sysdeps/ieee754/ldbl-96/gamma_product.c

   1 /* Compute a product of X, X+1, ..., with an error estimate.
   2    Copyright (C) 2013-2024 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-narrow-eval.h>
  21 #include <math_private.h>
  22 #include <float.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   long double x_full = (long double) x + (long double) x_eps;
  36   long double ret = x_full;
  37   for (int i = 1; i < n; i++)
  38     ret *= x_full + i;
  39
  40   double fret = math_narrow_eval ((double) ret);
  41   *eps = (ret - fret) / fret;
  42
  43   return fret;
  44 }