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
|
/* mpfr_round_raw_generic -- Generic rounding function
Copyright 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011 Free Software Foundation, Inc.
Contributed by the Arenaire and Caramel projects, INRIA.
This file is part of the GNU MPFR Library.
The GNU MPFR 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 3 of the License, or (at your
option) any later version.
The GNU MPFR 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 MPFR Library; see the file COPYING.LESSER. If not, see
http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
#ifndef flag
# error "ERROR: flag must be defined (0 / 1)"
#endif
#ifndef use_inexp
# error "ERROR: use_enexp must be defined (0 / 1)"
#endif
#ifndef mpfr_round_raw_generic
# error "ERROR: mpfr_round_raw_generic must be defined"
#endif
/*
* If flag = 0, puts in y the value of xp (with precision xprec and
* sign 1 if negative=0, -1 otherwise) rounded to precision yprec and
* direction rnd_mode. Supposes x is not zero nor NaN nor +/- Infinity
* (i.e. *xp != 0). In that case, the return value is a possible carry
* (0 or 1) that may happen during the rounding, in which case the result
* is a power of two.
*
* If inexp != NULL, put in *inexp the inexact flag of the rounding (0, 1, -1).
* In case of even rounding when rnd = MPFR_RNDN, put MPFR_EVEN_INEX (2) or
* -MPFR_EVEN_INEX (-2) in *inexp.
*
* If flag = 1, just returns whether one should add 1 or not for rounding.
*
* Note: yprec may be < MPFR_PREC_MIN; in particular, it may be equal
* to 1. In this case, the even rounding is done away from 0, which is
* a natural generalization. Indeed, a number with 1-bit precision can
* be seen as a denormalized number with more precision.
*/
int
mpfr_round_raw_generic(
#if flag == 0
mp_limb_t *yp,
#endif
const mp_limb_t *xp, mpfr_prec_t xprec,
int neg, mpfr_prec_t yprec, mpfr_rnd_t rnd_mode
#if use_inexp != 0
, int *inexp
#endif
)
{
mp_size_t xsize, nw;
mp_limb_t himask, lomask, sb;
int rw;
#if flag == 0
int carry;
#endif
#if use_inexp == 0
int *inexp;
#endif
if (use_inexp)
MPFR_ASSERTD(inexp != ((int*) 0));
MPFR_ASSERTD(neg == 0 || neg == 1);
if (flag && !use_inexp &&
(xprec <= yprec || MPFR_IS_LIKE_RNDZ (rnd_mode, neg)))
return 0;
xsize = (xprec-1)/GMP_NUMB_BITS + 1;
nw = yprec / GMP_NUMB_BITS;
rw = yprec & (GMP_NUMB_BITS - 1);
if (MPFR_UNLIKELY(xprec <= yprec))
{ /* No rounding is necessary. */
/* if yp=xp, maybe an overlap: MPN_COPY_DECR is ok when src <= dst */
if (MPFR_LIKELY(rw))
nw++;
MPFR_ASSERTD(nw >= 1);
MPFR_ASSERTD(nw >= xsize);
if (use_inexp)
*inexp = 0;
#if flag == 0
MPN_COPY_DECR(yp + (nw - xsize), xp, xsize);
MPN_ZERO(yp, nw - xsize);
#endif
return 0;
}
if (use_inexp || !MPFR_IS_LIKE_RNDZ(rnd_mode, neg))
{
mp_size_t k = xsize - nw - 1;
if (MPFR_LIKELY(rw))
{
nw++;
lomask = MPFR_LIMB_MASK (GMP_NUMB_BITS - rw);
himask = ~lomask;
}
else
{
lomask = ~(mp_limb_t) 0;
himask = ~(mp_limb_t) 0;
}
MPFR_ASSERTD(k >= 0);
