1 | |
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2 | #include <NTL/LLL.h> |
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3 | #include <NTL/fileio.h> |
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4 | #include <NTL/vec_xdouble.h> |
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5 | #include <NTL/vec_double.h> |
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6 | |
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7 | #include <NTL/new.h> |
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8 | |
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9 | NTL_START_IMPL |
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10 | |
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11 | |
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12 | static xdouble InnerProduct(xdouble *a, xdouble *b, long n) |
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13 | { |
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14 | xdouble s; |
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15 | long i; |
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16 | |
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17 | s = 0; |
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18 | for (i = 1; i <= n; i++) |
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19 | MulAdd(s, s, a[i], b[i]); |
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20 | |
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21 | return s; |
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22 | } |
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23 | |
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24 | |
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25 | static void RowTransform(vec_ZZ& A, vec_ZZ& B, const ZZ& MU1) |
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26 | // x = x - y*MU |
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27 | { |
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28 | static ZZ T, MU; |
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29 | long k; |
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30 | |
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31 | long n = A.length(); |
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32 | long i; |
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33 | |
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34 | MU = MU1; |
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35 | |
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36 | if (MU == 1) { |
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37 | for (i = 1; i <= n; i++) |
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38 | sub(A(i), A(i), B(i)); |
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39 | |
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40 | return; |
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41 | } |
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42 | |
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43 | if (MU == -1) { |
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44 | for (i = 1; i <= n; i++) |
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45 | add(A(i), A(i), B(i)); |
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46 | |
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47 | return; |
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48 | } |
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49 | |
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50 | if (MU == 0) return; |
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51 | |
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52 | if (NumTwos(MU) >= NTL_ZZ_NBITS) |
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53 | k = MakeOdd(MU); |
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54 | else |
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55 | k = 0; |
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56 | |
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57 | |
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58 | if (MU.WideSinglePrecision()) { |
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59 | long mu1; |
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60 | conv(mu1, MU); |
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61 | |
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62 | for (i = 1; i <= n; i++) { |
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63 | mul(T, B(i), mu1); |
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64 | if (k > 0) LeftShift(T, T, k); |
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65 | sub(A(i), A(i), T); |
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66 | } |
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67 | } |
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68 | else { |
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69 | for (i = 1; i <= n; i++) { |
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70 | mul(T, B(i), MU); |
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71 | if (k > 0) LeftShift(T, T, k); |
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72 | sub(A(i), A(i), T); |
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73 | } |
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74 | } |
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75 | } |
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76 | |
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77 | static void RowTransform2(vec_ZZ& A, vec_ZZ& B, const ZZ& MU1) |
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78 | // x = x + y*MU |
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79 | { |
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80 | static ZZ T, MU; |
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81 | long k; |
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82 | |
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83 | long n = A.length(); |
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84 | long i; |
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85 | |
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86 | MU = MU1; |
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87 | |
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88 | if (MU == 1) { |
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89 | for (i = 1; i <= n; i++) |
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90 | add(A(i), A(i), B(i)); |
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91 | |
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92 | return; |
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93 | } |
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94 | |
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95 | if (MU == -1) { |
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96 | for (i = 1; i <= n; i++) |
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97 | sub(A(i), A(i), B(i)); |
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98 | |
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99 | return; |
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100 | } |
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101 | |
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102 | if (MU == 0) return; |
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103 | |
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104 | if (NumTwos(MU) >= NTL_ZZ_NBITS) |
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105 | k = MakeOdd(MU); |
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106 | else |
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107 | k = 0; |
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108 | |
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109 | if (MU.WideSinglePrecision()) { |
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110 | long mu1; |
