i][j]); } } } /***************************************************************/ /* copy linearity from iQ to Q */ /***************************************************************/ void copy_linearity(lrs_dat *Q, lrs_dat *iQ) { long nlinearity; long i; long n=iQ->n; nlinearity = iQ->nlinearity; if (nlinearity > 0) { if(Q->linearity==NULL) Q->linearity = CALLOC ((nlinearity +1), sizeof (long)); for(i=0; i < nlinearity; i++) Q->linearity[i] = iQ->linearity[i]; Q->nlinearity = nlinearity; Q->polytope = FALSE; } if(iQ->vars != NULL ) { Q->vars = (long int*) CALLOC ((n + 3), sizeof (long)); for(i=0;i<=n+2;i++) Q->vars[i]=iQ->vars[i]; } } /***************************************************************/ void put_linearities_first(lrs_dat *Q, lrs_dic *P) { long nlinearity; long i, row; lrs_mp Temp; lrs_alloc_mp(Temp); nlinearity = Q->nlinearity; for(row=1; row <= nlinearity; row++) { if (Q->linearity[row-1] != row) { for(i=0;i<=P->d; i++) { copy(Temp, P->A[row][i]); copy(P->A[row][i], P->A[Q->linearity[row-1]][i]); copy(P->A[Q->linearity[row-1]][i], Temp); } copy(Temp, Q->Gcd[row]); copy(Q->Gcd[row], Q->Gcd[Q->linearity[row-1]]); copy(Q->Gcd[Q->linearity[row-1]], Temp); copy(Temp, Q->Lcm[row]); copy(Q->Lcm[row], Q->Lcm[Q->linearity[row-1]]); copy(Q->Lcm[Q->linearity[row-1]], Temp); Q->linearity[row-1] = row; } } lrs_clear_mp(Temp); } /***************************************************************/ /* Function to compute redundancies. redineq[i] = 1 if row i */ /* is redundant. Adapted from function in lrslib.c.*/ /***************************************************************/ long compute_redundancy(long *redineq, lrs_dic *P1, lrs_dat *Q1) { lrs_dic *P; lrs_dat *Q; long ineq; long d, m; long lastdv, index; lrs_mp_matrix Lin; m = P1->m_A; d = P1->d; if( (Q = lrs_alloc_dat("LRS GLOBALS")) == NULL) fel_abort("ERROR>Can't allocate memory for structures"); P=makecopy(Q,P1,Q1); if (lrs_getfirstbasis (&P, Q, &Lin, TRUE)==0 || overflow_detected) return (FALSE); m = P->m_A; d = P->d; lastdv = Q->lastdv; for(index = lastdv +1;index <= m+d; index++) { ineq = Q->inequality[index-lastdv]; /*test for linearity or redundancy */ redineq[ineq] = checkindex(P, Q, index, 0); if(redineq[ineq] == -1) /* indicates strictly redundant */ redineq[ineq]=1; } lrs_free_dic(P,Q); lrs_free_dat(Q); return (TRUE); } /******************************************************************/ /* project out column=col */ /******************************************************************/ long lrs_project_var(lrs_dic **iP, lrs_dat **iQ, long col, long verbose) { lrs_dic *P, *P1; lrs_dat *Q, *Q1; long *tgroups; long j, k, l, row; /* could do with less of these monsters */ lrs_mp Temp, Temp1, Lcm, div1, div2, Temp2, Temp3, Temp4, Temp5; lrs_alloc_mp(Temp); lrs_alloc_mp(Temp1);lrs_alloc_mp(Temp2); lrs_alloc_mp(Temp3); lrs_alloc_mp(Temp4);lrs_alloc_mp(Temp5); lrs_alloc_mp(Lcm); lrs_alloc_mp(div1);lrs_alloc_mp(div2); itomp(ZERO,Temp); itomp(ZERO,Temp1); itomp(ZERO,Temp2); itomp(ZERO,Temp3); itomp(ZERO,Temp4); itomp(ZERO,Temp5); P=(*iP); Q=(*iQ); tgroups = CALLOC ((Q->m+4), sizeof (long)); if (tgroups == NULL) fel_abort("ERROR>Can't allocate memory."); /* compute groupings tgroups[0] = # of rows with '0' in column 'col' */ lrs_compute_groups(Q, P, col, tgroups); /* check for overflow */ if (tgroups[Q->m +1] > 0) if (tgroups[Q->m + 2] > (MAXD/tgroups[Q->m +1])) fel_abort("ERROR>Overflow...too many rows produced."); /* create P1, Q1 */ if( (Q1 = lrs_alloc_dat("LRS GLOBALS")) == NULL) fel_abort("ERROR>Can't allocate memory for structures"); Q1->m = (tgroups[Q->m + 1]*tgroups[Q->m +2]) + tgroups[0]; Q1->n = (Q->n)-1; if(!Q->mplrs ) fprintf(lrs_ofp,"\n*allocating dictionary with %ld rows",Q1->m); if (( P1 = lrs_alloc_dic(Q1)) == NULL) fel_abort("ERROR>Can't allocate dictionary space"); row = 1; for(j = 1; j <= Q->m; j++) { if (tgroups[j] < 0) for(k=1; k <= Q->m; k++) { if (tgroups[k] > 0) { copy(div1, P->A[j][col]); copy(div2, P->A[k][col]); storesign(div1, POS); copy(Lcm, div1); lcm(Lcm, div2); copy(Temp, Lcm); copy(Temp1, div1); divint(Temp, Temp1, Temp2); copy(Temp, Lcm); copy(Temp1, div2); divint(Temp, Temp1, Temp3); for(l=0;l< col; l++) { copy(Temp, P->A[j][l]); copy(Temp1, P->A[k][l]); mulint(Temp,Temp2 ,Temp4); mulint(Temp1,Temp3,Temp5); addint(Temp4, Temp5, P1->A[row][l]); } for(l=col+1;ln; l++) { copy(Temp, P->A[j][l]); copy(Temp1, P->A[k][l]); mulint(Temp,Temp2 ,Temp4); mulint(Temp1,Temp3,Temp5); addint(Temp4, Temp5, P1->A[row][l-1]); } reducearray(P1->A[row], Q1->n); row++; } /* end if (tgroups[k]) */ } /* end for k */ } /* end for j*/ for(j=1;j<=Q->m;j++) { if (tgroups[j]==0) /* just copy row, coefficient was '0' */ { for(l=0;lA[row][l], P->A[j][l]); for(l=col+1;ln;l++) copy(P1->A[row][l-1], P->A[j][l]); reducearray(P1->A[row], Q1->n); row++; } } /* } end else */ lrs_free_dic(P, Q); lrs_free_dat(Q); for(row=1;row<=Q1->m;row++) { l = 0; for(j=1;jn; j++) if (zero(P1->A[row][j])) l++; } free(tgroups); lrs_clear_mp(Temp); lrs_clear_mp(Temp1);lrs_clear_mp(Temp2); lrs_clear_mp(Temp3); lrs_clear_mp(Temp4);lrs_clear_mp(Temp5); lrs_clear_mp(Lcm); lrs_clear_mp(div1);lrs_clear_mp(div2); /* returns system with redundancies */ (*iP) = P1; (*iQ) = Q1; return 0; } /* end lrs_project_var */ /*********************************************************************/ /* This is the main loop of the Fourier Elimination code derived */ /* an earlier code of Tallman Nkgau */ /*********************************************************************/ long fel_run(lrs_dic *P, lrs_dat *Qin, lrs_restart_dat *R) { lrs_dic *P1,*P2,*P3; lrs_dat *Q,*Q1,*Q2; long *redineq; long *remove; long *remainingvars; long i, j, k, l, m, col, row; long eqn; long m_begin; lrs_mp Temp, Temp1, div1; long messages=FALSE; long n = Qin->n; long remaining=n-1; /* for multiple rounds, number of remaining vars */ long debug=Qin->debug; long verbose=Qin->verbose; long nlinearity = Qin->nlinearity; long mplrs=Qin->mplrs; long nremove=Qin->vars[n+1]; long redundphase=Qin->redundphase; long rounds; long min=Qin->m; long nin=Qin->n; if(mplrs && R->rank != 1) /* only get consumer messages */ verbose=FALSE; /* for hull we only strip out the columns then remove redundancies */ if(Qin->hull) { extractcols(P,Qin); lrs_free_dic(P,Qin); return 0; } /* for H-rep we perform Fourier Elimination removing redundancies */ lrs_alloc_mp(Temp); lrs_alloc_mp(Temp1);lrs_alloc_mp(div1); itomp(ZERO,Temp); itomp(ZERO,Temp1); itomp(ZERO,div1); /* save Qin for later calls in mplrs */ /* make working copy in Q */ if( (Q = lrs_alloc_dat("LRS GLOBALS")) == NULL) fel_abort("ERROR>Can't allocate memory for structures"); Q->m=Qin->m; Q->n=Qin->n; Q->fel=TRUE; /* P3 just used to allocate the rest of Q */ if (( P3 = lrs_alloc_dic(Q)) == NULL) fel_abort("ERROR>Can't allocate dictionary space"); remainingvars = (long int*) CALLOC ((n + 3), sizeof (long)); for(i=1;i<=remaining;i++) remainingvars[i] = i; copy_linearity(Q, Qin); remove=Q->vars; rounds=remove[n+1]; if(Q->mplrs) rounds=1; for (i = 0; i < rounds; i++) /* main loop */ { if(i>0) /* after first iteration create redundant row free P from Q->Ain */ { if( (Q1 = lrs_alloc_dat("LRS GLOBALS")) == NULL) fel_abort("ERROR>Can't allocate memory for structures"); redineq=Q->redineq; Q1->m=Q->m-Q->redineq[0]; /* redineq[0]= # redunds last round */ Q1->n=Q->n; Q1->fel=TRUE; if (( P = lrs_alloc_dic(Q1)) == NULL) fel_abort("ERROR>Can't allocate dictionary space"); l=0; for(k=1;k<=Q->m;k++) if(redineq[k] != 1 && redineq[k] != -1) { l++; for(j=0;j<=P->d;j++) copy(P->A[l][j], Q->Ain[k][j]); } lrs_clear_mp_matrix(Q->Ain,min,nin); copy_linearity(Q1, Q); remove=Q1->vars; lrs_free_dat(Q ); Q=Q1; } Q->verbose=verbose; Q->debug=debug; m_begin=Q->m; col=lrs_next_col(Q,P,remove); if(!Q->mplrs) fprintf(lrs_ofp,"\n\n*iteration %ld removing column %ld",i+1,col); eqn= -1; for(l=1; l <= nlinearity; l++) if (!zero(P->A[l][col])) { eqn = l; /* use this linearity row to eliminate col */ break; } if (eqn > 0) { for(l=eqn-1;llinearity[l] = Q->linearity[l+1] -1; nlinearity--; Q->nlinearity = nlinearity; for(j=0;j<=P->d;j++) if ((j!=col) && !zero(P->A[eqn][j])) changesign(P->A[eqn][j]); copy(div1, P->A[eqn][col]); for(k=1;k<=P->m;k++) if (k!=eqn) { for(j=0;j<=P->d;j++) if (j!=col) { if (zero(P->A[k][col])) break; mulint(P->A[k][col], P->A[eqn][j], Temp); mulint(P->A[k][j], div1, Temp1); addint(Temp, Temp1, P->A[k][j]); if (negative(div1)) if (!zero(P->A[k][j])) changesign(P->A[k][j]); } itomp(0L, P->A[k][col]); reducearray(P->A[k], Q->n); } /* for k=1 ... */ /* resize P */ if( (Q1 = lrs_alloc_dat("LRS GLOBALS")) == NULL) fel_abort("ERROR>Can't allocate memory for structures"); Q1->m = Q->m -1; Q1->n = Q->n -1; Q1->fel=TRUE; copy_linearity(Q1, Q); remove=Q1->vars; if (( P1 = lrs_alloc_dic(Q1)) == NULL) fel_abort("ERROR>Can't allocate dictionary space"); copydicA(P1, P, eqn, col); } else /* eqn <= 0 eliminate inequality */ { if( (Q2 = lrs_alloc_dat("LRS GLOBALS")) == NULL) fel_abort("ERROR>Can't allocate memory for structures"); Q2->m = Q->m - Q->nlinearity; Q2->n = Q->n; if (( P2 = lrs_alloc_dic(Q2)) == NULL) fel_abort("ERROR>Can't allocate dictionary space"); for(row=Q->nlinearity+1;row<=Q->m; row++) for(l=0;l<=(Q->n)-1;l++) copy(P2->A[row-Q->nlinearity][l], P->A[row][l]); Q2->m = Q->m - Q->nlinearity; Q2->mplrs=mplrs; Q2->debug=Q->debug; lrs_project_var(&P2, &Q2, col, messages && verbose); if(debug) fprintf(lrs_ofp,"\n*exited lrs_project_var: Q2->m=%ld",Q2->m); if (verbose) felprint(P2,Q2); /* add back linearities getting new P, Q */ if( (Q1 = lrs_alloc_dat("LRS GLOBALS")) == NULL) fel_abort("ERROR>Can't allocate memory for structures"); Q1->m = Q->nlinearity + P2->m_A;; Q1->n = Q->n - 1; copy_linearity(Q1, Q); remove=Q1->vars; if (( P1 = lrs_alloc_dic(Q1)) == NULL) fel_abort("ERROR>Can't allocate dictionary space"); for(row=1;row<=Q->nlinearity; row++) { Q1->redineq[row]=2; for(l=0;lA[row][l], P->A[row][l]); for(l=col+1;l<=(Q->n)-1;l++) copy(P1->A[row][l-1], P->A[row][l]); } for(row=1;row<=P2->m_A; row++) { Q1->redineq[row+Q->nlinearity]=Q2->redineq[row]; for(l=0;l<=(Q1->n)-1;l++) copy(P1->A[row+Q->nlinearity][l], P2->A[row][l]); } lrs_free_dic(P2 , Q2 ); lrs_free_dat(Q2 ); } /* eqn <= 0 eliminate inequality */ if(i==0) { lrs_free_dic(P , Qin ); /* Qin retained for future rounds in mplrs */ lrs_free_dic(P3, Q ); /* P3 only used to allocate Q */ lrs_free_dat(Q); } else { lrs_free_dic(P , Q ); lrs_free_dat(Q); } P=P1; Q=Q1; /*2020.7.16 P,Q contain the new structure incl. redundancies and linearities*/ m=Q->m; R->m=m; Q->redundphase=redundphase; Q->verbose=verbose; if(mplrs && R->rank==0) /* boss does no work */ { lrs_free_dic(P1,Q1); free(R->redineq); R->redineq= (long int*) calloc ((m + 1), sizeof (long)); for(k=0;k<=m;k++) R->redineq[k]=1; for (i = 0; i nlinearity; i++) R->redineq[Q->linearity[i]] = 2L; R->count[6]=Q->nlinearity; if(Q->debug) { fprintf(lrs_ofp,"\n**R->rank=%ld R->redineq:",R->rank); for(k=1;k<=m;k++) fprintf(lrs_ofp," %ld",R->redineq[k]); fprintf(lrs_ofp,"\n"); } break; } /* if mplrs */ if(debug) { fprintf(lrs_ofp," \n*Rankk=%ld Q->m=%ld Q->redineq:\n",R->rank,Q->m); for(k=1;k<=m;k++) fprintf(lrs_ofp," %ld",Q->redineq[k]); fprintf(lrs_ofp,"\n"); } m=Q->m; Q->fel=TRUE; Q->debug=debug; Q->tid= R->rank; if(Q->mplrs) for(k=0;k<=m;k++) Q->redineq[k]=R->redineq[k]; min=Q->m; nin=Q->n; /* for deallocating Q->Ain later */ redund_run(P,Q); if(overflow_detected) /*2023.11.1*/ { if(Q->debug) fprintf(lrs_ofp," \n*overflow in fel"); lrs_free_dic(P,Q); goto cleanup; } if(Q->mplrs) for(k=0;k<=m;k++) R->redineq[k]=Q->redineq[k]; if(debug) if (!mplrs || R->rank == 1) { fprintf(lrs_ofp," \n*after redund rank=%ld:redineq:\n",R->rank); for(k=1;k<=m;k++) fprintf(lrs_ofp," %ld",Q->redineq[k]); fprintf(lrs_ofp,"\n"); } if ((!mplrs || R->rank==1) && verbose ) { fprintf(lrs_ofp, "\n*number of \t number after \t number of \t remaining\tcolumn \n"); fprintf(lrs_ofp, "*inequalties\t removing col\t redundancies\t rows \tremoved \n"); fprintf(lrs_ofp, "*%10ld ", m_begin); fprintf(lrs_ofp, "%10ld ", m); fprintf(lrs_ofp, "%10ld ", Q->redineq[0]); /* # redunds calculated in redund_print */ fprintf(lrs_ofp, "%10ld ", m-Q->redineq[0]); fprintf(lrs_ofp, "%10ld ", col); fprintf(lrs_ofp, "\n---------------------------------------------------------------------\n"); } // 2023.11.15 after first run mplrs loses track of the original vars if(!Q->mplrs) { remaining--; for(j=col;j<=remaining;j++) /*update remaining vars list */ remainingvars[j]= remainingvars[j+1]; if(remaining == 1) fprintf(lrs_ofp,"*original variable remaining:"); else fprintf(lrs_ofp,"*original vars remaining:"); for(j=1;j<=remaining;j++) fprintf(lrs_ofp," %ld",remainingvars[j]); fprintf(lrs_ofp,"\n"); } n=Q->n; if(i < nremove-1 && (!mplrs || R->rank==1)) /*remove option for next round */ { if(remove[n]==0) /* col removal in given order */ { fprintf(lrs_ofp,"eliminate %ld ",remove[n+1]); for (k = 0; k < remove[n+1];k++) fprintf(lrs_ofp," %ld",remove[k]); } else /* col removal in greedy order */ { fprintf(lrs_ofp,"project %ld ",n-nremove+i); for (k = 1; k < n;k++) { j=0; while(jm=Q->m; R->count[6]=Q->nlinearity; if(mplrs) /* mplrs does one round only */ { if(R->rank==1) break; } } /* for i= main loop */ cleanup: fflush(lrs_ofp); if(!Q->mplrs) lrs_clear_mp_matrix(Q->Ain,min,nin); lrs_free_dat(Q); lrs_clear_mp(Temp); lrs_clear_mp(Temp1);lrs_clear_mp(div1); free(remainingvars); return overflow_detected; } /* end of fel_run */ void felprint(lrs_dic *P,lrs_dat *Q) { long row; fprintf(lrs_ofp, "\nH-representation\n"); if (Q->nlinearity > 0) { fprintf(lrs_ofp, "linearity %ld", Q->nlinearity); for(row=0; rownlinearity;row++) fprintf(lrs_ofp, " %ld", Q->linearity[row]); fprintf(lrs_ofp, "\n"); } fprintf(lrs_ofp, "begin\n"); fprintf(lrs_ofp, "%ld %ld %s", Q->m, Q->n, "rational"); for(row=1;row<=Q->m; row++) lrs_printrow("", Q, P->A[row], P->d); fprintf(lrs_ofp, "\nend\n"); } void redundmask(lrs_dat *Q, lrs_restart_dat *R) /* 2023.12.15 obsolete, mplrs does this now */ { long i; long low=1; long s=0; long t=0; long m=Q->m; long hi=Q->m; // long verbose=Q->verbose; long debug=Q->debug; if(R->rank == 0) /*master do no checks */ hi=0; else if(R->rank == 1) /*consumer, check everything */ low=1; else { s=m/(R->size - 2); t=m % (R->size - 2); hi=0; for(i=2;i<=R->rank;i++) { low=hi+1; if(irank,R->size,low,hi); if(debug) { fprintf(lrs_ofp,"\n*R->redineq: "); for(i=1;i<=m;i++) fprintf(lrs_ofp," %ld",R->redineq[i]); } fflush(lrs_ofp); } /* note that mplrs only knows the new m value for the consumer rank=0 */ /* in all other cases we resize R */ if(R->rank != 1) { if(R->redineq != NULL) free(R->redineq); R->redineq= (long int*) calloc ((m + 1), sizeof (long)); for(i=0;i<=Q->m;i++) R->redineq[i]=1; for (i = 0; i nlinearity; i++) R->redineq[Q->linearity[i]] = 2L; } for(i=1;i<=m;i++) if(ihi) Q->redineq[i]=0; else Q->redineq[i]=R->redineq[i]; return; } /* redundmask */ /*****************end of fel routines***************************/ lrslib-073/lrslib.h0000777000175000017500000007073214625766605013043 0ustar avisavis/* lrslib.h (vertex enumeration using lexicographic reverse search) */ #define TITLE "lrslib_" #define VERSION "v.7.3_2024.5.30" #define AUTHOR "*Copyright (C) 1995,2024, David Avis avis@cs.mcgill.ca " /* This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA. */ /*Ver 6.1 major change is new lrsnash driver and library coded by Terje Lensberg */ /*Ver 6.0 major change is mplrs wrapper for multithreading coded by Skip Jordan */ /*Ver 5.0 major change is plrs wrapper for multithreading coded by Gary Roumanis */ /*Ver 4.2* library version */ /******************************************************************************/ /* See http://cgm.cs.mcgill.ca/~avis/C/lrs.html for usage instructions */ /******************************************************************************/ #define lrs_main suf(lrs_main) #define plrs_run suf(plrs_run) #define lrsv2_main suf(lrsv2_main) #define lrs_run suf(lrs_run) #define redund_run suf(redund_run) #define redund_print suf(redund_print) #define remove_artificial suf(remove_artificial) #define lrslong_overflow suf(lrslong_overflow) #define cache_misses suf(cache_misses) #define cache_tries suf(cache_tries) #define checkcobasic suf(checkcobasic) #define checkindex suf(checkindex) #define checkpoint suf(checkpoint) #define checkredund suf(checkredund) #define cleanupA suf(cleanupA) #define compute_redundancy suf(compute_redundancy) #define copy_dict suf(copy_dict) #define copydicA suf(copydicA) #define copy_linearity suf(copy_linearity) #define copy_Q suf(copy_Q) #define copy2_Q suf(copy2_Q) #define dan_selectpivot suf(dan_selectpivot) #define ran_selectpivot suf(ran_selectpivot) #define dict_count suf(dict_count) #define dict_limit suf(dict_limit) #define die_gracefully suf(die_gracefully) #define digits_overflow suf(digits_overflow) #define extractcols suf(extractcols) #define fel_run suf(fel_run) #define felprint suf(felprint) #define fel_abort suf(fel_abort) #define getabasis suf(getabasis) #define getnextoutput suf(getnextoutput) #define infile suf(infile) #define infileLen suf(infileLen) #define infilename suf(infilename) #define ismin suf(ismin) #define lexmin suf(lexmin) #define linear_dep suf(linear_dep) #define lprat suf(lprat) #define lreadrat suf(lreadrat) #define lrs_alloc_dat suf(lrs_alloc_dat) #define lrs_alloc_dic suf(lrs_alloc_dic) #define lrs_cache_to_file suf(lrs_cache_to_file) #define lrs_cfp suf(lrs_cfp) #define lrs_checkbound suf(lrs_checkbound) #define lrs_check_inequality suf(lrs_check_inequality) #define lrs_checkpoint_seconds suf(lrs_checkpoint_seconds) #define lrs_close suf(lrs_close) #define lrs_close_outputblock suf(lrs_close_outputblock) #define lrs_compute_groups suf(lrs_compute_groups) #define lrs_next_col suf(lrs_next_col) #define lrs_degenerate suf(lrs_degenerate) #define lrs_estimate suf(lrs_estimate) #define lrs_exit suf(lrs_exit) #define lrs_project_var suf(lrs_project_var) #define lrs_stdin_to_file suf(lrs_stdin_to_file) #define lrs_file_to_cache suf(lrs_file_to_cache) #define lrs_free_all_memory suf(lrs_free_all_memory) #define lrs_free_dat suf(lrs_free_dat) #define lrs_free_dic suf(lrs_free_dic) #define lrs_free_dic2 suf(lrs_free_dic2) #define lrs_getdic suf(lrs_getdic) #define lrs_getfirstbasis suf(lrs_getfirstbasis) #define lrs_getinput suf(lrs_getinput) #define lrs_getnextbasis suf(lrs_getnextbasis) #define lrs_getray suf(lrs_getray) #define lrs_getsolution suf(lrs_getsolution) #define lrs_getvertex suf(lrs_getvertex) #define lrs_global_count suf(lrs_global_count) #define lrs_global_list suf(lrs_global_list) #define lrs_init suf(lrs_init) #define lrs_setup suf(lrs_setup) #define lrs_setup_R suf(lrs_setup_R) #define lrs_reset suf(lrs_reset) #define lrs_leaf suf(lrs_leaf) #define lrs_lpoutput suf(lrs_lpoutput) #define lrs_open_outputblock suf(lrs_open_outputblock) #define lrs_post_output suf(lrs_post_output) #define lrs_printcobasis suf(lrs_printcobasis) #define lrs_print_header suf(lrs_print_header) #define lrs_printoutput suf(lrs_printoutput) #define lrs_printrow suf(lrs_printrow) #define lrs_printtotals suf(lrs_printtotals) #define lrs_ratio suf(lrs_ratio) #define lrs_read_dat suf(lrs_read_dat) #define lrs_read_dic suf(lrs_read_dic) #define lrs_return_unexplored suf(lrs_return_unexplored) #define lrs_set_digits suf(lrs_set_digits) #define lrs_set_obj suf(lrs_set_obj) #define lrs_set_obj_mp suf(lrs_set_obj_mp) #define lrs_set_row suf(lrs_set_row) #define lrs_set_row_mp suf(lrs_set_row_mp) #define lrs_solvelp suf(lrs_solvelp) #define lrs_solve_lp suf(lrs_solve_lp) #define lrs_warning suf(lrs_warning) #define lrsv2_overflow suf(lrsv2_overflow) #define makecopy suf(makecopy) #define makdedat suf(makedat) #define outfilename suf(outfilename) #define overflow suf(overflow) #define pivoting suf(pivoting) #define phaseone suf(phaseone) #define pimat suf(pimat) #define pivot suf(pivot) #define primalfeasible suf(primalfeasible) #define printA suf(printA) #define print_basis suf(print_basis) #define prawA suf(prawA) #define put_linearities_first suf(put_linearities_first) #define readfacets suf(readfacets) #define readvars suf(readvars) #define readlinearity suf(readlinearity) #define readredund suf(readredund) #define removecobasicindex suf(removecobasicindex) #define redundmask suf(redundmask) #define linextractcols suf(linextractcols) #define reorder suf(reorder) #define reorder1 suf(reorder1) #define rescaledet suf(rescaledet) #define rescalevolume suf(rescalevolume) #define resize suf(resize) #define restartpivots suf(restartpivots) #define reverse suf(reverse) #define save_basis suf(save_basis) #define selectpivot suf(selectpivot) #define timecheck suf(timecheck) #define tmpfilename suf(tmpfilename) #define update suf(update) #define updatevolume suf(updatevolume) #define update_R suf(update_R) #ifdef LRSLONG #define ARITH "lrslong.h" /* lrs long integer arithmetic package */ #else #if defined(GMP) || defined(FLINT) #define ARITH "lrsgmp.h" /* lrs wrapper for gmp multiple precsion arithmetic */ #else #define ARITH "lrsmp.h" /* lrs multiple precsion arithmetic */ #endif #endif #include ARITH #ifndef SIGNALS #include #include #define errcheck(s,e) if ((long)(e)==-1L){ perror(s);exit(1);} #endif #define CALLOC(n,s) xcalloc(n,s,__LINE__,__FILE__) /*********************/ /*global constants */ /*********************/ #define MAX_LRS_Q 10000L /* number of allocated dictionaries */ #define MAX_ROWS 100000000L /* maximum number of rows in dictionary */ #define MAXIMIZE 1L /* maximize the lp */ #define MINIMIZE 0L /* maximize the lp */ #define GE 1L /* constraint is >= */ #define EQ 0L /* constraint is linearity */ /*************/ /* typedefs */ /*************/ /******************************************************************************/ /* Indexing after initialization */ /* Basis Cobasis */ /* --------------------------------------- ----------------------------- */ /* | i |0|1| .... |lastdv|lastdv+1|...|m| | j | 0 | 1 | ... |d-1| d | */ /* |-----|+|+|++++++|++++++|--------|---|-| |----|---|---|-----|---|+++++| */ /* |B[i] |0|1| .... |lastdv|lastdv+1|...|m| |C[j]|m+1|m+2| ... |m+d|m+d+1| */ /* -----|+|+|++++++|++++++|????????|???|?| ----|???|???|-----|???|+++++| */ /* */ /* Row[i] is row location for B[i] Col[j] is column location for C[j] */ /* ----------------------------- ----------------------------- */ /* | i |0|1| ..........|m-1|m| | j | 0 | 1 | ... |d-1| d | */ /* |-------|+|-|-----------|---|-| |------|---|---|--- |---|++++| */ /* |Row[i] |0|1|...........|m-1|m| |Col[j]| 1 | 2 | ... | d | 0 | */ /* --------|+|*|***********|***|*| ------|***|***|*****|***|++++| */ /* */ /* + = remains invariant * = indices may be permuted ? = swapped by pivot */ /* */ /* m = number of input rows n= number of input columns */ /* input dimension inputd = n-1 (H-rep) or n (V-rep) */ /* lastdv = inputd-nredundcol (each redundant column removes a dec. var) */ /* working dimension d=lastdv-nlinearity (an input linearity removes a slack) */ /* obj function in row 0, index 0=B[0] col 0 has index m+d+1=C[d] */ /* H-rep: b-vector in col 0, A matrix in columns 1..n-1 */ /* V-rep: col 0 all zero, b-vector in col 1, A matrix in columns 1..n */ /******************************************************************************/ typedef struct lrs_dic_struct /* dynamic dictionary data */ { lrs_mp_matrix A; long m; /* A has m+1 rows, row 0 is cost row */ long m_A; /* =m or m-d if nonnegative flag set */ long d; /* A has d+1 columns, col 0 is b-vector */ long d_orig; /* value of d as A was allocated (E.G.) */ long lexflag; /* true if lexmin basis for this vertex */ long depth; /* depth of basis/vertex in reverse search tree */ long i, j; /* last pivot row and column pivot indices */ lrs_mp det; /* current determinant of basis */ lrs_mp objnum; /* objective numerator value */ lrs_mp objden; /* objective denominator value */ long *B, *Row; /* basis, row location indices */ long *C, *Col; /* cobasis, column location indices */ struct lrs_dic_struct *prev, *next; } lrs_dic; typedef struct lrs_dat /* global problem data */ { long *redineq; /* holds indices of rows for redundancy check */ lrs_mp_matrix Ain; /* used only in redund to hold input matrix */ lrs_mp_vector Gcd; /* Gcd of each row of numerators */ lrs_mp_vector Lcm; /* Lcm for each row of input denominators */ lrs_mp_vector output; /* One line of output dimensioned to n */ lrs_mp sumdet; /* sum of determinants */ lrs_mp Nvolume; /* volume numerator */ lrs_mp Dvolume; /* volume denominator */ lrs_mp boundn; /* objective bound numerator */ lrs_mp boundd; /* objective bound denominator */ long unbounded; /* lp unbounded */ char fname[4096]; /* program name: lrs redund fel nash */ char *projmess; /* holds project/eliminate input string */ /* initially holds order used to find starting */ /* basis, default: m,m-1,...,2,1 */ long *facet; /* cobasic indices for restart if needed */ long *redundcol; /* holds columns which are redundant */ long *inequality; /* indices of inequalities corr. to cobasic ind */ long *linearity; /* holds cobasic indices of input linearities */ long *vars; /* ordered list of vars for extract,project etc */ long *startcob; /* starting cobasis if given else zeroes */ long *minratio; /* used for lexicographic ratio test */ long *temparray; /* for sorting indices, dimensioned to d */ long *isave, *jsave; /* arrays for estimator, malloc'ed at start */ long inputd; /* input dimension: n-1 for H-rep, n for V-rep */ long m; /* number of rows in input file */ long n; /* number of columns in input file */ long lastdv; /* index of last dec. variable after preproc */ /* given by inputd-nredundcol */ long count[10]; /* count[0]=rays(facets)[1]=vertices(linearities)*/ /* [2]=cobases [3]=pivots [4]=integer vertices */ /* [5-7]=mplrs R [8]=max vertex/facet depth */ long startcount[5]; long deepest; /* max depth ever reached in search */ long nredundcol; /* number of redundant columns */ long nlinearity; /* number of input linearities */ long totalnodes; /* count total number of tree nodes evaluated */ long runs; /* probes for estimate function */ long seed; /* seed for random number generator */ double cest[10]; /* ests: 0=rays,1=vert,2=bases,3=vol,4=int vert */ long nextineq; /* start checking redundancy from this row:def=1*/ /**** flags ********** */ long allbases; /* TRUE if all bases should be printed */ long bound; /* TRUE if upper/lower bound on objective given */ long countonly; /* TRUE if only count totals should be output */ long debug; long dualdeg; /* TRUE if start dictionary is dual degenerate */ long etrace; /* turn off debug at basis # strace */ long extract; /* remove linearities if any and extractcols */ long frequency; /* frequency to print cobasis indices */ long geometric; /* TRUE if incident vertex prints after each ray */ long getvolume; /* do volume calculation */ long givenstart; /* TRUE if a starting cobasis is given */ long giveoutput; /* TRUE if output should be printed,used for supressing restart first output */ long redundphase; /* TRUE if mplrs consumer skips verifying output */ long hiddenlin; /* TRUE if hidden linearities exist */ long homogeneous; /* TRUE if all entries in column one are zero */ long hull; /* do convex hull computation if TRUE */ long incidence; /* print all tight inequalities (vertices/rays) */ long lponly; /* true if only lp solution wanted */ long long maxdepth; /* max depth to search to in treee */ long maximize; /* flag for LP maximization */ long maxoutput; /* if positive, maximum number of output lines */ long maxcobases; /* if positive, after maxcobasis unexplored subtrees reported */ long messages; /* TRUE for normal lrs output, FALSE for MPLRS and LRS_QUIET */ long minimize; /* flag for LP minimization */ long nincidence; /* number of incidences current basis */ long long maxincidence; /* prune if incidence >= maxincidence and... */ long long minprunedepth;/* ... depth >= minprunedepth */ long long mindepth; /* do not backtrack above mindepth */ long fel; /* TRUE if doing fourier elimination */ long mplrs; /* TRUE if compiled for mplrs */ long plrs; /* TRUE if compiled for plrs */ long nash; /* TRUE for computing nash equilibria */ long nonnegative; /* TRUE if last d constraints are nonnegativity */ long polytope; /* TRUE for facet computation of a polytope */ long printcobasis; /* TRUE if all cobasis should be printed */ long printslack; /* TRUE if indices of slack inequal. printed */ long redund; /* TRUE for computing nash equilibria */ long truncate; /* TRUE: truncate tree when moving from opt vert*/ long verbose; /* FALSE for minimalist output */ long restart; /* TRUE if restarting from some cobasis */ long strace; /* turn on debug at basis # strace */ long voronoi; /* compute voronoi vertices by transformation */ long long subtreesize; /* in estimate mode, iterates if cob_est >= subtreesize */ long testine; /* redund mode: find redundant inequalities */ long testlin; /* redund mode: find lin ind set of linearities */ long triangulation; /* TRUE: the cobases printed triangulate the polytope */ long newstart; /* TRUE: lrs is restarted with new arithmetic */ long fullredund; /* TRUE: all rows checked in a minrep/redund run */ /* variables for multithreading lrs */ long tid; /* thread index = 0 for single core */ long child; long threads; /* Variables for saving/restoring cobasis, db */ long id; /* numbered sequentially */ char *name; /* passed by user */ long saved_count[5]; /* Saves Q->count[*] */ long *saved_C; lrs_mp saved_det; lrs_mp saved_sumdet; long saved_depth; long saved_d; long saved_flag; /* There is something in the saved cobasis */ /* Variables for cacheing dictionaries, db */ lrs_dic *Qhead, *Qtail, *olddic; }lrs_dat, lrs_dat_p; /***************************/ /* mplrs hooks and hacks */ /***************************/ void lrs_open_outputblock(void); /* prevent mplrs output flushes */ void lrs_close_outputblock(void);/* re-enable mplrs output flushes */ void lrs_return_unexplored(lrs_dic *P,lrs_dat *Q); /* send cobasis data for unexplored nodes */ void lrs_post_output(const char *, const char *); /* lrs call to post_output */ /****************/ /* MPLRS */ /****************/ /* following provided by mplrs.c */ void post_output(const char *, const char *); void post_R(lrs_restart_dat *R); void open_outputblock(void); void close_outputblock(void); void mplrs_cleanstop(int checkpoint); void mplrs_emergencystop(const char *); /*******************************/ /* functions for external use */ /*******************************/ long lrsv2_main(int argc, char *argv[],lrs_dic **P,lrs_dat **Q, long overf,long stage,char *tmp,lrs_restart_dat *R); /* called from lrsX_main where X is arithmetic type */ long plrs_run(lrs_dic *P, lrs_dat *Q, lrs_restart_dat *R,char *tmp); /* parallel plrs loop inside lrsrv2_main */ long lrs_run ( lrs_dic *P, lrs_dat * Q); /* main reverse search function */ long redund_run ( lrs_dic *P, lrs_dat * Q); /* main redund loop */ void redund_print(lrs_dic *P,lrs_dat *Q); void remove_artificial(lrs_dic *P,lrs_dat *Q); /* used in minrep */ lrs_dat *lrs_alloc_dat (const char *name); /* allocate for lrs_dat structure "name" */ lrs_dic *lrs_alloc_dic (lrs_dat * Q); /* allocate for lrs_dic structure corr. to Q */ long lrs_estimate (lrs_dic * P, lrs_dat * Q); /* get estimates only and returns est number of cobases in subtree */ long lrs_read_dat (lrs_dat * Q, int argc, char *argv[]); /* read header and set up lrs_dat */ long lrs_read_dic (lrs_dic * P, lrs_dat * Q); /* read input and set up problem and lrs_dic */ long lrs_checkbound (lrs_dic *P, lrs_dat * Q); /* TRUE if current objective value exceeds specified bound */ long lrs_check_inequality (lrs_dic *P, lrs_dat * Q); /* max/min option used for V-rep testing */ long lrs_getfirstbasis (lrs_dic ** P_p, lrs_dat * Q, lrs_mp_matrix * Lin,long no_output); /* gets first basis, FALSE if none,P may get changed if lin. space Lin found no_output is TRUE supresses output headers P may get changed if lin. space Lin found */ void lrs_getinput(lrs_dic *P,lrs_dat *Q,long *num,long *den, long m, long d); /* reads input matrix b A in lrs/cdd format */ long lrs_getnextbasis (lrs_dic ** dict_p, lrs_dat * Q, long prune); /* gets next lrs tree basis, FALSE if none backtrack if prune is TRUE */ long lrs_getsolution (lrs_dic * P, lrs_dat * Q, lrs_mp_vector output, long col); long lrs_getray (lrs_dic * P, lrs_dat * Q, long col, long comment, lrs_mp_vector output); long lrs_getvertex (lrs_dic * P, lrs_dat * Q, lrs_mp_vector output); void lrs_close (const char *name); /* close lrs lib program "name" */ long lrs_init (const char *name); /* initialize lrslib and arithmetic package for prog "name" */ lrs_dic *lrs_setup(int argc, char *argv[], lrs_dat **Q, lrs_restart_dat *R); /* intialize P,P_orig,Q and read data */ lrs_dic *lrs_reset(lrs_dic *P_orig, lrs_dat *Q, lrs_restart_dat *R); /* restore P form P_orig reset Q using R */ void lrs_lpoutput(lrs_dic * P,lrs_dat * Q, lrs_mp_vector output); /* print LP primal and dual solutions */ void lrs_printcobasis (lrs_dic * P, lrs_dat * Q, long col); /* print cobasis for column col(verted or ray) */ void lrs_print_header(const char *name); void lrs_printoutput (lrs_dat * Q, lrs_mp_vector output); /* print output array */ void lrs_printrow (const char *name, lrs_dat * Q, lrs_mp_vector output, long rowd); /*print row of A matrix in output[0..rowd] */ void lrs_printsol (lrs_dic * P, lrs_dat * Q, long col, long comment); /* print out solution from col, comment= 0=normal,-1=geometric ray,1..inputd=linearity */ void lrs_printtotals (lrs_dic * P, lrs_dat * Q);/* print final totals for lrs */ long lrs_set_digits (long dec_digits ); /* set lrsmp digits to equiv. of decimal dec_digits */ void lrs_setup_R (lrs_dic * P, lrs_dat * Q, lrs_restart_dat * R); long lrs_solvelp (lrs_dic * P, lrs_dat * Q, long maximize);/* solve primal feas LP:TRUE bounded else FALSE */ void lrs_warning(lrs_dat *Q, char* type, char* ss); /* warnings sent to printer or mplrs */ long lrs_stdin_to_file (char *name); long lrs_file_to_cache(FILE *ifp); long lrs_cache_to_file(char *name, const char *args); /*******************************/ /* functions for internal use */ /*******************************/ /*******************************/ /* basic dictionary functions */ /*******************************/ long getabasis (lrs_dic * P, lrs_dat * Q, long order[]); /* Try to find a starting basis */ void getnextoutput (lrs_dic * P, lrs_dat * Q, long i, long col, lrs_mp out); /* get A[B[i][col] and copy to out */ long ismin (lrs_dic * P, lrs_dat * Q, long r, long s); /* test if A[r][s] is a min ratio for col s */ long lexmin (lrs_dic * P, lrs_dat * Q, long col); /* test A to see if current basis is lexmin */ void pivot (lrs_dic * P, lrs_dat * Q, long bas, long cob); /* Qpivot routine for array A */ long primalfeasible (lrs_dic * P, lrs_dat * Q); /* Do dual pivots to get primal feasibility */ long lrs_ratio (lrs_dic * P, lrs_dat * Q, long col); /* find lex min. ratio */ long removecobasicindex (lrs_dic * P, lrs_dat * Q, long k); /* remove C[k] from problem */ long linextractcols (lrs_dic * P, lrs_dat * Q); /* preprocess to remove input linearities */ long restartpivots (lrs_dic * P, lrs_dat * Q); /* restart problem from given cobasis */ long reverse (lrs_dic * P, lrs_dat * Q, long *r, long s); /* TRUE if B[*r] C[s] is a reverse lex-pos pivot */ long selectpivot (lrs_dic * P, lrs_dat * Q, long *r, long *s); /* select pivot indices using lexicographic rule */ long dan_selectpivot (lrs_dic * P, lrs_dat * Q, long *r, long *s); /* select pivot indices using dantzig-lex rule */ long ran_selectpivot (lrs_dic * P, lrs_dat * Q, long *r, long *s); /* select pivot indices using randomedge-lex rule */ void update (lrs_dic * P, lrs_dat * Q, long *i, long *j); /* update the B,C, LOC arrays after a pivot */ void updatevolume (lrs_dic * P, lrs_dat * Q); /* rescale determinant and update the volume */ /*******************************/ /* other functions using P,Q */ /*******************************/ long lrs_degenerate (lrs_dic * P, lrs_dat * Q); /* TRUE if the dictionary is primal degenerate */ long extractcols (lrs_dic * P, lrs_dat * Q); /* preprocess to just extract given cols */ void print_basis (FILE * fp, lrs_dat * Q); void printA (lrs_dic * P, lrs_dat * Q); /* print of dictionary, bases for debugging */ void prawA (lrs_dic * P, lrs_dat * Q); /* raw print of dictionary, bases for debugging */ void pimat (lrs_dic * P, long r, long s, lrs_mp Nt, const char *name); /* print the row r col s of A */ long readfacets (lrs_dat * Q, long facet[]); /* read and check facet list */ long readlinearity (lrs_dat * Q); /* read and check linearity list */ long readvars (lrs_dat * Q, char *name); /* read and check var list for extract or project */ long readredund (lrs_dat * Q); /* read and check redundancy list */ void rescaledet (lrs_dic * P, lrs_dat * Q, lrs_mp Vnum, lrs_mp Vden); /* rescale determinant to get its volume */ void rescalevolume (lrs_dic * P, lrs_dat * Q, lrs_mp Vnum, lrs_mp Vden); /* adjust volume for dimension */ long lrs_leaf(lrs_dic *P, lrs_dat *Q); /* true if current dictionary is leaf of reverse search tree */ void update_R(lrs_dic *P, lrs_dat *Q, lrs_restart_dat *R); void lrsv2_overflow(char *tmp,lrs_dic *P,lrs_dat *Q); /***************************************************/ /* Routines for redundancy checking */ /***************************************************/ long checkredund (lrs_dic * P, lrs_dat * Q);/* solve primal lp to check redund of obj fun. returns TRUE if redundant, else FALSE */ long checkcobasic (lrs_dic * P, lrs_dat * Q, long index); /* TRUE if index is cobasic and nondegenerate FALSE if basic, or degen. cobasic, where it will get pivoted out */ long checkindex (lrs_dic * P, lrs_dat * Q, long index, long phase); /* index=0 non-red.,1 red., 2 input linearity NOTE: row is returned all zero if redundant!! */ void cleanupA(lrs_dic * P, lrs_dat * Q);/* zero out duplicate rows from A*/ /***************************************************/ /* Routines for caching and restoring dictionaries */ /***************************************************/ void lrs_free_dic ( lrs_dic *P, lrs_dat *Q); void lrs_free_dic2 ( lrs_dic *P, lrs_dat *Q); /* same as lrs_free_dic but no cache*/ void lrs_free_dat ( lrs_dat *Q); void copy_dict (lrs_dat * global, lrs_dic * dest, lrs_dic * src); lrs_dat *copy_Q( lrs_dat *Q); /* allocate and return a copy of Q */ void copy2_Q(lrs_dat *Q1, lrs_dat *Q); /* copy arrays from Q to Q1 */ lrs_dic *alloc_memory (lrs_dat * Q); lrs_dic * lrs_getdic(lrs_dat *Q); lrs_dic *resize (lrs_dic * P, lrs_dat * Q); void lrs_free_all_memory(lrs_dic * P, lrs_dat * Q); /*******************************/ /* utilities */ /*******************************/ void lprat (const char *name, long Num, long Den); /* Print Num/Den without reducing */ long lreadrat (long *Num, long *Den); /* read a rational string and convert to long integers */ void reorder (long a[], long range); /* reorder array in increasing order with one misplaced element */ void reorder1 (long a[], long b[], long newone, long range); /* reorder array a in increasing order with misplaced element newone elements of b go along for the ride */ /***************************/ /* lp_solve like functions */ /***************************/ long lrs_solve_lp(lrs_dic *P, lrs_dat *Q);/* solve lp only for given dictionary */ void lrs_set_row(lrs_dic *P, lrs_dat *Q, long row, long num[], long den[], long ineq);/* load row i of dictionary from num[]/den[] ineq=GE */ void lrs_set_row_mp(lrs_dic *P, lrs_dat *Q, long row, lrs_mp_vector num, lrs_mp_vector den, long ineq);/* same as lrs_set_row except num/den is lrs_mp type */ void lrs_set_obj(lrs_dic *P, lrs_dat *Q, long num[], long den[], long max); /* set up objective function with coeffs num[]/den[] max=MAXIMIZE or MINIMIZE */ void lrs_set_obj_mp(lrs_dic *P, lrs_dat *Q, lrs_mp_vector num, lrs_mp_vector den, long max);/* same as lrs_set_obj but num/den has lrs_mp type */ /***************************/ /* functions for fel */ /***************************/ void copydicA(lrs_dic *P1, lrs_dic *P, long skip_row, long skip_col); void copy_linearity(lrs_dat *Q, lrs_dat *iQ); long fel_run(lrs_dic *iP, lrs_dat *iQ, lrs_restart_dat *R); void felprint(lrs_dic *P2, lrs_dat *Q2); void fel_abort(char str[]); void linear_dep(lrs_dic *P, lrs_dat *Q, long *Dep); void lrs_compute_groups(lrs_dat *Q, lrs_dic *P, long col, long *groups); long lrs_next_col(lrs_dat *Q, lrs_dic *P, long *remove); long lrs_project_var(lrs_dic **iP, lrs_dat **iQ, long col, long stat); long compute_redundancy(long *redineq, lrs_dic *P, lrs_dat *Q); void put_linearities_first(lrs_dat *Q, lrs_dic *P); lrs_dat *makedat(long n); lrs_dic *makecopy(lrs_dat *Q2,lrs_dic *P, lrs_dat *Q); void redundmask(lrs_dat *Q, lrs_restart_dat *R); /**************************************************************************/ lrslib-073/lrsnash.c0000777000175000017500000002230514625766602013207 0ustar avisavis/*********************************************************/ /* lrsnash is driver for computing all nash equilibria */ /* for two person games given by mxn payoff matrices A,B */ /* Usage: lrsnash [options] game [output file] */ /* */ /* game is a file containing: */ /* m n */ /* A (row by row) */ /* B (row by row) */ /* */ /* Derived from nash.c in lrslib-060 by */ /* Terje Lensberg, October 26, 2015: */ /* Simplified API via lrs_solve_nash(game *g) */ /*********************************************************/ /* Compile: gcc -O3 -o lrsnash lrsnash.c lrsnashlib.c lrslib.c lrsgmp.c -lgmp -DGMP */ char Usage[] = "usage (standard): %s [options...] \n" "usage (legacy): %s []\n" "type %s -h for more information\n\n"; char Helptext[] = "\nusage (standard): %s [options...] \n" " Input file structure: Input files to setupnash\n" " Input files can be specified separately, or by using wildcards, as in 'game*'\n" " Options:\n" " -v, --verbose Prints a trace of the solution process\n" " -d, --debug Dumps lots of information for debugging\n" " -p, --printgame Prints the payoff matrix for the game\n" " -s, --standard Promise that input files have standard structure\n" " -o, --outfile Send output to \n" " -h, --help Prints this text\n" " Short options can be grouped, as in '-ps' and '-do out.txt'\n" "usage (legacy): %s []\n" " Input file structure: Output files from setupnash\n" " Passing options with legacy input files produces an error\n" " (options must be specified in the input files)\n\n"; char LegacyMsg[] = "\nProcessing legacy input files. Alternatively, you may skip\n" "setupnash and pass its input file to this program.\n"; #include #include #include #include #include #include #include "lrsdriver.h" #include "lrslib.h" #include "lrsnashlib.h" //======================================================================== // Games //======================================================================== //----------------------------------------------------------------------------------------// // Reading games //----------------------------------------------------------------------------------------// char *Outfile = NULL; #ifdef LRSLONG #ifdef B128 char *name="*lrsnash2"; #else char *name="*lrsnash1"; #endif #else char *name="*lrsnash"; #endif //----------------------------------------------------------------------------------------// int openIO(void) { if (!lrs_init(name)) return FALSE; fprintf(stderr, "\n"); if(Outfile != NULL) { if ((lrs_ofp = fopen(Outfile, "w")) == NULL) { fprintf(stderr, "\nBad output file name\n"); return FALSE; } } return TRUE; } void closeIO(void) { if(lrs_ofp != stdout) fprintf(stdout, "\n"); lrs_close("lrsnash:"); } #define RECWARN(filename) fprintf(stderr, "\nWarning: Excess data in file %s.\n", filename); #define ERREXIT if(lrs_ofp != NULL) closeIO(); exit(1); #define FILEERROR(name) {fprintf(stderr, "\nError: Cannot find input file '%s'. \ Execution halted\n", name); ERREXIT} #define READERROR(name) {fprintf(stderr, "\nError: Premature end of input file '%s'. \ Execution halted\n", name); ERREXIT} void allocateGameStorage(game *g, const char *infile) { int i, pos; struct stat st; /* Get size of input file and use it to allocate storage for payoff strings. */ /* This provides enough space for adding string terminators ('\0'), because */ /* there is at least one whitespace character for every payoff number. */ stat(infile, &st); g->pstore = (char *) calloc(st.st_size, sizeof(char)); /* Initialize payoff matrices */ for(pos=0; pos<2; pos++) { g->payoff[pos] = (char ***) calloc(g->nstrats[ROW], sizeof(char **)); for (i=0;instrats[ROW];i++) g->payoff[pos][i] = (char **) calloc(g->nstrats[COL], sizeof(char *)); } } void freeGameStorage(game *g) { int i, pos; for(pos=0; pos<2; pos++) { for (i=0; instrats[ROW]; i++) free(g->payoff[pos][i]); free(g->payoff[pos]); } free(g->pstore); } //----------------------------------------------------------------------------------------// int readGame(game * g, const char *filename) { FILE *IN; long pos, s, t, nr, nc; char *p; g->name = (char *) calloc(strlen(filename)+1, sizeof(char)); strcpy(g->name, filename); if ((IN = fopen(filename, "r")) == NULL) FILEERROR(filename); if (fscanf(IN, "%ld %ld", &nr, &nc) < 2) READERROR(filename); /* get game dimensions */ g->nstrats[ROW] = nr; g->nstrats[COL] = nc; allocateGameStorage(g, filename); /* Read payoff matrices */ p = g->pstore; for (pos = 0; pos < 2; pos++) { for (s=0; snstrats[ROW]; s++) { for (t=0; tnstrats[COL]; t++) { if(fscanf(IN, "%s", p) < 1) READERROR(filename); g->payoff[pos][s][t] = p; p += strlen(p)+1; } } } if (fscanf(IN, "%1s", p) == 1) // Too many payoff entries RECWARN(filename); fclose(IN); return TRUE; } //----------------------------------------------------------------------------------------// //======================================================================== // Command line processing //======================================================================== // Flags to be set from command line options static long Print_game_flag; static long Standard_input_flag; void printUsage(const char *progname) { fprintf(stderr, Usage, progname, progname, progname); } void printInfo(const char *progname) { fprintf(stderr, Helptext, progname, progname); } //----------------------------------------------------------------------------------------// // Collects flags and reads list of games int getArgs(int argc, char **argv) { int c, error = FALSE; const char shortOptions[] = ":vdpsho:"; if (argc < 2) { printUsage(argv[0]); return FALSE; } while (1) { static struct option long_options[] = { {"verbose", no_argument, 0, 'v'}, {"debug", no_argument, 0, 'd'}, {"printgame", no_argument, 0, 'p'}, {"standard", no_argument, 0, 's'}, {"outfile", required_argument, 0, 'o'}, {"help", no_argument, 0, 'h'} // {0, 0, 0, 0} }; /* getopt_long stores the option index here. */ int option_index = 0; c = getopt_long(argc, argv, shortOptions, long_options, &option_index); /* Detect the end of the options. */ if (c == -1) break; switch (c) { case '?': fprintf(stderr, "\nError: Unknown option '-%c'.\n", optopt); error = TRUE; break; case ':': fprintf(stderr, "\nError: Missing argument to option '-%c'.\n", optopt); error = TRUE; break; case 'v': Verbose_flag = TRUE; break; case 'd': Debug_flag = TRUE; break; case 'p': Print_game_flag = TRUE; break; case 's': Standard_input_flag = TRUE; break; case 'h': printInfo(argv[0]); return FALSE; break; case 'o': Outfile = optarg; break; default: abort(); } } if(error) { fprintf(stderr, "Execution halted\n"); return FALSE; } return TRUE; } //----------------------------------------------------------------------------------------// // Checks if an input file is legacy (contains letters) int isLegacy(const char *filename) { FILE *fp; int i, n, foundLetter = FALSE; char buf[100]; if((fp = fopen(filename, "r")) == NULL) FILEERROR(filename); n = fread(buf, sizeof(char), 100, fp); for(i=0;i #include #include "lrsdriver.h" #include "lrslib.h" #include "lrsnashlib.h" static long FirstTime; /* set this to true for every new game to be solved */ long Debug_flag; long Verbose_flag; //======================================================================== // Standard solver. Modified version of main() from lrsNash //======================================================================== int lrs_solve_nash(game * g) { lrs_dic *P1; /* structure for holding current dictionary and indices */ lrs_dat *Q1, *Q2; /* structure for holding static problem data */ lrs_mp_vector output1; /* holds one line of output; ray,vertex,facet,linearity */ lrs_mp_vector output2; /* holds one line of output; ray,vertex,facet,linearity */ lrs_mp_matrix Lin; /* holds input linearities if any are found */ lrs_mp_matrix A2orig; lrs_dic *P2orig; /* we will save player 2's dictionary in getabasis */ long *linindex; /* for faster restart of player 2 */ long col; /* output column index for dictionary */ long startcol = 0; long prune = FALSE; /* if TRUE, getnextbasis will prune tree and backtrack */ long numequilib = 0; /* number of nash equilibria found */ long oldnum = 0; /* global variables lrs_ifp and lrs_ofp are file pointers for input and output */ /* they default to stdin and stdout, but may be overidden by command line parms. */ /*********************************************************************************/ /* Step 1: Allocate lrs_dat, lrs_dic and set up the problem */ /*********************************************************************************/ FirstTime=TRUE; /* This is done for each new game */ Q1 = lrs_alloc_dat("LRS globals"); /* allocate and init structure for static problem data */ if (Q1 == NULL) { return 0; } Q1->nash = TRUE; Q1->n = g->nstrats[ROW] + 2; Q1->m = g->nstrats[ROW] + g->nstrats[COL] + 1; Q1->debug = Debug_flag; Q1->verbose = Verbose_flag; P1 = lrs_alloc_dic(Q1); /* allocate and initialize lrs_dic */ if (P1 == NULL) { return 0; } BuildRep(P1, Q1, g, 1, 0); output1 = lrs_alloc_mp_vector(Q1->n + Q1->m); /* output holds one line of output from dictionary */ /* allocate and init structure for player 2's problem data */ Q2 = lrs_alloc_dat("LRS globals"); if (Q2 == NULL) { return 0; } Q2->debug = Debug_flag; Q2->verbose = Verbose_flag; Q2->nash = TRUE; Q2->n = g->nstrats[COL] + 2; Q2->m = g->nstrats[ROW] + g->nstrats[COL] + 1; P2orig = lrs_alloc_dic(Q2); /* allocate and initialize lrs_dic */ if (P2orig == NULL) { return 0; } BuildRep(P2orig, Q2, g, 0, 1); A2orig = P2orig->A; output2 = lrs_alloc_mp_vector(Q1->n + Q1->m); /* output holds one line of output from dictionary */ linindex = calloc((P2orig->m + P2orig->d + 2), sizeof(long)); /* for next time */ fprintf(lrs_ofp, "\n"); // fprintf (lrs_ofp, "***** %ld %ld rational\n", Q1->n, Q2->n); /*********************************************************************************/ /* Step 2: Find a starting cobasis from default of specified order */ /* P1 is created to hold active dictionary data and may be cached */ /* Lin is created if necessary to hold linearity space */ /* Print linearity space if any, and retrieve output from first dict. */ /*********************************************************************************/ if (!lrs_getfirstbasis(&P1, Q1, &Lin, TRUE)) return 1; if (Q1->dualdeg) { printf("\n*Warning! Dual degenerate, ouput may be incomplete"); printf("\n*Recommendation: Add dualperturb option before maximize in first input file\n"); } if (Q1->unbounded) { printf("\n*Warning! Unbounded starting dictionary for p1, output may be incomplete"); printf("\n*Recommendation: Change/remove maximize option, or include bounds \n"); } /* Pivot to a starting dictionary */ /* There may have been column redundancy */ /* If so the linearity space is obtained and redundant */ /* columns are removed. User can access linearity space */ /* from lrs_mp_matrix Lin dimensions nredundcol x d+1 */ if (Q1->homogeneous && Q1->hull) startcol++; /* col zero not treated as redundant */ for (col = startcol; col < Q1->nredundcol; col++) /* print linearity space */ lrs_printoutput(Q1, Lin[col]); /* Array Lin[][] holds the coeffs. */ /*********************************************************************************/ /* Step 3: Terminate if lponly option set, otherwise initiate a reverse */ /* search from the starting dictionary. Get output for each new dict. */ /*********************************************************************************/ /* We initiate reverse search from this dictionary */ /* getting new dictionaries until the search is complete */ /* User can access each output line from output which is */ /* vertex/ray/facet from the lrs_mp_vector output */ /* prune is TRUE if tree should be pruned at current node */ do { prune = lrs_checkbound(P1, Q1); if (!prune && lrs_getsolution(P1, Q1, output1, col)) { oldnum = numequilib; nash2_main(P1, Q1, P2orig, Q2, &numequilib, output2, linindex); if (numequilib > oldnum || Q1->verbose) { if (Q1->verbose) prat(" \np2's obj value: ", P1->objnum, P1->objden); lrs_nashoutput(Q1, output1, 1L); fprintf(lrs_ofp, "\n"); } } } while (lrs_getnextbasis(&P1, Q1, prune)); fprintf(lrs_ofp, "*Number of equilibria found: %ld", numequilib); fprintf(lrs_ofp, "\n*Player 1: vertices=%ld bases=%ld pivots=%ld", Q1->count[1], Q1->count[2], Q1->count[3]); fprintf(lrs_ofp, "\n*Player 2: vertices=%ld bases=%ld pivots=%ld", Q2->count[1], Q2->count[2], Q2->count[3]); lrs_clear_mp_vector(output1, Q1->m + Q1->n); lrs_clear_mp_vector(output2, Q1->m + Q1->n); lrs_free_dic(P1, Q1); /* deallocate lrs_dic */ lrs_free_dat(Q1); /* deallocate lrs_dat */ /* 2015.10.10 new code to clear P2orig */ Q2->Qhead = P2orig; /* reset this or you crash free_dic */ P2orig->A = A2orig; /* reset this or you crash free_dic */ lrs_free_dic(P2orig, Q2); /* deallocate lrs_dic */ lrs_free_dat(Q2); /* deallocate lrs_dat */ free(linindex); // lrs_close("nash:"); fprintf(lrs_ofp, "\n"); return 0; } /*********************************************/ /* end of nash driver */ /*********************************************/ /**********************************************************/ /* nash2_main is a second driver used in computing nash */ /* equilibria on a second polytope interleaved with first */ /**********************************************************/ long nash2_main(lrs_dic * P1, lrs_dat * Q1, lrs_dic * P2orig, lrs_dat * Q2, long *numequilib, lrs_mp_vector output, long linindex[]) { lrs_dic *P2; /* This can get resized, cached etc. Loaded from P2orig */ lrs_mp_matrix Lin; /* holds input linearities if any are found */ long col; /* output column index for dictionary */ long startcol = 0; long prune = FALSE; /* if TRUE, getnextbasis will prune tree and backtrack */ long nlinearity; long *linearity; static long firstwarning = TRUE; /* FALSE if dual deg warning for Q2 already given */ static long firstunbounded = TRUE; /* FALSE if dual deg warning for Q2 already given */ long i, j; /* global variables lrs_ifp and lrs_ofp are file pointers for input and output */ /* they default to stdin and stdout, but may be overidden by command line parms. */ /*********************************************************************************/ /* Step 1: Allocate lrs_dat, lrs_dic and set up the problem */ /*********************************************************************************/ P2 = lrs_getdic(Q2); copy_dict(Q2, P2, P2orig); /* Here we take the linearities generated by the current vertex of player 1*/ /* and append them to the linearity in player 2's input matrix */ /* next is the key magic linking player 1 and 2 */ /* be careful if you mess with this! */ linearity = Q2->linearity; nlinearity = 0; for (i = Q1->lastdv + 1; i <= P1->m; i++) { if (!zero(P1->A[P1->Row[i]][0])) { j = Q1->inequality[P1->B[i] - Q1->lastdv]; if (Q1->nlinearity == 0 || j < Q1->linearity[0]) linearity[nlinearity++] = j; } } /* add back in the linearity for probs summing to one */ if (Q1->nlinearity > 0) linearity[nlinearity++] = Q1->linearity[0]; /*sort linearities */ for (i = 1; i < nlinearity; i++) reorder(linearity, nlinearity); if (Q2->verbose) { fprintf(lrs_ofp, "\np2: linearities %ld", nlinearity); for (i = 0; i < nlinearity; i++) fprintf(lrs_ofp, " %ld", linearity[i]); } Q2->nlinearity = nlinearity; Q2->polytope = FALSE; /*********************************************************************************/ /* Step 2: Find a starting cobasis from default of specified order */ /* P2 is created to hold active dictionary data and may be cached */ /* Lin is created if necessary to hold linearity space */ /* Print linearity space if any, and retrieve output from first dict. */ /*********************************************************************************/ if (!lrs_getfirstbasis2(&P2, Q2, P2orig, &Lin, TRUE, linindex)) goto sayonara; if (firstwarning && Q2->dualdeg) { firstwarning = FALSE; printf("\n*Warning! Dual degenerate, ouput may be incomplete"); printf("\n*Recommendation: Add dualperturb option before maximize in second input file\n"); } if (firstunbounded && Q2->unbounded) { firstunbounded = FALSE; printf("\n*Warning! Unbounded starting dictionary for p2, output may be incomplete"); printf("\n*Recommendation: Change/remove maximize option, or include bounds \n"); } /* Pivot to a starting dictionary */ /* There may have been column redundancy */ /* If so the linearity space is obtained and redundant */ /* columns are removed. User can access linearity space */ /* from lrs_mp_matrix Lin dimensions nredundcol x d+1 */ if (Q2->homogeneous && Q2->hull) startcol++; /* col zero not treated as redundant */ /* for (col = startcol; col < Q2->nredundcol; col++) *//* print linearity space */ /*lrs_printoutput (Q2, Lin[col]); *//* Array Lin[][] holds the coeffs. */ /*********************************************************************************/ /* Step 3: Terminate if lponly option set, otherwise initiate a reverse */ /* search from the starting dictionary. Get output for each new dict. */ /*********************************************************************************/ /* We initiate reverse search from this dictionary */ /* getting new dictionaries until the search is complete */ /* User can access each output line from output which is */ /* vertex/ray/facet from the lrs_mp_vector output */ /* prune is TRUE if tree should be pruned at current node */ do { prune = lrs_checkbound(P2, Q2); col = 0; if (!prune && lrs_getsolution(P2, Q2, output, col)) { if (Q2->verbose) prat(" \np1's obj value: ", P2->objnum, P2->objden); if (lrs_nashoutput(Q2, output, 2L)) (*numequilib)++; } } while (lrs_getnextbasis(&P2, Q2, prune)); sayonara: lrs_free_dic(P2, Q2); return 0; } /*********************************************/ /* end of nash2_main */ /*********************************************/ /* In lrs_getfirstbasis and lrs_getnextbasis we use D instead of P */ /* since the dictionary P may change, ie. &P in calling routine */ #define D (*D_p) long lrs_getfirstbasis2(lrs_dic ** D_p, lrs_dat * Q, lrs_dic * P2orig, lrs_mp_matrix * Lin, long no_output, long linindex[]) /* gets first basis, FALSE if none */ /* P may get changed if lin. space Lin found */ /* no_output is TRUE supresses output headers */ { long i, j, k; /* assign local variables to structures */ lrs_mp_matrix A; long *B, *C, *Col; long *inequality; long *linearity; long hull = Q->hull; long m, d, lastdv, nlinearity, nredundcol; m = D->m; d = D->d; lastdv = Q->lastdv; nredundcol = 0L; /* will be set after getabasis */ nlinearity = Q->nlinearity; /* may be reset if new linearity read */ linearity = Q->linearity; A = D->A; B = D->B; C = D->C; Col = D->Col; inequality = Q->inequality; /* default is to look for starting cobasis using linearies first, then */ /* filling in from last rows of input as necessary */ /* linearity array is assumed sorted here */ /* note if restart/given start inequality indices already in place */ /* from nlinearity..d-1 */ for (i = 0; i < nlinearity; i++) /* put linearities first in the order */ inequality[i] = linearity[i]; k = 0; /* index for linearity array */ if (Q->givenstart) k = d; else k = nlinearity; for (i = m; i >= 1; i--) { j = 0; while (j < k && inequality[j] != i) j++; /* see if i is in inequality */ if (j == k) inequality[k++] = i; } if (Q->debug) { fprintf(lrs_ofp, "\n*Starting cobasis uses input row order"); for (i = 0; i < m; i++) fprintf(lrs_ofp, " %ld", inequality[i]); } if (!Q->maximize && !Q->minimize) for (j = 0; j <= d; j++) itomp(ZERO, A[0][j]); /* Now we pivot to standard form, and then find a primal feasible basis */ /* Note these steps MUST be done, even if restarting, in order to get */ /* the same index/inequality correspondance we had for the original prob. */ /* The inequality array is used to give the insertion order */ /* and is defaulted to the last d rows when givenstart=FALSE */ if (!getabasis2(D, Q, P2orig, inequality, linindex)) { return FALSE; } if (Q->debug) { fprintf(lrs_ofp, "\nafter getabasis2"); printA(D, Q); } nredundcol = Q->nredundcol; lastdv = Q->lastdv; d = D->d; /********************************************************************/ /* now we start printing the output file unless no output requested */ /********************************************************************/ if (!no_output || Q->debug) { fprintf(lrs_ofp, "\nV-representation"); /* Print linearity space */ /* Don't print linearity if first column zero in hull computation */ k = 0; if (nredundcol > k) { fprintf(lrs_ofp, "\nlinearity %ld ", nredundcol - k); /*adjust nredundcol for homog. */ for (i = 1; i <= nredundcol - k; i++) fprintf(lrs_ofp, " %ld", i); } /* end print of linearity space */ fprintf(lrs_ofp, "\nbegin"); fprintf(lrs_ofp, "\n***** %ld rational", Q->n); } /* end of if !no_output ....... */ /* Reset up the inequality array to remember which index is which input inequality */ /* inequality[B[i]-lastdv] is row number of the inequality with index B[i] */ /* inequality[C[i]-lastdv] is row number of the inequality with index C[i] */ for (i = 1; i <= m; i++) inequality[i] = i; if (nlinearity > 0) { /* some cobasic indices will be removed */ for (i = 0; i < nlinearity; i++) /* remove input linearity indices */ inequality[linearity[i]] = 0; k = 1; /* counter for linearities */ for (i = 1; i <= m - nlinearity; i++) { while (k <= m && inequality[k] == 0) k++; /* skip zeroes in corr. to linearity */ inequality[i] = inequality[k++]; } } /* end if linearity */ if (Q->debug) { fprintf(lrs_ofp, "\ninequality array initialization:"); for (i = 1; i <= m - nlinearity; i++) fprintf(lrs_ofp, " %ld", inequality[i]); } if (nredundcol > 0) { const unsigned int Qn = Q->n; *Lin = lrs_alloc_mp_matrix(nredundcol, Qn); for (i = 0; i < nredundcol; i++) { if (!