jaroslav@1258: /*
jaroslav@1258:  * Copyright (c) 1999, 2007, Oracle and/or its affiliates. All rights reserved.
jaroslav@1258:  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
jaroslav@1258:  *
jaroslav@1258:  * This code is free software; you can redistribute it and/or modify it
jaroslav@1258:  * under the terms of the GNU General Public License version 2 only, as
jaroslav@1258:  * published by the Free Software Foundation.  Oracle designates this
jaroslav@1258:  * particular file as subject to the "Classpath" exception as provided
jaroslav@1258:  * by Oracle in the LICENSE file that accompanied this code.
jaroslav@1258:  *
jaroslav@1258:  * This code is distributed in the hope that it will be useful, but WITHOUT
jaroslav@1258:  * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
jaroslav@1258:  * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
jaroslav@1258:  * version 2 for more details (a copy is included in the LICENSE file that
jaroslav@1258:  * accompanied this code).
jaroslav@1258:  *
jaroslav@1258:  * You should have received a copy of the GNU General Public License version
jaroslav@1258:  * 2 along with this work; if not, write to the Free Software Foundation,
jaroslav@1258:  * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
jaroslav@1258:  *
jaroslav@1258:  * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
jaroslav@1258:  * or visit www.oracle.com if you need additional information or have any
jaroslav@1258:  * questions.
jaroslav@1258:  */
jaroslav@1258: 
jaroslav@1258: package java.math;
jaroslav@1258: 
jaroslav@1258: /**
jaroslav@1258:  * A simple bit sieve used for finding prime number candidates. Allows setting
jaroslav@1258:  * and clearing of bits in a storage array. The size of the sieve is assumed to
jaroslav@1258:  * be constant to reduce overhead. All the bits of a new bitSieve are zero, and
jaroslav@1258:  * bits are removed from it by setting them.
jaroslav@1258:  *
jaroslav@1258:  * To reduce storage space and increase efficiency, no even numbers are
jaroslav@1258:  * represented in the sieve (each bit in the sieve represents an odd number).
jaroslav@1258:  * The relationship between the index of a bit and the number it represents is
jaroslav@1258:  * given by
jaroslav@1258:  * N = offset + (2*index + 1);
jaroslav@1258:  * Where N is the integer represented by a bit in the sieve, offset is some
jaroslav@1258:  * even integer offset indicating where the sieve begins, and index is the
jaroslav@1258:  * index of a bit in the sieve array.
jaroslav@1258:  *
jaroslav@1258:  * @see     BigInteger
jaroslav@1258:  * @author  Michael McCloskey
jaroslav@1258:  * @since   1.3
jaroslav@1258:  */
jaroslav@1258: class BitSieve {
jaroslav@1258:     /**
jaroslav@1258:      * Stores the bits in this bitSieve.
jaroslav@1258:      */
jaroslav@1258:     private long bits[];
jaroslav@1258: 
jaroslav@1258:     /**
jaroslav@1258:      * Length is how many bits this sieve holds.
jaroslav@1258:      */
jaroslav@1258:     private int length;
jaroslav@1258: 
jaroslav@1258:     /**
jaroslav@1258:      * A small sieve used to filter out multiples of small primes in a search
jaroslav@1258:      * sieve.
jaroslav@1258:      */
jaroslav@1258:     private static BitSieve smallSieve = new BitSieve();
jaroslav@1258: 
jaroslav@1258:     /**
jaroslav@1258:      * Construct a "small sieve" with a base of 0.  This constructor is
jaroslav@1258:      * used internally to generate the set of "small primes" whose multiples
jaroslav@1258:      * are excluded from sieves generated by the main (package private)
jaroslav@1258:      * constructor, BitSieve(BigInteger base, int searchLen).  The length
jaroslav@1258:      * of the sieve generated by this constructor was chosen for performance;
jaroslav@1258:      * it controls a tradeoff between how much time is spent constructing
jaroslav@1258:      * other sieves, and how much time is wasted testing composite candidates
jaroslav@1258:      * for primality.  The length was chosen experimentally to yield good
jaroslav@1258:      * performance.
jaroslav@1258:      */
jaroslav@1258:     private BitSieve() {
jaroslav@1258:         length = 150 * 64;
jaroslav@1258:         bits = new long[(unitIndex(length - 1) + 1)];
jaroslav@1258: 
jaroslav@1258:         // Mark 1 as composite
jaroslav@1258:         set(0);
jaroslav@1258:         int nextIndex = 1;
jaroslav@1258:         int nextPrime = 3;
jaroslav@1258: 
jaroslav@1258:         // Find primes and remove their multiples from sieve
jaroslav@1258:         do {
jaroslav@1258:             sieveSingle(length, nextIndex + nextPrime, nextPrime);
jaroslav@1258:             nextIndex = sieveSearch(length, nextIndex + 1);
jaroslav@1258:             nextPrime = 2*nextIndex + 1;
jaroslav@1258:         } while((nextIndex > 0) && (nextPrime < length));
jaroslav@1258:     }
jaroslav@1258: 
jaroslav@1258:     /**
jaroslav@1258:      * Construct a bit sieve of searchLen bits used for finding prime number
jaroslav@1258:      * candidates. The new sieve begins at the specified base, which must
jaroslav@1258:      * be even.
jaroslav@1258:      */
jaroslav@1258:     BitSieve(BigInteger base, int searchLen) {
jaroslav@1258:         /*
jaroslav@1258:          * Candidates are indicated by clear bits in the sieve. As a candidates
jaroslav@1258:          * nonprimality is calculated, a bit is set in the sieve to eliminate
jaroslav@1258:          * it. To reduce storage space and increase efficiency, no even numbers
jaroslav@1258:          * are represented in the sieve (each bit in the sieve represents an
jaroslav@1258:          * odd number).
