Author: luc
Date: Sun Mar 10 21:05:20 2013
New Revision: 1454920
URL: http://svn.apache.org/r1454920
Log:
Added utilities for prime numbers.
Thanks to Sébastien Riou.
JIRA: MATH-845
Added:
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/primes/
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/primes/PollardRho.java
(with props)
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/primes/Primes.java
(with props)
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/primes/SmallPrimes.java
(with props)
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/primes/package-info.java
(with props)
commons/proper/math/trunk/src/test/java/org/apache/commons/math3/primes/
commons/proper/math/trunk/src/test/java/org/apache/commons/math3/primes/PrimesTest.java
(with props)
Modified:
commons/proper/math/trunk/pom.xml
commons/proper/math/trunk/src/changes/changes.xml
Modified: commons/proper/math/trunk/pom.xml
URL:
http://svn.apache.org/viewvc/commons/proper/math/trunk/pom.xml?rev=1454920&r1=1454919&r2=1454920&view=diff
==============================================================================
--- commons/proper/math/trunk/pom.xml (original)
+++ commons/proper/math/trunk/pom.xml Sun Mar 10 21:05:20 2013
@@ -241,6 +241,9 @@
<name>Andreas Rieger</name>
</contributor>
<contributor>
+ <name>Sébastien Riou</name>
+ </contributor>
+ <contributor>
<name>Bill Rossi</name>
</contributor>
<contributor>
Modified: commons/proper/math/trunk/src/changes/changes.xml
URL:
http://svn.apache.org/viewvc/commons/proper/math/trunk/src/changes/changes.xml?rev=1454920&r1=1454919&r2=1454920&view=diff
==============================================================================
--- commons/proper/math/trunk/src/changes/changes.xml (original)
+++ commons/proper/math/trunk/src/changes/changes.xml Sun Mar 10 21:05:20 2013
@@ -55,6 +55,9 @@ This is a minor release: It combines bug
Changes to existing features were made in a backwards-compatible
way such as to allow drop-in replacement of the v3.1[.1] JAR file.
">
+ <action dev="luc" type="add" issue="MATH-845" due-to="Sébastien Riou" >
+ Added utilities for prime numbers.
+ </action>
<action dev="luc" type="fix" issue="MATH-936" >
Fixed generation of long random numbers between two bounds.
</action>
Added:
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/primes/PollardRho.java
URL:
http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math3/primes/PollardRho.java?rev=1454920&view=auto
==============================================================================
---
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/primes/PollardRho.java
(added)
+++
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/primes/PollardRho.java
Sun Mar 10 21:05:20 2013
@@ -0,0 +1,163 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math3.primes;
+
+import java.util.ArrayList;
+import java.util.List;
+
+import org.apache.commons.math3.util.FastMath;
+
+/**
+ * Implementation of the Pollard's rho factorization algorithm.
+ * @version $Id$
+ * @since 3.2
+ */
+class PollardRho {
+
+ /**
+ * Only static methods in this class
+ */
+ private PollardRho() {
+ }
+
+ /**
+ * Factorization using Pollard's rho algorithm.
+ * @param n number to factors, must be >0
+ * @return the list of prime factors of n.
+ */
+ public static List<Integer> primeFactors(int n) {
+ final List<Integer> factors = new ArrayList<Integer>();
+
+ n = SmallPrimes.smallTrialDivision(n, factors);
+ if (1 == n) {
+ return factors;
+ }
+
+ if (SmallPrimes.millerRabinPrimeTest(n)) {
+ factors.add(n);
+ return factors;
+ }
+
+ int divisor = rhoBrent(n);
+ factors.add(divisor);
+ factors.add(n / divisor);
+ return factors;
+ }
+
+ /**
+ * Implementation of the Pollard's rho factorization algorithm.
+ * This implementation follows the paper "An improved Monte Carlo
factorization algorithm" by Richard P. Brent.
+ * This avoid the triple computation of f(x) typically found in Pollard's
rho implementations. It also batch several gcd computation into 1.
+ * The backtracking is not implemented as we deal only with semi-prime.
+ * @param n number to factor, must be semi-prime.
+ * @return a prime factor of n.
