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 | |
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12 | static void RowTransform(vec_ZZ& A, vec_ZZ& B, const ZZ& MU1) |
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13 | // x = x - y*MU |
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14 | { |
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15 | static ZZ T, MU; |
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16 | long k; |
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17 | |
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18 | long n = A.length(); |
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19 | long i; |
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20 | |
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21 | MU = MU1; |
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22 | |
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23 | if (MU == 1) { |
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24 | for (i = 1; i <= n; i++) |
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25 | sub(A(i), A(i), B(i)); |
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26 | |
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27 | return; |
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28 | } |
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29 | |
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30 | if (MU == -1) { |
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31 | for (i = 1; i <= n; i++) |
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32 | add(A(i), A(i), B(i)); |
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33 | |
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34 | return; |
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35 | } |
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36 | |
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37 | if (MU == 0) return; |
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38 | |
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39 | if (NumTwos(MU) >= NTL_ZZ_NBITS) |
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40 | k = MakeOdd(MU); |
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41 | else |
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42 | k = 0; |
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43 | |
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44 | |
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45 | if (MU.WideSinglePrecision()) { |
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46 | long mu1; |
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47 | conv(mu1, MU); |
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48 | |
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49 | for (i = 1; i <= n; i++) { |
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50 | mul(T, B(i), mu1); |
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51 | if (k > 0) LeftShift(T, T, k); |
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52 | sub(A(i), A(i), T); |
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53 | } |
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54 | } |
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55 | else { |
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56 | for (i = 1; i <= n; i++) { |
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57 | mul(T, B(i), MU); |
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58 | if (k > 0) LeftShift(T, T, k); |
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59 | sub(A(i), A(i), T); |
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60 | } |
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61 | } |
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62 | } |
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63 | |
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64 | |
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65 | #define TR_BND (NTL_FDOUBLE_PRECISION/2.0) |
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66 | // Just to be safe!! |
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67 | |
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68 | static double max_abs(double *v, long n) |
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69 | { |
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70 | long i; |
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71 | double res, t; |
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72 | |
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73 | res = 0; |
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74 | |
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75 | for (i = 1; i <= n; i++) { |
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76 | t = fabs(v[i]); |
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77 | if (t > res) res = t; |
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78 | } |
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79 | |
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80 | return res; |
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81 | } |
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82 | |
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83 | |
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84 | static void RowTransformStart(double *a, long *in_a, long& in_float, long n) |
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85 | { |
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86 | long i; |
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87 | long inf = 1; |
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88 | |
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89 | for (i = 1; i <= n; i++) { |
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90 | in_a[i] = (a[i] < TR_BND && a[i] > -TR_BND); |
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91 | inf = inf & in_a[i]; |
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92 | } |
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93 | |
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94 | in_float = inf; |
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95 | } |
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96 | |
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97 | |
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98 | static void RowTransformFinish(vec_ZZ& A, double *a, long *in_a) |
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99 | { |
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100 | long n = A.length(); |
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101 | long i; |
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102 | |
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103 | for (i = 1; i <= n; i++) { |
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104 | if (in_a[i]) { |
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105 | conv(A(i), a[i]); |
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106 | } |
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107 | else { |
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108 | conv(a[i], A(i)); |
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109 | } |
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110 | } |
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111 | } |
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112 | |
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113 | |
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114 | static void RowTransform(vec_ZZ& A, vec_ZZ& B, const ZZ& MU1, |
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115 | double mu, double *a, double *b, long *in_a, |
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116 | double& max_a, double max_b, long& in_float) |
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117 | // x = x - y*MU |
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118 | { |
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119 | static ZZ T, MU; |
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120 | long k; |
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121 | |
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122 | long n = A.length(); |
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123 | long i; |
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124 | |
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125 | if (in_float) { |
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126 | max_a += fabs(mu)*max_b; |
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127 | if (max_a >= TR_BND) { |
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128 | in_float = 0; |
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129 | } |
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130 | } |
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131 | |
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132 | if (in_float) { |
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133 | if (mu == 1) { |
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134 | for (i = 1; i <= n; i++) |
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135 | a[i] -= b[i]; |