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111 | conv(mu1, MU); |
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112 | |
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113 | for (i = 1; i <= n; i++) { |
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114 | mul(T, B(i), mu1); |
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115 | if (k > 0) LeftShift(T, T, k); |
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116 | add(A(i), A(i), T); |
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117 | } |
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118 | } |
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119 | else { |
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120 | for (i = 1; i <= n; i++) { |
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121 | mul(T, B(i), MU); |
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122 | if (k > 0) LeftShift(T, T, k); |
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123 | add(A(i), A(i), T); |
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124 | } |
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125 | } |
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126 | } |
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127 | |
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128 | static |
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129 | void ComputeGS(mat_ZZ& B, xdouble **B1, xdouble **mu, xdouble *b, |
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130 | xdouble *c, long k, xdouble bound, long st, xdouble *buf) |
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131 | { |
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132 | long n = B.NumCols(); |
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133 | long i, j; |
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134 | xdouble s, t1, y, t; |
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135 | ZZ T1; |
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136 | |
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137 | xdouble *mu_k = mu[k]; |
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138 | |
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139 | if (st < k) { |
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140 | for (i = 1; i < st; i++) |
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141 | buf[i] = mu_k[i]*c[i]; |
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142 | } |
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143 | |
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144 | for (j = st; j <= k-1; j++) { |
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145 | if (b[k]*b[j] < NTL_FDOUBLE_PRECISION*NTL_FDOUBLE_PRECISION) { |
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146 | double z = 0; |
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147 | xdouble *B1_k = B1[k]; |
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148 | xdouble *B1_j = B1[j]; |
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149 | |
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150 | for (i = 1; i <= n; i++) |
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151 | z += B1_k[i].x * B1_j[i].x; |
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152 | |
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153 | s = z; |
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154 | } |
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155 | else { |
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156 | s = InnerProduct(B1[k], B1[j], n); |
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157 | |
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158 | if (s*s <= b[k]*b[j]/bound) { |
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159 | InnerProduct(T1, B(k), B(j)); |
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160 | conv(s, T1); |
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161 | } |
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162 | } |
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163 | |
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164 | xdouble *mu_j = mu[j]; |
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165 | |
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166 | t1 = 0; |
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167 | for (i = 1; i <= j-1; i++) |
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168 | MulAdd(t1, t1, mu_j[i], buf[i]); |
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169 | |
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170 | mu_k[j] = (buf[j] = (s - t1))/c[j]; |
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171 | } |
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172 | |
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173 | s = 0; |
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174 | for (j = 1; j <= k-1; j++) |
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175 | MulAdd(s, s, mu_k[j], buf[j]); |
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176 | |
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177 | c[k] = b[k] - s; |
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178 | } |
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179 | |
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180 | static xdouble red_fudge = to_xdouble(0); |
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181 | static long log_red = 0; |
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182 | |
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183 | static void init_red_fudge() |
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184 | { |
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185 | long i; |
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186 | |
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187 | log_red = long(0.50*NTL_DOUBLE_PRECISION); |
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188 | red_fudge = 1; |
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189 | |
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190 | for (i = log_red; i > 0; i--) |
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191 | red_fudge = red_fudge*0.5; |
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192 | } |
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193 | |
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194 | static void inc_red_fudge() |
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195 | { |
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196 | |
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197 | red_fudge = red_fudge * 2; |
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198 | log_red--; |
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199 | |
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200 | cerr << "LLL_XD: warning--relaxing reduction (" << log_red << ")\n"; |
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201 | |
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202 | if (log_red < 4) |
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203 | Error("LLL_XD: can not continue...sorry"); |
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204 | } |
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205 | |
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206 | |
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207 | |
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208 | static long verbose = 0; |
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209 | |
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210 | static unsigned long NumSwaps = 0; |
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211 | static double StartTime = 0; |
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212 | static double LastTime = 0; |
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213 | |