sb = xp[k] & lomask; /* First non-significant bits */
/* Rounding to nearest ? */
if (MPFR_LIKELY( rnd_mode == MPFR_RNDN) )
{
/* Rounding to nearest */
mp_limb_t rbmask = MPFR_LIMB_ONE << (GMP_NUMB_BITS - 1 - rw);
if (sb & rbmask) /* rounding bit */
sb &= ~rbmask; /* it is 1, clear it */
else
{
/* Rounding bit is 0, behave like rounding to 0 */
goto rnd_RNDZ;
}
while (MPFR_UNLIKELY(sb == 0) && k > 0)
sb = xp[--k];
/* rounding to nearest, with rounding bit = 1 */
if (MPFR_UNLIKELY(sb == 0)) /* Even rounding. */
{
/* sb == 0 && rnd_mode == MPFR_RNDN */
sb = xp[xsize - nw] & (himask ^ (himask << 1));
if (sb == 0)
{
if (use_inexp)
*inexp = 2*MPFR_EVEN_INEX*neg-MPFR_EVEN_INEX;
/* ((neg!=0)^(sb!=0)) ? MPFR_EVEN_INEX : -MPFR_EVEN_INEX;*/
/* Since neg = 0 or 1 and sb=0*/
#if flag == 1
return 0 /*sb != 0 && rnd_mode != MPFR_RNDZ */;
#else
MPN_COPY_INCR(yp, xp + xsize - nw, nw);
yp[0] &= himask;
return 0;
#endif
}
else
{
/* sb != 0 && rnd_mode == MPFR_RNDN */
if (use_inexp)
*inexp = MPFR_EVEN_INEX-2*MPFR_EVEN_INEX*neg;
/*((neg!=0)^(sb!=0))? MPFR_EVEN_INEX : -MPFR_EVEN_INEX; */
/*Since neg= 0 or 1 and sb != 0 */
goto rnd_RNDN_add_one_ulp;
}
}
else /* sb != 0 && rnd_mode == MPFR_RNDN*/
{
if (use_inexp)
/* *inexp = (neg == 0) ? 1 : -1; but since neg = 0 or 1 */
*inexp = 1-2*neg;
rnd_RNDN_add_one_ulp:
#if flag == 1
return 1; /*sb != 0 && rnd_mode != MPFR_RNDZ;*/
#else
carry = mpn_add_1 (yp, xp + xsize - nw, nw,
rw ?
MPFR_LIMB_ONE << (GMP_NUMB_BITS - rw)
: MPFR_LIMB_ONE);
yp[0] &= himask;
return carry;
#endif
}
}
/* Rounding to Zero ? */
else if (MPFR_IS_LIKE_RNDZ(rnd_mode, neg))
{
/* rnd_mode == MPFR_RNDZ */
rnd_RNDZ:
while (MPFR_UNLIKELY(sb == 0) && k > 0)
sb = xp[--k];
if (use_inexp)
/* rnd_mode == MPFR_RNDZ and neg = 0 or 1 */
/* (neg != 0) ^ (rnd_mode != MPFR_RNDZ)) ? 1 : -1);*/
*inexp = MPFR_UNLIKELY(sb == 0) ? 0 : (2*neg-1);
#if flag == 1
return 0; /*sb != 0 && rnd_mode != MPFR_RNDZ;*/
#else
MPN_COPY_INCR(yp, xp + xsize - nw, nw);
yp[0] &= himask;
return 0;
#endif
}
else
{
/* rnd_mode = Away */
while (MPFR_UNLIKELY(sb == 0) && k > 0)
sb = xp[--k];
if (MPFR_UNLIKELY(sb == 0))
{
/* sb = 0 && rnd_mode != MPFR_RNDZ */
if (use_inexp)
/* (neg != 0) ^ (rnd_mode != MPFR_RNDZ)) ? 1 : -1);*/
*inexp = 0;
#if flag == 1
return 0;
#else
MPN_COPY_INCR(yp, xp + xsize - nw, nw);
yp[0] &= himask;
return 0;
#endif
}
else
{
/* sb != 0 && rnd_mode != MPFR_RNDZ */
if (use_inexp)
/* (neg != 0) ^ (rnd_mode != MPFR_RNDZ)) ? 1 : -1);*/
*inexp = 1-2*neg;
#if flag == 1
return 1;
#else
carry = mpn_add_1(yp, xp + xsize - nw, nw,
rw ? MPFR_LIMB_ONE << (GMP_NUMB_BITS - rw)
: 1);
yp[0] &= himask;
return carry;
#endif
}
}
}
else
{
/* Roundind mode = Zero / No inexact flag */
#if flag == 1
return 0 /*sb != 0 && rnd_mode != MPFR_RNDZ*/;
#else
if (MPFR_LIKELY(rw))
{
nw++;
himask = ~MPFR_LIMB_MASK (GMP_NUMB_BITS - rw);
}
else
himask = ~(mp_limb_t) 0;
MPN_COPY_INCR(yp, xp + xsize - nw, nw);
yp[0] &= himask;
return 0;
#endif
}
}
#undef flag
#undef use_inexp
#undef mpfr_round_raw_generic
|
