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ae747c9b | 1 | /* -*-c-*- |
2 | * | |
12ed8a1f | 3 | * $Id$ |
ae747c9b | 4 | * |
5 | * Low-level arithmetic on binary polynomials | |
6 | * | |
7 | * (c) 2000 Straylight/Edgeware | |
8 | */ | |
9 | ||
45c0fd36 | 10 | /*----- Licensing notice --------------------------------------------------* |
ae747c9b | 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. | |
45c0fd36 | 18 | * |
ae747c9b | 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. | |
45c0fd36 | 23 | * |
ae747c9b | 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 | ||
ae747c9b | 30 | /*----- Header files ------------------------------------------------------*/ |
31 | ||
32 | #include <assert.h> | |
33 | ||
34 | #include "mpx.h" | |
35 | #include "mpscan.h" | |
36 | ||
37 | /*----- Main code ---------------------------------------------------------*/ | |
38 | ||
39 | /* --- @gfx_add@ --- * | |
40 | * | |
41 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit | |
42 | * @const mpw *av, *avl@ = first addend vector base and limit | |
43 | * @const mpw *bv, *bvl@ = second addend vector base and limit | |
44 | * | |
45 | * Returns: --- | |
46 | * | |
47 | * Use: Adds two %$\gf{2}$% polynomials. This is the same as | |
48 | * subtraction. | |
49 | */ | |
50 | ||
51 | void gfx_add(mpw *dv, mpw *dvl, | |
52 | const mpw *av, const mpw *avl, | |
53 | const mpw *bv, const mpw *bvl) | |
54 | { | |
55 | MPX_SHRINK(av, avl); | |
56 | MPX_SHRINK(bv, bvl); | |
57 | ||
58 | while (av < avl || bv < bvl) { | |
59 | mpw a, b; | |
60 | if (dv >= dvl) | |
61 | return; | |
62 | a = (av < avl) ? *av++ : 0; | |
63 | b = (bv < bvl) ? *bv++ : 0; | |
64 | *dv++ = a ^ b; | |
65 | } | |
66 | if (dv < dvl) | |
67 | MPX_ZERO(dv, dvl); | |
68 | } | |
69 | ||
70 | /* --- @gfx_acc@ --- * | |
71 | * | |
72 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit | |
73 | * @const mpw *av, *avl@ = addend vector base and limit | |
74 | * | |
75 | * Returns: --- | |
76 | * | |
77 | * Use: Adds the addend into the destination. This is considerably | |
78 | * faster than the three-address add call. | |
79 | */ | |
80 | ||
81 | void gfx_acc(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl) | |
82 | { | |
83 | size_t dlen, alen; | |
84 | ||
85 | MPX_SHRINK(av, avl); | |
86 | dlen = dvl - dv; | |
87 | alen = avl - av; | |
88 | if (dlen < alen) | |
89 | avl = av + dlen; | |
90 | while (av < avl) | |
91 | *dv++ ^= *av++; | |
92 | } | |
93 | ||
94 | /* --- @gfx_accshift@ --- * | |
95 | * | |
96 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit | |
97 | * @const mpw *av, *avl@ = addend vector base and limit | |
98 | * @size_t n@ = number of bits to shift | |
99 | * | |
100 | * Returns: --- | |
101 | * | |
