1#include <tommath.h>
2#ifdef BN_MP_EXTEUCLID_C
3/* LibTomMath, multiple-precision integer library -- Tom St Denis
4 *
5 * LibTomMath is a library that provides multiple-precision
6 * integer arithmetic as well as number theoretic functionality.
7 *
8 * The library was designed directly after the MPI library by
9 * Michael Fromberger but has been written from scratch with
10 * additional optimizations in place.
11 *
12 * The library is free for all purposes without any express
13 * guarantee it works.
14 *
15 * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
16 */
17
18/* Extended euclidean algorithm of (a, b) produces
19   a*u1 + b*u2 = u3
20 */
21int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3)
22{
23   mp_int u1,u2,u3,v1,v2,v3,t1,t2,t3,q,tmp;
24   int err;
25
26   if ((err = mp_init_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL)) != MP_OKAY) {
27      return err;
28   }
29
30   /* initialize, (u1,u2,u3) = (1,0,a) */
31   mp_set(&u1, 1);
32   if ((err = mp_copy(a, &u3)) != MP_OKAY)                                        { goto _ERR; }
33
34   /* initialize, (v1,v2,v3) = (0,1,b) */
35   mp_set(&v2, 1);
36   if ((err = mp_copy(b, &v3)) != MP_OKAY)                                        { goto _ERR; }
37
38   /* loop while v3 != 0 */
39   while (mp_iszero(&v3) == MP_NO) {
40       /* q = u3/v3 */
41       if ((err = mp_div(&u3, &v3, &q, NULL)) != MP_OKAY)                         { goto _ERR; }
42
43       /* (t1,t2,t3) = (u1,u2,u3) - (v1,v2,v3)q */
44       if ((err = mp_mul(&v1, &q, &tmp)) != MP_OKAY)                              { goto _ERR; }
45       if ((err = mp_sub(&u1, &tmp, &t1)) != MP_OKAY)                             { goto _ERR; }
46       if ((err = mp_mul(&v2, &q, &tmp)) != MP_OKAY)                              { goto _ERR; }
47       if ((err = mp_sub(&u2, &tmp, &t2)) != MP_OKAY)                             { goto _ERR; }
48       if ((err = mp_mul(&v3, &q, &tmp)) != MP_OKAY)                              { goto _ERR; }
49       if ((err = mp_sub(&u3, &tmp, &t3)) != MP_OKAY)                             { goto _ERR; }
50
51       /* (u1,u2,u3) = (v1,v2,v3) */
52       if ((err = mp_copy(&v1, &u1)) != MP_OKAY)                                  { goto _ERR; }
53       if ((err = mp_copy(&v2, &u2)) != MP_OKAY)                                  { goto _ERR; }
54       if ((err = mp_copy(&v3, &u3)) != MP_OKAY)                                  { goto _ERR; }
55
56       /* (v1,v2,v3) = (t1,t2,t3) */
57       if ((err = mp_copy(&t1, &v1)) != MP_OKAY)                                  { goto _ERR; }
58       if ((err = mp_copy(&t2, &v2)) != MP_OKAY)                                  { goto _ERR; }
59       if ((err = mp_copy(&t3, &v3)) != MP_OKAY)                                  { goto _ERR; }
60   }
61
62   /* make sure U3 >= 0 */
63   if (u3.sign == MP_NEG) {
64      mp_neg(&u1, &u1);
65      mp_neg(&u2, &u2);
66      mp_neg(&u3, &u3);
67   }
68
69   /* copy result out */
70   if (U1 != NULL) { mp_exch(U1, &u1); }
71   if (U2 != NULL) { mp_exch(U2, &u2); }
72   if (U3 != NULL) { mp_exch(U3, &u3); }
73
74   err = MP_OKAY;
75_ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL);
76   return err;
77}
78#endif
79
80/* $Source: /cvs/libtom/libtommath/bn_mp_exteuclid.c,v $ */
81/* $Revision: 1.4 $ */
82/* $Date: 2006/12/28 01:25:13 $ */
83