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More changes. Still embryonic.
[u/mdw/catacomb] / mpx-kmul.c
1 /* -*-c-*-
2 *
3 * $Id: mpx-kmul.c,v 1.3 1999/12/13 15:35:01 mdw Exp $
4 *
5 * Karatsuba's multiplication algorithm
6 *
7 * (c) 1999 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: mpx-kmul.c,v $
33 * Revision 1.3 1999/12/13 15:35:01 mdw
34 * Simplify and improve.
35 *
36 * Revision 1.2 1999/12/11 10:58:02 mdw
37 * Remove tweakable comments.
38 *
39 * Revision 1.1 1999/12/10 23:23:51 mdw
40 * Karatsuba-Ofman multiplication algorithm.
41 *
42 */
43
44 /*----- Header files ------------------------------------------------------*/
45
46 #include <assert.h>
47 #include <stdio.h>
48
49 #include "mpx.h"
50
51 /*----- Tweakables --------------------------------------------------------*/
52
53 #ifdef TEST_RIG
54 # undef KARATSUBA_CUTOFF
55 # define KARATSUBA_CUTOFF 2
56 #endif
57
58 /*----- Addition macros ---------------------------------------------------*/
59
60 #define UADD(dv, av, avl) do { \
61 mpw *_dv = (dv); \
62 const mpw *_av = (av), *_avl = (avl); \
63 mpw _c = 0; \
64 \
65 while (_av < _avl) { \
66 mpw _a, _b; \
67 mpd _x; \
68 _a = *_av++; \
69 _b = *_dv; \
70 _x = (mpd)_a + (mpd)_b + _c; \
71 *_dv++ = MPW(_x); \
72 _c = _x >> MPW_BITS; \
73 } \
74 while (_c) { \
75 mpd _x = (mpd)*_dv + (mpd)_c; \
76 *_dv++ = MPW(_x); \
77 _c = _x >> MPW_BITS; \
78 } \
79 } while (0)
80
81 #define UADD2(dv, dvl, av, avl, bv, bvl) do { \
82 mpw *_dv = (dv), *_dvl = (dvl); \
83 const mpw *_av = (av), *_avl = (avl); \
84 const mpw *_bv = (bv), *_bvl = (bvl); \
85 mpw _c = 0; \
86 \
87 while (_av < _avl || _bv < _bvl) { \
88 mpw _a, _b; \
89 mpd _x; \
90 _a = (_av < _avl) ? *_av++ : 0; \
91 _b = (_bv < _bvl) ? *_bv++ : 0; \
92 _x = (mpd)_a + (mpd)_b + _c; \
93 *_dv++ = MPW(_x); \
94 _c = _x >> MPW_BITS; \
95 } \
96 *_dv++ = _c; \
97 while (_dv < _dvl) \
98 *_dv++ = 0; \
99 } while (0)
100
101 #define USUB(dv, av, avl) do { \
102 mpw *_dv = (dv); \
103 const mpw *_av = (av), *_avl = (avl); \
104 mpw _c = 0; \
105 \
106 while (_av < _avl) { \
107 mpw _a, _b; \
108 mpd _x; \
109 _a = *_av++; \
110 _b = *_dv; \
111 _x = (mpd)_b - (mpd)_a - _c; \
112 *_dv++ = MPW(_x); \
113 if (_x >> MPW_BITS) \
114 _c = 1; \
115 else \
116 _c = 0; \
117 } \
118 while (_c) { \
119 mpd _x = (mpd)*_dv - (mpd)_c; \
120 *_dv++ = MPW(_x); \
121 if (_x >> MPW_BITS) \
122 _c = 1; \
123 else \
124 _c = 0; \
125 } \
126 } while (0)
127
128 /*----- Main code ---------------------------------------------------------*/
129
130 /* --- @mpx_kmul@ --- *
131 *
132 * Arguments: @mpw *dv, *dvl@ = pointer to destination buffer
133 * @const mpw *av, *avl@ = pointer to first argument
134 * @const mpw *bv, *bvl@ = pointer to second argument
135 * @mpw *sv, *svl@ = pointer to scratch workspace
136 *
137 * Returns: ---
138 *
139 * Use: Multiplies two multiprecision integers using Karatsuba's
140 * algorithm. This is rather faster than traditional long
141 * multiplication (e.g., @mpx_umul@) on large numbers, although
142 * more expensive on small ones.
