1/*	$NetBSD: bn_mp_n_root.c,v 1.2 2017/01/28 21:31:47 christos Exp $	*/
2
3#include <tommath.h>
4#ifdef BN_MP_N_ROOT_C
5/* LibTomMath, multiple-precision integer library -- Tom St Denis
6 *
7 * LibTomMath is a library that provides multiple-precision
8 * integer arithmetic as well as number theoretic functionality.
9 *
10 * The library was designed directly after the MPI library by
11 * Michael Fromberger but has been written from scratch with
12 * additional optimizations in place.
13 *
14 * The library is free for all purposes without any express
15 * guarantee it works.
16 *
17 * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
18 */
19
20/* find the n'th root of an integer
21 *
22 * Result found such that (c)**b <= a and (c+1)**b > a
23 *
24 * This algorithm uses Newton's approximation
25 * x[i+1] = x[i] - f(x[i])/f'(x[i])
26 * which will find the root in log(N) time where
27 * each step involves a fair bit.  This is not meant to
28 * find huge roots [square and cube, etc].
29 */
30int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
31{
32  mp_int  t1, t2, t3;
33  int     res, neg;
34
35  /* input must be positive if b is even */
36  if ((b & 1) == 0 && a->sign == MP_NEG) {
37    return MP_VAL;
38  }
39
40  if ((res = mp_init (&t1)) != MP_OKAY) {
41    return res;
42  }
43
44  if ((res = mp_init (&t2)) != MP_OKAY) {
45    goto LBL_T1;
46  }
47
48  if ((res = mp_init (&t3)) != MP_OKAY) {
49    goto LBL_T2;
50  }
51
52  /* if a is negative fudge the sign but keep track */
53  neg     = a->sign;
54  a->sign = MP_ZPOS;
55
56  /* t2 = 2 */
57  mp_set (&t2, 2);
58
59  do {
60    /* t1 = t2 */
61    if ((res = mp_copy (&t2, &t1)) != MP_OKAY) {
62      goto LBL_T3;
63    }
64
65    /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
66
67    /* t3 = t1**(b-1) */
68    if ((res = mp_expt_d (&t1, b - 1, &t3)) != MP_OKAY) {
69      goto LBL_T3;
70    }
71
72    /* numerator */
73    /* t2 = t1**b */
74    if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) {
75      goto LBL_T3;
76    }
77
78    /* t2 = t1**b - a */
79    if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) {
80      goto LBL_T3;
81    }
82
83    /* denominator */
84    /* t3 = t1**(b-1) * b  */
85    if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) {
86      goto LBL_T3;
87    }
88
89    /* t3 = (t1**b - a)/(b * t1**(b-1)) */
90    if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) {
91      goto LBL_T3;
92    }
93
94    if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) {
95      goto LBL_T3;
96    }
97  }  while (mp_cmp (&t1, &t2) != MP_EQ);
98
99  /* result can be off by a few so check */
100  for (;;) {
101    if ((res = mp_expt_d (&t1, b, &t2)) != MP_OKAY) {
102      goto LBL_T3;
103    }
104
105    if (mp_cmp (&t2, a) == MP_GT) {
106      if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) {
107         goto LBL_T3;
108      }
109    } else {
110      break;
111    }
112  }
113
114  /* reset the sign of a first */
115  a->sign = neg;
116
117  /* set the result */
118  mp_exch (&t1, c);
119
120  /* set the sign of the result */
121  c->sign = neg;
122
123  res = MP_OKAY;
124
125LBL_T3:mp_clear (&t3);
126LBL_T2:mp_clear (&t2);
127LBL_T1:mp_clear (&t1);
128  return res;
129}
130#endif
131
132/* Source: /cvs/libtom/libtommath/bn_mp_n_root.c,v  */
133/* Revision: 1.4  */
134/* Date: 2006/12/28 01:25:13  */
135