| /* |
| * Licensed to the Apache Software Foundation (ASF) under one or more |
| * contributor license agreements. See the NOTICE file distributed with |
| * this work for additional information regarding copyright ownership. |
| * The ASF licenses this file to You under the Apache License, Version 2.0 |
| * (the "License"); you may not use this file except in compliance with |
| * the License. You may obtain a copy of the License at |
| * |
| * http://www.apache.org/licenses/LICENSE-2.0 |
| * |
| * Unless required by applicable law or agreed to in writing, software |
| * distributed under the License is distributed on an "AS IS" BASIS, |
| * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| * See the License for the specific language governing permissions and |
| * limitations under the License. |
| */ |
| |
| package java.math; |
| |
| import java.util.Arrays; |
| |
| /** |
| * Provides primality probabilistic methods. |
| */ |
| class Primality { |
| |
| /** Just to denote that this class can't be instantiated. */ |
| private Primality() {} |
| |
| /** All prime numbers with bit length lesser than 10 bits. */ |
| private static final int[] primes = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, |
| 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, |
| 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, |
| 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, |
| 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, |
| 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, |
| 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, |
| 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, |
| 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, |
| 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, |
| 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, |
| 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, |
| 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, |
| 1013, 1019, 1021 }; |
| |
| /** All {@code BigInteger} prime numbers with bit length lesser than 10 bits. */ |
| private static final BigInteger BIprimes[] = new BigInteger[primes.length]; |
| |
| // /** |
| // * It encodes how many iterations of Miller-Rabin test are need to get an |
| // * error bound not greater than {@code 2<sup>(-100)</sup>}. For example: |
| // * for a {@code 1000}-bit number we need {@code 4} iterations, since |
| // * {@code BITS[3] < 1000 <= BITS[4]}. |
| // */ |
| // private static final int[] BITS = { 0, 0, 1854, 1233, 927, 747, 627, 543, |
| // 480, 431, 393, 361, 335, 314, 295, 279, 265, 253, 242, 232, 223, |
| // 216, 181, 169, 158, 150, 145, 140, 136, 132, 127, 123, 119, 114, |
| // 110, 105, 101, 96, 92, 87, 83, 78, 73, 69, 64, 59, 54, 49, 44, 38, |
| // 32, 26, 1 }; |
| // |
| // /** |
| // * It encodes how many i-bit primes there are in the table for |
| // * {@code i=2,...,10}. For example {@code offsetPrimes[6]} says that from |
| // * index {@code 11} exists {@code 7} consecutive {@code 6}-bit prime |
| // * numbers in the array. |
| // */ |
| // private static final int[][] offsetPrimes = { null, null, { 0, 2 }, |
| // { 2, 2 }, { 4, 2 }, { 6, 5 }, { 11, 7 }, { 18, 13 }, { 31, 23 }, |
| // { 54, 43 }, { 97, 75 } }; |
| |
| static {// To initialize the dual table of BigInteger primes |
| for (int i = 0; i < primes.length; i++) { |
| BIprimes[i] = BigInteger.valueOf(primes[i]); |
| } |
| } |
| |
| /** |
| * It uses the sieve of Eratosthenes to discard several composite numbers in |
| * some appropriate range (at the moment {@code [this, this + 1024]}). After |
| * this process it applies the Miller-Rabin test to the numbers that were |
| * not discarded in the sieve. |
| * |
| * @see BigInteger#nextProbablePrime() |
| */ |
| static BigInteger nextProbablePrime(BigInteger n) { |
| // PRE: n >= 0 |
| int i, j; |
| // int certainty; |
| int gapSize = 1024; // for searching of the next probable prime number |
| int[] modules = new int[primes.length]; |
| boolean isDivisible[] = new boolean[gapSize]; |
| BigInt ni = n.getBigInt(); |
| // If n < "last prime of table" searches next prime in the table |
| if (ni.bitLength() <= 10) { |
| int l = (int)ni.longInt(); |
| if (l < primes[primes.length - 1]) { |
| for (i = 0; l >= primes[i]; i++) {} |
| return BIprimes[i]; |
| } |
| } |
| |
| BigInt startPoint = ni.copy(); |
| BigInt probPrime = new BigInt(); |
| |
| // Fix startPoint to "next odd number": |
| startPoint.addPositiveInt(BigInt.remainderByPositiveInt(ni, 2) + 1); |
| |
| // // To set the improved certainty of Miller-Rabin |
| // j = startPoint.bitLength(); |
| // for (certainty = 2; j < BITS[certainty]; certainty++) { |
| // ; |
| // } |
| |
| // To calculate modules: N mod p1, N mod p2, ... for first primes. |
| for (i = 0; i < primes.length; i++) { |
| modules[i] = BigInt.remainderByPositiveInt(startPoint, primes[i]) - gapSize; |
| } |
| while (true) { |
| // At this point, all numbers in the gap are initialized as |
| // probably primes |
| Arrays.fill(isDivisible, false); |
| // To discard multiples of first primes |
| for (i = 0; i < primes.length; i++) { |
| modules[i] = (modules[i] + gapSize) % primes[i]; |
| j = (modules[i] == 0) ? 0 : (primes[i] - modules[i]); |
| for (; j < gapSize; j += primes[i]) { |
| isDivisible[j] = true; |
| } |
| } |
| // To execute Miller-Rabin for non-divisible numbers by all first |
| // primes |
| for (j = 0; j < gapSize; j++) { |
| if (!isDivisible[j]) { |
| probPrime.putCopy(startPoint); |
| probPrime.addPositiveInt(j); |
| if (probPrime.isPrime(100)) { |
| return new BigInteger(probPrime); |
| } |
| } |
| } |
| startPoint.addPositiveInt(gapSize); |
| } |
| } |
| |
| } |
