1 | |
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2 | |
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3 | #include <NTL/LLL.h> |
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4 | #include <NTL/fileio.h> |
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5 | |
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6 | #include <NTL/new.h> |
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7 | |
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8 | NTL_START_IMPL |
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9 | |
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10 | |
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11 | |
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12 | |
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13 | static void RowTransform(vec_ZZ& A, vec_ZZ& B, const ZZ& MU1) |
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14 | // x = x - y*MU |
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15 | { |
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16 | static ZZ T, MU; |
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17 | long k; |
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18 | |
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19 | long n = A.length(); |
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20 | long i; |
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21 | |
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22 | MU = MU1; |
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23 | |
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24 | if (MU == 1) { |
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25 | for (i = 1; i <= n; i++) |
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26 | sub(A(i), A(i), B(i)); |
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27 | |
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28 | return; |
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29 | } |
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30 | |
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31 | if (MU == -1) { |
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32 | for (i = 1; i <= n; i++) |
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33 | add(A(i), A(i), B(i)); |
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34 | |
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35 | return; |
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36 | } |
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37 | |
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38 | if (MU == 0) return; |
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39 | |
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40 | if (NumTwos(MU) >= NTL_ZZ_NBITS) |
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41 | k = MakeOdd(MU); |
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42 | else |
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43 | k = 0; |
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44 | |
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45 | |
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46 | if (MU.WideSinglePrecision()) { |
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47 | long mu1; |
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48 | conv(mu1, MU); |
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49 | |
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50 | for (i = 1; i <= n; i++) { |
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51 | mul(T, B(i), mu1); |
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52 | if (k > 0) LeftShift(T, T, k); |
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53 | sub(A(i), A(i), T); |
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54 | } |
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55 | } |
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56 | else { |
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57 | for (i = 1; i <= n; i++) { |
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58 | mul(T, B(i), MU); |
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59 | if (k > 0) LeftShift(T, T, k); |
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60 | sub(A(i), A(i), T); |
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61 | } |
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62 | } |
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63 | } |
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64 | |
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65 | static void RowTransform2(vec_ZZ& A, vec_ZZ& B, const ZZ& MU1) |
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66 | // x = x + y*MU |
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67 | { |
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68 | static ZZ T, MU; |
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69 | long k; |
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70 | |
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71 | long n = A.length(); |
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72 | long i; |
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73 | |
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74 | MU = MU1; |
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75 | |
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76 | if (MU == 1) { |
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77 | for (i = 1; i <= n; i++) |
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78 | add(A(i), A(i), B(i)); |
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79 | |
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80 | return; |
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81 | } |
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82 | |
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83 | if (MU == -1) { |
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84 | for (i = 1; i <= n; i++) |
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85 | sub(A(i), A(i), B(i)); |
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86 | |
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87 | return; |
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88 | } |
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89 | |
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90 | if (MU == 0) return; |
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91 | |
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92 | if (NumTwos(MU) >= NTL_ZZ_NBITS) |
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93 | k = MakeOdd(MU); |
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94 | else |
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95 | k = 0; |
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96 | |
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97 | if (MU.WideSinglePrecision()) { |
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98 | long mu1; |
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99 | conv(mu1, MU); |
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100 | |
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101 | for (i = 1; i <= n; i++) { |
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102 | mul(T, B(i), mu1); |
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103 | if (k > 0) LeftShift(T, T, k); |
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104 | add(A(i), A(i), T); |
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105 | } |
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106 | } |
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107 | else { |
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108 | for (i = 1; i <= n; i++) { |
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109 | mul(T, B(i), MU); |
