1  /* Compute a product of 1 + (T/X), 1 + (T/(X+1)), ....
       2     Copyright (C) 2015-2023 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 <mul_split.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    double ret = 0, ret_eps = 0;
      33    for (int i = 0; i < n; i++)
      34      {
      35        double xi = x + i;
      36        double quot = t / xi;
      37        double mhi, mlo;
      38        mul_split (&mhi, &mlo, quot, xi);
      39        double quot_lo = (t - mhi - mlo) / xi - t * x_eps / (xi * xi);
      40        /* We want (1 + RET + RET_EPS) * (1 + QUOT + QUOT_LO) - 1.  */
      41        double rhi, rlo;
      42        mul_split (&rhi, &rlo, ret, quot);
      43        double rpq = ret + quot;
      44        double rpq_eps = (ret - rpq) + quot;
      45        double nret = rpq + rhi;
      46        double nret_eps = (rpq - nret) + rhi;
      47        ret_eps += (rpq_eps + nret_eps + rlo + ret_eps * quot
      48  		  + quot_lo + quot_lo * (ret + ret_eps));
      49        ret = nret;
      50      }
      51    return ret + ret_eps;
      52  }