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
|
/* hgcd_reduce.c.
THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES. IT IS ONLY
SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
GUARANTEED THAT THEY'LL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
Copyright 2011, 2012 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"
/* Computes R -= A * B. Result must be non-negative. Normalized down
to size an, and resulting size is returned. */
static mp_size_t
submul (mp_ptr rp, mp_size_t rn,
mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
{
mp_ptr tp;
TMP_DECL;
ASSERT (bn > 0);
ASSERT (an >= bn);
ASSERT (rn >= an);
ASSERT (an + bn <= rn + 1);
TMP_MARK;
tp = TMP_ALLOC_LIMBS (an + bn);
mpn_mul (tp, ap, an, bp, bn);
ASSERT ((an + bn <= rn) || (tp[rn] == 0));
ASSERT_NOCARRY (mpn_sub (rp, rp, rn, tp, an + bn - (an + bn > rn)));
TMP_FREE;
while (rn > an && (rp[rn-1] == 0))
rn--;
return rn;
}
/* Computes (a, b) <-- M^{-1} (a; b) */
/* FIXME:
x Take scratch parameter, and figure out scratch need.
x Use some fallback for small M->n?
*/
static mp_size_t
hgcd_matrix_apply (const struct hgcd_matrix *M,
mp_ptr ap, mp_ptr bp,
mp_size_t n)
{
mp_size_t an, bn, un, vn, nn;
mp_size_t mn[2][2];
mp_size_t modn;
mp_ptr tp, sp, scratch;
mp_limb_t cy;
unsigned i, j;
TMP_DECL;
ASSERT ( (ap[n-1] | bp[n-1]) > 0);
an = n;
MPN_NORMALIZE (ap, an);
bn = n;
MPN_NORMALIZE (bp, bn);
for (i = 0; i < 2; i++)
for (j = 0; j < 2; j++)
{
mp_size_t k;
k = M->n;
MPN_NORMALIZE (M->p[i][j], k);
mn[i][j] = k;
}
ASSERT (mn[0][0] > 0);
ASSERT (mn[1][1] > 0);
ASSERT ( (mn[0][1] | mn[1][0]) > 0);
TMP_MARK;
if (mn[0][1] == 0)
{
/* A unchanged, M = (1, 0; q, 1) */
ASSERT (mn[0][0] == 1);
ASSERT (M->p[0][0][0] == 1);
ASSERT (mn[1][1] == 1);
ASSERT (M->p[1][1][0] == 1);
/* Put B <-- B - q A */
nn = submul (bp, bn, ap, an, M->p[1][0], mn[1][0]);
}
else if (mn[1][0] == 0)
{
/* B unchanged, M = (1, q; 0, 1) */
ASSERT (mn[0][0] == 1);
ASSERT (M->p[0][0][0] == 1);
ASSERT (mn[1][1] == 1);
ASSERT (M->p[1][1][0] == 1);
/* Put A <-- A - q * B */
nn = submul (ap, an, bp, bn, M->p[0][1], mn[0][1]);
}
else
{
/* A = m00 a + m01 b ==> a <= A / m00, b <= A / m01.
B = m10 a + m11 b ==> a <= B / m10, b <= B / m11. */
un = MIN (an - mn[0][0], bn - mn[1][0]) + 1;
vn = MIN (an - mn[0][1], bn - mn[1][1]) + 1;
nn = MAX (un, vn);
/* In the range of interest, mulmod_bnm1 should always beat mullo. */
modn = mpn_mulmod_bnm1_next_size (nn + 1);
TMP_ALLOC_LIMBS_3 (tp, modn,
sp, modn,
scratch, mpn_mulmod_bnm1_itch (modn, modn, M->n));
ASSERT (n <= 2*modn);
if (n > modn)
{
cy = mpn_add (ap, ap, modn, ap + modn, n - modn);
MPN_INCR_U (ap, modn, cy);
cy = mpn_add (bp, bp, modn, bp + modn, n - modn);
MPN_INCR_U (bp, modn, cy);
n = modn;
}
mpn_mulmod_bnm1 (tp, modn, ap, n, M->p[1][1], mn[1][1], scratch);
mpn_mulmod_bnm1 (sp, modn, bp, n, M->p[0][1], mn[0][1], scratch);
/* FIXME: Handle the small n case in some better way. */
if (n + mn[1][1] < modn)
MPN_ZERO (tp + n + mn[1][1], modn - n - mn[1][1]);
if (n + mn[0][1] < modn)
MPN_ZERO (sp + n + mn[0][1], modn - n - mn[0][1]);
cy = mpn_sub_n (tp, tp, sp, modn);
MPN_DECR_U (tp, modn, cy);
ASSERT (mpn_zero_p (tp + nn, modn - nn));
mpn_mulmod_bnm1 (sp, modn, ap, n, M->p[1][0], mn[1][0], scratch);
MPN_COPY (ap, tp, nn);
mpn_mulmod_bnm1 (tp, modn, bp, n, M->p[0][0], mn[0][0], scratch);
if (n + mn[1][0] < modn)
MPN_ZERO (sp + n + mn[1][0], modn - n - mn[1][0]);
if (n + mn[0][0] < modn)
MPN_ZERO (tp + n + mn[0][0], modn - n - mn[0][0]);
cy = mpn_sub_n (tp, tp, sp, modn);
MPN_DECR_U (tp, modn, cy);
ASSERT (mpn_zero_p (tp + nn, modn - nn));
MPN_COPY (bp, tp, nn);
while ( (ap[nn-1] | bp[nn-1]) == 0)
{
nn--;
ASSERT (nn > 0);
}
}
TMP_FREE;
return nn;
}
mp_size_t
mpn_hgcd_reduce_itch (mp_size_t n, mp_size_t p)
{
mp_size_t itch;
if (BELOW_THRESHOLD (n, HGCD_REDUCE_THRESHOLD))
{
itch = mpn_hgcd_itch (n-p);
/* For arbitrary p, the storage for _adjust is 2*(p + M->n) = 2 *
(p + ceil((n-p)/2) - 1 <= n + p - 1 */
if (itch < n + p - 1)
itch = n + p - 1;
}
else
{
itch = 2*(n-p) + mpn_hgcd_itch (n-p);
/* Currently, hgcd_matrix_apply allocates its own storage. */
}
return itch;
}
/* FIXME: Document storage need. */
mp_size_t
mpn_hgcd_reduce (struct hgcd_matrix *M,
mp_ptr ap, mp_ptr bp, mp_size_t n, mp_size_t p,
mp_ptr tp)
{
mp_size_t nn;
if (BELOW_THRESHOLD (n, HGCD_REDUCE_THRESHOLD))
{
nn = mpn_hgcd (ap + p, bp + p, n - p, M, tp);
if (nn > 0)
/* Needs 2*(p + M->n) <= 2*(floor(n/2) + ceil(n/2) - 1)
= 2 (n - 1) */
return mpn_hgcd_matrix_adjust (M, p + nn, ap, bp, p, tp);
}
else
{
MPN_COPY (tp, ap + p, n - p);
MPN_COPY (tp + n - p, bp + p, n - p);
if (mpn_hgcd_appr (tp, tp + n - p, n - p, M, tp + 2*(n-p)))
return hgcd_matrix_apply (M, ap, bp, n);
}
return 0;
}
|
