1 | include "basics/types.ma". |
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2 | include "basics/list.ma". |
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3 | include "common/Graphs.ma". |
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4 | include "common/Registers.ma". |
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5 | |
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6 | include "utilities/adt/table_adt.ma". |
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7 | include "utilities/adt/priority_set_adt.ma". |
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8 | include "utilities/adt/set_adt.ma". |
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9 | include "utilities/adt/set_table_adt.ma". |
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10 | include "utilities/adt/register_table.ma". |
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11 | |
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12 | definition vertex_set ≝ set vertex. |
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13 | definition vertex_priority_set ≝ priority_set vertex. |
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14 | definition vertex_set_table ≝ set_table vertex (set vertex). |
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15 | definition Register_set_table ≝ set_table vertex (set Register). |
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16 | definition Register_set ≝ set Register. |
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17 | |
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18 | record graph: Type[0] ≝ |
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19 | { |
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20 | ig_regmap : register_table; |
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21 | ig_ivv : vertex_set_table; |
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22 | ig_ivh : Register_set_table; |
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23 | ig_pvv : vertex_set; |
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24 | ig_pvh : Register_set; |
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25 | ig_degree : vertex_priority_set; |
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26 | ig_nmr : vertex_priority_set |
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27 | }. |
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28 | |
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29 | definition set_ivv ≝ |
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30 | λgraph. |
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31 | λivv: vertex_set_table. |
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32 | let regmap ≝ ig_regmap graph in |
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33 | let ivh ≝ ig_ivh graph in |
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34 | let pvv ≝ ig_pvv graph in |
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35 | let pvh ≝ ig_pvh graph in |
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36 | let degree ≝ ig_degree graph in |
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37 | let nmr ≝ ig_nmr graph in |
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38 | mk_graph |
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39 | regmap ivv ivh pvv pvh degree nmr. |
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40 | |
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41 | definition set_ivh ≝ |
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42 | λgraph. |
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43 | λivh: Register_set_table. |
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44 | let regmap ≝ ig_regmap graph in |
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45 | let ivv ≝ ig_ivv graph in |
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46 | let pvv ≝ ig_pvv graph in |
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47 | let pvh ≝ ig_pvh graph in |
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48 | let degree ≝ ig_degree graph in |
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49 | let nmr ≝ ig_nmr graph in |
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50 | mk_graph |
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51 | regmap ivv ivh pvv pvh degree nmr. |
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52 | |
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53 | definition set_degree ≝ |
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54 | λgraph. |
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55 | λdegree: vertex_priority_set. |
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56 | let regmap ≝ ig_regmap graph in |
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57 | let ivv ≝ ig_ivv graph in |
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58 | let ivh ≝ ig_ivh graph in |
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59 | let pvv ≝ ig_pvv graph in |
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60 | let pvh ≝ ig_pvh graph in |
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61 | let nmr ≝ ig_nmr graph in |
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62 | mk_graph |
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63 | regmap ivv ivh pvv pvh degree nmr. |
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64 | |
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65 | definition set_nmr ≝ |
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66 | λgraph. |
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67 | λnmr: vertex_priority_set. |
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68 | let regmap ≝ ig_regmap graph in |
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69 | let ivv ≝ ig_ivv graph in |
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70 | let ivh ≝ ig_ivh graph in |
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71 | let pvv ≝ ig_pvv graph in |
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72 | let pvh ≝ ig_pvh graph in |
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73 | let degree ≝ ig_degree graph in |
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74 | mk_graph |
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75 | regmap ivv ivh pvv pvh degree nmr. |
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76 | |
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77 | definition sg_neighboursv ≝ |
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78 | λgraph: graph. |
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79 | λv: vertex. |
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80 | set_tbl_find … v (ig_ivv graph). |
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81 | |
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82 | definition sg_existsvv ≝ |
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83 | λgraph. |
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84 | λv1. |
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85 | λv2. |
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86 | match sg_neighboursv graph v2 with |
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87 | [ None ⇒ false (* XXX: ok? *) |
