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annotate 3rdparty/libtommath/bn_mp_jacobi.c @ 0:2cf249471370

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convert mercurial for git
author Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
date Tue, 08 May 2018 16:09:12 +0900
parents
children
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rev   line source
0
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
1 #include <tommath_private.h>
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
2 #ifdef BN_MP_JACOBI_C
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
3 /* LibTomMath, multiple-precision integer library -- Tom St Denis
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
4 *
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
5 * LibTomMath is a library that provides multiple-precision
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
6 * integer arithmetic as well as number theoretic functionality.
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
7 *
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
8 * The library was designed directly after the MPI library by
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
9 * Michael Fromberger but has been written from scratch with
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
10 * additional optimizations in place.
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
11 *
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
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12 * The library is free for all purposes without any express
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
13 * guarantee it works.
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
14 *
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
15 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
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16 */
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
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17
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
18 /* computes the jacobi c = (a | n) (or Legendre if n is prime)
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
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19 * HAC pp. 73 Algorithm 2.149
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
20 * HAC is wrong here, as the special case of (0 | 1) is not
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
21 * handled correctly.
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
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22 */
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
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23 int mp_jacobi (mp_int * a, mp_int * n, int *c)
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
24 {
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
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25 mp_int a1, p1;
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
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26 int k, s, r, res;
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
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27 mp_digit residue;
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
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28
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
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29 /* if a < 0 return MP_VAL */
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
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30 if (mp_isneg(a) == MP_YES) {
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
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31 return MP_VAL;
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
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32 }
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
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33
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
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34 /* if n <= 0 return MP_VAL */
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
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35 if (mp_cmp_d(n, 0) != MP_GT) {
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
36 return MP_VAL;
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
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37 }
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
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38
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
39 /* step 1. handle case of a == 0 */
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
40 if (mp_iszero (a) == MP_YES) {
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
41 /* special case of a == 0 and n == 1 */
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
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42 if (mp_cmp_d (n, 1) == MP_EQ) {
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
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43 *c = 1;
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
44 } else {
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
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45 *c = 0;
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
46 }
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
47 return MP_OKAY;
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
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48 }
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
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49
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
50 /* step 2. if a == 1, return 1 */
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
51 if (mp_cmp_d (a, 1) == MP_EQ) {
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
52 *c = 1;
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
53 return MP_OKAY;
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
54 }
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
55
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
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56 /* default */
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
57 s = 0;
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
58
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
59 /* step 3. write a = a1 * 2**k */
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
60 if ((res = mp_init_copy (&a1, a)) != MP_OKAY) {
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
61 return res;
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
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62 }
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
63
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
64 if ((res = mp_init (&p1)) != MP_OKAY) {
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
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65 goto LBL_A1;
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
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66 }
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
67
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
68 /* divide out larger power of two */
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
69 k = mp_cnt_lsb(&a1);
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
70 if ((res = mp_div_2d(&a1, k, &a1, NULL)) != MP_OKAY) {
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
71 goto LBL_P1;
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
72 }
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
73
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
74 /* step 4. if e is even set s=1 */
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
75 if ((k & 1) == 0) {
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
76 s = 1;
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
77 } else {
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
78 /* else set s=1 if p = 1/7 (mod 8) or s=-1 if p = 3/5 (mod 8) */
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
79 residue = n->dp[0] & 7;
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
80
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
81 if ((residue == 1) || (residue == 7)) {
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
82 s = 1;
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
83 } else if ((residue == 3) || (residue == 5)) {
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
84 s = -1;
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
85 }
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
86 }
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
87
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
88 /* step 5. if p == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
89 if ( ((n->dp[0] & 3) == 3) && ((a1.dp[0] & 3) == 3)) {
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
90 s = -s;
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
91 }
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
92
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
93 /* if a1 == 1 we're done */
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
94 if (mp_cmp_d (&a1, 1) == MP_EQ) {
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
95 *c = s;
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
96 } else {
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
97 /* n1 = n mod a1 */
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
98 if ((res = mp_mod (n, &a1, &p1)) != MP_OKAY) {
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
99 goto LBL_P1;
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
100 }
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
101 if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) {
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
102 goto LBL_P1;
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
103 }
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
104 *c = s * r;
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
105 }
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
106
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
107 /* done */
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
108 res = MP_OKAY;
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
109 LBL_P1:mp_clear (&p1);
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
110 LBL_A1:mp_clear (&a1);
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
111 return res;
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
112 }
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
113 #endif
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
114
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
115 /* $Source$ */
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
116 /* $Revision$ */
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
117 /* $Date$ */