pax_global_header00006660000000000000000000000064122661426260014521gustar00rootroot0000000000000052 comment=77a80d83e99bbfa93c0b5e973f7931cd959dcba6 libmath-numeric-tower-clojure-0.0.4/000075500000000000000000000000001226614262600173775ustar00rootroot00000000000000libmath-numeric-tower-clojure-0.0.4/.gitignore000064400000000000000000000001771226614262600213740ustar00rootroot00000000000000*.jar .classpath .project .settings bin classes clojure-src.jar clojure-contrib.jar clojure.jar clojure-contrib-src.jar target libmath-numeric-tower-clojure-0.0.4/README.md000064400000000000000000000060641226614262600206640ustar00rootroot00000000000000clojure.math.numeric-tower ======================================== Formerly clojure.contrib.math Math functions that deal intelligently with the various types in Clojure's numeric tower, as well as math functions commonly found in Scheme implementations. Functions included: * (expt x y) - x to the yth power * (abs n) - absolute value of n * (gcd m n) - greatest common divisor of m and n * (lcm m n) - least common multiple of m and n * (floor x) - round down * (ceil x) - round up * (round x) - round to nearest * (sqrt x) - square root, exact if possible * (exact-integer-sqrt k) returns floor of square root and the "remainder" More documentation in docstrings. Releases and Dependency Information ======================================== Latest stable release: 0.0.4 * [All Released Versions](http://search.maven.org/#search%7Cgav%7C1%7Cg%3A%22org.clojure%22%20AND%20a%3A%22math.numeric-tower%22) * [Development Snapshot Versions](https://oss.sonatype.org/index.html#nexus-search;gav~org.clojure~math.numeric-tower~~~) [Leiningen](https://github.com/technomancy/leiningen) dependency information: ```clojure [org.clojure/math.numeric-tower "0.0.4"] ``` [Maven](http://maven.apache.org/) dependency information: ```xml org.clojure math.numeric-tower 0.0.4 ``` Example Usage ======================================== ```clojure (ns example.core (:require [clojure.math.numeric-tower :as math])) (defn- sqr "Uses the numeric tower expt to square a number" [x] (math/expt x 2)) (defn euclidean-squared-distance "Computes the Euclidean squared distance between two sequences" [a b] (reduce + (map (comp sqr -) a b))) (defn euclidean-distance "Computes the Euclidean distance between two sequences" [a b] (math/sqrt (euclidean-squared-distance a b))) (let [a [1 2 3 5 8 13 21] b [0 2 4 6 8 10 12]] (euclidean-distance a b)) ;;=> 9.643650760992955 ``` Refer to docstrings in the `clojure.math.numeric-tower` namespace for additional documentation. [API Documentation](http://clojure.github.com/math.numeric-tower/) Developer Information ======================================== * [GitHub project](https://github.com/clojure/math.numeric-tower) * [Bug Tracker](http://dev.clojure.org/jira/browse/MTOWER) * [Continuous Integration](http://build.clojure.org/job/math.numeric-tower/) * [Compatibility Test Matrix](http://build.clojure.org/job/math.numeric-tower-test-matrix/) Changelog ======================================== * Release 0.0.4 on 2014-01-16 * Adjust return type of expt to match base when power is 0. * (expt 3M 0) -> 1M * (expt 3N 0) -> 1N * Release 0.0.3 on 2013-12-29 * Minor improvement to sqrt of ratio. * Release 0.0.2 on 2012-11-23 * Added type hints to remove some reflective calls. * Release 0.0.1 on 2011-10-15 * Initial release. * Source-compatible with clojure.contrib.math, except for the name change. License ======================================== Distributed under the Eclipse Public License, the same as Clojure. libmath-numeric-tower-clojure-0.0.4/epl.html000064400000000000000000000305361226614262600210540ustar00rootroot00000000000000 Eclipse Public License - Version 1.0

