diff options
-rw-r--r-- | Makefile | 6 | ||||
-rw-r--r-- | backend/Asmexpandaux.ml | 16 | ||||
-rwxr-xr-x | configure | 11 | ||||
-rw-r--r-- | driver/Compiler.v | 2 | ||||
-rw-r--r-- | driver/ForwardSimulationBlock.v | 322 | ||||
-rw-r--r-- | extraction/extraction.v | 2 | ||||
-rw-r--r-- | mppa_k1c/Asm.v | 1859 | ||||
-rw-r--r-- | mppa_k1c/Asmblock.v | 1361 | ||||
-rw-r--r-- | mppa_k1c/Asmblockgen.v | 943 | ||||
-rw-r--r-- | mppa_k1c/Asmblockgenproof.v | 2143 | ||||
-rw-r--r-- | mppa_k1c/Asmblockgenproof0.v | 1081 | ||||
-rw-r--r-- | mppa_k1c/Asmblockgenproof1.v | 1633 | ||||
-rw-r--r-- | mppa_k1c/Asmexpand.ml | 111 | ||||
-rw-r--r-- | mppa_k1c/Asmgen.v | 837 | ||||
-rw-r--r-- | mppa_k1c/Asmgenproof.v | 1192 | ||||
-rw-r--r-- | mppa_k1c/Machblock.v | 355 | ||||
-rw-r--r-- | mppa_k1c/Machblockgen.v | 578 | ||||
-rw-r--r-- | mppa_k1c/Machblockgenproof.v | 629 | ||||
-rw-r--r-- | mppa_k1c/SelectLong.vp | 12 | ||||
-rw-r--r-- | mppa_k1c/TargetPrinter.ml | 265 | ||||
-rw-r--r-- | mppa_k1c/extractionMachdep.v | 2 | ||||
-rw-r--r-- | test/mppa/.gitignore | 19 | ||||
-rw-r--r-- | test/mppa/Makefile | 90 | ||||
-rw-r--r-- | test/mppa/builtins/clzll.c | 7 | ||||
-rw-r--r-- | test/mppa/builtins/stsud.c (renamed from test/mppa/general/stsud.c) | 0 | ||||
-rwxr-xr-x[-rw-r--r--] | test/mppa/check.sh | 34 | ||||
-rw-r--r-- | test/mppa/do_test.sh | 33 | ||||
-rw-r--r-- | test/mppa/generate.sh | 21 | ||||
-rw-r--r-- | test/mppa/instr/.gitignore (renamed from test/mppa/general/.gitignore) | 0 | ||||
-rw-r--r-- | test/mppa/instr/Makefile | 111 | ||||
-rw-r--r-- | test/mppa/instr/addw.c (renamed from test/mppa/general/addw.c) | 0 | ||||
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-rw-r--r-- | test/mppa/instr/branchzu.c (renamed from test/mppa/general/branchzu.c) | 0 | ||||
-rw-r--r-- | test/mppa/instr/call.c (renamed from test/mppa/general/call.c) | 0 | ||||
-rw-r--r-- | test/mppa/instr/cb.deqz.c (renamed from test/mppa/general/cb.deqz.c) | 0 | ||||
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-rw-r--r-- | test/mppa/instr/cb.dgtz.c (renamed from test/mppa/general/cb.dgtz.c) | 0 | ||||
-rw-r--r-- | test/mppa/instr/cb.dlez.c (renamed from test/mppa/general/cb.dlez.c) | 0 | ||||
-rw-r--r-- | test/mppa/instr/cb.dltz.c (renamed from test/mppa/general/cb.dltz.c) | 0 | ||||
-rw-r--r-- | test/mppa/instr/cb.dnez.c (renamed from test/mppa/general/cb.dnez.c) | 0 | ||||
-rw-r--r-- | test/mppa/instr/cb.wgez.c (renamed from test/mppa/general/cb.wgez.c) | 0 | ||||
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-rw-r--r-- | test/mppa/instr/cb.wltz.c (renamed from test/mppa/general/cb.wltz.c) | 0 | ||||
-rw-r--r-- | test/mppa/instr/compd.eq.c (renamed from test/mppa/general/compd.eq.c) | 0 | ||||
-rw-r--r-- | test/mppa/instr/compd.geu.c (renamed from test/mppa/general/compd.geu.c) | 0 | ||||
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-rw-r--r-- | test/mppa/instr/compd.gtu.c (renamed from test/mppa/general/compd.gtu.c) | 0 | ||||
-rw-r--r-- | test/mppa/instr/compd.le.c (renamed from test/mppa/general/compd.le.c) | 0 | ||||
-rw-r--r-- | test/mppa/instr/compd.leu.c (renamed from test/mppa/general/compd.leu.c) | 0 | ||||
-rw-r--r-- | test/mppa/instr/compd.lt.c (renamed from test/mppa/general/compd.lt.c) | 0 | ||||
-rw-r--r-- | test/mppa/instr/compd.ltu.c (renamed from test/mppa/general/compd.ltu.c) | 0 | ||||
