sysdeps/ieee754/ldbl-96/lgamma_product.c

   1 /* Compute a product of 1 + (T/X), 1 + (T/(X+1)), ....
   2    Copyright (C) 2015-2024 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_private.h>
  21 #include <float.h>
  22
  23 /* Compute the product of 1 + (T / (X + X_EPS)), 1 + (T / (X + X_EPS +
  24    1)), ..., 1 + (T / (X + X_EPS + N - 1)), minus 1.  X is such that
  25    all the values X + 1, ..., X + N - 1 are exactly representable, and
  26    X_EPS / X is small enough that factors quadratic in it can be
  27    neglected.  */
  28
  29 double
  30 __lgamma_product (double t, double x, double x_eps, int n)
  31 {
  32   long double x_full = (long double) x + (long double) x_eps;
  33   long double ret = 0;
  34   for (int i = 0; i < n; i++)
  35     ret += (t / (x_full + i)) * (1 + ret);
  36   return ret;
  37 }