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 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.

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 * particular file as subject to the "Classpath" exception as provided

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 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or

 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License

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 * accompanied this code).

 *

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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;

    }

}