102 | * Use: Shifts the argument left by %$n$% places and adds it to the | |
103 | * destination. This is a primitive used by multiplication and | |
104 | * division. | |
105 | */ | |
106 | ||
107 | void gfx_accshift(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, size_t n) | |
108 | { | |
109 | size_t c = n / MPW_BITS; | |
110 | mpw x = 0, y; | |
111 | size_t dlen, alen; | |
112 | ||
113 | /* --- Sort out the shift amounts --- */ | |
114 | ||
115 | if (dvl - dv < c) | |
116 | return; | |
117 | dv += c; | |
118 | n %= MPW_BITS; | |
119 | if (!n) { | |
120 | gfx_acc(dv, dvl, av, avl); | |
121 | return; | |
122 | } | |
123 | c = MPW_BITS - n; | |
124 | ||
125 | /* --- Sort out vector lengths --- */ | |
126 | ||
127 | MPX_SHRINK(av, avl); | |
128 | dlen = dvl - dv; | |
129 | alen = avl - av; | |
130 | if (dlen < alen) | |
131 | avl = av + dlen; | |
132 | ||
133 | /* --- Now do the hard work --- */ | |
134 | ||
135 | while (av < avl) { | |
136 | y = *av++; | |
137 | *dv++ ^= MPW((y << n) | (x >> c)); | |
138 | x = y; | |
139 | } | |
140 | if (dv < dvl) | |
141 | *dv++ ^= x >> c; | |
142 | } | |
143 | ||
144 | /* --- @gfx_mul@ --- * | |
145 | * | |
146 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit | |
147 | * @const mpw *av, *avl@ = first argument vector base and limit | |
148 | * @const mpw *bv, *bvl@ = second argument vector base and limit | |
149 | * | |
150 | * Returns: --- | |
151 | * | |
152 | * Use: Does multiplication of polynomials over %$\gf{2}$%. | |
153 | */ | |
154 | ||
155 | void gfx_mul(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, | |
156 | const mpw *bv, const mpw *bvl) | |
157 | { | |
158 | mpscan sc; | |
159 | const mpw *v; | |
160 | mpw *vv; | |
161 | mpw z; | |
162 | mpd x, y; | |
163 | ||
164 | MPX_SHRINK(av, avl); | |
165 | MPX_SHRINK(bv, bvl); | |
166 | MPSCAN_INITX(&sc, av, avl); | |
167 | MPX_ZERO(dv, dvl); | |
168 | ||
169 | while (bv < bvl && dv < dvl) { | |
170 | x = 0; | |
171 | for (v = av, vv = dv++; v < avl && vv < dvl; v++) { | |
172 | z = *bv; y = *v; | |
173 | while (z) { | |
174 | if (z & 1u) x ^= y; | |
175 | z >>= 1; y <<= 1; | |
176 | } | |
177 | *vv++ ^= MPW(x); | |
178 | x >>= MPW_BITS; | |
179 | } | |
180 | if (vv < dvl) | |
181 | *vv++ = MPW(x); | |
182 | bv++; | |
183 | } | |
184 | } | |
185 | ||
186 | /* --- @gfx_div@ --- * | |
187 | * | |
188 | * Arguments: @mpw *qv, *qvl@ = quotient vector base and limit | |
45c0fd36 MW |
189 | * @mpw *rv, *rvl@ = dividend/remainder vector base and limit |
190 | * @const mpw *dv, *dvl@ = divisor vector base and limit | |
ae747c9b | 191 | * |
45c0fd36 | 192 | * Returns: --- |
ae747c9b | 193 | * |
45c0fd36 | 194 | * Use: Performs division on polynomials over %$\gf{2}$%. |
ae747c9b | 195 | */ |
