1 | #include "mod2.h" |
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2 | |
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3 | #ifdef HAVE_MINOR |
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4 | |
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5 | #include "structs.h" |
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6 | #include "polys.h" |
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7 | #include <Minor.h> |
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8 | |
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9 | void MinorKey::reset() { |
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10 | _numberOfRowBlocks = 0; |
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11 | _numberOfColumnBlocks = 0; |
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12 | delete [] _rowKey; |
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13 | delete [] _columnKey; |
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14 | _rowKey = 0; |
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15 | _columnKey = 0; |
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16 | } |
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17 | |
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18 | MinorKey::MinorKey (const MinorKey& mk) { |
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19 | _numberOfRowBlocks = mk.getNumberOfRowBlocks(); |
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20 | _numberOfColumnBlocks = mk.getNumberOfColumnBlocks();; |
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21 | |
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22 | // allocate memory for new entries in _rowKey and _columnKey; |
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23 | _rowKey = new unsigned long[_numberOfRowBlocks]; |
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24 | _columnKey = new unsigned long[_numberOfColumnBlocks]; |
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25 | |
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26 | // copying values from parameter arrays to private arrays |
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27 | for (int r = 0; r < _numberOfRowBlocks; r++) |
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28 | _rowKey[r] = mk.getRowKey(r); |
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29 | for (int c = 0; c < _numberOfColumnBlocks; c++) |
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30 | _columnKey[c] = mk.getColumnKey(c); |
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31 | } |
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32 | |
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33 | MinorKey& MinorKey::operator=(const MinorKey& mk) { |
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34 | if (_numberOfRowBlocks != 0) delete [] _rowKey; |
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35 | if (_numberOfColumnBlocks != 0) delete [] _columnKey; |
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36 | _numberOfRowBlocks = 0; |
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37 | _numberOfColumnBlocks = 0; |
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38 | _rowKey = 0; |
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39 | _columnKey = 0; |
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40 | |
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41 | _numberOfRowBlocks = mk.getNumberOfRowBlocks(); |
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42 | _numberOfColumnBlocks = mk.getNumberOfColumnBlocks();; |
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43 | |
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44 | // allocate memory for new entries in _rowKey and _columnKey; |
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45 | _rowKey = new unsigned long[_numberOfRowBlocks]; |
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46 | _columnKey = new unsigned long[_numberOfColumnBlocks]; |
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47 | |
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48 | // copying values from parameter arrays to private arrays |
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49 | for (int r = 0; r < _numberOfRowBlocks; r++) |
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50 | _rowKey[r] = mk.getRowKey(r); |
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51 | for (int c = 0; c < _numberOfColumnBlocks; c++) |
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52 | _columnKey[c] = mk.getColumnKey(c); |
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53 | |
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54 | return *this; |
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55 | } |
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56 | |
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57 | void MinorKey::set(const int lengthOfRowArray, const unsigned long* rowKey, |
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58 | const int lengthOfColumnArray, const unsigned long* columnKey) { |
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59 | // free memory of _rowKey and _columnKey |
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60 | if (_numberOfRowBlocks > 0) { delete [] _rowKey; } |
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61 | if (_numberOfColumnBlocks > 0) { delete [] _columnKey; } |
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62 | |
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63 | _numberOfRowBlocks = lengthOfRowArray; |
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64 | _numberOfColumnBlocks = lengthOfColumnArray; |
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65 | |
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66 | // allocate memory for new entries in _rowKey and _columnKey; |
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67 | _rowKey = new unsigned long[_numberOfRowBlocks]; |
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68 | _columnKey = new unsigned long[_numberOfColumnBlocks]; |
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69 | |
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70 | // copying values from parameter arrays to private arrays |
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71 | for (int r = 0; r < _numberOfRowBlocks; r++) |
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72 | _rowKey[r] = rowKey[r]; |
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73 | for (int c = 0; c < _numberOfColumnBlocks; c++) |
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74 | _columnKey[c] = columnKey[c]; |
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75 | } |
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76 | |
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77 | MinorKey::MinorKey(const int lengthOfRowArray, const unsigned long* const rowKey, |
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78 | const int lengthOfColumnArray, const unsigned long* const columnKey) { |
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79 | _numberOfRowBlocks = lengthOfRowArray; |
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80 | _numberOfColumnBlocks = lengthOfColumnArray; |
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81 | |
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82 | // allocate memory for new entries in _rowKey and _columnKey; |
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83 | _rowKey = new unsigned long[_numberOfRowBlocks]; |
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84 | _columnKey = new unsigned long[_numberOfColumnBlocks]; |
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85 | |
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86 | // copying values from parameter arrays to private arrays |
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87 | for (int r = 0; r < _numberOfRowBlocks; r++) |
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88 | _rowKey[r] = rowKey[r]; |
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89 | |
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90 | for (int c = 0; c < _numberOfColumnBlocks; c++) |
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91 | _columnKey[c] = columnKey[c]; |
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92 | } |
