1 /* 2 * Licensed to the Apache Software Foundation (ASF) under one or more 3 * contributor license agreements. See the NOTICE file distributed with 4 * this work for additional information regarding copyright ownership. 5 * The ASF licenses this file to You under the Apache License, Version 2.0 6 * (the "License"); you may not use this file except in compliance with 7 * the License. You may obtain a copy of the License at 8 * 9 * http://www.apache.org/licenses/LICENSE-2.0 10 * 11 * Unless required by applicable law or agreed to in writing, software 12 * distributed under the License is distributed on an "AS IS" BASIS, 13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 14 * See the License for the specific language governing permissions and 15 * limitations under the License. 16 */ 17 18 // BEGIN android-note 19 // Since the original Harmony Code of the BigInteger class was strongly modified, 20 // in order to use the more efficient OpenSSL BIGNUM implementation, 21 // no android-modification-tags were placed, at all. 22 // END android-note 23 24 package java.math; 25 26 import java.util.Arrays; 27 28 /** 29 * Provides primality probabilistic methods. 30 */ 31 class Primality { 32 33 /** Just to denote that this class can't be instantiated. */ 34 private Primality() {} 35 36 /** All prime numbers with bit length lesser than 10 bits. */ 37 private static final int primes[] = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 38 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 39 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 40 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 41 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 42 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 43 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 44 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 45 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 46 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 47 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 48 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 49 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 50 1013, 1019, 1021 }; 51 52 /** All {@code BigInteger} prime numbers with bit length lesser than 10 bits. */ 53 private static final BigInteger BIprimes[] = new BigInteger[primes.length]; 54 55 // /** 56 // * It encodes how many iterations of Miller-Rabin test are need to get an 57 // * error bound not greater than {@code 2<sup>(-100)</sup>}. For example: 58 // * for a {@code 1000}-bit number we need {@code 4} iterations, since 59 // * {@code BITS[3] < 1000 <= BITS[4]}. 60 // */ 61 // private static final int[] BITS = { 0, 0, 1854, 1233, 927, 747, 627, 543, 62 // 480, 431, 393, 361, 335, 314, 295, 279, 265, 253, 242, 232, 223, 63 // 216, 181, 169, 158, 150, 145, 140, 136, 132, 127, 123, 119, 114, 64 // 110, 105, 101, 96, 92, 87, 83, 78, 73, 69, 64, 59, 54, 49, 44, 38, 65 // 32, 26, 1 }; 66 // 67 // /** 68 // * It encodes how many i-bit primes there are in the table for 69 // * {@code i=2,...,10}. For example {@code offsetPrimes[6]} says that from 70 // * index {@code 11} exists {@code 7} consecutive {@code 6}-bit prime 71 // * numbers in the array. 72 // */ 73 // private static final int[][] offsetPrimes = { null, null, { 0, 2 }, 74 // { 2, 2 }, { 4, 2 }, { 6, 5 }, { 11, 7 }, { 18, 13 }, { 31, 23 }, 75 // { 54, 43 }, { 97, 75 } }; 76 77 static {// To initialize the dual table of BigInteger primes 78 for (int i = 0; i < primes.length; i++) { 79 BIprimes[i] = BigInteger.valueOf(primes[i]); 80 } 81 } 82 83 /** 84 * It uses the sieve of Eratosthenes to discard several composite numbers in 85 * some appropriate range (at the moment {@code [this, this + 1024]}). After 86 * this process it applies the Miller-Rabin test to the numbers that were 87 * not discarded in the sieve. 88 * 89 * @see BigInteger#nextProbablePrime() 90 * @see #millerRabin(BigInteger, int) 91 */ 92 static BigInteger nextProbablePrime(BigInteger n) { 93 // PRE: n >= 0 94 int i, j; 95 // int certainty; 96 int gapSize = 1024; // for searching of the next probable prime number 97 int modules[] = new int[primes.length]; 98 boolean isDivisible[] = new boolean[gapSize]; 99 BigInt ni = n.bigInt; 100 // If n < "last prime of table" searches next prime in the table 101 if (ni.bitLength() <= 10) { 102 int l = (int)ni.longInt(); 103 if (l < primes[primes.length - 1]) { 104 for (i = 0; l >= primes[i]; i++) {} 105 return BIprimes[i]; 106 } 107 } 108 109 BigInt startPoint = ni.copy(); 110 BigInt probPrime = new BigInt(); 111 112 // Fix startPoint to "next odd number": 113 startPoint.addPositiveInt(BigInt.remainderByPositiveInt(ni, 2) + 1); 114 115 // // To set the improved certainty of Miller-Rabin 116 // j = startPoint.bitLength(); 117 // for (certainty = 2; j < BITS[certainty]; certainty++) { 118 // ; 119 // } 120 121 // To calculate modules: N mod p1, N mod p2, ... for first primes. 122 for (i = 0; i < primes.length; i++) { 123 modules[i] = BigInt.remainderByPositiveInt(startPoint, primes[i]) - gapSize; 124 } 125 while (true) { 126 // At this point, all numbers in the gap are initialized as 127 // probably primes 128 Arrays.fill(isDivisible, false); 129 // To discard multiples of first primes 130 for (i = 0; i < primes.length; i++) { 131 modules[i] = (modules[i] + gapSize) % primes[i]; 132 j = (modules[i] == 0) ? 0 : (primes[i] - modules[i]); 133 for (; j < gapSize; j += primes[i]) { 134 isDivisible[j] = true; 135 } 136 } 137 // To execute Miller-Rabin for non-divisible numbers by all first 138 // primes 139 for (j = 0; j < gapSize; j++) { 140 if (!isDivisible[j]) { 141 probPrime.putCopy(startPoint); 142 probPrime.addPositiveInt(j); 143 if (probPrime.isPrime(100, null, null)) { 144 return new BigInteger(probPrime); 145 } 146 } 147 } 148 startPoint.addPositiveInt(gapSize); 149 } 150 } 151 152 } 153