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136 | |
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137 | return; |
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138 | } |
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139 | |
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140 | if (mu == -1) { |
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141 | for (i = 1; i <= n; i++) |
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142 | a[i] += b[i]; |
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143 | |
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144 | return; |
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145 | } |
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146 | |
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147 | if (mu == 0) return; |
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148 | |
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149 | for (i = 1; i <= n; i++) |
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150 | a[i] -= mu*b[i]; |
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151 | |
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152 | |
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153 | return; |
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154 | } |
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155 | |
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156 | |
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157 | MU = MU1; |
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158 | |
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159 | if (MU == 1) { |
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160 | for (i = 1; i <= n; i++) { |
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161 | if (in_a[i] && a[i] < TR_BND && a[i] > -TR_BND && |
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162 | b[i] < TR_BND && b[i] > -TR_BND) { |
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163 | |
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164 | a[i] -= b[i]; |
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165 | } |
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166 | else { |
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167 | if (in_a[i]) { |
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168 | conv(A(i), a[i]); |
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169 | in_a[i] = 0; |
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170 | } |
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171 | |
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172 | sub(A(i), A(i), B(i)); |
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173 | } |
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174 | } |
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175 | return; |
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176 | } |
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177 | |
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178 | if (MU == -1) { |
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179 | for (i = 1; i <= n; i++) { |
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180 | if (in_a[i] && a[i] < TR_BND && a[i] > -TR_BND && |
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181 | b[i] < TR_BND && b[i] > -TR_BND) { |
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182 | |
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183 | a[i] += b[i]; |
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184 | } |
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185 | else { |
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186 | if (in_a[i]) { |
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187 | conv(A(i), a[i]); |
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188 | in_a[i] = 0; |
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189 | } |
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190 | |
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191 | add(A(i), A(i), B(i)); |
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192 | } |
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193 | } |
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194 | return; |
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195 | } |
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196 | |
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197 | if (MU == 0) return; |
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198 | |
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199 | double b_bnd = fabs(TR_BND/mu) - 1; |
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200 | if (b_bnd < 0) b_bnd = 0; |
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201 | |
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202 | if (NumTwos(MU) >= NTL_ZZ_NBITS) |
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203 | k = MakeOdd(MU); |
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204 | else |
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205 | k = 0; |
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206 | |
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207 | |
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208 | if (MU.WideSinglePrecision()) { |
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209 | long mu1; |
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210 | conv(mu1, MU); |
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211 | |
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212 | if (k > 0) { |
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213 | for (i = 1; i <= n; i++) { |
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214 | if (in_a[i]) { |
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215 | conv(A(i), a[i]); |
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216 | in_a[i] = 0; |
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217 | } |
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218 | |
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219 | mul(T, B(i), mu1); |
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220 | LeftShift(T, T, k); |
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221 | sub(A(i), A(i), T); |
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222 | } |
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223 | } |
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224 | else { |
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225 | for (i = 1; i <= n; i++) { |
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226 | if (in_a[i] && a[i] < TR_BND && a[i] > -TR_BND && |
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227 | b[i] < b_bnd && b[i] > -b_bnd) { |
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228 | |
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229 | a[i] -= b[i]*mu; |
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230 | } |
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231 | else { |
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232 | if (in_a[i]) { |
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233 | conv(A(i), a[i]); |
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234 | in_a[i] = 0; |
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235 | } |
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236 | mul(T, B(i), mu1); |
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237 | sub(A(i), A(i), T); |
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238 | } |
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239 | } |
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240 | } |
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241 | } |
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242 | else { |
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243 | for (i = 1; i <= n; i++) { |
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244 | if (in_a[i]) { |
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245 | conv(A(i), a[i]); |
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246 | in_a[i] = 0; |
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247 | } |
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248 | mul(T, B(i), MU); |
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249 | if (k > 0) LeftShift(T, T, k); |
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250 | sub(A(i), A(i), T); |
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251 | } |
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252 | } |
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253 | } |
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254 | |
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255 | static void RowTransform2(vec_ZZ& A, vec_ZZ& B, const ZZ& MU1) |
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256 | // x = x + y*MU |
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257 | |
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258 | { |
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259 | static ZZ T, MU; |
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260 | long k; |
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261 | |
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262 | long n = A.length(); |
