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| 1 | /* | ||
| 2 | * Copyright (c) 1999, 2007, Oracle and/or its affiliates. All rights reserved. | ||
| 3 | * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. | ||
| 4 | * | ||
| 5 | * This code is free software; you can redistribute it and/or modify it | ||
| 6 | * under the terms of the GNU General Public License version 2 only, as | ||
| 7 | * published by the Free Software Foundation. Oracle designates this | ||
| 8 | * particular file as subject to the "Classpath" exception as provided | ||
| 9 | * by Oracle in the LICENSE file that accompanied this code. | ||
| 10 | * | ||
| 11 | * This code is distributed in the hope that it will be useful, but WITHOUT | ||
| 12 | * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | ||
| 13 | * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | ||
| 14 | * version 2 for more details (a copy is included in the LICENSE file that | ||
| 15 | * accompanied this code). | ||
| 16 | * | ||
| 17 | * You should have received a copy of the GNU General Public License version | ||
| 18 | * 2 along with this work; if not, write to the Free Software Foundation, | ||
| 19 | * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. | ||
| 20 | * | ||
| 21 | * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA | ||
| 22 | * or visit www.oracle.com if you need additional information or have any | ||
| 23 | * questions. | ||
| 24 | */ | ||
| 25 | |||
| 26 | package java.math; | ||
| 27 | |||
| 28 | /** | ||
| 29 | * A simple bit sieve used for finding prime number candidates. Allows setting | ||
| 30 | * and clearing of bits in a storage array. The size of the sieve is assumed to | ||
| 31 | * be constant to reduce overhead. All the bits of a new bitSieve are zero, and | ||
| 32 | * bits are removed from it by setting them. | ||
| 33 | * | ||
| 34 | * To reduce storage space and increase efficiency, no even numbers are | ||
| 35 | * represented in the sieve (each bit in the sieve represents an odd number). | ||
| 36 | * The relationship between the index of a bit and the number it represents is | ||
| 37 | * given by | ||
| 38 | * N = offset + (2*index + 1); | ||
| 39 | * Where N is the integer represented by a bit in the sieve, offset is some | ||
| 40 | * even integer offset indicating where the sieve begins, and index is the | ||
| 41 | * index of a bit in the sieve array. | ||
| 42 | * | ||
| 43 | * @see BigInteger | ||
| 44 | * @author Michael McCloskey | ||
| 45 | * @since 1.3 | ||
| 46 | */ | ||
| 47 | class BitSieve { | ||
| 48 | /** | ||
| 49 | * Stores the bits in this bitSieve. | ||
| 50 | */ | ||
| 51 | private long bits[]; | ||
| 52 | |||
| 53 | /** | ||
| 54 | * Length is how many bits this sieve holds. | ||
| 55 | */ | ||
| 56 | private int length; | ||
| 57 | |||
| 58 | /** | ||
| 59 | * A small sieve used to filter out multiples of small primes in a search | ||
| 60 | * sieve. | ||
| 61 | */ | ||
| 62 | private static BitSieve smallSieve = new BitSieve(); | ||
| 63 | |||
| 64 | /** | ||
| 65 | * Construct a "small sieve" with a base of 0. This constructor is | ||
| 66 | * used internally to generate the set of "small primes" whose multiples | ||
| 67 | * are excluded from sieves generated by the main (package private) | ||
| 68 | * constructor, BitSieve(BigInteger base, int searchLen). The length | ||
| 69 | * of the sieve generated by this constructor was chosen for performance; | ||
| 70 | * it controls a tradeoff between how much time is spent constructing | ||
| 71 | * other sieves, and how much time is wasted testing composite candidates | ||
| 72 | * for primality. The length was chosen experimentally to yield good | ||
| 73 | * performance. | ||
| 74 | */ | ||
| 75 | private BitSieve() { | ||
| 76 | length = 150 * 64; | ||
| 77 | bits = new long[(unitIndex(length - 1) + 1)]; | ||
| 78 | |||
| 79 | // Mark 1 as composite | ||
| 80 | set(0); | ||
| 81 | int nextIndex = 1; | ||
| 82 | int nextPrime = 3; | ||
| 83 | |||
| 84 | // Find primes and remove their multiples from sieve | ||
| 85 | do { | ||
| 86 | sieveSingle(length, nextIndex + nextPrime, nextPrime); | ||
