1 | include "LTL/LTL_paolo.ma". |
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2 | include "ERTL/Interference_paolo.ma". |
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3 | include "ASM/Arithmetic.ma". |
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4 | include "joint/TranslateUtils_paolo.ma". |
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5 | |
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6 | (* Note: translation is complicated by having to preserve the carry bit and |
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7 | wanting to do it with as less boilerplate as possible. It could be somewhat |
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8 | simplified if constant and copy propagation was to be done after this pass: |
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9 | those optimisations would take care of the boilerplate for us.*) |
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10 | |
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11 | coercion Reg_to_dec : ∀r:Register.decision ≝ decision_colour on _r : Register to decision. |
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12 | |
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13 | inductive arg_decision : Type[0] ≝ |
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14 | | arg_decision_colour : Register → arg_decision |
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15 | | arg_decision_spill : ℕ → arg_decision |
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16 | | arg_decision_imm : Byte → arg_decision. |
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17 | |
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18 | coercion Reg_to_arg_dec : ∀r:Register.arg_decision ≝ arg_decision_colour on _r : Register to arg_decision. |
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19 | |
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20 | definition stacksize : |
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21 | ∀globals.ℕ → joint_internal_function globals ertl_params → ℕ ≝ |
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22 | λglobals. |
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23 | λspilled_no. |
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24 | λint_fun. |
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25 | spilled_no + joint_if_stacksize … int_fun. |
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26 | |
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27 | (* Paolo: I'm changing the following: before, spilled registers were |
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28 | assigned stack addresses going from SP + #frame_size - #stack_params |
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29 | excluded down to SP included. I am turning it upside down, so that |
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30 | the offset does not need the stack size to be computed *) |
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31 | |
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32 | definition preserve_carry_bit : |
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33 | ∀globals.bool → list (joint_seq ltl_params globals) → list (joint_seq ltl_params globals) ≝ |
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34 | λglobals,do_it,steps. |
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35 | if do_it then SAVE_CARRY :: steps @ [RESTORE_CARRY] else steps. |
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36 | |
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37 | definition set_dp_by_offset : |
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38 | ∀globals.Byte → list (joint_seq ltl_params globals) ≝ |
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39 | λglobals,off. |
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40 | [ 𝐀 ← off |
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41 | ; 𝐀 ← 𝐀 .Add. RegisterSPL |
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42 | ; RegisterDPL ← 𝐀 |
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43 | ; 𝐀 ← 0 |
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44 | ; 𝐀 ← 𝐀 .Addc. RegisterSPH |
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45 | ; RegisterDPH ← 𝐀 |
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46 | ]. |
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47 | |
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48 | definition get_stack: |
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49 | ∀globals.Register → Byte → list (joint_seq ltl_params globals) ≝ |
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50 | λglobals,r,off. |
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51 | set_dp_by_offset ? off @ |
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52 | [ LOAD … it it it ] @ |
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53 | if eq_Register r RegisterA then [ ] else [ r ← 𝐀 ]. |
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54 | |
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55 | definition set_stack_not_a : |
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56 | ∀globals.Byte → Register → list (joint_seq ltl_params globals) ≝ |
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57 | λglobals,off,r. |
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58 | set_dp_by_offset ? off @ |
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59 | [ 𝐀 ← r |
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60 | ; STORE … it it it ]. |
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61 | |
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62 | definition set_stack_a : |
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63 | ∀globals.Byte → list (joint_seq ltl_params globals) ≝ |
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64 | λglobals,off. |
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65 | [ RegisterST1 ← 𝐀 ] @ |
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66 | set_stack_not_a ? off RegisterST1. |
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67 | |
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68 | definition set_stack : |
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69 | ∀globals.Byte → Register → list (joint_seq ltl_params globals) ≝ |
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70 | λglobals,off,r. |
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71 | if eq_Register r RegisterA then |
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72 | set_stack_a ? off |
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73 | else |
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74 | set_stack_not_a ? off r. |
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75 | |
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76 | definition set_stack_int : |
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77 | ∀globals.Byte → Byte → list (joint_seq ltl_params globals) ≝ |
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78 | λglobals,off,int. |
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79 | set_dp_by_offset ? off @ |
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80 | [ 𝐀 ← int |
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81 | ; STORE … it it it ]. |
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82 | |
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83 | definition move : |
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84 | ∀globals.bool → decision → arg_decision → list (joint_seq ltl_params globals) ≝ |
