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Aperiodic Spectre tiling
This commit is contained in:
Zeno Rogue
@@ -382,6 +382,405 @@ vector<rule_recursive> rules_recursive = {
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{6, 6, 31, 31, 14},
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};
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vector<rule_base> spectre_rules_base = { rule_base
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{0, 0, 5, 5, -1},
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{0, 10, 7, 7, -1},
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{0, 11, 5, 8, -1},
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{0, 12, 5, 7, -1},
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{0, 13, 5, 6, -1},
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{0, 1, 3, 8, -1},
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{0, 2, 3, 7, -1},
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{0, 3, 3, 6, -1},
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{0, 4, 3, 5, -1},
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{0, 5, 1, 0, -1},
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{0, 6, 1, 13, -1},
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{0, 7, 1, 12, -1},
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{0, 8, 1, 11, -1},
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{0, 9, 7, 8, -1},
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{1, 0, 0, 5, -1},
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{1, 10, 7, 9, -1},
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{1, 11, 0, 8, -1},
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{1, 12, 0, 7, -1},
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{1, 1, 2, 6, -1},
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{1, 13, 0, 6, -1},
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{1, 2, 2, 5, -1},
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{1, 3, 2, 4, -1},
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{1, 4, 2, 13, 20},
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{1, 4, 3, 13, 14},
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{1, 4, 6, 13, 30},
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{1, 4, 7, 13, 26},
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{1, 4, 8, 13, 15},
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{1, 5, 2, 12, 20},
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{1, 5, 3, 12, 14},
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{1, 5, 6, 12, 30},
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{1, 5, 7, 12, 26},
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{1, 5, 8, 12, 15},
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{1, 6, 2, 11, 20},
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{1, 6, 3, 11, 14},
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{1, 6, 6, 11, 30},
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{1, 6, 7, 11, 26},
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{1, 6, 8, 11, 15},
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{1, 7, 2, 0, 13},
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{1, 7, 4, 0, 29},
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{1, 7, 4, 4, 14},
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{1, 7, 6, 0, 25},
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{1, 7, 8, 0, 9},
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{1, 8, 2, 13, 13},
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{1, 8, 4, 13, 29},
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{1, 8, 4, 3, 14},
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{1, 8, 6, 13, 25},
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{1, 8, 8, 13, 9},
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{1, 9, 2, 12, 13},
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{1, 9, 4, 12, 29},
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{1, 9, 4, 2, 14},
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{1, 9, 6, 12, 25},
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{1, 9, 8, 12, 9},
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{2, 0, 1, 7, 31},
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{2, 0, 2, 3, 27},
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{2, 0, 6, 3, 16},
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{2, 0, 8, 3, 22},
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{2, 10, 2, 11, 22},
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{2, 10, 2, 1, 32},
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{2, 10, 4, 11, 16},
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{2, 10, 7, 11, 31},
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{2, 11, 1, 6, 27},
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{2, 11, 2, 10, 22},
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{2, 11, 4, 10, 16},
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{2, 11, 7, 10, 31},
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{2, 1, 2, 10, 14},
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{2, 12, 1, 5, 27},
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{2, 12, 1, 9, 31},
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{2, 1, 2, 2, 27},
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{2, 12, 3, 1, 22},
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{2, 12, 5, 1, 16},
