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_double.h> |
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5 | |
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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 | static inline |
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12 | void CheckFinite(double *p) |
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13 | { |
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14 | if (!IsFinite(p)) Error("LLL_FP: numbers too big...use LLL_XD"); |
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15 | } |
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16 | |
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17 | static double InnerProduct(double *a, double *b, long n) |
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18 | { |
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19 | double s; |
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20 | long i; |
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21 | |
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22 | s = 0; |
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23 | for (i = 1; i <= n; i++) |
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24 | s += a[i]*b[i]; |
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25 | |
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26 | return s; |
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27 | } |
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28 | |
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29 | static void RowTransform(vec_ZZ& A, vec_ZZ& B, const ZZ& MU1) |
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30 | // x = x - y*MU |
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31 | { |
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32 | static ZZ T, MU; |
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33 | long k; |
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34 | |
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35 | long n = A.length(); |
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36 | long i; |
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37 | |
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38 | MU = MU1; |
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39 | |
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40 | if (MU == 1) { |
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41 | for (i = 1; i <= n; i++) |
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42 | sub(A(i), A(i), B(i)); |
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43 | |
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44 | return; |
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45 | } |
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46 | |
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47 | if (MU == -1) { |
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48 | for (i = 1; i <= n; i++) |
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49 | add(A(i), A(i), B(i)); |
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50 | |
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51 | return; |
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52 | } |
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53 | |
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54 | if (MU == 0) return; |
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55 | |
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56 | if (NumTwos(MU) >= NTL_ZZ_NBITS) |
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57 | k = MakeOdd(MU); |
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58 | else |
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59 | k = 0; |
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60 | |
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61 | |
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62 | if (MU.WideSinglePrecision()) { |
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63 | long mu1; |
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64 | conv(mu1, MU); |
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65 | |
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66 | for (i = 1; i <= n; i++) { |
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67 | mul(T, B(i), mu1); |
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68 | if (k > 0) LeftShift(T, T, k); |
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69 | sub(A(i), A(i), T); |
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70 | } |
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71 | } |
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72 | else { |
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73 | for (i = 1; i <= n; i++) { |
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74 | mul(T, B(i), MU); |
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75 | if (k > 0) LeftShift(T, T, k); |
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76 | sub(A(i), A(i), T); |
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77 | } |
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78 | } |
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79 | } |
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80 | |
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81 | |
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82 | #define TR_BND (NTL_FDOUBLE_PRECISION/2.0) |
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83 | // Just to be safe!! |
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84 | |
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85 | static double max_abs(double *v, long n) |
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86 | { |
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87 | long i; |
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88 | double res, t; |
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89 | |
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90 | res = 0; |
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91 | |
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92 | for (i = 1; i <= n; i++) { |
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93 | t = fabs(v[i]); |
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94 | if (t > res) res = t; |
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95 | } |
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96 | |
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97 | return res; |
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98 | } |
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99 | |
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100 | |
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101 | static void RowTransformStart(double *a, long *in_a, long& in_float, long n) |
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102 | { |
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103 | long i; |
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104 | long inf = 1; |
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105 | |
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106 | for (i = 1; i <= n; i++) { |
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107 | in_a[i] = (a[i] < TR_BND && a[i] > -TR_BND); |
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108 | inf = inf & in_a[i]; |
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109 | } |
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110 | |
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111 | in_float = inf; |
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112 | } |
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113 | |
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114 | |
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115 | static void RowTransformFinish(vec_ZZ& A, double *a, long *in_a) |
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116 | { |
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117 | long n = A.length(); |
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118 | long i; |
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119 | |
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120 | for (i = 1; i <= n; i++) { |
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121 | if (in_a[i]) { |
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122 | conv(A(i), a[i]); |
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123 | } |
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124 | else { |
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125 | conv(a[i], A(i)); |
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126 | CheckFinite(&a[i]); |
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127 | } |
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128 | } |
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129 | } |
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130 | |
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131 | |
