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

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  * published by the Free Software Foundation.  Oracle designates this

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

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  *

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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;

     }

 }