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{2, 13, 1, 4, 27},
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{2, 13, 1, 8, 31},
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{2, 13, 3, 0, 22},
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{2, 13, 5, 0, 16},
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{2, 1, 6, 10, 26},
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{2, 1, 6, 2, 16},
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{2, 1, 8, 2, 22},
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{2, 2, 2, 1, 20},
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{2, 2, 3, 1, 14},
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{2, 2, 6, 1, 30},
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{2, 2, 7, 1, 26},
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{2, 2, 8, 1, 15},
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{2, 3, 2, 0, 20},
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{2, 3, 3, 0, 14},
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{2, 3, 6, 0, 30},
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{2, 3, 7, 0, 26},
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{2, 3, 8, 0, 15},
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{2, 4, 1, 3, -1},
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{2, 5, 1, 2, -1},
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{2, 6, 1, 1, -1},
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{2, 7, 3, 4, -1},
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{2, 8, 3, 3, -1},
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{2, 9, 3, 2, -1},
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{3, 0, 2, 13, 22},
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{3, 0, 2, 3, 32},
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{3, 0, 4, 13, 16},
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{3, 0, 7, 13, 31},
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{3, 10, 4, 5, -1},
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{3, 11, 1, 6, 32},
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{3, 11, 8, 6, -1},
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{3, 1, 2, 12, 22},
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{3, 12, 1, 5, 32},
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{3, 1, 2, 2, 32},
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{3, 12, 8, 5, -1},
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{3, 13, 1, 4, 32},
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{3, 13, 8, 4, -1},
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{3, 1, 4, 12, 16},
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{3, 1, 7, 12, 31},
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{3, 2, 2, 9, -1},
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{3, 3, 2, 8, -1},
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{3, 4, 2, 7, -1},
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{3, 5, 0, 4, -1},
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{3, 6, 0, 3, -1},
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{3, 7, 0, 2, -1},
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{3, 8, 0, 1, -1},
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{3, 9, 4, 6, -1},
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{4, 0, 1, 7, 11},
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{4, 0, 4, 13, 21},
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{4, 0, 7, 13, 10},
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{4, 0, 8, 3, 28},
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{4, 10, 2, 11, 28},
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{4, 10, 6, 11, 19},
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{4, 10, 7, 11, 11},
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{4, 10, 8, 11, 23},
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{4, 11, 2, 10, 28},
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{4, 11, 6, 10, 19},
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{4, 11, 7, 10, 11},
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{4, 11, 8, 10, 23},
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{4, 12, 1, 9, 11},
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{4, 12, 3, 1, 28},
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{4, 12, 4, 1, 23},
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{4, 12, 7, 1, 19},
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{4, 13, 1, 8, 11},
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{4, 13, 3, 0, 28},
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{4, 13, 4, 0, 23},
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{4, 13, 7, 0, 19},
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{4, 1, 4, 12, 21},
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{4, 1, 7, 10, 32},
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{4, 1, 7, 12, 10},
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{4, 1, 8, 2, 28},
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{4, 2, 1, 9, 32},
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{4, 2, 8, 9, -1},
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{4, 3, 1, 8, 32},
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{4, 3, 8, 8, -1},
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{4, 4, 1, 7, 32},
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{4, 4, 8, 7, -1},
