1 /*
2 * Copyright (c) 2014, 2015, Oracle and/or its affiliates. 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. Oracle designates this
8 * particular file as subject to the "Classpath" exception as provided
9 * by Oracle 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 Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
22 * or visit www.oracle.com if you need additional information or have any
23 * questions.
24 */
25
26 /*
27 * @test
28 * @library ..
29 * @bug 8026236 8074460
30 * @summary test primality verification methods in BigInteger (use -Dseed=X to set PRNG seed)
31 * @author bpb
32 * @key randomness
33 */
34 import java.math.BigInteger;
35 import java.util.BitSet;
36 import java.util.List;
37 import java.util.NavigableSet;
38 import java.util.Set;
39 import java.util.SplittableRandom;
40 import java.util.TreeSet;
41 import static java.util.stream.Collectors.toCollection;
42 import static java.util.stream.Collectors.toList;
43
44 public class PrimeTest {
45
46 private static final int DEFAULT_UPPER_BOUND = 1299709; // 100000th prime
47 private static final int DEFAULT_CERTAINTY = 100;
48 private static final int NUM_NON_PRIMES = 10000;
49
50 /**
51 * Run the test.
52 *
53 * @param args The parameters.
54 * @throws Exception on failure
55 */
56 public static void main(String[] args) throws Exception {
57 // Prepare arguments
58 int upperBound = args.length > 0 ? Integer.valueOf(args[0]) : DEFAULT_UPPER_BOUND;
59 int certainty = args.length > 1 ? Integer.valueOf(args[1]) : DEFAULT_CERTAINTY;
60 boolean parallel = args.length > 2 ? Boolean.valueOf(args[2]) : true;
61
62 // Echo parameter settings
63 System.out.println("Upper bound = " + upperBound
64 + "\nCertainty = " + certainty
65 + "\nParallel = " + parallel);
66
67 // Get primes through specified bound (inclusive) and Integer.MAX_VALUE
68 NavigableSet<BigInteger> primes = getPrimes(upperBound);
69
70 // Check whether known primes are identified as such
71 boolean primeTest = checkPrime(primes, certainty, parallel);
72 System.out.println("Prime test result: " + (primeTest ? "SUCCESS" : "FAILURE"));
73 if (!primeTest) {
74 System.err.println("Prime test failed");
75 }
76
77 // Check whether known non-primes are not identified as primes
78 boolean nonPrimeTest = checkNonPrime(primes, certainty);
79 System.out.println("Non-prime test result: " + (nonPrimeTest ? "SUCCESS" : "FAILURE"));
80
81 boolean mersennePrimeTest = checkMersennePrimes(certainty);
82 System.out.println("Mersenne test result: " + (mersennePrimeTest ? "SUCCESS" : "FAILURE"));
83
84 if (!primeTest || !nonPrimeTest || !mersennePrimeTest) {
85 throw new Exception("PrimeTest FAILED!");
86 }
87
88 System.out.println("PrimeTest succeeded!");
89 }
90
91 /**
92 * Create a {@code BitSet} wherein a set bit indicates the corresponding
93 * index plus 2 is prime. That is, if bit N is set, then the integer N + 2
94 * is prime. The values 0 and 1 are intentionally excluded. See the
95 * <a
96 * href="http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes#Algorithm_description">
97 * Sieve of Eratosthenes</a> algorithm description for more information.
98 *
99 * @param upperBound The maximum prime to allow
100 * @return bits indicating which indexes represent primes
101 */
102 private static BitSet createPrimes(int upperBound) {
103 int nbits = upperBound - 1;
104 BitSet bs = new BitSet(nbits);
105 for (int p = 2; p * p < upperBound;) {
106 for (int i = p * p; i < nbits + 2; i += p) {
107 bs.set(i - 2, true);
108 }
109 do {
110 ++p;
111 } while (p > 1 && bs.get(p - 2));
112 }
113 bs.flip(0, nbits);
114 return bs;
115 }
116
117 /**
118 * Load the primes up to the specified bound (inclusive) into a
119 * {@code NavigableSet}, appending the prime {@code Integer.MAX_VALUE}.