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110 | if (k > 0) LeftShift(T, T, k); |
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111 | add(A(i), A(i), T); |
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112 | } |
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113 | } |
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114 | } |
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115 | |
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116 | void ComputeGS(const mat_ZZ& B, mat_RR& B1, |
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117 | mat_RR& mu, vec_RR& b, |
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118 | vec_RR& c, long k, const RR& bound, long st, |
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119 | vec_RR& buf, const RR& bound2) |
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120 | { |
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121 | long i, j; |
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122 | RR s, t, t1; |
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123 | ZZ T1; |
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124 | |
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125 | if (st < k) { |
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126 | for (i = 1; i < st; i++) |
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127 | mul(buf(i), mu(k,i), c(i)); |
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128 | } |
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129 | |
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130 | for (j = st; j <= k-1; j++) { |
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131 | InnerProduct(s, B1(k), B1(j)); |
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132 | |
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133 | sqr(t1, s); |
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134 | mul(t1, t1, bound); |
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135 | mul(t, b(k), b(j)); |
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136 | |
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137 | if (t >= bound2 && t >= t1) { |
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138 | InnerProduct(T1, B(k), B(j)); |
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139 | conv(s, T1); |
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140 | } |
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141 | |
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142 | clear(t1); |
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143 | for (i = 1; i <= j-1; i++) { |
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144 | mul(t, mu(j, i), buf(i)); |
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145 | add(t1, t1, t); |
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146 | } |
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147 | |
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148 | sub(t, s, t1); |
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149 | buf(j) = t; |
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150 | div(mu(k, j), t, c(j)); |
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151 | } |
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152 | |
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153 | |
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154 | clear(s); |
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155 | for (j = 1; j <= k-1; j++) { |
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156 | mul(t, mu(k, j), buf(j)); |
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157 | add(s, s, t); |
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158 | } |
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159 | |
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160 | sub(c(k), b(k), s); |
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161 | } |
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162 | |
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163 | static RR red_fudge; |
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164 | static long log_red = 0; |
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165 | |
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166 | static void init_red_fudge() |
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167 | { |
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168 | log_red = long(0.50*RR::precision()); |
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169 | |
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170 | power2(red_fudge, -log_red); |
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171 | } |
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172 | |
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173 | static void inc_red_fudge() |
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174 | { |
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175 | |
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176 | mul(red_fudge, red_fudge, 2); |
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177 | log_red--; |
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178 | |
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179 | if (log_red < 4) |
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180 | Error("LLL_RR: can not continue...sorry"); |
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181 | } |
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182 | |
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183 | |
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184 | |
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185 | |
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186 | static long verbose = 0; |
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187 | |
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188 | static unsigned long NumSwaps = 0; |
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189 | static double StartTime = 0; |
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190 | static double LastTime = 0; |
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191 | |
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192 | |
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193 | |
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194 | static void LLLStatus(long max_k, double t, long m, const mat_ZZ& B) |
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195 | { |
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196 | ZZ t1; |
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197 | long i; |
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198 | double prodlen = 0; |
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199 | |
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200 | for (i = 1; i <= m; i++) { |
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201 | InnerProduct(t1, B(i), B(i)); |
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202 | if (!IsZero(t1)) |
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203 | prodlen += log(t1); |
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204 | } |
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205 | |
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206 | LastTime = t; |
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207 | |
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208 | } |
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209 | |
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210 | |
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211 | |
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212 | static |
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213 | long ll_LLL_RR(mat_ZZ& B, mat_ZZ* U, const RR& delta, long deep, |
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214 | LLLCheckFct check, mat_RR& B1, mat_RR& mu, |
