1 | (* Pasted from Pottier's PP compiler *) |
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2 | |
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3 | (* This module implements a data structure for interference graphs. |
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4 | It provides functions that help construct, transform and inspect |
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5 | interference graphs. *) |
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6 | |
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7 | (* ------------------------------------------------------------------------- *) |
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8 | |
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9 | (* Vertices are represented as integers. We need sets of vertices, maps over |
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10 | vertices, maps of vertices to nonempty sets of vertices, maps of vertices |
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11 | to nonempty sets of hardware registers, and priority sets over vertices. *) |
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12 | |
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13 | module Vertex = struct |
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14 | |
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15 | module V = struct |
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16 | type t = int |
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17 | let compare = compare |
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18 | end |
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19 | |
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20 | include V |
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21 | |
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22 | module Set = Set.Make(V) |
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23 | |
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24 | module Map = MyMap.Make(V) |
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25 | |
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26 | end |
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27 | |
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28 | module VertexSetMap = |
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29 | SetMap.MakeHomo(Vertex.Set)(Vertex.Map) |
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30 | |
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31 | module I8051RegisterSetMap = |
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32 | SetMap.MakeHetero(I8051.RegisterSet)(Vertex.Map) |
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33 | |
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34 | module PrioritySet = |
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35 | PrioritySet.Make(Vertex) |
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36 | |
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37 | (* ------------------------------------------------------------------------- *) |
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38 | |
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39 | (* Each vertex maps to a set of pseudo-registers, which initially is a |
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40 | singleton set, but can grow due to coalescing. Conversely, each |
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41 | pseudo-register maps to a single vertex. *) |
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42 | |
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43 | module RegMap : sig |
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44 | |
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45 | type t |
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46 | |
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47 | (* [empty] is the empty map. *) |
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48 | |
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49 | val empty: t |
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50 | |
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51 | (* [forward] maps a vertex to a set of pseudo-registers. *) |
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52 | |
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53 | val forward: Vertex.t -> t -> Register.Set.t |
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54 | |
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55 | (* [backward] maps a pseudo-register to a vertex. *) |
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56 | |
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57 | val backward: Register.t -> t -> Vertex.t |
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58 | |
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59 | (* [add r v m] adds a relation between pseudo-register [r] and |
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60 | vertex [v], both of which are assumed fresh. *) |
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61 | |
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62 | val add: Register.t -> Vertex.t -> t -> t |
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63 | |
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64 | (* [fold f m accu] folds over all vertices. *) |
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65 | |
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66 | val fold: (Vertex.t -> Register.Set.t -> 'a -> 'a) -> t -> 'a -> 'a |
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67 | |
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68 | (* [coalesce x y m] coalesces vertices [x] and [y]. Vertex [x] is |
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69 | removed and the pseudo-registers associated with it become |
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70 | associated with [y] instead. *) |
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71 | |
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72 | val coalesce: Vertex.t -> Vertex.t -> t -> t |
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73 | |
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74 | (* [remove x m] removes vertex [x]. The pseudo-registers associated |
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75 | with [x] disappear. *) |
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76 | |
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77 | val remove: Vertex.t -> t -> t |
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78 | |
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79 | (* [restrict] keeps only those vertices that satisfy predicate [p]. *) |
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80 | |
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81 | val restrict: (Vertex.t -> bool) -> t -> t |
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82 | |
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83 | end = struct |
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84 | |
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85 | type t = { |
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86 | forward: Register.Set.t Vertex.Map.t; |
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87 | backward: Vertex.t Register.Map.t |
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88 | } |
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89 | |
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90 | let empty = { |
