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-rw-r--r--lib/mlibc/options/ansi/musl-generic-math/tgamma.c222
1 files changed, 0 insertions, 222 deletions
diff --git a/lib/mlibc/options/ansi/musl-generic-math/tgamma.c b/lib/mlibc/options/ansi/musl-generic-math/tgamma.c
deleted file mode 100644
index 28f6e0f..0000000
--- a/lib/mlibc/options/ansi/musl-generic-math/tgamma.c
+++ /dev/null
@@ -1,222 +0,0 @@
-/*
-"A Precision Approximation of the Gamma Function" - Cornelius Lanczos (1964)
-"Lanczos Implementation of the Gamma Function" - Paul Godfrey (2001)
-"An Analysis of the Lanczos Gamma Approximation" - Glendon Ralph Pugh (2004)
-
-approximation method:
-
- (x - 0.5) S(x)
-Gamma(x) = (x + g - 0.5) * ----------------
- exp(x + g - 0.5)
-
-with
- a1 a2 a3 aN
-S(x) ~= [ a0 + ----- + ----- + ----- + ... + ----- ]
- x + 1 x + 2 x + 3 x + N
-
-with a0, a1, a2, a3,.. aN constants which depend on g.
-
-for x < 0 the following reflection formula is used:
-
-Gamma(x)*Gamma(-x) = -pi/(x sin(pi x))
-
-most ideas and constants are from boost and python
-*/
-#include "libm.h"
-
-static const double pi = 3.141592653589793238462643383279502884;
-
-/* sin(pi x) with x > 0x1p-100, if sin(pi*x)==0 the sign is arbitrary */
-static double sinpi(double x)
-{
- int n;
-
- /* argument reduction: x = |x| mod 2 */
- /* spurious inexact when x is odd int */
- x = x * 0.5;
- x = 2 * (x - floor(x));
-
- /* reduce x into [-.25,.25] */
- n = 4 * x;
- n = (n+1)/2;
- x -= n * 0.5;
-
- x *= pi;
- switch (n) {
- default: /* case 4 */
- case 0:
- return __sin(x, 0, 0);
- case 1:
- return __cos(x, 0);
- case 2:
- return __sin(-x, 0, 0);
- case 3:
- return -__cos(x, 0);
- }
-}
-
-#define N 12
-//static const double g = 6.024680040776729583740234375;
-static const double gmhalf = 5.524680040776729583740234375;
-static const double Snum[N+1] = {
- 23531376880.410759688572007674451636754734846804940,
- 42919803642.649098768957899047001988850926355848959,
- 35711959237.355668049440185451547166705960488635843,
- 17921034426.037209699919755754458931112671403265390,
- 6039542586.3520280050642916443072979210699388420708,
- 1439720407.3117216736632230727949123939715485786772,
- 248874557.86205415651146038641322942321632125127801,
- 31426415.585400194380614231628318205362874684987640,
- 2876370.6289353724412254090516208496135991145378768,
- 186056.26539522349504029498971604569928220784236328,
- 8071.6720023658162106380029022722506138218516325024,
- 210.82427775157934587250973392071336271166969580291,
- 2.5066282746310002701649081771338373386264310793408,
-};
-static const double Sden[N+1] = {
- 0, 39916800, 120543840, 150917976, 105258076, 45995730, 13339535,
- 2637558, 357423, 32670, 1925, 66, 1,
-};
-/* n! for small integer n */
-static const double fact[] = {
- 1, 1, 2, 6, 24, 120, 720, 5040.0, 40320.0, 362880.0, 3628800.0, 39916800.0,
- 479001600.0, 6227020800.0, 87178291200.0, 1307674368000.0, 20922789888000.0,
