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
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
|
/* origin: FreeBSD /usr/src/lib/msun/src/s_remquol.c */
/*-
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#include "libm.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
long double remquol(long double x, long double y, int *quo)
{
return remquo(x, y, quo);
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
#define BIAS (LDBL_MAX_EXP - 1)
#if LDBL_MANL_SIZE > 32
typedef uint64_t manl_t;
#else
typedef uint32_t manl_t;
#endif
#if LDBL_MANH_SIZE > 32
typedef uint64_t manh_t;
#else
typedef uint32_t manh_t;
#endif
/*
* These macros add and remove an explicit integer bit in front of the
* fractional mantissa, if the architecture doesn't have such a bit by
* default already.
*/
#ifdef LDBL_IMPLICIT_NBIT
#define SET_NBIT(hx) ((hx) | (1ULL << LDBL_MANH_SIZE))
#define HFRAC_BITS LDBL_MANH_SIZE
#else
#define SET_NBIT(hx) (hx)
#define HFRAC_BITS (LDBL_MANH_SIZE - 1)
#endif
#define MANL_SHIFT (LDBL_MANL_SIZE - 1)
static const long double Zero[] = {0.0, -0.0};
/*
* Return the IEEE remainder and set *quo to the last n bits of the
* quotient, rounded to the nearest integer. We choose n=31 because
* we wind up computing all the integer bits of the quotient anyway as
* a side-effect of computing the remainder by the shift and subtract
* method. In practice, this is far more bits than are needed to use
* remquo in reduction algorithms.
*
* Assumptions:
* - The low part of the mantissa fits in a manl_t exactly.
* - The high part of the mantissa fits in an int64_t with enough room
* for an explicit integer bit in front of the fractional bits.
*/
long double remquol(long double x, long double y, int *quo)
{
union IEEEl2bits ux, uy;
int64_t hx,hz; /* We need a carry bit even if LDBL_MANH_SIZE is 32. */
manh_t hy;
manl_t lx,ly,lz;
int ix,iy,n,q,sx,sxy;
ux.e = x;
uy.e = y;
sx = ux.bits.sign;
sxy = sx ^ uy.bits.sign;
ux.bits.sign = 0; /* |x| */
uy.bits.sign = 0; /* |y| */
x = ux.e;
/* purge off exception values */
if ((uy.bits.exp|uy.bits.manh|uy.bits.manl)==0 || /* y=0 */
(ux.bits.exp == BIAS + LDBL_MAX_EXP) || /* or x not finite */
(uy.bits.exp == BIAS + LDBL_MAX_EXP &&
((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* or y is NaN */
return (x*y)/(x*y);
if (ux.bits.exp <= uy.bits.exp) {
if ((ux.bits.exp < uy.bits.exp) ||
(ux.bits.manh <= uy.bits.manh &&
(ux.bits.manh < uy.bits.manh ||
ux.bits.manl < uy.bits.manl))) {
q = 0;
goto fixup; /* |x|<|y| return x or x-y */
}
if (ux.bits.manh == uy.bits.manh && ux.bits.manl == uy.bits.manl) {
*quo = 1;
return Zero[sx]; /* |x|=|y| return x*0*/
}
}
/* determine ix = ilogb(x) */
if (ux.bits.exp == 0) { /* subnormal x */
ux.e *= 0x1.0p512;
ix = ux.bits.exp - (BIAS + 512);
} else {
ix = ux.bits.exp - BIAS;
}
/* determine iy = ilogb(y) */
if (uy.bits.exp == 0) { /* subnormal y */
uy.e *= 0x1.0p512;
iy = uy.bits.exp - (BIAS + 512);
} else {
iy = uy.bits.exp - BIAS;
}
/* set up {hx,lx}, {hy,ly} and align y to x */
hx = SET_NBIT(ux.bits.manh);
hy = SET_NBIT(uy.bits.manh);
lx = ux.bits.manl;
ly = uy.bits.manl;
/* fix point fmod */
n = ix - iy;
q = 0;
while (n--) {
hz = hx - hy;
lz = lx - ly;
if (lx < ly)
hz -= 1;
if (hz < 0) {
hx = hx + hx + (lx>>MANL_SHIFT);
lx = lx + lx;
} else {
hx = hz + hz + (lz>>MANL_SHIFT);
lx = lz + lz;
q++;
}
q <<= 1;
}
hz = hx - hy;
lz = lx - ly;
if (lx < ly)
hz -= 1;
if (hz >= 0) {
hx = hz;
lx = lz;
q++;
}
/* convert back to floating value and restore the sign */
if ((hx|lx) == 0) { /* return sign(x)*0 */
*quo = sxy ? -q : q;
return Zero[sx];
}
while (hx < (1ULL<<HFRAC_BITS)) { /* normalize x */
hx = hx + hx + (lx>>MANL_SHIFT);
lx = lx + lx;
iy -= 1;
}
ux.bits.manh = hx; /* The integer bit is truncated here if needed. */
ux.bits.manl = lx;
if (iy < LDBL_MIN_EXP) {
ux.bits.exp = iy + (BIAS + 512);
ux.e *= 0x1p-512;
} else {
ux.bits.exp = iy + BIAS;
}
ux.bits.sign = 0;
x = ux.e;
fixup:
y = fabsl(y);
if (y < LDBL_MIN * 2) {
if (x + x > y || (x + x == y && (q & 1))) {
q++;
x-=y;
}
} else if (x > 0.5*y || (x == 0.5*y && (q & 1))) {
q++;
x-=y;
}
ux.e = x;
ux.bits.sign ^= sx;
x = ux.e;
q &= 0x7fffffff;
*quo = sxy ? -q : q;
return x;
}
#endif
|
