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
|
/* mpfr_cmp2 -- exponent shift when subtracting two numbers.
Copyright 1999-2004, 2006-2017 Free Software Foundation, Inc.
Contributed by the AriC and Caramba 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. */
#define MPFR_NEED_LONGLONG_H
#include "mpfr-impl.h"
/* If |b| != |c|, puts the number of canceled bits when one subtracts |c|
from |b| in *cancel. Returns the sign of the difference (-1, 0, 1).
Assumes neither of b or c is NaN, +/- infinity, or +/- 0.
In other terms, if |b| != |c|, mpfr_cmp2 (b, c) returns
EXP(max(|b|,|c|)) - EXP(|b| - |c|).
*/
int
mpfr_cmp2 (mpfr_srcptr b, mpfr_srcptr c, mpfr_prec_t *cancel)
{
mp_limb_t *bp, *cp, bb, cc = 0, lastc = 0, dif, high_dif = 0;
mp_size_t bn, cn;
mpfr_uexp_t diff_exp;
mpfr_prec_t res = 0;
int sign;
/* b=c should not happen, since cmp2 is called only from agm (with
different variables) and from sub1 (if b=c, then sub1sp would be
called instead). So, no need for a particular optimization here. */
/* the cases b=0 or c=0 are also treated apart in agm and sub
(which calls sub1) */
MPFR_ASSERTD (MPFR_IS_PURE_FP(b));
MPFR_ASSERTD (MPFR_IS_PURE_FP(c));
if (MPFR_GET_EXP (b) >= MPFR_GET_EXP (c))
{
sign = 1;
diff_exp = (mpfr_uexp_t) MPFR_GET_EXP (b) - MPFR_GET_EXP (c);
bp = MPFR_MANT(b);
cp = MPFR_MANT(c);
bn = (MPFR_PREC(b) - 1) / GMP_NUMB_BITS;
cn = (MPFR_PREC(c) - 1) / GMP_NUMB_BITS; /* # of limbs of c minus 1 */
if (MPFR_UNLIKELY( diff_exp == 0 ))
{
while (bn >= 0 && cn >= 0 && bp[bn] == cp[cn])
{
bn--;
cn--;
res += GMP_NUMB_BITS;
}
if (MPFR_UNLIKELY (bn < 0))
{
if (MPFR_LIKELY (cn < 0)) /* b = c */
return 0;
bp = cp;
bn = cn;
cn = -1;
sign = -1;
}
if (MPFR_UNLIKELY (cn < 0))
/* c discards exactly the upper part of b */
{
unsigned int z;
MPFR_ASSERTD (bn >= 0);
while (bp[bn] == 0)
{
if (--bn < 0) /* b = c */
return 0;
res += GMP_NUMB_BITS;
}
count_leading_zeros(z, bp[bn]); /* bp[bn] <> 0 */
*cancel = res + z;
return sign;
}
MPFR_ASSERTD (bn >= 0);
MPFR_ASSERTD (cn >= 0);
MPFR_ASSERTD (bp[bn] != cp[cn]);
if (bp[bn] < cp[cn])
{
mp_limb_t *tp;
mp_size_t tn;
tp = bp; bp = cp; cp = tp;
tn = bn; bn = cn; cn = tn;
sign = -1;
}
}
} /* MPFR_EXP(b) >= MPFR_EXP(c) */
else /* MPFR_EXP(b) < MPFR_EXP(c) */
{
sign = -1;
diff_exp = (mpfr_uexp_t) MPFR_GET_EXP (c) - MPFR_GET_EXP (b);
bp = MPFR_MANT(c);
cp = MPFR_MANT(b);
bn = (MPFR_PREC(c) - 1) / GMP_NUMB_BITS;
cn = (MPFR_PREC(b) - 1) / GMP_NUMB_BITS;
}
/* now we have removed the identical upper limbs of b and c
(can happen only when diff_exp = 0), and after the possible
swap, we have |b| > |c|: bp[bn] > cc, bn >= 0, cn >= 0,
diff_exp = EXP(b) - EXP(c).
*/
if (MPFR_LIKELY (diff_exp < GMP_NUMB_BITS))
{
cc = cp[cn] >> diff_exp;
/* warning: a shift by GMP_NUMB_BITS may give wrong results */
if (diff_exp)
lastc = cp[cn] << (GMP_NUMB_BITS - diff_exp);
cn--;
}
else
diff_exp -= GMP_NUMB_BITS; /* cc = 0 */
dif = bp[bn--] - cc; /* necessarily dif >= 1 */
MPFR_ASSERTD(dif >= 1);
/* now high_dif = 0, dif >= 1, lastc is the neglected part of cp[cn+1] */
while (MPFR_UNLIKELY ((cn >= 0 || lastc != 0)
&& (high_dif == 0) && (dif == 1)))
{ /* dif=1 implies diff_exp = 0 or 1 */
bb = (bn >= 0) ? bp[bn] : 0;
cc = lastc;
if (cn >= 0)
{
if (diff_exp == 0)
{
cc += cp[cn];
}
else /* diff_exp = 1 */
{
cc += cp[cn] >> 1;
lastc = cp[cn] << (GMP_NUMB_BITS - 1);
}
}
else
lastc = 0;
high_dif = 1 - mpn_sub_n (&dif, &bb, &cc, 1);
bn--;
cn--;
res += GMP_NUMB_BITS;
}
/* (cn<0 and lastc=0) or (high_dif,dif)<>(0,1) */
if (MPFR_UNLIKELY (high_dif != 0)) /* high_dif == 1 */
{
res--;
MPFR_ASSERTD (res >= 0);
if (dif != 0)
{
*cancel = res;
return sign;
}
}
else /* high_dif == 0 */
{
unsigned int z;
count_leading_zeros(z, dif); /* dif > 1 here */
res += z;
if (MPFR_LIKELY(dif != (MPFR_LIMB_ONE << (GMP_NUMB_BITS - z - 1))))
{ /* dif is not a power of two */
*cancel = res;
return sign;
}
}
/* now result is res + (low(b) < low(c)) */
while (MPFR_UNLIKELY (bn >= 0 && (cn >= 0 || lastc != 0)))
{
if (diff_exp >= GMP_NUMB_BITS)
diff_exp -= GMP_NUMB_BITS;
else
{
cc = lastc;
if (cn >= 0)
{
cc += cp[cn] >> diff_exp;
if (diff_exp != 0)
lastc = cp[cn] << (GMP_NUMB_BITS - diff_exp);
}
else
lastc = 0;
cn--;
}
if (bp[bn] != cc)
{
*cancel = res + (bp[bn] < cc);
return sign;
}
bn--;
}
if (bn < 0)
{
if (lastc != 0)
res++;
else
{
while (cn >= 0 && cp[cn] == 0)
cn--;
if (cn >= 0)
res++;
}
}
*cancel = res;
return sign;
}
|
