### comparison libtommath/bn_mp_n_root.c @ 284:eed26cff980b

author Matt Johnston Wed, 08 Mar 2006 13:23:49 +0000 5ff8218bcee9
comparison
equal inserted replaced
283:bd240aa12ba7 284:eed26cff980b
1 #include <tommath.h>
2 #ifdef BN_MP_N_ROOT_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, [email protected], http://math.libtomcrypt.org
16 */
17
18 /* find the n'th root of an integer
19 *
20 * Result found such that (c)**b <= a and (c+1)**b > a
21 *
22 * This algorithm uses Newton's approximation
23 * x[i+1] = x[i] - f(x[i])/f'(x[i])
24 * which will find the root in log(N) time where
25 * each step involves a fair bit. This is not meant to
26 * find huge roots [square and cube, etc].
27 */
28 int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
29 {
30 mp_int t1, t2, t3;
31 int res, neg;
32
33 /* input must be positive if b is even */
34 if ((b & 1) == 0 && a->sign == MP_NEG) {
35 return MP_VAL;
36 }
37
38 if ((res = mp_init (&t1)) != MP_OKAY) {
39 return res;
40 }
41
42 if ((res = mp_init (&t2)) != MP_OKAY) {
43 goto LBL_T1;
44 }
45
46 if ((res = mp_init (&t3)) != MP_OKAY) {
47 goto LBL_T2;
48 }
49
50 /* if a is negative fudge the sign but keep track */
51 neg = a->sign;
52 a->sign = MP_ZPOS;
53
54 /* t2 = 2 */
55 mp_set (&t2, 2);
56
57 do {
58 /* t1 = t2 */
59 if ((res = mp_copy (&t2, &t1)) != MP_OKAY) {
60 goto LBL_T3;
61 }
62
63 /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
64
65 /* t3 = t1**(b-1) */
66 if ((res = mp_expt_d (&t1, b - 1, &t3)) != MP_OKAY) {
67 goto LBL_T3;
68 }
69
70 /* numerator */
71 /* t2 = t1**b */
72 if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) {
73 goto LBL_T3;
74 }
75
76 /* t2 = t1**b - a */
77 if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) {
78 goto LBL_T3;
79 }
80
81 /* denominator */
82 /* t3 = t1**(b-1) * b */
83 if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) {
84 goto LBL_T3;
85 }
86
87 /* t3 = (t1**b - a)/(b * t1**(b-1)) */
88 if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) {
89 goto LBL_T3;
90 }
91
92 if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) {
93 goto LBL_T3;
94 }
95 } while (mp_cmp (&t1, &t2) != MP_EQ);
96
97 /* result can be off by a few so check */
98 for (;;) {
99 if ((res = mp_expt_d (&t1, b, &t2)) != MP_OKAY) {
100 goto LBL_T3;
101 }
102
103 if (mp_cmp (&t2, a) == MP_GT) {
104 if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) {
105 goto LBL_T3;
106 }
107 } else {
108 break;
109 }
110 }
111
112 /* reset the sign of a first */
113 a->sign = neg;
114
115 /* set the result */
116 mp_exch (&t1, c);
117
118 /* set the sign of the result */
119 c->sign = neg;
120
121 res = MP_OKAY;
122
123 LBL_T3:mp_clear (&t3);
124 LBL_T2:mp_clear (&t2);
125 LBL_T1:mp_clear (&t1);
126 return res;
127 }
128 #endif