1 | include "ERTL/liveness.ma". |
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2 | include "utilities/Interference.ma". |
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3 | |
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4 | definition vertex ≝ register ⊎ Register. |
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5 | |
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6 | record graph: Type[0] ≝ |
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7 | { |
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8 | interferes: vertex → vertex → bool |
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9 | }. |
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10 | |
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11 | axiom create: ∀globals: list ident. ertl_internal_function globals → graph. |
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12 | |
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13 | inductive decision: Type[0] ≝ |
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14 | | decision_spill: decision |
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15 | | decision_colour: Register → decision. |
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16 | |
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17 | record coloured_graph (d: Type[0]): Type[1] ≝ |
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18 | { |
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19 | the_graph: graph; |
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20 | colouring: register → d; |
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21 | prop_colouring: ∀v1. ∀v2. (interferes the_graph (inl … v1) (inl … v2) = true) → colouring v1 ≠ colouring v2 |
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22 | }. |
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23 | |
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24 | definition initial_colouring ≝ coloured_graph decision. |
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25 | definition stack_colouring ≝ coloured_graph nat. |
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26 | |
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27 | (* |
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28 | definition build ≝ |
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29 | λglobals: list ident. |
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30 | λint_fun: ertl_internal_function globals. |
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31 | let liveafter ≝ analyse globals int_fun in |
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32 | let graph ≝ ig_create (ertl_if_locals globals int_fun) in |
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33 | let graph ≝ ig_mkiph graph (ertl_if_locals globals int_fun) RegistersForbidden in |
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34 | let graph ≝ |
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35 | foldi ? ? ? (λlabel. λstmt. λgraph. |
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36 | let live ≝ liveafter label in |
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37 | match eliminable globals live stmt with |
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38 | [ Some _ ⇒ graph |
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39 | | None ⇒ |
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40 | let defined ≝ defined globals stmt in |
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41 | let exceptions ≝ |
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42 | match stmt with |
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43 | [ joint_st_sequential seq l ⇒ |
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44 | match seq with |
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45 | [ joint_instr_move pair_reg ⇒ |
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46 | let reg_r ≝ \snd pair_reg in |
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47 | match reg_r with |
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48 | [ hardware hw ⇒ lattice_hsingleton hw |
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49 | | pseudo ps ⇒ lattice_psingleton ps |
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50 | ] |
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51 | | _ ⇒ ? |
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52 | ] |
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53 | | _ ⇒ ? |
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54 | ] |
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55 | in |
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56 | let graph ≝ ig_mki graph (lattice_diff live exceptions) defined in |
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57 | let graph ≝ |
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58 | match stmt with |
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59 | [ joint_st_sequential seq l ⇒ |
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60 | match seq with |
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61 | [ joint_instr_move pair_reg ⇒ |
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62 | let reg_l ≝ \fst pair_reg in |
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63 | let reg_r ≝ \snd pair_reg in |
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64 | match reg_l with |
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65 | [ pseudo ps1 ⇒ |
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66 | match reg_r with |
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67 | [ pseudo ps2 ⇒ ig_mkppp graph ps1 ps2 |
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68 | | hardware hw ⇒ ig_mkpph graph ps1 hw |
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69 | ] |
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70 | | hardware hw1 ⇒ |
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71 | match reg_r with |
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72 | [ pseudo ps ⇒ ig_mkpph graph ps hw1 |
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73 | | hardware hw2 ⇒ graph |
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74 | ] |
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75 | ] |
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76 | | _ ⇒ graph |
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77 | ] |
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78 | | _ ⇒ graph |
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79 | ] |
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80 | in graph |
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81 | ]) (ertl_if_graph globals int_fun) graph |
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82 | in |
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83 | 〈liveafter, graph〉. |
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84 | [*: @lattice_bottom ] (* XXX: matita bug here! *) |
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85 | qed. *) |
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