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91 | forward = Vertex.Map.empty; |
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92 | backward = Register.Map.empty |
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93 | } |
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94 | |
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95 | let forward v m = |
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96 | Vertex.Map.find v m.forward |
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97 | |
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98 | let backward r m = |
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99 | try |
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100 | Register.Map.find r m.backward |
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101 | with Not_found -> |
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102 | assert false (* bad pseudo-register *) |
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103 | |
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104 | let add r v m = { |
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105 | forward = Vertex.Map.add v (Register.Set.singleton r) m.forward; |
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106 | backward = Register.Map.add r v m.backward |
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107 | } |
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108 | |
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109 | let fold f m accu = |
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110 | Vertex.Map.fold f m.forward accu |
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111 | |
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112 | let coalesce x y m = |
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113 | let rx, forward = Vertex.Map.find_remove x m.forward in |
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114 | let forward = Vertex.Map.update y (Register.Set.union rx) forward in |
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115 | let backward = |
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116 | Register.Set.fold (fun r backward -> |
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117 | Register.Map.add r y backward |
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118 | ) rx m.backward |
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119 | in |
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120 | { |
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121 | forward = forward; |
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122 | backward = backward |
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123 | } |
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124 | |
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125 | let remove x m = |
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126 | let rx, forward = Vertex.Map.find_remove x m.forward in |
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127 | let backward = Register.Set.fold Register.Map.remove rx m.backward in |
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128 | { |
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129 | forward = forward; |
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130 | backward = backward |
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131 | } |
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132 | |
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133 | let restrict p m = { |
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134 | forward = Vertex.Map.restrict p m.forward; |
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135 | backward = Register.Map.restrict (fun r -> p (backward r m)) m.backward |
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136 | } |
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137 | |
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138 | end |
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139 | |
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140 | (* ------------------------------------------------------------------------- *) |
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141 | |
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142 | (* Graphs. *) |
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143 | |
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144 | type graph = { |
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145 | |
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146 | (* A two-way correspondence between vertices and pseudo-registers. |
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147 | This data structure is also used to keep a record of the set of |
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148 | all vertices. *) |
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149 | |
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150 | regmap: RegMap.t; |
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151 | |
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152 | (* Interference edges between two vertices: ``these two vertices |
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153 | cannot receive the same color''. *) |
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154 | |
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155 | ivv: VertexSetMap.t; |
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156 | |
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157 | (* Interference edges between a vertex and a hardware register: |
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158 | ``this vertex cannot receive this color''. *) |
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159 | |
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160 | ivh: I8051RegisterSetMap.t; |
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161 | |
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162 | (* Preference edges between two vertices: ``these two vertices |
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163 | should preferably receive the same color''. *) |
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164 | |
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165 | pvv: VertexSetMap.t; |
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166 | |
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167 | (* Preference edges between a vertex and a hardware register: |
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168 | ``this vertex should preferably receive this color''. *) |
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169 | |
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170 | pvh: I8051RegisterSetMap.t; |
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171 | |
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172 | (* The degree of each vertex [v], that is, the number of vertices |
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173 | and hardware registers that [v] interferes with, is recorded at |
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174 | all times. We use a ``priority set'' so as to be able to |
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175 | efficiently find a vertex of minimum degree. *) |
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176 | |
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177 | degree: PrioritySet.t; |
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178 | |
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179 | (* The degree of each *non-move-related* vertex [v]. This |
