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
|
#ifndef _MATH_PRIVATE_H_
#error "Never use <math_ldbl.h> directly; include <math_private.h> instead."
#endif
#include <sysdeps/ieee754/ldbl-128/math_ldbl.h>
#include <ieee754.h>
#include <stdint.h>
static inline void
ldbl_extract_mantissa (int64_t *hi64, uint64_t *lo64, int *exp, long double x)
{
/* We have 105 bits of mantissa plus one implicit digit. Since
106 bits are representable we use the first implicit digit for
the number before the decimal point and the second implicit bit
as bit 53 of the mantissa. */
uint64_t hi, lo;
int ediff;
union ibm_extended_long_double u;
u.ld = x;
*exp = u.d[0].ieee.exponent - IEEE754_DOUBLE_BIAS;
lo = ((uint64_t) u.d[1].ieee.mantissa0 << 32) | u.d[1].ieee.mantissa1;
hi = ((uint64_t) u.d[0].ieee.mantissa0 << 32) | u.d[0].ieee.mantissa1;
/* If the lower double is not a denomal or zero then set the hidden
53rd bit. */
if (u.d[1].ieee.exponent > 0x001)
{
lo |= (1ULL << 52);
lo = lo << 7; /* pre-shift lo to match ieee854. */
/* The lower double is normalized separately from the upper. We
may need to adjust the lower manitissa to reflect this. */
ediff = u.d[0].ieee.exponent - u.d[1].ieee.exponent;
if (ediff > 53)
lo = lo >> (ediff-53);
hi |= (1ULL << 52);
}
if ((u.d[0].ieee.negative != u.d[1].ieee.negative)
&& ((u.d[1].ieee.exponent != 0) && (lo != 0LL)))
{
hi--;
lo = (1ULL << 60) - lo;
if (hi < (1ULL << 52))
{
/* we have a borrow from the hidden bit, so shift left 1. */
hi = (hi << 1) | (lo >> 59);
lo = 0xfffffffffffffffLL & (lo << 1);
*exp = *exp - 1;
}
}
*lo64 = (hi << 60) | lo;
*hi64 = hi >> 4;
}
static inline long double
ldbl_insert_mantissa (int sign, int exp, int64_t hi64, u_int64_t lo64)
{
union ibm_extended_long_double u;
unsigned long hidden2, lzcount;
unsigned long long hi, lo;
u.d[0].ieee.negative = sign;
u.d[1].ieee.negative = sign;
u.d[0].ieee.exponent = exp + IEEE754_DOUBLE_BIAS;
u.d[1].ieee.exponent = exp-53 + IEEE754_DOUBLE_BIAS;
/* Expect 113 bits (112 bits + hidden) right justified in two longs.
The low order 53 bits (52 + hidden) go into the lower double */
lo = (lo64 >> 7)& ((1ULL << 53) - 1);
hidden2 = (lo64 >> 59) & 1ULL;
/* The high order 53 bits (52 + hidden) go into the upper double */
hi = (lo64 >> 60) & ((1ULL << 11) - 1);
hi |= (hi64 << 4);
if (lo != 0LL)
{
/* hidden2 bit of low double controls rounding of the high double.
If hidden2 is '1' then round up hi and adjust lo (2nd mantissa)
plus change the sign of the low double to compensate. */
if (hidden2)
{
hi++;
u.d[1].ieee.negative = !sign;
lo = (1ULL << 53) - lo;
}
/* The hidden bit of the lo mantissa is zero so we need to
normalize the it for the low double. Shift it left until the
hidden bit is '1' then adjust the 2nd exponent accordingly. */
if (sizeof (lo) == sizeof (long))
lzcount = __builtin_clzl (lo);
else if ((lo >> 32) != 0)
lzcount = __builtin_clzl ((long) (lo >> 32));
else
lzcount = __builtin_clzl ((long) lo) + 32;
lzcount = lzcount - 11;
if (lzcount > 0)
{
int expnt2 = u.d[1].ieee.exponent - lzcount;
if (expnt2 >= 1)
{
/* Not denormal. Normalize and set low exponent. */
lo = lo << lzcount;
u.d[1].ieee.exponent = expnt2;
}
else
{
/* Is denormal. */
lo = lo << (lzcount + expnt2);
u.d[1].ieee.exponent = 0;
}
}
}
else
{
u.d[1].ieee.negative = 0;
u.d[1].ieee.exponent = 0;
}
u.d[1].ieee.mantissa1 = lo & ((1ULL << 32) - 1);
u.d[1].ieee.mantissa0 = (lo >> 32) & ((1ULL << 20) - 1);
u.d[0].ieee.mantissa1 = hi & ((1ULL << 32) - 1);
u.d[0].ieee.mantissa0 = (hi >> 32) & ((1ULL << 20) - 1);
return u.ld;
}
/* Handy utility functions to pack/unpack/cononicalize and find the nearbyint
of long double implemented as double double. */
static inline long double
default_ldbl_pack (double a, double aa)
{
union ibm_extended_long_double u;
u.d[0].d = a;
u.d[1].d = aa;
return u.ld;
}
static inline void
default_ldbl_unpack (long double l, double *a, double *aa)
{
union ibm_extended_long_double u;
u.ld = l;
*a = u.d[0].d;
*aa = u.d[1].d;
}
#ifndef ldbl_pack
# define ldbl_pack default_ldbl_pack
#endif
#ifndef ldbl_unpack
# define ldbl_unpack default_ldbl_unpack
#endif
/* Convert a finite long double to canonical form.
Does not handle +/-Inf properly. */
static inline void
ldbl_canonicalize (double *a, double *aa)
{
double xh, xl;
xh = *a + *aa;
xl = (*a - xh) + *aa;
*a = xh;
*aa = xl;
}
/* Simple inline nearbyint (double) function .
Only works in the default rounding mode
but is useful in long double rounding functions. */
static inline double
ldbl_nearbyint (double a)
{
double two52 = 0x10000000000000LL;
if (__builtin_expect ((__builtin_fabs (a) < two52), 1))
{
if (__builtin_expect ((a > 0.0), 1))
{
a += two52;
a -= two52;
}
else if (__builtin_expect ((a < 0.0), 1))
{
a = two52 - a;
a = -(a - two52);
}
}
return a;
}
|