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libmath-numeric-tower-clojure-0.0.4/pom.xml000064400000000000000000000015761226614262600207250ustar00rootroot00000000000000 4.0.0 math.numeric-tower 0.0.4 ${project.artifactId} org.clojure pom.contrib 0.1.2 Mark Engelberg scm:git:git@github.com:clojure/math.numeric-tower.git scm:git:git@github.com:clojure/math.numeric-tower.git git@github.com:clojure/math.numeric-tower.git math.numeric-tower-0.0.4 libmath-numeric-tower-clojure-0.0.4/src/000075500000000000000000000000001226614262600201665ustar00rootroot00000000000000libmath-numeric-tower-clojure-0.0.4/src/main/000075500000000000000000000000001226614262600211125ustar00rootroot00000000000000libmath-numeric-tower-clojure-0.0.4/src/main/clojure/000075500000000000000000000000001226614262600225555ustar00rootroot00000000000000libmath-numeric-tower-clojure-0.0.4/src/main/clojure/clojure/000075500000000000000000000000001226614262600242205ustar00rootroot00000000000000libmath-numeric-tower-clojure-0.0.4/src/main/clojure/clojure/math/000075500000000000000000000000001226614262600251515ustar00rootroot00000000000000libmath-numeric-tower-clojure-0.0.4/src/main/clojure/clojure/math/numeric_tower.clj000064400000000000000000000216441226614262600305340ustar00rootroot00000000000000;;; math.clj: math functions that deal intelligently with the various ;;; types in Clojure's numeric tower, as well as math functions ;;; commonly found in Scheme implementations. ;; by Mark Engelberg (mark.engelberg@gmail.com) ;; May 21, 2011 (ns ^{:author "Mark Engelberg", :doc "Math functions that deal intelligently with the various types in Clojure's numeric tower, as well as math functions commonly found in Scheme implementations. expt - (expt x y) is x to the yth power, returns an exact number if the base is an exact number, and the power is an integer, otherwise returns a double. abs - (abs n) is the absolute value of n gcd - (gcd m n) returns the greatest common divisor of m and n lcm - (lcm m n) returns the least common multiple of m and n When floor, ceil, and round are passed doubles, we just defer to the corresponding functions in Java's Math library. Java's behavior is somewhat strange (floor and ceil return doubles rather than integers, and round on large doubles yields spurious results) but it seems best to match Java's semantics. On exact numbers (ratios and decimals), we can have cleaner semantics. floor - (floor n) returns the greatest integer less than or equal to n. If n is an exact number, floor returns an integer, otherwise a double. ceil - (ceil n) returns the least integer greater than or equal to n. If n is an exact number, ceil returns an integer, otherwise a double. round - (round n) rounds to the nearest integer. round always returns an integer. round rounds up for values exactly in between two integers. sqrt - Implements the sqrt behavior I'm accustomed to from PLT Scheme, specifically, if