kc3-lang/libquadmath/math/tgammaq.c

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• Hash : 4f659ab9
  Author : Thomas de Grivel
  Date : 2025-11-02T19:33:45
  

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• math/tgammaq.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 and
  		  Jakub Jelinek <jj@ultra.linux.cz, 1999.
  
     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 "quadmath-imp.h"
  __float128
  tgammaq (__float128 x)
  {
    int sign;
    __float128 ret;
    ret = __quadmath_gammaq_r (x, &sign);
    return sign < 0 ? -ret : ret;
  }
  
  /* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's
     approximation to gamma function.  */
  
  static const __float128 gamma_coeff[] =
    {
      0x1.5555555555555555555555555555p-4Q,
      -0xb.60b60b60b60b60b60b60b60b60b8p-12Q,
      0x3.4034034034034034034034034034p-12Q,
      -0x2.7027027027027027027027027028p-12Q,
      0x3.72a3c5631fe46ae1d4e700dca8f2p-12Q,
      -0x7.daac36664f1f207daac36664f1f4p-12Q,
      0x1.a41a41a41a41a41a41a41a41a41ap-8Q,
      -0x7.90a1b2c3d4e5f708192a3b4c5d7p-8Q,
      0x2.dfd2c703c0cfff430edfd2c703cp-4Q,
      -0x1.6476701181f39edbdb9ce625987dp+0Q,
      0xd.672219167002d3a7a9c886459cp+0Q,
      -0x9.cd9292e6660d55b3f712eb9e07c8p+4Q,
      0x8.911a740da740da740da740da741p+8Q,
      -0x8.d0cc570e255bf59ff6eec24b49p+12Q,
    };
  
  #define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0]))
  
  /* Return gamma (X), for positive X less than 1775, 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 __float128
  gammal_positive (__float128 x, int *exp2_adj)
  {
    int local_signgam;
    if (x < 0.5Q)
      {
        *exp2_adj = 0;
        return expq (__quadmath_lgammaq_r (x + 1, &local_signgam)) / x;
      }
    else if (x <= 1.5Q)
      {
        *exp2_adj = 0;
        return expq (__quadmath_lgammaq_r (x, &local_signgam));
      }
    else if (x < 12.5Q)
      {
        /* Adjust into the range for using exp (lgamma).  */
        *exp2_adj = 0;
        __float128 n = ceilq (x - 1.5Q);
        __float128 x_adj = x - n;
        __float128 eps;
        __float128 prod = __quadmath_gamma_productq (x_adj, 0, n, &eps);
        return (expq (__quadmath_lgammaq_r (x_adj, &local_signgam))
  	      * prod * (1 + eps));
      }
    else
      {
        __float128 eps = 0;
        __float128 x_eps = 0;
        __float128 x_adj = x;
        __float128 prod = 1;
        if (x < 24)
  	{
  	  /* Adjust into the range for applying Stirling's
  	     approximation.  */
  	  __float128 n = ceilq (24 - x);
  	  x_adj = x + n;
  	  x_eps = (x - (x_adj - n));
  	  prod = __quadmath_gamma_productq (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.  */
        __float128 exp_adj = -eps;
        __float128 x_adj_int = roundq (x_adj);
        __float128 x_adj_frac = x_adj - x_adj_int;
        int x_adj_log2;
        __float128 x_adj_mant = frexpq (x_adj, &x_adj_log2);
        if (x_adj_mant < M_SQRT1_2q)
  	{
  	  x_adj_log2--;
  	  x_adj_mant *= 2;
  	}
        *exp2_adj = x_adj_log2 * (int) x_adj_int;
        __float128 ret = (powq (x_adj_mant, x_adj)
  		       * exp2q (x_adj_log2 * x_adj_frac)
  		       * expq (-x_adj)
  		       * sqrtq (2 * M_PIq / x_adj)
  		       / prod);
        exp_adj += x_eps * logq (x_adj);
        __float128 bsum = gamma_coeff[NCOEFF - 1];
        __float128 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 * expm1q (exp_adj);
      }
  }
  
  __float128
  __quadmath_gammaq_r (__float128 x, int *signgamp)
  {
    int64_t hx;
    uint64_t lx;
    __float128 ret;
  
    GET_FLT128_WORDS64 (hx, lx, x);
  
    if (((hx & 0x7fffffffffffffffLL) | lx) == 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 < 0xffff000000000000ULL && rintq (x) == x)
      {
        /* Return value for integer x < 0 is NaN with invalid exception.  */
        *signgamp = 0;
        return (x - x) / (x - x);
      }
    if (hx == 0xffff000000000000ULL && lx == 0)
      {
        /* x == -Inf.  According to ISO this is NaN.  */
        *signgamp = 0;
        return x - x;
      }
    if ((hx & 0x7fff000000000000ULL) == 0x7fff000000000000ULL)
      {
        /* Positive infinity (return positive infinity) or NaN (return
  	 NaN).  */
        *signgamp = 0;
        return x + x;
      }
  
    if (x >= 1756)
      {
        /* Overflow.  */
        *signgamp = 0;
        return FLT128_MAX * FLT128_MAX;
      }
    else
      {
        SET_RESTORE_ROUNDF128 (FE_TONEAREST);
        if (x > 0)
  	{
  	  *signgamp = 0;
  	  int exp2_adj;
  	  ret = gammal_positive (x, &exp2_adj);
  	  ret = scalbnq (ret, exp2_adj);
  	}
        else if (x >= -FLT128_EPSILON / 4)
  	{
  	  *signgamp = 0;
  	  ret = 1 / x;
  	}
        else
  	{
  	  __float128 tx = truncq (x);
  	  *signgamp = (tx == 2 * truncq (tx / 2)) ? -1 : 1;
  	  if (x <= -1775)
  	    /* Underflow.  */
  	    ret = FLT128_MIN * FLT128_MIN;
  	  else
  	    {
  	      __float128 frac = tx - x;
  	      if (frac > 0.5Q)
  		frac = 1 - frac;
  	      __float128 sinpix = (frac <= 0.25Q
  				  ? sinq (M_PIq * frac)
  				  : cosq (M_PIq * (0.5Q - frac)));
  	      int exp2_adj;
  	      ret = M_PIq / (-x * sinpix
  			     * gammal_positive (-x, &exp2_adj));
  	      ret = scalbnq (ret, -exp2_adj);
  	      math_check_force_underflow_nonneg (ret);
  	    }
  	}
      }
    if (isinfq (ret) && x != 0)
      {
        if (*signgamp < 0)
  	return -(-copysignq (FLT128_MAX, ret) * FLT128_MAX);
        else
  	return copysignq (FLT128_MAX, ret) * FLT128_MAX;
      }
    else if (ret == 0)
      {
        if (*signgamp < 0)
  	return -(-copysignq (FLT128_MIN, ret) * FLT128_MIN);
        else
  	return copysignq (FLT128_MIN, ret) * FLT128_MIN;
      }
    else
      return ret;
  }
  

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