Coverage Report

Created: 2024-11-21 07:03

/src/libgmp/mpn/toom43_mul.c
Line
Count
Source
1
/* mpn_toom43_mul -- Multiply {ap,an} and {bp,bn} where an is nominally 4/3
2
   times as large as bn.  Or more accurately, bn < an < 2 bn.
3
4
   Contributed to the GNU project by Marco Bodrato.
5
6
   The idea of applying toom to unbalanced multiplication is due to Marco
7
   Bodrato and Alberto Zanoni.
8
9
   THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE.  IT IS ONLY
10
   SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES.  IN FACT, IT IS ALMOST
11
   GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
12
13
Copyright 2009, 2020 Free Software Foundation, Inc.
14
15
This file is part of the GNU MP Library.
16
17
The GNU MP Library is free software; you can redistribute it and/or modify
18
it under the terms of either:
19
20
  * the GNU Lesser General Public License as published by the Free
21
    Software Foundation; either version 3 of the License, or (at your
22
    option) any later version.
23
24
or
25
26
  * the GNU General Public License as published by the Free Software
27
    Foundation; either version 2 of the License, or (at your option) any
28
    later version.
29
30
or both in parallel, as here.
31
32
The GNU MP Library is distributed in the hope that it will be useful, but
33
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
34
or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
35
for more details.
36
37
You should have received copies of the GNU General Public License and the
38
GNU Lesser General Public License along with the GNU MP Library.  If not,
39
see https://www.gnu.org/licenses/.  */
40
41
42
#include "gmp-impl.h"
43
44
/* Evaluate in: -2, -1, 0, +1, +2, +inf
45
46
  <-s-><--n--><--n--><--n-->
47
   ___ ______ ______ ______
48
  |a3_|___a2_|___a1_|___a0_|
49
  |_b2_|___b1_|___b0_|
50
  <-t--><--n--><--n-->
51
52
  v0  =  a0             * b0          #   A(0)*B(0)
53
  v1  = (a0+ a1+ a2+ a3)*(b0+ b1+ b2) #   A(1)*B(1)      ah  <= 3  bh <= 2
54
  vm1 = (a0- a1+ a2- a3)*(b0- b1+ b2) #  A(-1)*B(-1)    |ah| <= 1 |bh|<= 1
55
  v2  = (a0+2a1+4a2+8a3)*(b0+2b1+4b2) #   A(2)*B(2)      ah  <= 14 bh <= 6
56
  vm2 = (a0-2a1+4a2-8a3)*(b0-2b1+4b2) #  A(-2)*B(-2)    |ah| <= 9 |bh|<= 4
57
  vinf=              a3 *         b2  # A(inf)*B(inf)
58
*/
59
60
void
61
mpn_toom43_mul (mp_ptr pp,
62
    mp_srcptr ap, mp_size_t an,
63
    mp_srcptr bp, mp_size_t bn, mp_ptr scratch)
64
104
{
65
104
  mp_size_t n, s, t;
66
104
  enum toom6_flags flags;
67
104
  mp_limb_t cy;
68
69
104
#define a0  ap
70
104
#define a1  (ap + n)
71
104
#define a2  (ap + 2 * n)
72
104
#define a3  (ap + 3 * n)
73
262
#define b0  bp
74
415
#define b1  (bp + n)
75
312
#define b2  (bp + 2 * n)
76
77
104
  n = 1 + (3 * an >= 4 * bn ? (an - 1) >> 2 : (bn - 1) / (size_t) 3);
78
79
104
  s = an - 3 * n;
80
104
  t = bn - 2 * n;
81
82
104
  ASSERT (0 < s && s <= n);
83
104
  ASSERT (0 < t && t <= n);
84
85
  /* This is true whenever an >= 25 or bn >= 19, I think. It
86
     guarantees that we can fit 5 values of size n+1 in the product
87
     area. */
88
104
  ASSERT (s+t >= 5);
89
90
104
#define v0    pp        /* 2n */
91
312
#define vm1   (scratch)        /* 2n+1 */
92
104
#define v1    (pp + 2*n)      /* 2n+1 */
93
208
#define vm2   (scratch + 2 * n + 1)    /* 2n+1 */
94
208
#define v2    (scratch + 4 * n + 2)    /* 2n+1 */
95
104
#define vinf  (pp + 5 * n)      /* s+t */
96
312
#define bs1    pp        /* n+1 */
97
1.60k
#define bsm1  (scratch + 2 * n + 2)    /* n+1 */
98
416
#define asm1  (scratch + 3 * n + 3)    /* n+1 */
99
208
#define asm2  (scratch + 4 * n + 4)    /* n+1 */
100
208
#define bsm2  (pp + n + 1)      /* n+1 */
101
208
#define bs2   (pp + 2 * n + 2)      /* n+1 */
102
208
#define as2   (pp + 3 * n + 3)      /* n+1 */
103
208
#define as1   (pp + 4 * n + 4)      /* n+1 */
104
105
  /* Total sccratch need is 6 * n + 3 + 1; we allocate one extra
