ae747c9b |
1 | /* -*-c-*- |
2 | * |
3 | * $Id: gfx.c,v 1.1 2000/10/08 15:49:37 mdw Exp $ |
4 | * |
5 | * Low-level arithmetic 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.c,v $ |
33 | * Revision 1.1 2000/10/08 15:49:37 mdw |
34 | * First glimmerings of binary polynomial arithmetic. |
35 | * |
36 | */ |
37 | |
38 | /*----- Header files ------------------------------------------------------*/ |
39 | |
40 | #include <assert.h> |
41 | |
42 | #include "mpx.h" |
43 | #include "mpscan.h" |
44 | |
45 | /*----- Main code ---------------------------------------------------------*/ |
46 | |
47 | /* --- @gfx_add@ --- * |
48 | * |
49 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
50 | * @const mpw *av, *avl@ = first addend vector base and limit |
51 | * @const mpw *bv, *bvl@ = second addend vector base and limit |
52 | * |
53 | * Returns: --- |
54 | * |
55 | * Use: Adds two %$\gf{2}$% polynomials. This is the same as |
56 | * subtraction. |
57 | */ |
58 | |
59 | void gfx_add(mpw *dv, mpw *dvl, |
60 | const mpw *av, const mpw *avl, |
61 | const mpw *bv, const mpw *bvl) |
62 | { |
63 | MPX_SHRINK(av, avl); |
64 | MPX_SHRINK(bv, bvl); |
65 | |
66 | while (av < avl || bv < bvl) { |
67 | mpw a, b; |
68 | if (dv >= dvl) |
69 | return; |
70 | a = (av < avl) ? *av++ : 0; |
71 | b = (bv < bvl) ? *bv++ : 0; |
72 | *dv++ = a ^ b; |
73 | } |
74 | if (dv < dvl) |
75 | MPX_ZERO(dv, dvl); |
76 | } |
77 | |
78 | /* --- @gfx_acc@ --- * |
79 | * |
80 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
81 | * @const mpw *av, *avl@ = addend vector base and limit |
82 | * |
83 | * Returns: --- |
84 | * |
85 | * Use: Adds the addend into the destination. This is considerably |
86 | * faster than the three-address add call. |
87 | */ |
88 | |
89 | void gfx_acc(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl) |
90 | { |
91 | size_t dlen, alen; |
92 | |
93 | MPX_SHRINK(av, avl); |
94 | dlen = dvl - dv; |
95 | alen = avl - av; |
96 | if (dlen < alen) |
97 | avl = av + dlen; |
98 | while (av < avl) |
99 | *dv++ ^= *av++; |
100 | } |
101 | |
102 | /* --- @gfx_accshift@ --- * |
103 | * |
104 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
105 | * @const mpw *av, *avl@ = addend vector base and limit |
106 | * @size_t n@ = number of bits to shift |
107 | * |
108 | * Returns: --- |
109 | * |
110 | * Use: Shifts the argument left by %$n$% places and adds it to the |
111 | * destination. This is a primitive used by multiplication and |
112 | * division. |
113 | */ |
114 | |
115 | void gfx_accshift(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, size_t n) |
116 | { |
117 | size_t c = n / MPW_BITS; |
118 | mpw x = 0, y; |
119 | size_t dlen, alen; |
120 | |
121 | /* --- Sort out the shift amounts --- */ |
122 | |
123 | if (dvl - dv < c) |
124 | return; |
125 | dv += c; |
126 | n %= MPW_BITS; |
127 | if (!n) { |
128 | gfx_acc(dv, dvl, av, avl); |
129 | return; |
130 | } |
131 | c = MPW_BITS - n; |
132 | |
133 | /* --- Sort out vector lengths --- */ |
134 | |
135 | MPX_SHRINK(av, avl); |
136 | dlen = dvl - dv; |
137 | alen = avl - av; |
138 | if (dlen < alen) |
139 | avl = av + dlen; |
140 | |
141 | /* --- Now do the hard work --- */ |
142 | |
143 | while (av < avl) { |
