math: handle denormals in Frexp, Ilogb, Ldexp, and Logb

Also:
* document special cases for Frexp and Ldexp
* handle ±Inf in Ldexp
* correctly return -0 on underflow in Ldexp
* test special cases for Ldexp
* test boundary cases for Frexp, Ilogb, Ldexp, and Logb

R=rsc
CC=golang-dev
https://golang.org/cl/3676041

1 files changed, 10 insertions, 0 deletions

diff --git a/src/pkg/math/bits.go b/src/pkg/math/bits.go
index 1a97e76799..a1dca3ed69 100644
--- a/src/pkg/math/bits.go
+++ b/src/pkg/math/bits.go
@@ -47,3 +47,13 @@ func IsInf(f float64, sign int) bool {
 	//	return sign >= 0 && x == uvinf || sign <= 0 && x == uvneginf;
 	return sign >= 0 && f > MaxFloat64 || sign <= 0 && f < -MaxFloat64
 }
+
+// normalize returns a normal number y and exponent exp
+// satisfying x == y × 2**exp. It assumes x is finite and non-zero.
+func normalize(x float64) (y float64, exp int) {
+	const SmallestNormal = 2.2250738585072014e-308 // 2**-1022
+	if Fabs(x) < SmallestNormal {
+		return x * (1 << 52), -52
+	}
+	return x, 0
+}