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263 | long i; |
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264 | |
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265 | MU = MU1; |
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266 | |
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267 | if (MU == 1) { |
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268 | for (i = 1; i <= n; i++) |
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269 | add(A(i), A(i), B(i)); |
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270 | |
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271 | return; |
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272 | } |
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273 | |
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274 | if (MU == -1) { |
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275 | for (i = 1; i <= n; i++) |
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276 | sub(A(i), A(i), B(i)); |
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277 | |
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278 | return; |
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279 | } |
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280 | |
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281 | if (MU == 0) return; |
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282 | |
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283 | if (NumTwos(MU) >= NTL_ZZ_NBITS) |
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284 | k = MakeOdd(MU); |
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285 | else |
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286 | k = 0; |
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287 | |
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288 | if (MU.WideSinglePrecision()) { |
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289 | long mu1; |
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290 | conv(mu1, MU); |
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291 | |
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292 | for (i = 1; i <= n; i++) { |
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293 | mul(T, B(i), mu1); |
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294 | if (k > 0) LeftShift(T, T, k); |
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295 | add(A(i), A(i), T); |
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296 | } |
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297 | } |
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298 | else { |
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299 | for (i = 1; i <= n; i++) { |
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300 | mul(T, B(i), MU); |
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301 | if (k > 0) LeftShift(T, T, k); |
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302 | add(A(i), A(i), T); |
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303 | } |
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304 | } |
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305 | } |
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306 | |
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307 | |
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308 | |
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309 | class GivensCache_FP { |
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310 | public: |
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311 | GivensCache_FP(long m, long n); |
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312 | ~GivensCache_FP(); |
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313 | |
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314 | void flush(); |
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315 | void selective_flush(long l); |
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316 | void swap(long l); |
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317 | void swap(); |
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318 | void touch(); |
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319 | void incr(); |
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320 | |
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321 | long sz; |
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322 | |
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323 | double **buf; |
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324 | long *bl; |
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325 | long *bv; |
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326 | long bp; |
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327 | }; |
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328 | |
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329 | |
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330 | GivensCache_FP::GivensCache_FP(long m, long n) |
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331 | { |
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332 | sz = min(m, n)/10; |
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333 | if (sz < 2) |
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334 | sz = 2; |
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335 | else if (sz > 20) |
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336 | sz = 20; |
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337 | |
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338 | typedef double *doubleptr; |
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339 | |
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340 | long i; |
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341 | buf = NTL_NEW_OP doubleptr[sz]; |
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342 | if (!buf) Error("out of memory"); |
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343 | for (i = 0; i < sz; i++) |
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344 | if (!(buf[i] = NTL_NEW_OP double[n+1])) Error("out of memory"); |
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345 | |
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346 | bl = NTL_NEW_OP long[sz]; |
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347 | if (!bl) Error("out of memory"); |
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348 | for (i = 0; i < sz; i++) bl[0] = 0; |
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349 | |
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350 | bv = NTL_NEW_OP long[sz]; |
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351 | if (!bv) Error("out of memory"); |
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352 | for (i = 0; i < sz; i++) bv[0] = 0; |
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353 | |
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354 | bp = 0; |
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355 | } |
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356 | |
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357 | GivensCache_FP::~GivensCache_FP() |
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358 | { |
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359 | long i; |
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360 | |
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361 | for (i = 0; i < sz; i++) delete [] buf[i]; |
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362 | delete [] buf; |
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363 | delete [] bl; |
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364 | delete [] bv; |
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365 | } |
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366 | |
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367 | void GivensCache_FP::flush() |
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368 | { |
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369 | long i; |
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370 | for (i = 0; i < sz; i++) bl[i] = 0; |
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371 | } |
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372 | |
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373 | void GivensCache_FP::selective_flush(long l) |
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374 | { |
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375 | long i; |
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376 | |
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377 | for (i = 0; i < sz; i++) |
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378 | if (bl[i] && bv[i] >= l) |
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379 | bl[i] = 0; |
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380 | } |
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381 | |
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382 | void GivensCache_FP::swap(long l) |
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383 | { |
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384 | long k = bl[bp]; |
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385 | long i; |
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386 | |
