/* 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 <mul_splitl.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.  */

long double

__lgamma_productl (long double t, long double x, long double x_eps, int n)

{

  long double ret = 0, ret_eps = 0;

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

    {

      long double xi = x + i;

      long double quot = t / xi;

      long double mhi, mlo;

      mul_splitl (&mhi, &mlo, quot, xi);

      long double quot_lo = (t - mhi - mlo) / xi - t * x_eps / (xi * xi);

      /* We want (1 + RET + RET_EPS) * (1 + QUOT + QUOT_LO) - 1.  */

      long double rhi, rlo;

      mul_splitl (&rhi, &rlo, ret, quot);

      long double rpq = ret + quot;

      long double rpq_eps = (ret - rpq) + quot;

      long double nret = rpq + rhi;

      long double nret_eps = (rpq - nret) + rhi;

      ret_eps += (rpq_eps + nret_eps + rlo + ret_eps * quot

		  + quot_lo + quot_lo * (ret + ret_eps));

      ret = nret;

    }

  return ret + ret_eps;

}