/* Compute a product of 1 + (T/X), 1 + (T/(X+1)), ....

   Copyright (C) 2015-2018 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 <float.h>

/* Compute the product of 1 + (T / (X + X_EPS)), 1 + (T / (X + X_EPS +

   1)), ..., 1 + (T / (X + X_EPS + N - 1)), minus 1.  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

__lgamma_product (double t, double x, double x_eps, int n)

{

  long double x_full = (long double) x + (long double) x_eps;

  long double ret = 0;

  for (int i = 0; i < n; i++)

    ret += (t / (x_full + i)) * (1 + ret);

  return ret;

}