*
     * It helps to consider the real number signif = absX * 2^(SIGNIFICAND_BITS - exponent).
     */
    int shift = exponent - SIGNIFICAND_BITS - 1;
    long twiceSignifFloor = absX.shiftRight(shift).longValue();
    long signifFloor = twiceSignifFloor >> 1;
    signifFloor &= SIGNIFICAND_MASK; // remove the implied bit

    /*
     * We round up if either the fractional part of signif is strictly greater than 0.5 (which is

            new Foo("b", 1, null));
    for (Foo a : instances) {
      for (Foo b : instances) {
        int comparedUsingComparisonChain = signum(comparatorUsingComparisonChain.compare(a, b));
        int comparedUsingComparatorMethods = signum(comparatorUsingComparatorMethods.compare(a, b));
        assertWithMessage("%s vs %s", a, b)
            .that(comparedUsingComparatorMethods)

      throw new IllegalArgumentException(role + " (" + x + ") must be > 0");
    }
    return x;
  }

  @CanIgnoreReturnValue
  static BigInteger checkPositive(String role, BigInteger x) {
    if (x.signum() <= 0) {
      throw new IllegalArgumentException(role + " (" + x + ") must be > 0");
    }
    return x;
  }

  @CanIgnoreReturnValue
  static int checkNonNegative(String role, int x) {
    if (x < 0) {

   */
  static BigInteger randomPositiveBigInteger(int numBits) {
    BigInteger result;
    do {
      result = randomNonNegativeBigInteger(numBits);
    } while (result.signum() == 0);
    return result;
  }

  /**
   * Generates a number in [0, 2^numBits) with an exponential distribution. The floor of the log2 of

   */
  static BigInteger randomPositiveBigInteger(int numBits) {
    BigInteger result;
    do {
      result = randomNonNegativeBigInteger(numBits);
    } while (result.signum() == 0);
    return result;
  }

  /**
   * Generates a number in [0, 2^numBits) with an exponential distribution. The floor of the log2 of

     *
     * It helps to consider the real number signif = absX * 2^(SIGNIFICAND_BITS - exponent).
     */
    int shift = exponent - SIGNIFICAND_BITS - 1;
    long twiceSignifFloor = absX.shiftRight(shift).longValue();
    long signifFloor = twiceSignifFloor >> 1;
    signifFloor &= SIGNIFICAND_MASK; // remove the implied bit

    /*
     * We round up if either the fractional part of signif is strictly greater than 0.5 (which is

    @Override
    double roundToDoubleArbitrarily(BigDecimal bigDecimal) {
      return bigDecimal.doubleValue();
    }

    @Override
    int sign(BigDecimal bigDecimal) {
      return bigDecimal.signum();
    }

    @Override
    BigDecimal toX(double d, RoundingMode mode) {
      return new BigDecimal(d);
    }

    @Override
    BigDecimal minus(BigDecimal a, BigDecimal b) {

    @Override
    double roundToDoubleArbitrarily(BigDecimal bigDecimal) {
      return bigDecimal.doubleValue();
    }

    @Override
    int sign(BigDecimal bigDecimal) {
      return bigDecimal.signum();
    }

    @Override
    BigDecimal toX(double d, RoundingMode mode) {
      return new BigDecimal(d);
    }

    @Override
    BigDecimal minus(BigDecimal a, BigDecimal b) {

     * deal with the cases where rounding towards 0 is wrong, which typically depends on the sign of
     * p / q.
     *
     * signum is 1 if p and q are both nonnegative or both negative, and -1 otherwise.
     */
    int signum = 1 | (int) ((p ^ q) >> (Long.SIZE - 1));
    boolean increment;
    switch (mode) {
      case UNNECESSARY:

        int expected = DoubleMath.fuzzyEquals(a, b, tolerance) ? 0 : Double.compare(a, b);
        int actual = DoubleMath.fuzzyCompare(a, b, tolerance);
        assertEquals(Integer.signum(expected), Integer.signum(actual));
      }
    }
  }

  public void testFuzzyCompareBadTolerance() {
    for (double tolerance : BAD_TOLERANCE_CANDIDATES) {