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1 | /* -*-c-*- |
2 | * |
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3 | * $Id$ |
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4 | * |
5 | * Basic arithmetic on binary polynomials |
6 | * |
7 | * (c) 2004 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 "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); |
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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); |
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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 | |
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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 | { |
182 | unsigned long m = mp_bits(f) - 1; |
183 | mp *u = MP_TWO; |
184 | mp *v = MP_NEW; |
185 | |
186 | m /= 2; |
187 | while (m) { |
188 | u = gf_sqr(u, u); |
189 | gf_div(0, &u, u, f); |
190 | v = gf_add(v, u, MP_TWO); |
191 | gf_gcd(&v, 0, 0, v, f); |
192 | if (!MP_EQ(v, MP_ONE)) break; |
193 | m--; |
194 | } |
195 | MP_DROP(u); |
196 | MP_DROP(v); |
197 | return (!m); |
198 | } |
199 | |
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200 | /*----- Test rig ----------------------------------------------------------*/ |
201 | |
202 | #ifdef TEST_RIG |
203 | |
204 | static int verify(const char *op, mp *expect, mp *result, mp *a, mp *b) |
205 | { |
206 | if (!MP_EQ(expect, result)) { |
207 | fprintf(stderr, "\n*** %s failed", op); |
208 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 16); |
209 | fputs("\n*** b = ", stderr); mp_writefile(b, stderr, 16); |
210 | fputs("\n*** result = ", stderr); mp_writefile(result, stderr, 16); |
211 | fputs("\n*** expect = ", stderr); mp_writefile(expect, stderr, 16); |
212 | fputc('\n', stderr); |
213 | return (0); |
214 | } |
215 | return (1); |
216 | } |
217 | |
218 | #define RIG(name, op) \ |
219 | static int t##name(dstr *v) \ |
220 | { \ |
221 | mp *a = *(mp **)v[0].buf; \ |
222 | mp *b = *(mp **)v[1].buf; \ |
223 | mp *r = *(mp **)v[2].buf; \ |
224 | mp *c = op(MP_NEW, a, b); \ |
225 | int ok = verify(#name, r, c, a, b); \ |
226 | mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(r); \ |
227 | assert(mparena_count(MPARENA_GLOBAL) == 0); \ |
228 | return (ok); \ |
229 | } |
230 | |
231 | RIG(add, gf_add) |
232 | RIG(mul, gf_mul) |
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233 | RIG(exp, gf_exp) |
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234 | |
235 | #undef RIG |
236 | |
237 | static int tsqr(dstr *v) |
238 | { |
239 | mp *a = *(mp **)v[0].buf; |
240 | mp *r = *(mp **)v[1].buf; |
241 | mp *c = MP_NEW; |
242 | int ok = 1; |
243 | c = gf_sqr(MP_NEW, a); |
244 | ok &= verify("sqr", r, c, a, MP_ZERO); |
245 | mp_drop(a); mp_drop(r); mp_drop(c); |
246 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
247 | return (ok); |
248 | } |
249 | |
250 | static int tdiv(dstr *v) |
251 | { |
252 | mp *a = *(mp **)v[0].buf; |
253 | mp *b = *(mp **)v[1].buf; |
254 | mp *q = *(mp **)v[2].buf; |
255 | mp *r = *(mp **)v[3].buf; |
256 | mp *c = MP_NEW, *d = MP_NEW; |
257 | int ok = 1; |
258 | gf_div(&c, &d, a, b); |
259 | ok &= verify("div(quotient)", q, c, a, b); |
260 | ok &= verify("div(remainder)", r, d, a, b); |
261 | mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(d); mp_drop(r); mp_drop(q); |
262 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
263 | return (ok); |
264 | } |
265 | |
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266 | static int tirred(dstr *v) |
267 | { |
268 | mp *a = *(mp **)v[0].buf; |
269 | int r = *(int *)v[1].buf; |
270 | int c = gf_irreduciblep(a); |
271 | int ok = 1; |
272 | if (r != c) { |
273 | ok = 0; |
274 | fprintf(stderr, "\n*** irred failed"); |
275 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 16); |
276 | fprintf(stderr, "\n*** r = %d\n", r); |
277 | fprintf(stderr, "*** c = %d\n", c); |
278 | } |
279 | mp_drop(a); |
280 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
281 | return (ok); |
282 | } |
283 | |
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284 | static test_chunk tests[] = { |
285 | { "add", tadd, { &type_mp, &type_mp, &type_mp, 0 } }, |
286 | { "mul", tmul, { &type_mp, &type_mp, &type_mp, 0 } }, |
287 | { "sqr", tsqr, { &type_mp, &type_mp, 0 } }, |
288 | { "div", tdiv, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
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289 | { "exp", texp, { &type_mp, &type_mp, &type_mp, 0 } }, |
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290 | { "irred", tirred, { &type_mp, &type_int, 0 } }, |
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291 | { 0, 0, { 0 } }, |
292 | }; |
293 | |
294 | int main(int argc, char *argv[]) |
295 | { |
296 | sub_init(); |
297 | test_run(argc, argv, tests, SRCDIR "/tests/gf"); |
298 | return (0); |
299 | } |
300 | |
301 | #endif |
302 | |
303 | /*----- That's all, folks -------------------------------------------------*/ |