[789] | 1 | include "RTLabs/syntax.ma". |
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| 2 | include "RTL/RTL.ma". |
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| 3 | include "common/AssocList.ma". |
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[1071] | 4 | include "common/FrontEndOps.ma". |
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[789] | 5 | include "common/Graphs.ma". |
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[1280] | 6 | include "joint/TranslateUtils.ma". |
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[1352] | 7 | include alias "ASM/BitVector.ma". |
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| 8 | include alias "arithmetics/nat.ma". |
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[789] | 9 | |
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[1047] | 10 | let rec register_freshes (runiverse: universe RegisterTag) (n: nat) on n ≝ |
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| 11 | match n with |
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[1281] | 12 | [ O ⇒ 〈[],runiverse〉 |
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| 13 | | S n' ⇒ |
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| 14 | let 〈r,runiverse〉 ≝ fresh … runiverse in |
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| 15 | let 〈res,runiverse〉 ≝ register_freshes runiverse n' in |
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| 16 | 〈r::res,runiverse〉 ]. |
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[1047] | 17 | |
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| 18 | definition complete_regs ≝ |
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[1280] | 19 | λglobals. |
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[1047] | 20 | λdef. |
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| 21 | λsrcrs1. |
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| 22 | λsrcrs2. |
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[1280] | 23 | if leb (length … srcrs2) (length … srcrs1) then |
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| 24 | let 〈def, added_regs〉 ≝ fresh_regs rtl_params0 globals def (minus (length ? srcrs1) (length ? srcrs2)) in |
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| 25 | 〈〈srcrs1, srcrs2 @ added_regs〉, added_regs〉 |
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| 26 | else |
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| 27 | let 〈def, added_regs〉 ≝ fresh_regs rtl_params0 globals def (minus (length ? srcrs2) (length ? srcrs1)) in |
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| 28 | 〈〈srcrs1 @ added_regs, srcrs2〉, added_regs〉. |
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[1047] | 29 | |
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[1280] | 30 | lemma complete_regs_length: |
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| 31 | ∀globals,def,left,right. |
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| 32 | |\fst (\fst (complete_regs globals def left right))| = |\snd (\fst (complete_regs globals def left right))|. |
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| 33 | #globals #def #left #right |
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[1521] | 34 | whd in match complete_regs; normalize nodelta |
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[1280] | 35 | @leb_elim normalize nodelta #H |
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[1521] | 36 | [ generalize in match (fresh_regs_length rtl_params0 globals def (minus (length … left) (length … right))); |
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| 37 | | generalize in match (fresh_regs_length rtl_params0 globals def (minus (length … right) (length … left)));] |
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[1280] | 38 | cases (fresh_regs ????) #def' #fresh normalize >append_length |
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[1521] | 39 | generalize in match H; -H; |
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| 40 | generalize in match (length … left); generalize in match (length … right); generalize in match (length … fresh); |
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| 41 | [ /2/ | #x #y #z #H generalize in match (not_le_to_lt … H); -H #H #E >E >commutative_plus |
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[1280] | 42 | <plus_minus_m_m /2/ ] |
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| 43 | qed. |
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[1064] | 44 | |
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[1053] | 45 | definition size_of_sig_type ≝ |
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[1052] | 46 | λsig. |
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| 47 | match sig with |
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[1047] | 48 | [ ASTint isize sign ⇒ |
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[1053] | 49 | let isize' ≝ match isize with [ I8 ⇒ 8 | I16 ⇒ 16 | I32 ⇒ 32 ] in |
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| 50 | isize' ÷ (nat_of_bitvector ? int_size) |
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| 51 | | ASTfloat _ ⇒ ? (* dpm: not implemented *) |
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| 52 | | ASTptr rgn ⇒ nat_of_bitvector ? ptr_size |
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[1047] | 53 | ]. |
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[1053] | 54 | cases not_implemented; |
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[1052] | 55 | qed. |
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[1047] | 56 | |
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[789] | 57 | inductive register_type: Type[0] ≝ |
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| 58 | | register_int: register → register_type |
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| 59 | | register_ptr: register → register → register_type. |
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| 60 | |
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[1515] | 61 | definition local_env ≝ identifier_map RegisterTag (list register). |
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[789] | 62 | |
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[1280] | 63 | definition mem_local_env : register → local_env → bool ≝ |
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[1515] | 64 | λr,e. member … e r. |
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[1052] | 65 | |
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[1280] | 66 | definition add_local_env : register → list register → local_env → local_env ≝ |
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[1515] | 67 | λr,v,e. add … e r v. |
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[1052] | 68 | |
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[1280] | 69 | definition find_local_env : register → local_env → list register ≝ |
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[1515] | 70 | λr: register.λenv. lookup_def … env r []. |
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[1052] | 71 | |
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[789] | 72 | definition initialize_local_env_internal ≝ |
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[1281] | 73 | λlenv_runiverse. |
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[1053] | 74 | λr_sig. |
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[1281] | 75 | let 〈lenv,runiverse〉 ≝ lenv_runiverse in |
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[1053] | 76 | let 〈r, sig〉 ≝ r_sig in |
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| 77 | let size ≝ size_of_sig_type sig in |
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[1281] | 78 | let 〈rs,runiverse〉 ≝ register_freshes runiverse size in |
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| 79 | 〈add_local_env r rs lenv,runiverse〉. |
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[789] | 80 | |
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| 81 | definition initialize_local_env ≝ |
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| 82 | λruniverse. |
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| 83 | λregisters. |
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[1053] | 84 | λresult. |
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[1050] | 85 | let registers ≝ registers @ |
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| 86 | match result with |
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| 87 | [ None ⇒ [ ] |
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| 88 | | Some rt ⇒ [ rt ] |
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| 89 | ] |
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| 90 | in |
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[1515] | 91 | foldl … initialize_local_env_internal 〈empty_map …,runiverse〉 registers. |
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[1280] | 92 | |
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[1050] | 93 | definition map_list_local_env_internal ≝ |
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[1280] | 94 | λlenv,res,r. res @ (find_local_env r lenv). |
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[1050] | 95 | |
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| 96 | definition map_list_local_env ≝ |
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[1280] | 97 | λlenv,regs. foldl … (map_list_local_env_internal lenv) [ ] regs. |
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[1050] | 98 | |
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[1053] | 99 | definition make_addr ≝ |
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| 100 | λA. |
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| 101 | λlst: list A. |
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[1343] | 102 | λprf: 2 = length A lst. |
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| 103 | match lst return λx. 2 = |x| → A × A with |
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[1053] | 104 | [ nil ⇒ λlst_nil_prf. ? |
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| 105 | | cons hd tl ⇒ λprf. |
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[1343] | 106 | match tl return λx. 1 = |x| → A × A with |
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[1053] | 107 | [ nil ⇒ λtl_nil_prf. ? |
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| 108 | | cons hd' tl' ⇒ λtl_cons_prf. 〈hd, hd'〉 |
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| 109 | ] ? |
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| 110 | ] prf. |
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| 111 | [1: normalize in lst_nil_prf; |
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[1343] | 112 | destruct(lst_nil_prf) |
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[1053] | 113 | |2: normalize in prf; |
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[1343] | 114 | @injective_S |
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[1066] | 115 | assumption |
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[1053] | 116 | |3: normalize in tl_nil_prf; |
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[1343] | 117 | destruct(tl_nil_prf) |
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| 118 | ] |
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[1053] | 119 | qed. |
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[1050] | 120 | |
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[789] | 121 | definition find_and_addr ≝ |
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[1280] | 122 | λr,lenv. make_addr ? (find_local_env r lenv). |
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[789] | 123 | |
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| 124 | definition rtl_args ≝ |
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[1280] | 125 | λregs_list,lenv. flatten … (map … (λr. find_local_env r lenv) regs_list). |
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[789] | 126 | |
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[1057] | 127 | definition translate_cst_int_internal ≝ |
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[1282] | 128 | λglobals,dest_lbl,r,i. sequential rtl_params_ globals (INT … r i) dest_lbl. |
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[1057] | 129 | |
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[1354] | 130 | definition split_into_bytes: |
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| 131 | ∀size. ∀int: bvint size. Σbytes: list Byte. |bytes| = size_intsize size ≝ |
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| 132 | λsize. |
