1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
|
/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001-2013 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 precision. */
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;
}
|
