001: /*
002: * Copyright 1999-2007 Sun Microsystems, Inc. All Rights Reserved.
003: * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
004: *
005: * This code is free software; you can redistribute it and/or modify it
006: * under the terms of the GNU General Public License version 2 only, as
007: * published by the Free Software Foundation. Sun designates this
008: * particular file as subject to the "Classpath" exception as provided
009: * by Sun in the LICENSE file that accompanied this code.
010: *
011: * This code is distributed in the hope that it will be useful, but WITHOUT
012: * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
013: * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
014: * version 2 for more details (a copy is included in the LICENSE file that
015: * accompanied this code).
016: *
017: * You should have received a copy of the GNU General Public License version
018: * 2 along with this work; if not, write to the Free Software Foundation,
019: * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
020: *
021: * Please contact Sun Microsystems, Inc., 4150 Network Circle, Santa Clara,
022: * CA 95054 USA or visit www.sun.com if you need additional information or
023: * have any questions.
024: */
025:
026: package java.math;
027:
028: /**
029: * A simple bit sieve used for finding prime number candidates. Allows setting
030: * and clearing of bits in a storage array. The size of the sieve is assumed to
031: * be constant to reduce overhead. All the bits of a new bitSieve are zero, and
032: * bits are removed from it by setting them.
033: *
034: * To reduce storage space and increase efficiency, no even numbers are
035: * represented in the sieve (each bit in the sieve represents an odd number).
036: * The relationship between the index of a bit and the number it represents is
037: * given by
038: * N = offset + (2*index + 1);
039: * Where N is the integer represented by a bit in the sieve, offset is some
040: * even integer offset indicating where the sieve begins, and index is the
041: * index of a bit in the sieve array.
042: *
043: * @see BigInteger
044: * @author Michael McCloskey
045: * @since 1.3
046: */
047: class BitSieve {
048: /**
049: * Stores the bits in this bitSieve.
050: */
051: private long bits[];
052:
053: /**
054: * Length is how many bits this sieve holds.
055: */
056: private int length;
057:
058: /**
059: * A small sieve used to filter out multiples of small primes in a search
060: * sieve.
061: */
062: private static BitSieve smallSieve = new BitSieve();
063:
064: /**
065: * Construct a "small sieve" with a base of 0. This constructor is
066: * used internally to generate the set of "small primes" whose multiples
067: * are excluded from sieves generated by the main (package private)
068: * constructor, BitSieve(BigInteger base, int searchLen). The length
069: * of the sieve generated by this constructor was chosen for performance;
070: * it controls a tradeoff between how much time is spent constructing
071: * other sieves, and how much time is wasted testing composite candidates
072: * for primality. The length was chosen experimentally to yield good
073: * performance.
074: */
075: private BitSieve() {
076: length = 150 * 64;
077: bits = new long[(unitIndex(length - 1) + 1)];
078:
079: // Mark 1 as composite
080: set(0);
081: int nextIndex = 1;
082: int nextPrime = 3;
083:
084: // Find primes and remove their multiples from sieve
085: do {
086: sieveSingle(length, nextIndex + nextPrime, nextPrime);
087: nextIndex = sieveSearch(length, nextIndex + 1);
088: nextPrime = 2 * nextIndex + 1;
089: } while ((nextIndex > 0) && (nextPrime < length));
090: }
091:
092: /**
093: * Construct a bit sieve of searchLen bits used for finding prime number
094: * candidates. The new sieve begins at the specified base, which must
095: * be even.
096: */
097: BitSieve(BigInteger base, int searchLen) {
098: /*
099: * Candidates are indicated by clear bits in the sieve. As a candidates
100: * nonprimality is calculated, a bit is set in the sieve to eliminate
101: * it. To reduce storage space and increase efficiency, no even numbers
102: * are represented in the sieve (each bit in the sieve represents an
103: * odd number).
104: */
105: bits = new long[(unitIndex(searchLen - 1) + 1)];
106: length = searchLen;
107: int start = 0;
108:
109: int step = smallSieve.sieveSearch(smallSieve.length, start);
110: int convertedStep = (step * 2) + 1;
111:
112: // Construct the large sieve at an even offset specified by base
113: MutableBigInteger r = new MutableBigInteger();
114: MutableBigInteger q = new MutableBigInteger();
115: do {
116: // Calculate base mod convertedStep
117: r.copyValue(base.mag);
118: r.divideOneWord(convertedStep, q);
119: start = r.value[r.offset];
120:
121: // Take each multiple of step out of sieve
122: start = convertedStep - start;
123: if (start % 2 == 0)
124: start += convertedStep;
125: sieveSingle(searchLen, (start - 1) / 2, convertedStep);
126:
127: // Find next prime from small sieve
128: step = smallSieve.sieveSearch(smallSieve.length, step + 1);
129: convertedStep = (step * 2) + 1;
130: } while (step > 0);
131: }
132:
133: /**
134: * Given a bit index return unit index containing it.
135: */
136: private static int unitIndex(int bitIndex) {
137: return bitIndex >>> 6;
138: }
139:
140: /**
141: * Return a unit that masks the specified bit in its unit.
142: */
143: private static long bit(int bitIndex) {
144: return 1L << (bitIndex & ((1 << 6) - 1));
145: }
146:
147: /**
148: * Get the value of the bit at the specified index.
149: */
150: private boolean get(int bitIndex) {
151: int unitIndex = unitIndex(bitIndex);
152: return ((bits[unitIndex] & bit(bitIndex)) != 0);
153: }
154:
155: /**
156: * Set the bit at the specified index.
157: */
158: private void set(int bitIndex) {
159: int unitIndex = unitIndex(bitIndex);
160: bits[unitIndex] |= bit(bitIndex);
161: }
162:
163: /**
164: * This method returns the index of the first clear bit in the search
165: * array that occurs at or after start. It will not search past the
166: * specified limit. It returns -1 if there is no such clear bit.
167: */
168: private int sieveSearch(int limit, int start) {
169: if (start >= limit)
170: return -1;
171:
172: int index = start;
173: do {
174: if (!get(index))
175: return index;
176: index++;
177: } while (index < limit - 1);
178: return -1;
179: }
180:
181: /**
182: * Sieve a single set of multiples out of the sieve. Begin to remove
183: * multiples of the specified step starting at the specified start index,
184: * up to the specified limit.
185: */
186: private void sieveSingle(int limit, int start, int step) {
187: while (start < limit) {
188: set(start);
189: start += step;
190: }
191: }
192:
193: /**
194: * Test probable primes in the sieve and return successful candidates.
195: */
196: BigInteger retrieve(BigInteger initValue, int certainty,
197: java.util.Random random) {
198: // Examine the sieve one long at a time to find possible primes
199: int offset = 1;
200: for (int i = 0; i < bits.length; i++) {
201: long nextLong = ~bits[i];
202: for (int j = 0; j < 64; j++) {
203: if ((nextLong & 1) == 1) {
204: BigInteger candidate = initValue.add(BigInteger
205: .valueOf(offset));
206: if (candidate.primeToCertainty(certainty, random))
207: return candidate;
208: }
209: nextLong >>>= 1;
210: offset += 2;
211: }
212: }
213: return null;
214: }
215: }
| 