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132 | static void RowTransform(vec_ZZ& A, vec_ZZ& B, const ZZ& MU1, |
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133 | double *a, double *b, long *in_a, |
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134 | double& max_a, double max_b, long& in_float) |
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135 | // x = x - y*MU |
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136 | { |
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137 | static ZZ T, MU; |
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138 | long k; |
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139 | double mu; |
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140 | |
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141 | conv(mu, MU1); |
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142 | CheckFinite(&mu); |
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143 | |
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144 | long n = A.length(); |
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145 | long i; |
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146 | |
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147 | if (in_float) { |
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148 | double mu_abs = fabs(mu); |
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149 | if (mu_abs > 0 && max_b > 0 && (mu_abs >= TR_BND || max_b >= TR_BND)) { |
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150 | in_float = 0; |
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151 | } |
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152 | else { |
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153 | max_a += mu_abs*max_b; |
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154 | if (max_a >= TR_BND) |
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155 | in_float = 0; |
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156 | } |
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157 | } |
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158 | |
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159 | if (in_float) { |
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160 | if (mu == 1) { |
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161 | for (i = 1; i <= n; i++) |
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162 | a[i] -= b[i]; |
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163 | |
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164 | return; |
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165 | } |
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166 | |
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167 | if (mu == -1) { |
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168 | for (i = 1; i <= n; i++) |
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169 | a[i] += b[i]; |
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170 | |
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171 | return; |
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172 | } |
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173 | |
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174 | if (mu == 0) return; |
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175 | |
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176 | for (i = 1; i <= n; i++) |
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177 | a[i] -= mu*b[i]; |
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178 | |
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179 | |
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180 | return; |
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181 | } |
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182 | |
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183 | |
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184 | MU = MU1; |
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185 | |
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186 | if (MU == 1) { |
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187 | for (i = 1; i <= n; i++) { |
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188 | if (in_a[i] && a[i] < TR_BND && a[i] > -TR_BND && |
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189 | b[i] < TR_BND && b[i] > -TR_BND) { |
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190 | |
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191 | a[i] -= b[i]; |
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192 | } |
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193 | else { |
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194 | if (in_a[i]) { |
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195 | conv(A(i), a[i]); |
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196 | in_a[i] = 0; |
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197 | } |
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198 | |
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199 | sub(A(i), A(i), B(i)); |
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200 | } |
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201 | } |
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202 | return; |
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203 | } |
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204 | |
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205 | if (MU == -1) { |
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206 | for (i = 1; i <= n; i++) { |
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207 | if (in_a[i] && a[i] < TR_BND && a[i] > -TR_BND && |
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208 | b[i] < TR_BND && b[i] > -TR_BND) { |
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209 | |
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210 | a[i] += b[i]; |
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211 | } |
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212 | else { |
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213 | if (in_a[i]) { |
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214 | conv(A(i), a[i]); |
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215 | in_a[i] = 0; |
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216 | } |
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217 | |
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218 | add(A(i), A(i), B(i)); |
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219 | } |
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220 | } |
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221 | return; |
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222 | } |
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223 | |
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224 | if (MU == 0) return; |
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225 | |
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226 | double b_bnd = fabs(TR_BND/mu) - 1; |
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227 | if (b_bnd < 0) b_bnd = 0; |
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228 | |
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229 | if (NumTwos(MU) >= NTL_ZZ_NBITS) |
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230 | k = MakeOdd(MU); |
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231 | else |
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232 | k = 0; |
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233 | |
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234 | |
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235 | if (MU.WideSinglePrecision()) { |
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236 | long mu1; |
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237 | conv(mu1, MU); |
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238 | |
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239 | if (k > 0) { |
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240 | for (i = 1; i <= n; i++) { |
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241 | if (in_a[i]) { |
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242 | conv(A(i), a[i]); |
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243 | in_a[i] = 0; |
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244 | } |
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245 | |
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246 | mul(T, B(i), mu1); |
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247 | LeftShift(T, T, k); |
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248 | sub(A(i), A(i), T); |
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249 | } |
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250 | } |
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251 | else { |
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252 | for (i = 1; i <= n; i++) { |