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88 | | Some neigh ⇒ set_member ? v1 neigh |
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89 | ]. |
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90 | |
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91 | definition sg_neighboursh ≝ |
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92 | λgraph. |
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93 | λv. |
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94 | set_tbl_find ? ? v (ig_ivh graph). |
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95 | |
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96 | definition sg_existsvh ≝ |
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97 | λgraph. |
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98 | λv. |
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99 | λh. |
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100 | match sg_neighboursh graph v with |
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101 | [ None ⇒ false (* XXX: ok? *) |
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102 | | Some neigh ⇒ set_member ? h neigh |
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103 | ]. |
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104 | |
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105 | definition sg_degree ≝ |
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106 | λgraph. |
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107 | λv. |
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108 | match sg_neighboursv graph v with |
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109 | [ None ⇒ None ? |
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110 | | Some neigh ⇒ |
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111 | match sg_neighboursh graph v with |
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112 | [ None ⇒ None ? |
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113 | | Some neigh' ⇒ Some ? ((set_size … neigh) + (set_size … neigh')) |
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114 | ] |
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115 | ]. |
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116 | |
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117 | definition sg_hwregs ≝ |
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118 | λgraph: graph. |
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119 | let union ≝ λkey: vertex. set_union ? in |
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120 | set_tbl_fold vertex ? ? union (ig_ivh graph) (set_empty Register). |
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121 | |
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122 | axiom sg_iter: Type[0]. (* XXX: todo when i can be bothered *) |
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123 | |
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124 | definition sg_mkvvi ≝ |
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125 | λgraph. |
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126 | λv1. |
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127 | λv2. |
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128 | set_ivv graph (set_tbl_homo_mkbiedge … v1 v2 (ig_ivv graph)). |
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129 | |
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130 | definition sg_mkvv ≝ |
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131 | λgraph. |
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132 | λv1. |
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133 | λv2. |
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134 | if eq_nat v1 v2 then |
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135 | graph |
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136 | else if sg_existsvv graph v1 v2 then |
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137 | graph |
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138 | else |
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139 | sg_mkvvi graph v1 v2. |
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140 | |
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141 | definition sg_rmvv ≝ |
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142 | λgraph. |
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143 | λv1. |
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144 | λv2. |
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145 | set_ivv graph (set_tbl_homo_rmbiedge … v1 v2 (ig_ivv graph)). |
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146 | |
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147 | definition sg_rmvvifx ≝ |
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148 | λgraph. |
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149 | λv1. |
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150 | λv2. |
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151 | if sg_existsvv graph v1 v2 then |
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152 | sg_rmvv graph v1 v2 |
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153 | else |
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154 | graph. |
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155 | |
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156 | definition sg_mkvhi ≝ |
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157 | λgraph. |
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158 | λv. |
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159 | λh. |
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160 | set_ivh graph (set_tbl_update … v (set_insert … h) (ig_ivh graph)). |
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161 | |
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162 | definition sg_mkvh ≝ |
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163 | λgraph. |
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164 | λv. |
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165 | λh. |
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166 | if sg_existsvh graph v h then |
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167 | graph |
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168 | else |
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169 | sg_mkvhi graph v h. |
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170 | |
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171 | definition sg_rmvh ≝ |
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172 | λgraph. |
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173 | λv. |
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174 | λh. |
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175 | set_ivh graph (set_tbl_update … v (set_remove … h) (ig_ivh graph)). |
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176 | |
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177 | definition sg_rmvhifx ≝ |
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178 | λgraph. |
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179 | λv. |
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180 | λh. |
