sysdeps/ieee754/dbl-64/mplog.c

/*
 * IBM Accurate Mathematical Library
 * written by International Business Machines Corp.
 * Copyright (C) 2001 Free Software Foundation
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU Lesser General Public License as published by
 * the Free Software Foundation; either version 2.1 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
 */
/************************************************************************/
/*                                                                      */
/*     MODULE_NAME:mplog.c                                              */
/*                                                                      */
/*     FUNCTIONS:  mplog                                                */
/*                                                                      */
/*     FILES NEEDED: endian.h mpa.h  mplog.h                            */
/*                    mpexp.c                                           */
/*                                                                      */
/* Multi-Precision logarithm function subroutine (for precision p >= 4, */
/* 2**(-1024) < x < 2**1024) and x is outside of the interval           */
/* [1-2**(-54),1+2**(-54)]. Upon entry, x should be set to the          */
/* multi-precision value of the input and y should be set into a multi- */
/* precision value of an approximation of log(x) with relative error    */
/* bound of at most 2**(-52). The routine improves the accuracy of y.   */
/*                                                                      */
/************************************************************************/
#include "endian.h"
#include "mpa.h"

void __mpexp(mp_no *, mp_no *, int);

void __mplog(mp_no *x, mp_no *y, int p) {
#include "mplog.h"
  int i,m;
#if 0
  int j,k,m1,m2,n;
  double a,b;
#endif
  static const int mp[33] = {0,0,0,0,0,1,1,2,2,2,2,3,3,3,3,3,3,3,3,
                             4,4,4,4,4,4,4,4,4,4,4,4,4,4};
  mp_no mpone = {0,{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
                    0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
                    0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}};
  mp_no mpt1,mpt2;

  /* Choose m and initiate mpone */
  m = mp[p];  mpone.e = 1;  mpone.d[0]=mpone.d[1]=ONE;

  /* Perform m newton iterations to solve for y: exp(y)-x=0.     */
  /* The iterations formula is:  y(n+1)=y(n)+(x*exp(-y(n))-1).   */
  __cpy(y,&mpt1,p);
  for (i=0; i<m; i++) {
    mpt1.d[0]=-mpt1.d[0];
    __mpexp(&mpt1,&mpt2,p);
    __mul(x,&mpt2,&mpt1,p);
    __sub(&mpt1,&mpone,&mpt2,p);
    __add(y,&mpt2,&mpt1,p);
    __cpy(&mpt1,y,p);
  }
  return;
}