Source: complex.go in package runtime


package runtime

inf2one returns a signed 1 if f is an infinity and a signed 0 otherwise. The sign of the result is the sign of f.

func inf2one(f float64) float64 {
	g := 0.0
	if isInf(f) {
		g = 1.0
	}
	return copysign(g, f)
}

func complex128div(n complex128, m complex128) complex128 {
	var e, f float64 // complex(e, f) = n/m

Algorithm for robust complex division as described in Robert L. Smith: Algorithm 116: Complex division. Commun. ACM 5(8): 435 (1962).

	if abs(real(m)) >= abs(imag(m)) {
		ratio := imag(m) / real(m)
		denom := real(m) + ratio*imag(m)
		e = (real(n) + imag(n)*ratio) / denom
		f = (imag(n) - real(n)*ratio) / denom
	} else {
		ratio := real(m) / imag(m)
		denom := imag(m) + ratio*real(m)
		e = (real(n)*ratio + imag(n)) / denom
		f = (imag(n)*ratio - real(n)) / denom
	}

Correct final result to infinities and zeros if applicable. Matches C99: ISO/IEC 9899:1999 - G.5.1 Multiplicative operators.


		a, b := real(n), imag(n)
		c, d := real(m), imag(m)

		switch {
		case m == 0 && (!isNaN(a) || !isNaN(b)):
			e = copysign(inf, c) * a
			f = copysign(inf, c) * b

		case (isInf(a) || isInf(b)) && isFinite(c) && isFinite(d):
			a = inf2one(a)
			b = inf2one(b)
			e = inf * (a*c + b*d)
			f = inf * (b*c - a*d)

		case (isInf(c) || isInf(d)) && isFinite(a) && isFinite(b):
			c = inf2one(c)
			d = inf2one(d)
			e = 0 * (a*c + b*d)
			f = 0 * (b*c - a*d)
		}
	}

	return complex(e, f)