8026236: Add PrimeTest for BigInteger
Test primality verification methods in BigInteger
Co-authored-by: Peter Levart <peter.levart@gmail.com>
Co-authored-by: Paul Sandoz <paul.sandoz@oracle.com>
Co-authored-by: Aleksey Shipilev <aleksey.shipilev@oracle.com>
Co-authored-by: Florian Weimer <fweimer@redhat.com>
Reviewed-by: psandoz
diff --git a/jdk/test/java/math/BigInteger/PrimeTest.java b/jdk/test/java/math/BigInteger/PrimeTest.java
new file mode 100644
index 0000000..85a7da1
--- /dev/null
+++ b/jdk/test/java/math/BigInteger/PrimeTest.java
@@ -0,0 +1,196 @@
+/*
+ * Copyright (c) 2014, 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
+ * @bug 8026236
+ * @summary test primality verification methods in BigInteger
+ * @author bpb
+ */
+import java.math.BigInteger;
+import java.util.BitSet;
+import java.util.List;
+import java.util.NavigableSet;
+import java.util.SplittableRandom;
+import java.util.TreeSet;
+import static java.util.stream.Collectors.toCollection;
+import static java.util.stream.Collectors.toList;
+import java.util.stream.IntStream;
+import java.util.stream.Stream;
+
+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<BigInteger> 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"));
+
+ if (!primeTest || !nonPrimeTest) {
+ 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
+ * <a
+ * href="http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes#Algorithm_description">
+ * Sieve of Eratosthenes</a> 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<BigInteger> getPrimes(int upperBound) {
+ BitSet bs = createPrimes(upperBound);
+ NavigableSet<BigInteger> 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(NavigableSet<BigInteger> 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 <i>not</i>
+ * prime numbers.
+ *
+ * @return true if and only if the test succeeds
+ */
+ private static boolean checkNonPrime(NavigableSet<BigInteger> 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.
+ List<BigInteger> nonPrimeBigInts = (new SplittableRandom())
+ .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;
+ }
+}
