sysdeps/ieee754/ldbl-128/gamma_productl.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_private.h>
  21 #include <fenv_private.h>
  22 #include <mul_splitl.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 _Float128
  33 __gamma_productl (_Float128 x, _Float128 x_eps, int n, _Float128 *eps)
  34 {
  35   SET_RESTORE_ROUNDL (FE_TONEAREST);
  36   _Float128 ret = x;
  37   *eps = x_eps / x;
  38   for (int i = 1; i < n; i++)
  39     {
  40       *eps += x_eps / (x + i);
  41       _Float128 lo;
  42       mul_splitl (&ret, &lo, ret, x + i);
  43       *eps += lo / ret;
  44     }
  45   return ret;
  46 }