java/math/BitSieve.java

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package java.math;

/**
 * A simple bit sieve used for finding prime number candidates. Allows setting
 * and clearing of bits in a storage array. The size of the sieve is assumed to
 * be constant to reduce overhead. All the bits of a new bitSieve are zero, and
 * bits are removed from it by setting them.
 *
 * To reduce storage space and increase efficiency, no even numbers are
 * represented in the sieve (each bit in the sieve represents an odd number).
 * The relationship between the index of a bit and the number it represents is
 * given by
 * N = offset + (2*index + 1);
 * Where N is the integer represented by a bit in the sieve, offset is some
 * even integer offset indicating where the sieve begins, and index is the
 * index of a bit in the sieve array.
 *
 * @see     BigInteger
 * @author  Michael McCloskey
 * @since   1.3
 */
class BitSieve {
    /**
     * Stores the bits in this bitSieve.
     */
    private long bits[];

    /**
     * Length is how many bits this sieve holds.
     */
    private int length;

    /**
     * A small sieve used to filter out multiples of small primes in a search
     * sieve.
     */
    private static BitSieve smallSieve = new BitSieve();

    /**
     * Construct a "small sieve" with a base of 0.  This constructor is
     * used internally to generate the set of "small primes" whose multiples
     * are excluded from sieves generated by the main (package private)
     * constructor, BitSieve(BigInteger base, int searchLen).  The length
     * of the sieve generated by this constructor was chosen for performance;
     * it controls a tradeoff between how much time is spent constructing
     * other sieves, and how much time is wasted testing composite candidates
     * for primality.  The length was chosen experimentally to yield good
     * performance.
     */
    private BitSieve() {
        length = 150 * 64;
        bits = new long[(unitIndex(length - 1) + 1)];

        // Mark 1 as composite
        set(0);
        int nextIndex = 1;
        int nextPrime = 3;

        // Find primes and remove their multiples from sieve
        do {
            sieveSingle(length, nextIndex + nextPrime, nextPrime);
            nextIndex = sieveSearch(length, nextIndex + 1);
            nextPrime = 2*nextIndex + 1;
        } while((nextIndex > 0) && (nextPrime < length));
    }

    /**
     * Construct a bit sieve of searchLen bits used for finding prime number
     * candidates. The new sieve begins at the specified base, which must
     * be even.
     */
    BitSieve(BigInteger base, int searchLen) {
        /*
         * Candidates are indicated by clear bits in the sieve. As a candidates
         * nonprimality is calculated, a bit is set in the sieve to eliminate
         * it. To reduce storage space and increase efficiency, no even numbers
         * are represented in the sieve (each bit in the sieve represents an
         * odd number).
         */
        bits = new long[(unitIndex(searchLen-1) + 1)];
        length = searchLen;
        int start = 0;

        int step = smallSieve.sieveSearch(smallSieve.length, start);
        int convertedStep = (step *2) + 1;

        // Construct the large sieve at an even offset specified by base
        MutableBigInteger b = new MutableBigInteger(base);
        MutableBigInteger q = new MutableBigInteger();
        do {
            // Calculate base mod convertedStep
            start = b.divideOneWord(convertedStep, q);

            // Take each multiple of step out of sieve
            start = convertedStep - start;
            if (start%2 == 0)
                start += convertedStep;
            sieveSingle(searchLen, (start-1)/2, convertedStep);

            // Find next prime from small sieve
            step = smallSieve.sieveSearch(smallSieve.length, step+1);
            convertedStep = (step *2) + 1;
        } while (step > 0);
    }

    /**
     * Given a bit index return unit index containing it.
     */
    private static int unitIndex(int bitIndex) {
        return bitIndex >>> 6;
    }

    /**
     * Return a unit that masks the specified bit in its unit.
     */
    private static long bit(int bitIndex) {
        return 1L << (bitIndex & ((1<<6) - 1));
    }

    /**
     * Get the value of the bit at the specified index.
     */
    private boolean get(int bitIndex) {
        int unitIndex = unitIndex(bitIndex);
        return ((bits[unitIndex] & bit(bitIndex)) != 0);
    }

    /**
     * Set the bit at the specified index.
     */
    private void set(int bitIndex) {
        int unitIndex = unitIndex(bitIndex);
        bits[unitIndex] |= bit(bitIndex);
    }

    /**
     * This method returns the index of the first clear bit in the search
     * array that occurs at or after start. It will not search past the
     * specified limit. It returns -1 if there is no such clear bit.
     */
    private int sieveSearch(int limit, int start) {
        if (start >= limit)
            return -1;

        int index = start;
        do {
            if (!get(index))
                return index;
            index++;
        } while(index < limit-1);
        return -1;
    }

    /**
     * Sieve a single set of multiples out of the sieve. Begin to remove
     * multiples of the specified step starting at the specified start index,
     * up to the specified limit.
     */
    private void sieveSingle(int limit, int start, int step) {
        while(start < limit) {
            set(start);
            start += step;
        }
    }

    /**
     * Test probable primes in the sieve and return successful candidates.
     */
    BigInteger retrieve(BigInteger initValue, int certainty, java.util.Random random) {
        // Examine the sieve one long at a time to find possible primes
        int offset = 1;
        for (int i=0; i<bits.length; i++) {
            long nextLong = ~bits[i];
            for (int j=0; j<64; j++) {
                if ((nextLong & 1) == 1) {
                    BigInteger candidate = initValue.add(
                                           BigInteger.valueOf(offset));
                    if (candidate.primeToCertainty(certainty, random))
                        return candidate;
                }
                nextLong >>>= 1;
                offset+=2;
            }
        }
        return null;
    }
}