glibc/sysdeps/ieee754/dbl-64/e_gamma_r.c
Joseph Myers 81dca813cc Use copysign functions not __copysign functions in glibc libm.
Continuing the move to use, within libm, public names for libm
functions that can be inlined as built-in functions on many
architectures, this patch moves calls to __copysign functions to call
the corresponding copysign names instead, with asm redirection to
__copysign when the calls are not inlined (all cases are inlined
except for IBM long double for powerpc soft-float / e500v1).  This
eliminates the need for an inline function defining __copysign in
terms of __builtin_copysign.

Tested for x86_64, and with build-many-glibcs.py.

	* include/math.h [!_ISOMAC && !(__FINITE_MATH_ONLY__ &&
	__FINITE_MATH_ONLY__ > 0) && !NO_MATH_REDIRECT]
	(MATH_REDIRECT_BINARY_ARGS): New macro.
	[!_ISOMAC && !(__FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ > 0)
	&& !NO_MATH_REDIRECT] (copysign): Redirect using MATH_REDIRECT.
	* sysdeps/alpha/fpu/s_copysign.c: Define NO_MATH_REDIRECT before
	header inclusion.
	* sysdeps/alpha/fpu/s_copysignf.c: Likewise.
	* sysdeps/ieee754/dbl-64/s_copysign.c: Likewise.
	* sysdeps/ieee754/float128/s_copysignf128.c: Likewise.
	* sysdeps/ieee754/flt-32/s_copysignf.c: Likewise.
	* sysdeps/ieee754/ldbl-128/s_copysignl.c: Likewise.
	* sysdeps/ieee754/ldbl-128ibm/s_copysignl.c: Likewise.
	* sysdeps/ieee754/ldbl-96/s_copysignl.c: Likewise.
	* sysdeps/powerpc/powerpc32/power4/fpu/multiarch/s_copysign.c:
	Likewise.
	* sysdeps/powerpc/powerpc32/power4/fpu/multiarch/s_copysignf.c:
	Likewise.
	* sysdeps/powerpc/powerpc64/fpu/multiarch/s_copysign.c: Likewise.
	* sysdeps/powerpc/powerpc64/fpu/multiarch/s_copysignf.c: Likewise.
	* sysdeps/riscv/rvd/s_copysign.c: Likewise.
	* sysdeps/riscv/rvf/s_copysignf.c: Likewise.
	* sysdeps/sparc/sparc32/sparcv9/fpu/multiarch/s_copysign.c:
	Likewise.
	* sysdeps/sparc/sparc32/sparcv9/fpu/multiarch/s_copysignf.c:
	Likewise.
	* sysdeps/generic/math_private_calls.h
	[!__MATH_DECLARING_LONG_DOUBLE || !NO_LONG_DOUBLE] (__copysign):
	Do not declare and define as an inline function.
	* math/divtc3.c (__divtc3): Use copysign functions instead of
	__copysign variants.
	* math/multc3.c (__multc3): Likewise.
	* sysdeps/generic/math-type-macros.h (M_COPYSIGN): Likewise.
	* sysdeps/ieee754/dbl-64/e_atan2.c (signArctan2): Likewise.
	* sysdeps/ieee754/dbl-64/e_atanh.c (__ieee754_atanh): Likewise.
	* sysdeps/ieee754/dbl-64/e_gamma_r.c (__ieee754_gamma_r):
	Likewise.
	* sysdeps/ieee754/dbl-64/e_jn.c (__ieee754_jn): Likewise.
	(__ieee754_yn): Likewise.
	* sysdeps/ieee754/dbl-64/s_asinh.c (__asinh): Likewise.
	* sysdeps/ieee754/dbl-64/s_atan.c (__signArctan): Likewise.
	* sysdeps/ieee754/dbl-64/s_scalbln.c (__scalbln): Likewise.
	* sysdeps/ieee754/dbl-64/s_scalbn.c (__scalbn): Likewise.
	* sysdeps/ieee754/dbl-64/s_sin.c (do_sin): Likewise.
	(__sin): Likewise.
	* sysdeps/ieee754/dbl-64/s_sincos.c (__sincos): Likewise.
	* sysdeps/ieee754/dbl-64/wordsize-64/s_nearbyint.c (__nearbyint):
	Likewise.