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214 | |
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215 | |
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216 | static void LLLStatus(long max_k, double t, long m, const mat_ZZ& B) |
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217 | { |
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218 | cerr << "---- LLL_XD status ----\n"; |
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219 | cerr << "elapsed time: "; |
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220 | PrintTime(cerr, t-StartTime); |
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221 | cerr << ", stage: " << max_k; |
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222 | cerr << ", rank: " << m; |
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223 | cerr << ", swaps: " << NumSwaps << "\n"; |
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224 | |
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225 | ZZ t1; |
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226 | long i; |
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227 | double prodlen = 0; |
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228 | |
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229 | for (i = 1; i <= m; i++) { |
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230 | InnerProduct(t1, B(i), B(i)); |
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231 | if (!IsZero(t1)) |
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232 | prodlen += log(t1); |
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233 | } |
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234 | |
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235 | cerr << "log of prod of lengths: " << prodlen/(2.0*log(2.0)) << "\n"; |
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236 | |
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237 | if (LLLDumpFile) { |
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238 | cerr << "dumping to " << LLLDumpFile << "..."; |
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239 | |
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240 | ofstream f; |
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241 | OpenWrite(f, LLLDumpFile); |
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242 | |
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243 | f << "["; |
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244 | for (i = 1; i <= m; i++) { |
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245 | f << B(i) << "\n"; |
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246 | } |
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247 | f << "]\n"; |
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248 | |
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249 | f.close(); |
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250 | |
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251 | cerr << "\n"; |
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252 | } |
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253 | |
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254 | LastTime = t; |
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255 | |
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256 | } |
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257 | |
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258 | |
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259 | static |
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260 | long ll_LLL_XD(mat_ZZ& B, mat_ZZ* U, xdouble delta, long deep, |
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261 | LLLCheckFct check, xdouble **B1, xdouble **mu, |
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262 | xdouble *b, xdouble *c, |
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263 | long m, long init_k, long &quit) |
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264 | { |
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265 | long n = B.NumCols(); |
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266 | |
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267 | long i, j, k, Fc1; |
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268 | ZZ MU; |
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269 | xdouble mu1; |
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270 | |
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271 | xdouble t1; |
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272 | ZZ T1; |
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273 | xdouble *tp; |
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274 | |
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275 | |
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276 | static xdouble bound = to_xdouble(0); |
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277 | |
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278 | |
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279 | if (bound == 0) { |
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280 | // we tolerate a 15% loss of precision in computing |
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281 | // inner products in ComputeGS. |
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282 | |
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283 | bound = 1; |
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284 | for (i = 2*long(0.15*NTL_DOUBLE_PRECISION); i > 0; i--) { |
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285 | bound = bound * 2; |
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286 | } |
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287 | } |
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288 | |
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289 | |
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290 | xdouble half = to_xdouble(0.5); |
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291 | xdouble half_plus_fudge = 0.5 + red_fudge; |
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292 | |
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293 | quit = 0; |
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294 | k = init_k; |
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295 | |
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296 | vec_long st_mem; |
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297 | st_mem.SetLength(m+2); |
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298 | long *st = st_mem.elts(); |
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299 | |
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300 | for (i = 1; i < k; i++) |
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301 | st[i] = i; |
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302 | |
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303 | for (i = k; i <= m+1; i++) |
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304 | st[i] = 1; |
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305 | |
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306 | xdouble *buf; |
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307 | buf = NTL_NEW_OP xdouble [m+1]; |
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308 | if (!buf) Error("out of memory in lll_LLL_XD"); |
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309 | |
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310 | long rst; |
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311 | long counter; |
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312 | |
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313 | long trigger_index; |
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314 | long small_trigger; |
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315 | long cnt; |
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316 | |
