1 /*
2 * Copyright 1999-2007 Sun Microsystems, Inc. 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. Sun designates this
8 * particular file as subject to the "Classpath" exception as provided
9 * by Sun 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 Sun Microsystems, Inc., 4150 Network Circle, Santa Clara,
22 * CA 95054 USA or visit www.sun.com if you need additional information or
23 * have any 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 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, java.util.Random random) {
197 // Examine the sieve one long at a time to find possible primes
198 int offset = 1;
199 for (int i=0; i<bits.length; i++) {
200 long nextLong = ~bits[i];
201 for (int j=0; j<64; j++) {
202 if ((nextLong & 1) == 1) {
203 BigInteger candidate = initValue.add(
204 BigInteger.valueOf(offset));
205 if (candidate.primeToCertainty(certainty, random))
206 return candidate;
207 }
208 nextLong >>>= 1;
209 offset+=2;
210 }
211 }
212 return null;
213 }
214 }
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