math: atan2 special cases (negative zero)

Added Signbit(), revised Copysign()

R=rsc
CC=golang-dev
https://golang.org/cl/822045

src/pkg/math/Makefile

@@ -69,6 +69,7 @@ ALLGOFILES=\
 	pow.go\
 	pow10.go\
 	remainder.go\
+	signbit.go\
 	sin.go\
 	sincos.go\
 	sinh.go\

src/pkg/math/all_test.go

@@ -466,6 +466,18 @@ var remainder = []float64{
 	8.734595415957246977711748e-01,
 	1.314075231424398637614104e+00,
 }
+var signbit = []bool{
+	false,
+	false,
+	true,
+	true,
+	false,
+	false,
+	false,
+	false,
+	false,
+	true,
+}
 var sin = []float64{
 	-9.6466616586009283766724726e-01,
 	9.9338225271646545763467022e-01,
@@ -653,8 +665,16 @@ var vfatan2SC = [][2]float64{
 	[2]float64{-Pi, 0},
 	[2]float64{-Pi, Inf(1)},
 	[2]float64{-Pi, NaN()},
+	[2]float64{-1 / Inf(1), Inf(-1)},     // -0, -Inf
+	[2]float64{-1 / Inf(1), -Pi},         // -0, -Pi
+	[2]float64{-1 / Inf(1), -1 / Inf(1)}, // -0, -0
+	[2]float64{-1 / Inf(1), 0},           // -0, +0
+	[2]float64{-1 / Inf(1), +Pi},         // -0, +Pi
+	[2]float64{-1 / Inf(1), Inf(1)},      // -0, +Inf
+	[2]float64{-1 / Inf(1), NaN()},       // -0, NaN
 	[2]float64{0, Inf(-1)},
 	[2]float64{0, -Pi},
+	[2]float64{0, -1 / Inf(1)}, // +0, -0
 	[2]float64{0, 0},
 	[2]float64{0, +Pi},
 	[2]float64{0, Inf(1)},
@@ -680,10 +700,18 @@ var atan2SC = []float64{
 	NaN(),
 	-Pi,
 	-Pi / 2,
-	-0,
+	-1 / Inf(1), // -0
+	NaN(),
+	-Pi,
+	-Pi,
+	-Pi, // -0, -0
+	-1 / Inf(1),
+	-1 / Inf(1),
+	-1 / Inf(1),
 	NaN(),
 	Pi,
 	Pi,
+	Pi, // +0, -0
 	0,
 	0,
 	0,
@@ -1107,6 +1135,21 @@ var powSC = []float64{
 	1,
 }
 
+var vfsignbitSC = []float64{
+	Inf(-1),
+	-1 / Inf(1), // -0
+	1 / Inf(1),  // +0
+	Inf(1),
+	NaN(),
+}
+var signbitSC = []bool{
+	true,
+	true,
+	false,
+	false,
+	false,
+}
+
 var vfsqrtSC = []float64{
 	Inf(-1),
 	-Pi,
@@ -1174,7 +1217,7 @@ func alike(a, b float64) bool {
 	case IsNaN(a) && IsNaN(b):
 		return true
 	case a == b:
-		return true
+		return Signbit(a) == Signbit(b)
 	}
 	return false
 }
@@ -1705,6 +1748,18 @@ func TestRemainder(t *testing.T) {
 	}
 }
 
+func TestSignbit(t *testing.T) {
+	for i := 0; i < len(vf); i++ {
+		if f := Signbit(vf[i]); signbit[i] != f {
+			t.Errorf("Signbit(%g) = %t, want %t\n", vf[i], f, signbit[i])
+		}
+	}
+	for i := 0; i < len(vfsignbitSC); i++ {
+		if f := Signbit(vfsignbitSC[i]); signbitSC[i] != f {
+			t.Errorf("Signbit(%g) = %t, want %t\n", vfsignbitSC[i], vfsignbitSC[i], f, signbitSC[i])
+		}
+	}
+}
 func TestSin(t *testing.T) {
 	for i := 0; i < len(vf); i++ {
 		if f := Sin(vf[i]); !close(sin[i], f) {
@@ -2150,6 +2205,12 @@ func BenchmarkRemainder(b *testing.B) {
 	}
 }
 
+func BenchmarkSignbit(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		Signbit(2.5)
+	}
+}
+
 func BenchmarkSin(b *testing.B) {
 	for i := 0; i < b.N; i++ {
 		Sin(.5)

src/pkg/math/atan2.go

@@ -11,8 +11,10 @@ package math
 // Special cases are (in order):
 //	Atan2(y, NaN) = NaN
 //	Atan2(NaN, x) = NaN
-//	Atan2(0, x>=0) = 0
-//	Atan2(0, x<0) = Pi
+//	Atan2(+0, x>=0) = +0
+//	Atan2(-0, x>=0) = -0
+//	Atan2(+0, x<=-0) = +Pi
+//	Atan2(-0, x<=-0) = -Pi
 //	Atan2(y>0, 0) = +Pi/2
 //	Atan2(y<0, 0) = -Pi/2
 //	Atan2(+Inf, +Inf) = +Pi/4
@@ -32,41 +34,29 @@ func Atan2(y, x float64) float64 {
 	case y != y || x != x: // IsNaN(y) || IsNaN(x):
 		return NaN()
 	case y == 0:
-		if x >= 0 {
-			return 0
+		if x >= 0 && !Signbit(x) {
+			return Copysign(0, y)
 		}
-		return Pi
+		return Copysign(Pi, y)
 	case x == 0:
-		if y > 0 {
-			return Pi / 2
-		}
-		return -Pi / 2
+		return Copysign(Pi/2, y)
 	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
+			case y < -MaxFloat64 || y > MaxFloat64: // IsInf(y, -1) || IsInf(y, 1):
+				return Copysign(Pi/4, y)
 			default:
-				return 0
+				return Copysign(0, y)
 			}
 		}
 		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
+		case y < -MaxFloat64 || y > MaxFloat64: // IsInf(y, -1) || IsInf(y, 1):
+			return Copysign(3*Pi/4, y)
 		default:
-			return -Pi
+			return Copysign(Pi, y)
 		}
 	case y < -MaxFloat64 || y > MaxFloat64: //IsInf(y, 0):
-		if y > MaxFloat64 { // IsInf(y, 1) {
-			return Pi / 2
-		}
-		return -Pi / 2
+		return Copysign(Pi/2, y)
 	}
 
 	// Call atan and determine the quadrant.

src/pkg/math/copysign.go

@@ -4,12 +4,9 @@
 
 package math
 
-
 // Copysign(x, y) returns a value with the magnitude
 // of x and the sign of y.
 func Copysign(x, y float64) float64 {
-	if x < 0 && y > 0 || x > 0 && y < 0 {
-		return -x
-	}
-	return x
+	const sign = 1 << 63
+	return Float64frombits(Float64bits(x)&^sign | Float64bits(y)&sign)
 }

src/pkg/math/signbit.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
+
+// Signbit returns true if x is negative or negative zero.
+func Signbit(x float64) bool {
+	return Float64bits(x)&(1<<63) != 0
+}