mirror of
https://sourceware.org/git/glibc.git
synced 2024-11-23 13:30:06 +00:00
126 lines
4.2 KiB
C
126 lines
4.2 KiB
C
/*
|
|
* IBM Accurate Mathematical Library
|
|
* written by International Business Machines Corp.
|
|
* Copyright (C) 2001-2014 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 */
|
|
/* calls to mpexp routine */
|
|
/*************************************************************************/
|
|
|
|
#include "mpa.h"
|
|
#include <math_private.h>
|
|
|
|
#include <stap-probe.h>
|
|
|
|
#ifndef SECTION
|
|
# define SECTION
|
|
#endif
|
|
|
|
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
|
|
SECTION
|
|
__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;
|
|
|
|
/* __HALFULP returns -10 or X^Y. */
|
|
res = __halfulp (x, y);
|
|
|
|
/* Return if the result was computed by __HALFULP. */
|
|
if (res >= 0)
|
|
return res;
|
|
|
|
/* Compute pow as long double. This is currently only used by powerpc, where
|
|
one may get 106 bits of accuracy. */
|
|
#ifdef USE_LONG_DOUBLE_FOR_MP
|
|
long double ldw, ldz, ldpp;
|
|
static const long double ldeps = 0x4.0p-96;
|
|
|
|
ldz = __ieee754_logl ((long double) x);
|
|
ldw = (long double) y *ldz;
|
|
ldpp = __ieee754_expl (ldw);
|
|
res = (double) (ldpp + ldeps);
|
|
res1 = (double) (ldpp - ldeps);
|
|
|
|
/* Return the result if it is accurate enough. */
|
|
if (res == res1)
|
|
return res;
|
|
#endif
|
|
|
|
/* Or else, calculate using multiple precision. P = 10 implies accuracy of
|
|
240 bits accuracy, since MP_NO has a radix of 2^24. */
|
|
p = 10;
|
|
__dbl_mp (x, &mpx, p);
|
|
__dbl_mp (y, &mpy, p);
|
|
__dbl_mp (z, &mpz, p);
|
|
|
|
/* z = x ^ y
|
|
log (z) = y * log (x)
|
|
z = exp (y * log (x)) */
|
|
__mplog (&mpx, &mpz, p);
|
|
__mul (&mpy, &mpz, &mpw, p);
|
|
__mpexp (&mpw, &mpp, p);
|
|
|
|
/* Add and subtract EPS to ensure that the result remains unchanged, i.e. we
|
|
have last bit accuracy. */
|
|
__add (&mpp, &eps, &mpr, p);
|
|
__mp_dbl (&mpr, &res, p);
|
|
__sub (&mpp, &eps, &mpr1, p);
|
|
__mp_dbl (&mpr1, &res1, p);
|
|
if (res == res1)
|
|
{
|
|
/* Track how often we get to the slow pow code plus
|
|
its input/output values. */
|
|
LIBC_PROBE (slowpow_p10, 4, &x, &y, &z, &res);
|
|
return res;
|
|
}
|
|
|
|
/* If we don't, then we repeat using a higher precision. 768 bits of
|
|
precision ought to be enough for anybody. */
|
|
p = 32;
|
|
__dbl_mp (x, &mpx, p);
|
|
__dbl_mp (y, &mpy, p);
|
|
__dbl_mp (z, &mpz, p);
|
|
__mplog (&mpx, &mpz, p);
|
|
__mul (&mpy, &mpz, &mpw, p);
|
|
__mpexp (&mpw, &mpp, p);
|
|
__mp_dbl (&mpp, &res, p);
|
|
|
|
/* Track how often we get to the uber-slow pow code plus
|
|
its input/output values. */
|
|
LIBC_PROBE (slowpow_p32, 4, &x, &y, &z, &res);
|
|
|
|
return res;
|
|
}
|