math: add Gamma function
R=rsc
CC=golang-dev
https://golang.org/cl/649041
diff --git a/src/pkg/math/Makefile b/src/pkg/math/Makefile
index 3b82a78..a92a50e 100644
--- a/src/pkg/math/Makefile
+++ b/src/pkg/math/Makefile
@@ -53,6 +53,7 @@
floor.go\
fmod.go\
frexp.go\
+ gamma.go\
hypot.go\
hypot_port.go\
logb.go\
diff --git a/src/pkg/math/all_test.go b/src/pkg/math/all_test.go
index 8cb5756..b28a1f4 100644
--- a/src/pkg/math/all_test.go
+++ b/src/pkg/math/all_test.go
@@ -286,6 +286,18 @@
fi{9.1265404584042750000e-01, 1},
fi{-5.4287029803597508250e-01, 4},
}
+var gamma = []float64{
+ 2.3254348370739963835386613898e+01,
+ 2.991153837155317076427529816e+03,
+ -4.561154336726758060575129109e+00,
+ 7.719403468842639065959210984e-01,
+ 1.6111876618855418534325755566e+05,
+ 1.8706575145216421164173224946e+00,
+ 3.4082787447257502836734201635e+01,
+ 1.579733951448952054898583387e+00,
+ 9.3834586598354592860187267089e-01,
+ -2.093995902923148389186189429e-05,
+}
var lgamma = []fi{
fi{3.146492141244545774319734e+00, 1},
fi{8.003414490659126375852113e+00, 1},
@@ -736,6 +748,21 @@
fi{NaN(), 0},
}
+var vfgammaSC = []float64{
+ Inf(-1),
+ -3,
+ 0,
+ Inf(1),
+ NaN(),
+}
+var gammaSC = []float64{
+ Inf(-1),
+ Inf(1),
+ Inf(1),
+ Inf(1),
+ NaN(),
+}
+
var vfhypotSC = [][2]float64{
[2]float64{Inf(-1), Inf(-1)},
[2]float64{Inf(-1), 0},
@@ -1278,6 +1305,19 @@
}
}
+func TestGamma(t *testing.T) {
+ for i := 0; i < len(vf); i++ {
+ if f := Gamma(vf[i]); !close(gamma[i], f) {
+ t.Errorf("Gamma(%g) = %g, want %g\n", vf[i], f, gamma[i])
+ }
+ }
+ for i := 0; i < len(vfgammaSC); i++ {
+ if f := Gamma(vfgammaSC[i]); !alike(gammaSC[i], f) {
+ t.Errorf("Gamma(%g) = %g, want %g\n", vfgammaSC[i], f, gammaSC[i])
+ }
+ }
+}
+
func TestHypot(t *testing.T) {
for i := 0; i < len(vf); i++ {
a := Fabs(1e200 * tanh[i] * Sqrt(2))
@@ -1748,6 +1788,12 @@
}
}
+func BenchmarkGamma(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ Gamma(2.5)
+ }
+}
+
func BenchmarkHypot(b *testing.B) {
for i := 0; i < b.N; i++ {
Hypot(3, 4)
diff --git a/src/pkg/math/gamma.go b/src/pkg/math/gamma.go
new file mode 100644
index 0000000..4c5b17d
--- /dev/null
+++ b/src/pkg/math/gamma.go
@@ -0,0 +1,188 @@
+// 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
+
+// The original C code, the long comment, and the constants
+// below are from http://netlib.sandia.gov/cephes/cprob/gamma.c.
+// The go code is a simplified version of the original C.
+//
+// tgamma.c
+//
+// Gamma function
+//
+// SYNOPSIS:
+//
+// double x, y, tgamma();
+// extern int signgam;
+//
+// y = tgamma( x );
+//
+// DESCRIPTION:
+//
+// Returns gamma function of the argument. The result is
+// correctly signed, and the sign (+1 or -1) is also
+// returned in a global (extern) variable named signgam.
+// This variable is also filled in by the logarithmic gamma
+// function lgamma().
+//
+// Arguments |x| <= 34 are reduced by recurrence and the function
+// approximated by a rational function of degree 6/7 in the
+// interval (2,3). Large arguments are handled by Stirling's
+// formula. Large negative arguments are made positive using
+// a reflection formula.
+//
+// ACCURACY:
+//
+// Relative error:
+// arithmetic domain # trials peak rms
+// DEC -34, 34 10000 1.3e-16 2.5e-17
+// IEEE -170,-33 20000 2.3e-15 3.3e-16
+// IEEE -33, 33 20000 9.4e-16 2.2e-16
+// IEEE 33, 171.6 20000 2.3e-15 3.2e-16
+//
+// Error for arguments outside the test range will be larger
+// owing to error amplification by the exponential function.
