libquadmath/math/lgammaq_product.c

   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 }