(Q->homogeneous && Q->hull && i == 0)) { /* skip redund col 1 for homog. hull */ lrs_getray(D, Q, Col[0], D->C[0] + i - hull, (*Lin)[i]); /* adjust index for deletions */ } if (!removecobasicindex(D, Q, 0L)) { lrs_clear_mp_matrix(*Lin, nredundcol, Qn); return FALSE; } } } /* end if nredundcol > 0 */ if (Q->verbose) { fprintf(lrs_ofp, "\nNumber of pivots for starting dictionary: %ld", Q->count[3]); } /* Do dual pivots to get primal feasibility */ if (!primalfeasible(D, Q)) { if (Q->verbose) { fprintf(lrs_ofp, "\nNumber of pivots for feasible solution: %ld", Q->count[3]); fprintf(lrs_ofp, " - No feasible solution"); } return FALSE; } if (Q->verbose) { fprintf(lrs_ofp, "\nNumber of pivots for feasible solution: %ld", Q->count[3]); } /* Now solve LP if objective function was given */ if (Q->maximize || Q->minimize) { Q->unbounded = !lrs_solvelp(D, Q, Q->maximize); /* check to see if objective is dual degenerate */ j = 1; while (j <= d && !zero(A[0][j])) j++; if (j <= d) Q->dualdeg = TRUE; } else /* re-initialize cost row to -det */ { for (j = 1; j <= d; j++) { copy(A[0][j], D->det); storesign(A[0][j], NEG); } itomp(ZERO, A[0][0]); /* zero optimum objective value */ } /* reindex basis to 0..m if necessary */ /* we use the fact that cobases are sorted by index value */ if (Q->debug) printA(D, Q); while (C[0] <= m) { i = C[0]; //j = inequality[B[i] - lastdv]; //inequality[B[i] - lastdv] = inequality[C[0] - lastdv]; //inequality[C[0] - lastdv] = j; C[0] = B[i]; B[i] = i; reorder1(C, Col, ZERO, d); } if (Q->debug) { fprintf(lrs_ofp, "\n*Inequality numbers for indices %ld .. %ld : ", lastdv + 1, m + d); for (i = 1; i <= m - nlinearity; i++) fprintf(lrs_ofp, " %ld ", inequality[i]); printA(D, Q); } if (Q->restart) { if (Q->debug) fprintf(lrs_ofp, "\nPivoting to restart co-basis"); if (!restartpivots(D, Q)) return FALSE; D->lexflag = lexmin(D, Q, ZERO); /* see if lexmin basis */ if (Q->debug) printA(D, Q); } /* Check to see if necessary to resize */ if (Q->inputd > D->d) *D_p = resize(D, Q); return TRUE; } /********* end of lrs_getfirstbasis ***************/ long getabasis2(lrs_dic * P, lrs_dat * Q, lrs_dic * P2orig, long order[], long linindex[]) /* Pivot Ax<=b to standard form */ /*Try to find a starting basis by pivoting in the variables x[1]..x[d] */ /*If there are any input linearities, these appear first in order[] */ /* Steps: (a) Try to pivot out basic variables using order */ /* Stop if some linearity cannot be made to leave basis */ /* (b) Permanently remove the cobasic indices of linearities */ /* (c) If some decision variable cobasic, it is a linearity, */ /* and will be removed. */ { /* 2015.10.10 linindex now preallocated and received as parameter so we can free it */ // static long firsttime = TRUE; /* stays true until first valid dictionary built */ long i, j, k; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *B = P->B; long *C = P->C; long *Row = P->Row; long *Col = P->Col; long *linearity = Q->linearity; long *redundcol = Q->redundcol; long m, d, nlinearity; long nredundcol = 0L; /* will be calculated here */ m = P->m; d = P->d; nlinearity = Q->nlinearity; //2015.9.15 /* after first time we update the change in linearities from the last time, saving many pivots */ if (!FirstTime) { for (i = 1; i <= m + d; i++) linindex[i] = FALSE; if (Q->debug) fprintf(lrs_ofp, "\nlindex ="); for (i = 0; i < nlinearity; i++) { linindex[d + linearity[i]] = TRUE; if (Q->debug) fprintf(lrs_ofp, " %ld", d + linearity[i]); } for (i = 1; i <= m; i++) { if (linindex[B[i]]) { /* pivot out unwanted linearities */ k = 0; while (k < d && (linindex[C[k]] || zero(A[Row[i]][Col[k]]))) k++; if (k < d) { j = i; /* note this index changes in update, cannot use i!) */ if (C[k] > B[j]) /* decrease i or we may skip a linearity */ i--; pivot(P, Q, j, k); update(P, Q, &j, &k); } else { /* this is not necessarily an error, eg. two identical rows/cols in payoff matrix */ if (!zero(A[Row[i]][0])) { /* error condition */ if (Q->debug || Q->verbose) { fprintf(lrs_ofp, "\n*Infeasible linearity i=%ld B[i]=%ld", i, B[i]); if (Q->debug) printA(P, Q); } return (FALSE); } if (Q->debug || Q->verbose) { fprintf(lrs_ofp, "\n*Couldn't remove linearity i=%ld B[i]=%ld", i, B[i]); } } } /* if linindex */ } /* for i .. */ } else { /* we have not had a successful dictionary built from the given linearities */ /* standard lrs processing is done on only the first call to getabasis2 */ if (Q->debug) { fprintf(lrs_ofp, "\ngetabasis from inequalities given in order"); for (i = 0; i < m; i++) fprintf(lrs_ofp, " %ld", order[i]); } for (j = 0; j < m; j++) { i = 0; while (i <= m && B[i] != d + order[j]) i++; /* find leaving basis index i */ if (j < nlinearity && i > m) { /* cannot pivot linearity to cobasis */ if (Q->debug) printA(P, Q); #ifndef LRS_QUIET fprintf(lrs_ofp, "\nCannot find linearity in the basis"); #endif return FALSE; } if (i <= m) { /* try to do a pivot */ k = 0; while (C[k] <= d && zero(A[Row[i]][Col[k]])) k++; if (C[k] <= d) { pivot(P, Q, i, k); update(P, Q, &i, &k); } else if (j < nlinearity) { /* cannot pivot linearity to cobasis */ if (zero(A[Row[i]][0])) { #ifndef LRS_QUIET fprintf(lrs_ofp, "*Input linearity in row %ld is redundant--skipped\n", order[j]); #endif linearity[j] = 0; } else { if (Q->debug) printA(P, Q); if (Q->debug || Q->verbose) fprintf(lrs_ofp, "\nInconsistent linearities"); return FALSE; } } /* end if j < nlinearity */ } /* end of if i <= m .... */ } /* end of for */ /* update linearity array to get rid of redundancies */ i = 0; k = 0; /* counters for linearities */ while (k < nlinearity) { while (k < nlinearity && linearity[k] == 0) k++; if (k < nlinearity) linearity[i++] = linearity[k++]; } nlinearity = i; /* lrs bug fix, 2009.6.27, nash 2015.9.16 */ Q->nlinearity = i; /* column dependencies now can be recorded */ /* redundcol contains input column number 0..n-1 where redundancy is */ k = 0; while (k < d && C[k] <= d) { if (C[k] <= d) /* decision variable still in cobasis */ redundcol[nredundcol++] = C[k] - Q->hull; /* adjust for hull indices */ k++; } /* now we know how many decision variables remain in problem */ Q->nredundcol = nredundcol; Q->lastdv = d - nredundcol; /* 2015.9.15 bug fix : we needed first *successful* time */ FirstTime = FALSE; } /* else firsttime ... we have built a dictionary from the given linearities */ /* we continue from here after loading dictionary */ if (Q->debug) { fprintf(lrs_ofp, "\nend of first phase of getabasis2: "); fprintf(lrs_ofp, "lastdv=%ld nredundcol=%ld", Q->lastdv, Q->nredundcol); fprintf(lrs_ofp, "\nredundant cobases:"); for (i = 0; i < nredundcol; i++) fprintf(lrs_ofp, " %ld", redundcol[i]); printA(P, Q); } /* here we save dictionary for use next time, *before* we resize */ copy_dict(Q, P2orig, P); /* Remove linearities from cobasis for rest of computation */ /* This is done in order so indexing is not screwed up */ for (i = 0; i < nlinearity; i++) { /* find cobasic index */ k = 0; while (k < d && C[k] != linearity[i] + d) k++; if (k >= d) { if (Q->debug || Q->verbose) { fprintf(lrs_ofp, "\nCould not remove cobasic index"); } /* not neccesarily an error as eg., could be repeated row/col in payoff */ } else { removecobasicindex(P, Q, k); d = P->d; } } if (Q->debug && nlinearity > 0) printA(P, Q); /* set index value for first slack variable */ /* Check feasability */ if (Q->givenstart) { i = Q->lastdv + 1; while (i <= m && !negative(A[Row[i]][0])) i++; if (i <= m) fprintf(lrs_ofp, "\n*Infeasible startingcobasis - will be modified"); } return TRUE; } /* end of getabasis2 */ long lrs_nashoutput(lrs_dat * Q, lrs_mp_vector output, long player) { long i; long origin = TRUE; /* do not print the origin for either player */ for (i = 1; i < Q->n; i++) if (!zero(output[i])) origin = FALSE; if (origin) return FALSE; fprintf(lrs_ofp, "%ld ", player); for (i = 1; i < Q->n; i++) prat("", output[i], output[0]); fprintf(lrs_ofp, "\n"); fflush(lrs_ofp); return TRUE; } /* end lrs_nashoutput */ //======================================================================== // Old style solver. Included for backward compatibility //======================================================================== int lrs_solve_nash_legacy (int argc, char *argv[]) // Handles legacy input files { lrs_dic *P1; /* structure for holding current dictionary and indices */ lrs_dat *Q1,*Q2; /* structure for holding static problem data */ lrs_mp_vector output1; /* holds one line of output; ray,vertex,facet,linearity */ lrs_mp_vector output2; /* holds one line of output; ray,vertex,facet,linearity */ lrs_mp_matrix Lin; /* holds input linearities if any are found */ lrs_mp_matrix A2orig; lrs_dic *P2orig; /* we will save player 2's dictionary in getabasis */ long *linindex; /* for faster restart of player 2 */ long col; /* output column index for dictionary */ long startcol = 0; long prune = FALSE; /* if TRUE, getnextbasis will prune tree and backtrack */ long numequilib=0; /* number of nash equilibria found */ long oldnum=0; /* global variables lrs_ifp and lrs_ofp are file pointers for input and output */ /* they default to stdin and stdout, but may be overidden by command line parms. */ if(argc <= 2 ) { printf("Usage: %s input1 input2 [outputfile] \n", argv[0]); return 1; } /*************************************************** Step 0: Do some global initialization that should only be done once, no matter how many lrs_dat records are allocated. db ***************************************************/ if ( !lrs_init ("\n*nash:")) return 1; /*********************************************************************************/ /* Step 1: Allocate lrs_dat, lrs_dic and set up the problem */ /*********************************************************************************/ Q1 = lrs_alloc_dat ("LRS globals"); /* allocate and init structure for static problem data */ if (Q1 == NULL) return 1; Q1->nash=TRUE; if (!lrs_read_dat (Q1, argc, argv)) /* read first part of problem data to get dimensions */ return 1; /* and problem type: H- or V- input representation */ strcpy(Q1->fname,"nash"); /* program name */ P1 = lrs_alloc_dic (Q1); /* allocate and initialize lrs_dic */ if (P1 == NULL) return 1; if (!lrs_read_dic (P1, Q1)) /* read remainder of input to setup P1 and Q1 */ return 1; output1 = lrs_alloc_mp_vector (Q1->n + Q1->m); /* output holds one line of output from dictionary */ /* allocate and init structure for player 2's problem data */ printf ("\n*Second input taken from file %s\n", argv[2]); Q2 = lrs_alloc_dat ("LRS globals"); if (Q2 == NULL) return 1; strcpy(Q2->fname,"nash"); /* program name */ Q2->nash=TRUE; if (!lrs_read_dat (Q2, 2, argv)) /* read first part of problem data to get dimensions */ return 1; /* and problem type: H- or V- input representation */ if (Q2->nlinearity > 0) free(Q2->linearity); /* we will start again */ Q2->linearity = CALLOC ((Q2->m + 2), sizeof (long)); P2orig = lrs_alloc_dic (Q2); /* allocate and initialize lrs_dic */ if (P2orig == NULL) return 1; if (!lrs_read_dic (P2orig, Q2)) /* read remainder of input to setup P2 and Q2 */ return 1; A2orig = P2orig->A; output2 = lrs_alloc_mp_vector (Q1->n + Q1->m); /* output holds one line of output from dictionary */ linindex = calloc ((P2orig->m + P2orig->d + 2), sizeof (long)); /* for next time*/ fprintf (lrs_ofp, "\n***** %ld %ld rational\n", Q1->n, Q2->n); /*********************************************************************************/ /* Step 2: Find a starting cobasis from default of specified order */ /* P1 is created to hold active dictionary data and may be cached */ /* Lin is created if necessary to hold linearity space */ /* Print linearity space if any, and retrieve output from first dict. */ /*********************************************************************************/ if (!lrs_getfirstbasis (&P1, Q1, &Lin, TRUE)) return 1; if (Q1->dualdeg) { printf("\n*Warning! Dual degenerate, ouput may be incomplete"); printf("\n*Recommendation: Add dualperturb option before maximize in first input file\n"); } if (Q1->unbounded) { printf("\n*Warning! Unbounded starting dictionary for p1, output may be incomplete"); printf("\n*Recommendation: Change/remove maximize option, or include bounds \n"); } /* Pivot to a starting dictionary */ /* There may have been column redundancy */ /* If so the linearity space is obtained and redundant */ /* columns are removed. User can access linearity space */ /* from lrs_mp_matrix Lin dimensions nredundcol x d+1 */ if (Q1->homogeneous && Q1->hull) startcol++; /* col zero not treated as redundant */ for (col = startcol; col < Q1->nredundcol; col++) /* print linearity space */ lrs_printoutput (Q1, Lin[col]); /* Array Lin[][] holds the coeffs. */ /*********************************************************************************/ /* Step 3: Terminate if lponly option set, otherwise initiate a reverse */ /* search from the starting dictionary. Get output for each new dict. */ /*********************************************************************************/ /* We initiate reverse search from this dictionary */ /* getting new dictionaries until the search is complete */ /* User can access each output line from output which is */ /* vertex/ray/facet from the lrs_mp_vector output */ /* prune is TRUE if tree should be pruned at current node */ do { prune=lrs_checkbound(P1,Q1); if (!prune && lrs_getsolution (P1, Q1, output1, col)) { oldnum=numequilib; nash2_main(P1,Q1,P2orig,Q2,&numequilib,output2,linindex); if (numequilib > oldnum || Q1->verbose) { if(Q1->verbose) prat(" \np2's obj value: ",P1->objnum,P1->objden); lrs_nashoutput (Q1, output1, 1L); fprintf (lrs_ofp, "\n"); } } } while (lrs_getnextbasis (&P1, Q1, prune)); fprintf(lrs_ofp,"\n*Number of equilibria found: %ld",numequilib); fprintf (lrs_ofp,"\n*Player 1: vertices=%ld bases=%ld pivots=%ld", Q1->count[1], Q1->count[2],Q1->count[3]); fprintf (lrs_ofp,"\n*Player 2: vertices=%ld bases=%ld pivots=%ld", Q2->count[1], Q2->count[2],Q2->count[3]); lrs_clear_mp_vector(output1, Q1->m + Q1->n); lrs_clear_mp_vector(output2, Q1->m + Q1->n); lrs_free_dic (P1,Q1); /* deallocate lrs_dic */ lrs_free_dat (Q1); /* deallocate lrs_dat */ /* 2015.10.10 new code to clear P2orig */ Q2->Qhead = P2orig; /* reset this or you crash free_dic */ P2orig->A=A2orig; /* reset this or you crash free_dic */ lrs_free_dic (P2orig,Q2); /* deallocate lrs_dic */ lrs_free_dat (Q2); /* deallocate lrs_dat */ free (linindex); lrs_close ("nash:"); return 0; } /*********************************************/ /* end of nash driver */ /*********************************************/ //========================================================================== // Building the problem representations (adapted from Gambit-enummixed) //========================================================================== // // These two functions are based upon the program setupnash.c from the // lrslib distribution, and the user's guide documentation. // There are two separate functions, one for each player's problem. // According to the user's guide, the ordering of the constraint rows // is significant, and differs between the players; for player 1's problem // the nonnegativity constraints come first, whereas for player 2's problem // they appear later. Experiments suggest this is in fact true, and // reversing them breaks something. // //----------------------------------------------------------------------------------------// void FillNonnegativityRows(lrs_dic * P, lrs_dat * Q, int firstRow, int lastRow, int n) { const int MAXCOL = 1000; /* maximum number of columns */ long num[MAXCOL], den[MAXCOL]; long row, col; for (row = firstRow; row <= lastRow; row++) { num[0] = 0; den[0] = 1; for (col = 1; col < n; col++) { num[col] = (row - firstRow + 1 == col) ? 1 : 0; den[col] = 1; } lrs_set_row(P, Q, row, num, den, GE); } } long str2rat (lrs_mp Na, lrs_mp Da, char *str) { /* Based on readrat in lrsgmp.c */ /* convert rational or integer to lrs_mp */ /* returns true if denominator is not one */ char num[MAXINPUT], den[MAXINPUT]; atoaa (str, num, den); /*convert rational to num/dem strings */ atomp (num, Na); if (den[0] == '\0') { itomp (1L, Da); return (FALSE); } atomp (den, Da); return (TRUE); } //----------------------------------------------------------------------------------------// void FillConstraintRows(lrs_dic * P, lrs_dat * Q, const game * g, int p1, int p2, int firstRow) { lrs_mp_vector Num, Den; char *onePayoff; int row, s, t, d; d = P->d; // Should equal g->nstrats[p2] + 1? Num = lrs_alloc_mp_vector(d+1); Den = lrs_alloc_mp_vector(d+1); for (row = firstRow; row < firstRow + g->nstrats[p1]; row++) { itomp (ZERO, Num[0]); itomp (ONE, Den[0]); s = row - firstRow; for (t = 0; t < g->nstrats[p2]; t++) { onePayoff = p1 == ROW ? g->payoff[p1][s][t] : g->payoff[p1][t][s]; str2rat(Num[t + 1], Den[t + 1], onePayoff); if(!zero(Num[t + 1])) changesign(Num[t + 1]); } itomp (ONE, Num[g->nstrats[p2] + 1]); itomp (ONE, Den[g->nstrats[p2] + 1]); lrs_set_row_mp(P, Q, row, Num, Den, GE); } lrs_clear_mp_vector(Num,d+1); lrs_clear_mp_vector(Den,d+1); } //----------------------------------------------------------------------------------------// void FillLinearityRow(lrs_dic * P, lrs_dat * Q, int m, int n) { const int MAXCOL = 1000; /* maximum number of columns */ long num[MAXCOL], den[MAXCOL]; int i; num[0] = -1; den[0] = 1; for (i = 1; i < n - 1; i++) { num[i] = 1; den[i] = 1; } num[n - 1] = 0; den[n - 1] = 1; lrs_set_row(P, Q, m, num, den, EQ); } // // TL added this to get first row of ones. Don't know if it's needed //----------------------------------------------------------------------------------------// void FillFirstRow(lrs_dic * P, lrs_dat * Q, int n) { const int MAXCOL = 1000; /* maximum number of columns */ long num[MAXCOL], den[MAXCOL]; int i; for (i = 0; i < n; i++) { num[i] = 1; den[i] = 1; } lrs_set_row(P, Q, 0, num, den, GE); } // // Build the H-representation for player p1 //----------------------------------------------------------------------------------------// void BuildRep(lrs_dic * P, lrs_dat * Q, const game * g, int p1, int p2) { long m = Q->m; /* number of inequalities */ long n = Q->n; if (p1 == 0) { FillConstraintRows(P, Q, g, p1, p2, 1); FillNonnegativityRows(P, Q, g->nstrats[p1] + 1, g->nstrats[ROW] + g->nstrats[COL], n); } else { FillNonnegativityRows(P, Q, 1, g->nstrats[p2], n); FillConstraintRows(P, Q, g, p1, p2, g->nstrats[p2] + 1); // 1 here } FillLinearityRow(P, Q, m, n); // TL added this to get first row of ones. (Is this necessary?) FillFirstRow(P, Q, n); } //----------------------------------------------------------------------------------------// void printGame(game * g) { int s, t, pos, len; int *fwidth[2]; /* Storage for field witdths. g->nstrats[COL] columns for both players */ fwidth[ROW] = (int *)calloc(g->nstrats[COL], sizeof(int)); fwidth[COL] = (int *)calloc(g->nstrats[COL], sizeof(int)); /* Get column widths for output*/ for(pos=0; pos<2; pos++) { for (t = 0; t < g->nstrats[COL]; t++) { fwidth[pos][t] = 0; for (s = 0; s < g->nstrats[ROW]; s++) { len = strlen(g->payoff[pos][s][t]); if(len > fwidth[pos][t]) fwidth[pos][t] = len; } } } /* print payoffs */ fprintf(lrs_ofp, "\n--------------------------------------------------------------------------------\n"); fprintf(lrs_ofp, "%s payoff matrix:\n", g->name); for (s = 0; s < g->nstrats[ROW]; s++) { for (t = 0; t < g->nstrats[COL]; t++) fprintf(lrs_ofp, "%*s, %-*s ", fwidth[ROW][t], g->payoff[ROW][s][t], fwidth[COL][t], g->payoff[COL][s][t]); fprintf(lrs_ofp, "\n"); } fprintf(lrs_ofp, "\nNash equilibria:\n"); fflush(lrs_ofp); free(fwidth[ROW]); free(fwidth[COL]); } void resetNashSolver() { FirstTime = TRUE; } /******************** end of lrsnashlib.c ***************************/ lrslib-073/lrsnashlib.h0000777000175000017500000000432714625766570013713 0ustar avisavis/*******************************************************/ /* lrsnashlib is a library of routines for computing */ /* computing all nash equilibria for two person games */ /* given by mxn payoff matrices A,B */ /* */ /* */ /* Main user callable function is */ /* lrs_solve_nash(game *g) */ /* */ /* Sample driver: lrsnash.c */ /* Derived from nash.c in lrslib-060 */ /* by Terje Lensberg, October 26, 2015: */ /*******************************************************/ /* minor mod 2018.2.12 to set Q->fname="nash" */ /*************/ /* Games */ /*************/ #define ROW 0 #define COL 1 typedef struct { char *name; long nstrats[2]; char *pstore; // Storage for payoffs char ***payoff[2]; // Pointers to payoffs } game; int lrs_solve_nash(game * g); long nash2_main(lrs_dic * P1, lrs_dat * Q1, lrs_dic * P2orig, lrs_dat * Q2, long *numequilib, lrs_mp_vector output, long linindex[]); /* lrs driver, argv[2]= 2nd input file for nash equilibria */ long lrs_getfirstbasis2(lrs_dic ** D_p, lrs_dat * Q, lrs_dic * P2orig, lrs_mp_matrix * Lin, long no_output, long linindex[]); long getabasis2(lrs_dic * P, lrs_dat * Q, lrs_dic * P2orig, long order[], long linindex[]); long lrs_nashoutput(lrs_dat * Q, lrs_mp_vector output, long player); /* returns TRUE and prints output if not the origin */ int lrs_solve_nash_legacy (int argc, char *argv[]); void BuildRep(lrs_dic * P, lrs_dat * Q, const game * g, int p1, int p2); void FillFirstRow(lrs_dic * P, lrs_dat * Q, int n); void FillLinearityRow(lrs_dic * P, lrs_dat * Q, int m, int n); void FillConstraintRows(lrs_dic * P, lrs_dat * Q, const game * g, int p1, int p2, int firstRow); void FillNonnegativityRows(lrs_dic * P, lrs_dat * Q, int firstRow, int lastRow, int n); void printGame(game * g); void resetNashSolver(); /* Call this function for every new game to be solved */ extern long Debug_flag; extern long Verbose_flag; lrslib-073/lrsrestart.h0000777000175000017500000000611114625766573013753 0ustar avisavistypedef struct lrs_restart_dat /* for restarting from a given cobasis */ { long *facet; /* cobasic indices for restart */ long overide; /* TRUE if Q parameters should be updated */ long restart; /* TRUE if we supply restart cobasis */ long lrs; /* TRUE if we are doing a lrs run */ long m; /* number of input rows */ long d; /* number of cobasic indices */ long count[10]; /* count[0]=rays(facets) [1]=verts. [2]=base [3]=pivots */ /* count[4]=integer vertices [5]=1 for hull */ /* [6]=nlinearities [7]=deepest */ long depth; /* depth of restart node */ long maxcobases; /* if positive, after maxcobasis unexplored subtrees reported */ long long maxdepth; /* max depth to search to in treee */ long long mindepth; /* do not backtrack above mindepth */ long printcobasis; /* TRUE if option set in lrs, mplrs renumbers */ long redund; /* TRUE if we are doing a redund run */ long fel; /* TRUE if we are doing a fel run */ long testlin; /* TRUE if we test for hidden linearities */ long redundphase; /* TRUE if relative interior point exists */ long messages; /* TRUE if lrs should post_output messages */ long *redineq; /* a list of row numbers to check redundancy */ long size; /* number of processes in mplrs MPI run */ long rank; /* my ID. * 0: master, 1: consumer, 2...size-1: workers*/ } lrs_restart_dat; lrs_restart_dat* lrs_alloc_restart(); /********************************************************************************** Usage of lrs_restart_dat for communication between lrs and mplrs lrs mode: ----------------------------------------------------------------------------------- redund mode: ----------------------------------------------------------------------------------- fel mode: (fel=TRUE redund=lrs=FALSE ) rank=0 mplrs expects lrs to return m where m+1 is the dimension of redineq after one variable has been eliminated. Currently lrs allocs redineq and initializes redineq[i]=1 (is this necessary?) rank=2,...,np-2 mplrs expects eacher worker to return a redineq array with same dimension m with redineq[i]=2 linearity, =1 possibly redundant, =-1 surely redundant, =0 otherwise mplrs copies the non-zero values into its own redineq array. After all workers finish mplrs chooses the worker with the most "1" values and converts them to "-1" rank=1 after all workers terminated mplrs supplies its redineq array lrs does a redund_run and produces ouput **********************************************************************************/ lrslib-073/makefile0000777000175000017500000003432714626240523013066 0ustar avisavis#makefile for lrslib-073 2024.2.2 # default make requires a compiler with __int128 and openMP support (eg. gcc v.4.2 or later) # and installation of the GMP library. Otherwise make the alternative choices below. # if all else fails use %make lrs64 to compile # mplrs requires OpenMPI to be installed (including mpicc) #try uncommenting next line if cc is the default C compiler #CC = gcc7 CC ?= gcc # or gcc7 #GMP library installed - try this first! GMP=-DGMP -lgmp MINI= #GMP library is not installed - try second #GMP=-DGMP -DMGMP #MINI=${ARITH}mini-gmp.c #compilers supporting openMP (eg gcc 4.2 and later) PLRSFLAGS=-fopenmp -DPLRS #compilers without openMP support - try second #PLRSFLAGS= #compilers supporting _int128 (eg gcc 4.2 and later) BITS=-DB128 MPLRSOBJ2=lrslib2-mplrs.o lrslong2-mplrs.o LRSOBJ2=lrslib2.o lrslong2.o #compilers without _int128 support (equivalent to make lrs64 in v.7.2) #BITS= #MPLRSOBJ2= #LRSOBJ2= #legacy lrs and mplrs #CFLAGS = -g -Wall -I ${ARITH} CFLAGS = -O3 -Wall -I ${ARITH} #use this if you want only output file contain data between begin/end lines #CFLAGS = -O3 -Wall -I ${ARITH} -DLRS_QUIET #ARITH= ARITH=lrsarith-011/ #Apple clang doesn't support OpenMP - change PLRSFLAGS so default builds #on macOS #comment this out if you have OpenMP support and are using an Apple compiler $(eval APPLE_CHECK := $(shell $(CC) --version | grep Apple | wc -l)) ifeq ($(APPLE_CHECK),1) $(info OpenMP support not found, disabling OpenMP parallel build) PLRSFLAGS= endif default: lrs lrsgmp #default: lrs mplrs lrsgmp mplrsgmp # add -DTIMES if your compiler does *not* support ptimes() and get_time() # add -DSIGNALS if your compiler does *not* support #make lrs lrs,lrsgmp hybrid and gmp versions #make mplrs mplrs,mplrsgmp hybrid and gmp versions, make sure mpicc and OpenMPI library is installed #make mplrs64 mplrs,mplrsgmp for compilers without 128 bit support #make flint lrs and mplrs with FLINT arithmetic #make single makes lrs with various arithmetic packages (depending on compiler),lrsnash #make singlemplrs makes mplrs with various arithmetic packages (depending on compiler) #make allmp uses native mp and long arithmetic #make demo various demo programs for lrslib #make lrsnash Nash equilibria for 2-person games: lrsnash (gmp), lrsnash1 (64bit), lrsnash2 (128bit) #make clean removes binaries #INCLUDEDIR = /usr/include #LIBDIR = /usr/lib #Kyoto machines usage INCLUDEDIR = /usr/local/include LIBDIR = /usr/local/lib SHLIB_CFLAGS = -fPIC mpicxx=mpicc LRSOBJ=lrs.o lrslong1.o lrslib1.o lrslibgmp.o lrsgmp.o lrsdriver.o LRSOBJMP=lrs.o lrslong1.o lrslong2.o lrslib1.o lrslib2.o lrslibmp.o lrsmp.o lrsdriver.o MPLRSOBJ=lrslong1-mplrs.o lrslib1-mplrs.o lrslibgmp-mplrs.o lrsgmp-mplrs.o lrsdriver-mplrs.o mplrs.o MPLRSOBJ64=lrslong1-mplrs.o lrslib1-mplrs.o lrslibgmp-mplrs.o lrsgmp-mplrs.o lrsdriver-mplrs.o mplrs64.o lrs: ${LRSOBJ} ${LRSOBJ2} $(CC) ${CFLAGS} ${PLRSFLAGS} -DMA ${BITS} -L${LIBDIR} -o lrs ${LRSOBJ} ${LRSOBJ2} ${MINI} ${GMP} ln -s -f lrs redund ln -s -f lrs minrep ln -s -f lrs fel lrsMP: ${LRSOBJMP} $(CC) ${CFLAGS} ${PLRSFLAGS} -DMA ${BITS} -o lrsMP ${LRSOBJMP} $(CC) -O3 hvref.c -o hvref ln -s -f lrs redund lrs.o: lrs.c $(CC) ${CFLAGS} -DMA ${BITS} -c -o lrs.o lrs.c lrs64.o: lrs.c $(CC) ${CFLAGS} -DMA -c -o lrs64.o lrs.c lrslong1.o: ${ARITH}lrslong.c ${ARITH}lrslong.h $(CC) ${CFLAGS} -DMA -DSAFE -DLRSLONG -c -o lrslong1.o ${ARITH}lrslong.c lrslib1.o: lrslib.c lrslib.h $(CC) ${CFLAGS} ${PLRSFLAGS} -DMA -DSAFE -DLRSLONG -c -o lrslib1.o lrslib.c lrslong2.o: ${ARITH}lrslong.c ${ARITH}lrslong.h $(CC) ${CFLAGS} -DMA -DSAFE ${BITS} -DLRSLONG -c -o lrslong2.o ${ARITH}lrslong.c lrslib2.o: lrslib.c lrslib.h $(CC) ${CFLAGS} ${PLRSFLAGS} -DMA -DSAFE ${BITS} -DLRSLONG -c -o lrslib2.o lrslib.c lrslibgmp.o: lrslib.c lrslib.h $(CC) ${CFLAGS} ${PLRSFLAGS} -DMA -I${INCLUDEDIR} -c -o lrslibgmp.o lrslib.c ${GMP} lrslibmp.o: lrslib.c lrslib.h $(CC) ${CFLAGS} ${PLRSFLAGS} -DMA -DMP -c -o lrslibmp.o lrslib.c lrsgmp.o: ${ARITH}lrsgmp.c ${ARITH}lrsgmp.h $(CC) ${CFLAGS} -DMA -I${INCLUDEDIR} -c -o lrsgmp.o ${ARITH}lrsgmp.c ${GMP} lrsmp.o: ${ARITH}lrsmp.c ${ARITH}lrsmp.h $(CC) ${CFLAGS} -DMA -DMP -c -o lrsmp.o ${ARITH}lrsmp.c inedel: inedel.c ${ARITH}lrsgmp.h ${ARITH}lrsgmp.c $(CC) ${CFLAGS} -I${INCLUDEDIR} -L${LIBDIR} -DGMP -o inedel inedel.c ${ARITH}lrsgmp.c -lgmp polyv: polyv.c ${ARITH}lrsgmp.h ${ARITH}lrsgmp.c $(CC) $(CFLAGS) -I${INCLUDEDIR} -L${LIBDIR} -DGMP -o polyv polyv.c ${ARITH}lrsgmp.c -lgmp lrslong1-mplrs.o: ${ARITH}lrslong.c ${ARITH}lrslong.h $(mpicxx) ${CFLAGS} -DTIMES -DSIGNALS -DMA -DSAFE -DLRSLONG -DMPLRS -c -o lrslong1-mplrs.o ${ARITH}lrslong.c lrslong2-mplrs.o: ${ARITH}lrslong.c ${ARITH}lrslong.h $(mpicxx) ${CFLAGS} -DTIMES -DSIGNALS -DMA -DSAFE ${BITS} -DLRSLONG -DMPLRS -c -o lrslong2-mplrs.o ${ARITH}lrslong.c lrslib1-mplrs.o: lrslib.c lrslib.h $(mpicxx) ${CFLAGS} -DTIMES -DSIGNALS -DMA -DSAFE -DLRSLONG -DMPLRS -c -o lrslib1-mplrs.o lrslib.c lrslib2-mplrs.o: lrslib.c lrslib.h $(mpicxx) ${CFLAGS} -DTIMES -DSIGNALS -DMA -DSAFE ${BITS} -DLRSLONG -DMPLRS -c -o lrslib2-mplrs.o lrslib.c lrslibgmp-mplrs.o: lrslib.c lrslib.h $(mpicxx) ${CFLAGS} -DMA -DTIMES -DSIGNALS ${GMP} -DMPLRS -I${INCLUDEDIR} -c -o lrslibgmp-mplrs.o lrslib.c lrsgmp-mplrs.o: ${ARITH}lrsgmp.c ${ARITH}lrsgmp.h $(mpicxx) ${CFLAGS} -DMA -DTIMES -DSIGNALS ${GMP} -DMPLRS -I${INCLUDEDIR} -c -o lrsgmp-mplrs.o ${ARITH}lrsgmp.c lrsdriver-mplrs.o: lrsdriver.c lrsdriver.h lrslib.h $(mpicxx) $(CFLAGS) -c -DMPLRS -o lrsdriver-mplrs.o lrsdriver.c mplrs.o: mplrs.c mplrs.h lrslib.h ${ARITH}lrsgmp.h $(mpicxx) ${CFLAGS} -I${INCLUDEDIR} ${GMP} -DMA -DMPLRS -DTIMES ${BITS} -DSIGNALS -D_WITH_GETLINE -c -o mplrs.o mplrs.c mplrs64.o: mplrs.c mplrs.h lrslib.h ${ARITH}lrsgmp.h $(mpicxx) ${CFLAGS} -I${INCLUDEDIR} ${GMP} -DMA -DMPLRS -DTIMES -DSIGNALS -D_WITH_GETLINE -c -o mplrs64.o mplrs.c mplrs: ${MPLRSOBJ} ${MPLRSOBJ2} $(mpicxx) ${CFLAGS} -DTIMES -DSIGNALS -D_WITH_GETLINE -DMPLRS -DMA ${BITS} -L${LIBDIR} -o mplrs ${MPLRSOBJ} ${MPLRSOBJ2} ${MINI} ${GMP} mplrs64: ${MPLRSOBJ64} mplrsgmp $(mpicxx) ${CFLAGS} -DTIMES -DSIGNALS -D_WITH_GETLINE -DMPLRS -DMA -L${LIBDIR} -o mplrs ${MPLRSOBJ64} -lgmp mplrsgmp: mplrs.c mplrs.h lrslib.c lrslib.h ${ARITH}lrsgmp.c ${ARITH}lrsgmp.h lrsdriver.h lrsdriver.c $(mpicxx) ${CFLAGS} -DTIMES -DSIGNALS -D_WITH_GETLINE -DMPLRS -DGMP -I${INCLUDEDIR} mplrs.c lrslib.c ${ARITH}lrsgmp.c lrsdriver.c -L${LIBDIR} -o mplrsgmp -lgmp mplrs1: mplrs.c mplrs.h lrslib.c lrslib.h ${ARITH}lrslong.c ${ARITH}lrslong.h lrsdriver.h lrsdriver.c $(mpicxx) ${CFLAGS} -DTIMES -DSIGNALS -D_WITH_GETLINE -DMPLRS -DSAFE -DLRSLONG mplrs.c lrslib.c ${ARITH}lrslong.c lrsdriver.c -o mplrs1 mplrs2: mplrs.c mplrs.h lrslib.c lrslib.h ${ARITH}lrslong.c ${ARITH}lrslong.h lrsdriver.h lrsdriver.c $(mpicxx) ${CFLAGS} -DTIMES -DSIGNALS -D_WITH_GETLINE -DMPLRS -DSAFE -DLRSLONG ${BITS} mplrs.c lrslib.c ${ARITH}lrslong.c lrsdriver.c -o mplrs2 mplrsmp: mplrs.c mplrs.h lrslib.c lrslib.h ${ARITH}lrsmp.c ${ARITH}lrsmp.h lrsdriver.h lrsdriver.c $(mpicxx) ${CFLAGS} -DMP -DTIMES -DSIGNALS -D_WITH_GETLINE -DMPLRS mplrs.c lrslib.c ${ARITH}lrsmp.c lrsdriver.c -o mplrsmp singlemplrs: mplrs1 mplrs2 flint: lrs.c lrslib.c lrslib.h ${ARITH}lrsgmp.c ${ARITH}lrsgmp.h @test -d ${INCLUDEDIR}/flint || { echo ${INCLUDEDIR}/flint not found; exit 1; } $(CC) -O3 -DFLINT ${PLRSFLAGS} -I/usr/local/include/flint lrs.c lrslib.c ${ARITH}lrsgmp.c lrsdriver.c -L/usr/local/lib -Wl,-rpath=/usr/local/lib -lflint -o lrsflint -lgmp mplrsflint: mplrs.c mplrs.h lrslib.c lrslib.h ${ARITH}lrsgmp.c ${ARITH}lrsgmp.h lrsdriver.c lrsdriver.h ${mpicxx} ${CFLAGS} -DTIMES -DSIGNALS -D_WITH_GETLINE -DFLINT -I${INCLUDEDIR}/flint -DMPLRS -o mplrsflint mplrs.c lrsdriver.c lrslib.c ${ARITH}lrsgmp.c -L${LIBDIR} -lflint -lgmp lrsgmp: lrs.c lrslib.c lrslib.h ${ARITH}lrsgmp.c ${ARITH}lrsgmp.h lrsdriver.h lrsdriver.c $(CC) ${CFLAGS} ${PLRSFLAGS} -I${INCLUDEDIR} -o lrsgmp lrs.c lrslib.c ${ARITH}lrsgmp.c lrsdriver.c -L${LIBDIR} ${MINI} ${GMP} single: lrs.c ${ARITH}lrslong.c ${ARITH}lrslong.h lrslib.c lrslib.h ${ARITH}lrsgmp.c ${ARITH}lrsgmp.h lrsdriver.h lrsdriver.c $(CC) ${CFLAGS} ${PLRSFLAGS} -DSAFE -DLRSLONG -o lrs1 lrs.c lrslib.c ${ARITH}lrslong.c lrsdriver.c $(CC) ${CFLAGS} ${PLRSFLAGS} ${BITS} -DSAFE -DLRSLONG -o lrs2 lrs.c lrslib.c ${ARITH}lrslong.c lrsdriver.c $(CC) ${CFLAGS} ${PLRSFLAGS} -DMP -o lrsmp lrs.c lrslib.c lrsdriver.c ${ARITH}lrsmp.c $(CC) ${CFLAGS} ${PLRSFLAGS} -DGMP -I${INCLUDEDIR} -o lrsgmp lrs.c lrslib.c ${ARITH}lrsgmp.c lrsdriver.c -L${LIBDIR} -lgmp $(CC) ${CFLAGS} ${PLRSFLAGS} -DMGMP -DGMP -I${INCLUDEDIR} -o lrsmgmp lrs.c lrslib.c ${ARITH}lrsgmp.c lrsdriver.c ${ARITH}mini-gmp.c allmp: lrs.c lrslib.c lrslib.h ${ARITH}lrsmp.c ${ARITH}lrsmp.h lrsdriver.h lrsdriver.c $(CC) ${CFLAGS} ${PLRSFLAGS} -DMP -o lrsmp lrs.c lrslib.c lrsdriver.c ${ARITH}lrsmp.c $(CC) ${CFLAGS} ${PLRSFLAGS} -DSAFE -DLRSLONG -o lrs1 lrs.c lrslib.c lrsdriver.c ${ARITH}lrslong.c $(CC) ${CFLAGS} ${PLRSFLAGS} -DSAFE -DLRSLONG ${BITS} -o lrs2 lrs.c lrslib.c lrsdriver.c ${ARITH}lrslong.c $(CC) ${CFLAGS} -DMP -DLRS_QUIET -o lrsnash lrsnash.c lrsnashlib.c lrslib.c lrsdriver.c ${ARITH}lrsmp.c $(CC) ${CFLAGS} -DMP -o setupnash setupnash.c lrslib.c lrsdriver.c ${ARITH}lrsmp.c $(CC) ${CFLAGS} -DMP -o setupnash2 setupnash2.c lrslib.c lrsdriver.c ${ARITH}lrsmp.c $(CC) ${CFLAGS} -o 2nash 2nash.c demo: lpdemo1.c lrslib.c lrsdriver.c lrslib.h ${ARITH}lrsgmp.c ${ARITH}lrsgmp.h $(CC) ${CFLAGS} -I${INCLUDEDIR} -L${LIBDIR} -o lpdemo1 lpdemo1.c lrslib.c lrsdriver.c ${ARITH}lrsgmp.c -lgmp -DGMP $(CC) ${CFLAGS} -I${INCLUDEDIR} -L${LIBDIR} -o lpdemo lpdemo.c lrslib.c lrsdriver.c ${ARITH}lrsgmp.c -lgmp -DGMP $(CC) ${CFLAGS} -I${INCLUDEDIR} -L${LIBDIR} -o lpdemo2 lpdemo2.c lrslib.c lrsdriver.c ${ARITH}lrsgmp.c -lgmp -DGMP $(CC) ${CFLAGS} -I${INCLUDEDIR} -L${LIBDIR} -o vedemo vedemo.c lrslib.c lrsdriver.c ${ARITH}lrsgmp.c -lgmp -DGMP $(CC) ${CFLAGS} -I${INCLUDEDIR} -L${LIBDIR} -o chdemo chdemo.c lrslib.c lrsdriver.c ${ARITH}lrsgmp.c -lgmp -DGMP lrsnash: lrsnash.c nashdemo.c lrsnashlib.c lrslib.c lrsnashlib.h lrslib.h ${ARITH}lrsgmp.c ${ARITH}lrsgmp.h ${ARITH}lrslong.h lrsdriver.h lrsdriver.c $(CC) ${CFLAGS} -I${INCLUDEDIR} -L${LIBDIR} -o lrsnashgmp lrsnash.c lrsnashlib.c lrslib.c ${ARITH}lrsgmp.c lrsdriver.c ${MINI} ${GMP} $(CC) ${CFLAGS} -DNASH -I${INCLUDEDIR} -L${LIBDIR} -o lrsnash1 lrsnash.c lrsnashlib.c lrslib.c ${ARITH}lrslong.c lrsdriver.c -DLRSLONG -DSAFE $(CC) ${CFLAGS} -DNASH -I${INCLUDEDIR} -L${LIBDIR} -o lrsnash2 lrsnash.c lrsnashlib.c lrslib.c ${ARITH}lrslong.c lrsdriver.c -DLRSLONG -DSAFE ${BITS} $(CC) ${CFLAGS} -I${INCLUDEDIR} -L${LIBDIR} -o nashdemo nashdemo.c lrsnashlib.c lrslib.c ${ARITH}lrsgmp.c lrsdriver.c ${MINI} ${GMP} $(CC) ${CFLAGS} -DMP -o setupnash setupnash.c lrslib.c lrsdriver.c ${ARITH}lrsmp.c $(CC) ${CFLAGS} -DMP -o setupnash2 setupnash2.c lrslib.c lrsdriver.c ${ARITH}lrsmp.c $(CC) ${CFLAGS} -I${INCLUDEDIR} -L${LIBDIR} -o 2nash 2nash.c cp lrsnashgmp lrsnash ###################################################################### # From here on the author is David Bremner to whom you should turn for help # # Shared library variables SONAME ?=liblrs.so.1 SOMINOR ?=.0.0 SHLIB ?=$(SONAME)$(SOMINOR) SHLINK ?=liblrs.so SHLIBOBJ2=lrslib2-shr.o lrslong2-shr.o # for 32 bit machines # SHLIBOBJ2= SHLIBOBJ=lrslong1-shr.o lrslib1-shr.o \ lrslibgmp-shr.o lrsgmp-shr.o lrsdriver-shr.o \ ${SHLIBOBJ2} SHLIBBIN=lrs-shared lrsnash-shared # Building (linking) the shared library, and relevant symlinks. ${SHLIB}: ${SHLIBOBJ} $(CC) -shared -Wl,-soname=$(SONAME) $(SHLIBFLAGS) -o $@ ${SHLIBOBJ} -lgmp ${SONAME}: ${SHLIB} ln -sf ${SHLIB} ${SONAME} ${SHLINK}: ${SONAME} ln -sf $< $@ # binaries linked against the shared library all-shared: ${SHLIBBIN} lrs-shared: ${SHLINK} lrs-shared.o $(CC) $^ -o $@ -L . -llrs lrsnash-shared: ${SHLINK} lrsnash.c $(CC) ${CFLAGS} -DGMP -DMA lrsnash.c lrsnashlib.c -I${INCLUDEDIR} -o $@ -L . -llrs -lgmp # driver object files lrs-shared.o: lrs.c $(CC) ${CFLAGS} -DMA ${BITS} -L${LIBDIR} -c -o $@ lrs.c # build object files for the shared library lrslib1-shr.o: lrslib.c lrslib.h $(CC) ${CFLAGS} ${SHLIB_CFLAGS} -DMA -DSAFE -DLRSLONG -c -o $@ lrslib.c lrsdriver-shr.o: lrsdriver.c $(CC) ${CFLAGS} ${SHLIB_CFLAGS} -c -o $@ $< lrslong1-shr.o: ${ARITH}lrslong.c ${ARITH}lrslong.h $(CC) ${CFLAGS} ${SHLIB_CFLAGS} -DMA -DSAFE -DLRSLONG -c -o $@ ${ARITH}lrslong.c lrslong2-shr.o: ${ARITH}lrslong.c ${ARITH}lrslong.h $(CC) ${CFLAGS} ${SHLIB_CFLAGS} -DMA -DSAFE ${BITS} -DLRSLONG -c -o $@ ${ARITH}lrslong.c lrslibgmp-shr.o: lrslib.c lrslib.h $(CC) ${CFLAGS} ${SHLIB_CFLAGS} -DMA -DGMP -I${INCLUDEDIR} -c -o $@ lrslib.c lrsgmp-shr.o: ${ARITH}lrsgmp.c ${ARITH}lrsgmp.h $(CC) ${CFLAGS} ${SHLIB_CFLAGS} -DMA -DGMP -I${INCLUDEDIR} -c -o $@ ${ARITH}lrsgmp.c lrslib2-shr.o: lrslib.c lrslib.h $(CC) ${CFLAGS} ${SHLIB_CFLAGS} -DMA -DSAFE ${BITS} -DLRSLONG -c -o $@ lrslib.c ###################################################################### # install targets # where to install binaries, libraries, include files prefix ?= /usr/local INSTALL_INCLUDES=lrslib.h lrsdriver.h ${ARITH}lrsgmp.h ${ARITH}lrslong.h ${ARITH}lrsmp.h lrsrestart.h install: all-shared install-common mkdir -p $(DESTDIR)${prefix}/bin for file in ${SHLIBBIN}; do cp $${file} $(DESTDIR)${prefix}/bin/$$(basename $$file -shared); done mkdir -p $(DESTDIR)${prefix}/lib install -t $(DESTDIR)${prefix}/lib $(SHLIB) cd $(DESTDIR)${prefix}/lib && ln -sf $(SHLIB) $(SHLINK) cd $(DESTDIR)${prefix}/lib && ln -sf $(SHLIB) $(SONAME) install-common: mkdir -p $(DESTDIR)${prefix}/include/lrslib install -t $(DESTDIR)${prefix}/include/lrslib ${INSTALL_INCLUDES} ###################################################################### clean: rm -f lrs lrs1 lrsgmp lrsmgmp lpdemo lpdemo1 lpdemo2 mplrs1 mplrs mplrsmp mplrsgmp lrs2 mplrs2 lrsflint mplrsflint rm -f *.o *.exe *.so redund fel minrep rm -f lrsmp lrsMP hvref setupnash setupnash2 lrsnashgmp lrsnash lrsnash1 lrsnash2 nashdemo 2nash vedemo polyv inedel rm -f ${LRSOBJ} ${LRSOBJ64} ${SHLIBOBJ} ${SHLIB} ${SONAME} ${SHLINK} rm -f ${SHLIBBIN} lrslib-073/man/0000777000175000017500000000000014625766600012135 5ustar avisavislrslib-073/man/html/0000777000175000017500000000000014625766600013101 5ustar avisavislrslib-073/man/html/index.html0000777000175000017500000000256014625766577015121 0ustar avisavis Manpage of lrslib

