Mercurial > dropbear
annotate libtommath/bn_s_mp_karatsuba_mul.c @ 1861:2b3a8026a6ce
Add re-exec for server
This allows ASLR to re-randomize the address
space for every connection, preventing some
vulnerabilities from being exploitable by
repeated probing.
Overhead (memory and time) is yet to be confirmed.
At present this is only enabled on Linux. Other BSD platforms
with fexecve() would probably also work though have not been tested.
author | Matt Johnston <matt@ucc.asn.au> |
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date | Sun, 30 Jan 2022 10:14:56 +0800 |
parents | 1051e4eea25a |
children |
rev | line source |
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1692
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Update LibTomMath to 1.2.0 (#84)
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1 #include "tommath_private.h" |
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2 #ifdef BN_S_MP_KARATSUBA_MUL_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 /* c = |a| * |b| using Karatsuba Multiplication using |
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7 * three half size multiplications |
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8 * |
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9 * Let B represent the radix [e.g. 2**MP_DIGIT_BIT] and |
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10 * let n represent half of the number of digits in |
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11 * the min(a,b) |
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12 * |
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13 * a = a1 * B**n + a0 |
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14 * b = b1 * B**n + b0 |
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15 * |
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16 * Then, a * b => |
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17 a1b1 * B**2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B + a0b0 |
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18 * |
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19 * Note that a1b1 and a0b0 are used twice and only need to be |
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20 * computed once. So in total three half size (half # of |
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21 * digit) multiplications are performed, a0b0, a1b1 and |
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22 * (a1+b1)(a0+b0) |
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23 * |
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24 * Note that a multiplication of half the digits requires |
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25 * 1/4th the number of single precision multiplications so in |
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26 * total after one call 25% of the single precision multiplications |
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27 * are saved. Note also that the call to mp_mul can end up back |
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28 * in this function if the a0, a1, b0, or b1 are above the threshold. |
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29 * This is known as divide-and-conquer and leads to the famous |
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30 * O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than |
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31 * the standard O(N**2) that the baseline/comba methods use. |
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32 * Generally though the overhead of this method doesn't pay off |
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33 * until a certain size (N ~ 80) is reached. |
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34 */ |
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35 mp_err s_mp_karatsuba_mul(const mp_int *a, const mp_int *b, mp_int *c) |
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36 { |
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37 mp_int x0, x1, y0, y1, t1, x0y0, x1y1; |
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38 int B; |
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39 mp_err err = MP_MEM; /* default the return code to an error */ |
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40 |
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41 /* min # of digits */ |
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42 B = MP_MIN(a->used, b->used); |
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43 |
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44 /* now divide in two */ |
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45 B = B >> 1; |
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46 |
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47 /* init copy all the temps */ |
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48 if (mp_init_size(&x0, B) != MP_OKAY) { |
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49 goto LBL_ERR; |
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50 } |
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51 if (mp_init_size(&x1, a->used - B) != MP_OKAY) { |
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52 goto X0; |
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53 } |
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54 if (mp_init_size(&y0, B) != MP_OKAY) { |
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55 goto X1; |
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56 } |
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57 if (mp_init_size(&y1, b->used - B) != MP_OKAY) { |
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58 goto Y0; |
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59 } |
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60 |
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61 /* init temps */ |
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62 if (mp_init_size(&t1, B * 2) != MP_OKAY) { |
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63 goto Y1; |
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64 } |
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65 if (mp_init_size(&x0y0, B * 2) != MP_OKAY) { |
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66 goto T1; |
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67 } |
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68 if (mp_init_size(&x1y1, B * 2) != MP_OKAY) { |
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69 goto X0Y0; |
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70 } |
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71 |
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72 /* now shift the digits */ |
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73 x0.used = y0.used = B; |
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74 x1.used = a->used - B; |
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75 y1.used = b->used - B; |
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76 |
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77 { |
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78 int x; |
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79 mp_digit *tmpa, *tmpb, *tmpx, *tmpy; |
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80 |
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81 /* we copy the digits directly instead of using higher level functions |
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82 * since we also need to shift the digits |
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83 */ |
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84 tmpa = a->dp; |
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85 tmpb = b->dp; |
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86 |
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87 tmpx = x0.dp; |
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88 tmpy = y0.dp; |
