3 * Basic arithmetic on binary polynomials
5 * (c) 2004 Straylight/Edgeware
8 /*----- Licensing notice --------------------------------------------------*
10 * This file is part of Catacomb.
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
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17 * Catacomb is distributed in the hope that it will be useful,
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19 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
20 * GNU Library General Public License for more details.
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,
28 /*----- Header files ------------------------------------------------------*/
32 /*----- Macros ------------------------------------------------------------*/
34 #define MAX(x, y) ((x) >= (y) ? (x) : (y))
36 /*----- Main code ---------------------------------------------------------*/
40 * Arguments: @mp *d@ = destination
41 * @mp *a, *b@ = sources
43 * Returns: Result, @a@ added to @b@.
46 mp *gf_add(mp *d, mp *a, mp *b)
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;
57 * Arguments: @mp *d@ = destination
58 * @mp *a, *b@ = sources
60 * Returns: Result, @a@ multiplied by @b@.
63 mp *gf_mul(mp *d, mp *a, mp *b)
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);
72 size_t m = MAX(MP_LEN(a), MP_LEN(b));
74 MP_DEST(d, 2 * m, a->f | b->f | MP_UNDEF);
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);
80 d->f = (a->f | b->f) & MP_BURN;
89 * Arguments: @mp *d@ = destination
92 * Returns: Result, @a@ squared.
95 mp *gf_sqr(mp *d, mp *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;
106 /* --- @gf_div@ --- *
108 * Arguments: @mp **qq, **rr@ = destination, quotient and remainder
109 * @mp *a, *b@ = sources
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@.
118 void gf_div(mp **qq, mp **rr, mp *a, mp *b)
120 mp *r = rr ? *rr : MP_NEW;
121 mp *q = qq ? *qq : MP_NEW;
123 /* --- Set the remainder up right --- */
130 MP_DEST(r, MP_LEN(b) + 2, a->f | b->f);
132 /* --- Fix up the quotient too --- */
135 MP_DEST(q, MP_LEN(r), r->f | MP_UNDEF);
138 /* --- Perform the calculation --- */
140 gfx_div(q->v, q->vl, r->v, r->vl, b->v, b->vl);
142 /* --- Sort out the sign of the results --- *
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@.
149 q->f = (r->f | b->f) & MP_BURN;
150 r->f = (r->f | b->f) & MP_BURN;
152 /* --- Store the return values --- */
171 /* --- @gf_irreduciblep@ --- *
173 * Arguments: @mp *f@ = a polynomial
175 * Returns: Nonzero if the polynomial is irreducible; otherwise zero.
178 int gf_irreduciblep(mp *f)
186 else if (MP_LEN(f) == 1) {
187 if (f->v[0] < 2) return (0);
188 if (f->v[0] < 4) return (1);
190 m = (mp_bits(f) - 1)/2;
194 v = gf_add(v, u, MP_TWO);
195 gf_gcd(&v, 0, 0, v, f);
196 if (!MP_EQ(v, MP_ONE)) break;
204 /*----- Test rig ----------------------------------------------------------*/
208 static int verify(const char *op, mp *expect, mp *result, mp *a, mp *b)
210 if (!MP_EQ(expect, result)) {
211 fprintf(stderr, "\n*** %s failed", op);
212 fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 16);
213 fputs("\n*** b = ", stderr); mp_writefile(b, stderr, 16);
214 fputs("\n*** result = ", stderr); mp_writefile(result, stderr, 16);
215 fputs("\n*** expect = ", stderr); mp_writefile(expect, stderr, 16);
222 #define RIG(name, op) \
223 static int t##name(dstr *v) \
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); \
241 static int tsqr(dstr *v)
243 mp *a = *(mp **)v[0].buf;
244 mp *r = *(mp **)v[1].buf;
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);
254 static int tdiv(dstr *v)
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;
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);
270 static int tirred(dstr *v)
272 mp *a = *(mp **)v[0].buf;
273 int r = *(int *)v[1].buf;
274 int c = gf_irreduciblep(a);
278 fprintf(stderr, "\n*** irred failed");
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);
284 assert(mparena_count(MPARENA_GLOBAL) == 0);
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 } },
293 { "exp", texp, { &type_mp, &type_mp, &type_mp, 0 } },
294 { "irred", tirred, { &type_mp, &type_int, 0 } },
298 int main(int argc, char *argv[])
301 test_run(argc, argv, tests, SRCDIR "/t/gf");
307 /*----- That's all, folks -------------------------------------------------*/