lrslib man pages

lrslib(5)            Main package description

lrsarith(5)        Multiprecision arithmetic package description

lrsscripts(5)        Various scripts for basic lrslib functions

Main programs

lrs (1)   mplrs(1)   redund/minrep(1)   fel(1)   lrsnash(1)   hvref(1)   polyv(1)

lrs home page

lrslib-073/man/html/man1/0000777000175000017500000000000014625766600013735 5ustar avisavislrslib-073/man/html/man1/fel.1.html0000777000175000017500000002056314625766577015556 0ustar avisavisContent-type: text/html; charset=UTF-8 Man page of fel

fel

Section: lrslib 7.3 (1)
Updated: 2024.1.10
Index Return to Main Contents
 

Name

fel - Project an H-representation or V-representation onto a subset of columns.  

Synopsis

fel [input-file] [output-file]
mpirun -np [procs] mplrs -fel [input-file] [output-file] [option...]
 

Description

fel is an alias of lrs which can also perform these functions via
the eliminate and project options.

H-representation.
The input is projected onto a given set of columns using Fourier-Motzkin elimination. An H-representation is output after each iteration. mplrs -fel is a fully parallel version that performs one iteration only, see mplrs(1).
V-representation.
The specified columns are extracted and redundant rows are removed. The output can be can be piped directly into lrs. Not implemented in mplrs.

 

Options

These options are placed after the end statement.

eliminate k i_1 i_2 ... i_k (new in v7.2)
(H-representation) Eliminates k variables in an H-representation corresponding to cols i_1 .. i_k by projection onto the remaining variables using the Fourier-Motzkin method. Variables are eliminated in the order given and redundancy is removed after each iteration.
(V-representation) Delete the k given columns from the input matrix and remove redundancies (cf. extract where redundancies are not removed).
Column indices are between 1 and n-1 and column zero cannot be eliminated. The output is a valid lrs input file.

project k i_1 i_2 ... i_k (new in v7.2)
(H-representation) Project the polyhedron onto the k variables corresponding to cols i_1 .. i_k using the Fourier-Motzkin method. Column indices are between 1 and n-1 and column zero is automatically retained. Variables not contained in the list are eliminated using a heuristic which chooses the column which minimizes the product of the number of positive and negative entries. Redundancy is removed after each iteration using linear programming.
(V-representation) Extract the k given columns from the input matrix and remove redundancies. Column indices are between 1 and n-1 and column zero is automatically extracted (cf. extract where redundancies are not removed).
The output as a valid lrs input file.

See also extract in lrs(1).

verbose

For an H-representation give, for each iteration, statistics on how many new inequaties were created and how many of these were redundant. See Example below.

 

Example

(1) Project onto columns 1 and 3 in an H-representation


 % cat cube.ine
 cube.ine
 H-representation
 begin
 6 4 rational
 1  1  0  0
 1  0  1  0
 1  0  0  1
 1 -1  0  0
 1  0  0 -1
 1  0 -1  0
 end
 project 2 1 3
 verbose


 % fel cube.ine
 fel:lrslib_v.7.3_2024.1.10(64bit,lrslong.h,hybrid_arithmetic)
 *Input taken from  cube.ine
 cube
 
 *switching to fel mode
 *project 2  1 3 
 *after removing column 2
 *checking for redundant rows only
 H-representation
 begin
 4 3 rational
  0  1  0 
  1 -1  0 
  1  0 -1 
 -1  0  1 
 end
 *number of       number after    number of       remaining      column  
 *inequalties     removing col    redundancies     rows          removed 
 *         7              6             2             4             2    
 --------------------------------------------------------------------


 
 *original vars remaining: 1 3

(2) Eliminate columns 1,2,3 from a V-representation


 % cat cp4.ext
 V-representation
 begin
 8 7 rational
  1  0  0  0  0  0  0 
  1  0  1  1  1  1  0 
  1  1  1  0  0  1  1 
  1  1  0  0  1  1  0 
  1  0  0  1  0  1  1 
  1  1  1  1  0  0  0 
  1  0  1  0  1  0  1 
  1  1  0  1  1  0  1 
 end
 eliminate 3 1 2 3 
 
 % lrs cp4.ext
 lrs:lrslib_v.7.3_2024.1.12(64bit,lrslong.h,hybrid_arithmetic)
 *Input taken from  cp4.ext
 cp4
 
 *switching to fel mode
 *eliminate 3  1 2 3 
 *checking for redundant rows only
 V-representation
 begin
 4 4 rational
  1  1  1  0 
  1  0  1  1 
  1  0  0  0 
  1  1  0  1 
 end
 *columns retained: 0 4 5 6

 

Notes

1.
FAQ page
https://inf.ethz.ch/personal/fukudak/polyfaq/polyfaq.html
2.
User's guide for lrslib
http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html
 

Author

David Avis <avis at cs dot mcgill dot ca >  

See also

lrs(1), mplrs(1), lrslib(5),

 

Index

Name
Synopsis
Description
Options
Example
Notes
Author
See also
This document was created by man2html, using the manual pages.
Time: 07:33:14 GMT, January 31, 2024 lrslib-073/man/html/man1/hvref.1.html0000777000175000017500000001166414625766577016124 0ustar avisavisContent-type: text/html; charset=UTF-8 Man page of xref|hvref

xref|hvref

Section: lrslib 7.3 (1)
Updated: 2023.1.4
Index Return to Main Contents
 

Name

xref|hvref - produce a cross reference list between H- and V-representations.
   

Synopsis

xref [input-file]
hvref [input-file]
 

Description

These programs are part of and must be compiled with lrslib which is a C library. All computations are done in exact arithmetic.

xref and hvref produce a cross reference list between H- and V-representations.

xref/hvref Cross reference listing between V- and H-representations

In the example below we start from an H-representation of cube.ine but the same steps apply to the V-representation cube.ext. It is recommended to first remove any redundancies from the input file using redund.

1. Add printcobasis and incidence options to cube.ine and run lrs.
 % cat cube.ine
 cube
 H-representation
 begin
 6 4 rational
  0  1  0  0
  0  0  1  0
  0  0  0  1
  1 -1  0  0
  1  0 -1  0
  1  0  0 -1
 end
 printcobasis
 incidence
  % lrs cube.ine cube.ext

2. Run xref on the output file cube.ext getting cube.ext.ex


 % xref cube.ext
 % cat cube.ext.ex lg% cat cube.ext.x
 V-representation
     1   4 5 6    #
     2   1 5 6    #
     3   2 4 6    #
     4   1 2 6    #
     5   3 4 5    #
     6   1 3 5    #
     7   2 3 4    #
     8   1 2 3    #

3. Edit the file cube.ext.x to insert a second line that contains two integers

rows maxindex

where rows >= # output lines in cube.ext.x
      maxindex >= # input lines in cube.ine

or just use 0 0 and run hvref, the output will tell you which values to use.

% hvref cube.ext.x % hvref cube.ext.x


 V-representation
 8 8
 1: 4 5 6
 2: 1 5 6
 3: 2 4 6
 4: 1 2 6
 5: 3 4 5
 6: 1 3 5
 7: 2 3 4
 8: 1 2 3
 
 H-representation
 6 8
 1: 2 4 6 8
 2: 3 4 7 8
 3: 5 6 7 8
 4: 1 3 5 7
 5: 1 2 5 6
 6: 1 2 3 4
 input rows=8 maxindex=6
 

 

Notes

1.
FAQ page
https://inf.ethz.ch/personal/fukudak/polyfaq/polyfaq.html
2.
User's guide for lrslib
http://cgm.cs.mcgill.ca/~avis/C/lrslib/USERGUIDE.html
 

Author

David Avis <avis at cs dot mcgill dot ca >  

See also

mplrs(1), lrslib(5), lrsnash(1)

 

Index

Name
Synopsis
Description
Notes
Author
See also
This document was created by man2html, using the manual pages.
Time: 07:33:14 GMT, January 31, 2024 lrslib-073/man/html/man1/lrs.1.html0000777000175000017500000005646114625766577015616 0ustar avisavisContent-type: text/html; charset=UTF-8 Man page of lrs

lrs

Section: lrs 7.3 (1)
Updated: 2023.1.4
Index Return to Main Contents
 

Name

lrs - Convert between representations of convex polyhedra, remove redundant inequalities, convex hull computation, volume, triangulation, solution to linear programs in exact precision.  

Synopsis

lrs|plrs [input-file] [output-file]
redund|minrep [input-file] [output-file] See: redund(1)
fel [input-file] [output-file] See: fel(1)
hvref/xref [input-file] See: xref(1)
 

Description

These programs are part of and must be compiled with lrslib which is a C library. All computations are done in exact arithmetic.

A polyhedron can be described by a list of inequalities (H-representation) or by a list of its vertices and extreme rays (V-representation).

lrs converts an H-representation of a polyhedron to its V-representation and vice versa, known respectively as the vertex enumeration and facet enumeration problems (see Example (1) below). For V-representations the volume can be computed and a triangulation produced. lrs can also be used to solve a linear program, remove linearities from a system, and extract a subset of columns.
plrs is a primitive multi-threaded version of lrs that gives some speedup on shared memory machines. See threads option. For a fully parallel version see mplrs(1)

redund|minrep
These are aliases of lrs which can also perform these functions via the redund, redund_list and testlin options. For a more complete description and examples see redund(1).
H-representation: redundant inequalities in an input H-representation are removed and the remaining inequalities output. In addition minrep checks for hidden linearities.
V-representation: outputs all extreme points and extreme rays, often called the convex hull problem. In addition minrep checks for hidden linearities.

fel projects an input H-representation onto a given set of variables using Fourier-Motzkin elimination. For a V-representation it extracts the specified columns. The output is non-redundant and can be can be piped directly into lrs. This is an alias of lrs which can also perform these functions via the eliminate and project options.

hvref/xref produce a cross reference list between H- and V-representations. See xref(1).

mplrs is Skip Jordan's parallel wrapper based on MPI for lrs/redund using the same input and output formats. See: mplrs(1)

Fukuda's FAQ page[1] contains a more detailed introduction to the problem, along with many useful tips for the new user. User's guide for lsrslib[8]

 

File formats

File formats were developed jointly with Komei Fukuda and are compatible with cdd/cddlib[2].
The input for lrs/redund is an H- or V-representation of a polyhedron.


 name
 H-representation [or V-representation]
 {options}
 {linearities}
 begin
  m n rational [or integer]
 {input matrix}
 end 
 {options}

name is a user supplied name for the polyhedron.  Comments may appear before the begin or after the end and should begin with a special character such as "*".

If the representation is not specified H-representation is assumed. The input coefficients are read in free format, and are not checked for type. Coefficients are separated by white space. m is the number of rows and n the number of columns of the input matrix.  

H-representation

m is the number of input rows, each being an inequality or equation.
n is the number of input columns and d=n-1 is the dimension of the input.
An inequality or equation of the form:

b + a_1 x_1 + ... + a_d x_d >=  0

b + a_1 x_1 + ... + a_d x_d =  0

is input as the line:

b  a_1 ... a_d

The coefficients can be entered as integers or rationals in the format x/y. To distinguish an equation a linearity option must be supplied before the begin line (see below).  

V-representation

m is the number of input rows, each being a vertex, ray or line.
n is the number of input columns and d=n-1 is dimension of the input.
Each vertex is given in the form:

1   v_1   v_1 ... v_d

Each ray is given in the form:

0   r_1   r_2...   r_d

where r_1  ...   r_d is a point on the ray.

There must be at least one vertex in each file. For bounded polyhedra there will be no rays entered. The coefficients can be entered as integers or rationals in the format x/y. An input line can be specified as a ray and then included in the linearity option (see below).

Note for cdd users: Note the input files for lrs are read in free format. lrs will look for exactly m*n rationals or integers separated by white space (blank, carriage return, tab etc.). lrs will not "drop" extra columns of input if n is less than the number of columns supplied.

 

Options

Almost all options are placed after the end statement, maintaining compatibility with cdd. Where this is not the case, it will be mentioned explicitly.

allbases This option instructs lrs to list each vertex (or facet) for each of its bases. This option is often combined with printcobasis.

bound  x (H-representation only). Either the maximize or minimize option should be selected. x is an integer or rational. For maximization (resp. minimization) the reverse search tree is truncated  whenever the current objective value is less (resp. more) than x.

cache n     (default n=50)
lrs stores the latest  n dictionaries in the reverse search tree. This speeds up the backtracking step, but requires more memory.

debug  startingcobasis endingcobasis
Print out cryptic but detailed trace, dictionaries etc. starting at #B=startingcobasis and ending at #B=endingcobasis. debug 0 0 gives a complete trace.

digits n (lrsmp arithmetic only - placed before the begin statement)
n is the maximum number of decimal digits to be used. If this is exceeded the program terminates with a message and can usually be restarted with the restart option. The default is set to 100 digits. At the end of a run a message is given informing the user of the maximum integer size encountered.

dualperturb If lrs is executed with the maximize or minimize option, the reverse search tree is rooted at an optimum vertex for this function. If there are multiple optimum vertices, the output will often not be complete. This option gives a small perturbation to the objective to avoid this. A warning message is given if the starting dictionary is dual degenerate.

estimates k
Estimate the output size. Used in conjunction with maxdepth and seed. See: Estimation[3].

eliminate k i_1 i_2 ... i_k (see fel(1))
(H-representation) Eliminates k variables in an H-representation corresponding to cols i_1 .. i_k by projection onto the remaining variables using the Fourier-Motzkin method. Variables are eliminated in the order given and redundancy is removed after each iteration.
(V-representation) Delete the k given columns from the input matrix and remove redundancies (cf. extract where redundancies are not removed).
Column indices are between 1 and n-1 and column zero cannot be eliminated. The output is a valid lrs input file. See also project and extract

extract [ k i_1 i_2 ... i_k ]
(H-representation) A preprocessing step to remove linearities (if any) in an H-representation and resize the A matrix. The output as a valid lrs input file. The resulting file will not contain any equations but may not be full dimensional as there may be additional linearities in the remaining inequalities. Options in the input file are stripped. The user can specify the k columns i_1 i_2 ... i_k to retain otherwise if k=0 or is ommitted the lex-min set of columns are retained, equivalent to the the order 1,2,..n-1. Linearly dependent columns are skipped and additional indices are taken from 1,2,...,n-1 as necessary. If there are no linearities in the input file the given columns are retained and the other ones are deleted.
(V-representation) Extract the given columns from the input file outputing a valid lrs input file. Options are stripped.

geometric   (H-representation  or voronoi option only) Each ray is printed together with the vertex with which it is incident.

incidence This option automatically switches on printcobasis. For input H-representation, indices of all input inequalities that contain the vertex/ray that is about to be output. For input V-representation, indices of all input vertices/rays that lie on the facet that is about to be output. A starred index indicates that this vertex  is also in the cobasis, but is not contained in the facet. It arises due to the lifting operation used with input V-representations.

linearity  k  i_1  i_2  ...  i_k (placed before begin statement)
(H-representation) The k rows i_1  i_2  ...  i_k  of the input file represent equations. (V-representation) The k rows, which should have a zero in column 1, represent lines in space (rather than rays).

lponly Solve the LP given by the input H-representation with objective function specified by the maximize or minimize options and terminate. Use with verbose option to get dual variables. See: Linear Programming[4].

maxcobases k
The search will be truncated after k cobases have been generated.

maxdepth k
The search will be truncated at depth k. All bases with depth less than or equal to k will be computed.  k is  a non-negative integer, and this option is used for estimates - see Estimation[3]. Note: For H-representations, rays at depth k will not be reported. For V-representations, facets at depth k will not be reported.

maximize  b  a_1 ... a_{n-1}  
minimize  b  a_1 ... a_{n-1}  
(H-representation) The starting vertex maximizes (or minimizes) the function  b + a_1 x_1+ ... + a_{n-1} x_{n-1}.
The dualperturb option may be needed to avoid dual degeneracy. Often used with lponly.
(V-representation, v.7.2) The input file row numbers maximizing(minimizing) the function are output along with the optimum value. Using verbose the optimizing lines are also printed. With minimization a facet gives an optimum value of zero, a negative value indicates infeasibility and a positive value indicates strong redundancy.

maxincidence n k
Prunes the search tree when the depth is at least k and the current vertex/facet has incidence at least n. Using verbose a message is printed whenever the search tree is pruned.

maxoutput n
Limits number of output lines produced (either vertices+rays or facets) to n

mindepth k
Backtracking will be terminated at depth k.

nonnegative (This option must come before the begin statement - H-representation only)   Bug: Can only be used if the origin is a vertex of the polyhedron  For problems where the input is an H-representation of the form b+Ax>=0, x>=0 (ie. all variables non-negative, all constraints inequalities) it is not necessary to give the non-negative constraints explicitly if the nonnegative option is used. This option cannot be used for V-representations, or with the linearity option (in which case the linearities will be treated as inequalities). This option may be used with redund , but the implied nonnegativity constraints are not tested themselves for redundancy.

project k i_1 i_2 ... i_k (see fel(1))
(H-representation) Project the polyhedron onto the k variables corresponding to cols i_1 .. i_k using the Fourier-Motzkin method. Column indices are between 1 and n-1 and column zero is automatically retained. Variables not contained in the list are eliminated using a heuristic which chooses the column which minimizes the product of the number of positive and negative entries. Redundancy is removed after each iteration using linear programming.
(V-representation) Extract the k given columns from the input matrix and remove redundancies. Column indices are between 1 and n-1 and column zero is automatically extracted (cf. extract where redundancies are not removed).
The output as a valid lrs input file. See also eliminate and extract

printcobasis k
Every k-th cobasis is printed. If k is omitted, the cobasis is printed for each vertex/ray/facet that is output. For a long run it is useful to print the cobasis occasionally so that the program can be restarted if necessary. H-representation: the cobasis is a list the indices of the inequalities from the input file that define the current vertex or ray. For rays the cobasis is the cobasis of the vertex from which the ray emanates. One of the indices is starred, this indicates the inequality to be dropped from the cobasis to define the ray. If the allbases option is used, all cobases will be printed. V-representation: the cobasis is a list of the input vertices/rays that define the current facet. See option incidence for more information.

printslack (H-representation only) A list of the indices of the input inequalities that are satisfied strictly for the current vertex, ie. corresponding slack variable is positive. If nonnegative is set, the list will also include indices n+i for each decision variable x_i which is positive.

redund start end (see redund(1))
Check input lines with line numbers from start to end and remove any redundant lines.
redund 0 0 will check all input lines.

redund_list k i_1 i_2 ... i_k (see redund(1))
Check the k input line numbers with indices i_1 i_2 ... i_k and remove any redundant lines.

restart  V# R# B# depth {facet #s or vertex/ray #s}
lrs can be restarted from any known cobasis. The calculation will proceed to normal termination. All of the information is contained in the output from a printcobasis option.  The order of the indices is very important, enter them exactly as they appear in the output from the previously terminated run.

seed k
Set the random number generator seed=k. Used with estimates.

startingcobasis i_1  i_2  ...  i_{n-1}
lrs will start from the given cobasis which which is a list of the inequalities (for H-representation) or vertices/rays (for V-representation) that define it. If it is invalid, or this option is not specified, lrs will find its own starting cobasis.

testlin (before the begin line only) H-representation only (new 7.3)
redund An LP test will be made for hidden linearities at the beginning of the run and is reported. If there are no hidden linearities one LP per constraint tests for redundancy. (mplrs can be run with no verification step.) If hidden linearities exist two LPs per constraint search for hidden linearities and remove redundancies. In both cases the run ends with a minimum set of linearities and inequalities (ie. no hidden inequalities or duplicates) and the dimension is reported. (mplrs will find all linearities but some non redundant inequalities may be eliminated, so a second run is required.)
lrs If neither redund or redund_list options are present the initial LP test is made, reported and the run halted. Otherwise same as redund above.

threads n (new in 7.3, currently for plrs1,plrs2,plrsgmp,plrsmp and script plrs)
Multithreaded lrs using openMP for a parallel for loop at depth 0 in the search tree. Disabled for mplrs. If n is not specified the default openMP max threads is used.

truncate The reverse search tree is truncated(pruned)  whenever a new vertex is encountered. Note: This does note necessarily produce the set of all vertices adjacent to the optimum vertex in the polyhedron, but just a subset of them.

verbose Print slightly more detailed information about the run.

volume (V-representation only) Compute the volume and, if the verbose option is also included, output a triangulation. See Volume Computation[5].

voronoi (V-representation  only - place immediately after end statement)
Compute Voronoi diagram - see Voronoi Diagrams[6].  

Arithmetic

From version 7.1 lrs/redund/mplrs use hybrid arithmetic with overflow checking, starting in 64bit integers, moving to 128bit (if available) and then GMP. Overflow checking is conservative to improve performance: eg. with 64 bit arithmetic, a*b triggers overflow if either a or b is at least 2^31, and a+b triggers an overflow if either a or b is at least 2^62. Typically problems that can be solved in 64bits run 3-4 times faster than with GMP and inputs solvable in 128bits run twice as fast as GMP.

Various arithmetic versions are available and can be built from the makefile:

lrs1 Fixed length 64 bit integer arithmetic, terminates on overflow.

lrs2 Fixed length 128 bit integer arithmetic, terminates on overflow.

lrsmp Built in extended precision integer arithmetic, uses digits option above.

lrsgmp GNU MP which must be installed first from https://gmplib.org/.

lrsflint FLINT hybrid arithmetic which must be installed first from http://www.flintlib.org/

 

Examples

(1) Convert the H-representation of a cube given cube by 6 the six inequalities
-1 <= x_i <= 1 , i=1,2,3 into its V-representation consisting of 8 vertices.


