1 | #include <tommath.h> |
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2 | #ifdef BN_MP_TOOM_MUL_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 | * The library is free for all purposes without any express |
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13 | * guarantee it works. |
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14 | * |
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15 | * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com |
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16 | */ |
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17 | |
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18 | /* multiplication using the Toom-Cook 3-way algorithm |
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19 | * |
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20 | * Much more complicated than Karatsuba but has a lower |
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21 | * asymptotic running time of O(N**1.464). This algorithm is |
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22 | * only particularly useful on VERY large inputs |
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23 | * (we're talking 1000s of digits here...). |
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24 | */ |
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25 | int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c) |
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26 | { |
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27 | mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2; |
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28 | int res, B; |
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29 | |
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30 | /* init temps */ |
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31 | if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4, |
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32 | &a0, &a1, &a2, &b0, &b1, |
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33 | &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) { |
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34 | return res; |
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35 | } |
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36 | |
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37 | /* B */ |
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38 | B = MIN(a->used, b->used) / 3; |
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39 | |
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40 | /* a = a2 * B**2 + a1 * B + a0 */ |
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41 | if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) { |
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42 | goto ERR; |
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43 | } |
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44 | |
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45 | if ((res = mp_copy(a, &a1)) != MP_OKAY) { |
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46 | goto ERR; |
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47 | } |
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48 | mp_rshd(&a1, B); |
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49 | mp_mod_2d(&a1, DIGIT_BIT * B, &a1); |
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50 | |
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51 | if ((res = mp_copy(a, &a2)) != MP_OKAY) { |
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52 | goto ERR; |
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53 | } |
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54 | mp_rshd(&a2, B*2); |
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55 | |
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56 | /* b = b2 * B**2 + b1 * B + b0 */ |
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57 | if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) { |
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58 | goto ERR; |
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59 | } |
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60 | |
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61 | if ((res = mp_copy(b, &b1)) != MP_OKAY) { |
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62 | goto ERR; |
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63 | } |
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64 | mp_rshd(&b1, B); |
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65 | mp_mod_2d(&b1, DIGIT_BIT * B, &b1); |
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66 | |
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67 | if ((res = mp_copy(b, &b2)) != MP_OKAY) { |
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68 | goto ERR; |
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69 | } |
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70 | mp_rshd(&b2, B*2); |
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71 | |
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72 | /* w0 = a0*b0 */ |
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73 | if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) { |
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74 | goto ERR; |
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75 | } |
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76 | |
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77 | /* w4 = a2 * b2 */ |
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78 | if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) { |
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79 | goto ERR; |
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80 | } |
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81 | |
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82 | /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */ |
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83 | if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) { |
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84 | goto ERR; |
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85 | } |
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86 | if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) { |
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87 | goto ERR; |
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88 | } |
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89 | if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) { |
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90 | goto ERR; |
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91 | } |
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92 | if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) { |
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93 | goto ERR; |
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94 | } |
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95 | |
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96 | if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) { |
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97 | goto ERR; |
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98 | } |
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99 | if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) { |
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100 | goto ERR; |
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101 | } |
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102 | if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) { |
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103 | goto ERR; |
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104 | } |
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105 | if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) { |
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106 | goto ERR; |
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107 | } |
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108 | |
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109 | if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) { |
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110 | goto ERR; |
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111 | } |
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112 | |
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113 | /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */ |
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114 | if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) { |
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115 | goto ERR; |
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116 | } |
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117 | if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) { |
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118 | goto ERR; |
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119 | } |
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120 | if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) { |
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121 | goto ERR; |
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122 | } |
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123 | if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) { |
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124 | goto ERR; |
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125 | } |
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126 | |
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127 | if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) { |
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128 | goto ERR; |
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129 | } |
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130 | if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) { |
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131 | goto ERR; |
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132 | } |
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133 | if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) { |
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134 | goto ERR; |
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135 | } |
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136 | if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) { |
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137 | goto ERR; |
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138 | } |
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139 | |
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140 | if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) { |
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141 | goto ERR; |
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142 | } |
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143 | |
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144 | |
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145 | /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */ |
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146 | if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) { |