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| 133 | match size return λsize.∀int: bvint size. Σbytes. |bytes| = size_intsize size with |
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| 134 | [ I8 ⇒ λint. ? | I16 ⇒ λint. ? | I32 ⇒ λint. ? ]. |
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| 135 | [ %[@[int]] // |
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| 136 | | %[@(let 〈h,l〉 ≝ split ? 8 … int in [l;h])] cases (split ????) // |
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| 137 | | %[@(let 〈h1,l〉 ≝ split ? 8 … int in |
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| 138 | let 〈h2,l〉 ≝ split ? 8 … l in |
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| 139 | let 〈h3,l〉 ≝ split ? 8 … l in |
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| 140 | [l;h3;h2;h1])] |
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| 141 | cases (split ????) #h1 #l normalize |
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| 142 | cases (split ????) #h2 #l normalize |
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| 143 | cases (split ????) // ] |
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| 144 | qed. |
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[1308] | 145 | |
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| 146 | lemma eqb_implies_eq: |
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| 147 | ∀m, n: nat. |
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| 148 | eqb m n = true → m = n. |
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| 149 | #M |
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| 150 | elim M |
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| 151 | [1: #N normalize |
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| 152 | cases N |
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| 153 | [1: normalize // |
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| 154 | |2: #M' normalize #HYP destruct(HYP) |
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| 155 | ] |
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| 156 | |2: #M' #IND_HYP #N |
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| 157 | normalize |
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| 158 | cases N |
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| 159 | [1: normalize #HYP destruct(HYP) |
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| 160 | |2: #M'' normalize #HYP |
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| 161 | @eq_f @(IND_HYP M'') |
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| 162 | assumption |
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| 163 | ] |
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| 164 | ] |
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| 165 | qed. |
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| 166 | |
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[1325] | 167 | definition translate_op: ∀globals. ? → list register → list register → list register → |
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| 168 | label → label → rtl_internal_function globals → rtl_internal_function globals ≝ |
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| 169 | λglobals: list ident. |
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| 170 | λop. |
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| 171 | λdestrs: list register. |
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| 172 | λsrcrs1: list register. |
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| 173 | λsrcrs2: list register. |
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| 174 | λstart_lbl: label. |
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| 175 | λdest_lbl: label. |
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| 176 | λdef: rtl_internal_function globals. |
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| 177 | match reduce_strong register register srcrs1 srcrs2 with |
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[1601] | 178 | [ mk_Sig reduced first_reduced_proof ⇒ |
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[1325] | 179 | let srcrsl_common ≝ \fst (\fst reduced) in |
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| 180 | let srcrsr_common ≝ \fst (\snd reduced) in |
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| 181 | let srcrsl_rest ≝ \snd (\fst reduced) in |
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| 182 | let srcrsr_rest ≝ \snd (\snd reduced) in |
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| 183 | let srcrs_rest ≝ srcrsl_rest @ srcrsr_rest in |
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| 184 | match reduce_strong register register destrs srcrsl_common with |
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[1601] | 185 | [ mk_Sig reduced second_reduced_proof ⇒ |
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[1325] | 186 | let destrs_common ≝ \fst (\fst reduced) in |
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| 187 | let destrs_rest ≝ \snd (\fst reduced) in |
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| 188 | match reduce_strong register register destrs_rest srcrs_rest with |
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[1601] | 189 | [ mk_Sig reduced third_reduced_proof ⇒ |
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[1325] | 190 | let destrs_cted ≝ \fst (\fst reduced) in |
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| 191 | let destrs_rest ≝ \snd (\fst reduced) in |
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| 192 | let srcrs_cted ≝ \fst (\snd reduced) in |
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| 193 | let 〈def, tmpr〉 ≝ fresh_reg rtl_params0 globals def in |
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| 194 | let insts_init ≝ [ |
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| 195 | sequential … (CLEAR_CARRY …); |
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| 196 | sequential … (INT rtl_params_ globals tmpr (zero …)) |
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| 197 | ] in |
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| 198 | let f_add ≝ λdestr. λsrcr1. λsrcr2. sequential … (OP2 rtl_params_ globals op destr srcr1 srcr2) in |
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| 199 | let insts_add ≝ map3 ? ? ? ? f_add destrs_common srcrsl_common srcrsr_common ? ? in |
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| 200 | let f_add_cted ≝ λdestr. λsrcr. sequential … (OP2 rtl_params_ globals op destr srcr tmpr) in |
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| 201 | let insts_add_cted ≝ map2 … f_add_cted destrs_cted srcrs_cted ? in |
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| 202 | let f_rest ≝ λdestr. sequential … (OP2 rtl_params_ globals op destr tmpr tmpr) in |
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| 203 | let insts_rest ≝ map … f_rest destrs_rest in |
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| 204 | adds_graph rtl_params1 globals (insts_init @ insts_add @ insts_add_cted @ insts_rest) start_lbl dest_lbl def |
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| 205 | ] |
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| 206 | ] |
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| 207 | ]. |
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| 208 | [1: @third_reduced_proof |
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| 209 | |3: @first_reduced_proof |
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| 210 | |*: cases daemon (* XXX: some of these look like they may be false *) |
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| 211 | ] |
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| 212 | qed. |
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| 213 | |
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[1307] | 214 | let rec translate_cst |
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| 215 | (globals: list ident) (cst: constant) (destrs: list register) |
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| 216 | (start_lbl: label) (dest_lbl: label) (def: rtl_internal_function globals) |
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| 217 | on cst: rtl_internal_function globals ≝ |
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| 218 | match cst with |
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| 219 | [ Ointconst size const ⇒ |
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| 220 | match destrs with |
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[1308] | 221 | [ nil ⇒ add_graph … start_lbl (GOTO … dest_lbl) def |
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| 222 | | _ ⇒ |
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| 223 | let size' ≝ size_intsize size in |
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| 224 | match eqb size' (|destrs|) return λx. (eqb size' (|destrs|)) = x → rtl_internal_function globals with |
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| 225 | [ true ⇒ λgood_case. |
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| 226 | match split_into_bytes size const with |
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[1601] | 227 | [ mk_Sig bytes bytes_length_proof ⇒ |
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[1308] | 228 | let mapped ≝ map2 … (λd. λb. (sequential … (INT rtl_params_ globals d b))) destrs bytes ? in |
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| 229 | adds_graph rtl_params1 globals mapped start_lbl dest_lbl def |
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| 230 | ] |
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| 231 | | false ⇒ λbad_case. ? |
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| 232 | ] (refl … (eqb size' (|destrs|))) |
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[1307] | 233 | ] |
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| 234 | | Ofloatconst float ⇒ ⊥ |
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[1308] | 235 | | Oaddrsymbol id offset ⇒ |
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| 236 | let 〈r1, r2〉 ≝ make_addr … destrs ? in |
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[1325] | 237 | let def ≝ add_graph rtl_params1 globals start_lbl (sequential … (ADDRESS rtl_params_ globals id ? r1 r2) dest_lbl) def in |
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| 238 | let def ≝ translate_op globals Addc [r1] [r1] [r2] start_lbl dest_lbl def in |
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| 239 | def |
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[1308] | 240 | | Oaddrstack offset ⇒ |
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| 241 | let 〈r1, r2〉 ≝ make_addr … destrs ? in |
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[1343] | 242 | let def ≝ add_graph rtl_params1 globals start_lbl (sequential … (extension rtl_params_ globals (rtl_st_ext_stack_address r1 r2)) dest_lbl) def in |
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[1325] | 243 | let def ≝ translate_op globals Addc [r1] [r1] [r2] start_lbl dest_lbl def in |
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| 244 | def |
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[1307] | 245 | ]. |
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[1308] | 246 | [1: >bytes_length_proof |
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| 247 | cut(size' = |destrs|) |
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| 248 | [1: @eqb_implies_eq |
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| 249 | assumption |
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| 250 | |2: #EQ_HYP |
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| 251 | <EQ_HYP % |
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| 252 | ] |
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[1325] | 253 | |2: cases daemon (* XXX: bad case where destrs is of the wrong length *) |
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| 254 | |3: cases not_implemented (* XXX: float, error_float in o'caml *) |
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| 255 | |*: cases daemon (* XXX: various proofs to be filled in *) |
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[1307] | 256 | ]. |
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[1315] | 257 | qed. |
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[1307] | 258 | |
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[1059] | 259 | definition translate_move_internal ≝ |
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[1280] | 260 | λglobals. |
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[1059] | 261 | λdestr: register. |