-rw-r--r-- | test/mppa/instr/compd.ne.c (renamed from test/mppa/general/compd.ne.c) | 0 | ||||
-rw-r--r-- | test/mppa/instr/compw.eq.c (renamed from test/mppa/general/compw.eq.c) | 0 | ||||
-rw-r--r-- | test/mppa/instr/compw.geu.c (renamed from test/mppa/general/compw.geu.c) | 0 | ||||
-rw-r--r-- | test/mppa/instr/compw.gt.c (renamed from test/mppa/general/compw.gt.c) | 0 | ||||
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-rw-r--r-- | test/mppa/instr/div2.c (renamed from test/mppa/general/div2.c) | 0 | ||||
-rw-r--r-- | test/mppa/instr/for.c (renamed from test/mppa/general/for.c) | 0 | ||||
-rw-r--r-- | test/mppa/instr/forvar.c (renamed from test/mppa/general/forvar.c) | 0 | ||||
-rw-r--r-- | test/mppa/instr/forvarl.c (renamed from test/mppa/general/forvarl.c) | 0 | ||||
-rw-r--r-- | test/mppa/instr/framework.h (renamed from test/mppa/general/framework.h) | 2 | ||||
-rw-r--r-- | test/mppa/instr/lbs.c (renamed from test/mppa/general/lbs.c) | 0 | ||||
-rw-r--r-- | test/mppa/instr/lbz.c (renamed from test/mppa/general/lbz.c) | 0 | ||||
-rw-r--r-- | test/mppa/instr/muld.c (renamed from test/mppa/general/muld.c) | 0 | ||||
-rw-r--r-- | test/mppa/instr/mulw.c (renamed from test/mppa/general/mulw.c) | 0 | ||||
-rw-r--r-- | test/mppa/instr/negd.c (renamed from test/mppa/general/negd.c) | 0 | ||||
-rw-r--r-- | test/mppa/instr/ord.c (renamed from test/mppa/general/ord.c) | 0 | ||||
-rw-r--r-- | test/mppa/instr/sbfd.c (renamed from test/mppa/general/sbfd.c) | 0 | ||||
-rw-r--r-- | test/mppa/instr/sbfw.c (renamed from test/mppa/general/sbfw.c) | 0 | ||||
-rw-r--r-- | test/mppa/instr/simple.c (renamed from test/mppa/general/simple.c) | 0 | ||||
-rw-r--r-- | test/mppa/instr/sllw.c (renamed from test/mppa/general/sllw.c) | 0 | ||||
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-rw-r--r-- | test/mppa/instr/udivd.c (renamed from test/mppa/general/udivd.c) | 0 | ||||
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-rw-r--r-- | test/mppa/lib/.gitignore | 2 | ||||
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-rw-r--r-- | test/mppa/mmult/.gitignore | 7 | ||||
-rw-r--r-- | test/mppa/mmult/Makefile | 99 | ||||
-rw-r--r-- | test/mppa/mmult/README.md | 17 | ||||
-rw-r--r-- | test/mppa/mmult/mmult.c | 44 | ||||
-rw-r--r-- | test/mppa/prng/.gitignore | 3 | ||||
-rw-r--r-- | test/mppa/prng/Makefile | 69 | ||||
-rw-r--r-- | test/mppa/prng/README.md | 17 | ||||
-rw-r--r-- | test/mppa/prng/prng.c (renamed from test/mppa/lib/prng.c) | 11 | ||||
-rw-r--r-- | test/mppa/prng/prng.h (renamed from test/mppa/lib/prng.h) | 0 | ||||
-rw-r--r-- | test/mppa/prng/types.h (renamed from test/mppa/lib/types.h) | 0 | ||||
-rw-r--r-- | test/mppa/sort/.gitignore | 18 | ||||
-rw-r--r-- | test/mppa/sort/Makefile | 123 | ||||
-rw-r--r-- | test/mppa/sort/README.md | 17 | ||||
-rw-r--r-- | test/mppa/sort/insertion.c | 17 | ||||
-rw-r--r-- | test/mppa/sort/main.c (renamed from test/mppa/sort/test.c) | 9 | ||||
-rw-r--r-- | test/mppa/sort/merge.c | 25 | ||||
-rw-r--r-- | test/mppa/sort/selection.c | 21 | ||||
-rwxr-xr-x | test/mppa/test.sh | 6 |
105 files changed, 10302 insertions, 3910 deletions
