sysdeps/ieee754/dbl-64/mpexp.c

   1
   2 /*
   3  * IBM Accurate Mathematical Library
   4  * Copyright (c) International Business Machines Corp., 2001
   5  *
   6  * This program is free software; you can redistribute it and/or modify
   7  * it under the terms of the GNU  Lesser General Public License as published by
   8  * the Free Software Foundation; either version 2 of the License, or
   9  * (at your option) any later version.
  10  *
  11  * This program is distributed in the hope that it will be useful,
  12  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  13  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  14  * GNU General Public License for more details.
  15  *
  16  * You should have received a copy of the GNU Lesser General Public License
  17  * along with this program; if not, write to the Free Software
  18  * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
  19  */
  20 /*************************************************************************/
  21 /*   MODULE_NAME:mpexp.c                                                 */
  22 /*                                                                       */
  23 /*   FUNCTIONS: mpexp                                                    */
  24 /*                                                                       */
  25 /*   FILES NEEDED: mpa.h endian.h mpexp.h                                */
  26 /*                 mpa.c                                                 */
  27 /*                                                                       */
  28 /* Multi-Precision exponential function subroutine                       */
  29 /*   (  for p >= 4, 2**(-55) <= abs(x) <= 1024     ).                    */
  30 /*************************************************************************/
  31
  32 #include "endian.h"
  33 #include "mpa.h"
  34 #include "mpexp.h"
  35
  36 /* Multi-Precision exponential function subroutine (for p >= 4,          */
  37 /* 2**(-55) <= abs(x) <= 1024).                                          */
  38 void __mpexp(mp_no *x, mp_no *y, int p) {
  39
  40   int i,j,k,m,m1,m2,n;
  41   double a,b;
  42   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,
  43                              6,6,6,6,7,7,7,7,8,8,8,8,8};
  44   static const int m1p[33]= {0,0,0,0,17,23,23,28,27,38,42,39,43,47,43,47,50,54,
  45                                57,60,64,67,71,74,68,71,74,77,70,73,76,78,81};
  46   static const int m1np[7][18] = {
  47                  { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
  48                  { 0, 0, 0, 0,36,48,60,72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
  49                  { 0, 0, 0, 0,24,32,40,48,56,64,72, 0, 0, 0, 0, 0, 0, 0},
  50                  { 0, 0, 0, 0,17,23,29,35,41,47,53,59,65, 0, 0, 0, 0, 0},
  51                  { 0, 0, 0, 0, 0, 0,23,28,33,38,42,47,52,57,62,66, 0, 0},
  52                  { 0, 0, 0, 0, 0, 0, 0, 0,27, 0, 0,39,43,47,51,55,59,63},
  53                  { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,43,47,50,54}};
  54   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,
  55                     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,
  56                     0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}};
  57   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,
  58                     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,
  59                     0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}};
  60   mp_no mps,mpak,mpt1,mpt2;
  61
  62   /* Choose m,n and compute a=2**(-m) */
  63   n = np[p];    m1 = m1p[p];    a = twomm1[p].d;
  64   for (i=0; i<EX; i++)  a *= RADIXI;
  65   for (   ; i>EX; i--)  a *= RADIX;
  66   b = X[1]*RADIXI;   m2 = 24*EX;
  67   for (; b<HALF; m2--)  { a *= TWO;   b *= TWO; }
  68   if (b == HALF) {
  69     for (i=2; i<=p; i++) { if (X[i]!=ZERO)  break; }
  70     if (i==p+1)  { m2--;  a *= TWO; }
  71   }
  72   if ((m=m1+m2) <= 0) {
  73     m=0;  a=ONE;
  74     for (i=n-1; i>0; i--,n--) { if (m1np[i][p]+m2>0)  break; }
  75   }
  76
  77   /* Compute s=x*2**(-m). Put result in mps */
  78   __dbl_mp(a,&mpt1,p);
  79   __mul(x,&mpt1,&mps,p);
  80
  81   /* Evaluate the polynomial. Put result in mpt2 */
  82   mpone.e=1;   mpone.d[0]=ONE;   mpone.d[1]=ONE;
  83   mpk.e = 1;   mpk.d[0] = ONE;   mpk.d[1]=nn[n].d;
  84   __dvd(&mps,&mpk,&mpt1,p);
  85   __add(&mpone,&mpt1,&mpak,p);
  86   for (k=n-1; k>1; k--) {
  87     __mul(&mps,&mpak,&mpt1,p);
  88     mpk.d[1]=nn[k].d;
  89     __dvd(&mpt1,&mpk,&mpt2,p);
  90     __add(&mpone,&mpt2,&mpak,p);
  91   }
  92   __mul(&mps,&mpak,&mpt1,p);
  93   __add(&mpone,&mpt1,&mpt2,p);
  94
  95   /* Raise polynomial value to the power of 2**m. Put result in y */
  96   for (k=0,j=0; k<m; ) {
  97     __mul(&mpt2,&mpt2,&mpt1,p);  k++;
  98     if (k==m)  { j=1;  break; }
  99     __mul(&mpt1,&mpt1,&mpt2,p);  k++;
 100   }
 101   if (j)  __cpy(&mpt1,y,p);
 102   else    __cpy(&mpt2,y,p);
 103   return;
 104 }