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89 for (x = 0; x < B; x++) { |
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90 *tmpx++ = *tmpa++; |
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91 *tmpy++ = *tmpb++; |
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92 } |
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93 |
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94 tmpx = x1.dp; |
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95 for (x = B; x < a->used; x++) { |
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96 *tmpx++ = *tmpa++; |
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97 } |
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98 |
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99 tmpy = y1.dp; |
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100 for (x = B; x < b->used; x++) { |
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101 *tmpy++ = *tmpb++; |
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102 } |
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103 } |
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104 |
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105 /* only need to clamp the lower words since by definition the |
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106 * upper words x1/y1 must have a known number of digits |
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107 */ |
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108 mp_clamp(&x0); |
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109 mp_clamp(&y0); |
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110 |
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111 /* now calc the products x0y0 and x1y1 */ |
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112 /* after this x0 is no longer required, free temp [x0==t2]! */ |
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113 if (mp_mul(&x0, &y0, &x0y0) != MP_OKAY) { |
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114 goto X1Y1; /* x0y0 = x0*y0 */ |
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115 } |
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116 if (mp_mul(&x1, &y1, &x1y1) != MP_OKAY) { |
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117 goto X1Y1; /* x1y1 = x1*y1 */ |
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118 } |
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119 |
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120 /* now calc x1+x0 and y1+y0 */ |
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121 if (s_mp_add(&x1, &x0, &t1) != MP_OKAY) { |
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122 goto X1Y1; /* t1 = x1 - x0 */ |
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123 } |
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124 if (s_mp_add(&y1, &y0, &x0) != MP_OKAY) { |
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125 goto X1Y1; /* t2 = y1 - y0 */ |
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126 } |
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127 if (mp_mul(&t1, &x0, &t1) != MP_OKAY) { |
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128 goto X1Y1; /* t1 = (x1 + x0) * (y1 + y0) */ |
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129 } |
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130 |
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131 /* add x0y0 */ |
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132 if (mp_add(&x0y0, &x1y1, &x0) != MP_OKAY) { |
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133 goto X1Y1; /* t2 = x0y0 + x1y1 */ |
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134 } |
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135 if (s_mp_sub(&t1, &x0, &t1) != MP_OKAY) { |
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136 goto X1Y1; /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */ |
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137 } |
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138 |
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139 /* shift by B */ |
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140 if (mp_lshd(&t1, B) != MP_OKAY) { |
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141 goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */ |
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142 } |
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143 if (mp_lshd(&x1y1, B * 2) != MP_OKAY) { |
1051e4eea25a
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144 goto X1Y1; /* x1y1 = x1y1 << 2*B */ |
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|
145 } |
1051e4eea25a
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|
146 |
1051e4eea25a
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147 if (mp_add(&x0y0, &t1, &t1) != MP_OKAY) { |
1051e4eea25a
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parents:
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148 goto X1Y1; /* t1 = x0y0 + t1 */ |
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|
149 } |
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150 if (mp_add(&t1, &x1y1, c) != MP_OKAY) { |
1051e4eea25a
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parents:
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151 goto X1Y1; /* t1 = x0y0 + t1 + x1y1 */ |
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|
152 } |
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|
153 |
1051e4eea25a
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154 /* Algorithm succeeded set the return code to MP_OKAY */ |
1051e4eea25a
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155 err = MP_OKAY; |
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156 |
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157 X1Y1: |
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158 mp_clear(&x1y1); |
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159 X0Y0: |
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160 mp_clear(&x0y0); |
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Steffen Jaeckel <s@jaeckel.eu>
parents:
diff
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|
161 T1: |
1051e4eea25a
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Steffen Jaeckel <s@jaeckel.eu>
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|
162 mp_clear(&t1); |
1051e4eea25a
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Steffen Jaeckel <s@jaeckel.eu>
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|
163 Y1: |
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164 mp_clear(&y1); |
1051e4eea25a
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Steffen Jaeckel <s@jaeckel.eu>
parents:
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|
165 Y0: |
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Steffen Jaeckel <s@jaeckel.eu>
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|
166 mp_clear(&y0); |
1051e4eea25a
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Steffen Jaeckel <s@jaeckel.eu>
parents:
diff
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|
167 X1: |
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|
168 mp_clear(&x1); |
1051e4eea25a
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Steffen Jaeckel <s@jaeckel.eu>
parents:
diff
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|
169 X0: |
1051e4eea25a
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Steffen Jaeckel <s@jaeckel.eu>
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|
170 mp_clear(&x0); |
1051e4eea25a
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Steffen Jaeckel <s@jaeckel.eu>
parents:
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|
171 LBL_ERR: |
1051e4eea25a
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|
172 return err; |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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|
173 } |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff
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|
174 #endif |