| 87 | nextIndex = sieveSearch(length, nextIndex + 1); | ||
| 88 | nextPrime = 2*nextIndex + 1; | ||
| 89 | } while((nextIndex > 0) && (nextPrime < length)); | ||
| 90 | } | ||
| 91 | |||
| 92 | /** | ||
| 93 | * Construct a bit sieve of searchLen bits used for finding prime number | ||
| 94 | * candidates. The new sieve begins at the specified base, which must | ||
| 95 | * be even. | ||
| 96 | */ | ||
| 97 | BitSieve(BigInteger base, int searchLen) { | ||
| 98 | /* | ||
| 99 | * 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 b = new MutableBigInteger(base); | ||
| 114 | MutableBigInteger q = new MutableBigInteger(); | ||
| 115 | do { | ||
| 116 | // Calculate base mod convertedStep | ||
| 117 | start = b.divideOneWord(convertedStep, q); | ||
| 118 | |||
| 119 | // Take each multiple of step out of sieve | ||
| 120 | start = convertedStep - start; | ||
| 121 | if (start%2 == 0) | ||
| 122 | start += convertedStep; | ||
| 123 | sieveSingle(searchLen, (start-1)/2, convertedStep); | ||
| 124 | |||
| 125 | // Find next prime from small sieve | ||
| 126 | step = smallSieve.sieveSearch(smallSieve.length, step+1); | ||
| 127 | convertedStep = (step *2) + 1; | ||
| 128 | } while (step > 0); | ||
| 129 | } | ||
| 130 | |||
| 131 | /** | ||
| 132 | * Given a bit index return unit index containing it. | ||
| 133 | */ | ||
| 134 | private static int unitIndex(int bitIndex) { | ||
| 135 | return bitIndex >>> 6; | ||
| 136 | } | ||
| 137 | |||
| 138 | /** | ||
| 139 | * Return a unit that masks the specified bit in its unit. | ||
| 140 | */ | ||
| 141 | private static long bit(int bitIndex) { | ||
| 142 | return 1L << (bitIndex & ((1<<6) - 1)); | ||
| 143 | } | ||
| 144 | |||
| 145 | /** | ||
| 146 | * Get the value of the bit at the specified index. | ||
| 147 | */ | ||
| 148 | private boolean get(int bitIndex) { | ||
| 149 | int unitIndex = unitIndex(bitIndex); | ||
| 150 | return ((bits[unitIndex] & bit(bitIndex)) != 0); | ||
| 151 | } | ||
| 152 | |||
| 153 | /** | ||
| 154 | * Set the bit at the specified index. | ||
| 155 | */ | ||
| 156 | private void set(int bitIndex) { | ||
| 157 | int unitIndex = unitIndex(bitIndex); | ||
| 158 | bits[unitIndex] |= bit(bitIndex); | ||
| 159 | } | ||
| 160 | |||
| 161 | /** | ||
| 162 | * This method returns the index of the first clear bit in the search | ||
| 163 | * array that occurs at or after start. It will not search past the | ||
| 164 | * specified limit. It returns -1 if there is no such clear bit. | ||
| 165 | */ | ||
| 166 | private int sieveSearch(int limit, int start) { | ||
| 167 | if (start >= limit) | ||
| 168 | return -1; | ||
| 169 | |||
| 170 | int index = start; | ||
| 171 | do { | ||
| 172 | if (!get(index)) | ||
| 173 | return index; | ||
| 174 | index++; | ||
| 175 | } while(index < limit-1); | ||
| 176 | return -1; | ||
| 177 | } | ||
| 178 | |||
| 179 | /** | ||
| 180 | * Sieve a single set of multiples out of the sieve. Begin to remove | ||
| 181 | * multiples of the specified step starting at the specified start index, | ||
| 182 | * up to the specified limit. | ||
| 183 | */ | ||
| 184 | private void sieveSingle(int limit, int start, int step) { | ||
| 185 | while(start < limit) { | ||
| 186 | set(start); | ||
| 187 | start += step; | ||
| 188 | } | ||
| 189 | } | ||
| 190 | |||
| 191 | /** | ||
| 192 | * Test probable primes in the sieve and return successful candidates. | ||
| 193 | */ | ||
| 194 | BigInteger retrieve(BigInteger initValue, int certainty, java.util.Random random) { | ||
| 195 | // Examine the sieve one long at a time to find possible primes | ||
| 196 | int offset = 1; | ||
| 197 | for (int i=0; i<bits.length; i++) { | ||
| 198 | long nextLong = ~bits[i]; | ||
| 199 | for (int j=0; j<64; j++) { | ||
| 200 | if ((nextLong & 1) == 1) { | ||
| 201 | BigInteger candidate = initValue.add( | ||
| 202 | BigInteger.valueOf(offset)); | ||
| 203 | if (candidate.primeToCertainty(certainty, random)) | ||
| 204 | return candidate; | ||
| 205 | } | ||
| 206 | nextLong >>>= 1; | ||
| 207 | offset+=2; | ||
| 208 | } | ||
| 209 | } | ||
| 210 | return null; | ||
| 211 | } | ||
| 212 | } | ||