 % cat cube.ine
 cube.ine
 H-representation
 begin
 6 4 rational
 1  1  0  0
 1  0  1  0
 1  0  0  1
 1 -1  0  0
 1  0  0 -1
 1  0 -1  0
 end


 % lrs cube.ine


 *lrs:lrslib v.6.3 2018.4.11(64bit,lrslong.h,overflow checking)
 *Input taken from file cube.ine
 cube.ine
 V-representation
 begin
 ***** 4 rational
 1  1  1  1
 1 -1  1  1
 1  1 -1  1
 1 -1 -1  1
 1  1  1 -1
 1 -1  1 -1
 1  1 -1 -1
 1 -1 -1 -1
 end
 *Totals: vertices=8 rays=0 bases=8 integer_vertices=8

 

Notes

1.
FAQ page
https://inf.ethz.ch/personal/fukudak/polyfaq/polyfaq.html
2.
cdd
https://inf.ethz.ch/personal/fukudak/cdd_home/
3.
Estimation.
http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html#Estimation
4.
Linear Programming
http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html#Linear%20Programming
5.
Volume Computation.
http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html#Volume%20Computation
6.
Voronoi Diagrams.
http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html#Voronoi%20Diagrams
7.
redund: extreme point enumeration and eliminating redundant inequalities
http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html#redund
8.
User's guide for lrslib
http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html
 

Author

David Avis <avis at cs dot mcgill dot ca >  

See also

mplrs(1), lrslib(5), lrsnash(1)

 

Index

Name
Synopsis
Description
File formats
H-representation
V-representation
Options
Arithmetic
Examples
Notes
Author
See also
This document was created by man2html, using the manual pages.
Time: 07:33:14 GMT, January 31, 2024 lrslib-073/man/html/man1/lrsnash.1.html0000777000175000017500000001500414625766600016437 0ustar avisavisContent-type: text/html; charset=UTF-8 Man page of lrsnash

lrsnash

Section: lrslib 7.3 (1)
Updated: 2024.1.31
Index Return to Main Contents
 

Name

lrsnash:   Compute Nash-equibria in 2-person games.  

Synopsis

lrsnash  [options...] [input-file]
lrsnash1 [options...] [input-file]
lrsnash2 [options...] [input-file]
nashdemo 

options:
    -v, --verbose         Prints a trace of the solution process
    -d, --debug           Dumps lots of information for debugging
    -p, --printgame       Prints the payoff matrix for the game
    -s, --standard        Promise that input files have standard structure
    -o, --outfile <file>  Send output to <file>
    -h, --help            Prints this text
     Short options can be grouped, as in '-ps' and '-do out.txt'

 

Description

These C programs are distributed as part of the lsrslib[2] package and must be compiled with it.

Alice has a payoff matrix A and Bob has a playoff matrix B, both of dimension m by n. Alice assigns probabilities x to the rows and Bob y to the columns. Alice receives payoff x^T A y and Bob receives x^T B y. A Nash equilibriam occurs for pairs x,y for which neither player can improve their expected payoff by unilateraly changing strategies.

lrsnash is an application of lrs for finding Nash-equilibria in 2-person matrix games using a method described in [1]. It uses GMP exact extended precision arithmetic.

lrsnash1 is the same as lrsnash except that it uses 64 bit exact arithmetic and terminates if overflow is detected. It is about 3-4 times faster.

lrsnash2 is the same as lrsnash except that it uses 128 bit exact arithmetic and terminates if overflow is detected. It is about twice as fast. It requires a C compiler with __int128 support (eg. gcc v. 4.6.0 or later).

nashdemo is a simple template for lrsnash. It builds two 3x4 matrices A and B and computes their equilibria.

The running time may be significantly different depending on the order of the two matrices in the input. For large problems it may be advantageous to run lrsnash twice in parallel with the matrices in different orders. There is also a more complex legacy input format recognized by lrsnash that is described in [1].

 

File formats

The input file consists of two integers m and n on line 1 followed by two mxn payoff matrices A and B:


 m n                                            
 A          (row by row)                    
 B          (row by row)      

 

Example

The input file game has two 3x2 payoff matrices:


 %cat game


 3 2
 
 0 6
 2 5
 3 3
 
 1 0
 0 2
 4 3


 % lrsnash game
 
 2  1/3  2/3  4 
 1  2/3  1/3  0  2/3 
 
 2  2/3  1/3  3 
 1  0  1/3  2/3  8/3 
 
 2  1  0  3 
 1  0  0  1  4 
 
 *Number of equilibria found: 3
 *Player 1: vertices=5 bases=5 pivots=8
 *Player 2: vertices=3 bases=1 pivots=8

Interpretation There are 3 Nash equilibria. For the first one:


 2  1/3  2/3  4    
Bob(player 2) plays column 1 and 2 with probablilities y=(1/3, 2/3) and the payoff to Alice(player 1) is 4.


 1  2/3  1/3  0  2/3
Alice plays rows 1,2,3 with probabilities x=(2/3, 1/3, 0) and the payoff to Bob is 2/3.

 

Notes

1.
D. Avis, G. Rosenberg, R. Savani, B. von Stengel, Enumeration of Nash Equilibria for Two-Player Games, Economic Theory 42(2009) 9-37
2.
User's guide for lrslib
http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html
 

Authors

David Avis and Terje Lensberg  

See also

lrslib(5)

 

Index

Name
Synopsis
Description
File formats
Example
Notes
Authors
See also
This document was created by man2html, using the manual pages.
Time: 07:33:14 GMT, January 31, 2024 lrslib-073/man/html/man1/minrep.1.html0000777000175000017500000002221114625766600016255 0ustar avisavisContent-type: text/html; charset=UTF-8 Man page of redund|minrep

redund|minrep

Section: lrslib 7.3 (1)
Updated: 2024.1.10
Index Return to Main Contents
 

Name

redund|minrep - Remove redundant inequalities from an H-representation or redundant vertices (non-extreme points) from a V-representation. minrep also identifies hidden linearities.  

Synopsis

redund [input-file] [output-file]
minrep [input-file] [output-file]
mpirun -np [procs] mplrs -minrep [input-file] [output-file] [option...]
 

Description

redund and minrep are aliases to lrs which is part of

the C library lrslib(5). This functionality can also be performed by lrs directly by using the options described below. All computations are done in exact arithmetic. For input file descriptions see lrs(1). A parallel version of minrep is given by mplrs -minrep. The -redund option performs the same function and is retained for legacy. (see mplrs(1))

redund
H-representation: redundant inequalities in an input H-representation are removed and the remaining inequalities output. Hidden linearities are not detected unless the testlin option is included, in which case the output is a minimum representation and the dimension is reported.
V-representation: outputs all extreme points and extreme rays, often called the convex hull problem. The testlin option cause linearities to be detected and explicitly output.
Outputs can be piped directly into lrs. redund is a link to lrs which can also perform these functions via the testlin, redund and redund_list options. mplrs -redund always sets the testlin option, so always produces minimum representations.

minrep
Equivalent to redund with the testlin option.

With no options minrep|redund will process the entire input file.

redund start end
Check input lines with line numbers from start to end and remove any redundant lines.
redund 0 0 will check all input lines.

redund_list k i_1 i_2 ... i_k
Check the k input line numbers with indices i_1 i_2 ... i_k and remove any redundant lines.

testlin (before the begin line only) (new 7.3)
An LP test will be made for hidden linearities at the beginning of the run and is reported. If there are no hidden linearities one LP per constraint tests for redundancy. (mplrs can be run with no verification step.) If hidden linearities exist two LPs per constraint search for hidden linearities and remove redundancies. In both cases the run ends with a minimum set of linearities and inequalities (ie. no hidden inequalities or duplicates) and the dimension is reported. (mplrs will find all linearities but some non redundant inequalities may be eliminated, so a second run is required.)

verbose
As each input line is checked a message is printed telling its status

 *nr :non-redundant 
 *re :redundant 
 *sr :strongly redundant
For an H-representation strongly redundant means the feasible region lies in its open half-space. For a V-representation it means that the point lies in the (relative) interior of the convex hull.
In addition minrep may report
 *li :linearity  

Examples

(1) Remove hidden linearities and minimum representation of an H-representation.
 % cat cube.ine
 H-representation
 begin
 7 4 rational
  0  1  0  0 
  0  0  1  0 
  0  0  0  1 
  1 -1  0  0 
  1  0 -1  0 
  1  0  0 -1 
 -1  0  0  1
 end
 verbose
 
 % minrep cube.ine
 minrep:lrslib_v.7.3_2024.1.10(64bit,lrslong.h,hybrid_arithmetic)
 *Input taken from  cube.ine
 *hidden linearities exist
 *finding minimum representation
 *nr 0  1  0  0 
 *nr 0  0  1  0 
 *sr 0  0  0  1 
 *nr 1 -1  0  0 
 *nr 1  0 -1  0 
 *li 1  0  0 -1 
 *li-1  0  0  1 
 *linearity in row=6 removed or in cobasis, independent
 *linearity in row=7 dependent, made redundant
 H-representation
 linearity 1 1
 begin
 5 4 rational
  1  0  0 -1 
  0  1  0  0 
  0  0  1  0 
  1 -1  0  0 
  1  0 -1  0 
 end
 
 *input had 7 rows and 4 columns
 * 2 redundant row(s) found
  3 7
 * 1 hidden linearity found
 

(2) Compute the extreme points of a set of 10 points in R^3


 % cat c.ext
 V-representation
 begin
 10 4 rational
 1  1  1  1 
 1  0  1  1 
 1 1/2 0 1/3
 1  1  1  0 
 1  0  1  0 
 1  1  0  0 
 1  0  0  0 
 1  0 1/3 1/4
 1  1  0  1 
 1  0  0  1 
 end


 % redund c.ext


 *redund:lrslib v.7.2 2020.6.8(64bit,lrslong.h,hybrid arithmetic)
 *Input taken from  c.ext
 V-representation
 begin
 8 4 rational
 1  1  1  1 
 1  0  1  1 
 1  1  1  0 
 1  0  1  0 
 1  1  0  0 
 1  0  0  0 
 1  1  0  1 
 1  0  0  1 
 end
 *Input had 10 rows and 4 columns
 * 2 redundant row(s) found:
 3 8

 

Notes

1.
FAQ page
https://inf.ethz.ch/personal/fukudak/polyfaq/polyfaq.html
2.
redund: extreme point enumeration and eliminating redundant inequalities
http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html#redund
3.
User's guide for lrslib
http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html
 

Author

David Avis <avis at cs dot mcgill dot ca >  

See also

lrs(1), mplrs(1), lrslib(5),

 

Index

Name
Synopsis
Description
Examples
Notes
Author
See also
This document was created by man2html, using the manual pages.
Time: 07:33:14 GMT, January 31, 2024 lrslib-073/man/html/man1/mplrs.1.html0000777000175000017500000001753714625766600016137 0ustar avisavisContent-type: text/html; charset=UTF-8 Man page of mplrs

mplrs

Section: mplrs 7.3 (1)
Updated: 2024.2.5
Index Return to Main Contents
 

Name

mplrs - Convert between representations of convex polyhedra, remove redundant inequalities, do Fourier-Motzkin elimination (parallel version).  

Synopsis

mpirun -np num_proc mplrs infile [outfile] [option...]

 

Description

A polyhedron can be described by a list of inequalities (H-representation) or by a list of its vertices and extreme rays (V-representation). mplrs is a parallel version of lrs, and converts an H-representation of a polyhedron to its V-representation, and vice versa.  These problems are known respectively as the vertex enumeration and convex hull problems. With lrs options redund or redund_list in the input file it will do parallel execution of minrep (computing a minimum representation), see redund(1). With lrs options project or eliminate in the input file it will do parallel execution of fel (Fourier-Motkin elimination).

 

Usage

The number of processors num_proc specified to mpirun should be 4 or higher. Some lrs input file options are not supported by mplrs.

 

Options

mplrs supports the following options, where default values are given in brackets.

-checkp <checkpoint file> if mplrs is terminated by -stop or -time then it can be restarted using this <checkpoint file> and -restart
-countonly don't output vertices/rays/facets, just count them
-freq <file> store frequency data in <file> for use by gnuplot, see below
-hist <file>store parallelization data in <file> for use by gnuplot, see below
-id <initial depth> [2] the depth of the original tree search to populate the job list L
-lmax <int>[lmin] if job list |L|>np*lmax then then maxc is replaced by maxc*scale
-lmin <int>[3] if job list |L|<np*lmin then the maxd parameter is set for all producers
-maxbuf <n>[500] controls maximum size of worker output buffers
-maxc <maxcobases>[50 (*scale)] a producer stops and returns all subtrees that are not leaves to L after generating  maxc nodes   
-maxd <depth>[0] a producer returns all subtrees that are not leaves at depth maxd. Zero if not used
-minheight jobs are scheduled in increasing order by height in the search tree (default is LIFO)
-queue jobs are scheduled in FIFO order (default is LIFO)
-restart <checkpoint file> restart mplrs using previously created <checkpoint file>. If used with -checkp file names should be different!
-scale <int>[100] used by lmax
-stop <stopfile> terminate mplrs if a file with name <stopfile> is created in the current directory
-stopafter <n> exit after approximately <n> cobases have been computed (no guarantee about how many vertices/rays/facets computed)
-temp <prefix>[/tmp/] store a temporary file for each process. Should be specified if /tmp not writeable. Using " -temp  ./ " will write temporary files to the current directory
-time <seconds> terminate mplrs after <seconds> of elapsed time
redund/fel options
-j <int>[1] if non-zero splits the run into <int> jobs per worker, over-riding rows and lastrows
-lastp <int>[10] the percentage of jobs to use lastrows
-lastrows <int>[10] the number of rows for the last lastp jobs
-minrep removes redundant inequalities, finds hidden linearities and outputs a minimum representation of the input file. This ignores any project or eliminate option present in the input file
-redund same as -minrep, maintained for legacy purposes.
-rows <int>[60] the number of rows per job
 

-hist file format

Example line:

   54.118141 94 279 94 0 0 373


   time since execution began in seconds (54.118141 here)
   number of busy workers (94 here)
   current size of job list (279 here)
   number of workers that may return unfinished jobs (94 here)
   unused (0 here)
   unused (0 here)
   total number of jobs that have been in the job list (373 here)

The second and fourth entries are similar and can differ due to latencies.

 

-freq file format

One integer per line corresponding to the size of a subtree explored by a worker.  

Example

Input file mp5.ine is run with 8 processors. This produced 378 subtrees that were enumerated in parallel using 6 producer cores,  1 core controlling the run and 1 core collecting the output. 

      mai20% mpirun -np 8 mplrs mp5.ine mp5.mplrs
      *mplrs:lrslib v.6.0 2015.7.13(lrsgmp.h)8 processes
      *Copyright (C) 1995,2015, David Avis   avis@cs.mcgill.ca
      *Input taken from mp5.ine
      *Output written to: mp5.mplrs
      *Starting depth of 2 maxcobases=50 maxdepth=0 lmin=3 lmax=3 scale=100
      *Phase 1 time: 0 seconds.
      *Total number of jobs: 378, L became empty 4 times
      *Totals: vertices=32 rays=0 bases=9041 integer-vertices=16
      *Elapsed time: 1 seconds.
      2.285u 0.137s 0:01.86 129.5%    0+0k 0+9976io 36pf+0w
 

Author

Charles Jordan <skip at res dot otaru-uc dot ac dot jp >  

See also

lrs(1), lrslib(5)

 

Index

Name
Synopsis
Description
Usage
Options
-hist file format
-freq file format
Example
Author
See also
This document was created by man2html, using the manual pages.
Time: 06:04:25 GMT, February 05, 2024 lrslib-073/man/html/man1/plrs.1.html0000777000175000017500000005646114625766577015776 0ustar avisavisContent-type: text/html; charset=UTF-8 Man page of lrs

lrs

Section: lrs 7.3 (1)
Updated: 2023.1.4
Index Return to Main Contents
 

Name

lrs - Convert between representations of convex polyhedra, remove redundant inequalities, convex hull computation, volume, triangulation, solution to linear programs in exact precision.  

Synopsis

lrs|plrs [input-file] [output-file]
redund|minrep [input-file] [output-file] See: redund(1)
fel [input-file] [output-file] See: fel(1)
hvref/xref [input-file] See: xref(1)
 

Description

These programs are part of and must be compiled with lrslib which is a C library. All computations are done in exact arithmetic.

A polyhedron can be described by a list of inequalities (H-representation) or by a list of its vertices and extreme rays (V-representation).

lrs converts an H-representation of a polyhedron to its V-representation and vice versa, known respectively as the vertex enumeration and facet enumeration problems (see Example (1) below). For V-representations the volume can be computed and a triangulation produced. lrs can also be used to solve a linear program, remove linearities from a system, and extract a subset of columns.
plrs is a primitive multi-threaded version of lrs that gives some speedup on shared memory machines. See threads option. For a fully parallel version see mplrs(1)

redund|minrep
These are aliases of lrs which can also perform these functions via the redund, redund_list and testlin options. For a more complete description and examples see redund(1).
H-representation: redundant inequalities in an input H-representation are removed and the remaining inequalities output. In addition minrep checks for hidden linearities.
V-representation: outputs all extreme points and extreme rays, often called the convex hull problem. In addition minrep checks for hidden linearities.

fel projects an input H-representation onto a given set of variables using Fourier-Motzkin elimination. For a V-representation it extracts the specified columns. The output is non-redundant and can be can be piped directly into lrs. This is an alias of lrs which can also perform these functions via the eliminate and project options.

hvref/xref produce a cross reference list between H- and V-representations. See xref(1).

mplrs is Skip Jordan's parallel wrapper based on MPI for lrs/redund using the same input and output formats. See: mplrs(1)

Fukuda's FAQ page[1] contains a more detailed introduction to the problem, along with many useful tips for the new user. User's guide for lsrslib[8]

 

File formats

File formats were developed jointly with Komei Fukuda and are compatible with cdd/cddlib[2].
The input for lrs/redund is an H- or V-representation of a polyhedron.


 name
 H-representation [or V-representation]
 {options}
 {linearities}
 begin
  m n rational [or integer]
 {input matrix}
 end 
 {options}

name is a user supplied name for the polyhedron.  Comments may appear before the begin or after the end and should begin with a special character such as "*".

If the representation is not specified H-representation is assumed. The input coefficients are read in free format, and are not checked for type. Coefficients are separated by white space. m is the number of rows and n the number of columns of the input matrix.  

H-representation

m is the number of input rows, each being an inequality or equation.
n is the number of input columns and d=n-1 is the dimension of the input.
An inequality or equation of the form:

b + a_1 x_1 + ... + a_d x_d >=  0

b + a_1 x_1 + ... + a_d x_d =  0

is input as the line:

b  a_1 ... a_d

The coefficients can be entered as integers or rationals in the format x/y. To distinguish an equation a linearity option must be supplied before the begin line (see below).  

V-representation

m is the number of input rows, each being a vertex, ray or line.
n is the number of input columns and d=n-1 is dimension of the input.
Each vertex is given in the form:

1   v_1   v_1 ... v_d

Each ray is given in the form:

0   r_1   r_2...   r_d

where r_1  ...   r_d is a point on the ray.

There must be at least one vertex in each file. For bounded polyhedra there will be no rays entered. The coefficients can be entered as integers or rationals in the format x/y. An input line can be specified as a ray and then included in the linearity option (see below).

Note for cdd users: Note the input files for lrs are read in free format. lrs will look for exactly m*n rationals or integers separated by white space (blank, carriage return, tab etc.). lrs will not "drop" extra columns of input if n is less than the number of columns supplied.

 

Options

Almost all options are placed after the end statement, maintaining compatibility with cdd. Where this is not the case, it will be mentioned explicitly.

allbases This option instructs lrs to list each vertex (or facet) for each of its bases. This option is often combined with printcobasis.

bound  x (H-representation only). Either the maximize or minimize option should be selected. x is an integer or rational. For maximization (resp. minimization) the reverse search tree is truncated  whenever the current objective value is less (resp. more) than x.

cache n     (default n=50)
lrs stores the latest  n dictionaries in the reverse search tree. This speeds up the backtracking step, but requires more memory.

debug  startingcobasis endingcobasis
Print out cryptic but detailed trace, dictionaries etc. starting at #B=startingcobasis and ending at #B=endingcobasis. debug 0 0 gives a complete trace.

digits n (lrsmp arithmetic only - placed before the begin statement)
n is the maximum number of decimal digits to be used. If this is exceeded the program terminates with a message and can usually be restarted with the restart option. The default is set to 100 digits. At the end of a run a message is given informing the user of the maximum integer size encountered.

dualperturb If lrs is executed with the maximize or minimize option, the reverse search tree is rooted at an optimum vertex for this function. If there are multiple optimum vertices, the output will often not be complete. This option gives a small perturbation to the objective to avoid this. A warning message is given if the starting dictionary is dual degenerate.

estimates k
Estimate the output size. Used in conjunction with maxdepth and seed. See: Estimation[3].

eliminate k i_1 i_2 ... i_k (see fel(1))
(H-representation) Eliminates k variables in an H-representation corresponding to cols i_1 .. i_k by projection onto the remaining variables using the Fourier-Motzkin method. Variables are eliminated in the order given and redundancy is removed after each iteration.
(V-representation) Delete the k given columns from the input matrix and remove redundancies (cf. extract where redundancies are not removed).
Column indices are between 1 and n-1 and column zero cannot be eliminated. The output is a valid lrs input file. See also project and extract

extract [ k i_1 i_2 ... i_k ]
(H-representation) A preprocessing step to remove linearities (if any) in an H-representation and resize the A matrix. The output as a valid lrs input file. The resulting file will not contain any equations but may not be full dimensional as there may be additional linearities in the remaining inequalities. Options in the input file are stripped. The user can specify the k columns i_1 i_2 ... i_k to retain otherwise if k=0 or is ommitted the lex-min set of columns are retained, equivalent to the the order 1,2,..n-1. Linearly dependent columns are skipped and additional indices are taken from 1,2,...,n-1 as necessary. If there are no linearities in the input file the given columns are retained and the other ones are deleted.
(V-representation) Extract the given columns from the input file outputing a valid lrs input file. Options are stripped.

geometric   (H-representation  or voronoi option only) Each ray is printed together with the vertex with which it is incident.

incidence This option automatically switches on printcobasis. For input H-representation, indices of all input inequalities that contain the vertex/ray that is about to be output. For input V-representation, indices of all input vertices/rays that lie on the facet that is about to be output. A starred index indicates that this vertex  is also in the cobasis, but is not contained in the facet. It arises due to the lifting operation used with input V-representations.

linearity  k  i_1  i_2  ...  i_k (placed before begin statement)
(H-representation) The k rows i_1  i_2  ...  i_k  of the input file represent equations. (V-representation) The k rows, which should have a zero in column 1, represent lines in space (rather than rays).

lponly Solve the LP given by the input H-representation with objective function specified by the maximize or minimize options and terminate. Use with verbose option to get dual variables. See: Linear Programming[4].

maxcobases k
The search will be truncated after k cobases have been generated.

maxdepth k
The search will be truncated at depth k. All bases with depth less than or equal to k will be computed.  k is  a non-negative integer, and this option is used for estimates - see Estimation[3]. Note: For H-representations, rays at depth k will not be reported. For V-representations, facets at depth k will not be reported.

maximize  b  a_1 ... a_{n-1}  
minimize  b  a_1 ... a_{n-1}  
(H-representation) The starting vertex maximizes (or minimizes) the function  b + a_1 x_1+ ... + a_{n-1} x_{n-1}.
The dualperturb option may be needed to avoid dual degeneracy. Often used with lponly.
(V-representation, v.7.2) The input file row numbers maximizing(minimizing) the function are output along with the optimum value. Using verbose the optimizing lines are also printed. With minimization a facet gives an optimum value of zero, a negative value indicates infeasibility and a positive value indicates strong redundancy.

maxincidence n k
Prunes the search tree when the depth is at least k and the current vertex/facet has incidence at least n. Using verbose a message is printed whenever the search tree is pruned.

maxoutput n
Limits number of output lines produced (either vertices+rays or facets) to n

mindepth k
Backtracking will be terminated at depth k.

nonnegative (This option must come before the begin statement - H-representation only)   Bug: Can only be used if the origin is a vertex of the polyhedron  For problems where the input is an H-representation of the form b+Ax>=0, x>=0 (ie. all variables non-negative, all constraints inequalities) it is not necessary to give the non-negative constraints explicitly if the nonnegative option is used. This option cannot be used for V-representations, or with the linearity option (in which case the linearities will be treated as inequalities). This option may be used with redund , but the implied nonnegativity constraints are not tested themselves for redundancy.

project k i_1 i_2 ... i_k (see fel(1))
(H-representation) Project the polyhedron onto the k variables corresponding to cols i_1 .. i_k using the Fourier-Motzkin method. Column indices are between 1 and n-1 and column zero is automatically retained. Variables not contained in the list are eliminated using a heuristic which chooses the column which minimizes the product of the number of positive and negative entries. Redundancy is removed after each iteration using linear programming.
(V-representation) Extract the k given columns from the input matrix and remove redundancies. Column indices are between 1 and n-1 and column zero is automatically extracted (cf. extract where redundancies are not removed).
The output as a valid lrs input file. See also eliminate and extract

printcobasis k
Every k-th cobasis is printed. If k is omitted, the cobasis is printed for each vertex/ray/facet that is output. For a long run it is useful to print the cobasis occasionally so that the program can be restarted if necessary. H-representation: the cobasis is a list the indices of the inequalities from the input file that define the current vertex or ray. For rays the cobasis is the cobasis of the vertex from which the ray emanates. One of the indices is starred, this indicates the inequality to be dropped from the cobasis to define the ray. If the allbases option is used, all cobases will be printed. V-representation: the cobasis is a list of the input vertices/rays that define the current facet. See option incidence for more information.

printslack (H-representation only) A list of the indices of the input inequalities that are satisfied strictly for the current vertex, ie. corresponding slack variable is positive. If nonnegative is set, the list will also include indices n+i for each decision variable x_i which is positive.

redund start end (see redund(1))
Check input lines with line numbers from start to end and remove any redundant lines.
redund 0 0 will check all input lines.

redund_list k i_1 i_2 ... i_k (see redund(1))
Check the k input line numbers with indices i_1 i_2 ... i_k and remove any redundant lines.

restart  V# R# B# depth {facet #s or vertex/ray #s}
lrs can be restarted from any known cobasis. The calculation will proceed to normal termination. All of the information is contained in the output from a printcobasis option.  The order of the indices is very important, enter them exactly as they appear in the output from the previously terminated run.

seed k
Set the random number generator seed=k. Used with estimates.

startingcobasis i_1  i_2  ...  i_{n-1}
lrs will start from the given cobasis which which is a list of the inequalities (for H-representation) or vertices/rays (for V-representation) that define it. If it is invalid, or this option is not specified, lrs will find its own starting cobasis.

testlin (before the begin line only) H-representation only (new 7.3)
redund An LP test will be made for hidden linearities at the beginning of the run and is reported. If there are no hidden linearities one LP per constraint tests for redundancy. (mplrs can be run with no verification step.) If hidden linearities exist two LPs per constraint search for hidden linearities and remove redundancies. In both cases the run ends with a minimum set of linearities and inequalities (ie. no hidden inequalities or duplicates) and the dimension is reported. (mplrs will find all linearities but some non redundant inequalities may be eliminated, so a second run is required.)
lrs If neither redund or redund_list options are present the initial LP test is made, reported and the run halted. Otherwise same as redund above.

threads n (new in 7.3, currently for plrs1,plrs2,plrsgmp,plrsmp and script plrs)
Multithreaded lrs using openMP for a parallel for loop at depth 0 in the search tree. Disabled for mplrs. If n is not specified the default openMP max threads is used.

truncate The reverse search tree is truncated(pruned)  whenever a new vertex is encountered. Note: This does note necessarily produce the set of all vertices adjacent to the optimum vertex in the polyhedron, but just a subset of them.

verbose Print slightly more detailed information about the run.

volume (V-representation only) Compute the volume and, if the verbose option is also included, output a triangulation. See Volume Computation[5].

voronoi (V-representation  only - place immediately after end statement)
Compute Voronoi diagram - see Voronoi Diagrams[6].  

Arithmetic

From version 7.1 lrs/redund/mplrs use hybrid arithmetic with overflow checking, starting in 64bit integers, moving to 128bit (if available) and then GMP. Overflow checking is conservative to improve performance: eg. with 64 bit arithmetic, a*b triggers overflow if either a or b is at least 2^31, and a+b triggers an overflow if either a or b is at least 2^62. Typically problems that can be solved in 64bits run 3-4 times faster than with GMP and inputs solvable in 128bits run twice as fast as GMP.

Various arithmetic versions are available and can be built from the makefile:

lrs1 Fixed length 64 bit integer arithmetic, terminates on overflow.

lrs2 Fixed length 128 bit integer arithmetic, terminates on overflow.

lrsmp Built in extended precision integer arithmetic, uses digits option above.

lrsgmp GNU MP which must be installed first from https://gmplib.org/.

lrsflint FLINT hybrid arithmetic which must be installed first from http://www.flintlib.org/

 

Examples

(1) Convert the H-representation of a cube given cube by 6 the six inequalities
-1 <= x_i <= 1 , i=1,2,3 into its V-representation consisting of 8 vertices.


 % cat cube.ine
 cube.ine
 H-representation
 begin
 6 4 rational
 1  1  0  0
 1  0  1  0
 1  0  0  1
 1 -1  0  0
 1  0  0 -1
 1  0 -1  0
 end


 % lrs cube.ine


 *lrs:lrslib v.6.3 2018.4.11(64bit,lrslong.h,overflow checking)
 *Input taken from file cube.ine
 cube.ine
 V-representation
 begin
 ***** 4 rational
 1  1  1  1
 1 -1  1  1
 1  1 -1  1
 1 -1 -1  1
 1  1  1 -1
 1 -1  1 -1
 1  1 -1 -1
 1 -1 -1 -1
 end
 *Totals: vertices=8 rays=0 bases=8 integer_vertices=8

 

Notes

1.
FAQ page
https://inf.ethz.ch/personal/fukudak/polyfaq/polyfaq.html
2.
cdd
https://inf.ethz.ch/personal/fukudak/cdd_home/
3.
Estimation.
http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html#Estimation
4.
Linear Programming
http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html#Linear%20Programming
5.
Volume Computation.
http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html#Volume%20Computation
6.
Voronoi Diagrams.
http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html#Voronoi%20Diagrams
7.
redund: extreme point enumeration and eliminating redundant inequalities
http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html#redund
8.
User's guide for lrslib
http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html
 

Author

David Avis <avis at cs dot mcgill dot ca >  

See also

mplrs(1), lrslib(5), lrsnash(1)

 

Index

Name
Synopsis
Description
File formats
H-representation
V-representation
Options
Arithmetic
Examples
Notes
Author
See also
This document was created by man2html, using the manual pages.
Time: 07:33:14 GMT, January 31, 2024 lrslib-073/man/html/man1/polyv.1.html0000777000175000017500000002150014625766577016151 0ustar avisavisContent-type: text/html; charset=UTF-8 Man page of polyv

polyv

Section: polyv 7.3 (1)
Updated: 2023.10.21
Index Return to Main Contents
 

Name

polyv - utility to create and verify logical formulas checking properties of given H/V representations using logic solvers.  

Synopsis

polyv [input-files]
 

Description

The input file or files are H- or V-representations of polyhedra in lrs format, and the output is a logical formula in SMT-LIB 2.6 format. Behavior depends on the options and number of input files provided. In many cases, it is easier and faster to use lrs, mplrs or other tools to check the following questions directly. polyv is an alternative approach intended for some examples where the direct approach is difficult.

First, polyv can be given a single H-representation defining a polyhedron P, along with a list of variables for a projection of P and an inequality I to test. The question is whether we have the same projection when I is deleted from P. If so we say I is redundant for the projection, otherwise it is non-redundant. polyv allows the use of SMT solvers to decide this question without performing the projection explicitly, producing a formula that is satisfiable iff the I is non-redundant for the projection. In addition, polyv it produce lrs inputs that verify witnesses of non-redundancy produced by an SMT solver.

Next, polyv can be given two representations defining polyhedra P and Q, where H-representations may contain projections. The question is whether P and Q are different polyhedra: polyv produces a formula that is satisfiable iff there is a point contained in exactly one of P and Q.

Finally, polyv can be given three representations defining polyhedra P, Q and R. The question is whether the intersection of P and Q is different from R: polyv produces a formula that is satisfiable iff there is a point contained in exactly one of R and the intersection.

 

File formats

The input file is in lrs format (see lrs(1)) consisting of (a) an H-representation of a polyhedron, (b) a projection to a subset of variables given by the project or eliminate options, and (c) an inequality to test given by the redund or redund_list options. Note that only "linearity", "redund", "redund_list", "project" and "eliminate" options are supported, and the combination of redund/redund_list and project/eliminate options is both unique to polyv and required.

The output is in SMT-LIB 2.6 format using logic LRA. Solvers such as z3 or cvc5 support this logic. See The SMT-LIB Standard: Version 2.6 for details.

 

Usage

polyv [input-file] produces a logical formula satisfiable iff the first inequality given in a redund/redund_list option is redundant after projection according to a project/eliminate option. The solver can produce witnesses for non-redundant inequalities, i.e. an assignment to the variables whose image is in the projection only if the inequality is removed. No witness is produced if the inequality is redundant.

A witness of non-redundancy can be verified using two certificates. The first certificate specifies that the assignment to the variables is feasible when the inequality in question is removed. The second certificate asserts that when this inequality is added, no feasible assignment has the same projection. Certificates are produced using the following options.

polyv -c 1 [input-file] reads a witness of non-redundancy on standard input and produces an lrs input file that should be feasible. The options in the input file should be the same as when the formula was produced.

polyv -c 2 [input-file] reads a witness of non-redundancy on standard input and produces an lrs input file that should be infeasible. The options in the input file should be the same as when the formula was produced.

polyv [input-file-1] [input-file-2] given two H/V representations, produces a logical formula satisfiable iff they define different polyhedra. Projections are supported in H-representations using the project or eliminate option. This can be used to e.g. verify H/V equivalency or fel projections.

polyv [input-file-1] [input-file-2] [input-file-3] given three H/V representations, produces a logical formula satisfiable iff the intersection of polyhedra defined by input-file-1 and input-file-2 is not defined by input-file-3. Projections are supported in H-representations using the project or eliminate option.

 

Examples

(1) Check if the first inequality in cp4.ine is redundant for projections.
(a) To check for redundancy after the first variable is eliminated, add options "redund_list 1 1" and "eliminate 1 1" to cp4.ine. Then:


 % polyv cp4.ine > cp4-11.smt
 % z3 cp4-11.smt > cp4-11.out    
or

 % cvc5 -L smt --produce-models cp4-11.smt > cp4-11.out 

The first line of cp4-11.out reads "sat" indicating that inequality 1 is non-redundant for eliminating variable 1. We can check the witness:


 % polyv -c 1 cp4.ine < cp4-11.out | lrs
 % polyv -c 2 cp4.ine < cp4-11.out | lrs

The first certificate is feasible and second infeasible, so the witness proves non-redundancy for the projection.
(b) To check for redunancy after variables 1 and 2 are eliminated, add options "redund_list 1 1" and "eliminate 2 1 2" to cp4.ine. Then


 % polyv cp4.ine > cp4-112.smt
 % z3 cp4-112.smt > cp4-112.out
or

 % cvc5 -L smt --produce-models cp4-112.smt > cp4-112.out

The first line of cp4-112.out reads "unsat" indicating that inequality 1 is redundant for eliminating variables 1 and 2. In this case there is no witness.

(2) Check if given H- and V- representations define different polyhedra.
(a) To check whether mp5.ine and mp5.ext (produced using lrs) define different polyhedra:


 % polyv mp5.ine mp5.ext > mp5hv.smt
 % z3 mp5hv.smt > mp5hv.out

The first line of mp5hv.out reads "unsat" indicating that these two representations do not define different polyhedra (i.e. they are equivalent).
(b) After removing the last vertex (the origin) from mp5.ext to create
    mp5missing.ext:


 % polyv mp5.ine mp5missing.ext > mp5hvm.smt
 % z3 mp5hvm.smt > mp5hvm.out

The first line of mp5hvm.out reads "sat" indicating that these two representations define different polyhedra.
Note that the H-representations are allowed to include projections.

