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
|
/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001-2015 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 urem.c */
/* */
/* FUNCTION: uremainder */
/* */
/* An ultimate remainder routine. Given two IEEE double machine numbers x */
/* ,y it computes the correctly rounded (to nearest) value of remainder */
/* of dividing x by y. */
/* Assumption: Machine arithmetic operations are performed in */
/* round to nearest mode of IEEE 754 standard. */
/* */
/* ************************************************************************/
#include "endian.h"
#include "mydefs.h"
#include "urem.h"
#include "MathLib.h"
#include <math.h>
#include <math_private.h>
/**************************************************************************/
/* An ultimate remainder routine. Given two IEEE double machine numbers x */
/* ,y it computes the correctly rounded (to nearest) value of remainder */
/**************************************************************************/
double
__ieee754_remainder (double x, double y)
{
double z, d, xx;
int4 kx, ky, n, nn, n1, m1, l;
mynumber u, t, w = { { 0, 0 } }, v = { { 0, 0 } }, ww = { { 0, 0 } }, r;
u.x = x;
t.x = y;
kx = u.i[HIGH_HALF] & 0x7fffffff; /* no sign for x*/
t.i[HIGH_HALF] &= 0x7fffffff; /*no sign for y */
ky = t.i[HIGH_HALF];
/*------ |x| < 2^1023 and 2^-970 < |y| < 2^1024 ------------------*/
if (kx < 0x7fe00000 && ky < 0x7ff00000 && ky >= 0x03500000)
{
SET_RESTORE_ROUND_NOEX (FE_TONEAREST);
if (kx + 0x00100000 < ky)
return x;
if ((kx - 0x01500000) < ky)
{
z = x / t.x;
v.i[HIGH_HALF] = t.i[HIGH_HALF];
d = (z + big.x) - big.x;
xx = (x - d * v.x) - d * (t.x - v.x);
if (d - z != 0.5 && d - z != -0.5)
return (xx != 0) ? xx : ((x > 0) ? ZERO.x : nZERO.x);
else
{
if (fabs (xx) > 0.5 * t.x)
return (z > d) ? xx - t.x : xx + t.x;
else
return xx;
}
} /* (kx<(ky+0x01500000)) */
else
{
r.x = 1.0 / t.x;
n = t.i[HIGH_HALF];
nn = (n & 0x7ff00000) + 0x01400000;
w.i[HIGH_HALF] = n;
ww.x = t.x - w.x;
l = (kx - nn) & 0xfff00000;
n1 = ww.i[HIGH_HALF];
m1 = r.i[HIGH_HALF];
while (l > 0)
{
r.i[HIGH_HALF] = m1 - l;
z = u.x * r.x;
w.i[HIGH_HALF] = n + l;
ww.i[HIGH_HALF] = (n1) ? n1 + l : n1;
d = (z + big.x) - big.x;
u.x = (u.x - d * w.x) - d * ww.x;
l = (u.i[HIGH_HALF] & 0x7ff00000) - nn;
}
r.i[HIGH_HALF] = m1;
w.i[HIGH_HALF] = n;
ww.i[HIGH_HALF] = n1;
z = u.x * r.x;
d = (z + big.x) - big.x;
u.x = (u.x - d * w.x) - d * ww.x;
if (fabs (u.x) < 0.5 * t.x)
return (u.x != 0) ? u.x : ((x > 0) ? ZERO.x : nZERO.x);
else
if (fabs (u.x) > 0.5 * t.x)
return (d > z) ? u.x + t.x : u.x - t.x;
else
{
z = u.x / t.x; d = (z + big.x) - big.x;
return ((u.x - d * w.x) - d * ww.x);
}
}
} /* (kx<0x7fe00000&&ky<0x7ff00000&&ky>=0x03500000) */
else
{
if (kx < 0x7fe00000 && ky < 0x7ff00000 && (ky > 0 || t.i[LOW_HALF] != 0))
{
y = fabs (y) * t128.x;
z = __ieee754_remainder (x, y) * t128.x;
z = __ieee754_remainder (z, y) * tm128.x;
return z;
}
else
{
if ((kx & 0x7ff00000) == 0x7fe00000 && ky < 0x7ff00000 &&
(ky > 0 || t.i[LOW_HALF] != 0))
{
y = fabs (y);
z = 2.0 * __ieee754_remainder (0.5 * x, y);
d = fabs (z);
if (d <= fabs (d - y))
return z;
else
return (z > 0) ? z - y : z + y;
}
else /* if x is too big */
{
if (ky == 0 && t.i[LOW_HALF] == 0) /* y = 0 */
return (x * y) / (x * y);
else if (kx >= 0x7ff00000 /* x not finite */
|| (ky > 0x7ff00000 /* y is NaN */
|| (ky == 0x7ff00000 && t.i[LOW_HALF] != 0)))
return (x * y) / (x * y);
else
return x;
}
}
}
}
strong_alias (__ieee754_remainder, __remainder_finite)
|