144 | y = *av++; |
145 | *dv++ ^= MPW((y << n) | (x >> c)); |
146 | x = y; |
147 | } |
148 | if (dv < dvl) |
149 | *dv++ ^= x >> c; |
150 | } |
151 | |
152 | /* --- @gfx_mul@ --- * |
153 | * |
154 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
155 | * @const mpw *av, *avl@ = first argument vector base and limit |
156 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
157 | * |
158 | * Returns: --- |
159 | * |
160 | * Use: Does multiplication of polynomials over %$\gf{2}$%. |
161 | */ |
162 | |
163 | void gfx_mul(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, |
164 | const mpw *bv, const mpw *bvl) |
165 | { |
166 | mpscan sc; |
167 | const mpw *v; |
168 | mpw *vv; |
169 | mpw z; |
170 | mpd x, y; |
171 | |
172 | MPX_SHRINK(av, avl); |
173 | MPX_SHRINK(bv, bvl); |
174 | MPSCAN_INITX(&sc, av, avl); |
175 | MPX_ZERO(dv, dvl); |
176 | |
177 | while (bv < bvl && dv < dvl) { |
178 | x = 0; |
179 | for (v = av, vv = dv++; v < avl && vv < dvl; v++) { |
180 | z = *bv; y = *v; |
181 | while (z) { |
182 | if (z & 1u) x ^= y; |
183 | z >>= 1; y <<= 1; |
184 | } |
185 | *vv++ ^= MPW(x); |
186 | x >>= MPW_BITS; |
187 | } |
188 | if (vv < dvl) |
189 | *vv++ = MPW(x); |
190 | bv++; |
191 | } |
192 | } |
193 | |
194 | /* --- @gfx_div@ --- * |
195 | * |
196 | * Arguments: @mpw *qv, *qvl@ = quotient vector base and limit |
197 | * @mpw *rv, *rvl@ = dividend/remainder vector base and limit |
198 | * @const mpw *dv, *dvl@ = divisor vector base and limit |
199 | * |
200 | * Returns: --- |
201 | * |
202 | * Use: Performs division on polynomials over %$\gf{2}$%. |
203 | */ |
204 | |
205 | void gfx_div(mpw *qv, mpw *qvl, mpw *rv, mpw *rvl, |
206 | const mpw *dv, const mpw *dvl) |
207 | { |
208 | size_t dlen, rlen, qlen; |
209 | size_t dbits; |
210 | mpw *rvv, *rvd; |
211 | unsigned rvm, n, qi; |
212 | mpw q; |
213 | |
214 | MPX_SHRINK(rv, rvl); |
215 | MPX_SHRINK(dv, dvl); |
216 | assert(((void)"division by zero in gfx_div", dv < dvl)); |
217 | MPX_BITS(dbits, dv, dvl); |
218 | dlen = dvl - dv; |
219 | rlen = rvl - rv; |
220 | qlen = qvl - qv; |
221 | |
222 | MPX_ZERO(qv, qvl); |
223 | if (dlen > rlen) |
224 | return; |
225 | rvd = rvl - dlen; |
226 | rvv = rvl - 1; |
227 | rvm = 1 << (MPW_BITS - 1); |
228 | n = MPW_BITS - (dbits % MPW_BITS); |
229 | if (n == MPW_BITS) |
230 | n = 0; |
231 | q = 0; |
232 | qi = rvd - rv; |
233 | |
234 | for (;;) { |
235 | q <<= 1; |
236 | if (*rvv & rvm) { |
237 | q |= 1; |
238 | gfx_accshift(rvd, rvl, dv, dvl, n); |
239 | } |
240 | rvm >>= 1; |
241 | if (!rvm) { |
242 | rvm = 1 << (MPW_BITS - 1); |
243 | rvv--; |
244 | } |
245 | if (n) |
246 | n--; |
247 | else { |
248 | if (qi < qlen) |
249 | qv[qi] = q; |
250 | q = 0; |
251 | qi--; |
252 | if (rvd == rv) |
253 | break; |
254 | n = MPW_BITS - 1; |
255 | rvd--; |
256 | } |
257 | } |
258 | } |
259 | |
260 | /*----- Test rig ----------------------------------------------------------*/ |
261 | |
262 | #ifdef TEST_RIG |
263 | |
264 | #include <mLib/alloc.h> |
265 | #include <mLib/dstr.h> |
266 | #include <mLib/quis.h> |
267 | #include <mLib/testrig.h> |
268 | |
269 | #define ALLOC(v, vl, sz) do { \ |
270 | size_t _sz = (sz); \ |
271 | mpw *_vv = xmalloc(MPWS(_sz)); \ |