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215 | vec_RR& b, vec_RR& c, long m, long init_k, long &quit) |
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216 | { |
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217 | long n = B.NumCols(); |
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218 | |
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219 | long i, j, k, Fc1; |
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220 | ZZ MU; |
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221 | RR mu1, t1, t2, cc; |
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222 | ZZ T1; |
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223 | |
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224 | RR bound; |
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225 | |
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226 | // we tolerate a 15% loss of precision in computing |
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227 | // inner products in ComputeGS. |
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228 | |
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229 | power2(bound, 2*long(0.15*RR::precision())); |
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230 | |
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231 | |
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232 | RR bound2; |
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233 | |
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234 | power2(bound2, 2*RR::precision()); |
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235 | |
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236 | |
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237 | quit = 0; |
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238 | k = init_k; |
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239 | |
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240 | vec_long st_mem; |
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241 | st_mem.SetLength(m+2); |
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242 | long *st = st_mem.elts(); |
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243 | |
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244 | for (i = 1; i < k; i++) |
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245 | st[i] = i; |
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246 | |
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247 | for (i = k; i <= m+1; i++) |
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248 | st[i] = 1; |
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249 | |
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250 | vec_RR buf; |
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251 | buf.SetLength(m); |
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252 | |
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253 | long rst; |
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254 | long counter; |
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255 | |
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256 | long trigger_index; |
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257 | long small_trigger; |
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258 | long cnt; |
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259 | |
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260 | RR half; |
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261 | conv(half, 0.5); |
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262 | RR half_plus_fudge; |
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263 | add(half_plus_fudge, half, red_fudge); |
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264 | |
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265 | long max_k = 0; |
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266 | double tt; |
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267 | |
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268 | while (k <= m) { |
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269 | |
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270 | if (k > max_k) { |
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271 | max_k = k; |
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272 | } |
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273 | |
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274 | if (verbose) { |
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275 | tt = GetTime(); |
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276 | |
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277 | if (tt > LastTime + LLLStatusInterval) |
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278 | LLLStatus(max_k, tt, m, B); |
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279 | } |
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280 | |
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281 | |
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282 | if (st[k] == k) |
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283 | rst = 1; |
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284 | else |
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285 | rst = k; |
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286 | |
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287 | if (st[k] < st[k+1]) st[k+1] = st[k]; |
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288 | ComputeGS(B, B1, mu, b, c, k, bound, st[k], buf, bound2); |
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289 | st[k] = k; |
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290 | |
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291 | counter = 0; |
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292 | trigger_index = k; |
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293 | small_trigger = 0; |
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294 | cnt = 0; |
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295 | |
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296 | do { |
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297 | // size reduction |
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298 | |
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299 | counter++; |
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300 | if (counter > 10000) { |
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301 | //cerr << "LLL_XD: warning--possible infinite loop\n"; |
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302 | counter = 0; |
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303 | } |
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304 | |
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305 | |
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306 | Fc1 = 0; |
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307 | |
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308 | for (j = rst-1; j >= 1; j--) { |
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309 | abs(t1, mu(k,j)); |
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310 | if (t1 > half_plus_fudge) { |
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311 | |
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312 | if (!Fc1) { |
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313 | if (j > trigger_index || |
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314 | (j == trigger_index && small_trigger)) { |
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315 | |
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316 | cnt++; |
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317 | |
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318 | if (cnt > 10) { |
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319 | inc_red_fudge(); |
