1 | include "RTL/RTLTailcall.ma". |
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2 | include "utilities/RegisterSet.ma". |
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3 | include "common/Identifiers.ma". |
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4 | include "ERTL/ERTL.ma". |
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5 | include "joint/TranslateUtils.ma". |
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6 | |
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7 | definition save_hdws ≝ |
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8 | λglobals,l. |
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9 | let save_hdws_internal ≝ |
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10 | λdestr_srcr.λstart_lbl. |
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11 | let 〈destr, srcr〉 ≝ destr_srcr in |
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12 | adds_graph ertl_params1 globals [ sequential ertl_params_ … (MOVE … 〈pseudo destr,hardware srcr〉) ] start_lbl |
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13 | in |
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14 | map ? ? save_hdws_internal l. |
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15 | |
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16 | definition restore_hdws ≝ |
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17 | λglobals,l. |
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18 | let restore_hdws_internal ≝ |
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19 | λsrcr_destr: register × Register. |
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20 | λstart_lbl: label. |
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21 | let 〈srcr, destr〉 ≝ srcr_destr in |
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22 | adds_graph ertl_params1 globals [ sequential ertl_params_ … (MOVE … 〈hardware destr, pseudo srcr〉) ] start_lbl |
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23 | in |
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24 | map ? ? restore_hdws_internal l. |
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25 | |
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26 | definition get_params_hdw ≝ |
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27 | λglobals. |
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28 | λparams: list register. |
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29 | match params with |
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30 | [ nil ⇒ [λstart_lbl: label. adds_graph ertl_params1 globals [ GOTO … ] start_lbl] |
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31 | | _ ⇒ |
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32 | let l ≝ zip_pottier ? ? params RegisterParams in |
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33 | save_hdws globals l ]. |
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34 | |
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35 | definition get_param_stack ≝ |
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36 | λglobals. |
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37 | λoff: nat. |
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38 | λdestr. |
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39 | λstart_lbl, dest_lbl: label. |
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40 | λdef. |
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41 | let 〈def, addr1〉 ≝ fresh_reg … def in |
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42 | let 〈def, addr2〉 ≝ fresh_reg … def in |
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43 | let 〈def, tmpr〉 ≝ fresh_reg … def in |
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44 | let 〈carry, int_offset〉 ≝ half_add ? (bitvector_of_nat ? off) int_size in |
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45 | adds_graph ertl_params1 globals [ |
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46 | sequential ertl_params_ … (extension … (ertl_st_ext_frame_size addr1)); |
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47 | sequential ertl_params_ … (INT … tmpr int_offset); |
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48 | sequential ertl_params_ … (OP2 … Sub addr1 addr1 tmpr); |
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49 | sequential ertl_params_ … (MOVE … 〈pseudo tmpr, hardware RegisterSPL〉); |
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50 | sequential ertl_params_ … (OP2 … Add addr1 addr1 tmpr); |
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51 | sequential ertl_params_ … (INT … addr2 (bitvector_of_nat 8 0)); |
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52 | sequential ertl_params_ … (MOVE … 〈pseudo tmpr, hardware RegisterSPH〉); |
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53 | sequential ertl_params_ … (OP2 … Addc addr2 addr2 tmpr); |
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54 | sequential ertl_params_ … (LOAD … destr addr1 addr2) |
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55 | ] start_lbl dest_lbl def. |
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56 | |
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57 | definition get_params_stack ≝ |
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58 | λglobals,params. |
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59 | match params with |
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60 | [ nil ⇒ [ λstart_lbl. adds_graph … [GOTO …] start_lbl ] |
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61 | | _ ⇒ mapi ? ? (get_param_stack globals) params ]. |
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62 | |
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63 | definition get_params ≝ |
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64 | λglobals,params. |
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65 | let n ≝ min (length … params) (length … RegisterParams) in |
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66 | let 〈hdw_params, stack_params〉 ≝ list_split … n params in |
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67 | let hdw_params ≝ get_params_hdw globals hdw_params in |
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68 | hdw_params @ (get_params_stack … stack_params). |
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69 | |
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70 | definition add_prologue ≝ |
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71 | λglobals. |