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{4, 5, 3, 10, -1},
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{4, 6, 3, 9, -1},
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{4, 7, 5, 4, -1},
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{4, 8, 5, 3, -1},
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{4, 9, 5, 2, -1},
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{5, 0, 2, 13, 28},
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{5, 0, 6, 13, 19},
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{5, 0, 7, 13, 11},
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{5, 0, 8, 13, 23},
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{5, 10, 7, 5, -1},
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{5, 11, 6, 6, -1},
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{5, 1, 2, 12, 28},
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{5, 12, 6, 5, -1},
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{5, 13, 6, 4, -1},
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{5, 1, 6, 12, 19},
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{5, 1, 7, 12, 11},
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{5, 1, 8, 12, 23},
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{5, 2, 4, 9, -1},
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{5, 3, 4, 8, -1},
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{5, 4, 4, 7, -1},
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{5, 5, 0, 0, -1},
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{5, 6, 0, 13, -1},
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{5, 7, 0, 12, -1},
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{5, 8, 0, 11, -1},
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{5, 9, 7, 6, -1},
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{6, 0, 1, 7, 17},
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{6, 0, 2, 3, 12},
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{6, 0, 6, 3, 24},
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{6, 10, 2, 1, 18},
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{6, 10, 4, 11, 24},
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{6, 10, 6, 1, 29},
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{6, 10, 7, 11, 17},
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{6, 10, 8, 1, 13},
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{6, 11, 1, 6, 12},
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{6, 11, 4, 10, 24},
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{6, 11, 7, 10, 17},
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{6, 12, 1, 5, 12},
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{6, 12, 1, 9, 17},
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{6, 1, 2, 2, 12},
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{6, 12, 5, 1, 24},
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{6, 13, 1, 4, 12},
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{6, 13, 1, 8, 17},
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{6, 13, 5, 0, 24},
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{6, 1, 6, 10, 11},
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{6, 1, 6, 2, 24},
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{6, 2, 2, 1, 28},
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{6, 2, 6, 1, 19},
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{6, 2, 7, 1, 11},
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{6, 2, 8, 1, 23},
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{6, 3, 2, 0, 28},
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{6, 3, 6, 0, 19},
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{6, 3, 7, 0, 11},
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{6, 3, 8, 0, 23},
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{6, 4, 5, 13, -1},
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{6, 5, 5, 12, -1},
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{6, 6, 5, 11, -1},
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{6, 7, 7, 4, -1},
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{6, 8, 7, 3, -1},
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{6, 9, 7, 2, -1},
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{7, 0, 2, 3, 18},
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{7, 0, 4, 13, 24},
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{7, 0, 6, 3, 29},
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{7, 0, 7, 13, 17},
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{7, 0, 8, 3, 13},
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{7, 10, 2, 11, 13},
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{7, 10, 4, 11, 29},
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{7, 10, 4, 1, 14},
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{7, 10, 6, 11, 25},
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{7, 10, 8, 11, 9},
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{7, 11, 1, 6, 18},
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{7, 11, 2, 10, 13},
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{7, 11, 4, 10, 29},
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{7, 11, 6, 10, 25},
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{7, 11, 8, 10, 9},
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{7, 12, 1, 5, 18},
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{7, 1, 2, 2, 18},
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{7, 12, 3, 1, 13},
