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1 /* |
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2 * Copyright 1999-2007 Sun Microsystems, Inc. All Rights Reserved. |
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3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. |
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4 * |
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5 * This code is free software; you can redistribute it and/or modify it |
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6 * under the terms of the GNU General Public License version 2 only, as |
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7 * published by the Free Software Foundation. Sun designates this |
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8 * particular file as subject to the "Classpath" exception as provided |
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9 * by Sun in the LICENSE file that accompanied this code. |
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10 * |
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11 * This code is distributed in the hope that it will be useful, but WITHOUT |
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12 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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13 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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14 * version 2 for more details (a copy is included in the LICENSE file that |
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15 * accompanied this code). |
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16 * |
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17 * You should have received a copy of the GNU General Public License version |
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18 * 2 along with this work; if not, write to the Free Software Foundation, |
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19 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. |
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20 * |
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21 * Please contact Sun Microsystems, Inc., 4150 Network Circle, Santa Clara, |
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22 * CA 95054 USA or visit www.sun.com if you need additional information or |
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23 * have any questions. |
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24 */ |
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25 |
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26 package java.math; |
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27 |
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28 /** |
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29 * A simple bit sieve used for finding prime number candidates. Allows setting |
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30 * and clearing of bits in a storage array. The size of the sieve is assumed to |
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31 * be constant to reduce overhead. All the bits of a new bitSieve are zero, and |
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32 * bits are removed from it by setting them. |
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33 * |
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34 * To reduce storage space and increase efficiency, no even numbers are |
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35 * represented in the sieve (each bit in the sieve represents an odd number). |
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36 * The relationship between the index of a bit and the number it represents is |
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37 * given by |
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38 * N = offset + (2*index + 1); |
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39 * Where N is the integer represented by a bit in the sieve, offset is some |
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40 * even integer offset indicating where the sieve begins, and index is the |
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41 * index of a bit in the sieve array. |
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42 * |
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43 * @see BigInteger |
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44 * @author Michael McCloskey |
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45 * @since 1.3 |
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46 */ |
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47 class BitSieve { |
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48 /** |
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49 * Stores the bits in this bitSieve. |
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50 */ |
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51 private long bits[]; |
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52 |
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53 /** |
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54 * Length is how many bits this sieve holds. |
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55 */ |
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56 private int length; |
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57 |
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58 /** |
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59 * A small sieve used to filter out multiples of small primes in a search |
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60 * sieve. |
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61 */ |
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62 private static BitSieve smallSieve = new BitSieve(); |
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63 |
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64 /** |
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65 * Construct a "small sieve" with a base of 0. This constructor is |
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66 * used internally to generate the set of "small primes" whose multiples |
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67 * are excluded from sieves generated by the main (package private) |
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68 * constructor, BitSieve(BigInteger base, int searchLen). The length |
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69 * of the sieve generated by this constructor was chosen for performance; |
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70 * it controls a tradeoff between how much time is spent constructing |
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71 * other sieves, and how much time is wasted testing composite candidates |
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72 * for primality. The length was chosen experimentally to yield good |
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73 * performance. |
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74 */ |
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75 private BitSieve() { |
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76 length = 150 * 64; |
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77 bits = new long[(unitIndex(length - 1) + 1)]; |
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78 |
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79 // Mark 1 as composite |
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80 set(0); |
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81 int nextIndex = 1; |
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82 int nextPrime = 3; |
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83 |
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84 // Find primes and remove their multiples from sieve |
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85 do { |
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86 sieveSingle(length, nextIndex + nextPrime, nextPrime); |
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87 nextIndex = sieveSearch(length, nextIndex + 1); |
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88 nextPrime = 2*nextIndex + 1; |
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89 } while((nextIndex > 0) && (nextPrime < length)); |
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90 } |
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91 |
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92 /** |
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93 * Construct a bit sieve of searchLen bits used for finding prime number |
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94 * candidates. The new sieve begins at the specified base, which must |
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95 * be even. |
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96 */ |
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97 BitSieve(BigInteger base, int searchLen) { |
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98 /* |
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99 * Candidates are indicated by clear bits in the sieve. As a candidates |
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100 * nonprimality is calculated, a bit is set in the sieve to eliminate |
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101 * it. To reduce storage space and increase efficiency, no even numbers |