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93 | |
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94 | MinorKey::~MinorKey() { |
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95 | // free memory of _rowKey and _columnKey |
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96 | delete [] _rowKey; |
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97 | delete [] _columnKey; |
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98 | } |
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99 | |
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100 | void MinorKey::print() const { |
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101 | cout << this->toString(); |
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102 | } |
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103 | |
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104 | int MinorKey::getAbsoluteRowIndex(const int i) const { |
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105 | // This method is to return the absolute (0-based) index of the i-th row encoded in \a this. |
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106 | // Example: bit-pattern of rows: "10010001101", i = 3: |
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107 | // This should yield the 0-based absolute index of the 3-rd bit (counted from the right), i.e. 7. |
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108 | |
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109 | int matchedBits = -1; // counter for matched bits; this needs to reach i, then we're done |
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110 | for (int block = 0; block < getNumberOfRowBlocks(); block ++) { // start with lowest bits, i.e. in block No. 0 |
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111 | unsigned long blockBits = getRowKey(block); // the bits in this block of 32 bits |
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112 | unsigned long shiftedBit = 1; |
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113 | int exponent = 0; |
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114 | // The invariant "shiftedBit = 2^exponent" will hold throughout the entire while loop. |
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115 | while (exponent < 32) { |
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116 | if (shiftedBit & blockBits) matchedBits++; |
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117 | if (matchedBits == i) return exponent + (32 * block); |
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118 | shiftedBit = shiftedBit << 1; |
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119 | exponent++; |
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120 | } |
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121 | } |
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122 | // We should never reach this line of code. |
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123 | assert(false); |
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124 | } |
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125 | |
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126 | int MinorKey::getAbsoluteColumnIndex(const int i) const { |
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127 | // This method is to return the absolute (0-based) index of the i-th column encoded in \a this. |
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128 | // Example: bit-pattern of columns: "10010001101", i = 3: |
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129 | // This should yield the 0-based absolute index of the 3-rd bit (counted from the right), i.e. 7. |
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130 | |
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131 | int matchedBits = -1; // counter for matched bits; this needs to reach i, then we're done |
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132 | for (int block = 0; block < getNumberOfColumnBlocks(); block ++) { // start with lowest bits, i.e. in block No. 0 |
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133 | unsigned long blockBits = getColumnKey(block); // the bits in this block of 32 bits |
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134 | unsigned long shiftedBit = 1; |
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135 | int exponent = 0; |
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136 | // The invariant "shiftedBit = 2^exponent" will hold throughout the entire while loop. |
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137 | while (exponent < 32) { |
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138 | if (shiftedBit & blockBits) matchedBits++; |
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139 | if (matchedBits == i) return exponent + (32 * block); |
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140 | shiftedBit = shiftedBit << 1; |
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141 | exponent++; |
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142 | } |
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143 | } |
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144 | // We should never reach this line of code. |
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145 | assert(false); |
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146 | } |
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147 | |
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148 | void MinorKey::getAbsoluteRowIndices(int* const target) const { |
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149 | int i = 0; // index for filling the target array |
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150 | for (int block = 0; block < getNumberOfRowBlocks(); block ++) { // start with lowest bits, i.e. in block No. 0 |
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151 | unsigned long blockBits = getRowKey(block); // the bits in this block of 32 bits |
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152 | unsigned long shiftedBit = 1; |
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153 | int exponent = 0; |
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154 | // The invariant "shiftedBit = 2^exponent" will hold throughout the entire while loop. |
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155 | while (exponent < 32) { |
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156 | if (shiftedBit & blockBits) target[i++] = exponent + (32 * block); |
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157 | shiftedBit = shiftedBit << 1; |
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158 | exponent++; |
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159 | } |
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160 | } |
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161 | return; |
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162 | } |
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163 | |
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164 | void MinorKey::getAbsoluteColumnIndices(int* const target) const { |
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165 | int i = 0; // index for filling the target array |
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166 | for (int block = 0; block < getNumberOfColumnBlocks(); block ++) { // start with lowest bits, i.e. in block No. 0 |
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167 | unsigned long blockBits = getColumnKey(block); // the bits in this block of 32 bits |
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168 | unsigned long shiftedBit = 1; |
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169 | int exponent = 0; |
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170 | // The invariant "shiftedBit = 2^exponent" will hold throughout the entire while loop. |
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171 | while (exponent < 32) { |
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172 | if (shiftedBit & blockBits) target[i++] = exponent + (32 * block); |
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173 | shiftedBit = shiftedBit << 1; |
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174 | exponent++; |
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175 | } |
