| |
| /* |
| * 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:mpexp.c */ |
| /* */ |
| /* FUNCTIONS: mpexp */ |
| /* */ |
| /* FILES NEEDED: mpa.h endian.h mpexp.h */ |
| /* mpa.c */ |
| /* */ |
| /* Multi-Precision exponential function subroutine */ |
| /* ( for p >= 4, 2**(-55) <= abs(x) <= 1024 ). */ |
| /*************************************************************************/ |
| |
| #include "endian.h" |
| #include "mpa.h" |
| #include "mpexp.h" |
| |
| /* Multi-Precision exponential function subroutine (for p >= 4, */ |
| /* 2**(-55) <= abs(x) <= 1024). */ |
| void __mpexp(mp_no *x, mp_no *y, int p) { |
| |
| int i,j,k,m,m1,m2,n; |
| double a,b; |
| 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, |
| 6,6,6,6,7,7,7,7,8,8,8,8,8}; |
| static const int m1p[33]= {0,0,0,0,17,23,23,28,27,38,42,39,43,47,43,47,50,54, |
| 57,60,64,67,71,74,68,71,74,77,70,73,76,78,81}; |
| static const int m1np[7][18] = { |
| { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, |
| { 0, 0, 0, 0,36,48,60,72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, |
| { 0, 0, 0, 0,24,32,40,48,56,64,72, 0, 0, 0, 0, 0, 0, 0}, |
| { 0, 0, 0, 0,17,23,29,35,41,47,53,59,65, 0, 0, 0, 0, 0}, |
| { 0, 0, 0, 0, 0, 0,23,28,33,38,42,47,52,57,62,66, 0, 0}, |
| { 0, 0, 0, 0, 0, 0, 0, 0,27, 0, 0,39,43,47,51,55,59,63}, |
| { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,43,47,50,54}}; |
| 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, |
| 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 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, |
| 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 mps,mpak,mpt1,mpt2; |
| |
| /* Choose m,n and compute a=2**(-m) */ |
| n = np[p]; m1 = m1p[p]; a = twomm1[p].d; |
| for (i=0; i<EX; i++) a *= RADIXI; |
| for ( ; i>EX; i--) a *= RADIX; |
| b = X[1]*RADIXI; m2 = 24*EX; |
| for (; b<HALF; m2--) { a *= TWO; b *= TWO; } |
| if (b == HALF) { |
| for (i=2; i<=p; i++) { if (X[i]!=ZERO) break; } |
| if (i==p+1) { m2--; a *= TWO; } |
| } |
| if ((m=m1+m2) <= 0) { |
| m=0; a=ONE; |
| for (i=n-1; i>0; i--,n--) { if (m1np[i][p]+m2>0) break; } |
| } |
| |
| /* Compute s=x*2**(-m). Put result in mps */ |
| __dbl_mp(a,&mpt1,p); |
| __mul(x,&mpt1,&mps,p); |
| |
| /* Evaluate the polynomial. Put result in mpt2 */ |
| mpone.e=1; mpone.d[0]=ONE; mpone.d[1]=ONE; |
| mpk.e = 1; mpk.d[0] = ONE; mpk.d[1]=nn[n].d; |
| __dvd(&mps,&mpk,&mpt1,p); |
| __add(&mpone,&mpt1,&mpak,p); |
| for (k=n-1; k>1; k--) { |
| __mul(&mps,&mpak,&mpt1,p); |
| mpk.d[1]=nn[k].d; |
| __dvd(&mpt1,&mpk,&mpt2,p); |
| __add(&mpone,&mpt2,&mpak,p); |
| } |
| __mul(&mps,&mpak,&mpt1,p); |
| __add(&mpone,&mpt1,&mpt2,p); |
| |
| /* Raise polynomial value to the power of 2**m. Put result in y */ |
| for (k=0,j=0; k<m; ) { |
| __mul(&mpt2,&mpt2,&mpt1,p); k++; |
| if (k==m) { j=1; break; } |
| __mul(&mpt1,&mpt1,&mpt2,p); k++; |
| } |
| if (j) __cpy(&mpt1,y,p); |
| else __cpy(&mpt2,y,p); |
| return; |
| } |