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));
    }
  }

      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));
    }
  }

      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;

    public abstract boolean noAddOverflow(long a, long b);

    public abstract boolean noMulOverflow(int a, int b);

    public abstract boolean noMulOverflow(long a, long b);
  }

  private final int[] factorials = new int[ARRAY_SIZE];
  private final int[][] binomials = new int[ARRAY_SIZE][2];
  private final int[][] nonnegInt = new int[ARRAY_SIZE][2];
  private final long[][] nonnegLong = new long[ARRAY_SIZE][2];

    public abstract boolean noAddOverflow(long a, long b);

    public abstract boolean noMulOverflow(int a, int b);

    public abstract boolean noMulOverflow(long a, long b);
  }

  private final int[] factorials = new int[ARRAY_SIZE];
  private final int[][] binomials = new int[ARRAY_SIZE][2];
  private final int[][] nonnegInt = new int[ARRAY_SIZE][2];
  private final long[][] nonnegLong = new long[ARRAY_SIZE][2];

      return BigInteger.valueOf(LongMath.factorials[n]);
    }

    // Pre-allocate space for our list of intermediate BigIntegers.
    int approxSize = IntMath.divide(n * IntMath.log2(n, CEILING), Long.SIZE, CEILING);
    ArrayList<BigInteger> bignums = new ArrayList<>(approxSize);

    // Start from the pre-computed maximum long factorial.
    int startingNumber = LongMath.factorials.length;

  public void testConstantsFactorials() {
    long expected = 1;
    for (int i = 0; i < LongMath.factorials.length; i++, expected *= i) {
      assertEquals(expected, LongMath.factorials[i]);
    }
    try {
      LongMath.checkedMultiply(
          LongMath.factorials[LongMath.factorials.length - 1], LongMath.factorials.length);
      fail("Expected ArithmeticException");
    } catch (ArithmeticException expect) {
    }

  public void testConstantsFactorials() {
    long expected = 1;
    for (int i = 0; i < LongMath.factorials.length; i++, expected *= i) {
      assertEquals(expected, LongMath.factorials[i]);
    }
    try {
      LongMath.checkedMultiply(
          LongMath.factorials[LongMath.factorials.length - 1], LongMath.factorials.length);
      fail("Expected ArithmeticException");
    } catch (ArithmeticException expect) {
    }

    if (k > (n >> 1)) {
      k = n - k;
    }
    switch (k) {
      case 0:
        return 1;
      case 1:
        return n;
      default:
        if (n < factorials.length) {
          return factorials[n] / (factorials[k] * factorials[n - k]);
        } else if (k >= biggestBinomials.length || n > biggestBinomials[k]) {
          return Long.MAX_VALUE;