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ceb3f0c0 | 1 | /* -*-c-*- |
2 | * | |
f4535c64 | 3 | * $Id$ |
ceb3f0c0 | 4 | * |
5 | * Basic arithmetic on binary polynomials | |
6 | * | |
7 | * (c) 2004 Straylight/Edgeware | |
8 | */ | |
9 | ||
45c0fd36 | 10 | /*----- Licensing notice --------------------------------------------------* |
ceb3f0c0 | 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 | * |
ceb3f0c0 | 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 | * |
ceb3f0c0 | 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 | ||
ceb3f0c0 | 30 | /*----- Header files ------------------------------------------------------*/ |
31 | ||
32 | #include "gf.h" | |
33 | ||
34 | /*----- Macros ------------------------------------------------------------*/ | |
35 | ||
36 | #define MAX(x, y) ((x) >= (y) ? (x) : (y)) | |
37 | ||
38 | /*----- Main code ---------------------------------------------------------*/ | |
39 | ||
40 | /* --- @gf_add@ --- * | |
41 | * | |
42 | * Arguments: @mp *d@ = destination | |
43 | * @mp *a, *b@ = sources | |
44 | * | |
45 | * Returns: Result, @a@ added to @b@. | |
46 | */ | |
47 | ||
48 | mp *gf_add(mp *d, mp *a, mp *b) | |
49 | { | |
50 | MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)), (a->f | b->f) & MP_BURN); | |
51 | gfx_add(d->v, d->vl, a->v, a->vl, b->v, b->vl); | |
52 | d->f = (a->f | b->f) & MP_BURN; | |
53 | MP_SHRINK(d); | |
54 | return (d); | |
55 | } | |
56 | ||
57 | /* --- @gf_mul@ --- * | |
58 | * | |
59 | * Arguments: @mp *d@ = destination | |
60 | * @mp *a, *b@ = sources | |
61 | * | |
62 | * Returns: Result, @a@ multiplied by @b@. | |
63 | */ | |
64 | ||
65 | mp *gf_mul(mp *d, mp *a, mp *b) | |
66 | { | |
67 | a = MP_COPY(a); | |
68 | b = MP_COPY(b); | |
69 | ||
70 | if (MP_LEN(a) <= MPK_THRESH || MP_LEN(b) <= GFK_THRESH) { | |
71 | MP_DEST(d, MP_LEN(a) + MP_LEN(b), a->f | b->f | MP_UNDEF); | |
72 | gfx_mul(d->v, d->vl, a->v, a->vl, b->v, b->vl); | |
73 | } else { | |
74 | size_t m = MAX(MP_LEN(a), MP_LEN(b)); | |
75 | mpw *s; | |
76 | MP_DEST(d, 2 * m, a->f | b->f | MP_UNDEF); | |
432c4e18 | 77 | s = mpalloc(d->a, 3 * m); |
78 | gfx_kmul(d->v, d->vl, a->v, a->vl, b->v, b->vl, s, s + 3 * m); | |
ceb3f0c0 | 79 | mpfree(d->a, s); |
80 | } | |
81 | ||
82 | d->f = (a->f | b->f) & MP_BURN; | |
83 | MP_SHRINK(d); | |
84 | MP_DROP(a); | |
85 | MP_DROP(b); | |
86 | return (d); | |
87 | } | |
88 | ||
89 | /* --- @gf_sqr@ --- * | |
90 | * | |
91 | * Arguments: @mp *d@ = destination | |
92 | * @mp *a@ = source | |
93 | * | |
94 | * Returns: Result, @a@ squared. | |
95 | */ | |
96 | ||
97 | mp *gf_sqr(mp *d, mp *a) | |
98 | { | |
99 | MP_COPY(a); | |
100 | MP_DEST(d, 2 * MP_LEN(a), a->f & MP_BURN); | |
101 | gfx_sqr(d->v, d->vl, a->v, a->vl); | |
102 | d->f = a->f & MP_BURN; | |
103 | MP_SHRINK(d); | |
104 | MP_DROP(a); | |
105 | return (d); | |
106 | } | |
107 | ||
108 | /* --- @gf_div@ --- * | |
109 | * | |
110 | * Arguments: @mp **qq, **rr@ = destination, quotient and remainder | |
111 | * @mp *a, *b@ = sources | |
112 | * | |
113 | * Use: Calculates the quotient and remainder when @a@ is divided by | |
