compiler: implement complex division

This is hard to do correctly, so copy the relevant files from the Go
compiler itself.

For related discussions:
* https://github.com/golang/go/issues/14644
* https://github.com/golang/go/issues/29846

src/runtime/complex.go

@@ -0,0 +1,65 @@
+// Copyright 2010 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+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 complex64div(n complex64, m complex64) complex64 {
+	return complex64(complex128div(complex128(n), complex128(m)))
+}
+
+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
+	}
+
+	if isNaN(e) && isNaN(f) {
+		// 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)
+}