 

Notes

1.
SMT-Lib Standards
http://smtlib.cs.uiowa.edu/language.shtml
2.
z3
https://github.com/Z3Prover/z3/wiki
3.
cvc5
https://cvc5.github.io/
 

Author

Charles Jordan <skip at res dot otaru-uc dot ac dot jp >  

See also

lrslib(5), lrs(1)

 

Index

Name
Synopsis
Description
File formats
Usage
Examples
Notes
Author
See also
This document was created by man2html, using the manual pages.
Time: 07:33:14 GMT, January 31, 2024 lrslib-073/man/html/man1/redund.1.html0000777000175000017500000002221114625766577016261 0ustar avisavisContent-type: text/html; charset=UTF-8 Man page of redund|minrep

redund|minrep

Section: lrslib 7.3 (1)
Updated: 2024.1.10
Index Return to Main Contents
 

Name

redund|minrep - Remove redundant inequalities from an H-representation or redundant vertices (non-extreme points) from a V-representation. minrep also identifies hidden linearities.  

Synopsis

redund [input-file] [output-file]
minrep [input-file] [output-file]
mpirun -np [procs] mplrs -minrep [input-file] [output-file] [option...]
 

Description

redund and minrep are aliases to lrs which is part of

the C library lrslib(5). This functionality can also be performed by lrs directly by using the options described below. All computations are done in exact arithmetic. For input file descriptions see lrs(1). A parallel version of minrep is given by mplrs -minrep. The -redund option performs the same function and is retained for legacy. (see mplrs(1))

redund
H-representation: redundant inequalities in an input H-representation are removed and the remaining inequalities output. Hidden linearities are not detected unless the testlin option is included, in which case the output is a minimum representation and the dimension is reported.
V-representation: outputs all extreme points and extreme rays, often called the convex hull problem. The testlin option cause linearities to be detected and explicitly output.
Outputs can be piped directly into lrs. redund is a link to lrs which can also perform these functions via the testlin, redund and redund_list options. mplrs -redund always sets the testlin option, so always produces minimum representations.

minrep
Equivalent to redund with the testlin option.

With no options minrep|redund will process the entire input file.

redund start end
Check input lines with line numbers from start to end and remove any redundant lines.
redund 0 0 will check all input lines.

redund_list k i_1 i_2 ... i_k
Check the k input line numbers with indices i_1 i_2 ... i_k and remove any redundant lines.

testlin (before the begin line only) (new 7.3)
An LP test will be made for hidden linearities at the beginning of the run and is reported. If there are no hidden linearities one LP per constraint tests for redundancy. (mplrs can be run with no verification step.) If hidden linearities exist two LPs per constraint search for hidden linearities and remove redundancies. In both cases the run ends with a minimum set of linearities and inequalities (ie. no hidden inequalities or duplicates) and the dimension is reported. (mplrs will find all linearities but some non redundant inequalities may be eliminated, so a second run is required.)

verbose
As each input line is checked a message is printed telling its status

 *nr :non-redundant 
 *re :redundant 
 *sr :strongly redundant
For an H-representation strongly redundant means the feasible region lies in its open half-space. For a V-representation it means that the point lies in the (relative) interior of the convex hull.
In addition minrep may report
 *li :linearity  

Examples

(1) Remove hidden linearities and minimum representation of an H-representation.
 % cat cube.ine
 H-representation
 begin
 7 4 rational
  0  1  0  0 
  0  0  1  0 
  0  0  0  1 
  1 -1  0  0 
  1  0 -1  0 
  1  0  0 -1 
 -1  0  0  1
 end
 verbose
 
 % minrep cube.ine
 minrep:lrslib_v.7.3_2024.1.10(64bit,lrslong.h,hybrid_arithmetic)
 *Input taken from  cube.ine
 *hidden linearities exist
 *finding minimum representation
 *nr 0  1  0  0 
 *nr 0  0  1  0 
 *sr 0  0  0  1 
 *nr 1 -1  0  0 
 *nr 1  0 -1  0 
 *li 1  0  0 -1 
 *li-1  0  0  1 
 *linearity in row=6 removed or in cobasis, independent
 *linearity in row=7 dependent, made redundant
 H-representation
 linearity 1 1
 begin
 5 4 rational
  1  0  0 -1 
  0  1  0  0 
  0  0  1  0 
  1 -1  0  0 
  1  0 -1  0 
 end
 
 *input had 7 rows and 4 columns
 * 2 redundant row(s) found
  3 7
 * 1 hidden linearity found
 

(2) Compute the extreme points of a set of 10 points in R^3


 % cat c.ext
 V-representation
 begin
 10 4 rational
 1  1  1  1 
 1  0  1  1 
 1 1/2 0 1/3
 1  1  1  0 
 1  0  1  0 
 1  1  0  0 
 1  0  0  0 
 1  0 1/3 1/4
 1  1  0  1 
 1  0  0  1 
 end


 % redund c.ext


 *redund:lrslib v.7.2 2020.6.8(64bit,lrslong.h,hybrid arithmetic)
 *Input taken from  c.ext
 V-representation
 begin
 8 4 rational
 1  1  1  1 
 1  0  1  1 
 1  1  1  0 
 1  0  1  0 
 1  1  0  0 
 1  0  0  0 
 1  1  0  1 
 1  0  0  1 
 end
 *Input had 10 rows and 4 columns
 * 2 redundant row(s) found:
 3 8

 

Notes

1.
FAQ page
https://inf.ethz.ch/personal/fukudak/polyfaq/polyfaq.html
2.
redund: extreme point enumeration and eliminating redundant inequalities
http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html#redund
3.
User's guide for lrslib
http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html
 

Author

David Avis <avis at cs dot mcgill dot ca >  

See also

lrs(1), mplrs(1), lrslib(5),

 

Index

Name
Synopsis
Description
Examples
Notes
Author
See also
This document was created by man2html, using the manual pages.
Time: 07:33:14 GMT, January 31, 2024 lrslib-073/man/html/man1/xref.1.html0000777000175000017500000001166414625766577015756 0ustar avisavisContent-type: text/html; charset=UTF-8 Man page of xref|hvref

xref|hvref

Section: lrslib 7.3 (1)
Updated: 2023.1.4
Index Return to Main Contents
 

Name

xref|hvref - produce a cross reference list between H- and V-representations.
   

Synopsis

xref [input-file]
hvref [input-file]
 

Description

These programs are part of and must be compiled with lrslib which is a C library. All computations are done in exact arithmetic.

xref and hvref produce a cross reference list between H- and V-representations.

xref/hvref Cross reference listing between V- and H-representations

In the example below we start from an H-representation of cube.ine but the same steps apply to the V-representation cube.ext. It is recommended to first remove any redundancies from the input file using redund.

1. Add printcobasis and incidence options to cube.ine and run lrs.
 % cat cube.ine
 cube
 H-representation
 begin
 6 4 rational
  0  1  0  0
  0  0  1  0
  0  0  0  1
  1 -1  0  0
  1  0 -1  0
  1  0  0 -1
 end
 printcobasis
 incidence
  % lrs cube.ine cube.ext

2. Run xref on the output file cube.ext getting cube.ext.ex


 % xref cube.ext
 % cat cube.ext.ex lg% cat cube.ext.x
 V-representation
     1   4 5 6    #
     2   1 5 6    #
     3   2 4 6    #
     4   1 2 6    #
     5   3 4 5    #
     6   1 3 5    #
     7   2 3 4    #
     8   1 2 3    #

3. Edit the file cube.ext.x to insert a second line that contains two integers

rows maxindex

where rows >= # output lines in cube.ext.x
      maxindex >= # input lines in cube.ine

or just use 0 0 and run hvref, the output will tell you which values to use.

% hvref cube.ext.x % hvref cube.ext.x


 V-representation
 8 8
 1: 4 5 6
 2: 1 5 6
 3: 2 4 6
 4: 1 2 6
 5: 3 4 5
 6: 1 3 5
 7: 2 3 4
 8: 1 2 3
 
 H-representation
 6 8
 1: 2 4 6 8
 2: 3 4 7 8
 3: 5 6 7 8
 4: 1 3 5 7
 5: 1 2 5 6
 6: 1 2 3 4
 input rows=8 maxindex=6
 

 

Notes

1.
FAQ page
https://inf.ethz.ch/personal/fukudak/polyfaq/polyfaq.html
2.
User's guide for lrslib
http://cgm.cs.mcgill.ca/~avis/C/lrslib/USERGUIDE.html
 

Author

David Avis <avis at cs dot mcgill dot ca >  

See also

mplrs(1), lrslib(5), lrsnash(1)

 

Index

Name
Synopsis
Description
Notes
Author
See also
This document was created by man2html, using the manual pages.
Time: 07:33:14 GMT, January 31, 2024 lrslib-073/man/html/man5/0000777000175000017500000000000014625766600013741 5ustar avisavislrslib-073/man/html/man5/lrsarith.5.html0000777000175000017500000001310314625766600016623 0ustar avisavisContent-type: text/html; charset=UTF-8 Man page of lrsarith

lrsarith

Section: lrsarith 1.1 (5)
Updated: 2022.1.19
Index Return to Main Contents
 

Name

lrsarith: library routines for exact precision integer and rational arithmetic from lrslib with sample programs. 64bit integer, 128bit integer, GMP, lrslib MP, and FLINT arithmetic packages are supported. as well as hybrid arithmetic. Overflow checking is done for 64bit and 128bit arithmetic.  

Synopsis

lrslong.h lrslong.c [64bit and 128bit arithmetic]
lrsgmp.h lrsgmp.c [GMP and FLINT arithmetic] (requires external library)
lrsmp.h lrsmp.c [lrslib MP arithmetic]
 

Description

This package was extracted from version 7.1 of lrslib which uses hybrid arithmetic with overflow checking, starting in 64bit integers, moving to 128bit (if available) and then GMP. Overflow checking is conservative to improve performance: eg. with 64 bit arithmetic, a*b triggers overflow if either a or b is at least 2^31, and a+b triggers an overflow if either a or b is at least 2^62. Typically problems that can be solved in 64bits run 3-4 times faster than with GMP and inputs solvable in 128bits run twice as fast as GMP. A rational number is represented by a pair of integers, however the user must keep track of the numerator and denominators manually. Operations for rational arithmetic are included.

Various test programs are available and can be built from the makefile:

% make fixed

Build the programs fixed1, fixed1n, fixed2, fixed2n, fixedmp, fixedgmp that read an integer k and repeatedly square it 6 times.

% make hybrid  (% make mp use internal MP arithmetic instead of GMP)

Build the program hybrid (and fixed1, fixed2, fixedgmp) that runs through the three arithmetic packages as needed.

% make coll  (% make flint make FLINT arithmetic version)

Reverse search code for building a Collatz tree with largest value maxn in all arithmetic versions.

% make test 

Test the arithmetic constants used in overflow checking.  

Initialization

lrs_mp_init(digits,fpin,fpout);

digits: maximum number of decimal digits in MP arithmetic else set digits=0

fpin, fpout: input and output file pointers, eg, stdin, stdout  

Types

Fixed arithmetic is handled by defining a generic integer type and a set of generic operations. A generic integer a, integer vector v and integer matrix A are defined

lrs_mp a; lrs_mp_vector v; lrs_mp_matrix A;

allocated

lrs_alloc_mp(a); v=lrs_alloc_mp_vector(n); A=lrs_alloc_mp_matrix(m,n);

and freed

lrs_clear_mp(a); lrs_clear_mp_vector(n); lrs_clear_mp_matrix(m,n);

where m and n are the dimensions.  

Operations

Operations using lrs_mp integers are written generically. The most basic ones are below and a complete list is included in lrslong.h. Operations may be implemented as macros which may evaluate their arguments more than once. Arguments should not be expressions with potential side effects. Here, a,b,c,d,e are lrs_mp integers, i is a long long int and the equivalent C code is given in parenthesis.

addint(a,b,c) (c=a+b) /* a and b should be different */

changesign(a) (a = -a)

compare(a,b) (a ? b and returns -1,0,1 for <,=,>)

copy(a,b) (a=b)

decint(a,b) (a=a-b)

divint(a,b,c) (c=a/b a=a%b)

exactdivint(a,b,c) (c=a/b)

itomp(i,a); (a=i)

linint(a, ka, b, kb) (a=a*ka+b*kb for ka, kb long long integers)

mp_greater(a, b) (a>b)

mulint(a,b,c) (c=a*b) /* b and c may be the same */

negative(a) (a<0)

one(a) (a == 1)

pmp("string",a) (print "string" followed by a to lrs_ofp)

positive(a) (a>0)

qpiv(a,b,c,d,e) (a=(a*b-c*d)/e where the division is exact )

sign(a) (a < 0 ? NEG : POS)

storesign(a, i) (a = labs(a) * i)

subint(a,b,c) (c=a-b)

zero(a) (a == 0)

 

Notes

User's guide for lrslib

http://cgm.cs.mcgill.ca/~avis/C/lrslib/USERGUIDE.html
 

Author

David Avis <avis at cs dot mcgill dot ca >  

See also

lrslib(5),

 

Index

Name
Synopsis
Description
Initialization
Types
Operations
Notes
Author
See also
This document was created by man2html, using the manual pages.
Time: 07:33:14 GMT, January 31, 2024 lrslib-073/man/html/man5/lrslib.5.html0000777000175000017500000001277114625766600016274 0ustar avisavisContent-type: text/html; charset=UTF-8 Man page of lrslib

lrslib

Section: lrslib 7.3 (5)
Updated: 2024.01.31
Index Return to Main Contents
 

Name

lrslib: Convert between representations of convex polyhedra, remove redundant inequalities, find minimum representations, convex hull computation, solve linear programs in exact precision, compute Nash-equibria in 2-person games.  

Synopsis

lrs [input-file] [output-file]
redund [input-file] [output-file]
minrep [input-file] [output-file]
fel [input-file] [output-file]
mpirun -np num-proc mplrs input-file [output-file] [options]
lrsnash [options] [input-file]
hvref/xvref [input-file]
polyv [input-file]
 

Description

A polyhedron can be described by a list of inequalities (H-representation) or as by a list of its vertices and extreme rays (V-representation). lrslib is a C library containing programs to manipulate these representations. All computations are done in exact arithmetic.

lrs(1) converts an H-representation of a polyhedron to its V-representation and vice versa, known respectively as the vertex enumeration and facet enumeration problems (see Example (1) below). lrs can also be used to solve a linear program, remove linearities from a system, and extract a subset of columns.

redund(1) removes redundant inequalities in an input H-representation and outputs the remaining inequalities. For a V-representation input it outputs all extreme points and extreme rays. Both outputs can be piped directly into lrs. redund is a link to lrs which performs these functions via the redund and redund_list options.

minrep(1) performs the same functions as redund(1) but in addition searches for hidden linearities in the input. These are made explicit in the output which is a minimum representation of the polyhedron.

fel(1) projects an input H-representation onto a given set of variables using Fourier-Motzkin elimination. For a V-representation it extracts the specified columns. The output is non-redundant and can be can be piped directly into lrs. fel is a link to lrs which performs these functions via the eliminate and project options.

mplrs(1) is Skip Jordan's parallel wrapper for lrs/redund/minrep/fel.

lrsnash(1) is Terje Lensberg's application of lrs for finding Nash-equilibria in 2-person games.

hvref(1) xvref(1) produce a cross reference list between H- and V-representations.

polyv(1) is Skip Jordan's utility to create logical formulas for checking equivalence between H- and V- representations or determining whether a given inequality is redundant after eliminating variables, without eliminating the variables.

 

Arithmetic

lrsarith(5) From version 7.1 lrs/redund/mplrs use hybrid arithmetic with overflow checking, starting in 64bit integers, moving to 128bit (if available) and then GMP. Overflow checking is conservative to improve performance: eg. with 64 bit arithmetic, a*b triggers overflow if either a or b is at least 2^31, and a+b triggers an overflow if either a or b is at least 2^62. Typically problems that can be solved in 64bits run 3-4 times faster than with GMP and inputs solvable in 128bits run twice as fast as GMP.

Various arithmetic versions are available and can be built from the makefile.

 

Notes

User's guide for lrslib

http://cgm.cs.mcgill.ca/~avis/C/lrslib/USERGUIDE.html
 

Author

David Avis <avis at cs dot mcgill dot ca >  

See Also

lrs (1), redund(1), minrep(1), mplrs(1), fel(1), lrsnash(1), hvref(1), xvref(1), polyv(1), lrsarith(5)

 

Index

Name
Synopsis
Description
Arithmetic
Notes
Author
See Also
This document was created by man2html, using the manual pages.
Time: 07:33:14 GMT, January 31, 2024 lrslib-073/man/html/man5/lrsscripts.5.html0000777000175000017500000001324114625766600017206 0ustar avisavisContent-type: text/html; charset=UTF-8 Man page of lrsscripts

lrsscripts

Section: lrslib 7.2 (5)
Updated: 2022.02.15
Index Return to Main Contents
 

Name

lrsscripts: some (fragile) shell functions to perform common lrslib operations. caveat emptor !  

Synopsis

mfel input-file [output-file [procs ] ]
mlrs input-file [output-file [procs [cptime [cpindex] ] ]
tlrs input-file [output-file [procs ]
plotV|plotR lrs-output-file [maxdepth [maxcobases] ]
plotL [histogram-file]
projred [-solver SMT-solver] ine-file [output file]

 

Description

mfel:

multiprocessor version of fel(1) which performs multiple rounds of Fourier-Motzkin elimination as specified in either a project or eliminate option in the input file. mplrs performs only one iteration and terminates. procs (if specified) is the number of processors to use (assigned according to the default-hostfile), otherwise all available processors on the current machine are used.

mlrs: simple interface to mplrs(1) that is similar to lrs(1) and in addition does automatic checkpoint/restart for long runs. procs (if specified) is the number of processors to use (assigned according to the default-hostfile), otherwise all available processors on the current machine are used. cptime (if specified) is the time in seconds until a checkpoint/restart is made, default 86400 secs (1 day). Checkpoint data is written into a file named input-file.cpN, where N=0,1,2,... is assigned consecutively. cpindex (if specified) is a valid value of N and causes a restart from checkpoint file input-file.cpN. Other mplrs(1) command line parameters are default values.

tlrs: Runs naive hybrid arithmetic for multithreaded lrs using the binaries tlrs1, tlrs2, tlrsgmp. procs (if specified) is the number of threads to use. If omitted or zero the default openMP maximum thread count is used.

plotV(requires gnuplot be installed): produces a PDF file named <lrs-output-file>V.pdf that gives a plot of each vertex or facet along with its height in the reverse search tree. lrs-output-file should be an lrs/mplrs output file produced when the printcobasis is included in the input file for the run.

plotR(requires gnuplot be installed): performs a similar task to plotV for cones producing the file <lrs-output-file>H.pdf where the height of each ray is plotted.

plotL(requires gnuplot be installed): plotL produces a realtime view of an mplrs run that uses the command line option "-hist <histogram-file>". If histogram-file is not specified hist is the assumed file name. A PDF file named <histogram-file>.pdf is produced. The first plot has 3 graphs showing the number of processors working, the size of the job queue L, and message requests pending, all versus elapsed time on the x-axis. The second histogram shows the size of the subtrees explored by producers. The root of the subtree is not counted in this size. Note that a producer stops after (possibly scaled) maxc nodes are explored, but in backtracking some additional leaves may be discovered. So the size of the largest subtree may be slightly larger than maxc.

projred(requires inedel, polyv(1) and external SMT solver be installed): simple wrapper for polyv(1) that tests and greedily removes inequalities that are redundant after a projection, without doing the projection. Repeatedly calls polyv(1) and the specified SMT solver (z3 by default), removing inequalities determined to be redundant for the given projection. The output is produced in [output file] or on standard output if no output file is specified. The output file will produce the same projection as the original input. Inequalities and projection to test are given as options in the input file, see polyv(1) for details.

 

Notes

User's guide for lrslib

http://cgm.cs.mcgill.ca/~avis/C/lrslib/USERGUIDE.html
 

Author

David Avis <avis at cs dot mcgill dot ca >  

See Also

lrs(1), mplrs(1), fel(1), polyv(1), lrslib(5)

 