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180 | information is partially redundant with the [degree] field |
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181 | above. It is nevertheless required in order to be able to |
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182 | efficiently find a *non-move-related* vertex of minimum |
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183 | degree. *) |
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184 | |
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185 | nmr: PrioritySet.t; |
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186 | |
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187 | } |
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188 | |
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189 | (* ------------------------------------------------------------------------- *) |
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190 | |
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191 | (* Our graphs are made up of two subgraphs: the subgraph formed by the |
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192 | interference edges alone and the one formed by the preference edges |
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193 | alone. |
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194 | |
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195 | In order to allow more code sharing, we define functions that allow |
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196 | dealing with a single subgraph at a time. They provide operations |
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197 | such as inspecting the neighbors of a vertex, adding edges, |
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198 | removing edges, coalescing two vertices, removing a vertex, etc. |
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199 | |
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200 | We first define functions that deal with a ``generic'' subgraph, |
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201 | then (via inheritance) specialize them to deal with the |
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202 | interference subgraph and the preference subgraph with their |
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203 | specific features. *) |
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204 | |
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205 | class virtual subgraph = object (self) |
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206 | |
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207 | (* These methods provide access to the fields of the [graph] data |
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208 | structure that define the subgraph of interest. All data is |
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209 | stored in the [graph] data structure. The object [self] has no |
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210 | state and holds no data. *) |
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211 | |
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212 | method virtual getvv: graph -> VertexSetMap.t |
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213 | method virtual setvv: graph -> VertexSetMap.t -> graph |
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214 | method virtual getvh: graph -> I8051RegisterSetMap.t |
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215 | method virtual setvh: graph -> I8051RegisterSetMap.t -> graph |
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216 | |
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217 | (* Accessing the neighbors of a vertex and testing whether edges |
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218 | exist. *) |
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219 | |
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220 | method neighborsv graph v = |
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221 | VertexSetMap.find v (self#getvv graph) |
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222 | |
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223 | method existsvv graph v1 v2 = |
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224 | Vertex.Set.mem v1 (self#neighborsv graph v2) |
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225 | |
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226 | method neighborsh graph v = |
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227 | I8051RegisterSetMap.find v (self#getvh graph) |
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228 | |
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229 | method existsvh graph v h = |
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230 | I8051.RegisterSet.mem h (self#neighborsh graph v) |
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231 | |
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232 | (* [degree graph v] is the degree of vertex [v] with respect to the |
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233 | subgraph. *) |
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234 | |
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235 | method degree graph v = |
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236 | Vertex.Set.cardinal (self#neighborsv graph v) + I8051.RegisterSet.cardinal (self#neighborsh graph v) |
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237 | |
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238 | (* [hwregs graph] is the set of all hardware registers mentioned in |
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239 | the subgraph. *) |
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240 | |
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241 | method hwregs graph = |
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242 | let union _ = I8051.RegisterSet.union in |
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243 | Vertex.Map.fold union (self#getvh graph) I8051.RegisterSet.empty |
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244 | |
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245 | (* [iter graph fvv fvh] iterates over all edges in the subgraph. |
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246 | Vertex-to-vertex edges are presented only once. *) |
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247 | |
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248 | method iter graph fvv fvh = |
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249 | Vertex.Map.iter (fun vertex neighbors -> |
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250 | Vertex.Set.iter (fun neighbor -> |
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251 | if vertex < neighbor then |
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252 | fvv vertex neighbor |
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253 | ) neighbors |
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254 | ) (self#getvv graph); |
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255 | Vertex.Map.iter (fun vertex neighbors -> |
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256 | I8051.RegisterSet.iter (fun neighbor -> |
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257 | fvh vertex neighbor |
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258 | ) neighbors |
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259 | ) (self#getvh graph) |