@@ -95,7 +95,9 @@ BACKEND=\ Debugvar.v Debugvarproof.v \ Mach.v \ Bounds.v Stacklayout.v Stacking.v Stackingproof.v \ - Asm.v Asmgen.v Asmgenproof0.v Asmgenproof1.v Asmgenproof.v + Machblock.v Machblockgen.v Machblockgenproof.v \ + Asmblock.v Asmblockgen.v Asmblockgenproof0.v Asmblockgenproof1.v Asmblockgenproof.v \ + Asm.v Asmgen.v Asmgenproof.v # C front-end modules (in cfrontend/) @@ -118,7 +120,7 @@ PARSER=Cabs.v Parser.v # Putting everything together (in driver/) -DRIVER=Compopts.v Compiler.v Complements.v +DRIVER=Compopts.v Compiler.v Complements.v ForwardSimulationBlock.v # All source files diff --git a/backend/Asmexpandaux.ml b/backend/Asmexpandaux.ml index 23fef3f2..62c4a702 100644 --- a/backend/Asmexpandaux.ml +++ b/backend/Asmexpandaux.ml @@ -26,7 +26,9 @@ let emit i = current_code := i :: !current_code (* Generation of fresh labels *) -let dummy_function = { fn_code = []; fn_sig = signature_main } +(** dummy_funtion is now defined in Asm.v *) +(* let dummy_function = { fn_code = []; fn_sig = signature_main } *) + let current_function = ref dummy_function let next_label = ref (None: label option) @@ -39,7 +41,7 @@ let new_label () = List.fold_left (fun next instr -> match instr with - | PExpand (Plabel l) -> if P.lt l next then next else P.succ l + | Plabel l -> if P.lt l next then next else P.succ l | _ -> next) P.one (!current_function).fn_code in @@ -100,17 +102,17 @@ let expand_debug id sp preg simple l = let get_lbl = function | None -> let lbl = new_label () in - emit (PExpand (Plabel lbl)); + emit (Plabel lbl); lbl | Some lbl -> lbl in let rec aux lbl scopes = function | [] -> () - | (PExpand (Pbuiltin(EF_debug (kind,txt,_x),args,_) as i))::rest -> + | (Pbuiltin(EF_debug (kind,txt,_x),args,_) as i)::rest -> let kind = (P.to_int kind) in begin match kind with | 1-> - emit (PExpand i);aux lbl scopes rest + emit i; aux lbl scopes rest | 2 -> aux lbl scopes rest | 3 -> @@ -142,11 +144,11 @@ let expand_debug id sp preg simple l = | _ -> aux None scopes rest end - | (PExpand (Plabel lbl))::rest -> simple (PExpand (Plabel lbl)); aux (Some lbl) scopes rest + | (Plabel lbl)::rest -> simple (Plabel lbl); aux (Some lbl) scopes rest | i::rest -> simple i; aux None scopes rest in (* We need to move all closing debug annotations before the last real statement *) let rec move_debug acc bcc = function - | (PExpand (Pbuiltin(EF_debug (kind,_,_),_,_)) as i)::rest -> + | (Pbuiltin(EF_debug (kind,_,_),_,_)) as i::rest -> let kind = (P.to_int kind) in if kind = 1 then move_debug acc (i::bcc) rest (* Do not move debug line *) @@ -414,16 +414,17 @@ fi if test "$arch" = "mppa_k1c"; then #model_options="-march=rv64imafd -mabi=lp64d" # FIXME - maybe later add it for NodeOS & cie - model_options=-m64 + #model_options=-m64 + model_options= abi="standard" - casm="${toolprefix}gcc" + casm="k1-mbr-gcc" casm_options="$model_options -c" - cc="${toolprefix}gcc $model_options" - clinker="${toolprefix}gcc" + cc="k1-mbr-gcc $model_options" + clinker="k1-mbr-gcc" bindir="$HOME/.usr/bin" libdir="$HOME/.usr/lib" clinker_options="$model_options -L$libdir -Wl,-rpath=$libdir" - cprepro="${toolprefix}gcc" + cprepro="k1-mbr-gcc" cprepro_options="$model_options -std=c99 -U__GNUC__ -E" libmath="-lm" system="linux" diff --git a/driver/Compiler.v b/driver/Compiler.v index 75247f71..1cb5bd36 100644 --- a/driver/Compiler.v +++ b/driver/Compiler.v @@ -404,7 +404,7 @@ Ltac DestructM := eapply compose_forward_simulations. eapply