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320 | add(half_plus_fudge, half, red_fudge); |
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321 | cnt = 0; |
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322 | } |
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323 | } |
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324 | |
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325 | trigger_index = j; |
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326 | small_trigger = (t1 < 4); |
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327 | } |
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328 | |
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329 | Fc1 = 1; |
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330 | |
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331 | mu1 = mu(k,j); |
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332 | if (sign(mu1) >= 0) { |
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333 | sub(mu1, mu1, half); |
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334 | ceil(mu1, mu1); |
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335 | } |
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336 | else { |
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337 | add(mu1, mu1, half); |
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338 | floor(mu1, mu1); |
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339 | } |
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340 | |
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341 | if (mu1 == 1) { |
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342 | for (i = 1; i <= j-1; i++) |
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343 | sub(mu(k,i), mu(k,i), mu(j,i)); |
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344 | } |
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345 | else if (mu1 == -1) { |
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346 | for (i = 1; i <= j-1; i++) |
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347 | add(mu(k,i), mu(k,i), mu(j,i)); |
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348 | } |
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349 | else { |
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350 | for (i = 1; i <= j-1; i++) { |
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351 | mul(t2, mu1, mu(j,i)); |
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352 | sub(mu(k,i), mu(k,i), t2); |
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353 | } |
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354 | } |
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355 | |
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356 | |
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357 | conv(MU, mu1); |
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358 | |
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359 | sub(mu(k,j), mu(k,j), mu1); |
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360 | |
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361 | RowTransform(B(k), B(j), MU); |
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362 | if (U) RowTransform((*U)(k), (*U)(j), MU); |
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363 | } |
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364 | } |
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365 | |
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366 | if (Fc1) { |
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367 | for (i = 1; i <= n; i++) |
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368 | conv(B1(k, i), B(k, i)); |
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369 | |
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370 | InnerProduct(b(k), B1(k), B1(k)); |
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371 | ComputeGS(B, B1, mu, b, c, k, bound, 1, buf, bound2); |
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372 | } |
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373 | } while (Fc1); |
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374 | |
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375 | if (check && (*check)(B(k))) |
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376 | quit = 1; |
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377 | |
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378 | if (IsZero(b(k))) { |
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379 | for (i = k; i < m; i++) { |
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380 | // swap i, i+1 |
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381 | swap(B(i), B(i+1)); |
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382 | swap(B1(i), B1(i+1)); |
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383 | swap(b(i), b(i+1)); |
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384 | if (U) swap((*U)(i), (*U)(i+1)); |
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385 | } |
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386 | |
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387 | for (i = k; i <= m+1; i++) st[i] = 1; |
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388 | |
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389 | m--; |
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390 | if (quit) break; |
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391 | continue; |
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392 | } |
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393 | |
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394 | if (quit) break; |
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395 | |
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396 | if (deep > 0) { |
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397 | // deep insertions |
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398 | |
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399 | cc = b(k); |
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400 | long l = 1; |
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401 | while (l <= k-1) { |
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402 | mul(t1, delta, c(l)); |
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403 | if (t1 > cc) break; |
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404 | sqr(t1, mu(k,l)); |
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405 | mul(t1, t1, c(l)); |
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406 | sub(cc, cc, t1); |
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407 | l++; |
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408 | } |
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409 | |
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410 | if (l <= k-1 && (l <= deep || k-l <= deep)) { |
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411 | // deep insertion at position l |
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412 | |
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413 | for (i = k; i > l; i--) { |
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414 | // swap rows i, i-1 |
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415 | swap(B(i), B(i-1)); |
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416 | swap(B1(i), B1(i-1)); |
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417 | swap(mu(i), mu(i-1)); |
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418 | swap(b(i), b(i-1)); |
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419 | if (U) swap((*U)(i), (*U)(i-1)); |
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420 | } |
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421 | |
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422 | k = l; |
