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annotate libtommath/bn_mp_log_u32.c @ 1793:f90e681b8b8c

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merge
author Matt Johnston <matt@ucc.asn.au>
date Fri, 29 Jan 2021 21:59:12 +0800
parents 1051e4eea25a
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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1 #include "tommath_private.h"
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2 #ifdef BN_MP_LOG_U32_C
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3 /* LibTomMath, multiple-precision integer library -- Tom St Denis */
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4 /* SPDX-License-Identifier: Unlicense */
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5
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6 /* Compute log_{base}(a) */
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7 static mp_word s_pow(mp_word base, mp_word exponent)
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8 {
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9 mp_word result = 1uLL;
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10 while (exponent != 0u) {
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11 if ((exponent & 1u) == 1u) {
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12 result *= base;
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13 }
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14 exponent >>= 1;
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15 base *= base;
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16 }
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17
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18 return result;
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19 }
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20
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21 static mp_digit s_digit_ilogb(mp_digit base, mp_digit n)
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22 {
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23 mp_word bracket_low = 1uLL, bracket_mid, bracket_high, N;
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24 mp_digit ret, high = 1uL, low = 0uL, mid;
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25
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26 if (n < base) {
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27 return 0uL;
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28 }
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29 if (n == base) {
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30 return 1uL;
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31 }
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32
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33 bracket_high = (mp_word) base ;
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34 N = (mp_word) n;
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35
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36 while (bracket_high < N) {
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37 low = high;
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38 bracket_low = bracket_high;
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39 high <<= 1;
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40 bracket_high *= bracket_high;
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41 }
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42
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43 while (((mp_digit)(high - low)) > 1uL) {
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44 mid = (low + high) >> 1;
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45 bracket_mid = bracket_low * s_pow(base, (mp_word)(mid - low));
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46
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47 if (N < bracket_mid) {
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48 high = mid ;
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49 bracket_high = bracket_mid ;
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50 }
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51 if (N > bracket_mid) {
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52 low = mid ;
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53 bracket_low = bracket_mid ;
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54 }
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55 if (N == bracket_mid) {
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56 return (mp_digit) mid;
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57 }
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58 }
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59
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60 if (bracket_high == N) {
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61 ret = high;
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62 } else {
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63 ret = low;
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64 }
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65
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66 return ret;
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67 }
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68
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69 /* TODO: output could be "int" because the output of mp_radix_size is int, too,
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70 as is the output of mp_bitcount.
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71 With the same problem: max size is INT_MAX * MP_DIGIT not INT_MAX only!
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72 */
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73 mp_err mp_log_u32(const mp_int *a, uint32_t base, uint32_t *c)
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74 {
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75 mp_err err;
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76 mp_ord cmp;
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77 uint32_t high, low, mid;
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78 mp_int bracket_low, bracket_high, bracket_mid, t, bi_base;
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79
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80 err = MP_OKAY;
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81
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82 if (a->sign == MP_NEG) {
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83 return MP_VAL;
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84 }
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85
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86 if (MP_IS_ZERO(a)) {
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87 return MP_VAL;
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88 }
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89
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90 if (base < 2u) {
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91 return MP_VAL;
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92 }
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93
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94 /* A small shortcut for bases that are powers of two. */
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95 if ((base & (base - 1u)) == 0u) {
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96 int y, bit_count;
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97 for (y=0; (y < 7) && ((base & 1u) == 0u); y++) {
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98 base >>= 1;
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99 }
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100 bit_count = mp_count_bits(a) - 1;
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101 *c = (uint32_t)(bit_count/y);
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102 return MP_OKAY;
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103 }
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104
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105 if (a->used == 1) {
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106 *c = (uint32_t)s_digit_ilogb(base, a->dp[0]);
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107 return err;
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108 }
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109
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110 cmp = mp_cmp_d(a, base);
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111 if ((cmp == MP_LT) || (cmp == MP_EQ)) {
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112 *c = cmp == MP_EQ;
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113 return err;
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114 }
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115
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116 if ((err =
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117 mp_init_multi(&bracket_low, &bracket_high,
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118 &bracket_mid, &t, &bi_base, NULL)) != MP_OKAY) {
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119 return err;
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120 }
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121
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122 low = 0u;
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123 mp_set(&bracket_low, 1uL);
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124 high = 1u;
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125
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126 mp_set(&bracket_high, base);
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127
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128 /*
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129 A kind of Giant-step/baby-step algorithm.
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130 Idea shamelessly stolen from https://programmingpraxis.com/2010/05/07/integer-logarithms/2/
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131 The effect is asymptotic, hence needs benchmarks to test if the Giant-step should be skipped
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132 for small n.
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133 */
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134 while (mp_cmp(&bracket_high, a) == MP_LT) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
135 low = high;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
136 if ((err = mp_copy(&bracket_high, &bracket_low)) != MP_OKAY) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
137 goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
138 }
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
139 high <<= 1;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
140 if ((err = mp_sqr(&bracket_high, &bracket_high)) != MP_OKAY) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
141 goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
142 }
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
143 }
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
144 mp_set(&bi_base, base);
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
145
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Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
146 while ((high - low) > 1u) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
147 mid = (high + low) >> 1;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
148
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Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
149 if ((err = mp_expt_u32(&bi_base, (uint32_t)(mid - low), &t)) != MP_OKAY) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
150 goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
151 }
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
152 if ((err = mp_mul(&bracket_low, &t, &bracket_mid)) != MP_OKAY) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
153 goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
154 }
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
155 cmp = mp_cmp(a, &bracket_mid);
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
156 if (cmp == MP_LT) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
157 high = mid;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
158 mp_exch(&bracket_mid, &bracket_high);
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
159 }
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
160 if (cmp == MP_GT) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
161 low = mid;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
162 mp_exch(&bracket_mid, &bracket_low);
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
163 }
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
164 if (cmp == MP_EQ) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
165 *c = mid;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
166 goto LBL_END;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
167 }
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
168 }
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
169
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
170 *c = (mp_cmp(&bracket_high, a) == MP_EQ) ? high : low;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
171
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
172 LBL_END:
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
173 LBL_ERR:
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
174 mp_clear_multi(&bracket_low, &bracket_high, &bracket_mid,
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
175 &t, &bi_base, NULL);
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
176 return err;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
177 }
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
178
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
179
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
180 #endif