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176 | } |
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177 | return; |
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178 | } |
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179 | |
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180 | int MinorKey::getRelativeRowIndex(const int i) const { |
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181 | // This method is to return the relative (0-based) index of the row with absolute index \c i. |
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182 | // Example: bit-pattern of rows: "10010001101", i = 7: |
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183 | // This should yield the 0-based relative index of the bit corresponding to row no. 7, |
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184 | // i.e. 3. |
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185 | |
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186 | int matchedBits = -1; // counter for matched bits; this is going to contain our return value |
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187 | for (int block = 0; block < getNumberOfRowBlocks(); block ++) { // start with lowest bits, i.e. in block No. 0 |
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188 | unsigned long blockBits = getRowKey(block); // the bits in this block of 32 bits |
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189 | unsigned long shiftedBit = 1; |
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190 | int exponent = 0; |
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191 | // The invariant "shiftedBit = 2^exponent" will hold throughout the entire while loop. |
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192 | while (exponent < 32) { |
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193 | if (shiftedBit & blockBits) matchedBits++; |
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194 | if (exponent + (32 * block) == i) return matchedBits; |
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195 | shiftedBit = shiftedBit << 1; |
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196 | exponent++; |
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197 | } |
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198 | } |
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199 | // We should never reach this line of code. |
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200 | assert(false); |
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201 | } |
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202 | |
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203 | int MinorKey::getRelativeColumnIndex(const int i) const { |
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204 | // This method is to return the relative (0-based) index of the column with absolute index \c i. |
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205 | // Example: bit-pattern of columns: "10010001101", i = 7: |
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206 | // This should yield the 0-based relative index of the bit corresponding to column no. 7, |
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207 | // i.e. 3. |
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208 | |
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209 | int matchedBits = -1; // counter for matched bits; this is going to contain our return value |
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210 | for (int block = 0; block < getNumberOfColumnBlocks(); block ++) { // start with lowest bits, i.e. in block No. 0 |
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211 | unsigned long blockBits = getColumnKey(block); // the bits in this block of 32 bits |
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212 | unsigned long shiftedBit = 1; |
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213 | int exponent = 0; |
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214 | // The invariant "shiftedBit = 2^exponent" will hold throughout the entire while loop. |
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215 | while (exponent < 32) { |
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216 | if (shiftedBit & blockBits) matchedBits++; |
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217 | if (exponent + (32 * block) == i) return matchedBits; |
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218 | shiftedBit = shiftedBit << 1; |
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219 | exponent++; |
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220 | } |
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221 | } |
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222 | // We should never reach this line of code. |
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223 | assert(false); |
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224 | } |
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225 | |
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226 | unsigned long MinorKey::getRowKey(const int blockIndex) const { |
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227 | return _rowKey[blockIndex]; |
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228 | } |
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229 | |
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230 | unsigned long MinorKey::getColumnKey(const int blockIndex) const { |
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231 | return _columnKey[blockIndex]; |
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232 | } |
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233 | |
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234 | int MinorKey::getNumberOfRowBlocks() const { |
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235 | return _numberOfRowBlocks; |
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236 | } |
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237 | |
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238 | int MinorKey::getNumberOfColumnBlocks() const { |
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239 | return _numberOfColumnBlocks; |
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240 | } |
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241 | |
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242 | int MinorKey::getSetBits(const int a) const { |
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243 | int b = 0; |
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244 | if (a == 1) { // rows |
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245 | for (int i = 0; i < _numberOfRowBlocks; i++) { |
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246 | unsigned long m = _rowKey[i]; |
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247 | unsigned long k = 1; |
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248 | for (int j = 0; j < 32; j++) { |
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249 | // k = 2^j |
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250 | if (m & k) b++; |
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251 | k = k << 1; |
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252 | } |
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253 | } |
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254 | } |
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255 | else { // columns |
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256 | for (int i = 0; i < _numberOfColumnBlocks; i++) { |
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257 | unsigned long m = _columnKey[i]; |
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258 | unsigned long k = 1; |
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259 | for (int j = 0; j < 32; j++) { |
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260 | // k = 2^j |
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261 | if (m & k) b++; |
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262 | k = k << 1; |
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263 | } |
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264 | } |
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265 | } |
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266 | return b; |
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267 | } |
