math: use portable Exp instead of 387 instructions on 386

The 387 implementation is less accurate and slower.

name     old time/op  new time/op  delta
Exp-8    29.7ns ± 2%  24.0ns ± 2%  -19.08%  (p=0.000 n=10+10)

This makes Gamma more accurate too.

Change-Id: Iad33b9cce0b087ccbce3e08ba7a6d285c4999d02
Reviewed-on: https://go-review.googlesource.com/30230
Run-TryBot: Russ Cox <rsc@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Quentin Smith <quentin@golang.org>
Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>

diff --git a/src/math/all_test.go b/src/math/all_test.go
index 7d604b3e8baf73f66360f9a38bcfd8558925523f..882400527b24d2aa52898e92049ed1c3546900b6 100644 (file)
--- a/src/math/all_test.go
+++ b/src/math/all_test.go
@@ -1974,7 +1974,7 @@ func TestExp(t *testing.T) {
 
 func testExp(t *testing.T, Exp func(float64) float64, name string) {
        for i := 0; i < len(vf); i++ {
-               if f := Exp(vf[i]); !close(exp[i], f) {
+               if f := Exp(vf[i]); !veryclose(exp[i], f) {
                        t.Errorf("%s(%g) = %g, want %g", name, vf[i], f, exp[i])
                }
        }

diff --git a/src/math/exp_386.s b/src/math/exp_386.s
index 18a92efd3ecef5e82c7336ace46c1ecb38a5ac1a..9d63295c60bac9cbed3321eee92c56cc1df35fe2 100644 (file)
--- a/src/math/exp_386.s
+++ b/src/math/exp_386.s
@@ -6,36 +6,6 @@
 
 // func Exp(x float64) float64
 TEXT ·Exp(SB),NOSPLIT,$0
-// test bits for not-finite
-       MOVL    x_hi+4(FP), AX
-       ANDL    $0x7ff00000, AX
-       CMPL    AX, $0x7ff00000
-       JEQ     not_finite
-       FLDL2E                // F0=log2(e)
-       FMULD   x+0(FP), F0   // F0=x*log2(e)
-       FMOVD   F0, F1        // F0=x*log2(e), F1=x*log2(e)
-       FRNDINT               // F0=int(x*log2(e)), F1=x*log2(e)
-       FSUBD   F0, F1        // F0=int(x*log2(e)), F1=x*log2(e)-int(x*log2(e))
-       FXCHD   F0, F1        // F0=x*log2(e)-int(x*log2(e)), F1=int(x*log2(e))
-       F2XM1                 // F0=2**(x*log2(e)-int(x*log2(e)))-1, F1=int(x*log2(e))
-       FLD1                  // F0=1, F1=2**(x*log2(e)-int(x*log2(e)))-1, F2=int(x*log2(e))
-       FADDDP  F0, F1        // F0=2**(x*log2(e)-int(x*log2(e))), F1=int(x*log2(e))
-       FSCALE                // F0=e**x, F1=int(x*log2(e))
-       FMOVDP  F0, F1        // F0=e**x
-       FMOVDP  F0, ret+8(FP)
-       RET
-not_finite:
-// test bits for -Inf
-       MOVL    x_hi+4(FP), BX
-       MOVL    x_lo+0(FP), CX
-       CMPL    BX, $0xfff00000
-       JNE     not_neginf
-       CMPL    CX, $0
-       JNE     not_neginf
-       FLDZ                  // F0=0
-       FMOVDP  F0, ret+8(FP)
-       RET
-not_neginf:
-       MOVL    CX, ret_lo+8(FP)
-       MOVL    BX, ret_hi+12(FP)
-       RET
+       // Used to use 387 assembly (FLDL2E+F2XM1) here,
+       // but it was both slower and less accurate than the portable Go code.
+       JMP ·exp(SB)