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253 | if (in_a[i] && a[i] < TR_BND && a[i] > -TR_BND && |
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254 | b[i] < b_bnd && b[i] > -b_bnd) { |
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255 | |
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256 | a[i] -= b[i]*mu; |
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257 | } |
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258 | else { |
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259 | if (in_a[i]) { |
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260 | conv(A(i), a[i]); |
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261 | in_a[i] = 0; |
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262 | } |
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263 | mul(T, B(i), mu1); |
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264 | sub(A(i), A(i), T); |
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265 | } |
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266 | } |
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267 | } |
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268 | } |
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269 | else { |
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270 | for (i = 1; i <= n; i++) { |
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271 | if (in_a[i]) { |
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272 | conv(A(i), a[i]); |
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273 | in_a[i] = 0; |
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274 | } |
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275 | mul(T, B(i), MU); |
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276 | if (k > 0) LeftShift(T, T, k); |
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277 | sub(A(i), A(i), T); |
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278 | } |
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279 | } |
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280 | } |
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281 | |
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282 | static void RowTransform2(vec_ZZ& A, vec_ZZ& B, const ZZ& MU1) |
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283 | // x = x + y*MU |
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284 | |
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285 | { |
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286 | static ZZ T, MU; |
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287 | long k; |
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288 | |
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289 | long n = A.length(); |
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290 | long i; |
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291 | |
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292 | MU = MU1; |
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293 | |
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294 | if (MU == 1) { |
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295 | for (i = 1; i <= n; i++) |
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296 | add(A(i), A(i), B(i)); |
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297 | |
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298 | return; |
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299 | } |
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300 | |
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301 | if (MU == -1) { |
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302 | for (i = 1; i <= n; i++) |
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303 | sub(A(i), A(i), B(i)); |
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304 | |
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305 | return; |
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306 | } |
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307 | |
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308 | if (MU == 0) return; |
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309 | |
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310 | if (NumTwos(MU) >= NTL_ZZ_NBITS) |
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311 | k = MakeOdd(MU); |
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312 | else |
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313 | k = 0; |
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314 | |
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315 | if (MU.WideSinglePrecision()) { |
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316 | long mu1; |
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317 | conv(mu1, MU); |
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318 | |
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319 | for (i = 1; i <= n; i++) { |
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320 | mul(T, B(i), mu1); |
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321 | if (k > 0) LeftShift(T, T, k); |
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322 | add(A(i), A(i), T); |
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323 | } |
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324 | } |
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325 | else { |
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326 | for (i = 1; i <= n; i++) { |
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327 | mul(T, B(i), MU); |
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328 | if (k > 0) LeftShift(T, T, k); |
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329 | add(A(i), A(i), T); |
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330 | } |
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331 | } |
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332 | } |
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333 | |
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334 | static |
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335 | void ComputeGS(mat_ZZ& B, double **B1, double **mu, double *b, |
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336 | double *c, long k, double bound, long st, double *buf) |
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337 | |
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338 | { |
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339 | long n = B.NumCols(); |
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340 | long i, j; |
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341 | double s, t1, y, t; |
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342 | |
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343 | ZZ T1; |
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344 | long test; |
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345 | |
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346 | double *mu_k = mu[k]; |
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347 | |
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348 | if (st < k) { |
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349 | for (i = 1; i < st; i++) |
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350 | buf[i] = mu_k[i]*c[i]; |
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351 | } |
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352 | |
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353 | for (j = st; j <= k-1; j++) { |
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354 | s = InnerProduct(B1[k], B1[j], n); |
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355 | |
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356 | // test = b[k]*b[j] >= NTL_FDOUBLE_PRECISION^2 |
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357 | |
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358 | test = (b[k]/NTL_FDOUBLE_PRECISION >= NTL_FDOUBLE_PRECISION/b[j]); |
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359 | |
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360 | // test = test && s^2 <= b[k]*b[j]/bound, |
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361 | // but we compute it in a strange way to avoid overflow |
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362 | |
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363 | if (test && (y = fabs(s)) != 0) { |
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364 | t = y/b[j]; |
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365 | t1 = b[k]/y; |
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366 | if (t <= 1) |
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367 | test = (t*bound <= t1); |
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368 | else if (t1 >= 1) |
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369 | test = (t <= t1/bound); |
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370 | else |
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371 | test = 0; |
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372 | } |
