253 lines
9.5 KiB
Java
253 lines
9.5 KiB
Java
/*
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* Copyright (c) 2014, 2022, Oracle and/or its affiliates. All rights reserved.
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* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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*
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* This code is free software; you can redistribute it and/or modify it
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* under the terms of the GNU General Public License version 2 only, as
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* published by the Free Software Foundation.
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*
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* This code is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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* version 2 for more details (a copy is included in the LICENSE file that
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* accompanied this code).
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*
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* You should have received a copy of the GNU General Public License version
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* 2 along with this work; if not, write to the Free Software Foundation,
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* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
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*
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* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
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* or visit www.oracle.com if you need additional information or have any
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* questions.
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*/
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/*
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* @test
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* @library /test/lib
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* @build jdk.test.lib.RandomFactory
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* @run main PrimeTest
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* @bug 8026236 8074460 8078672 8294593
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* @summary test primality verification methods in BigInteger (use -Dseed=X to set PRNG seed)
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* @author bpb
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* @key randomness
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*/
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import java.math.BigInteger;
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import java.util.BitSet;
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import java.util.List;
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import java.util.NavigableSet;
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import java.util.Set;
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import java.util.SplittableRandom;
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import java.util.TreeSet;
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import jdk.test.lib.RandomFactory;
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import static java.util.stream.Collectors.toCollection;
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import static java.util.stream.Collectors.toList;
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public class PrimeTest {
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private static final int DEFAULT_UPPER_BOUND = 1299709; // 100000th prime
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private static final int DEFAULT_CERTAINTY = 100;
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private static final int NUM_NON_PRIMES = 10000;
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/**
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* Run the test.
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*
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* @param args The parameters.
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* @throws Exception on failure
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*/
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public static void main(String[] args) throws Exception {
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// Prepare arguments
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int upperBound = args.length > 0 ? Integer.valueOf(args[0]) : DEFAULT_UPPER_BOUND;
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int certainty = args.length > 1 ? Integer.valueOf(args[1]) : DEFAULT_CERTAINTY;
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boolean parallel = args.length > 2 ? Boolean.valueOf(args[2]) : true;
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// Echo parameter settings
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System.out.println("Upper bound = " + upperBound
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+ "\nCertainty = " + certainty
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+ "\nParallel = " + parallel);
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// Get primes through specified bound (inclusive) and Integer.MAX_VALUE
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NavigableSet<BigInteger> primes = getPrimes(upperBound);
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// Check whether known primes are identified as such
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boolean primeTest = checkPrime(primes, certainty, parallel);
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System.out.println("Prime test result: " + (primeTest ? "SUCCESS" : "FAILURE"));
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if (!primeTest) {
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System.err.println("Prime test failed");
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}
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// Check whether known non-primes are not identified as primes
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boolean nonPrimeTest = checkNonPrime(primes, certainty);
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System.out.println("Non-prime test result: " + (nonPrimeTest ? "SUCCESS" : "FAILURE"));
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boolean mersennePrimeTest = checkMersennePrimes(certainty);
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System.out.println("Mersenne test result: " + (mersennePrimeTest ? "SUCCESS" : "FAILURE"));
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if (!primeTest || !nonPrimeTest || !mersennePrimeTest) {
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throw new Exception("PrimeTest FAILED!");
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}
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if (!checkHugeFails()) {
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throw new Exception("Primality test on huge integer should fail but succeeded");
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}
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System.out.println("PrimeTest succeeded!");
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}
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/**
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* Create a {@code BitSet} wherein a set bit indicates the corresponding
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* index plus 2 is prime. That is, if bit N is set, then the integer N + 2
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* is prime. The values 0 and 1 are intentionally excluded. See the
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* <a
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* href="http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes#Algorithm_description">
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* Sieve of Eratosthenes</a> algorithm description for more information.
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*
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* @param upperBound The maximum prime to allow
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* @return bits indicating which indexes represent primes
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*/
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private static BitSet createPrimes(int upperBound) {
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int nbits = upperBound - 1;
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BitSet bs = new BitSet(nbits);
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for (int p = 2; p * p < upperBound;) {
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for (int i = p * p; i < nbits + 2; i += p) {
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bs.set(i - 2, true);
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}
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do {
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++p;
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} while (p > 1 && bs.get(p - 2));
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}
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bs.flip(0, nbits);
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return bs;
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}
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/**
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* Load the primes up to the specified bound (inclusive) into a
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* {@code NavigableSet}, appending the prime {@code Integer.MAX_VALUE}.