the input is an exact number, and is a square of an exact number, the output will be exact. The downside is that for the common case (inexact square root), some extra computation is done to look for an exact square root first. So if you need blazingly fast square root performance, and you know you're just going to need a double result, you're better off calling java's Math/sqrt, or alternatively, you could just convert your input to a double before calling this sqrt function. If Clojure ever gets complex numbers, then this function will need to be updated (so negative inputs yield complex outputs). exact-integer-sqrt - Implements a math function from the R6RS Scheme standard. (exact-integer-sqrt k) where k is a non-negative integer, returns [s r] where k = s^2+r and k < (s+1)^2. In other words, it returns the floor of the square root and the \"remainder\". "} clojure.math.numeric-tower) ;; so this code works with both 1.2.x and 1.3.0: (def ^{:private true} minus (first [-' -])) (def ^{:private true} mult (first [*' *])) (def ^{:private true} plus (first [+' +])) (def ^{:private true} dec* (first [dec' dec])) (def ^{:private true} inc* (first [inc' inc])) ;; feature testing macro, based on suggestion from Chas Emerick: (defmacro when-available [sym & body] (try (when (resolve sym) (list* 'do body)) (catch ClassNotFoundException _#))) (defn- expt-int [base pow] (loop [n pow, y (num 1), z base] (let [t (even? n), n (quot n 2)] (cond t (recur n y (mult z z)) (zero? n) (mult z y) :else (recur n (mult z y) (mult z z)))))) (defn expt "(expt base pow) is base to the pow power. Returns an exact number if the base is an exact number and the power is an integer, otherwise returns a double." [base pow] (if (and (not (float? base)) (integer? pow)) (cond (pos? pow) (expt-int base pow) (zero? pow) (cond (= (type base) BigDecimal) 1M (= (type base) java.math.BigInteger) (java.math.BigInteger. "1") (when-available clojure.lang.BigInt (= (type base) clojure.lang.BigInt)) (when-available clojure.lang.BigInt (bigint 1)) :else 1) :else (/ 1 (expt-int base (minus pow)))) (Math/pow base pow))) (defn abs "(abs n) is the absolute value of n" [n] (cond (not (number? n)) (throw (IllegalArgumentException. "abs requires a number")) (neg? n) (minus n) :else n)) (defprotocol MathFunctions (floor [n] "(floor n) returns the greatest integer less than or equal to n. If n is an exact number, floor returns an integer, otherwise a double.") (ceil [n] "(ceil n) returns the least integer greater than or equal to n. If n is an exact number, ceil returns an integer, otherwise a double.") (round [n] "(round n) rounds to the nearest integer. round always returns an integer. Rounds up for values exactly in between two integers.") (integer-length [n] "Length of integer in binary") (sqrt [n] "Square root, but returns exact number if possible.")) (declare sqrt-integer) (declare sqrt-ratio) (declare sqrt-decimal) (extend-type Integer MathFunctions (floor [n] n) (ceil [n] n) (round [n] n) (integer-length [n] (- 32 (Integer/numberOfLeadingZeros n))) (sqrt [n] (sqrt-integer n))) (extend-type Long MathFunctions (floor [n] n) (ceil [n] n) (round [n] n) (integer-length [n] (- 64 (Long/numberOfLeadingZeros n))) (sqrt [n] (sqrt-integer n))) (extend-type java.math.BigInteger MathFunctions (floor [n] n) (ceil [n] n) (round [n] n) (integer-length [n] (.bitLength n)) (sqrt [n] (sqrt-integer n))) (when-available clojure.lang.BigInt (extend-type clojure.lang.BigInt MathFunctions (floor [n] n) (ceil [n] n) (round [n] n) (integer-length [n] (.bitLength n)) (sqrt [n] (sqrt-integer n)))) (extend-type java.math.BigDecimal MathFunctions (floor [n] (bigint (.setScale n 0 BigDecimal/ROUND_FLOOR))) (ceil [n] (bigint (.setScale n 0 BigDecimal/ROUND_CEILING))) (round [n] (floor (+ n 0.5M))) (sqrt [n] (sqrt-decimal n))) (extend-type clojure.lang.Ratio MathFunctions (floor [n] (if (pos? n) (quot (. n numerator) (. n denominator)) (dec* (quot (. n numerator) (. n denominator))))) (ceil [n] (if (pos? n) (inc* (quot (. n numerator) (. n denominator))) (quot (. n numerator) (. n denominator)))) (round [n] (floor (+ n 1/2))) (sqrt [n] (sqrt-ratio n))) (extend-type Double MathFunctions (floor [n] (Math/floor n)) (ceil [n] (Math/ceil n)) (round [n] (Math/round n)) ;(round (bigdec n))) (sqrt [n] (Math/sqrt n))) (extend-type Float MathFunctions (floor [n] (Math/floor n)) (ceil [n] (Math/ceil n)) (round [n] (Math/round n)) ;(round (bigdec n))) (sqrt [n] (Math/sqrt n))) (defn gcd "(gcd a b) returns the greatest common divisor of a and b" [a b] (if (or (not (integer? a)) (not (integer? b))) (throw (IllegalArgumentException. "gcd requires two integers")) (loop [a (abs a) b (abs b)] (if (zero? b) a, (recur b (mod a b)))))) (defn lcm "(lcm a b) returns the least common multiple of a and b" [a b] (when (or (not (integer? a)) (not (integer? b))) (throw (IllegalArgumentException. "lcm requires two integers"))) (cond (zero? a) 0 (zero? b) 0 :else (abs (mult b (quot a (gcd a b)))))) ;; Produces the largest integer less than or equal to the square root of n ;; Input n must be a non-negative integer (defn- integer-sqrt [n] (cond (> n 24) (let [n-len (integer-length n)] (loop [init-value (if (even? n-len) (expt 2 (quot n-len 2)) (expt 2 (inc* (quot n-len 2))))] (let [iterated-value (quot (plus init-value (quot n init-value)) 2)] (if (>= iterated-value init-value) init-value (recur iterated-value))))) (> n 15) 4 (> n 8) 3 (> n 3) 2 (> n 0) 1 (> n -1) 0)) (defn exact-integer-sqrt "(exact-integer-sqrt n) expects a non-negative integer n, and returns [s r] where n = s^2+r and n < (s+1)^2. In other words, it returns the floor of the square root and the 'remainder'. For example, (exact-integer-sqrt 15) is [3 6] because 15 = 3^2+6." [n] (if (or (not (integer? n)) (neg? n)) (throw (IllegalArgumentException. "exact-integer-sqrt requires a non-negative integer")) (let [isqrt (integer-sqrt n), error (minus n (mult isqrt isqrt))] [isqrt error]))) (defn- sqrt-integer [n] (if (neg? n) Double/NaN (let [isqrt (integer-sqrt n), error (minus n (mult isqrt isqrt))] (if (zero? error) isqrt (Math/sqrt n))))) (defn- sqrt-ratio [^clojure.lang.Ratio n] (if (neg? n) Double/NaN (let [numerator (.numerator n), denominator (.denominator n), sqrtnum (sqrt numerator)] (if (float? sqrtnum) (Math/sqrt n) (let [sqrtden (sqrt denominator)] (if (float? sqrtden) (Math/sqrt n) (/ sqrtnum sqrtden))))))) (defn- sqrt-decimal [n] (if (neg? n) Double/NaN (let [frac (rationalize n), sqrtfrac (sqrt frac)] (if (ratio? sqrtfrac) (/ (BigDecimal. (.numerator ^clojure.lang.Ratio sqrtfrac)) (BigDecimal. (.denominator ^clojure.lang.Ratio