Mercurial > dropbear
annotate libtommath/bn_mp_div.c @ 1671:5c8913b7464c
Mention Ed25519 in dropbearkey man (#94)
author | Vladislav Grishenko <themiron@users.noreply.github.com> |
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date | Mon, 25 May 2020 18:28:27 +0500 |
parents | f52919ffd3b1 |
children | 1051e4eea25a |
rev | line source |
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1 #include "tommath_private.h" |
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2 #ifdef BN_MP_DIV_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 #ifdef BN_MP_DIV_SMALL |
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16 |
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17 /* slower bit-bang division... also smaller */ |
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18 int mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d) |
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19 { |
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20 mp_int ta, tb, tq, q; |
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21 int res, n, n2; |
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22 |
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23 /* is divisor zero ? */ |
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24 if (mp_iszero(b) == MP_YES) { |
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25 return MP_VAL; |
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26 } |
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27 |
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28 /* if a < b then q=0, r = a */ |
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29 if (mp_cmp_mag(a, b) == MP_LT) { |
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30 if (d != NULL) { |
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31 res = mp_copy(a, d); |
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32 } else { |
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33 res = MP_OKAY; |
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34 } |
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35 if (c != NULL) { |
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36 mp_zero(c); |
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37 } |
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38 return res; |
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39 } |
1436 | 40 |
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41 /* init our temps */ |
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42 if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL)) != MP_OKAY) { |
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43 return res; |
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44 } |
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45 |
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46 |
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47 mp_set(&tq, 1uL); |
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48 n = mp_count_bits(a) - mp_count_bits(b); |
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49 if (((res = mp_abs(a, &ta)) != MP_OKAY) || |
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50 ((res = mp_abs(b, &tb)) != MP_OKAY) || |
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51 ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) || |
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52 ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) { |
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53 goto LBL_ERR; |
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54 } |
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55 |
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56 while (n-- >= 0) { |
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57 if (mp_cmp(&tb, &ta) != MP_GT) { |
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58 if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) || |
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59 ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) { |
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60 goto LBL_ERR; |
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61 } |
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62 } |
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63 if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) || |
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64 ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) { |
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65 goto LBL_ERR; |
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66 } |
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67 } |
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68 |
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69 /* now q == quotient and ta == remainder */ |
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70 n = a->sign; |
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71 n2 = (a->sign == b->sign) ? MP_ZPOS : MP_NEG; |
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72 if (c != NULL) { |
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73 mp_exch(c, &q); |
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74 c->sign = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2; |
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75 } |
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76 if (d != NULL) { |
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77 mp_exch(d, &ta); |
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78 d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n; |
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79 } |
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80 LBL_ERR: |
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81 mp_clear_multi(&ta, &tb, &tq, &q, NULL); |
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82 return res; |
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83 } |
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84 |
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85 #else |
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86 |
1436 | 87 /* integer signed division. |
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88 * c*b + d == a [e.g. a/b, c=quotient, d=remainder] |
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89 * HAC pp.598 Algorithm 14.20 |
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90 * |
1436 | 91 * Note that the description in HAC is horribly |
92 * incomplete. For example, it doesn't consider | |
93 * the case where digits are removed from 'x' in | |
94 * the inner loop. It also doesn't consider the | |
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95 * case that y has fewer than three digits, etc.. |
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96 * |
1436 | 97 * The overall algorithm is as described as |
284
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98 * 14.20 from HAC but fixed to treat these cases. |
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99 */ |
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100 int mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d) |
284
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101 { |
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102 mp_int q, x, y, t1, t2; |
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103 int res, n, t, i, norm, neg; |
284
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104 |
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105 /* is divisor zero ? */ |
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106 if (mp_iszero(b) == MP_YES) { |
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107 return MP_VAL; |
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108 } |
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109 |
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110 /* if a < b then q=0, r = a */ |
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111 if (mp_cmp_mag(a, b) == MP_LT) { |
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112 if (d != NULL) { |
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113 res = mp_copy(a, d); |
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114 } else { |
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115 res = MP_OKAY; |
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116 } |
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117 if (c != NULL) { |
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118 mp_zero(c); |
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119 } |
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120 return res; |
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121 } |
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122 |
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123 if ((res = mp_init_size(&q, a->used + 2)) != MP_OKAY) { |
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124 return res; |
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125 } |
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126 q.used = a->used + 2; |
284
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127 |
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128 if ((res = mp_init(&t1)) != MP_OKAY) { |
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129 goto LBL_Q; |
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130 } |
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131 |
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132 if ((res = mp_init(&t2)) != MP_OKAY) { |
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133 goto LBL_T1; |
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134 } |
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135 |
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136 if ((res = mp_init_copy(&x, a)) != MP_OKAY) { |
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137 goto LBL_T2; |
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138 } |
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139 |
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140 if ((res = mp_init_copy(&y, b)) != MP_OKAY) { |
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141 goto LBL_X; |
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142 } |
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143 |
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144 /* fix the sign */ |
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145 neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG; |
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146 x.sign = y.sign = MP_ZPOS; |
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147 |
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148 /* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */ |
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149 norm = mp_count_bits(&y) % DIGIT_BIT; |
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150 if (norm < (DIGIT_BIT - 1)) { |
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151 norm = (DIGIT_BIT - 1) - norm; |
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152 if ((res = mp_mul_2d(&x, norm, &x)) != MP_OKAY) { |
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153 goto LBL_Y; |