114 | * @b@. The destinations @*qq@ and @*rr@ must be distinct. | |
115 | * Either of @qq@ or @rr@ may be null to indicate that the | |
116 | * result is irrelevant. (Discarding both results is silly.) | |
117 | * There is a performance advantage if @a == *rr@. | |
118 | */ | |
119 | ||
120 | void gf_div(mp **qq, mp **rr, mp *a, mp *b) | |
121 | { | |
122 | mp *r = rr ? *rr : MP_NEW; | |
123 | mp *q = qq ? *qq : MP_NEW; | |
124 | ||
125 | /* --- Set the remainder up right --- */ | |
126 | ||
127 | b = MP_COPY(b); | |
128 | a = MP_COPY(a); | |
129 | if (r) | |
130 | MP_DROP(r); | |
131 | r = a; | |
132 | MP_DEST(r, MP_LEN(b) + 2, a->f | b->f); | |
133 | ||
134 | /* --- Fix up the quotient too --- */ | |
135 | ||
136 | r = MP_COPY(r); | |
137 | MP_DEST(q, MP_LEN(r), r->f | MP_UNDEF); | |
138 | MP_DROP(r); | |
139 | ||
140 | /* --- Perform the calculation --- */ | |
141 | ||
142 | gfx_div(q->v, q->vl, r->v, r->vl, b->v, b->vl); | |
143 | ||
144 | /* --- Sort out the sign of the results --- * | |
145 | * | |
146 | * If the signs of the arguments differ, and the remainder is nonzero, I | |
147 | * must add one to the absolute value of the quotient and subtract the | |
148 | * remainder from @b@. | |
149 | */ | |
150 | ||
151 | q->f = (r->f | b->f) & MP_BURN; | |
152 | r->f = (r->f | b->f) & MP_BURN; | |
153 | ||
154 | /* --- Store the return values --- */ | |
155 | ||
156 | MP_DROP(b); | |
157 | ||
158 | if (!qq) | |
159 | MP_DROP(q); | |
160 | else { | |
161 | MP_SHRINK(q); | |
162 | *qq = q; | |
163 | } | |
164 | ||
165 | if (!rr) | |
166 | MP_DROP(r); | |
167 | else { | |
168 | MP_SHRINK(r); | |
169 | *rr = r; | |
170 | } | |
171 | } | |
172 | ||
432c4e18 | 173 | /* --- @gf_irreduciblep@ --- * |
174 | * | |
175 | * Arguments: @mp *f@ = a polynomial | |
176 | * | |
177 | * Returns: Nonzero if the polynomial is irreducible; otherwise zero. | |
178 | */ | |
179 | ||
180 | int gf_irreduciblep(mp *f) | |
181 | { | |
00f096fc | 182 | unsigned long m; |
432c4e18 | 183 | mp *u = MP_TWO; |
184 | mp *v = MP_NEW; | |
185 | ||
00f096fc MW |
186 | if (MP_ZEROP(f)) |
187 | return (0); | |
188 | else if (MP_LEN(f) == 1) { | |
189 | if (f->v[0] < 2) return (0); | |
190 | if (f->v[0] < 4) return (1); | |
191 | } | |
192 | m = (mp_bits(f) - 1)/2; | |
432c4e18 | 193 | while (m) { |
194 | u = gf_sqr(u, u); | |
195 | gf_div(0, &u, u, f); | |
196 | v = gf_add(v, u, MP_TWO); | |
197 | gf_gcd(&v, 0, 0, v, f); | |
198 | if (!MP_EQ(v, MP_ONE)) break; | |
199 | m--; | |
200 | } | |
201 | MP_DROP(u); | |
202 | MP_DROP(v); | |
203 | return (!m); | |
204 | } | |
205 | ||
ceb3f0c0 | 206 | /*----- Test rig ----------------------------------------------------------*/ |
207 | ||
208 | #ifdef TEST_RIG | |
209 | ||
210 | static int verify(const char *op, mp *expect, mp *result, mp *a, mp *b) | |
211 | { | |
212 | if (!MP_EQ(expect, result)) { | |
213 | fprintf(stderr, "\n*** %s failed", op); | |
45c0fd36 MW |
214 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 16); |
215 | fputs("\n*** b = ", stderr); mp_writefile(b, stderr, 16); | |
ceb3f0c0 | 216 | fputs("\n*** result = ", stderr); mp_writefile(result, stderr, 16); |