+ */
+ static int rhoBrent(final int n){
+ final int x0 = 2;
+ final int m = 25;
+ int cst = SmallPrimes.PRIMES_LAST;
+ int y = x0;
+ int r = 1;
+ do {
+ int x = y;
+ for (int i = 0; i < r; i++) {
+ final long y2 = ((long) y) * y;
+ y = (int) ((y2 + cst) % n);
+ }
+ int k = 0;
+ do {
+ final int bound = FastMath.min(m, r - k);
+ int q = 1;
+ for (int i = -3; i < bound; i++) { //start at -3 to ensure we
enter this loop at least 3 times
+ final long y2 = ((long) y) * y;
+ y = (int) ((y2 + cst) % n);
+ final long divisor = FastMath.abs(x - y);
+ if (0 == divisor) {
+ cst += SmallPrimes.PRIMES_LAST;
+ k = -m;
+ y = x0;
+ r = 1;
+ break;
+ }
+ final long prod = divisor * q;
+ q = (int) (prod % n);
+ if (0 == q) {
+ return gcdPositive(FastMath.abs((int) divisor), n);
+ }
+ }
+ final int out = gcdPositive(FastMath.abs(q), n);
+ if (1 != out) {
+ return out;
+ }
+ k = k + m;
+ } while (k < r);
+ r = 2 * r;
+ } while (true);
+ }
+
+ /**
+ * Gcd between two positive numbers
+ * <p>
+ * Gets the greatest common divisor of two numbers,
+ * using the "binary gcd" method which avoids division and modulo
+ * operations. See Knuth 4.5.2 algorithm B. This algorithm is due to Josef
+ * Stein (1961).
+ * </p>
+ * Special cases:
+ * <ul>
+ * <li>The result of {@code gcd(x, x)}, {@code gcd(0, x)} and
+ * {@code gcd(x, 0)} is the value of {@code x}.
+ * <li>The invocation {@code gcd(0, 0)} is the only one which returns
+ * {@code 0}.</li>
+ * </ul>
+ * @param a first number, must be >=0
+ * @param b second number, must be >=0
+ * @return gcd(a,b)
+ */
+ static int gcdPositive(int a, int b){
+ // both a and b must be positive, it is not checked here
+ //gdc(a,0) = a
+ if (a == 0) {
+ return b;
+ } else if (b == 0) {
+ return a;
+ }
+
+ //make a and b odd, keep in mind the common power of twos
+ final int aTwos = Integer.numberOfTrailingZeros(a);
+ a >>= aTwos;
+ final int bTwos = Integer.numberOfTrailingZeros(b);
+ b >>= bTwos;
+ final int shift = FastMath.min(aTwos, bTwos);
+
+ //a and b >0
+ //if a > b then gdc(a,b) = gcd(a-b,b)
+ //if a < b then gcd(a,b) = gcd(b-a,a)
+ //so next a is the absolute difference and next b is the minimum of
current values
+ while (a != b) {
+ final int delta = a - b;
+ b = FastMath.min(a, b);
+ a = FastMath.abs(delta);
+ //for speed optimization:
+ //remove any power of two in a as b is guaranteed to be odd
throughout all iterations
+ a >>= Integer.numberOfTrailingZeros(a);
+ }
+
+ //gcd(a,a) = a, just "add" the common power of twos
+ return a << shift;
+ }
+}
Propchange:
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/primes/PollardRho.java
------------------------------------------------------------------------------
svn:eol-style = native
Propchange:
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/primes/PollardRho.java
------------------------------------------------------------------------------
svn:keywords = "Author Date Id Revision"
Added:
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/primes/Primes.java
URL:
http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math3/primes/Primes.java?rev=1454920&view=auto
==============================================================================
---
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/primes/Primes.java
(added)
+++
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/primes/Primes.java
Sun Mar 10 21:05:20 2013
@@ -0,0 +1,127 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math3.primes;
+
+import org.apache.commons.math3.exception.MathIllegalArgumentException;
+import org.apache.commons.math3.exception.util.LocalizedFormats;
+
+import java.util.List;
+
+
+/**
+ * Methods related to prime numbers in the range of <code>int</code>:
+ * <ul>
+ * <li>primality test</li>
+ * <li>prime number generation</li>
+ * <li>factorization</li>
+ * </ul>
+ * {@link Math}.