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373 | |
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374 | if (test) { |
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375 | InnerProduct(T1, B(k), B(j)); |
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376 | conv(s, T1); |
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377 | } |
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378 | |
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379 | double *mu_j = mu[j]; |
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380 | |
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381 | t1 = 0; |
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382 | for (i = 1; i <= j-1; i++) { |
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383 | t1 += mu_j[i]*buf[i]; |
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384 | } |
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385 | |
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386 | mu_k[j] = (buf[j] = (s - t1))/c[j]; |
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387 | } |
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388 | |
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389 | #if (!NTL_EXT_DOUBLE) |
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390 | |
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391 | // Kahan summation |
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392 | |
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393 | double c1; |
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394 | |
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395 | s = c1 = 0; |
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396 | for (j = 1; j <= k-1; j++) { |
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397 | y = mu_k[j]*buf[j] - c1; |
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398 | t = s+y; |
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399 | c1 = t-s; |
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400 | c1 = c1-y; |
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401 | s = t; |
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402 | } |
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403 | |
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404 | |
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405 | #else |
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406 | |
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407 | s = 0; |
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408 | for (j = 1; j <= k-1; j++) |
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409 | s += mu_k[j]*buf[j]; |
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410 | |
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411 | #endif |
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412 | |
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413 | c[k] = b[k] - s; |
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414 | } |
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415 | |
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416 | static double red_fudge = 0; |
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417 | static long log_red = 0; |
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418 | |
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419 | static long verbose = 0; |
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420 | |
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421 | char *LLLDumpFile = 0; |
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422 | |
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423 | static unsigned long NumSwaps = 0; |
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424 | static double RR_GS_time = 0; |
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425 | static double StartTime = 0; |
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426 | static double LastTime = 0; |
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427 | |
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428 | |
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429 | |
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430 | static void init_red_fudge() |
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431 | { |
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432 | long i; |
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433 | |
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434 | log_red = long(0.50*NTL_DOUBLE_PRECISION); |
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435 | red_fudge = 1; |
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436 | |
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437 | for (i = log_red; i > 0; i--) |
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438 | red_fudge = red_fudge*0.5; |
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439 | } |
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440 | |
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441 | static void inc_red_fudge() |
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442 | { |
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443 | |
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444 | red_fudge = red_fudge * 2; |
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445 | log_red--; |
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446 | |
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447 | |
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448 | if (log_red < 4) |
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449 | Error("LLL_FP: too much loss of precision...stop!"); |
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450 | } |
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451 | |
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452 | |
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453 | void ComputeGS(const mat_ZZ& B, mat_RR& B1, |
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454 | mat_RR& mu, vec_RR& b, |
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455 | vec_RR& c, long k, const RR& bound, long st, |
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456 | vec_RR& buf, const RR& bound2); |
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457 | |
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458 | |
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459 | |
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460 | static void RR_GS(mat_ZZ& B, double **B1, double **mu, |
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461 | double *b, double *c, double *buf, long prec, |
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462 | long rr_st, long k, long m_orig, |
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463 | mat_RR& rr_B1, mat_RR& rr_mu, |
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464 | vec_RR& rr_b, vec_RR& rr_c) |
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465 | { |
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466 | double tt; |
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467 | |
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468 | tt = GetTime(); |
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469 | |
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470 | if (rr_st > k) Error("LLL_FP: can not continue!!!"); |
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471 | |
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472 | long old_p = RR::precision(); |
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473 | RR::SetPrecision(prec); |
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474 | |
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475 | long n = B.NumCols(); |
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476 | |
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477 | rr_B1.SetDims(k, n); |
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478 | rr_mu.SetDims(k, m_orig); |
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479 | rr_b.SetLength(k); |
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480 | rr_c.SetLength(k); |
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481 | |
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482 | vec_RR rr_buf; |
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483 | rr_buf.SetLength(k); |
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484 | |
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485 | long i, j; |
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486 | |
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487 | for (i = rr_st; i <= k; i++) |
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488 | for (j = 1; j <= n; j++) |
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489 | conv(rr_B1(i, j), B(i, j)); |
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490 | |
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491 | for (i = rr_st; i <= k; i++) |