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{7, 12, 4, 1, 9},
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{7, 12, 5, 1, 29},
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{7, 12, 7, 1, 25},
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{7, 13, 1, 4, 18},
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{7, 13, 3, 0, 13},
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{7, 13, 4, 0, 9},
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{7, 13, 5, 0, 29},
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{7, 13, 7, 0, 25},
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{7, 1, 4, 12, 24},
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{7, 1, 6, 2, 29},
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{7, 1, 7, 12, 17},
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{7, 1, 8, 2, 13},
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{7, 2, 6, 9, -1},
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{7, 3, 6, 8, -1},
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{7, 4, 6, 7, -1},
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{7, 5, 5, 10, -1},
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{7, 6, 5, 9, -1},
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{7, 7, 0, 10, -1},
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{7, 8, 0, 9, -1},
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{7, 9, 1, 10, -1},
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{8, 0, 1, 7, 10},
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{8, 0, 2, 3, 33},
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{8, 0, 6, 3, 21},
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{8, 10, 4, 11, 21},
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{8, 10, 7, 11, 10},
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{8, 10, 8, 1, 28},
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{8, 11, 1, 6, 33},
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{8, 11, 4, 10, 21},
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{8, 11, 7, 10, 10},
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{8, 12, 1, 5, 33},
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{8, 12, 1, 9, 10},
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{8, 1, 2, 2, 33},
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{8, 12, 5, 1, 21},
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{8, 13, 1, 4, 33},
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{8, 13, 1, 8, 10},
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{8, 13, 5, 0, 21},
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{8, 1, 6, 10, 31},
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{8, 1, 6, 2, 21},
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{8, 1, 8, 10, 16},
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{8, 2, 2, 1, 22},
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{8, 2, 4, 1, 16},
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{8, 2, 7, 1, 31},
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{8, 3, 2, 0, 22},
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{8, 3, 4, 0, 16},
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{8, 3, 7, 0, 31},
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{8, 4, 3, 13, -1},
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{8, 5, 3, 12, -1},
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{8, 6, 3, 11, -1},
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{8, 7, 4, 4, -1},
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{8, 8, 4, 3, -1},
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{8, 9, 4, 2, -1},
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};
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vector<rule_recursive> spectre_rules_recursive = { rule_recursive
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{0, 1, 27, -1, 20},
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{0, 1, 9, 18, 10},
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{0, 2, 32, -1, 14},
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{0, 3, 11, -1, 29},
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{0, 3, 9, 32, 10},
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{0, 4, 15, 31, 33},
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{0, 4, 17, -1, 25},
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{0, 4, 9, 27, 10},
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{0, 5, 15, 17, 33},
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{0, 5, 9, 12, 10},
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{0, 6, 15, 11, 33},
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{0, 6, 30, 32, 12},
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{0, 7, 15, 10, 33},
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{0, 7, 9, 33, 10},
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{1, 0, 10, 26, 9},
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{1, 0, 20, -1, 27},
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{1, 1, 21, 17, 23},
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{1, 1, 23, 25, 21},
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{1, 2, 13, -1, 31},
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{1, 2, 21, 11, 23},
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{1, 3, 21, 31, 23},
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{1, 4, 19, 26, 24},