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260 | |
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261 | (* [mkvv graph v1 v2] adds an edge between vertices [v1] and [v2]. *) |
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262 | |
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263 | method mkvv graph v1 v2 = |
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264 | if v1 = v2 then |
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265 | graph (* avoid creating self-edge *) |
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266 | else if self#existsvv graph v1 v2 then |
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267 | graph (* avoid re-adding an existing edge *) |
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268 | else |
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269 | self#mkvvi graph v1 v2 |
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270 | |
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271 | method mkvvi graph v1 v2 = |
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272 | self#setvv graph (VertexSetMap.mkbiedge v1 v2 (self#getvv graph)) |
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273 | |
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274 | (* [rmvv graph v1 v2] removes an edge between vertices [v1] and [v2]. |
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275 | [rmvvifx] removes an edge if it exists. *) |
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276 | |
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277 | method rmvv graph v1 v2 = |
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278 | assert (self#existsvv graph v1 v2); |
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279 | self#setvv graph (VertexSetMap.rmbiedge v1 v2 (self#getvv graph)) |
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280 | |
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281 | method rmvvifx graph v1 v2 = |
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282 | if self#existsvv graph v1 v2 then |
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283 | self#rmvv graph v1 v2 |
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284 | else |
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285 | graph |
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286 | |
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287 | (* [mkvh graph v h] adds an edge between vertex [v] and hardware |
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288 | register [h]. *) |
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289 | |
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290 | method mkvh graph v h = |
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291 | if self#existsvh graph v h then |
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292 | graph (* avoid re-adding an existing edge *) |
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293 | else |
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294 | self#mkvhi graph v h |
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295 | |
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296 | method mkvhi graph v h = |
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297 | self#setvh graph (I8051RegisterSetMap.update v (I8051.RegisterSet.add h) (self#getvh graph)) |
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298 | |
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299 | (* [rmvh v h] removes an edge between vertex [v] and hardware |
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300 | register [h]. [rmvhifx] removes an edge if it exists. *) |
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301 | |
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302 | method rmvh graph v h = |
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303 | assert (self#existsvh graph v h); |
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304 | self#setvh graph (I8051RegisterSetMap.update v (I8051.RegisterSet.remove h) (self#getvh graph)) |
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305 | |
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306 | method rmvhifx graph v h = |
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307 | if self#existsvh graph v h then |
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308 | self#rmvh graph v h |
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309 | else |
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310 | graph |
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311 | |
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312 | (* [coalesce graph x y] turns every neighbor [w] or [h] of [x] into |
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313 | a neighbor of [y] instead. [w] ranges over both vertices and |
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314 | hardware registers. *) |
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315 | |
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316 | method coalesce graph x y = |
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317 | let graph = |
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318 | Vertex.Set.fold (fun w graph -> |
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319 | self#mkvv (self#rmvv graph x w) y w |
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320 | ) (self#neighborsv graph x) graph |
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321 | in |
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322 | let graph = |
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323 | I8051.RegisterSet.fold (fun h graph -> |
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324 | self#mkvh (self#rmvh graph x h) y h |
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325 | ) (self#neighborsh graph x) graph |
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326 | in |
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327 | graph |
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328 | |
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329 | (* [coalesceh graph x h] turns every neighbor [w] of [x] into a |
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330 | neighbor of [h] instead. [w] ranges over both vertices and |
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331 | hardware registers. Edges between two hardware registers are not |
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332 | recorded. *) |
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333 | |
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334 | method coalesceh graph x h = |
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335 | let graph = |
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336 | Vertex.Set.fold (fun w graph -> |
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337 | self#mkvh (self#rmvv graph x w) w h |
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338 | ) (self#neighborsv graph x) graph |
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339 | in |
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340 | let graph = |
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341 | I8051.RegisterSet.fold (fun k graph -> |
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342 | self#rmvh graph x k |
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343 | ) (self#neighborsh graph x) graph |
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344 | in |
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345 | graph |