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492 | InnerProduct(rr_b(i), rr_B1(i), rr_B1(i)); |
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493 | |
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494 | |
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495 | |
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496 | RR bound; |
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497 | power2(bound, 2*long(0.15*RR::precision())); |
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498 | |
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499 | RR bound2; |
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500 | power2(bound2, 2*RR::precision()); |
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501 | |
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502 | for (i = rr_st; i <= k; i++) |
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503 | ComputeGS(B, rr_B1, rr_mu, rr_b, rr_c, i, bound, 1, rr_buf, bound2); |
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504 | |
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505 | for (i = rr_st; i <= k; i++) |
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506 | for (j = 1; j <= n; j++) { |
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507 | conv(B1[i][j], rr_B1(i,j)); |
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508 | CheckFinite(&B1[i][j]); |
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509 | } |
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510 | |
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511 | for (i = rr_st; i <= k; i++) |
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512 | for (j = 1; j <= i-1; j++) { |
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513 | conv(mu[i][j], rr_mu(i,j)); |
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514 | } |
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515 | |
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516 | for (i = rr_st; i <= k; i++) { |
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517 | conv(b[i], rr_b(i)); |
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518 | CheckFinite(&b[i]); |
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519 | } |
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520 | |
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521 | |
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522 | for (i = rr_st; i <= k; i++) { |
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523 | conv(c[i], rr_c(i)); |
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524 | CheckFinite(&c[i]); |
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525 | } |
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526 | |
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527 | for (i = 1; i <= k-1; i++) { |
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528 | conv(buf[i], rr_buf[i]); |
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529 | } |
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530 | |
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531 | |
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532 | RR::SetPrecision(old_p); |
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533 | |
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534 | tt = GetTime()-tt; |
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535 | RR_GS_time += tt; |
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536 | } |
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537 | |
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538 | void ComputeGS(const mat_ZZ& B, mat_RR& mu, vec_RR& c) |
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539 | { |
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540 | long n = B.NumCols(); |
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541 | long k = B.NumRows(); |
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542 | |
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543 | mat_RR B1; |
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544 | vec_RR b; |
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545 | |
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546 | B1.SetDims(k, n); |
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547 | mu.SetDims(k, k); |
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548 | b.SetLength(k); |
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549 | c.SetLength(k); |
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550 | |
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551 | vec_RR buf; |
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552 | buf.SetLength(k); |
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553 | |
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554 | long i, j; |
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555 | |
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556 | for (i = 1; i <= k; i++) |
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557 | for (j = 1; j <= n; j++) |
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558 | conv(B1(i, j), B(i, j)); |
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559 | |
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560 | for (i = 1; i <= k; i++) |
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561 | InnerProduct(b(i), B1(i), B1(i)); |
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562 | |
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563 | |
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564 | |
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565 | RR bound; |
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566 | power2(bound, 2*long(0.15*RR::precision())); |
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567 | |
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568 | RR bound2; |
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569 | power2(bound2, 2*RR::precision()); |
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570 | |
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571 | |
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572 | for (i = 1; i <= k; i++) |
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573 | ComputeGS(B, B1, mu, b, c, i, bound, 1, buf, bound2); |
---|
574 | |
---|
575 | } |
---|
576 | |
---|
577 | |
---|
578 | |
---|
579 | |
---|
580 | |
---|
581 | static |
---|
582 | long ll_LLL_FP(mat_ZZ& B, mat_ZZ* U, double delta, long deep, |
---|
583 | LLLCheckFct check, double **B1, double **mu, |
---|
584 | double *b, double *c, |
---|
585 | long m, long init_k, long &quit) |
---|
586 | { |
---|
587 | long n = B.NumCols(); |
---|
588 | |
---|
589 | long i, j, k, Fc1; |
---|
590 | ZZ MU; |
---|
591 | double mu1; |
---|
592 | |
---|
593 | double t1; |
---|
594 | ZZ T1; |
---|
595 | double *tp; |
---|
596 | |
---|
597 | |
---|
598 | static double bound = 0; |
---|
599 | |
---|
600 | if (bound == 0) { |
---|
601 | // we tolerate a 15% loss of precision in computing |
---|
602 | // inner products in ComputeGS. |
---|
603 | |
---|
604 | bound = 1; |
---|
605 | for (i = 2*long(0.15*NTL_DOUBLE_PRECISION); i > 0; i--) |
---|
606 | bound = bound * 2; |
---|
607 | } |
---|
608 | |
---|
609 | double half_plus_fudge = 0.5 + red_fudge; |
---|
610 | |
---|
611 | quit = 0; |
---|
612 | k = init_k; |
---|
613 | |
---|
614 | |
---|
615 | vec_long st_mem; |
---|
616 | st_mem.SetLength(m+2); |
---|
617 | long *st = st_mem.elts(); |
---|
618 | |
---|
619 | for (i = 1; i < k; i++) |
---|
620 | st[i] = i; |
---|
621 | |
---|
622 | for (i = k; i <= m+1; i++) |
---|
623 | st[i] = 1; |
---|
624 | |
---|
625 | double *buf; |
---|
626 | buf = NTL_NEW_OP double [m+1]; |
---|
627 | if (!buf) Error("out of memory in lll_LLL_FP"); |
---|
628 | |
---|
629 | vec_long in_vec_mem; |
---|
630 | in_vec_mem.SetLength(n+1); |
---|
631 | long *in_vec = in_vec_mem.elts(); |
---|
632 | |
---|
633 | double *max_b; |
---|
634 | max_b = NTL_NEW_OP double [m+1]; |
---|
635 | if (!max_b) Error("out of memory in lll_LLL_FP"); |
---|
636 | |
---|
637 | for (i = 1; i <= m; i++) |
---|
638 | max_b[i] = max_abs(B1[i], n); |
---|
639 | |
---|
640 | long in_float; |
---|
641 | |
---|
642 | long rst; |
---|
643 | long counter; |
---|
644 | long start_over; |
---|
645 | |
---|
646 | long trigger_index; |
---|
647 | long small_trigger; |
---|
648 | long cnt; |
---|
649 | |
---|
650 | mat_RR rr_B1; |
---|
651 | mat_RR rr_mu; |
---|
652 | vec_RR rr_c; |
---|
653 | vec_RR rr_b; |
---|
654 | |
---|
655 | long m_orig = m; |
---|
656 | |
---|
657 | long rr_st = 1; |
---|
658 | |
---|
659 | long max_k = 0; |
---|
660 | |
---|
661 | long prec = RR::precision(); |
---|
662 | |
---|
663 | double tt; |
---|
664 | |
---|
665 | long swap_cnt = 0; |
---|
666 | |
---|
667 | |
---|
668 | while (k <= m) { |
---|
669 | |
---|
670 | if (k > max_k) { |
---|
671 | max_k = k; |
---|
672 | swap_cnt = 0; |
---|
673 | } |
---|
674 | |
---|
675 | if (k < rr_st) rr_st = k; |
---|
676 | |
---|
677 | if (st[k] == k) |