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102 * are represented in the sieve (each bit in the sieve represents an |
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103 * odd number). |
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104 */ |
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105 bits = new long[(unitIndex(searchLen-1) + 1)]; |
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106 length = searchLen; |
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107 int start = 0; |
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108 |
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109 int step = smallSieve.sieveSearch(smallSieve.length, start); |
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110 int convertedStep = (step *2) + 1; |
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111 |
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112 // Construct the large sieve at an even offset specified by base |
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113 MutableBigInteger r = new MutableBigInteger(); |
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114 MutableBigInteger q = new MutableBigInteger(); |
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115 do { |
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116 // Calculate base mod convertedStep |
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117 r.copyValue(base.mag); |
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118 r.divideOneWord(convertedStep, q); |
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119 start = r.value[r.offset]; |
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120 |
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121 // Take each multiple of step out of sieve |
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122 start = convertedStep - start; |
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123 if (start%2 == 0) |
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124 start += convertedStep; |
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125 sieveSingle(searchLen, (start-1)/2, convertedStep); |
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126 |
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127 // Find next prime from small sieve |
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128 step = smallSieve.sieveSearch(smallSieve.length, step+1); |
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129 convertedStep = (step *2) + 1; |
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130 } while (step > 0); |
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131 } |
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132 |
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133 /** |
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134 * Given a bit index return unit index containing it. |
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135 */ |
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136 private static int unitIndex(int bitIndex) { |
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137 return bitIndex >>> 6; |
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138 } |
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139 |
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140 /** |
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141 * Return a unit that masks the specified bit in its unit. |
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142 */ |
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143 private static long bit(int bitIndex) { |
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144 return 1L << (bitIndex & ((1<<6) - 1)); |
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145 } |
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146 |
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147 /** |
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148 * Get the value of the bit at the specified index. |
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149 */ |
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150 private boolean get(int bitIndex) { |
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151 int unitIndex = unitIndex(bitIndex); |
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152 return ((bits[unitIndex] & bit(bitIndex)) != 0); |
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153 } |
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154 |
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155 /** |
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156 * Set the bit at the specified index. |
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157 */ |
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158 private void set(int bitIndex) { |
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159 int unitIndex = unitIndex(bitIndex); |
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160 bits[unitIndex] |= bit(bitIndex); |
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161 } |
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162 |
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163 /** |
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164 * This method returns the index of the first clear bit in the search |
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165 * array that occurs at or after start. It will not search past the |
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166 * specified limit. It returns -1 if there is no such clear bit. |
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167 */ |
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168 private int sieveSearch(int limit, int start) { |
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169 if (start >= limit) |
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170 return -1; |
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171 |
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172 int index = start; |
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173 do { |
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174 if (!get(index)) |
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175 return index; |
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176 index++; |
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177 } while(index < limit-1); |
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178 return -1; |
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179 } |
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180 |
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181 /** |
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182 * Sieve a single set of multiples out of the sieve. Begin to remove |
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183 * multiples of the specified step starting at the specified start index, |
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184 * up to the specified limit. |
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185 */ |
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186 private void sieveSingle(int limit, int start, int step) { |
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187 while(start < limit) { |
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188 set(start); |
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189 start += step; |
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190 } |
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191 } |
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192 |
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193 /** |
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194 * Test probable primes in the sieve and return successful candidates. |
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195 */ |
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196 BigInteger retrieve(BigInteger initValue, int certainty, java.util.Random random) { |
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197 // Examine the sieve one long at a time to find possible primes |
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198 int offset = 1; |
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199 for (int i=0; i<bits.length; i++) { |
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200 long nextLong = ~bits[i]; |
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201 for (int j=0; j<64; j++) { |
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202 if ((nextLong & 1) == 1) { |
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203 BigInteger candidate = initValue.add( |
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204 BigInteger.valueOf(offset)); |
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205 if (candidate.primeToCertainty(certainty, random)) |
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206 return candidate; |
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207 } |
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208 nextLong >>>= 1; |
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209 offset+=2; |
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210 } |
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211 } |
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212 return null; |
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213 } |
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214 } |