math: update Gamma special cases

Match new C99 values for special cases.

Fixes #2977.

R=rsc, golang-dev
CC=golang-dev
https://golang.org/cl/5972058

diff --git a/src/pkg/math/all_test.go b/src/pkg/math/all_test.go
index ed66a42fb0088b851b3ac29ca5e5233a705506f8..8cbead1ab706630ad2927b7cc54a11e3ce720922 100644 (file)
--- a/src/pkg/math/all_test.go
+++ b/src/pkg/math/all_test.go
@@ -1128,11 +1128,11 @@ var vfgammaSC = []float64{
        NaN(),
 }
 var gammaSC = []float64{
+       NaN(),
+       NaN(),
        Inf(-1),
        Inf(1),
        Inf(1),
-       Inf(1),
-       Inf(1),
        NaN(),
 }
 

diff --git a/src/pkg/math/gamma.go b/src/pkg/math/gamma.go
index 7c6f421bad1a2a1a6912dbd26552632ddd0ddd9e..8b053cb85ffc92050d62ee829a220eb666d8c42a 100644 (file)
--- a/src/pkg/math/gamma.go
+++ b/src/pkg/math/gamma.go
@@ -113,16 +113,23 @@ func stirling(x float64) float64 {
 // Gamma(x) returns the Gamma function of x.
 //
 // Special cases are:
-//     Gamma(±Inf) = ±Inf
+//     Gamma(+Inf) = +Inf
+//     Gamma(+0) = +Inf
+//     Gamma(-0) = -Inf
+//     Gamma(x) = NaN for integer x < 0
+//     Gamma(-Inf) = NaN
 //     Gamma(NaN) = NaN
-// Large values overflow to +Inf.
-// Zero and negative integer arguments return ±Inf.
 func Gamma(x float64) float64 {
        const Euler = 0.57721566490153286060651209008240243104215933593992 // A001620
        // special cases
        switch {
-       case IsInf(x, -1) || IsNaN(x):
-               return x
+       case isNegInt(x) || IsInf(x, -1) || IsNaN(x):
+               return NaN()
+       case x == 0:
+               if Signbit(x) {
+                       return Inf(-1)
+               }
+               return Inf(1)
        case x < -170.5674972726612 || x > 171.61447887182298:
                return Inf(1)
        }
@@ -185,3 +192,11 @@ small:
        }
        return z / ((1 + Euler*x) * x)
 }
+
+func isNegInt(x float64) bool {
+       if x < 0 {
+               _, xf := Modf(x)
+               return xf == 0
+       }
+       return false
+}