match_if_simulation. eassumption. exact Debugvarproof.transf_program_correct. eapply compose_forward_simulations. - eapply Stackingproof.transf_program_correct with (return_address_offset := Asmgenproof0.return_address_offset). + eapply Stackingproof.transf_program_correct with (return_address_offset := Asmgenproof.return_address_offset). exact Asmgenproof.return_address_exists. eassumption. eapply Asmgenproof.transf_program_correct; eassumption. diff --git a/driver/ForwardSimulationBlock.v b/driver/ForwardSimulationBlock.v new file mode 100644 index 00000000..dc8beb29 --- /dev/null +++ b/driver/ForwardSimulationBlock.v @@ -0,0 +1,322 @@ +(*** + +Auxiliary lemmas on starN and forward_simulation +in order to prove the forward simulation of Mach -> Machblock. + +***) + +Require Import Relations. +Require Import Wellfounded. +Require Import Coqlib. +Require Import Events. +Require Import Globalenvs. +Require Import Smallstep. + + +Local Open Scope nat_scope. + + +(** Auxiliary lemma on starN *) +Section starN_lemma. + +Variable L: semantics. + +Local Hint Resolve starN_refl starN_step Eapp_assoc. + +Lemma starN_split n s t s': + starN (step L) (globalenv L) n s t s' -> + forall m k, n=m+k -> + exists (t1 t2:trace) s0, starN (step L) (globalenv L) m s t1 s0 /\ starN (step L) (globalenv L) k s0 t2 s' /\ t=t1**t2. +Proof. + induction 1; simpl. + + intros m k H; assert (X: m=0); try omega. + assert (X0: k=0); try omega. + subst; repeat (eapply ex_intro); intuition eauto. + + intros m; destruct m as [| m']; simpl. + - intros k H2; subst; repeat (eapply ex_intro); intuition eauto. + - intros k H2. inversion H2. + exploit (IHstarN m' k); eauto. intro. + destruct H3 as (t5 & t6 & s0 & H5 & H6 & H7). + repeat (eapply ex_intro). + instantiate (1 := t6); instantiate (1 := t1 ** t5); instantiate (1 := s0). + intuition eauto. subst. auto. +Qed. + +Lemma starN_tailstep n s t1 s': + starN (step L) (globalenv L) n s t1 s' -> + forall (t t2:trace) s'', + Step L s' t2 s'' -> t = t1 ** t2 -> starN (step L) (globalenv L) (S n) s t s''. +Proof. + induction 1; simpl. + + intros t t1 s0; autorewrite with trace_rewrite. + intros; subst; eapply starN_step; eauto. + autorewrite with trace_rewrite; auto. + + intros. eapply starN_step; eauto. + intros; subst; autorewrite with trace_rewrite; auto. +Qed. + +End starN_lemma. + + + +(** General scheme from a "match_states" relation *) + +Section ForwardSimuBlock_REL. + +Variable L1 L2: semantics. + + +(** Hypothèses de la preuve *) + +Variable dist_end_block: state L1 -> nat. + +Hypothesis simu_mid_block: + forall s1 t s1', Step L1 s1 t s1' -> (dist_end_block s1)<>0 -> t = E0 /\ dist_end_block s1=S (dist_end_block s1'). + +Hypothesis public_preserved: + forall id, Senv.public_symbol (symbolenv L2) id = Senv.public_symbol (symbolenv L1) id. + +Variable match_states: state L1 -> state L2 -> Prop. + +Hypothesis match_initial_states: + forall s1, initial_state L1 s1 -> exists s2, match_states s1 s2 /\ initial_state L2 s2. + +Hypothesis match_final_states: + forall s1 s2 r, final_state L1 s1 r -> match_states s1 s2 -> final_state L2 s2 r. + +Hypothesis final_states_end_block: + forall s1 t s1' r, Step L1 s1 t s1' -> final_state L1 s1' r -> dist_end_block s1 = 0. + +Hypothesis simu_end_block: + forall s1 t s1' s2, starN (step L1) (globalenv