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| 262 | λsrcr: register. |
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[1283] | 263 | sequential rtl_params_ globals (MOVE … 〈destr,srcr〉). |
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[1057] | 264 | |
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[1059] | 265 | definition translate_move ≝ |
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[1280] | 266 | λglobals. |
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[1059] | 267 | λdestrs: list register. |
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| 268 | λsrcrs: list register. |
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| 269 | λstart_lbl: label. |
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[1071] | 270 | match reduce_strong register register destrs srcrs with |
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[1601] | 271 | [ mk_Sig crl_crr len_proof ⇒ |
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[1060] | 272 | let commonl ≝ \fst (\fst crl_crr) in |
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| 273 | let commonr ≝ \fst (\snd crl_crr) in |
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| 274 | let restl ≝ \snd (\fst crl_crr) in |
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| 275 | let restr ≝ \snd (\snd crl_crr) in |
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[1283] | 276 | let f_common ≝ translate_move_internal globals in |
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[1280] | 277 | let translate1 ≝ adds_graph rtl_params1 … (map2 … f_common commonl commonr ?) in |
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| 278 | let translate2 ≝ translate_cst … (Ointconst ? (repr I8 0)) restl in (* should this be 8? *) |
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| 279 | add_translates … [ translate1 ; translate2 ] start_lbl |
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[1060] | 280 | ]. |
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| 281 | @len_proof |
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| 282 | qed. |
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| 283 | |
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| 284 | let rec make |
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| 285 | (A: Type[0]) (elt: A) (n: nat) on n ≝ |
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| 286 | match n with |
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| 287 | [ O ⇒ [ ] |
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| 288 | | S n' ⇒ elt :: make A elt n' |
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| 289 | ]. |
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| 290 | |
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| 291 | lemma make_length: |
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| 292 | ∀A: Type[0]. |
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| 293 | ∀elt: A. |
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| 294 | ∀n: nat. |
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| 295 | n = length ? (make A elt n). |
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| 296 | #A #ELT #N |
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| 297 | elim N |
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| 298 | [ normalize % |
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| 299 | | #N #IH |
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| 300 | normalize <IH % |
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| 301 | ] |
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| 302 | qed. |
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| 303 | |
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| 304 | definition translate_cast_unsigned ≝ |
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[1280] | 305 | λglobals. |
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[1060] | 306 | λdestrs. |
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| 307 | λstart_lbl. |
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| 308 | λdest_lbl. |
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[1280] | 309 | λdef: joint_internal_function … (rtl_params globals). |
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| 310 | let 〈def, tmp_zero〉 ≝ fresh_reg … def in |
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| 311 | let zeros ≝ make … tmp_zero (length … destrs) in |
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| 312 | add_translates … [ |
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| 313 | adds_graph rtl_params1 … [ |
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[1283] | 314 | sequential rtl_params_ … (INT rtl_params_ ? tmp_zero (bitvector_of_nat ? 0)) |
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[1060] | 315 | ]; |
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[1280] | 316 | translate_move globals destrs zeros |
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[1060] | 317 | ] start_lbl dest_lbl def. |
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| 318 | |
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[1285] | 319 | definition translate_cast_signed: |
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| 320 | ∀globals: list ident. list register → ? → label → label → rtl_internal_function globals → rtl_internal_function globals ≝ |
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| 321 | λglobals: list ident. |
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[1060] | 322 | λdestrs. |
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| 323 | λsrcr. |
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| 324 | λstart_lbl. |
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| 325 | λdest_lbl. |
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| 326 | λdef. |
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[1280] | 327 | let 〈def, tmp_128〉 ≝ fresh_reg … def in |
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| 328 | let 〈def, tmp_255〉 ≝ fresh_reg … def in |
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| 329 | let 〈def, tmpr〉 ≝ fresh_reg … def in |
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| 330 | let 〈def, dummy〉 ≝ fresh_reg … def in |
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[1060] | 331 | let insts ≝ [ |
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[1285] | 332 | sequential … (INT rtl_params_ globals tmp_128 (bitvector_of_nat ? 128)); |
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| 333 | sequential … (OP2 rtl_params_ globals And tmpr tmp_128 srcr); |
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| 334 | sequential … (OPACCS rtl_params_ globals DivuModu tmpr dummy tmpr tmp_128); |
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| 335 | sequential … (INT rtl_params_ globals tmp_255 (bitvector_of_nat ? 255)); |
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| 336 | sequential … (OPACCS rtl_params_ globals Mul tmpr dummy tmpr tmp_255) |
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| 337 | ] |
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| 338 | in |
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[1280] | 339 | let srcrs ≝ make … tmpr (length … destrs) in |
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[1285] | 340 | add_translates rtl_params1 globals [ |
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| 341 | adds_graph rtl_params1 globals insts; |
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| 342 | translate_move globals destrs srcrs |
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[1060] | 343 | ] start_lbl dest_lbl def. |
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| 344 | |
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| 345 | definition translate_cast ≝ |
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[1285] | 346 | λglobals: list ident. |
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| 347 | λsrc_size: nat. |
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| 348 | λsrc_sign: signedness. |
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| 349 | λdest_size: nat. |
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| 350 | λdestrs: list register. |
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| 351 | λsrcrs: list register. |
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[1066] | 352 | match |srcrs| return λx. |srcrs| = x → ? with |
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[1285] | 353 | [ O ⇒ λzero_prf. adds_graph rtl_params1 globals [ ] |
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[1060] | 354 | | S n' ⇒ λsucc_prf. |
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| 355 | if ltb dest_size src_size then |
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[1285] | 356 | translate_move globals destrs srcrs |
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[1060] | 357 | else |
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[1071] | 358 | match reduce_strong register register destrs srcrs with |
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[1601] | 359 | [ mk_Sig crl len_proof ⇒ |
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[1060] | 360 | let commonl ≝ \fst (\fst crl) in |
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| 361 | let commonr ≝ \fst (\snd crl) in |
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| 362 | let restl ≝ \snd (\fst crl) in |
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| 363 | let restr ≝ \snd (\snd crl) in |
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[1285] | 364 | let insts_common ≝ translate_move globals commonl commonr in |
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[1060] | 365 | let sign_reg ≝ last_safe ? srcrs ? in |
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| 366 | let insts_sign ≝ |
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| 367 | match src_sign with |
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[1285] | 368 | [ Unsigned ⇒ translate_cast_unsigned globals restl |
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| 369 | | Signed ⇒ translate_cast_signed globals restl sign_reg |
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[1060] | 370 | ] |
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| 371 | in |
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[1285] | 372 | add_translates rtl_params1 globals [ insts_common; insts_sign ] |
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[1060] | 373 | ] |
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| 374 | ] (refl ? (|srcrs|)). |
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| 375 | >succ_prf // |
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| 376 | qed. |
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| 377 | |
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| 378 | definition translate_negint ≝ |
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[1285] | 379 | λglobals: list ident. |
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| 380 | λdestrs: list register. |
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| 381 | λsrcrs: list register. |
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| 382 | λstart_lbl: label. |
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| 383 | λdest_lbl: label. |
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| 384 | λdef: rtl_internal_function globals. |
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| 385 | λprf: |destrs| = |srcrs|. (* assert in caml code *) |
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| 386 | let 〈def, tmpr〉 ≝ fresh_reg rtl_params0 globals def in |
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| 387 | let f_cmpl ≝ λdestr. λsrcr. sequential rtl_params_ globals (OP1 rtl_params1 globals Cmpl destr srcr) in |
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| 388 | let insts_cmpl ≝ map2 … f_cmpl destrs srcrs prf in |
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[1060] | 389 | let insts_init ≝ [ |
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[1285] | 390 | sequential … (SET_CARRY …); |
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| 391 | sequential … (INT rtl_params_ globals tmpr (zero ?)) |
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[1060] | 392 | ] in |
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[1285] | 393 | let f_add ≝ λdestr. sequential … (OP2 rtl_params_ globals Addc destr destr tmpr) in |
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[1060] | 394 | let insts_add ≝ map … f_add destrs in |
