math: Atan2 special cases and tests; atan2_386

Added special cases, tests and benchmarks for Atan2;
added 386 FPU version of Atan2.

R=rsc
CC=golang-dev
https://golang.org/cl/201068

src/pkg/math/Makefile

@@ -12,6 +12,7 @@ OFILES_amd64=\
 OFILES_386=\
 	asin_386.$O\
 	atan_386.$O\
+	atan2_386.$O\
 	exp_386.$O\
 	fabs_386.$O\
 	floor_386.$O\

src/pkg/math/all_test.go

@@ -100,6 +100,18 @@ var atanh = []float64{
 	1.8459947964298794318714228e-01,
 	-1.3273186910532645867272502e+00,
 }
+var atan2 = []float64{
+	1.1088291730037004444527075e+00,
+	9.1218183188715804018797795e-01,
+	1.5984772603216203736068915e+00,
+	2.0352918654092086637227327e+00,
+	8.0391819139044720267356014e-01,
+	1.2861075249894661588866752e+00,
+	1.0889904479131695712182587e+00,
+	1.3044821793397925293797357e+00,
+	1.3902530903455392306872261e+00,
+	2.2859857424479142655411058e+00,
+}
 var ceil = []float64{
 	5.0000000000000000e+00,
 	8.0000000000000000e+00,
@@ -427,6 +439,64 @@ var atanhSC = []float64{
 	NaN(),
 	NaN(),
 }
+var vfatan2SC = [][2]float64{
+	[2]float64{Inf(-1), Inf(-1)},
+	[2]float64{Inf(-1), -Pi},
+	[2]float64{Inf(-1), 0},
+	[2]float64{Inf(-1), +Pi},
+	[2]float64{Inf(-1), Inf(1)},
+	[2]float64{Inf(-1), NaN()},
+	[2]float64{-Pi, Inf(-1)},
+	[2]float64{-Pi, 0},
+	[2]float64{-Pi, Inf(1)},
+	[2]float64{-Pi, NaN()},
+	[2]float64{0, Inf(-1)},
+	[2]float64{0, -Pi},
+	[2]float64{0, 0},
+	[2]float64{0, +Pi},
+	[2]float64{0, Inf(1)},
+	[2]float64{0, NaN()},
+	[2]float64{+Pi, Inf(-1)},
+	[2]float64{+Pi, 0},
+	[2]float64{+Pi, Inf(1)},
+	[2]float64{+Pi, NaN()},
+	[2]float64{Inf(1), Inf(-1)},
+	[2]float64{Inf(1), -Pi},
+	[2]float64{Inf(1), 0},
+	[2]float64{Inf(1), +Pi},
+	[2]float64{Inf(1), Inf(1)},
+	[2]float64{Inf(1), NaN()},
+	[2]float64{NaN(), NaN()},
+}
+var atan2SC = []float64{
+	-3 * Pi / 4,
+	-Pi / 2,
+	-Pi / 2,
+	-Pi / 2,
+	-Pi / 4,
+	NaN(),
+	-Pi,
+	-Pi / 2,
+	-0,
+	NaN(),
+	Pi,
+	Pi,
+	0,
+	0,
+	0,
+	NaN(),
+	Pi,
+	Pi / 2,
+	0,
+	NaN(),
+	3 * Pi / 4,
+	Pi / 2,
+	Pi / 2,
+	Pi / 2,
+	Pi / 4,
+	NaN(),
+	NaN(),
+}
 
 var vfceilSC = []float64{
 	Inf(-1),
@@ -851,6 +921,19 @@ func TestAtanh(t *testing.T) {
 	}
 }
 
