1 /* 2 * Copyright (c) 2014, 2015, Oracle and/or its affiliates. All rights reserved. 3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. 4 * 5 * This code is free software; you can redistribute it and/or modify it 6 * under the terms of the GNU General Public License version 2 only, as 7 * published by the Free Software Foundation. Oracle designates this 8 * particular file as subject to the "Classpath" exception as provided 9 * by Oracle in the LICENSE file that accompanied this code. 10 * 11 * This code is distributed in the hope that it will be useful, but WITHOUT 12 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or 13 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 14 * version 2 for more details (a copy is included in the LICENSE file that 15 * accompanied this code). 16 * 17 * You should have received a copy of the GNU General Public License version 18 * 2 along with this work; if not, write to the Free Software Foundation, 19 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. 20 * 21 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA 22 * or visit www.oracle.com if you need additional information or have any 23 * questions. 24 */ 25 26 /* 27 * @test 28 * @library .. 29 * @bug 8026236 8074460 30 * @summary test primality verification methods in BigInteger (use -Dseed=X to set PRNG seed) 31 * @author bpb 32 */ 33 import java.math.BigInteger; 34 import java.util.BitSet; 35 import java.util.List; 36 import java.util.NavigableSet; 37 import java.util.Set; 38 import java.util.SplittableRandom; 39 import java.util.TreeSet; 40 import static java.util.stream.Collectors.toCollection; 41 import static java.util.stream.Collectors.toList; 42 43 public class PrimeTest { 44 45 private static final int DEFAULT_UPPER_BOUND = 1299709; // 100000th prime 46 private static final int DEFAULT_CERTAINTY = 100; 47 private static final int NUM_NON_PRIMES = 10000; 48 49 /** 50 * Run the test. 51 * 52 * @param args The parameters. 53 * @throws Exception on failure 54 */ 55 public static void main(String[] args) throws Exception { 56 // Prepare arguments 57 int upperBound = args.length > 0 ? Integer.valueOf(args[0]) : DEFAULT_UPPER_BOUND; 58 int certainty = args.length > 1 ? Integer.valueOf(args[1]) : DEFAULT_CERTAINTY; 59 boolean parallel = args.length > 2 ? Boolean.valueOf(args[2]) : true; 60 61 // Echo parameter settings 62 System.out.println("Upper bound = " + upperBound 63 + "\nCertainty = " + certainty 64 + "\nParallel = " + parallel); 65 66 // Get primes through specified bound (inclusive) and Integer.MAX_VALUE 67 NavigableSet<BigInteger> primes = getPrimes(upperBound); 68 69 // Check whether known primes are identified as such 70 boolean primeTest = checkPrime(primes, certainty, parallel); 71 System.out.println("Prime test result: " + (primeTest ? "SUCCESS" : "FAILURE")); 72 if (!primeTest) { 73 System.err.println("Prime test failed"); 74 } 75 76 // Check whether known non-primes are not identified as primes 77 boolean nonPrimeTest = checkNonPrime(primes, certainty); 78 System.out.println("Non-prime test result: " + (nonPrimeTest ? "SUCCESS" : "FAILURE")); 79 80 boolean mersennePrimeTest = checkMersennePrimes(certainty); 81 System.out.println("Mersenne test result: " + (mersennePrimeTest ? "SUCCESS" : "FAILURE")); 82 83 if (!primeTest || !nonPrimeTest || !mersennePrimeTest) { 84 throw new Exception("PrimeTest FAILED!"); 85 } 86 87 System.out.println("PrimeTest succeeded!"); 88 } 89 90 /** 91 * Create a {@code BitSet} wherein a set bit indicates the corresponding 92 * index plus 2 is prime. That is, if bit N is set, then the integer N + 2 93 * is prime. The values 0 and 1 are intentionally excluded. See the 94 * <a 95 * href="http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes#Algorithm_description"> 96 * Sieve of Eratosthenes</a> algorithm description for more information. 97 * 98 * @param upperBound The maximum prime to allow 99 * @return bits indicating which indexes represent primes 100 */ 101 private static BitSet createPrimes(int upperBound) { 102 int nbits = upperBound - 1; 103 BitSet bs = new BitSet(nbits); 104 for (int p = 2; p * p < upperBound;) { 105 for (int i = p * p; i < nbits + 2; i += p) { 106 bs.set(i - 2, true); 107 } 108 do { 109 ++p; 110 } while (p > 1 && bs.get(p - 2)); 111 } 112 bs.flip(0, nbits); 113 return bs; 114 } 115 116 /** 117 * Load the primes up to the specified bound (inclusive) into a 118 * {@code NavigableSet}, appending the prime {@code Integer.MAX_VALUE}. 