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[1285] | 395 | adds_graph rtl_params1 globals (insts_cmpl @ insts_init @ insts_add) start_lbl dest_lbl def. |
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[1060] | 396 | |
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[1285] | 397 | definition translate_notbool: ∀globals. list register → list register → label → label → rtl_internal_function globals → rtl_internal_function globals ≝ |
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| 398 | λglobals: list ident. |
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| 399 | λdestrs: list register. |
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| 400 | λsrcrs: list register. |
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| 401 | λstart_lbl: label. |
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| 402 | λdest_lbl: label. |
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| 403 | λdef: rtl_internal_function globals. |
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[1060] | 404 | match destrs with |
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[1285] | 405 | [ nil ⇒ add_graph rtl_params1 globals start_lbl (GOTO … start_lbl) def |
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[1060] | 406 | | cons destr destrs ⇒ |
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[1285] | 407 | let 〈def, tmpr〉 ≝ fresh_reg rtl_params0 globals def in |
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| 408 | let 〈def, tmp_srcrs〉 ≝ fresh_regs rtl_params0 globals def (length ? srcrs) in |
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| 409 | let save_srcrs ≝ translate_move globals tmp_srcrs srcrs in |
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| 410 | let init_destr ≝ sequential … (INT rtl_params_ globals destr (bitvector_of_nat ? 1)) in |
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[1060] | 411 | let f ≝ λtmp_srcr. [ |
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[1285] | 412 | sequential … (CLEAR_CARRY rtl_params_ globals); |
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| 413 | sequential … (INT rtl_params_ globals tmpr (zero ?)); |
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| 414 | sequential … (OP2 rtl_params_ globals Sub tmpr tmpr tmp_srcr); |
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| 415 | sequential … (INT rtl_params_ globals tmpr (zero ?)); |
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| 416 | sequential … (OP2 rtl_params_ globals Addc tmpr tmpr tmpr); |
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| 417 | sequential … (OP2 rtl_params_ globals Xor destr destr tmpr) |
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[1060] | 418 | ] in |
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[1285] | 419 | let insts ≝ init_destr :: (flatten … (map … f tmp_srcrs)) in |
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| 420 | let epilogue ≝ translate_cst globals (Ointconst I8 (zero …)) destrs in |
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| 421 | add_translates rtl_params1 globals [ |
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| 422 | save_srcrs; adds_graph rtl_params1 globals insts; epilogue |
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[1060] | 423 | ] start_lbl dest_lbl def |
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| 424 | ]. |
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| 425 | |
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[1066] | 426 | (* TODO: examine this properly. This is a change from the O'caml code due |
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| 427 | to us dropping the explicit use of a cast destination size field. We |
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| 428 | instead infer the size of the cast's destination from the context. Is |
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| 429 | this correct? |
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| 430 | *) |
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[1064] | 431 | definition translate_op1 ≝ |
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[1286] | 432 | λglobals: list ident. |
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[1529] | 433 | λty, ty'. |
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| 434 | λop1: unary_operation ty ty'. |
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[1064] | 435 | λdestrs: list register. |
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| 436 | λsrcrs: list register. |
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[1062] | 437 | λprf: |destrs| = |srcrs|. |
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[1064] | 438 | λstart_lbl: label. |
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| 439 | λdest_lbl: label. |
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[1286] | 440 | λdef: rtl_internal_function globals. |
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[1060] | 441 | match op1 with |
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[1529] | 442 | [ Ocastint src_size src_sign _ _ ⇒ |
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[1066] | 443 | let dest_size ≝ |destrs| * 8 in |
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| 444 | let src_size ≝ bitsize_of_intsize src_size in |
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[1286] | 445 | translate_cast globals src_size src_sign dest_size destrs srcrs start_lbl dest_lbl def |
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[1529] | 446 | | Onegint _ _ ⇒ |
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[1286] | 447 | translate_negint globals destrs srcrs start_lbl dest_lbl def prf |
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[1529] | 448 | | Onotbool _ _ _ _ ⇒ |
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[1286] | 449 | translate_notbool globals destrs srcrs start_lbl dest_lbl def |
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[1529] | 450 | | Onotint _ _ ⇒ |
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[1286] | 451 | let f ≝ λdestr. λsrcr. sequential rtl_params_ globals (OP1 … Cmpl destr srcr) in |
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[1060] | 452 | let l ≝ map2 … f destrs srcrs prf in |
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[1286] | 453 | adds_graph rtl_params1 globals l start_lbl dest_lbl def |
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[1529] | 454 | | Optrofint _ _ r ⇒ |
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[1286] | 455 | translate_move globals destrs srcrs start_lbl dest_lbl def |
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[1529] | 456 | | Ointofptr _ _ r ⇒ |
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[1286] | 457 | translate_move globals destrs srcrs start_lbl dest_lbl def |
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[1529] | 458 | | Oid _ ⇒ |
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[1286] | 459 | translate_move globals destrs srcrs start_lbl dest_lbl def |
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[1066] | 460 | | _ ⇒ ? (* float operations implemented in runtime *) |
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[1060] | 461 | ]. |
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[1066] | 462 | cases not_implemented |
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| 463 | qed. |
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[1057] | 464 | |
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[1062] | 465 | let rec translate_mul1 |
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[1286] | 466 | (globals: list ident) (dummy: register) (tmpr: register) |
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| 467 | (destrs: list register) (srcrs1: list register) (srcr2: register) |
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| 468 | (start_lbl: label) |
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| 469 | on srcrs1 ≝ |
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[1062] | 470 | match destrs with |
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[1286] | 471 | [ nil ⇒ adds_graph rtl_params1 globals [ GOTO … ] start_lbl |
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[1062] | 472 | | cons destr tl ⇒ |
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| 473 | match tl with |
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| 474 | [ nil ⇒ |
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| 475 | match srcrs1 with |
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| 476 | [ nil ⇒ |
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[1286] | 477 | adds_graph rtl_params1 globals [ |
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| 478 | sequential … (INT rtl_params_ globals tmpr (zero …)); |
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| 479 | sequential … (OP2 rtl_params_ globals Addc destr destr tmpr) |
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[1062] | 480 | ] start_lbl |
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| 481 | | cons srcr1 tl' ⇒ |
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[1286] | 482 | adds_graph rtl_params1 globals [ |
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| 483 | sequential … (OPACCS rtl_params_ globals Mul tmpr dummy srcr2 srcr1); |
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| 484 | sequential … (OP2 rtl_params_ globals Addc destr destr tmpr) |
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[1062] | 485 | ] start_lbl |
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| 486 | ] |
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| 487 | | cons destr2 destrs ⇒ |
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| 488 | match srcrs1 with |
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| 489 | [ nil ⇒ |
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[1286] | 490 | add_translates rtl_params1 globals [ |
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| 491 | adds_graph rtl_params1 globals [ |
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| 492 | sequential … (INT rtl_params_ globals tmpr (zero …)); |
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| 493 | sequential … (OP2 rtl_params_ globals Addc destr destr tmpr); |
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| 494 | sequential … (OP2 rtl_params_ globals Addc destr2 tmpr tmpr) |
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[1062] | 495 | ]; |
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[1286] | 496 | translate_cst globals (Ointconst I8 (zero …)) destrs |
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[1062] | 497 | ] start_lbl |
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| 498 | | cons srcr1 srcrs1 ⇒ |
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| 499 | match destrs with |
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| 500 | [ nil ⇒ |
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[1286] | 501 | add_translates rtl_params1 globals [ |
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| 502 | adds_graph rtl_params1 globals [ |
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| 503 | sequential … (INT rtl_params_ globals tmpr (zero …)); |
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| 504 | sequential … (OP2 rtl_params_ globals Addc destr destr tmpr); |
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| 505 | sequential … (OP2 rtl_params_ globals Addc destr2 tmpr tmpr) |
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[1062] | 506 | ]; |
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[1286] | 507 | translate_cst globals (Ointconst I8 (zero ?)) destrs |
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[1062] | 508 | ] start_lbl |
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| 509 | | cons destr2 destrs ⇒ |
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[1286] | 510 | add_translates rtl_params1 globals [ |
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| 511 | adds_graph rtl_params1 globals [ |
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| 512 | sequential … (OPACCS rtl_params_ globals Mul tmpr destr2 srcr2 srcr1); |
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| 513 | sequential … (OP2 rtl_params_ globals Addc destr destr tmpr) |
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[1062] | 514 | ]; |
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[1286] | 515 | translate_mul1 globals dummy tmpr (destr2 :: destrs) srcrs1 srcr2 |
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[1062] | 516 | ] start_lbl |
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| 517 | ] |
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| 518 | ] |
