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
|
/* mpn_toom_interpolate_8pts -- Interpolate for toom54, 63, 72.
Contributed to the GNU project by Marco Bodrato.
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 2009, 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 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/. */
#include "gmp.h"
#include "gmp-impl.h"
#define BINVERT_3 MODLIMB_INVERSE_3
#define BINVERT_15 \
((((GMP_NUMB_MAX >> (GMP_NUMB_BITS % 4)) / 15) * 14 * 16 & GMP_NUMB_MAX) + 15)
#define BINVERT_45 ((BINVERT_15 * BINVERT_3) & GMP_NUMB_MASK)
#ifndef mpn_divexact_by3
#if HAVE_NATIVE_mpn_pi1_bdiv_q_1
#define mpn_divexact_by3(dst,src,size) mpn_pi1_bdiv_q_1(dst,src,size,3,BINVERT_3,0)
#else
#define mpn_divexact_by3(dst,src,size) mpn_divexact_1(dst,src,size,3)
#endif
#endif
#ifndef mpn_divexact_by45
#if GMP_NUMB_BITS % 12 == 0
#define mpn_divexact_by45(dst,src,size) \
(63 & 19 * mpn_bdiv_dbm1 (dst, src, size, __GMP_CAST (mp_limb_t, GMP_NUMB_MASK / 45)))
#else
#if HAVE_NATIVE_mpn_pi1_bdiv_q_1
#define mpn_divexact_by45(dst,src,size) mpn_pi1_bdiv_q_1(dst,src,size,45,BINVERT_45,0)
#else
#define mpn_divexact_by45(dst,src,size) mpn_divexact_1(dst,src,size,45)
#endif
#endif
#endif
#if HAVE_NATIVE_mpn_sublsh2_n_ip1
#define DO_mpn_sublsh2_n(dst,src,n,ws) mpn_sublsh2_n_ip1(dst,src,n)
#else
#define DO_mpn_sublsh2_n(dst,src,n,ws) DO_mpn_sublsh_n(dst,src,n,2,ws)
#endif
#if HAVE_NATIVE_mpn_sublsh_n
#define DO_mpn_sublsh_n(dst,src,n,s,ws) mpn_sublsh_n (dst,dst,src,n,s)
#else
static mp_limb_t
DO_mpn_sublsh_n (mp_ptr dst, mp_srcptr src, mp_size_t n, unsigned int s, mp_ptr ws)
{
#if USE_MUL_1 && 0
return mpn_submul_1(dst,src,n,CNST_LIMB(1) <<(s));
#else
mp_limb_t __cy;
__cy = mpn_lshift (ws,src,n,s);
return __cy + mpn_sub_n (dst,dst,ws,n);
#endif
}
#endif
#if HAVE_NATIVE_mpn_subrsh
#define DO_mpn_subrsh(dst,nd,src,ns,s,ws) mpn_subrsh (dst,nd,src,ns,s)
#else
/* This is not a correct definition, it assumes no carry */
#define DO_mpn_subrsh(dst,nd,src,ns,s,ws) \
do { \
mp_limb_t __cy; \
MPN_DECR_U (dst, nd, src[0] >> s); \
__cy = DO_mpn_sublsh_n (dst, src + 1, ns - 1, GMP_NUMB_BITS - s, ws); \
MPN_DECR_U (dst + ns - 1, nd - ns + 1, __cy); \
} while (0)
#endif
/* Interpolation for Toom-4.5 (or Toom-4), using the evaluation
points: infinity(4.5 only), 4, -4, 2, -2, 1, -1, 0. More precisely,
we want to compute f(2^(GMP_NUMB_BITS * n)) for a polynomial f of
degree 7 (or 6), given the 8 (rsp. 7) values:
r1 = limit at infinity of f(x) / x^7,
r2 = f(4),
r3 = f(-4),
r4 = f(2),
r5 = f(-2),
r6 = f(1),
r7 = f(-1),
r8 = f(0).
All couples of the form f(n),f(-n) must be already mixed with
toom_couple_handling(f(n),...,f(-n),...)
The result is stored in {pp, spt + 7*n (or 6*n)}.
At entry, r8 is stored at {pp, 2n},
r5 is stored at {pp + 3n, 3n + 1}.
The other values are 2n+... limbs each (with most significant limbs small).
All intermediate results are positive.
Inputs are destroyed.