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72 | λparams: list register. |
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73 | λsral. |
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74 | λsrah. |
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75 | λsregs. |
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76 | λdef. |
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77 | let start_lbl ≝ joint_if_entry … (ertl_params globals) def in |
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78 | let 〈tmp_lbl, def〉 ≝ fresh_label … def in |
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79 | match lookup … (joint_if_code … def) start_lbl |
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80 | return λx. x ≠ None ? → ertl_internal_function globals with |
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81 | [ None ⇒ λnone_absrd. ⊥ |
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82 | | Some last_stmt ⇒ λsome_prf. |
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83 | let def ≝ |
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84 | add_translates … |
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85 | ((adds_graph ertl_params1 … [ |
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86 | sequential ertl_params_ … (extension ertl_params__ globals ertl_st_ext_new_frame) |
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87 | ]) :: |
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88 | (adds_graph ertl_params1 … [ |
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89 | sequential ertl_params_ … (POP … sral); |
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90 | sequential ertl_params_ … (POP … srah) |
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91 | ]) :: |
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92 | (save_hdws … sregs) @ |
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93 | (get_params … params)) |
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94 | start_lbl tmp_lbl def |
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95 | in |
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96 | add_graph … tmp_lbl last_stmt def |
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97 | ] ?. |
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98 | [ cases start_lbl #x #H cases daemon (* @H *) (*CSC: XXXX, no Russell *) |
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99 | | cases (none_absrd) /2/ ] |
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100 | qed. |
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101 | |
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102 | definition save_return ≝ |
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103 | λglobals. |
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104 | λret_regs. |
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105 | λstart_lbl: label. |
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106 | λdest_lbl: label. |
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107 | λdef: ertl_internal_function globals. |
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108 | let 〈def, tmpr〉 ≝ fresh_reg … def in |
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109 | match reduce_strong ? ? RegisterSTS ret_regs with |
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110 | [ dp crl crl_proof ⇒ |
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111 | let commonl ≝ \fst (\fst crl) in |
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112 | let commonr ≝ \fst (\snd crl) in |
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113 | let restl ≝ \snd (\fst crl) in |
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114 | let restr ≝ \snd (\snd crl) in |
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115 | let init_tmpr ≝ sequential ertl_params_ … (INT … tmpr (zero …)) in |
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116 | let f_save ≝ λst. λr. sequential ertl_params_ … (MOVE … 〈hardware st, pseudo r〉) in |
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117 | let saves ≝ map2 … f_save commonl commonr crl_proof in |
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118 | let f_default ≝ λst. sequential ertl_params_ … (MOVE … 〈hardware st, pseudo tmpr〉) in |
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119 | let defaults ≝ map … f_default restl in |
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120 | adds_graph ertl_params1 … (init_tmpr :: saves @ defaults) start_lbl dest_lbl def |
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121 | ]. |
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122 | |
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123 | definition assign_result ≝ |
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124 | λglobals.λstart_lbl: label. |
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125 | match reduce_strong ? ? RegisterRets RegisterSTS with |
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126 | [ dp crl crl_proof ⇒ |
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127 | let commonl ≝ \fst (\fst crl) in |
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128 | let commonr ≝ \fst (\snd crl) in |
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129 | let f ≝ λret. λst. sequential ertl_params_ globals (MOVE … 〈hardware ret, hardware st〉) in |
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130 | let insts ≝ map2 ? ? ? f commonl commonr crl_proof in |
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131 | adds_graph ertl_params1 … insts start_lbl |
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132 | ]. |
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133 | |
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134 | definition add_epilogue ≝ |
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135 | λglobals. |
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136 | λret_regs. |
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137 | λsral. |
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138 | λsrah. |
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139 | λsregs. |
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140 | λdef. |
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141 | let start_lbl ≝ joint_if_exit … (ertl_params globals) def in |
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142 | let 〈tmp_lbl, def〉 ≝ fresh_label … def in |
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143 | match lookup … (joint_if_code … def) start_lbl |