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423 | continue; |
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424 | } |
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425 | } // end deep insertions |
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426 | |
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427 | // test LLL reduction condition |
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428 | |
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429 | if (k <= 1) { |
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430 | k++; |
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431 | } |
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432 | else { |
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433 | sqr(t1, mu(k,k-1)); |
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434 | mul(t1, t1, c(k-1)); |
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435 | add(t1, t1, c(k)); |
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436 | mul(t2, delta, c(k-1)); |
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437 | if (t2 > t1) { |
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438 | // swap rows k, k-1 |
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439 | swap(B(k), B(k-1)); |
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440 | swap(B1(k), B1(k-1)); |
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441 | swap(mu(k), mu(k-1)); |
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442 | swap(b(k), b(k-1)); |
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443 | if (U) swap((*U)(k), (*U)(k-1)); |
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444 | |
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445 | k--; |
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446 | NumSwaps++; |
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447 | } |
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448 | else { |
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449 | k++; |
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450 | } |
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451 | } |
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452 | } |
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453 | |
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454 | if (verbose) { |
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455 | LLLStatus(m+1, GetTime(), m, B); |
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456 | } |
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457 | |
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458 | |
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459 | return m; |
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460 | } |
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461 | |
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462 | static |
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463 | long LLL_RR(mat_ZZ& B, mat_ZZ* U, const RR& delta, long deep, |
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464 | LLLCheckFct check) |
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465 | { |
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466 | long m = B.NumRows(); |
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467 | long n = B.NumCols(); |
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468 | |
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469 | long i, j; |
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470 | long new_m, dep, quit; |
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471 | RR s; |
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472 | ZZ MU; |
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473 | RR mu1; |
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474 | |
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475 | RR t1; |
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476 | ZZ T1; |
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477 | |
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478 | init_red_fudge(); |
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479 | |
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480 | if (U) ident(*U, m); |
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481 | |
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482 | mat_RR B1; // approximates B |
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483 | B1.SetDims(m, n); |
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484 | |
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485 | |
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486 | mat_RR mu; |
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487 | mu.SetDims(m, m); |
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488 | |
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489 | vec_RR c; // squared lengths of Gramm-Schmidt basis vectors |
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490 | c.SetLength(m); |
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491 | |
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492 | vec_RR b; // squared lengths of basis vectors |
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493 | b.SetLength(m); |
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494 | |
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495 | |
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496 | for (i = 1; i <=m; i++) |
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497 | for (j = 1; j <= n; j++) |
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498 | conv(B1(i, j), B(i, j)); |
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499 | |
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500 | |
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501 | |
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502 | for (i = 1; i <= m; i++) { |
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503 | InnerProduct(b(i), B1(i), B1(i)); |
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504 | } |
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505 | |
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506 | |
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507 | new_m = ll_LLL_RR(B, U, delta, deep, check, B1, mu, b, c, m, 1, quit); |
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508 | dep = m - new_m; |
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509 | m = new_m; |
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510 | |
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511 | if (dep > 0) { |
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512 | // for consistency, we move all of the zero rows to the front |
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513 | |
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514 | for (i = 0; i < m; i++) { |
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515 | swap(B(m+dep-i), B(m-i)); |
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516 | if (U) swap((*U)(m+dep-i), (*U)(m-i)); |
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517 | } |
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518 | } |
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519 | |
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520 | |
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521 | return m; |
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522 | } |
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523 | |
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524 | |
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525 | |
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526 | long LLL_RR(mat_ZZ& B, double delta, long deep, |
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527 | LLLCheckFct check, long verb) |
