mirror of
https://sourceware.org/git/glibc.git
synced 2024-12-15 15:40:12 +00:00
94 lines
3.8 KiB
C
94 lines
3.8 KiB
C
/*
|
|
* IBM Accurate Mathematical Library
|
|
* written by International Business Machines Corp.
|
|
* Copyright (C) 2001-2012 Free Software Foundation, Inc.
|
|
*
|
|
* 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, see <http://www.gnu.org/licenses/>.
|
|
*/
|
|
/*************************************************************************/
|
|
/* 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;
|
|
}
|