math: more special cases for signed zero

R=rsc
CC=golang-dev
https://golang.org/cl/937042

src/pkg/math/asin.go

@@ -14,16 +14,20 @@ package math
 
 // Asin returns the arcsine of x.
 //
-// Special case is:
+// Special cases are:
+//	Asin(±0) = ±0
 //	Asin(x) = NaN if x < -1 or x > 1
 func Asin(x float64) float64 {
+	if x == 0 {
+		return x // special case
+	}
 	sign := false
 	if x < 0 {
 		x = -x
 		sign = true
 	}
 	if x > 1 {
-		return NaN()
+		return NaN() // special case
 	}
 
 	temp := Sqrt(1 - x*x)

src/pkg/math/atan.go

@@ -47,7 +47,14 @@ func satan(arg float64) float64 {
 }
 
 // Atan returns the arctangent of x.
+//
+// Special cases are:
+//	Atan(±0) = ±0
+//	Atan(±Inf) = ±Pi/2
 func Atan(x float64) float64 {
+	if x == 0 {
+		return x
+	}
 	if x > 0 {
 		return satan(x)
 	}

src/pkg/math/cbrt.go

@@ -15,8 +15,8 @@ package math
 // Cbrt returns the cube root of its argument.
 //
 // Special cases are:
-//	Exp(+Inf) = +Inf
-//	Exp(-Inf) = -Inf
+//	Exp(±0) = ±0
+//	Exp(±Inf) = ±Inf
 //	Exp(NaN) = NaN
 func Cbrt(x float64) float64 {
 	const (
@@ -37,7 +37,7 @@ func Cbrt(x float64) float64 {
 	// when compiler does it for us
 	// special cases
 	switch {
-	case x != x || x < -MaxFloat64 || x > MaxFloat64: // IsNaN(x) || IsInf(x, 0):
+	case x == 0 || x != x || x < -MaxFloat64 || x > MaxFloat64: // x == 0 || IsNaN(x) || IsInf(x, 0):
 		return x
 	}
 	sign := false

src/pkg/math/fabs.go

@@ -11,8 +11,11 @@ package math
 //	Fabs(-Inf) = +Inf
 //	Fabs(NaN) = NaN
 func Fabs(x float64) float64 {
-	if x < 0 {
+	switch {
+	case x < 0:
 		return -x
+	case x == 0:
+		return 0 // return correctly fabs(-0)
 	}
 	return x
 }

src/pkg/math/floor.go

@@ -14,7 +14,7 @@ package math
 func Floor(x float64) float64 {
 	// TODO(rsc): Remove manual inlining of IsNaN, IsInf
 	// when compiler does it for us
-	if x != x || x > MaxFloat64 || x < -MaxFloat64 { // IsNaN(x) || IsInf(x, 0)
+	if x == 0 || x != x || x > MaxFloat64 || x < -MaxFloat64 { // x == 0 || IsNaN(x) || IsInf(x, 0)
 		return x
 	}
 	if x < 0 {
@@ -45,7 +45,7 @@ func Ceil(x float64) float64 { return -Floor(-x) }
 func Trunc(x float64) float64 {
 	// TODO(rsc): Remove manual inlining of IsNaN, IsInf
 	// when compiler does it for us
-	if x != x || x > MaxFloat64 || x < -MaxFloat64 { // IsNaN(x) || IsInf(x, 0)
+	if x == 0 || x != x || x > MaxFloat64 || x < -MaxFloat64 { // x == 0 || IsNaN(x) || IsInf(x, 0)
 		return x
 	}
 	d, _ := Modf(x)

src/pkg/math/frexp.go

@@ -14,10 +14,9 @@ func Frexp(f float64) (frac float64, exp int) {
 	// special cases
 	switch {
 	case f == 0:
-		return
+		return f, 0 // correctly return -0
 	case f < -MaxFloat64 || f > MaxFloat64 || f != f: // IsInf(f, 0) || IsNaN(f):
-		frac = f
-		return
+		return f, 0
 	}
 	x := Float64bits(f)
 	exp = int((x>>shift)&mask) - bias

src/pkg/math/ldexp.go

@@ -10,7 +10,10 @@ func Ldexp(frac float64, exp int) float64 {
 	// TODO(rsc): Remove manual inlining of IsNaN, IsInf
 	// when compiler does it for us
 	// special cases
-	if frac != frac { // IsNaN(frac)
+	switch {
+	case frac == 0:
+		return frac // correctly return -0
+	case frac != frac: // IsNaN(frac):
 		return NaN()
 	}
 	x := Float64bits(frac)