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144 | return λx. x ≠ None ? → ertl_internal_function globals with |
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145 | [ None ⇒ λnone_absrd. ⊥ |
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146 | | Some last_stmt ⇒ λsome_prf. |
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147 | let def ≝ |
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148 | add_translates ertl_params1 … ( |
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149 | [save_return globals ret_regs] @ |
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150 | restore_hdws … sregs @ |
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151 | [adds_graph ertl_params1 … [ |
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152 | sequential ertl_params_ … (PUSH … srah); |
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153 | sequential ertl_params_ … (PUSH … sral) |
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154 | ]] @ |
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155 | [adds_graph ertl_params1 … [ |
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156 | sequential ertl_params_ … (extension … ertl_st_ext_del_frame) |
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157 | ]] @ |
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158 | [assign_result globals] |
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159 | ) start_lbl tmp_lbl def |
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160 | in |
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161 | let def' ≝ add_graph … tmp_lbl last_stmt def in |
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162 | set_joint_if_exit … tmp_lbl def' ? |
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163 | ] ?. |
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164 | [ cases start_lbl #x #H cases daemon (* @H *) (* CSC: XXXX *) |
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165 | | cases (none_absrd) /2/ |
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166 | | cases daemon (* CSC: XXXXX *) |
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167 | ] |
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168 | qed. |
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169 | |
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170 | |
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171 | definition allocate_regs ≝ |
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172 | λglobals. |
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173 | λrs. |
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174 | λsaved: rs_set rs. |
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175 | λdef. |
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176 | let allocate_regs_internal ≝ |
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177 | λr: Register. |
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178 | λdef_sregs. |
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179 | let 〈def, sregs〉 ≝ def_sregs in |
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180 | let 〈def, r'〉 ≝ fresh_reg ertl_params0 globals def in |
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181 | 〈def, 〈r', r〉 :: sregs〉 |
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182 | in |
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183 | rs_fold ? ? allocate_regs_internal saved 〈def, [ ]〉. |
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184 | |
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185 | definition add_pro_and_epilogue ≝ |
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186 | λglobals. |
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187 | λparams. |
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188 | λret_regs. |
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189 | λdef. |
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190 | match fresh_regs_strong … globals def 2 with |
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191 | [ dp def_sra def_sra_proof ⇒ |
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192 | let def ≝ \fst def_sra in |
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193 | let sra ≝ \snd def_sra in |
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194 | let sral ≝ nth_safe ? 0 sra ? in |
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195 | let srah ≝ nth_safe ? 1 sra ? in |
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196 | let 〈def, sregs〉 ≝ allocate_regs … register_list_set RegisterCalleeSaved def in |
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197 | let def ≝ add_prologue … params sral srah sregs def in |
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198 | let def ≝ add_epilogue … ret_regs sral srah sregs def in |
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199 | def |
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200 | ]. |
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201 | >def_sra_proof // |
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202 | qed. |
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203 | |
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204 | definition set_params_hdw ≝ |
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205 | λglobals,params. |
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206 | match params with |
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207 | [ nil ⇒ [ λstart_lbl. adds_graph … [GOTO …] start_lbl] |
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208 | | _ ⇒ |
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209 | let l ≝ zip_pottier ? ? params RegisterParams in |
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210 | restore_hdws globals l |
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211 | ]. |
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212 | |
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213 | definition set_param_stack ≝ |
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214 | λglobals. |
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215 | λoff. |
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216 | λsrcr. |
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217 | λstart_lbl: label. |
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218 | λdest_lbl: label. |
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219 | λdef: ertl_internal_function globals. |
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220 | let 〈def, addr1〉 ≝ fresh_reg … def in |
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221 | let 〈def, addr2〉 ≝ fresh_reg … def in |
