annotate libtommath/bn_mp_n_root_ex.c @ 1436:60fc6476e044

Update to libtommath v1.0
author Matt Johnston <matt@ucc.asn.au>
date Sat, 24 Jun 2017 22:37:14 +0800
parents
children 8bba51a55704
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
1436
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
1 #include <tommath_private.h>
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
2 #ifdef BN_MP_N_ROOT_EX_C
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
3 /* LibTomMath, multiple-precision integer library -- Tom St Denis
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
4 *
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
5 * LibTomMath is a library that provides multiple-precision
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
6 * integer arithmetic as well as number theoretic functionality.
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
7 *
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
8 * The library was designed directly after the MPI library by
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
9 * Michael Fromberger but has been written from scratch with
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
10 * additional optimizations in place.
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
11 *
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
12 * The library is free for all purposes without any express
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
13 * guarantee it works.
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
14 *
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
15 * Tom St Denis, [email protected], http://libtom.org
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
16 */
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
17
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
18 /* find the n'th root of an integer
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
19 *
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
20 * Result found such that (c)**b <= a and (c+1)**b > a
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
21 *
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
22 * This algorithm uses Newton's approximation
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
23 * x[i+1] = x[i] - f(x[i])/f'(x[i])
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
24 * which will find the root in log(N) time where
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
25 * each step involves a fair bit. This is not meant to
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
26 * find huge roots [square and cube, etc].
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
27 */
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
28 int mp_n_root_ex (mp_int * a, mp_digit b, mp_int * c, int fast)
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
29 {
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
30 mp_int t1, t2, t3;
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
31 int res, neg;
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
32
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
33 /* input must be positive if b is even */
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
34 if (((b & 1) == 0) && (a->sign == MP_NEG)) {
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
35 return MP_VAL;
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
36 }
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
37
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
38 if ((res = mp_init (&t1)) != MP_OKAY) {
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
39 return res;
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
40 }
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
41
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
42 if ((res = mp_init (&t2)) != MP_OKAY) {
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
43 goto LBL_T1;
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
44 }
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
45
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
46 if ((res = mp_init (&t3)) != MP_OKAY) {
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
47 goto LBL_T2;
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
48 }
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
49
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
50 /* if a is negative fudge the sign but keep track */
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
51 neg = a->sign;
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
52 a->sign = MP_ZPOS;
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
53
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
54 /* t2 = 2 */
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
55 mp_set (&t2, 2);
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
56
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
57 do {
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
58 /* t1 = t2 */
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
59 if ((res = mp_copy (&t2, &t1)) != MP_OKAY) {
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
60 goto LBL_T3;
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
61 }
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
62
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
63 /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
64
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
65 /* t3 = t1**(b-1) */
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
66 if ((res = mp_expt_d_ex (&t1, b - 1, &t3, fast)) != MP_OKAY) {
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
67 goto LBL_T3;
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
68 }
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
69
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
70 /* numerator */
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
71 /* t2 = t1**b */
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
72 if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) {
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
73 goto LBL_T3;
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
74 }
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
75
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
76 /* t2 = t1**b - a */
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
77 if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) {
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
78 goto LBL_T3;
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
79 }
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
80
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
81 /* denominator */
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
82 /* t3 = t1**(b-1) * b */
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
83 if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) {
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
84 goto LBL_T3;
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
85 }
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
86
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
87 /* t3 = (t1**b - a)/(b * t1**(b-1)) */
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
88 if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) {
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
89 goto LBL_T3;
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
90 }
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
91
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
92 if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) {
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
93 goto LBL_T3;
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
94 }
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
95 } while (mp_cmp (&t1, &t2) != MP_EQ);
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
96
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
97 /* result can be off by a few so check */
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
98 for (;;) {
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
99 if ((res = mp_expt_d_ex (&t1, b, &t2, fast)) != MP_OKAY) {
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
100 goto LBL_T3;
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
101 }
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
102
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
103 if (mp_cmp (&t2, a) == MP_GT) {
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
104 if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) {
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
105 goto LBL_T3;
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
106 }
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
107 } else {
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
108 break;
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
109 }
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
110 }
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
111
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
112 /* reset the sign of a first */
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
113 a->sign = neg;
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
114
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
115 /* set the result */
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
116 mp_exch (&t1, c);
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
117
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
118 /* set the sign of the result */
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
119 c->sign = neg;
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
120
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
121 res = MP_OKAY;
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
122
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
123 LBL_T3:mp_clear (&t3);
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
124 LBL_T2:mp_clear (&t2);
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
125 LBL_T1:mp_clear (&t1);
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
126 return res;
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
127 }
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
128 #endif
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
129
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
130 /* $Source$ */
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
131 /* $Revision$ */
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
132 /* $Date$ */