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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;
}
}