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222 | let 〈def, tmpr〉 ≝ fresh_reg … def in |
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223 | let 〈ignore, int_off〉 ≝ half_add ? off int_size in |
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224 | adds_graph ertl_params1 … [ |
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225 | sequential ertl_params_ … (INT … addr1 int_off); |
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226 | sequential ertl_params_ … (MOVE … 〈pseudo tmpr, hardware RegisterSPL〉); |
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227 | sequential ertl_params_ … (CLEAR_CARRY …); |
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228 | sequential ertl_params_ … (OP2 … Sub addr1 tmpr addr1); |
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229 | sequential ertl_params_ … (MOVE … 〈pseudo tmpr, hardware RegisterSPH〉); |
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230 | sequential ertl_params_ … (INT … addr2 (zero ?)); |
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231 | sequential ertl_params_ … (OP2 … Sub addr2 tmpr addr2); |
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232 | sequential ertl_params_ … (STORE … addr1 addr2 srcr) |
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233 | ] start_lbl dest_lbl def. |
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234 | |
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235 | definition set_params_stack ≝ |
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236 | λglobals,params. |
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237 | match params with |
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238 | [ nil ⇒ [ λstart_lbl. adds_graph ertl_params1 globals [GOTO …] start_lbl] |
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239 | | _ ⇒ |
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240 | let f ≝ λi. λr. set_param_stack … (bitvector_of_nat ? i) r in |
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241 | mapi ? ? f params]. |
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242 | |
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243 | definition set_params ≝ |
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244 | λglobals,params. |
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245 | let n ≝ min (|params|) (|RegisterParams|) in |
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246 | let hdw_stack_params ≝ split ? params n ? in |
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247 | let hdw_params ≝ \fst hdw_stack_params in |
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248 | let stack_params ≝ \snd hdw_stack_params in |
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249 | set_params_hdw globals hdw_params @ set_params_stack globals stack_params. |
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250 | /2/ |
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251 | qed. |
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252 | |
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253 | definition fetch_result ≝ |
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254 | λglobals. |
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255 | λret_regs. |
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256 | λstart_lbl: label. |
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257 | match reduce_strong ? ? RegisterSTS RegisterRets with |
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258 | [ dp crl first_crl_proof ⇒ |
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259 | let commonl ≝ \fst (\fst crl) in |
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260 | let commonr ≝ \fst (\snd crl) in |
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261 | let f_save ≝ λst. λret. sequential ertl_params_ globals (MOVE … 〈hardware st, hardware ret〉) in |
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262 | let saves ≝ map2 ? ? ? f_save commonl commonr ? in |
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263 | match reduce_strong ? ? ret_regs RegisterSTS with |
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264 | [ dp crl second_crl_proof ⇒ |
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265 | let commonl ≝ \fst (\fst crl) in |
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266 | let commonr ≝ \fst (\snd crl) in |
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267 | let f_restore ≝ λr. λst. sequential ertl_params_ … (MOVE … 〈pseudo r, hardware st〉) in |
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268 | let restores ≝ map2 ? ? ? f_restore commonl commonr ? in |
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269 | adds_graph ertl_params1 … (saves @ restores) start_lbl]]. |
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270 | [@second_crl_proof | @first_crl_proof] |
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271 | qed. |
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272 | |
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273 | definition translate_call_id ≝ |
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274 | λglobals,f. |
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275 | λargs. |
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276 | λret_regs. |
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277 | λstart_lbl. |
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278 | λdest_lbl. |
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279 | λdef. |
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280 | let nb_args ≝ |args| in |
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281 | add_translates ertl_params1 globals ( |
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282 | set_params … args @ [ |
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283 | adds_graph ertl_params1 … [ sequential ertl_params_ … (CALL_ID … f nb_args it) ]; |
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284 | fetch_result … ret_regs |
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285 | ] |
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286 | ) start_lbl dest_lbl def. |
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287 | |
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288 | definition translate_stmt : |
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289 | ∀globals: list ident. label → rtlntc_statement globals → ertl_internal_function globals → ertl_internal_function globals |
