Mercurial > dropbear
annotate libtommath/bn_mp_div.c @ 1901:4e36e3a95084
Fix tarball retention-days
author | Matt Johnston <matt@ucc.asn.au> |
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date | Thu, 24 Mar 2022 12:26:09 +0800 |
parents | 1051e4eea25a |
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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) { |
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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 |
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128 /* normalize both x and y, ensure that y >= b/2, [b == 2**MP_DIGIT_BIT] */ |
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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} } */ |
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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]); |
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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 |
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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 |
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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 } |
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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 |