217 | fputs("\n*** expect = ", stderr); mp_writefile(expect, stderr, 16); | |
218 | fputc('\n', stderr); | |
219 | return (0); | |
220 | } | |
221 | return (1); | |
222 | } | |
223 | ||
224 | #define RIG(name, op) \ | |
225 | static int t##name(dstr *v) \ | |
226 | { \ | |
227 | mp *a = *(mp **)v[0].buf; \ | |
228 | mp *b = *(mp **)v[1].buf; \ | |
229 | mp *r = *(mp **)v[2].buf; \ | |
230 | mp *c = op(MP_NEW, a, b); \ | |
231 | int ok = verify(#name, r, c, a, b); \ | |
232 | mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(r); \ | |
233 | assert(mparena_count(MPARENA_GLOBAL) == 0); \ | |
234 | return (ok); \ | |
235 | } | |
236 | ||
237 | RIG(add, gf_add) | |
238 | RIG(mul, gf_mul) | |
f4535c64 | 239 | RIG(exp, gf_exp) |
ceb3f0c0 | 240 | |
241 | #undef RIG | |
242 | ||
243 | static int tsqr(dstr *v) | |
244 | { | |
245 | mp *a = *(mp **)v[0].buf; | |
246 | mp *r = *(mp **)v[1].buf; | |
247 | mp *c = MP_NEW; | |
248 | int ok = 1; | |
249 | c = gf_sqr(MP_NEW, a); | |
250 | ok &= verify("sqr", r, c, a, MP_ZERO); | |
251 | mp_drop(a); mp_drop(r); mp_drop(c); | |
252 | assert(mparena_count(MPARENA_GLOBAL) == 0); | |
253 | return (ok); | |
254 | } | |
255 | ||
256 | static int tdiv(dstr *v) | |
257 | { | |
258 | mp *a = *(mp **)v[0].buf; | |
259 | mp *b = *(mp **)v[1].buf; | |
260 | mp *q = *(mp **)v[2].buf; | |
261 | mp *r = *(mp **)v[3].buf; | |
262 | mp *c = MP_NEW, *d = MP_NEW; | |
263 | int ok = 1; | |
264 | gf_div(&c, &d, a, b); | |
265 | ok &= verify("div(quotient)", q, c, a, b); | |
266 | ok &= verify("div(remainder)", r, d, a, b); | |
267 | mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(d); mp_drop(r); mp_drop(q); | |
268 | assert(mparena_count(MPARENA_GLOBAL) == 0); | |
269 | return (ok); | |
270 | } | |
271 | ||
432c4e18 | 272 | static int tirred(dstr *v) |
273 | { | |
274 | mp *a = *(mp **)v[0].buf; | |
275 | int r = *(int *)v[1].buf; | |
276 | int c = gf_irreduciblep(a); | |
277 | int ok = 1; | |
278 | if (r != c) { | |
279 | ok = 0; | |
280 | fprintf(stderr, "\n*** irred failed"); | |
45c0fd36 MW |
281 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 16); |
282 | fprintf(stderr, "\n*** r = %d\n", r); | |
283 | fprintf(stderr, "*** c = %d\n", c); | |
432c4e18 | 284 | } |
285 | mp_drop(a); | |
286 | assert(mparena_count(MPARENA_GLOBAL) == 0); | |
287 | return (ok); | |
288 | } | |
289 | ||
ceb3f0c0 | 290 | static test_chunk tests[] = { |
291 | { "add", tadd, { &type_mp, &type_mp, &type_mp, 0 } }, | |
292 | { "mul", tmul, { &type_mp, &type_mp, &type_mp, 0 } }, | |
293 | { "sqr", tsqr, { &type_mp, &type_mp, 0 } }, | |
294 | { "div", tdiv, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, | |
f4535c64 | 295 | { "exp", texp, { &type_mp, &type_mp, &type_mp, 0 } }, |
432c4e18 | 296 | { "irred", tirred, { &type_mp, &type_int, 0 } }, |
ceb3f0c0 | 297 | { 0, 0, { 0 } }, |
298 | }; | |
299 | ||
300 | int main(int argc, char *argv[]) | |
301 | { | |
302 | sub_init(); | |
303 | test_run(argc, argv, tests, SRCDIR "/tests/gf"); | |
304 | return (0); | |
305 | } | |
306 | ||
307 | #endif | |
308 | ||
309 | /*----- That's all, folks -------------------------------------------------*/ |