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Added utilities for prime numbers. 

Thanks to Sébastien Riou.

JIRA: MATH-845

git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1454920 13f79535-47bb-0310-9956-ffa450edef68
This commit is contained in:
Luc Maisonobe 2013-03-10 21:05:20 +00:00
parent ca139a75fe
commit c99413d2e9
7 changed files with 674 additions and 0 deletions
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3
pom.xml
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@ -240,6 +240,9 @@
<contributor>
<name>Andreas Rieger</name>
</contributor>
<contributor>
<name>S&#233;bastien Riou</name>
</contributor>
<contributor>
<name>Bill Rossi</name>
</contributor>

3
src/changes/changes.xml
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@ -55,6 +55,9 @@ This is a minor release: It combines bug fixes and new features.
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>

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src/main/java/org/apache/commons/math3/primes/PollardRho.java Normal file
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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.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;
}
}

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src/main/java/org/apache/commons/math3/primes/Primes.java Normal file
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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 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);
}
}

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src/main/java/org/apache/commons/math3/primes/SmallPrimes.java Normal file
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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.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
}
}

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src/main/java/org/apache/commons/math3/primes/package-info.java Normal file
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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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/*
* 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());
}
}
}