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181 | if sg_existsvh graph v h then |
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182 | sg_rmvh graph v h |
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183 | else |
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184 | graph. |
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185 | |
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186 | definition sg_coalesce ≝ |
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187 | λg. |
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188 | λx. |
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189 | λy. |
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190 | match sg_neighboursv g x with |
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191 | [ None ⇒ None ? |
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192 | | Some neigh ⇒ |
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193 | let graph ≝ set_fold ? graph (λw. λg. |
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194 | sg_mkvv (sg_rmvv g x w) y w) neigh g |
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195 | in |
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196 | match sg_neighboursh g x with |
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197 | [ None ⇒ None ? |
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198 | | Some neigh ⇒ |
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199 | let graph ≝ set_fold ? ? (λh. λg. |
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200 | sg_mkvh (sg_rmvh g x h) y h) neigh g |
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201 | in |
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202 | Some … graph |
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203 | ] |
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204 | ]. |
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205 | |
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206 | definition sg_coalesceh ≝ |
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207 | λg. |
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208 | λx. |
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209 | λh. |
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210 | match sg_neighboursv g x with |
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211 | [ None ⇒ None ? |
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212 | | Some neigh ⇒ |
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213 | let graph ≝ set_fold ? graph (λw. λg. |
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214 | sg_mkvh (sg_rmvv g x w) w h) neigh g |
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215 | in |
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216 | match sg_neighboursh g x with |
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217 | [ None ⇒ None ? |
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218 | | Some neigh ⇒ |
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219 | let graph ≝ set_fold ? ? (λk. λg. |
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220 | sg_rmvh graph x k) neigh g |
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221 | in |
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222 | Some … graph |
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223 | ] |
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224 | ]. |
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225 | |
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226 | definition sg_remove ≝ |
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227 | λg. |
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228 | λx. |
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229 | match sg_neighboursv g x with |
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230 | [ None ⇒ None ? |
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231 | | Some neigh ⇒ |
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232 | let graph ≝ |
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233 | set_fold … (λw. λgraph. |
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234 | sg_rmvv graph x w) neigh g |
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235 | in |
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236 | match sg_neighboursh graph x with |
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237 | [ None ⇒ None ? |
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238 | | Some neigh ⇒ |
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239 | let graph ≝ set_fold … (λh. λg. |
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240 | sg_rmvh g x h) neigh graph |
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241 | in |
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242 | Some ? graph |
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243 | ] |
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244 | ]. |
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245 | |
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246 | definition ig_mkvvi ≝ |
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247 | λgraph. |
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248 | λv1. |
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249 | λv2. |
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250 | let graph ≝ sg_mkvvi graph v1 v2 in |
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251 | let graph ≝ sg_rmvvifx graph v1 v2 in |
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252 | let degree' ≝ pset_increment ? v1 (repr 1) (pset_increment ? v2 (repr 1) (ig_degree graph)) in |
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253 | let nmr' ≝ pset_incrementifx ? v1 (repr 1) (pset_incrementifx ? v2 (repr 1) (ig_nmr graph)) in |
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254 | set_degree (set_nmr graph nmr') degree'. |
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255 | |
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256 | definition ig_rmvv ≝ |
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257 | λgraph. |
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258 | λv1. |
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259 | λv2. |
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260 | let graph ≝ sg_rmvv graph v1 v2 in |
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261 | let degree' ≝ pset_increment ? v1 (neg (repr 1)) (pset_increment ? v2 (neg (repr 1)) (ig_degree graph)) in |
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262 | let nmr' ≝ pset_incrementifx ? v1 (neg (repr 1)) (pset_incrementifx ? v2 (neg (repr 1)) (ig_nmr graph)) in |
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263 | set_degree (set_nmr graph nmr') degree'. |
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264 | |
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265 | definition ig_mkvhi ≝ |
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266 | λgraph. |
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267 | λv. |
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268 | λh. |
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269 | let graph ≝ sg_mkvhi graph v h in |