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346 | |
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347 | (* [remove graph x] removes all edges carried by vertex [x]. *) |
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348 | |
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349 | method remove graph x = |
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350 | let graph = |
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351 | Vertex.Set.fold (fun w graph -> |
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352 | self#rmvv graph x w |
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353 | ) (self#neighborsv graph x) graph |
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354 | in |
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355 | let graph = |
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356 | I8051.RegisterSet.fold (fun h graph -> |
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357 | self#rmvh graph x h |
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358 | ) (self#neighborsh graph x) graph |
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359 | in |
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360 | graph |
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361 | |
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362 | end |
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363 | |
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364 | (* ------------------------------------------------------------------------- *) |
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365 | |
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366 | (* The interference subgraph. |
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367 | |
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368 | This is a subgraph with the following specific features: (1) the |
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369 | degree of every vertex is recorded in the [degree] field of the |
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370 | [graph] data structure; (2) the degree of every non-move-related |
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371 | vertex is recorded in the [nmr] field of the [graph] data |
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372 | structure; (3) creating an edge in the interference subgraph |
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373 | automatically destroys a corresponding edge in the preference |
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374 | subgraph. *) |
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375 | |
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376 | class interference (preference : preference Lazy.t) = object (self) |
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377 | |
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378 | inherit subgraph as super |
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379 | |
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380 | method getvv graph = graph.ivv |
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381 | method setvv graph m = { graph with ivv = m } |
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382 | method getvh graph = graph.ivh |
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383 | method setvh graph m = { graph with ivh = m } |
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384 | |
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385 | (* Override the edge creation and destruction methods. *) |
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386 | |
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387 | method mkvvi graph v1 v2 = |
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388 | let graph = super#mkvvi graph v1 v2 in |
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389 | let graph = (Lazy.force preference)#rmvvifx graph v1 v2 in (* do not constrain an existing preference edge *) |
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390 | { graph with |
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391 | degree = PrioritySet.increment v1 1 (PrioritySet.increment v2 1 graph.degree); |
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392 | nmr = PrioritySet.incrementifx v1 1 (PrioritySet.incrementifx v2 1 graph.nmr); |
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393 | } |
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394 | |
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395 | method rmvv graph v1 v2 = |
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396 | let graph = super#rmvv graph v1 v2 in |
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397 | { graph with |
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398 | degree = PrioritySet.increment v1 (-1) (PrioritySet.increment v2 (-1) graph.degree); |
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399 | nmr = PrioritySet.incrementifx v1 (-1) (PrioritySet.incrementifx v2 (-1) graph.nmr); |
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400 | } |
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401 | |
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402 | method mkvhi graph v h = |
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403 | let graph = super#mkvhi graph v h in |
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404 | let graph = (Lazy.force preference)#rmvhifx graph v h in (* do not constrain an existing preference edge *) |
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405 | { graph with |
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406 | degree = PrioritySet.increment v 1 graph.degree; |
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407 | nmr = PrioritySet.incrementifx v 1 graph.nmr; |
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408 | } |
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409 | |
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410 | method rmvh graph v h = |
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411 | let graph = super#rmvh graph v h in |
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412 | { graph with |
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413 | degree = PrioritySet.increment v (-1) graph.degree; |
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414 | nmr = PrioritySet.incrementifx v (-1) graph.nmr; |
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415 | } |
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416 | |
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417 | end |
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418 | |
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419 | (* ------------------------------------------------------------------------- *) |
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420 | |
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421 | (* The preference subgraph. |
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422 | |
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423 | This is a subgraph with the following specific features: (1) an |
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424 | edge in the preference subgraph cannot be created if a |
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425 | corresponding edge exists in the interference subgraph; (2) adding |
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426 | an edge can make a vertex move-related, which requires taking that |