+ *
+ * @version $Id$
+ * @since 3.2
+ */
+public class Primes {
+ /**
+ * Only static methods in this class
+ */
+ private Primes() {
+ }
+
+ /**
+ * Primality test: tells if the argument is a (provable) prime or not.</p>
+ * It uses the Miller-Rabin probabilistic test in such a way that result
is always guaranteed: it uses the firsts prime numbers as successive base
+ * (see Handbook of applied cryptography by Menezes, table 4.1)
+ *
+ * @param n number to test.
+ * @return true if n is prime. (All numbers <2 return false).
+ */
+ public static boolean isPrime(int n) {
+ if (n < 2) {
+ return false;
+ }
+
+ for (int p : SmallPrimes.PRIMES) {
+ if (0 == (n % p)) {
+ return n == p;
+ }
+ }
+ return SmallPrimes.millerRabinPrimeTest(n);
+ }
+
+ /**
+ * Return the smallest prime superior or equal to n.
+ *
+ * @param n a positive number.
+ * @return the smallest prime superior or equal to n.
+ * @throws MathIllegalArgumentException if n <0.
+ */
+ public static int nextPrime(int n) {
+ if (n < 0) {
+ throw new
MathIllegalArgumentException(LocalizedFormats.NUMBER_TOO_SMALL, n, 0);
+ }
+ if (n == 2) {
+ return 2;
+ }
+ n = n | 1;//make sur n is odd
+ if (n == 1) {
+ return 2;
+ }
+
+ if (isPrime(n)) {
+ return n;
+ }
+
+ //prepare entry in the +2, +4 loop:
+ //n should not be a multiple of 3
+ final int rem = n % 3;
+ if (0 == rem) {// if n%3==0
+ n += 2;//n%3==2
+ } else if (1 == rem) {//if n%3==1
+ //if (isPrime(n)) return n;
+ n += 4;//n%3==2
+ }
+ while (true) { //this loop skips all multiple of 3
+ if (isPrime(n)) {
+ return n;
+ }
+ n += 2;//n%3==1
+ if (isPrime(n)) {
+ return n;
+ }
+ n += 4;//n%3==2
+ }
+ }
+
+ /**
+ * Prime factors decomposition
+ *
+ * @param n number to factorize: must be >=2
+ * @return list of prime factors of n
+ * @throws MathIllegalArgumentException if n <2.
+ */
+ public static List<Integer> primeFactors(int n) {
+
+ if (n < 2) {
+ throw new
MathIllegalArgumentException(LocalizedFormats.NUMBER_TOO_SMALL, n, 2);
+ }
+ //slower than trial div unless we do an awful lot of computation (then
it finally gets JIT-compiled efficiently
+ //List<Integer> out = PollardRho.primeFactors(n);
+ return SmallPrimes.trialDivision(n);
+
+ }
+
+}
Propchange:
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/primes/Primes.java
------------------------------------------------------------------------------
svn:eol-style = native
Propchange:
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/primes/Primes.java
------------------------------------------------------------------------------
svn:keywords = "Author Date Id Revision"
Added:
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/primes/SmallPrimes.java
URL:
http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math3/primes/SmallPrimes.java?rev=1454920&view=auto
==============================================================================
---
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/primes/SmallPrimes.java
(added)
+++
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/primes/SmallPrimes.java
Sun Mar 10 21:05:20 2013
@@ -0,0 +1,186 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math3.primes;
+
+
+import java.math.BigInteger;
+import java.util.ArrayList;
+import java.util.List;
+
+import org.apache.commons.math3.util.FastMath;
+
+/**
+ * Utility methods to work on primes within the <code>int</code> range.
+ * @version $Id$
+ * @since 3.2
+ */
+class SmallPrimes {
+
+ /**
+ * The 512 firsts prime numbers
+ * It contains all primes smaller or equal to the cubic square of
Integer.MAX_VALUE.
+ * As a result, <code>int</code> numbers which are not reduced by those
primes are garanteed to be either prime or semi prime.