---|
678 | rst = 1; |
---|
679 | else |
---|
680 | rst = k; |
---|
681 | |
---|
682 | if (st[k] < st[k+1]) st[k+1] = st[k]; |
---|
683 | ComputeGS(B, B1, mu, b, c, k, bound, st[k], buf); |
---|
684 | CheckFinite(&c[k]); |
---|
685 | st[k] = k; |
---|
686 | |
---|
687 | if (swap_cnt > 200000) { |
---|
688 | RR_GS(B, B1, mu, b, c, buf, prec, |
---|
689 | rr_st, k, m_orig, rr_B1, rr_mu, rr_b, rr_c); |
---|
690 | if (rr_st < st[k+1]) st[k+1] = rr_st; |
---|
691 | rr_st = k+1; |
---|
692 | rst = k; |
---|
693 | swap_cnt = 0; |
---|
694 | } |
---|
695 | |
---|
696 | counter = 0; |
---|
697 | trigger_index = k; |
---|
698 | small_trigger = 0; |
---|
699 | cnt = 0; |
---|
700 | |
---|
701 | long thresh = 10; |
---|
702 | long sz=0, new_sz; |
---|
703 | |
---|
704 | long did_rr_gs = 0; |
---|
705 | |
---|
706 | |
---|
707 | do { |
---|
708 | // size reduction |
---|
709 | |
---|
710 | counter++; |
---|
711 | if ((counter & 127) == 0) { |
---|
712 | |
---|
713 | new_sz = 0; |
---|
714 | for (j = 1; j <= n; j++) |
---|
715 | new_sz += NumBits(B(k,j)); |
---|
716 | |
---|
717 | if ((counter >> 7) == 1 || new_sz < sz) { |
---|
718 | sz = new_sz; |
---|
719 | } |
---|
720 | } |
---|
721 | |
---|
722 | Fc1 = 0; |
---|
723 | start_over = 0; |
---|
724 | |
---|
725 | for (j = rst-1; j >= 1; j--) { |
---|
726 | t1 = fabs(mu[k][j]); |
---|
727 | if (t1 > half_plus_fudge) { |
---|
728 | |
---|
729 | |
---|
730 | if (!Fc1) { |
---|
731 | if (j > trigger_index || |
---|
732 | (j == trigger_index && small_trigger)) { |
---|
733 | |
---|
734 | cnt++; |
---|
735 | |
---|
736 | if (cnt > thresh) { |
---|
737 | if (log_red <= 15) { |
---|
738 | |
---|
739 | while (log_red > 10) |
---|
740 | inc_red_fudge(); |
---|
741 | |
---|
742 | half_plus_fudge = 0.5 + red_fudge; |
---|
743 | |
---|
744 | if (!did_rr_gs) { |
---|
745 | RR_GS(B, B1, mu, b, c, buf, prec, |
---|
746 | rr_st, k, m_orig, rr_B1, rr_mu, rr_b, rr_c); |
---|
747 | if (rr_st < st[k+1]) st[k+1] = rr_st; |
---|
748 | rr_st = k+1; |
---|
749 | did_rr_gs = 1; |
---|
750 | rst = k; |
---|
751 | trigger_index = k; |
---|
752 | small_trigger = 0; |
---|
753 | start_over = 1; |
---|
754 | break; |
---|
755 | } |
---|
756 | } |
---|
757 | else { |
---|
758 | inc_red_fudge(); |
---|
759 | half_plus_fudge = 0.5 + red_fudge; |
---|
760 | cnt = 0; |
---|
761 | } |
---|
762 | } |
---|
763 | } |
---|
764 | |
---|
765 | trigger_index = j; |
---|
766 | small_trigger = (t1 < 4); |
---|
767 | |
---|
768 | Fc1 = 1; |
---|
769 | if (k < rr_st) rr_st = k; |
---|
770 | RowTransformStart(B1[k], in_vec, in_float, n); |
---|
771 | } |
---|
772 | |
---|
773 | |
---|
774 | mu1 = mu[k][j]; |
---|
775 | if (mu1 >= 0) |
---|
776 | mu1 = ceil(mu1-0.5); |
---|
777 | else |
---|
778 | mu1 = floor(mu1+0.5); |
---|
779 | |
---|
780 | double *mu_k = mu[k]; |
---|
781 | double *mu_j = mu[j]; |
---|
782 | |
---|
783 | if (mu1 == 1) { |
---|
784 | for (i = 1; i <= j-1; i++) |
---|
785 | mu_k[i] -= mu_j[i]; |
---|
786 | } |
---|
787 | else if (mu1 == -1) { |
---|
788 | for (i = 1; i <= j-1; i++) |
---|
789 | mu_k[i] += mu_j[i]; |
---|
790 | } |
---|
791 | else { |
---|
792 | for (i = 1; i <= j-1; i++) |
---|
793 | mu_k[i] -= mu1*mu_j[i]; |
---|
794 | } |
---|
795 | |
---|
796 | mu_k[j] -= mu1; |
---|
797 | |
---|
798 | conv(MU, mu1); |
---|
799 | |
---|
800 | RowTransform(B(k), B(j), MU, B1[k], B1[j], in_vec, |
---|
801 | max_b[k], max_b[j], in_float); |
---|
802 | if (U) RowTransform((*U)(k), (*U)(j), MU); |
---|
803 | } |
---|
804 | } |
---|
805 | |
---|
806 | |
---|
807 | if (Fc1) { |
---|
808 | RowTransformFinish(B(k), B1[k], in_vec); |
---|
809 | max_b[k] = max_abs(B1[k], n); |
---|
810 | |
---|
811 | if (!did_rr_gs) { |
---|
812 | b[k] = InnerProduct(B1[k], B1[k], n); |
---|
813 | CheckFinite(&b[k]); |
---|
814 | |
---|
815 | ComputeGS(B, B1, mu, b, c, k, bound, 1, buf); |
---|
816 | CheckFinite(&c[k]); |
---|
817 | } |
---|
818 | else { |
---|
819 | RR_GS(B, B1, mu, b, c, buf, prec, |
---|
820 | rr_st, k, m_orig, rr_B1, rr_mu, rr_b, rr_c); |
---|
821 | rr_st = k+1; |
---|
822 | } |
---|
823 | |
---|
824 | rst = k; |
---|
825 | } |
---|
826 | } while (Fc1 || start_over); |
---|
827 | |
---|
828 | if (check && (*check)(B(k))) |
---|
829 | quit = 1; |
---|
830 | |
---|
831 | if (b[k] == 0) { |
---|
832 | for (i = k; i < m; i++) { |
---|
833 | // swap i, i+1 |
---|
834 | swap(B(i), B(i+1)); |
---|
835 | tp = B1[i]; B1[i] = B1[i+1]; B1[i+1] = tp; |
---|
836 | t1 = b[i]; b[i] = b[i+1]; b[i+1] = t1; |
---|
837 | t1 = max_b[i]; max_b[i] = max_b[i+1]; max_b[i+1] = t1; |
---|
838 | if (U) swap((*U)(i), (*U)(i+1)); |
---|
839 | } |
---|
840 | |
---|
841 | for (i = k; i <= m+1; i++) st[i] = 1; |
---|
842 | if (k < rr_st) rr_st = k; |
---|
843 | |
---|
844 | m--; |
---|
845 | if (quit) break; |
---|
846 | continue; |
---|
847 | } |
---|
848 | |
---|
849 | if (quit) break; |
---|
850 | |
---|
851 | if (deep > 0) { |
---|
852 | // deep insertions |
---|
853 | |
---|
854 | double cc = b[k]; |
---|
855 | long l = 1; |
---|
856 | while (l <= k-1 && delta*c[l] <= cc) { |
---|
857 | cc = cc - mu[k][l]*mu[k][l]*c[l]; |
---|
858 | l++; |
---|
859 | } |
---|
860 | |
---|
861 | if (l <= k-1 && (l <= deep || k-l <= deep)) { |
---|
862 | // deep insertion at position l |
---|
863 | |
---|
864 | for (i = k; i > l; i--) { |
---|
865 | // swap rows i, i-1 |
---|
866 | swap(B(i), B(i-1)); |
---|
867 | tp = B1[i]; B1[i] = B1[i-1]; B1[i-1] = tp; |
---|
868 | tp = mu[i]; mu[i] = mu[i-1]; mu[i-1] = tp; |
---|
869 | t1 = b[i]; b[i] = b[i-1]; b[i-1] = t1; |
---|
870 | t1 = max_b[i]; max_b[i] = max_b[i-1]; max_b[i-1] = t1; |
---|
871 | if (U) swap((*U)(i), (*U)(i-1)); |
---|
872 | } |
---|
873 | |
---|
874 | k = l; |
---|
875 | NumSwaps++; |
---|
876 | swap_cnt++; |
---|
877 | continue; |
---|
878 | } |
---|
879 | } // end deep insertions |
---|
880 | |
---|
881 | // test LLL reduction condition |
---|
882 | |
---|
883 | if (k > 1 && delta*c[k-1] > c[k] + mu[k][k-1]*mu[k][k-1]*c[k-1]) { |
---|
884 | // swap rows k, k-1 |
---|
885 | swap(B(k), B(k-1)); |
---|
886 | tp = B1[k]; B1[k] = B1[k-1]; B1[k-1] = tp; |
---|
887 | tp = mu[k]; mu[k] = mu[k-1]; mu[k-1] = tp; |
---|
888 | t1 = b[k]; b[k] = b[k-1]; b[k-1] = t1; |
---|
889 | t1 = max_b[k]; max_b[k] = max_b[k-1]; max_b[k-1] = t1; |
---|
890 | if (U) swap((*U)(k), (*U)(k-1)); |
---|
891 | |
---|
892 | k--; |
---|
893 | NumSwaps++; |
---|
894 | swap_cnt++; |
---|
895 | // cout << "-\n"; |
---|
896 | } |
---|
897 | else { |
---|
898 | |
---|
899 | k++; |
---|
900 | // cout << "+\n"; |
---|
901 | } |
---|
902 | |
---|
903 | } |
---|
904 | |
---|
905 | delete [] buf; |
---|
906 | delete [] max_b; |
---|
907 | |
---|
908 | return m; |
---|
909 | } |
---|
910 | |
---|
911 | |
---|
912 | |
---|
913 | |
---|
914 | |
---|
915 | static |
---|
916 | long LLL_FP(mat_ZZ& B, mat_ZZ* U, double delta, long deep, |
---|
917 | LLLCheckFct check) |
---|
918 | { |
---|
919 | long m = B.NumRows(); |
---|
920 | long n = B.NumCols(); |
---|
921 | |
---|
922 | long i, j; |
---|
923 | long new_m, dep, quit; |
---|
924 | ZZ MU; |
---|
925 | |
---|
926 | ZZ T1; |
---|
927 | |
---|
928 | init_red_fudge(); |
---|
929 | |
---|
930 | if (U) ident(*U, m); |
---|
931 | |
---|
932 | double **B1; // approximates B |
---|
933 | |
---|
934 | typedef double *doubleptr; |
---|
935 | |
---|
936 | B1 = NTL_NEW_OP doubleptr[m+1]; |
---|
937 | if (!B1) Error("LLL_FP: out of memory"); |
---|
938 | |
---|
939 | for (i = 1; i <= m; i++) { |
---|
940 | B1[i] = NTL_NEW_OP double[n+1]; |
---|
941 | if (!B1[i]) Error("LLL_FP: out of memory"); |
---|
942 | } |
---|
943 | |
---|
944 | double **mu; |
---|
945 | mu = NTL_NEW_OP doubleptr[m+1]; |
---|
946 | if (!mu) Error("LLL_FP: out of memory"); |
---|
947 | |
---|
948 | for (i = 1; i <= m; i++) { |
---|
949 | mu[i] = NTL_NEW_OP double[m+1]; |
---|
950 | if (!mu[i]) Error("LLL_FP: out of memory"); |
---|
951 | } |
---|
952 | |
---|
953 | double *c; // squared lengths of Gramm-Schmidt basis vectors |
---|
954 | |
---|
955 | c = NTL_NEW_OP double[m+1]; |
---|
956 | if (!c) Error("LLL_FP: out of memory"); |
---|
957 | |
---|
958 | double *b; // squared lengths of basis vectors |
---|
959 | |
---|
960 | b = NTL_NEW_OP double[m+1]; |
---|
961 | if (!b) Error("LLL_FP: out of memory"); |
---|
962 | |
---|
963 | |
---|
964 | for (i = 1; i <=m; i++) |
---|
965 | for (j = 1; j <= n; j++) { |
---|
966 | conv(B1[i][j], B(i, j)); |
---|
967 | CheckFinite(&B1[i][j]); |
---|
968 | } |
---|
969 | |
---|
970 | |
---|
971 | for (i = 1; i <= m; i++) { |
---|
972 | b[i] = InnerProduct(B1[i], B1[i], n); |
---|
973 | CheckFinite(&b[i]); |
---|
974 | } |
---|
975 | |
---|
976 | new_m = ll_LLL_FP(B, U, delta, deep, check, B1, mu, b, c, m, 1, quit); |
---|
977 | dep = m - new_m; |
---|
978 | m = new_m; |
---|
979 | |
---|
980 | if (dep > 0) { |
---|
981 | // for consistency, we move all of the zero rows to the front |
---|
982 | |
---|
983 | for (i = 0; i < m; i++) { |
---|
984 | swap(B(m+dep-i), B(m-i)); |
---|