143 *
144 * The destination must be twice as large as the larger
145 * argument. The scratch space must be twice as large as the
146 * larger argument, plus the magic number @KARATSUBA_SLOP@.
147 */
148
149 void mpx_kmul(mpw *dv, mpw *dvl,
150 const mpw *av, const mpw *avl,
151 const mpw *bv, const mpw *bvl,
152 mpw *sv, mpw *svl)
153 {
154 const mpw *avm, *bvm;
155 size_t m;
156
157 /* --- Dispose of easy cases to @mpx_umul@ --- *
158 *
159 * Karatsuba is only a win on large numbers, because of all the
160 * recursiveness and bookkeeping. The recursive calls make a quick check
161 * to see whether to bottom out to @mpx_umul@ which should help quite a
162 * lot, but sometimes the only way to know is to make sure...
163 */
164
165 MPX_SHRINK(av, avl);
166 MPX_SHRINK(bv, bvl);
167
168 if (avl - av <= KARATSUBA_CUTOFF || bvl - bv <= KARATSUBA_CUTOFF) {
169 mpx_umul(dv, dvl, av, avl, bv, bvl);
170 return;
171 }
172
173 /* --- How the algorithm works --- *
174 *
175 * Let %$A = xb + y$% and %$B = ub + v$%. Then, simply by expanding, %$AB
176 * = x u b^2 + b(x v + y u) + y v$%. That's not helped any, because I've
177 * got four multiplications, each four times easier than the one I started
178 * with. However, note that I can rewrite the coefficient of %$b$% as
179 * %$xv + yu = (x + y)(u + v) - xu - yv$%. The terms %$xu$% and %$yv$%
180 * I've already calculated, and that leaves only one more multiplication to
181 * do. So now I have three multiplications, each four times easier, and
182 * that's a win.
183 */
184
185 /* --- First things --- *
186 *
187 * Sort out where to break the factors in half. I'll choose the midpoint
188 * of the largest one, since this minimizes the amount of work I have to do
189 * most effectively.
190 */
191
192 if (avl - av > bvl - bv) {
193 m = (avl - av + 1) >> 1;
194 avm = av + m;
195 if (bvl - bv > m)
196 bvm = bv + m;
197 else
198 bvm = bvl;
199 } else {
200 m = (bvl - bv + 1) >> 1;
201 bvm = bv + m;
202 if (avl - av > m)
203 avm = av + m;
204 else
205 avm = avl;
206 }
207
208 assert(((void)"Destination too small for Karatsuba multiply",
209 dvl - dv >= 4 * m));
210 assert(((void)"Not enough workspace for Karatsuba multiply",
211 svl - sv >= 4 * m));
212
213 /* --- Sort out the middle term --- */
214
215 {
216 mpw *bsv = sv + m + 1, *ssv = bsv + m + 1;
217 mpw *rdv = dv + m, *rdvl = rdv + 2 * (m + 2);
218
219 UADD2(sv, bsv, av, avm, avm, avl);
220 UADD2(bsv, ssv, bv, bvm, bvm, bvl);
221 if (m > KARATSUBA_CUTOFF)
222 mpx_kmul(rdv, rdvl, sv, bsv, bsv, ssv, ssv, svl);
223 else
224 mpx_umul(rdv, rdvl, sv, bsv, bsv, ssv);
225 }
226
227 /* --- Sort out the other two terms --- */
