1  /* Compute a product of X, X+1, ..., with an error estimate.
       2     Copyright (C) 2013-2023 Free Software Foundation, Inc.
       3     This file is part of the GNU C Library.
       4  
       5     The GNU C Library is free software; you can redistribute it and/or
       6     modify it under the terms of the GNU Lesser General Public
       7     License as published by the Free Software Foundation; either
       8     version 2.1 of the License, or (at your option) any later version.
       9  
      10     The GNU C Library is distributed in the hope that it will be useful,
      11     but WITHOUT ANY WARRANTY; without even the implied warranty of
      12     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
      13     Lesser General Public License for more details.
      14  
      15     You should have received a copy of the GNU Lesser General Public
      16     License along with the GNU C Library; if not, see
      17     <https://www.gnu.org/licenses/>.  */
      18  
      19  #include <math.h>
      20  #include <math_private.h>
      21  #include <fenv_private.h>
      22  #include <mul_split.h>
      23  
      24  /* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N
      25     - 1, in the form R * (1 + *EPS) where the return value R is an
      26     approximation to the product and *EPS is set to indicate the
      27     approximate error in the return value.  X is such that all the
      28     values X + 1, ..., X + N - 1 are exactly representable, and X_EPS /
      29     X is small enough that factors quadratic in it can be
      30     neglected.  */
      31  
      32  double
      33  __gamma_product (double x, double x_eps, int n, double *eps)
      34  {
      35    SET_RESTORE_ROUND (FE_TONEAREST);
      36    double ret = x;
      37    *eps = x_eps / x;
      38    for (int i = 1; i < n; i++)
      39      {
      40        *eps += x_eps / (x + i);
      41        double lo;
      42        mul_split (&ret, &lo, ret, x + i);
      43        *eps += lo / ret;
      44      }
      45    return ret;
      46  }