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
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
|
/* Software floating-point emulation.
Convert a _BitInt to _Decimal64.
Copyright (C) 2023 Free Software Foundation, Inc.
This file is part of GCC.
GCC is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free
Software Foundation; either version 3, or (at your option) any later
version.
GCC 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 General Public License
for more details.
Under Section 7 of GPL version 3, you are granted additional
permissions described in the GCC Runtime Library Exception, version
3.1, as published by the Free Software Foundation.
You should have received a copy of the GNU General Public License and
a copy of the GCC Runtime Library Exception along with this program;
see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
<http://www.gnu.org/licenses/>. */
#include "soft-fp.h"
#include "bitint.h"
#ifdef __BITINT_MAXWIDTH__
extern _Decimal64 __bid_floatbitintdd (const UBILtype *, SItype);
_Decimal64
__bid_floatbitintdd (const UBILtype *i, SItype iprec)
{
iprec = bitint_reduce_prec (&i, iprec);
USItype aiprec = iprec < 0 ? -iprec : iprec;
USItype in = (aiprec + BIL_TYPE_SIZE - 1) / BIL_TYPE_SIZE;
USItype idx = BITINT_END (0, in - 1);
UBILtype msb = i[idx];
UDItype mantissa;
SItype exponent = 0;
UBILtype inexact = 0;
union { _Decimal64 d; UDItype u; } u, ui;
if (aiprec % BIL_TYPE_SIZE)
{
if (iprec > 0)
msb &= ((UBILtype) 1 << (aiprec % BIL_TYPE_SIZE)) - 1;
else
msb |= (UBILtype) -1 << (aiprec % BIL_TYPE_SIZE);
}
if (iprec < 0)
{
SItype n = sizeof (0ULL) * __CHAR_BIT__ + 1 - __builtin_clzll (~msb);
aiprec = (in - 1) * BIL_TYPE_SIZE + n;
}
else if (msb == 0)
aiprec = 1;
else
{
SItype n = sizeof (0ULL) * __CHAR_BIT__ - __builtin_clzll (msb);
aiprec = (in - 1) * BIL_TYPE_SIZE + n;
}
/* Number of bits in (_BitInt(2048)) 9999999999999999e+369DD. */
if (aiprec > 1279 + (iprec < 0))
{
ovf:
if (iprec < 0)
u.d = -9000000000000000e+369DD;
else
u.d = 9000000000000000e+369DD;
__asm ("" : "+g" (u.d));
u.d += u.d;
__asm ("" : "+g" (u.d));
goto done;
}
/* Bit precision of 9999999999999999uwb. */
if (aiprec >= 54)
{
USItype pow10_limbs, q_limbs, q2_limbs, j;
USItype exp_bits = 0, e;
UDItype m;
UBILtype *buf;
/* First do a possibly large divide smaller enough such that
we only need to check remainder for 0 or non-0 and then
we'll do further division. */
if (aiprec >= 54 + 4 + 10)
{
exp_bits = (aiprec - 54 - 4) / 10;
exponent = exp_bits * 3;
/* Upper estimate for pow10 (exponent) bits. */
exp_bits = exp_bits * 10 - exp_bits / 30;
}
pow10_limbs = (exp_bits + BIL_TYPE_SIZE - 1) / BIL_TYPE_SIZE;
/* 72 is the highest number of quotient bits needed on
aiprec range of [68, 1279]. E.g. if aiprec is 1277,
exponent will be 363 and exp_bits 1206. 1277 - 1206 + 1
is 72. Unfortunately that means the result doesn't fit into
UDItype... */
q_limbs = (72 + BIL_TYPE_SIZE - 1) / BIL_TYPE_SIZE;
q2_limbs = 64 / BIL_TYPE_SIZE;
buf = __builtin_alloca ((q_limbs + pow10_limbs * 2 + q2_limbs + 2)
* sizeof (UBILtype));
if (exponent)
{
__bid_pow10bitint (buf + q_limbs, exp_bits, exponent);
__divmodbitint4 (buf, q_limbs * BIL_TYPE_SIZE,
buf + q_limbs + pow10_limbs,
pow10_limbs * BIL_TYPE_SIZE,
i, iprec < 0 ? -aiprec : aiprec,
buf + q_limbs, exp_bits);
if (iprec < 0)
bitint_negate (buf + BITINT_END (q_limbs - 1, 0),
buf + BITINT_END (q_limbs - 1, 0), q_limbs);
inexact = buf[q_limbs + pow10_limbs];
