math: add Exp2; 386 FPU versions of Exp2 and Log1p

Added tests and benchmarks for Exp2 (special cases same
as Exp). Log1p also enhances speed of inverse hyperbolics.

R=rsc
CC=golang-dev
https://golang.org/cl/206058

src/pkg/math/Makefile

@@ -14,11 +14,13 @@ OFILES_386=\
 	atan_386.$O\
 	atan2_386.$O\
 	exp_386.$O\
+	exp2_386.$O\
 	fabs_386.$O\
 	floor_386.$O\
 	fmod_386.$O\
 	hypot_386.$O\
 	log_386.$O\
+	log1p_386.$O\
 	modf_386.$O\
 	sin_386.$O\
 	sqrt_386.$O\

src/pkg/math/all_test.go

@@ -208,6 +208,18 @@ var expm1 = []float64{
 	1.842068661871398836913874273e-02,
 	-8.3193870863553801814961137573e-02,
 }
+var exp2 = []float64{
+	3.1537839463286288034313104e+01,
+	2.1361549283756232296144849e+02,
+	8.2537402562185562902577219e-01,
+	3.1021158628740294833424229e-02,
+	7.9581744110252191462569661e+02,
+	7.6019905892596359262696423e+00,
+	3.7506882048388096973183084e+01,
+	6.6250893439173561733216375e+00,
+	3.5438267900243941544605339e+00,
+	2.4281533133513300984289196e-03,
+}
 var fdim = []float64{
 	4.9790119248836735e+00,
 	7.7388724745781045e+00,
@@ -1078,6 +1090,19 @@ func TestExpm1(t *testing.T) {
 	}
 }
 
+func TestExp2(t *testing.T) {
+	for i := 0; i < len(vf); i++ {
+		if f := Exp2(vf[i]); !close(exp2[i], f) {
+			t.Errorf("Exp2(%g) = %g, want %g\n", vf[i], f, exp2[i])
+		}
+	}
+	for i := 0; i < len(vfexpSC); i++ {
+		if f := Exp2(vfexpSC[i]); !alike(expSC[i], f) {
+			t.Errorf("Exp2(%g) = %g, want %g\n", vfexpSC[i], f, expSC[i])
+		}
+	}
+}
+
 func TestFdim(t *testing.T) {
 	for i := 0; i < len(vf); i++ {
 		if f := Fdim(vf[i], 0); fdim[i] != f {
@@ -1492,6 +1517,12 @@ func BenchmarkExpm1(b *testing.B) {
 	}
 }
 
+func BenchmarkExp2(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		Exp(.5)
+	}
+}
+
 func BenchmarkFloor(b *testing.B) {
 	for i := 0; i < b.N; i++ {
 		Floor(.5)

src/pkg/math/exp.go

@@ -139,3 +139,8 @@ 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_386.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 Exp2(x float64) float64
+TEXT ·Exp2(SB),7,$0
+// test bits for not-finite
+	MOVL    x+4(FP), AX
+	ANDL    $0x7ff00000, AX
+	CMPL    AX, $0x7ff00000
+	JEQ     not_finite
+	FMOVD   x+0(FP), F0   // F0=x
+	FMOVD   F0, F1        // F0=x, F1=x
+	FRNDINT               // F0=int(x), F1=x
+	FSUBD   F0, F1        // F0=int(x), F1=x-int(x)
+	FXCHD   F0, F1        // F0=x-int(x), F1=int(x)
+	F2XM1                 // F0=2**(x-int(x))-1, F1=int(x)
+	FLD1                  // F0=1, F1=2**(x-int(x))-1, F2=int(x)
+	FADDDP  F0, F1        // F0=2**(x-int(x)), F1=int(x)
+	FSCALE                // F0=2**x, F1=int(x)
+	FMOVDP  F0, F1        // F0=2**x
+	FMOVDP  F0, r+8(FP)
+	RET
+not_finite:
+// test bits for -Inf
+	MOVL    x+4(FP), BX
+	MOVL    x+0(FP), CX
+	CMPL    BX, $0xfff00000
+	JNE     not_neginf
+	CMPL    CX, $0
+	JNE     not_neginf
+	MOVL    $0, r+8(FP)
+	MOVL    $0, r+12(FP)
+	RET
+not_neginf:
+	MOVL    CX, r+8(FP)
+	MOVL    BX, r+12(FP)
+	RET

src/pkg/math/exp2_decl.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
+
+func Exp2(x float64) float64

src/pkg/math/log1p_386.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 Log1p(x float64) float64
+TEXT ·Log1p(SB),7,$0
+	FMOVD   $(2.928932188134524e-01), F0
+	FMOVD   x+0(FP), F0  // F0=x, F1=1-sqrt(2)/2 = 0.29289321881345247559915564
+	FABS                 // F0=|x|, F1=1-sqrt(2)/2
+	FUCOMPP F0, F1       // compare F0 to F1
+	FSTSW   AX
+	FLDLN2               // F0=log(2)
+	ANDW    $0x0100, AX
+	JEQ     use_fyl2x    // jump if F0 >= F1
+	FMOVD   x+0(FP), F0  // F0=x, F1=log(2)
+	FYL2XP1              // F0=log(1+x)=log2(1+x)*log(2)
+	FMOVDP  F0, r+8(FP)
+	RET
+use_fyl2x:
+	FLD1                 // F0=1, F2=log(2)
+	FADDD   x+0(FP), F0  // F0=1+x, F1=log(2)
+	FYL2X                // F0=log(1+x)=log2(1+x)*log(2)
+	FMOVDP  F0, r+8(FP)
+	RET
+

src/pkg/math/log1p_decl.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
+
+func Log1p(x float64) float64