Mercurial > dropbear
annotate libtommath/bn_mp_n_root_ex.c @ 1684:d5d25ce2a2ed
cast to fix warning
author | Matt Johnston <matt@ucc.asn.au> |
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date | Tue, 26 May 2020 19:57:28 +0800 |
parents | f52919ffd3b1 |
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rev | line source |
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1 #include "tommath_private.h" |
1436 | 2 #ifdef BN_MP_N_ROOT_EX_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 * | |
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12 * SPDX-License-Identifier: Unlicense |
1436 | 13 */ |
14 | |
15 /* find the n'th root of an integer | |
16 * | |
17 * Result found such that (c)**b <= a and (c+1)**b > a | |
18 * | |
19 * This algorithm uses Newton's approximation | |
20 * x[i+1] = x[i] - f(x[i])/f'(x[i]) | |
21 * which will find the root in log(N) time where | |
22 * each step involves a fair bit. This is not meant to | |
23 * find huge roots [square and cube, etc]. | |
24 */ | |
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25 int mp_n_root_ex(const mp_int *a, mp_digit b, mp_int *c, int fast) |
1436 | 26 { |
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27 mp_int t1, t2, t3, a_; |
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28 int res; |
1436 | 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 } |
1436 | 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 } |
1436 | 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 } |
1436 | 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 } |
1436 | 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; |
1436 | 50 |
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51 /* t2 = 2 */ |
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52 mp_set(&t2, 2uL); |
1436 | 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 } |
1436 | 59 |
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60 /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */ |
1436 | 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 } |
1436 | 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) { |
1436 | 70 goto LBL_T3; |
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 } |
1436 | 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); |
1436 | 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 } |
1436 | 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 } |
1436 | 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; |
1436 | 116 |
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117 LBL_T3: |
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118 mp_clear(&t3); |
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119 LBL_T2: |
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120 mp_clear(&t2); |
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121 LBL_T1: |
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122 mp_clear(&t1); |
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123 return res; |
1436 | 124 } |
125 #endif | |
126 | |
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127 /* ref: HEAD -> master, tag: v1.1.0 */ |
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128 /* git commit: 08549ad6bc8b0cede0b357a9c341c5c6473a9c55 */ |
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129 /* commit time: 2019-01-28 20:32:32 +0100 */ |