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
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
|
/*
* 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:halfulp.c */
/* */
/* FUNCTIONS:halfulp */
/* FILES NEEDED: mydefs.h dla.h endian.h */
/* uroot.c */
/* */
/*Routine halfulp(double x, double y) computes x^y where result does */
/*not need rounding. If the result is closer to 0 than can be */
/*represented it returns 0. */
/* In the following cases the function does not compute anything */
/*and returns a negative number: */
/*1. if the result needs rounding, */
/*2. if y is outside the interval [0, 2^20-1], */
/*3. if x can be represented by x=2**n for some integer n. */
/************************************************************************/
#include "endian.h"
#include "mydefs.h"
#include <dla.h>
#include <math_private.h>
#ifndef SECTION
# define SECTION
#endif
static const int4 tab54[32] = {
262143, 11585, 1782, 511, 210, 107, 63, 42,
30, 22, 17, 14, 12, 10, 9, 7,
7, 6, 5, 5, 5, 4, 4, 4,
3, 3, 3, 3, 3, 3, 3, 3
};
double
SECTION
__halfulp (double x, double y)
{
mynumber v;
double z, u, uu;
#ifndef DLA_FMS
double j1, j2, j3, j4, j5;
#endif
int4 k, l, m, n;
if (y <= 0) /*if power is negative or zero */
{
v.x = y;
if (v.i[LOW_HALF] != 0)
return -10.0;
v.x = x;
if (v.i[LOW_HALF] != 0)
return -10.0;
if ((v.i[HIGH_HALF] & 0x000fffff) != 0)
return -10; /* if x =2 ^ n */
k = ((v.i[HIGH_HALF] & 0x7fffffff) >> 20) - 1023; /* find this n */
z = (double) k;
return (z * y == -1075.0) ? 0 : -10.0;
}
/* if y > 0 */
v.x = y;
if (v.i[LOW_HALF] != 0)
return -10.0;
v.x = x;
/* case where x = 2**n for some integer n */
if (((v.i[HIGH_HALF] & 0x000fffff) | v.i[LOW_HALF]) == 0)
{
k = (v.i[HIGH_HALF] >> 20) - 1023;
return (((double) k) * y == -1075.0) ? 0 : -10.0;
}
v.x = y;
k = v.i[HIGH_HALF];
m = k << 12;
l = 0;
while (m)
{
m = m << 1; l++;
}
n = (k & 0x000fffff) | 0x00100000;
n = n >> (20 - l); /* n is the odd integer of y */
k = ((k >> 20) - 1023) - l; /* y = n*2**k */
if (k > 5)
return -10.0;
if (k > 0)
for (; k > 0; k--)
n *= 2;
if (n > 34)
return -10.0;
k = -k;
if (k > 5)
return -10.0;
/* now treat x */
while (k > 0)
{
z = __ieee754_sqrt (x);
EMULV (z, z, u, uu, j1, j2, j3, j4, j5);
if (((u - x) + uu) != 0)
break;
x = z;
k--;
}
if (k)
return -10.0;
/* it is impossible that n == 2, so the mantissa of x must be short */
v.x = x;
if (v.i[LOW_HALF])
return -10.0;
k = v.i[HIGH_HALF];
m = k << 12;
l = 0;
while (m)
{
m = m << 1; l++;
}
m = (k & 0x000fffff) | 0x00100000;
m = m >> (20 - l); /* m is the odd integer of x */
/* now check whether the length of m**n is at most 54 bits */
if (m > tab54[n - 3])
return -10.0;
/* yes, it is - now compute x**n by simple multiplications */
u = x;
for (k = 1; k < n; k++)
u = u * x;
return u;
}
|