106
     limb, because products will overwrite 2n+2 limbs. */
107
108
104
#define a0a2  scratch
109
574
#define b0b2  scratch
110
104
#define a1a3  asm1
111
520
#define b1d   bsm1
112
113
  /* Compute as2 and asm2.  */
114
104
  flags = (enum toom6_flags) (toom6_vm2_neg & mpn_toom_eval_dgr3_pm2 (as2, asm2, ap, n, s, a1a3));
115
116
  /* Compute bs2 and bsm2.  */
117
104
  b1d[n] = mpn_lshift (b1d, b1, n, 1);      /*       2b1      */
118
104
#if HAVE_NATIVE_mpn_addlsh2_n
119
104
  cy = mpn_addlsh2_n (b0b2, b0, b2, t);     /*  4b2      + b0 */
120
#else
121
  cy  = mpn_lshift (b0b2, b2, t, 2);      /*  4b2           */
122
  cy += mpn_add_n (b0b2, b0b2, b0, t);      /*  4b2      + b0 */
123
#endif
124
104
  if (t != n)
125
54
    cy = mpn_add_1 (b0b2 + t, b0 + t, n - t, cy);
126
104
  b0b2[n] = cy;
127
128
#if HAVE_NATIVE_mpn_add_n_sub_n
129
  if (mpn_cmp (b0b2, b1d, n+1) < 0)
130
    {
131
      mpn_add_n_sub_n (bs2, bsm2, b1d, b0b2, n+1);
132
      flags = (enum toom6_flags) (flags ^ toom6_vm2_neg);
133
    }
134
  else
135
    {
136
      mpn_add_n_sub_n (bs2, bsm2, b0b2, b1d, n+1);
137
    }
138
#else
139
104
  mpn_add_n (bs2, b0b2, b1d, n+1);
140
104
  if (mpn_cmp (b0b2, b1d, n+1) < 0)
141
84
    {
142
84
      mpn_sub_n (bsm2, b1d, b0b2, n+1);
143
84
      flags = (enum toom6_flags) (flags ^ toom6_vm2_neg);
144
84
    }
145
20
  else
146
20
    {
147
20
      mpn_sub_n (bsm2, b0b2, b1d, n+1);
148
20
    }
149
104
#endif
150
151
  /* Compute as1 and asm1.  */
152
104
  flags = (enum toom6_flags) (flags ^ (toom6_vm1_neg & mpn_toom_eval_dgr3_pm1 (as1, asm1, ap, n, s, a0a2)));
153
154
  /* Compute bs1 and bsm1.  */
155
104
  bsm1[n] = mpn_add (bsm1, b0, n, b2, t);
156
#if HAVE_NATIVE_mpn_add_n_sub_n
157
  if (bsm1[n] == 0 && mpn_cmp (bsm1, b1, n) < 0)
158
    {
159
      cy = mpn_add_n_sub_n (bs1, bsm1, b1, bsm1, n);
160
      bs1[n] = cy >> 1;
161
      flags = (enum toom6_flags) (flags ^ toom6_vm1_neg);
162
    }
163
  else
164
    {
165
      cy = mpn_add_n_sub_n (bs1, bsm1, bsm1, b1, n);
166
      bs1[n] = bsm1[n] + (cy >> 1);
167
      bsm1[n]-= cy & 1;
168
    }
169
#else
170
104
  bs1[n] = bsm1[n] + mpn_add_n (bs1, bsm1, b1, n);
171
104
  if (bsm1[n] == 0 && mpn_cmp (bsm1, b1, n) < 0)
172
54
    {
173
54
      mpn_sub_n (bsm1, b1, bsm1, n);
174
54
      flags = (enum toom6_flags) (flags ^ toom6_vm1_neg);
175
54
    }
176
50
  else
177
50
    {
178
50
      bsm1[n] -= mpn_sub_n (bsm1, bsm1, b1, n);
179
50
    }
180
104
#endif
181
182
104
  ASSERT (as1[n] <= 3);
183
104
  ASSERT (bs1[n] <= 2);
184
104
  ASSERT (asm1[n] <= 1);
185
104
  ASSERT (bsm1[n] <= 1);
186
104
  ASSERT (as2[n] <=14);
187
104
  ASSERT (bs2[n] <= 6);
188
104
  ASSERT (asm2[n] <= 9);
189
104
  ASSERT (bsm2[n] <= 4);
190
191
  /* vm1, 2n+1 limbs */
192
104
  vm1[2*n] = 0;
193
104
  mpn_mul_n (vm1, asm1, bsm1, n + (asm1[n] | bsm1[n]));  /* W4 */
194
195
  /* vm2, 2n+1 limbs */
196
104
  mpn_mul_n (vm2, asm2, bsm2, n+1);  /* W2 */
197
198
  /* v2, 2n+1 limbs */
199
104
  mpn_mul_n (v2, as2, bs2, n+1);  /* W1 */
200
201
  /* v1, 2n+1 limbs */
202
104
  mpn_mul_n (v1, as1, bs1, n+1);  /* W3 */
203
204
  /* vinf, s+t limbs */   /* W0 */
205
104
  if (s > t)  mpn_mul (vinf, a3, s, b2, t);
206
66
  else        mpn_mul (vinf, b2, t, a3, s);
207
208
  /* v0, 2n limbs */
209
104
  mpn_mul_n (v0, ap, bp, n);  /* W5 */
210
211
104
  mpn_toom_interpolate_6pts (pp, n, flags, vm1, vm2, v2, t + s);
212
213
104
#undef v0
214
104
#undef vm1
215
104
#undef v1
216
104
#undef vm2
217
104
#undef v2
218
104
#undef vinf
219
104
#undef bs1
220
104
#undef bs2
221
104
#undef bsm1
222
104
#undef bsm2
223
104
#undef asm1
224
104
#undef asm2
225
/* #undef as1 */
226
/* #undef as2 */
227
104
#undef a0a2
228
104
#undef b0b2
229
104
#undef a1a3
230
104
#undef b1d
231
104
#undef a0
232
104
#undef a1
233
104
#undef a2
234
104
#undef a3
235
104
#undef b0
236
104
#undef b1
237
104
#undef b2
238
104
}