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 * ORACLE PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
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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;
 }
}