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
|
/* Copyright (C) 1995-2025 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library 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.
The GNU C Library 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 the GNU C Library; if not, see
<https://www.gnu.org/licenses/>. */
#include <ieee754.h>
#include <errno.h>
#include <float.h>
#include <math.h>
#include "gmp.h"
#include "gmp-impl.h"
/* Convert a multi-precision integer of the needed number of bits (106
for long double) and an integral power of two to a `long double' in
IBM extended format. */
long double
__mpn_construct_long_double (mp_srcptr frac_ptr, int expt, int sign)
{
union ibm_extended_long_double u;
unsigned long lzcount;
unsigned long long hi, lo;
int exponent2;
u.d[0].ieee.negative = sign;
u.d[1].ieee.negative = sign;
u.d[0].ieee.exponent = expt + IEEE754_DOUBLE_BIAS;
u.d[1].ieee.exponent = 0;
exponent2 = expt - 53 + IEEE754_DOUBLE_BIAS;
#if BITS_PER_MP_LIMB == 32
/* The low order 53 bits (52 + hidden) go into the lower double */
lo = frac_ptr[0];
lo |= (frac_ptr[1] & ((1LL << (53 - 32)) - 1)) << 32;
/* The high order 53 bits (52 + hidden) go into the upper double */
hi = (frac_ptr[1] >> (53 - 32)) & ((1 << 11) - 1);
hi |= ((unsigned long long) frac_ptr[2]) << 11;
hi |= ((unsigned long long) frac_ptr[3]) << (32 + 11);
#elif BITS_PER_MP_LIMB == 64
/* The low order 53 bits (52 + hidden) go into the lower double */
lo = frac_ptr[0] & (((mp_limb_t) 1 << 53) - 1);
/* The high order 53 bits (52 + hidden) go into the upper double */
hi = (frac_ptr[0] >> 53) & (((mp_limb_t) 1 << 11) - 1);
hi |= (frac_ptr[1] << 11);
#else
#error "mp_limb size " BITS_PER_MP_LIMB "not accounted for"
#endif
if ((hi & (1LL << 52)) == 0 && (hi | lo) != 0)
{
/* denormal number */
unsigned long long val = hi ? hi : lo;
if (sizeof (val) == sizeof (long))
lzcount = __builtin_clzl (val);
else if ((val >> 32) != 0)
lzcount = __builtin_clzl ((long) (val >> 32));
else
lzcount = __builtin_clzl ((long) val) + 32;
if (hi)
lzcount = lzcount - (64 - 53);
else
lzcount = lzcount + 53 - (64 - 53);
if (lzcount > u.d[0].ieee.exponent)
{
lzcount = u.d[0].ieee.exponent;
u.d[0].ieee.exponent = 0;
exponent2 -= lzcount;
}
else
{
u.d[0].ieee.exponent -= (lzcount - 1);
exponent2 -= (lzcount - 1);
}
if (lzcount <= 53)
{
hi = (hi << lzcount) | (lo >> (53 - lzcount));
lo = (lo << lzcount) & ((1LL << 53) - 1);
}
else
{
hi = lo << (lzcount - 53);
lo = 0;
}
}
if (lo != 0)
{
/* hidden bit of low double controls rounding of the high double.
If hidden is '1' and either the explicit mantissa is non-zero
or hi is odd, then round up hi and adjust lo (2nd mantissa)
plus change the sign of the low double to compensate. */
if ((lo & (1LL << 52)) != 0
&& ((hi & 1) != 0 || (lo & ((1LL << 52) - 1)) != 0))
{
hi++;
if ((hi & (1LL << 53)) != 0)
{
hi >>= 1;
u.d[0].ieee.exponent++;
if (u.d[0].ieee.exponent == IEEE754_DOUBLE_BIAS + DBL_MAX_EXP)
{
/* Overflow. The appropriate overflowed result must
be produced (if an infinity, that means the low
part must be zero). */
__set_errno (ERANGE);
return (sign ? -LDBL_MAX : LDBL_MAX) * LDBL_MAX;
}
}
u.d[1].ieee.negative = !sign;
lo = (1LL << 53) - lo;
}
/* Normalize the low double. Shift the mantissa left until
the hidden bit is '1' and adjust the 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 - (64 - 53);
lo <<= lzcount;
exponent2 -= lzcount;
if (exponent2 > 0)
u.d[1].ieee.exponent = exponent2;
else if (exponent2 > -53)
lo >>= 1 - exponent2;
else
lo = 0;
}
else
u.d[1].ieee.negative = 0;
u.d[1].ieee.mantissa1 = lo;
u.d[1].ieee.mantissa0 = lo >> 32;
u.d[0].ieee.mantissa1 = hi;
u.d[0].ieee.mantissa0 = hi >> 32;
return u.ld;
}
|
