1 2 /* 3 * IBM Accurate Mathematical Library 4 * written by International Business Machines Corp. 5 * Copyright (C) 2001 Free Software Foundation 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, write to the Free Software 19 * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. 20 */ 21 /************************************************************************/ 22 /* */ 23 /* MODULE_NAME:mplog.c */ 24 /* */ 25 /* FUNCTIONS: mplog */ 26 /* */ 27 /* FILES NEEDED: endian.h mpa.h mplog.h */ 28 /* mpexp.c */ 29 /* */ 30 /* Multi-Precision logarithm function subroutine (for precision p >= 4, */ 31 /* 2**(-1024) < x < 2**1024) and x is outside of the interval */ 32 /* [1-2**(-54),1+2**(-54)]. Upon entry, x should be set to the */ 33 /* multi-precision value of the input and y should be set into a multi- */ 34 /* precision value of an approximation of log(x) with relative error */ 35 /* bound of at most 2**(-52). The routine improves the accuracy of y. */ 36 /* */ 37 /************************************************************************/ 38 #include "endian.h" 39 #include "mpa.h" 40 41 void __mpexp(mp_no *, mp_no *, int); 42 43 void __mplog(mp_no *x, mp_no *y, int p) { 44 #include "mplog.h" 45 int i,m; 46 #if 0 47 int j,k,m1,m2,n; 48 double a,b; 49 #endif 50 static const int mp[33] = {0,0,0,0,0,1,1,2,2,2,2,3,3,3,3,3,3,3,3, 51 4,4,4,4,4,4,4,4,4,4,4,4,4,4}; 52 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, 53 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, 54 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}}; 55 mp_no mpt1,mpt2; 56 57 /* Choose m and initiate mpone */ 58 m = mp[p]; mpone.e = 1; mpone.d[0]=mpone.d[1]=ONE; 59 60 /* Perform m newton iterations to solve for y: exp(y)-x=0. */ 61 /* The iterations formula is: y(n+1)=y(n)+(x*exp(-y(n))-1). */ 62 __cpy(y,&mpt1,p); 63 for (i=0; i<m; i++) { 64 mpt1.d[0]=-mpt1.d[0]; 65 __mpexp(&mpt1,&mpt2,p); 66 __mul(x,&mpt2,&mpt1,p); 67 __sub(&mpt1,&mpone,&mpt2,p); 68 __add(y,&mpt2,&mpt1,p); 69 __cpy(&mpt1,y,p); 70 } 71 return; 72 } 73