985 | if (U) swap((*U)(m+dep-i), (*U)(m-i)); |
---|
986 | } |
---|
987 | } |
---|
988 | |
---|
989 | |
---|
990 | // clean-up |
---|
991 | |
---|
992 | for (i = 1; i <= m; i++) { |
---|
993 | delete [] B1[i]; |
---|
994 | } |
---|
995 | |
---|
996 | delete [] B1; |
---|
997 | |
---|
998 | for (i = 1; i <= m; i++) { |
---|
999 | delete [] mu[i]; |
---|
1000 | } |
---|
1001 | |
---|
1002 | delete [] mu; |
---|
1003 | |
---|
1004 | delete [] c; |
---|
1005 | |
---|
1006 | delete [] b; |
---|
1007 | |
---|
1008 | return m; |
---|
1009 | } |
---|
1010 | |
---|
1011 | |
---|
1012 | |
---|
1013 | long LLL_FP(mat_ZZ& B, double delta, long deep, LLLCheckFct check, |
---|
1014 | long verb) |
---|
1015 | { |
---|
1016 | verbose = verb; |
---|
1017 | RR_GS_time = 0; |
---|
1018 | NumSwaps = 0; |
---|
1019 | if (verbose) { |
---|
1020 | StartTime = GetTime(); |
---|
1021 | LastTime = StartTime; |
---|
1022 | } |
---|
1023 | |
---|
1024 | if (delta < 0.50 || delta >= 1) Error("LLL_FP: bad delta"); |
---|
1025 | if (deep < 0) Error("LLL_FP: bad deep"); |
---|
1026 | return LLL_FP(B, 0, delta, deep, check); |
---|
1027 | } |
---|
1028 | |
---|
1029 | long LLL_FP(mat_ZZ& B, mat_ZZ& U, double delta, long deep, |
---|
1030 | LLLCheckFct check, long verb) |
---|
1031 | { |
---|
1032 | verbose = verb; |
---|
1033 | RR_GS_time = 0; |
---|
1034 | NumSwaps = 0; |
---|
1035 | if (verbose) { |
---|
1036 | StartTime = GetTime(); |
---|
1037 | LastTime = StartTime; |
---|
1038 | } |
---|
1039 | |
---|
1040 | if (delta < 0.50 || delta >= 1) Error("LLL_FP: bad delta"); |
---|
1041 | if (deep < 0) Error("LLL_FP: bad deep"); |
---|
1042 | return LLL_FP(B, &U, delta, deep, check); |
---|
1043 | } |
---|
1044 | |
---|
1045 | |
---|
1046 | |
---|
1047 | static vec_double BKZConstant; |
---|
1048 | |
---|
1049 | static |
---|
1050 | void ComputeBKZConstant(long beta, long p) |
---|
1051 | { |
---|
1052 | const double c_PI = 3.14159265358979323846264338328; |
---|
1053 | const double LogPI = 1.14472988584940017414342735135; |
---|
1054 | |
---|
1055 | BKZConstant.SetLength(beta-1); |
---|
1056 | |
---|
1057 | vec_double Log; |
---|
1058 | Log.SetLength(beta); |
---|
1059 | |
---|
1060 | |
---|
1061 | long i, j, k; |
---|
1062 | double x, y; |
---|
1063 | |
---|
1064 | for (j = 1; j <= beta; j++) |
---|
1065 | Log(j) = log(double(j)); |
---|
1066 | |
---|
1067 | for (i = 1; i <= beta-1; i++) { |
---|
1068 | // First, we compute x = gamma(i/2)^{2/i} |
---|
1069 | |
---|
1070 | k = i/2; |
---|
1071 | |
---|
1072 | if ((i & 1) == 0) { // i even |
---|
1073 | x = 0; |
---|
1074 | for (j = 1; j <= k; j++) |
---|
1075 | x = x + Log(j); |
---|
1076 | |
---|
1077 | x = x * (1/double(k)); |
---|
1078 | |
---|
1079 | x = exp(x); |
---|
1080 | } |
---|
1081 | else { // i odd |
---|
1082 | x = 0; |
---|
1083 | for (j = k + 2; j <= 2*k + 2; j++) |
---|
1084 | x = x + Log(j); |
---|
1085 | |
---|
1086 | x = 0.5*LogPI + x - 2*(k+1)*Log(2); |
---|
1087 | |
---|
1088 | x = x * (2.0/double(i)); |
---|
1089 | |
---|
1090 | x = exp(x); |
---|
1091 | } |
---|
1092 | |
---|
1093 | // Second, we compute y = 2^{2*p/i} |
---|
1094 | |
---|
1095 | y = -(2*p/double(i))*Log(2); |
---|
1096 | y = exp(y); |
---|
1097 | |
---|
1098 | BKZConstant(i) = x*y/c_PI; |
---|
1099 | } |
---|
1100 | } |
---|
1101 | |
---|
1102 | static vec_double BKZThresh; |
---|
1103 | |
---|
1104 | static |
---|
1105 | void ComputeBKZThresh(double *c, long beta) |
---|
1106 | { |
---|
1107 | BKZThresh.SetLength(beta-1); |
---|
1108 | |
---|
1109 | long i; |
---|
1110 | double x; |
---|
1111 | |
---|
1112 | x = 0; |
---|
1113 | |
---|
1114 | for (i = 1; i <= beta-1; i++) { |
---|
1115 | x += log(c[i-1]); |
---|
1116 | BKZThresh(i) = exp(x/double(i))*BKZConstant(i); |
---|
1117 | if (!IsFinite(&BKZThresh(i))) BKZThresh(i) = 0; |
---|
1118 | } |
---|
1119 | } |
---|
1120 | |
---|
1121 | static |
---|
1122 | long BKZ_FP(mat_ZZ& BB, mat_ZZ* UU, double delta, |
---|
1123 | long beta, long prune, LLLCheckFct check) |
---|
1124 | { |
---|
1125 | |
---|
1126 | |
---|
1127 | |
---|
1128 | long m = BB.NumRows(); |
---|
1129 | long n = BB.NumCols(); |
---|
1130 | long m_orig = m; |
---|
1131 | |
---|
1132 | long i, j; |
---|
1133 | ZZ MU; |
---|
1134 | |
---|
1135 | double t1; |
---|
1136 | ZZ T1; |
---|
1137 | double *tp; |
---|
1138 | |
---|
1139 | init_red_fudge(); |
---|
1140 | |
---|
1141 | mat_ZZ B; |
---|
1142 | B = BB; |
---|
1143 | |
---|
1144 | B.SetDims(m+1, n); |
---|
1145 | |
---|
1146 | |
---|
1147 | double **B1; // approximates B |
---|
1148 | |
---|
1149 | typedef double *doubleptr; |
---|
1150 | |
---|
1151 | B1 = NTL_NEW_OP doubleptr[m+2]; |
---|
1152 | if (!B1) Error("BKZ_FP: out of memory"); |
---|
1153 | |
---|
1154 | for (i = 1; i <= m+1; i++) { |
---|
1155 | B1[i] = NTL_NEW_OP double[n+1]; |
---|
1156 | if (!B1[i]) Error("BKZ_FP: out of memory"); |
---|
1157 | } |
---|
1158 | |
---|
1159 | double **mu; |
---|
1160 | mu = NTL_NEW_OP doubleptr[m+2]; |
---|
1161 | if (!mu) Error("LLL_FP: out of memory"); |
---|
1162 | |
---|
1163 | for (i = 1; i <= m+1; i++) { |
---|
1164 | mu[i] = NTL_NEW_OP double[m+1]; |
---|
1165 | if (!mu[i]) Error("BKZ_FP: out of memory"); |
---|
1166 | } |
---|
1167 | |
---|
1168 | |
---|
1169 | double *c; // squared lengths of Gramm-Schmidt basis vectors |
---|
1170 | |
---|
1171 | c = NTL_NEW_OP double[m+2]; |
---|
1172 | if (!c) Error("BKZ_FP: out of memory"); |
---|
1173 | |
---|
1174 | double *b; // squared lengths of basis vectors |
---|
1175 | |
---|
1176 | b = NTL_NEW_OP double[m+2]; |
---|
1177 | if (!b) Error("BKZ_FP: out of memory"); |
---|
1178 | |
---|
1179 | double cbar; |
---|
1180 | |
---|
1181 | double *ctilda; |
---|
1182 | ctilda = NTL_NEW_OP double[m+2]; |
---|
1183 | if (!ctilda) Error("BKZ_FP: out of memory"); |
---|
1184 | |
---|
1185 | double *vvec; |
---|
1186 | vvec = NTL_NEW_OP double[m+2]; |
---|
1187 | if (!vvec) Error("BKZ_FP: out of memory"); |
---|
1188 | |
---|
1189 | double *yvec; |
---|
1190 | yvec = NTL_NEW_OP double[m+2]; |
---|
1191 | if (!yvec) Error("BKZ_FP: out of memory"); |
---|
1192 | |
---|
1193 | double *uvec; |
---|
1194 | uvec = NTL_NEW_OP double[m+2]; |
---|
1195 | if (!uvec) Error("BKZ_FP: out of memory"); |
---|
1196 | |
---|
1197 | double *utildavec; |
---|
1198 | utildavec = NTL_NEW_OP double[m+2]; |
---|
1199 | if (!utildavec) Error("BKZ_FP: out of memory"); |
---|
1200 | |
---|
1201 | |
---|
1202 | long *Deltavec; |
---|
1203 | Deltavec = NTL_NEW_OP long[m+2]; |
---|
1204 | if (!Deltavec) Error("BKZ_FP: out of memory"); |
---|
1205 | |
---|
1206 | long *deltavec; |
---|
1207 | deltavec = NTL_NEW_OP long[m+2]; |
---|
1208 | if (!deltavec) Error("BKZ_FP: out of memory"); |
---|
1209 | |
---|
1210 | mat_ZZ Ulocal; |
---|
1211 | mat_ZZ *U; |
---|
1212 | |
---|
1213 | if (UU) { |
---|
1214 | Ulocal.SetDims(m+1, m); |
---|
1215 | for (i = 1; i <= m; i++) |
---|
1216 | conv(Ulocal(i, i), 1); |
---|
1217 | U = &Ulocal; |
---|
1218 | } |
---|
1219 | else |
---|
1220 | U = 0; |
---|
1221 | |
---|
1222 | long quit; |
---|
1223 | long new_m; |
---|
1224 | long z, jj, kk; |
---|
1225 | long s, t; |
---|
1226 | long h; |
---|
1227 | double eta; |
---|
1228 | |
---|
1229 | |
---|
1230 | for (i = 1; i <=m; i++) |
---|
1231 | for (j = 1; j <= n; j++) { |
---|
1232 | conv(B1[i][j], B(i, j)); |
---|
1233 | CheckFinite(&B1[i][j]); |
---|
1234 | } |
---|
1235 | |
---|
1236 | |
---|
1237 | for (i = 1; i <= m; i++) { |
---|
1238 | b[i] = InnerProduct(B1[i], B1[i], n); |
---|
1239 | CheckFinite(&b[i]); |
---|
1240 | } |
---|
1241 | |
---|
1242 | |
---|
1243 | |
---|
1244 | m = ll_LLL_FP(B, U, delta, 0, check, B1, mu, b, c, m, 1, quit); |
---|
1245 | |
---|
1246 | double tt; |
---|
1247 | |
---|
1248 | double enum_time = 0; |
---|
1249 | unsigned long NumIterations = 0; |
---|
1250 | unsigned long NumTrivial = 0; |
---|
1251 | unsigned long NumNonTrivial = 0; |
---|
1252 | unsigned long NumNoOps = 0; |
---|
1253 | |
---|
1254 | long verb = verbose; |
---|
1255 | |
---|
1256 | verbose = 0; |
---|
1257 | |
---|
1258 | long clean = 1; |
---|
1259 | |
---|
1260 | if (m < m_orig) { |
---|
1261 | for (i = m_orig+1; i >= m+2; i--) { |
---|
1262 | // swap i, i-1 |
---|
1263 | |
---|
1264 | swap(B(i), B(i-1)); |
---|
1265 | if (U) swap((*U)(i), (*U)(i-1)); |
---|
1266 | } |
---|
1267 | } |
---|
1268 | |
---|
1269 | if (!quit && m > 1) { |
---|
1270 | if (beta > m) beta = m; |
---|
1271 | |
---|
1272 | if (prune > 0) |
---|
1273 | ComputeBKZConstant(beta, prune); |
---|
1274 | |
---|
1275 | z = 0; |
---|
1276 | jj = 0; |
---|
1277 | |
---|
1278 | while (z < m-1) { |
---|
1279 | jj++; |
---|
1280 | kk = min(jj+beta-1, m); |
---|
1281 | |
---|
1282 | if (jj == m) { |
---|
1283 | jj = 1; |
---|
1284 | kk = beta; |
---|
1285 | clean = 1; |
---|
1286 | } |
---|
1287 | |
---|
1288 | // ENUM |
---|
1289 | |
---|
1290 | double tt1; |
---|
1291 | |
---|
1292 | if (verb) { |
---|
1293 | tt1 = GetTime(); |
---|
1294 | } |
---|
1295 | |
---|
1296 | |
---|