+ */
+ public static final int[] PRIMES = {2,
+ 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61,
67, 71, 73,
+ 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149,
151, 157, 163, 167, 173, 179,
+ 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251,
257, 263, 269, 271, 277, 281, 283,
+ 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373,
379, 383, 389, 397, 401, 409, 419,
+ 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491,
499, 503, 509, 521, 523, 541, 547,
+ 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619,
631, 641, 643, 647, 653, 659, 661,
+ 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757,
761, 769, 773, 787, 797, 809, 811,
+ 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887,
907, 911, 919, 929, 937, 941, 947,
+ 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031,
1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087,
+ 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163,
1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229,
+ 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301,
1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381,
+ 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459,
1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523,
+ 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601,
1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663,
+ 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747,
1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823,
+ 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907,
1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993,
+ 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069,
2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131,
+ 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237,
2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293,
+ 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377,
2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437,
+ 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543,
2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621,
+ 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693,
2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749,
+ 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837,
2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909,
+ 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011,
3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083,
+ 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191,
3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259,
+ 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347,
3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433,
+ 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527,
3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581,
+ 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671};
+ /**
+ * The last number in PRIMES
+ */
+ public static final int PRIMES_LAST = PRIMES[PRIMES.length - 1];
+
+ /**
+ * Only static methods in this class
+ */
+ private SmallPrimes() {
+ }
+
+ /**
+ * Extract small factors.
+ * @param n the number to factor, must be >0.
+ * @param factors the list where to add the factors.
+ * @return the part of n which remains to be factored, it is either a
prime or a semi-prime
+ */
+ public static int smallTrialDivision(int n, final List<Integer> factors) {
+ for (int p : PRIMES) {
+ while (0 == n % p) {
+ n = n / p;
+ factors.add(p);
+ }
+ }
+ return n;
+ }
+
+ /**
+ * Extract factors in the range <code>PRIME_LAST+2</code> to
<code>maxFactors</code>
+ * @param n the number to factorize, must be >= PRIME_LAST+2 and must not
contain any factor below PRIME_LAST+2
+ * @param maxFactor the upper bound of trial division: if it is reach, the
methods gives up and return n.
+ * @param factors the list where to add the factors.
+ * @return n or 1 if factorization is completed.
+ */
+ public static int boundedTrialDivision(int n, int maxFactor, List<Integer>
factors) {
+ int f = PRIMES_LAST + 2;
+ // no check is done about n >= f
+ while (f <= maxFactor) {
+ if (0 == n % f) {
+ n = n / f;
+ factors.add(f);
+ break;
+ }
+ f += 4;
+ if (0 == n % f) {
+ n = n / f;
+ factors.add(f);
+ break;
+ }
+ f += 2;
+ }
+ if (n != 1) {
+ factors.add(n);
+ }
+ return n;
+ }
+
+ /**
+ * Factorization by trial division
+ * @param n the number to factorize
+ * @return the list of prime factors of n
+ */
+ public static List<Integer> trialDivision(int n){
+ final List<Integer> factors = new ArrayList<Integer>(32);
+ n = smallTrialDivision(n, factors);
+ if (1 == n) {
+ return factors;
+ }
+ // here we are sure that n is either a prime or a semi prime
+ final int bound = (int) FastMath.sqrt(n);
+ boundedTrialDivision(n, bound, factors);
+ return factors;
+ }
+
+ /**
+ * Miller-Rabin probabilistic primality test for int type, used in such a
way that result is always guaranteed.
+ * It uses the prime numbers as successive base therefore it is garanteed
to be always correct. (see Handbook of applied cryptography by Menezes, table
4.1)
+ *
+ * @param n number to test: an odd integer >= 3
+ * @return true if n is prime. false if n is definitely composite.
