1 /* mpn_toom52_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 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--><--n-->
47 ___ ______ ______ ______ ______
48 |a4_|___a3_|___a2_|___a1_|___a0_|
49 |b1|___b0_|
50 <t-><--n-->
51
52 v0 = a0 * b0 # A(0)*B(0)
53 v1 = (a0+ a1+ a2+ a3+ a4)*(b0+ b1) # A(1)*B(1) ah <= 4 bh <= 1
54 vm1 = (a0- a1+ a2- a3+ a4)*(b0- b1) # A(-1)*B(-1) |ah| <= 2 bh = 0
55 v2 = (a0+2a1+4a2+8a3+16a4)*(b0+2b1) # A(2)*B(2) ah <= 30 bh <= 2
56 vm2 = (a0-2a1+4a2-8a3+16a4)*(b0-2b1) # A(-2)*B(-2) |ah| <= 20 |bh|<= 1
57 vinf= a4 * b1 # A(inf)*B(inf)
58
59 Some slight optimization in evaluation are taken from the paper:
60 "Towards Optimal Toom-Cook Multiplication for Univariate and
61 Multivariate Polynomials in Characteristic 2 and 0."
62 */
63
64 void
65 mpn_toom52_mul (mp_ptr pp,
66 mp_srcptr ap, mp_size_t an,
67 mp_srcptr bp, mp_size_t bn, mp_ptr scratch)
68 {
69 mp_size_t n, s, t;
70 enum toom6_flags flags;
71
72 #define a0 ap
73 #define a1 (ap + n)
74 #define a2 (ap + 2 * n)
75 #define a3 (ap + 3 * n)
76 #define a4 (ap + 4 * n)
77 #define b0 bp
78 #define b1 (bp + n)
79
80 n = 1 + (2 * an >= 5 * bn ? (an - 1) / (size_t) 5 : (bn - 1) >> 1);
81
82 s = an - 4 * n;
83 t = bn - n;
84
85 ASSERT (0 < s && s <= n);
86 ASSERT (0 < t && t <= n);
87
88 /* Ensures that 5 values of n+1 limbs each fits in the product area.
89 Borderline cases are an = 32, bn = 8, n = 7, and an = 36, bn = 9,
90 n = 8. */
91 ASSERT (s+t >= 5);
92
93 #define v0 pp /* 2n */
94 #define vm1 (scratch) /* 2n+1 */
95 #define v1 (pp + 2 * n) /* 2n+1 */
96 #define vm2 (scratch + 2 * n + 1) /* 2n+1 */
97 #define v2 (scratch + 4 * n + 2) /* 2n+1 */
98 #define vinf (pp + 5 * n) /* s+t */
99 #define bs1 pp /* n+1 */
100 #define bsm1 (scratch + 2 * n + 2) /* n */
101 #define asm1 (scratch + 3 * n + 3) /* n+1 */
102 #define asm2 (scratch + 4 * n + 4) /* n+1 */
103 #define bsm2 (pp + n + 1) /* n+1 */
104 #define bs2 (pp + 2 * n + 2) /* n+1 */
105 #define as2 (pp + 3 * n + 3) /* n+1 */
106 #define as1 (pp + 4 * n + 4) /* n+1 */
107
108 /* Scratch need is 6 * n + 3 + 1. We need one extra limb, because
109 products will overwrite 2n+2 limbs. */
110
111 #define a0a2 scratch
112 #define a1a3 asm1
113
114 /* Compute as2 and asm2. */
115 flags = (enum toom6_flags) (toom6_vm2_neg & mpn_toom_eval_pm2 (as2, asm2, 4, ap, n, s, a1a3));
116
117 /* Compute bs1 and bsm1. */
118 if (t == n)
119 {
120 #if HAVE_NATIVE_mpn_add_n_sub_n
121 mp_limb_t cy;
122
123 if (mpn_cmp (b0, b1, n) < 0)
124 {
125 cy = mpn_add_n_sub_n (bs1, bsm1, b1, b0, n);
126 flags = (enum toom6_flags) (flags ^ toom6_vm1_neg);
127 }
128 else
129 {
130 cy = mpn_add_n_sub_n (bs1, bsm1, b0, b1, n);
131 }
