Mercurial > hg > Members > anatofuz > MoarVM

annotate 3rdparty/libtommath/bn_mp_n_root_ex.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
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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_N_ROOT_EX_C
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
3 /* LibTomMath, multiple-precision integer library -- Tom St Denis
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
4 *
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
5 * LibTomMath is a library that provides multiple-precision
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
6 * integer arithmetic as well as number theoretic functionality.
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
7 *
2cf249471370 convert mercurial for git
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
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
10 * additional optimizations in place.
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
11 *
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
12 * The library is free for all purposes without any express
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
13 * guarantee it works.
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
14 *
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
15 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
16 */
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
17
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
18 /* find the n'th root of an integer
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
19 *
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
20 * Result found such that (c)**b <= a and (c+1)**b > a
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
21 *
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
22 * This algorithm uses Newton's approximation
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
23 * x[i+1] = x[i] - f(x[i])/f'(x[i])
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
24 * which will find the root in log(N) time where
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
25 * each step involves a fair bit. This is not meant to
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
26 * find huge roots [square and cube, etc].
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
27 */
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
28 int mp_n_root_ex (mp_int * a, mp_digit b, mp_int * c, int fast)
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
29 {
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
30 mp_int t1, t2, t3;
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
31 int res, neg;
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
32
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
33 /* input must be positive if b is even */
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
34 if (((b & 1) == 0) && (a->sign == MP_NEG)) {
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
35 return MP_VAL;
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
36 }
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
37
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
38 if ((res = mp_init (&t1)) != MP_OKAY) {
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
39 return res;
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
40 }
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
41
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
42 if ((res = mp_init (&t2)) != MP_OKAY) {
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
43 goto LBL_T1;
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
44 }
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
45
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
46 if ((res = mp_init (&t3)) != MP_OKAY) {
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
47 goto LBL_T2;
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
48 }
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
49
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
50 /* if a is negative fudge the sign but keep track */
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
51 neg = a->sign;
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
52 a->sign = MP_ZPOS;
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
53
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
54 /* t2 = 2 */
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
55 mp_set (&t2, 2);
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
56
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
57 do {
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
58 /* t1 = t2 */
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
59 if ((res = mp_copy (&t2, &t1)) != MP_OKAY) {
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
60 goto LBL_T3;
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
61 }
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
62
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
63 /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
64
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
65 /* t3 = t1**(b-1) */
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
66 if ((res = mp_expt_d_ex (&t1, b - 1, &t3, fast)) != MP_OKAY) {
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
67 goto LBL_T3;
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
68 }
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
69
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
70 /* numerator */
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
71 /* t2 = t1**b */
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
72 if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) {
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
73 goto LBL_T3;
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
74 }
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
75
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
76 /* t2 = t1**b - a */
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
77 if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) {
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
78 goto LBL_T3;
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
79 }
2cf249471370 convert mercurial for git
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 /* denominator */
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
82 /* t3 = t1**(b-1) * b */
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
83 if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) {
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
84 goto LBL_T3;
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
85 }
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
86
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
87 /* t3 = (t1**b - a)/(b * t1**(b-1)) */
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
88 if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) {
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
89 goto LBL_T3;
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
90 }
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 if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) {
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
93 goto LBL_T3;
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
94 }
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
95 } while (mp_cmp (&t1, &t2) != MP_EQ);
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
96
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
97 /* result can be off by a few so check */
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
98 for (;;) {
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
99 if ((res = mp_expt_d_ex (&t1, b, &t2, fast)) != MP_OKAY) {
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
100 goto LBL_T3;
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
101 }
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
102
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
103 if (mp_cmp (&t2, a) == MP_GT) {
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
104 if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) {
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
105 goto LBL_T3;
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
106 }
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
107 } else {
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
108 break;
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
109 }
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
110 }
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
111
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
112 /* reset the sign of a first */
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
113 a->sign = neg;
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
114
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
115 /* set the result */
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
116 mp_exch (&t1, c);
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
117
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
118 /* set the sign of the result */
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
119 c->sign = neg;
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
120
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
121 res = MP_OKAY;
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
122
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
123 LBL_T3:mp_clear (&t3);
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
124 LBL_T2:mp_clear (&t2);
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
125 LBL_T1:mp_clear (&t1);
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
126 return res;
2cf249471370 convert mercurial for git
Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
127 }
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128 #endif
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129
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130 /* $Source$ */
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131 /* $Revision$ */
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132 /* $Date$ */