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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: gfx-kmul.c,v 1.3 2004/03/27 17:54:11 mdw Exp $ |
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4 | * |
5 | * Karatsuba's multiplication algorithm on binary polynomials |
6 | * |
7 | * (c) 2000 Straylight/Edgeware |
8 | */ |
9 | |
10 | /*----- Licensing notice --------------------------------------------------* |
11 | * |
12 | * This file is part of Catacomb. |
13 | * |
14 | * Catacomb is free software; you can redistribute it and/or modify |
15 | * it under the terms of the GNU Library General Public License as |
16 | * published by the Free Software Foundation; either version 2 of the |
17 | * License, or (at your option) any later version. |
18 | * |
19 | * Catacomb is distributed in the hope that it will be useful, |
20 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
21 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
22 | * GNU Library General Public License for more details. |
23 | * |
24 | * You should have received a copy of the GNU Library General Public |
25 | * License along with Catacomb; if not, write to the Free |
26 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
27 | * MA 02111-1307, USA. |
28 | */ |
29 | |
30 | /*----- Revision history --------------------------------------------------* |
31 | * |
32 | * $Log: gfx-kmul.c,v $ |
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33 | * Revision 1.3 2004/03/27 17:54:11 mdw |
34 | * Standard curves and curve checking. |
35 | * |
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36 | * Revision 1.2 2002/10/09 00:36:03 mdw |
37 | * Fix bounds on workspace for Karatsuba operations. |
38 | * |
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39 | * Revision 1.1 2000/10/08 15:49:37 mdw |
40 | * First glimmerings of binary polynomial arithmetic. |
41 | * |
42 | */ |
43 | |
44 | /*----- Header files ------------------------------------------------------*/ |
45 | |
46 | #include <assert.h> |
47 | #include <stdio.h> |
48 | |
49 | #include "gfx.h" |
50 | #include "karatsuba.h" |
51 | |
52 | /*----- Tweakables --------------------------------------------------------*/ |
53 | |
54 | #ifdef TEST_RIG |
55 | # undef GFK_THRESH |
56 | # define GFK_THRESH 1 |
57 | #endif |
58 | |
59 | /*----- Main code ---------------------------------------------------------*/ |
60 | |
61 | /* --- @gfx_kmul@ --- * |
62 | * |
63 | * Arguments: @mpw *dv, *dvl@ = pointer to destination buffer |
64 | * @const mpw *av, *avl@ = pointer to first argument |
65 | * @const mpw *bv, *bvl@ = pointer to second argument |
66 | * @mpw *sv, *svl@ = pointer to scratch workspace |
67 | * |
68 | * Returns: --- |
69 | * |
70 | * Use: Multiplies two binary polynomials using Karatsuba's |
71 | * algorithm. This is rather faster than traditional long |
72 | * multiplication (e.g., @gfx_umul@) on polynomials with large |
73 | * degree, although more expensive on small ones. |
74 | * |
75 | * The destination must be twice as large as the larger |
76 | * argument. The scratch space must be twice as large as the |
77 | * larger argument. |
78 | */ |
79 | |
80 | void gfx_kmul(mpw *dv, mpw *dvl, |
81 | const mpw *av, const mpw *avl, |
82 | const mpw *bv, const mpw *bvl, |
83 | mpw *sv, mpw *svl) |
84 | { |
85 | const mpw *avm, *bvm; |
86 | size_t m; |
87 | |
88 | /* --- Dispose of easy cases to @mpx_umul@ --- * |
89 | * |
90 | * Karatsuba is only a win on large numbers, because of all the |
91 | * recursiveness and bookkeeping. The recursive calls make a quick check |
92 | * to see whether to bottom out to @gfx_umul@ which should help quite a |
93 | * lot, but sometimes the only way to know is to make sure... |
94 | */ |
95 | |
96 | MPX_SHRINK(av, avl); |
97 | MPX_SHRINK(bv, bvl); |
98 | |
99 | if (avl - av <= GFK_THRESH || bvl - bv <= GFK_THRESH) { |
100 | gfx_mul(dv, dvl, av, avl, bv, bvl); |
101 | return; |
102 | } |
103 | |
104 | /* --- How the algorithm works --- * |
105 | * |
106 | * Let %$A = xb + y$% and %$B = ub + v$%. Then, simply by expanding, |
107 | * %$AB = x u b^2 + b(x v + y u) + y v$%. That's not helped any, because |
108 | * I've got four multiplications, each four times easier than the one I |
109 | * started with. However, note that I can rewrite the coefficient of %$b$% |
110 | * as %$xv + yu = (x + y)(u + v) - xu - yv$%. The terms %$xu$% and %$yv$% |