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268 | |
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269 | MinorKey MinorKey::getSubMinorKey (const int absoluteEraseRowIndex, |
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270 | const int absoluteEraseColumnIndex) const { |
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271 | int rowBlock = absoluteEraseRowIndex / 32; |
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272 | int exponent = absoluteEraseRowIndex % 32; |
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273 | unsigned long newRowBits = getRowKey(rowBlock) - (1 << exponent); |
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274 | int highestRowBlock = getNumberOfRowBlocks() - 1; |
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275 | // highestRowBlock will finally contain the highest block index with non-zero bit pattern |
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276 | if ((newRowBits == 0) && (rowBlock == highestRowBlock)) { |
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277 | // we have thus nullified the highest block; |
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278 | // we can now forget about the highest block... |
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279 | highestRowBlock -= 1; |
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280 | while (getRowKey(highestRowBlock) == 0) // ...and maybe even some more zero-blocks |
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281 | highestRowBlock -= 1; |
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282 | } |
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283 | // highestRowBlock now contains the highest row block index with non-zero bit pattern |
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284 | |
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285 | int columnBlock = absoluteEraseColumnIndex / 32; |
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286 | exponent = absoluteEraseColumnIndex % 32; |
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287 | unsigned long newColumnBits = getColumnKey(columnBlock) - (1 << exponent); |
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288 | int highestColumnBlock = getNumberOfColumnBlocks() - 1; |
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289 | // highestColumnBlock will finally contain the highest block index with non-zero bit pattern |
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290 | if ((newColumnBits == 0) && (columnBlock == highestColumnBlock)) { |
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291 | // we have thus nullified the highest block; |
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292 | // we can now forget about the highest block... |
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293 | highestColumnBlock -= 1; |
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294 | while (getColumnKey(highestColumnBlock) == 0) // ...and maybe even some more zero-blocks |
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295 | highestColumnBlock -= 1; |
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296 | } |
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297 | // highestColumnBlock now contains the highest column block index with non-zero bit pattern |
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298 | |
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299 | MinorKey result(highestRowBlock + 1, _rowKey, highestColumnBlock + 1, _columnKey); |
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300 | // This is just a copy with maybe some leading bit blocks omitted. We still need to re-define |
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301 | // the row block at index 'rowBlock' and the column block at index 'columnBlock': |
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302 | if ((newRowBits != 0) || (rowBlock < getNumberOfRowBlocks() - 1)) result.setRowKey(rowBlock, newRowBits); |
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303 | if ((newColumnBits != 0) || (columnBlock < getNumberOfColumnBlocks() - 1)) result.setColumnKey(columnBlock, newColumnBits); |
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304 | |
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305 | if (result.getSetBits(1) != result.getSetBits(2)) { // asserts that the number of selected rows and columns are equal |
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306 | cout << endl; |
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307 | this->print(); |
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308 | cout << endl; |
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309 | result.print(); |
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310 | cout << endl; |
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311 | cout << "rows: " << result.getSetBits(1) << " / columns: " << result.getSetBits(2); |
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312 | cout << endl; |
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313 | cout << "row to be erased: " << absoluteEraseRowIndex << " / column to be erased: " << absoluteEraseColumnIndex << endl; |
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314 | assert(false); |
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315 | } |
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316 | |
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317 | return result; |
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318 | } |
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319 | |
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320 | void MinorKey::setRowKey (const int blockIndex, const unsigned long rowKey) { |
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321 | _rowKey[blockIndex] = rowKey; |
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322 | } |
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323 | |
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324 | void MinorKey::setColumnKey (const int blockIndex, const unsigned long columnKey) { |
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325 | _columnKey[blockIndex] = columnKey; |
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326 | } |
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327 | |
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328 | int MinorKey::compare (const MinorKey& that) const { |
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329 | // compare by rowKeys first; in case of equality, use columnKeys |
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330 | if (this->getNumberOfRowBlocks() < that.getNumberOfRowBlocks()) |
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331 | return -1; |
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332 | if (this->getNumberOfRowBlocks() > that.getNumberOfRowBlocks()) |
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333 | return 1; |
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334 | // Here, numbers of rows are equal. |
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335 | for (int r = this->getNumberOfRowBlocks() - 1; r >= 0; r--) { |
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336 | if (this->getRowKey(r) < that.getRowKey(r)) return -1; |
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337 | if (this->getRowKey(r) > that.getRowKey(r)) return 1; |
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338 | } |
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339 | // Here, this and that encode ecaxtly the same sets of rows. |
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340 | // Now, we take a look at the columns. |
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341 | if (this->getNumberOfColumnBlocks() < that.getNumberOfColumnBlocks()) |
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342 | return -1; |
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343 | if (this->getNumberOfColumnBlocks() > that.getNumberOfColumnBlocks()) |
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344 | return 1; |
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345 | // Here, numbers of columns are equal. |
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346 | for (int c = this->getNumberOfColumnBlocks() - 1; c >= 0; c--) { |