272 | mpw *_vvl = _vv + _sz; \ |
273 | (v) = _vv; \ |
274 | (vl) = _vvl; \ |
275 | } while (0) |
276 | |
277 | #define LOAD(v, vl, d) do { \ |
278 | const dstr *_d = (d); \ |
279 | mpw *_v, *_vl; \ |
280 | ALLOC(_v, _vl, MPW_RQ(_d->len)); \ |
281 | mpx_loadb(_v, _vl, _d->buf, _d->len); \ |
282 | (v) = _v; \ |
283 | (vl) = _vl; \ |
284 | } while (0) |
285 | |
286 | #define MAX(x, y) ((x) > (y) ? (x) : (y)) |
287 | |
288 | static void dumpmp(const char *msg, const mpw *v, const mpw *vl) |
289 | { |
290 | fputs(msg, stderr); |
291 | MPX_SHRINK(v, vl); |
292 | while (v < vl) |
293 | fprintf(stderr, " %08lx", (unsigned long)*--vl); |
294 | fputc('\n', stderr); |
295 | } |
296 | |
297 | static int vadd(dstr *v) |
298 | { |
299 | mpw *a, *al; |
300 | mpw *b, *bl; |
301 | mpw *c, *cl; |
302 | mpw *d, *dl; |
303 | int ok = 1; |
304 | |
305 | LOAD(a, al, &v[0]); |
306 | LOAD(b, bl, &v[1]); |
307 | LOAD(c, cl, &v[2]); |
308 | ALLOC(d, dl, MAX(al - a, bl - b) + 1); |
309 | |
310 | gfx_add(d, dl, a, al, b, bl); |
311 | if (!mpx_ueq(d, dl, c, cl)) { |
312 | fprintf(stderr, "\n*** vadd 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); |
321 | return (ok); |
322 | } |
323 | |
324 | static int vmul(dstr *v) |
325 | { |
326 | mpw *a, *al; |
327 | mpw *b, *bl; |
328 | mpw *c, *cl; |
329 | mpw *d, *dl; |
330 | int ok = 1; |
331 | |
332 | LOAD(a, al, &v[0]); |
333 | LOAD(b, bl, &v[1]); |
334 | LOAD(c, cl, &v[2]); |
335 | ALLOC(d, dl, (al - a) + (bl - b)); |
336 | |
337 | gfx_mul(d, dl, a, al, b, bl); |
338 | if (!mpx_ueq(d, dl, c, cl)) { |
339 | fprintf(stderr, "\n*** vmul failed\n"); |
340 | dumpmp(" a", a, al); |
341 | dumpmp(" b", b, bl); |
342 | dumpmp("expected", c, cl); |
343 | dumpmp(" result", d, dl); |
344 | ok = 0; |
345 | } |
346 | |
347 | free(a); free(b); free(c); free(d); |
348 | return (ok); |
349 | } |
350 | |
351 | static int vdiv(dstr *v) |
352 | { |
353 | mpw *a, *al; |
354 | mpw *b, *bl; |
355 | mpw *q, *ql; |
356 | mpw *r, *rl; |
357 | mpw *qq, *qql; |
358 | int ok = 1; |
359 | |
360 | ALLOC(a, al, MPW_RQ(v[0].len) + 2); mpx_loadb(a, al, v[0].buf, v[0].len); |
361 | LOAD(b, bl, &v[1]); |
362 | LOAD(q, ql, &v[2]); |
363 | LOAD(r, rl, &v[3]); |
364 | ALLOC(qq, qql, al - a); |
365 | |
366 | gfx_div(qq, qql, a, al, b, bl); |
367 | if (!mpx_ueq(qq, qql, q, ql) || |
368 | !mpx_ueq(a, al, r, rl)) { |
369 | fprintf(stderr, "\n*** vdiv failed\n"); |
370 | dumpmp(" divisor", b, bl); |
371 | dumpmp("expect r", r, rl); |
372 | dumpmp("result r", a, al); |
373 | dumpmp("expect q", q, ql); |
374 | dumpmp("result q", qq, qql); |
375 | ok = 0; |
376 | } |
377 | |
378 | free(a); free(b); free(r); free(q); free(qq); |
379 | return (ok); |
380 | } |
381 | |
382 | static test_chunk defs[] = { |
383 | { "add", vadd, { &type_hex, &type_hex, &type_hex, 0 } }, |
384 | { "mul", vmul, { &type_hex, &type_hex, &type_hex, 0 } }, |
385 | { "div", vdiv, { &type_hex, &type_hex, &type_hex, &type_hex, 0 } }, |
386 | { 0, 0, { 0 } } |
387 | }; |
388 | |
389 | int main(int argc, char *argv[]) |
390 | { |
391 | test_run(argc, argv, defs, SRCDIR"/tests/gfx"); |
392 | return (0); |
393 | } |
394 | |
395 | #endif |
396 | |
397 | /*----- That's all, folks -------------------------------------------------*/ |