3 * $Id: gf-arith.c,v 1.3 2004/03/27 17:54:11 mdw Exp $
5 * Basic arithmetic on binary polynomials
7 * (c) 2004 Straylight/Edgeware
10 /*----- Licensing notice --------------------------------------------------*
12 * This file is part of Catacomb.
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.
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.
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,
30 /*----- Revision history --------------------------------------------------*
32 * $Log: gf-arith.c,v $
33 * Revision 1.3 2004/03/27 17:54:11 mdw
34 * Standard curves and curve checking.
36 * Revision 1.2 2004/03/21 22:52:06 mdw
37 * Merge and close elliptic curve branch.
39 * Revision 1.1.2.1 2004/03/21 22:39:46 mdw
40 * Elliptic curves on binary fields work.
44 /*----- Header files ------------------------------------------------------*/
48 /*----- Macros ------------------------------------------------------------*/
50 #define MAX(x, y) ((x) >= (y) ? (x) : (y))
52 /*----- Main code ---------------------------------------------------------*/
56 * Arguments: @mp *d@ = destination
57 * @mp *a, *b@ = sources
59 * Returns: Result, @a@ added to @b@.
62 mp
*gf_add(mp
*d
, mp
*a
, mp
*b
)
64 MP_DEST(d
, MAX(MP_LEN(a
), MP_LEN(b
)), (a
->f
| b
->f
) & MP_BURN
);
65 gfx_add(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
);
66 d
->f
= (a
->f
| b
->f
) & MP_BURN
;
73 * Arguments: @mp *d@ = destination
74 * @mp *a, *b@ = sources
76 * Returns: Result, @a@ multiplied by @b@.
79 mp
*gf_mul(mp
*d
, mp
*a
, mp
*b
)
84 if (MP_LEN(a
) <= MPK_THRESH
|| MP_LEN(b
) <= GFK_THRESH
) {
85 MP_DEST(d
, MP_LEN(a
) + MP_LEN(b
), a
->f
| b
->f
| MP_UNDEF
);
86 gfx_mul(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
);
88 size_t m
= MAX(MP_LEN(a
), MP_LEN(b
));
90 MP_DEST(d
, 2 * m
, a
->f
| b
->f
| MP_UNDEF
);
91 s
= mpalloc(d
->a
, 3 * m
);
92 gfx_kmul(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
, s
, s
+ 3 * m
);
96 d
->f
= (a
->f
| b
->f
) & MP_BURN
;
103 /* --- @gf_sqr@ --- *
105 * Arguments: @mp *d@ = destination
108 * Returns: Result, @a@ squared.
111 mp
*gf_sqr(mp
*d
, mp
*a
)
114 MP_DEST(d
, 2 * MP_LEN(a
), a
->f
& MP_BURN
);
115 gfx_sqr(d
->v
, d
->vl
, a
->v
, a
->vl
);
116 d
->f
= a
->f
& MP_BURN
;
122 /* --- @gf_div@ --- *
124 * Arguments: @mp **qq, **rr@ = destination, quotient and remainder
125 * @mp *a, *b@ = sources
127 * Use: Calculates the quotient and remainder when @a@ is divided by
128 * @b@. The destinations @*qq@ and @*rr@ must be distinct.
129 * Either of @qq@ or @rr@ may be null to indicate that the
130 * result is irrelevant. (Discarding both results is silly.)
131 * There is a performance advantage if @a == *rr@.
134 void gf_div(mp
**qq
, mp
**rr
, mp
*a
, mp
*b
)
136 mp
*r
= rr ?
*rr
: MP_NEW
;
137 mp
*q
= qq ?
*qq
: MP_NEW
;
139 /* --- Set the remainder up right --- */
146 MP_DEST(r
, MP_LEN(b
) + 2, a
->f
| b
->f
);
148 /* --- Fix up the quotient too --- */
151 MP_DEST(q
, MP_LEN(r
), r
->f
| MP_UNDEF
);
154 /* --- Perform the calculation --- */
156 gfx_div(q
->v
, q
->vl
, r
->v
, r
->vl
, b
->v
, b
->vl
);
158 /* --- Sort out the sign of the results --- *
160 * If the signs of the arguments differ, and the remainder is nonzero, I
161 * must add one to the absolute value of the quotient and subtract the
162 * remainder from @b@.