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270 | let graph ≝ sg_rmvhifx graph v h in |
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271 | let degree ≝ pset_increment ? v (repr 1) (ig_degree graph) in |
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272 | let nmr ≝ pset_incrementifx ? v (repr 1) (ig_nmr graph) in |
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273 | set_degree (set_nmr graph nmr) degree. |
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274 | |
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275 | definition ig_rmvh ≝ |
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276 | λgraph. |
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277 | λv. |
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278 | λh. |
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279 | let graph ≝ sg_rmvh graph v h in |
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280 | let degree ≝ pset_increment ? v (neg (repr 1)) (ig_degree graph) in |
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281 | let nmr ≝ pset_incrementifx ? v (neg (repr 1)) (ig_nmr graph) in |
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282 | set_degree (set_nmr graph nmr) degree. |
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283 | |
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284 | definition pref_nmr ≝ |
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285 | λgraph. |
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286 | λv. |
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287 | match sg_neighboursv graph v with |
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288 | [ None ⇒ false (* XXX: ok? *) |
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289 | | Some neigh ⇒ |
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290 | match sg_neighboursh graph v with |
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291 | [ None ⇒ false |
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292 | | Some neigh' ⇒ |
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293 | andb (set_is_empty ? neigh) (set_is_empty ? neigh') |
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294 | ] |
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295 | ]. |
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296 | |
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297 | definition pref_mkcheck ≝ |
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298 | λgraph. |
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299 | λv. |
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300 | if pref_nmr graph v then |
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301 | let nmr' ≝ pset_remove ? v (ig_nmr graph) in |
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302 | set_nmr graph nmr' |
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303 | else |
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304 | graph. |
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305 | |
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306 | definition pref_mkvvi ≝ |
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307 | λgraph. |
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308 | λv1. |
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309 | λv2. |
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310 | if sg_existsvv graph v1 v2 then |
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311 | graph |
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312 | else |
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313 | let graph ≝ pref_mkcheck graph v1 in |
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314 | let graph ≝ pref_mkcheck graph v2 in |
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315 | sg_mkvvi graph v1 v2. |
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316 | |
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317 | definition pref_mkvhi ≝ |
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318 | λgraph. |
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319 | λv. |
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320 | λh. |
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321 | if sg_existsvh graph v h then |
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322 | graph |
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323 | else |
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324 | let graph ≝ pref_mkcheck graph v in |
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325 | sg_mkvhi graph v h. |
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326 | |
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327 | (* XXX: look at this carefully *) |
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328 | definition pref_rmcheck ≝ |
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329 | λgraph. |
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330 | λv. |
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331 | if pref_nmr graph v then |
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332 | match pset_lookup ? v (ig_degree graph) with |
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333 | [ None ⇒ graph (* XXX: ok? *) |
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334 | | Some pref ⇒ |
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335 | let nmr ≝ pset_insert ? v pref (ig_nmr graph) in |
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336 | set_nmr graph nmr |
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337 | ] |
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338 | else |
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339 | graph. |
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340 | |
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341 | definition pref_rmvv ≝ |
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342 | λgraph. |
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343 | λv1. |
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344 | λv2. |
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345 | let graph ≝ sg_rmvv graph v1 v2 in |
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346 | let graph ≝ pref_rmcheck graph v1 in |
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347 | let graph ≝ pref_rmcheck graph v2 in |
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348 | graph. |
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349 | |
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350 | definition pref_rmvh ≝ |
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351 | λgraph. |
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352 | λv. |
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353 | λh. |
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354 | let graph ≝ sg_rmvh graph v h in |
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355 | let graph ≝ pref_rmcheck graph v in |
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356 | graph. |
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357 | |
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358 | |
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359 | |
