Mercurial > dropbear
annotate libtommath/bn_mp_div.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 |
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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 /* SPDX-License-Identifier: Unlicense */ |
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5 |
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6 #ifdef BN_MP_DIV_SMALL |
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7 |
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8 /* slower bit-bang division... also smaller */ |
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9 mp_err mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d) |
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10 { |
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11 mp_int ta, tb, tq, q; |
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12 int n, n2; |
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13 mp_err err; |
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14 |
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15 /* is divisor zero ? */ |
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16 if (MP_IS_ZERO(b)) { |
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17 return MP_VAL; |
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18 } |
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19 |
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20 /* if a < b then q=0, r = a */ |
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21 if (mp_cmp_mag(a, b) == MP_LT) { |
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22 if (d != NULL) { |
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23 err = mp_copy(a, d); |
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24 } else { |
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25 err = MP_OKAY; |
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26 } |
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27 if (c != NULL) { |
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28 mp_zero(c); |
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29 } |
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30 return err; |
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31 } |
1436 | 32 |
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33 /* init our temps */ |
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34 if ((err = mp_init_multi(&ta, &tb, &tq, &q, NULL)) != MP_OKAY) { |
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35 return err; |
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36 } |
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37 |
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38 |
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39 mp_set(&tq, 1uL); |
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40 n = mp_count_bits(a) - mp_count_bits(b); |
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41 if ((err = mp_abs(a, &ta)) != MP_OKAY) goto LBL_ERR; |
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42 if ((err = mp_abs(b, &tb)) != MP_OKAY) goto LBL_ERR; |
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43 if ((err = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) goto LBL_ERR; |
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44 if ((err = mp_mul_2d(&tq, n, &tq)) != MP_OKAY) goto LBL_ERR; |
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45 |
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46 while (n-- >= 0) { |
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47 if (mp_cmp(&tb, &ta) != MP_GT) { |
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48 if ((err = mp_sub(&ta, &tb, &ta)) != MP_OKAY) goto LBL_ERR; |
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49 if ((err = mp_add(&q, &tq, &q)) != MP_OKAY) goto LBL_ERR; |
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50 } |
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51 if ((err = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) goto LBL_ERR; |
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52 if ((err = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY) goto LBL_ERR; |
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53 } |
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54 |
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55 /* now q == quotient and ta == remainder */ |
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56 n = a->sign; |
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57 n2 = (a->sign == b->sign) ? MP_ZPOS : MP_NEG; |
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58 if (c != NULL) { |
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59 mp_exch(c, &q); |
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60 c->sign = MP_IS_ZERO(c) ? MP_ZPOS : n2; |
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61 } |
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62 if (d != NULL) { |
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63 mp_exch(d, &ta); |
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64 d->sign = MP_IS_ZERO(d) ? MP_ZPOS : n; |
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65 } |
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66 LBL_ERR: |
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67 mp_clear_multi(&ta, &tb, &tq, &q, NULL); |
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68 return err; |
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69 } |
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70 |
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71 #else |
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72 |
1436 | 73 /* integer signed division. |
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74 * c*b + d == a [e.g. a/b, c=quotient, d=remainder] |
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75 * HAC pp.598 Algorithm 14.20 |
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76 * |
1436 | 77 * Note that the description in HAC is horribly |
78 * incomplete. For example, it doesn't consider | |
79 * the case where digits are removed from 'x' in | |
80 * the inner loop. It also doesn't consider the | |
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81 * case that y has fewer than three digits, etc.. |
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82 * |
1436 | 83 * The overall algorithm is as described as |
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84 * 14.20 from HAC but fixed to treat these cases. |
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85 */ |
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86 mp_err mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d) |
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87 { |
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88 mp_int q, x, y, t1, t2; |
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89 int n, t, i, norm; |
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90 mp_sign neg; |
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91 mp_err err; |
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92 |
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93 /* is divisor zero ? */ |
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94 if (MP_IS_ZERO(b)) { |
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|
95 return MP_VAL; |
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96 } |
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97 |
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98 /* if a < b then q=0, r = a */ |
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99 if (mp_cmp_mag(a, b) == MP_LT) { |
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100 if (d != NULL) { |
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101 err = mp_copy(a, d); |
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102 } else { |
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103 err = MP_OKAY; |
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104 } |
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105 if (c != NULL) { |
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106 mp_zero(c); |
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107 } |
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108 return err; |
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109 } |
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110 |
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111 if ((err = mp_init_size(&q, a->used + 2)) != MP_OKAY) { |
1051e4eea25a
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112 return err; |
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113 } |
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114 q.used = a->used + 2; |
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115 |
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116 if ((err = mp_init(&t1)) != MP_OKAY) goto LBL_Q; |
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117 |
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118 if ((err = mp_init(&t2)) != MP_OKAY) goto LBL_T1; |
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119 |
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120 if ((err = mp_init_copy(&x, a)) != MP_OKAY) goto LBL_T2; |
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121 |
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122 if ((err = mp_init_copy(&y, b)) != MP_OKAY) goto LBL_X; |
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123 |
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124 /* fix the sign */ |
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125 neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG; |
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126 x.sign = y.sign = MP_ZPOS; |
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127 |
1692
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128 /* normalize both x and y, ensure that y >= b/2, [b == 2**MP_DIGIT_BIT] */ |
1051e4eea25a
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129 norm = mp_count_bits(&y) % MP_DIGIT_BIT; |