111 | * I've already calculated, and that leaves only one more multiplication to |
112 | * do. So now I have three multiplications, each four times easier, and |
113 | * that's a win. |
114 | */ |
115 | |
116 | /* --- First things --- * |
117 | * |
118 | * Sort out where to break the factors in half. I'll choose the midpoint |
119 | * of the larger one, since this minimizes the amount of work I have to do |
120 | * most effectively. |
121 | */ |
122 | |
123 | if (avl - av > bvl - bv) { |
124 | m = (avl - av + 1) >> 1; |
125 | avm = av + m; |
126 | if (bvl - bv > m) |
127 | bvm = bv + m; |
128 | else |
129 | bvm = bvl; |
130 | } else { |
131 | m = (bvl - bv + 1) >> 1; |
132 | bvm = bv + m; |
133 | if (avl - av > m) |
134 | avm = av + m; |
135 | else |
136 | avm = avl; |
137 | } |
138 | |
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139 | /* --- Sort out the middle term --- */ |
140 | |
141 | { |
142 | mpw *bsv = sv + m, *ssv = bsv + m; |
143 | mpw *rdv = dv + m, *rdvl = rdv + 2 * m; |
144 | |
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145 | assert(rdvl <= dvl); |
146 | assert(ssv <= svl); |
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147 | UXOR2(sv, bsv, av, avm, avm, avl); |
148 | UXOR2(bsv, ssv, bv, bvm, bvm, bvl); |
149 | if (m > GFK_THRESH) |
150 | gfx_kmul(rdv, rdvl, sv, bsv, bsv, ssv, ssv, svl); |
151 | else |
152 | gfx_mul(rdv, rdvl, sv, bsv, bsv, ssv); |
153 | } |
154 | |
155 | /* --- Sort out the other two terms --- */ |
156 | |
157 | { |
158 | mpw *svm = sv + m, *ssv = svm + m; |
159 | mpw *tdv = dv + m; |
160 | mpw *rdv = tdv + m; |
161 | |
162 | if (avl == avm || bvl == bvm) |
163 | MPX_ZERO(rdv + m, dvl); |
164 | else { |
165 | if (m > GFK_THRESH) |
166 | gfx_kmul(sv, ssv, avm, avl, bvm, bvl, ssv, svl); |
167 | else |
168 | gfx_mul(sv, ssv, avm, avl, bvm, bvl); |
169 | MPX_COPY(rdv + m, dvl, svm, ssv); |
170 | UXOR(rdv, sv, svm); |
171 | UXOR(tdv, sv, ssv); |
172 | } |
173 | |
174 | if (m > GFK_THRESH) |
175 | gfx_kmul(sv, ssv, av, avm, bv, bvm, ssv, svl); |
176 | else |
177 | gfx_mul(sv, ssv, av, avm, bv, bvm); |
178 | MPX_COPY(dv, tdv, sv, svm); |
179 | UXOR(tdv, sv, ssv); |
180 | UXOR(tdv, svm, ssv); |
181 | } |
182 | } |
183 | |
184 | /*----- Test rig ----------------------------------------------------------*/ |
185 | |
186 | #ifdef TEST_RIG |
187 | |
188 | #include <mLib/alloc.h> |
189 | #include <mLib/testrig.h> |
190 | |
191 | #define ALLOC(v, vl, sz) do { \ |
192 | size_t _sz = (sz); \ |
193 | mpw *_vv = xmalloc(MPWS(_sz)); \ |
194 | mpw *_vvl = _vv + _sz; \ |
195 | (v) = _vv; \ |
196 | (vl) = _vvl; \ |
197 | } while (0) |
198 | |
199 | #define LOAD(v, vl, d) do { \ |
200 | const dstr *_d = (d); \ |
201 | mpw *_v, *_vl; \ |
202 | ALLOC(_v, _vl, MPW_RQ(_d->len)); \ |
203 | mpx_loadb(_v, _vl, _d->buf, _d->len); \ |
204 | (v) = _v; \ |
205 | (vl) = _vl; \ |
206 | } while (0) |
207 | |
208 | #define MAX(x, y) ((x) > (y) ? (x) : (y)) |
209 | |
210 | static void dumpmp(const char *msg, const mpw *v, const mpw *vl) |
211 | { |
212 | fputs(msg, stderr); |
213 | MPX_SHRINK(v, vl); |
214 | while (v < vl) |
215 | fprintf(stderr, " %08lx", (unsigned long)*--vl); |
216 | fputc('\n', stderr); |
217 | } |
218 | |
219 | static int mul(dstr *v) |
220 | { |
221 | mpw *a, *al; |
222 | mpw *b, *bl; |
223 | mpw *c, *cl; |
224 | mpw *d, *dl; |
225 | mpw *s, *sl; |
226 | size_t m; |
227 | int ok = 1; |
228 | |
229 | LOAD(a, al, &v[0]); |
230 | LOAD(b, bl, &v[1]); |
231 | LOAD(c, cl, &v[2]); |
232 | m = MAX(al - a, bl - b) + 1; |
233 | ALLOC(d, dl, 2 * m); |
234 | ALLOC(s, sl, 2 * m); |
235 | |
236 | gfx_kmul(d, dl, a, al, b, bl, s, sl); |
237 | if (!mpx_ueq(d, dl, c, cl)) { |
238 | fprintf(stderr, "\n*** mul failed\n"); |
239 | dumpmp(" a", a, al); |
240 | dumpmp(" b", b, bl); |
241 | dumpmp("expected", c, cl); |
242 | dumpmp(" result", d, dl); |
243 | ok = 0; |
244 | } |
245 | |
246 | free(a); free(b); free(c); free(d); free(s); |
247 | return (ok); |
248 | } |
249 | |
250 | static test_chunk defs[] = { |
251 | { "mul", mul, { &type_hex, &type_hex, &type_hex, 0 } }, |
252 | { 0, 0, { 0 } } |
253 | }; |
254 | |
255 | int main(int argc, char *argv[]) |
256 | { |
257 | test_run(argc, argv, defs, SRCDIR"/tests/gfx"); |
258 | return (0); |
259 | } |
260 | |
261 | #endif |
262 | |
263 | /*----- That's all, folks -------------------------------------------------*/ |