1 /* 2 * Copyright (c) 2014, 2017, 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 /test/lib 29 * @build jdk.test.lib.RandomFactory 30 * @run main PrimeTest 31 * @bug 8026236 8074460 8078672 32 * @summary test primality verification methods in BigInteger (use -Dseed=X to set PRNG seed) 33 * @author bpb 34 * @key randomness 35 */ 36 import java.math.BigInteger; 37 import java.util.BitSet; 38 import java.util.List; 39 import java.util.NavigableSet; 40 import java.util.Set; 41 import java.util.SplittableRandom; 42 import java.util.TreeSet; 43 import jdk.test.lib.RandomFactory; 44 import static java.util.stream.Collectors.toCollection; 45 import static java.util.stream.Collectors.toList; 46 47 public class PrimeTest { 48 49 private static final int DEFAULT_UPPER_BOUND = 1299709; // 100000th prime 50 private static final int DEFAULT_CERTAINTY = 100; 51 private static final int NUM_NON_PRIMES = 10000; 52 53 /** 54 * Run the test. 55 * 56 * @param args The parameters. 57 * @throws Exception on failure 58 */ 59 public static void main(String[] args) throws Exception { 60 // Prepare arguments 61 int upperBound = args.length > 0 ? Integer.valueOf(args[0]) : DEFAULT_UPPER_BOUND; 62 int certainty = args.length > 1 ? Integer.valueOf(args[1]) : DEFAULT_CERTAINTY; 63 boolean parallel = args.length > 2 ? Boolean.valueOf(args[2]) : true; 64 65 // Echo parameter settings 66 System.out.println("Upper bound = " + upperBound 67 + "\nCertainty = " + certainty 68 + "\nParallel = " + parallel); 69 70 // Get primes through specified bound (inclusive) and Integer.MAX_VALUE 71 NavigableSet<BigInteger> primes = getPrimes(upperBound); 72 73 // Check whether known primes are identified as such 74 boolean primeTest = checkPrime(primes, certainty, parallel); 75 System.out.println("Prime test result: " + (primeTest ? "SUCCESS" : "FAILURE")); 76 if (!primeTest) { 77 System.err.println("Prime test failed"); 78 } 79 80 // Check whether known non-primes are not identified as primes 81 boolean nonPrimeTest = checkNonPrime(primes, certainty); 82 System.out.println("Non-prime test result: " + (nonPrimeTest ? "SUCCESS" : "FAILURE")); 83 84 boolean mersennePrimeTest = checkMersennePrimes(certainty); 85 System.out.println("Mersenne test result: " + (mersennePrimeTest ? "SUCCESS" : "FAILURE")); 86 87 if (!primeTest || !nonPrimeTest || !mersennePrimeTest) { 88 throw new Exception("PrimeTest FAILED!"); 89 } 90 91 System.out.println("PrimeTest succeeded!"); 92 } 93 94 /** 95 * Create a {@code BitSet} wherein a set bit indicates the corresponding 96 * index plus 2 is prime. That is, if bit N is set, then the integer N + 2 97 * is prime. The values 0 and 1 are intentionally excluded. See the 98 * <a 99 * href="http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes#Algorithm_description"> 100 * Sieve of Eratosthenes</a> algorithm description for more information. 101 * 102 * @param upperBound The maximum prime to allow 103 * @return bits indicating which indexes represent primes 104 */ 105 private static BitSet createPrimes(int upperBound) { 106 int nbits = upperBound - 1; 107 BitSet bs = new BitSet(nbits); 108 for (int p = 2; p * p < upperBound;) { 109 for (int i = p * p; i < nbits + 2; i += p) { 110 bs.set(i - 2, true); 111 } 112 do { 113 ++p; 114 } while (p > 1 && bs.get(p - 2)); 115 } 116 bs.flip(0, nbits); 117 return bs; 118 } 119 120 /** 121 * Load the primes up to the specified bound (inclusive) into a 122 * {@code NavigableSet}, appending the prime {@code Integer.MAX_VALUE}. 