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annotate libtommath/bn_mp_n_root_ex.c @ 1680:5e763ad6e2e0

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author Matt Johnston <matt@ucc.asn.au>
date Sun, 24 May 2020 13:34:19 +0800
parents f52919ffd3b1
children
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diff changeset
1 #include "tommath_private.h"
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2 #ifdef BN_MP_N_ROOT_EX_C
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3 /* LibTomMath, multiple-precision integer library -- Tom St Denis
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4 *
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5 * LibTomMath is a library that provides multiple-precision
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6 * integer arithmetic as well as number theoretic functionality.
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7 *
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8 * The library was designed directly after the MPI library by
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9 * Michael Fromberger but has been written from scratch with
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10 * additional optimizations in place.
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11 *
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12 * SPDX-License-Identifier: Unlicense
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13 */
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14
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15 /* find the n'th root of an integer
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16 *
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17 * Result found such that (c)**b <= a and (c+1)**b > a
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18 *
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19 * This algorithm uses Newton's approximation
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20 * x[i+1] = x[i] - f(x[i])/f'(x[i])
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21 * which will find the root in log(N) time where
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22 * each step involves a fair bit. This is not meant to
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23 * find huge roots [square and cube, etc].
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24 */
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25 int mp_n_root_ex(const mp_int *a, mp_digit b, mp_int *c, int fast)
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26 {
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27 mp_int t1, t2, t3, a_;
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28 int res;
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29
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30 /* input must be positive if b is even */
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31 if (((b & 1u) == 0u) && (a->sign == MP_NEG)) {
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32 return MP_VAL;
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33 }
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34
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35 if ((res = mp_init(&t1)) != MP_OKAY) {
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36 return res;
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37 }
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38
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39 if ((res = mp_init(&t2)) != MP_OKAY) {
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40 goto LBL_T1;
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41 }
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42
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43 if ((res = mp_init(&t3)) != MP_OKAY) {
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44 goto LBL_T2;
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45 }
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46
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47 /* if a is negative fudge the sign but keep track */
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48 a_ = *a;
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49 a_.sign = MP_ZPOS;
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50
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51 /* t2 = 2 */
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52 mp_set(&t2, 2uL);
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53
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54 do {
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55 /* t1 = t2 */
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56 if ((res = mp_copy(&t2, &t1)) != MP_OKAY) {
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57 goto LBL_T3;
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58 }
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59
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60 /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
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61
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62 /* t3 = t1**(b-1) */
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63 if ((res = mp_expt_d_ex(&t1, b - 1u, &t3, fast)) != MP_OKAY) {
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64 goto LBL_T3;
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65 }
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66
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67 /* numerator */
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68 /* t2 = t1**b */
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69 if ((res = mp_mul(&t3, &t1, &t2)) != MP_OKAY) {
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70 goto LBL_T3;
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71 }
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72
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73 /* t2 = t1**b - a */
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74 if ((res = mp_sub(&t2, &a_, &t2)) != MP_OKAY) {
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75 goto LBL_T3;
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76 }
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77
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78 /* denominator */
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79 /* t3 = t1**(b-1) * b */
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80 if ((res = mp_mul_d(&t3, b, &t3)) != MP_OKAY) {
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81 goto LBL_T3;
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82 }
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83
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84 /* t3 = (t1**b - a)/(b * t1**(b-1)) */
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85 if ((res = mp_div(&t2, &t3, &t3, NULL)) != MP_OKAY) {
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86 goto LBL_T3;
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87 }
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88
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89 if ((res = mp_sub(&t1, &t3, &t2)) != MP_OKAY) {
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90 goto LBL_T3;
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91 }
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92 } while (mp_cmp(&t1, &t2) != MP_EQ);
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93
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94 /* result can be off by a few so check */
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95 for (;;) {
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96 if ((res = mp_expt_d_ex(&t1, b, &t2, fast)) != MP_OKAY) {
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97 goto LBL_T3;
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98 }
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99
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100 if (mp_cmp(&t2, &a_) == MP_GT) {
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101 if ((res = mp_sub_d(&t1, 1uL, &t1)) != MP_OKAY) {
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102 goto LBL_T3;
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103 }
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104 } else {
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105 break;
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106 }
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107 }
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108
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109 /* set the result */
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110 mp_exch(&t1, c);
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111
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112 /* set the sign of the result */
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113 c->sign = a->sign;
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114
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115 res = MP_OKAY;
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116
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parents: 1470
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117 LBL_T3:
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
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118 mp_clear(&t3);
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parents: 1470
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119 LBL_T2:
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
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120 mp_clear(&t2);
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
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121 LBL_T1:
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
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122 mp_clear(&t1);
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
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123 return res;
1436
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
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124 }
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
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125 #endif
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parents:
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126
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
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127 /* ref: HEAD -> master, tag: v1.1.0 */
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
128 /* git commit: 08549ad6bc8b0cede0b357a9c341c5c6473a9c55 */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
129 /* commit time: 2019-01-28 20:32:32 +0100 */