PrimeTest.java

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 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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/*
 * @test
 * @bug 8026236
 * @summary test primality verification methods in BigInteger
 * @author bpb
 * @key randomness
 */
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;
    }
}