/* Compute a product of X, X+1, ..., with an error estimate.

   Copyright (C) 2013-2018 Free Software Foundation, Inc.

   This file is part of the GNU C Library.

   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 <math.h>

#include <math_private.h>

#include <mul_split.h>

/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N

   - 1, in the form R * (1 + *EPS) where the return value R is an

   approximation to the product and *EPS is set to indicate the

   approximate error in the return value.  X is such that all the

   values X + 1, ..., X + N - 1 are exactly representable, and X_EPS /

   X is small enough that factors quadratic in it can be

   neglected.  */

double

__gamma_product (double x, double x_eps, int n, double *eps)

{

  SET_RESTORE_ROUND (FE_TONEAREST);

  double ret = x;

  *eps = x_eps / x;

  for (int i = 1; i < n; i++)

    {

      *eps += x_eps / (x + i);

      double lo;

      mul_split (&ret, &lo, ret, x + i);

      *eps += lo / ret;

    }

  return ret;

}