mirror of
https://sourceware.org/git/glibc.git
synced 2024-12-05 11:11:04 +00:00
581c785bf3
I used these shell commands: ../glibc/scripts/update-copyrights $PWD/../gnulib/build-aux/update-copyright (cd ../glibc && git commit -am"[this commit message]") and then ignored the output, which consisted lines saying "FOO: warning: copyright statement not found" for each of 7061 files FOO. I then removed trailing white space from math/tgmath.h, support/tst-support-open-dev-null-range.c, and sysdeps/x86_64/multiarch/strlen-vec.S, to work around the following obscure pre-commit check failure diagnostics from Savannah. I don't know why I run into these diagnostics whereas others evidently do not. remote: *** 912-#endif remote: *** 913: remote: *** 914- remote: *** error: lines with trailing whitespace found ... remote: *** error: sysdeps/unix/sysv/linux/statx_cp.c: trailing lines
220 lines
6.2 KiB
C
220 lines
6.2 KiB
C
/* Implementation of gamma function according to ISO C.
|
|
Copyright (C) 1997-2022 Free Software Foundation, Inc.
|
|
This file is part of the GNU C Library.
|
|
|
|
The GNU C Library is free software; you can redistribute it and/or
|
|
modify it under the terms of the GNU Lesser General Public
|
|
License as published by the Free Software Foundation; either
|
|
version 2.1 of the License, or (at your option) any later version.
|
|
|
|
The GNU C Library is distributed in the hope that it will be useful,
|
|
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
|
|
Lesser General Public License for more details.
|
|
|
|
You should have received a copy of the GNU Lesser General Public
|
|
License along with the GNU C Library; if not, see
|
|
<https://www.gnu.org/licenses/>. */
|
|
|
|
#include <math.h>
|
|
#include <math_private.h>
|
|
#include <fenv_private.h>
|
|
#include <math-underflow.h>
|
|
#include <float.h>
|
|
#include <libm-alias-finite.h>
|
|
|
|
/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's
|
|
approximation to gamma function. */
|
|
|
|
static const long double gamma_coeff[] =
|
|
{
|
|
0x1.555555555555555555555555558p-4L,
|
|
-0xb.60b60b60b60b60b60b60b60b6p-12L,
|
|
0x3.4034034034034034034034034p-12L,
|
|
-0x2.7027027027027027027027027p-12L,
|
|
0x3.72a3c5631fe46ae1d4e700dca9p-12L,
|
|
-0x7.daac36664f1f207daac36664f2p-12L,
|
|
0x1.a41a41a41a41a41a41a41a41a4p-8L,
|
|
-0x7.90a1b2c3d4e5f708192a3b4c5ep-8L,
|
|
0x2.dfd2c703c0cfff430edfd2c704p-4L,
|
|
-0x1.6476701181f39edbdb9ce625988p+0L,
|
|
0xd.672219167002d3a7a9c886459cp+0L,
|
|
-0x9.cd9292e6660d55b3f712eb9e08p+4L,
|
|
0x8.911a740da740da740da740da74p+8L,
|
|
};
|
|
|
|
#define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0]))
|
|
|
|
/* Return gamma (X), for positive X less than 191, in the form R *
|
|
2^(*EXP2_ADJ), where R is the return value and *EXP2_ADJ is set to
|
|
avoid overflow or underflow in intermediate calculations. */
|
|
|
|
static long double
|
|
gammal_positive (long double x, int *exp2_adj)
|
|
{
|
|
int local_signgam;
|
|
if (x < 0.5L)
|
|
{
|
|
*exp2_adj = 0;
|
|
return __ieee754_expl (__ieee754_lgammal_r (x + 1, &local_signgam)) / x;
|
|
}
|
|
else if (x <= 1.5L)
|
|
{
|
|
*exp2_adj = 0;
|
|
return __ieee754_expl (__ieee754_lgammal_r (x, &local_signgam));
|
|
}
|
|
else if (x < 11.5L)
|
|
{
|
|
/* Adjust into the range for using exp (lgamma). */
|
|
*exp2_adj = 0;
|
|
long double n = ceill (x - 1.5L);
|
|
long double x_adj = x - n;
|
|
long double eps;
|
|
long double prod = __gamma_productl (x_adj, 0, n, &eps);
|
|
return (__ieee754_expl (__ieee754_lgammal_r (x_adj, &local_signgam))
|
|
* prod * (1.0L + eps));
|
|
}
|
|
else
|
|
{
|
|
long double eps = 0;
|
|
long double x_eps = 0;
|
|
long double x_adj = x;
|
|
long double prod = 1;
|
|
if (x < 23.0L)
|
|
{
|
|
/* Adjust into the range for applying Stirling's
|
|
approximation. */
|
|
long double n = ceill (23.0L - x);
|
|
x_adj = x + n;
|
|
x_eps = (x - (x_adj - n));
|
|
prod = __gamma_productl (x_adj - n, x_eps, n, &eps);
|
|
}
|
|
/* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)).