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317 | long max_k = 0; |
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318 | |
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319 | double tt; |
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320 | |
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321 | |
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322 | while (k <= m) { |
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323 | |
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324 | if (k > max_k) { |
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325 | max_k = k; |
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326 | } |
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327 | |
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328 | if (verbose) { |
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329 | tt = GetTime(); |
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330 | |
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331 | if (tt > LastTime + LLLStatusInterval) |
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332 | LLLStatus(max_k, tt, m, B); |
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333 | } |
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334 | |
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335 | |
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336 | if (st[k] == k) |
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337 | rst = 1; |
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338 | else |
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339 | rst = k; |
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340 | |
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341 | if (st[k] < st[k+1]) st[k+1] = st[k]; |
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342 | ComputeGS(B, B1, mu, b, c, k, bound, st[k], buf); |
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343 | st[k] = k; |
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344 | |
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345 | counter = 0; |
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346 | trigger_index = k; |
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347 | small_trigger = 0; |
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348 | cnt = 0; |
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349 | |
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350 | do { |
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351 | // size reduction |
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352 | |
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353 | counter++; |
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354 | if (counter > 10000) { |
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355 | cerr << "LLL_XD: warning--possible infinite loop\n"; |
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356 | counter = 0; |
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357 | } |
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358 | |
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359 | |
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360 | Fc1 = 0; |
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361 | |
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362 | for (j = rst-1; j >= 1; j--) { |
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363 | t1 = fabs(mu[k][j]); |
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364 | if (t1 > half_plus_fudge) { |
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365 | |
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366 | if (!Fc1) { |
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367 | if (j > trigger_index || |
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368 | (j == trigger_index && small_trigger)) { |
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369 | |
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370 | cnt++; |
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371 | |
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372 | if (cnt > 10) { |
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373 | inc_red_fudge(); |
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374 | half_plus_fudge = 0.5 + red_fudge; |
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375 | cnt = 0; |
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376 | } |
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377 | } |
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378 | |
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379 | trigger_index = j; |
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380 | small_trigger = (t1 < 4); |
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381 | } |
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382 | |
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383 | |
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384 | Fc1 = 1; |
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385 | |
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386 | mu1 = mu[k][j]; |
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387 | if (mu1 >= 0) |
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388 | mu1 = ceil(mu1-half); |
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389 | else |
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390 | mu1 = floor(mu1+half); |
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391 | |
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392 | |
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393 | xdouble *mu_k = mu[k]; |
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394 | xdouble *mu_j = mu[j]; |
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395 | |
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396 | if (mu1 == 1) { |
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397 | for (i = 1; i <= j-1; i++) |
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398 | mu_k[i] -= mu_j[i]; |
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399 | } |
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400 | else if (mu1 == -1) { |
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401 | for (i = 1; i <= j-1; i++) |
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402 | mu_k[i] += mu_j[i]; |
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403 | } |
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404 | else { |
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405 | for (i = 1; i <= j-1; i++) |
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406 | MulSub(mu_k[i], mu_k[i], mu1, mu_j[i]); |
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407 | } |
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408 | |
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409 | mu_k[j] -= mu1; |
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410 | |
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411 | conv(MU, mu1); |
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412 | |
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413 | // cout << j << " " << MU << "\n"; |
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414 | |
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415 | RowTransform(B(k), B(j), MU); |
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416 | if (U) RowTransform((*U)(k), (*U)(j), MU); |
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417 | } |
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418 | } |
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419 | |
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420 | if (Fc1) { |
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421 | for (i = 1; i <= n; i++) |
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422 | conv(B1[k][i], B(k, i)); |