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85 | λglobals,carry_lives_after,dst,src. |
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86 | match dst with |
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87 | [ decision_colour dstr ⇒ |
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88 | match src with |
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89 | [ arg_decision_colour srcr ⇒ |
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90 | if eq_Register dstr srcr then [ ] else |
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91 | if eq_Register dstr RegisterA then [ 𝐀 ← srcr ] else |
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92 | if eq_Register srcr RegisterA then [ dstr ← 𝐀 ] else |
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93 | [ 𝐀 ← srcr ; dstr ← 𝐀] |
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94 | | arg_decision_spill srco ⇒ |
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95 | preserve_carry_bit ? carry_lives_after |
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96 | (get_stack ? dstr srco) |
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97 | | arg_decision_imm int ⇒ |
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98 | [ 𝐀 ← int ] @ |
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99 | if eq_Register dstr RegisterA then [ ] else |
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100 | [ dstr ← 𝐀 ] |
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101 | ] |
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102 | | decision_spill dsto ⇒ |
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103 | match src with |
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104 | [ arg_decision_colour srcr ⇒ |
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105 | preserve_carry_bit ? carry_lives_after |
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106 | (set_stack ? dsto srcr) |
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107 | | arg_decision_spill srco ⇒ |
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108 | if eqb srco dsto then [ ] else |
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109 | preserve_carry_bit ? carry_lives_after |
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110 | (get_stack ? RegisterA srco @ |
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111 | set_stack ? dsto RegisterA) |
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112 | | arg_decision_imm int ⇒ |
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113 | preserve_carry_bit ? carry_lives_after |
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114 | (set_stack_int ? dsto int) |
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115 | ] |
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116 | ]. |
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117 | |
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118 | definition arg_is_spilled : arg_decision → bool ≝ |
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119 | λx.match x with [ arg_decision_spill _ ⇒ true | _ ⇒ false ]. |
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120 | definition is_spilled : decision → bool ≝ |
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121 | λx.match x with [ decision_spill _ ⇒ true | _ ⇒ false ]. |
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122 | |
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123 | definition newframe : |
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124 | ∀globals.ℕ → list (joint_seq ltl_params globals) ≝ |
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125 | λglobals,stack_sz. |
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126 | [ CLEAR_CARRY … |
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127 | ; 𝐀 ← RegisterSPL |
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128 | ; 𝐀 ← 𝐀 .Sub. stack_sz |
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129 | ; RegisterSPL ← 𝐀 |
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130 | ; 𝐀 ← RegisterSPH |
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131 | ; 𝐀 ← 𝐀 .Sub. 0 |
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132 | ; RegisterSPL ← 𝐀 |
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133 | ]. |
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134 | |
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135 | definition delframe : |
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136 | ∀globals.ℕ → list (joint_seq ltl_params globals) ≝ |
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137 | λglobals,stack_sz. |
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138 | [ 𝐀 ← RegisterSPL |
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139 | ; 𝐀 ← 𝐀 .Add. stack_sz |
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140 | ; RegisterSPL ← 𝐀 |
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141 | ; 𝐀 ← RegisterSPH |
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142 | ; 𝐀 ← 𝐀 .Addc. 0 |
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143 | ; RegisterSPL ← 𝐀 |
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144 | ]. |
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145 | |
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146 | definition commutative : Op2 → bool ≝ |
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147 | λop.match op with |
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148 | [ Add ⇒ true |
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149 | | Addc ⇒ true |
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150 | | Or ⇒ true |
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151 | | Xor ⇒ true |
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152 | | And ⇒ true |
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153 | | _ ⇒ false |
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154 | ]. |
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155 | |
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156 | definition uses_carry : Op2 → bool ≝ |
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157 | λop.match op with |
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158 | [ Addc ⇒ true |
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159 | | Sub ⇒ true |
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160 | | _ ⇒ false |
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161 | ]. |
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162 | |
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163 | definition sets_carry : Op2 → bool ≝ |
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164 | λop.match op with |
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165 | [ Add ⇒ true |
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166 | | Addc ⇒ true |
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167 | | Sub ⇒ true |
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168 | | _ ⇒ false |
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169 | ]. |
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170 | |
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171 | definition translate_op2 : |
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172 | ∀globals.bool→ Op2 → decision → arg_decision → arg_decision → list (joint_seq ltl_params globals) ≝ |
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173 | λglobals,carry_lives_after,op,dst,arg1,arg2. |
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174 | (* this won't preserve the carry bit if op does not set it: left to next function *) |
