sysdeps/ieee754/dbl-64/mplog.c

   1 /*
   2  * IBM Accurate Mathematical Library
   3  * written by International Business Machines Corp.
   4  * Copyright (C) 2001-2015 Free Software Foundation, Inc.
   5  *
   6  * This program is free software; you can redistribute it and/or modify
   7  * it under the terms of the GNU Lesser General Public License as published by
   8  * the Free Software Foundation; either version 2.1 of the License, or
   9  * (at your option) any later version.
  10  *
  11  * This program is distributed in the hope that it will be useful,
  12  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  13  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  14  * GNU Lesser General Public License for more details.
  15  *
  16  * You should have received a copy of the GNU Lesser General Public License
  17  * along with this program; if not, see <http://www.gnu.org/licenses/>.
  18  */
  19 /************************************************************************/
  20 /*                                                                      */
  21 /*     MODULE_NAME:mplog.c                                              */
  22 /*                                                                      */
  23 /*     FUNCTIONS:  mplog                                                */
  24 /*                                                                      */
  25 /*     FILES NEEDED: endian.h mpa.h  mplog.h                            */
  26 /*                    mpexp.c                                           */
  27 /*                                                                      */
  28 /* Multi-Precision logarithm function subroutine (for precision p >= 4, */
  29 /* 2**(-1024) < x < 2**1024) and x is outside of the interval           */
  30 /* [1-2**(-54),1+2**(-54)]. Upon entry, x should be set to the          */
  31 /* multi-precision value of the input and y should be set into a multi- */
  32 /* precision value of an approximation of log(x) with relative error    */
  33 /* bound of at most 2**(-52). The routine improves the accuracy of y.   */
  34 /*                                                                      */
  35 /************************************************************************/
  36 #include "endian.h"
  37 #include "mpa.h"
  38
  39 void
  40 __mplog (mp_no *x, mp_no *y, int p)
  41 {
  42   int i, m;
  43   static const int mp[33] =
  44     {
  45       0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3,
  46       4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4
  47     };
  48   mp_no mpt1, mpt2;
  49
  50   /* Choose m.  */
  51   m = mp[p];
  52
  53   /* Perform m newton iterations to solve for y: exp(y) - x = 0.  The
  54      iterations formula is:  y(n + 1) = y(n) + (x * exp(-y(n)) - 1).   */
  55   __cpy (y, &mpt1, p);
  56   for (i = 0; i < m; i++)
  57     {
  58       mpt1.d[0] = -mpt1.d[0];
  59       __mpexp (&mpt1, &mpt2, p);
  60       __mul (x, &mpt2, &mpt1, p);
  61       __sub (&mpt1, &__mpone, &mpt2, p);
  62       __add (y, &mpt2, &mpt1, p);
  63       __cpy (&mpt1, y, p);
  64     }
  65 }