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 }