213 lines
5.7 KiB
C
213 lines
5.7 KiB
C
/* Implementation of gamma function according to ISO C.
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Copyright (C) 1997-2017 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<http://www.gnu.org/licenses/>. */
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#include <math.h>
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#include <math_private.h>
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#include <float.h>
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/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's
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approximation to gamma function. */
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static const float gamma_coeff[] =
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{
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0x1.555556p-4f,
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-0xb.60b61p-12f,
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0x3.403404p-12f,
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};
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#define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0]))
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/* Return gamma (X), for positive X less than 42, in the form R *
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2^(*EXP2_ADJ), where R is the return value and *EXP2_ADJ is set to
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avoid overflow or underflow in intermediate calculations. */
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static float
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gammaf_positive (float x, int *exp2_adj)
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{
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int local_signgam;
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if (x < 0.5f)
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{
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*exp2_adj = 0;
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return __ieee754_expf (__ieee754_lgammaf_r (x + 1, &local_signgam)) / x;
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}
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else if (x <= 1.5f)
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{
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*exp2_adj = 0;
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return __ieee754_expf (__ieee754_lgammaf_r (x, &local_signgam));
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}
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else if (x < 2.5f)
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{
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*exp2_adj = 0;
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float x_adj = x - 1;
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return (__ieee754_expf (__ieee754_lgammaf_r (x_adj, &local_signgam))
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* x_adj);
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}
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else
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{
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float eps = 0;
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float x_eps = 0;
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float x_adj = x;
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float prod = 1;
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if (x < 4.0f)
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{
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/* Adjust into the range for applying Stirling's
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approximation. */
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float n = __ceilf (4.0f - x);
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x_adj = math_narrow_eval (x + n);
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x_eps = (x - (x_adj - n));
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prod = __gamma_productf (x_adj - n, x_eps, n, &eps);
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}
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/* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)).
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Compute gamma (X_ADJ + X_EPS) using Stirling's approximation,
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starting by computing pow (X_ADJ, X_ADJ) with a power of 2
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factored out. */
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float exp_adj = -eps;
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float x_adj_int = __roundf (x_adj);
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float x_adj_frac = x_adj - x_adj_int;
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int x_adj_log2;
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float x_adj_mant = __frexpf (x_adj, &x_adj_log2);
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if (x_adj_mant < (float) M_SQRT1_2)
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{
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x_adj_log2--;
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x_adj_mant *= 2.0f;
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}
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*exp2_adj = x_adj_log2 * (int) x_adj_int;
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float ret = (__ieee754_powf (x_adj_mant, x_adj)
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* __ieee754_exp2f (x_adj_log2 * x_adj_frac)
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* __ieee754_expf (-x_adj)
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* __ieee754_sqrtf (2 * (float) M_PI / x_adj)
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/ prod);
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exp_adj += x_eps * __ieee754_logf (x_adj);
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float bsum = gamma_coeff[NCOEFF - 1];
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float x_adj2 = x_adj * x_adj;
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for (size_t i = 1; i <= NCOEFF - 1; i++)
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bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i];
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exp_adj += bsum / x_adj;
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return ret + ret * __expm1f (exp_adj);
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}
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}
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float
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__ieee754_gammaf_r (float x, int *signgamp)
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{
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int32_t hx;
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float ret;
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GET_FLOAT_WORD (hx, x);
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if (__glibc_unlikely ((hx & 0x7fffffff) == 0))
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{
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/* Return value for x == 0 is Inf with divide by zero exception. */
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*signgamp = 0;
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return 1.0 / x;
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}
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if (__builtin_expect (hx < 0, 0)
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&& (uint32_t) hx < 0xff800000 && __rintf (x) == x)
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{
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/* Return value for integer x < 0 is NaN with invalid exception. */
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*signgamp = 0;
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return (x - x) / (x - x);
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}
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if (__glibc_unlikely (hx == 0xff800000))
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{
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/* x == -Inf. According to ISO this is NaN. */
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*signgamp = 0;
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return x - x;
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}
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if (__glibc_unlikely ((hx & 0x7f800000) == 0x7f800000))
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{
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/* Positive infinity (return positive infinity) or NaN (return
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NaN). */
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*signgamp = 0;
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return x + x;
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}
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if (x >= 36.0f)
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{
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/* Overflow. */
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*signgamp = 0;
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ret = math_narrow_eval (FLT_MAX * FLT_MAX);
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return ret;
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}
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else
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{
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SET_RESTORE_ROUNDF (FE_TONEAREST);
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if (x > 0.0f)
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{
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*signgamp = 0;
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int exp2_adj;
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float tret = gammaf_positive (x, &exp2_adj);
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ret = __scalbnf (tret, exp2_adj);
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}
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else if (x >= -FLT_EPSILON / 4.0f)
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{
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*signgamp = 0;
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ret = 1.0f / x;
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}
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else
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{
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float tx = __truncf (x);
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*signgamp = (tx == 2.0f * __truncf (tx / 2.0f)) ? -1 : 1;
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if (x <= -42.0f)
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/* Underflow. */
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ret = FLT_MIN * FLT_MIN;
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else
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{
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float frac = tx - x;
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if (frac > 0.5f)
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frac = 1.0f - frac;
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float sinpix = (frac <= 0.25f
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? __sinf ((float) M_PI * frac)
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: __cosf ((float) M_PI * (0.5f - frac)));
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int exp2_adj;
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float tret = (float) M_PI / (-x * sinpix
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* gammaf_positive (-x, &exp2_adj));
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ret = __scalbnf (tret, -exp2_adj);
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math_check_force_underflow_nonneg (ret);
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}
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}
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ret = math_narrow_eval (ret);
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}
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if (isinf (ret) && x != 0)
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{
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if (*signgamp < 0)
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{
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ret = math_narrow_eval (-__copysignf (FLT_MAX, ret) * FLT_MAX);
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ret = -ret;
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}
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else
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ret = math_narrow_eval (__copysignf (FLT_MAX, ret) * FLT_MAX);
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return ret;
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}
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else if (ret == 0)
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{
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if (*signgamp < 0)
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{
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ret = math_narrow_eval (-__copysignf (FLT_MIN, ret) * FLT_MIN);
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ret = -ret;
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}
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else
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ret = math_narrow_eval (__copysignf (FLT_MIN, ret) * FLT_MIN);
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return ret;
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}
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else
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return ret;
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}
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strong_alias (__ieee754_gammaf_r, __gammaf_r_finite)
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