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
|
/* e_fmodl.c -- long double version of e_fmod.c.
* Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* fmodq(x,y)
* Return x mod y in exact arithmetic
* Method: shift and subtract
*/
#include "quadmath-imp.h"
static const __float128 one = 1.0, Zero[] = {0.0, -0.0,};
__float128
fmodq (__float128 x, __float128 y)
{
int64_t n,hx,hy,hz,ix,iy,sx,i;
uint64_t lx,ly,lz;
GET_FLT128_WORDS64(hx,lx,x);
GET_FLT128_WORDS64(hy,ly,y);
sx = hx&0x8000000000000000ULL; /* sign of x */
hx ^=sx; /* |x| */
hy &= 0x7fffffffffffffffLL; /* |y| */
/* purge off exception values */
if((hy|ly)==0||(hx>=0x7fff000000000000LL)|| /* y=0,or x not finite */
((hy|((ly|-ly)>>63))>0x7fff000000000000LL)) /* or y is NaN */
return (x*y)/(x*y);
if(hx<=hy) {
if((hx<hy)||(lx<ly)) return x; /* |x|<|y| return x */
if(lx==ly)
return Zero[(uint64_t)sx>>63]; /* |x|=|y| return x*0*/
}
/* determine ix = ilogb(x) */
if(hx<0x0001000000000000LL) { /* subnormal x */
if(hx==0) {
for (ix = -16431, i=lx; i>0; i<<=1) ix -=1;
} else {
for (ix = -16382, i=hx<<15; i>0; i<<=1) ix -=1;
}
} else ix = (hx>>48)-0x3fff;
/* determine iy = ilogb(y) */
if(hy<0x0001000000000000LL) { /* subnormal y */
if(hy==0) {
for (iy = -16431, i=ly; i>0; i<<=1) iy -=1;
} else {
for (iy = -16382, i=hy<<15; i>0; i<<=1) iy -=1;
}
} else iy = (hy>>48)-0x3fff;
/* set up {hx,lx}, {hy,ly} and align y to x */
if(ix >= -16382)
hx = 0x0001000000000000LL|(0x0000ffffffffffffLL&hx);
else { /* subnormal x, shift x to normal */
n = -16382-ix;
if(n<=63) {
hx = (hx<<n)|(lx>>(64-n));
lx <<= n;
} else {
hx = lx<<(n-64);
lx = 0;
}
}
if(iy >= -16382)
hy = 0x0001000000000000LL|(0x0000ffffffffffffLL&hy);
else { /* subnormal y, shift y to normal */
n = -16382-iy;
if(n<=63) {
hy = (hy<<n)|(ly>>(64-n));
ly <<= n;
} else {
hy = ly<<(n-64);
ly = 0;
}
}
/* fix point fmod */
n = ix - iy;
while(n--) {
hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
if(hz<0){hx = hx+hx+(lx>>63); lx = lx+lx;}
else {
if((hz|lz)==0) /* return sign(x)*0 */
return Zero[(uint64_t)sx>>63];
hx = hz+hz+(lz>>63); lx = lz+lz;
}
}
hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
if(hz>=0) {hx=hz;lx=lz;}
/* convert back to floating value and restore the sign */
if((hx|lx)==0) /* return sign(x)*0 */
return Zero[(uint64_t)sx>>63];
while(hx<0x0001000000000000LL) { /* normalize x */
hx = hx+hx+(lx>>63); lx = lx+lx;
iy -= 1;
}
if(iy>= -16382) { /* normalize output */
hx = ((hx-0x0001000000000000LL)|((iy+16383)<<48));
SET_FLT128_WORDS64(x,hx|sx,lx);
} else { /* subnormal output */
n = -16382 - iy;
if(n<=48) {
lx = (lx>>n)|((uint64_t)hx<<(64-n));
hx >>= n;
} else if (n<=63) {
lx = (hx<<(64-n))|(lx>>n); hx = sx;
} else {
lx = hx>>(n-64); hx = sx;
}
SET_FLT128_WORDS64(x,hx|sx,lx);
x *= one; /* create necessary signal */
}
return x; /* exact output */
}
|