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528 | { |
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529 | verbose = verb; |
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530 | NumSwaps = 0; |
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531 | if (verbose) { |
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532 | StartTime = GetTime(); |
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533 | LastTime = StartTime; |
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534 | } |
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535 | |
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536 | if (delta < 0.50 || delta >= 1) Error("LLL_RR: bad delta"); |
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537 | if (deep < 0) Error("LLL_RR: bad deep"); |
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538 | RR Delta; |
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539 | conv(Delta, delta); |
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540 | return LLL_RR(B, 0, Delta, deep, check); |
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541 | } |
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542 | |
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543 | long LLL_RR(mat_ZZ& B, mat_ZZ& U, double delta, long deep, |
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544 | LLLCheckFct check, long verb) |
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545 | { |
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546 | verbose = verb; |
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547 | NumSwaps = 0; |
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548 | if (verbose) { |
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549 | StartTime = GetTime(); |
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550 | LastTime = StartTime; |
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551 | } |
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552 | |
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553 | if (delta < 0.50 || delta >= 1) Error("LLL_RR: bad delta"); |
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554 | if (deep < 0) Error("LLL_RR: bad deep"); |
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555 | RR Delta; |
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556 | conv(Delta, delta); |
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557 | return LLL_RR(B, &U, Delta, deep, check); |
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558 | } |
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559 | |
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560 | |
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561 | |
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562 | static vec_RR BKZConstant; |
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563 | |
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564 | static |
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565 | void ComputeBKZConstant(long beta, long p) |
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566 | { |
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567 | RR c_PI; |
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568 | ComputePi(c_PI); |
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569 | |
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570 | RR LogPI = log(c_PI); |
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571 | |
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572 | BKZConstant.SetLength(beta-1); |
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573 | |
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574 | vec_RR Log; |
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575 | Log.SetLength(beta); |
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576 | |
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577 | |
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578 | long i, j, k; |
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579 | RR x, y; |
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580 | |
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581 | for (j = 1; j <= beta; j++) |
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582 | Log(j) = log(to_RR(j)); |
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583 | |
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584 | for (i = 1; i <= beta-1; i++) { |
---|
585 | // First, we compute x = gamma(i/2)^{2/i} |
---|
586 | |
---|
587 | k = i/2; |
---|
588 | |
---|
589 | if ((i & 1) == 0) { // i even |
---|
590 | x = 0; |
---|
591 | for (j = 1; j <= k; j++) |
---|
592 | x += Log(j); |
---|
593 | |
---|
594 | x = exp(x/k); |
---|
595 | |
---|
596 | } |
---|
597 | else { // i odd |
---|
598 | x = 0; |
---|
599 | for (j = k + 2; j <= 2*k + 2; j++) |
---|
600 | x += Log(j); |
---|
601 | |
---|
602 | x += 0.5*LogPI - 2*(k+1)*Log(2); |
---|
603 | |
---|
604 | x = exp(2*x/i); |
---|
605 | } |
---|
606 | |
---|
607 | // Second, we compute y = 2^{2*p/i} |
---|
608 | |
---|
609 | y = exp(-(2*p/to_RR(i))*Log(2)); |
---|
610 | |
---|
611 | BKZConstant(i) = x*y/c_PI; |
---|
612 | } |
---|
613 | |
---|
614 | } |
---|
615 | |
---|
616 | static vec_RR BKZThresh; |
---|
617 | |
---|
618 | static |
---|
619 | void ComputeBKZThresh(RR *c, long beta) |
---|
620 | { |
---|
621 | BKZThresh.SetLength(beta-1); |
---|
622 | |
---|
623 | long i; |
---|
624 | RR x; |
---|
625 | RR t1; |
---|
626 | |
---|
627 | x = 0; |
---|
628 | |
---|
629 | for (i = 1; i <= beta-1; i++) { |
---|
630 | log(t1, c[i-1]); |
---|
631 | add(x, x, t1); |
---|
632 | div(t1, x, i); |
---|
633 | exp(t1, t1); |
---|
634 | mul(BKZThresh(i), t1, BKZConstant(i)); |
---|
635 | } |
---|
636 | } |
---|
637 | |
---|
638 | |
---|
639 | |
---|
640 | |
---|
641 | static |
---|
642 | void BKZStatus(double tt, double enum_time, unsigned long NumIterations, |
---|
643 | unsigned long NumTrivial, unsigned long NumNonTrivial, |
---|
644 | unsigned long NumNoOps, long m, |
---|
645 | const mat_ZZ& B) |
---|
646 | { |
---|
647 | |
---|
648 | ZZ t1; |
---|
649 | long i; |
---|
650 | double prodlen = 0; |
---|
651 | |
---|
652 | for (i = 1; i <= m; i++) { |
---|
653 | InnerProduct(t1, B(i), B(i)); |
---|
654 | if (!IsZero(t1)) |
---|
655 | prodlen += log(t1); |
---|
656 | } |
---|
657 | |
---|
658 | LastTime = tt; |
---|
659 | |
---|
660 | } |
---|
661 | |
---|
662 | |
---|
663 | |
---|
664 | |
---|
665 | static |
---|
666 | long BKZ_RR(mat_ZZ& BB, mat_ZZ* UU, const RR& delta, |
---|
667 | long beta, long prune, LLLCheckFct check) |
---|
668 | { |
---|
669 | long m = BB.NumRows(); |
---|
670 | long n = BB.NumCols(); |
---|
671 | long m_orig = m; |
---|
672 | |
---|
673 | long i, j; |
---|
674 | ZZ MU; |
---|
675 | |
---|
676 | RR t1, t2; |
---|
677 | ZZ T1; |
---|
678 | |
---|
679 | init_red_fudge(); |
---|
680 | |
---|
681 | mat_ZZ B; |
---|
682 | B = BB; |
---|
683 | |
---|
684 | B.SetDims(m+1, n); |
---|
685 | |
---|
686 | |
---|
687 | mat_RR B1; |
---|
688 | B1.SetDims(m+1, n); |
---|
689 | |
---|
690 | mat_RR mu; |
---|
691 | mu.SetDims(m+1, m); |
---|
692 | |
---|
693 | vec_RR c; |
---|
694 | c.SetLength(m+1); |
---|
695 | |
---|
696 | vec_RR b; |
---|
697 | b.SetLength(m+1); |
---|
698 | |
---|
699 | RR cbar; |
---|
700 | |
---|
701 | vec_RR ctilda; |
---|
702 | ctilda.SetLength(m+1); |
---|
703 | |
---|
704 | vec_RR vvec; |
---|
705 | vvec.SetLength(m+1); |
---|
706 | |
---|
707 | vec_RR yvec; |
---|
708 | yvec.SetLength(m+1); |
---|
709 | |
---|
710 | vec_RR uvec; |
---|
711 | uvec.SetLength(m+1); |
---|
712 | |
---|
713 | vec_RR utildavec; |
---|
714 | utildavec.SetLength(m+1); |
---|
715 | |
---|
716 | vec_long Deltavec; |
---|
717 | Deltavec.SetLength(m+1); |
---|
718 | |
---|
719 | vec_long deltavec; |
---|
720 | deltavec.SetLength(m+1); |
---|
721 | |
---|
722 | mat_ZZ Ulocal; |
---|
