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 /* MODULE_NAME:mpexp.c */ 23 /* */ 24 /* FUNCTIONS: mpexp */ 25 /* */ 26 /* FILES NEEDED: mpa.h endian.h mpexp.h */ 27 /* mpa.c */ 28 /* */ 29 /* Multi-Precision exponential function subroutine */ 30 /* ( for p >= 4, 2**(-55) <= abs(x) <= 1024 ). */ 31 /*************************************************************************/ 32 33 #include "endian.h" 34 #include "mpa.h" 35 #include "mpexp.h" 36 37 /* Multi-Precision exponential function subroutine (for p >= 4, */ 38 /* 2**(-55) <= abs(x) <= 1024). */ 39 void __mpexp(mp_no *x, mp_no *y, int p) { 40 41 int i,j,k,m,m1,m2,n; 42 double a,b; 43 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, 44 6,6,6,6,7,7,7,7,8,8,8,8,8}; 45 static const int m1p[33]= {0,0,0,0,17,23,23,28,27,38,42,39,43,47,43,47,50,54, 46 57,60,64,67,71,74,68,71,74,77,70,73,76,78,81}; 47 static const int m1np[7][18] = { 48 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 49 { 0, 0, 0, 0,36,48,60,72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 50 { 0, 0, 0, 0,24,32,40,48,56,64,72, 0, 0, 0, 0, 0, 0, 0}, 51 { 0, 0, 0, 0,17,23,29,35,41,47,53,59,65, 0, 0, 0, 0, 0}, 52 { 0, 0, 0, 0, 0, 0,23,28,33,38,42,47,52,57,62,66, 0, 0}, 53 { 0, 0, 0, 0, 0, 0, 0, 0,27, 0, 0,39,43,47,51,55,59,63}, 54 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,43,47,50,54}}; 55 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, 56 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0, 57 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 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, 59 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0, 60 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}}; 61 mp_no mps,mpak,mpt1,mpt2; 62 63 /* Choose m,n and compute a=2**(-m) */ 64 n = np[p]; m1 = m1p[p]; a = twomm1[p].d; 65 for (i=0; i<EX; i++) a *= RADIXI; 66 for ( ; i>EX; i--) a *= RADIX; 67 b = X[1]*RADIXI; m2 = 24*EX; 68 for (; b<HALF; m2--) { a *= TWO; b *= TWO; } 69 if (b == HALF) { 70 for (i=2; i<=p; i++) { if (X[i]!=ZERO) break; } 71 if (i==p+1) { m2--; a *= TWO; } 72 } 73 if ((m=m1+m2) <= 0) { 74 m=0; a=ONE; 75 for (i=n-1; i>0; i--,n--) { if (m1np[i][p]+m2>0) break; } 76 } 77 78 /* Compute s=x*2**(-m). Put result in mps */ 79 __dbl_mp(a,&mpt1,p); 80 __mul(x,&mpt1,&mps,p); 81 82 /* Evaluate the polynomial. Put result in mpt2 */ 83 mpone.e=1; mpone.d[0]=ONE; mpone.d[1]=ONE; 84 mpk.e = 1; mpk.d[0] = ONE; mpk.d[1]=nn[n].d; 85 __dvd(&mps,&mpk,&mpt1,p); 86 __add(&mpone,&mpt1,&mpak,p); 87 for (k=n-1; k>1; k--) { 88 __mul(&mps,&mpak,&mpt1,p); 89 mpk.d[1]=nn[k].d; 90 __dvd(&mpt1,&mpk,&mpt2,p); 91 __add(&mpone,&mpt2,&mpak,p); 92 } 93 __mul(&mps,&mpak,&mpt1,p); 94 __add(&mpone,&mpt1,&mpt2,p); 95 96 /* Raise polynomial value to the power of 2**m. Put result in y */ 97 for (k=0,j=0; k<m; ) { 98 __mul(&mpt2,&mpt2,&mpt1,p); k++; 99 if (k==m) { j=1; break; } 100 __mul(&mpt1,&mpt1,&mpt2,p); k++; 101 } 102 if (j) __cpy(&mpt1,y,p); 103 else __cpy(&mpt2,y,p); 104 return; 105 } 106