| /* |
| * IBM Accurate Mathematical Library |
| * written by International Business Machines Corp. |
| * Copyright (C) 2001, 2006 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 */ |
| /* recompute. */ |
| /*************************************************************************/ |
| |
| #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; |
| long double ldw, ldz, ldpp; |
| static const long double ldeps = 0x4.0p-96; |
| |
| 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 */ |
| |
| /* Compute pow as long double, 106 bits */ |
| ldz = __ieee754_logl ((long double) x); |
| ldw = (long double) y *ldz; |
| ldpp = __ieee754_expl (ldw); |
| res = (double) (ldpp + ldeps); |
| res1 = (double) (ldpp - ldeps); |
| |
| if (res != res1) /* if result still not accurate enough */ |
| { /* use mpa for higher persision. */ |
| mp_no mpx, mpy, mpz, mpw, mpp, mpr, mpr1; |
| static const mp_no eps = { -3, {1.0, 4.0} }; |
| int p; |
| |
| p = 10; /* p=precision 240 bits */ |
| __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; |
| |
| /* if we get here result wasn't calculated exactly, continue for |
| more exact calculation using 768 bits. */ |
| p = 32; |
| __dbl_mp (x, &mpx, p); |
| __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; |
| } |