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/*
* IBM Accurate Mathematical Library
* Copyright (c) International Business Machines Corp., 2001
*
* 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 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 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,j,k,m,m1,m2,n;
double a,b;
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;
}
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