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154 } |
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155 if ((res = mp_mul_2d(&y, norm, &y)) != MP_OKAY) { |
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156 goto LBL_Y; |
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157 } |
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158 } else { |
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159 norm = 0; |
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160 } |
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161 |
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162 /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */ |
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163 n = x.used - 1; |
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164 t = y.used - 1; |
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165 |
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166 /* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */ |
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167 if ((res = mp_lshd(&y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */ |
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168 goto LBL_Y; |
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169 } |
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170 |
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171 while (mp_cmp(&x, &y) != MP_LT) { |
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172 ++(q.dp[n - t]); |
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173 if ((res = mp_sub(&x, &y, &x)) != MP_OKAY) { |
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174 goto LBL_Y; |
1436 | 175 } |
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176 } |
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177 |
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178 /* reset y by shifting it back down */ |
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179 mp_rshd(&y, n - t); |
1436 | 180 |
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181 /* step 3. for i from n down to (t + 1) */ |
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182 for (i = n; i >= (t + 1); i--) { |
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183 if (i > x.used) { |
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184 continue; |
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185 } |
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186 |
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187 /* step 3.1 if xi == yt then set q{i-t-1} to b-1, |
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188 * otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */ |
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189 if (x.dp[i] == y.dp[t]) { |
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190 q.dp[(i - t) - 1] = ((mp_digit)1 << (mp_digit)DIGIT_BIT) - (mp_digit)1; |
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191 } else { |
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192 mp_word tmp; |
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193 tmp = (mp_word)x.dp[i] << (mp_word)DIGIT_BIT; |
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194 tmp |= (mp_word)x.dp[i - 1]; |
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195 tmp /= (mp_word)y.dp[t]; |
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196 if (tmp > (mp_word)MP_MASK) { |
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197 tmp = MP_MASK; |
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198 } |
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199 q.dp[(i - t) - 1] = (mp_digit)(tmp & (mp_word)MP_MASK); |
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200 } |
284
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201 |
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202 /* while (q{i-t-1} * (yt * b + y{t-1})) > |
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203 xi * b**2 + xi-1 * b + xi-2 |
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204 |
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205 do q{i-t-1} -= 1; |
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206 */ |
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207 q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] + 1uL) & (mp_digit)MP_MASK; |
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208 do { |
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209 q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] - 1uL) & (mp_digit)MP_MASK; |
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210 |
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211 /* find left hand */ |
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212 mp_zero(&t1); |
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213 t1.dp[0] = ((t - 1) < 0) ? 0u : y.dp[t - 1]; |
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214 t1.dp[1] = y.dp[t]; |
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215 t1.used = 2; |
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216 if ((res = mp_mul_d(&t1, q.dp[(i - t) - 1], &t1)) != MP_OKAY) { |
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217 goto LBL_Y; |
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218 } |
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219 |
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220 /* find right hand */ |
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221 t2.dp[0] = ((i - 2) < 0) ? 0u : x.dp[i - 2]; |
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222 t2.dp[1] = ((i - 1) < 0) ? 0u : x.dp[i - 1]; |
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223 t2.dp[2] = x.dp[i]; |
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224 t2.used = 3; |
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225 } while (mp_cmp_mag(&t1, &t2) == MP_GT); |
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226 |
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227 /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */ |
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228 if ((res = mp_mul_d(&y, q.dp[(i - t) - 1], &t1)) != MP_OKAY) { |
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229 goto LBL_Y; |
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230 } |
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231 |
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232 if ((res = mp_lshd(&t1, (i - t) - 1)) != MP_OKAY) { |
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233 goto LBL_Y; |
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234 } |
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235 |
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236 if ((res = mp_sub(&x, &t1, &x)) != MP_OKAY) { |
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237 goto LBL_Y; |
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238 } |
284
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239 |
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240 /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */ |
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241 if (x.sign == MP_NEG) { |
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242 if ((res = mp_copy(&y, &t1)) != MP_OKAY) { |
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243 goto LBL_Y; |
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244 } |
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245 if ((res = mp_lshd(&t1, (i - t) - 1)) != MP_OKAY) { |
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246 goto LBL_Y; |
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247 } |
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248 if ((res = mp_add(&x, &t1, &x)) != MP_OKAY) { |
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249 goto LBL_Y; |
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250 } |
1436 | 251 |
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252 q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] - 1uL) & MP_MASK; |
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253 } |
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254 } |
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255 |
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256 /* now q is the quotient and x is the remainder |
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257 * [which we have to normalize] |
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258 */ |
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259 |
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260 /* get sign before writing to c */ |
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261 x.sign = (x.used == 0) ? MP_ZPOS : a->sign; |
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262 |
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263 if (c != NULL) { |
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264 mp_clamp(&q); |
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265 mp_exch(&q, c); |
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266 c->sign = neg; |
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267 } |
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268 |
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269 if (d != NULL) { |
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270 if ((res = mp_div_2d(&x, norm, &x, NULL)) != MP_OKAY) { |
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271 goto LBL_Y; |
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272 } |
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273 mp_exch(&x, d); |
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274 } |
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275 |
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276 res = MP_OKAY; |
284
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277 |
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278 LBL_Y: |
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279 mp_clear(&y); |
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280 LBL_X: |
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281 mp_clear(&x); |
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282 LBL_T2: |
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283 mp_clear(&t2); |
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284 LBL_T1: |
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285 mp_clear(&t1); |
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286 LBL_Q: |
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287 mp_clear(&q); |
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288 return res; |
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289 } |
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290 |
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291 #endif |
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292 |
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293 #endif |
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294 |
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295 /* ref: HEAD -> master, tag: v1.1.0 */ |
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296 /* git commit: 08549ad6bc8b0cede0b357a9c341c5c6473a9c55 */ |
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297 /* commit time: 2019-01-28 20:32:32 +0100 */ |