132 bs1[n] = cy >> 1;
133 #else
134 bs1[n] = mpn_add_n (bs1, b0, b1, n);
135 if (mpn_cmp (b0, b1, n) < 0)
136 {
137 mpn_sub_n (bsm1, b1, b0, n);
138 flags = (enum toom6_flags) (flags ^ toom6_vm1_neg);
139 }
140 else
141 {
142 mpn_sub_n (bsm1, b0, b1, n);
143 }
144 #endif
145 }
146 else
147 {
148 bs1[n] = mpn_add (bs1, b0, n, b1, t);
149 if (mpn_zero_p (b0 + t, n - t) && mpn_cmp (b0, b1, t) < 0)
150 {
151 mpn_sub_n (bsm1, b1, b0, t);
152 MPN_ZERO (bsm1 + t, n - t);
153 flags = (enum toom6_flags) (flags ^ toom6_vm1_neg);
154 }
155 else
156 {
157 mpn_sub (bsm1, b0, n, b1, t);
158 }
159 }
160
161 /* Compute bs2 and bsm2, recycling bs1 and bsm1. bs2=bs1+b1; bsm2=bsm1-b1 */
162 mpn_add (bs2, bs1, n+1, b1, t);
163 if (flags & toom6_vm1_neg)
164 {
165 bsm2[n] = mpn_add (bsm2, bsm1, n, b1, t);
166 flags = (enum toom6_flags) (flags ^ toom6_vm2_neg);
167 }
168 else
169 {
170 bsm2[n] = 0;
171 if (t == n)
172 {
173 if (mpn_cmp (bsm1, b1, n) < 0)
174 {
175 mpn_sub_n (bsm2, b1, bsm1, n);
176 flags = (enum toom6_flags) (flags ^ toom6_vm2_neg);
177 }
178 else
179 {
180 mpn_sub_n (bsm2, bsm1, b1, n);
181 }
182 }
183 else
184 {
185 if (mpn_zero_p (bsm1 + t, n - t) && mpn_cmp (bsm1, b1, t) < 0)
186 {
187 mpn_sub_n (bsm2, b1, bsm1, t);
188 MPN_ZERO (bsm2 + t, n - t);
189 flags = (enum toom6_flags) (flags ^ toom6_vm2_neg);
190 }
191 else
192 {
193 mpn_sub (bsm2, bsm1, n, b1, t);
194 }
195 }
196 }
197
198 /* Compute as1 and asm1. */
199 flags = (enum toom6_flags) (flags ^ (toom6_vm1_neg & mpn_toom_eval_pm1 (as1, asm1, 4, ap, n, s, a0a2)));
200
201 ASSERT (as1[n] <= 4);
202 ASSERT (bs1[n] <= 1);
203 ASSERT (asm1[n] <= 2);
204 /* ASSERT (bsm1[n] <= 1); */
205 ASSERT (as2[n] <=30);
206 ASSERT (bs2[n] <= 2);
207 ASSERT (asm2[n] <= 20);
208 ASSERT (bsm2[n] <= 1);
209
210 /* vm1, 2n+1 limbs */
211 mpn_mul (vm1, asm1, n+1, bsm1, n); /* W4 */
212
213 /* vm2, 2n+1 limbs */
214 mpn_mul_n (vm2, asm2, bsm2, n+1); /* W2 */
215
216 /* v2, 2n+1 limbs */
217 mpn_mul_n (v2, as2, bs2, n+1); /* W1 */
218
219 /* v1, 2n+1 limbs */
220 mpn_mul_n (v1, as1, bs1, n+1); /* W3 */
221
222 /* vinf, s+t limbs */ /* W0 */
223 if (s > t) mpn_mul (vinf, a4, s, b1, t);
224 else mpn_mul (vinf, b1, t, a4, s);
225
226 /* v0, 2n limbs */
227 mpn_mul_n (v0, ap, bp, n); /* W5 */
228
229 mpn_toom_interpolate_6pts (pp, n, flags, vm1, vm2, v2, t + s);
230
231 #undef v0
232 #undef vm1
233 #undef v1
234 #undef vm2
235 #undef v2
236 #undef vinf
237 #undef bs1
238 #undef bs2
239 #undef bsm1
240 #undef bsm2
241 #undef asm1
242 #undef asm2
243 #undef as1
244 #undef as2
245 #undef a0a2
246 #undef b0b2
247 #undef a1a3
248 #undef a0
249 #undef a1
250 #undef a2
251 #undef a3
252 #undef b0
253 #undef b1
254 #undef b2
255
256 }