196 | ||
197 | void gfx_div(mpw *qv, mpw *qvl, mpw *rv, mpw *rvl, | |
198 | const mpw *dv, const mpw *dvl) | |
199 | { | |
200 | size_t dlen, rlen, qlen; | |
201 | size_t dbits; | |
202 | mpw *rvv, *rvd; | |
203 | unsigned rvm, n, qi; | |
204 | mpw q; | |
205 | ||
206 | MPX_SHRINK(rv, rvl); | |
207 | MPX_SHRINK(dv, dvl); | |
208 | assert(((void)"division by zero in gfx_div", dv < dvl)); | |
209 | MPX_BITS(dbits, dv, dvl); | |
210 | dlen = dvl - dv; | |
211 | rlen = rvl - rv; | |
212 | qlen = qvl - qv; | |
213 | ||
214 | MPX_ZERO(qv, qvl); | |
215 | if (dlen > rlen) | |
216 | return; | |
217 | rvd = rvl - dlen; | |
218 | rvv = rvl - 1; | |
219 | rvm = 1 << (MPW_BITS - 1); | |
220 | n = MPW_BITS - (dbits % MPW_BITS); | |
221 | if (n == MPW_BITS) | |
222 | n = 0; | |
223 | q = 0; | |
224 | qi = rvd - rv; | |
225 | ||
226 | for (;;) { | |
227 | q <<= 1; | |
228 | if (*rvv & rvm) { | |
229 | q |= 1; | |
230 | gfx_accshift(rvd, rvl, dv, dvl, n); | |
231 | } | |
232 | rvm >>= 1; | |
233 | if (!rvm) { | |
234 | rvm = 1 << (MPW_BITS - 1); | |
235 | rvv--; | |
236 | } | |
237 | if (n) | |
238 | n--; | |
239 | else { | |
240 | if (qi < qlen) | |
241 | qv[qi] = q; | |
242 | q = 0; | |
243 | qi--; | |
244 | if (rvd == rv) | |
245 | break; | |
246 | n = MPW_BITS - 1; | |
247 | rvd--; | |
248 | } | |
249 | } | |
250 | } | |
251 | ||
252 | /*----- Test rig ----------------------------------------------------------*/ | |
253 | ||
254 | #ifdef TEST_RIG | |
255 | ||
256 | #include <mLib/alloc.h> | |
257 | #include <mLib/dstr.h> | |
258 | #include <mLib/quis.h> | |
259 | #include <mLib/testrig.h> | |
260 | ||
261 | #define ALLOC(v, vl, sz) do { \ | |
262 | size_t _sz = (sz); \ | |
263 | mpw *_vv = xmalloc(MPWS(_sz)); \ | |
264 | mpw *_vvl = _vv + _sz; \ | |
265 | (v) = _vv; \ | |
266 | (vl) = _vvl; \ | |
267 | } while (0) | |
268 | ||
269 | #define LOAD(v, vl, d) do { \ | |
270 | const dstr *_d = (d); \ | |
271 | mpw *_v, *_vl; \ | |
272 | ALLOC(_v, _vl, MPW_RQ(_d->len)); \ | |
273 | mpx_loadb(_v, _vl, _d->buf, _d->len); \ | |
274 | (v) = _v; \ | |
275 | (vl) = _vl; \ | |
276 | } while (0) | |
277 | ||
278 | #define MAX(x, y) ((x) > (y) ? (x) : (y)) | |
45c0fd36 | 279 | |
ae747c9b | 280 | static void dumpmp(const char *msg, const mpw *v, const mpw *vl) |
281 | { | |
282 | fputs(msg, stderr); | |
283 | MPX_SHRINK(v, vl); | |
284 | while (v < vl) | |
285 | fprintf(stderr, " %08lx", (unsigned long)*--vl); | |
286 | fputc('\n', stderr); | |
287 | } | |
288 | ||
289 | static int vadd(dstr *v) | |
290 | { | |
291 | mpw *a, *al; | |
292 | mpw *b, *bl; | |
293 | mpw *c, *cl; | |
294 | mpw *d, *dl; | |
295 | int ok = 1; | |
296 | ||
297 | LOAD(a, al, &v[0]); | |
298 | LOAD(b, bl, &v[1]); | |
299 | LOAD(c, cl, &v[2]); | |
