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
|
/*
* 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: uroot.c */
/* */
/* FUNCTION: usqrt */
/* */
/* FILES NEEDED: dla.h endian.h mydefs.h uroot.h */
/* uroot.tbl */
/* */
/* An ultimate sqrt routine. Given an IEEE double machine number x */
/* it computes the correctly rounded (to nearest) value of square */
/* root of x. */
/* Assumption: Machine arithmetic operations are performed in */
/* round to nearest mode of IEEE 754 standard. */
/* */
/*********************************************************************/
#include <math_private.h>
typedef unsigned int int4;
typedef union {int4 i[4]; long double x; double d[2]; } mynumber;
static const mynumber
t512 = {{0x5ff00000, 0x00000000, 0x00000000, 0x00000000 }}, /* 2^512 */
tm256 = {{0x2ff00000, 0x00000000, 0x00000000, 0x00000000 }}; /* 2^-256 */
static const double
two54 = 1.80143985094819840000e+16, /* 0x4350000000000000 */
twom54 = 5.55111512312578270212e-17; /* 0x3C90000000000000 */
/*********************************************************************/
/* An ultimate sqrt routine. Given an IEEE double machine number x */
/* it computes the correctly rounded (to nearest) value of square */
/* root of x. */
/*********************************************************************/
long double __ieee754_sqrtl(long double x)
{
static const long double big = 134217728.0, big1 = 134217729.0;
long double t,s,i;
mynumber a,c;
int4 k, l, m;
int n;
double d;
a.x=x;
k=a.i[0] & 0x7fffffff;
/*----------------- 2^-1022 <= | x |< 2^1024 -----------------*/
if (k>0x000fffff && k<0x7ff00000) {
if (x < 0) return (big1-big1)/(big-big);
l = (k&0x001fffff)|0x3fe00000;
if (((a.i[2] & 0x7fffffff) | a.i[3]) != 0) {
n = (int) ((l - k) * 2) >> 21;
m = (a.i[2] >> 20) & 0x7ff;
if (m == 0) {
a.d[1] *= two54;
m = ((a.i[2] >> 20) & 0x7ff) - 54;
}
m += n;
if ((int) m > 0)
a.i[2] = (a.i[2] & 0x800fffff) | (m << 20);
else if ((int) m <= -54) {
a.i[2] &= 0x80000000;
a.i[3] = 0;
} else {
m += 54;
a.i[2] = (a.i[2] & 0x800fffff) | (m << 20);
a.d[1] *= twom54;
}
}
a.i[0] = l;
s = a.x;
d = __ieee754_sqrt (a.d[0]);
c.i[0] = 0x20000000+((k&0x7fe00000)>>1);
c.i[1] = 0;
c.i[2] = 0;
c.i[3] = 0;
i = d;
t = 0.5L * (i + s / i);
i = 0.5L * (t + s / t);
return c.x * i;
}
else {
if (k>=0x7ff00000) {
if (a.i[0] == 0xfff00000 && a.i[1] == 0)
return (big1-big1)/(big-big); /* sqrt (-Inf) = NaN. */
return x; /* sqrt (NaN) = NaN, sqrt (+Inf) = +Inf. */
}
if (x == 0) return x;
if (x < 0) return (big1-big1)/(big-big);
return tm256.x*__ieee754_sqrtl(x*t512.x);
}
}
strong_alias (__ieee754_sqrtl, __sqrtl_finite)
|