- 355687428096000.0, 6402373705728000.0, 121645100408832000.0,
- 2432902008176640000.0, 51090942171709440000.0, 1124000727777607680000.0,
-};
-
-/* S(x) rational function for positive x */
-static double S(double x)
-{
- double_t num = 0, den = 0;
- int i;
-
- /* to avoid overflow handle large x differently */
- if (x < 8)
- for (i = N; i >= 0; i--) {
- num = num * x + Snum[i];
- den = den * x + Sden[i];
- }
- else
- for (i = 0; i <= N; i++) {
- num = num / x + Snum[i];
- den = den / x + Sden[i];
- }
- return num/den;
-}
-
-double tgamma(double x)
-{
- union {double f; uint64_t i;} u = {x};
- double absx, y;
- double_t dy, z, r;
- uint32_t ix = u.i>>32 & 0x7fffffff;
- int sign = u.i>>63;
-
- /* special cases */
- if (ix >= 0x7ff00000)
- /* tgamma(nan)=nan, tgamma(inf)=inf, tgamma(-inf)=nan with invalid */
- return x + INFINITY;
- if (ix < (0x3ff-54)<<20)
- /* |x| < 2^-54: tgamma(x) ~ 1/x, +-0 raises div-by-zero */
- return 1/x;
-
- /* integer arguments */
- /* raise inexact when non-integer */
- if (x == floor(x)) {
- if (sign)
- return 0/0.0;
- if (x <= sizeof fact/sizeof *fact)
- return fact[(int)x - 1];
- }
-
- /* x >= 172: tgamma(x)=inf with overflow */
- /* x =< -184: tgamma(x)=+-0 with underflow */
- if (ix >= 0x40670000) { /* |x| >= 184 */
- if (sign) {
- FORCE_EVAL((float)(0x1p-126/x));
- if (floor(x) * 0.5 == floor(x * 0.5))
- return 0;
- return -0.0;
- }
- x *= 0x1p1023;
- return x;
- }
-
- absx = sign ? -x : x;
-
- /* handle the error of x + g - 0.5 */
- y = absx + gmhalf;
- if (absx > gmhalf) {
- dy = y - absx;
- dy -= gmhalf;
- } else {
- dy = y - gmhalf;
- dy -= absx;
- }
-
- z = absx - 0.5;
- r = S(absx) * exp(-y);
- if (x < 0) {
- /* reflection formula for negative x */
- /* sinpi(absx) is not 0, integers are already handled */
- r = -pi / (sinpi(absx) * absx * r);
- dy = -dy;
- z = -z;
- }
- r += dy * (gmhalf+0.5) * r / y;
- z = pow(y, 0.5*z);
- y = r * z * z;
- return y;
-}
-
-#if 0
-double __lgamma_r(double x, int *sign)
-{
- double r, absx;
-
- *sign = 1;
-
- /* special cases */
- if (!isfinite(x))
- /* lgamma(nan)=nan, lgamma(+-inf)=inf */
- return x*x;
-
- /* integer arguments */
- if (x == floor(x) && x <= 2) {
- /* n <= 0: lgamma(n)=inf with divbyzero */
- /* n == 1,2: lgamma(n)=0 */
- if (x <= 0)
- return 1/0.0;
- return 0;
- }
-
- absx = fabs(x);
-
- /* lgamma(x) ~ -log(|x|) for tiny |x| */
- if (absx < 0x1p-54) {
- *sign = 1 - 2*!!signbit(x);
- return -log(absx);
- }
-
- /* use tgamma for smaller |x| */
- if (absx < 128) {
- x = tgamma(x);
- *sign = 1 - 2*!!signbit(x);
- return log(fabs(x));
- }
-
- /* second term (log(S)-g) could be more precise here.. */
- /* or with stirling: (|x|-0.5)*(log(|x|)-1) + poly(1/|x|) */
- r = (absx-0.5)*(log(absx+gmhalf)-1) + (log(S(absx)) - (gmhalf+0.5));
- if (x < 0) {
- /* reflection formula for negative x */
- x = sinpi(absx);
- *sign = 2*!!signbit(x) - 1;
- r = log(pi/(fabs(x)*absx)) - r;
- }
- return r;
-}
-
-weak_alias(__lgamma_r, lgamma_r);
-#endif