723 | mat_ZZ *U; |
---|
724 | |
---|
725 | if (UU) { |
---|
726 | Ulocal.SetDims(m+1, m); |
---|
727 | for (i = 1; i <= m; i++) |
---|
728 | conv(Ulocal(i, i), 1); |
---|
729 | U = &Ulocal; |
---|
730 | } |
---|
731 | else |
---|
732 | U = 0; |
---|
733 | |
---|
734 | long quit; |
---|
735 | long new_m; |
---|
736 | long z, jj, kk; |
---|
737 | long s, t; |
---|
738 | long h; |
---|
739 | |
---|
740 | |
---|
741 | for (i = 1; i <=m; i++) |
---|
742 | for (j = 1; j <= n; j++) |
---|
743 | conv(B1(i, j), B(i, j)); |
---|
744 | |
---|
745 | |
---|
746 | for (i = 1; i <= m; i++) { |
---|
747 | InnerProduct(b(i), B1(i), B1(i)); |
---|
748 | } |
---|
749 | |
---|
750 | // cerr << "\n"; |
---|
751 | // cerr << "first LLL\n"; |
---|
752 | |
---|
753 | m = ll_LLL_RR(B, U, delta, 0, check, B1, mu, b, c, m, 1, quit); |
---|
754 | |
---|
755 | double tt; |
---|
756 | |
---|
757 | double enum_time = 0; |
---|
758 | unsigned long NumIterations = 0; |
---|
759 | unsigned long NumTrivial = 0; |
---|
760 | unsigned long NumNonTrivial = 0; |
---|
761 | unsigned long NumNoOps = 0; |
---|
762 | |
---|
763 | long verb = verbose; |
---|
764 | |
---|
765 | verbose = 0; |
---|
766 | |
---|
767 | |
---|
768 | if (m < m_orig) { |
---|
769 | for (i = m_orig+1; i >= m+2; i--) { |
---|
770 | // swap i, i-1 |
---|
771 | |
---|
772 | swap(B(i), B(i-1)); |
---|
773 | if (U) swap((*U)(i), (*U)(i-1)); |
---|
774 | } |
---|
775 | } |
---|
776 | |
---|
777 | long clean = 1; |
---|
778 | |
---|
779 | if (!quit && m > 1) { |
---|
780 | // cerr << "continuing\n"; |
---|
781 | |
---|
782 | if (beta > m) beta = m; |
---|
783 | |
---|
784 | if (prune > 0) |
---|
785 | ComputeBKZConstant(beta, prune); |
---|
786 | |
---|
787 | z = 0; |
---|
788 | jj = 0; |
---|
789 | |
---|
790 | while (z < m-1) { |
---|
791 | jj++; |
---|
792 | kk = min(jj+beta-1, m); |
---|
793 | |
---|
794 | if (jj == m) { |
---|
795 | jj = 1; |
---|
796 | kk = beta; |
---|
797 | clean = 1; |
---|
798 | } |
---|
799 | |
---|
800 | if (verb) { |
---|
801 | tt = GetTime(); |
---|
802 | if (tt > LastTime + LLLStatusInterval) |
---|
803 | BKZStatus(tt, enum_time, NumIterations, NumTrivial, |
---|
804 | NumNonTrivial, NumNoOps, m, B); |
---|
805 | } |
---|
806 | |
---|
807 | // ENUM |
---|
808 | |
---|
809 | double tt1; |
---|
810 | |
---|
811 | if (verb) { |
---|
812 | tt1 = GetTime(); |
---|
813 | } |
---|
814 | |
---|
815 | if (prune > 0) |
---|
816 | ComputeBKZThresh(&c(jj), kk-jj+1); |
---|
817 | |
---|
818 | cbar = c(jj); |
---|
819 | conv(utildavec(jj), 1); |
---|
820 | conv(uvec(jj), 1); |
---|
821 | |
---|
822 | conv(yvec(jj), 0); |
---|
823 | conv(vvec(jj), 0); |
---|
824 | Deltavec(jj) = 0; |
---|
825 | |
---|
826 | |
---|
827 | s = t = jj; |
---|
828 | deltavec(jj) = 1; |
---|
829 | |
---|
830 | for (i = jj+1; i <= kk+1; i++) { |
---|
831 | conv(ctilda(i), 0); |
---|
832 | conv(uvec(i), 0); |
---|
833 | conv(utildavec(i), 0); |
---|
834 | conv(yvec(i), 0); |
---|
835 | Deltavec(i) = 0; |
---|
836 | conv(vvec(i), 0); |
---|
837 | deltavec(i) = 1; |
---|
838 | } |
---|
839 | |
---|
840 | long enum_cnt = 0; |
---|
841 | |
---|
842 | while (t <= kk) { |
---|
843 | if (verb) { |
---|
844 | enum_cnt++; |
---|
845 | if (enum_cnt > 100000) { |
---|
846 | enum_cnt = 0; |
---|
847 | tt = GetTime(); |
---|
848 | if (tt > LastTime + LLLStatusInterval) { |
---|
849 | enum_time += tt - tt1; |
---|
850 | tt1 = tt; |
---|
851 | BKZStatus(tt, enum_time, NumIterations, NumTrivial, |
---|
852 | NumNonTrivial, NumNoOps, m, B); |
---|
853 | } |
---|
854 | } |
---|
855 | } |
---|
856 | |
---|
857 | |
---|
858 | add(t1, yvec(t), utildavec(t)); |
---|
859 | sqr(t1, t1); |
---|
860 | mul(t1, t1, c(t)); |
---|
861 | add(ctilda(t), ctilda(t+1), t1); |
---|
862 | |
---|
863 | if (prune > 0 && t > jj) |
---|
864 | sub(t1, cbar, BKZThresh(t-jj)); |
---|
865 | else |
---|
866 | t1 = cbar; |
---|
867 | |
---|
868 | |
---|
869 | if (ctilda(t) <t1) { |
---|
870 | if (t > jj) { |
---|
871 | t--; |
---|
872 | clear(t1); |
---|
873 | for (i = t+1; i <= s; i++) { |
---|
874 | mul(t2, utildavec(i), mu(i,t)); |
---|
875 | add(t1, t1, t2); |
---|
876 | } |
---|
877 | |
---|
878 | yvec(t) = t1; |
---|
879 | negate(t1, t1); |
---|
880 | if (sign(t1) >= 0) { |
---|
881 | sub(t1, t1, 0.5); |
---|
882 | ceil(t1, t1); |
---|
883 | } |
---|
884 | else { |
---|
885 | add(t1, t1, 0.5); |
---|
886 | floor(t1, t1); |
---|
887 | } |
---|
888 | |
---|
889 | utildavec(t) = t1; |
---|
890 | vvec(t) = t1; |
---|
891 | Deltavec(t) = 0; |
---|
892 | |
---|
893 | negate(t1, t1); |
---|
894 | |
---|
895 | if (t1 < yvec(t)) |
---|
896 | deltavec(t) = -1; |
---|
897 | else |
---|
898 | deltavec(t) = 1; |
---|
899 | } |
---|
900 | else { |
---|
901 | cbar = ctilda(jj); |
---|
902 | for (i = jj; i <= kk; i++) { |
---|
903 | uvec(i) = utildavec(i); |
---|
904 | } |
---|
905 | } |
---|
906 | } |
---|
907 | else { |
---|
908 | t++; |
---|
909 | s = max(s, t); |
---|
910 | if (t < s) Deltavec(t) = -Deltavec(t); |
---|
911 | if (Deltavec(t)*deltavec(t) >= 0) Deltavec(t) += deltavec(t); |
---|
912 | add(utildavec(t), vvec(t), Deltavec(t)); |
---|
913 | } |
---|
914 | } |
---|
915 | |
---|
916 | if (verb) { |
---|
917 | tt1 = GetTime() - tt1; |
---|
918 | enum_time += tt1; |
---|
919 | } |
---|
920 | |
---|
921 | NumIterations++; |
---|
922 | |
---|
923 | h = min(kk+1, m); |
---|
924 | |
---|
925 | mul(t1, red_fudge, -8); |
---|
926 | add(t1, t1, delta); |
---|
927 | mul(t1, t1, c(jj)); |
---|
928 | |
---|
929 | if (t1 > cbar) { |
---|
930 | |
---|
931 | clean = 0; |
---|
932 | |
---|
933 | // we treat the case that the new vector is b_s (jj < s <= kk) |
---|
934 | // as a special case that appears to occur most of the time. |
---|
935 | |
---|
936 | s = 0; |
---|
937 | for (i = jj+1; i <= kk; i++) { |
---|
938 | if (uvec(i) != 0) { |
---|
939 | if (s == 0) |
---|
940 | s = i; |
---|
941 | else |
---|
942 | s = -1; |
---|
943 | } |
---|
944 | } |
---|
945 | |
---|
946 | if (s == 0) Error("BKZ_RR: internal error"); |
---|
947 | |
---|
948 | if (s > 0) { |
---|
949 | // special case |
---|
950 | // cerr << "special case\n"; |
---|
951 | |
---|
952 | NumTrivial++; |
---|
953 | |
---|
954 | for (i = s; i > jj; i--) { |
---|
955 | // swap i, i-1 |
---|
956 | swap(B(i-1), B(i)); |
---|
957 | swap(B1(i-1), B1(i)); |
---|
958 | swap(b(i-1), b(i)); |
---|
959 | if (U) swap((*U)(i-1), (*U)(i)); |
---|
960 | } |
---|
961 | |
---|
962 | new_m = ll_LLL_RR(B, U, delta, 0, check, |
---|
963 | B1, mu, b, c, h, jj, quit); |
---|
964 | if (new_m != h) Error("BKZ_RR: internal error"); |
---|
965 | if (quit) break; |
---|
966 | } |
---|
967 | else { |
---|
968 | // the general case |
---|
969 | |
---|
970 | NumNonTrivial++; |
---|
971 | |
---|
972 | for (i = 1; i <= n; i++) conv(B(m+1, i), 0); |
---|
973 | |
---|
974 | if (U) { |
---|
975 | for (i = 1; i <= m_orig; i++) |
---|
976 | conv((*U)(m+1, i), 0); |
---|
977 | } |
---|
978 | |
---|
979 | for (i = jj; i <= kk; i++) { |
---|
980 | if (uvec(i) == 0) continue; |
---|
981 | conv(MU, uvec(i)); |
---|
982 | RowTransform2(B(m+1), B(i), MU); |
---|
983 | if (U) RowTransform2((*U)(m+1), (*U)(i), MU); |
---|
984 | } |
---|
985 | |
---|
986 | for (i = m+1; i >= jj+1; i--) { |
---|
987 | // swap i, i-1 |
---|
988 | swap(B(i-1), B(i)); |
---|
989 | swap(B1(i-1), B1(i)); |
---|
990 | swap(b(i-1), b(i)); |
---|
991 | if (U) swap((*U)(i-1), (*U)(i)); |
---|
992 | } |
---|
993 | |
---|
994 | for (i = 1; i <= n; i++) |
---|
995 | conv(B1(jj, i), B(jj, i)); |
---|
996 | |
---|
997 | InnerProduct(b(jj), B1(jj), B1(jj)); |
---|
998 | |
---|
999 | if (b(jj) == 0) Error("BKZ_RR: internal error"); |
---|
1000 | |
---|
1001 | // remove linear dependencies |
---|
1002 | |
---|
1003 | // cerr << "general case\n"; |
---|
1004 | new_m = ll_LLL_RR(B, U, delta, 0, 0, B1, mu, b, c, kk+1, jj, quit); |