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423 | |
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424 | b[k] = InnerProduct(B1[k], B1[k], n); |
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425 | ComputeGS(B, B1, mu, b, c, k, bound, 1, buf); |
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426 | } |
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427 | } while (Fc1); |
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428 | |
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429 | if (check && (*check)(B(k))) |
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430 | quit = 1; |
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431 | |
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432 | if (b[k] == 0) { |
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433 | for (i = k; i < m; i++) { |
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434 | // swap i, i+1 |
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435 | swap(B(i), B(i+1)); |
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436 | tp = B1[i]; B1[i] = B1[i+1]; B1[i+1] = tp; |
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437 | t1 = b[i]; b[i] = b[i+1]; b[i+1] = t1; |
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438 | if (U) swap((*U)(i), (*U)(i+1)); |
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439 | } |
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440 | |
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441 | for (i = k; i <= m+1; i++) st[i] = 1; |
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442 | |
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443 | m--; |
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444 | if (quit) break; |
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445 | continue; |
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446 | } |
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447 | |
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448 | if (quit) break; |
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449 | |
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450 | if (deep > 0) { |
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451 | // deep insertions |
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452 | |
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453 | xdouble cc = b[k]; |
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454 | long l = 1; |
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455 | while (l <= k-1 && delta*c[l] <= cc) { |
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456 | cc = cc - mu[k][l]*mu[k][l]*c[l]; |
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457 | l++; |
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458 | } |
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459 | |
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460 | if (l <= k-1 && (l <= deep || k-l <= deep)) { |
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461 | // deep insertion at position l |
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462 | |
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463 | for (i = k; i > l; i--) { |
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464 | // swap rows i, i-1 |
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465 | swap(B(i), B(i-1)); |
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466 | tp = B1[i]; B1[i] = B1[i-1]; B1[i-1] = tp; |
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467 | tp = mu[i]; mu[i] = mu[i-1]; mu[i-1] = tp; |
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468 | t1 = b[i]; b[i] = b[i-1]; b[i-1] = t1; |
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469 | if (U) swap((*U)(i), (*U)(i-1)); |
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470 | } |
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471 | |
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472 | k = l; |
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473 | continue; |
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474 | } |
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475 | } // end deep insertions |
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476 | |
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477 | // test LLL reduction condition |
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478 | |
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479 | if (k > 1 && delta*c[k-1] > c[k] + mu[k][k-1]*mu[k][k-1]*c[k-1]) { |
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480 | // swap rows k, k-1 |
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481 | swap(B(k), B(k-1)); |
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482 | tp = B1[k]; B1[k] = B1[k-1]; B1[k-1] = tp; |
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483 | tp = mu[k]; mu[k] = mu[k-1]; mu[k-1] = tp; |
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484 | t1 = b[k]; b[k] = b[k-1]; b[k-1] = t1; |
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485 | if (U) swap((*U)(k), (*U)(k-1)); |
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486 | |
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487 | k--; |
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488 | NumSwaps++; |
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489 | |
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490 | // cout << "- " << k << "\n"; |
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491 | } |
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492 | else { |
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493 | k++; |
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494 | // cout << "+ " << k << "\n"; |
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495 | } |
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496 | } |
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497 | |
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498 | if (verbose) { |
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499 | LLLStatus(m+1, GetTime(), m, B); |
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500 | } |
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501 | |
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502 | |
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503 | delete [] buf; |
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504 | |
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505 | return m; |
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506 | } |
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507 | |
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508 | |
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509 | |
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510 | |
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511 | static |
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512 | long LLL_XD(mat_ZZ& B, mat_ZZ* U, xdouble delta, long deep, |
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513 | LLLCheckFct check) |
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514 | { |
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515 | long m = B.NumRows(); |
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516 | long n = B.NumCols(); |
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517 | |
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518 | long i, j; |
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519 | long new_m, dep, quit; |
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520 | xdouble s; |
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521 | ZZ MU; |
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522 | xdouble mu1; |
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523 | |
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524 | xdouble t1; |
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525 | ZZ T1; |
