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