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427 | vertex out of the [nmr] set; conversely, removing an edge can make |
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428 | a vertex non-move-related, which requires adding that vertex to the |
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429 | [nmr] set. *) |
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430 | |
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431 | and preference (interference : interference Lazy.t) = object (self) |
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432 | |
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433 | inherit subgraph as super |
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434 | |
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435 | method getvv graph = graph.pvv |
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436 | method setvv graph m = { graph with pvv = m } |
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437 | method getvh graph = graph.pvh |
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438 | method setvh graph m = { graph with pvh = m } |
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439 | |
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440 | (* [nmr graph v] tells whether vertex [v] is non-move-related. *) |
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441 | |
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442 | method nmr graph v = |
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443 | Vertex.Set.is_empty (self#neighborsv graph v) && |
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444 | I8051.RegisterSet.is_empty (self#neighborsh graph v) |
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445 | |
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446 | (* [mkcheck graph v] moves [v] out of the [nmr] set if [v] is |
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447 | non-move-related. *) |
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448 | |
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449 | method mkcheck graph v = |
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450 | if self#nmr graph v then |
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451 | { graph with |
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452 | nmr = PrioritySet.remove v graph.nmr } |
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453 | else |
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454 | graph |
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455 | |
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456 | (* Override the edge creation methods. *) |
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457 | |
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458 | method mkvvi graph v1 v2 = |
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459 | if (Lazy.force interference)#existsvv graph v1 v2 then |
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460 | graph (* avoid creating constrained preference edge *) |
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461 | else |
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462 | let graph = self#mkcheck graph v1 in |
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463 | let graph = self#mkcheck graph v2 in |
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464 | super#mkvvi graph v1 v2 |
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465 | |
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466 | method mkvhi graph v h = |
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467 | if (Lazy.force interference)#existsvh graph v h then |
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468 | graph (* avoid creating constrained preference edge *) |
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469 | else |
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470 | let graph = self#mkcheck graph v in |
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471 | super#mkvhi graph v h |
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472 | |
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473 | (* [rmcheck graph v] moves [v] into the [nmr] set if [v] is |
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474 | non-move-related. *) |
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475 | |
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476 | method rmcheck graph v = |
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477 | if self#nmr graph v then |
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478 | { graph with |
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479 | nmr = PrioritySet.add v (PrioritySet.priority v graph.degree) graph.nmr |
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480 | } |
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481 | else |
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482 | graph |
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483 | |
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484 | (* Override the edge destruction methods. *) |
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485 | |
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486 | method rmvv graph v1 v2 = |
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487 | let graph = super#rmvv graph v1 v2 in |
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488 | let graph = self#rmcheck graph v1 in |
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489 | let graph = self#rmcheck graph v2 in |
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490 | graph |
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491 | |
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492 | method rmvh graph v h = |
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493 | let graph = super#rmvh graph v h in |
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494 | let graph = self#rmcheck graph v in |
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495 | graph |
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496 | |
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497 | end |
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498 | |
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499 | (* ------------------------------------------------------------------------- *) |
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500 | |
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501 | (* Because the interference and preference subgraphs are mutually |
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502 | referential, a recursive definition is required. It is made |
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503 | somewhat inelegant by Objective Caml's insistence on using the |
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504 | [Lazy] mechanism. *) |
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505 | |
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506 | let rec interference = lazy (new interference preference) |
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507 | and preference = lazy (new preference interference) |
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508 | let interference = Lazy.force interference |
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509 | let preference = Lazy.force preference |
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510 | |
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511 | (* ------------------------------------------------------------------------- *) |