L1) (S (dist_end_block s1)) s1 t s1' -> match_states s1 s2 -> exists s2', Step L2 s2 t s2' /\ match_states s1' s2'. + + +(** Introduction d'une sémantique par bloc sur L1 appelée "memoL1" *) + +Local Hint Resolve starN_refl starN_step. + +Definition follows_in_block (head current: state L1): Prop := + dist_end_block head >= dist_end_block current + /\ starN (step L1) (globalenv L1) (minus (dist_end_block head) (dist_end_block current)) head E0 current. + +Lemma follows_in_block_step (head previous next: state L1): + forall t, follows_in_block head previous -> Step L1 previous t next -> (dist_end_block previous)<>0 -> follows_in_block head next. +Proof. + intros t [H1 H2] H3 H4. + destruct (simu_mid_block _ _ _ H3 H4) as [H5 H6]; subst. + constructor 1. + + omega. + + cutrewrite (dist_end_block head - dist_end_block next = S (dist_end_block head - dist_end_block previous)). + - eapply starN_tailstep; eauto. + - omega. +Qed. + +Lemma follows_in_block_init (head current: state L1): + forall t, Step L1 head t current -> (dist_end_block head)<>0 -> follows_in_block head current. +Proof. + intros t H3 H4. + destruct (simu_mid_block _ _ _ H3 H4) as [H5 H6]; subst. + constructor 1. + + omega. + + cutrewrite (dist_end_block head - dist_end_block current = 1). + - eapply starN_tailstep; eauto. + - omega. +Qed. + + +Record memostate := { + real: state L1; + memorized: option (state L1); + memo_star: forall head, memorized = Some head -> follows_in_block head real; + memo_final: forall r, final_state L1 real r -> memorized = None +}. + +Definition head (s: memostate): state L1 := + match memorized s with + | None => real s + | Some s' => s' + end. + +Lemma head_followed (s: memostate): follows_in_block (head s) (real s). +Proof. + destruct s as [rs ms Hs]. simpl. + destruct ms as [ms|]; unfold head; simpl; auto. + constructor 1. + omega. + cutrewrite ((dist_end_block rs - dist_end_block rs)%nat=O). + + apply starN_refl; auto. + + omega. +Qed. + +Inductive is_well_memorized (s s': memostate): Prop := + | StartBloc: + dist_end_block (real s) <> O -> + memorized s = None -> + memorized s' = Some (real s) -> + is_well_memorized s s' + | MidBloc: + dist_end_block (real s) <> O -> + memorized s <> None -> + memorized s' = memorized s -> + is_well_memorized s s' + | ExitBloc: + dist_end_block (real s) = O -> + memorized s' = None -> + is_well_memorized s s'. + +Local Hint Resolve StartBloc MidBloc ExitBloc. + +Definition memoL1 := {| + state := memostate; + genvtype := genvtype L1; + step := fun ge s t s' => + step L1 ge (real s) t (real s') + /\ is_well_memorized s s' ; + initial_state := fun s => initial_state L1 (real s) /\ memorized s = None; + final_state := fun s r => final_state L1 (real s) r; + globalenv:= globalenv L1; + symbolenv:= symbolenv L1 +|}. + + +(** Preuve des 2 forward simulations: L1 -> memoL1 et memoL1 -> L2 *) + +Lemma discr_dist_end s: + {dist_end_block s = O} + {dist_end_block s <> O}. +Proof. + destruct (dist_end_block s); simpl; intuition. +Qed. + +Lemma memo_simulation_step: + forall s1 t s1', Step L1 s1 t s1' -> + forall s2, s1 = (real s2) -> exists s2', Step memoL1 s2 t s2' /\ s1' = (real s2'). +Proof. + intros s1 t s1' H1 [rs2 ms2 Hmoi] H2. simpl in H2; subst. + destruct (discr_dist_end rs2) as [H3 | H3]. + + refine (ex_intro _ {|real:=s1'; memorized:=None |} _); simpl. + intuition. + + destruct ms2 as [s|]. + - refine (ex_intro _ {|real:=s1'; memorized:=Some s |} _); simpl. + intuition. + - refine (ex_intro _ {|real:=s1'; memorized:=Some rs2 |} _); simpl. + intuition. + Unshelve. + * intros; discriminate. + * intros; auto. + * intros head X; injection X; clear X; intros; subst. + eapply follows_in_block_step; eauto. + * intros r X; erewrite final_states_end_block in H3; intuition eauto. + * intros head X; injection X; clear X; intros; subst. + eapply follows_in_block_init; eauto. + * intros r X; erewrite final_states_end_block in H3; intuition eauto. +Qed. + +Lemma forward_memo_simulation_1: forward_simulation L1 memoL1. +Proof. + apply forward_simulation_step with (match_states:=fun s1 s2 => s1 = (real s2)); auto. + + intros s1 H; eapply ex_intro with (x:={|real:=s1; memorized:=None |}); simpl. + intuition. + + intros; subst; auto. + + intros; exploit memo_simulation_step; eauto. + Unshelve. + * intros; discriminate. + * auto. +Qed. + +Lemma forward_memo_simulation_2: forward_simulation memoL1 L2. +Proof. + unfold memoL1; simpl. + apply forward_simulation_opt with (measure:=fun s => dist_end_block (real s)) (match_states:=fun s1 s2 => match_states (head s1) s2); simpl; auto. + + intros s1 [H0 H1]; destruct (match_initial_states (real s1) H0). + unfold head; rewrite H1. + intuition eauto. + + intros s1 s2 r X H0; unfold head in X. + erewrite memo_final in X; eauto. + + intros s1 t s1' [H1 H2] s2 H; subst. + destruct H2 as [ H0 H2 H3 | H0 H2 H3 | H0 H2]. + - (* StartBloc *) + constructor 2. destruct (simu_mid_block (real s1) t (real s1')) as [H5 H4]; auto. + unfold head in * |- *. rewrite H2 in H. rewrite H3. rewrite H4. intuition. + - (* MidBloc *) + constructor 2. destruct (simu_mid_block (real s1) t (real s1')) as [H5 H4]; auto. + unfold head in * |- *. rewrite H3. rewrite H4. intuition. + destruct (memorized s1); simpl; auto. tauto. + - (* EndBloc *) + constructor 1. + destruct (simu_end_block (head s1) t (real s1') s2) as (s2' & H3 & H4); auto. + * destruct (head_followed s1) as [H4 H3]. + cutrewrite (dist_end_block (head s1) - dist_end_block (real s1) = dist_end_block (head s1)) in H3; try omega. + eapply starN_tailstep; eauto. + * unfold head; rewrite H2; simpl. intuition eauto. +Qed. + +Lemma forward_simulation_block_rel: forward_simulation L1 L2. +Proof. + eapply compose_forward_simulations. + eapply forward_memo_simulation_1. + apply forward_memo_simulation_2. +Qed. + + +End ForwardSimuBlock_REL. + + + +(* An instance of the previous scheme, when there is a translation from L1 states to L2 states + +Here, we do not require that the sequence of S2 states does exactly match the sequence of L1 states by trans_state. +This is because the exact matching is broken in Machblock on "goto" instruction (due to the find_label). + +However, the Machblock state after a goto remains "equivalent" to the trans_state of the Mach state in the sense of "equiv_on_next_step" below... + +*) + +Section ForwardSimuBlock_TRANS. + +Variable L1 L2: semantics. + +Variable trans_state: state L1 -> state L2. + +Definition equiv_on_next_step (P Q: Prop) s2_a s2_b: Prop := + (P -> (forall t s', Step L2 s2_a t s' <-> Step L2 s2_b t s')) /\ (Q -> (forall r, (final_state L2 s2_a r) <-> (final_state L2 s2_b r))). + +Definition