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387 | i = 0; |
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388 | while (i < sz && bl[i] != l) |
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389 | i++; |
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390 | |
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391 | if (i < sz) { |
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392 | bl[bp] = l; |
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393 | bl[i] = k; |
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394 | } |
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395 | else |
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396 | bl[bp] = l; |
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397 | |
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398 | selective_flush(l); |
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399 | } |
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400 | |
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401 | void GivensCache_FP::swap() |
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402 | { |
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403 | swap(bl[bp] - 1); |
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404 | } |
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405 | |
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406 | void GivensCache_FP::touch() |
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407 | { |
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408 | long k = bl[bp]; |
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409 | bl[bp] = 0; |
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410 | selective_flush(k); |
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411 | } |
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412 | |
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413 | void GivensCache_FP::incr() |
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414 | { |
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415 | long k = bl[bp]; |
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416 | long k1 = k+1; |
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417 | long i; |
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418 | |
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419 | i = 0; |
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420 | while (i < sz && bl[i] != k1) |
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421 | i++; |
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422 | |
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423 | if (i < sz) { |
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424 | bp = i; |
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425 | return; |
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426 | } |
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427 | |
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428 | i = 0; |
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429 | while (i < sz && bl[i] != 0) |
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430 | i++; |
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431 | |
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432 | if (i < sz) { |
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433 | bp = i; |
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434 | return; |
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435 | } |
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436 | |
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437 | long max_val = 0; |
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438 | long max_index = 0; |
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439 | for (i = 0; i < sz; i++) { |
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440 | long t = labs(bl[i]-k1); |
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441 | if (t > max_val) { |
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442 | max_val = t; |
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443 | max_index = i; |
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444 | } |
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445 | } |
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446 | |
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447 | bp = max_index; |
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448 | bl[max_index] = 0; |
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449 | } |
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450 | |
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451 | |
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452 | static |
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453 | void GivensComputeGS(double **B1, double **mu, double **aux, long k, long n, |
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454 | GivensCache_FP& cache) |
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455 | { |
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456 | long i, j; |
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457 | |
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458 | double c, s, a, b, t; |
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459 | |
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460 | double *p = mu[k]; |
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461 | |
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462 | double *pp = cache.buf[cache.bp]; |
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463 | |
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464 | if (!cache.bl[cache.bp]) { |
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465 | for (j = 1; j <= n; j++) |
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466 | pp[j] = B1[k][j]; |
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467 | |
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468 | long backoff; |
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469 | backoff = k/4; |
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470 | if (backoff < 2) |
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471 | backoff = 2; |
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472 | else if (backoff > cache.sz + 2) |
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473 | backoff = cache.sz + 2; |
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474 | |
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475 | long ub = k-(backoff-1); |
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476 | |
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477 | for (i = 1; i < ub; i++) { |
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478 | double *cptr = mu[i]; |
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479 | double *sptr = aux[i]; |
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480 | |
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481 | for (j = n; j > i; j--) { |
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482 | c = cptr[j]; |
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483 | s = sptr[j]; |
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484 | |
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485 | a = c*pp[j-1] - s*pp[j]; |
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486 | b = s*pp[j-1] + c*pp[j]; |
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487 | |
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488 | pp[j-1] = a; |
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489 | pp[j] = b; |
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490 | } |
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491 | |
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492 | pp[i] = pp[i]/mu[i][i]; |
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493 | } |
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494 | |
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495 | cache.bl[cache.bp] = k; |
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496 | cache.bv[cache.bp] = k-backoff; |
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497 | } |
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498 | |
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499 | for (j = 1; j <= n; j++) |
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500 | p[j] = pp[j]; |
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501 | |
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502 | for (i = max(cache.bv[cache.bp]+1, 1); i < k; i++) { |
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503 | double *cptr = mu[i]; |
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504 | double *sptr = aux[i]; |
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505 | |
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506 | for (j = n; j > i; j--) { |
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507 | c = cptr[j]; |
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508 | s = sptr[j]; |
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509 | |
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510 | a = c*p[j-1] - s*p[j]; |
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511 | b = s*p[j-1] + c*p[j]; |