123 * 124 * @param upperBound The maximum prime to allow 125 * @return a set of primes 126 */ 127 private static NavigableSet<BigInteger> getPrimes(int upperBound) { 128 BitSet bs = createPrimes(upperBound); 129 NavigableSet<BigInteger> primes = bs.stream() 130 .mapToObj(p -> BigInteger.valueOf(p + 2)) 131 .collect(toCollection(TreeSet::new)); 132 primes.add(BigInteger.valueOf(Integer.MAX_VALUE)); 133 System.out.println(String.format("Created %d primes", primes.size())); 134 return primes; 135 } 136 137 /** 138 * Verifies whether the fraction of probable primes detected is at least 1 - 139 * 1/2^certainty. 140 * 141 * @return true if and only if the test succeeds 142 */ 143 private static boolean checkPrime(Set<BigInteger> primes, 144 int certainty, 145 boolean parallel) { 146 long probablePrimes = (parallel ? primes.parallelStream() : primes.stream()) 147 .filter(bi -> bi.isProbablePrime(certainty)) 148 .count(); 149 150 // N = certainty / 2 151 // Success if p/t >= 1 - 1/4^N 152 // or (p/t)*4^N >= 4^N - 1 153 // or p*4^N >= t*(4^N - 1) 154 BigInteger p = BigInteger.valueOf(probablePrimes); 155 BigInteger t = BigInteger.valueOf(primes.size()); 156 BigInteger fourToTheC = BigInteger.valueOf(4).pow(certainty / 2); 157 BigInteger fourToTheCMinusOne = fourToTheC.subtract(BigInteger.ONE); 158 BigInteger left = p.multiply(fourToTheC); 159 BigInteger right = t.multiply(fourToTheCMinusOne); 160 161 if (left.compareTo(right) < 0) { 162 System.err.println("Probable prime certainty test failed"); 163 } 164 165 return left.compareTo(right) >= 0; 166 } 167 168 /** 169 * Verifies whether all {@code BigInteger}s in the tested range for which 170 * {@code isProbablePrime()} returns {@code false} are <i>not</i> 171 * prime numbers. 172 * 173 * @return true if and only if the test succeeds 174 */ 175 private static boolean checkNonPrime(NavigableSet<BigInteger> primes, 176 int certainty) { 177 int maxPrime = DEFAULT_UPPER_BOUND; 178 try { 179 maxPrime = primes.last().intValueExact(); 180 } catch (ArithmeticException e) { 181 // ignore it 182 } 183 184 // Create a list of non-prime BigIntegers. 185 SplittableRandom splitRandom = RandomFactory.getSplittableRandom(); 186 List<BigInteger> nonPrimeBigInts = (splitRandom) 187 .ints(NUM_NON_PRIMES, 2, maxPrime).mapToObj(BigInteger::valueOf) 188 .filter(b -> !b.isProbablePrime(certainty)).collect(toList()); 189 190 // If there are any non-probable primes also in the primes list then fail. 191 boolean failed = nonPrimeBigInts.stream().anyMatch(primes::contains); 192 193 // In the event, print which purported non-primes were actually prime. 194 if (failed) { 195 for (BigInteger bigInt : nonPrimeBigInts) { 196 if (primes.contains(bigInt)) { 197 System.err.println("Prime value thought to be non-prime: " + bigInt); 198 } 199 } 200 } 201 202 return !failed; 203 } 204 205 /** 206 * Verifies whether a specified subset of Mersenne primes are correctly 207 * identified as being prime. See 208 * <a href="https://en.wikipedia.org/wiki/Mersenne_prime">Mersenne prime</a> 209 * for more information. 210 * 211 * @return true if and only if the test succeeds 212 */ 213 private static boolean checkMersennePrimes(int certainty) { 214 int[] MERSENNE_EXPONENTS = { 215 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 216 2281, 3217, 4253, // uncomment remaining array elements to make this test run a long time 217 /* 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 218 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 219 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 220 30402457, 32582657, 37156667, 42643801, 43112609, 57885161 */ 221 }; 222 System.out.println("Checking first "+MERSENNE_EXPONENTS.length+" Mersenne primes"); 223 224 boolean result = true; 225 for (int n : MERSENNE_EXPONENTS) { 226 BigInteger mp = BigInteger.ONE.shiftLeft(n).subtract(BigInteger.ONE); 227 if (!mp.isProbablePrime(certainty)) { 228 System.err.println("Mp with p = "+n+" not classified as prime"); 229 result = false; 230 } 231 } 232 233 return result; 234 } 235 }