for (j = 1; j < pow10_limbs; ++j)
inexact |= buf[q_limbs + pow10_limbs + j];
}
else
{
__builtin_memcpy (buf + BITINT_END (q_limbs - in + 1, 0), i,
(in - 1) * sizeof (UBILtype));
buf[BITINT_END (q_limbs - in, in - 1)] = msb;
if (iprec < 0)
bitint_negate (buf + BITINT_END (q_limbs - 1, 0),
buf + BITINT_END (q_limbs - 1, 0), in);
if (q_limbs > in)
__builtin_memset (buf + BITINT_END (0, in), '\0',
(q_limbs - in) * sizeof (UBILtype));
}
e = 0;
#if BIL_TYPE_SIZE == 64
m = buf[BITINT_END (1, 0)];
#elif BIL_TYPE_SIZE == 32
m = (UDItype) buf[1] << 32 | buf[BITINT_END (2, 0)];
#else
# error Unsupported BIL_TYPE_SIZE
#endif
if (buf[BITINT_END (0, q_limbs - 1)])
{
if (buf[BITINT_END (0, q_limbs - 1)] > 0x5)
{
/* 1000000000000000000000wb */
if (buf[BITINT_END (0, q_limbs - 1)] > 0x36
|| (buf[BITINT_END (0, q_limbs - 1)] == 0x36
&& m >= (UDItype) 0x35c9adc5dea00000))
e = 6;
else
e = 5;
}
/* 100000000000000000000wb */
else if (buf[BITINT_END (0, q_limbs - 1)] == 0x5
&& m >= (UDItype) 0x6bc75e2d63100000)
e = 5;
else
e = 4;
}
else if (m >= (UDItype) 1000000000000000000)
{
if (m >= (UDItype) 10000000000000000000ULL)
e = 4;
else
e = 3;
}
else if (m >= (UDItype) 100000000000000000)
e = 2;
else if (m >= (UDItype) 10000000000000000)
e = 1;
exponent += e;
if (exponent > 369)
goto ovf;
if (e)
{
UBILtype rem, half;
__bid_pow10bitint (buf + q_limbs + pow10_limbs * 2,
BIL_TYPE_SIZE, e);
__divmodbitint4 (buf + q_limbs + pow10_limbs * 2 + 1,
q2_limbs * BIL_TYPE_SIZE,
buf + q_limbs + pow10_limbs * 2 + 1 + q2_limbs,
BIL_TYPE_SIZE,
buf, q_limbs * BIL_TYPE_SIZE,
buf + q_limbs + pow10_limbs * 2, BIL_TYPE_SIZE);
half = buf[q_limbs + pow10_limbs * 2] / 2;
rem = buf[q_limbs + pow10_limbs * 2 + 1 + q2_limbs];
if (inexact)
{
/* If first division discovered some non-0 digits
and this second division is by 10, e.g.
for XXXXXX5499999999999 or XXXXXX5000000000001
if first division is by 10^12 and second by 10^1,
doing rem |= 1 wouldn't change the 5. Similarly
for rem 4 doing rem |= 1 would change it to 5,
but we don't want to change it in that case. */
if (e == 1)
{
if (rem == 5)
rem = 6;
else if (rem != 4)
rem |= 1;
}
else
rem |= 1;
}
/* Set inexact to 0, 1, 2, 3 depending on if remainder
of the divisions is exact 0, smaller than 10^exponent / 2,
exactly 10^exponent / 2 or greater than that. */
if (rem >= half)
inexact = 2 + (rem > half);
else
inexact = (rem != 0);
#if BIL_TYPE_SIZE == 64
mantissa = buf[q_limbs + pow10_limbs * 2 + 1];
#else
mantissa
= ((UDItype)
buf[q_limbs + pow10_limbs * 2 + 1 + BITINT_END (0, 1)] << 32
| buf[q_limbs + pow10_limbs * 2 + 1 + BITINT_END (1, 0)]);
#endif
}
else
#if BIL_TYPE_SIZE == 64
mantissa = buf[BITINT_END (1, 0)];
#else
mantissa = (UDItype) buf[1] << 32 | buf[BITINT_END (2, 0)];
#endif
}
else
{
#if BIL_TYPE_SIZE == 64
mantissa = msb;
#else
if (in == 1)
mantissa = iprec < 0 ? (UDItype) (BILtype) msb : (UDItype) msb;
else
mantissa = (UDItype) msb << 32 | i[BITINT_END (1, 0)];
#endif
if (iprec < 0)
mantissa = -mantissa;
}
exponent += 398;
if (mantissa >= (UDItype) 0x20000000000000)
u.u = (((((iprec < 0) << 2) | (UDItype) 3) << 61)
| (((UDItype) exponent) << 51)
| (mantissa ^ (UDItype) 0x20000000000000));
else
u.u = ((((UDItype) (iprec < 0)) << 63)
| (((UDItype) exponent) << 53)
| mantissa);
if (inexact)
{
ui.u = ((((UDItype) (iprec < 0)) << 63)
| (((UDItype) (exponent - 1)) << 53)
| (inexact + 3));
__asm ("" : "+g" (u.d));
__asm ("" : "+g" (ui.d));
u.d += ui.d;
__asm ("" : "+g" (u.d));
}
done:
return u.d;
}
#endif
|