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526 | |
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527 | init_red_fudge(); |
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528 | |
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529 | if (U) ident(*U, m); |
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530 | |
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531 | xdouble **B1; // approximates B |
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532 | |
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533 | typedef xdouble *xdoubleptr; |
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534 | |
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535 | B1 = NTL_NEW_OP xdoubleptr[m+1]; |
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536 | if (!B1) Error("LLL_XD: out of memory"); |
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537 | |
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538 | for (i = 1; i <= m; i++) { |
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539 | B1[i] = NTL_NEW_OP xdouble[n+1]; |
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540 | if (!B1[i]) Error("LLL_XD: out of memory"); |
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541 | } |
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542 | |
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543 | xdouble **mu; |
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544 | mu = NTL_NEW_OP xdoubleptr[m+1]; |
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545 | if (!mu) Error("LLL_XD: out of memory"); |
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546 | |
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547 | for (i = 1; i <= m; i++) { |
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548 | mu[i] = NTL_NEW_OP xdouble[m+1]; |
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549 | if (!mu[i]) Error("LLL_XD: out of memory"); |
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550 | } |
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551 | |
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552 | xdouble *c; // squared lengths of Gramm-Schmidt basis vectors |
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553 | |
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554 | c = NTL_NEW_OP xdouble[m+1]; |
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555 | if (!c) Error("LLL_XD: out of memory"); |
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556 | |
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557 | xdouble *b; // squared lengths of basis vectors |
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558 | |
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559 | b = NTL_NEW_OP xdouble[m+1]; |
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560 | if (!b) Error("LLL_XD: out of memory"); |
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561 | |
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562 | |
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563 | |
---|
564 | for (i = 1; i <=m; i++) |
---|
565 | for (j = 1; j <= n; j++) |
---|
566 | conv(B1[i][j], B(i, j)); |
---|
567 | |
---|
568 | |
---|
569 | |
---|
570 | for (i = 1; i <= m; i++) { |
---|
571 | b[i] = InnerProduct(B1[i], B1[i], n); |
---|
572 | } |
---|
573 | |
---|
574 | |
---|
575 | new_m = ll_LLL_XD(B, U, delta, deep, check, B1, mu, b, c, m, 1, quit); |
---|
576 | dep = m - new_m; |
---|
577 | m = new_m; |
---|
578 | |
---|
579 | if (dep > 0) { |
---|
580 | // for consistency, we move all of the zero rows to the front |
---|
581 | |
---|
582 | for (i = 0; i < m; i++) { |
---|
583 | swap(B(m+dep-i), B(m-i)); |
---|
584 | if (U) swap((*U)(m+dep-i), (*U)(m-i)); |
---|
585 | } |
---|
586 | } |
---|
587 | |
---|
588 | |
---|
589 | // clean-up |
---|
590 | |
---|
591 | for (i = 1; i <= m; i++) { |
---|
592 | delete [] B1[i]; |
---|
593 | } |
---|
594 | |
---|
595 | delete [] B1; |
---|
596 | |
---|
597 | for (i = 1; i <= m; i++) { |
---|
598 | delete [] mu[i]; |
---|
599 | } |
---|
600 | |
---|
601 | delete [] mu; |
---|
602 | |
---|
603 | delete [] c; |
---|
604 | |
---|
605 | delete [] b; |
---|
606 | |
---|
607 | return m; |
---|
608 | } |
---|
609 | |
---|
610 | |
---|
611 | |
---|
612 | long LLL_XD(mat_ZZ& B, double delta, long deep, |
---|
613 | LLLCheckFct check, long verb) |
---|
614 | { |
---|
615 | verbose = verb; |
---|
616 | NumSwaps = 0; |
---|
617 | if (verbose) { |
---|
618 | StartTime = GetTime(); |
---|
619 | LastTime = StartTime; |
---|
620 | } |
---|
621 | |
---|
622 | if (delta < 0.50 || delta >= 1) Error("LLL_XD: bad delta"); |
---|
623 | if (deep < 0) Error("LLL_XD: bad deep"); |
---|
624 | return LLL_XD(B, 0, to_xdouble(delta), deep, check); |
---|
625 | } |
---|
626 | |
---|
627 | long LLL_XD(mat_ZZ& B, mat_ZZ& U, double delta, long deep, |
---|
628 | LLLCheckFct check, long verb) |
---|
629 | { |
---|
630 | verbose = verb; |
---|
631 | NumSwaps = 0; |
---|
632 | if (verbose) { |
---|
633 | StartTime = GetTime(); |
---|
634 | LastTime = StartTime; |
---|
635 | } |
---|
636 | |
---|
637 | |
---|
638 | if (delta < 0.50 || delta >= 1) Error("LLL_XD: bad delta"); |
---|
639 | if (deep < 0) Error("LLL_XD: bad deep"); |
---|
640 | return LLL_XD(B, &U, to_xdouble(delta), deep, check); |
---|
641 | } |
---|
642 | |
---|
643 | |
---|
644 | |
---|
645 | static vec_xdouble BKZConstant; |
---|
646 | |
---|
647 | static |
---|
648 | void ComputeBKZConstant(long beta, long p) |
---|
649 | { |
---|
650 | const double c_PI = 3.14159265358979323846264338328; |
---|
651 | const double LogPI = 1.14472988584940017414342735135; |
---|
652 | |
---|
653 | BKZConstant.SetLength(beta-1); |
---|
654 | |
---|
655 | vec_double Log; |
---|
656 | Log.SetLength(beta); |
---|
657 | |
---|
658 | |
---|
659 | long i, j, k; |
---|
660 | double x, y; |
---|
661 | |
---|
662 | for (j = 1; j <= beta; j++) |
---|
663 | Log(j) = log(double(j)); |
---|
664 | |
---|
665 | for (i = 1; i <= beta-1; i++) { |
---|
666 | // First, we compute x = gamma(i/2)^{2/i} |
---|
667 | |
---|
668 | k = i/2; |
---|
669 | |
---|
670 | if ((i & 1) == 0) { // i even |
---|
671 | x = 0; |
---|
672 | for (j = 1; j <= k; j++) |
---|
673 | x = x + Log(j); |
---|
674 | |
---|
675 | x = x * (1/double(k)); |
---|
676 | |
---|
677 | x = exp(x); |
---|
678 | } |
---|
679 | else { // i odd |
---|
680 | x = 0; |
---|
681 | for (j = k + 2; j <= 2*k + 2; j++) |
---|
682 | x = x + Log(j); |
---|
683 | |
---|
684 | x = 0.5*LogPI + x - 2*(k+1)*Log(2); |
---|
685 | |
---|
686 | x = x * (2.0/double(i)); |
---|
687 | |
---|
688 | x = exp(x); |
---|
689 | } |
---|
690 | |
---|
691 | // Second, we compute y = 2^{2*p/i} |
---|
692 | |
---|
693 | y = -(2*p/double(i))*Log(2); |
---|
694 | y = exp(y); |
---|
695 | |
---|
696 | BKZConstant(i) = x*y/c_PI; |
---|
697 | } |
---|
698 | } |
---|
699 | |
---|
700 | static vec_xdouble BKZThresh; |
---|
701 | |
---|
702 | static |
---|
703 | void ComputeBKZThresh(xdouble *c, long beta) |
---|
704 | { |
---|
705 | BKZThresh.SetLength(beta-1); |
---|
706 | |
---|
707 | long i; |
---|
708 | double x; |
---|
709 | |
---|
710 | x = 0; |
---|
711 | |
---|
712 | for (i = 1; i <= beta-1; i++) { |
---|
713 | x += log(c[i-1]); |
---|
714 | BKZThresh(i) = xexp(x/double(i))*BKZConstant(i); |
---|
715 | } |
---|
716 | } |
---|
717 | |
---|
718 | |
---|
719 | static |
---|
720 | void BKZStatus(double tt, double enum_time, long NumIterations, |
---|
721 | long NumTrivial, long NumNonTrivial, long NumNoOps, long m, |
---|
722 | const mat_ZZ& B) |
---|
723 | { |
---|
724 | cerr << "---- BKZ_XD status ----\n"; |
---|
725 | cerr << "elapsed time: "; |
---|
726 | PrintTime(cerr, tt-StartTime); |
---|
727 | cerr << ", enum time: "; |
---|
728 | PrintTime(cerr, enum_time); |
---|
729 | cerr << ", iter: " << NumIterations << "\n"; |
---|
730 | cerr << "triv: " << NumTrivial; |
---|
