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
194
195
196
197
|
/* Copyright (C) 1995-2024 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 "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"
#include <ieee754.h>
#include <float.h>
#include <math.h>
#include <stdlib.h>
/* Convert a `long double' in IBM extended format to a multi-precision
integer representing the significand scaled up by its number of
bits (106 for long double) and an integral power of two (MPN
frexpl). */
/* When signs differ, the actual value is the difference between the
significant double and the less significant double. Sometimes a
bit can be lost when we borrow from the significant mantissa. */
#define EXTRA_INTERNAL_PRECISION (7)
mp_size_t
__mpn_extract_long_double (mp_ptr res_ptr, mp_size_t size,
int *expt, int *is_neg,
long double value)
{
union ibm_extended_long_double u;
unsigned long long hi, lo;
int ediff;
u.ld = value;
*is_neg = u.d[0].ieee.negative;
*expt = (int) u.d[0].ieee.exponent - IEEE754_DOUBLE_BIAS;
lo = ((long long) u.d[1].ieee.mantissa0 << 32) | u.d[1].ieee.mantissa1;
hi = ((long long) u.d[0].ieee.mantissa0 << 32) | u.d[0].ieee.mantissa1;
/* Hold 7 extra bits of precision in the mantissa. This allows
the normalizing shifts below to prevent losing precision when
the signs differ and the exponents are sufficiently far apart. */
lo <<= EXTRA_INTERNAL_PRECISION;
/* If the lower double is not a denormal or zero then set the hidden
53rd bit. */
if (u.d[1].ieee.exponent != 0)
lo |= 1ULL << (52 + EXTRA_INTERNAL_PRECISION);
else
lo = lo << 1;
/* 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 - 53;
if (ediff > 0)
{
if (ediff < 64)
lo = lo >> ediff;
else
lo = 0;
}
else if (ediff < 0)
lo = lo << -ediff;
/* The high double may be rounded and the low double reflects the
difference between the long double and the rounded high double
value. This is indicated by a difference between the signs of the
high and low doubles. */
if (u.d[0].ieee.negative != u.d[1].ieee.negative
&& lo != 0)
{
lo = (1ULL << (53 + EXTRA_INTERNAL_PRECISION)) - lo;
if (hi == 0)
{
/* we have a borrow from the hidden bit, so shift left 1. */
hi = 0x000ffffffffffffeLL | (lo >> (52 + EXTRA_INTERNAL_PRECISION));
lo = 0x0fffffffffffffffLL & (lo << 1);
(*expt)--;
}
else
hi--;
}
#if BITS_PER_MP_LIMB == 32
/* Combine the mantissas to be contiguous. */
res_ptr[0] = lo >> EXTRA_INTERNAL_PRECISION;
res_ptr[1] = (hi << (53 - 32)) | (lo >> (32 + EXTRA_INTERNAL_PRECISION));
res_ptr[2] = hi >> 11;
res_ptr[3] = hi >> (32 + 11);
#define N 4
#elif BITS_PER_MP_LIMB == 64
/* Combine the two mantissas to be contiguous. */
res_ptr[0] = (hi << 53) | (lo >> EXTRA_INTERNAL_PRECISION);
res_ptr[1] = hi >> 11;
#define N 2
#else
#error "mp_limb size " BITS_PER_MP_LIMB "not accounted for"
#endif
/* The format does not fill the last limb. There are some zeros. */
#define NUM_LEADING_ZEROS (BITS_PER_MP_LIMB \
- (LDBL_MANT_DIG - ((N - 1) * BITS_PER_MP_LIMB)))
if (u.d[0].ieee.exponent == 0)
{
/* A biased exponent of zero is a special case.
Either it is a zero or it is a denormal number. */
if (res_ptr[0] == 0 && res_ptr[1] == 0
&& res_ptr[N - 2] == 0 && res_ptr[N - 1] == 0) /* Assumes N<=4. */
/* It's zero. */
*expt = 0;
else
{
/* It is a denormal number, meaning it has no implicit leading
one bit, and its exponent is in fact the format minimum. We
use DBL_MIN_EXP instead of LDBL_MIN_EXP below because the
latter describes the properties of both parts together, but
the exponent is computed from the high part only. */
int cnt;
#if N == 2
if (res_ptr[N - 1] != 0)
{
count_leading_zeros (cnt, res_ptr[N - 1]);
cnt -= NUM_LEADING_ZEROS;
res_ptr[N - 1] = res_ptr[N - 1] << cnt
| (res_ptr[0] >> (BITS_PER_MP_LIMB - cnt));
res_ptr[0] <<= cnt;
*expt = DBL_MIN_EXP - 1 - cnt;
}
else
{
count_leading_zeros (cnt, res_ptr[0]);
if (cnt >= NUM_LEADING_ZEROS)
{
res_ptr[N - 1] = res_ptr[0] << (cnt - NUM_LEADING_ZEROS);
res_ptr[0] = 0;
}
else
{
res_ptr[N - 1] = res_ptr[0] >> (NUM_LEADING_ZEROS - cnt);
res_ptr[0] <<= BITS_PER_MP_LIMB - (NUM_LEADING_ZEROS - cnt);
}
*expt = DBL_MIN_EXP - 1
- (BITS_PER_MP_LIMB - NUM_LEADING_ZEROS) - cnt;
}
#else
int j, k, l;
for (j = N - 1; j > 0; j--)
if (res_ptr[j] != 0)
break;
count_leading_zeros (cnt, res_ptr[j]);
cnt -= NUM_LEADING_ZEROS;
l = N - 1 - j;
if (cnt < 0)
{
cnt += BITS_PER_MP_LIMB;
l--;
}
if (!cnt)
for (k = N - 1; k >= l; k--)
res_ptr[k] = res_ptr[k-l];
else
{
for (k = N - 1; k > l; k--)
res_ptr[k] = res_ptr[k-l] << cnt
| res_ptr[k-l-1] >> (BITS_PER_MP_LIMB - cnt);
res_ptr[k--] = res_ptr[0] << cnt;
}
for (; k >= 0; k--)
res_ptr[k] = 0;
*expt = DBL_MIN_EXP - 1 - l * BITS_PER_MP_LIMB - cnt;
#endif
}
}
else
/* Add the implicit leading one bit for a normalized number. */
res_ptr[N - 1] |= (mp_limb_t) 1 << (LDBL_MANT_DIG - 1
- ((N - 1) * BITS_PER_MP_LIMB));
return N;
}
|
