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author | Ian Lance Taylor <ian@gcc.gnu.org> | 2010-12-03 04:34:57 +0000 |
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committer | Ian Lance Taylor <ian@gcc.gnu.org> | 2010-12-03 04:34:57 +0000 |
commit | 7a9389330e91acc3ed05deac2d198af25d13cf3c (patch) | |
tree | 38fe54a4f38ede5d949c915d66191f24a6fe5153 /libgo/go/math/gamma.go | |
parent | 1aa6700378e5188a853c018256113ce6e1fb5c05 (diff) | |
download | gcc-7a9389330e91acc3ed05deac2d198af25d13cf3c.tar.gz |
Add Go frontend, libgo library, and Go testsuite.
gcc/:
* gcc.c (default_compilers): Add entry for ".go".
* common.opt: Add -static-libgo as a driver option.
* doc/install.texi (Configuration): Mention libgo as an option for
--enable-shared. Mention go as an option for --enable-languages.
* doc/invoke.texi (Overall Options): Mention .go as a file name
suffix. Mention go as a -x option.
* doc/frontends.texi (G++ and GCC): Mention Go as a supported
language.
* doc/sourcebuild.texi (Top Level): Mention libgo.
* doc/standards.texi (Standards): Add section on Go language.
Move references for other languages into their own section.
* doc/contrib.texi (Contributors): Mention that I contributed the
Go frontend.
gcc/testsuite/:
* lib/go.exp: New file.
* lib/go-dg.exp: New file.
* lib/go-torture.exp: New file.
* lib/target-supports.exp (check_compile): Match // Go.
From-SVN: r167407
Diffstat (limited to 'libgo/go/math/gamma.go')
-rw-r--r-- | libgo/go/math/gamma.go | 188 |
1 files changed, 188 insertions, 0 deletions
diff --git a/libgo/go/math/gamma.go b/libgo/go/math/gamma.go new file mode 100644 index 00000000000..4c5b17d05c7 --- /dev/null +++ b/libgo/go/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) +} |