math: document more special cases

Acosh, Asinh, Atanh, Ceil, Floor, Trunc, Mod and Remainder affected. These changes add some non-finite arguments and results (and -0.0 results).

R=rsc, golang-dev
CC=golang-dev
https://golang.org/cl/5469046

src/pkg/math/acosh.go

@@ -36,6 +36,7 @@ package math
 // Acosh(x) calculates the inverse hyperbolic cosine of x.
 //
 // Special cases are:
+//	Acosh(+Inf) = +Inf
 //	Acosh(x) = NaN if x < 1
 //	Acosh(NaN) = NaN
 func Acosh(x float64) float64 {

src/pkg/math/asinh.go

@@ -33,6 +33,7 @@ package math
 // Asinh(x) calculates the inverse hyperbolic sine of x.
 //
 // Special cases are:
+//	Asinh(±0) = ±0
 //	Asinh(±Inf) = ±Inf
 //	Asinh(NaN) = NaN
 func Asinh(x float64) float64 {

src/pkg/math/atanh.go

@@ -39,9 +39,10 @@ package math
 // Atanh(x) calculates the inverse hyperbolic tangent of x.
 //
 // Special cases are:
-//	Atanh(x) = NaN if x < -1 or x > 1
 //	Atanh(1) = +Inf
+//	Atanh(±0) = ±0
 //	Atanh(-1) = -Inf
+//	Atanh(x) = NaN if x < -1 or x > 1
 //	Atanh(NaN) = NaN
 func Atanh(x float64) float64 {
 	const NearZero = 1.0 / (1 << 28) // 2**-28

src/pkg/math/floor.go

@@ -7,6 +7,7 @@ package math
 // Floor returns the greatest integer value less than or equal to x.
 //
 // Special cases are:
+//	Floor(±0) = ±0
 //	Floor(±Inf) = ±Inf
 //	Floor(NaN) = NaN
 func Floor(x float64) float64 {
@@ -29,6 +30,7 @@ func Floor(x float64) float64 {
 // Ceil returns the least integer value greater than or equal to x.
 //
 // Special cases are:
+//	Ceil(±0) = ±0
 //	Ceil(±Inf) = ±Inf
 //	Ceil(NaN) = NaN
 func Ceil(x float64) float64 { return -Floor(-x) }
@@ -36,6 +38,7 @@ func Ceil(x float64) float64 { return -Floor(-x) }
 // Trunc returns the integer value of x.
 //
 // Special cases are:
+//	Trunc(±0) = ±0
 //	Trunc(±Inf) = ±Inf
 //	Trunc(NaN) = NaN
 func Trunc(x float64) float64 {

src/pkg/math/mod.go

@@ -13,8 +13,11 @@ package math
 // sign agrees with that of x.
 //
 // Special cases are:
-//	if x is not finite, Mod returns NaN
-//	if y is 0 or NaN, Mod returns NaN
+//	Mod(±Inf, y) = NaN
+//	Mod(NaN, y) = NaN
+//	Mod(x, 0) = NaN
+//	Mod(x, ±Inf) = x
+//	Mod(x, NaN) = NaN
 func Mod(x, y float64) float64 {
 	// TODO(rsc): Remove manual inlining of IsNaN, IsInf
 	// when compiler does it for us.

src/pkg/math/nextafter.go

@@ -10,6 +10,7 @@ package math
 // Special cases are:
 //	Nextafter(NaN, y) = NaN
 //	Nextafter(x, NaN) = NaN
+//	Nextafter(0, y) = -0, if y < 0
 func Nextafter(x, y float64) (r float64) {
 	// TODO(rsc): Remove manual inlining of IsNaN
 	// when compiler does it for us

src/pkg/math/remainder.go

@@ -29,11 +29,11 @@ package math
 // Remainder returns the IEEE 754 floating-point remainder of x/y.
 //
 // Special cases are:
-//	Remainder(x, NaN) = NaN
+//	Remainder(±Inf, y) = NaN
 //	Remainder(NaN, y) = NaN
-//	Remainder(Inf, y) = NaN
 //	Remainder(x, 0) = NaN
-//	Remainder(x, Inf) = x
+//	Remainder(x, ±Inf) = x
+//	Remainder(x, NaN) = NaN
 func Remainder(x, y float64) float64 {
 	const (
 		Tiny    = 4.45014771701440276618e-308 // 0x0020000000000000