1  /* Compute a product of 1 + (T/X), 1 + (T/(X+1)), ....
       2     Copyright (C) 2015-2018 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     <http://www.gnu.org/licenses/>.  */
      18  
      19  #include "quadmath-imp.h"
      20  
      21  /* Compute the product of 1 + (T / (X + X_EPS)), 1 + (T / (X + X_EPS +
      22     1)), ..., 1 + (T / (X + X_EPS + N - 1)), minus 1.  X is such that
      23     all the values X + 1, ..., X + N - 1 are exactly representable, and
      24     X_EPS / X is small enough that factors quadratic in it can be
      25     neglected.  */
      26  
      27  __float128
      28  __quadmath_lgamma_productq (__float128 t, __float128 x, __float128 x_eps, int n)
      29  {
      30    __float128 ret = 0, ret_eps = 0;
      31    for (int i = 0; i < n; i++)
      32      {
      33        __float128 xi = x + i;
      34        __float128 quot = t / xi;
      35        __float128 mhi, mlo;
      36        mul_splitq (&mhi, &mlo, quot, xi);
      37        __float128 quot_lo = (t - mhi - mlo) / xi - t * x_eps / (xi * xi);
      38        /* We want (1 + RET + RET_EPS) * (1 + QUOT + QUOT_LO) - 1.  */
      39        __float128 rhi, rlo;
      40        mul_splitq (&rhi, &rlo, ret, quot);
      41        __float128 rpq = ret + quot;
      42        __float128 rpq_eps = (ret - rpq) + quot;
      43        __float128 nret = rpq + rhi;
      44        __float128 nret_eps = (rpq - nret) + rhi;
      45        ret_eps += (rpq_eps + nret_eps + rlo + ret_eps * quot
      46  		  + quot_lo + quot_lo * (ret + ret_eps));
      47        ret = nret;
      48      }
      49    return ret + ret_eps;
      50  }