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512 | |
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513 | (* Inspecting interference graphs. *) |
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514 | |
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515 | (* [ipp graph v] is the set of vertices that the vertex [v] interferes |
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516 | with. *) |
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517 | |
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518 | let ipp graph v = |
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519 | interference#neighborsv graph v |
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520 | |
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521 | (* [iph graph v] is the set of hardware registers that the vertex [v] |
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522 | interferes with. *) |
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523 | |
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524 | let iph graph v = |
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525 | interference#neighborsh graph v |
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526 | |
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527 | (* [ppp graph v] is the set of vertices that should preferably be |
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528 | assigned the same color as the vertex [v]. *) |
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529 | |
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530 | let ppp graph v = |
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531 | preference#neighborsv graph v |
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532 | |
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533 | (* [pph graph v] is the set of hardware registers that [v] should |
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534 | preferably be assigned. *) |
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535 | |
---|
536 | let pph graph v = |
---|
537 | preference#neighborsh graph v |
---|
538 | |
---|
539 | (* [degree graph v] is the degree of the vertex [v], that is, the number |
---|
540 | of vertices and hardware registers that [v] interferes with. *) |
---|
541 | |
---|
542 | let degree graph v = |
---|
543 | PrioritySet.priority v graph.degree |
---|
544 | |
---|
545 | (* [lowest graph] returns [Some (v, d)], where the vertex [v] has |
---|
546 | minimum degree [d], or returns [None] if the graph is empty. *) |
---|
547 | |
---|
548 | let lowest graph = |
---|
549 | PrioritySet.lowest graph.degree |
---|
550 | |
---|
551 | (* [lowest_non_move_related graph] returns [Some (v, d)], where the |
---|
552 | vertex [v] has minimum degree [d] among the vertices that are not |
---|
553 | move-related, or returns [None] if all vertices are move-related. A |
---|
554 | vertex is move-related if it carries a preference edge. *) |
---|
555 | |
---|
556 | let lowest_non_move_related graph = |
---|
557 | PrioritySet.lowest graph.nmr |
---|
558 | |
---|
559 | (* [fold f graph accu] folds over all vertices. *) |
---|
560 | |
---|
561 | let fold f graph accu = |
---|
562 | RegMap.fold (fun v _ accu -> f v accu) graph.regmap accu |
---|
563 | |
---|
564 | (* [minimum f graph] returns a vertex [v] such that the value of [f x] |
---|
565 | is minimal. The values returned by [f] are compared using Objective |
---|
566 | Caml's generic comparison operator [<]. If the graph is empty, |
---|
567 | [None] is returned. *) |
---|
568 | |
---|
569 | let minimum f graph = |
---|
570 | match |
---|
571 | fold (fun w accu -> |
---|
572 | let dw = f w in |
---|
573 | match accu with |
---|
574 | | None -> |
---|
575 | Some (dw, w) |
---|
576 | | Some (dv, v) -> |
---|
577 | if dw < dv then |
---|
578 | Some (dw, w) |
---|
579 | else |
---|
580 | accu |
---|
581 | ) graph None |
---|
582 | with |
---|
583 | | None -> |
---|
584 | None |
---|
585 | | Some (_, v) -> |
---|
586 | Some v |
---|
587 | |
---|
588 | (* [pppick graph p] returns an arbitrary preference edge that |
---|
589 | satisfies the predicate [p], if the graph contains one. *) |
---|
590 | |
---|
591 | type ppedge = |
---|
592 | Vertex.t * Vertex.t |
---|
593 | |
---|
594 | let pppick graph p = |
---|
595 | VertexSetMap.pick graph.pvv p |
---|
596 | |
---|
597 | (* [phpick graph p] returns an arbitrary preference edge that |
---|
598 | satisfies the predicate [p], if the graph contains one. *) |
---|
599 | |
---|
600 | type phedge = |
---|
601 | Vertex.t * I8051.register |
---|
602 | |
---|
603 | let phpick graph p = |
---|
604 | I8051RegisterSetMap.pick graph.pvh p |
---|
605 | |
---|
606 | (* ------------------------------------------------------------------------- *) |
---|
607 | |
---|
608 | (* Constructing interference graphs. *) |
---|
609 | |
---|
610 | (* [create regs] creates an interference graph whose vertices are |
---|
611 | the pseudo-registers [regs] and that does not have any edges. *) |
---|
612 | |
---|
613 | let create regs = |
---|
614 | let (_ : int), regmap, degree = |
---|
615 | Register.Set.fold (fun r (v, regmap, degree) -> |
---|
616 | v+1, |
---|
617 | RegMap.add r v regmap, |
---|
618 | PrioritySet.add v 0 degree |
---|
619 | ) regs (0, RegMap.empty, PrioritySet.empty) |
---|
620 | in |
---|
621 | { |
---|
622 | regmap = regmap; |
---|
623 | ivv = Vertex.Map.empty; |
---|
624 | ivh = Vertex.Map.empty; |
---|
625 | pvv = Vertex.Map.empty; |
---|
626 | pvh = Vertex.Map.empty; |
---|
627 | degree = degree; |
---|
628 | nmr = degree |
---|
629 | } |
---|
630 | |
---|
631 | (* [lookup graph r] returns the graph vertex associated with |
---|
632 | pseudo-register [r]. *) |
---|
633 | |
---|
634 | let lookup graph r = |
---|
635 | RegMap.backward r graph.regmap |
---|
636 | |
---|
637 | (* Conversely, [registers graph v] returns the set of pseudo-registers |
---|
638 | associated with vertex [v]. *) |
---|
639 | |
---|
640 | let registers graph v = |
---|
641 | RegMap.forward v graph.regmap |
---|
642 | |
---|
643 | (* [mkipp graph regs1 regs2] adds interference edges between all pairs |
---|
644 | of pseudo-registers [r1] and [r2], where [r1] ranges over [regs1], |
---|
645 | [r2] ranges over [regs2], and [r1] and [r2] are distinct. *) |
---|
646 | |
---|
647 | let mkipp graph regs1 regs2 = |
---|
648 | Register.Set.fold (fun r1 graph -> |
---|
649 | let v1 = lookup graph r1 in |
---|
650 | Register.Set.fold (fun r2 graph -> |
---|
651 | interference#mkvv graph v1 (lookup graph r2) |
---|
652 | ) regs2 graph |
---|
653 | ) regs1 graph |
---|
654 | |
---|
655 | (* [mkiph graph regs hwregs] adds interference edges between all pairs |
---|
656 | of a pseudo-register [r] and a hardware register [hwr], where [r] |
---|
657 | ranges over [regs] and [hwr] ranges over [hwregs]. *) |
---|
658 | |
---|
659 | let mkiph graph regs hwregs = |
---|
660 | Register.Set.fold (fun r graph -> |
---|
661 | let v = lookup graph r in |
---|
662 | I8051.RegisterSet.fold (fun h graph -> |
---|
663 | interference#mkvh graph v h |
---|
664 | ) hwregs graph |
---|
665 | ) regs graph |
---|
666 | |
---|
667 | (* [mki graph regs1 regs2] adds interference edges between all pairs |
---|
668 | of (pseudo- or hardware) registers [r1] and [r2], where [r1] ranges |
---|
669 | over [regs1], [r2] ranges over [regs2], and [r1] and [r2] are |
---|
670 | distinct. *) |
---|
671 | |
---|
672 | let mki graph (regs1, hwregs1) (regs2, hwregs2) = |
---|
673 | let graph = mkipp graph regs1 regs2 in |
---|