match_states s1 s2: Prop := + equiv_on_next_step (exists t s1', Step L1 s1 t s1') (exists r, final_state L1 s1 r) s2 (trans_state s1). + +Lemma match_states_trans_state s1: match_states s1 (trans_state s1). +Proof. + unfold match_states, equiv_on_next_step. intuition. +Qed. + +Variable dist_end_block: state L1 -> nat. + +Hypothesis simu_mid_block: + forall s1 t s1', Step L1 s1 t s1' -> (dist_end_block s1)<>0 -> t = E0 /\ dist_end_block s1=S (dist_end_block s1'). + +Hypothesis public_preserved: + forall id, Senv.public_symbol (symbolenv L2) id = Senv.public_symbol (symbolenv L1) id. + +Hypothesis match_initial_states: + forall s1, initial_state L1 s1 -> exists s2, match_states s1 s2 /\ initial_state L2 s2. + +Hypothesis match_final_states: + forall s1 r, final_state L1 s1 r -> final_state L2 (trans_state s1) r. + +Hypothesis final_states_end_block: + forall s1 t s1' r, Step L1 s1 t s1' -> final_state L1 s1' r -> dist_end_block s1 = 0. + +Hypothesis simu_end_block: + forall s1 t s1', starN (step L1) (globalenv L1) (S (dist_end_block s1)) s1 t s1' -> exists s2', Step L2 (trans_state s1) t s2' /\ match_states s1' s2'. + +Lemma forward_simulation_block_trans: forward_simulation L1 L2. +Proof. + eapply forward_simulation_block_rel with (dist_end_block:=dist_end_block) (match_states:=match_states); try tauto. + + (* final_states *) intros s1 s2 r H1 [H2 H3]. rewrite H3; eauto. + + (* simu_end_block *) + intros s1 t s1' s2 H1 [H2a H2b]. exploit simu_end_block; eauto. + intros (s2' & H3 & H4); econstructor 1; intuition eauto. + rewrite H2a; auto. + inversion_clear H1. eauto. +Qed. + +End ForwardSimuBlock_TRANS. diff --git a/extraction/extraction.v b/extraction/extraction.v index 8ac776ef..6ab2ce3a 100644 --- a/extraction/extraction.v +++ b/extraction/extraction.v @@ -167,7 +167,7 @@ Set Extraction AccessOpaque. Cd "extraction". Separate Extraction - Asmgen.addptrofs + Asm.dummy_function Asmgen.addptrofs Asmgen.storeind_ptr Compiler.transf_c_program Compiler.transf_cminor_program Cexec.do_initial_state Cexec.do_step Cexec.at_final_state Ctypes.merge_attributes Ctypes.remove_attributes Ctypes.build_composite_env diff --git a/mppa_k1c/Asm.v b/mppa_k1c/Asm.v index 9de80a15..c142185c 100644 --- a/mppa_k1c/Asm.v +++ b/mppa_k1c/Asm.v @@ -1,1363 +1,496 @@ -(* *********************************************************************) -(* *) -(* The Compcert verified compiler *) -(* *) -(* Xavier Leroy, INRIA Paris-Rocquencourt *) -(* Prashanth Mundkur, SRI International *) -(* *) -(* Copyright Institut National de Recherche en Informatique et en *) -(* Automatique. All rights reserved. This file is distributed *) -(* under the terms of the INRIA Non-Commercial License Agreement. *) -(* *) -(* The contributions by Prashanth Mundkur are reused and adapted *) -(* under the terms of a Contributor License Agreement between *) -(* SRI International and INRIA. *) -(* *) -(* *********************************************************************) - -(** Abstract syntax and semantics for K1c assembly language. *) - -Require Import Coqlib. -Require Import Maps. -Require Import AST. -Require Import Integers. -Require Import Floats. -Require Import Values. -Require Import Memory. -Require Import Events. -Require Import Globalenvs. -Require Import Smallstep. -Require Import Locations. -Require