Commit | Line | Data |
---|---|---|
ceb3f0c0 | 1 | /* -*-c-*- |
ceb3f0c0 | 2 | * |
3 | * Basic arithmetic on binary polynomials | |
4 | * | |
5 | * (c) 2004 Straylight/Edgeware | |
6 | */ | |
7 | ||
45c0fd36 | 8 | /*----- Licensing notice --------------------------------------------------* |
ceb3f0c0 | 9 | * |
10 | * This file is part of Catacomb. | |
11 | * | |
12 | * Catacomb is free software; you can redistribute it and/or modify | |
13 | * it under the terms of the GNU Library General Public License as | |
14 | * published by the Free Software Foundation; either version 2 of the | |
15 | * License, or (at your option) any later version. | |
45c0fd36 | 16 | * |
ceb3f0c0 | 17 | * Catacomb is distributed in the hope that it will be useful, |
18 | * but WITHOUT ANY WARRANTY; without even the implied warranty of | |
19 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
20 | * GNU Library General Public License for more details. | |
45c0fd36 | 21 | * |
ceb3f0c0 | 22 | * You should have received a copy of the GNU Library General Public |
23 | * License along with Catacomb; if not, write to the Free | |
24 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, | |
25 | * MA 02111-1307, USA. | |
26 | */ | |
27 | ||
ceb3f0c0 | 28 | /*----- Header files ------------------------------------------------------*/ |
29 | ||
30 | #include "gf.h" | |
31 | ||
32 | /*----- Macros ------------------------------------------------------------*/ | |
33 | ||
34 | #define MAX(x, y) ((x) >= (y) ? (x) : (y)) | |
35 | ||
36 | /*----- Main code ---------------------------------------------------------*/ | |
37 | ||
38 | /* --- @gf_add@ --- * | |
39 | * | |
40 | * Arguments: @mp *d@ = destination | |
41 | * @mp *a, *b@ = sources | |
42 | * | |
43 | * Returns: Result, @a@ added to @b@. | |
44 | */ | |
45 | ||
46 | mp *gf_add(mp *d, mp *a, mp *b) | |
47 | { | |
48 | MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)), (a->f | b->f) & MP_BURN); | |
49 | gfx_add(d->v, d->vl, a->v, a->vl, b->v, b->vl); | |
50 | d->f = (a->f | b->f) & MP_BURN; | |
51 | MP_SHRINK(d); | |
52 | return (d); | |
53 | } | |
54 | ||
55 | /* --- @gf_mul@ --- * | |
56 | * | |
57 | * Arguments: @mp *d@ = destination | |
58 | * @mp *a, *b@ = sources | |
59 | * | |
60 | * Returns: Result, @a@ multiplied by @b@. | |
61 | */ | |
62 | ||
63 | mp *gf_mul(mp *d, mp *a, mp *b) | |
64 | { | |
65 | a = MP_COPY(a); | |
66 | b = MP_COPY(b); | |
67 | ||
68 | if (MP_LEN(a) <= MPK_THRESH || MP_LEN(b) <= GFK_THRESH) { | |
69 | MP_DEST(d, MP_LEN(a) + MP_LEN(b), a->f | b->f | MP_UNDEF); | |
70 | gfx_mul(d->v, d->vl, a->v, a->vl, b->v, b->vl); | |
71 | } else { | |
72 | size_t m = MAX(MP_LEN(a), MP_LEN(b)); | |
73 | mpw *s; | |
74 | MP_DEST(d, 2 * m, a->f | b->f | MP_UNDEF); | |
432c4e18 | 75 | s = mpalloc(d->a, 3 * m); |
76 | gfx_kmul(d->v, d->vl, a->v, a->vl, b->v, b->vl, s, s + 3 * m); | |
ceb3f0c0 | 77 | mpfree(d->a, s); |
78 | } | |
79 | ||
80 | d->f = (a->f | b->f) & MP_BURN; | |
81 | MP_SHRINK(d); | |
82 | MP_DROP(a); | |
83 | MP_DROP(b); | |
84 | return (d); | |
85 | } | |
86 | ||
87 | /* --- @gf_sqr@ --- * | |
88 | * | |
89 | * Arguments: @mp *d@ = destination | |
90 | * @mp *a@ = source | |
91 | * | |
92 | * Returns: Result, @a@ squared. | |
93 | */ | |
94 | ||
95 | mp *gf_sqr(mp *d, mp *a) | |
96 | { | |
97 | MP_COPY(a); | |
98 | MP_DEST(d, 2 * MP_LEN(a), a->f & MP_BURN); | |