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290 | ≝ |
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291 | λglobals. |
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292 | λlbl. |
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293 | λstmt. |
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294 | λdef. |
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295 | match stmt with |
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296 | [ GOTO lbl' ⇒ add_graph … lbl (GOTO … lbl') def |
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297 | | RETURN ⇒ add_graph … lbl (RETURN …) def |
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298 | | sequential seq lbl' ⇒ |
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299 | match seq with |
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300 | [ PUSH _ ⇒ ⊥ (*CSC: XXXX should not be in the syntax *) |
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301 | | POP _ ⇒ ⊥ (*CSC: XXXX should not be in the syntax *) |
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302 | | CALL_ID f args ret_regs ⇒ |
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303 | translate_call_id … f args ret_regs lbl lbl' def |
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304 | | MOVE rs ⇒ |
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305 | let 〈r1,r2〉 ≝ rs in |
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306 | let rs ≝ 〈pseudo r1, pseudo r2〉 in |
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307 | add_graph ertl_params1 ? lbl (sequential … (MOVE … rs) lbl') def |
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308 | | extension ext ⇒ |
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309 | match ext with |
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310 | [ rtlntc_st_ext_call_ptr _ _ _ _ ⇒ ⊥ (*CSC: XXXX not implemented in OCaml too *) |
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311 | | rtlntc_st_ext_stack_address r1 r2 ⇒ |
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312 | adds_graph ertl_params1 … [ |
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313 | sequential ertl_params_ … (MOVE … 〈pseudo r1, hardware RegisterSPL〉); |
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314 | sequential ertl_params_ … (MOVE … 〈pseudo r2, hardware RegisterSPH〉) |
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315 | ] lbl lbl' def] |
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316 | (*CSC: everything is just copied to re-type it from now on; |
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317 | the problem is call_id that takes different parameters, but that is pattern-matched |
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318 | above. It could be made nicer at the cost of making all the rest of the code uglier *) |
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319 | | COST_LABEL cost_lbl ⇒ add_graph ertl_params1 … lbl (sequential … (COST_LABEL … cost_lbl) lbl') def |
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320 | | ADDRESS x prf r1 r2 ⇒ add_graph ertl_params1 … lbl (sequential … (ADDRESS … x prf r1 r2) lbl') def |
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321 | | INT r i ⇒ add_graph ertl_params1 … lbl (sequential … (INT … r i) lbl') def |
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322 | | OPACCS op destr1 destr2 srcr1 srcr2 ⇒ |
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323 | add_graph ertl_params1 … lbl (sequential … (OPACCS … op destr1 destr2 srcr1 srcr2) lbl') def |
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324 | | OP1 op1 destr srcr ⇒ |
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325 | add_graph ertl_params1 … lbl (sequential … (OP1 … op1 destr srcr) lbl') def |
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326 | | OP2 op2 destr srcr1 srcr2 ⇒ |
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327 | add_graph ertl_params1 … lbl (sequential … (OP2 … op2 destr srcr1 srcr2) lbl') def |
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328 | | CLEAR_CARRY ⇒ |
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329 | add_graph ertl_params1 … lbl (sequential … (CLEAR_CARRY …) lbl') def |
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330 | | SET_CARRY ⇒ |
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331 | add_graph ertl_params1 … lbl (sequential … (SET_CARRY …) lbl') def |
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332 | | LOAD destr addr1 addr2 ⇒ |
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333 | add_graph ertl_params1 … lbl (sequential … (LOAD … destr addr1 addr2) lbl') def |
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334 | | STORE addr1 addr2 srcr ⇒ |
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335 | add_graph ertl_params1 … lbl (sequential … (STORE … addr1 addr2 srcr) lbl') def |
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336 | | COND srcr lbl_true ⇒ |
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337 | add_graph ertl_params1 … lbl (sequential … (COND … srcr lbl_true) lbl') def |
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338 | | COMMENT msg ⇒ |
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339 | add_graph ertl_params1 … lbl (sequential … (COMMENT … msg) lbl') def |
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340 | ]]. |
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341 | @not_implemented (*CSC: XXXX spurious things in the syntax and ptr_calls *) |
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342 | qed. |
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343 | |
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344 | (* hack with empty graphs used here *) |
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345 | definition translate_funct_internal ≝ |
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346 | λglobals.λdef:rtlntc_internal_function globals. |
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347 | let nb_params ≝ |joint_if_params ?? def| in |
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348 | let added_stacksize ≝ max 0 (nb_params - |RegisterParams|) in |
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349 | let new_locals ≝ nub_by ? (eq_identifier ?) ((joint_if_locals … def) @ (joint_if_params … def)) in |
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350 | let entry' ≝ joint_if_entry … def in |
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351 | let exit' ≝ joint_if_exit … def in |