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347 | if (this->getColumnKey(c) < that.getColumnKey(c)) return -1; |
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348 | if (this->getColumnKey(c) > that.getColumnKey(c)) return 1; |
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349 | } |
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350 | // Here, this and that encode exactly the same sets of rows and columns. |
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351 | return 0; |
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352 | } |
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353 | |
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354 | // just to make the compiler happy; |
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355 | // this method should never be called |
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356 | bool MinorKey::operator==(const MinorKey& mk) const { |
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357 | assert(false); |
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358 | return this->compare(mk) == 0; |
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359 | } |
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360 | |
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361 | // just to make the compiler happy; |
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362 | // this method should never be called |
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363 | bool MinorKey::operator<(const MinorKey& mk) const { |
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364 | assert(false); |
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365 | return this->compare(mk) == -1; |
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366 | } |
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367 | |
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368 | void MinorKey::selectFirstRows (const int k, const MinorKey& mk) { |
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369 | int hitBits = 0; // the number of bits we have hit; in the end, this has to be equal to k, |
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370 | // the dimension of the minor |
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371 | int blockIndex = -1; // the index of the current long in mk |
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372 | unsigned long highestLong = 0; // the new highest block of this MinorKey |
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373 | // We determine which longs of mk we can copy. Their indices will be 0, 1, ..., blockIndex - 1. |
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374 | // And highestLong is going to capture the highest long (which may be only a portion of |
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375 | // the corresponding long in mk. We loop until hitBits = k: |
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376 | while (hitBits < k) { |
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377 | blockIndex++; |
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378 | highestLong = 0; |
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379 | unsigned long currentLong = mk.getRowKey(blockIndex); |
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380 | unsigned long shiftedBit = 1; |
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381 | int exponent = 0; |
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382 | // invariant in the loop: shiftedBit = 2^exponent |
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383 | while (exponent < 32 && hitBits < k) { |
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384 | if (shiftedBit & currentLong) { |
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385 | highestLong += shiftedBit; |
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386 | hitBits++; |
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387 | } |
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388 | shiftedBit = shiftedBit << 1; |
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389 | exponent++; |
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390 | } |
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391 | } |
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392 | // free old memory |
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393 | delete [] _rowKey; _rowKey = 0; |
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394 | _numberOfRowBlocks = blockIndex + 1; |
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395 | // allocate memory for new entries in _rowKey; |
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396 | _rowKey = new unsigned long[_numberOfRowBlocks]; |
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397 | // copying values from mk to this MinorKey |
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398 | for (int r = 0; r < blockIndex; r++) |
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399 | _rowKey[r] = mk.getRowKey(r); |
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400 | _rowKey[blockIndex] = highestLong; |
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401 | } |
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402 | |
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403 | void MinorKey::selectFirstColumns (const int k, const MinorKey& mk) { |
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404 | int hitBits = 0; // the number of bits we have hit; in the end, this has to be equal to k, |
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405 | // the dimension of the minor |
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406 | int blockIndex = -1; // the index of the current long in mk |
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407 | unsigned long highestLong = 0; // the new highest block of this MinorKey |
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408 | // We determine which longs of mk we can copy. Their indices will be 0, 1, ..., blockIndex - 1. |
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409 | // And highestLong is going to capture the highest long (which may be only a portion of |
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410 | // the corresponding long in mk. We loop until hitBits = k: |
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411 | while (hitBits < k) { |
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412 | blockIndex++; |
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413 | highestLong = 0; |
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414 | unsigned long currentLong = mk.getColumnKey(blockIndex); |
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415 | unsigned long shiftedBit = 1; |
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416 | int exponent = 0; |
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417 | // invariant in the loop: shiftedBit = 2^exponent |
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418 | while (exponent < 32 && hitBits < k) { |
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419 | if (shiftedBit & currentLong) { |
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420 | highestLong += shiftedBit; |
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421 | hitBits++; |
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422 | } |
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423 | shiftedBit = shiftedBit << 1; |
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424 | exponent++; |
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425 | } |
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426 | } |
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427 | // free old memory |
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428 | delete [] _columnKey; _columnKey = 0; |
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429 | _numberOfColumnBlocks = blockIndex + 1; |
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430 | // allocate memory for new entries in _columnKey; |
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431 | _columnKey = new unsigned long[_numberOfColumnBlocks]; |
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432 | // copying values from mk to this MinorKey |
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433 | for (int c = 0; c < blockIndex; c++) |