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*
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* @param upperBound The maximum prime to allow
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* @return a set of primes
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*/
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private static NavigableSet<BigInteger> getPrimes(int upperBound) {
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BitSet bs = createPrimes(upperBound);
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NavigableSet<BigInteger> primes = bs.stream()
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.mapToObj(p -> BigInteger.valueOf(p + 2))
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.collect(toCollection(TreeSet::new));
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primes.add(BigInteger.valueOf(Integer.MAX_VALUE));
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System.out.println(String.format("Created %d primes", primes.size()));
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return primes;
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}
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/**
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* Verifies whether the fraction of probable primes detected is at least 1 -
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* 1/2^certainty.
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*
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* @return true if and only if the test succeeds
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*/
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private static boolean checkPrime(Set<BigInteger> primes,
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int certainty,
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boolean parallel) {
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long probablePrimes = (parallel ? primes.parallelStream() : primes.stream())
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.filter(bi -> bi.isProbablePrime(certainty))
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.count();
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// N = certainty / 2
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// Success if p/t >= 1 - 1/4^N
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// or (p/t)*4^N >= 4^N - 1
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// or p*4^N >= t*(4^N - 1)
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BigInteger p = BigInteger.valueOf(probablePrimes);
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BigInteger t = BigInteger.valueOf(primes.size());
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BigInteger fourToTheC = BigInteger.valueOf(4).pow(certainty / 2);
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BigInteger fourToTheCMinusOne = fourToTheC.subtract(BigInteger.ONE);
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BigInteger left = p.multiply(fourToTheC);
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BigInteger right = t.multiply(fourToTheCMinusOne);
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if (left.compareTo(right) < 0) {
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System.err.println("Probable prime certainty test failed");
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}
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return left.compareTo(right) >= 0;
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}
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/**
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* Verifies whether all {@code BigInteger}s in the tested range for which
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* {@code isProbablePrime()} returns {@code false} are <i>not</i>
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* prime numbers.
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*
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* @return true if and only if the test succeeds
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*/
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private static boolean checkNonPrime(NavigableSet<BigInteger> primes,
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int certainty) {
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int maxPrime = DEFAULT_UPPER_BOUND;
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try {
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maxPrime = primes.last().intValueExact();
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} catch (ArithmeticException e) {
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// ignore it
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}
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// Create a list of non-prime BigIntegers.
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SplittableRandom splitRandom = RandomFactory.getSplittableRandom();
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List<BigInteger> nonPrimeBigInts = (splitRandom)
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.ints(NUM_NON_PRIMES, 2, maxPrime).mapToObj(BigInteger::valueOf)
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.filter(b -> !b.isProbablePrime(certainty)).collect(toList());
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// If there are any non-probable primes also in the primes list then fail.
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boolean failed = nonPrimeBigInts.stream().anyMatch(primes::contains);
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// In the event, print which purported non-primes were actually prime.
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if (failed) {
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for (BigInteger bigInt : nonPrimeBigInts) {
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if (primes.contains(bigInt)) {
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System.err.println("Prime value thought to be non-prime: " + bigInt);
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}
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}
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}
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return !failed;
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}
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/**
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* Verifies whether a specified subset of Mersenne primes are correctly
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* identified as being prime. See
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* <a href="https://en.wikipedia.org/wiki/Mersenne_prime">Mersenne prime</a>
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* for more information.
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*
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* @return true if and only if the test succeeds
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*/
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private static boolean checkMersennePrimes(int certainty) {
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int[] MERSENNE_EXPONENTS = {
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2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203,
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2281, 3217, 4253, // uncomment remaining array elements to make this test run a long time
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/* 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497,
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86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269,
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2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951,
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30402457, 32582657, 37156667, 42643801, 43112609, 57885161 */
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};
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System.out.println("Checking first "+MERSENNE_EXPONENTS.length+" Mersenne primes");
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boolean result = true;
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for (int n : MERSENNE_EXPONENTS) {
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BigInteger mp = BigInteger.ONE.shiftLeft(n).subtract(BigInteger.ONE);
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if (!mp.isProbablePrime(certainty)) {
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System.err.println("Mp with p = "+n+" not classified as prime");
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result = false;
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}
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}
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return result;
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}
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private static boolean checkHugeFails() {
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try {
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// huge odd integer
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BigInteger a = BigInteger.ONE.shiftLeft(500_000_000 + 1)
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.setBit(0);
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a.isProbablePrime(1);
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// not expected to reach here
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return false;
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} catch (ArithmeticException e) {
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// this is the expected behavior
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return true;
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}
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}
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}
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