99 | gfx_sqr(d->v, d->vl, a->v, a->vl); | |
100 | d->f = a->f & MP_BURN; | |
101 | MP_SHRINK(d); | |
102 | MP_DROP(a); | |
103 | return (d); | |
104 | } | |
105 | ||
106 | /* --- @gf_div@ --- * | |
107 | * | |
108 | * Arguments: @mp **qq, **rr@ = destination, quotient and remainder | |
109 | * @mp *a, *b@ = sources | |
110 | * | |
111 | * Use: Calculates the quotient and remainder when @a@ is divided by | |
112 | * @b@. The destinations @*qq@ and @*rr@ must be distinct. | |
113 | * Either of @qq@ or @rr@ may be null to indicate that the | |
114 | * result is irrelevant. (Discarding both results is silly.) | |
115 | * There is a performance advantage if @a == *rr@. | |
116 | */ | |
117 | ||
118 | void gf_div(mp **qq, mp **rr, mp *a, mp *b) | |
119 | { | |
120 | mp *r = rr ? *rr : MP_NEW; | |
121 | mp *q = qq ? *qq : MP_NEW; | |
122 | ||
123 | /* --- Set the remainder up right --- */ | |
124 | ||
125 | b = MP_COPY(b); | |
126 | a = MP_COPY(a); | |
127 | if (r) | |
128 | MP_DROP(r); | |
129 | r = a; | |
130 | MP_DEST(r, MP_LEN(b) + 2, a->f | b->f); | |
131 | ||
132 | /* --- Fix up the quotient too --- */ | |
133 | ||
134 | r = MP_COPY(r); | |
135 | MP_DEST(q, MP_LEN(r), r->f | MP_UNDEF); | |
136 | MP_DROP(r); | |
137 | ||
138 | /* --- Perform the calculation --- */ | |
139 | ||
140 | gfx_div(q->v, q->vl, r->v, r->vl, b->v, b->vl); | |
141 | ||
142 | /* --- Sort out the sign of the results --- * | |
143 | * | |
144 | * If the signs of the arguments differ, and the remainder is nonzero, I | |
145 | * must add one to the absolute value of the quotient and subtract the | |
146 | * remainder from @b@. | |
147 | */ | |
148 | ||
149 | q->f = (r->f | b->f) & MP_BURN; | |
150 | r->f = (r->f | b->f) & MP_BURN; | |
151 | ||
152 | /* --- Store the return values --- */ | |
153 | ||
154 | MP_DROP(b); | |
155 | ||
156 | if (!qq) | |
157 | MP_DROP(q); | |
158 | else { | |
159 | MP_SHRINK(q); | |
160 | *qq = q; | |
161 | } | |
162 | ||
163 | if (!rr) | |
164 | MP_DROP(r); | |
165 | else { | |
166 | MP_SHRINK(r); | |
167 | *rr = r; | |
168 | } | |
169 | } | |
170 | ||
432c4e18 | 171 | /* --- @gf_irreduciblep@ --- * |
172 | * | |
173 | * Arguments: @mp *f@ = a polynomial | |
174 | * | |
175 | * Returns: Nonzero if the polynomial is irreducible; otherwise zero. | |
176 | */ | |
177 | ||
178 | int gf_irreduciblep(mp *f) | |
179 | { | |
00f096fc | 180 | unsigned long m; |
432c4e18 | 181 | mp *u = MP_TWO; |
182 | mp *v = MP_NEW; | |
183 | ||
00f096fc MW |
184 | if (MP_ZEROP(f)) |
185 | return (0); | |
186 | else if (MP_LEN(f) == 1) { | |
187 | if (f->v[0] < 2) return (0); | |
188 | if (f->v[0] < 4) return (1); | |
189 | } | |
190 | m = (mp_bits(f) - 1)/2; | |
432c4e18 | 191 | while (m) { |
192 | u = gf_sqr(u, u); | |
193 | gf_div(0, &u, u, f); | |
194 | v = gf_add(v, u, MP_TWO); | |
195 | gf_gcd(&v, 0, 0, v, f); | |
196 | if (!MP_EQ(v, MP_ONE)) break; | |
197 | m--; | |
198 | } | |
199 | MP_DROP(u); | |
200 | MP_DROP(v); | |
201 | return (!m); | |
202 | } | |
203 | ||
ceb3f0c0 | 204 | /*----- Test rig ----------------------------------------------------------*/ |
205 | ||
206 | #ifdef TEST_RIG | |
207 | ||
208 | static int verify(const char *op, mp *expect, mp *result, mp *a, mp *b) | |
209 | { | |
210 | if (!MP_EQ(expect, result)) { | |
211 | fprintf(stderr, "\n*** %s failed", op); | |
45c0fd36 MW |