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175 | (* if op uses carry bit (⇒ it sets it too) it must be preserved before the op *) |
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176 | (preserve_carry_bit ? |
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177 | (uses_carry op ∧ (arg_is_spilled arg1 ∨ arg_is_spilled arg2)) |
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178 | (move ? false RegisterB arg2 @ |
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179 | move ? false RegisterA arg1) @ |
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180 | [ 𝐀 ← 𝐀 .op. RegisterB ] @ |
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181 | (* it op sets the carry bit and it is needed afterwards it must be preserved here *) |
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182 | move ? (sets_carry op ∧ carry_lives_after) dst RegisterA). |
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183 | |
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184 | definition translate_op2_smart : |
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185 | ∀globals.bool → Op2 → decision → arg_decision → arg_decision → list (joint_seq ltl_params globals) ≝ |
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186 | λglobals,carry_lives_after,op,dst,arg1,arg2. |
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187 | (* if op does not set carry bit (⇒ it does not use it either) then it must be |
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188 | preserved *) |
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189 | preserve_carry_bit ? |
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190 | (¬sets_carry op ∧ carry_lives_after ∧ |
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191 | (arg_is_spilled arg1 ∨ arg_is_spilled arg2 ∨ is_spilled dst)) |
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192 | (match arg2 with |
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193 | [ arg_decision_colour arg2r ⇒ |
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194 | move ? (uses_carry op) RegisterA arg1 @ |
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195 | [ 𝐀 ← 𝐀 .op. arg2r ] @ |
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196 | move ? (sets_carry op ∧ carry_lives_after) dst RegisterA |
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197 | | arg_decision_imm arg2i ⇒ |
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198 | move ? (uses_carry op) RegisterA arg1 @ |
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199 | [ 𝐀 ← 𝐀 .op. arg2i ] @ |
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200 | move ? (sets_carry op ∧ carry_lives_after) dst RegisterA |
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201 | | _ ⇒ |
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202 | if commutative op then |
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203 | match arg1 with |
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204 | [ arg_decision_colour arg1r ⇒ |
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205 | move ? (uses_carry op) RegisterA arg2 @ |
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206 | [ 𝐀 ← 𝐀 .op. arg1r ] @ |
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207 | move ? (sets_carry op ∧ carry_lives_after) dst RegisterA |
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208 | | arg_decision_imm arg1i ⇒ |
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209 | move ? (uses_carry op) RegisterA arg2 @ |
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210 | [ 𝐀 ← 𝐀 .op. arg1i ] @ |
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211 | move ? (sets_carry op ∧ carry_lives_after) dst RegisterA |
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212 | | _ ⇒ |
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213 | translate_op2 ? carry_lives_after op dst arg1 arg2 |
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214 | ] |
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215 | else |
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216 | translate_op2 ? carry_lives_after op dst arg1 arg2 |
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217 | ]). |
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218 | |
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219 | definition dec_to_arg_dec : decision → arg_decision ≝ |
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220 | λd.match d with |
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221 | [ decision_colour r ⇒ arg_decision_colour r |
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222 | | decision_spill n ⇒ arg_decision_spill n |
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223 | ]. |
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224 | |
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225 | coercion dec_arg_dec : ∀d:decision.arg_decision ≝ dec_to_arg_dec on _d : decision to arg_decision. |
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226 | |
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227 | definition translate_op1 : |
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228 | ∀globals.bool → Op1 → decision → decision → list (joint_seq ltl_params globals) ≝ |
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229 | λglobals,carry_lives_after,op,dst,arg. |
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230 | let preserve_carry ≝ carry_lives_after ∧ (is_spilled dst ∨ is_spilled arg) in |
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231 | preserve_carry_bit ? preserve_carry |
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232 | (move ? false RegisterA arg @ |
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233 | OP1 … op it it :: |
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234 | move ? false dst RegisterA). |
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235 | |
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236 | definition translate_opaccs : |
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237 | ∀globals.bool → OpAccs → decision → decision → arg_decision → arg_decision → list (joint_seq ltl_params globals) ≝ |
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238 | λglobals,carry_lives_after,op,dst1,dst2,arg1,arg2. |
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239 | (* OPACCS always has dead carry bit and sets it to zero *) |
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240 | move ? false RegisterB arg2 @ |
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241 | move ? false RegisterA arg1 @ |
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242 | OPACCS … op it it it it :: |
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243 | move ? false dst1 RegisterA @ |
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244 | move ? false dst2 RegisterB @ |
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245 | if carry_lives_after ∧ (is_spilled dst1 ∨ is_spilled dst2) then |
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246 | [CLEAR_CARRY ??] |
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247 | else [ ]. |
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248 | |
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249 | (* does not preserve carry bit *) |
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250 | definition move_to_dp : |
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251 | ∀globals.arg_decision → arg_decision → list (joint_seq ltl_params globals) ≝ |
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252 | λglobals,arg1,arg2. |
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253 | if ¬arg_is_spilled arg1 then |