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512 | |
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513 | p[j-1] = a; |
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514 | p[j] = b; |
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515 | } |
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516 | |
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517 | p[i] = p[i]/mu[i][i]; |
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518 | } |
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519 | |
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520 | for (j = n; j > k; j--) { |
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521 | a = p[j-1]; |
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522 | b = p[j]; |
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523 | |
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524 | if (b == 0) { |
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525 | c = 1; |
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526 | s = 0; |
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527 | } |
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528 | else if (fabs(b) > fabs(a)) { |
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529 | t = -a/b; |
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530 | s = 1/sqrt(1 + t*t); |
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531 | c = s*t; |
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532 | } |
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533 | else { |
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534 | t = -b/a; |
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535 | c = 1/sqrt(1 + t*t); |
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536 | s = c*t; |
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537 | } |
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538 | |
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539 | p[j-1] = c*a - s*b; |
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540 | p[j] = c; |
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541 | aux[k][j] = s; |
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542 | } |
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543 | |
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544 | if (k > n+1) Error("G_LLL_FP: internal error"); |
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545 | if (k > n) p[k] = 0; |
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546 | |
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547 | for (i = 1; i <= k; i++) |
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548 | if (!IsFinite(&p[i])) Error("G_LLL_FP...numbers too big"); |
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549 | } |
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550 | |
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551 | static double red_fudge = 0; |
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552 | static long log_red = 0; |
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553 | |
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554 | static long verbose = 0; |
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555 | |
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556 | static unsigned long NumSwaps = 0; |
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557 | static double StartTime = 0; |
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558 | static double LastTime = 0; |
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559 | |
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560 | |
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561 | |
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562 | static void G_LLLStatus(long max_k, double t, long m, const mat_ZZ& B) |
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563 | { |
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564 | cerr << "---- G_LLL_FP status ----\n"; |
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565 | cerr << "elapsed time: "; |
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566 | PrintTime(cerr, t-StartTime); |
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567 | cerr << ", stage: " << max_k; |
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568 | cerr << ", rank: " << m; |
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569 | cerr << ", swaps: " << NumSwaps << "\n"; |
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570 | |
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571 | ZZ t1; |
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572 | long i; |
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573 | double prodlen = 0; |
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574 | |
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575 | for (i = 1; i <= m; i++) { |
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576 | InnerProduct(t1, B(i), B(i)); |
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577 | if (!IsZero(t1)) |
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578 | prodlen += log(t1); |
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579 | } |
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580 | |
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581 | cerr << "log of prod of lengths: " << prodlen/(2.0*log(2.0)) << "\n"; |
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582 | |
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583 | if (LLLDumpFile) { |
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584 | cerr << "dumping to " << LLLDumpFile << "..."; |
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585 | |
---|
586 | ofstream f; |
---|
587 | OpenWrite(f, LLLDumpFile); |
---|
588 | |
---|
589 | f << "["; |
---|
590 | for (i = 1; i <= m; i++) { |
---|
591 | f << B(i) << "\n"; |
---|
592 | } |
---|
593 | f << "]\n"; |
---|
594 | |
---|
595 | f.close(); |
---|
596 | |
---|
597 | cerr << "\n"; |
---|
598 | } |
---|
599 | |
---|
600 | LastTime = t; |
---|
601 | |
---|
602 | } |
---|
603 | |
---|
604 | static void init_red_fudge() |
---|
605 | { |
---|
606 | long i; |
---|
607 | |
---|
608 | log_red = long(0.50*NTL_DOUBLE_PRECISION); |
---|
609 | red_fudge = 1; |
---|
610 | |
---|
611 | for (i = log_red; i > 0; i--) |
---|
612 | red_fudge = red_fudge*0.5; |
---|
613 | } |
---|
614 | |
---|
615 | static void inc_red_fudge() |
---|
616 | { |
---|
617 | |
---|
618 | red_fudge = red_fudge * 2; |
---|
619 | log_red--; |
---|
620 | |
---|
621 | |
---|
622 | cerr << "G_LLL_FP: warning--relaxing reduction (" << log_red << ")\n"; |
---|
623 | |
---|
624 | if (log_red < 4) |
---|
625 | Error("G_LLL_FP: too much loss of precision...stop!"); |
---|
626 | } |
---|
627 | |
---|
628 | |
---|
629 | #if 0 |
---|
630 | |
---|
631 | static void print_mus(double **mu, long k) |
---|
632 | { |
---|
633 | long i; |
---|
634 | |
---|
635 | for (i = k-1; i >= 1; i--) |
---|
636 | cerr << mu[k][i] << " "; |
---|
637 | cerr << "\n"; |
---|
638 | } |
---|
639 | |
---|
640 | #endif |
---|
641 | |
---|
642 | |
---|
643 | |
---|
644 | static |
---|
645 | long ll_G_LLL_FP(mat_ZZ& B, mat_ZZ* U, double delta, long deep, |
---|
646 | LLLCheckFct check, double **B1, double **mu, |
---|
647 | double **aux, |
---|
648 | long m, long init_k, long &quit, GivensCache_FP& cache) |
---|
649 | { |
---|
650 | long n = B.NumCols(); |
---|
651 | |
---|
652 | long i, j, k, Fc1; |
---|
653 | ZZ MU; |
---|
654 | double mu1; |
---|
655 | |
---|
656 | double t1; |
---|
657 | ZZ T1; |
---|
658 | double *tp; |
---|
659 | |
---|
660 | double half_plus_fudge = 0.5 + red_fudge; |
---|
661 | |
---|
662 | quit = 0; |
---|
663 | k = init_k; |
---|
664 | |
---|
665 | vec_long in_vec_mem; |
---|
666 | in_vec_mem.SetLength(n+1); |
---|
667 | long *in_vec = in_vec_mem.elts(); |
---|
668 | |
---|
669 | double *max_b; |
---|
670 | max_b = NTL_NEW_OP double [m+1]; |
---|
671 | if (!max_b) Error("out of memory in lll_G_LLL_FP"); |
---|
672 | |
---|
673 | for (i = 1; i <= m; i++) |
---|
674 | max_b[i] = max_abs(B1[i], n); |
---|
675 | |
---|
676 | long in_float; |
---|
677 | |
---|
678 | long counter; |
---|
679 | |
---|
680 | long trigger_index; |
---|
681 | long small_trigger; |
---|
682 | long cnt; |
---|
683 | |
---|
684 | |
---|
685 | long max_k = 0; |
---|
686 | |
---|
687 | double tt; |
---|
688 | |
---|
689 | long swap_cnt = 0; |
---|
690 | |
---|
691 | cache.flush(); |
---|
692 | |
---|
693 | while (k <= m) { |
---|
694 | |
---|
695 | if (k > max_k) { |
---|
696 | max_k = k; |
---|
697 | swap_cnt = 0; |
---|
698 | } |
---|
699 | |
---|
700 | if (verbose) { |
---|
701 | tt = GetTime(); |
---|
702 | |
---|
703 | if (tt > LastTime + LLLStatusInterval) |
---|
704 | G_LLLStatus(max_k, tt, m, B); |
---|
705 | } |
---|
706 | |
---|
707 | GivensComputeGS(B1, mu, aux, k, n, cache); |
---|
708 | |
---|
709 | if (swap_cnt > 200000) { |
---|
710 | cerr << "G_LLL_FP: swap loop?\n"; |
---|
711 | swap_cnt = 0; |
---|
712 | } |
---|
713 | |
---|
714 | counter = 0; |
---|
715 | trigger_index = k; |
---|
716 | small_trigger = 0; |
---|
717 | cnt = 0; |
---|
718 | |
---|
719 | long sz=0, new_sz; |
---|
720 | |
---|
721 | do { |
---|