	* sysdeps/ieee754/dbl-64/wordsize-64/s_scalbln.c (__scalbln):
	Likewise.
	* sysdeps/ieee754/dbl-64/wordsize-64/s_scalbn.c (__scalbn):
	Likewise.
	* sysdeps/ieee754/flt-32/e_atanhf.c (__ieee754_atanhf): Likewise.
	* sysdeps/ieee754/flt-32/e_gammaf_r.c (__ieee754_gammaf_r):
	Likewise.
	* sysdeps/ieee754/flt-32/e_jnf.c (__ieee754_jnf): Likewise.
	(__ieee754_ynf): Likewise.
	* sysdeps/ieee754/flt-32/s_asinhf.c (__asinhf): Likewise.
	* sysdeps/ieee754/flt-32/s_scalbnf.c (__scalbnf): Likewise.
	* sysdeps/ieee754/k_standard.c (__kernel_standard): Likewise.
	* sysdeps/ieee754/ldbl-128/e_gammal_r.c (__ieee754_gammal_r):
	Likewise.
	* sysdeps/ieee754/ldbl-128/e_jnl.c (__ieee754_jnl): Likewise.
	(__ieee754_ynl): Likewise.
	* sysdeps/ieee754/ldbl-128/s_scalblnl.c (__scalblnl): Likewise.
	* sysdeps/ieee754/ldbl-128/s_scalbnl.c (__scalbnl): Likewise.
	* sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c (__ieee754_gammal_r):
	Likewise.
	* sysdeps/ieee754/ldbl-128ibm/e_jnl.c (__ieee754_jnl): Likewise.
	(__ieee754_ynl): Likewise.
	* sysdeps/ieee754/ldbl-128ibm/s_fmal.c (__fmal): Likewise.
	* sysdeps/ieee754/ldbl-128ibm/s_scalblnl.c (__scalblnl): Likewise.
	* sysdeps/ieee754/ldbl-128ibm/s_scalbnl.c (__scalbnl): Likewise.
	* sysdeps/ieee754/ldbl-96/e_gammal_r.c (__ieee754_gammal_r):
	Likewise.
	* sysdeps/ieee754/ldbl-96/e_jnl.c (__ieee754_jnl): Likewise.
	(__ieee754_ynl)
	* sysdeps/ieee754/ldbl-96/s_asinhl.c (__asinhl): Likewise.
	* sysdeps/ieee754/ldbl-96/s_scalblnl.c (__scalblnl): Likewise.
	* sysdeps/ieee754/ldbl-opt/nldbl-copysign.c (copysignl): Likewise.
	* sysdeps/powerpc/power5+/fpu/s_modf.c (__modf): Likewise.
	* sysdeps/powerpc/power5+/fpu/s_modff.c (__modff): Likewise.
2018-09-27 20:04:48 +00:00

224 lines
6.1 KiB
C

/* Implementation of gamma function according to ISO C.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
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
<http://www.gnu.org/licenses/>. */
#include <math.h>
#include <math-narrow-eval.h>
#include <math_private.h>
#include <fenv_private.h>
#include <math-underflow.h>
#include <float.h>
/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's
approximation to gamma function. */
static const double gamma_coeff[] =
{
0x1.5555555555555p-4,
-0xb.60b60b60b60b8p-12,
0x3.4034034034034p-12,
-0x2.7027027027028p-12,
0x3.72a3c5631fe46p-12,
-0x7.daac36664f1f4p-12,
};
#define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0]))
/* Return gamma (X), for positive X less than 184, 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 double
gamma_positive (double x, int *exp2_adj)
{
int local_signgam;
if (x < 0.5)
{
*exp2_adj = 0;
return __ieee754_exp (__ieee754_lgamma_r (x + 1, &local_signgam)) / x;
}
else if (x <= 1.5)
{
*exp2_adj = 0;
return __ieee754_exp (__ieee754_lgamma_r (x, &local_signgam));
}
else if (x < 6.5)
{
/* Adjust into the range for using exp (lgamma). */
*exp2_adj = 0;
double n = ceil (x - 1.5);
double x_adj = x - n;
double eps;
double prod = __gamma_product (x_adj, 0, n, &eps);