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254 | move ? false RegisterDPH arg2 @ |
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255 | (* does not change dph because arg1 is not spilled *) |
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256 | move ? false RegisterDPL arg1 |
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257 | else if ¬arg_is_spilled arg2 then |
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258 | move ? false RegisterDPL arg1 @ |
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259 | (* does not change dpl because arg2 is not spilled *) |
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260 | move ? false RegisterDPH arg2 |
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261 | else |
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262 | (* using B as temporary, as moving spilled registers tampers with DPTR *) |
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263 | move ? false RegisterB arg1 @ |
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264 | move ? false RegisterDPH arg2 @ |
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265 | move ? false RegisterDPL RegisterB. |
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266 | |
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267 | definition translate_store : |
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268 | ∀globals.bool → arg_decision → arg_decision → arg_decision → list (joint_seq ltl_params globals) ≝ |
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269 | λglobals,carry_lives_after,addr1,addr2,src. |
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270 | (* requires src != RegisterA and RegisterB *) |
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271 | preserve_carry_bit ? (carry_lives_after ∧ |
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272 | (arg_is_spilled addr1 ∨ arg_is_spilled addr1 ∨ arg_is_spilled src)) |
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273 | (let move_to_dptr ≝ move_to_dp ? addr1 addr2 in |
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274 | (if arg_is_spilled src then |
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275 | move ? false RegisterST0 src @ |
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276 | move_to_dptr @ |
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277 | [ 𝐀 ← RegisterST0] |
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278 | else move_to_dptr) @ |
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279 | [STORE … it it it]). |
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280 | |
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281 | definition translate_load : |
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282 | ∀globals.bool → decision → arg_decision → arg_decision → list (joint_seq ltl_params globals) ≝ |
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283 | λglobals,carry_lives_after,dst,addr1,addr2. |
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284 | preserve_carry_bit ? (carry_lives_after ∧ |
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285 | (is_spilled dst ∨ arg_is_spilled addr1 ∨ arg_is_spilled addr1)) |
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286 | (move_to_dp ? addr1 addr2 @ |
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287 | [ LOAD … it it it ] @ |
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288 | move ? false dst RegisterA). |
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289 | |
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290 | definition translate_address : |
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291 | ∀globals.bool → ∀i.member i (eq_identifier ?) globals → decision → decision → |
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292 | list (joint_seq ltl_params globals) ≝ |
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293 | λglobals,carry_lives_after,id,prf,addr1,addr2. |
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294 | preserve_carry_bit ? (carry_lives_after ∧ (is_spilled addr1 ∨ is_spilled addr2)) |
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295 | (ADDRESS ltl_params ? id prf it it :: |
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296 | move ? false addr1 RegisterDPL @ |
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297 | move ? false addr2 RegisterDPH). |
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298 | |
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299 | definition translate_step: |
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300 | ∀globals.∀after : valuation register_lattice. |
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301 | coloured_graph after → |
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302 | ℕ → label → joint_step ertl_params globals → seq_block ltl_params globals (joint_step ltl_params globals) ≝ |
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303 | λglobals,after,grph,stack_sz,lbl,s. |
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304 | let lookup ≝ λr.colouring … grph (inl … r) in |
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305 | let lookup_arg ≝ λa.match a with |
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306 | [ Reg r ⇒ lookup r |
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307 | | Imm b ⇒ arg_decision_imm b |
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308 | ] in |
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309 | let carry_lives_after ≝ hlives RegisterCarry (after lbl) in |
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310 | let move ≝ move globals carry_lives_after in |
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311 | match s with |
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312 | [ step_seq s' ⇒ |
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313 | match s' return λ_.seq_block ltl_params globals (joint_step ltl_params globals) with |
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314 | [ COMMENT c ⇒ COMMENT … c |
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315 | | COST_LABEL cost_lbl ⇒ COST_LABEL … cost_lbl |
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316 | | POP r ⇒ |
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317 | POP … it :: |
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318 | move (lookup r) RegisterA |
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319 | | PUSH a ⇒ |
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320 | move RegisterA (lookup_arg a) @ |
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321 | [ PUSH … it ] |
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322 | | STORE addr1 addr2 srcr ⇒ |
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323 | translate_store ? carry_lives_after |
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324 | (lookup_arg addr1) |
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325 | (lookup_arg addr2) |
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326 | (lookup_arg srcr) |
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327 | | LOAD dstr addr1 addr2 ⇒ |
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328 | translate_load ? carry_lives_after |
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329 | (lookup dstr) |
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330 | (lookup_arg addr1) |
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331 | (lookup_arg addr2) |
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332 | | CLEAR_CARRY ⇒ CLEAR_CARRY … |