jaroslav@1258:          */
jaroslav@1258:         bits = new long[(unitIndex(searchLen-1) + 1)];
jaroslav@1258:         length = searchLen;
jaroslav@1258:         int start = 0;
jaroslav@1258: 
jaroslav@1258:         int step = smallSieve.sieveSearch(smallSieve.length, start);
jaroslav@1258:         int convertedStep = (step *2) + 1;
jaroslav@1258: 
jaroslav@1258:         // Construct the large sieve at an even offset specified by base
jaroslav@1258:         MutableBigInteger b = new MutableBigInteger(base);
jaroslav@1258:         MutableBigInteger q = new MutableBigInteger();
jaroslav@1258:         do {
jaroslav@1258:             // Calculate base mod convertedStep
jaroslav@1258:             start = b.divideOneWord(convertedStep, q);
jaroslav@1258: 
jaroslav@1258:             // Take each multiple of step out of sieve
jaroslav@1258:             start = convertedStep - start;
jaroslav@1258:             if (start%2 == 0)
jaroslav@1258:                 start += convertedStep;
jaroslav@1258:             sieveSingle(searchLen, (start-1)/2, convertedStep);
jaroslav@1258: 
jaroslav@1258:             // Find next prime from small sieve
jaroslav@1258:             step = smallSieve.sieveSearch(smallSieve.length, step+1);
jaroslav@1258:             convertedStep = (step *2) + 1;
jaroslav@1258:         } while (step > 0);
jaroslav@1258:     }
jaroslav@1258: 
jaroslav@1258:     /**
jaroslav@1258:      * Given a bit index return unit index containing it.
jaroslav@1258:      */
jaroslav@1258:     private static int unitIndex(int bitIndex) {
jaroslav@1258:         return bitIndex >>> 6;
jaroslav@1258:     }
jaroslav@1258: 
jaroslav@1258:     /**
jaroslav@1258:      * Return a unit that masks the specified bit in its unit.
jaroslav@1258:      */
jaroslav@1258:     private static long bit(int bitIndex) {
jaroslav@1258:         return 1L << (bitIndex & ((1<<6) - 1));
jaroslav@1258:     }
jaroslav@1258: 
jaroslav@1258:     /**
jaroslav@1258:      * Get the value of the bit at the specified index.
jaroslav@1258:      */
jaroslav@1258:     private boolean get(int bitIndex) {
jaroslav@1258:         int unitIndex = unitIndex(bitIndex);
jaroslav@1258:         return ((bits[unitIndex] & bit(bitIndex)) != 0);
jaroslav@1258:     }
jaroslav@1258: 
jaroslav@1258:     /**
jaroslav@1258:      * Set the bit at the specified index.
jaroslav@1258:      */
jaroslav@1258:     private void set(int bitIndex) {
jaroslav@1258:         int unitIndex = unitIndex(bitIndex);
jaroslav@1258:         bits[unitIndex] |= bit(bitIndex);
jaroslav@1258:     }
jaroslav@1258: 
jaroslav@1258:     /**
jaroslav@1258:      * This method returns the index of the first clear bit in the search
jaroslav@1258:      * array that occurs at or after start. It will not search past the
jaroslav@1258:      * specified limit. It returns -1 if there is no such clear bit.
jaroslav@1258:      */
jaroslav@1258:     private int sieveSearch(int limit, int start) {
jaroslav@1258:         if (start >= limit)
jaroslav@1258:             return -1;
jaroslav@1258: 
jaroslav@1258:         int index = start;
jaroslav@1258:         do {
jaroslav@1258:             if (!get(index))
jaroslav@1258:                 return index;
jaroslav@1258:             index++;
jaroslav@1258:         } while(index < limit-1);
jaroslav@1258:         return -1;
jaroslav@1258:     }
jaroslav@1258: 
jaroslav@1258:     /**
jaroslav@1258:      * Sieve a single set of multiples out of the sieve. Begin to remove
jaroslav@1258:      * multiples of the specified step starting at the specified start index,
jaroslav@1258:      * up to the specified limit.
jaroslav@1258:      */
jaroslav@1258:     private void sieveSingle(int limit, int start, int step) {
jaroslav@1258:         while(start < limit) {
jaroslav@1258:             set(start);
jaroslav@1258:             start += step;
jaroslav@1258:         }
jaroslav@1258:     }
jaroslav@1258: 
jaroslav@1258:     /**
jaroslav@1258:      * Test probable primes in the sieve and return successful candidates.
jaroslav@1258:      */
jaroslav@1258:     BigInteger retrieve(BigInteger initValue, int certainty, java.util.Random random) {
jaroslav@1258:         // Examine the sieve one long at a time to find possible primes
jaroslav@1258:         int offset = 1;
jaroslav@1258:         for (int i=0; i<bits.length; i++) {
jaroslav@1258:             long nextLong = ~bits[i];
jaroslav@1258:             for (int j=0; j<64; j++) {
jaroslav@1258:                 if ((nextLong & 1) == 1) {
jaroslav@1258:                     BigInteger candidate = initValue.add(
jaroslav@1258:                                            BigInteger.valueOf(offset));
jaroslav@1258:                     if (candidate.primeToCertainty(certainty, random))
jaroslav@1258:                         return candidate;
jaroslav@1258:                 }
jaroslav@1258:                 nextLong >>>= 1;
jaroslav@1258:                 offset+=2;
jaroslav@1258:             }
jaroslav@1258:         }
jaroslav@1258:         return null;
jaroslav@1258:     }
jaroslav@1258: }