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130 if (norm < (MP_DIGIT_BIT - 1)) { |
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131 norm = (MP_DIGIT_BIT - 1) - norm; |
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132 if ((err = mp_mul_2d(&x, norm, &x)) != MP_OKAY) goto LBL_Y; |
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133 if ((err = mp_mul_2d(&y, norm, &y)) != MP_OKAY) goto LBL_Y; |
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134 } else { |
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135 norm = 0; |
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136 } |
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137 |
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138 /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */ |
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139 n = x.used - 1; |
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140 t = y.used - 1; |
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141 |
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142 /* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */ |
1692
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143 /* y = y*b**{n-t} */ |
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144 if ((err = mp_lshd(&y, n - t)) != MP_OKAY) goto LBL_Y; |
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145 |
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146 while (mp_cmp(&x, &y) != MP_LT) { |
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147 ++(q.dp[n - t]); |
1692
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148 if ((err = mp_sub(&x, &y, &x)) != MP_OKAY) goto LBL_Y; |
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|
149 } |
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150 |
1655
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151 /* reset y by shifting it back down */ |
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152 mp_rshd(&y, n - t); |
1436 | 153 |
1655
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154 /* step 3. for i from n down to (t + 1) */ |
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155 for (i = n; i >= (t + 1); i--) { |
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156 if (i > x.used) { |
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157 continue; |
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158 } |
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|
159 |
1655
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160 /* step 3.1 if xi == yt then set q{i-t-1} to b-1, |
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161 * otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */ |
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|
162 if (x.dp[i] == y.dp[t]) { |
1692
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163 q.dp[(i - t) - 1] = ((mp_digit)1 << (mp_digit)MP_DIGIT_BIT) - (mp_digit)1; |
1655
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|
164 } else { |
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|
165 mp_word tmp; |
1692
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166 tmp = (mp_word)x.dp[i] << (mp_word)MP_DIGIT_BIT; |
1655
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167 tmp |= (mp_word)x.dp[i - 1]; |
f52919ffd3b1
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168 tmp /= (mp_word)y.dp[t]; |
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169 if (tmp > (mp_word)MP_MASK) { |
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|
170 tmp = MP_MASK; |
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171 } |
f52919ffd3b1
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|
172 q.dp[(i - t) - 1] = (mp_digit)(tmp & (mp_word)MP_MASK); |
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|
173 } |
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174 |
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|
175 /* while (q{i-t-1} * (yt * b + y{t-1})) > |
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176 xi * b**2 + xi-1 * b + xi-2 |
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177 |
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178 do q{i-t-1} -= 1; |
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179 */ |
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180 q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] + 1uL) & (mp_digit)MP_MASK; |
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|
181 do { |
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182 q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] - 1uL) & (mp_digit)MP_MASK; |
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183 |
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|
184 /* find left hand */ |
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185 mp_zero(&t1); |
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186 t1.dp[0] = ((t - 1) < 0) ? 0u : y.dp[t - 1]; |
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187 t1.dp[1] = y.dp[t]; |
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188 t1.used = 2; |
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189 if ((err = mp_mul_d(&t1, q.dp[(i - t) - 1], &t1)) != MP_OKAY) goto LBL_Y; |
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190 |
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191 /* find right hand */ |
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192 t2.dp[0] = ((i - 2) < 0) ? 0u : x.dp[i - 2]; |
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193 t2.dp[1] = x.dp[i - 1]; /* i >= 1 always holds */ |
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194 t2.dp[2] = x.dp[i]; |
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195 t2.used = 3; |
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196 } while (mp_cmp_mag(&t1, &t2) == MP_GT); |
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197 |
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198 /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */ |
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199 if ((err = mp_mul_d(&y, q.dp[(i - t) - 1], &t1)) != MP_OKAY) goto LBL_Y; |
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200 |
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201 if ((err = mp_lshd(&t1, (i - t) - 1)) != MP_OKAY) goto LBL_Y; |
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202 |
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203 if ((err = mp_sub(&x, &t1, &x)) != MP_OKAY) goto LBL_Y; |
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204 |
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205 /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */ |
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206 if (x.sign == MP_NEG) { |
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207 if ((err = mp_copy(&y, &t1)) != MP_OKAY) goto LBL_Y; |
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208 if ((err = mp_lshd(&t1, (i - t) - 1)) != MP_OKAY) goto LBL_Y; |
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209 if ((err = mp_add(&x, &t1, &x)) != MP_OKAY) goto LBL_Y; |
1436 | 210 |
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211 q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] - 1uL) & MP_MASK; |
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212 } |
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213 } |
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214 |
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215 /* now q is the quotient and x is the remainder |
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216 * [which we have to normalize] |
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217 */ |
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218 |
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219 /* get sign before writing to c */ |
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220 x.sign = (x.used == 0) ? MP_ZPOS : a->sign; |
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221 |
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222 if (c != NULL) { |
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223 mp_clamp(&q); |
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224 mp_exch(&q, c); |
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225 c->sign = neg; |
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226 } |
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227 |
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228 if (d != NULL) { |
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229 if ((err = mp_div_2d(&x, norm, &x, NULL)) != MP_OKAY) goto LBL_Y; |
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230 mp_exch(&x, d); |
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231 } |
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232 |
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233 err = MP_OKAY; |
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234 |
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235 LBL_Y: |
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236 mp_clear(&y); |
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237 LBL_X: |
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238 mp_clear(&x); |
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239 LBL_T2: |
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240 mp_clear(&t2); |
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241 LBL_T1: |
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242 mp_clear(&t1); |
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243 LBL_Q: |
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244 mp_clear(&q); |
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245 return err; |
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246 } |
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247 |
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248 #endif |
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249 |
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250 #endif |