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147 | goto ERR; |
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148 | } |
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149 | if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) { |
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150 | goto ERR; |
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151 | } |
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152 | if ((res = mp_add(&b2, &b1, &tmp2)) != MP_OKAY) { |
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153 | goto ERR; |
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154 | } |
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155 | if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) { |
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156 | goto ERR; |
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157 | } |
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158 | if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) { |
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159 | goto ERR; |
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160 | } |
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161 | |
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162 | /* now solve the matrix |
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163 | |
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164 | 0 0 0 0 1 |
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165 | 1 2 4 8 16 |
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166 | 1 1 1 1 1 |
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167 | 16 8 4 2 1 |
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168 | 1 0 0 0 0 |
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169 | |
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170 | using 12 subtractions, 4 shifts, |
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171 | 2 small divisions and 1 small multiplication |
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172 | */ |
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173 | |
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174 | /* r1 - r4 */ |
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175 | if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) { |
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176 | goto ERR; |
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177 | } |
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178 | /* r3 - r0 */ |
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179 | if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) { |
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180 | goto ERR; |
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181 | } |
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182 | /* r1/2 */ |
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183 | if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) { |
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184 | goto ERR; |
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185 | } |
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186 | /* r3/2 */ |
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187 | if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) { |
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188 | goto ERR; |
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189 | } |
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190 | /* r2 - r0 - r4 */ |
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191 | if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) { |
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192 | goto ERR; |
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193 | } |
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194 | if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) { |
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195 | goto ERR; |
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196 | } |
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197 | /* r1 - r2 */ |
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198 | if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) { |
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199 | goto ERR; |
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200 | } |
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201 | /* r3 - r2 */ |
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202 | if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) { |
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203 | goto ERR; |
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204 | } |
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205 | /* r1 - 8r0 */ |
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206 | if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) { |
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207 | goto ERR; |
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208 | } |
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209 | if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) { |
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210 | goto ERR; |
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211 | } |
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212 | /* r3 - 8r4 */ |
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213 | if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) { |
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214 | goto ERR; |
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215 | } |
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216 | if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) { |
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217 | goto ERR; |
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218 | } |
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219 | /* 3r2 - r1 - r3 */ |
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220 | if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) { |
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221 | goto ERR; |
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222 | } |
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223 | if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) { |
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224 | goto ERR; |
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225 | } |
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226 | if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) { |
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227 | goto ERR; |
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228 | } |
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229 | /* r1 - r2 */ |
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230 | if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) { |
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231 | goto ERR; |
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232 | } |
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233 | /* r3 - r2 */ |
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234 | if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) { |
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235 | goto ERR; |
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236 | } |
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237 | /* r1/3 */ |
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238 | if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) { |
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239 | goto ERR; |
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240 | } |
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241 | /* r3/3 */ |
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242 | if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) { |
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243 | goto ERR; |
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244 | } |
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245 | |
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246 | /* at this point shift W[n] by B*n */ |
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247 | if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) { |
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248 | goto ERR; |
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249 | } |
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250 | if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) { |
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251 | goto ERR; |
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252 | } |
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253 | if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) { |
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254 | goto ERR; |
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255 | } |
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256 | if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) { |
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257 | goto ERR; |
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258 | } |
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259 | |
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260 | if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) { |
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261 | goto ERR; |
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262 | } |
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263 | if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) { |
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264 | goto ERR; |
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265 | } |
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266 | if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) { |
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267 | goto ERR; |
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268 | } |
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269 | if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) { |
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270 | goto ERR; |
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271 | } |
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272 | |
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273 | ERR: |
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274 | mp_clear_multi(&w0, &w1, &w2, &w3, &w4, |
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275 | &a0, &a1, &a2, &b0, &b1, |
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276 | &b2, &tmp1, &tmp2, NULL); |
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277 | return res; |
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278 | } |
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279 | |
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280 | #endif |
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281 | |
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282 | /* $Source: /cvsroot/tcl/libtommath/bn_mp_toom_mul.c,v $ */ |
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283 | /* $Revision: 1.1.1.4 $ */ |
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284 | /* $Date: 2006/12/01 00:08:11 $ */ |
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