228
229 {
230 mpw *svm = sv + m, *svn = svm + m, *ssv = svn + 4;
231 mpw *tdv = dv + m;
232 mpw *rdv = tdv + m;
233
234 if (avl == avm || bvl == bvm)
235 MPX_ZERO(rdv + m + 1, dvl);
236 else {
237 if (m > KARATSUBA_CUTOFF)
238 mpx_kmul(sv, ssv, avm, avl, bvm, bvl, ssv, svl);
239 else
240 mpx_umul(sv, ssv, avm, avl, bvm, bvl);
241 MPX_COPY(rdv + m + 1, dvl, svm + 1, svn);
242 UADD(rdv, sv, svm + 1);
243 USUB(tdv, sv, svn);
244 }
245
246 if (m > KARATSUBA_CUTOFF)
247 mpx_kmul(sv, ssv, av, avm, bv, bvm, ssv, svl);
248 else
249 mpx_umul(sv, ssv, av, avm, bv, bvm);
250 MPX_COPY(dv, tdv, sv, svm);
251 USUB(tdv, sv, svn);
252 UADD(tdv, svm, svn);
253 }
254 }
255
256 /*----- Test rig ----------------------------------------------------------*/
257
258 #ifdef TEST_RIG
259
260 #include <mLib/alloc.h>
261 #include <mLib/testrig.h>
262
263 #include "mpscan.h"
264
265 #define ALLOC(v, vl, sz) do { \
266 size_t _sz = (sz); \
267 mpw *_vv = xmalloc(MPWS(_sz)); \
268 mpw *_vvl = _vv + _sz; \
269 (v) = _vv; \
270 (vl) = _vvl; \
271 } while (0)
272
273 #define LOAD(v, vl, d) do { \
274 const dstr *_d = (d); \
275 mpw *_v, *_vl; \
276 ALLOC(_v, _vl, MPW_RQ(_d->len)); \
277 mpx_loadb(_v, _vl, _d->buf, _d->len); \
278 (v) = _v; \
279 (vl) = _vl; \
280 } while (0)
281
282 #define MAX(x, y) ((x) > (y) ? (x) : (y))
283
284 static void dumpmp(const char *msg, const mpw *v, const mpw *vl)
285 {
286 fputs(msg, stderr);
287 MPX_SHRINK(v, vl);
288 while (v < vl)
289 fprintf(stderr, " %08lx", (unsigned long)*--vl);
290 fputc('\n', stderr);
291 }
292
293 static int umul(dstr *v)
294 {
295 mpw *a, *al;
296 mpw *b, *bl;
297 mpw *c, *cl;
298 mpw *d, *dl;
299 mpw *s, *sl;
300 size_t m;
301 int ok = 1;
302
303 LOAD(a, al, &v[0]);
304 LOAD(b, bl, &v[1]);
305 LOAD(c, cl, &v[2]);
306 m = MAX(al - a, bl - b) + 1;
307 ALLOC(d, dl, 2 * m);
308 ALLOC(s, sl, 2 * m + 32);
309
310 mpx_kmul(d, dl, a, al, b, bl, s, sl);
311 if (MPX_UCMP(d, dl, !=, c, cl)) {
312 fprintf(stderr, "\n*** umul failed\n");
313 dumpmp(" a", a, al);
314 dumpmp(" b", b, bl);
315 dumpmp("expected", c, cl);
316 dumpmp(" result", d, dl);
317 ok = 0;
318 }
319
320 free(a); free(b); free(c); free(d); free(s);
321 return (ok);
322 }
323
324 static test_chunk defs[] = {
325 { "umul", umul, { &type_hex, &type_hex, &type_hex, 0 } },
326 { 0, 0, { 0 } }
327 };
328
329 int main(int argc, char *argv[])
330 {
331 test_run(argc, argv, defs, SRCDIR"/tests/mpx");
332 return (0);
333 }
334
335 #endif
336
337 /*----- That's all, folks -------------------------------------------------*/
Catacomb cryptographic library (downstream of http://git.distorted.org.uk/~mdw/catacomb/)