120 *
121 * @param upperBound The maximum prime to allow
122 * @return a set of primes
123 */
124 private static NavigableSet<BigInteger> getPrimes(int upperBound) {
125 BitSet bs = createPrimes(upperBound);
126 NavigableSet<BigInteger> primes = bs.stream()
127 .mapToObj(p -> BigInteger.valueOf(p + 2))
128 .collect(toCollection(TreeSet::new));
129 primes.add(BigInteger.valueOf(Integer.MAX_VALUE));
130 System.out.println(String.format("Created %d primes", primes.size()));
131 return primes;
132 }
133
134 /**
135 * Verifies whether the fraction of probable primes detected is at least 1 -
136 * 1/2^certainty.
137 *
138 * @return true if and only if the test succeeds
139 */
140 private static boolean checkPrime(Set<BigInteger> primes,
141 int certainty,
142 boolean parallel) {
143 long probablePrimes = (parallel ? primes.parallelStream() : primes.stream())
144 .filter(bi -> bi.isProbablePrime(certainty))
145 .count();
146
147 // N = certainty / 2
148 // Success if p/t >= 1 - 1/4^N
149 // or (p/t)*4^N >= 4^N - 1
150 // or p*4^N >= t*(4^N - 1)
151 BigInteger p = BigInteger.valueOf(probablePrimes);
152 BigInteger t = BigInteger.valueOf(primes.size());
153 BigInteger fourToTheC = BigInteger.valueOf(4).pow(certainty / 2);
154 BigInteger fourToTheCMinusOne = fourToTheC.subtract(BigInteger.ONE);
155 BigInteger left = p.multiply(fourToTheC);
156 BigInteger right = t.multiply(fourToTheCMinusOne);
157
158 if (left.compareTo(right) < 0) {
159 System.err.println("Probable prime certainty test failed");
160 }
161
162 return left.compareTo(right) >= 0;
163 }
164
165 /**
166 * Verifies whether all {@code BigInteger}s in the tested range for which
167 * {@code isProbablePrime()} returns {@code false} are <i>not</i>
168 * prime numbers.
169 *
170 * @return true if and only if the test succeeds
171 */
172 private static boolean checkNonPrime(NavigableSet<BigInteger> primes,
173 int certainty) {
174 int maxPrime = DEFAULT_UPPER_BOUND;
175 try {
176 maxPrime = primes.last().intValueExact();
177 } catch (ArithmeticException e) {
178 // ignore it
179 }
180
181 // Create a list of non-prime BigIntegers.
182 RandomSeed rndSeed = new RandomSeed(true);
183 System.out.println("Random number generator seed = " + rndSeed.getSeed());
184 List<BigInteger> nonPrimeBigInts = (rndSeed.getSplittableRandom())
185 .ints(NUM_NON_PRIMES, 2, maxPrime).mapToObj(BigInteger::valueOf)
186 .filter(b -> !b.isProbablePrime(certainty)).collect(toList());
187
188 // If there are any non-probable primes also in the primes list then fail.
189 boolean failed = nonPrimeBigInts.stream().anyMatch(primes::contains);
190
191 // In the event, print which purported non-primes were actually prime.
192 if (failed) {
193 for (BigInteger bigInt : nonPrimeBigInts) {
194 if (primes.contains(bigInt)) {
195 System.err.println("Prime value thought to be non-prime: " + bigInt);
196 }
197 }
198 }
199
200 return !failed;
201 }
202
203 /**
204 * Verifies whether a specified subset of Mersenne primes are correctly
205 * identified as being prime. See
206 * <a href="https://en.wikipedia.org/wiki/Mersenne_prime">Mersenne prime</a>
207 * for more information.
208 *
209 * @return true if and only if the test succeeds
210 */
211 private static boolean checkMersennePrimes(int certainty) {
212 int[] MERSENNE_EXPONENTS = {
213 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203,
214 2281, 3217, 4253, // uncomment remaining array elements to make this test run a long time
215 /* 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497,
216 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269,
217 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951,
218 30402457, 32582657, 37156667, 42643801, 43112609, 57885161 */
219 };
220 System.out.println("Checking first "+MERSENNE_EXPONENTS.length+" Mersenne primes");
221
222 boolean result = true;
223 for (int n : MERSENNE_EXPONENTS) {
224 BigInteger mp = BigInteger.ONE.shiftLeft(n).subtract(BigInteger.ONE);
225 if (!mp.isProbablePrime(certainty)) {
226 System.err.println("Mp with p = "+n+" not classified as prime");
227 result = false;
228 }
229 }
230
231 return result;
232 }
233 }