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glibc  2.9
mpexp.c
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00001 
00002 /*
00003  * IBM Accurate Mathematical Library
00004  * written by International Business Machines Corp.
00005  * Copyright (C) 2001 Free Software Foundation
00006  *
00007  * This program is free software; you can redistribute it and/or modify
00008  * it under the terms of the GNU  Lesser General Public License as published by
00009  * the Free Software Foundation; either version 2.1 of the License, or
00010  * (at your option) any later version.
00011  *
00012  * This program is distributed in the hope that it will be useful,
00013  * but WITHOUT ANY WARRANTY; without even the implied warranty of
00014  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
00015  * GNU Lesser General Public License for more details.
00016  *
00017  * You should have received a copy of the GNU Lesser General Public License
00018  * along with this program; if not, write to the Free Software
00019  * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
00020  */
00021 /*************************************************************************/
00022 /*   MODULE_NAME:mpexp.c                                                 */
00023 /*                                                                       */
00024 /*   FUNCTIONS: mpexp                                                    */
00025 /*                                                                       */
00026 /*   FILES NEEDED: mpa.h endian.h mpexp.h                                */
00027 /*                 mpa.c                                                 */
00028 /*                                                                       */
00029 /* Multi-Precision exponential function subroutine                       */
00030 /*   (  for p >= 4, 2**(-55) <= abs(x) <= 1024     ).                    */
00031 /*************************************************************************/
00032 
00033 #include "endian.h"
00034 #include "mpa.h"
00035 #include "mpexp.h"
00036 
00037 /* Multi-Precision exponential function subroutine (for p >= 4,          */
00038 /* 2**(-55) <= abs(x) <= 1024).                                          */
00039 void __mpexp(mp_no *x, mp_no *y, int p) {
00040 
00041   int i,j,k,m,m1,m2,n;
00042   double a,b;
00043   static const int np[33] = {0,0,0,0,3,3,4,4,5,4,4,5,5,5,6,6,6,6,6,6,
00044                              6,6,6,6,7,7,7,7,8,8,8,8,8};
00045   static const int m1p[33]= {0,0,0,0,17,23,23,28,27,38,42,39,43,47,43,47,50,54,
00046                                57,60,64,67,71,74,68,71,74,77,70,73,76,78,81};
00047   static const int m1np[7][18] = {
00048                  { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
00049                  { 0, 0, 0, 0,36,48,60,72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
00050                  { 0, 0, 0, 0,24,32,40,48,56,64,72, 0, 0, 0, 0, 0, 0, 0},
00051                  { 0, 0, 0, 0,17,23,29,35,41,47,53,59,65, 0, 0, 0, 0, 0},
00052                  { 0, 0, 0, 0, 0, 0,23,28,33,38,42,47,52,57,62,66, 0, 0},
00053                  { 0, 0, 0, 0, 0, 0, 0, 0,27, 0, 0,39,43,47,51,55,59,63},
00054                  { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,43,47,50,54}};
00055   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,
00056                     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,
00057                     0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}};
00058   mp_no mpk   = {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,
00059                     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,
00060                     0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}};
00061   mp_no mps,mpak,mpt1,mpt2;
00062 
00063   /* Choose m,n and compute a=2**(-m) */
00064   n = np[p];    m1 = m1p[p];    a = twomm1[p].d;
00065   for (i=0; i<EX; i++)  a *= RADIXI;
00066   for (   ; i>EX; i--)  a *= RADIX;
00067   b = X[1]*RADIXI;   m2 = 24*EX;
00068   for (; b<HALF; m2--)  { a *= TWO;   b *= TWO; }
00069   if (b == HALF) {
00070     for (i=2; i<=p; i++) { if (X[i]!=ZERO)  break; }
00071     if (i==p+1)  { m2--;  a *= TWO; }
00072   }
00073   if ((m=m1+m2) <= 0) {
00074     m=0;  a=ONE;
00075     for (i=n-1; i>0; i--,n--) { if (m1np[i][p]+m2>0)  break; }
00076   }
00077 
00078   /* Compute s=x*2**(-m). Put result in mps */
00079   __dbl_mp(a,&mpt1,p);
00080   __mul(x,&mpt1,&mps,p);
00081 
00082   /* Evaluate the polynomial. Put result in mpt2 */
00083   mpone.e=1;   mpone.d[0]=ONE;   mpone.d[1]=ONE;
00084   mpk.e = 1;   mpk.d[0] = ONE;   mpk.d[1]=nn[n].d;
00085   __dvd(&mps,&mpk,&mpt1,p);
00086   __add(&mpone,&mpt1,&mpak,p);
00087   for (k=n-1; k>1; k--) {
00088     __mul(&mps,&mpak,&mpt1,p);
00089     mpk.d[1]=nn[k].d;
00090     __dvd(&mpt1,&mpk,&mpt2,p);
00091     __add(&mpone,&mpt2,&mpak,p);
00092   }
00093   __mul(&mps,&mpak,&mpt1,p);
00094   __add(&mpone,&mpt1,&mpt2,p);
00095 
00096   /* Raise polynomial value to the power of 2**m. Put result in y */
00097   for (k=0,j=0; k<m; ) {
00098     __mul(&mpt2,&mpt2,&mpt1,p);  k++;
00099     if (k==m)  { j=1;  break; }
00100     __mul(&mpt1,&mpt1,&mpt2,p);  k++;
00101   }
00102   if (j)  __cpy(&mpt1,y,p);
00103   else    __cpy(&mpt2,y,p);
00104   return;
00105 }