165 q
->f
= (r
->f
| b
->f
) & MP_BURN
;
166 r
->f
= (r
->f
| b
->f
) & MP_BURN
;
168 /* --- Store the return values --- */
187 /* --- @gf_irreduciblep@ --- *
189 * Arguments: @mp *f@ = a polynomial
191 * Returns: Nonzero if the polynomial is irreducible; otherwise zero.
194 int gf_irreduciblep(mp
*f
)
196 unsigned long m
= mp_bits(f
) - 1;
204 v
= gf_add(v
, u
, MP_TWO
);
205 gf_gcd(&v
, 0, 0, v
, f
);
206 if (!MP_EQ(v
, MP_ONE
)) break;
214 /*----- Test rig ----------------------------------------------------------*/
218 static int verify(const char *op
, mp
*expect
, mp
*result
, mp
*a
, mp
*b
)
220 if (!MP_EQ(expect
, result
)) {
221 fprintf(stderr
, "\n*** %s failed", op
);
222 fputs("\n*** a = ", stderr
); mp_writefile(a
, stderr
, 16);
223 fputs("\n*** b = ", stderr
); mp_writefile(b
, stderr
, 16);
224 fputs("\n*** result = ", stderr
); mp_writefile(result
, stderr
, 16);
225 fputs("\n*** expect = ", stderr
); mp_writefile(expect
, stderr
, 16);
232 #define RIG(name, op) \
233 static int t##name(dstr *v) \
235 mp *a = *(mp **)v[0].buf; \
236 mp *b = *(mp **)v[1].buf; \
237 mp *r = *(mp **)v[2].buf; \
238 mp *c = op(MP_NEW, a, b); \
239 int ok = verify(#name, r, c, a, b); \
240 mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(r); \
241 assert(mparena_count(MPARENA_GLOBAL) == 0); \
250 static int tsqr(dstr
*v
)
252 mp
*a
= *(mp
**)v
[0].buf
;
253 mp
*r
= *(mp
**)v
[1].buf
;
256 c
= gf_sqr(MP_NEW
, a
);
257 ok
&= verify("sqr", r
, c
, a
, MP_ZERO
);
258 mp_drop(a
); mp_drop(r
); mp_drop(c
);
259 assert(mparena_count(MPARENA_GLOBAL
) == 0);
263 static int tdiv(dstr
*v
)
265 mp
*a
= *(mp
**)v
[0].buf
;
266 mp
*b
= *(mp
**)v
[1].buf
;
267 mp
*q
= *(mp
**)v
[2].buf
;
268 mp
*r
= *(mp
**)v
[3].buf
;
269 mp
*c
= MP_NEW
, *d
= MP_NEW
;
271 gf_div(&c
, &d
, a
, b
);
272 ok
&= verify("div(quotient)", q
, c
, a
, b
);
273 ok
&= verify("div(remainder)", r
, d
, a
, b
);
274 mp_drop(a
); mp_drop(b
); mp_drop(c
); mp_drop(d
); mp_drop(r
); mp_drop(q
);
275 assert(mparena_count(MPARENA_GLOBAL
) == 0);
279 static int tirred(dstr
*v
)
281 mp
*a
= *(mp
**)v
[0].buf
;
282 int r
= *(int *)v
[1].buf
;
283 int c
= gf_irreduciblep(a
);
287 fprintf(stderr
, "\n*** irred failed");
288 fputs("\n*** a = ", stderr
); mp_writefile(a
, stderr
, 16);
289 fprintf(stderr
, "\n*** r = %d\n", r
);
290 fprintf(stderr
, "*** c = %d\n", c
);
293 assert(mparena_count(MPARENA_GLOBAL
) == 0);
297 static test_chunk tests
[] = {
298 { "add", tadd
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
299 { "mul", tmul
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
300 { "sqr", tsqr
, { &type_mp
, &type_mp
, 0 } },
301 { "div", tdiv
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
, 0 } },
302 { "irred", tirred
, { &type_mp
, &type_int
, 0 } },
306 int main(int argc
, char *argv
[])
309 test_run(argc
, argv
, tests
, SRCDIR
"/tests/gf");
315 /*----- That's all, folks -------------------------------------------------*/