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
|
/* mpn_toom3_sqr -- Square {ap,an}.
Contributed to the GNU project by Torbjorn Granlund.
THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE. IT IS ONLY
SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
Copyright 2006, 2007, 2008 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 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 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 Lesser General Public
License for more details.
You should have received a copy of the GNU Lesser General Public License
along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */
/*
Things to work on:
1. Trim allocation. The allocations for as1 and asm1 could be
avoided by instead reusing the pp area and the scratch area.
2. Use new toom functions for the recursive calls.
*/
#include "gmp.h"
#include "gmp-impl.h"
/* Evaluate in: -1, 0, +1, +2, +inf
<-s-><--n--><--n--><--n-->
___ ______ ______ ______
|a3_|___a2_|___a1_|___a0_|
|_b1_|___b0_|
<-t--><--n-->
v0 = a0 * b0 # A(0)*B(0)
v1 = (a0+ a1+ a2)*(b0+ b1+ b2) # A(1)*B(1) ah <= 2 bh <= 2
vm1 = (a0- a1+ a2)*(b0- b1+ b2) # A(-1)*B(-1) |ah| <= 1 bh <= 1
v2 = (a0+2a1+4a2)*(b0+2b1+4b2) # A(2)*B(2) ah <= 6 bh <= 6
vinf= a2 * b2 # A(inf)*B(inf)
*/
#if TUNE_PROGRAM_BUILD
#define MAYBE_sqr_basecase 1
#define MAYBE_sqr_toom3 1
#else
#define MAYBE_sqr_basecase \
(SQR_TOOM3_THRESHOLD < 3 * SQR_KARATSUBA_THRESHOLD)
#define MAYBE_sqr_toom3 \
(SQR_TOOM4_THRESHOLD >= 3 * SQR_TOOM3_THRESHOLD)
#endif
#define TOOM3_SQR_N_REC(p, a, n, ws) \
do { \
if (MAYBE_sqr_basecase \
&& BELOW_THRESHOLD (n, SQR_KARATSUBA_THRESHOLD)) \
mpn_sqr_basecase (p, a, n); \
else if (! MAYBE_sqr_toom3 \
|| BELOW_THRESHOLD (n, SQR_TOOM3_THRESHOLD)) \
mpn_kara_sqr_n (p, a, n, ws); \
else \
mpn_toom3_sqr_n (p, a, n, ws); \
} while (0)
void
mpn_toom3_sqr (mp_ptr pp,
mp_srcptr ap, mp_size_t an,
mp_ptr scratch)
{
mp_size_t n, s;
mp_limb_t cy, vinf0;
mp_ptr gp;
mp_ptr as1, asm1, as2;
TMP_DECL;
#define a0 ap
#define a1 (ap + n)
#define a2 (ap + 2*n)
n = (an + 2) / (size_t) 3;
s = an - 2 * n;
ASSERT (0 < s && s <= n);
TMP_MARK;
as1 = TMP_SALLOC_LIMBS (n + 1);
asm1 = TMP_SALLOC_LIMBS (n + 1);
as2 = TMP_SALLOC_LIMBS (n + 1);
gp = pp;
/* Compute as1 and asm1. */
cy = mpn_add (gp, a0, n, a2, s);
#if HAVE_NATIVE_mpn_addsub_n
if (cy == 0 && mpn_cmp (gp, a1, n) < 0)
{
cy = mpn_addsub_n (as1, asm1, a1, gp, n);
as1[n] = 0;
asm1[n] = 0;
}
else
{
cy2 = mpn_addsub_n (as1, asm1, gp, a1, n);
as1[n] = cy + (cy2 >> 1);
asm1[n] = cy - (cy & 1);
}
#else
as1[n] = cy + mpn_add_n (as1, gp, a1, n);
if (cy == 0 && mpn_cmp (gp, a1, n) < 0)
{
mpn_sub_n (asm1, a1, gp, n);
asm1[n] = 0;
}
else
{
cy -= mpn_sub_n (asm1, gp, a1, n);
asm1[n] = cy;
}
#endif
/* Compute as2. */
#if HAVE_NATIVE_mpn_addlsh1_n
cy = mpn_addlsh1_n (as2, a1, a2, s);
if (s != n)
cy = mpn_add_1 (as2 + s, a1 + s, n - s, cy);
cy = 2 * cy + mpn_addlsh1_n (as2, a0, as2, n);
#else
cy = mpn_lshift (as2, a2, s, 1);
cy += mpn_add_n (as2, a1, as2, s);
if (s != n)
cy = mpn_add_1 (as2 + s, a1 + s, n - s, cy);
cy = 2 * cy + mpn_lshift (as2, as2, n, 1);
cy += mpn_add_n (as2, a0, as2, n);
#endif
as2[n] = cy;
ASSERT (as1[n] <= 2);
ASSERT (asm1[n] <= 1);
#define v0 pp /* 2n */
#define v1 (pp + 2 * n) /* 2n+1 */
#define vinf (pp + 4 * n) /* s+s */
#define vm1 scratch /* 2n+1 */
#define v2 (scratch + 2 * n + 1) /* 2n+2 */
#define scratch_out (scratch + 4 * n + 4)
/* vm1, 2n+1 limbs */
#ifdef SMALLER_RECURSION
TOOM3_SQR_N_REC (vm1, asm1, n, scratch_out);
cy = 0;
if (asm1[n] != 0)
cy = asm1[n] + mpn_add_n (vm1 + n, vm1 + n, asm1, n);
if (asm1[n] != 0)
cy += mpn_add_n (vm1 + n, vm1 + n, asm1, n);
vm1[2 * n] = cy;
#else
TOOM3_SQR_N_REC (vm1, asm1, n + 1, scratch_out);
#endif
TOOM3_SQR_N_REC (v2, as2, n + 1, scratch_out); /* v2, 2n+1 limbs */
TOOM3_SQR_N_REC (vinf, a2, s, scratch_out); /* vinf, s+s limbs */
vinf0 = vinf[0]; /* v1 overlaps with this */
#ifdef SMALLER_RECURSION
/* v1, 2n+1 limbs */
TOOM3_SQR_N_REC (v1, as1, n, scratch_out);
if (as1[n] == 1)
{
cy = as1[n] + mpn_add_n (v1 + n, v1 + n, as1, n);
}
else if (as1[n] != 0)
{
#if HAVE_NATIVE_mpn_addlsh1_n
cy = 2 * as1[n] + mpn_addlsh1_n (v1 + n, v1 + n, as1, n);
#else
cy = 2 * as1[n] + mpn_addmul_1 (v1 + n, as1, n, CNST_LIMB(2));
#endif
}
else
cy = 0;
if (as1[n] == 1)
{
cy += mpn_add_n (v1 + n, v1 + n, as1, n);
}
else if (as1[n] != 0)
{
#if HAVE_NATIVE_mpn_addlsh1_n
cy += mpn_addlsh1_n (v1 + n, v1 + n, as1, n);
#else
cy += mpn_addmul_1 (v1 + n, as1, n, CNST_LIMB(2));
#endif
}
v1[2 * n] = cy;
#else
cy = vinf[1];
TOOM3_SQR_N_REC (v1, as1, n + 1, scratch_out);
vinf[1] = cy;
#endif
TOOM3_SQR_N_REC (v0, ap, n, scratch_out); /* v0, 2n limbs */
mpn_toom_interpolate_5pts (pp, v2, vm1, n, s + s, 1, vinf0, scratch_out);
TMP_FREE;
}
|
