sysdeps/ieee754/flt-32/e_gammaf_r.c

   1 /* Implementation of gamma function according to ISO C.
   2    Copyright (C) 1997-2014 Free Software Foundation, Inc.
   3    This file is part of the GNU C Library.
   4    Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
   5
   6    The GNU C Library is free software; you can redistribute it and/or
   7    modify it under the terms of the GNU Lesser General Public
   8    License as published by the Free Software Foundation; either
   9    version 2.1 of the License, or (at your option) any later version.
  10
  11    The GNU C Library is distributed in the hope that it will be useful,
  12    but WITHOUT ANY WARRANTY; without even the implied warranty of
  13    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  14    Lesser General Public License for more details.
  15
  16    You should have received a copy of the GNU Lesser General Public
  17    License along with the GNU C Library; if not, see
  18    <http://www.gnu.org/licenses/>.  */
  19
  20 #include <math.h>
  21 #include <math_private.h>
  22 #include <float.h>
  23
  24 /* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's
  25    approximation to gamma function.  */
  26
  27 static const float gamma_coeff[] =
  28   {
  29     0x1.555556p-4f,
  30     -0xb.60b61p-12f,
  31     0x3.403404p-12f,
  32   };
  33
  34 #define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0]))
  35
  36 /* Return gamma (X), for positive X less than 42, in the form R *
  37    2^(*EXP2_ADJ), where R is the return value and *EXP2_ADJ is set to
  38    avoid overflow or underflow in intermediate calculations.  */
  39
  40 static float
  41 gammaf_positive (float x, int *exp2_adj)
  42 {
  43   int local_signgam;
  44   if (x < 0.5f)
  45     {
  46       *exp2_adj = 0;
  47       return __ieee754_expf (__ieee754_lgammaf_r (x + 1, &local_signgam)) / x;
  48     }
  49   else if (x <= 1.5f)
  50     {
  51       *exp2_adj = 0;
  52       return __ieee754_expf (__ieee754_lgammaf_r (x, &local_signgam));
  53     }
  54   else if (x < 2.5f)
  55     {
  56       *exp2_adj = 0;
  57       float x_adj = x - 1;
  58       return (__ieee754_expf (__ieee754_lgammaf_r (x_adj, &local_signgam))
  59               * x_adj);
  60     }
  61   else
  62     {
  63       float eps = 0;
  64       float x_eps = 0;
  65       float x_adj = x;
  66       float prod = 1;
  67       if (x < 4.0f)
  68         {
  69           /* Adjust into the range for applying Stirling's
  70              approximation.  */
  71           float n = __ceilf (4.0f - x);
  72 #if FLT_EVAL_METHOD != 0
  73           volatile
  74 #endif
  75           float x_tmp = x + n;
  76           x_adj = x_tmp;
  77           x_eps = (x - (x_adj - n));
  78           prod = __gamma_productf (x_adj - n, x_eps, n, &eps);
  79         }
  80       /* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)).
  81          Compute gamma (X_ADJ + X_EPS) using Stirling's approximation,
  82          starting by computing pow (X_ADJ, X_ADJ) with a power of 2
  83          factored out.  */
  84       float exp_adj = -eps;
  85       float x_adj_int = __roundf (x_adj);
  86       float x_adj_frac = x_adj - x_adj_int;
  87       int x_adj_log2;
  88       float x_adj_mant = __frexpf (x_adj, &x_adj_log2);
  89       if (x_adj_mant < (float) M_SQRT1_2)
  90         {
  91           x_adj_log2--;
  92           x_adj_mant *= 2.0f;
  93         }
  94       *exp2_adj = x_adj_log2 * (int) x_adj_int;
  95       float ret = (__ieee754_powf (x_adj_mant, x_adj)
  96                    * __ieee754_exp2f (x_adj_log2 * x_adj_frac)
  97                    * __ieee754_expf (-x_adj)
  98                    * __ieee754_sqrtf (2 * (float) M_PI / x_adj)
  99                    / prod);
 100       exp_adj += x_eps * __ieee754_logf (x);
 101       float bsum = gamma_coeff[NCOEFF - 1];
 102       float x_adj2 = x_adj * x_adj;
 103       for (size_t i = 1; i <= NCOEFF - 1; i++)
 104         bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i];
 105       exp_adj += bsum / x_adj;
 106       return ret + ret * __expm1f (exp_adj);
 107     }
 108 }
 109
 110 float
 111 __ieee754_gammaf_r (float x, int *signgamp)
 112 {
 113   int32_t hx;
 114
 115   GET_FLOAT_WORD (hx, x);
 116
 117   if (__builtin_expect ((hx & 0x7fffffff) == 0, 0))
 118     {
 119       /* Return value for x == 0 is Inf with divide by zero exception.  */
 120       *signgamp = 0;
 121       return 1.0 / x;
 122     }
 123   if (__builtin_expect (hx < 0, 0)
 124       && (u_int32_t) hx < 0xff800000 && __rintf (x) == x)
 125     {
 126       /* Return value for integer x < 0 is NaN with invalid exception.  */
 127       *signgamp = 0;
 128       return (x - x) / (x - x);
 129     }
 130   if (__builtin_expect (hx == 0xff800000, 0))
 131     {
 132       /* x == -Inf.  According to ISO this is NaN.  */
 133       *signgamp = 0;
 134       return x - x;
 135     }
 136   if (__builtin_expect ((hx & 0x7f800000) == 0x7f800000, 0))
 137     {
 138       /* Positive infinity (return positive infinity) or NaN (return
 139          NaN).  */
 140       *signgamp = 0;
 141       return x + x;
 142     }
 143
 144   if (x >= 36.0f)
 145     {
 146       /* Overflow.  */
 147       *signgamp = 0;
 148       return FLT_MAX * FLT_MAX;
 149     }
 150   else if (x > 0.0f)
 151     {
 152       *signgamp = 0;
 153       int exp2_adj;
 154       float ret = gammaf_positive (x, &exp2_adj);
 155       return __scalbnf (ret, exp2_adj);
 156     }
 157   else if (x >= -FLT_EPSILON / 4.0f)
 158     {
 159       *signgamp = 0;
 160       return 1.0f / x;
 161     }
 162   else
 163     {
 164       float tx = __truncf (x);
 165       *signgamp = (tx == 2.0f * __truncf (tx / 2.0f)) ? -1 : 1;
 166       if (x <= -42.0f)
 167         /* Underflow.  */
 168         return FLT_MIN * FLT_MIN;
 169       float frac = tx - x;
 170       if (frac > 0.5f)
 171         frac = 1.0f - frac;
 172       float sinpix = (frac <= 0.25f
 173                       ? __sinf ((float) M_PI * frac)
 174                       : __cosf ((float) M_PI * (0.5f - frac)));
 175       int exp2_adj;
 176       float ret = (float) M_PI / (-x * sinpix
 177                                   * gammaf_positive (-x, &exp2_adj));
 178       return __scalbnf (ret, -exp2_adj);
 179     }
 180 }
 181 strong_alias (__ieee754_gammaf_r, __gammaf_r_finite)