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| 519 | ] |
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| 520 | ]. |
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| 521 | |
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| 522 | definition translate_muli ≝ |
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[1286] | 523 | λglobals: list ident. |
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[1062] | 524 | λdummy: register. |
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| 525 | λtmpr: register. |
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| 526 | λdestrs: list register. |
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| 527 | λtmp_destrs: list register. |
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| 528 | λsrcrs1: list register. |
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| 529 | λdummy_lbl: label. |
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| 530 | λi: nat. |
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[1325] | 531 | λi_prf: i ≤ |tmp_destrs|. |
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[1063] | 532 | λtranslates: list ?. |
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| 533 | λsrcr2i: register. |
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[1286] | 534 | let 〈tmp_destrs1, tmp_destrs2〉 ≝ split … tmp_destrs i i_prf in |
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[1063] | 535 | let tmp_destrs2' ≝ |
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| 536 | match tmp_destrs2 with |
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| 537 | [ nil ⇒ [ ] |
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| 538 | | cons tmp_destr2 tmp_destrs2 ⇒ [ |
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[1286] | 539 | adds_graph rtl_params1 globals [ |
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| 540 | sequential rtl_params_ globals (CLEAR_CARRY …); |
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| 541 | sequential … (INT rtl_params_ globals tmp_destr2 (zero …)) |
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[1063] | 542 | ]; |
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[1286] | 543 | translate_mul1 globals dummy tmpr tmp_destrs2 srcrs1 srcr2i; |
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| 544 | translate_cst globals (Ointconst I8 (zero …)) tmp_destrs1; |
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| 545 | adds_graph rtl_params1 globals [ |
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| 546 | sequential rtl_params_ globals (CLEAR_CARRY …) |
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[1063] | 547 | ]; |
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[1286] | 548 | translate_op globals Addc destrs destrs tmp_destrs |
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[1063] | 549 | ] |
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| 550 | ] |
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| 551 | in |
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| 552 | translates @ tmp_destrs2'. |
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[1356] | 553 | |
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| 554 | let rec remove_n_first_internal |
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| 555 | (b: Type[0]) (n: nat) (the_list: list b) (i: nat) |
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| 556 | on the_list ≝ |
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| 557 | match the_list with |
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| 558 | [ nil ⇒ [ ] |
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| 559 | | cons hd tl ⇒ |
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| 560 | match eqb i n with |
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| 561 | [ true ⇒ the_list |
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| 562 | | false ⇒ remove_n_first_internal b n tl (S i) |
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| 563 | ] |
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| 564 | ]. |
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| 565 | |
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| 566 | definition remove_n_first ≝ |
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| 567 | λb: Type[0]. |
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| 568 | λn: nat. |
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| 569 | λthe_list: list b. |
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| 570 | remove_n_first_internal b n the_list 0. |
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| 571 | |
---|
| 572 | axiom plus_m_n_eq_o_to_lt_m_o: |
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| 573 | ∀m, n, o: nat. |
---|
| 574 | m + n = o → m ≤ o. |
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| 575 | |
---|
| 576 | include alias "arithmetics/nat.ma". |
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| 577 | |
---|
| 578 | axiom minus_m_n_Sp_to_minus_m_Sn_p: |
---|
| 579 | ∀m, n, p: nat. |
---|
| 580 | minus m n = S p → minus m (S n) = p. |
---|
| 581 | |
---|
| 582 | let rec foldi_strong_internal |
---|
| 583 | (a: Type[0]) (b: Type[0]) (reference: nat) (the_list: list b) |
---|
| 584 | (f: ∀j: nat. ∀proof: lt j (|the_list|). a → b → a) (seed: a) |
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| 585 | (counter: nat) (counter_proof: minus reference counter = |the_list|) |
---|
| 586 | on the_list: a ≝ |
---|
| 587 | match the_list return λx. the_list = x → (minus reference counter = |x|) → a with |
---|
| 588 | [ nil ⇒ λidentity. λbase_case. seed |
---|
| 589 | | cons hd tl ⇒ λidentity. λstep_case. |
---|
| 590 | let f' ≝ λj: nat. λproof: j < |tl|. f j ? in |
---|
| 591 | foldi_strong_internal a b reference tl f' (f counter ? seed hd) (S counter) ? |
---|
| 592 | ] (refl … the_list) counter_proof. |
---|
[1358] | 593 | [1: cases daemon (* XXX: to do *) |
---|
[1356] | 594 | |2: generalize in match counter_proof; |
---|
| 595 | >identity |
---|
| 596 | #HYP |
---|
| 597 | normalize in HYP:(???%); |
---|
| 598 | generalize in match (minus_m_n_Sp_to_minus_m_Sn_p reference counter (|tl|) HYP); |
---|
| 599 | #ASSM assumption |
---|
| 600 | |3: >identity |
---|
| 601 | normalize |
---|
| 602 | normalize in proof; |
---|
| 603 | generalize in match(le_S … proof); |
---|
| 604 | #HYP assumption |
---|
| 605 | ] |
---|
| 606 | qed. |
---|
[1358] | 607 | |
---|
| 608 | definition foldi_strong ≝ |
---|
[1356] | 609 | λa: Type[0]. |
---|
| 610 | λb: Type[0]. |
---|
| 611 | λthe_list: list b. |
---|
[1358] | 612 | λf: (∀i: nat. ∀proof: i < |the_list|. a → b → a). |
---|
[1356] | 613 | λseed: a. |
---|
[1358] | 614 | foldi_strong_internal a b (|the_list|) the_list f seed 0 ?. |
---|
[1356] | 615 | // |
---|
| 616 | qed. |
---|
[1343] | 617 | |
---|
[1063] | 618 | definition translate_mul ≝ |
---|
[1287] | 619 | λglobals: list ident. |
---|
[1063] | 620 | λdestrs: list register. |
---|
| 621 | λsrcrs1: list register. |
---|
| 622 | λsrcrs2: list register. |
---|
[1343] | 623 | λregs_proof: |destrs| = |srcrs2|. |
---|
[1063] | 624 | λstart_lbl: label. |
---|
| 625 | λdest_lbl: label. |
---|
[1287] | 626 | λdef: rtl_internal_function globals. |
---|
| 627 | let 〈def, dummy〉 ≝ fresh_reg rtl_params0 globals def in |
---|
| 628 | let 〈def, tmpr〉 ≝ fresh_reg rtl_params0 globals def in |
---|
[1331] | 629 | match fresh_regs_strong rtl_params0 globals def (|destrs|) with |
---|
[1601] | 630 | [ mk_Sig def_tmp_destrs tmp_destrs_prf ⇒ |
---|
[1331] | 631 | let def ≝ \fst def_tmp_destrs in |
---|
| 632 | let tmp_destrs ≝ \snd def_tmp_destrs in |
---|
| 633 | let 〈def, fresh_srcrs1〉 ≝ fresh_regs rtl_params0 globals def (|srcrs1|) in |
---|
| 634 | let 〈def, fresh_srcrs2〉 ≝ fresh_regs rtl_params0 globals def (|srcrs2|) in |
---|
| 635 | let insts_init ≝ [ |
---|
| 636 | translate_move globals fresh_srcrs1 srcrs1; |
---|
| 637 | translate_move globals fresh_srcrs2 srcrs2; |
---|
| 638 | translate_cst globals (Ointconst I8 (zero …)) destrs |
---|
| 639 | ] |
---|
| 640 | in |
---|
| 641 | let f ≝ translate_muli globals dummy tmpr destrs tmp_destrs fresh_srcrs1 start_lbl in |
---|
[1358] | 642 | let f' ≝ λi. λi_proof: i < |srcrs2|. f i ? in |
---|
[1343] | 643 | let insts_mul ≝ foldi_strong … srcrs2 f' [ ] in |
---|
[1331] | 644 | add_translates rtl_params1 globals (insts_init @ insts_mul) start_lbl dest_lbl def |
---|
| 645 | ]. |
---|
| 646 | >tmp_destrs_prf |
---|
[1343] | 647 | >regs_proof |
---|
[1358] | 648 | /2/ |
---|
[1331] | 649 | qed. |
---|
[1062] | 650 | |
---|
[1064] | 651 | definition translate_divumodu8 ≝ |
---|
[1287] | 652 | λglobals: list ident. |
---|
[1064] | 653 | λorder: bool. |
---|
| 654 | λdestrs: list register. |
---|
| 655 | λsrcr1: register. |
---|
| 656 | λsrcr2: register. |
---|
| 657 | λstart_lbl: label. |
---|
| 658 | λdest_lbl: label. |
---|
[1287] | 659 | λdef: rtl_internal_function globals. |
---|
[1064] | 660 | match destrs with |
---|
[1287] | 661 | [ nil ⇒ add_graph rtl_params1 globals start_lbl (GOTO … dest_lbl) def |
---|
[1064] | 662 | | cons destr destrs ⇒ |
---|
[1287] | 663 | let 〈def, dummy〉 ≝ fresh_reg rtl_params0 globals def in |
---|
[1064] | 664 | let 〈destr1, destr2〉 ≝ match order with [ true ⇒ 〈destr, dummy〉 | _ ⇒ 〈dummy, destr〉 ] in |
---|
[1287] | 665 | let inst_div ≝ adds_graph rtl_params1 globals [ |
---|
| 666 | sequential rtl_params_ globals (OPACCS … DivuModu destr1 destr2 srcr1 srcr2) |
---|
[1064] | 667 | ] |
---|
| 668 | in |
---|
[1287] | 669 | let insts_rest ≝ translate_cst globals (Ointconst I8 (zero ?)) destrs in |
---|
| 670 | add_translates rtl_params1 globals [ inst_div; insts_rest ] start_lbl dest_lbl def |
---|
[1064] | 671 | ]. |
---|
[1063] | 672 | |
---|
[1287] | 673 | definition translate_ne: ∀globals: list ident. ? → ? → ? → ? → ? → ? → rtl_internal_function globals ≝ |
---|
| 674 | λglobals: list ident. |
---|
[1064] | 675 | λdestrs: list register. |
---|
| 676 | λsrcrs1: list register. |
---|
| 677 | λsrcrs2: list register. |
---|
| 678 | λstart_lbl: label. |
---|
| 679 | λdest_lbl: label. |
---|
[1287] | 680 | λdef: rtl_internal_function globals. |
---|
[1064] | 681 | match destrs with |
---|
[1287] | 682 | [ nil ⇒ add_graph rtl_params1 globals start_lbl (GOTO … dest_lbl) def |
---|
[1064] | 683 | | cons destr destrs ⇒ |
---|
[1287] | 684 | let 〈def, tmpr〉 ≝ fresh_reg rtl_params0 globals def in |
---|
| 685 | let 〈def, tmp_zero〉 ≝ fresh_reg rtl_params0 globals def in |
---|
| 686 | let 〈def, tmp_srcrs1〉 ≝ fresh_regs rtl_params0 globals def (|srcrs1|) in |
---|
| 687 | let save_srcrs1 ≝ translate_move globals tmp_srcrs1 srcrs1 in |
---|
| 688 | let 〈def, tmp_srcrs2〉 ≝ fresh_regs rtl_params0 globals def (|srcrs2|) in |
---|
| 689 | let save_srcrs2 ≝ translate_move globals tmp_srcrs2 srcrs2 in |
---|
[1071] | 690 | match reduce_strong register register tmp_srcrs1 tmp_srcrs2 with |
---|
[1601] | 691 | [ mk_Sig crl their_proof ⇒ |
---|
[1064] | 692 | let commonl ≝ \fst (\fst crl) in |
---|
| 693 | let commonr ≝ \fst (\snd crl) in |
---|
| 694 | let restl ≝ \snd (\snd crl) in |
---|
| 695 | let restr ≝ \snd (\snd crl) in |
---|
[1293] | 696 | let rest ≝ restl @ restr in |
---|
[1064] | 697 | let inits ≝ [ |
---|
[1287] | 698 | sequential … (INT rtl_params_ globals destr (zero …)); |
---|
| 699 | sequential … (INT rtl_params_ globals tmp_zero (zero …)) |
---|
[1064] | 700 | ] |
---|
| 701 | in |
---|
| 702 | let f_common ≝ λtmp_srcr1. λtmp_srcr2. [ |
---|
[1287] | 703 | sequential … (CLEAR_CARRY …); |
---|
| 704 | sequential … (OP2 rtl_params_ globals Sub tmpr tmp_srcr1 tmp_srcr2); |
---|
| 705 | sequential … (OP2 rtl_params_ globals Or destr destr tmpr) |
---|
[1064] | 706 | ] |
---|
| 707 | in |
---|
[1287] | 708 | let insts_common ≝ flatten … (map2 … f_common commonl commonr ?) in |
---|
[1064] | 709 | let f_rest ≝ λtmp_srcr. [ |
---|
[1287] | 710 | sequential … (CLEAR_CARRY …); |
---|
| 711 | sequential … (OP2 rtl_params_ globals Sub tmpr tmp_zero tmp_srcr); |
---|
| 712 | sequential … (OP2 rtl_params_ globals Or destr destr tmpr) |
---|
[1064] | 713 | ] |
---|
| 714 | in |
---|
[1287] | 715 | let insts_rest ≝ flatten … (map … f_rest rest) in |
---|
[1064] | 716 | let insts ≝ inits @ insts_common @ insts_rest in |
---|
[1287] | 717 | let epilogue ≝ translate_cst globals (Ointconst I8 (zero …)) destrs in |
---|
| 718 | add_translates rtl_params1 globals [ |
---|
| 719 | save_srcrs1; save_srcrs2; adds_graph rtl_params1 globals insts; epilogue |
---|
[1064] | 720 | ] start_lbl dest_lbl def |
---|
| 721 | ] |
---|
| 722 | ]. |
---|
[1293] | 723 | @their_proof |
---|
[1064] | 724 | qed. |
---|
| 725 | |
---|
| 726 | definition translate_eq_reg ≝ |
---|