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434 | _columnKey[c] = mk.getColumnKey(c); |
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435 | _columnKey[blockIndex] = highestLong; |
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436 | } |
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437 | |
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438 | bool MinorKey::selectNextRows (const int k, const MinorKey& mk) { |
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439 | // We need to compute the set of k rows which must all be contained in mk. |
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440 | // AND: This set must be the least possible of this kind which is larger |
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441 | // than the currently encoded set of rows. (Here, '<' is w.r.t. to the natural |
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442 | // ordering on multi-indices. |
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443 | // Example: mk encodes the rows according to the bit pattern 11010111, k = 3, this |
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444 | // MinorKey encodes 10010100. Then, the method must shift the set of rows in |
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445 | // this MinorKey to 11000001 (, and return true). |
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446 | |
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447 | // The next two variables will finally name a row which is |
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448 | // (1) currently not yet among the rows in this MinorKey, but |
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449 | // (2) among the rows in mk, and |
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450 | // (3) which is "higher" than the lowest row in this MinorKey, and |
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451 | // (4) which is the lowest possible choice such that (1) - (3) hold. |
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452 | // If we should not be able to find such a row, then there is no next subset of rows. |
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453 | // In this case, the method will return false; otherwise always true. |
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454 | int newBitBlockIndex = 0; // the block index of the bit |
---|
455 | unsigned long newBitToBeSet = 0; // the bit as 2^e, where 0 <= e <= 31 |
---|
456 | |
---|
457 | int blockCount = this->getNumberOfRowBlocks(); // number of longs (representing rows) in this MinorKey |
---|
458 | int mkBlockIndex = mk.getNumberOfRowBlocks(); // for iterating along the blocks of mk |
---|
459 | |
---|
460 | int hitBits = 0; // the number of bits we have hit |
---|
461 | int bitCounter = 0; // for storing the number of bits hit before a specific moment; see below |
---|
462 | |
---|
463 | while (hitBits < k) { |
---|
464 | mkBlockIndex--; |
---|
465 | unsigned long currentLong = mk.getRowKey(mkBlockIndex); |
---|
466 | unsigned long shiftedBit = 1 << 31; // initially, this equals 2^31, i.e. the highest bit |
---|
467 | while (hitBits < k && shiftedBit > 0) { |
---|
468 | if (blockCount - 1 >= mkBlockIndex && |
---|
469 | shiftedBit & this->getRowKey(mkBlockIndex)) hitBits++; |
---|
470 | else if (shiftedBit & currentLong) { |
---|
471 | newBitToBeSet = shiftedBit; |
---|
472 | newBitBlockIndex = mkBlockIndex; |
---|
473 | bitCounter = hitBits; // So, whenever we set newBitToBeSet, we want to remember the momentary |
---|
474 | // number of hit bits. This will later be needed; see below. |
---|
475 | } |
---|
476 | shiftedBit = shiftedBit >> 1; |
---|
477 | } |
---|
478 | } |
---|
479 | |
---|
480 | if (newBitToBeSet == 0) { |
---|
481 | return false; |
---|
482 | } |
---|
483 | else { |
---|
484 | // Note that the following must hold when reaching this line of code: |
---|
485 | // (1) The row with bit newBitToBeSet in this->getRowKey(newBitBlockIndex) is currently |
---|
486 | // not among the rows in this MinorKey, but |
---|
487 | // (2) it is among the rows in mk, and |
---|
488 | // (3) it is higher than the lowest row in this MinorKey, and |
---|
489 | // (4) it is the lowest possible choice such that (1) - (3) hold. |
---|
490 | // In the above example, we would reach this line with |
---|
491 | // newBitToBeSet == 2^6 and bitCounter == 1 (resulting from the bit 2^7). |
---|
492 | |
---|
493 | if (blockCount - 1 < newBitBlockIndex) { // In this case, _rowKey is to small. |
---|
494 | // free old memory |
---|
495 | delete [] _rowKey; _rowKey = 0; |
---|
496 | _numberOfRowBlocks = newBitBlockIndex + 1; |
---|
497 | // allocate memory for new entries in _rowKey; |
---|
498 | _rowKey = new unsigned long[_numberOfRowBlocks]; |
---|
499 | } |
---|
500 | else { |
---|
501 | // We need to delete all bits in _rowKey[newBitBlockIndex] that are below newBitToBeSet: |
---|
502 | unsigned long aLong = this->getRowKey(newBitBlockIndex); |
---|
503 | unsigned long deleteBit = newBitToBeSet >> 1; // in example: = 2^5 |
---|
504 | while (deleteBit > 0) { |
---|
505 | if (aLong & deleteBit) aLong -= deleteBit; |
---|
506 | deleteBit = deleteBit >> 1; |
---|
507 | }; |
---|
508 | _rowKey[newBitBlockIndex] = aLong; |
---|
509 | // ...and we delete all entries in _rowKey[i] for 0 <= i < newBitBlockIndex |
---|
510 | for (int i = 0; i < newBitBlockIndex; i++) |
---|
511 | _rowKey[i] = 0; |
---|
512 | } |
---|
513 | |
---|
514 | // We have now deleted all bits from _rowKey[...] below the bit 2^newBitToBeSet. |
---|
515 | // In the example we shall have at this point: _rowKey[...] = 10000000. |
---|
516 | // Now let's set the new bit: |
---|
517 | _rowKey[newBitBlockIndex] += newBitToBeSet; // _rowKey[newBitBlockIndex] = 11000000 |
---|
518 | bitCounter++; // This is now the number of correct bits in _rowKey[...]; i.e. in the |
---|
519 | // example this will be equal to 2. |
---|
520 | |
---|
521 | // Now we only need to fill _rowKey[...] with the lowest possible bits until it |
---|
522 | // consists of exactly k bits. (We know that we need to set exactly (k - bitCounter) |
---|
523 | // additional bits.) |
---|
524 | mkBlockIndex = -1; |
---|
525 | while (bitCounter < k) { |
---|
526 | mkBlockIndex++; |
---|
527 | unsigned long currentLong = mk.getRowKey(mkBlockIndex); |
---|
528 | unsigned long shiftedBit = 1; |
---|
529 | int exponent = 0; |
---|
530 | // invariant: shiftedBit = 2^exponent |
---|
531 | while (bitCounter < k && exponent < 32) { |
---|
532 | if (shiftedBit & currentLong) { |
---|
533 | _rowKey[mkBlockIndex] += shiftedBit; |
---|
534 | bitCounter++; |
---|
535 | }; |
---|
536 | shiftedBit = shiftedBit << 1; |
---|
537 | exponent++; |
---|
538 | } |
---|
539 | }; |
---|
540 | // in the example, we shall obtain _rowKey[...] = 11000001 |
---|
541 | |
---|
542 | return true; |
---|
543 | } |
---|
544 | } |
---|
545 | |
---|
546 | bool MinorKey::selectNextColumns (const int k, const MinorKey& mk) { |
---|
547 | // We need to compute the set of k columns which must all be contained in mk. |
---|
548 | // AND: This set must be the least possible of this kind which is larger |
---|
549 | // than the currently encoded set of columns. (Here, '<' is w.r.t. to the natural |
---|
550 | // ordering on multi-indices. |
---|
551 | // Example: mk encodes the columns according to the bit pattern 11010111, k = 3, this |
---|
552 | // MinorKey encodes 10010100. Then, the method must shift the set of columns in |
---|
553 | // this MinorKey to 11000001 (, and return true). |
---|
554 | |
---|
555 | // The next two variables will finally name a columns which is |
---|
556 | // (1) currently not yet among the columns in this MinorKey, but |
---|
557 | // (2) among the columns in mk, and |
---|
558 | // (3) which is "higher" than the lowest columns in this MinorKey, and |
---|
559 | // (4) which is the lowest possible choice such that (1) - (3) hold. |
---|
560 | // If we should not be able to find such a columns, then there is no next subset of columns. |
---|
561 | // In this case, the method will return false; otherwise always true. |
---|
562 | int newBitBlockIndex = 0; // the block index of the bit |
---|
563 | unsigned long newBitToBeSet = 0; // the bit as 2^e, where 0 <= e <= 31 |
---|
564 | |
---|