*/
void
mpn_toom_interpolate_8pts (mp_ptr pp, mp_size_t n,
mp_ptr r3, mp_ptr r7,
mp_size_t spt, mp_ptr ws)
{
mp_limb_signed_t cy;
mp_ptr r5, r1;
r5 = (pp + 3 * n); /* 3n+1 */
r1 = (pp + 7 * n); /* spt */
/******************************* interpolation *****************************/
DO_mpn_subrsh(r3+n, 2 * n + 1, pp, 2 * n, 4, ws);
cy = DO_mpn_sublsh_n (r3, r1, spt, 12, ws);
MPN_DECR_U (r3 + spt, 3 * n + 1 - spt, cy);
DO_mpn_subrsh(r5+n, 2 * n + 1, pp, 2 * n, 2, ws);
cy = DO_mpn_sublsh_n (r5, r1, spt, 6, ws);
MPN_DECR_U (r5 + spt, 3 * n + 1 - spt, cy);
r7[3*n] -= mpn_sub_n (r7+n, r7+n, pp, 2 * n);
cy = mpn_sub_n (r7, r7, r1, spt);
MPN_DECR_U (r7 + spt, 3 * n + 1 - spt, cy);
ASSERT_NOCARRY(mpn_sub_n (r3, r3, r5, 3 * n + 1));
ASSERT_NOCARRY(mpn_rshift(r3, r3, 3 * n + 1, 2));
ASSERT_NOCARRY(mpn_sub_n (r5, r5, r7, 3 * n + 1));
ASSERT_NOCARRY(mpn_sub_n (r3, r3, r5, 3 * n + 1));
mpn_divexact_by45 (r3, r3, 3 * n + 1);
ASSERT_NOCARRY(mpn_divexact_by3 (r5, r5, 3 * n + 1));
ASSERT_NOCARRY(DO_mpn_sublsh2_n (r5, r3, 3 * n + 1, ws));
/* last interpolation steps... */
/* ... are mixed with recomposition */
/***************************** recomposition *******************************/
/*
pp[] prior to operations:
|_H r1|_L r1|____||_H r5|_M_r5|_L r5|_____|_H r8|_L r8|pp
summation scheme for remaining operations:
|____8|n___7|n___6|n___5|n___4|n___3|n___2|n____|n____|pp
|_H r1|_L r1|____||_H*r5|_M r5|_L r5|_____|_H_r8|_L r8|pp
||_H r3|_M r3|_L*r3|
||_H_r7|_M_r7|_L_r7|
||-H r3|-M r3|-L*r3|
||-H*r5|-M_r5|-L_r5|
*/
cy = mpn_add_n (pp + n, pp + n, r7, n); /* Hr8+Lr7-Lr5 */
cy-= mpn_sub_n (pp + n, pp + n, r5, n);
if (0 > cy)
MPN_DECR_U (r7 + n, 2*n + 1, 1);
else
MPN_INCR_U (r7 + n, 2*n + 1, cy);
cy = mpn_sub_n (pp + 2*n, r7 + n, r5 + n, n); /* Mr7-Mr5 */
MPN_DECR_U (r7 + 2*n, n + 1, cy);
cy = mpn_add_n (pp + 3*n, r5, r7+ 2*n, n+1); /* Hr7+Lr5 */
r5[3*n]+= mpn_add_n (r5 + 2*n, r5 + 2*n, r3, n); /* Hr5+Lr3 */
cy-= mpn_sub_n (pp + 3*n, pp + 3*n, r5 + 2*n, n+1); /* Hr7-Hr5+Lr5-Lr3 */
if (UNLIKELY(0 > cy))
MPN_DECR_U (r5 + n + 1, 2*n, 1);
else
MPN_INCR_U (r5 + n + 1, 2*n, cy);
ASSERT_NOCARRY(mpn_sub_n(pp + 4*n, r5 + n, r3 + n, 2*n +1)); /* Mr5-Mr3,Hr5-Hr3 */
cy = mpn_add_1 (pp + 6*n, r3 + n, n, pp[6*n]);
MPN_INCR_U (r3 + 2*n, n + 1, cy);
cy = mpn_add_n (pp + 7*n, pp + 7*n, r3 + 2*n, n);
if (LIKELY(spt != n))
MPN_INCR_U (pp + 8*n, spt - n, cy + r3[3*n]);
else
ASSERT (r3[3*n] | cy == 0);
}
|