Index

Name
Synopsis
Description
Notes
Author
See Also
This document was created by man2html, using the manual pages.
Time: 07:33:14 GMT, January 31, 2024 lrslib-073/man/man1/0000777000175000017500000000000014625766600012771 5ustar avisavislrslib-073/man/man1/fel.10000777000175000017500000001254314625766600013631 0ustar avisavis.TH "fel" "1" "2024.1.10 " "January 2024" "lrslib 7.3" .\" ----------------------------------------------------------------- .\" * Define some portability stuff .\" ----------------------------------------------------------------- .\" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .\" http://bugs.debian.org/507673 .\" http://lists.gnu.org/archive/html/groff/2009-02/msg00013.html .\" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .ie \n(.g .ds Aq \(aq .el .ds Aq ' .\" ----------------------------------------------------------------- .\" * set default formatting .\" ----------------------------------------------------------------- .\" disable hyphenation .nh .\" disable justification (adjust text to left margin only) .ad l .\" ----------------------------------------------------------------- .\" * MAIN CONTENT STARTS HERE * .\" ----------------------------------------------------------------- .SS "Name" fel - Project an H-representation or V-representation onto a subset of columns. .SS "Synopsis" .HP \w'\fBfel\fR\ [input-file] [output-file]\ 'u \fBfel\fR\ \fI[input-file] [output-file]\fR .HP \w'\fBmpirun\fR\ \fR\fBmplrs\fR\ [input-file] [output-file]\ 'u \fBmpirun\fR\ -np [procs] \fBmplrs -fel\fR\ \fI[input-file] [output-file] [option...]\fR .SS "Description" \fBfel\fR is an alias of \fRlrs\fR which can also perform these functions via the \fBeliminate\fR and \fBproject\fR options. .PP \fIH-representation\fR. .br The input is projected onto a given set of columns using Fourier-Motzkin elimination. An H-representation is output after each iteration. \fBmplrs -fel\fR is a fully parallel version that performs one iteration only, see \fBmplrs(1)\fR. .br \fIV-representation\fR. .br The specified columns are extracted and redundant rows are removed. The output can be can be piped directly into \fBlrs\fR. Not implemented in \fBmplrs\fR. .SS "Options" .PP These options are placed \fBafter\fR the end statement. .PP \fBeliminate k i_1 i_2 ... i_k \fR (new in v7.2) .br \fI(H-representation)\fR Eliminates k variables in an H-representation corresponding to cols i_1 .. i_k by projection onto the remaining variables using the Fourier-Motzkin method. Variables are eliminated in the order given and redundancy is removed after each iteration. .br \fI(V-representation)\fR Delete the k given columns from the input matrix and remove redundancies (cf. \fBextract\fR where redundancies are not removed). .br Column indices are between 1 and n-1 and column zero cannot be eliminated. The output is a valid lrs input file. .PP \fBproject k i_1 i_2 ... i_k \fR (new in v7.2) .br \fI(H-representation)\fR Project the polyhedron onto the k variables corresponding to cols i_1 .. i_k using the Fourier-Motzkin method. Column indices are between 1 and n-1 and column zero is automatically retained. Variables not contained in the list are eliminated using a heuristic which chooses the column which minimizes the product of the number of positive and negative entries. Redundancy is removed after each iteration using linear programming. .br \fI(V-representation)\fR Extract the k given columns from the input matrix and remove redundancies. Column indices are between 1 and n-1 and column zero is automatically extracted (cf. \fBextract\fR where redundancies are not removed). .br The output as a valid lrs input file. .PP See also \fBextract\fR in \fBlrs(1)\fR. \fBverbose\fR .PP For an H-representation give, for each iteration, statistics on how many new inequaties were created and how many of these were redundant. See \fBExample\fR below. .SS "Example" (1) Project onto columns 1 and 3 in an H-representation % cat cube.ine cube.ine H-representation begin 6 4 rational 1 1 0 0 1 0 1 0 1 0 0 1 1 -1 0 0 1 0 0 -1 1 0 -1 0 end project 2 1 3 verbose % fel cube.ine fel:lrslib_v.7.3_2024.1.10(64bit,lrslong.h,hybrid_arithmetic) *Input taken from cube.ine cube *switching to fel mode *project 2 1 3 *after removing column 2 *checking for redundant rows only H-representation begin 4 3 rational 0 1 0 1 -1 0 1 0 -1 -1 0 1 end *number of number after number of remaining column *inequalties removing col redundancies rows removed * 7 6 2 4 2 -------------------------------------------------------------------- *original vars remaining: 1 3 (2) Eliminate columns 1,2,3 from a V-representation % cat cp4.ext V-representation begin 8 7 rational 1 0 0 0 0 0 0 1 0 1 1 1 1 0 1 1 1 0 0 1 1 1 1 0 0 1 1 0 1 0 0 1 0 1 1 1 1 1 1 0 0 0 1 0 1 0 1 0 1 1 1 0 1 1 0 1 end eliminate 3 1 2 3 % lrs cp4.ext lrs:lrslib_v.7.3_2024.1.12(64bit,lrslong.h,hybrid_arithmetic) *Input taken from cp4.ext cp4 *switching to fel mode *eliminate 3 1 2 3 *checking for redundant rows only V-representation begin 4 4 rational 1 1 1 0 1 0 1 1 1 0 0 0 1 1 0 1 end *columns retained: 0 4 5 6 .SS "Notes" .IP " 1." 4 FAQ page .RS 4 \%https://inf.ethz.ch/personal/fukudak/polyfaq/polyfaq.html .RE .IP "2." 4 User's guide for lrslib .RS 4 \%http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html .RE .SS Author David Avis .SS "See also" .BR lrs (1), .BR mplrs (1), .BR lrslib (5), lrslib-073/man/man1/hvref.10000777000175000017500000000000014625766600015204 2xref.1ustar avisavislrslib-073/man/man1/lrs.10000777000175000017500000005057214625766600013667 0ustar avisavis.TH "lrs" "1" "2023.1.4 " "January 2023" "lrs 7.3" .\" ----------------------------------------------------------------- .\" * Define some portability stuff .\" ----------------------------------------------------------------- .\" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .\" http://bugs.debian.org/507673 .\" http://lists.gnu.org/archive/html/groff/2009-02/msg00013.html .\" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .ie \n(.g .ds Aq \(aq .el .ds Aq ' .\" ----------------------------------------------------------------- .\" * set default formatting .\" ----------------------------------------------------------------- .\" disable hyphenation .nh .\" disable justification (adjust text to left margin only) .ad l .\" ----------------------------------------------------------------- .\" * MAIN CONTENT STARTS HERE * .\" ----------------------------------------------------------------- .SS "Name" lrs - Convert between representations of convex polyhedra, remove redundant inequalities, convex hull computation, volume, triangulation, solution to linear programs in exact precision. .SS "Synopsis" .HP \w'\fBlrs\fR\ [input-file] [output-file]\ 'u \fBlrs\fR\ \fI[input-file] [output-file]\fR .HP \w'\fBredund\fR\ [input-file] [output-file]\ 'u \fBredund|minrep\fR\ \fI[input-file] [output-file]\fR \fBSee: redund(1) \fR .HP \w'\fBfel\fR\ [input-file] [output-file]\ 'u \fBfel\fR\ \fI[input-file] [output-file]\fR \fBSee: fel(1)\fR .HP \w'\fBhvref/xref\fR\ [input-file] \ 'u \fBhvref/xref\fR\ \fI[input-file]\fR \fBSee: xref(1)\fR .SS "Description" .PP These programs are part of and must be compiled with \fIlrslib\fR which is a C library. All computations are done in exact arithmetic. .PP A polyhedron can be described by a list of inequalities (\fIH\-representation)\fR or by a list of its vertices and extreme rays (\fIV\-representation)\fR\&. .PP \fIlrs\fR converts an H\-representation of a polyhedron to its V\-representation and vice versa, known respectively as the \fIvertex enumeration\fR and \fIfacet enumeration\fR problems\& (see Example (1) below). For V-representations the volume can be computed and a triangulation. From v7.3 \fIlrs\fR is multi-threaded giving some partial parallelization that gives some speedup on shared memory machines. See \fBthreads\fR option. For a fully parallel version see \fBmplrs(1) \fR. \fIlrs\fR can also be used to solve a linear program and perform, using options, the functions of \fIredund, minrep, fel\fR and can extract a subset of columns. .PP \fIredund|minrep\fR .br These are aliases of \fIlrs\fR which can also perform these functions via the \fBredund\fR, \fBredund_list\fR and \fBtestlin\fR options. For a more complete description and examples see \fBredund(1)\fR. .br \fIH-representation:\fR redundant inequalities in an input H-representation are removed and the remaining inequalities output. In addition \fIminrep\fR checks for hidden linearities. .br \fIV-representation:\fR outputs all extreme points and extreme rays, often called the \fIconvex hull\fR problem. In addition \fIminrep\fR checks for hidden linearities. .PP \fIfel\fR projects an input H-representation onto a given set of variables using Fourier-Motzkin elimination. For a V-representation it extracts the specified columns. The output is non-redundant and can be can be piped directly into \fIlrs\fR. This is an alias of \fIlrs\fR which can also perform these functions via the \fBeliminate\fR and \fBproject\fR options. .PP \fIhvref/xref\fR\ produce a cross reference list between H- and V-representations. See \fBxref(1)\fR. .PP \fImplrs\fR is Skip Jordan's parallel wrapper based on MPI for \fIlrs/redund\fR using the same input and output formats. See: \fBmplrs(1)\fR .PP Fukuda's \fBFAQ page\fR[1] contains a more detailed introduction to the problem, along with many useful tips for the new user\&. User's guide for \fBlsrslib\fR[8] .SS "File formats" .PP File formats were developed jointly with Komei Fukuda and are compatible with \fBcdd/cddlib\fR[2]. .br The input for \fIlrs/redund\fR is an H\- or V\-representation of a polyhedron\&. name H-representation [\fIor\fR V-representation] {options} {linearities} begin m n rational [\fIor\fR integer] {input matrix} end {options} \fIname\fR is a user supplied name for the polyhedron\&.\ \& Comments may appear before the begin or after the end and should begin with a special character such as "*"\&. .PP If the representation is not specified H\-representation is assumed. The input coefficients are read in free format, and are not checked for type\&. Coefficients are separated by white space\&. m is the number of rows and n the number of columns of the input matrix\&. .SS "H\-representation" .PP m is the number of input rows, each being an inequality or equation. .br n is the number of input columns and d=n-1 is the dimension of the input. .br An inequality or equation of the form: .PP b + a_1 x_1 + \&.\&.\&. + a_d x_d >=\ \& 0\& .PP b + a_1 x_1 + \&.\&.\&. + a_d x_d =\ \& 0\& .PP is input as the line: .PP b \ a_1 \&.\&.\&. a_d .PP The coefficients can be entered as integers or rationals in the format x/y\&. To distinguish an equation a \fBlinearity\fR option must be supplied before the \fBbegin\fR line (see below). .SS "V\-representation" .PP m is the number of input rows, each being a vertex, ray or line. .br n is the number of input columns and d=n-1 is dimension of the input. .br Each vertex is given in the form: .PP 1 \ v_1 \ \ v_1 \&.\&.\&.\ v_d .PP Each ray is given in the form: .PP 0\ \&\ \& r_1 \&\ \& r_2\&.\&.\&.\ \&\ \& r_d .PP where r_1 \ \&.\&.\&.\ \&\ \& r_d is a point on the ray\&. .PP There must be at least one vertex in each file\&. For bounded polyhedra there will be no rays entered\&. The coefficients can be entered as integers or rationals in the format x/y\&. An input line can be specified as a ray and then included in the \fBlinearity\fR option (see below). .PP \fBNote for cdd users\fR: Note the input files for \fIlrs\fR are read in free format. \fIlrs\fR will look for exactly m*n rationals or integers separated by white space (blank, carriage return, tab etc\&.). \fIlrs\fR will not "drop" extra columns of input if n is less than the number of columns supplied\&. .SS "Options" .PP Almost all options are placed \fBafter\fR the end statement, maintaining compatibility with \fIcdd\fR\&. Where this is not the case, it will be mentioned explicitly\&. .PP \fBallbases\fR This option instructs \fIlrs\fR to list each vertex (or facet) for each of its bases\&. This option is often combined with printcobasis\&. .PP \fBbound\ \& x \fR (H\-representation only). Either the maximize or minimize option should be selected\&. x is an integer or rational\&. For maximization (resp\&. minimization) the reverse search tree is truncated\ \& whenever the current objective value is less (resp\&. more) than x\&. .PP \fBcache n\fR \ \ \ \ (default n=50) .br \fIlrs\fR stores the latest\ \& n dictionaries in the reverse search tree\&. This speeds up the backtracking step, but requires more memory\&. .PP \fBdebug\ \& startingcobasis endingcobasis\fR .br Print out cryptic but detailed trace, dictionaries etc\&. starting at #B=startingcobasis and ending at #B=endingcobasis\&. \fBdebug 0 0\fR gives a complete trace\&. .PP \fBdigits n\fR (lrsmp arithmetic only - placed before the begin statement) .br n is the maximum number of decimal digits to be used\&. If this is exceeded the program terminates with a message and can usually be restarted with the \fbrestart\fR option. The default is set to 100 digits\&. At the end of a run a message is given informing the user of the maximum integer size encountered\&. .PP \fBdualperturb\fR If lrs is executed with the \fBmaximize\fR or \fBminimize\fR option, the reverse search tree is rooted at an optimum vertex for this function\&. If there are multiple optimum vertices, the output will often not be complete\&. This option gives a small perturbation to the objective to avoid this\&. A warning message is given if the starting dictionary is dual degenerate\&. .PP \fBestimates k\fR .br Estimate the output size\&. Used in conjunction with \fBmaxdepth\fR and \fBseed\fR. See: \fBEstimation\fR[3]. .PP \fBeliminate k i_1 i_2 ... i_k \fR (see \fBfel(1)\fR) .br \fI(H-representation)\fR Eliminates k variables in an H-representation corresponding to cols i_1 .. i_k by projection onto the remaining variables using the Fourier-Motzkin method. Variables are eliminated in the order given and redundancy is removed after each iteration. .br \fI(V-representation)\fR Delete the k given columns from the input matrix and remove redundancies (cf. \fBextract\fR where redundancies are not removed). .br Column indices are between 1 and n-1 and column zero cannot be eliminated. The output is a valid lrs input file. See also \fBproject\fR and \fBextract\fR .PP \fBextract [ k i_1 i_2 ... i_k ] \fR .br \fI(H-representation)\fR A preprocessing step to remove linearities (if any) in an H-representation and resize the A matrix. The output as a valid lrs input file. The resulting file will not contain any equations but may not be full dimensional as there may be additional linearities in the remaining inequalities. Options in the input file are stripped. The user can specify the k columns i_1 i_2 ... i_k to retain otherwise if k=0 or is ommitted the lex-min set of columns are retained, equivalent to the the order 1,2,..n-1. Linearly dependent columns are skipped and additional indices are taken from 1,2,...,n-1 as necessary. If there are no linearities in the input file the given columns are retained and the other ones are deleted. .br \fI(V-representation)\fR Extract the given columns from the input file outputing a valid lrs input file. Options are stripped. .PP \fBgeometric\ \&\ \&\fR \fI(H\-representation\ \& or voronoi option only)\fR Each ray is printed together with the vertex with which it is incident\&. .PP \fBincidence\fR This option automatically switches on \fBprintcobasis\fR. For input H\-representation, indices of all input inequalities that contain the vertex/ray that is about to be output\&. For input V\-representation, indices of all input vertices/rays that lie on the facet that is about to be output\&. A starred index indicates that this vertex\ \& is also in the cobasis, but is not contained in the facet\&. It arises due to the lifting operation used with input V\-representations\&. .PP \fBlinearity\ \& k\ \& i_1 \ i_2 \ \&... \ i_k \fR (placed before begin statement) .br (H-representation) The k rows i_1 \ i_2 \ \&... \ i_k \fR \ of the input file represent equations\&. (V-representation) The k rows, which should have a zero in column 1, represent lines in space (rather than rays). .PP \fBlponly\fR Solve the LP given by the input H-representation with objective function specified by the \fBmaximize\fR or \fBminimize\fR options and terminate. Use with \fBverbose\fR option to get dual variables. See: \fBLinear Programming\fR[4]. .PP \fBmaxcobases k\fR .br The search will be truncated after k\& cobases have been generated. .PP \fBmaxdepth k\fR .br The search will be truncated at depth k\&. All bases with depth less than or equal to k will be computed\&.\ \& k is\ \& a non\-negative integer, and this option is used for estimates \- see \fBEstimation\fR[3]. \fBNote\fR: For H\-representations, rays at depth k will not be reported\&. For V\-representations, facets at depth k will not be reported\&. .PP \fBmaximize\ \& b \ a_1 \&.\&.\&. a_{n-1} \fR\ \& .br \fBminimize\ \& b \ a_1 \&.\&.\&. a_{n-1} \fR\ \& .br \fI(H\-representation)\fR The starting vertex maximizes (or minimizes) the function \ b + a_1 x_1+ \&.\&.\&. + a_{n-1} x_{n-1}. .br The \fBdualperturb\fR option may be needed to avoid dual degeneracy\&. Often used with \fBlponly\fR. .br \fI(V\-representation, v.7.2)\fR The input file row numbers maximizing(minimizing) the function are output along with the optimum value. Using \fBverbose\fR the optimizing lines are also printed. With minimization a facet gives an optimum value of zero, a negative value indicates infeasibility and a positive value indicates strong redundancy. .PP \fBmaxincidence n k\fR .br Prunes the search tree when the depth is at least k and the current vertex/facet has incidence at least n. Using \fBverbose\fR a message is printed whenever the search tree is pruned. .PP \fBmaxoutput n\fR .br Limits number of output lines produced (either vertices+rays or facets) to n .PP \fBmindepth k\fR .br Backtracking will be terminated at depth k. .PP \fBnonnegative\fR (This option must come before the begin statement - H\-representation only) \ \& Bug: Can only be used if the origin is a vertex of the polyhedron\ \& For problems where the input is an H\-representation of the form b+Ax>=0, x>=0 (ie\&. all variables non\-negative, all constraints inequalities) it is not necessary to give the non\-negative constraints explicitly if the nonnegative option is used\&. This option cannot be used for V\-representations, or with the linearity option (in which case the linearities will be treated as inequalities)\&. This option may be used with redund , but the implied nonnegativity constraints are not tested themselves for redundancy\&. .PP \fBproject k i_1 i_2 ... i_k \fR (see \fBfel(1)\fR) .br \fI(H-representation)\fR Project the polyhedron onto the k variables corresponding to cols i_1 .. i_k using the Fourier-Motzkin method. Column indices are between 1 and n-1 and column zero is automatically retained. Variables not contained in the list are eliminated using a heuristic which chooses the column which minimizes the product of the number of positive and negative entries. Redundancy is removed after each iteration using linear programming. .br \fI(V-representation)\fR Extract the k given columns from the input matrix and remove redundancies. Column indices are between 1 and n-1 and column zero is automatically extracted (cf. \fBextract\fR where redundancies are not removed). .br The output as a valid lrs input file. See also \fBeliminate\fR and \fBextract\fR .PP \fBprintcobasis\ k\fR .br Every k-th cobasis is printed. If k is omitted, the cobasis is printed for each vertex/ray/facet that is output\&. For a long run it is useful to print the cobasis occasionally so that the program can be restarted if necessary\&. \fIH\-representation\fR: the cobasis is a list the indices of the inequalities from the input file that define the current vertex or ray\&. For rays the cobasis is the cobasis of the vertex from which the ray emanates\&. One of the indices is starred, this indicates the inequality to be dropped from the cobasis to define the ray\&. If the \fBallbases\fR option is used, all cobases will be printed\&. \fIV\-representation\fR: the cobasis is a list of the input vertices/rays that define the current facet\&. See option \fBincidence\fR for more information\&. .PP \fBprintslack\fR (H\-representation only) A list of the indices of the input inequalities that are satisfied strictly for the current vertex, ie\&. corresponding slack variable is positive\&. If nonnegative is set, the list will also include indices n+i for each decision variable x_i which is positive\&. .PP \fBredund start end \fR (see \fBredund(1)\fR) .br Check input lines with line numbers from start to end and remove any redundant lines. .br \fBredund 0 0\fR will check all input lines. .PP \fBredund_list k i_1 i_2 ... i_k\fR (see \fBredund(1)\fR) .br Check the k input line numbers with indices i_1 i_2 ... i_k and remove any redundant lines. .PP \fBrestart\ \& V# R# B# depth {facet #s or vertex/ray #s\fR} .br \fIlrs\fR can be restarted from any known cobasis\&. The calculation will proceed to normal termination\&. All of the information is contained in the output from a \fBprintcobasis\fR option\&.\ \& The \fBorder of the indices is very important,\fR enter them exactly as they appear in the output from the previously terminated run\&. .PP Note that if some cobasic index is followed by a "*",\ \& then the index only, without the "*", is included in the restart line\&. \fBCaution:\fR When restarting, output from the restart dictionary may be duplicated, and the final totals of number of vertices/rays/facets may reflect this\&. .PP \fBseed k\fR .br Set the random number generator seed=k. Used with \fBestimates\fR. .PP \fBstartingcobasis i_1 \ i_2 \ ... \ i_{n-1}\fR .br lrs will start from the given cobasis which which is a list of the inequalities (for H\-representation) or vertices/rays (for V\-representation) that define it. If it is invalid, or this option is not specified, \fIlrs\fR will find its own starting cobasis\&. .PP \fBtestlin\fR \fB(before the begin line only)\fR \fIH-representation\fR only (new 7.3) .br An LP test will be made for hidden linearities in the input file. If neither \fBredund\fR or \fBredund_list\fR options are present the initial LP test is made, reported and the run halted. Otherwise the run is equivalent to \fIminrep\fR. .PP \fBthreads n\fR (new in 7.3, disabled for mplrs) .br Multithreaded lrs for the H-V conversion problem using openMP. A parallel search of the reverse search tree is performed at depth 1. If n is not specified the default openMP max threads is used. .PP \fBtruncate\fR The reverse search tree is truncated(pruned) whenever a new vertex is encountered\&. Note: This does note necessarily produce the set of all vertices adjacent to the optimum vertex in the polyhedron, but just a subset of them\&. .PP \fBverbose\fR Print slightly more detailed information about the run\&. .PP \fBvolume\fR (V\-representation only) Compute the volume and, if the \fBverbose\fR option is also included, output a \fBtriangulation\fR. See \fBVolume Computation\fR[5]. .PP \fBvoronoi\fR (V\-representation\ \& only \- place immediately after end statement) .br Compute Voronoi diagram \- see \fBVoronoi Diagrams\fR[6]. .SS "Arithmetic" From version 7.1 \fIlrs/redund/mplrs\fR use hybrid arithmetic with overflow checking, starting in 64bit integers, moving to 128bit (if available) and then GMP. Overflow checking is conservative to improve performance: eg. with 64 bit arithmetic, a*b triggers overflow if either a or b is at least 2^31, and a+b triggers an overflow if either a or b is at least 2^62. Typically problems that can be solved in 64bits run 3-4 times faster than with GMP and inputs solvable in 128bits run twice as fast as GMP. .PP Various arithmetic versions are available and can be built from the makefile: .PP \fBlrs1\fR Fixed length 64 bit integer arithmetic, terminates on overflow. .PP \fBlrs2\fR Fixed length 128 bit integer arithmetic, terminates on overflow. .PP \fBlrsmp\fR Built in extended precision integer arithmetic, uses \fBdigits\fR option above. .PP \fBlrsgmp\fR GNU MP which must be installed first from https://gmplib.org/. .PP \fBlrsflint\fR FLINT hybrid arithmetic which must be installed first from http://www.flintlib.org/ .SS "Examples" .PP (1) Convert the H-representation of a cube given cube by 6 the six inequalities .br -1 <= x_i <= 1 , i=1,2,3 into its V-representation consisting of 8 vertices. .PP % cat cube.ine cube.ine H-representation begin 6 4 rational 1 1 0 0 1 0 1 0 1 0 0 1 1 -1 0 0 1 0 0 -1 1 0 -1 0 end % lrs cube.ine *lrs:lrslib v.6.3 2018.4.11(64bit,lrslong.h,overflow checking) *Input taken from file cube.ine cube.ine V-representation begin ***** 4 rational 1 1 1 1 1 -1 1 1 1 1 -1 1 1 -1 -1 1 1 1 1 -1 1 -1 1 -1 1 1 -1 -1 1 -1 -1 -1 end *Totals: vertices=8 rays=0 bases=8 integer_vertices=8 .SS "Notes" .IP " 1." 4 FAQ page .RS 4 \%https://inf.ethz.ch/personal/fukudak/polyfaq/polyfaq.html .RE .IP " 2." 4 cdd .RS 4 \%https://inf.ethz.ch/personal/fukudak/cdd_home/ .RE .IP " 3." 4 Estimation. .RS 4 \%http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html#Estimation .RE .IP " 4." 4 Linear Programming .RS 4 \%http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html#Linear%20Programming .RE .IP " 5." 4 Volume Computation. .RS 4 \%http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html#Volume%20Computation .RE .IP "6." 4 Voronoi Diagrams. .RS 4 \%http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html#Voronoi%20Diagrams .RE .IP "7." 4 redund: extreme point enumeration and eliminating redundant inequalities .RS 4 \%http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html#redund .RE .IP "8." 4 User's guide for lrslib .RS 4 \%http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html .RE .SS Author David Avis .SS "See also" .BR mplrs (1), .BR lrslib (5), .BR lrsnash (1) lrslib-073/man/man1/lrsnash.10000777000175000017500000001073314625766600014534 0ustar avisavis.TH "lrsnash" "1" "2024.1.31" "January 2024" "lrslib 7.3" .\" ----------------------------------------------------------------- .\" * Define some portability stuff .\" ----------------------------------------------------------------- .\" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .\" http://bugs.debian.org/507673 .\" http://lists.gnu.org/archive/html/groff/2009-02/msg00013.html .\" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .ie (.g .ds Aq \(aq .el .ds Aq ' .\" ----------------------------------------------------------------- .\" * set default formatting .\" ----------------------------------------------------------------- .\" disable hyphenation .nh .\" disable justification (adjust text to left margin only) .ad l .\" ----------------------------------------------------------------- .\" * MAIN CONTENT STARTS HERE * .\" ----------------------------------------------------------------- .SS "Name" lrsnash: \ Compute Nash-equibria in 2-person games\&. .SS "Synopsis" .HP \w'\fBlrsnash\fR \ [options...] [input-file] \ 'u \fBlrsnash\fR \ [options...] [input-file] .HP \w'\fBlrsnash1\fR\ [options...] [input-file] \ 'u \fBlrsnash1\fR\ [options...] [input-file] .HP \w'\fBlrsnash2\fR\ [options...] [input-file] \ 'u \fBlrsnash2\fR\ [options...] [input-file] .HP \w'\fBnashdemo\fR\ \ 'u \fBnashdemo\fR\ .PP options: -v, --verbose Prints a trace of the solution process -d, --debug Dumps lots of information for debugging -p, --printgame Prints the payoff matrix for the game -s, --standard Promise that input files have standard structure -o, --outfile Send output to -h, --help Prints this text Short options can be grouped, as in '-ps' and '-do out.txt' .SS Description .PP These C programs are distributed as part of the \fBlsrslib\fR[2] package and must be compiled with it. Alice has a payoff matrix A and Bob has a playoff matrix B, both of dimension m by n. Alice assigns probabilities x to the rows and Bob y to the columns. Alice receives payoff x^T A y and Bob receives x^T B y. A Nash equilibriam occurs for pairs x,y for which neither player can improve their expected payoff by unilateraly changing strategies. .PP \fIlrsnash\fR is an application of \fIlrs\fR for finding Nash-equilibria in 2-person matrix games using a method described in \u[1]. It uses GMP exact extended precision arithmetic. \fIlrsnash1\fR is the same as \fIlrsnash\fR except that it uses 64 bit exact arithmetic and terminates if overflow is detected. It is about 3-4 times faster. \fIlrsnash2\fR is the same as \fIlrsnash\fR except that it uses 128 bit exact arithmetic and terminates if overflow is detected. It is about twice as fast. It requires a C compiler with __int128 support (eg. gcc v. 4.6.0 or later). \fInashdemo\fR is a simple template for \fIlrsnash\fR. It builds two 3x4 matrices A and B and computes their equilibria. The running time may be significantly different depending on the order of the two matrices in the input. For large problems it may be advantageous to run \fIlrsnash\fR twice in parallel with the matrices in different orders. There is also a more complex legacy input format recognized by \fIlrsnash\fR that is described in \u[1]. .SS File formats .PP The input file consists of two integers m and n on line 1 followed by two mxn payoff matrices A and B: m n A (row by row) B (row by row) .SS Example The input file game has two 3x2 payoff matrices: %cat game 3 2 0 6 2 5 3 3 1 0 0 2 4 3 % lrsnash game 2 1/3 2/3 4 1 2/3 1/3 0 2/3 2 2/3 1/3 3 1 0 1/3 2/3 8/3 2 1 0 3 1 0 0 1 4 *Number of equilibria found: 3 *Player 1: vertices=5 bases=5 pivots=8 *Player 2: vertices=3 bases=1 pivots=8 \fBInterpretation\fR There are 3 Nash equilibria. For the first one: 2 1/3 2/3 4 .br Bob(player 2) plays column 1 and 2 with probablilities y=(1/3, 2/3) and the payoff to Alice(player 1) is 4. 1 2/3 1/3 0 2/3 .br Alice plays rows 1,2,3 with probabilities x=(2/3, 1/3, 0) and the payoff to Bob is 2/3. .SS Notes .IP 1. 4 D. Avis, G. Rosenberg, R. Savani, B. von Stengel, \fIEnumeration of Nash Equilibria for Two-Player Games\fR, Economic Theory 42(2009) 9-37 .IP 2. 4 User's guide for lrslib .RS 4 \%http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html .RE .SS Authors David Avis and Terje Lensberg .SS "See also" .BR lrslib (5) lrslib-073/man/man1/minrep.10000777000175000017500000000000014625766600015701 2redund.1ustar avisavislrslib-073/man/man1/mplrs.10000777000175000017500000001450714625766600014222 0ustar avisavis.TH "mplrs" "1" "2024.2.5" "February 2024" "mplrs 7.3" .\" ----------------------------------------------------------------- .\" * Define some portability stuff .\" ----------------------------------------------------------------- .\" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .\" http://bugs.debian.org/507673 .\" http://lists.gnu.org/archive/html/groff/2009-02/msg00013.html .\" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .ie \n(.g .ds Aq \(aq .el .ds Aq ' .\" ----------------------------------------------------------------- .\" * set default formatting .\" ----------------------------------------------------------------- .\" disable hyphenation .nh .\" disable justification (adjust text to left margin only) .ad l .\" ----------------------------------------------------------------- .\" * MAIN CONTENT STARTS HERE * .\" ----------------------------------------------------------------- .SS "Name" mplrs \- Convert between representations of convex polyhedra, remove redundant inequalities, do Fourier-Motzkin elimination (parallel version)\&. .SS "Synopsis" .HP \w'\fB\ mpirun\ \fR\fBmplrs\fR\ 'u \fB mpirun \fR \-np \fInum_proc\ \fR\fBmplrs\fR \fIinfile\fR [\fIoutfile\fR] [\fIoption\fR...] .br .SS "Description" .PP A polyhedron can be described by a list of inequalities (\fIH\-representation)\fR or by a list of its vertices and extreme rays (\fIV\-representation)\fR\&. \fImplrs\fR is a parallel version of lrs, and converts an H\-representation of a polyhedron to its V\-representation, and vice versa\&.\ \& These problems are known respectively as the \fIvertex enumeration\fR and \fIconvex hull problems\fR\&. With \fBlrs\fR options \fBredund\fR or \fBredund_list\fR in the input file it will do parallel execution of \fBminrep\fR (computing a minimum representation), see \fBredund(1)\fR. With \fBlrs\fR options \fBproject\fR or \fBeliminate\fR in the input file it will do parallel execution of \fBfel\fR (Fourier-Motkin elimination). .PP .SS "Usage" .PP The number of processors \fInum_proc\fR specified to \fBmpirun\fR should be 4 or higher. Some lrs input file options are not supported by \fBmplrs\fR. .PP .SS "Options" .PP \fBmplrs\fR supports the following options, where default values are given in brackets\&. .RS 4 \fB\-checkp \fR if mplrs is terminated by \-stop or \-time then it can be restarted using this and \-restart .RE .RS 4 \fB\-countonly\fR don\*(Aqt output vertices/rays/facets, just count them .RE .RS 4 \fB\-freq \fR store frequency data in for use by gnuplot, see below .RE .RS 4 \fB\-hist \fRstore parallelization data in for use by gnuplot, see below .RE .RS 4 \fB\-id \fR [2] the depth of the original tree search to populate the job list L .RE .RS 4 \fB\-lmax \fR[lmin] if job list |L|>np*lmax then then maxc is replaced by maxc*scale .RE .RS 4 \fB\-lmin \fR[3] if job list |L|\fR[500] controls maximum size of worker output buffers .RE .RS 4 \fB\-maxc \fR[50 (*scale)] a producer stops and returns all subtrees that are not leaves to L after generating\ \& maxc nodes\ \&\ \&\ \& .RE .RS 4 \fB\-maxd \fR[0] a producer returns all subtrees that are not leaves at depth maxd\&. Zero if not used .RE .RS 4 \fB\-minheight\fR jobs are scheduled in increasing order by height in the search tree (default is LIFO) .RE .RS 4 \fB\-queue\fR jobs are scheduled in FIFO order (default is LIFO) .RE .RS 4 \fB\-restart \fR restart mplrs using previously created \&. If used with \-checkp file names should be different! .RE .RS 4 \fB\-scale \fR[100] used by lmax .RE .RS 4 \fB\-stop \fR terminate mplrs if a file with name is created in the current directory .RE .RS 4 \fB\-stopafter \fR exit after approximately cobases have been computed (no guarantee about how many vertices/rays/facets computed) .RE .RS 4 \fB\-temp \fR[/tmp/] store a temporary file for each process\&. Should be specified if /tmp not writeable\&. Using " \-temp\ \& \&./ " will write temporary files to the current directory .RE .RS 4 \fB\-time \fR terminate mplrs after of elapsed time .RE \fB redund/fel options .RS 4 \fB\-j \fR[1] if non-zero splits the run into jobs per worker, over-riding rows and lastrows .RE .RS 4 \fB\-lastp \fR[10] the percentage of jobs to use lastrows .RE .RS 4 \fB\-lastrows \fR[10] the number of rows for the last lastp jobs .RE .RS 4 \fB\-minrep\fR removes redundant inequalities, finds hidden linearities and outputs a minimum representation of the input file. This ignores any \fBproject\fR or \fBeliminate\fR option present in the input file .RE .RS 4 \fB\-rows \fR[60] the number of rows per job .RE .SS "-hist file format" Example line: .RS 4 54.118141 94 279 94 0 0 373 time since execution began in seconds (54.118141 here) number of busy workers (94 here) current size of job list (279 here) number of workers that may return unfinished jobs (94 here) unused (0 here) unused (0 here) total number of jobs that have been in the job list (373 here) .RE The second and fourth entries are similar and can differ due to latencies. .SS "-freq file format" One integer per line corresponding to the size of a subtree explored by a worker. .SS "Example" .PP Input file mp5\&.ine is run with 8 processors\&. This produced 378 subtrees that were enumerated in parallel using 6 producer cores,\ \& 1 core controlling the run and 1 core collecting the output\&. .sp .if n \{\ .RS 4 .\} .nf mai20% mpirun \-np 8 mplrs mp5\&.ine mp5\&.mplrs *mplrs:lrslib v\&.6\&.0 2015\&.7\&.13(lrsgmp\&.h)8 processes *Copyright (C) 1995,2015, David Avis\ \&\ \& avis@cs\&.mcgill\&.ca *Input taken from mp5\&.ine *Output written to: mp5\&.mplrs *Starting depth of 2 maxcobases=50 maxdepth=0 lmin=3 lmax=3 scale=100 *Phase 1 time: 0 seconds\&. *Total number of jobs: 378, L became empty 4 times *Totals: vertices=32 rays=0 bases=9041 integer\-vertices=16 *Elapsed time: 1 seconds\&. 2\&.285u 0\&.137s 0:01\&.86 129\&.5%\ \&\ \&\ \& 0+0k 0+9976io 36pf+0w .fi .if n \{\ .RE .\} .SS Author Charles Jordan .SS "See also" .BR lrs (1), .BR lrslib (5) lrslib-073/man/man1/polyv.10000777000175000017500000001704014625766600014231 0ustar avisavis.TH "polyv" "1" "2023.10.21" "October 2023" "polyv 7.3" .\" ----------------------------------------------------------------- .\" * Define some portability stuff .\" ----------------------------------------------------------------- .\" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .\" http://bugs.debian.org/507673 .\" http://lists.gnu.org/archive/html/groff/2009-02/msg00013.html .\" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .ie \n(.g .ds Aq \(aq .el .ds Aq ' .\" ----------------------------------------------------------------- .\" * set default formatting .\" ----------------------------------------------------------------- .\" disable hyphenation .nh .\" disable justification (adjust text to left margin only) .ad l .\" ----------------------------------------------------------------- .\" * MAIN CONTENT STARTS HERE * .\" ----------------------------------------------------------------- .SS "Name" polyv - utility to create and verify logical formulas checking properties of given H/V representations using logic solvers. .SS "Synopsis" .HP \w'\fBpolyv\fR\ [input-files]\ 'u \fBpolyv\fR\ \fI[input-files]\fR .SS "Description" .PP The input file or files are H- or V-representations of polyhedra in \fIlrs\fR format, and the output is a logical formula in \fISMT\-LIB\fR 2.6 format. Behavior depends on the options and number of input files provided. In many cases, it is easier and faster to use \fIlrs\fR, \fImplrs\fR or other tools to check the following questions directly. \fIpolyv\fR is an alternative approach intended for some examples where the direct approach is difficult. First, \fIpolyv\fR can be given a single H-representation defining a polyhedron P, along with a list of variables for a projection of P and an inequality I to test. The question is whether we have the same projection when I is deleted from P. If so we say I is redundant for the projection, otherwise it is non-redundant. \fIpolyv\fR allows the use of SMT solvers to decide this question without performing the projection explicitly, producing a formula that is satisfiable iff the I is non-redundant for the projection. In addition, \fIpolyv\fR it produce \fIlrs\fR inputs that verify witnesses of non-redundancy produced by an SMT solver. Next, \fIpolyv\fR can be given two representations defining polyhedra P and Q, where H-representations may contain projections. The question is whether P and Q are different polyhedra: \fIpolyv\fR produces a formula that is satisfiable iff there is a point contained in exactly one of P and Q. Finally, \fIpolyv\fR can be given three representations defining polyhedra P, Q and R. The question is whether the intersection of P and Q is different from R: \fIpolyv\fR produces a formula that is satisfiable iff there is a point contained in exactly one of R and the intersection. .SS "File formats" .PP The input file is in \fIlrs\fR format (see .BR lrs (1) ) consisting of (a) an H-representation of a polyhedron, (b) a projection to a subset of variables given by the \fIproject\fR or \fIeliminate\fR options, and (c) an inequality to test given by the \fIredund\fR or \fIredund_list\fR options. Note that only "linearity", "redund", "redund_list", "project" and "eliminate" options are supported, and the combination of redund/redund_list and project/eliminate options is both unique to polyv and required. .PP The output is in \fISMT\-LIB\fR 2.6 format using logic \fILRA\fR. Solvers such as \fIz3\fR or \fIcvc5\fR support this logic. See The SMT-LIB Standard: Version 2.6 for details. .SS "Usage" .PP \fBpolyv\fR\ [input-file] produces a logical formula satisfiable iff the first inequality given in a redund/redund_list option is redundant after projection according to a project/eliminate option. The solver can produce witnesses for non-redundant inequalities, i.e. an assignment to the variables whose image is in the projection only if the inequality is removed. No witness is produced if the inequality is redundant. .PP A witness of non-redundancy can be verified using two certificates. The first certificate specifies that the assignment to the variables is feasible when the inequality in question is removed. The second certificate asserts that when this inequality is added, no feasible assignment has the same projection. Certificates are produced using the following options. .PP \fBpolyv\fR\ -c 1 [input-file] reads a witness of non-redundancy on standard input and produces an lrs input file that should be feasible. The options in the input file should be the same as when the formula was produced. .PP \fBpolyv\fR\ -c 2 [input-file] reads a witness of non-redundancy on standard input and produces an lrs input file that should be infeasible. The options in the input file should be the same as when the formula was produced. .PP \fBpolyv\fR\ [input-file-1] [input-file-2] given two H/V representations, produces a logical formula satisfiable iff they define different polyhedra. Projections are supported in H-representations using the project or eliminate option. This can be used to e.g. verify H/V equivalency or fel projections. .PP \fBpolyv\fR\ [input-file-1] [input-file-2] [input-file-3] given three H/V representations, produces a logical formula satisfiable iff the intersection of polyhedra defined by input-file-1 and input-file-2 is not defined by input-file-3. Projections are supported in H-representations using the project or eliminate option. .SS "Examples" .PP (1) Check if the first inequality in cp4.ine is redundant for projections. .br (a) To check for redundancy after the first variable is eliminated, add options "redund_list 1 1" and "eliminate 1 1" to cp4.ine. Then: % polyv cp4.ine > cp4\-11.smt % z3 cp4\-11.smt > cp4\-11.out .br or .br % cvc5 -L smt --produce-models cp4\-11.smt > cp4\-11.out The first line of cp4\-11.out reads "sat" indicating that inequality 1 is non-redundant for eliminating variable 1. We can check the witness: % polyv -c 1 cp4.ine < cp4\-11.out | lrs % polyv -c 2 cp4.ine < cp4\-11.out | lrs The first certificate is feasible and second infeasible, so the witness proves non-redundancy for the projection. .br (b) To check for redunancy after variables 1 and 2 are eliminated, add options "redund_list 1 1" and "eliminate 2 1 2" to cp4.ine. Then % polyv cp4.ine > cp4\-112.smt % z3 cp4\-112.smt > cp4\-112.out .br or .br % cvc5 -L smt --produce-models cp4\-112.smt > cp4\-112.out The first line of cp4\-112.out reads "unsat" indicating that inequality 1 is redundant for eliminating variables 1 and 2. In this case there is no witness. .PP (2) Check if given H- and V- representations define different polyhedra. .br (a) To check whether mp5.ine and mp5.ext (produced using lrs) define different polyhedra: % polyv mp5.ine mp5.ext > mp5hv.smt % z3 mp5hv.smt > mp5hv.out The first line of mp5hv.out reads "unsat" indicating that these two representations do not define different polyhedra (i.e. they are equivalent). .br (b) After removing the last vertex (the origin) from mp5.ext to create mp5missing.ext: % polyv mp5.ine mp5missing.ext > mp5hvm.smt % z3 mp5hvm.smt > mp5hvm.out The first line of mp5hvm.out reads "sat" indicating that these two representations define different polyhedra. .br Note that the H-representations are allowed to include projections. .SS "Notes" .IP " 1." 