return (__ieee754_exp (__ieee754_lgamma_r (x_adj, &local_signgam))
* prod * (1.0 + eps));
}
else
{
double eps = 0;
double x_eps = 0;
double x_adj = x;
double prod = 1;
if (x < 12.0)
{
/* Adjust into the range for applying Stirling's
approximation. */
double n = ceil (12.0 - x);
x_adj = math_narrow_eval (x + n);
x_eps = (x - (x_adj - n));
prod = __gamma_product (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. */
double exp_adj = -eps;
double x_adj_int = round (x_adj);
double x_adj_frac = x_adj - x_adj_int;
int x_adj_log2;
double x_adj_mant = __frexp (x_adj, &x_adj_log2);
if (x_adj_mant < M_SQRT1_2)
{
x_adj_log2--;
x_adj_mant *= 2.0;
}
*exp2_adj = x_adj_log2 * (int) x_adj_int;
double ret = (__ieee754_pow (x_adj_mant, x_adj)
* __ieee754_exp2 (x_adj_log2 * x_adj_frac)
* __ieee754_exp (-x_adj)
* sqrt (2 * M_PI / x_adj)
/ prod);
exp_adj += x_eps * __ieee754_log (x_adj);
double bsum = gamma_coeff[NCOEFF - 1];
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 * __expm1 (exp_adj);
}
}
double
__ieee754_gamma_r (double x, int *signgamp)
{
int32_t hx;
uint32_t lx;
double ret;
EXTRACT_WORDS (hx, lx, x);
if (__glibc_unlikely (((hx & 0x7fffffff) | lx) == 0))
{
/* Return value for x == 0 is Inf with divide by zero exception. */
*signgamp = 0;
return 1.0 / x;
}
if (__builtin_expect (hx < 0, 0)
&& (uint32_t) hx < 0xfff00000 && rint (x) == x)
{
/* Return value for integer x < 0 is NaN with invalid exception. */
*signgamp = 0;
return (x - x) / (x - x);
}
if (__glibc_unlikely ((unsigned int) hx == 0xfff00000 && lx == 0))
{
/* x == -Inf. According to ISO this is NaN. */
*signgamp = 0;
return x - x;
}
if (__glibc_unlikely ((hx & 0x7ff00000) == 0x7ff00000))
{
/* Positive infinity (return positive infinity) or NaN (return
NaN). */
*signgamp = 0;
return x + x;
}
if (x >= 172.0)
{
/* Overflow. */
*signgamp = 0;
ret = math_narrow_eval (DBL_MAX * DBL_MAX);
return ret;
}
else
{
SET_RESTORE_ROUND (FE_TONEAREST);
if (x > 0.0)
{
*signgamp = 0;
int exp2_adj;
double tret = gamma_positive (x, &exp2_adj);
ret = __scalbn (tret, exp2_adj);
}
else if (x >= -DBL_EPSILON / 4.0)
{
*signgamp = 0;
ret = 1.0 / x;
}
else
{
double tx = trunc (x);
*signgamp = (tx == 2.0 * trunc (tx / 2.0)) ? -1 : 1;
if (x <= -184.0)
/* Underflow. */
ret = DBL_MIN * DBL_MIN;
else
{
double frac = tx - x;
if (frac > 0.5)
frac = 1.0 - frac;
double sinpix = (frac <= 0.25
? __sin (M_PI * frac)
: __cos (M_PI * (0.5 - frac)));
int exp2_adj;
double tret = M_PI / (-x * sinpix
* gamma_positive (-x, &exp2_adj));
ret = __scalbn (tret, -exp2_adj);
math_check_force_underflow_nonneg (ret);
}
}
ret = math_narrow_eval (ret);
}
if (isinf (ret) && x != 0)
{
if (*signgamp < 0)
{
ret = math_narrow_eval (-copysign (DBL_MAX, ret) * DBL_MAX);
ret = -ret;
}
else
ret = math_narrow_eval (copysign (DBL_MAX, ret) * DBL_MAX);
return ret;
}
else if (ret == 0)
{
if (*signgamp < 0)
{
ret = math_narrow_eval (-copysign (DBL_MIN, ret) * DBL_MIN);
ret = -ret;
}
else
ret = math_narrow_eval (copysign (DBL_MIN, ret) * DBL_MIN);
return ret;
}
else
return ret;
}
strong_alias (__ieee754_gamma_r, __gamma_r_finite)