| /* |
| * 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:slowpow.c */ |
| /* */ |
| /* FUNCTION:slowpow */ |
| /* */ |
| /*FILES NEEDED:mpa.h */ |
| /* mpa.c mpexp.c mplog.c halfulp.c */ |
| /* */ |
| /* Given two IEEE double machine numbers y,x , routine computes the */ |
| /* correctly rounded (to nearest) value of x^y. Result calculated by */ |
| /* multiplication (in halfulp.c) or if result isn't accurate enough */ |
| /* then routine converts x and y into multi-precision doubles and */ |
| /* calls to mpexp routine */ |
| /*************************************************************************/ |
| |
| #include "mpa.h" |
| #include "math_private.h" |
| |
| void __mpexp(mp_no *x, mp_no *y, int p); |
| void __mplog(mp_no *x, mp_no *y, int p); |
| double ulog(double); |
| double __halfulp(double x,double y); |
| |
| double __slowpow(double x, double y, double z) { |
| double res,res1; |
| mp_no mpx, mpy, mpz,mpw,mpp,mpr,mpr1; |
| static const mp_no eps = {-3,{1.0,4.0}}; |
| int p; |
| |
| res = __halfulp(x,y); /* halfulp() returns -10 or x^y */ |
| if (res >= 0) return res; /* if result was really computed by halfulp */ |
| /* else, if result was not really computed by halfulp */ |
| p = 10; /* p=precision */ |
| __dbl_mp(x,&mpx,p); |
| __dbl_mp(y,&mpy,p); |
| __dbl_mp(z,&mpz,p); |
| __mplog(&mpx, &mpz, p); /* log(x) = z */ |
| __mul(&mpy,&mpz,&mpw,p); /* y * z =w */ |
| __mpexp(&mpw, &mpp, p); /* e^w =pp */ |
| __add(&mpp,&eps,&mpr,p); /* pp+eps =r */ |
| __mp_dbl(&mpr, &res, p); |
| __sub(&mpp,&eps,&mpr1,p); /* pp -eps =r1 */ |
| __mp_dbl(&mpr1, &res1, p); /* converting into double precision */ |
| if (res == res1) return res; |
| |
| p = 32; /* if we get here result wasn't calculated exactly, continue */ |
| __dbl_mp(x,&mpx,p); /* for more exact calculation */ |
| __dbl_mp(y,&mpy,p); |
| __dbl_mp(z,&mpz,p); |
| __mplog(&mpx, &mpz, p); /* log(c)=z */ |
| __mul(&mpy,&mpz,&mpw,p); /* y*z =w */ |
| __mpexp(&mpw, &mpp, p); /* e^w=pp */ |
| __mp_dbl(&mpp, &res, p); /* converting into double precision */ |
| return res; |
| } |