/* * Copyright (c) 2014, 2015, Oracle and/or its affiliates. All rights reserved. * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. * * This code is free software; you can redistribute it and/or modify it * under the terms of the GNU General Public License version 2 only, as * published by the Free Software Foundation. Oracle designates this * particular file as subject to the "Classpath" exception as provided * by Oracle in the LICENSE file that accompanied this code. * * This code is distributed in the hope that it will be useful, but WITHOUT * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License * version 2 for more details (a copy is included in the LICENSE file that * accompanied this code). * * You should have received a copy of the GNU General Public License version * 2 along with this work; if not, write to the Free Software Foundation, * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. * * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA * or visit www.oracle.com if you need additional information or have any * questions. */ /* * @test * @library .. * @bug 8026236 8074460 * @summary test primality verification methods in BigInteger (use -Dseed=X to set PRNG seed) * @author bpb * @key randomness */ import java.math.BigInteger; import java.util.BitSet; import java.util.List; import java.util.NavigableSet; import java.util.Set; import java.util.SplittableRandom; import java.util.TreeSet; import static java.util.stream.Collectors.toCollection; import static java.util.stream.Collectors.toList; public class PrimeTest { private static final int DEFAULT_UPPER_BOUND = 1299709; // 100000th prime private static final int DEFAULT_CERTAINTY = 100; private static final int NUM_NON_PRIMES = 10000; /** * Run the test. * * @param args The parameters. * @throws Exception on failure */ public static void main(String[] args) throws Exception { // Prepare arguments int upperBound = args.length > 0 ? Integer.valueOf(args[0]) : DEFAULT_UPPER_BOUND; int certainty = args.length > 1 ? Integer.valueOf(args[1]) : DEFAULT_CERTAINTY; boolean parallel = args.length > 2 ? Boolean.valueOf(args[2]) : true; // Echo parameter settings System.out.println("Upper bound = " + upperBound + "\nCertainty = " + certainty + "\nParallel = " + parallel); // Get primes through specified bound (inclusive) and Integer.MAX_VALUE NavigableSet primes = getPrimes(upperBound); // Check whether known primes are identified as such boolean primeTest = checkPrime(primes, certainty, parallel); System.out.println("Prime test result: " + (primeTest ? "SUCCESS" : "FAILURE")); if (!primeTest) { System.err.println("Prime test failed"); } // Check whether known non-primes are not identified as primes boolean nonPrimeTest = checkNonPrime(primes, certainty); System.out.println("Non-prime test result: " + (nonPrimeTest ? "SUCCESS" : "FAILURE")); boolean mersennePrimeTest = checkMersennePrimes(certainty); System.out.println("Mersenne test result: " + (mersennePrimeTest ? "SUCCESS" : "FAILURE")); if (!primeTest || !nonPrimeTest || !mersennePrimeTest) { throw new Exception("PrimeTest FAILED!"); } System.out.println("PrimeTest succeeded!"); } /** * Create a {@code BitSet} wherein a set bit indicates the corresponding * index plus 2 is prime. That is, if bit N is set, then the integer N + 2 * is prime. The values 0 and 1 are intentionally excluded. See the * * Sieve of Eratosthenes algorithm description for more information. * * @param upperBound The maximum prime to allow * @return bits indicating which indexes represent primes */ private static BitSet createPrimes(int upperBound) { int nbits = upperBound - 1; BitSet bs = new BitSet(nbits); for (int p = 2; p * p < upperBound;) { for (int i = p * p; i < nbits + 2; i += p) { bs.set(i - 2, true); } do { ++p; } while (p > 1 && bs.get(p - 2)); } bs.flip(0, nbits); return bs; } /** * Load the primes up to the specified bound (inclusive) into a * {@code NavigableSet}, appending the prime {@code Integer.MAX_VALUE}. * * @param upperBound The maximum prime to allow * @return a set of primes */ private static NavigableSet getPrimes(int upperBound) { BitSet bs = createPrimes(upperBound); NavigableSet primes = bs.stream() .mapToObj(p -> BigInteger.valueOf(p + 2)) .collect(toCollection(TreeSet::new)); primes.add(BigInteger.valueOf(Integer.MAX_VALUE)); System.out.println(String.format("Created %d primes", primes.size())); return primes; } /** * Verifies whether the fraction of probable primes detected is at least 1 - * 1/2^certainty. * * @return true if and only if the test succeeds */ private static boolean checkPrime(Set primes, int certainty, boolean parallel) { long probablePrimes = (parallel ? primes.parallelStream() : primes.stream()) .filter(bi -> bi.isProbablePrime(certainty)) .count(); // N = certainty / 2 // Success if p/t >= 1 - 1/4^N // or (p/t)*4^N >= 4^N - 1 // or p*4^N >= t*(4^N - 1) BigInteger p = BigInteger.valueOf(probablePrimes); BigInteger t = BigInteger.valueOf(primes.size()); BigInteger fourToTheC = BigInteger.valueOf(4).pow(certainty / 2); BigInteger fourToTheCMinusOne = fourToTheC.subtract(BigInteger.ONE); BigInteger left = p.multiply(fourToTheC); BigInteger right = t.multiply(fourToTheCMinusOne); if (left.compareTo(right) < 0) { System.err.println("Probable prime certainty test failed"); } return left.compareTo(right) >= 0; } /** * Verifies whether all {@code BigInteger}s in the tested range for which * {@code isProbablePrime()} returns {@code false} are not * prime numbers. * * @return true if and only if the test succeeds */ private static boolean checkNonPrime(NavigableSet primes, int certainty) { int maxPrime = DEFAULT_UPPER_BOUND; try { maxPrime = primes.last().intValueExact(); } catch (ArithmeticException e) { // ignore it } // Create a list of non-prime BigIntegers. RandomSeed rndSeed = new RandomSeed(true); System.out.println("Random number generator seed = " + rndSeed.getSeed()); List nonPrimeBigInts = (rndSeed.getSplittableRandom()) .ints(NUM_NON_PRIMES, 2, maxPrime).mapToObj(BigInteger::valueOf) .filter(b -> !b.isProbablePrime(certainty)).collect(toList()); // If there are any non-probable primes also in the primes list then fail. boolean failed = nonPrimeBigInts.stream().anyMatch(primes::contains); // In the event, print which purported non-primes were actually prime. if (failed) { for (BigInteger bigInt : nonPrimeBigInts) { if (primes.contains(bigInt)) { System.err.println("Prime value thought to be non-prime: " + bigInt); } } } return !failed; } /** * Verifies whether a specified subset of Mersenne primes are correctly * identified as being prime. See * Mersenne prime * for more information. * * @return true if and only if the test succeeds */ private static boolean checkMersennePrimes(int certainty) { int[] MERSENNE_EXPONENTS = { 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, // uncomment remaining array elements to make this test run a long time /* 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667, 42643801, 43112609, 57885161 */ }; System.out.println("Checking first "+MERSENNE_EXPONENTS.length+" Mersenne primes"); boolean result = true; for (int n : MERSENNE_EXPONENTS) { BigInteger mp = BigInteger.ONE.shiftLeft(n).subtract(BigInteger.ONE); if (!mp.isProbablePrime(certainty)) { System.err.println("Mp with p = "+n+" not classified as prime"); result = false; } } return result; } }