}

  @Benchmark
  int factorial(int reps) {
    int tmp = 0;
    for (int i = 0; i < reps; i++) {
      int j = i & ARRAY_MASK;
      tmp += IntMath.factorial(factorial[j]);
    }
    return tmp;
  }

  @Benchmark
  int binomial(int reps) {
    int tmp = 0;
    for (int i = 0; i < reps; i++) {
      int j = i & ARRAY_MASK;
      tmp += IntMath.binomial(factorial[j], binomial[j]);
    }

  }

  @Benchmark
  int factorial(int reps) {
    int tmp = 0;
    for (int i = 0; i < reps; i++) {
      int j = i & ARRAY_MASK;
      tmp += IntMath.factorial(factorial[j]);
    }
    return tmp;
  }

  @Benchmark
  int binomial(int reps) {
    int tmp = 0;
    for (int i = 0; i < reps; i++) {
      int j = i & ARRAY_MASK;
      tmp += IntMath.binomial(factorial[j], binomial[j]);
    }

      tmp += Double.doubleToRawLongBits(DoubleMath.log2(positiveDoubles[j]));
    }
    return tmp;
  }

  @Benchmark
  long factorial(int reps) {
    long tmp = 0;
    for (int i = 0; i < reps; i++) {
      int j = i & ARRAY_MASK;
      tmp += Double.doubleToRawLongBits(DoubleMath.factorial(factorials[j]));
    }
    return tmp;
  }

  @Benchmark
  int isMathematicalInteger(int reps) {
    int tmp = 0;

      tmp += Double.doubleToRawLongBits(DoubleMath.log2(positiveDoubles[j]));
    }
    return tmp;
  }

  @Benchmark
  long factorial(int reps) {
    long tmp = 0;
    for (int i = 0; i < reps; i++) {
      int j = i & ARRAY_MASK;
      tmp += Double.doubleToRawLongBits(DoubleMath.factorial(factorials[j]));
    }
    return tmp;
  }

  @Benchmark
  int isMathematicalInteger(int reps) {
    int tmp = 0;

      binomials[i] = RANDOM_SOURCE.nextInt(factorials[i] + 1);
    }
  }

  /** Previous version of BigIntegerMath.factorial, kept for timing purposes. */
  private static BigInteger oldSlowFactorial(int n) {
    if (n <= 20) {
      return BigInteger.valueOf(LongMath.factorial(n));
    } else {
      int k = 20;
      return BigInteger.valueOf(LongMath.factorial(k)).multiply(oldSlowFactorial(k, n));
    }
  }

   * <p>This uses an efficient binary recursive algorithm to compute the factorial with balanced
   * multiplies. It also removes all the 2s from the intermediate products (shifting them back in at
   * the end).
   *
   * @throws IllegalArgumentException if {@code n < 0}
   */
  public static BigInteger factorial(int n) {
    checkNonNegative("n", n);

    // If the factorial is small enough, just use LongMath to do it.

   * Double.MAX_VALUE}.
   *
   * <p>The result is within 1 ulp of the true value.
   *
   * @throws IllegalArgumentException if {@code n < 0}
   */
  public static double factorial(int n) {
    checkNonNegative("n", n);
    if (n > MAX_FACTORIAL) {
      return Double.POSITIVE_INFINITY;
    } else {
      // Multiplying the last (n & 0xf) values into their own accumulator gives a more accurate

      double actual = BigIntegerMath.factorial(i).doubleValue();
      double result = DoubleMath.factorial(i);
      assertThat(result).isWithin(Math.ulp(actual)).of(actual);
    }
  }

  public void testFactorialTooHigh() {
    assertThat(DoubleMath.factorial(DoubleMath.MAX_FACTORIAL + 1)).isPositiveInfinity();
    assertThat(DoubleMath.factorial(DoubleMath.MAX_FACTORIAL + 20)).isPositiveInfinity();
  }

  }

  // Depends on the correctness of BigIntegerMath.factorial
  private static void runBinomialTest(int firstN, int lastN) {
    for (int n = firstN; n <= lastN; n++) {
      for (int k = 0; k <= n; k++) {
        BigInteger expected =
            BigIntegerMath.factorial(n)
                .divide(BigIntegerMath.factorial(k))
                .divide(BigIntegerMath.factorial(n - k));

   *
   * @throws IllegalArgumentException if {@code n < 0}
   */
  public static int factorial(int n) {
    checkNonNegative("n", n);
    return (n < factorials.length) ? factorials[n] : Integer.MAX_VALUE;
  }

  private static final int[] factorials = {
    1,
    1,
    1 * 2,
    1 * 2 * 3,
    1 * 2 * 3 * 4,
    1 * 2 * 3 * 4 * 5,
    1 * 2 * 3 * 4 * 5 * 6,