sqrtfrac))) sqrtfrac)))) libmath-numeric-tower-clojure-0.0.4/src/test/000075500000000000000000000000001226614262600211455ustar00rootroot00000000000000libmath-numeric-tower-clojure-0.0.4/src/test/clojure/000075500000000000000000000000001226614262600226105ustar00rootroot00000000000000libmath-numeric-tower-clojure-0.0.4/src/test/clojure/clojure/000075500000000000000000000000001226614262600242535ustar00rootroot00000000000000libmath-numeric-tower-clojure-0.0.4/src/test/clojure/clojure/math/000075500000000000000000000000001226614262600252045ustar00rootroot00000000000000libmath-numeric-tower-clojure-0.0.4/src/test/clojure/clojure/math/test_numeric_tower.clj000064400000000000000000000064141226614262600316240ustar00rootroot00000000000000(ns clojure.math.test-numeric-tower (:use clojure.test clojure.math.numeric-tower)) (deftest test-expt (are [x y] (= x y) (expt 2 3) 8 (expt (expt 2 16) 2) (expt 2 32) (expt 4/3 2) 16/9 (expt 2 -10) 1/1024 (expt 0.5M 2) 0.25M (expt 5 4.2) (Math/pow 5 4.2) (expt 5.3 4) (Math/pow 5.3 4) (expt 5.3 4) (Math/pow 5.3 4) (expt 2 0) 1 (expt (java.math.BigInteger. "4") 0) (java.math.BigInteger. "1") (expt 4M 0) 1M (expt 8M 1) 8M (expt 16M 16) 18446744073709551616M)) (when-available clojure.lang.BigInt (deftest test-expt-bigint (are [x y] (= x y) (expt (bigint 4) 0) (bigint 1)))) (deftest test-abs (are [x y] (= x y) (abs -2) 2 (abs 0) 0 (abs 5) 5 (abs 123456789123456789) 123456789123456789 (abs -123456789123456789) 123456789123456789 (abs 5/3) 5/3 (abs -4/3) 4/3 (abs 4.3M) 4.3M (abs -4.3M) 4.3M (abs 2.8) 2.8 (abs -2.8) 2.8)) (deftest test-gcd (are [x y] (= x y) (gcd 4 3) 1 (gcd 24 12) 12 (gcd 24 27) 3 (gcd 1 0) 1 (gcd 0 1) 1 (gcd 0 0) 0) (is (thrown? IllegalArgumentException (gcd nil 0))) (is (thrown? IllegalArgumentException (gcd 0 nil))) (is (thrown? IllegalArgumentException (gcd 7.0 0)))) (deftest test-lcm (are [x y] (= x y) (lcm 2 3) 6 (lcm 3 2) 6 (lcm -2 3) 6 (lcm 2 -3) 6 (lcm -2 -3) 6 (lcm 4 10) 20 (lcm 1 0) 0 (lcm 0 1) 0 (lcm 0 0) 0) (is (thrown? IllegalArgumentException (lcm nil 0))) (is (thrown? IllegalArgumentException (lcm 0 nil))) (is (thrown? IllegalArgumentException (lcm 7.0 0)))) (deftest test-floor (are [x y] (== x y) (floor 6) 6 (floor -6) -6 (floor 123456789123456789) 123456789123456789 (floor -123456789123456789) -123456789123456789 (floor 4/3) 1 (floor -4/3) -2 (floor 4.3M) 4 (floor -4.3M) -5 (floor 4.3) 4.0 (floor -4.3) -5.0)) (deftest test-ceil (are [x y] (== x y) (ceil 6) 6 (ceil -6) -6 (ceil 123456789123456789) 123456789123456789 (ceil -123456789123456789) -123456789123456789 (ceil 4/3) 2 (ceil -4/3) -1 (ceil 4.3M) 5 (ceil -4.3M) -4 (ceil 4.3) 5.0 (ceil -4.3) -4.0)) (deftest test-round (are [x y] (== x y) (round 6) 6 (round -6) -6 (round 123456789123456789) 123456789123456789 (round -123456789123456789) -123456789123456789 (round 4/3) 1 (round 5/3) 2 (round 5/2) 3 (round -4/3) -1 (round -5/3) -2 (round -5/2) -2 (round 4.3M) 4 (round 4.7M) 5 (round -4.3M) -4 (round -4.7M) -5 (round 4.5M) 5 (round -4.5M) -4 (round 4.3) 4 (round 4.7) 5 (round -4.3) -4 (round -4.7) -5 (round 4.5) 5 (round -4.5) -4)) (deftest test-sqrt (are [x y] (= x y) (sqrt 9) 3 (sqrt 16/9) 4/3 (sqrt 0.25M) 0.5M (sqrt 2) (Math/sqrt 2))) (deftest test-exact-integer-sqrt (are [x y] (= x y) (exact-integer-sqrt 15) [3 6] (exact-integer-sqrt (inc (expt 2 32))) [(expt 2 16) 1] (exact-integer-sqrt 1000000000000) [1000000 0]))