4 SMT-Lib Standards .RS 4 \%http://smtlib.cs.uiowa.edu/language.shtml .RE .IP " 2." 4 z3 .RS 4 \%https://github.com/Z3Prover/z3/wiki .RE .IP " 3." 4 cvc5 .RS 4 \%https://cvc5.github.io/ .RE .SS Author Charles Jordan .SS "See also" .BR lrslib (5), .BR lrs (1) lrslib-073/man/man1/redund.10000777000175000017500000001452214625766600014343 0ustar avisavis.TH "redund|minrep" "1" "2024.1.10 " "January 2024" "lrslib 7.3" .\" ----------------------------------------------------------------- .\" * Define some portability stuff .\" ----------------------------------------------------------------- .\" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .\" http://bugs.debian.org/507673 .\" http://lists.gnu.org/archive/html/groff/2009-02/msg00013.html .\" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .ie \n(.g .ds Aq \(aq .el .ds Aq ' .\" ----------------------------------------------------------------- .\" * set default formatting .\" ----------------------------------------------------------------- .\" disable hyphenation .nh .\" disable justification (adjust text to left margin only) .ad l .\" ----------------------------------------------------------------- .\" * MAIN CONTENT STARTS HERE * .\" ----------------------------------------------------------------- .SS "Name" redund|minrep - Remove redundant inequalities from an H-representation or redundant vertices (non-extreme points) from a V-representation. \fBminrep\fR also identifies hidden linearities. .SS "Synopsis" .HP \w'\fBredund\fR\ [input-file] [output-file]\ 'u \fBredund\fR\ \fI[input-file] [output-file]\fR .HP \w'\fBminrep\fR\ [input-file] [output-file]\ 'u \fBminrep\fR\ \fI[input-file] [output-file]\fR .HP \w'\fBmpirun\fR\ \fR\fBmplrs\fR\ [input-file] [output-file]\ 'u \fBmpirun\fR\ -np [procs] \fBmplrs -minrep\fR\ \fI[input-file] [output-file] [option...]\fR .SS "Description" .PP \fBredund\fR and \fBminrep\fR are aliases to \fBlrs\fR which is part of the C library \fBlrslib(5)\fR. This functionality can also be performed by \fBlrs\fR directly by using the options described below. All computations are done in exact arithmetic. For input file descriptions see \fBlrs(1)\fR. A parallel version of \fBminrep\fR is given by \fBmplrs -minrep\fR. The \fB-redund\fR option performs the same function and is retained for legacy. (see \fBmplrs(1)\fR) .PP \fIredund\fR .br \fIH-representation:\fR redundant inequalities in an input H-representation are removed and the remaining inequalities output\&. Hidden linearities are not detected unless the \fBtestlin\fR option is included, in which case the output is a minimum representation and the dimension is reported. .br \fIV-representation:\fR outputs all extreme points and extreme rays, often called the \fIconvex hull\fR problem. The \fBtestlin\fR option cause linearities to be detected and explicitly output. .br Outputs can be piped directly into \fIlrs\fR. \fIredund\fR is a link to \fIlrs\fR which can also perform these functions via the \fBtestlin\fR, \fBredund\fR and \fBredund_list\fR options. \fBmplrs -redund\fR always sets the \fBtestlin\fR option, so always produces minimum representations. .PP \fIminrep\fR .br Equivalent to \fBredund\fR with the \fBtestlin\fR option. .PP With no options minrep|redund will process the entire input file. .PP \fBredund start end \fR .br Check input lines with line numbers from start to end and remove any redundant lines. .br \fBredund 0 0\fR will check all input lines. .PP \fBredund_list k i_1 i_2 ... i_k\fR .br Check the k input line numbers with indices i_1 i_2 ... i_k and remove any redundant lines. .PP \fBtestlin\fR \fB(before the begin line only)\fR (new 7.3) .br \fIredund\fR An LP test will be made for hidden linearities at the beginning of the run and is reported. If there are no hidden linearities one LP per constraint tests for redundancy. If hidden linearities exist two LPs per constraint search for hidden linearities and remove redundancies. In both cases the run ends with a minimum set of linearities and inequalities (ie. no hidden inequalities or duplicates) and the dimension is reported. .br \fIlrs\fR If neither \fBredund\fR or \fBredund_list\fR options are present the initial LP test is made, reported and the run halted. Otherwise as above for \fIredund\fR. .br \fImplrs\fR This option is ignored. In redund/minrep mode a minimum representation is always found. .PP \fBverbose\fR .br As each input line is checked a message is printed telling its status .br *nr :non-redundant *re :redundant *sr :strongly redundant .br For an H-representation strongly redundant means the feasible region lies in its open half-space. For a V-representation it means that the point lies in the (relative) interior of the convex hull. .br In addition \fIminrep\fR may report *li :linearity .SS "Examples" .PP (1) Remove hidden linearities and minimum representation of an H-representation. % cat cube.ine H-representation begin 7 4 rational 0 1 0 0 0 0 1 0 0 0 0 1 1 -1 0 0 1 0 -1 0 1 0 0 -1 -1 0 0 1 end verbose % minrep cube.ine minrep:lrslib_v.7.3_2024.1.10(64bit,lrslong.h,hybrid_arithmetic) *Input taken from cube.ine *hidden linearities exist *finding minimum representation *nr 0 1 0 0 *nr 0 0 1 0 *sr 0 0 0 1 *nr 1 -1 0 0 *nr 1 0 -1 0 *li 1 0 0 -1 *li-1 0 0 1 *linearity in row=6 removed or in cobasis, independent *linearity in row=7 dependent, made redundant H-representation linearity 1 1 begin 5 4 rational 1 0 0 -1 0 1 0 0 0 0 1 0 1 -1 0 0 1 0 -1 0 end *input had 7 rows and 4 columns * 2 redundant row(s) found 3 7 * 1 hidden linearity found .PP (2) Compute the extreme points of a set of 10 points in R^3 .PP % cat c.ext V-representation begin 10 4 rational 1 1 1 1 1 0 1 1 1 1/2 0 1/3 1 1 1 0 1 0 1 0 1 1 0 0 1 0 0 0 1 0 1/3 1/4 1 1 0 1 1 0 0 1 end % redund c.ext *redund:lrslib v.7.2 2020.6.8(64bit,lrslong.h,hybrid arithmetic) *Input taken from c.ext V-representation begin 8 4 rational 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 0 1 1 0 0 1 0 0 0 1 1 0 1 1 0 0 1 end *Input had 10 rows and 4 columns * 2 redundant row(s) found: 3 8 .SS "Notes" .IP " 1." 4 FAQ page .RS 4 \%https://inf.ethz.ch/personal/fukudak/polyfaq/polyfaq.html .RE .IP "2." 4 redund: extreme point enumeration and eliminating redundant inequalities .RS 4 \%http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html#redund .RE .IP "3." 4 User's guide for lrslib .RS 4 \%http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html .RE .SS Author David Avis .SS "See also" .BR lrs (1), .BR mplrs (1), .BR lrslib (5), lrslib-073/man/man1/xref.10000777000175000017500000000615514625766600014031 0ustar avisavis.TH "xref|hvref" "1" "2023.1.4 " "January 2024" "lrslib 7.3" .\" ----------------------------------------------------------------- .\" * Define some portability stuff .\" ----------------------------------------------------------------- .\" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .\" http://bugs.debian.org/507673 .\" http://lists.gnu.org/archive/html/groff/2009-02/msg00013.html .\" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .ie \n(.g .ds Aq \(aq .el .ds Aq ' .\" ----------------------------------------------------------------- .\" * set default formatting .\" ----------------------------------------------------------------- .\" disable hyphenation .nh .\" disable justification (adjust text to left margin only) .ad l .\" ----------------------------------------------------------------- .\" * MAIN CONTENT STARTS HERE * .\" ----------------------------------------------------------------- .SS "Name" xref|hvref - produce a cross reference list between H- and V-representations. .SS "Synopsis" .HP \w'\fBxref\fR\ [input-file] \ 'u \fBxref\fR\ \fI[input-file]\fR .HP \w'\fBhvref\fR\ [input-file] \ 'u \fBhvref\fR\ \fI[input-file]\fR .SS "Description" .PP These programs are part of and must be compiled with \fIlrslib\fR which is a C library. All computations are done in exact arithmetic. .PP \fIxref\fR and \fIhvref\fR\ produce a cross reference list between H- and V-representations. .PP \fBxref/hvref\fR Cross reference listing between V- and H-representations In the example below we start from an H-representation of cube.ine but the same steps apply to the V-representation cube.ext. It is recommended to first remove any redundancies from the input file using redund. 1. Add \fBprintcobasis\fR and \fBincidence\fR options to cube.ine and run \fblrs\fR. % cat cube.ine cube H-representation begin 6 4 rational 0 1 0 0 0 0 1 0 0 0 0 1 1 -1 0 0 1 0 -1 0 1 0 0 -1 end printcobasis incidence % lrs cube.ine cube.ext 2. Run xref on the output file cube.ext getting cube.ext.ex % xref cube.ext % cat cube.ext.ex lg% cat cube.ext.x V-representation 1 4 5 6 # 2 1 5 6 # 3 2 4 6 # 4 1 2 6 # 5 3 4 5 # 6 1 3 5 # 7 2 3 4 # 8 1 2 3 # 3. Edit the file cube.ext.x to insert a second line that contains two integers rows maxindex where rows >= # output lines in cube.ext.x maxindex >= # input lines in cube.ine or just use 0 0 and run hvref, the output will tell you which values to use. % hvref cube.ext.x % hvref cube.ext.x V-representation 8 8 1: 4 5 6 2: 1 5 6 3: 2 4 6 4: 1 2 6 5: 3 4 5 6: 1 3 5 7: 2 3 4 8: 1 2 3 H-representation 6 8 1: 2 4 6 8 2: 3 4 7 8 3: 5 6 7 8 4: 1 3 5 7 5: 1 2 5 6 6: 1 2 3 4 input rows=8 maxindex=6 .SS "Notes" .IP " 1." 4 FAQ page .RS 4 \%https://inf.ethz.ch/personal/fukudak/polyfaq/polyfaq.html .RE .IP " 2." 4 User's guide for lrslib .RS 4 \%http://cgm.cs.mcgill.ca/~avis/C/lrslib/USERGUIDE.html .RE .SS Author David Avis .SS "See also" .BR mplrs (1), .BR lrslib (5), .BR lrsnash (1) lrslib-073/man/man2h0000777000175000017500000000047014625766600013071 0ustar avisavis#!/bin/csh # run this in man folder which contains a html folder with copy of man subfolders: man1 man5 etc # on Debian install: sudo apt-get install man2html cd man1 foreach i (*.1 ) man2html -r < $i >! ../html/man1/$i.html end cd ../man5 foreach i (*.5 ) man2html -r < $i >! ../html/man5/$i.html end cd .. lrslib-073/man/man5/0000777000175000017500000000000014625766577013012 5ustar avisavislrslib-073/man/man5/lrsarith.50000777000175000017500000001215714625766577014741 0ustar avisavis.TH "lrsarith" "5" "2022.1.19" "January 2022" "lrsarith 1.1" .\" ----------------------------------------------------------------- .\" * Define some portability stuff .\" ----------------------------------------------------------------- .\" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .\" http://bugs.debian.org/507673 .\" http://lists.gnu.org/archive/html/groff/2009-02/msg00013.html .\" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .ie \n(.g .ds Aq \(aq .el .ds Aq ' .\" ----------------------------------------------------------------- .\" * set default formatting .\" ----------------------------------------------------------------- .\" disable hyphenation .nh .\" disable justification (adjust text to left margin only) .ad l .\" ----------------------------------------------------------------- .\" * MAIN CONTENT STARTS HERE * .\" ----------------------------------------------------------------- .SS "Name" lrsarith: library routines for exact precision integer and rational arithmetic from lrslib with sample programs. 64bit integer, 128bit integer, GMP, lrslib MP, and FLINT arithmetic packages are supported. as well as hybrid arithmetic. Overflow checking is done for 64bit and 128bit arithmetic. .SS "Synopsis" .HP \w'\fBlrslong.h lrslong.c\fR\ [64bit and 128bit arithmetic with overflow handling]\ \fBlrslong.h lrslong.c\fR\ \fI[64bit and 128bit arithmetic]\fR .HP \w'\fBlrsgmp.h lrsgmp.c\fR\ [GMP and FLINT arithmetic]\ \fBlrsgmp.h lrsgmp.c\fR\ \fI[GMP and FLINT arithmetic]\fR (requires external library) .HP \w'\fBlrsmp.h lrsmp.c\fR\ [lrslib MP arithmetic]\ \fBlrsmp.h lrsmp.c\fR\ \fI[lrslib MP arithmetic]\fR .SS "Description" .PP This package was extracted from version 7.1 of lrslib which uses hybrid arithmetic with overflow checking, starting in 64bit integers, moving to 128bit (if available) and then GMP. Overflow checking is conservative to improve performance: eg. with 64 bit arithmetic, a*b triggers overflow if either a or b is at least 2^31, and a+b triggers an overflow if either a or b is at least 2^62. Typically problems that can be solved in 64bits run 3-4 times faster than with GMP and inputs solvable in 128bits run twice as fast as GMP. A rational number is represented by a pair of integers, however the user must keep track of the numerator and denominators manually. Operations for rational arithmetic are included. Various test programs are available and can be built from the makefile: .PP \fI% make fixed\fR Build the programs fixed1, fixed1n, fixed2, fixed2n, fixedmp, fixedgmp that read an integer k and repeatedly square it 6 times. .PP \fI% make hybrid\fR\ (% make mp use internal MP arithmetic instead of GMP) Build the program hybrid (and fixed1, fixed2, fixedgmp) that runs through the three arithmetic packages as needed. .PP \fI% make coll\fR\ (% make flint make FLINT arithmetic version) Reverse search code for building a Collatz tree with largest value maxn in all arithmetic versions. .PP \fI% make test\fR\ Test the arithmetic constants used in overflow checking. .SS "Initialization" lrs_mp_init(digits,fpin,fpout); digits: maximum number of decimal digits in MP arithmetic else set digits=0 fpin, fpout: input and output file pointers, eg, stdin, stdout .SS "Types" Fixed arithmetic is handled by defining a generic integer type and a set of generic operations. A generic integer a, integer vector v and integer matrix A are defined lrs_mp a; lrs_mp_vector v; lrs_mp_matrix A; allocated lrs_alloc_mp(a); v=lrs_alloc_mp_vector(n); A=lrs_alloc_mp_matrix(m,n); and freed lrs_clear_mp(a); lrs_clear_mp_vector(n); lrs_clear_mp_matrix(m,n); where m and n are the dimensions. .SS "Operations" Operations using lrs_mp integers are written generically. The most basic ones are below and a complete list is included in lrslong.h. Operations may be implemented as macros which may evaluate their arguments more than once. Arguments should not be expressions with potential side effects. Here, a,b,c,d,e are lrs_mp integers, i is a long long int and the equivalent C code is given in parenthesis. addint(a,b,c) (c=a+b) /* a and b should be different */ changesign(a) (a = -a) compare(a,b) (a ? b and returns -1,0,1 for <,=,>) copy(a,b) (a=b) decint(a,b) (a=a-b) divint(a,b,c) (c=a/b a=a%b) exactdivint(a,b,c) (c=a/b) itomp(i,a); (a=i) linint(a, ka, b, kb) (a=a*ka+b*kb for ka, kb long long integers) mp_greater(a, b) (a>b) mulint(a,b,c) (c=a*b) /* b and c may be the same */ negative(a) (a<0) one(a) (a == 1) pmp("string",a) (print "string" followed by a to lrs_ofp) positive(a) (a>0) qpiv(a,b,c,d,e) (a=(a*b-c*d)/e where the division is exact ) sign(a) (a < 0 ? NEG : POS) storesign(a, i) (a = labs(a) * i) subint(a,b,c) (c=a-b) zero(a) (a == 0) .SS "Notes" .PP User's guide for lrslib .RS 4 \%http://cgm.cs.mcgill.ca/~avis/C/lrslib/USERGUIDE.html .RE .SS Author David Avis .SS "See also" .BR lrslib (5), lrslib-073/man/man5/lrslib.50000777000175000017500000001165414625766577014401 0ustar avisavis.TH "lrslib" "5" "2024.01.31" "January 2024" "lrslib 7.3" .\" ----------------------------------------------------------------- .\" * Define some portability stuff .\" ----------------------------------------------------------------- .\" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .\" http://bugs.debian.org/507673 .\" http://lists.gnu.org/archive/html/groff/2009-02/msg00013.html .\" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .ie \n(.g .ds Aq \(aq .el .ds Aq ' .\" ----------------------------------------------------------------- .\" * set default formatting .\" ----------------------------------------------------------------- .\" disable hyphenation .nh .\" disable justification (adjust text to left margin only) .ad l .\" ----------------------------------------------------------------- .\" * MAIN CONTENT STARTS HERE * .\" ----------------------------------------------------------------- .SS "Name" lrslib: Convert between representations of convex polyhedra, remove redundant inequalities, find minimum representations, convex hull computation, solve linear programs in exact precision, compute Nash-equibria in 2-person games\&. .SS "Synopsis" .HP \w'\fBlrs\fR\ [input-file] [output-file]\ 'u \fBlrs\fR\ \fI[input-file] [output-file]\fR .HP \w'\fBredund\fR\ [input-file] [output-file]\ 'u \fBredund\fR\ \fI[input-file] [output-file]\fR .HP \w'\fBminrep\fR\ [input-file] [output-file]\ 'u \fBminrep\fR\ \fI[input-file] [output-file]\fR .HP \w'\fBfel\fR\ [input-file] [output-file]\ 'u \fBfel\fR\ \fI[input-file] [output-file]\fR .HP \w'\fBmpirun\fR -np \fInum_proc\fR \fBmplrs\fR\ \fIinput-file [output-file] [options...]\fR\ 'u \fBmpirun\fR -np \fInum-proc\fR \fBmplrs\fR\ \fIinput-file [output-file] [options]\fR .HP \w'\fBlrsnash\fR\ [input-file] \ 'u \fBlrsnash\fR\ \fI[options] [input-file] \fR .HP \w'\fBhvref/xref\fR\ [input-file] \ 'u \fBhvref/xvref\fR\ \fI[input-file]\fR .HP \w'\fBhvref/xref\fR\ [input-file] \ 'u \fBpolyv\fR\ \fI[input-file]\fR .SS "Description" .LP A polyhedron can be described by a list of inequalities (\fIH\-representation)\fR or as by a list of its vertices and extreme rays (\fIV\-representation)\fR\&. \fIlrslib\fR is a C library containing programs to manipulate these representations. All computations are done in exact arithmetic. .PP lrs(1) converts an H\-representation of a polyhedron to its V\-representation and vice versa, known respectively as the \fIvertex enumeration\fR and \fIfacet enumeration\fR problems\& (see Example (1) below). lrs can also be used to solve a linear program, remove linearities from a system, and extract a subset of columns. .PP redund(1) removes redundant inequalities in an input H-representation and outputs the remaining inequalities\&. For a V-representation input it outputs all extreme points and extreme rays. Both outputs can be piped directly into \fIlrs\fR. \fIredund\fR is a link to \fIlrs\fR which performs these functions via the \fBredund\fR and \fBredund_list\fR options. .PP minrep(1) performs the same functions as redund(1) but in addition searches for hidden linearities in the input. These are made explicit in the output which is a minimum representation of the polyhedron. .PP fel(1) projects an input H-representation onto a given set of variables using Fourier-Motzkin elimination. For a V-representation it extracts the specified columns. The output is non-redundant and can be can be piped directly into \fIlrs\fR. \fIfel\fR is a link to \fIlrs\fR which performs these functions via the \fBeliminate\fR and \fBproject\fR options. .PP mplrs(1) is Skip Jordan's parallel wrapper for \fIlrs/redund/minrep/fel\fR. .PP lrsnash(1) is Terje Lensberg's application of \fIlrs\fR for finding Nash-equilibria in 2-person games\&. .PP hvref(1) xvref(1) produce a cross reference list between H- and V-representations. .PP polyv(1) is Skip Jordan's utility to create logical formulas for checking equivalence between H- and V- representations or determining whether a given inequality is redundant after eliminating variables, without eliminating the variables. .RE .SS "Arithmetic" lrsarith(5) From version 7.1 \fIlrs/redund/mplrs\fR use hybrid arithmetic with overflow checking, starting in 64bit integers, moving to 128bit (if available) and then GMP. Overflow checking is conservative to improve performance: eg. with 64 bit arithmetic, a*b triggers overflow if either a or b is at least 2^31, and a+b triggers an overflow if either a or b is at least 2^62. Typically problems that can be solved in 64bits run 3-4 times faster than with GMP and inputs solvable in 128bits run twice as fast as GMP. .PP Various arithmetic versions are available and can be built from the makefile. .SS "Notes" .PP User's guide for lrslib .RS 4 \%http://cgm.cs.mcgill.ca/~avis/C/lrslib/USERGUIDE.html .RE .SS Author David Avis .SS "See Also" lrs (1), redund(1), minrep(1), mplrs(1), fel(1), lrsnash(1), hvref(1), xvref(1), polyv(1), lrsarith(5) lrslib-073/man/man5/lrsscripts.50000777000175000017500000001174114625766577015317 0ustar avisavis.TH "lrsscripts" "5" "2022.02.15" "February 2022" "lrslib 7.2" .\" ----------------------------------------------------------------- .\" * Define some portability stuff .\" ----------------------------------------------------------------- .\" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .\" http://bugs.debian.org/507673 .\" http://lists.gnu.org/archive/html/groff/2009-02/msg00013.html .\" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .ie \n(.g .ds Aq \(aq .el .ds Aq ' .\" ----------------------------------------------------------------- .\" * set default formatting .\" ----------------------------------------------------------------- .\" disable hyphenation .nh .\" disable justification (adjust text to left margin only) .ad l .\" ----------------------------------------------------------------- .\" * MAIN CONTENT STARTS HERE * .\" ----------------------------------------------------------------- .SS "Name" lrsscripts: some (fragile) shell functions to perform common lrslib operations. \fIcaveat emptor\fR \&! .SS "Synopsis" .HP \fBmfel\fR \fIinput-file [output-file [procs ] ]\fR .HP \fBmlrs\fR\ \fIinput-file [output-file [procs [cptime [cpindex] ] ]\fR .HP \fBtlrs\fR\ \fIinput-file [output-file [procs ]\fR .HP \fBplotV|plotR\fR \fIlrs-output-file [maxdepth [maxcobases] ]\fR .HP \fBplotL\fR [\fIhistogram-file\fR] .HP \fBprojred\fR \fI[-solver SMT-solver] ine-file [output file]\fR .SS "Description" \fBmfel\fR: multiprocessor version of \fBfel(1)\fR which performs multiple rounds of Fourier-Motzkin elimination as specified in either a project or eliminate option in the input file. \fBmplrs\fR performs only one iteration and terminates. \fIprocs\fR (if specified) is the number of processors to use (assigned according to the default-hostfile), otherwise all available processors on the current machine are used. \fBmlrs\fR: simple interface to \fBmplrs(1)\fR that is similar to \fBlrs(1)\fR and in addition does automatic checkpoint/restart for long runs. \fIprocs\fR (if specified) is the number of processors to use (assigned according to the default-hostfile), otherwise all available processors on the current machine are used. \fIcptime\fR (if specified) is the time in seconds until a checkpoint/restart is made, default 86400 secs (1 day). Checkpoint data is written into a file named input-file.cpN, where N=0,1,2,... is assigned consecutively. \fBcpindex\fR (if specified) is a valid value of N and causes a restart from checkpoint file input-file.cpN. Other \fBmplrs(1)\fR command line parameters are default values. \fBtlrs\fR: Runs naive hybrid arithmetic for multithreaded lrs using the binaries tlrs1, tlrs2, tlrsgmp. \fIprocs\fR (if specified) is the number of threads to use. If omitted or zero the default openMP maximum thread count is used. \fBplotV\fR(requires \fBgnuplot\fR be installed): produces a PDF file named V.pdf that gives a plot of each vertex or facet along with its height in the reverse search tree. \fIlrs-output-file\fR should be an \fBlrs/mplrs\fR output file produced when the \fIprintcobasis\fR is included in the input file for the run. \fBplotR\fR(requires \fBgnuplot\fR be installed): performs a similar task to \fBplotV\fR for cones producing the file H.pdf where the height of each ray is plotted. \fBplotL\fR(requires \fBgnuplot\fR be installed): \fBplotL\fR produces a realtime view of an \fBmplrs\fR run that uses the command line option "-hist ". If \fIhistogram-file\fR is not specified \fIhist\fR is the assumed file name. A PDF file named \fI.pdf\fR is produced. The first plot has 3 graphs showing the number of processors working, the size of the job queue L, and message requests pending, all versus elapsed time on the x-axis. The second histogram shows the size of the subtrees explored by producers. The root of the subtree is not counted in this size. Note that a producer stops after (possibly scaled) maxc nodes are explored, but in backtracking some additional leaves may be discovered. So the size of the largest subtree may be slightly larger than maxc. \fBprojred\fR(requires \fBinedel\fR, \fBpolyv(1)\fR and external SMT solver be installed): simple wrapper for \fBpolyv(1)\fR that tests and greedily removes inequalities that are redundant after a projection, without doing the projection. Repeatedly calls \fBpolyv(1)\fR and the specified SMT solver (\fBz3\fR by default), removing inequalities determined to be redundant for the given projection. The output is produced in \fI[output file]\fR or on standard output if no output file is specified. The output file will produce the same projection as the original input. Inequalities and projection to test are given as options in the input file, see \fBpolyv(1)\fR for details. .SS "Notes" .PP User's guide for lrslib .RS 4 \%http://cgm.cs.mcgill.ca/~avis/C/lrslib/USERGUIDE.html .RE .SS Author David Avis .SS "See Also" lrs(1), mplrs(1), fel(1), polyv(1), lrslib(5) lrslib-073/mit.ine0000777000175000017500000005041514625766576012674 0ustar avisavismit.ine begin 729 9 integer 0 2 2 -4 0 4 0 1 0 72 0 0 -4 -4 -2 0 0 0 216 -2 -2 -10 -12 -6 0 0 0 192 -4 -2 -8 -8 -8 0 0 0 288 -12 6 8 -16 -8 0 0 0 96 -4 2 0 -4 -4 0 0 0 144 -5 1 -4 -6 -6 0 0 0 288 -8 -2 -10 -12 -12 0 0 0 96 -4 2 -4 -2 -4 0 0 0 240 -7 -1 -10 -8 -10 0 0 0 288 -8 -2 -12 -8 -12 0 0 0 288 -8 -2 -8 -16 -8 0 0 0 96 -4 2 -8 0 0 0 0 0 0 0 6 -8 4 8 0 0 0 0 4 6 -8 0 8 0 0 0 24 2 2 -4 -2 2 0 0 0 864 -24 -6 -40 -16 -32 0 0 0 24 0 0 -2 -2 2 0 0 0 0 4 10 -16 0 24 0 0 0 0 1 1 -4 0 12 0 0 0 0 0 6 -16 8 40 0 0 0 96 -4 2 -16 16 32 0 0 0 288 -8 -2 -16 0 0 0 0 0 96 -4 2 8 -8 8 0 0 0 288 -8 -2 8 -24 24 0 0 0 0 0 2 -8 8 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0 2 -10 -4 0 0 -2 576 -18 0 4 -24 -16 -4 0 -8 448 -14 0 1 -19 -14 -3 0 -5 576 -18 0 -3 -23 -22 -3 0 -5 192 -6 0 5 -7 -6 -3 0 -3 192 -6 0 13 -7 -6 -5 0 -3 64 -4 4 20 -4 24 4 2 -4 2304 -56 -32 -96 -96 -96 16 10 0 768 -30 0 -32 -28 -32 8 6 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 end verbose lrslib-073/mp5.ext0000777000175000017500000000266514625766605012626 0ustar avisavismp5 V-representation begin 32 11 rational 1 1 1 1 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 1 0 1 2/3 2/3 2/3 2/3 2/3 2/3 2/3 2/3 2/3 2/3 1 1 0 1 1 1 0 0 1 1 0 1 0 1 1 1 1 1 1 0 0 0 1 2/3 2/3 1/3 1/3 2/3 1/3 1/3 1/3 1/3 2/3 1 0 1 0 1 1 0 1 1 0 1 1 1 1 0 1 0 1 0 1 0 1 1 1/3 2/3 2/3 2/3 1/3 1/3 1/3 2/3 2/3 2/3 1 0 1 1 0 1 1 0 0 1 1 1 1 1 1 0 0 0 1 0 1 1 1 1/3 1/3 2/3 2/3 2/3 1/3 1/3 1/3 1/3 2/3 1 0 0 0 1 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 2/3 1/3 2/3 2/3 1/3 2/3 2/3 1/3 1/3 2/3 1 1/3 2/3 1/3 1/3 1/3 2/3 2/3 1/3 1/3 2/3 1 2/3 1/3 1/3 1/3 1/3 1/3 1/3 2/3 2/3 2/3 1 0 0 1 0 0 1 0 1 0 1 1 2/3 2/3 2/3 1/3 2/3 2/3 1/3 2/3 1/3 1/3 1 1 0 1 0 1 0 1 1 0 1 1 2/3 1/3 1/3 2/3 1/3 1/3 2/3 2/3 1/3 1/3 1 1/3 1/3 1/3 2/3 2/3 2/3 1/3 2/3 1/3 1/3 1 1/3 1/3 1/3 1/3 2/3 2/3 2/3 2/3 2/3 2/3 1 0 1 0 0 1 0 0 1 1 0 1 2/3 1/3 2/3 1/3 1/3 2/3 1/3 1/3 2/3 1/3 1 1/3 2/3 1/3 2/3 1/3 2/3 1/3 1/3 2/3 1/3 1 1/3 1/3 2/3 1/3 2/3 1/3 2/3 1/3 2/3 1/3 1 1 1 0 0 0 1 1 1 1 0 1 1/3 2/3 2/3 1/3 1/3 1/3 2/3 2/3 1/3 1/3 1 1 0 0 0 1 1 1 0 0 0 1 2/3 2/3 1/3 2/3 2/3 1/3 2/3 1/3 2/3 1/3 1 0 0 0 0 0 0 0 0 0 0 end volume lrslib-073/mp5.ine0000777000175000017500000000210014625766517012563 0ustar avisavismp5 *metric polytope on 5 points H-representation begin 40 11 integer 2 -1 -1 0 0 -1 0 0 0 0 0 0 1 1 0 0 -1 0 0 0 0 0 0 -1 0 1 0 0 1 0 0 0 0 0 1 0 1 0 0 -1 0 0 0 0 0 -1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 -1 0 0 0 0 0 -1 1 0 0 0 0 1 0 0 0 0 1 -1 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 -1 0 0 0 0 -1 0 1 0 0 0 0 1 0 0 0 1 0 -1 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 -1 0 0 0 0 1 1 0 0 0 0 0 -1 0 0 0 1 -1 0 0 0 0 0 1 0 0 0 -1 1 0 0 0 0 0 1 2 0 0 0 0 -1 -1 0 -1 0 0 0 0 0 0 0 1 1 0 -1 0 0 0 0 0 0 0 -1 1 0 1 0 0 0 0 0 0 0 1 -1 0 1 0 0 2 0 0 0 0 -1 0 -1 0 -1 0 0 0 0 0 0 1 0 1 0 -1 0 0 0 0 0 0 -1 0 1 0 1 0 0 0 0 0 0 1 0 -1 0 1 0 2 0 0 0 0 0 -1 -1 0 0 -1 0 0 0 0 0 0 -1 1 0 0 1 0 0 0 0 0 0 1 -1 0 0 1 0 0 0 0 0 0 1 1 0 0 -1 2 0 0 0 0 0 0 0 -1 -1 -1 0 0 0 0 0 0 0 0 1 -1 1 0 0 0 0 0 0 0 0 -1 1 1 0 0 0 0 0 0 0 0 1 1 -1 0 -1 1 0 0 1 0 0 0 0 0 0 1 -1 0 0 1 0 0 0 0 0 2 -1 0 -1 0 0 -1 0 0 0 0 0 1 0 -1 0 0 1 0 0 0 0 2 -1 0 0 -1 0 0 -1 0 0 0 0 1 0 0 -1 0 0 1 0 0 0 2 0 -1 -1 0 0 0 0 -1 0 0 2 0 -1 0 -1 0 0 0 0 -1 0 2 0 0 -1 -1 0 0 0 0 0 -1 end *project 8 1 2 3 4 5 6 7 8 verbose lrslib-073/mplrs.c0000777000175000017500000033575114625766517012713 0ustar avisavis/* mplrs.c: MPI version This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. Author: Charles Jordan skip@res.otaru-uc.ac.jp Based on plrs.cpp by Gary Roumanis Initial lrs Author: David Avis avis@cs.mcgill.ca */ /* #include "lrslib.h" */ /* included in mplrs.h */ #include "mplrs.h" #include #include #include #include #include #include #include /* global variables */ mplrsv mplrs; /* state of this process */ masterv master; /* state of the master */ consumerv consumer; /* state of the consumer */ char argv0[] = "mplrs-internal"; /* warning removal for C++ */ /****************** * initialization * ******************/ int main(int argc, char **argv) { mplrs_init(argc, argv); mprintf2(("%d: initialized on %s\n",mplrs.rank,mplrs.host)); if (mplrs.size<3) return mplrs_fallback(); if (mplrs.rank == MASTER) return mplrs_master(); else if (mplrs.rank == CONSUMER) return mplrs_consumer(); else return mplrs_worker(); } void mplrs_init(int argc, char **argv) { int count; int header[9]; time_t curt = time(NULL); char *tim, *tim1; long *wred = NULL; /* redineq for redund */ /* make timestamp for filenames */ tim = ctime(&curt); tim1 = tim+4; tim1[3] = tim1[6] = '_'; tim1[15]='\0'; /* start MPI */ MPI_Init(&argc, &argv); MPI_Comm_rank(MPI_COMM_WORLD, &mplrs.rank); MPI_Comm_size(MPI_COMM_WORLD, &mplrs.size); MPI_Get_processor_name(mplrs.host, &count); /* lrs_mp_init to get correct MAXDl etc when CONS not defined */ lrs_mp_init(0, stdin, stdout); /* allocate mp for volume calculation, from plrs */ lrs_alloc_mp(mplrs.tN); lrs_alloc_mp(mplrs.tD); lrs_alloc_mp(mplrs.Vnum); lrs_alloc_mp(mplrs.Vden); lrs_alloc_mp(mplrs.Tnum); lrs_alloc_mp(mplrs.Tden); itomp(ZERO, mplrs.Vnum); itomp(ONE, mplrs.Vden); gettimeofday(&mplrs.start, NULL); mplrs_initstrucs(); /* initialize default values of globals */ /* process commandline arguments, set input and output files */ mplrs_commandline(argc, argv); if (mplrs.rank == MASTER) { /* open input file for reading on master, histogram * file for writing on master, if used. */ mplrs_initfiles(); master_sendfile(); /* may have produced warnings from stage 0 lrs, flush them. */ if (mplrs.output_list == NULL) /* need to prod consumer */ post_output("warning"," "); /* see waiting_initial */ mplrs.dummyout=0; /*avoid unitialized valgrind message*/ process_output(); /* before starting a flush */ clean_outgoing_buffers(); } else { /* open output file for writing on consumer, open histogram file * for writing on consumer, if used. */ if (mplrs.rank == CONSUMER) mplrs_initfiles(); /* receive input file from master */ MPI_Recv(header, 9, MPI_INT, 0, 20, MPI_COMM_WORLD, MPI_STATUS_IGNORE); count = header[0]; mplrs.abortinit = header[3]; mplrs.fel = header[4]; mplrs.nohiddenl = header[7]; mplrs.input = malloc(sizeof(char)*(count+1)); if (!mplrs.abortinit) /* don't need if aborting, may be big */ MPI_Recv(mplrs.input, header[0], MPI_CHAR, 0, 20, MPI_COMM_WORLD, MPI_STATUS_IGNORE); mplrs.input[count] = '\0'; mplrs.redund = mplrs.fel; /* TODO: this is a hack; do better */ mplrs.renumber = header[5]; mplrs.testlin = header[6]; if (mplrs.rank == CONSUMER) { consumer.felfallback = header[8]; if (mplrs.abortinit) consumer.final_print = 0; } /* workers don't need to look for non-existent linearities */ if (!mplrs.abortinit && mplrs.nohiddenl == 1 && mplrs.rank!=CONSUMER) remove_option(mplrs.input, count, "testlin"); mprintf2(("%d: redund,fel,testlin,renumber,nohiddenl:%d,%d,%d,%d,%d\n", mplrs.rank, mplrs.redund, mplrs.fel, mplrs.testlin, mplrs.renumber, mplrs.nohiddenl)); mplrs.m = header[2]; /* get temporary filename needed for worker files */ mplrs_init_tfn(tim1); if (mplrs.fel && mplrs.rank == CONSUMER) { consumer.m = header[2]; consumer.redineq = calloc(header[2]+1, sizeof(long)); } else if (header[1]>0 && mplrs.rank == CONSUMER) /* sigh ... */ { consumer.redineq = calloc((header[2]+1), sizeof(long)); mplrs.redund = 1; } else if (header[1]>0) mplrs.redund = 1; /* we will need a secound parallel round */ /* not used on consumer */ if (mplrs.redund && mplrs.testlin && !mplrs.nohiddenl && mplrs.rank!=CONSUMER) { mplrs.minrep_nonfinal = 1; mplrs.redineq = calloc(header[2]+1, sizeof(long)); } } /* setup signals -- * TERM checkpoint to checkpoint file, or output file if none & exit * HUP ditto */ signal(SIGTERM, mplrs_caughtsig); signal(SIGHUP, mplrs_caughtsig); free(wred); } /* if we catch a signal, set a flag to exit */ void mplrs_caughtsig(int sig) { if (mplrs.caughtsig<2) mplrs.caughtsig = 1; signal(sig, mplrs_caughtsig); return; } /* if we've caught a signal, tell the master about it */ void mplrs_handlesigs(void) { float junk = 0; /* 0: caught a signal */ if (mplrs.caughtsig != 1) return; /* we want to stop, so no need to hurry and queue the send */ MPI_Send(&junk, 1, MPI_FLOAT, MASTER, 9, MPI_COMM_WORLD); mplrs.caughtsig = 2; /* handled */ return; } /* signal the master that we want to stop, * can try to checkpoint. Use mplrs to give * output if desired. * Does not return to caller ... ugly */ /* not used and untested as of 3/16/2023 */ void mplrs_cleanstop(int checkpoint) { MPI_Request req = MPI_REQUEST_NULL; char *cobasis = NULL; float junk; int header[8]={0}; int flag = 0, len; unsigned long ncob = 0; mprintf(("%d: in cleanstop\n", mplrs.rank)); if (checkpoint) junk = 1; else junk = -1; /* inform master, wait for reply */ MPI_Send(&junk, 1, MPI_FLOAT, MASTER, 9, MPI_COMM_WORLD); MPI_Recv(&junk, 1, MPI_FLOAT,MASTER,9,MPI_COMM_WORLD,MPI_STATUS_IGNORE); /* needs to do usual cleanup / exit of a worker. callstack is * unpredictable though, so exit() and don't return. */ /* leaks: starting_cobasis (mplrs_worker) */ /* do_work cleanup*/ remove(mplrs.tfn); /* delete temporary file */ /* mplrs_worker cleanup */ mplrs.outputblock = 0; process_output(); process_curwarn(); return_unfinished_cobases(); clean_outgoing_buffers(); /* mplrs_worker start of loop ... */ MPI_Isend(&ncob, 1, MPI_UNSIGNED, MASTER, 6, MPI_COMM_WORLD, &req); while (1) { MPI_Test(&req, &flag, MPI_STATUS_IGNORE); if (flag) { mprintf3(("%d: clean_stop incoming message from 0\n", mplrs.rank)); MPI_Recv(header, 8, MPI_INT, MASTER, MPI_ANY_TAG, MPI_COMM_WORLD, MPI_STATUS_IGNORE); if (header[0] == -1) /* no more work to do */ { mplrs_worker_finished(); exit(0); } else /* forget this cobasis */ { len = header[0]; cobasis = malloc(sizeof(char)*(len+1)); MPI_Recv(cobasis, len, MPI_CHAR, MASTER, MPI_ANY_TAG, MPI_COMM_WORLD, MPI_STATUS_IGNORE); cobasis[len] = '\0'; mprintf3(("%d: got %s, throwing away\n", mplrs.rank, cobasis)); free(cobasis); return_unfinished_cobases(); clean_outgoing_buffers(); MPI_Isend(&ncob, 1, MPI_UNSIGNED, MASTER, 6, MPI_COMM_WORLD, &req); } } clean_outgoing_buffers(); } /* mplrs_worker */ } /* terminate immediately and ungracefully after printing the string */ void mplrs_emergencystop(const char *msg) { int ret; fprintf(stderr, "%s",msg); ret = MPI_Abort(MPI_COMM_WORLD, 1); exit(ret); } /* we're in a redund run, make blocks of <= master.rows * from redineq and add to L * if master.rows = 0, split evenly for testing */ void add_redund_jobs(long rcount, long m) { long *nums; long nlinearities = mplrs.R->count[6]; /* secret hidden bit */ int i=1,j,k,h; long c = 0; unsigned long extra = 0; unsigned int njobs; unsigned int cutoff = 0; /* number of jobs before lastp, lastrows */ int ex = 0; if (rcount == 0) { /* can happen in round 2 in minrep mode - we may find hidden * linearities but no weakly redundant lines. * could happen with redund 0 0 on empty H-reps, but lrs rejects * them in stage 0 */ mprintf(("M: in add_redund_jobs but rcount==0, no jobs to make\n")); return; } /* option -j overrides -rows -lastrows -lastp */ if (master.j > 0) { master.rows = master.lastrows = rcount / (master.j * (mplrs.size - 2)); extra = rcount % (master.j * (mplrs.size - 2)); mprintf(("M: -j option, setting rows to %u, splitting %lu extra rows evenly to get %u jobs per worker\n", master.rows, extra, master.j)); } if (master.rows > rcount/(mplrs.size-2)) master.rows = 0; if (master.rows==0) { if (m>mplrs.size-2) { master.rows = rcount / (mplrs.size-2); extra = rcount%(mplrs.size-2); if (master.rows == 0) /* prevent divide by 0 below, * min job size is 1 row */ master.rows = 1; /* note rcount is not 0 */ } else master.rows = 1; } if (master.lastrows == 0 || master.lastrows > master.rows || master.lastp<=0 || master.lastp>100) /* disable bad values */ master.lastrows = master.rows; njobs = (rcount / master.rows) + (rcount%master.rows>0 ? 1 : 0); if (extra>0) /* if we're splitting evenly and doesn't divide evenly,*/ { /* put ex (1) many extra rows in the first extra rows */ ex = 1; njobs--; } cutoff = (float)(100-master.lastp)/100.0 * njobs; while (ccutoff) { mprintf3(("M: after %lu jobs switching to lastrows (%u %u %u)\n", master.size_L, njobs, master.lastp, master.lastrows)); master.rows = master.lastrows; } nums = malloc(sizeof(long)*(master.rows+ex+nlinearities)); for (j=0; j<(master.rows+ex) && credineq[i++]==1) { nums[j++] = i-1; c++; break; } } } for (k=0; kredineq[h] == 2) nums[j + (k++)] = -1 * h; if (extra>0) extra--; if (extra==0) ex=0; mprintf3(("M: adding redund job (%u rows) to L:", j)); for (k=0; k