[1287] | 727 | λglobals: list ident. |
---|
[1064] | 728 | λtmp_zero: register. |
---|
| 729 | λtmp_one: register. |
---|
| 730 | λtmpr1: register. |
---|
| 731 | λtmpr2: register. |
---|
| 732 | λdestr: register. |
---|
| 733 | λdummy_lbl: label. |
---|
| 734 | λsrcr12: register × register. |
---|
| 735 | let 〈srcr1, srcr2〉 ≝ srcr12 in |
---|
[1287] | 736 | [ sequential … (CLEAR_CARRY …); |
---|
| 737 | sequential rtl_params_ globals (OP2 rtl_params_ globals Sub tmpr1 srcr1 srcr2); |
---|
| 738 | sequential … (OP2 rtl_params_ globals Addc tmpr1 tmp_zero tmp_zero); |
---|
| 739 | sequential … (OP2 rtl_params_ globals Sub tmpr2 srcr2 srcr1); |
---|
| 740 | sequential … (OP2 rtl_params_ globals Addc tmpr2 tmp_zero tmp_zero); |
---|
| 741 | sequential … (OP2 rtl_params_ globals Or tmpr1 tmpr1 tmpr2); |
---|
| 742 | sequential … (OP2 rtl_params_ globals Xor tmpr1 tmpr1 tmp_one); |
---|
| 743 | sequential … (OP2 rtl_params_ globals And destr destr tmpr1) ]. |
---|
[1064] | 744 | |
---|
| 745 | definition translate_eq_list ≝ |
---|
[1287] | 746 | λglobals: list ident. |
---|
[1064] | 747 | λtmp_zero: register. |
---|
| 748 | λtmp_one: register. |
---|
| 749 | λtmpr1: register. |
---|
| 750 | λtmpr2: register. |
---|
| 751 | λdestr: register. |
---|
| 752 | λleq: list (register × register). |
---|
| 753 | λdummy_lbl: label. |
---|
[1287] | 754 | let f ≝ translate_eq_reg globals tmp_zero tmp_one tmpr1 tmpr2 destr dummy_lbl in |
---|
| 755 | (sequential … (INT rtl_params_ globals destr (bitvector_of_nat ? 1))) :: |
---|
| 756 | flatten … (map … f leq). |
---|
[1064] | 757 | |
---|
| 758 | definition translate_atom ≝ |
---|
[1287] | 759 | λglobals: list ident. |
---|
[1064] | 760 | λtmp_zero: register. |
---|
| 761 | λtmp_one: register. |
---|
| 762 | λtmpr1: register. |
---|
| 763 | λtmpr2: register. |
---|
| 764 | λtmpr3: register. |
---|
| 765 | λdestr: register. |
---|
| 766 | λdummy_lbl: label. |
---|
| 767 | λleq: list (register × register). |
---|
| 768 | λsrcr1: register. |
---|
| 769 | λsrcr2: register. |
---|
[1287] | 770 | translate_eq_list globals tmp_zero tmp_one tmpr1 tmpr2 tmpr3 leq dummy_lbl @ |
---|
| 771 | [ sequential … (CLEAR_CARRY …); |
---|
| 772 | sequential … (OP2 rtl_params_ globals Sub tmpr1 srcr1 srcr2); |
---|
| 773 | sequential … (OP2 rtl_params_ globals Addc tmpr1 tmp_zero tmp_zero); |
---|
| 774 | sequential … (OP2 rtl_params_ globals And tmpr3 tmpr3 tmpr1); |
---|
| 775 | sequential … (OP2 rtl_params_ globals Or destr destr tmpr3) ]. |
---|
[1064] | 776 | |
---|
| 777 | definition translate_lt_main ≝ |
---|
[1287] | 778 | λglobals: list ident. |
---|
[1064] | 779 | λtmp_zero: register. |
---|
| 780 | λtmp_one: register. |
---|
| 781 | λtmpr1: register. |
---|
| 782 | λtmpr2: register. |
---|
| 783 | λtmpr3: register. |
---|
| 784 | λdestr: register. |
---|
| 785 | λdummy_lbl: label. |
---|
| 786 | λsrcrs1: list register. |
---|
| 787 | λsrcrs2: list register. |
---|
| 788 | λproof: |srcrs1| = |srcrs2|. |
---|
| 789 | let f ≝ λinsts_leq. λsrcr1. λsrcr2. |
---|
| 790 | let 〈insts, leq〉 ≝ insts_leq in |
---|
[1287] | 791 | let added_insts ≝ translate_atom globals tmp_zero tmp_one tmpr1 tmpr2 tmpr3 destr dummy_lbl leq srcr1 srcr2 in |
---|
[1064] | 792 | 〈insts @ added_insts, leq @ [〈srcr1, srcr2〉]〉 |
---|
| 793 | in |
---|
[1287] | 794 | \fst (fold_left2 … f 〈[ ], [ ]〉 srcrs1 srcrs2 proof). |
---|
[1064] | 795 | |
---|
| 796 | definition fresh_regs_strong: |
---|
[1287] | 797 | ∀globals. rtl_internal_function globals → ∀n: nat. Σfresh: (rtl_internal_function globals) × (list register). |\snd fresh| = n ≝ |
---|
| 798 | λglobals: list ident. |
---|
[1064] | 799 | λdef. |
---|
| 800 | λn. |
---|
[1287] | 801 | fresh_regs rtl_params0 globals def n. |
---|
[1064] | 802 | @fresh_regs_length |
---|
| 803 | qed. |
---|
| 804 | |
---|
| 805 | definition complete_regs_strong: |
---|
[1287] | 806 | ∀globals: list ident. rtl_internal_function globals → list register → list register → Σcomplete: (list register) × (list register) × (list register). |\fst (\fst complete)| = |\snd (\fst complete)| ≝ |
---|
| 807 | λglobals: list ident. |
---|
[1064] | 808 | λdef. |
---|
| 809 | λleft. |
---|
| 810 | λright. |
---|
[1287] | 811 | complete_regs globals def left right. |
---|
[1064] | 812 | @complete_regs_length |
---|
| 813 | qed. |
---|
| 814 | |
---|
| 815 | definition translate_lt ≝ |
---|
[1287] | 816 | λglobals: list ident. |
---|
[1064] | 817 | λdestrs: list register. |
---|
[1306] | 818 | λprf_destrs: 0 < |destrs|. |
---|
[1064] | 819 | λsrcrs1: list register. |
---|
| 820 | λsrcrs2: list register. |
---|
| 821 | λstart_lbl: label. |
---|
| 822 | λdest_lbl: label. |
---|
[1287] | 823 | λdef: rtl_internal_function globals. |
---|
[1064] | 824 | match destrs with |
---|
[1287] | 825 | [ nil ⇒ add_graph rtl_params1 globals start_lbl (GOTO … dest_lbl) def |
---|
[1064] | 826 | | _ ⇒ |
---|
[1287] | 827 | match fresh_regs_strong globals def (|destrs|) with |
---|
[1601] | 828 | [ mk_Sig def_tmp_destrs tmp_destrs_proof ⇒ |
---|
[1064] | 829 | let def ≝ \fst def_tmp_destrs in |
---|
| 830 | let tmp_destrs ≝ \snd def_tmp_destrs in |
---|
| 831 | let tmp_destr ≝ hd_safe ? tmp_destrs ? in |
---|
[1287] | 832 | let 〈def, tmp_zero〉 ≝ fresh_reg rtl_params1 globals def in |
---|
| 833 | let 〈def, tmp_one〉 ≝ fresh_reg rtl_params1 globals def in |
---|
| 834 | let 〈def, tmpr1〉 ≝ fresh_reg rtl_params1 globals def in |
---|
| 835 | let 〈def, tmpr2〉 ≝ fresh_reg rtl_params1 globals def in |
---|
| 836 | let 〈def, tmpr3〉 ≝ fresh_reg rtl_params1 globals def in |
---|
| 837 | match complete_regs_strong globals def srcrs1 srcrs2 with |
---|
[1601] | 838 | [ mk_Sig srcrs12_added srcrs12_proof ⇒ |
---|
[1064] | 839 | let srcrs1 ≝ \fst (\fst srcrs12_added) in |
---|
| 840 | let srcrs2 ≝ \snd (\fst srcrs12_added) in |
---|
| 841 | let added ≝ \snd srcrs12_added in |
---|
[1287] | 842 | let srcrs1' ≝ rev … srcrs1 in |
---|
| 843 | let srcrs2' ≝ rev … srcrs2 in |
---|
[1064] | 844 | let insts_init ≝ [ |
---|
[1287] | 845 | translate_cst globals (Ointconst I8 (zero ?)) tmp_destrs; |
---|
| 846 | translate_cst globals (Ointconst I8 (zero ?)) added; |
---|
| 847 | adds_graph rtl_params1 globals [ |
---|
| 848 | sequential rtl_params_ globals (INT rtl_params_ globals tmp_zero (zero …)); |
---|
| 849 | sequential rtl_params_ globals (INT rtl_params_ globals tmp_one (bitvector_of_nat … 1)) |
---|
[1064] | 850 | ] |
---|
| 851 | ] |
---|
| 852 | in |
---|
| 853 | let insts_main ≝ |
---|
[1287] | 854 | translate_lt_main globals tmp_zero tmp_one tmpr1 tmpr2 tmpr3 tmp_destr start_lbl srcrs1' srcrs2' ? in |
---|
| 855 | let insts_main ≝ [ adds_graph rtl_params1 globals insts_main ] in |
---|
| 856 | let insts_exit ≝ [ translate_move globals destrs tmp_destrs ] in |
---|
| 857 | add_translates rtl_params1 globals (insts_init @ insts_main @ insts_exit) start_lbl dest_lbl def |
---|
[1064] | 858 | ] |
---|
| 859 | ] |
---|
| 860 | ]. |
---|
| 861 | [2: >tmp_destrs_proof @prf_destrs |
---|
| 862 | |1: normalize nodelta |
---|
[1529] | 863 | generalize in match srcrs12_proof; |
---|
[1064] | 864 | #HYP >rev_length >rev_length @HYP |
---|
| 865 | ] |
---|
| 866 | qed. |
---|
| 867 | |
---|
| 868 | definition add_128_to_last ≝ |
---|
[1287] | 869 | λglobals: list ident. |
---|
[1064] | 870 | λtmp_128: register. |
---|
| 871 | λrs. |
---|
| 872 | λprf: 0 < |rs|. |
---|
| 873 | λstart_lbl: label. |
---|
| 874 | match rs with |
---|
[1287] | 875 | [ nil ⇒ adds_graph rtl_params1 globals [ ] start_lbl |
---|
[1064] | 876 | | _ ⇒ |
---|
[1287] | 877 | let r ≝ last_safe … rs prf in |
---|
| 878 | adds_graph rtl_params1 globals [ |
---|
| 879 | sequential rtl_params_ globals (OP2 rtl_params_ globals Add r r tmp_128) |
---|
[1064] | 880 | ] start_lbl |
---|
| 881 | ]. |
---|
| 882 | |
---|
| 883 | definition translate_lts ≝ |
---|
[1287] | 884 | λglobals: list ident. |
---|
[1064] | 885 | λdestrs: list register. |
---|
[1306] | 886 | λdestrs_prf: 0 < |destrs|. |
---|
[1064] | 887 | λsrcrs1: list register. |
---|
| 888 | λsrcrs2: list register. |
---|
| 889 | λsrcrs1_lt_prf: 0 < |srcrs1|. |
---|
[1066] | 890 | λsrcrs2_lt_prf: 0 < |srcrs2|. |
---|
[1064] | 891 | λstart_lbl: label. |
---|
| 892 | λdest_lbl: label. |
---|
[1287] | 893 | λdef: rtl_internal_function globals. |
---|
| 894 | match fresh_regs_strong globals def (|srcrs1|) with |
---|
[1601] | 895 | [ mk_Sig def_tmp_srcrs1 srcrs1_prf ⇒ |
---|
[1064] | 896 | let def ≝ \fst def_tmp_srcrs1 in |
---|
| 897 | let tmp_srcrs1 ≝ \snd def_tmp_srcrs1 in |
---|
[1287] | 898 | match fresh_regs_strong globals def (|srcrs2|) with |
---|
[1601] | 899 | [ mk_Sig def_tmp_srcrs2 srcrs2_prf ⇒ |
---|
[1064] | 900 | let def ≝ \fst def_tmp_srcrs2 in |
---|
| 901 | let tmp_srcrs2 ≝ \snd def_tmp_srcrs2 in |
---|
[1287] | 902 | let 〈def, tmp_128〉 ≝ fresh_reg rtl_params0 globals def in |
---|
| 903 | add_translates rtl_params1 globals [ |
---|
| 904 | translate_move globals tmp_srcrs1 srcrs1; |
---|
| 905 | translate_move globals tmp_srcrs2 srcrs2; |
---|
| 906 | adds_graph rtl_params1 globals [ |
---|
| 907 | sequential rtl_params_ globals (INT rtl_params_ globals tmp_128 (bitvector_of_nat ? 128)) |
---|
[1064] | 908 | ]; |
---|
[1287] | 909 | add_128_to_last globals tmp_128 tmp_srcrs1 ?; |
---|
| 910 | add_128_to_last globals tmp_128 tmp_srcrs2 ?; |
---|
| 911 | translate_lt globals destrs destrs_prf tmp_srcrs1 tmp_srcrs2 |
---|
[1064] | 912 | ] start_lbl dest_lbl def |
---|
| 913 | ] |
---|
| 914 | ]. |
---|
[1066] | 915 | [1: >srcrs1_prf @srcrs1_lt_prf |
---|
| 916 | |2: >srcrs2_prf @srcrs2_lt_prf |
---|
[1064] | 917 | ] |
---|
| 918 | qed. |
---|
| 919 | |
---|
| 920 | definition translate_op2 ≝ |
---|
[1288] | 921 | λglobals: list ident. |
---|
[1064] | 922 | λop2. |
---|
| 923 | λdestrs: list register. |
---|
[1306] | 924 | λdestrs_prf: 0 < |destrs|. |
---|
[1064] | 925 | λsrcrs1: list register. |
---|
| 926 | λsrcrs2: list register. |
---|
[1343] | 927 | λsrcrs2_destrs_prf: |srcrs2| = |destrs|. |
---|
| 928 | λsrcrs1_destrs_prf: |srcrs1| = |destrs|. |
---|
[1064] | 929 | λstart_lbl: label. |
---|
| 930 | λdest_lbl: label. |
---|
[1288] | 931 | λdef: rtl_internal_function globals. |
---|
[1064] | 932 | match op2 with |
---|
[1066] | 933 | [ Oadd ⇒ |
---|
[1288] | 934 | translate_op globals Addc destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
[1066] | 935 | | Oaddp ⇒ |
---|
[1288] | 936 | translate_op globals Addc destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
[1066] | 937 | | Osub ⇒ |
---|
[1288] | 938 | translate_op globals Sub destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
[1066] | 939 | | Osubpi ⇒ |
---|
[1288] | 940 | translate_op globals Sub destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
[1066] | 941 | | Osubpp sz ⇒ |
---|
[1288] | 942 | translate_op globals Sub destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
[1066] | 943 | | Omul ⇒ |
---|
[1331] | 944 | translate_mul globals destrs srcrs1 srcrs2 ? start_lbl dest_lbl def |
---|
[1066] | 945 | | Odivu ⇒ |
---|
[1288] | 946 | match srcrs1 return λx. 0 < |x| → rtl_internal_function globals with |
---|
[1066] | 947 | [ cons hd tl ⇒ λcons_prf. |
---|
| 948 | match tl with |
---|
[1288] | 949 | [ nil ⇒ translate_divumodu8 globals true destrs hd (hd_safe register srcrs2 ?) start_lbl dest_lbl def |
---|
[1066] | 950 | | _ ⇒ ? (* not implemented *) |
---|
| 951 | ] |
---|
| 952 | | nil ⇒ λnil_absrd. ? |
---|
[1343] | 953 | ] ? |
---|
[1066] | 954 | | Omodu ⇒ |
---|
[1288] | 955 | match srcrs1 return λx. 0 < |x| → rtl_internal_function globals with |
---|
[1066] | 956 | [ cons hd tl ⇒ λcons_prf. |
---|
| 957 | match tl with |
---|
[1288] | 958 | [ nil ⇒ translate_divumodu8 globals false destrs hd (hd_safe register srcrs2 ?) start_lbl dest_lbl def |
---|
[1066] | 959 | | _ ⇒ ? (* not implemented *) |
---|
| 960 | ] |
---|
| 961 | | nil ⇒ λnil_absrd. ? |
---|
[1343] | 962 | ] ? |
---|
[1066] | 963 | | Oand ⇒ |
---|
[1288] | 964 | translate_op globals And destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
[1066] | 965 | | Oor ⇒ |
---|
[1288] | 966 | translate_op globals Or destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
[1066] | 967 | | Oxor ⇒ |
---|
[1288] | 968 | translate_op globals Xor destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
[1066] | 969 | | Ocmp c ⇒ |
---|
[1064] | 970 | match c with |
---|
[1066] | 971 | [ Ceq ⇒ |
---|
[1288] | 972 | add_translates rtl_params1 globals [ |
---|
| 973 | translate_ne globals destrs srcrs1 srcrs2; |
---|
[1529] | 974 | translate_op1 globals ?? (Onotbool (ASTint I8 Unsigned) I8 Unsigned I) destrs destrs (refl ? (|destrs|)) |
---|
[1064] | 975 | ] start_lbl dest_lbl def |