119 * 120 * @param upperBound The maximum prime to allow 121 * @return a set of primes 122 */ 123 private static NavigableSet<BigInteger> getPrimes(int upperBound) { 124 BitSet bs = createPrimes(upperBound); 125 NavigableSet<BigInteger> primes = bs.stream() 126 .mapToObj(p -> BigInteger.valueOf(p + 2)) 127 .collect(toCollection(TreeSet::new)); 128 primes.add(BigInteger.valueOf(Integer.MAX_VALUE)); 129 System.out.println(String.format("Created %d primes", primes.size())); 130 return primes; 131 } 132 133 /** 134 * Verifies whether the fraction of probable primes detected is at least 1 - 135 * 1/2^certainty. 136 * 137 * @return true if and only if the test succeeds 138 */ 139 private static boolean checkPrime(Set<BigInteger> primes, 140 int certainty, 141 boolean parallel) { 142 long probablePrimes = (parallel ? primes.parallelStream() : primes.stream()) 143 .filter(bi -> bi.isProbablePrime(certainty)) 144 .count(); 145 146 // N = certainty / 2 147 // Success if p/t >= 1 - 1/4^N 148 // or (p/t)*4^N >= 4^N - 1 149 // or p*4^N >= t*(4^N - 1) 150 BigInteger p = BigInteger.valueOf(probablePrimes); 151 BigInteger t = BigInteger.valueOf(primes.size()); 152 BigInteger fourToTheC = BigInteger.valueOf(4).pow(certainty / 2); 153 BigInteger fourToTheCMinusOne = fourToTheC.subtract(BigInteger.ONE); 154 BigInteger left = p.multiply(fourToTheC); 155 BigInteger right = t.multiply(fourToTheCMinusOne); 156 157 if (left.compareTo(right) < 0) { 158 System.err.println("Probable prime certainty test failed"); 159 } 160 161 return left.compareTo(right) >= 0; 162 } 163 164 /** 165 * Verifies whether all {@code BigInteger}s in the tested range for which 166 * {@code isProbablePrime()} returns {@code false} are <i>not</i> 167 * prime numbers. 168 * 169 * @return true if and only if the test succeeds 170 */ 171 private static boolean checkNonPrime(NavigableSet<BigInteger> primes, 172 int certainty) { 173 int maxPrime = DEFAULT_UPPER_BOUND; 174 try { 175 maxPrime = primes.last().intValueExact(); 176 } catch (ArithmeticException e) { 177 // ignore it 178 } 179 180 // Create a list of non-prime BigIntegers. 181 RandomSeed rndSeed = new RandomSeed(true); 182 System.out.println("Random number generator seed = " + rndSeed.getSeed()); 183 List<BigInteger> nonPrimeBigInts = (rndSeed.getSplittableRandom()) 184 .ints(NUM_NON_PRIMES, 2, maxPrime).mapToObj(BigInteger::valueOf) 185 .filter(b -> !b.isProbablePrime(certainty)).collect(toList()); 186 187 // If there are any non-probable primes also in the primes list then fail. 188 boolean failed = nonPrimeBigInts.stream().anyMatch(primes::contains); 189 190 // In the event, print which purported non-primes were actually prime. 191 if (failed) { 192 for (BigInteger bigInt : nonPrimeBigInts) { 193 if (primes.contains(bigInt)) { 194 System.err.println("Prime value thought to be non-prime: " + bigInt); 195 } 196 } 197 } 198 199 return !failed; 200 } 201 202 /** 203 * Verifies whether a specified subset of Mersenne primes are correctly 204 * identified as being prime. See 205 * <a href="https://en.wikipedia.org/wiki/Mersenne_prime">Mersenne prime</a> 206 * for more information. 207 * 208 * @return true if and only if the test succeeds 209 */ 210 private static boolean checkMersennePrimes(int certainty) { 211 int[] MERSENNE_EXPONENTS = { 212 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 213 2281, 3217, 4253, // uncomment remaining array elements to make this test run a long time 214 /* 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 215 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 216 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 217 30402457, 32582657, 37156667, 42643801, 43112609, 57885161 */ 218 }; 219 System.out.println("Checking first "+MERSENNE_EXPONENTS.length+" Mersenne primes"); 220 221 boolean result = true; 222 for (int n : MERSENNE_EXPONENTS) { 223 BigInteger mp = BigInteger.ONE.shiftLeft(n).subtract(BigInteger.ONE); 224 if (!mp.isProbablePrime(certainty)) { 225 System.err.println("Mp with p = "+n+" not classified as prime"); 226 result = false; 227 } 228 } 229 230 return result; 231 } 232 }