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annotate libtommath/bn_s_mp_karatsuba_mul.c @ 1714:c0f12eaf95c9

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author Matt Johnston <matt@ucc.asn.au>
date Thu, 11 Jun 2020 00:09:15 +0800
parents 1051e4eea25a
children
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1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
1 #include "tommath_private.h"
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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2 #ifdef BN_S_MP_KARATSUBA_MUL_C
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parents:
diff changeset
3 /* LibTomMath, multiple-precision integer library -- Tom St Denis */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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4 /* SPDX-License-Identifier: Unlicense */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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5
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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6 /* c = |a| * |b| using Karatsuba Multiplication using
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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parents:
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7 * three half size multiplications
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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8 *
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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9 * Let B represent the radix [e.g. 2**MP_DIGIT_BIT] and
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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10 * let n represent half of the number of digits in
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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diff changeset
11 * the min(a,b)
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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12 *
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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13 * a = a1 * B**n + a0
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
14 * b = b1 * B**n + b0
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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parents:
diff changeset
15 *
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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16 * Then, a * b =>
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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17 a1b1 * B**2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B + a0b0
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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18 *
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Steffen Jaeckel <s@jaeckel.eu>
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19 * Note that a1b1 and a0b0 are used twice and only need to be
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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20 * computed once. So in total three half size (half # of
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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21 * digit) multiplications are performed, a0b0, a1b1 and
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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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
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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25 * 1/4th the number of single precision multiplications so in
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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26 * total after one call 25% of the single precision multiplications
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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27 * are saved. Note also that the call to mp_mul can end up back
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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parents:
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28 * in this function if the a0, a1, b0, or b1 are above the threshold.
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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29 * This is known as divide-and-conquer and leads to the famous
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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30 * O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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31 * the standard O(N**2) that the baseline/comba methods use.
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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32 * Generally though the overhead of this method doesn't pay off
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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33 * until a certain size (N ~ 80) is reached.
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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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;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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38 int B;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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39 mp_err err = MP_MEM; /* default the return code to an error */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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40
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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41 /* min # of digits */
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42 B = MP_MIN(a->used, b->used);
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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43
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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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) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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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) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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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) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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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
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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82 * since we also need to shift the digits
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
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83 */
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Steffen Jaeckel <s@jaeckel.eu>
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84 tmpa = a->dp;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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85 tmpb = b->dp;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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86
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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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++) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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90 *tmpx++ = *tmpa++;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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91 *tmpy++ = *tmpb++;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
92 }
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
93
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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94 tmpx = x1.dp;
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parents:
diff changeset
95 for (x = B; x < a->used; x++) {
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96 *tmpx++ = *tmpa++;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
97 }
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
98
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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99 tmpy = y1.dp;
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100 for (x = B; x < b->used; x++) {
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parents:
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101 *tmpy++ = *tmpb++;
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Steffen Jaeckel <s@jaeckel.eu>
parents:
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102 }
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Steffen Jaeckel <s@jaeckel.eu>
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diff changeset
103 }
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Steffen Jaeckel <s@jaeckel.eu>
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diff changeset
104
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Steffen Jaeckel <s@jaeckel.eu>
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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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Steffen Jaeckel <s@jaeckel.eu>
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108 mp_clamp(&x0);
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Steffen Jaeckel <s@jaeckel.eu>
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109 mp_clamp(&y0);
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parents:
diff changeset
110
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111 /* now calc the products x0y0 and x1y1 */
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parents:
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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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parents:
diff changeset
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) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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125 goto X1Y1; /* t2 = y1 - y0 */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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parents:
diff changeset
126 }
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
127 if (mp_mul(&t1, &x0, &t1) != MP_OKAY) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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parents:
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128 goto X1Y1; /* t1 = (x1 + x0) * (y1 + y0) */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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129 }
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Steffen Jaeckel <s@jaeckel.eu>
parents:
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130
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Steffen Jaeckel <s@jaeckel.eu>
parents:
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131 /* add x0y0 */
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Steffen Jaeckel <s@jaeckel.eu>
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132 if (mp_add(&x0y0, &x1y1, &x0) != MP_OKAY) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
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133 goto X1Y1; /* t2 = x0y0 + x1y1 */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
134 }
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
135 if (s_mp_sub(&t1, &x0, &t1) != MP_OKAY) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
136 goto X1Y1; /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
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137 }
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 /* shift by B */
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Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
140 if (mp_lshd(&t1, B) != MP_OKAY) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
141 goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */
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 if (mp_lshd(&x1y1, B * 2) != MP_OKAY) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
144 goto X1Y1; /* x1y1 = x1y1 << 2*B */
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Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
145 }
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
146
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
147 if (mp_add(&x0y0, &t1, &t1) != MP_OKAY) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
148 goto X1Y1; /* t1 = x0y0 + t1 */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
149 }
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
150 if (mp_add(&t1, &x1y1, c) != MP_OKAY) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
151 goto X1Y1; /* t1 = x0y0 + t1 + x1y1 */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
152 }
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
153
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
154 /* Algorithm succeeded set the return code to MP_OKAY */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
155 err = MP_OKAY;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
156
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
157 X1Y1:
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Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
158 mp_clear(&x1y1);
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
159 X0Y0:
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
160 mp_clear(&x0y0);
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
161 T1:
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
162 mp_clear(&t1);
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
163 Y1:
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
164 mp_clear(&y1);
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
165 Y0:
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
166 mp_clear(&y0);
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
167 X1:
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
168 mp_clear(&x1);
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
169 X0:
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
170 mp_clear(&x0);
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
171 LBL_ERR:
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Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
172 return err;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
173 }
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
174 #endif