/*
* 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);
}
}
}