|
|
Compute gamma (X_ADJ + X_EPS) using Stirling's approximation,
|
|
starting by computing pow (X_ADJ, X_ADJ) with a power of 2
|
|
factored out. */
|
|
long double exp_adj = -eps;
|
|
long double x_adj_int = roundl (x_adj);
|
|
long double x_adj_frac = x_adj - x_adj_int;
|
|
int x_adj_log2;
|
|
long double x_adj_mant = __frexpl (x_adj, &x_adj_log2);
|
|
if (x_adj_mant < M_SQRT1_2l)
|
|
{
|
|
x_adj_log2--;
|
|
x_adj_mant *= 2.0L;
|
|
}
|
|
*exp2_adj = x_adj_log2 * (int) x_adj_int;
|
|
long double ret = (__ieee754_powl (x_adj_mant, x_adj)
|
|
* __ieee754_exp2l (x_adj_log2 * x_adj_frac)
|
|
* __ieee754_expl (-x_adj)
|
|
* sqrtl (2 * M_PIl / x_adj)
|
|
/ prod);
|
|
exp_adj += x_eps * __ieee754_logl (x_adj);
|
|
long double bsum = gamma_coeff[NCOEFF - 1];
|
|
long double x_adj2 = x_adj * x_adj;
|
|
for (size_t i = 1; i <= NCOEFF - 1; i++)
|
|
bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i];
|
|
exp_adj += bsum / x_adj;
|
|
return ret + ret * __expm1l (exp_adj);
|
|
}
|
|
}
|
|
|
|
long double
|
|
__ieee754_gammal_r (long double x, int *signgamp)
|
|
{
|
|
int64_t hx;
|
|
double xhi;
|
|
long double ret;
|
|
|
|
xhi = ldbl_high (x);
|
|
EXTRACT_WORDS64 (hx, xhi);
|
|
|
|
if ((hx & 0x7fffffffffffffffLL) == 0)
|
|
{
|
|
/* Return value for x == 0 is Inf with divide by zero exception. */
|
|
*signgamp = 0;
|
|
return 1.0 / x;
|
|
}
|
|
if (hx < 0 && (uint64_t) hx < 0xfff0000000000000ULL && rintl (x) == x)
|
|
{
|
|
/* Return value for integer x < 0 is NaN with invalid exception. */
|
|
*signgamp = 0;
|
|
return (x - x) / (x - x);
|
|
}
|
|
if (hx == 0xfff0000000000000ULL)
|
|
{
|
|
/* x == -Inf. According to ISO this is NaN. */
|
|
*signgamp = 0;
|
|
return x - x;
|
|
}
|
|
if ((hx & 0x7ff0000000000000ULL) == 0x7ff0000000000000ULL)
|
|
{
|
|
/* Positive infinity (return positive infinity) or NaN (return
|
|
NaN). */
|
|
*signgamp = 0;
|
|
return x + x;
|
|
}
|
|
|
|
if (x >= 172.0L)
|
|
{
|
|
/* Overflow. */
|
|
*signgamp = 0;
|
|
return LDBL_MAX * LDBL_MAX;
|
|
}
|
|
else
|
|
{
|
|
SET_RESTORE_ROUNDL (FE_TONEAREST);
|
|
if (x > 0.0L)
|
|
{
|
|
*signgamp = 0;
|
|
int exp2_adj;
|
|
ret = gammal_positive (x, &exp2_adj);
|
|
ret = __scalbnl (ret, exp2_adj);
|
|
}
|
|
else if (x >= -0x1p-110L)
|
|
{
|
|
*signgamp = 0;
|
|
ret = 1.0L / x;
|
|
}
|
|
else
|
|
{
|
|
long double tx = truncl (x);
|
|
*signgamp = (tx == 2.0L * truncl (tx / 2.0L)) ? -1 : 1;
|
|
if (x <= -191.0L)
|
|
/* Underflow. */
|
|
ret = LDBL_MIN * LDBL_MIN;
|
|
else
|
|
{
|
|
long double frac = tx - x;
|
|
if (frac > 0.5L)
|
|
frac = 1.0L - frac;
|
|
long double sinpix = (frac <= 0.25L
|
|
? __sinl (M_PIl * frac)
|
|
: __cosl (M_PIl * (0.5L - frac)));
|
|
int exp2_adj;
|
|
ret = M_PIl / (-x * sinpix
|
|
* gammal_positive (-x, &exp2_adj));
|
|
ret = __scalbnl (ret, -exp2_adj);
|
|
math_check_force_underflow_nonneg (ret);
|
|
}
|
|
}
|
|
}
|
|
if (isinf (ret) && x != 0)
|
|
{
|
|
if (*signgamp < 0)
|
|
return -(-copysignl (LDBL_MAX, ret) * LDBL_MAX);
|
|
else
|
|
return copysignl (LDBL_MAX, ret) * LDBL_MAX;
|
|
}
|
|
else if (ret == 0)
|
|
{
|
|
if (*signgamp < 0)
|
|
return -(-copysignl (LDBL_MIN, ret) * LDBL_MIN);
|
|
else
|
|
return copysignl (LDBL_MIN, ret) * LDBL_MIN;
|
|
}
|
|
else
|
|
return ret;
|
|
}
|
|
libm_alias_finite (__ieee754_gammal_r, __gammal_r)
|