millerrabintest.java

来自「一个一元曲线多项式数值演示例子」· Java 代码 · 共 133 行

package numbercruncher.primeutils;

import java.util.*;

import numbercruncher.mathutils.*;

/**
 * An implemention of the the Miller-Rabin test for primality.
 */
public class MillerRabinTest {
  private static MillerRabinStatus status = new MillerRabinStatus();

  /** number to test for primality */
  private int p;
  /** number of times to run the test */
  private int iterations;

  /** caller of the test */
  private MillerRabinCaller caller;

  /**
   * Constructor.
   * @param p the number to test for primality
   * @param iterations the number of times to run the test
   * @param caller the caller of the test
   */
  public MillerRabinTest(int p, int iterations,
                         MillerRabinCaller caller) {
    this.p = p;
    this.iterations = iterations;
    this.caller = caller;
  }

  /**
   * Perform the Miller-Rabin test.
   * @return true if p is probably prime, false if p is composite
   */
  public boolean test() {
    Random random = new Random(0);
    int k = p - 1;
    int s = 0;

    // Shift k to the right s bits to make it odd.
    while ( (k & 1) == 0) {
      k >>= 1;
      ++s;
    }

    status.k = k;
    status.s = s;

    // Run the test with different random base values.
    for (int i = 0; i < iterations; ++i) {

      // Generate a random integer base b.
      int b;
      while ( (b = random.nextInt(p)) <= 1) {
        ; // want 1 < b < p
      }

      status.b = b;

      // Composite?
      if (!test(k, s, b)) {
        return false; // definitely composite
      }
    }

    return true; // most likely prime
  }

  /**
   * Perform the Miller-Rabin test.
   * @param k the value of p-1 shifted right until it is odd
   * @param s the number of right shifts
   * @return true if p is probably prime, false if p is composite
   */
  private boolean test(int k, int s, int b) {
    int pm1 = p - 1;
    int sm1 = s - 1;

    status.i = 0;
    status.code = MillerRabinStatus.DONT_KNOW_YET;

    int r = ModuloArithmetic.raise(b, k, p); // b^k (mod p)
    status.r = r;

    if (r == 1) {
      status.code = MillerRabinStatus.PROBABLY_PRIME;
      reportStatus();

      return true; // probably prime
    }

    // Loop at most s-1 times.
    int i = 0;
    while (r != pm1) {
      reportStatus();
      status.i = ++i;

      if (i > sm1) {
        status.code = MillerRabinStatus.DEFINITELY_COMPOSITE;
        return false; // definitely composite
      }

      r = ModuloArithmetic.raise(r, 2, p); // r^2 (mod p)
      status.r = r;

      if (r == 1) {
        status.code = MillerRabinStatus.DEFINITELY_COMPOSITE;
        reportStatus();

        return false; // definitely composite
      }
    }

    status.code = MillerRabinStatus.PROBABLY_PRIME;
    reportStatus();

    return true; // probably prime
  }

  /**
   * Report the test status back to the caller.
   * @param status the test status
   */
  private void reportStatus() {
    if (caller != null) {
      caller.reportStatus(status);
    }
  }
}