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{1, 4, 22, 31, 22},
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{1, 5, 12, -1, 30},
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{1, 5, 19, 11, 24},
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{1, 5, 22, 17, 22},
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{1, 6, 16, 32, 28},
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{1, 6, 21, 10, 23},
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{1, 6, 22, 11, 22},
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{1, 6, 23, 19, 21},
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{1, 7, 19, 31, 24},
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{1, 7, 22, 10, 22},
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{2, 0, 14, -1, 32},
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{2, 1, 23, 29, 21},
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{2, 1, 31, -1, 13},
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{2, 3, 18, -1, 26},
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{2, 4, 23, 16, 21},
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{2, 5, 10, -1, 9},
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{2, 5, 23, 24, 21},
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{2, 6, 12, -1, 30},
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{2, 7, 23, 21, 21},
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{3, 0, 10, 14, 9},
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{3, 0, 29, -1, 11},
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{3, 1, 23, 13, 21},
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{3, 2, 26, -1, 18},
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{3, 4, 12, -1, 30},
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{3, 4, 19, 14, 24},
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{3, 4, 23, 22, 21},
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{3, 6, 23, 28, 21},
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{3, 6, 31, -1, 13},
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{3, 7, 10, -1, 9},
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{4, 0, 10, 20, 9},
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||||
{4, 0, 25, -1, 17},
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{4, 0, 33, 13, 15},
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{4, 1, 22, 13, 22},
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||||
{4, 1, 24, 18, 19},
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||||
{4, 2, 21, 28, 23},
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{4, 3, 21, 22, 23},
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{4, 3, 24, 32, 19},
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{4, 3, 30, -1, 12},
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{4, 4, 16, 14, 28},
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||||
{4, 4, 19, 20, 24},
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||||
{4, 4, 22, 22, 22},
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||||
{4, 4, 24, 27, 19},
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||||
{4, 4, 28, 32, 16},
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||||
{4, 5, 19, 28, 24},
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||||
{4, 5, 24, 12, 19},
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||||
{4, 5, 28, 18, 16},
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||||
{4, 6, 22, 28, 22},
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||||
{4, 7, 19, 22, 24},
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||||
{4, 7, 24, 33, 19},
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||||
{5, 0, 10, 30, 9},
|
||||
{5, 0, 33, 25, 15},
|
||||
{5, 1, 22, 25, 22},
|
||||
{5, 1, 24, 29, 19},
|
||||
{5, 1, 30, -1, 12},
|
||||
{5, 2, 21, 19, 23},
|
||||
{5, 2, 9, -1, 10},
|
||||
{5, 4, 16, 26, 28},
|
||||
{5, 4, 19, 30, 24},
|
||||
{5, 4, 24, 16, 19},
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||||
{5, 5, 16, 11, 28},
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||||
{5, 5, 19, 19, 24},
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||||
{5, 5, 24, 24, 19},
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||||
{5, 5, 28, 29, 16},
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||||
{5, 6, 22, 19, 22},
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||||
{5, 7, 16, 31, 28},
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||||
{5, 7, 24, 21, 19},
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||||
{6, 0, 12, 14, 30},
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||||
{6, 0, 33, 29, 15},
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||||
{6, 1, 21, 24, 23},
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||||
{6, 1, 22, 29, 22},
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||||
{6, 1, 23, 9, 21},
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||||
{6, 1, 28, 14, 16},
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||||
{6, 2, 30, -1, 12},
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||||
{6, 3, 13, -1, 31},
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||||
{6, 3, 21, 16, 23},
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||||
{6, 4, 22, 16, 22},
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||||
{6, 5, 22, 24, 22},
|
||||
{6, 6, 21, 21, 23},
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||||
