math/cmplx: define Pow(0, x) for problematic values of x.

Currently it's always zero, but that is inconsistent with math.Pow
and also plain wrong.
This is a proposal for how it should be defined.
Fixes #7583.

LGTM=rsc
R=golang-codereviews, iant, gobot, rsc
CC=golang-codereviews
https://golang.org/cl/76940044

src/pkg/math/cmplx/cmath_test.go

@@ -656,6 +656,19 @@ func TestPolar(t *testing.T) {
 	}
 }
 func TestPow(t *testing.T) {
+	// Special cases for Pow(0, c).
+	var zero = complex(0, 0)
+	zeroPowers := [][2]complex128{
+		{0, 1 + 0i},
+		{1.5, 0 + 0i},
+		{-1.5, complex(math.Inf(0), 0)},
+		{-1.5 + 1.5i, Inf()},
+	}
+	for _, zp := range zeroPowers {
+		if f := Pow(zero, zp[0]); f != zp[1] {
+			t.Errorf("Pow(%g, %g) = %g, want %g", zero, zp[0], f, zp[1])
+		}
+	}
 	var a = complex(3.0, 3.0)
 	for i := 0; i < len(vc); i++ {
 		if f := Pow(a, vc[i]); !cSoclose(pow[i], f, 4e-15) {

src/pkg/math/cmplx/pow.go

@@ -43,7 +43,25 @@ import "math"
 //    IEEE      -10,+10     30000       9.4e-15     1.5e-15
 
 // Pow returns x**y, the base-x exponential of y.
+// For generalized compatiblity with math.Pow:
+// Pow(0, ±0) returns 1+0i
+// Pow(0, c) for real(c)<0 returns Inf+0i if imag(c) is zero, otherwise Inf+Inf i.
 func Pow(x, y complex128) complex128 {
+	if x == 0 { // Guaranteed also true for x == -0.
+		r, i := real(y), imag(y)
+		switch {
+		case r == 0:
+			return 1
+		case r < 0:
+			if i == 0 {
+				return complex(math.Inf(1), 0)
+			}
+			return Inf()
+		case r > 0:
+			return 0
+		}
+		panic("not reached")
+	}
 	modulus := Abs(x)
 	if modulus == 0 {
 		return complex(0, 0)