731 | cerr << ", nontriv: " << NumNonTrivial; |
---|
732 | cerr << ", no ops: " << NumNoOps; |
---|
733 | cerr << ", rank: " << m; |
---|
734 | cerr << ", swaps: " << NumSwaps << "\n"; |
---|
735 | |
---|
736 | |
---|
737 | |
---|
738 | ZZ t1; |
---|
739 | long i; |
---|
740 | double prodlen = 0; |
---|
741 | |
---|
742 | for (i = 1; i <= m; i++) { |
---|
743 | InnerProduct(t1, B(i), B(i)); |
---|
744 | if (!IsZero(t1)) |
---|
745 | prodlen += log(t1); |
---|
746 | } |
---|
747 | |
---|
748 | cerr << "log of prod of lengths: " << prodlen/(2.0*log(2.0)) << "\n"; |
---|
749 | |
---|
750 | |
---|
751 | if (LLLDumpFile) { |
---|
752 | cerr << "dumping to " << LLLDumpFile << "..."; |
---|
753 | |
---|
754 | ofstream f; |
---|
755 | OpenWrite(f, LLLDumpFile); |
---|
756 | |
---|
757 | f << "["; |
---|
758 | for (i = 1; i <= m; i++) { |
---|
759 | f << B(i) << "\n"; |
---|
760 | } |
---|
761 | f << "]\n"; |
---|
762 | |
---|
763 | f.close(); |
---|
764 | |
---|
765 | cerr << "\n"; |
---|
766 | } |
---|
767 | |
---|
768 | LastTime = tt; |
---|
769 | |
---|
770 | } |
---|
771 | |
---|
772 | |
---|
773 | static |
---|
774 | long BKZ_XD(mat_ZZ& BB, mat_ZZ* UU, xdouble delta, |
---|
775 | long beta, long prune, LLLCheckFct check) |
---|
776 | { |
---|
777 | long m = BB.NumRows(); |
---|
778 | long n = BB.NumCols(); |
---|
779 | long m_orig = m; |
---|
780 | |
---|
781 | long i, j; |
---|
782 | ZZ MU; |
---|
783 | |
---|
784 | xdouble t1; |
---|
785 | ZZ T1; |
---|
786 | xdouble *tp; |
---|
787 | |
---|
788 | init_red_fudge(); |
---|
789 | |
---|
790 | mat_ZZ B; |
---|
791 | B = BB; |
---|
792 | |
---|
793 | B.SetDims(m+1, n); |
---|
794 | |
---|
795 | |
---|
796 | xdouble **B1; // approximates B |
---|
797 | |
---|
798 | typedef xdouble *xdoubleptr; |
---|
799 | |
---|
800 | B1 = NTL_NEW_OP xdoubleptr[m+2]; |
---|
801 | if (!B1) Error("BKZ_XD: out of memory"); |
---|
802 | |
---|
803 | for (i = 1; i <= m+1; i++) { |
---|
804 | B1[i] = NTL_NEW_OP xdouble[n+1]; |
---|
805 | if (!B1[i]) Error("BKZ_XD: out of memory"); |
---|
806 | } |
---|
807 | |
---|
808 | xdouble **mu; |
---|
809 | mu = NTL_NEW_OP xdoubleptr[m+2]; |
---|
810 | if (!mu) Error("BKZ_XD: out of memory"); |
---|
811 | |
---|
812 | for (i = 1; i <= m+1; i++) { |
---|
813 | mu[i] = NTL_NEW_OP xdouble[m+1]; |
---|
814 | if (!mu[i]) Error("BKZ_XD: out of memory"); |
---|
815 | } |
---|
816 | |
---|
817 | xdouble *c; // squared lengths of Gramm-Schmidt basis vectors |
---|
818 | |
---|
819 | c = NTL_NEW_OP xdouble[m+2]; |
---|
820 | if (!c) Error("BKZ_XD: out of memory"); |
---|
821 | |
---|
822 | xdouble *b; // squared lengths of basis vectors |
---|
823 | |
---|
824 | b = NTL_NEW_OP xdouble[m+2]; |
---|
825 | if (!b) Error("BKZ_XD: out of memory"); |
---|
826 | |
---|
827 | xdouble cbar; |
---|
828 | |
---|
829 | xdouble *ctilda; |
---|
830 | ctilda = NTL_NEW_OP xdouble[m+2]; |
---|
831 | if (!ctilda) Error("BKZ_XD: out of memory"); |
---|
832 | |
---|
833 | xdouble *vvec; |
---|
834 | vvec = NTL_NEW_OP xdouble[m+2]; |
---|
835 | if (!vvec) Error("BKZ_XD: out of memory"); |
---|
836 | |
---|
837 | xdouble *yvec; |
---|
838 | yvec = NTL_NEW_OP xdouble[m+2]; |
---|
839 | if (!yvec) Error("BKZ_XD: out of memory"); |
---|
840 | |
---|
841 | xdouble *uvec; |
---|
842 | uvec = NTL_NEW_OP xdouble[m+2]; |
---|
843 | if (!uvec) Error("BKZ_XD: out of memory"); |
---|
844 | |
---|
845 | xdouble *utildavec; |
---|
846 | utildavec = NTL_NEW_OP xdouble[m+2]; |
---|
847 | if (!utildavec) Error("BKZ_XD: out of memory"); |
---|
848 | |
---|
849 | |
---|
850 | long *Deltavec; |
---|
851 | Deltavec = NTL_NEW_OP long[m+2]; |
---|
852 | if (!Deltavec) Error("BKZ_XD: out of memory"); |
---|
853 | |
---|
854 | long *deltavec; |
---|
855 | deltavec = NTL_NEW_OP long[m+2]; |
---|
856 | if (!deltavec) Error("BKZ_XD: out of memory"); |
---|
857 | |
---|
858 | mat_ZZ Ulocal; |
---|
859 | mat_ZZ *U; |
---|
860 | |
---|
861 | if (UU) { |
---|
862 | Ulocal.SetDims(m+1, m); |
---|
863 | for (i = 1; i <= m; i++) |
---|
864 | conv(Ulocal(i, i), 1); |
---|
865 | U = &Ulocal; |
---|
866 | } |
---|
867 | else |
---|
868 | U = 0; |
---|
869 | |
---|
870 | long quit; |
---|
871 | long new_m; |
---|
872 | long z, jj, kk; |
---|
873 | long s, t; |
---|
874 | long h; |
---|
875 | xdouble eta; |
---|
876 | |
---|
877 | |
---|
878 | for (i = 1; i <=m; i++) |
---|
879 | for (j = 1; j <= n; j++) |
---|
880 | conv(B1[i][j], B(i, j)); |
---|
881 | |
---|
882 | |
---|
883 | for (i = 1; i <= m; i++) { |
---|
884 | b[i] = InnerProduct(B1[i], B1[i], n); |
---|
885 | } |
---|
886 | |
---|
887 | // cerr << "\n"; |
---|
888 | // cerr << "first LLL\n"; |
---|
889 | |
---|
890 | m = ll_LLL_XD(B, U, delta, 0, check, B1, mu, b, c, m, 1, quit); |
---|
891 | |
---|
892 | double tt; |
---|
893 | |
---|
894 | double enum_time = 0; |
---|
895 | long NumIterations = 0; |
---|
896 | long NumTrivial = 0; |
---|
897 | long NumNonTrivial = 0; |
---|
898 | long NumNoOps = 0; |
---|
899 | |
---|
900 | long verb = verbose; |
---|
901 | |
---|
902 | verbose = 0; |
---|
903 | |
---|
904 | |
---|
905 | |
---|
906 | if (m < m_orig) { |
---|
907 | for (i = m_orig+1; i >= m+2; i--) { |
---|
908 | // swap i, i-1 |
---|
909 | |
---|
910 | swap(B(i), B(i-1)); |
---|
911 | if (U) swap((*U)(i), (*U)(i-1)); |
---|
912 | } |
---|
913 | } |
---|
914 | |
---|
915 | long clean = 1; |
---|
916 | |
---|
917 | if (!quit && m > 1) { |
---|
918 | // cerr << "continuing\n"; |
---|
919 | if (beta > m) beta = m; |
---|
920 | |
---|
921 | if (prune > 0) |
---|
922 | ComputeBKZConstant(beta, prune); |
---|
923 | |
---|
924 | z = 0; |
---|
925 | jj = 0; |
---|
926 | |
---|
927 | while (z < m-1) { |
---|
928 | jj++; |
---|
929 | kk = min(jj+beta-1, m); |
---|
930 | |
---|
931 | if (jj == m) { |
---|
932 | jj = 1; |
---|
933 | kk = beta; |
---|
934 | clean = 1; |
---|
935 | } |
---|
936 | |
---|
937 | if (verb) { |
---|
938 | tt = GetTime(); |
---|
939 | if (tt > LastTime + LLLStatusInterval) |
---|
940 | BKZStatus(tt, enum_time, NumIterations, NumTrivial, |
---|
941 | NumNonTrivial, NumNoOps, m, B); |
---|
942 | } |
---|
943 | |
---|
944 | // ENUM |
---|
945 | |
---|
946 | double tt1; |
---|
947 | |
---|
948 | if (verb) { |
---|
949 | tt1 = GetTime(); |
---|
950 | } |
---|
951 | |
---|
952 | if (prune > 0) |
---|
953 | ComputeBKZThresh(&c[jj], kk-jj+1); |
---|
954 | |
---|
955 | cbar = c[jj]; |
---|
956 | utildavec[jj] = uvec[jj] = 1; |
---|
957 | |
---|
958 | yvec[jj] = vvec[jj] = 0; |
---|
959 | Deltavec[jj] = 0; |
---|
960 | |
---|
961 | |
---|
962 | s = t = jj; |
---|
963 | deltavec[jj] = 1; |
---|
964 | |
---|
965 | for (i = jj+1; i <= kk+1; i++) { |
---|
966 | ctilda[i] = uvec[i] = utildavec[i] = yvec[i] = 0; |
---|
967 | Deltavec[i] = 0; |
---|
968 | vvec[i] = 0; |
---|
969 | deltavec[i] = 1; |
---|
970 | } |
---|
971 | |
---|
972 | long enum_cnt = 0; |
---|
973 | |
---|
974 | while (t <= kk) { |
---|
975 | if (verb) { |
---|
976 | enum_cnt++; |
---|
977 | if (enum_cnt > 100000) { |
---|
978 | enum_cnt = 0; |
---|
979 | tt = GetTime(); |
---|
980 | if (tt > LastTime + LLLStatusInterval) { |
---|
981 | enum_time += tt - tt1; |
---|
982 | tt1 = tt; |
---|
983 | BKZStatus(tt, enum_time, NumIterations, NumTrivial, |
---|
984 | NumNonTrivial, NumNoOps, m, B); |
---|
985 | } |
---|
986 | } |
---|
987 | } |
---|
988 | |
---|
989 | |
---|
990 | ctilda[t] = ctilda[t+1] + |
---|
991 | (yvec[t]+utildavec[t])*(yvec[t]+utildavec[t])*c[t]; |
---|
992 | |
---|
993 | if (prune > 0 && t > jj) { |
---|
994 | eta = BKZThresh(t-jj); |
---|
995 | } |
---|
996 | else |
---|
997 | eta = 0; |
---|
998 | |
---|
999 | if (ctilda[t] < cbar - eta) { |
---|
1000 | if (t > jj) { |
---|
1001 | t--; |
---|
1002 | t1 = 0; |
---|
1003 | for (i = t+1; i <= s; i++) { |
---|
1004 | t1 += utildavec[i]*mu[i][t]; |
---|
1005 | } |
---|
1006 | |
---|
1007 | |
---|
1008 | yvec[t] = t1; |
---|
1009 | t1 = -t1; |