{6, 6, 23, 23, 21},
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||||
{6, 7, 12, -1, 30},
|
||||
{6, 7, 19, 16, 24},
|
||||
{6, 7, 22, 21, 22},
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||||
{7, 0, 10, 15, 9},
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||||
{7, 0, 33, 9, 15},
|
||||
{7, 1, 22, 9, 22},
|
||||
{7, 1, 24, 13, 19},
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||||
{7, 2, 21, 23, 23},
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||||
{7, 3, 9, -1, 10},
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||||
{7, 4, 19, 15, 24},
|
||||
{7, 4, 24, 22, 19},
|
||||
{7, 5, 19, 23, 24},
|
||||
{7, 5, 28, 13, 16},
|
||||
{7, 6, 22, 23, 22},
|
||||
{7, 6, 24, 28, 19},
|
||||
{7, 6, 30, -1, 12},
|
||||
{7, 7, 16, 16, 28},
|
||||
{7, 7, 28, 28, 16},
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||||
};
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|
||||
EX ld hat_param = 1;
|
||||
EX ld hat_param_imag = 0;
|
||||
|
||||
@@ -390,6 +789,8 @@ struct hrmap_hat : hrmap {
|
||||
// always generate the same way
|
||||
std::mt19937 hatrng;
|
||||
|
||||
bool is_spectre;
|
||||
|
||||
int hatrand(int i) {
|
||||
return hatrng() % i;
|
||||
}
|
||||
@@ -412,6 +813,9 @@ struct hrmap_hat : hrmap {
|
||||
memo_matrix adj_memo[2][2][14][14];
|
||||
vector<vector<memo_matrix>> long_transformations;
|
||||
|
||||
vector<rule_base> get_rules_base() { return is_spectre ? spectre_rules_base : rules_base; }
|
||||
vector<rule_recursive> get_rules_recursive() { return is_spectre ? spectre_rules_recursive : rules_recursive; }
|
||||
|
||||
void fill_transform_levels(int lev) {
|
||||
int clev = isize(long_transformations);
|
||||
while(clev <= lev) {
|
||||
@@ -439,11 +843,11 @@ struct hrmap_hat : hrmap {
|
||||
else unknown++;
|
||||
};
|
||||
|
||||
if(clev == 1) for(auto& b: rules_base) {
|
||||
if(clev == 1) for(auto& b: get_rules_base()) {
|
||||
products_equal(lt[0][b.id0+1], adj2(b.id0==0, fix(b.edge0), b.id1==0, fix(b.edge1)), lt[1][b.master_connection+1], lt[0][b.id1+1]);
|
||||
}
|
||||
|
||||
if(clev >= 2) for(auto& b: rules_recursive) {
|
||||
if(clev >= 2) for(auto& b: get_rules_recursive()) {
|
||||
products_equal(lt[clev][b.id0+1], lt[clev-1][b.child+1], lt[clev][b.parent+1], lt[clev][b.id1+1]);
|
||||
}
|
||||
|
||||
@@ -464,6 +868,8 @@ struct hrmap_hat : hrmap {
|
||||
|
||||
void init() {
|
||||
|
||||
relations = 34;
|
||||
|
||||
transmatrix T = Id;
|
||||
auto& hc = hatcorners[0];
|
||||
hc.clear();
|
||||
@@ -535,14 +941,22 @@ struct hrmap_hat : hrmap {
|
||||
for(auto& h: hc) h = gpushxto0(ctr) * h;
|
||||
};
|
||||
|
||||
if(hat_param_imag) {
|
||||
if(is_spectre) {
|
||||
println(hlog, "eshort = ", eshort, " elong = ", elong);
|
||||
swap(eshort, elong);
|
||||
swap(eshorti, elongi);
|
||||
hat(hatcorners[1]);
|
||||
}
|
||||
else if(hat_param_imag) {
|
||||
eshorti *= -1;
|
||||
elongi *= -1;
|
||||
hat(hatcorners[1]);
|
||||
}
|
||||
else hatcorners[1] = hc;
|
||||
for(auto& h: hc) h = MirrorX * h;
|
||||
reverse(hatcorners[1].begin(), hatcorners[1].end());
|
||||
if(!is_spectre) {
|
||||
for(auto& h: hc) h = MirrorX * h;
|
||||
reverse(hatcorners[1].begin(), hatcorners[1].end());
|
||||
}
|
||||
|
||||
if(q == 6) {
|
||||
ld phi = (1 + sqrt(5)) / 2;
|
||||
@@ -577,7 +991,7 @@ struct hrmap_hat : hrmap {
|
||||
long_transformations.clear();
|
||||
}
|
||||
|
||||
constexpr static int relations = 34;
|
||||
int relations;
|
||||
|
||||
// heptagons represent clusters
|
||||
// heptagon->distance is 0 for clusters of hats, d+1 for supercluster of heptagon d
|
||||
@@ -622,7 +1036,7 @@ struct hrmap_hat : hrmap {
|
||||
}
|
||||
return h1;
|
||||
}
|
||||
if(dir <= 7 - h->zebraval) {
|
||||
if(dir <= (is_spectre ? 8 : 7) - h->zebraval) {
|
||||
// create child
|
||||
auto h1 = init_heptagon(relations);
|
||||
h1->distance = h->distance - 1;
|
||||
@@ -635,11 +1049,13 @@ struct hrmap_hat : hrmap {
|
||||
createStep(h, 0);
|
||||
int id = h->c.spin(0)-1;
|
||||
indenter ind(2);
|
||||
for(auto& ru: rules_recursive) {
|
||||
if(ru.id0 == id && ru.child == dir) {
|
||||
for(auto& ru: get_rules_recursive()) {
|
||||
int i0 = ru.id0, i1 = ru.id1;
|
||||
if((h->distance & 1) && is_spectre) swap(i0, i1);
|
||||
if(i0 == id && ru.child == dir) {
|
||||
heptagon *h1 = get_step(h->move(0), ru.parent);
|
||||
if(!h1) continue;
|
||||
heptagon *h2 = get_step(h1, ru.id1+1);
|
||||
heptagon *h2 = get_step(h1, i1+1);
|
||||
if(!h2) continue;
|
||||
h->c.connect(dir, h2, ru.rev_child, false);
|
||||
return h2;
|
||||
@@ -662,7 +1078,7 @@ struct hrmap_hat : hrmap {
|
||||
void find_cell_connection(cell *c, int d) override {
|
||||
int id = hat_id(c);
|
||||
indenter ind(2);
|
||||
for(auto& ru: rules_base) {
|
||||
for(auto& ru: get_rules_base()) {
|
||||
if(ru.id0 == id && ru.edge0 == fix(d)) {
|
||||
heptagon *h = get_step(c->master, ru.master_connection);
|
||||
if(!h) continue;
|
||||
@@ -728,12 +1144,13 @@ struct hrmap_hat : hrmap {
|
||||
void build_cells(heptagon *h) {
|
||||
if(h->c7) return;
|
||||
auto& ha = hats[h];
|
||||
ha.resize(8 - h->zebraval);
|
||||
ha.resize((is_spectre ? 9 : 8) - h->zebraval);
|
||||
for(auto& hac: ha) hac = newCell(isize(hatcorners[0]), h);
|
||||
h->c7 = ha[0];
|
||||
}
|
||||
|
||||
hrmap_hat() {
|
||||
is_spectre = geometry == gAperiodicSpectre;
|
||||
hatrng.seed(37);
|
||||
init();
|
||||
origin = init_heptagon(relations);
|
||||
|
||||
Reference in New Issue
Block a user