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
|
/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001, 2005 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: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"
double __ieee754_sqrt(double x);
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 __halfulp(double x, double y)
{
mynumber v;
double z,u,uu,j1,j2,j3,j4,j5;
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;
}
|