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333 | | SET_CARRY ⇒ CLEAR_CARRY … |
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334 | | OP2 op dst arg1 arg2 ⇒ |
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335 | translate_op2_smart ? carry_lives_after op |
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336 | (lookup dst) |
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337 | (lookup_arg arg1) |
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338 | (lookup_arg arg2) |
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339 | | OP1 op dst arg ⇒ |
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340 | translate_op1 ? carry_lives_after op |
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341 | (lookup dst) |
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342 | (lookup arg) |
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343 | | MOVE pair_regs ⇒ |
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344 | let lookup_move_dst ≝ λx.match x return λ_.decision with |
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345 | [ PSD r ⇒ lookup r |
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346 | | HDW r ⇒ r |
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347 | ] in |
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348 | let dst ≝ lookup_move_dst (\fst pair_regs) in |
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349 | let src ≝ |
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350 | match \snd pair_regs return λ_.arg_decision with |
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351 | [ REG r ⇒ lookup_move_dst r |
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352 | | INT b ⇒ arg_decision_imm b |
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353 | ] in |
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354 | move dst src |
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355 | | ADDRESS lbl prf dpl dph ⇒ |
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356 | translate_address ? carry_lives_after |
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357 | lbl prf (lookup dpl) (lookup dph) |
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358 | | OPACCS op dst1 dst2 arg1 arg2 ⇒ |
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359 | translate_opaccs ? carry_lives_after op |
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360 | (lookup dst1) (lookup dst2) |
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361 | (lookup_arg arg1) (lookup_arg arg2) |
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362 | | extension_seq ext ⇒ |
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363 | match ext with |
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364 | [ ertl_new_frame ⇒ newframe ? stack_sz |
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365 | | ertl_del_frame ⇒ delframe ? stack_sz |
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366 | | ertl_frame_size r ⇒ |
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367 | move (lookup r) (arg_decision_imm stack_sz) |
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368 | ] |
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369 | | CALL_ID f n_args _ ⇒ CALL_ID ltl_params ? f n_args it |
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370 | | extension_call abs ⇒ match abs in void with [ ] |
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371 | ] |
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372 | | COND r ltrue ⇒ |
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373 | 〈move RegisterA (lookup r),COND … it ltrue〉 |
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374 | ]. |
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375 | |
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376 | definition translate_fin_step: |
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377 | ∀globals.label → joint_fin_step ertl_params → seq_block ltl_params globals (joint_fin_step ltl_params) ≝ |
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378 | λglobals,lbl,s. |
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379 | match s return λ_.seq_block ltl_params globals (joint_fin_step ltl_params) with |
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380 | [ RETURN ⇒ RETURN ? |
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381 | | GOTO l ⇒ GOTO ? l |
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382 | | tailcall abs ⇒ match abs in void with [ ] |
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383 | ]. |
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384 | |
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385 | definition translate_internal: ∀globals: list ident. |
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386 | ertl_internal_function globals → joint_internal_function globals ltl_params ≝ |
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387 | λglobals: list ident. |
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388 | λint_fun: ertl_internal_function globals. |
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389 | (* initialize graph *) |
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390 | let entry ≝ pi1 … (joint_if_entry … int_fun) in |
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391 | let exit ≝ pi1 … (joint_if_exit … int_fun) in |
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392 | let graph ≝ add ? ? (empty_map ? (joint_statement ??)) entry (GOTO … exit) in |
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393 | let graph ≝ add ? ? graph exit (RETURN …) in |
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394 | (* colour registers *) |
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395 | let after ≝ analyse_liveness globals int_fun in |
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396 | let coloured_graph ≝ build after in |
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397 | (* compute new stack size *) |
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398 | let stack_sz ≝ spilled_no … coloured_graph + joint_if_stacksize … int_fun in |
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399 | (* initialize internal function *) |
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400 | let init ≝ mk_joint_internal_function globals ltl_params |
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401 | (joint_if_luniverse … int_fun) |
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402 | (joint_if_runiverse … int_fun) |
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403 | it it [ ] stack_sz graph entry exit in |
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404 | graph_translate … |
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405 | init |
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406 | (translate_step … coloured_graph stack_sz) |
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407 | (translate_fin_step …) |
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408 | int_fun. |
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409 | >graph_code_has_point @map_mem_prop |
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410 | [@graph_add_lookup] @graph_add |
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411 | qed. |
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412 | |
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413 | definition ertl_to_ltl: ertl_program → ltl_program ≝ |
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414 | λp.transform_program … p (λvarnames. transf_fundef … (translate_internal varnames)). |
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