sysdeps/ieee754/ldbl-96/gamma_productl.c

   1 /* Compute a product of X, X+1, ..., with an error estimate.
   2    Copyright (C) 2013-2015 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 <math.h>
  20 #include <math_private.h>
  21 #include <float.h>
  22
  23 /* Calculate X * Y exactly and store the result in *HI + *LO.  It is
  24    given that the values are small enough that no overflow occurs and
  25    large enough (or zero) that no underflow occurs.  */
  26
  27 static inline void
  28 mul_split (long double *hi, long double *lo, long double x, long double y)
  29 {
  30 #ifdef __FP_FAST_FMAL
  31   /* Fast built-in fused multiply-add.  */
  32   *hi = x * y;
  33   *lo = __builtin_fmal (x, y, -*hi);
  34 #elif defined FP_FAST_FMAL
  35   /* Fast library fused multiply-add, compiler before GCC 4.6.  */
  36   *hi = x * y;
  37   *lo = __fmal (x, y, -*hi);
  38 #else
  39   /* Apply Dekker's algorithm.  */
  40   *hi = x * y;
  41 # define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1)
  42   long double x1 = x * C;
  43   long double y1 = y * C;
  44 # undef C
  45   x1 = (x - x1) + x1;
  46   y1 = (y - y1) + y1;
  47   long double x2 = x - x1;
  48   long double y2 = y - y1;
  49   *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
  50 #endif
  51 }
  52
  53 /* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N
  54    - 1, in the form R * (1 + *EPS) where the return value R is an
  55    approximation to the product and *EPS is set to indicate the
  56    approximate error in the return value.  X is such that all the
  57    values X + 1, ..., X + N - 1 are exactly representable, and X_EPS /
  58    X is small enough that factors quadratic in it can be
  59    neglected.  */
  60
  61 long double
  62 __gamma_productl (long double x, long double x_eps, int n, long double *eps)
  63 {
  64   SET_RESTORE_ROUNDL (FE_TONEAREST);
  65   long double ret = x;
  66   *eps = x_eps / x;
  67   for (int i = 1; i < n; i++)
  68     {
  69       *eps += x_eps / (x + i);
  70       long double lo;
  71       mul_split (&ret, &lo, ret, x + i);
  72       *eps += lo / ret;
  73     }
  74   return ret;
  75 }