722 | // size reduction |
---|
723 | |
---|
724 | counter++; |
---|
725 | if ((counter & 127) == 0) { |
---|
726 | |
---|
727 | new_sz = 0; |
---|
728 | for (j = 1; j <= n; j++) |
---|
729 | new_sz += NumBits(B(k,j)); |
---|
730 | |
---|
731 | if ((counter >> 7) == 1 || new_sz < sz) { |
---|
732 | sz = new_sz; |
---|
733 | } |
---|
734 | else { |
---|
735 | cerr << "G_LLL_FP: warning--infinite loop? (" << k << ")\n"; |
---|
736 | } |
---|
737 | } |
---|
738 | |
---|
739 | Fc1 = 0; |
---|
740 | |
---|
741 | for (j = k-1; j >= 1; j--) { |
---|
742 | t1 = fabs(mu[k][j]); |
---|
743 | if (t1 > half_plus_fudge) { |
---|
744 | |
---|
745 | |
---|
746 | if (!Fc1) { |
---|
747 | if (j > trigger_index || |
---|
748 | (j == trigger_index && small_trigger)) { |
---|
749 | |
---|
750 | cnt++; |
---|
751 | |
---|
752 | if (cnt > 10) { |
---|
753 | inc_red_fudge(); |
---|
754 | half_plus_fudge = 0.5 + red_fudge; |
---|
755 | cnt = 0; |
---|
756 | } |
---|
757 | } |
---|
758 | |
---|
759 | trigger_index = j; |
---|
760 | small_trigger = (t1 < 4); |
---|
761 | |
---|
762 | Fc1 = 1; |
---|
763 | RowTransformStart(B1[k], in_vec, in_float, n); |
---|
764 | } |
---|
765 | |
---|
766 | |
---|
767 | mu1 = mu[k][j]; |
---|
768 | if (mu1 >= 0) |
---|
769 | mu1 = ceil(mu1-0.5); |
---|
770 | else |
---|
771 | mu1 = floor(mu1+0.5); |
---|
772 | |
---|
773 | double *mu_k = mu[k]; |
---|
774 | double *mu_j = mu[j]; |
---|
775 | |
---|
776 | if (mu1 == 1) { |
---|
777 | for (i = 1; i <= j-1; i++) |
---|
778 | mu_k[i] -= mu_j[i]; |
---|
779 | } |
---|
780 | else if (mu1 == -1) { |
---|
781 | for (i = 1; i <= j-1; i++) |
---|
782 | mu_k[i] += mu_j[i]; |
---|
783 | } |
---|
784 | else { |
---|
785 | for (i = 1; i <= j-1; i++) |
---|
786 | mu_k[i] -= mu1*mu_j[i]; |
---|
787 | } |
---|
788 | |
---|
789 | mu_k[j] -= mu1; |
---|
790 | |
---|
791 | conv(MU, mu1); |
---|
792 | |
---|
793 | RowTransform(B(k), B(j), MU, mu1, B1[k], B1[j], in_vec, |
---|
794 | max_b[k], max_b[j], in_float); |
---|
795 | if (U) RowTransform((*U)(k), (*U)(j), MU); |
---|
796 | } |
---|
797 | } |
---|
798 | |
---|
799 | |
---|
800 | if (Fc1) { |
---|
801 | RowTransformFinish(B(k), B1[k], in_vec); |
---|
802 | max_b[k] = max_abs(B1[k], n); |
---|
803 | cache.touch(); |
---|
804 | GivensComputeGS(B1, mu, aux, k, n, cache); |
---|
805 | } |
---|
806 | } while (Fc1); |
---|
807 | |
---|
808 | if (check && (*check)(B(k))) |
---|
809 | quit = 1; |
---|
810 | |
---|
811 | if (IsZero(B(k))) { |
---|
812 | for (i = k; i < m; i++) { |
---|
813 | // swap i, i+1 |
---|
814 | swap(B(i), B(i+1)); |
---|
815 | tp = B1[i]; B1[i] = B1[i+1]; B1[i+1] = tp; |
---|
816 | t1 = max_b[i]; max_b[i] = max_b[i+1]; max_b[i+1] = t1; |
---|
817 | if (U) swap((*U)(i), (*U)(i+1)); |
---|
818 | } |
---|
819 | |
---|
820 | cache.flush(); |
---|
821 | |
---|
822 | m--; |
---|
823 | if (quit) break; |
---|
824 | continue; |
---|
825 | } |
---|
826 | |
---|
827 | if (quit) break; |
---|
828 | |
---|
829 | if (deep > 0) { |
---|
830 | // deep insertions |
---|
831 | |
---|
832 | Error("sorry...deep insertions not implemented"); |
---|
833 | } // end deep insertions |
---|
834 | |
---|
835 | // test G_LLL reduction condition |
---|
836 | |
---|
837 | if (k > 1 && |
---|
838 | sqrt(delta - mu[k][k-1]*mu[k][k-1])*fabs(mu[k-1][k-1]) > |
---|
839 | fabs(mu[k][k])) { |
---|
840 | // swap rows k, k-1 |
---|
841 | |
---|
842 | swap(B(k), B(k-1)); |
---|
843 | tp = B1[k]; B1[k] = B1[k-1]; B1[k-1] = tp; |
---|
844 | t1 = max_b[k]; max_b[k] = max_b[k-1]; max_b[k-1] = t1; |
---|
845 | if (U) swap((*U)(k), (*U)(k-1)); |
---|
846 | |
---|
847 | cache.swap(); |
---|
848 | |
---|
849 | k--; |
---|
850 | NumSwaps++; |
---|
851 | swap_cnt++; |
---|
852 | // cout << "-\n"; |
---|
853 | } |
---|
854 | else { |
---|
855 | |
---|
856 | cache.incr(); |
---|
857 | |
---|
858 | k++; |
---|
859 | // cout << "+\n"; |
---|
860 | } |
---|
861 | |
---|
862 | } |
---|
863 | |
---|
864 | if (verbose) { |
---|
865 | G_LLLStatus(m+1, GetTime(), m, B); |
---|
866 | } |
---|
867 | |
---|
868 | |
---|
869 | delete [] max_b; |
---|
870 | |
---|
871 | return m; |
---|
872 | } |
---|
873 | |
---|
874 | |
---|
875 | |
---|
876 | |
---|
877 | |
---|
878 | static |
---|
879 | long G_LLL_FP(mat_ZZ& B, mat_ZZ* U, double delta, long deep, |
---|
880 | LLLCheckFct check) |
---|
881 | { |
---|
882 | long m = B.NumRows(); |
---|
883 | long n = B.NumCols(); |
---|
884 | |
---|
885 | long i, j; |
---|
886 | long new_m, dep, quit; |
---|
887 | ZZ MU; |
---|
888 | |
---|
889 | ZZ T1; |
---|
890 | |
---|
891 | init_red_fudge(); |
---|
892 | |
---|
893 | if (U) ident(*U, m); |
---|
894 | |
---|
895 | double **B1; // approximates B |
---|
896 | |
---|
897 | typedef double *doubleptr; |
---|
898 | |
---|
899 | B1 = NTL_NEW_OP doubleptr[m+1]; |
---|
900 | if (!B1) Error("G_LLL_FP: out of memory"); |
---|
901 | |
---|
902 | for (i = 1; i <= m; i++) { |
---|
903 | B1[i] = NTL_NEW_OP double[n+1]; |
---|
904 | if (!B1[i]) Error("G_LLL_FP: out of memory"); |
---|
905 | } |
---|
906 | |
---|
907 | double **mu; |
---|
908 | mu = NTL_NEW_OP doubleptr[m+1]; |
---|
909 | if (!mu) Error("G_LLL_FP: out of memory"); |
---|
910 | |
---|
911 | for (i = 1; i <= m; i++) { |
---|
912 | mu[i] = NTL_NEW_OP double[n+2]; |
---|
913 | if (!mu[i]) Error("G_LLL_FP: out of memory"); |
---|
914 | } |
---|
915 | |
---|
916 | double **aux; |
---|
917 | aux = NTL_NEW_OP doubleptr[m+1]; |
---|
918 | if (!aux) Error("G_LLL_FP: out of memory"); |
---|
919 | |
---|
920 | for (i = 1; i <= m; i++) { |
---|
921 | aux[i] = NTL_NEW_OP double[n+1]; |
---|
922 | if (!aux[i]) Error("G_LLL_FP: out of memory"); |
---|
923 | } |
---|
924 | |
---|
925 | for (i = 1; i <=m; i++) |
---|
926 | for (j = 1; j <= n; j++) |
---|
927 | conv(B1[i][j], B(i, j)); |
---|
928 | |
---|
929 | |
---|
930 | for (i = 1; i <= m; i++) |
---|
931 | for (j = 1; j <= n; j++) |
---|
932 | if (!IsFinite(&B1[i][j])) |
---|
933 | Error("G_LLL_FP: numbers too big...use G_LLL_XD"); |
---|
934 | |
---|
935 | GivensCache_FP cache(m, n); |
---|
936 | |
---|
937 | new_m = ll_G_LLL_FP(B, U, delta, deep, check, B1, mu, aux, m, 1, quit, cache); |
---|
938 | dep = m - new_m; |
---|
939 | m = new_m; |
---|
940 | |
---|
941 | if (dep > 0) { |
---|
942 | // for consistency, we move all of the zero rows to the front |
---|
943 | |
---|
944 | for (i = 0; i < m; i++) { |
---|
945 | swap(B(m+dep-i), B(m-i)); |
---|
946 | if (U) swap((*U)(m+dep-i), (*U)(m-i)); |
---|
947 | } |
---|
948 | } |
---|
949 | |
---|
950 | |
---|
951 | // clean-up |
---|
952 | |
---|
953 | for (i = 1; i <= m; i++) { |
---|
954 | delete [] B1[i]; |
---|
955 | } |
---|
956 | |
---|
957 | delete [] B1; |
---|
958 | |
---|
959 | for (i = 1; i <= m; i++) { |
---|
960 | delete [] mu[i]; |
---|
961 | } |
---|
962 | |
---|
963 | delete [] mu; |
---|
964 | |
---|
965 | for (i = 1; i <= m; i++) { |
---|
966 | delete [] aux[i]; |
---|
967 | } |
---|
968 | |
---|
969 | delete [] aux; |
---|
970 | |
---|
971 | return m; |
---|
972 | } |
---|
973 | |
---|
974 | |
---|
975 | |
---|
976 | long G_LLL_FP(mat_ZZ& B, double delta, long deep, LLLCheckFct check, |
---|
977 | long verb) |
---|
978 | { |
---|
979 | verbose = verb; |
---|
980 | NumSwaps = 0; |
---|
981 | if (verbose) { |
---|
982 | StartTime = GetTime(); |
---|
983 | LastTime = StartTime; |
---|
984 | } |
---|
985 | |
---|
986 | if (delta < 0.50 || delta >= 1) Error("G_LLL_FP: bad delta"); |
---|
987 | if (deep < 0) Error("G_LLL_FP: bad deep"); |
---|
988 | return G_LLL_FP(B, 0, delta, deep, check); |
---|
989 | } |
---|
990 | |
---|
991 | long G_LLL_FP(mat_ZZ& B, mat_ZZ& U, double delta, long deep, |
---|
992 | LLLCheckFct check, long verb) |
---|
993 | { |
---|
994 | verbose = verb; |
---|
995 | NumSwaps = 0; |
---|
996 | if (verbose) { |
---|
997 | StartTime = GetTime(); |
---|
998 | LastTime = StartTime; |
---|
999 | } |
---|
1000 | |
---|
1001 | if (delta < 0.50 || delta >= 1) Error("G_LLL_FP: bad delta"); |
---|
1002 | if (deep < 0) Error("G_LLL_FP: bad deep"); |
---|
1003 | return G_LLL_FP(B, &U, delta, deep, check); |
---|
1004 | } |
---|
1005 | |
---|
1006 | |
---|
1007 | |
---|
1008 | static vec_double G_BKZConstant; |
---|
1009 | |
---|
1010 | static |
---|
1011 | void ComputeG_BKZConstant(long beta, long p) |
---|
1012 | { |
---|
1013 | const double c_PI = 3.14159265358979323846264338328; |
---|
1014 | const double LogPI = 1.14472988584940017414342735135; |
---|
1015 | |
---|
1016 | G_BKZConstant.SetLength(beta-1); |
---|
1017 | |
---|
1018 | vec_double Log; |
---|
1019 | Log.SetLength(beta); |
---|
1020 | |
---|
1021 | |
---|
1022 | long i, j, k; |
---|
1023 | double x, y; |
---|
1024 | |
---|
1025 | for (j = 1; j <= beta; j++) |
---|
1026 | Log(j) = log(double(j)); |
---|
1027 | |
---|
1028 | for (i = 1; i <= beta-1; i++) { |
---|
1029 | // First, we compute x = gamma(i/2)^{2/i} |
---|
1030 | |
---|
1031 | k = i/2; |
---|
1032 | |
---|
1033 | if ((i & 1) == 0) { // i even |
---|
1034 | x = 0; |
---|
1035 | for (j = 1; j <= k; j++) |
---|
1036 | x = x + Log(j); |
---|
1037 | |
---|
1038 | x = x * (1/double(k)); |
---|
1039 | |
---|
1040 | x = exp(x); |
---|
1041 | } |
---|
1042 | else { // i odd |
---|
1043 | x = 0; |
---|
1044 | for (j = k + 2; j <= 2*k + 2; j++) |
