Function Equal

util.go:24–45

Equal returns true if a and b are equal within an absolute tolerance of Epsilon or within a relative tolerance of Epsilon (relative to the largest of the two).

(a, b float64)

// Equal returns true if a and b are equal within an absolute tolerance of Epsilon or within a relative tolerance of Epsilon (relative to the largest of the two).
func Equal(a, b float64) bool {
	// avoid math.Abs
	if a < b {
		return b-a <= Epsilon
	}
	return a-b <= Epsilon
	//return math.Abs(a-b) <= Epsilon // this is much quicker

	// See https://floating-point-gui.de/errors/comparison/ and
	// https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/
	// for more information. To be blunt, the code below may not be appropriate for all cases,
	// especially for small numbers. Since most comparisons involve millimeter scale (the
	// coordinates in a canvas), this is probably OK. We should make sure that computations
	// resulting in small numbers (below Epsilon) should be insignificant in their difference.
	diff := math.Abs(a - b)
	abs := a == b || diff <= Epsilon // handle infinities and absolute epsilon
	if !abs && (a != 0.0 || b != 0.0) {
		// handle relative epsilon for large numbers (relative to largest number)
		return diff/math.Max(math.Abs(a), math.Abs(b)) <= Epsilon
	}
	return abs
}

// Interval returns true if f is in closed interval [lower-Epsilon,upper+Epsilon] where lower and upper can be interchanged.
func Interval(f, lower, upper float64) bool {