---|
1005 | |
---|
1006 | if (new_m != kk) Error("BKZ_RR: internal error"); |
---|
1007 | |
---|
1008 | // remove zero vector |
---|
1009 | |
---|
1010 | for (i = kk+2; i <= m+1; i++) { |
---|
1011 | // swap i, i-1 |
---|
1012 | swap(B(i-1), B(i)); |
---|
1013 | swap(B1(i-1), B1(i)); |
---|
1014 | swap(b(i-1), b(i)); |
---|
1015 | if (U) swap((*U)(i-1), (*U)(i)); |
---|
1016 | } |
---|
1017 | |
---|
1018 | quit = 0; |
---|
1019 | if (check) { |
---|
1020 | for (i = 1; i <= kk; i++) |
---|
1021 | if ((*check)(B(i))) { |
---|
1022 | quit = 1; |
---|
1023 | break; |
---|
1024 | } |
---|
1025 | } |
---|
1026 | |
---|
1027 | if (quit) break; |
---|
1028 | |
---|
1029 | if (h > kk) { |
---|
1030 | // extend reduced basis |
---|
1031 | |
---|
1032 | new_m = ll_LLL_RR(B, U, delta, 0, check, |
---|
1033 | B1, mu, b, c, h, h, quit); |
---|
1034 | |
---|
1035 | if (new_m != h) Error("BKZ_RR: internal error"); |
---|
1036 | if (quit) break; |
---|
1037 | } |
---|
1038 | } |
---|
1039 | |
---|
1040 | z = 0; |
---|
1041 | } |
---|
1042 | else { |
---|
1043 | // LLL_RR |
---|
1044 | // cerr << "progress\n"; |
---|
1045 | |
---|
1046 | NumNoOps++; |
---|
1047 | |
---|
1048 | if (!clean) { |
---|
1049 | new_m = |
---|
1050 | ll_LLL_RR(B, U, delta, 0, check, B1, mu, b, c, h, h, quit); |
---|
1051 | if (new_m != h) Error("BKZ_RR: internal error"); |
---|
1052 | if (quit) break; |
---|
1053 | } |
---|
1054 | |
---|
1055 | z++; |
---|
1056 | } |
---|
1057 | } |
---|
1058 | } |
---|
1059 | |
---|
1060 | if (verb) { |
---|
1061 | BKZStatus(GetTime(), enum_time, NumIterations, NumTrivial, NumNonTrivial, |
---|
1062 | NumNoOps, m, B); |
---|
1063 | } |
---|
1064 | |
---|
1065 | |
---|
1066 | // clean up |
---|
1067 | |
---|
1068 | if (m_orig > m) { |
---|
1069 | // for consistency, we move zero vectors to the front |
---|
1070 | |
---|
1071 | for (i = m+1; i <= m_orig; i++) { |
---|
1072 | swap(B(i), B(i+1)); |
---|
1073 | if (U) swap((*U)(i), (*U)(i+1)); |
---|
1074 | } |
---|
1075 | |
---|
1076 | for (i = 0; i < m; i++) { |
---|
1077 | swap(B(m_orig-i), B(m-i)); |
---|
1078 | if (U) swap((*U)(m_orig-i), (*U)(m-i)); |
---|
1079 | } |
---|
1080 | } |
---|
1081 | |
---|
1082 | B.SetDims(m_orig, n); |
---|
1083 | BB = B; |
---|
1084 | |
---|
1085 | if (U) { |
---|
1086 | U->SetDims(m_orig, m_orig); |
---|
1087 | *UU = *U; |
---|
1088 | } |
---|
1089 | |
---|
1090 | return m; |
---|
1091 | } |
---|
1092 | |
---|
1093 | long BKZ_RR(mat_ZZ& BB, mat_ZZ& UU, double delta, |
---|
1094 | long beta, long prune, LLLCheckFct check, long verb) |
---|
1095 | { |
---|
1096 | verbose = verb; |
---|
1097 | NumSwaps = 0; |
---|
1098 | if (verbose) { |
---|
1099 | StartTime = GetTime(); |
---|
1100 | LastTime = StartTime; |
---|
1101 | } |
---|
1102 | |
---|
1103 | if (delta < 0.50 || delta >= 1) Error("BKZ_RR: bad delta"); |
---|
1104 | if (beta < 2) Error("BKZ_RR: bad block size"); |
---|
1105 | |
---|
1106 | RR Delta; |
---|
1107 | conv(Delta, delta); |
---|
1108 | |
---|
1109 | return BKZ_RR(BB, &UU, Delta, beta, prune, check); |
---|
1110 | } |
---|
1111 | |
---|
1112 | long BKZ_RR(mat_ZZ& BB, double delta, |
---|
1113 | long beta, long prune, LLLCheckFct check, long verb) |
---|
1114 | { |
---|
1115 | verbose = verb; |
---|
1116 | NumSwaps = 0; |
---|
1117 | if (verbose) { |
---|
1118 | StartTime = GetTime(); |
---|
1119 | LastTime = StartTime; |
---|
1120 | } |
---|
1121 | |
---|
1122 | if (delta < 0.50 || delta >= 1) Error("BKZ_RR: bad delta"); |
---|
1123 | if (beta < 2) Error("BKZ_RR: bad block size"); |
---|
1124 | |
---|
1125 | RR Delta; |
---|
1126 | conv(Delta, delta); |
---|
1127 | |
---|
1128 | return BKZ_RR(BB, 0, Delta, beta, prune, check); |
---|
1129 | } |
---|
1130 | |
---|
1131 | |
---|
1132 | |
---|
1133 | |
---|
1134 | void NearVector(vec_ZZ& ww, const mat_ZZ& BB, const vec_ZZ& a) |
---|
1135 | { |
---|
1136 | long n = BB.NumCols(); |
---|
1137 | |
---|
1138 | if (n != BB.NumRows()) |
---|
1139 | Error("NearVector: matrix must be square"); |
---|
1140 | |
---|
1141 | if (n != a.length()) |
---|
1142 | Error("NearVector: dimension mismatch"); |
---|
1143 | |
---|
1144 | long i, j; |
---|
1145 | mat_ZZ B; |
---|
1146 | |
---|
1147 | B.SetDims(n+1, n); |
---|
1148 | for (i = 1; i <= n; i++) |
---|
1149 | B(i) = BB(i); |
---|
1150 | |
---|
1151 | B(n+1) = a; |
---|
1152 | |
---|
1153 | mat_RR B1, mu; |
---|
1154 | vec_RR b, c; |
---|
1155 | |
---|
1156 | B1.SetDims(n+1, n); |
---|
1157 | mu.SetDims(n+1, n+1); |
---|
1158 | b.SetLength(n+1); |
---|
1159 | c.SetLength(n+1); |
---|
1160 | |
---|
1161 | vec_RR buf; |
---|
1162 | buf.SetLength(n+1); |
---|
1163 | |
---|
1164 | |
---|
1165 | for (i = 1; i <= n+1; i++) |
---|
1166 | for (j = 1; j <= n; j++) |
---|
1167 | conv(B1(i, j), B(i, j)); |
---|
1168 | |
---|
1169 | for (i = 1; i <= n+1; i++) |
---|
1170 | InnerProduct(b(i), B1(i), B1(i)); |
---|
1171 | |
---|
1172 | |
---|
1173 | |
---|
1174 | RR bound; |
---|
1175 | power2(bound, 2*long(0.15*RR::precision())); |
---|
1176 | |
---|
1177 | RR bound2; |
---|
1178 | power2(bound2, 2*RR::precision()); |
---|
1179 | |
---|
1180 | |
---|
1181 | for (i = 1; i <= n+1; i++) |
---|
1182 | ComputeGS(B, B1, mu, b, c, i, bound, 1, buf, bound2); |
---|
1183 | |
---|
1184 | init_red_fudge(); |
---|
1185 | |
---|
1186 | RR half; |
---|
1187 | conv(half, 0.5); |
---|
1188 | RR half_plus_fudge; |
---|
1189 | add(half_plus_fudge, half, red_fudge); |
---|
1190 | |
---|
1191 | RR t1, t2, mu1; |
---|
1192 | ZZ MU; |
---|
1193 | |
---|
1194 | long trigger_index = n+1; |
---|
1195 | long small_trigger = 0; |
---|
1196 | long cnt = 0; |
---|
1197 | |
---|
1198 | long Fc1; |
---|
1199 | |
---|
1200 | vec_ZZ w; |
---|
1201 | w.SetLength(n); |
---|
1202 | clear(w); |
---|
1203 | |
---|
1204 | do { |
---|
1205 | Fc1 = 0; |
---|
1206 | |
---|
1207 | for (j = n; j >= 1; j--) { |
---|
1208 | abs(t1, mu(n+1,j)); |
---|
1209 | if (t1 > half_plus_fudge) { |
---|
1210 | |
---|
1211 | if (!Fc1) { |
---|
1212 | if (j > trigger_index || |
---|
1213 | (j == trigger_index && small_trigger)) { |
---|
1214 | |
---|
1215 | cnt++; |
---|
1216 | |
---|
1217 | if (cnt > 10) { |
---|
1218 | inc_red_fudge(); |
---|
1219 | add(half_plus_fudge, half, red_fudge); |
---|
1220 | cnt = 0; |
---|
1221 | } |
---|
1222 | } |
---|
1223 | |
---|
1224 | trigger_index = j; |
---|
1225 | small_trigger = (t1 < 4); |
---|
1226 | } |
---|
1227 | |
---|
1228 | Fc1 = 1; |
---|
1229 | |
---|
1230 | mu1 = mu(n+1,j); |
---|
1231 | if (sign(mu1) >= 0) { |
---|
1232 | sub(mu1, mu1, half); |
---|
1233 | ceil(mu1, mu1); |
---|
1234 | } |
---|
1235 | else { |
---|
1236 | add(mu1, mu1, half); |
---|
1237 | floor(mu1, mu1); |
---|
1238 | } |
---|
1239 | |
---|
1240 | if (mu1 == 1) { |
---|
1241 | for (i = 1; i <= j-1; i++) |
---|
1242 | sub(mu(n+1,i), mu(n+1,i), mu(j,i)); |
---|
1243 | } |
---|
1244 | else if (mu1 == -1) { |
---|
1245 | for (i = 1; i <= j-1; i++) |
---|
1246 | add(mu(n+1,i), mu(n+1,i), mu(j,i)); |
---|
1247 | } |
---|
1248 | else { |
---|
1249 | for (i = 1; i <= j-1; i++) { |
---|
1250 | mul(t2, mu1, mu(j,i)); |
---|
1251 | sub(mu(n+1,i), mu(n+1,i), t2); |
---|
1252 | } |
---|
1253 | } |
---|
1254 | |
---|
1255 | |
---|
1256 | conv(MU, mu1); |
---|
1257 | |
---|
1258 | sub(mu(n+1,j), mu(n+1,j), mu1); |
---|
1259 | |
---|
1260 | RowTransform(B(n+1), B(j), MU); |
---|
1261 | RowTransform2(w, B(j), MU); |
---|
1262 | } |
---|
1263 | } |
---|
1264 | |
---|
1265 | if (Fc1) { |
---|
1266 | for (i = 1; i <= n; i++) |
---|
1267 | conv(B1(n+1, i), B(n+1, i)); |
---|
1268 | |
---|
1269 | InnerProduct(b(n+1), B1(n+1), B1(n+1)); |
---|
1270 | ComputeGS(B, B1, mu, b, c, n+1, bound, 1, buf, bound2); |
---|
1271 | } |
---|
1272 | } while (Fc1); |
---|
1273 | |
---|
1274 | ww = w; |
---|
1275 | } |
---|
1276 | |
---|
1277 | NTL_END_IMPL |
---|