---|
[1288] | 976 | | Cne ⇒ translate_ne globals destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
| 977 | | Clt ⇒ translate_lts globals destrs destrs_prf srcrs1 srcrs2 ? ? start_lbl dest_lbl def |
---|
| 978 | | Cgt ⇒ translate_lts globals destrs destrs_prf srcrs2 srcrs1 ? ? start_lbl dest_lbl def |
---|
[1066] | 979 | | Cle ⇒ |
---|
[1288] | 980 | add_translates rtl_params1 globals [ |
---|
| 981 | translate_lts globals destrs destrs_prf srcrs2 srcrs1 ? ?; |
---|
[1529] | 982 | translate_op1 globals ?? (Onotbool (ASTint I8 Unsigned) I8 Unsigned I) destrs destrs (refl ? (|destrs|)) |
---|
[1064] | 983 | ] start_lbl dest_lbl def |
---|
[1066] | 984 | | Cge ⇒ |
---|
[1288] | 985 | add_translates rtl_params1 globals [ |
---|
| 986 | translate_lts globals destrs destrs_prf srcrs1 srcrs2 ? ?; |
---|
[1529] | 987 | translate_op1 globals ?? (Onotbool (ASTint I8 Unsigned) I8 Unsigned I) destrs destrs (refl ? (|destrs|)) |
---|
[1064] | 988 | ] start_lbl dest_lbl def |
---|
| 989 | ] |
---|
[1066] | 990 | | Ocmpu c ⇒ |
---|
| 991 | match c with |
---|
| 992 | [ Ceq ⇒ |
---|
[1288] | 993 | add_translates rtl_params1 globals [ |
---|
| 994 | translate_ne globals destrs srcrs1 srcrs2; |
---|
[1529] | 995 | translate_op1 globals ?? (Onotbool (ASTint I8 Unsigned) I8 Unsigned I) destrs destrs (refl ? (|destrs|)) |
---|
[1066] | 996 | ] start_lbl dest_lbl def |
---|
[1288] | 997 | | Cne ⇒ translate_ne globals destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
| 998 | | Clt ⇒ translate_lt globals destrs destrs_prf srcrs1 srcrs2 start_lbl dest_lbl def |
---|
| 999 | | Cgt ⇒ translate_lt globals destrs destrs_prf srcrs2 srcrs1 start_lbl dest_lbl def |
---|
[1066] | 1000 | | Cle ⇒ |
---|
[1288] | 1001 | add_translates rtl_params1 globals [ |
---|
| 1002 | translate_lt globals destrs destrs_prf srcrs2 srcrs1; |
---|
[1529] | 1003 | translate_op1 globals ?? (Onotbool (ASTint I8 Unsigned) I8 Unsigned I) destrs destrs (refl ? (|destrs|)) |
---|
[1066] | 1004 | ] start_lbl dest_lbl def |
---|
| 1005 | | Cge ⇒ |
---|
[1288] | 1006 | add_translates rtl_params1 globals [ |
---|
| 1007 | translate_lt globals destrs destrs_prf srcrs1 srcrs2; |
---|
[1529] | 1008 | translate_op1 globals ?? (Onotbool (ASTint I8 Unsigned) I8 Unsigned I) destrs destrs (refl ? (|destrs|)) |
---|
[1066] | 1009 | ] start_lbl dest_lbl def |
---|
| 1010 | ] |
---|
| 1011 | | Ocmpp c ⇒ |
---|
| 1012 | match c with |
---|
| 1013 | [ Ceq ⇒ |
---|
[1288] | 1014 | add_translates rtl_params1 globals [ |
---|
| 1015 | translate_ne globals destrs srcrs1 srcrs2; |
---|
[1529] | 1016 | translate_op1 globals ?? (Onotbool (ASTint I8 Unsigned) I8 Unsigned I) destrs destrs (refl ? (|destrs|)) |
---|
[1066] | 1017 | ] start_lbl dest_lbl def |
---|
[1288] | 1018 | | Cne ⇒ translate_ne globals destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
| 1019 | | Clt ⇒ translate_lt globals destrs destrs_prf srcrs1 srcrs2 start_lbl dest_lbl def |
---|
| 1020 | | Cgt ⇒ translate_lt globals destrs destrs_prf srcrs2 srcrs1 start_lbl dest_lbl def |
---|
[1066] | 1021 | | Cle ⇒ |
---|
[1288] | 1022 | add_translates rtl_params1 globals [ |
---|
| 1023 | translate_lt globals destrs destrs_prf srcrs2 srcrs1; |
---|
[1529] | 1024 | translate_op1 globals ?? (Onotbool (ASTint I8 Unsigned) I8 Unsigned I) destrs destrs (refl ? (|destrs|)) |
---|
[1066] | 1025 | ] start_lbl dest_lbl def |
---|
| 1026 | | Cge ⇒ |
---|
[1288] | 1027 | add_translates rtl_params1 globals [ |
---|
| 1028 | translate_lt globals destrs destrs_prf srcrs1 srcrs2; |
---|
[1529] | 1029 | translate_op1 globals ?? (Onotbool (ASTint I8 Unsigned) I8 Unsigned I) destrs destrs (refl ? (|destrs|)) |
---|
[1066] | 1030 | ] start_lbl dest_lbl def |
---|
| 1031 | ] |
---|
| 1032 | | _ ⇒ ? (* assert false, implemented in run time or float op *) |
---|
| 1033 | ]. |
---|
[1343] | 1034 | [1: |
---|
| 1035 | @sym_eq |
---|
| 1036 | assumption |
---|
| 1037 | |3,8,19,22,24,25: |
---|
| 1038 | >srcrs1_destrs_prf |
---|
| 1039 | assumption |
---|
| 1040 | |4,9: |
---|
| 1041 | normalize in nil_absrd; |
---|
| 1042 | cases(not_le_Sn_O 0) |
---|
| 1043 | #HYP cases(HYP nil_absrd) |
---|
| 1044 | |5,10,20,21,23,26: |
---|
| 1045 | >srcrs2_destrs_prf |
---|
| 1046 | assumption |
---|
| 1047 | |*: |
---|
| 1048 | cases not_implemented (* XXX: yes, really *) |
---|
[1066] | 1049 | ] |
---|
| 1050 | qed. |
---|
| 1051 | |
---|
[1288] | 1052 | definition translate_cond: ∀globals: list ident. list register → label → label → label → rtl_internal_function globals → rtl_internal_function globals ≝ |
---|
| 1053 | λglobals: list ident. |
---|
[1066] | 1054 | λsrcrs: list register. |
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| 1055 | λstart_lbl: label. |
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| 1056 | λlbl_true: label. |
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| 1057 | λlbl_false: label. |
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[1288] | 1058 | λdef: rtl_internal_function globals. |
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| 1059 | let 〈def, tmpr〉 ≝ fresh_reg rtl_params0 globals def in |
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| 1060 | let 〈tmp_lbl, def〉 ≝ fresh_label rtl_params1 globals def in |
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| 1061 | let init ≝ sequential rtl_params_ globals (INT rtl_params_ globals tmpr (zero …)) in |
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| 1062 | let f ≝ λsrcr. sequential rtl_params_ globals (OP2 rtl_params_ globals Or tmpr tmpr srcr) in |
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| 1063 | let def ≝ adds_graph rtl_params1 globals (init :: (map ? ? f srcrs)) start_lbl tmp_lbl def in |
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[1290] | 1064 | add_graph rtl_params1 globals tmp_lbl (sequential rtl_params_ globals (COND rtl_params_ globals tmpr lbl_true) lbl_false) def. |
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[1066] | 1065 | |
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| 1066 | definition translate_load ≝ |
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[1292] | 1067 | λglobals: list ident. |
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[1066] | 1068 | λaddr. |
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[1343] | 1069 | λaddr_prf: 2 = |addr|. |
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[1066] | 1070 | λdestrs: list register. |
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| 1071 | λstart_lbl: label. |
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| 1072 | λdest_lbl: label. |
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[1292] | 1073 | λdef: rtl_internal_function globals. |
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| 1074 | match fresh_regs_strong rtl_params0 globals def (|addr|) with |
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[1601] | 1075 | [ mk_Sig def_save_addr save_addr_prf ⇒ |
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[1066] | 1076 | let def ≝ \fst def_save_addr in |
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| 1077 | let save_addr ≝ \snd def_save_addr in |
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[1292] | 1078 | match fresh_regs_strong rtl_params0 globals def (|addr|) with |
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[1601] | 1079 | [ mk_Sig def_tmp_addr tmp_addr_prf ⇒ |
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[1066] | 1080 | let def ≝ \fst def_tmp_addr in |
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| 1081 | let tmp_addr ≝ \snd def_tmp_addr in |
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[1292] | 1082 | let 〈tmp_addr1, tmp_addr2〉 ≝ make_addr … tmp_addr ? in |
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| 1083 | let 〈def, tmpr〉 ≝ fresh_reg rtl_params0 globals def in |
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[1343] | 1084 | let 〈def, dummy〉 ≝ fresh_reg rtl_params0 globals def in |
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[1292] | 1085 | let insts_save_addr ≝ translate_move globals save_addr addr in |
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[1066] | 1086 | let f ≝ λtranslates_off. λr. |
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| 1087 | let 〈translates, off〉 ≝ translates_off in |
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| 1088 | let translates ≝ translates @ [ |
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[1292] | 1089 | adds_graph rtl_params1 globals [ |
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| 1090 | sequential rtl_params_ globals (INT rtl_params_ globals tmpr off) |
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[1066] | 1091 | ]; |
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[1343] | 1092 | translate_op2 globals Oaddp tmp_addr ? save_addr [dummy; tmpr] ? ?; |
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[1292] | 1093 | adds_graph rtl_params1 globals [ |
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| 1094 | sequential rtl_params_ globals (LOAD rtl_params_ globals r tmp_addr1 tmp_addr2) |
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[1066] | 1095 | ] |
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| 1096 | ] |
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| 1097 | in |
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[1292] | 1098 | let 〈carry, result〉 ≝ half_add … off int_size in |
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[1066] | 1099 | 〈translates, result〉 |
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| 1100 | in |
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[1292] | 1101 | let 〈translates, ignore〉 ≝ foldl … f 〈[ ], (zero ?)〉 destrs in |
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| 1102 | add_translates rtl_params1 globals (insts_save_addr :: translates) start_lbl dest_lbl def |
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[1066] | 1103 | ] |
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| 1104 | ]. |
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[1343] | 1105 | [1: >tmp_addr_prf >save_addr_prf % |
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| 1106 | |2: >save_addr_prf >tmp_addr_prf |
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| 1107 | @addr_prf |
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[1066] | 1108 | |3: >tmp_addr_prf normalize |
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[1343] | 1109 | <addr_prf // |
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| 1110 | |4: >tmp_addr_prf assumption |
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[1066] | 1111 | ] |
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| 1112 | qed. |
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| 1113 | |
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| 1114 | definition translate_store ≝ |
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[1292] | 1115 | λglobals: list ident. |
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[1066] | 1116 | λaddr. |
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[1343] | 1117 | λaddr_prf: 2 = |addr|. |
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[1066] | 1118 | λsrcrs: list register. |
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| 1119 | λstart_lbl: label. |
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| 1120 | λdest_lbl: label. |
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[1292] | 1121 | λdef: rtl_internal_function globals. |
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| 1122 | match fresh_regs_strong rtl_params0 globals def (|addr|) with |
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[1601] | 1123 | [ mk_Sig def_tmp_addr tmp_addr_prf ⇒ |
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[1066] | 1124 | let def ≝ \fst def_tmp_addr in |
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| 1125 | let tmp_addr ≝ \snd def_tmp_addr in |
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[1292] | 1126 | let 〈tmp_addr1, tmp_addr2〉 ≝ make_addr … tmp_addr ? in |
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| 1127 | let 〈def, tmpr〉 ≝ fresh_reg rtl_params0 globals def in |
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[1343] | 1128 | let 〈def, dummy〉 ≝ fresh_reg rtl_params0 globals def in |
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[1066] | 1129 | let f ≝ λtranslate_off. λsrcr. |
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| 1130 | let 〈translates, off〉 ≝ translate_off in |
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| 1131 | let translates ≝ translates @ [ |
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[1292] | 1132 | adds_graph rtl_params1 globals [ |