565 | int blockCount = this->getNumberOfColumnBlocks(); // number of longs (representing columns) in this MinorKey |
---|
566 | int mkBlockIndex = mk.getNumberOfColumnBlocks(); // for iterating along the blocks of mk |
---|
567 | |
---|
568 | int hitBits = 0; // the number of bits we have hit |
---|
569 | int bitCounter = 0; // for storing the number of bits hit before a specific moment; see below |
---|
570 | |
---|
571 | while (hitBits < k) { |
---|
572 | mkBlockIndex--; |
---|
573 | unsigned long currentLong = mk.getColumnKey(mkBlockIndex); |
---|
574 | unsigned long shiftedBit = 1 << 31; // initially, this equals 2^31, i.e. the highest bit |
---|
575 | while (hitBits < k && shiftedBit > 0) { |
---|
576 | if (blockCount - 1 >= mkBlockIndex && |
---|
577 | shiftedBit & this->getColumnKey(mkBlockIndex)) hitBits++; |
---|
578 | else if (shiftedBit & currentLong) { |
---|
579 | newBitToBeSet = shiftedBit; |
---|
580 | newBitBlockIndex = mkBlockIndex; |
---|
581 | bitCounter = hitBits; // So, whenever we set newBitToBeSet, we want to remember the momentary |
---|
582 | // number of hit bits. This will later be needed; see below. |
---|
583 | } |
---|
584 | shiftedBit = shiftedBit >> 1; |
---|
585 | } |
---|
586 | } |
---|
587 | |
---|
588 | if (newBitToBeSet == 0) { |
---|
589 | return false; |
---|
590 | } |
---|
591 | else { |
---|
592 | // Note that the following must hold when reaching this line of code: |
---|
593 | // (1) The columns with bit newBitToBeSet in this->getColumnKey(newBitBlockIndex) is currently |
---|
594 | // not among the columns in this MinorKey, but |
---|
595 | // (2) it is among the columns in mk, and |
---|
596 | // (3) it is higher than the lowest columns in this MinorKey, and |
---|
597 | // (4) it is the lowest possible choice such that (1) - (3) hold. |
---|
598 | // In the above example, we would reach this line with |
---|
599 | // newBitToBeSet == 2^6 and bitCounter == 1 (resulting from the bit 2^7). |
---|
600 | |
---|
601 | if (blockCount - 1 < newBitBlockIndex) { // In this case, _columnKey is to small. |
---|
602 | // free old memory |
---|
603 | delete [] _columnKey; _columnKey = 0; |
---|
604 | _numberOfColumnBlocks = newBitBlockIndex + 1; |
---|
605 | // allocate memory for new entries in _columnKey; |
---|
606 | _columnKey = new unsigned long[_numberOfColumnBlocks]; |
---|
607 | } |
---|
608 | else { |
---|
609 | // We need to delete all bits in _columnKey[newBitBlockIndex] that are below newBitToBeSet: |
---|
610 | unsigned long aLong = this->getColumnKey(newBitBlockIndex); |
---|
611 | unsigned long deleteBit = newBitToBeSet >> 1; // in example: = 2^5 |
---|
612 | while (deleteBit > 0) { |
---|
613 | if (aLong & deleteBit) aLong -= deleteBit; |
---|
614 | deleteBit = deleteBit >> 1; |
---|
615 | }; |
---|
616 | _columnKey[newBitBlockIndex] = aLong; |
---|
617 | // ...and we delete all entries in _columnKey[i] for 0 <= i < newBitBlockIndex |
---|
618 | for (int i = 0; i < newBitBlockIndex; i++) |
---|
619 | _columnKey[i] = 0; |
---|
620 | } |
---|
621 | |
---|
622 | // We have now deleted all bits from _columnKey[...] below the bit 2^newBitToBeSet. |
---|
623 | // In the example we shall have at this point: _columnKey[...] = 10000000. |
---|
624 | // Now let's set the new bit: |
---|
625 | _columnKey[newBitBlockIndex] += newBitToBeSet; // _columnKey[newBitBlockIndex] = 11000000 |
---|
626 | bitCounter++; // This is now the number of correct bits in _columnKey[...]; i.e. in the |
---|
627 | // example this will be equal to 2. |
---|
628 | |
---|
629 | // Now we only need to fill _columnKey[...] with the lowest possible bits until it |
---|
630 | // consists of exactly k bits. (We know that we need to set exactly (k - bitCounter) |
---|
631 | // additional bits.) |
---|
632 | mkBlockIndex = -1; |
---|
633 | while (bitCounter < k) { |
---|
634 | mkBlockIndex++; |
---|
635 | unsigned long currentLong = mk.getColumnKey(mkBlockIndex); |
---|
636 | unsigned long shiftedBit = 1; |
---|
637 | int exponent = 0; |
---|
638 | // invariant: shiftedBit = 2^exponent |
---|
639 | while (bitCounter < k && exponent < 32) { |
---|
640 | if (shiftedBit & currentLong) { |
---|
641 | _columnKey[mkBlockIndex] += shiftedBit; |
---|
642 | bitCounter++; |
---|
643 | }; |
---|
644 | shiftedBit = shiftedBit << 1; |
---|
645 | exponent++; |
---|
646 | } |
---|
647 | }; |
---|
648 | // in the example, we shall obtain _columnKey[...] = 11000001 |
---|
649 | |
---|
650 | return true; |
---|
651 | } |
---|
652 | } |
---|
653 | |
---|
654 | string MinorKey::toString() const { |
---|
655 | char h[32]; |
---|
656 | string t = ""; |
---|
657 | string s = "("; |
---|
658 | for (int r = this->getNumberOfRowBlocks() - 1; r >= 0; r--) { |
---|
659 | sprintf(h, "%ld", this->getRowKey(r)); t += h; |
---|
660 | if (r < this->getNumberOfRowBlocks() - 1) |
---|
661 | t = string(32 - t.length(), '0') + t; |
---|
662 | s += t; |
---|
663 | } |
---|
664 | s += ", "; |
---|
665 | for (int c = this->getNumberOfColumnBlocks() - 1; c >= 0; c--) { |
---|
666 | sprintf(h, "%ld", this->getColumnKey(c)); t += h; |
---|
667 | if (c < this->getNumberOfColumnBlocks() - 1) |
---|
668 | t = string(32 - t.length(), '0') + t; |
---|
669 | s += t; |
---|
670 | } |
---|
671 | s += ")"; |
---|
672 | return s; |
---|
673 | } |
---|
674 | |
---|
675 | int MinorValue::_RankingStrategy = -1; |
---|
676 | |
---|
677 | long MinorValue::getWeight () const |
---|
678 | { |
---|
679 | assert(false); // must be overridden in derived classes |
---|
680 | return 0; |
---|
681 | } |
---|
682 | |
---|
683 | // just to make the compiler happy; |
---|
684 | // this method should never be called |
---|
685 | bool MinorValue::operator==(const MinorValue& mv) const { |
---|
686 | assert(false); |
---|
687 | return (this == &mv); // compare addresses of both objects |
---|
688 | } |
---|
689 | |
---|
690 | string MinorValue::toString () const |
---|
691 | { |
---|
692 | assert(false); // must be overridden in derived classes |
---|
693 | return ""; |
---|
694 | } |
---|
695 | |
---|
696 | // just to make the compiler happy; |
---|
697 | // this method should never be called |
---|
698 | bool MinorValue::operator<(const MinorValue& mv) const { |
---|
699 | assert(false); |
---|
700 | return (this < &mv); // compare addresses of both objects |
---|
701 | } |
---|
702 | |
---|
703 | long MinorValue::getRetrievals() const { |
---|
704 | return _retrievals; |
---|
705 | } |
---|
706 | |
---|
707 | void MinorValue::incrementRetrievals() { |
---|
708 | _retrievals++; |
---|
709 | } |
---|
710 | |
---|
711 | long MinorValue::getPotentialRetrievals() const { |
---|
712 | return _potentialRetrievals; |
---|
713 | } |
---|
714 | |
---|
715 | long MinorValue::getMultiplications() const { |
---|
716 | return _multiplications; |
---|
717 | } |
---|
718 | |
---|
719 | long MinorValue::getAdditions() const { |
---|
720 | return _additions; |
---|
721 | } |
---|
722 | |
---|
723 | long MinorValue::getAccumulatedMultiplications() const { |
---|
724 | return _accumulatedMult; |
---|
725 | } |
---|
726 | |
---|
727 | long MinorValue::getAccumulatedAdditions() const { |
---|
728 | return _accumulatedSum; |
---|
729 | } |
---|
730 | |
---|
731 | void MinorValue::print() const { |
---|
732 | cout << this->toString(); |
---|
733 | } |
---|
734 | |
---|
735 | |
---|
736 | void MinorValue::SetRankingStrategy(const int rankingStrategy) { |
---|
737 | _RankingStrategy = rankingStrategy; |
---|
738 | if (_RankingStrategy == 6) { |
---|
739 | // initialize the random generator with system time |
---|
740 | srand ( time(NULL) ); |
---|
741 | } |
---|
742 | } |
---|
743 | |
---|
744 | int MinorValue::GetRankingStrategy() { |
---|
745 | return _RankingStrategy; |
---|
746 | } |
---|
747 | |
---|
748 | // this is for generically accessing the rank measure regardless of |
---|
749 | // which strategy has been set |
---|
750 | int MinorValue::getUtility () const { |
---|
751 | switch (this->GetRankingStrategy()) { |
---|
752 | case 1: return this->rankMeasure1(); |
---|
753 | case 2: return this->rankMeasure2(); |
---|
754 | case 3: return this->rankMeasure3(); |
---|
755 | case 4: return this->rankMeasure4(); |
---|
756 | case 5: return this->rankMeasure5(); |
---|
757 | default: return this->rankMeasure1(); |
---|
758 | } |
---|
759 | } |
---|
760 | |