---|
1045 | x = x + Log(j); |
---|
1046 | |
---|
1047 | x = 0.5*LogPI + x - 2*(k+1)*Log(2); |
---|
1048 | |
---|
1049 | x = x * (2.0/double(i)); |
---|
1050 | |
---|
1051 | x = exp(x); |
---|
1052 | } |
---|
1053 | |
---|
1054 | // Second, we compute y = 2^{2*p/i} |
---|
1055 | |
---|
1056 | y = -(2*p/double(i))*Log(2); |
---|
1057 | y = exp(y); |
---|
1058 | |
---|
1059 | G_BKZConstant(i) = x*y/c_PI; |
---|
1060 | } |
---|
1061 | } |
---|
1062 | |
---|
1063 | static vec_double G_BKZThresh; |
---|
1064 | |
---|
1065 | static |
---|
1066 | void ComputeG_BKZThresh(double *c, long beta) |
---|
1067 | { |
---|
1068 | G_BKZThresh.SetLength(beta-1); |
---|
1069 | |
---|
1070 | long i; |
---|
1071 | double x; |
---|
1072 | |
---|
1073 | x = 0; |
---|
1074 | |
---|
1075 | for (i = 1; i <= beta-1; i++) { |
---|
1076 | x += log(c[i-1]); |
---|
1077 | G_BKZThresh(i) = exp(x/double(i))*G_BKZConstant(i); |
---|
1078 | if (!IsFinite(&G_BKZThresh(i))) G_BKZThresh(i) = 0; |
---|
1079 | } |
---|
1080 | } |
---|
1081 | |
---|
1082 | static |
---|
1083 | void G_BKZStatus(double tt, double enum_time, long NumIterations, |
---|
1084 | long NumTrivial, long NumNonTrivial, long NumNoOps, long m, |
---|
1085 | const mat_ZZ& B) |
---|
1086 | { |
---|
1087 | cerr << "---- G_BKZ_FP status ----\n"; |
---|
1088 | cerr << "elapsed time: "; |
---|
1089 | PrintTime(cerr, tt-StartTime); |
---|
1090 | cerr << ", enum time: "; |
---|
1091 | PrintTime(cerr, enum_time); |
---|
1092 | cerr << ", iter: " << NumIterations << "\n"; |
---|
1093 | cerr << "triv: " << NumTrivial; |
---|
1094 | cerr << ", nontriv: " << NumNonTrivial; |
---|
1095 | cerr << ", no ops: " << NumNoOps; |
---|
1096 | cerr << ", rank: " << m; |
---|
1097 | cerr << ", swaps: " << NumSwaps << "\n"; |
---|
1098 | |
---|
1099 | |
---|
1100 | |
---|
1101 | ZZ t1; |
---|
1102 | long i; |
---|
1103 | double prodlen = 0; |
---|
1104 | |
---|
1105 | for (i = 1; i <= m; i++) { |
---|
1106 | InnerProduct(t1, B(i), B(i)); |
---|
1107 | if (!IsZero(t1)) |
---|
1108 | prodlen += log(t1); |
---|
1109 | } |
---|
1110 | |
---|
1111 | cerr << "log of prod of lengths: " << prodlen/(2.0*log(2.0)) << "\n"; |
---|
1112 | |
---|
1113 | |
---|
1114 | if (LLLDumpFile) { |
---|
1115 | cerr << "dumping to " << LLLDumpFile << "..."; |
---|
1116 | |
---|
1117 | ofstream f; |
---|
1118 | OpenWrite(f, LLLDumpFile); |
---|
1119 | |
---|
1120 | f << "["; |
---|
1121 | for (i = 1; i <= m; i++) { |
---|
1122 | f << B(i) << "\n"; |
---|
1123 | } |
---|
1124 | f << "]\n"; |
---|
1125 | |
---|
1126 | f.close(); |
---|
1127 | |
---|
1128 | cerr << "\n"; |
---|
1129 | } |
---|
1130 | |
---|
1131 | LastTime = tt; |
---|
1132 | |
---|
1133 | } |
---|
1134 | |
---|
1135 | |
---|
1136 | |
---|
1137 | static |
---|
1138 | long G_BKZ_FP(mat_ZZ& BB, mat_ZZ* UU, double delta, |
---|
1139 | long beta, long prune, LLLCheckFct check) |
---|
1140 | { |
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1141 | |
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1142 | |
---|
1143 | |
---|
1144 | long m = BB.NumRows(); |
---|
1145 | long n = BB.NumCols(); |
---|
1146 | long m_orig = m; |
---|
1147 | |
---|
1148 | long i, j; |
---|
1149 | ZZ MU; |
---|
1150 | |
---|
1151 | double t1; |
---|
1152 | ZZ T1; |
---|
1153 | double *tp; |
---|
1154 | |
---|
1155 | init_red_fudge(); |
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1156 | |
---|
1157 | mat_ZZ B; |
---|
1158 | B = BB; |
---|
1159 | |
---|
1160 | B.SetDims(m+1, n); |
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1161 | |
---|
1162 | |
---|
1163 | double **B1; // approximates B |
---|
1164 | |
---|
1165 | typedef double *doubleptr; |
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1166 | |
---|
1167 | B1 = NTL_NEW_OP doubleptr[m+2]; |
---|
1168 | if (!B1) Error("G_BKZ_FP: out of memory"); |
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1169 | |
---|
1170 | for (i = 1; i <= m+1; i++) { |
---|
1171 | B1[i] = NTL_NEW_OP double[n+1]; |
---|
1172 | if (!B1[i]) Error("G_BKZ_FP: out of memory"); |
---|
1173 | } |
---|
1174 | |
---|
1175 | double **mu; |
---|
1176 | mu = NTL_NEW_OP doubleptr[m+2]; |
---|
1177 | if (!mu) Error("G_LLL_FP: out of memory"); |
---|
1178 | |
---|
1179 | for (i = 1; i <= m+1; i++) { |
---|
1180 | mu[i] = NTL_NEW_OP double[n+2]; |
---|
1181 | if (!mu[i]) Error("G_BKZ_FP: out of memory"); |
---|
1182 | } |
---|
1183 | |
---|
1184 | double **aux; |
---|
1185 | aux = NTL_NEW_OP doubleptr[m+2]; |
---|
1186 | if (!aux) Error("G_LLL_FP: out of memory"); |
---|
1187 | |
---|
1188 | for (i = 1; i <= m+1; i++) { |
---|
1189 | aux[i] = NTL_NEW_OP double[n+1]; |
---|
1190 | if (!aux[i]) Error("G_BKZ_FP: out of memory"); |
---|
1191 | } |
---|
1192 | |
---|
1193 | |
---|
1194 | double *c; // squared lengths of Gramm-Schmidt basis vectors |
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1195 | |
---|
1196 | c = NTL_NEW_OP double[m+2]; |
---|
1197 | if (!c) Error("G_BKZ_FP: out of memory"); |
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1198 | |
---|
1199 | double cbar; |
---|
1200 | |
---|
1201 | double *ctilda; |
---|
1202 | ctilda = NTL_NEW_OP double[m+2]; |
---|
1203 | if (!ctilda) Error("G_BKZ_FP: out of memory"); |
---|
1204 | |
---|
1205 | double *vvec; |
---|
1206 | vvec = NTL_NEW_OP double[m+2]; |
---|
1207 | if (!vvec) Error("G_BKZ_FP: out of memory"); |
---|
1208 | |
---|
1209 | double *yvec; |
---|
1210 | yvec = NTL_NEW_OP double[m+2]; |
---|
1211 | if (!yvec) Error("G_BKZ_FP: out of memory"); |
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1212 | |
---|
1213 | double *uvec; |
---|
1214 | uvec = NTL_NEW_OP double[m+2]; |
---|
1215 | if (!uvec) Error("G_BKZ_FP: out of memory"); |
---|
1216 | |
---|
1217 | double *utildavec; |
---|
1218 | utildavec = NTL_NEW_OP double[m+2]; |
---|
1219 | if (!utildavec) Error("G_BKZ_FP: out of memory"); |
---|
1220 | |
---|
1221 | |
---|
1222 | long *Deltavec; |
---|
1223 | Deltavec = NTL_NEW_OP long[m+2]; |
---|
1224 | if (!Deltavec) Error("G_BKZ_FP: out of memory"); |
---|
1225 | |
---|
1226 | long *deltavec; |
---|
1227 | deltavec = NTL_NEW_OP long[m+2]; |
---|
1228 | if (!deltavec) Error("G_BKZ_FP: out of memory"); |
---|
1229 | |
---|
1230 | mat_ZZ Ulocal; |
---|
1231 | mat_ZZ *U; |
---|
1232 | |
---|
1233 | if (UU) { |
---|
1234 | Ulocal.SetDims(m+1, m); |
---|
1235 | for (i = 1; i <= m; i++) |
---|
1236 | conv(Ulocal(i, i), 1); |
---|
1237 | U = &Ulocal; |
---|
1238 | } |
---|
1239 | else |
---|
1240 | U = 0; |
---|
1241 | |
---|
1242 | long quit; |
---|
1243 | long new_m; |
---|
1244 | long z, jj, kk; |
---|
1245 | long s, t; |
---|
1246 | long h; |
---|
1247 | double eta; |
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1248 | |
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1249 | |
---|
1250 | for (i = 1; i <=m; i++) |
---|
1251 | for (j = 1; j <= n; j++) { |
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1252 | conv(B1[i][j], B(i, j)); |
---|
1253 | if (!IsFinite(&B1[i][j])) |
---|
1254 | Error("G_BKZ_FP: numbers too big...use G_BKZ_XD"); |
---|
1255 | } |
---|
1256 | |
---|
1257 | |
---|
1258 | GivensCache_FP cache(m, n); |
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1259 | |
---|
1260 | m = ll_G_LLL_FP(B, U, delta, 0, check, B1, mu, aux, m, 1, quit, cache); |
---|
1261 | |
---|
1262 | double tt; |
---|
1263 | |
---|
1264 | double enum_time = 0; |
---|
1265 | long NumIterations = 0; |
---|
1266 | long NumTrivial = 0; |
---|
1267 | long NumNonTrivial = 0; |
---|
1268 | long NumNoOps = 0; |
---|
1269 | |
---|
1270 | long verb = verbose; |
---|
1271 | |
---|
1272 | verbose = 0; |
---|
1273 | |
---|
1274 | long clean = 1; |
---|
1275 | |
---|
1276 | if (m < m_orig) { |
---|
1277 | for (i = m_orig+1; i >= m+2; i--) { |
---|
1278 | // swap i, i-1 |
---|
1279 | |
---|
1280 | swap(B(i), B(i-1)); |
---|
1281 | if (U) swap((*U)(i), (*U)(i-1)); |
---|
1282 | } |
---|
1283 | } |
---|
1284 | |
---|
1285 | if (!quit && m > 1) { |
---|
1286 | if (beta > m) beta = m; |
---|
1287 | |
---|
1288 | if (prune > 0) |
---|
1289 | ComputeG_BKZConstant(beta, prune); |
---|
1290 | |
---|
1291 | z = 0; |
---|
1292 | jj = 0; |
---|
1293 | |
---|
1294 | while (z < m-1) { |
---|
1295 | jj++; |
---|
1296 | kk = min(jj+beta-1, m); |
---|
1297 | |
---|
1298 | if (jj == m) { |
---|
1299 | jj = 1; |
---|
1300 | kk = beta; |
---|
1301 | clean = 1; |
---|
1302 | } |
---|
1303 | |
---|
1304 | if (verb) { |
---|
1305 | tt = GetTime(); |
---|
1306 | if (tt > LastTime + LLLStatusInterval) |
---|
1307 | G_BKZStatus(tt, enum_time, NumIterations, NumTrivial, |
---|
1308 | NumNonTrivial, NumNoOps, m, B); |
---|
1309 | } |
---|
1310 | |
---|
1311 | |
---|
1312 | // ENUM |
---|
1313 | |
---|
1314 | double tt1; |
---|
1315 | |
---|
1316 | if (verb) { |
---|
1317 | tt1 = GetTime(); |
---|
1318 | } |
---|
1319 | |
---|
1320 | for (i = jj; i <= kk; i++) { |
---|
1321 | c[i] = mu[i][i]*mu[i][i]; |
---|
1322 | if (!IsFinite(&c[i])) Error("numbers too big...use G_BKZ_XD"); |
---|
1323 | } |
---|
1324 | |
---|
1325 | if (prune > 0) |
---|
1326 | ComputeG_BKZThresh(&c[jj], kk-jj+1); |
---|
1327 | |
---|
1328 | cbar = c[jj]; |
---|
1329 | utildavec[jj] = uvec[jj] = 1; |
---|
1330 | |
---|