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360 | definition ig_create ≝ |
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361 | λregs. |
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362 | let 〈ignore_int, table'', priority''〉 ≝ |
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363 | foldr … (λr. λv_table_priority'. |
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364 | let 〈v, table', priority'〉 ≝ v_table_priority' in |
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365 | let table'' ≝ rt_add r v table' in |
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366 | let priority'' ≝ ps_insert ? v 0 priority' in |
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367 | 〈v + 1, table'', priority''〉) 〈0, rt_empty …, ps_empty …〉 regs |
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368 | in |
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369 | mk_graph table'' (set_tbl_empty …) (set_tbl_empty …) (set_empty …) |
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370 | (set_empty …) priority'' priority''. |
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371 | |
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372 | |
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373 | |
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374 | definition ig_mkipp ≝ |
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375 | λset_impl. |
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376 | λgraph: interference_graph set_impl. |
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377 | λregs1. |
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378 | λregs2. |
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379 | set_fold … (ig_Reg_set … graph) (λr1. λgraph. |
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380 | let v1 ≝ lookup … graph r1 in |
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381 | set_fold … (ig_Reg_set … graph) (λr2. λgraph. |
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382 | ig_mkvv … |
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383 | |
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384 | let mkipp graph regs1 regs2 = |
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385 | Register.Set.fold (fun r1 graph -> |
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386 | let v1 = lookup graph r1 in |
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387 | Register.Set.fold (fun r2 graph -> |
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388 | interference#mkvv graph v1 (lookup graph r2) |
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389 | ) regs2 graph |
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390 | ) regs1 graph |
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391 | |
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392 | axiom ig_mkiph: graph → list register → list Register → |
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393 | graph. |
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394 | |
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395 | definition ig_mki: graph → (list register) × (list Register) → |
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396 | (list register) × (list Register) → graph ≝ |
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397 | λgraph. |
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398 | λregs1_hwregs1. |
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399 | λregs2_hwregs2. |
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400 | let 〈regs1, hwregs1〉 ≝ regs1_hwregs1 in |
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401 | let 〈regs2, hwregs2〉 ≝ regs2_hwregs2 in |
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402 | let graph ≝ ig_mkipp graph regs1 regs2 in |
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403 | let graph ≝ ig_mkiph graph regs1 hwregs2 in |
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404 | let graph ≝ ig_mkiph graph regs2 hwregs1 in |
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405 | graph. |
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406 | |
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407 | axiom ig_mkppp: interference_graph → register → register → interference_graph. |
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408 | axiom ig_mkpph: interference_graph → register → Register → interference_graph. |
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409 | axiom ig_coalesce: interference_graph → vertex → vertex → interference_graph. |
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410 | axiom ig_coalesceh: interference_graph → vertex → Register → interference_graph. |
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411 | axiom ig_remove: interference_graph → vertex → interference_graph. |
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412 | axiom ig_freeze: interference_graph → vertex → interference_graph. |
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413 | axiom ig_restrict: interference_graph → (vertex → bool) → interference_graph. |
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414 | axiom ig_droph: interference_graph → interference_graph. |
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415 | axiom ig_lookup: interference_graph → register → vertex. |
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416 | axiom ig_registers: interference_graph → vertex → list register. |
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417 | axiom ig_degree: interference_graph → vertex → nat. |
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418 | axiom ig_lowest: interference_graph → option (vertex × nat). |
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419 | axiom ig_lowest_non_move_related: interference_graph → option (vertex × nat). |
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420 | axiom ig_minimum: ∀A: Type[0]. ∀ord: A → A → order. (vertex → A) → |
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421 | interference_graph → option vertex. |
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422 | axiom ig_fold: ∀A: Type[0]. (vertex → A → A) → interference_graph → A → A. |
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423 | axiom ig_ipp: interference_graph → vertex → vertex_set. |
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424 | axiom ig_iph: interference_graph → vertex → list Register. |
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425 | axiom ig_ppp: interference_graph → vertex → vertex_set. |
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426 | axiom ig_pph: interference_graph → vertex → list Register. |
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427 | definition ig_ppedge ≝ vertex × vertex. |
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428 | axiom ig_pppick: interference_graph → (ig_ppedge → bool) → option ig_ppedge. |
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429 | definition ig_phedge ≝ vertex × Register. |
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430 | axiom ig_phpick: interference_graph → (ig_phedge → bool) → option ig_phedge. |
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