5 * Extended GCD calculation
7 * (c) 1999 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 /*----- Header files ------------------------------------------------------*/
34 /*----- Main code ---------------------------------------------------------*/
38 * Arguments: @mp **gcd, **xx, **yy@ = where to write the results
39 * @mp *a, *b@ = sources (must be nonzero)
43 * Use: Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that
44 * @ax + by = gcd(a, b)@. This is useful for computing modular
48 void mp_gcd(mp
**gcd
, mp
**xx
, mp
**yy
, mp
*a
, mp
*b
)
50 mp
*x
= MP_ONE
, *X
= MP_ZERO
;
51 mp
*y
= MP_ZERO
, *Y
= MP_ONE
;
61 /* --- Sort out some initial flags --- */
71 /* --- Ensure that @a@ is larger than @b@ --- *
73 * Use absolute values here!
76 if (MPX_UCMP(a
->v
, a
->vl
, <, b
->v
, b
->vl
)) {
77 { mp
*t
= a
; a
= b
; b
= t
; }
81 /* --- Check for zeroness --- */
83 if (MP_EQ(b
, MP_ZERO
)) {
85 /* --- Store %$|a|$% as the GCD --- */
88 if (*gcd
) MP_DROP(*gcd
);
98 /* --- Store %$1$% and %$0$% in the appropriate bins --- */
102 mp
**t
= xx
; xx
= yy
; yy
= t
;
105 if (*xx
) MP_DROP(*xx
);
106 if (MP_EQ(a
, MP_ZERO
))
114 if (*yy
) MP_DROP(*yy
);
121 /* --- Force the signs on the arguments and take copies --- */
126 MP_SPLIT(a
); a
->f
&= ~MP_NEG
;
127 MP_SPLIT(b
); b
->f
&= ~MP_NEG
;
132 /* --- Main extended Euclidean algorithm --- */
134 while (!MP_ZEROP(v
)) {
136 mp_div(&q
, &u
, u
, v
);
138 t
= mp_mul(MP_NEW
, X
, q
);
140 MP_DROP(x
); x
= X
; X
= t
;
141 t
= mp_mul(MP_NEW
, Y
, q
);
143 MP_DROP(y
); y
= Y
; Y
= t
;
152 if (*gcd
) MP_DROP(*gcd
);
157 /* --- Perform a little normalization --- *
159 * Ensure that the coefficient returned is positive, if there is only one.
160 * If there are two, favour @y@. Of course, if the original arguments were
161 * negative then I'll need to twiddle their signs as well.
166 /* --- If @a@ and @b@ got swapped, swap the coefficients back --- */
169 mp
*t
= x
; x
= y
; y
= t
;
173 /* --- Sort out the signs --- *
175 * Note that %$ax + by = a(x - b) + b(y + a)$%.
177 * This is currently bodgy. It needs sorting out at some time.
185 } while (MP_NEGP(y
));
187 while (MP_CMP(y
, >=, a
)) {
198 while (MP_CMP(x
, >=, b
))
203 /* --- Twiddle the signs --- */
210 /* --- Store the results --- */
215 if (*xx
) MP_DROP(*xx
);
222 if (*yy
) MP_DROP(*yy
);
228 MP_DROP(X
); MP_DROP(Y
);
229 MP_DROP(a
); MP_DROP(b
);
232 /* -- @mp_modinv@ --- *
234 * Arguments: @mp *d@ = destination
238 * Returns: The inverse %$x^{-1} \bmod p$%.
240 * Use: Computes a modular inverse. An assertion fails if %$p$%
244 mp
*mp_modinv(mp
*d
, mp
*x
, mp
*p
)
247 mp_gcd(&g
, 0, &d
, p
, x
);
248 assert(MP_EQ(g
, MP_ONE
));
253 /*----- Test rig ----------------------------------------------------------*/
257 static int modinv(dstr
*v
)
260 mp
*x
= *(mp
**)v
[0].buf
;
261 mp
*m
= *(mp
**)v
[1].buf
;
262 mp
*r
= *(mp
**)v
[2].buf
;
264 mp
*y
= mp_modinv(MP_NEW
, x
, m
);
266 fputs("\n*** mp_modinv failed", stderr
);
267 fputs("\nx = ", stderr
); mp_writefile(x
, stderr
, 10);
268 fputs("\nm = ", stderr
); mp_writefile(m
, stderr
, 10);
269 fputs("\nexpect = ", stderr
); mp_writefile(r
, stderr
, 10);
270 fputs("\nresult = ", stderr
); mp_writefile(y
, stderr
, 10);
273 MP_DROP(x
); MP_DROP(m
); MP_DROP(r
); MP_DROP(y
);
274 assert(mparena_count(MPARENA_GLOBAL
) == 0);
278 static int gcd(dstr
*v
)
281 mp
*a
= *(mp
**)v
[0].buf
;
282 mp
*b
= *(mp
**)v
[1].buf
;
283 mp
*g
= *(mp
**)v
[2].buf
;
284 mp
*x
= *(mp
**)v
[3].buf
;
285 mp
*y
= *(mp
**)v
[4].buf
;
287 mp
*gg
= MP_NEW
, *xx
= MP_NEW
, *yy
= MP_NEW
;
288 mp_gcd(&gg
, &xx
, &yy
, a
, b
);
290 fputs("\n*** mp_gcd(x) failed", stderr
);
291 fputs("\na = ", stderr
); mp_writefile(a
, stderr
, 10);
292 fputs("\nb = ", stderr
); mp_writefile(b
, stderr
, 10);
293 fputs("\nexpect = ", stderr
); mp_writefile(x
, stderr
, 10);
294 fputs("\nresult = ", stderr
); mp_writefile(xx
, stderr
, 10);
299 fputs("\n*** mp_gcd(y) failed", stderr
);
300 fputs("\na = ", stderr
); mp_writefile(a
, stderr
, 10);
301 fputs("\nb = ", stderr
); mp_writefile(b
, stderr
, 10);
302 fputs("\nexpect = ", stderr
); mp_writefile(y
, stderr
, 10);
303 fputs("\nresult = ", stderr
); mp_writefile(yy
, stderr
, 10);
309 mp
*ax
= mp_mul(MP_NEW
, a
, xx
);
310 mp
*by
= mp_mul(MP_NEW
, b
, yy
);
311 ax
= mp_add(ax
, ax
, by
);
313 fputs("\n*** (Alternative result found.)\n", stderr
);
319 fputs("\n*** mp_gcd(gcd) failed", stderr
);
320 fputs("\na = ", stderr
); mp_writefile(a
, stderr
, 10);
321 fputs("\nb = ", stderr
); mp_writefile(b
, stderr
, 10);
322 fputs("\nexpect = ", stderr
); mp_writefile(g
, stderr
, 10);
323 fputs("\nresult = ", stderr
); mp_writefile(gg
, stderr
, 10);
327 MP_DROP(a
); MP_DROP(b
); MP_DROP(g
); MP_DROP(x
); MP_DROP(y
);
328 MP_DROP(gg
); MP_DROP(xx
); MP_DROP(yy
);
329 assert(mparena_count(MPARENA_GLOBAL
) == 0);
333 static test_chunk tests
[] = {
334 { "gcd", gcd
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
, &type_mp
, 0 } },
335 { "modinv", modinv
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
339 int main(int argc
, char *argv
[])
342 test_run(argc
, argv
, tests
, SRCDIR
"/tests/mp");
348 /*----- That's all, folks -------------------------------------------------*/