674 | let graph = mkiph graph regs1 hwregs2 in |
---|
675 | let graph = mkiph graph regs2 hwregs1 in |
---|
676 | graph |
---|
677 | |
---|
678 | (* [mkppp graph r1 r2] adds a preference edge between the |
---|
679 | pseudo-registers [r1] and [r2]. *) |
---|
680 | |
---|
681 | let mkppp graph r1 r2 = |
---|
682 | let v1 = lookup graph r1 |
---|
683 | and v2 = lookup graph r2 in |
---|
684 | let graph = preference#mkvv graph v1 v2 in |
---|
685 | graph |
---|
686 | |
---|
687 | (* [mkpph graph r h] adds a preference edge between the |
---|
688 | pseudo-register [r] and the hardware register [h]. *) |
---|
689 | |
---|
690 | let mkpph graph r h = |
---|
691 | let v = lookup graph r in |
---|
692 | let graph = preference#mkvh graph v h in |
---|
693 | graph |
---|
694 | |
---|
695 | (* ------------------------------------------------------------------------- *) |
---|
696 | |
---|
697 | (* Displaying interference graphs. *) |
---|
698 | |
---|
699 | open Printf |
---|
700 | |
---|
701 | let hwregs graph = |
---|
702 | I8051.RegisterSet.union (interference#hwregs graph) (preference#hwregs graph) |
---|
703 | |
---|
704 | let print_vertex graph v = |
---|
705 | Register.Set.print (registers graph v) |
---|
706 | |
---|
707 | let print f graph = |
---|
708 | |
---|
709 | fprintf f "graph G {\n"; |
---|
710 | (* fprintf f "size=\"6, 3\";\n"; (* in inches *)*) |
---|
711 | fprintf f "orientation = landscape;\n"; |
---|
712 | fprintf f "rankdir = LR;\n"; |
---|
713 | fprintf f "ratio = compress;\n\n"; (* compress or fill or auto *) |
---|
714 | |
---|
715 | RegMap.fold (fun vertex regs () -> |
---|
716 | fprintf f "r%d [ label=\"%s\" ] ;\n" vertex (Register.Set.print regs) |
---|
717 | ) graph.regmap (); |
---|
718 | |
---|
719 | I8051.RegisterSet.iter (fun hwr -> |
---|
720 | let name = I8051.print_register hwr in |
---|
721 | fprintf f "hwr%s [ label=\"$%s\" ] ;\n" name name |
---|
722 | ) (hwregs graph); |
---|
723 | |
---|
724 | interference#iter graph |
---|
725 | (fun vertex neighbor -> |
---|
726 | fprintf f "r%d -- r%d ;\n" vertex neighbor) |
---|
727 | (fun vertex neighbor -> |
---|
728 | fprintf f "r%d -- hwr%s ;\n" vertex (I8051.print_register neighbor)); |
---|
729 | |
---|
730 | preference#iter graph |
---|
731 | (fun vertex neighbor -> |
---|
732 | fprintf f "r%d -- r%d [ style = dashed ] ;\n" vertex neighbor) |
---|
733 | (fun vertex neighbor -> |
---|
734 | fprintf f "r%d -- hwr%s [ style = dashed ] ;\n" vertex (I8051.print_register neighbor)); |
---|
735 | |
---|
736 | fprintf f "\n}\n" |
---|
737 | |
---|
738 | (* ------------------------------------------------------------------------- *) |
---|
739 | |
---|
740 | (* Coalescing. *) |
---|
741 | |
---|
742 | (* [coalesce graph v1 v2] is a new graph where the vertices [v1] and [v2] |
---|
743 | are coalesced. The new coalesced vertex is known under the name [v2]. *) |
---|
744 | |
---|
745 | let coalesce graph x y = |
---|
746 | |
---|
747 | assert (x <> y); (* attempt to coalesce one vertex with itself *) |
---|
748 | assert (not (interference#existsvv graph x y)); (* attempt to coalesce two interfering vertices *) |
---|
749 | |
---|
750 | (* Perform coalescing in the two subgraphs. *) |
---|
751 | |
---|
752 | let graph = interference#coalesce graph x y in |
---|
753 | let graph = preference#coalesce graph x y in |
---|
754 | |
---|
755 | (* Remove [x] from all tables. *) |
---|
756 | |
---|
757 | { |
---|
758 | graph with |
---|
759 | regmap = RegMap.coalesce x y graph.regmap; |
---|
760 | ivh = Vertex.Map.remove x graph.ivh; |
---|
761 | pvh = Vertex.Map.remove x graph.pvh; |
---|
762 | degree = PrioritySet.remove x graph.degree; |
---|
763 | nmr = PrioritySet.remove x graph.nmr; |
---|
764 | } |
---|
765 | |
---|
766 | (* [coalesceh graph v h] coalesces the vertex [v] with the hardware register |
---|
767 | [h]. This produces a new graph where [v] no longer exists and all edges |
---|
768 | leading to [v] are replaced with edges leading to [h]. *) |
---|
769 | |
---|
770 | let coalesceh graph x h = |
---|
771 | |
---|
772 | assert (not (interference#existsvh graph x h)); (* attempt to coalesce interfering entities *) |
---|
773 | |
---|
774 | (* Perform coalescing in the two subgraphs. *) |
---|
775 | |
---|
776 | let graph = interference#coalesceh graph x h in |
---|
777 | let graph = preference#coalesceh graph x h in |
---|
778 | |
---|
779 | (* Remove [x] from all tables. *) |
---|
780 | |
---|
781 | { |
---|
782 | graph with |
---|
783 | regmap = RegMap.remove x graph.regmap; |
---|
784 | ivh = Vertex.Map.remove x graph.ivh; |
---|
785 | pvh = Vertex.Map.remove x graph.pvh; |
---|
786 | degree = PrioritySet.remove x graph.degree; |
---|
787 | nmr = PrioritySet.remove x graph.nmr; |
---|
788 | } |
---|
789 | |
---|
790 | (* ------------------------------------------------------------------------- *) |
---|
791 | |
---|
792 | (* [freeze graph x] is a new graph where all preference edges carried |
---|
793 | by [x] are removed. *) |
---|
794 | |
---|
795 | let freeze graph x = |
---|
796 | preference#remove graph x |
---|
797 | |
---|
798 | (* ------------------------------------------------------------------------- *) |
---|
799 | |
---|
800 | (* Removal. *) |
---|
801 | |
---|
802 | (* [remove graph v] is a new graph where vertex [v] is removed. *) |
---|
803 | |
---|
804 | let remove graph v = |
---|
805 | |
---|
806 | (* Remove all edges carried by [v]. *) |
---|
807 | |
---|
808 | let graph = interference#remove graph v in |
---|
809 | let graph = preference#remove graph v in |
---|
810 | |
---|
811 | (* Remove [v] from all tables. *) |
---|
812 | |
---|
813 | { |
---|
814 | graph with |
---|
815 | regmap = RegMap.remove v graph.regmap; |
---|
816 | degree = PrioritySet.remove v graph.degree; |
---|
817 | nmr = PrioritySet.remove v graph.nmr; |
---|
818 | } |
---|
819 | |
---|
820 | (* ------------------------------------------------------------------------- *) |
---|
821 | |
---|
822 | (* [mkdeg graph] recomputes degree information from scratch. *) |
---|
823 | |
---|
824 | let mkdeg graph = |
---|
825 | let degree, nmr = |
---|
826 | fold (fun v (degree, nmr) -> |
---|
827 | let d = interference#degree graph v in |
---|
828 | PrioritySet.add v d degree, |
---|
829 | if preference#nmr graph v then PrioritySet.add v d nmr else nmr |
---|
830 | ) graph (PrioritySet.empty, PrioritySet.empty) |
---|
831 | in |
---|
832 | { graph with |
---|
833 | degree = degree; |
---|
834 | nmr = nmr; |
---|
835 | } |
---|
836 | |
---|
837 | (* [restrict graph p] is a new graph where only those vertices that |
---|
838 | satisfy predicate [p] are kept. The same effect could be obtained |
---|
839 | by repeated application of [remove], but [restrict] is likely to be |
---|
840 | more efficient if many vertices are removed. *) |
---|
841 | |
---|
842 | let restrict graph p = |
---|
843 | mkdeg { |
---|
844 | graph with |
---|
845 | regmap = RegMap.restrict p graph.regmap; |
---|
846 | ivv = VertexSetMap.restrict p graph.ivv; |
---|
847 | ivh = Vertex.Map.restrict p graph.ivh; |
---|
848 | pvv = VertexSetMap.restrict p graph.pvv; |
---|
849 | pvh = Vertex.Map.restrict p graph.pvh; |
---|
850 | } |
---|
851 | |
---|
852 | (* [droph graph] is a new graph where all information concerning hardware |
---|
853 | registers has been dropped. *) |
---|
854 | |
---|
855 | let droph graph = |
---|
856 | mkdeg { |
---|
857 | graph with |
---|
858 | ivh = Vertex.Map.empty; |
---|
859 | pvh = Vertex.Map.empty; |
---|
860 | } |
---|
861 | |
---|