math: faster Cbrt

For amd64, from 127 to 105 ns/op; for 386, from 208 to 169 ns/op.

R=rsc, golang-dev
CC=golang-dev
https://golang.org/cl/5412056

diff --git a/src/pkg/math/cbrt.go b/src/pkg/math/cbrt.go
index d2b7e910b84868aaa807fc2dc5e0916e195f8447..09edc0eae881ab6f8c6b827898bb03ccde796c3a 100644 (file)
--- a/src/pkg/math/cbrt.go
+++ b/src/pkg/math/cbrt.go
@@ -45,22 +45,21 @@ func Cbrt(x float64) float64 {
                x = -x
                sign = true
        }
-       // Reduce argument
-       f, e := Frexp(x)
+       // Reduce argument and estimate cube root
+       f, e := Frexp(x) // 0.5 <= f < 1.0
        m := e % 3
        if m > 0 {
                m -= 3
                e -= m // e is multiple of 3
        }
-       f = Ldexp(f, m) // 0.125 <= f < 1.0
-
-       // Estimate cube root
        switch m {
        case 0: // 0.5 <= f < 1.0
                f = A1*f + A2 - A3/(A4+f)
-       case -1: // 0.25 <= f < 0.5
+       case -1:
+               f *= 0.5 // 0.25 <= f < 0.5
                f = B1*f + B2 - B3/(B4+f)
-       default: // 0.125 <= f < 0.25
+       default: // m == -2
+               f *= 0.25 // 0.125 <= f < 0.25
                f = C1*f + C2 - C3/(C4+f)
        }
        y := Ldexp(f, e/3) // e/3 = exponent of cube root