math: faster Sincos
Sincos via sincos.go is 35.4 ns/op, via sincos_amd64.s is 37.4 ns/op on 2.53 GHz Intel Core 2 Duo (Mac OS X).
R=rsc, golang-dev
CC=golang-dev
https://golang.org/cl/5447045
diff --git a/src/pkg/math/Makefile b/src/pkg/math/Makefile
index 5472dc1..ad012b64c 100644
--- a/src/pkg/math/Makefile
+++ b/src/pkg/math/Makefile
@@ -15,7 +15,6 @@
exp_amd64.$O\
hypot_amd64.$O\
log_amd64.$O\
- sincos_amd64.$O\
sqrt_amd64.$O\
OFILES_386=\
diff --git a/src/pkg/math/sincos.go b/src/pkg/math/sincos.go
index e8261bc..f5412fd 100644
--- a/src/pkg/math/sincos.go
+++ b/src/pkg/math/sincos.go
@@ -4,9 +4,66 @@
package math
+// Coefficients _sin[] and _cos[] are found in pkg/math/sin.go.
+
// Sincos(x) returns Sin(x), Cos(x).
//
// Special conditions are:
+// Sincos(±0) = ±0, 1
// Sincos(±Inf) = NaN, NaN
// Sincos(NaN) = NaN, NaN
-func Sincos(x float64) (sin, cos float64) { return Sin(x), Cos(x) }
+func Sincos(x float64) (sin, cos float64) {
+ const (
+ PI4A = 7.85398125648498535156E-1 // 0x3fe921fb40000000, Pi/4 split into three parts
+ PI4B = 3.77489470793079817668E-8 // 0x3e64442d00000000,
+ PI4C = 2.69515142907905952645E-15 // 0x3ce8469898cc5170,
+ M4PI = 1.273239544735162542821171882678754627704620361328125 // 4/pi
+ )
+ // TODO(rsc): Remove manual inlining of IsNaN, IsInf
+ // when compiler does it for us
+ // special cases
+ switch {
+ case x == 0:
+ return x, 1 // return ±0.0, 1.0
+ case x != x || x < -MaxFloat64 || x > MaxFloat64: // IsNaN(x) || IsInf(x, 0):
+ return NaN(), NaN()
+ }
+
+ // make argument positive
+ sinSign, cosSign := false, false
+ if x < 0 {
+ x = -x
+ sinSign = true
+ }
+
+ j := int64(x * M4PI) // integer part of x/(Pi/4), as integer for tests on the phase angle
+ y := float64(j) // integer part of x/(Pi/4), as float
+
+ if j&1 == 1 { // map zeros to origin
+ j += 1
+ y += 1
+ }
+ j &= 7 // octant modulo 2Pi radians (360 degrees)
+ if j > 3 { // reflect in x axis
+ j -= 4
+ sinSign, cosSign = !sinSign, !cosSign
+ }
+ if j > 1 {
+ cosSign = !cosSign
+ }
+
+ z := ((x - y*PI4A) - y*PI4B) - y*PI4C // Extended precision modular arithmetic
+ zz := z * z
+ cos = 1.0 - 0.5*zz + zz*zz*((((((_cos[0]*zz)+_cos[1])*zz+_cos[2])*zz+_cos[3])*zz+_cos[4])*zz+_cos[5])
+ sin = z + z*zz*((((((_sin[0]*zz)+_sin[1])*zz+_sin[2])*zz+_sin[3])*zz+_sin[4])*zz+_sin[5])
+ if j == 1 || j == 2 {
+ sin, cos = cos, sin
+ }
+ if cosSign {
+ cos = -cos
+ }
+ if sinSign {
+ sin = -sin
+ }
+ return
+}