---|
761 | // here are some sensible caching strategies: |
---|
762 | int MinorValue::rankMeasure1 () const { |
---|
763 | // number of actually performed multiplications |
---|
764 | return this->getMultiplications(); |
---|
765 | } |
---|
766 | |
---|
767 | int MinorValue::rankMeasure2 () const { |
---|
768 | // accumulated number of performed multiplications, i.e. all including nested multiplications |
---|
769 | return this->getAccumulatedMultiplications(); |
---|
770 | } |
---|
771 | |
---|
772 | int MinorValue::rankMeasure3 () const { |
---|
773 | // number of performed multiplications, weighted with the ratio of |
---|
774 | // not yet performed retrievals over the maximal number of retrievals |
---|
775 | return this->getMultiplications() * (this->getPotentialRetrievals() - this->getRetrievals()) |
---|
776 | / this->getPotentialRetrievals(); |
---|
777 | } |
---|
778 | |
---|
779 | int MinorValue::rankMeasure4 () const { |
---|
780 | // number of performed multiplications, |
---|
781 | // multiplied with the number of not yet performed retrievals |
---|
782 | return this->getMultiplications() * (this->getPotentialRetrievals() - this->getRetrievals()); |
---|
783 | } |
---|
784 | |
---|
785 | int MinorValue::rankMeasure5 () const { |
---|
786 | // number of not yet performed retrievals; |
---|
787 | // tends to cache entries longer when they are going to be retrieved more often in the future |
---|
788 | return this->getPotentialRetrievals() - this->getRetrievals(); |
---|
789 | } |
---|
790 | |
---|
791 | long LongMinorValue::getWeight () const { |
---|
792 | // put measure for size of MinorValue here, i.e. number of monomials in polynomial; |
---|
793 | // so far, we use the accumulated number of multiplications (i.e., including all nested ones) |
---|
794 | // to simmulate the size of a polynomial |
---|
795 | return _accumulatedMult; |
---|
796 | } |
---|
797 | |
---|
798 | LongMinorValue::LongMinorValue (const long result, const int multiplications, const int additions, |
---|
799 | const int accumulatedMultiplications, const int accumulatedAdditions, |
---|
800 | const int retrievals, const int potentialRetrievals) { |
---|
801 | _result = result; |
---|
802 | _multiplications = multiplications; |
---|
803 | _additions = additions; |
---|
804 | _accumulatedMult = accumulatedMultiplications; |
---|
805 | _accumulatedSum = accumulatedAdditions; |
---|
806 | _potentialRetrievals = potentialRetrievals; |
---|
807 | _retrievals = retrievals; |
---|
808 | } |
---|
809 | |
---|
810 | LongMinorValue::LongMinorValue () { |
---|
811 | _result = -1; |
---|
812 | _multiplications = -1; |
---|
813 | _additions = -1; |
---|
814 | _accumulatedMult = -1; |
---|
815 | _accumulatedSum = -1; |
---|
816 | _potentialRetrievals = -1; |
---|
817 | _retrievals = -1; |
---|
818 | } |
---|
819 | |
---|
820 | LongMinorValue::~LongMinorValue() |
---|
821 | { |
---|
822 | } |
---|
823 | |
---|
824 | long LongMinorValue::getResult() const { |
---|
825 | return _result; |
---|
826 | } |
---|
827 | |
---|
828 | string LongMinorValue::toString () const { |
---|
829 | char h[10]; |
---|
830 | |
---|
831 | // Let's see whether a cache has been used to compute this MinorValue: |
---|
832 | bool cacheHasBeenUsed = true; |
---|
833 | if (this->getRetrievals() == -1) cacheHasBeenUsed = false; |
---|
834 | |
---|
835 | sprintf(h, "%ld", this->getResult()); |
---|
836 | string s = h; |
---|
837 | s += " [retrievals: "; |
---|
838 | if (cacheHasBeenUsed) { sprintf(h, "%ld", this->getRetrievals()); s += h; } |
---|
839 | else s += "/"; |
---|
840 | s += " (of "; |
---|
841 | if (cacheHasBeenUsed) { sprintf(h, "%ld", this->getPotentialRetrievals()); s += h; } |
---|
842 | else s += "/"; |
---|
843 | s += "), *: "; |
---|
844 | sprintf(h, "%ld", this->getMultiplications()); s += h; |
---|
845 | s += " (accumulated: "; |
---|
846 | sprintf(h, "%ld", this->getAccumulatedMultiplications()); s += h; |
---|
847 | s += "), +: "; |
---|
848 | sprintf(h, "%ld", this->getAdditions()); s += h; |
---|
849 | s += " (accumulated: "; |
---|
850 | sprintf(h, "%ld", this->getAccumulatedAdditions()); s += h; |
---|
851 | s += "), rank: "; |
---|
852 | if (cacheHasBeenUsed) { sprintf(h, "%d", this->getUtility()); s += h; } |
---|
853 | else s += "/"; |
---|
854 | s += "]"; |
---|
855 | return s; |
---|
856 | } |
---|
857 | |
---|
858 | LongMinorValue::LongMinorValue (const LongMinorValue& mv) { |
---|
859 | _result = mv.getResult(); |
---|
860 | _retrievals = mv.getRetrievals(); |
---|
861 | _potentialRetrievals = mv.getPotentialRetrievals(); |
---|
862 | _multiplications = mv.getMultiplications(); |
---|
863 | _additions = mv.getAdditions(); |
---|
864 | _accumulatedMult = mv.getAccumulatedMultiplications(); |
---|
865 | _accumulatedSum = mv.getAccumulatedAdditions(); |
---|
866 | } |
---|
867 | |
---|
868 | PolyMinorValue::PolyMinorValue (const poly result, const int multiplications, const int additions, |
---|
869 | const int accumulatedMultiplications, const int accumulatedAdditions, |
---|
870 | const int retrievals, const int potentialRetrievals) { |
---|
871 | _result = pCopy(result); |
---|
872 | // std::cout << std::endl << "PolyMinorValue creator, " << pString(_result); |
---|
873 | _multiplications = multiplications; |
---|
874 | _additions = additions; |
---|
875 | _accumulatedMult = accumulatedMultiplications; |
---|
876 | _accumulatedSum = accumulatedAdditions; |
---|
877 | _potentialRetrievals = potentialRetrievals; |
---|
878 | _retrievals = retrievals; |
---|
879 | } |
---|
880 | |
---|
881 | PolyMinorValue::PolyMinorValue () { |
---|
882 | _result = pISet(0); |
---|
883 | // std::cout << std::endl << "PolyMinorValue creator, " << pString(_result) << " STANDARD!"; |
---|
884 | _multiplications = -1; |
---|
885 | _additions = -1; |
---|
886 | _accumulatedMult = -1; |
---|
887 | _accumulatedSum = -1; |
---|
888 | _potentialRetrievals = -1; |
---|
889 | _retrievals = -1; |
---|
890 | } |
---|
891 | |
---|
892 | PolyMinorValue::~PolyMinorValue() |
---|
893 | { |
---|
894 | // p_Delete(&_result, currRing); |
---|
895 | } |
---|
896 | |
---|
897 | poly PolyMinorValue::getResult() const { |
---|
898 | return _result; |
---|
899 | } |
---|
900 | |
---|
901 | long PolyMinorValue::getWeight () const { |
---|
902 | // put measure for size of PolyMinorValue here, e.g. the number of monomials |
---|
903 | // the cached polynomial |
---|
904 | return pLength(_result); // the number of monomials in the polynomial |
---|
905 | } |
---|
906 | |
---|
907 | string PolyMinorValue::toString () const { |
---|
908 | char h[10]; |
---|
909 | |
---|
910 | // Let's see whether a cache has been used to compute this MinorValue: |
---|
911 | bool cacheHasBeenUsed = true; |
---|
912 | if (this->getRetrievals() == -1) cacheHasBeenUsed = false; |
---|
913 | |
---|
914 | string s = pString(_result); |
---|
915 | s += " [retrievals: "; |
---|
916 | if (cacheHasBeenUsed) { sprintf(h, "%ld", this->getRetrievals()); s += h; } |
---|
917 | else s += "/"; |
---|
918 | s += " (of "; |
---|
919 | if (cacheHasBeenUsed) { sprintf(h, "%ld", this->getPotentialRetrievals()); s += h; } |
---|
920 | else s += "/"; |
---|
921 | s += "), *: "; |
---|
922 | sprintf(h, "%ld", this->getMultiplications()); s += h; |
---|
923 | s += " (accumulated: "; |
---|
924 | sprintf(h, "%ld", this->getAccumulatedMultiplications()); s += h; |
---|
925 | s += "), +: "; |
---|
926 | sprintf(h, "%ld", this->getAdditions()); s += h; |
---|
927 | s += " (accumulated: "; |
---|
928 | sprintf(h, "%ld", this->getAccumulatedAdditions()); s += h; |
---|
929 | s += "), rank: "; |
---|
930 | if (cacheHasBeenUsed) { sprintf(h, "%d", this->getUtility()); s += h; } |
---|
931 | else s += "/"; |
---|
932 | s += "]"; |
---|
933 | return s; |
---|
934 | } |
---|
935 | |
---|
936 | PolyMinorValue::PolyMinorValue (const PolyMinorValue& mv) { |
---|
937 | _result = mv.getResult(); |
---|
938 | _retrievals = mv.getRetrievals(); |
---|
939 | _potentialRetrievals = mv.getPotentialRetrievals(); |
---|
940 | _multiplications = mv.getMultiplications(); |
---|
941 | _additions = mv.getAdditions(); |
---|
942 | _accumulatedMult = mv.getAccumulatedMultiplications(); |
---|
943 | _accumulatedSum = mv.getAccumulatedAdditions(); |
---|
944 | } |
---|
945 | |
---|
946 | #endif // HAVE_MINOR |
---|