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352 | let graph' ≝ add ? ? (empty_map ? ?) entry' (GOTO … entry') in |
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353 | let graph' ≝ add ? ? graph' exit' (GOTO … exit') in |
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354 | let def' ≝ |
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355 | mk_joint_internal_function globals (ertl_params globals) |
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356 | (joint_if_luniverse … def) (joint_if_runiverse … def) it |
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357 | nb_params new_locals ((joint_if_stacksize … def) + added_stacksize) |
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358 | graph' ? ? in |
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359 | let def' ≝ foldi ? ? ? (translate_stmt globals) (joint_if_code … def) def' in |
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360 | add_pro_and_epilogue ? (joint_if_params ?? def) (joint_if_result ?? def) def'. |
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361 | whd in match ertl_params (* CSC: Matita's bug here; not enough/too much reduction |
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362 | makes the next application fail. Why? *) |
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363 | % |
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364 | [ @entry' | @graph_add_lookup @graph_add |
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365 | | @exit' | @graph_add ] |
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366 | qed. |
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367 | |
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368 | definition generate ≝ |
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369 | λglobals. |
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370 | λstmt. |
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371 | λdef: joint_internal_function … (ertl_params globals). |
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372 | let 〈entry, def〉 ≝ fresh_label … def in |
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373 | let graph ≝ add … (joint_if_code … def) entry stmt in |
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374 | set_joint_if_graph … (ertl_params globals) graph def ??. |
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375 | [ (*% [ @entry | @graph_add ]*) cases daemon (*CSC: XXX *) |
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376 | | (*cases (joint_if_exit … def) #LBL #LBL_PRF % [ @LBL | @graph_add_lookup @LBL_PRF |
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377 | *) cases daemon (*CSC: XXX *) |
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378 | ] |
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379 | qed. |
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380 | |
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381 | let rec find_and_remove_first_cost_label_internal (globals: list ident) |
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382 | (def: ertl_internal_function globals) (lbl: label) (num_nodes: nat) |
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383 | on num_nodes ≝ |
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384 | match num_nodes with |
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385 | [ O ⇒ 〈None ?, def〉 |
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386 | | S num_nodes' ⇒ |
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387 | match lookup … (joint_if_code … def) lbl with |
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388 | [ None ⇒ 〈None ?, def〉 |
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389 | | Some stmt ⇒ |
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390 | match stmt with |
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391 | [ sequential inst lbl ⇒ |
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392 | match inst with |
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393 | [ COST_LABEL cost_lbl ⇒ |
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394 | 〈Some … cost_lbl, add_graph ertl_params1 globals lbl (GOTO … lbl) def〉 |
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395 | | _ ⇒ find_and_remove_first_cost_label_internal globals def lbl num_nodes' ] |
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396 | | RETURN ⇒ 〈None …, def〉 |
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397 | | GOTO lbl ⇒ find_and_remove_first_cost_label_internal globals def lbl num_nodes' |
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398 | ]]]. |
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399 | |
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400 | definition find_and_remove_first_cost_label ≝ |
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401 | λglobals,def. |
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402 | find_and_remove_first_cost_label_internal globals def (joint_if_entry … def) (graph_num_nodes ? (joint_if_code … def)). |
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403 | |
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404 | definition move_first_cost_label_up_internal ≝ |
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405 | λglobals,def. |
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406 | let 〈cost_label, def〉 ≝ find_and_remove_first_cost_label … def in |
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407 | match cost_label with |
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408 | [ None ⇒ def |
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409 | | Some cost_label ⇒ generate … (sequential ertl_params_ globals (COST_LABEL … cost_label) (joint_if_entry … def)) def |
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410 | ]. |
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411 | |
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412 | definition translate_funct ≝ λglobals,def. (move_first_cost_label_up_internal … (translate_funct_internal globals def)). |
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413 | |
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414 | definition translate : rtl_program → ertl_program ≝ |
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415 | λp. |
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416 | let p ≝ tailcall_simplify p in (* tailcall simplification here *) |
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417 | transform_program ??? p (transf_fundef ?? (translate_funct …)). |
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