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| 1133 | sequential rtl_params_ globals (INT rtl_params_ globals tmpr off) |
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[1066] | 1134 | ]; |
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[1343] | 1135 | translate_op2 globals Oaddp tmp_addr … addr [dummy; tmpr] ? ?; |
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[1292] | 1136 | adds_graph rtl_params1 globals [ |
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| 1137 | sequential rtl_params_ globals (STORE rtl_params_ globals tmp_addr1 tmp_addr2 srcr) |
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[1066] | 1138 | ] |
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| 1139 | ] |
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| 1140 | in |
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[1292] | 1141 | let 〈carry, result〉 ≝ half_add … off int_size in |
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[1066] | 1142 | 〈translates, result〉 |
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| 1143 | in |
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[1306] | 1144 | let 〈translates, ignore〉 ≝ foldl … f 〈[ ], zero …〉 srcrs in |
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[1292] | 1145 | add_translates rtl_params1 globals translates start_lbl dest_lbl def |
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[1066] | 1146 | ]. |
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[1343] | 1147 | [1: >tmp_addr_prf % |
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[1066] | 1148 | |2: >tmp_addr_prf normalize |
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[1343] | 1149 | <addr_prf // |
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| 1150 | |3: >tmp_addr_prf <addr_prf // |
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| 1151 | |4: >tmp_addr_prf @addr_prf |
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[1066] | 1152 | ] |
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| 1153 | qed. |
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| 1154 | |
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[1293] | 1155 | axiom fake_label: label. |
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| 1156 | |
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| 1157 | (* XXX: following conversation with CSC about the mix up in extension statements |
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[1296] | 1158 | and extension instructions in RTL, use fake_label in calls to |
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| 1159 | tailcall_* instructions. *) |
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[1066] | 1160 | definition translate_stmt ≝ |
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[1292] | 1161 | λglobals: list ident. |
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[1281] | 1162 | λlenv: local_env. |
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[1066] | 1163 | λlbl: label. |
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| 1164 | λstmt. |
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[1292] | 1165 | λdef: rtl_internal_function globals. |
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[1066] | 1166 | match stmt with |
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[1282] | 1167 | [ St_skip lbl' ⇒ add_graph … lbl (GOTO … lbl') def |
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[1293] | 1168 | | St_cost cost_lbl lbl' ⇒ add_graph rtl_params1 globals lbl (sequential rtl_params_ globals (COST_LABEL rtl_params_ globals cost_lbl) lbl') def |
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[1066] | 1169 | | St_const destr cst lbl' ⇒ |
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[1293] | 1170 | translate_cst globals cst (find_local_env destr lenv) lbl lbl' def |
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[1529] | 1171 | | St_op1 ty ty' op1 destr srcr lbl' ⇒ |
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| 1172 | translate_op1 globals ty ty' op1 (find_local_env destr lenv) (find_local_env srcr lenv) … lbl lbl' def |
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[1066] | 1173 | | St_op2 op2 destr srcr1 srcr2 lbl' ⇒ |
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[1306] | 1174 | translate_op2 globals op2 (find_local_env destr lenv) ? (find_local_env srcr1 lenv) (find_local_env srcr2 lenv) ? ? lbl lbl' def |
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[1307] | 1175 | (* XXX: should we be ignoring this? *) |
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[1066] | 1176 | | St_load ignore addr destr lbl' ⇒ |
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[1306] | 1177 | translate_load globals (find_local_env addr lenv) ? (find_local_env destr lenv) lbl lbl' def |
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[1307] | 1178 | (* XXX: should we be ignoring this? *) |
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[1066] | 1179 | | St_store ignore addr srcr lbl' ⇒ |
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[1306] | 1180 | translate_store globals (find_local_env addr lenv) ? (find_local_env srcr lenv) lbl lbl' def |
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[1066] | 1181 | | St_call_id f args retr lbl' ⇒ |
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| 1182 | match retr with |
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| 1183 | [ Some retr ⇒ |
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[1293] | 1184 | add_graph rtl_params1 globals lbl (sequential … (CALL_ID rtl_params1 globals f (rtl_args args lenv) (find_local_env retr lenv)) lbl') def |
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| 1185 | | None ⇒ add_graph rtl_params1 globals lbl (sequential … (CALL_ID rtl_params1 globals f (rtl_args args lenv) [ ]) lbl') def |
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[1066] | 1186 | ] |
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| 1187 | | St_call_ptr f args retr lbl' ⇒ |
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| 1188 | match retr with |
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| 1189 | [ None ⇒ |
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| 1190 | let 〈f1, f2〉 ≝ find_and_addr f lenv ? in |
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[1293] | 1191 | add_graph rtl_params1 globals lbl (sequential … (extension … (rtl_st_ext_call_ptr f1 f2 (rtl_args args lenv) [ ])) lbl') def |
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[1066] | 1192 | | Some retr ⇒ |
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| 1193 | let 〈f1, f2〉 ≝ find_and_addr f lenv ? in |
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[1293] | 1194 | add_graph rtl_params1 globals lbl (sequential … (extension … (rtl_st_ext_call_ptr f1 f2 (rtl_args args lenv) (find_local_env retr lenv))) lbl') def |
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[1066] | 1195 | ] |
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| 1196 | | St_tailcall_id f args ⇒ |
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[1293] | 1197 | add_graph rtl_params1 globals lbl (sequential rtl_params_ globals (extension rtl_params_ globals (rtl_st_ext_tailcall_id f (rtl_args args lenv))) fake_label) def |
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[1066] | 1198 | | St_tailcall_ptr f args ⇒ |
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| 1199 | let 〈f1, f2〉 ≝ find_and_addr f lenv ? in |
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[1293] | 1200 | add_graph rtl_params1 globals lbl (sequential rtl_params_ globals (extension rtl_params1 globals (rtl_st_ext_tailcall_ptr f1 f2 (rtl_args args lenv))) fake_label) def |
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[1066] | 1201 | | St_cond r lbl_true lbl_false ⇒ |
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[1292] | 1202 | translate_cond globals (find_local_env r lenv) lbl lbl_true lbl_false def |
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[1066] | 1203 | | St_jumptable r l ⇒ ? (* assert false: not implemented yet *) |
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[1292] | 1204 | | St_return ⇒ add_graph rtl_params1 globals lbl (RETURN …) def |
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[1064] | 1205 | ]. |
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[1067] | 1206 | [10: cases not_implemented (* jtable case *) |
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| 1207 | |*: cases daemon (* TODO: proofs regarding lengths of lists, examine! *) |
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| 1208 | ] |
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| 1209 | qed. |
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[1064] | 1210 | |
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[1073] | 1211 | (* XXX: we use a "hack" here to circumvent the proof obligations required to |
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| 1212 | create res, an empty internal_function record. we insert into our graph |
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| 1213 | the start and end nodes to ensure that they are in, and place dummy |
---|
| 1214 | skip instructions at these nodes. *) |
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[1067] | 1215 | definition translate_internal ≝ |
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[1293] | 1216 | λglobals: list ident. |
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| 1217 | λdef. |
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[1067] | 1218 | let runiverse ≝ f_reggen def in |
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[1281] | 1219 | let 〈lenv,runiverse〉 ≝ initialize_local_env runiverse |
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[1068] | 1220 | (f_params def @ f_locals def) (f_result def) in |
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[1292] | 1221 | let params ≝ map_list_local_env lenv (map … \fst (f_params def)) in |
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| 1222 | let locals ≝ map_list_local_env lenv (map … \fst (f_locals def)) in |
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[1149] | 1223 | let result ≝ |
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[1068] | 1224 | match (f_result def) with |
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| 1225 | [ None ⇒ [ ] |
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| 1226 | | Some r_typ ⇒ |
---|
| 1227 | let 〈r, typ〉 ≝ r_typ in |
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| 1228 | find_local_env r lenv |
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[1053] | 1229 | ] |
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[1068] | 1230 | in |
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| 1231 | let luniverse' ≝ f_labgen def in |
---|
| 1232 | let runiverse' ≝ runiverse in |
---|
| 1233 | let result' ≝ result in |
---|
| 1234 | let params' ≝ params in |
---|
| 1235 | let locals' ≝ locals in |
---|
| 1236 | let stack_size' ≝ f_stacksize def in |
---|
| 1237 | let entry' ≝ f_entry def in |
---|
| 1238 | let exit' ≝ f_exit def in |
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[1293] | 1239 | let graph' ≝ add LabelTag ? (empty_map LabelTag ?) entry' (GOTO rtl_params_ globals entry') in |
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| 1240 | let graph' ≝ add LabelTag ? graph' exit' (GOTO rtl_params_ globals exit') in |
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[1068] | 1241 | let res ≝ |
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[1281] | 1242 | mk_joint_internal_function … (rtl_params globals) luniverse' runiverse' result' params' |
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| 1243 | locals' stack_size' graph' ? ? in |
---|
[1293] | 1244 | foldi … (translate_stmt globals … lenv) (f_graph def) res. |
---|
[1281] | 1245 | [ % [@entry' | @graph_add_lookup @graph_add] |
---|
| 1246 | | % [@exit' | @graph_add]] |
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[1073] | 1247 | qed. |
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[1053] | 1248 | |
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[1239] | 1249 | (*CSC: here we are not doing any alignment on variables, like it is done in OCaml |
---|
| 1250 | because of CompCert heritage *) |
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[1293] | 1251 | definition rtlabs_to_rtl: RTLabs_program → rtl_program ≝ |
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| 1252 | λp. transform_program … p (transf_fundef … (translate_internal (prog_var_names …))). |
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