Repository: commons-numbers Updated Branches: refs/heads/master eed94bfe8 -> 1eaba643f
NUMBERS-20: Establish baseline of files copied from [math]. Project: http://git-wip-us.apache.org/repos/asf/commons-numbers/repo Commit: http://git-wip-us.apache.org/repos/asf/commons-numbers/commit/996a3a45 Tree: http://git-wip-us.apache.org/repos/asf/commons-numbers/tree/996a3a45 Diff: http://git-wip-us.apache.org/repos/asf/commons-numbers/diff/996a3a45 Branch: refs/heads/master Commit: 996a3a45d5dc92383064594a950b23667df56f21 Parents: b37c9f1 Author: Ray DeCampo <r...@decampo.org> Authored: Sun Apr 16 13:04:34 2017 -0400 Committer: Ray DeCampo <r...@decampo.org> Committed: Thu Apr 20 18:23:48 2017 -0400 ---------------------------------------------------------------------- .../apache/commons/numbers/primes/Primes.java | 126 +++++++++++++ .../commons/numbers/primes/SmallPrimes.java | 188 +++++++++++++++++++ .../commons/numbers/primes/package-info.java | 20 ++ .../commons/numbers/primes/PrimesTest.java | 174 +++++++++++++++++ 4 files changed, 508 insertions(+) ---------------------------------------------------------------------- http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/996a3a45/commons-numbers-primes/src/main/java/org/apache/commons/numbers/primes/Primes.java ---------------------------------------------------------------------- diff --git a/commons-numbers-primes/src/main/java/org/apache/commons/numbers/primes/Primes.java b/commons-numbers-primes/src/main/java/org/apache/commons/numbers/primes/Primes.java new file mode 100644 index 0000000..db75ccc --- /dev/null +++ b/commons-numbers-primes/src/main/java/org/apache/commons/numbers/primes/Primes.java @@ -0,0 +1,126 @@ +/* + * 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.math4.primes; + +import org.apache.commons.math4.exception.MathIllegalArgumentException; +import org.apache.commons.math4.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> + * + * @since 3.2 + */ +public class Primes { + + /** + * Hide utility 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 a result is 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 greater than or equal to n. + * + * @param n a positive number. + * @return the smallest prime greater than 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 |= 1;//make sure 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); + } + return SmallPrimes.trialDivision(n); + + } + +} http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/996a3a45/commons-numbers-primes/src/main/java/org/apache/commons/numbers/primes/SmallPrimes.java ---------------------------------------------------------------------- diff --git a/commons-numbers-primes/src/main/java/org/apache/commons/numbers/primes/SmallPrimes.java b/commons-numbers-primes/src/main/java/org/apache/commons/numbers/primes/SmallPrimes.java new file mode 100644 index 0000000..6f329e3 --- /dev/null +++ b/commons-numbers-primes/src/main/java/org/apache/commons/numbers/primes/SmallPrimes.java @@ -0,0 +1,188 @@ +/* + * 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.math4.primes; + + +import java.math.BigInteger; +import java.util.ArrayList; +import java.util.List; + +import org.apache.commons.math4.util.FastMath; + +/** + * Utility methods to work on primes within the <code>int</code> range. + * @since 3.2 + */ +class SmallPrimes { + + /** + * The first 512 prime numbers. + * <p> + * 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 guaranteed + * 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]; + + /** + * Hide utility 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 /= 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 reached, the method gives up and returns 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 /= f; + factors.add(f); + break; + } + f += 4; + if (0 == n % f) { + 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 factor + * @return the list of prime factors of n + */ + public static List<Integer> trialDivision(int n){ + final List<Integer> factors = new ArrayList<>(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 a result is always guaranteed. + * <p> + * It uses the prime numbers as successive base therefore it is guaranteed 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 + } +} + http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/996a3a45/commons-numbers-primes/src/main/java/org/apache/commons/numbers/primes/package-info.java ---------------------------------------------------------------------- diff --git a/commons-numbers-primes/src/main/java/org/apache/commons/numbers/primes/package-info.java b/commons-numbers-primes/src/main/java/org/apache/commons/numbers/primes/package-info.java new file mode 100644 index 0000000..076ec31 --- /dev/null +++ b/commons-numbers-primes/src/main/java/org/apache/commons/numbers/primes/package-info.java @@ -0,0 +1,20 @@ +/* + * 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.math4.primes; http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/996a3a45/commons-numbers-primes/src/test/java/org/apache/commons/numbers/primes/PrimesTest.java ---------------------------------------------------------------------- diff --git a/commons-numbers-primes/src/test/java/org/apache/commons/numbers/primes/PrimesTest.java b/commons-numbers-primes/src/test/java/org/apache/commons/numbers/primes/PrimesTest.java new file mode 100644 index 0000000..831a86e --- /dev/null +++ b/commons-numbers-primes/src/test/java/org/apache/commons/numbers/primes/PrimesTest.java @@ -0,0 +1,174 @@ +/* + * 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.math4.primes; + + +import java.util.HashSet; +import java.util.List; + +import org.apache.commons.math4.exception.MathIllegalArgumentException; +import org.apache.commons.math4.exception.util.LocalizedFormats; +import org.apache.commons.math4.primes.Primes; +import org.apache.commons.math4.primes.SmallPrimes; +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.assertFalse(Primes.isPrime(i)); + } + for (int i:NOT_PRIMES) { + Assert.assertFalse(Primes.isPrime(i)); + } + for (int i:PRIMES) { + Assert.assertTrue(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<>(); + 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()); + } + } +}