1297 | if (prune > 0) |
---|
1298 | ComputeBKZThresh(&c[jj], kk-jj+1); |
---|
1299 | |
---|
1300 | |
---|
1301 | cbar = c[jj]; |
---|
1302 | utildavec[jj] = uvec[jj] = 1; |
---|
1303 | |
---|
1304 | yvec[jj] = vvec[jj] = 0; |
---|
1305 | Deltavec[jj] = 0; |
---|
1306 | |
---|
1307 | |
---|
1308 | s = t = jj; |
---|
1309 | deltavec[jj] = 1; |
---|
1310 | |
---|
1311 | for (i = jj+1; i <= kk+1; i++) { |
---|
1312 | ctilda[i] = uvec[i] = utildavec[i] = yvec[i] = 0; |
---|
1313 | Deltavec[i] = 0; |
---|
1314 | vvec[i] = 0; |
---|
1315 | deltavec[i] = 1; |
---|
1316 | } |
---|
1317 | |
---|
1318 | long enum_cnt = 0; |
---|
1319 | |
---|
1320 | while (t <= kk) { |
---|
1321 | |
---|
1322 | ctilda[t] = ctilda[t+1] + |
---|
1323 | (yvec[t]+utildavec[t])*(yvec[t]+utildavec[t])*c[t]; |
---|
1324 | |
---|
1325 | if (prune > 0 && t > jj) { |
---|
1326 | eta = BKZThresh(t-jj); |
---|
1327 | } |
---|
1328 | else |
---|
1329 | eta = 0; |
---|
1330 | |
---|
1331 | if (ctilda[t] < cbar - eta) { |
---|
1332 | if (t > jj) { |
---|
1333 | t--; |
---|
1334 | t1 = 0; |
---|
1335 | for (i = t+1; i <= s; i++) |
---|
1336 | t1 += utildavec[i]*mu[i][t]; |
---|
1337 | yvec[t] = t1; |
---|
1338 | t1 = -t1; |
---|
1339 | if (t1 >= 0) |
---|
1340 | t1 = ceil(t1-0.5); |
---|
1341 | else |
---|
1342 | t1 = floor(t1+0.5); |
---|
1343 | utildavec[t] = vvec[t] = t1; |
---|
1344 | Deltavec[t] = 0; |
---|
1345 | if (utildavec[t] > -yvec[t]) |
---|
1346 | deltavec[t] = -1; |
---|
1347 | else |
---|
1348 | deltavec[t] = 1; |
---|
1349 | } |
---|
1350 | else { |
---|
1351 | cbar = ctilda[jj]; |
---|
1352 | for (i = jj; i <= kk; i++) { |
---|
1353 | uvec[i] = utildavec[i]; |
---|
1354 | } |
---|
1355 | } |
---|
1356 | } |
---|
1357 | else { |
---|
1358 | t++; |
---|
1359 | s = max(s, t); |
---|
1360 | if (t < s) Deltavec[t] = -Deltavec[t]; |
---|
1361 | if (Deltavec[t]*deltavec[t] >= 0) Deltavec[t] += deltavec[t]; |
---|
1362 | utildavec[t] = vvec[t] + Deltavec[t]; |
---|
1363 | } |
---|
1364 | } |
---|
1365 | |
---|
1366 | if (verb) { |
---|
1367 | tt1 = GetTime() - tt1; |
---|
1368 | enum_time += tt1; |
---|
1369 | } |
---|
1370 | |
---|
1371 | NumIterations++; |
---|
1372 | |
---|
1373 | h = min(kk+1, m); |
---|
1374 | |
---|
1375 | if ((delta - 8*red_fudge)*c[jj] > cbar) { |
---|
1376 | |
---|
1377 | clean = 0; |
---|
1378 | |
---|
1379 | // we treat the case that the new vector is b_s (jj < s <= kk) |
---|
1380 | // as a special case that appears to occur most of the time. |
---|
1381 | |
---|
1382 | s = 0; |
---|
1383 | for (i = jj+1; i <= kk; i++) { |
---|
1384 | if (uvec[i] != 0) { |
---|
1385 | if (s == 0) |
---|
1386 | s = i; |
---|
1387 | else |
---|
1388 | s = -1; |
---|
1389 | } |
---|
1390 | } |
---|
1391 | |
---|
1392 | if (s == 0) Error("BKZ_FP: internal error"); |
---|
1393 | |
---|
1394 | if (s > 0) { |
---|
1395 | // special case |
---|
1396 | |
---|
1397 | NumTrivial++; |
---|
1398 | |
---|
1399 | for (i = s; i > jj; i--) { |
---|
1400 | // swap i, i-1 |
---|
1401 | swap(B(i-1), B(i)); |
---|
1402 | if (U) swap((*U)(i-1), (*U)(i)); |
---|
1403 | tp = B1[i-1]; B1[i-1] = B1[i]; B1[i] = tp; |
---|
1404 | t1 = b[i-1]; b[i-1] = b[i]; b[i] = t1; |
---|
1405 | } |
---|
1406 | |
---|
1407 | // cerr << "special case\n"; |
---|
1408 | new_m = ll_LLL_FP(B, U, delta, 0, check, |
---|
1409 | B1, mu, b, c, h, jj, quit); |
---|
1410 | if (new_m != h) Error("BKZ_FP: internal error"); |
---|
1411 | if (quit) break; |
---|
1412 | } |
---|
1413 | else { |
---|
1414 | // the general case |
---|
1415 | |
---|
1416 | NumNonTrivial++; |
---|
1417 | |
---|
1418 | for (i = 1; i <= n; i++) conv(B(m+1, i), 0); |
---|
1419 | |
---|
1420 | if (U) { |
---|
1421 | for (i = 1; i <= m_orig; i++) |
---|
1422 | conv((*U)(m+1, i), 0); |
---|
1423 | } |
---|
1424 | |
---|
1425 | for (i = jj; i <= kk; i++) { |
---|
1426 | if (uvec[i] == 0) continue; |
---|
1427 | conv(MU, uvec[i]); |
---|
1428 | RowTransform2(B(m+1), B(i), MU); |
---|
1429 | if (U) RowTransform2((*U)(m+1), (*U)(i), MU); |
---|
1430 | } |
---|
1431 | |
---|
1432 | for (i = m+1; i >= jj+1; i--) { |
---|
1433 | // swap i, i-1 |
---|
1434 | swap(B(i-1), B(i)); |
---|
1435 | if (U) swap((*U)(i-1), (*U)(i)); |
---|
1436 | tp = B1[i-1]; B1[i-1] = B1[i]; B1[i] = tp; |
---|
1437 | t1 = b[i-1]; b[i-1] = b[i]; b[i] = t1; |
---|
1438 | } |
---|
1439 | |
---|
1440 | for (i = 1; i <= n; i++) { |
---|
1441 | conv(B1[jj][i], B(jj, i)); |
---|
1442 | CheckFinite(&B1[jj][i]); |
---|
1443 | } |
---|
1444 | |
---|
1445 | b[jj] = InnerProduct(B1[jj], B1[jj], n); |
---|
1446 | CheckFinite(&b[jj]); |
---|
1447 | |
---|
1448 | if (b[jj] == 0) Error("BKZ_FP: internal error"); |
---|
1449 | |
---|
1450 | // remove linear dependencies |
---|
1451 | |
---|
1452 | // cerr << "general case\n"; |
---|
1453 | new_m = ll_LLL_FP(B, U, delta, 0, 0, B1, mu, b, c, kk+1, jj, quit); |
---|
1454 | |
---|
1455 | if (new_m != kk) Error("BKZ_FP: internal error"); |
---|
1456 | |
---|
1457 | // remove zero vector |
---|
1458 | |
---|
1459 | for (i = kk+2; i <= m+1; i++) { |
---|
1460 | // swap i, i-1 |
---|
1461 | swap(B(i-1), B(i)); |
---|
1462 | if (U) swap((*U)(i-1), (*U)(i)); |
---|
1463 | tp = B1[i-1]; B1[i-1] = B1[i]; B1[i] = tp; |
---|
1464 | t1 = b[i-1]; b[i-1] = b[i]; b[i] = t1; |
---|
1465 | } |
---|
1466 | |
---|
1467 | quit = 0; |
---|
1468 | if (check) { |
---|
1469 | for (i = 1; i <= kk; i++) |
---|
1470 | if ((*check)(B(i))) { |
---|
1471 | quit = 1; |
---|
1472 | break; |
---|
1473 | } |
---|
1474 | } |
---|
1475 | |
---|
1476 | if (quit) break; |
---|
1477 | |
---|
1478 | if (h > kk) { |
---|
1479 | // extend reduced basis |
---|
1480 | |
---|
1481 | new_m = ll_LLL_FP(B, U, delta, 0, check, |
---|
1482 | B1, mu, b, c, h, h, quit); |
---|
1483 | |
---|
1484 | if (new_m != h) Error("BKZ_FP: internal error"); |
---|
1485 | if (quit) break; |
---|
1486 | } |
---|
1487 | } |
---|
1488 | |
---|
1489 | z = 0; |
---|
1490 | } |
---|
1491 | else { |
---|
1492 | // LLL_FP |
---|
1493 | // cerr << "progress\n"; |
---|
1494 | |
---|
1495 | NumNoOps++; |
---|
1496 | |
---|
1497 | if (!clean) { |
---|
1498 | new_m = |
---|
1499 | ll_LLL_FP(B, U, delta, 0, check, B1, mu, b, c, h, h, quit); |
---|
1500 | if (new_m != h) Error("BKZ_FP: internal error"); |
---|
1501 | if (quit) break; |
---|
1502 | } |
---|
1503 | |
---|
1504 | z++; |
---|
1505 | } |
---|
1506 | } |
---|
1507 | } |
---|
1508 | |
---|
1509 | |
---|
1510 | // clean up |
---|
1511 | |
---|
1512 | |
---|
1513 | if (m_orig > m) { |
---|
1514 | // for consistency, we move zero vectors to the front |
---|
1515 | |
---|
1516 | for (i = m+1; i <= m_orig; i++) { |
---|
1517 | swap(B(i), B(i+1)); |
---|
1518 | if (U) swap((*U)(i), (*U)(i+1)); |
---|
1519 | } |
---|
1520 | |
---|
1521 | for (i = 0; i < m; i++) { |
---|
1522 | swap(B(m_orig-i), B(m-i)); |
---|
1523 | if (U) swap((*U)(m_orig-i), (*U)(m-i)); |
---|
1524 | } |
---|
1525 | } |
---|
1526 | |
---|
1527 | B.SetDims(m_orig, n); |
---|
1528 | BB = B; |
---|
1529 | |
---|
1530 | if (U) { |
---|
1531 | U->SetDims(m_orig, m_orig); |
---|
1532 | *UU = *U; |
---|
1533 | } |
---|
1534 | |
---|
1535 | for (i = 1; i <= m+1; i++) { |
---|
1536 | delete [] B1[i]; |
---|
1537 | } |
---|
1538 | |
---|
1539 | delete [] B1; |
---|
1540 | |
---|
1541 | for (i = 1; i <= m+1; i++) { |
---|
1542 | delete [] mu[i]; |
---|
1543 | } |
---|
1544 | |
---|
1545 | delete [] mu; |
---|
1546 | |
---|
1547 | delete [] c; |
---|
1548 | delete [] b; |
---|
1549 | delete [] ctilda; |
---|
1550 | delete [] vvec; |
---|
1551 | delete [] yvec; |
---|
1552 | delete [] uvec; |
---|
1553 | delete [] utildavec; |
---|
1554 | delete [] Deltavec; |
---|
1555 | delete [] deltavec; |
---|
1556 | |
---|
1557 | return m; |
---|
1558 | } |
---|
1559 | |
---|
1560 | long BKZ_FP(mat_ZZ& BB, mat_ZZ& UU, double delta, |
---|
1561 | long beta, long prune, LLLCheckFct check, long verb) |
---|
1562 | { |
---|
1563 | verbose = verb; |
---|
1564 | RR_GS_time = 0; |
---|
1565 | NumSwaps = 0; |
---|
1566 | if (verbose) { |
---|
1567 | StartTime = GetTime(); |
---|
1568 | LastTime = StartTime; |
---|
1569 | } |
---|
1570 | |
---|
1571 | if (delta < 0.50 || delta >= 1) Error("BKZ_FP: bad delta"); |
---|
1572 | if (beta < 2) Error("BKZ_FP: bad block size"); |
---|
1573 | |
---|
1574 | return BKZ_FP(BB, &UU, delta, beta, prune, check); |
---|
1575 | } |
---|
1576 | |
---|
1577 | long BKZ_FP(mat_ZZ& BB, double delta, |
---|
1578 | long beta, long prune, LLLCheckFct check, long verb) |
---|
1579 | { |
---|
1580 | verbose = verb; |
---|
1581 | RR_GS_time = 0; |
---|
1582 | NumSwaps = 0; |
---|
1583 | if (verbose) { |
---|
1584 | StartTime = GetTime(); |
---|
1585 | LastTime = StartTime; |
---|
1586 | } |
---|
1587 | |
---|
1588 | if (delta < 0.50 || delta >= 1) Error("BKZ_FP: bad delta"); |
---|
1589 | if (beta < 2) Error("BKZ_FP: bad block size"); |
---|
1590 | |
---|
1591 | return BKZ_FP(BB, 0, delta, beta, prune, check); |
---|
1592 | } |
---|
1593 | |
---|
1594 | |
---|
1595 | NTL_END_IMPL |
---|