// It's definitely safe to multiply into numerator and denominator.
              numerator *= n;
              denominator *= i;
              numeratorBits += nBits;
            } else {
              // It might not be safe to multiply into numerator and denominator,
              // so multiply (numerator / denominator) into result.
              result = multiplyFraction(result, numerator, denominator);
              numerator = n;

func TestCeilFrac(t *testing.T) {
	cases := []struct {
		numerator, denominator, ceiling int64
	}{
		{0, 1, 0},
		{-1, 2, 0},
		{1, 2, 1},
		{1, 1, 1},
		{3, 2, 2},
		{54, 11, 5},
		{45, 11, 5},
		{-4, 3, -1},
		{4, -3, -1},
		{-4, -3, 2},
		{3, 0, 0},
	}
	for i, testCase := range cases {
		ceiling := ceilFrac(testCase.numerator, testCase.denominator)
		if ceiling != testCase.ceiling {

}

// ceilFrac takes a numerator and denominator representing a fraction
// and returns its ceiling. If denominator is 0, it returns 0 instead
// of crashing.
func ceilFrac(numerator, denominator int64) (ceil int64) {
	if denominator == 0 {
		// do nothing on invalid input
		return ceil
	}
	// Make denominator positive
	if denominator < 0 {
		numerator = -numerator
		denominator = -denominator
	}