/* * Copyright (c) 1999, 2007, Oracle and/or its affiliates. All rights reserved. * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. * * This code is free software; you can redistribute it and/or modify it * under the terms of the GNU General Public License version 2 only, as * published by the Free Software Foundation. Oracle designates this * particular file as subject to the "Classpath" exception as provided * by Oracle in the LICENSE file that accompanied this code. * * This code is distributed in the hope that it will be useful, but WITHOUT * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License * version 2 for more details (a copy is included in the LICENSE file that * accompanied this code). * * You should have received a copy of the GNU General Public License version * 2 along with this work; if not, write to the Free Software Foundation, * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. * * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA * or visit www.oracle.com if you need additional information or have any * questions. */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; }}
/*
* Copyright (c) 1999, 2007, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
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;
}
}