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comparison bn_mp_n_root.c @ 2:86e0b50a9b58 libtommath-orig ltm-0.30-orig

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ltm 0.30 orig import
author Matt Johnston <matt@ucc.asn.au>
date Mon, 31 May 2004 18:25:22 +0000
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children d29b64170cf0
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-1:000000000000 2:86e0b50a9b58
1 /* LibTomMath, multiple-precision integer library -- Tom St Denis
2 *
3 * LibTomMath is a library that provides multiple-precision
4 * integer arithmetic as well as number theoretic functionality.
5 *
6 * The library was designed directly after the MPI library by
7 * Michael Fromberger but has been written from scratch with
8 * additional optimizations in place.
9 *
10 * The library is free for all purposes without any express
11 * guarantee it works.
12 *
13 * Tom St Denis, [email protected], http://math.libtomcrypt.org
14 */
15 #include <tommath.h>
16
17 /* find the n'th root of an integer
18 *
19 * Result found such that (c)**b <= a and (c+1)**b > a
20 *
21 * This algorithm uses Newton's approximation
22 * x[i+1] = x[i] - f(x[i])/f'(x[i])
23 * which will find the root in log(N) time where
24 * each step involves a fair bit. This is not meant to
25 * find huge roots [square and cube, etc].
26 */
27 int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
28 {
29 mp_int t1, t2, t3;
30 int res, neg;
31
32 /* input must be positive if b is even */
33 if ((b & 1) == 0 && a->sign == MP_NEG) {
34 return MP_VAL;
35 }
36
37 if ((res = mp_init (&t1)) != MP_OKAY) {
38 return res;
39 }
40
41 if ((res = mp_init (&t2)) != MP_OKAY) {
42 goto __T1;
43 }
44
45 if ((res = mp_init (&t3)) != MP_OKAY) {
46 goto __T2;
47 }
48
49 /* if a is negative fudge the sign but keep track */
50 neg = a->sign;
51 a->sign = MP_ZPOS;
52
53 /* t2 = 2 */
54 mp_set (&t2, 2);
55
56 do {
57 /* t1 = t2 */
58 if ((res = mp_copy (&t2, &t1)) != MP_OKAY) {
59 goto __T3;
60 }
61
62 /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
63
64 /* t3 = t1**(b-1) */
65 if ((res = mp_expt_d (&t1, b - 1, &t3)) != MP_OKAY) {
66 goto __T3;
67 }
68
69 /* numerator */
70 /* t2 = t1**b */
71 if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) {
72 goto __T3;
73 }
74
75 /* t2 = t1**b - a */
76 if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) {
77 goto __T3;
78 }
79
80 /* denominator */
81 /* t3 = t1**(b-1) * b */
82 if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) {
83 goto __T3;
84 }
85
86 /* t3 = (t1**b - a)/(b * t1**(b-1)) */
87 if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) {
88 goto __T3;
89 }
90
91 if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) {
92 goto __T3;
93 }
94 } while (mp_cmp (&t1, &t2) != MP_EQ);
95
96 /* result can be off by a few so check */
97 for (;;) {
98 if ((res = mp_expt_d (&t1, b, &t2)) != MP_OKAY) {
99 goto __T3;
100 }
101
102 if (mp_cmp (&t2, a) == MP_GT) {
103 if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) {
104 goto __T3;
105 }
106 } else {
107 break;
108 }
109 }
110
111 /* reset the sign of a first */
112 a->sign = neg;
113
114 /* set the result */
115 mp_exch (&t1, c);
116
117 /* set the sign of the result */
118 c->sign = neg;
119
120 res = MP_OKAY;
121
122 __T3:mp_clear (&t3);
123 __T2:mp_clear (&t2);
124 __T1:mp_clear (&t1);
125 return res;
126 }