+func TestAtan2(t *testing.T) {
+	for i := 0; i < len(vf); i++ {
+		if f := Atan2(10, vf[i]); !veryclose(atan2[i], f) {
+			t.Errorf("Atan2(10, %g) = %g, want %g\n", vf[i], f, atan2[i])
+		}
+	}
+	for i := 0; i < len(vfatan2SC); i++ {
+		if f := Atan2(vfatan2SC[i][0], vfatan2SC[i][1]); !alike(atan2SC[i], f) {
+			t.Errorf("Atan2(%g, %g) = %g, want %g\n", vfatan2SC[i][0], vfatan2SC[i][1], f, atan2SC[i])
+		}
+	}
+}
+
 func TestCeil(t *testing.T) {
 	for i := 0; i < len(vf); i++ {
 		if f := Ceil(vf[i]); ceil[i] != f {
@@ -1254,6 +1337,12 @@ func BenchmarkAtanh(b *testing.B) {
 	}
 }
 
+func BenchmarkAtan2(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		Atan2(.5, 1)
+	}
+}
+
 func BenchmarkCeil(b *testing.B) {
 	for i := 0; i < b.N; i++ {
 		Ceil(.5)

src/pkg/math/atan2.go

@@ -7,14 +7,69 @@ package math
 // Atan2 returns the arc tangent of y/x, using
 // the signs of the two to determine the quadrant
 // of the return value.
+//
+// Special cases are (in order):
+//	Atan2(y, NaN) = NaN
+//	Atan2(NaN, x) = NaN
+//	Atan2(0, x>=0) = 0
+//	Atan2(0, x<0) = Pi
+//	Atan2(y>0, 0) = +Pi/2
+//	Atan2(y<0, 0) = -Pi/2
+//	Atan2(+Inf, +Inf) = +Pi/4
+//	Atan2(-Inf, +Inf) = -Pi/4
+//	Atan2(+Inf, -Inf) = 3Pi/4
+//	Atan2(-Inf, -Inf) = -3Pi/4
+//	Atan2(y, +Inf) = 0
+//	Atan2(y>0, -Inf) = +Pi
+//	Atan2(y<0, -Inf) = -Pi
+//	Atan2(+Inf, x) = +Pi/2
+//	Atan2(-Inf, x) = -Pi/2
 func Atan2(y, x float64) float64 {
-	// Determine the quadrant and call atan.
+	// TODO(rsc): Remove manual inlining of IsNaN, IsInf
-	if y+x == y {
+	// when compiler does it for us
-		if y >= 0 {
+	// special cases
+	switch {
+	case y != y || x != x: // IsNaN(y) || IsNaN(x):
+		return NaN()
+	case y == 0:
+		if x >= 0 {
+			return 0
+		}
+		return Pi
+	case x == 0:
+		if y > 0 {
+			return Pi / 2
+		}
+		return -Pi / 2
+	case x < -MaxFloat64 || x > MaxFloat64: // IsInf(x, 0):
+		if x > MaxFloat64 { // IsInf(x, 1) {
+			switch {
+			case y > MaxFloat64: // IsInf(y, 1):
+				return Pi / 4
+			case y < -MaxFloat64: // IsInf(y, -1):
+				return -Pi / 4
+			default:
+				return 0
+			}
+		}
+		switch {
+		case y > MaxFloat64: //IsInf(y, 1):
+			return 3 * Pi / 4
+		case y < -MaxFloat64: //IsInf(y, -1):
+			return -3 * Pi / 4
+		case y > 0:
+			return Pi
+		default:
+			return -Pi
+		}
+	case y < -MaxFloat64 || y > MaxFloat64: //IsInf(y, 0):
+		if y > MaxFloat64 { // IsInf(y, 1) {
 			return Pi / 2
 		}
 		return -Pi / 2
 	}
+
+	// Call atan and determine the quadrant.
 	q := Atan(y / x)
 	if x < 0 {
 		if q <= 0 {

src/pkg/math/atan2_386.s

@@ -0,0 +1,11 @@
+// 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 Atan2(y, x float64) float64	// =atan(y/x)
+TEXT ·Atan2(SB),7,$0
+	FMOVD   y+0(FP), F0  // F0=y
+	FMOVD   x+8(FP), F0  // F0=x, F1=y
+	FPATAN               // F0=atan(F1/F0)
+	FMOVDP  F0, r+16(FP)
+	RET

src/pkg/math/atan2_decl.go

@@ -0,0 +1,7 @@
+// 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 Atan2(y, x float64) float64