math: amd64 versions of exp and fabs

Benchmark of exp to 28 ns/op from 64 ns/op,
on 2.53GHz Intel Core 2 Duo.

R=rsc
CC=golang-dev
https://golang.org/cl/1594041

src/pkg/math/Makefile

@@ -7,6 +7,8 @@ include ../../Make.$(GOARCH)
 TARG=math
 
 OFILES_amd64=\
+	exp_amd64.$O\
+	fabs_amd64.$O\
 	fdim_amd64.$O\
 	sqrt_amd64.$O\
 
@@ -48,6 +50,7 @@ ALLGOFILES=\
 	copysign.go\
 	erf.go\
 	exp.go\
+	exp2.go\
 	expm1.go\
 	fabs.go\
 	fdim.go\

src/pkg/math/all_test.go

@@ -2343,9 +2343,9 @@ func BenchmarkExp2(b *testing.B) {
 	}
 }
 
-func BenchmarkFloor(b *testing.B) {
+func BenchmarkFabs(b *testing.B) {
 	for i := 0; i < b.N; i++ {
-		Floor(.5)
+		Fabs(.5)
 	}
 }
 
@@ -2355,6 +2355,12 @@ func BenchmarkFdim(b *testing.B) {
 	}
 }
 
+func BenchmarkFloor(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		Floor(.5)
+	}
+}
+
 func BenchmarkFmax(b *testing.B) {
 	for i := 0; i < b.N; i++ {
 		Fmax(10, 3)
@@ -2445,15 +2451,15 @@ func BenchmarkLogb(b *testing.B) {
 	}
 }
 
-func BenchmarkLog10(b *testing.B) {
+func BenchmarkLog1p(b *testing.B) {
 	for i := 0; i < b.N; i++ {
-		Log10(.5)
+		Log1p(.5)
 	}
 }
 
-func BenchmarkLog1p(b *testing.B) {
+func BenchmarkLog10(b *testing.B) {
 	for i := 0; i < b.N; i++ {
-		Log1p(.5)
+		Log10(.5)
 	}
 }
 

src/pkg/math/exp.go

@@ -139,8 +139,3 @@ func Exp(x float64) float64 {
 	// TODO(rsc): make sure Ldexp can handle boundary k
 	return Ldexp(y, k)
 }
-
-// Exp2 returns 2**x, the base-2 exponential of x.
-//
-// Special cases are the same as Exp.
-func Exp2(x float64) float64 { return Exp(x * Ln2) }

src/pkg/math/exp2.go

+// Copyright 2010 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package math
+
+// Exp2 returns 2**x, the base-2 exponential of x.
+//
+// Special cases are the same as Exp.
+func Exp2(x float64) float64 { return Exp(x * Ln2) }

src/pkg/math/exp_amd64.s

+// Copyright 2010 The Go Authors.  All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// The method is based on a paper by Naoki Shibata: "Efficient evaluation
+// methods of elementary functions suitable for SIMD computation", Proc.
+// of International Supercomputing Conference 2010 (ISC'10), pp. 25 -- 32
+// (May 2010). The paper is available at
+// http://www.springerlink.com/content/340228x165742104/
+//
+// The original code and the constants below are from the author's
+// implementation available at http://freshmeat.net/projects/sleef.
+// The README file says, "The software is in public domain.
+// You can use the software without any obligation."
+//
+// This code is a simplified version of the original.
+
+#define LN2 0.6931471805599453094172321214581766 // log_e(2)
+#define LOG2E 1.4426950408889634073599246810018920 // 1/LN2
+#define LN2U 0.69314718055966295651160180568695068359375 // upper half LN2
+#define LN2L 0.28235290563031577122588448175013436025525412068e-12 // lower half LN2
+
+// func Exp(x float64) float64
+TEXT ·Exp(SB),7,$0
+// test bits for not-finite
+	MOVQ    x+0(FP), AX
+	MOVQ    $0x7ff0000000000000, BX
+	ANDQ    BX, AX
+	CMPQ    BX, AX
+	JEQ     not_finite
+	MOVSD   x+0(FP), X0
+	MOVSD   $LOG2E, X1
+	MULSD   X0, X1
+	CVTTSD2SQ X1, BX // BX = exponent
+	CVTSQ2SD BX, X1
+	MOVSD   $LN2U, X2
+	MULSD   X1, X2
+	SUBSD   X2, X0
+	MOVSD   $LN2L, X2
+	MULSD   X1, X2
+	SUBSD   X2, X0
+	// reduce argument
+	MOVSD   $0.0625, X1
+	MULSD   X1, X0
+	// Taylor series evaluation
+	MOVSD   $2.4801587301587301587e-5, X1
+	MULSD   X0, X1
+	MOVSD   $1.9841269841269841270e-4, X2
+	ADDSD   X2, X1
+	MULSD   X0, X1
+	MOVSD   $1.3888888888888888889e-3, X2
+	ADDSD   X2, X1
+	MULSD   X0, X1
+	MOVSD   $8.3333333333333333333e-3, X2
+	ADDSD   X2, X1
+	MULSD   X0, X1
+	MOVSD   $4.1666666666666666667e-2, X2
+	ADDSD   X2, X1
+	MULSD   X0, X1
+	MOVSD   $1.6666666666666666667e-1, X2
+	ADDSD   X2, X1
+	MULSD   X0, X1
+	MOVSD   $0.5, X2
+	ADDSD   X2, X1
+	MULSD   X0, X1
+	MOVSD   $1.0, X2
+	ADDSD   X2, X1
+	MULSD   X1, X0
+	MOVSD   $2.0, X1
+	ADDSD   X0, X1
+	MULSD   X1, X0
+	MOVSD   $2.0, X1
+	ADDSD   X0, X1
+	MULSD   X1, X0
+	MOVSD   $2.0, X1
+	ADDSD   X0, X1
+	MULSD   X1, X0
+	MOVSD   $2.0, X1
+	ADDSD   X0, X1
+	MULSD   X1, X0
+	MOVSD   $1.0, X1
+	ADDSD   X1, X0
+	// return ldexp(fr, exp)
+	MOVQ    $0x3ff, AX // bias + 1
+	ADDQ    AX, BX
+	MOVQ    BX, X1
+	MOVQ    $52, AX // shift
+	MOVQ    AX, X2
+	PSLLQ   X2, X1
+	MULSD   X1, X0
+	MOVSD   X0, r+8(FP)
+	RET
+not_finite:
+// test bits for -Inf
+	MOVQ    x+0(FP), AX
+	MOVQ    $0xfff0000000000000, BX
+	CMPQ    BX, AX
+	JNE     not_neginf
+	XORQ    AX, AX
+	MOVQ    AX, r+8(FP)
+	RET
+not_neginf:
+	MOVQ    AX, r+8(FP)
+	RET

src/pkg/math/fabs_amd64.s

+// Copyright 2010 The Go Authors.  All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// func Fabs(x float64) float64
+TEXT ·Fabs(SB),7,$0
+	MOVQ   $(1<<63), BX
+	MOVQ   BX, X0 // movsd $(-0.0), x0
+	MOVSD  x+0(FP), X1
+	ANDNPD X1, X0
+	MOVSD  X0, r+8(FP)
+	RET