1331 | yvec[jj] = vvec[jj] = 0; |
---|
1332 | Deltavec[jj] = 0; |
---|
1333 | |
---|
1334 | |
---|
1335 | s = t = jj; |
---|
1336 | deltavec[jj] = 1; |
---|
1337 | |
---|
1338 | for (i = jj+1; i <= kk+1; i++) { |
---|
1339 | ctilda[i] = uvec[i] = utildavec[i] = yvec[i] = 0; |
---|
1340 | Deltavec[i] = 0; |
---|
1341 | vvec[i] = 0; |
---|
1342 | deltavec[i] = 1; |
---|
1343 | } |
---|
1344 | |
---|
1345 | long enum_cnt = 0; |
---|
1346 | |
---|
1347 | while (t <= kk) { |
---|
1348 | if (verb) { |
---|
1349 | enum_cnt++; |
---|
1350 | if (enum_cnt > 100000) { |
---|
1351 | enum_cnt = 0; |
---|
1352 | tt = GetTime(); |
---|
1353 | if (tt > LastTime + LLLStatusInterval) { |
---|
1354 | enum_time += tt - tt1; |
---|
1355 | tt1 = tt; |
---|
1356 | G_BKZStatus(tt, enum_time, NumIterations, NumTrivial, |
---|
1357 | NumNonTrivial, NumNoOps, m, B); |
---|
1358 | } |
---|
1359 | } |
---|
1360 | } |
---|
1361 | |
---|
1362 | ctilda[t] = ctilda[t+1] + |
---|
1363 | (yvec[t]+utildavec[t])*(yvec[t]+utildavec[t])*c[t]; |
---|
1364 | |
---|
1365 | if (prune > 0 && t > jj) { |
---|
1366 | eta = G_BKZThresh(t-jj); |
---|
1367 | } |
---|
1368 | else |
---|
1369 | eta = 0; |
---|
1370 | |
---|
1371 | if (ctilda[t] < cbar - eta) { |
---|
1372 | if (t > jj) { |
---|
1373 | t--; |
---|
1374 | t1 = 0; |
---|
1375 | for (i = t+1; i <= s; i++) |
---|
1376 | t1 += utildavec[i]*mu[i][t]; |
---|
1377 | yvec[t] = t1; |
---|
1378 | t1 = -t1; |
---|
1379 | if (t1 >= 0) |
---|
1380 | t1 = ceil(t1-0.5); |
---|
1381 | else |
---|
1382 | t1 = floor(t1+0.5); |
---|
1383 | utildavec[t] = vvec[t] = t1; |
---|
1384 | Deltavec[t] = 0; |
---|
1385 | if (utildavec[t] > -yvec[t]) |
---|
1386 | deltavec[t] = -1; |
---|
1387 | else |
---|
1388 | deltavec[t] = 1; |
---|
1389 | } |
---|
1390 | else { |
---|
1391 | cbar = ctilda[jj]; |
---|
1392 | for (i = jj; i <= kk; i++) { |
---|
1393 | uvec[i] = utildavec[i]; |
---|
1394 | } |
---|
1395 | } |
---|
1396 | } |
---|
1397 | else { |
---|
1398 | t++; |
---|
1399 | s = max(s, t); |
---|
1400 | if (t < s) Deltavec[t] = -Deltavec[t]; |
---|
1401 | if (Deltavec[t]*deltavec[t] >= 0) Deltavec[t] += deltavec[t]; |
---|
1402 | utildavec[t] = vvec[t] + Deltavec[t]; |
---|
1403 | } |
---|
1404 | } |
---|
1405 | |
---|
1406 | if (verb) { |
---|
1407 | tt1 = GetTime() - tt1; |
---|
1408 | enum_time += tt1; |
---|
1409 | } |
---|
1410 | |
---|
1411 | NumIterations++; |
---|
1412 | |
---|
1413 | h = min(kk+1, m); |
---|
1414 | |
---|
1415 | if ((delta - 8*red_fudge)*c[jj] > cbar) { |
---|
1416 | |
---|
1417 | clean = 0; |
---|
1418 | |
---|
1419 | // we treat the case that the new vector is b_s (jj < s <= kk) |
---|
1420 | // as a special case that appears to occur most of the time. |
---|
1421 | |
---|
1422 | s = 0; |
---|
1423 | for (i = jj+1; i <= kk; i++) { |
---|
1424 | if (uvec[i] != 0) { |
---|
1425 | if (s == 0) |
---|
1426 | s = i; |
---|
1427 | else |
---|
1428 | s = -1; |
---|
1429 | } |
---|
1430 | } |
---|
1431 | |
---|
1432 | if (s == 0) Error("G_BKZ_FP: internal error"); |
---|
1433 | |
---|
1434 | if (s > 0) { |
---|
1435 | // special case |
---|
1436 | |
---|
1437 | NumTrivial++; |
---|
1438 | |
---|
1439 | for (i = s; i > jj; i--) { |
---|
1440 | // swap i, i-1 |
---|
1441 | swap(B(i-1), B(i)); |
---|
1442 | if (U) swap((*U)(i-1), (*U)(i)); |
---|
1443 | tp = B1[i-1]; B1[i-1] = B1[i]; B1[i] = tp; |
---|
1444 | } |
---|
1445 | |
---|
1446 | // cerr << "special case\n"; |
---|
1447 | new_m = ll_G_LLL_FP(B, U, delta, 0, check, |
---|
1448 | B1, mu, aux, h, jj, quit, cache); |
---|
1449 | if (new_m != h) Error("G_BKZ_FP: internal error"); |
---|
1450 | if (quit) break; |
---|
1451 | } |
---|
1452 | else { |
---|
1453 | // the general case |
---|
1454 | |
---|
1455 | NumNonTrivial++; |
---|
1456 | |
---|
1457 | for (i = 1; i <= n; i++) conv(B(m+1, i), 0); |
---|
1458 | |
---|
1459 | if (U) { |
---|
1460 | for (i = 1; i <= m_orig; i++) |
---|
1461 | conv((*U)(m+1, i), 0); |
---|
1462 | } |
---|
1463 | |
---|
1464 | for (i = jj; i <= kk; i++) { |
---|
1465 | if (uvec[i] == 0) continue; |
---|
1466 | conv(MU, uvec[i]); |
---|
1467 | RowTransform2(B(m+1), B(i), MU); |
---|
1468 | if (U) RowTransform2((*U)(m+1), (*U)(i), MU); |
---|
1469 | } |
---|
1470 | |
---|
1471 | for (i = m+1; i >= jj+1; i--) { |
---|
1472 | // swap i, i-1 |
---|
1473 | swap(B(i-1), B(i)); |
---|
1474 | if (U) swap((*U)(i-1), (*U)(i)); |
---|
1475 | tp = B1[i-1]; B1[i-1] = B1[i]; B1[i] = tp; |
---|
1476 | } |
---|
1477 | |
---|
1478 | for (i = 1; i <= n; i++) |
---|
1479 | conv(B1[jj][i], B(jj, i)); |
---|
1480 | |
---|
1481 | if (IsZero(B(jj))) Error("G_BKZ_FP: internal error"); |
---|
1482 | |
---|
1483 | // remove linear dependencies |
---|
1484 | |
---|
1485 | // cerr << "general case\n"; |
---|
1486 | new_m = ll_G_LLL_FP(B, U, delta, 0, 0, B1, mu, aux, |
---|
1487 | kk+1, jj, quit, cache); |
---|
1488 | |
---|
1489 | if (new_m != kk) Error("G_BKZ_FP: internal error"); |
---|
1490 | |
---|
1491 | // remove zero vector |
---|
1492 | |
---|
1493 | for (i = kk+2; i <= m+1; i++) { |
---|
1494 | // swap i, i-1 |
---|
1495 | swap(B(i-1), B(i)); |
---|
1496 | if (U) swap((*U)(i-1), (*U)(i)); |
---|
1497 | tp = B1[i-1]; B1[i-1] = B1[i]; B1[i] = tp; |
---|
1498 | } |
---|
1499 | |
---|
1500 | quit = 0; |
---|
1501 | if (check) { |
---|
1502 | for (i = 1; i <= kk; i++) |
---|
1503 | if ((*check)(B(i))) { |
---|
1504 | quit = 1; |
---|
1505 | break; |
---|
1506 | } |
---|
1507 | } |
---|
1508 | |
---|
1509 | if (quit) break; |
---|
1510 | |
---|
1511 | if (h > kk) { |
---|
1512 | // extend reduced basis |
---|
1513 | |
---|
1514 | new_m = ll_G_LLL_FP(B, U, delta, 0, check, |
---|
1515 | B1, mu, aux, h, h, quit, cache); |
---|
1516 | |
---|
1517 | if (new_m != h) Error("G_BKZ_FP: internal error"); |
---|
1518 | if (quit) break; |
---|
1519 | } |
---|
1520 | } |
---|
1521 | |
---|
1522 | z = 0; |
---|
1523 | } |
---|
1524 | else { |
---|
1525 | // G_LLL_FP |
---|
1526 | // cerr << "progress\n"; |
---|
1527 | |
---|
1528 | NumNoOps++; |
---|
1529 | |
---|
1530 | if (!clean) { |
---|
1531 | new_m = ll_G_LLL_FP(B, U, delta, 0, check, B1, mu, aux, |
---|
1532 | h, h, quit, cache); |
---|
1533 | if (new_m != h) Error("G_BKZ_FP: internal error"); |
---|
1534 | if (quit) break; |
---|
1535 | } |
---|
1536 | |
---|
1537 | z++; |
---|
1538 | } |
---|
1539 | } |
---|
1540 | } |
---|
1541 | |
---|
1542 | |
---|
1543 | if (verb) { |
---|
1544 | G_BKZStatus(GetTime(), enum_time, NumIterations, NumTrivial, NumNonTrivial, |
---|
1545 | NumNoOps, m, B); |
---|
1546 | } |
---|
1547 | |
---|
1548 | // clean up |
---|
1549 | |
---|
1550 | |
---|
1551 | if (m_orig > m) { |
---|
1552 | // for consistency, we move zero vectors to the front |
---|
1553 | |
---|
1554 | for (i = m+1; i <= m_orig; i++) { |
---|
1555 | swap(B(i), B(i+1)); |
---|
1556 | if (U) swap((*U)(i), (*U)(i+1)); |
---|
1557 | } |
---|
1558 | |
---|
1559 | for (i = 0; i < m; i++) { |
---|
1560 | swap(B(m_orig-i), B(m-i)); |
---|
1561 | if (U) swap((*U)(m_orig-i), (*U)(m-i)); |
---|
1562 | } |
---|
1563 | } |
---|
1564 | |
---|
1565 | B.SetDims(m_orig, n); |
---|
1566 | BB = B; |
---|
1567 | |
---|
1568 | if (U) { |
---|
1569 | U->SetDims(m_orig, m_orig); |
---|
1570 | *UU = *U; |
---|
1571 | } |
---|
1572 | |
---|
1573 | for (i = 1; i <= m+1; i++) { |
---|
1574 | delete [] B1[i]; |
---|
1575 | } |
---|
1576 | |
---|
1577 | delete [] B1; |
---|
1578 | |
---|
1579 | for (i = 1; i <= m+1; i++) { |
---|
1580 | delete [] mu[i]; |
---|
1581 | } |
---|
1582 | |
---|
1583 | delete [] mu; |
---|
1584 | |
---|
1585 | for (i = 1; i <= m+1; i++) { |
---|
1586 | delete [] aux[i]; |
---|
1587 | } |
---|
1588 | |
---|
1589 | delete [] aux; |
---|
1590 | |
---|
1591 | delete [] c; |
---|
1592 | delete [] ctilda; |
---|
1593 | delete [] vvec; |
---|
1594 | delete [] yvec; |
---|
1595 | delete [] uvec; |
---|
1596 | delete [] utildavec; |
---|
1597 | delete [] Deltavec; |
---|
1598 | delete [] deltavec; |
---|
1599 | |
---|
1600 | return m; |
---|
1601 | } |
---|
1602 | |
---|
1603 | long G_BKZ_FP(mat_ZZ& BB, mat_ZZ& UU, double delta, |
---|
1604 | long beta, long prune, LLLCheckFct check, long verb) |
---|
1605 | { |
---|
1606 | verbose = verb; |
---|
1607 | NumSwaps = 0; |
---|
1608 | if (verbose) { |
---|
1609 | StartTime = GetTime(); |
---|
1610 | LastTime = StartTime; |
---|
1611 | } |
---|
1612 | |
---|
1613 | if (delta < 0.50 || delta >= 1) Error("G_BKZ_FP: bad delta"); |
---|
1614 | if (beta < 2) Error("G_BKZ_FP: bad block size"); |
---|
1615 | |
---|
1616 | return G_BKZ_FP(BB, &UU, delta, beta, prune, check); |
---|
1617 | } |
---|
1618 | |
---|
1619 | long G_BKZ_FP(mat_ZZ& BB, double delta, |
---|
1620 | long beta, long prune, LLLCheckFct check, long verb) |
---|
1621 | { |
---|
1622 | verbose = verb; |
---|
1623 | NumSwaps = 0; |
---|
1624 | if (verbose) { |
---|
1625 | StartTime = GetTime(); |
---|
1626 | LastTime = StartTime; |
---|
1627 | } |
---|
1628 | |
---|
1629 | if (delta < 0.50 || delta >= 1) Error("G_BKZ_FP: bad delta"); |
---|
1630 | if (beta < 2) Error("G_BKZ_FP: bad block size"); |
---|
1631 | |
---|
1632 | return G_BKZ_FP(BB, 0, delta, beta, prune, check); |
---|
1633 | } |
---|
1634 | |
---|
1635 | NTL_END_IMPL |
---|