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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: gfx.c,v 1.2 2004/04/08 01:36:15 mdw Exp $ |
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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 | |
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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 |
189 | * @mpw *rv, *rvl@ = dividend/remainder vector base and limit |
190 | * @const mpw *dv, *dvl@ = divisor vector base and limit |
191 | * |
192 | * Returns: --- |
193 | * |
194 | * Use: Performs division on polynomials over %$\gf{2}$%. |
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)) |
279 | |
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"); |
305 | dumpmp(" a", a, al); |
306 | dumpmp(" b", b, bl); |
307 | dumpmp("expected", c, cl); |
308 | dumpmp(" result", d, dl); |
309 | ok = 0; |
310 | } |
311 | |
312 | free(a); free(b); free(c); free(d); |
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"); |
332 | dumpmp(" a", a, al); |
333 | dumpmp(" b", b, bl); |
334 | dumpmp("expected", c, cl); |
335 | dumpmp(" result", d, dl); |
336 | ok = 0; |
337 | } |
338 | |
339 | free(a); free(b); free(c); free(d); |
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 | |
370 | free(a); free(b); free(r); free(q); free(qq); |
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 -------------------------------------------------*/ |