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
|
/* mpz_congruent_p -- test congruence of two mpz's.
Copyright 2001, 2002, 2005 Free Software Foundation, Inc.
This file is part of the GNU MP Library.
The GNU MP Library is free software; you can redistribute it and/or modify
it under the terms of either:
* 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.
or
* the GNU General Public License as published by the Free Software
Foundation; either version 2 of the License, or (at your option) any
later version.
or both in parallel, as here.
The GNU MP 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 General Public License
for more details.
You should have received copies of the GNU General Public License and the
GNU Lesser General Public License along with the GNU MP Library. If not,
see https://www.gnu.org/licenses/. */
#include "gmp-impl.h"
#include "longlong.h"
/* For big divisors this code is only very slightly better than the user
doing a combination of mpz_sub and mpz_tdiv_r, but it's quite convenient,
and perhaps in the future can be improved, in similar ways to
mpn_divisible_p perhaps.
The csize==1 / dsize==1 special case makes mpz_congruent_p as good as
mpz_congruent_ui_p on relevant operands, though such a combination
probably doesn't occur often.
Alternatives:
If c<d then it'd work to just form a%d and compare a and c (either as
a==c or a+c==d depending on the signs), but the saving from avoiding the
abs(a-c) calculation would be small compared to the division.
Similarly if both a<d and c<d then it would work to just compare a and c
(a==c or a+c==d), but this isn't considered a particularly important case
and so isn't done for the moment.
Low zero limbs on d could be stripped and the corresponding limbs of a
and c tested and skipped, but doing so would introduce a borrow when a
and c differ in sign and have non-zero skipped limbs. It doesn't seem
worth the complications to do this, since low zero limbs on d should
occur only rarely. */
int
mpz_congruent_p (mpz_srcptr a, mpz_srcptr c, mpz_srcptr d)
{
mp_size_t asize, csize, dsize, sign;
mp_srcptr ap, cp, dp;
mp_ptr xp;
mp_limb_t alow, clow, dlow, dmask, r;
int result;
TMP_DECL;
dsize = SIZ(d);
if (UNLIKELY (dsize == 0))
return (mpz_cmp (a, c) == 0);
dsize = ABS(dsize);
dp = PTR(d);
if (ABSIZ(a) < ABSIZ(c))
MPZ_SRCPTR_SWAP (a, c);
asize = SIZ(a);
csize = SIZ(c);
sign = (asize ^ csize);
asize = ABS(asize);
ap = PTR(a);
if (csize == 0)
return mpn_divisible_p (ap, asize, dp, dsize);
csize = ABS(csize);
cp = PTR(c);
alow = ap[0];
clow = cp[0];
dlow = dp[0];
/* Check a==c mod low zero bits of dlow. This might catch a few cases of
a!=c quickly, and it helps the csize==1 special cases below. */
dmask = LOW_ZEROS_MASK (dlow) & GMP_NUMB_MASK;
alow = (sign >= 0 ? alow : -alow);
if (((alow-clow) & dmask) != 0)
return 0;
if (csize == 1)
{
if (dsize == 1)
{
cong_1:
if (sign < 0)
NEG_MOD (clow, clow, dlow);
if (ABOVE_THRESHOLD (asize, BMOD_1_TO_MOD_1_THRESHOLD))
{
r = mpn_mod_1 (ap, asize, dlow);
if (clow < dlow)
return r == clow;
else
return r == (clow % dlow);
}
if ((dlow & 1) == 0)
{
/* Strip low zero bits to get odd d required by modexact. If
d==e*2^n then a==c mod d if and only if both a==c mod e and
a==c mod 2^n, the latter having been done above. */
unsigned twos;
count_trailing_zeros (twos, dlow);
dlow >>= twos;
}
r = mpn_modexact_1c_odd (ap, asize, dlow, clow);
return r == 0 || r == dlow;
}
/* dlow==0 is avoided since we don't want to bother handling extra low
zero bits if dsecond is even (would involve borrow if a,c differ in
sign and alow,clow!=0). */
if (dsize == 2 && dlow != 0)
{
mp_limb_t dsecond = dp[1];
if (dsecond <= dmask)
{
unsigned twos;
count_trailing_zeros (twos, dlow);
dlow = (dlow >> twos) | (dsecond << (GMP_NUMB_BITS-twos));
ASSERT_LIMB (dlow);
/* dlow will be odd here, so the test for it even under cong_1
is unnecessary, but the rest of that code is wanted. */
goto cong_1;
}
}
}
TMP_MARK;
xp = TMP_ALLOC_LIMBS (asize+1);
/* calculate abs(a-c) */
if (sign >= 0)
{
/* same signs, subtract */
if (asize > csize || mpn_cmp (ap, cp, asize) >= 0)
ASSERT_NOCARRY (mpn_sub (xp, ap, asize, cp, csize));
else
ASSERT_NOCARRY (mpn_sub_n (xp, cp, ap, asize));
MPN_NORMALIZE (xp, asize);
}
else
{
/* different signs, add */
mp_limb_t carry;
carry = mpn_add (xp, ap, asize, cp, csize);
xp[asize] = carry;
asize += (carry != 0);
}
result = mpn_divisible_p (xp, asize, dp, dsize);
TMP_FREE;
return result;
}
|