+ */
+ public static boolean millerRabinPrimeTest(final int n) {
+ final int nMinus1 = n - 1;
+ final int s = Integer.numberOfTrailingZeros(nMinus1);
+ final int r = nMinus1 >> s;
+ //r must be odd, it is not checked here
+ int t = 1;
+ if (n >= 2047) {
+ t = 2;
+ }
+ if (n >= 1373653) {
+ t = 3;
+ }
+ if (n >= 25326001) {
+ t = 4;
+ } // works up to 3.2 billion, int range stops at 2.7 so we are safe :-)
+ BigInteger br = BigInteger.valueOf(r);
+ BigInteger bn = BigInteger.valueOf(n);
+
+ for (int i = 0; i < t; i++) {
+ BigInteger a = BigInteger.valueOf(SmallPrimes.PRIMES[i]);
+ BigInteger bPow = a.modPow(br, bn);
+ int y = bPow.intValue();
+ if ((1 != y) && (y != nMinus1)) {
+ int j = 1;
+ while ((j <= s - 1) && (nMinus1 != y)) {
+ long square = ((long) y) * y;
+ y = (int) (square % n);
+ if (1 == y) {
+ return false;
+ } //definitely composite
+ j++;
+ }
+ if (nMinus1 != y) {
+ return false;
+ } //definitely composite
+ }
+ }
+ return true; //definitely prime
+ }
+}
+
Propchange:
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/primes/SmallPrimes.java
------------------------------------------------------------------------------
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commons/proper/math/trunk/src/main/java/org/apache/commons/math3/primes/package-info.java
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commons/proper/math/trunk/src/main/java/org/apache/commons/math3/primes/package-info.java
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commons/proper/math/trunk/src/main/java/org/apache/commons/math3/primes/package-info.java
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+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+/**
+ * Methods related to prime numbers like primality test, factor decomposition.
+ */
+package org.apache.commons.math3.primes;
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commons/proper/math/trunk/src/test/java/org/apache/commons/math3/primes/PrimesTest.java
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commons/proper/math/trunk/src/test/java/org/apache/commons/math3/primes/PrimesTest.java
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commons/proper/math/trunk/src/test/java/org/apache/commons/math3/primes/PrimesTest.java
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+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math3.primes;
+
+
+import java.util.HashSet;
+import java.util.List;
+
+import org.apache.commons.math3.exception.MathIllegalArgumentException;
+import org.apache.commons.math3.exception.util.LocalizedFormats;
+import org.junit.Assert;
+import org.junit.Test;
+
+public class PrimesTest {
+
+ public static final int[] PRIMES = {//primes here have been verified one
by one using Dario Alejandro Alpern's tool, see
http://www.alpertron.com.ar/ECM.HTM
+ 2,3,5,7,11,13,17,19,23,29,31,43,47,53,71,73,79,89,97,
+ 107,137,151,157,271,293,331,409,607,617,683,829,
+ 1049,1103,1229,1657,
+ 2039,2053,//around first boundary in miller-rabin
+ 2251,2389,2473,2699,3271,3389,3449,5653,6449,6869,9067,9091,
+ 11251,12433,12959,22961,41047,46337,65413,80803,91577,92693,
+ 118423,656519,795659,
+ 1373639,1373677,//around second boundary in miller-rabin
+ 588977,952381,
+ 1013041,1205999,2814001,
+ 22605091,
+ 25325981,25326023,//around third boundary in miller-rabin
+ 100000007,715827881,
+ 2147483647//Integer.MAX_VALUE
+ };
+
+ public static final int[] NOT_PRIMES = {//composite chosen at random +
particular values used in algorithms such as boundaries for millerRabin
+ 4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,
+ 275,
+ 2037,2041,2045,2046,2047,2048,2049,2051,2055,//around first
boundary in miller-rabin
+ 9095,
+ 463465,
+
1373637,1373641,1373651,1373652,1373653,1373654,1373655,1373673,1373675,1373679,//around