212 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 16); |
213 | fputs("\n*** b = ", stderr); mp_writefile(b, stderr, 16); | |
ceb3f0c0 | 214 | fputs("\n*** result = ", stderr); mp_writefile(result, stderr, 16); |
215 | fputs("\n*** expect = ", stderr); mp_writefile(expect, stderr, 16); | |
216 | fputc('\n', stderr); | |
217 | return (0); | |
218 | } | |
219 | return (1); | |
220 | } | |
221 | ||
222 | #define RIG(name, op) \ | |
223 | static int t##name(dstr *v) \ | |
224 | { \ | |
225 | mp *a = *(mp **)v[0].buf; \ | |
226 | mp *b = *(mp **)v[1].buf; \ | |
227 | mp *r = *(mp **)v[2].buf; \ | |
228 | mp *c = op(MP_NEW, a, b); \ | |
229 | int ok = verify(#name, r, c, a, b); \ | |
230 | mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(r); \ | |
231 | assert(mparena_count(MPARENA_GLOBAL) == 0); \ | |
232 | return (ok); \ | |
233 | } | |
234 | ||
235 | RIG(add, gf_add) | |
236 | RIG(mul, gf_mul) | |
f4535c64 | 237 | RIG(exp, gf_exp) |
ceb3f0c0 | 238 | |
239 | #undef RIG | |
240 | ||
241 | static int tsqr(dstr *v) | |
242 | { | |
243 | mp *a = *(mp **)v[0].buf; | |
244 | mp *r = *(mp **)v[1].buf; | |
245 | mp *c = MP_NEW; | |
246 | int ok = 1; | |
247 | c = gf_sqr(MP_NEW, a); | |
248 | ok &= verify("sqr", r, c, a, MP_ZERO); | |
249 | mp_drop(a); mp_drop(r); mp_drop(c); | |
250 | assert(mparena_count(MPARENA_GLOBAL) == 0); | |
251 | return (ok); | |
252 | } | |
253 | ||
254 | static int tdiv(dstr *v) | |
255 | { | |
256 | mp *a = *(mp **)v[0].buf; | |
257 | mp *b = *(mp **)v[1].buf; | |
258 | mp *q = *(mp **)v[2].buf; | |
259 | mp *r = *(mp **)v[3].buf; | |
260 | mp *c = MP_NEW, *d = MP_NEW; | |
261 | int ok = 1; | |
262 | gf_div(&c, &d, a, b); | |
263 | ok &= verify("div(quotient)", q, c, a, b); | |
264 | ok &= verify("div(remainder)", r, d, a, b); | |
265 | mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(d); mp_drop(r); mp_drop(q); | |
266 | assert(mparena_count(MPARENA_GLOBAL) == 0); | |
267 | return (ok); | |
268 | } | |
269 | ||
432c4e18 | 270 | static int tirred(dstr *v) |
271 | { | |
272 | mp *a = *(mp **)v[0].buf; | |
273 | int r = *(int *)v[1].buf; | |
274 | int c = gf_irreduciblep(a); | |
275 | int ok = 1; | |
276 | if (r != c) { | |
277 | ok = 0; | |
278 | fprintf(stderr, "\n*** irred failed"); | |
45c0fd36 MW |
279 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 16); |
280 | fprintf(stderr, "\n*** r = %d\n", r); | |
281 | fprintf(stderr, "*** c = %d\n", c); | |
432c4e18 | 282 | } |
283 | mp_drop(a); | |
284 | assert(mparena_count(MPARENA_GLOBAL) == 0); | |
285 | return (ok); | |
286 | } | |
287 | ||
ceb3f0c0 | 288 | static test_chunk tests[] = { |
289 | { "add", tadd, { &type_mp, &type_mp, &type_mp, 0 } }, | |
290 | { "mul", tmul, { &type_mp, &type_mp, &type_mp, 0 } }, | |
291 | { "sqr", tsqr, { &type_mp, &type_mp, 0 } }, | |
292 | { "div", tdiv, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, | |
f4535c64 | 293 | { "exp", texp, { &type_mp, &type_mp, &type_mp, 0 } }, |
432c4e18 | 294 | { "irred", tirred, { &type_mp, &type_int, 0 } }, |
ceb3f0c0 | 295 | { 0, 0, { 0 } }, |
296 | }; | |
297 | ||
298 | int main(int argc, char *argv[]) | |
299 | { | |
300 | sub_init(); | |
0f00dc4c | 301 | test_run(argc, argv, tests, SRCDIR "/t/gf"); |
ceb3f0c0 | 302 | return (0); |
303 | } | |
304 | ||
305 | #endif | |
306 | ||
307 | /*----- That's all, folks -------------------------------------------------*/ |