sysdeps/ieee754/dbl-64/mplog.c

   1
   2 /*
   3  * IBM Accurate Mathematical Library
   4  * written by International Business Machines Corp.
   5  * Copyright (C) 2001-2012 Free Software Foundation, Inc.
   6  *
   7  * This program is free software; you can redistribute it and/or modify
   8  * it under the terms of the GNU Lesser General Public License as published by
   9  * the Free Software Foundation; either version 2.1 of the License, or
  10  * (at your option) any later version.
  11  *
  12  * This program is distributed in the hope that it will be useful,
  13  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  14  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  15  * GNU Lesser General Public License for more details.
  16  *
  17  * You should have received a copy of the GNU Lesser General Public License
  18  * along with this program; if not, see <http://www.gnu.org/licenses/>.
  19  */
  20 /************************************************************************/
  21 /*                                                                      */
  22 /*     MODULE_NAME:mplog.c                                              */
  23 /*                                                                      */
  24 /*     FUNCTIONS:  mplog                                                */
  25 /*                                                                      */
  26 /*     FILES NEEDED: endian.h mpa.h  mplog.h                            */
  27 /*                    mpexp.c                                           */
  28 /*                                                                      */
  29 /* Multi-Precision logarithm function subroutine (for precision p >= 4, */
  30 /* 2**(-1024) < x < 2**1024) and x is outside of the interval           */
  31 /* [1-2**(-54),1+2**(-54)]. Upon entry, x should be set to the          */
  32 /* multi-precision value of the input and y should be set into a multi- */
  33 /* precision value of an approximation of log(x) with relative error    */
  34 /* bound of at most 2**(-52). The routine improves the accuracy of y.   */
  35 /*                                                                      */
  36 /************************************************************************/
  37 #include "endian.h"
  38 #include "mpa.h"
  39
  40 void __mpexp(mp_no *, mp_no *, int);
  41
  42 void __mplog(mp_no *x, mp_no *y, int p) {
  43   int i,m;
  44   static const int mp[33] = {0,0,0,0,0,1,1,2,2,2,2,3,3,3,3,3,3,3,3,
  45                              4,4,4,4,4,4,4,4,4,4,4,4,4,4};
  46   mp_no mpt1,mpt2;
  47
  48   /* Choose m */
  49   m = mp[p];
  50
  51   /* Perform m newton iterations to solve for y: exp(y)-x=0.     */
  52   /* The iterations formula is:  y(n+1)=y(n)+(x*exp(-y(n))-1).   */
  53   __cpy(y,&mpt1,p);
  54   for (i=0; i<m; i++) {
  55     mpt1.d[0]=-mpt1.d[0];
  56     __mpexp(&mpt1,&mpt2,p);
  57     __mul(x,&mpt2,&mpt1,p);
  58     __sub(&mpt1,&mpone,&mpt2,p);
  59     __add(y,&mpt2,&mpt1,p);
  60     __cpy(&mpt1,y,p);
  61   }
  62   return;
  63 }