+//
+// Cephes Math Library Release 2.8: June, 2000
+// Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
+//
+// The readme file at http://netlib.sandia.gov/cephes/ says:
+// Some software in this archive may be from the book _Methods and
+// Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
+// International, 1989) or from the Cephes Mathematical Library, a
+// commercial product. In either event, it is copyrighted by the author.
+// What you see here may be used freely but it comes with no support or
+// guarantee.
+//
+// The two known misprints in the book are repaired here in the
+// source listings for the gamma function and the incomplete beta
+// integral.
+//
+// Stephen L. Moshier
+// moshier@na-net.ornl.gov
+
+var _P = []float64{
+ 1.60119522476751861407e-04,
+ 1.19135147006586384913e-03,
+ 1.04213797561761569935e-02,
+ 4.76367800457137231464e-02,
+ 2.07448227648435975150e-01,
+ 4.94214826801497100753e-01,
+ 9.99999999999999996796e-01,
+}
+var _Q = []float64{
+ -2.31581873324120129819e-05,
+ 5.39605580493303397842e-04,
+ -4.45641913851797240494e-03,
+ 1.18139785222060435552e-02,
+ 3.58236398605498653373e-02,
+ -2.34591795718243348568e-01,
+ 7.14304917030273074085e-02,
+ 1.00000000000000000320e+00,
+}
+var _S = []float64{
+ 7.87311395793093628397e-04,
+ -2.29549961613378126380e-04,
+ -2.68132617805781232825e-03,
+ 3.47222221605458667310e-03,
+ 8.33333333333482257126e-02,
+}
+
+// Gamma function computed by Stirling's formula.
+// The polynomial is valid for 33 <= x <= 172.
+func stirling(x float64) float64 {
+ const (
+ SqrtTwoPi = 2.506628274631000502417
+ MaxStirling = 143.01608
+ )
+ w := 1 / x
+ w = 1 + w*((((_S[0]*w+_S[1])*w+_S[2])*w+_S[3])*w+_S[4])
+ y := Exp(x)
+ if x > MaxStirling { // avoid Pow() overflow
+ v := Pow(x, 0.5*x-0.25)
+ y = v * (v / y)
+ } else {
+ y = Pow(x, x-0.5) / y
+ }
+ y = SqrtTwoPi * y * w
+ return y
+}
+
+// Gamma(x) returns the Gamma function of x.
+//
+// Special cases are:
+// Gamma(Inf) = Inf
+// Gamma(-Inf) = -Inf
+// Gamma(NaN) = NaN
+// Large values overflow to +Inf.
+// Negative integer values equal ±Inf.
+func Gamma(x float64) float64 {
+ const Euler = 0.57721566490153286060651209008240243104215933593992 // A001620
+ // special cases
+ switch {
+ case x < -MaxFloat64 || x != x: // IsInf(x, -1) || IsNaN(x):
+ return x
+ case x < -170.5674972726612 || x > 171.61447887182298:
+ return Inf(1)
+ }
+ q := Fabs(x)
+ p := Floor(q)
+ if q > 33 {
+ if x >= 0 {
+ return stirling(x)
+ }
+ signgam := 1
+ if ip := int(p); ip&1 == 0 {
+ signgam = -1
+ }
+ z := q - p
+ if z > 0.5 {
+ p = p + 1
+ z = q - p
+ }
+ z = q * Sin(Pi*z)
+ if z == 0 {
+ return Inf(signgam)
+ }
+ z = Pi / (Fabs(z) * stirling(q))
+ return float64(signgam) * z
+ }
+
+ // Reduce argument
+ z := float64(1)
+ for x >= 3 {
+ x = x - 1
+ z = z * x
+ }
+ for x < 0 {
+ if x > -1e-09 {
+ goto small
+ }
+ z = z / x
+ x = x + 1
+ }
+ for x < 2 {
+ if x < 1e-09 {
+ goto small
+ }
+ z = z / x
+ x = x + 1
+ }
+
+ if x == 2 {
+ return z
+ }
+
+ x = x - 2
+ p = (((((x*_P[0]+_P[1])*x+_P[2])*x+_P[3])*x+_P[4])*x+_P[5])*x + _P[6]
+ q = ((((((x*_Q[0]+_Q[1])*x+_Q[2])*x+_Q[3])*x+_Q[4])*x+_Q[5])*x+_Q[6])*x + _Q[7]
+ return z * p / q
+
+small:
+ if x == 0 {
+ return Inf(1)
+ }
+ return z / ((1 + Euler*x) * x)
+}