---|
1010 | if (t1 >= 0) |
---|
1011 | t1 = ceil(t1-0.5); |
---|
1012 | else |
---|
1013 | t1 = floor(t1+0.5); |
---|
1014 | |
---|
1015 | utildavec[t] = vvec[t] = t1; |
---|
1016 | Deltavec[t] = 0; |
---|
1017 | if (utildavec[t] > -yvec[t]) |
---|
1018 | deltavec[t] = -1; |
---|
1019 | else |
---|
1020 | deltavec[t] = 1; |
---|
1021 | } |
---|
1022 | else { |
---|
1023 | cbar = ctilda[jj]; |
---|
1024 | for (i = jj; i <= kk; i++) { |
---|
1025 | uvec[i] = utildavec[i]; |
---|
1026 | } |
---|
1027 | } |
---|
1028 | } |
---|
1029 | else { |
---|
1030 | t++; |
---|
1031 | s = max(s, t); |
---|
1032 | if (t < s) Deltavec[t] = -Deltavec[t]; |
---|
1033 | if (Deltavec[t]*deltavec[t] >= 0) Deltavec[t] += deltavec[t]; |
---|
1034 | utildavec[t] = vvec[t] + Deltavec[t]; |
---|
1035 | } |
---|
1036 | } |
---|
1037 | |
---|
1038 | if (verb) { |
---|
1039 | tt1 = GetTime() - tt1; |
---|
1040 | enum_time += tt1; |
---|
1041 | } |
---|
1042 | |
---|
1043 | NumIterations++; |
---|
1044 | |
---|
1045 | h = min(kk+1, m); |
---|
1046 | |
---|
1047 | if ((delta-8*red_fudge)*c[jj] > cbar) { |
---|
1048 | |
---|
1049 | clean = 0; |
---|
1050 | |
---|
1051 | // we treat the case that the new vector is b_s (jj < s <= kk) |
---|
1052 | // as a special case that appears to occur most of the time. |
---|
1053 | |
---|
1054 | s = 0; |
---|
1055 | for (i = jj+1; i <= kk; i++) { |
---|
1056 | if (uvec[i] != 0) { |
---|
1057 | if (s == 0) |
---|
1058 | s = i; |
---|
1059 | else |
---|
1060 | s = -1; |
---|
1061 | } |
---|
1062 | } |
---|
1063 | |
---|
1064 | if (s == 0) Error("BKZ_XD: internal error"); |
---|
1065 | |
---|
1066 | if (s > 0) { |
---|
1067 | // special case |
---|
1068 | |
---|
1069 | NumTrivial++; |
---|
1070 | |
---|
1071 | for (i = s; i > jj; i--) { |
---|
1072 | // swap i, i-1 |
---|
1073 | swap(B(i-1), B(i)); |
---|
1074 | if (U) swap((*U)(i-1), (*U)(i)); |
---|
1075 | tp = B1[i-1]; B1[i-1] = B1[i]; B1[i] = tp; |
---|
1076 | t1 = b[i-1]; b[i-1] = b[i]; b[i] = t1; |
---|
1077 | } |
---|
1078 | |
---|
1079 | // cerr << "special case\n"; |
---|
1080 | new_m = ll_LLL_XD(B, U, delta, 0, check, |
---|
1081 | B1, mu, b, c, h, jj, quit); |
---|
1082 | if (new_m != h) Error("BKZ_XD: internal error"); |
---|
1083 | if (quit) break; |
---|
1084 | } |
---|
1085 | else { |
---|
1086 | // the general case |
---|
1087 | |
---|
1088 | NumNonTrivial++; |
---|
1089 | |
---|
1090 | for (i = 1; i <= n; i++) conv(B(m+1, i), 0); |
---|
1091 | |
---|
1092 | if (U) { |
---|
1093 | for (i = 1; i <= m_orig; i++) |
---|
1094 | conv((*U)(m+1, i), 0); |
---|
1095 | } |
---|
1096 | |
---|
1097 | for (i = jj; i <= kk; i++) { |
---|
1098 | if (uvec[i] == 0) continue; |
---|
1099 | conv(MU, uvec[i]); |
---|
1100 | RowTransform2(B(m+1), B(i), MU); |
---|
1101 | if (U) RowTransform2((*U)(m+1), (*U)(i), MU); |
---|
1102 | } |
---|
1103 | |
---|
1104 | for (i = m+1; i >= jj+1; i--) { |
---|
1105 | // swap i, i-1 |
---|
1106 | swap(B(i-1), B(i)); |
---|
1107 | if (U) swap((*U)(i-1), (*U)(i)); |
---|
1108 | tp = B1[i-1]; B1[i-1] = B1[i]; B1[i] = tp; |
---|
1109 | t1 = b[i-1]; b[i-1] = b[i]; b[i] = t1; |
---|
1110 | } |
---|
1111 | |
---|
1112 | for (i = 1; i <= n; i++) |
---|
1113 | conv(B1[jj][i], B(jj, i)); |
---|
1114 | |
---|
1115 | b[jj] = InnerProduct(B1[jj], B1[jj], n); |
---|
1116 | |
---|
1117 | if (b[jj] == 0) Error("BKZ_XD: internal error"); |
---|
1118 | |
---|
1119 | // remove linear dependencies |
---|
1120 | |
---|
1121 | // cerr << "general case\n"; |
---|
1122 | new_m = ll_LLL_XD(B, U, delta, 0, 0, B1, mu, b, c, kk+1, jj, quit); |
---|
1123 | |
---|
1124 | if (new_m != kk) Error("BKZ_XD: internal error"); |
---|
1125 | |
---|
1126 | // remove zero vector |
---|
1127 | |
---|
1128 | for (i = kk+2; i <= m+1; i++) { |
---|
1129 | // swap i, i-1 |
---|
1130 | swap(B(i-1), B(i)); |
---|
1131 | if (U) swap((*U)(i-1), (*U)(i)); |
---|
1132 | tp = B1[i-1]; B1[i-1] = B1[i]; B1[i] = tp; |
---|
1133 | t1 = b[i-1]; b[i-1] = b[i]; b[i] = t1; |
---|
1134 | } |
---|
1135 | |
---|
1136 | quit = 0; |
---|
1137 | if (check) { |
---|
1138 | for (i = 1; i <= kk; i++) |
---|
1139 | if ((*check)(B(i))) { |
---|
1140 | quit = 1; |
---|
1141 | break; |
---|
1142 | } |
---|
1143 | } |
---|
1144 | |
---|
1145 | if (quit) break; |
---|
1146 | |
---|
1147 | if (h > kk) { |
---|
1148 | // extend reduced basis |
---|
1149 | |
---|
1150 | new_m = ll_LLL_XD(B, U, delta, 0, check, |
---|
1151 | B1, mu, b, c, h, h, quit); |
---|
1152 | |
---|
1153 | if (new_m != h) Error("BKZ_XD: internal error"); |
---|
1154 | if (quit) break; |
---|
1155 | } |
---|
1156 | } |
---|
1157 | |
---|
1158 | z = 0; |
---|
1159 | } |
---|
1160 | else { |
---|
1161 | // LLL_XD |
---|
1162 | // cerr << "progress\n"; |
---|
1163 | |
---|
1164 | NumNoOps++; |
---|
1165 | |
---|
1166 | if (!clean) { |
---|
1167 | new_m = |
---|
1168 | ll_LLL_XD(B, U, delta, 0, check, B1, mu, b, c, h, h, quit); |
---|
1169 | if (new_m != h) Error("BKZ_XD: internal error"); |
---|
1170 | if (quit) break; |
---|
1171 | } |
---|
1172 | |
---|
1173 | z++; |
---|
1174 | } |
---|
1175 | } |
---|
1176 | } |
---|
1177 | |
---|
1178 | if (verb) { |
---|
1179 | BKZStatus(GetTime(), enum_time, NumIterations, NumTrivial, NumNonTrivial, |
---|
1180 | NumNoOps, m, B); |
---|
1181 | } |
---|
1182 | |
---|
1183 | |
---|
1184 | // clean up |
---|
1185 | |
---|
1186 | if (m_orig > m) { |
---|
1187 | // for consistency, we move zero vectors to the front |
---|
1188 | |
---|
1189 | for (i = m+1; i <= m_orig; i++) { |
---|
1190 | swap(B(i), B(i+1)); |
---|
1191 | if (U) swap((*U)(i), (*U)(i+1)); |
---|
1192 | } |
---|
1193 | |
---|
1194 | for (i = 0; i < m; i++) { |
---|
1195 | swap(B(m_orig-i), B(m-i)); |
---|
1196 | if (U) swap((*U)(m_orig-i), (*U)(m-i)); |
---|
1197 | } |
---|
1198 | } |
---|
1199 | |
---|
1200 | B.SetDims(m_orig, n); |
---|
1201 | BB = B; |
---|
1202 | |
---|
1203 | if (U) { |
---|
1204 | U->SetDims(m_orig, m_orig); |
---|
1205 | *UU = *U; |
---|
1206 | } |
---|
1207 | |
---|
1208 | for (i = 1; i <= m+1; i++) { |
---|
1209 | delete [] B1[i]; |
---|
1210 | } |
---|
1211 | |
---|
1212 | delete [] B1; |
---|
1213 | |
---|
1214 | for (i = 1; i <= m+1; i++) { |
---|
1215 | delete [] mu[i]; |
---|
1216 | } |
---|
1217 | |
---|
1218 | delete [] mu; |
---|
1219 | |
---|
1220 | |
---|
1221 | delete [] c; |
---|
1222 | delete [] b; |
---|
1223 | delete [] ctilda; |
---|
1224 | delete [] vvec; |
---|
1225 | delete [] yvec; |
---|
1226 | delete [] uvec; |
---|
1227 | delete [] utildavec; |
---|
1228 | delete [] Deltavec; |
---|
1229 | delete [] deltavec; |
---|
1230 | |
---|
1231 | return m; |
---|
1232 | } |
---|
1233 | |
---|
1234 | long BKZ_XD(mat_ZZ& BB, mat_ZZ& UU, double delta, |
---|
1235 | long beta, long prune, LLLCheckFct check, long verb) |
---|
1236 | { |
---|
1237 | verbose = verb; |
---|
1238 | NumSwaps = 0; |
---|
1239 | if (verbose) { |
---|
1240 | StartTime = GetTime(); |
---|
1241 | LastTime = StartTime; |
---|
1242 | } |
---|
1243 | |
---|
1244 | |
---|
1245 | if (delta < 0.50 || delta >= 1) Error("BKZ_XD: bad delta"); |
---|
1246 | if (beta < 2) Error("BKZ_XD: bad block size"); |
---|
1247 | |
---|
1248 | return BKZ_XD(BB, &UU, to_xdouble(delta), beta, prune, check); |
---|
1249 | } |
---|
1250 | |
---|
1251 | long BKZ_XD(mat_ZZ& BB, double delta, |
---|
1252 | long beta, long prune, LLLCheckFct check, long verb) |
---|
1253 | { |
---|
1254 | verbose = verb; |
---|
1255 | NumSwaps = 0; |
---|
1256 | if (verbose) { |
---|
1257 | StartTime = GetTime(); |
---|
1258 | LastTime = StartTime; |
---|
1259 | } |
---|
1260 | |
---|
1261 | |
---|
1262 | |
---|
1263 | if (delta < 0.50 || delta >= 1) Error("BKZ_XD: bad delta"); |
---|
1264 | if (beta < 2) Error("BKZ_XD: bad block size"); |
---|
1265 | |
---|
1266 | return BKZ_XD(BB, 0, to_xdouble(delta), beta, prune, check); |
---|
1267 | } |
---|
1268 | |
---|
1269 | NTL_END_IMPL |
---|