second boundary in miller-rabin
+
25325979,25325983,25325993,25325997,25325999,25326001,25326003,25326007,25326009,25326011,25326021,25326025,//around
third boundary in miller-rabin
+ 100000005,
+
1073741341,1073741823,2147473649,2147483641,2147483643,2147483645,2147483646};
+
+ public static final int[] BELOW_2 = {
+ Integer.MIN_VALUE,-1,0,1};
+
+ void assertPrimeFactorsException(int n, Throwable expected) {
+ try {
+ Primes.primeFactors(n);
+ Assert.fail("Exception not thrown");
+ } catch (Throwable e) {
+ Assert.assertEquals(expected.getClass(), e.getClass());
+ if (expected.getMessage() != null) {
+ Assert.assertEquals(expected.getMessage(), e.getMessage());
+ }
+ }
+ }
+ void assertNextPrimeException(int n, Throwable expected){
+ try {
+ Primes.nextPrime(n);
+ Assert.fail("Exception not thrown");
+ } catch(Throwable e) {
+ Assert.assertEquals(expected.getClass(), e.getClass());
+ if (expected.getMessage() != null) {
+ Assert.assertEquals(expected.getMessage(), e.getMessage());
+ }
+ }
+ }
+
+ @Test
+ public void testNextPrime() {
+
+ Assert.assertEquals(2, Primes.nextPrime(0));
+ Assert.assertEquals(2, Primes.nextPrime(1));
+ Assert.assertEquals(2, Primes.nextPrime(2));
+ Assert.assertEquals(3, Primes.nextPrime(3));
+ Assert.assertEquals(5, Primes.nextPrime(4));
+ Assert.assertEquals(5, Primes.nextPrime(5));
+
+ for (int i = 0; i < SmallPrimes.PRIMES.length - 1; i++) {
+ for (int j = SmallPrimes.PRIMES[i] + 1; j <= SmallPrimes.PRIMES[i
+ 1]; j++) {
+ Assert.assertEquals(SmallPrimes.PRIMES[i+1],
Primes.nextPrime(j));
+ }
+ }
+
+ Assert.assertEquals(25325981, Primes.nextPrime(25325981));
+ for (int i = 25325981 + 1; i <= 25326023; i++) {
+ Assert.assertEquals(25326023, Primes.nextPrime(i));
+ }
+
+ Assert.assertEquals(Integer.MAX_VALUE,
Primes.nextPrime(Integer.MAX_VALUE - 10));
+ Assert.assertEquals(Integer.MAX_VALUE,
Primes.nextPrime(Integer.MAX_VALUE - 1));
+ Assert.assertEquals(Integer.MAX_VALUE,
Primes.nextPrime(Integer.MAX_VALUE));
+
+ assertNextPrimeException(Integer.MIN_VALUE, new
MathIllegalArgumentException(LocalizedFormats.NUMBER_TOO_SMALL,Integer.MIN_VALUE,0));
+ assertNextPrimeException(-1, new
MathIllegalArgumentException(LocalizedFormats.NUMBER_TOO_SMALL,-1,0));
+ assertNextPrimeException(-13, new
MathIllegalArgumentException(LocalizedFormats.NUMBER_TOO_SMALL,-13,0));
+ }
+
+ @Test
+ public void testIsPrime() throws Exception {
+ for (int i : BELOW_2) {
+ Assert.assertEquals(false,Primes.isPrime(i));
+ }
+ for (int i:NOT_PRIMES) {
+ Assert.assertEquals(false,Primes.isPrime(i));
+ }
+ for (int i:PRIMES) {
+ Assert.assertEquals(true,Primes.isPrime(i));
+ }
+ }
+
+ static int sum(List<Integer> numbers){
+ int out = 0;
+ for (int i:numbers) {
+ out += i;
+ }
+ return out;
+ }
+ static int product(List<Integer> numbers) {
+ int out = 1;
+ for (int i : numbers) {
+ out *= i;
+ }
+ return out;
+ }
+ static final HashSet<Integer> PRIMES_SET = new HashSet<Integer>();
+ static {
+ for (int p : PRIMES) {
+ PRIMES_SET.add(p);
+ }
+ }
+ static void checkPrimeFactors(List<Integer> factors){
+ for (int p : factors) {
+ if (!PRIMES_SET.contains(p)) {
+ Assert.fail("Not found in primes list: " + p);
+ }
+ }
+ }
+
+ @Test
+ public void testPrimeFactors() throws Exception {
+ for (int i : BELOW_2) {
+ assertPrimeFactorsException(i, new
MathIllegalArgumentException(LocalizedFormats.NUMBER_TOO_SMALL,i,2));
+ }
+ for (int i : NOT_PRIMES) {
+ List<Integer> factors = Primes.primeFactors(i);
+ checkPrimeFactors(factors);
+ int prod = product(factors);
+ Assert.assertEquals(i, prod);
+ }
+ for (int i : PRIMES) {
+ List<Integer> factors = Primes.primeFactors(i);
+ Assert.assertEquals(i, (int)factors.get(0));
+ Assert.assertEquals(1, factors.size());
+ }
+ }
+}
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