300 | ALLOC(d, dl, MAX(al - a, bl - b) + 1); | |
301 | ||
302 | gfx_add(d, dl, a, al, b, bl); | |
303 | if (!mpx_ueq(d, dl, c, cl)) { | |
304 | fprintf(stderr, "\n*** vadd failed\n"); | |
45c0fd36 MW |
305 | dumpmp(" a", a, al); |
306 | dumpmp(" b", b, bl); | |
ae747c9b | 307 | dumpmp("expected", c, cl); |
308 | dumpmp(" result", d, dl); | |
309 | ok = 0; | |
310 | } | |
311 | ||
12ed8a1f | 312 | xfree(a); xfree(b); xfree(c); xfree(d); |
ae747c9b | 313 | return (ok); |
314 | } | |
315 | ||
316 | static int vmul(dstr *v) | |
317 | { | |
318 | mpw *a, *al; | |
319 | mpw *b, *bl; | |
320 | mpw *c, *cl; | |
321 | mpw *d, *dl; | |
322 | int ok = 1; | |
323 | ||
324 | LOAD(a, al, &v[0]); | |
325 | LOAD(b, bl, &v[1]); | |
326 | LOAD(c, cl, &v[2]); | |
327 | ALLOC(d, dl, (al - a) + (bl - b)); | |
328 | ||
329 | gfx_mul(d, dl, a, al, b, bl); | |
330 | if (!mpx_ueq(d, dl, c, cl)) { | |
331 | fprintf(stderr, "\n*** vmul failed\n"); | |
45c0fd36 MW |
332 | dumpmp(" a", a, al); |
333 | dumpmp(" b", b, bl); | |
ae747c9b | 334 | dumpmp("expected", c, cl); |
335 | dumpmp(" result", d, dl); | |
336 | ok = 0; | |
337 | } | |
338 | ||
12ed8a1f | 339 | xfree(a); xfree(b); xfree(c); xfree(d); |
ae747c9b | 340 | return (ok); |
341 | } | |
342 | ||
343 | static int vdiv(dstr *v) | |
344 | { | |
345 | mpw *a, *al; | |
346 | mpw *b, *bl; | |
347 | mpw *q, *ql; | |
348 | mpw *r, *rl; | |
349 | mpw *qq, *qql; | |
350 | int ok = 1; | |
351 | ||
352 | ALLOC(a, al, MPW_RQ(v[0].len) + 2); mpx_loadb(a, al, v[0].buf, v[0].len); | |
353 | LOAD(b, bl, &v[1]); | |
354 | LOAD(q, ql, &v[2]); | |
355 | LOAD(r, rl, &v[3]); | |
356 | ALLOC(qq, qql, al - a); | |
357 | ||
358 | gfx_div(qq, qql, a, al, b, bl); | |
359 | if (!mpx_ueq(qq, qql, q, ql) || | |
360 | !mpx_ueq(a, al, r, rl)) { | |
361 | fprintf(stderr, "\n*** vdiv failed\n"); | |
362 | dumpmp(" divisor", b, bl); | |
363 | dumpmp("expect r", r, rl); | |
364 | dumpmp("result r", a, al); | |
365 | dumpmp("expect q", q, ql); | |
366 | dumpmp("result q", qq, qql); | |
367 | ok = 0; | |
368 | } | |
369 | ||
12ed8a1f | 370 | xfree(a); xfree(b); xfree(r); xfree(q); xfree(qq); |
ae747c9b | 371 | return (ok); |
372 | } | |
373 | ||
374 | static test_chunk defs[] = { | |
375 | { "add", vadd, { &type_hex, &type_hex, &type_hex, 0 } }, | |
376 | { "mul", vmul, { &type_hex, &type_hex, &type_hex, 0 } }, | |
377 | { "div", vdiv, { &type_hex, &type_hex, &type_hex, &type_hex, 0 } }, | |
378 | { 0, 0, { 0 } } | |
379 | }; | |
380 | ||
381 | int main(int argc, char *argv[]) | |
382 | { | |
383 | test_run(argc, argv, defs, SRCDIR"/tests/gfx"); | |
384 | return (0); | |
385 | } | |
386 | ||
387 | #endif | |
388 | ||
389 | /*----- That's all, folks -------------------------------------------------*/ |