Stacklayout. -Require Import Conventions. - -(** * Abstract syntax *) - -(** General Purpose registers. *) - -Inductive gpreg: Type := - | GPR0: gpreg | GPR1: gpreg | GPR2: gpreg | GPR3: gpreg | GPR4: gpreg - | GPR5: gpreg | GPR6: gpreg | GPR7: gpreg | GPR8: gpreg | GPR9: gpreg - | GPR10: gpreg | GPR11: gpreg | GPR12: gpreg | GPR13: gpreg | GPR14: gpreg - | GPR15: gpreg | GPR16: gpreg | GPR17: gpreg | GPR18: gpreg | GPR19: gpreg - | GPR20: gpreg | GPR21: gpreg | GPR22: gpreg | GPR23: gpreg | GPR24: gpreg - | GPR25: gpreg | GPR26: gpreg | GPR27: gpreg | GPR28: gpreg | GPR29: gpreg - | GPR30: gpreg | GPR31: gpreg | GPR32: gpreg | GPR33: gpreg | GPR34: gpreg - | GPR35: gpreg | GPR36: gpreg | GPR37: gpreg | GPR38: gpreg | GPR39: gpreg - | GPR40: gpreg | GPR41: gpreg | GPR42: gpreg | GPR43: gpreg | GPR44: gpreg - | GPR45: gpreg | GPR46: gpreg | GPR47: gpreg | GPR48: gpreg | GPR49: gpreg - | GPR50: gpreg | GPR51: gpreg | GPR52: gpreg | GPR53: gpreg | GPR54: gpreg - | GPR55: gpreg | GPR56: gpreg | GPR57: gpreg | GPR58: gpreg | GPR59: gpreg - | GPR60: gpreg | GPR61: gpreg | GPR62: gpreg | GPR63: gpreg. - -Definition ireg := gpreg. -Definition freg := gpreg. - -Lemma ireg_eq: forall (x y: ireg), {x=y} + {x<>y}. -Proof. decide equality. Defined. - -Lemma freg_eq: forall (x y: freg), {x=y} + {x<>y}. -Proof. decide equality. Defined. - -(** We model the following registers of the RISC-V architecture. *) - -Inductive preg: Type := - | IR: gpreg -> preg (**r integer registers *) - | FR: gpreg -> preg (**r float registers *) - | RA: preg (**r return address *) - | PC: preg. (**r program counter *) - -Coercion IR: gpreg >-> preg. -Coercion FR: gpreg >-> preg. - -Lemma preg_eq: forall (x y: preg), {x=y} + {x<>y}. -Proof. decide equality. apply ireg_eq. apply freg_eq. Defined. - -Module PregEq. - Definition t := preg. - Definition eq := preg_eq. -End PregEq. - -Module Pregmap := EMap(PregEq). - -(** Conventional names for stack pointer ([SP]) and return address ([RA]). *) - -Notation "'SP'" := GPR12 (only parsing) : asm. -Notation "'FP'" := GPR10 (only parsing) : asm. -Notation "'RTMP'" := GPR31 (only parsing) : asm. - -Inductive btest: Type := - | BTdnez (**r Double Not Equal to Zero *) - | BTdeqz (**r Double Equal to Zero *) - | BTdltz (**r Double Less Than Zero *) - | BTdgez (**r Double Greater Than or Equal to Zero *) - | BTdlez (**r Double Less Than or Equal to Zero *) - | BTdgtz (**r Double Greater Than Zero *) -(*| BTodd (**r Odd (LSB Set) *) - | BTeven (**r Even (LSB Clear) *) -*)| BTwnez (**r Word Not Equal to Zero *) - | BTweqz (**r Word Equal to Zero *) - | BTwltz (**r Word Less Than Zero *) - | BTwgez (**r Word Greater Than or Equal to Zero *) - | BTwlez (**r Word Less Than or Equal to Zero *) - | BTwgtz (**r Word Greater Than Zero *) - . - -Inductive itest: Type := - | ITne (**r Not Equal *) - | ITeq (**r Equal *) - | ITlt (**r Less Than *) - | ITge (**r Greater Than or Equal *) - | ITle (**r Less Than or Equal *) - | ITgt (**r Greater Than *) - | ITneu (**r Unsigned Not Equal *) - | ITequ (**r Unsigned Equal *) - | ITltu (**r Less Than Unsigned *) - | ITgeu (**r Greater Than or Equal Unsigned *) - | ITleu (**r Less Than or Equal Unsigned *) - | ITgtu (**r Greater Than Unsigned *) - (* Not used yet *) - | ITall (**r All Bits Set in Mask *) - | ITnall (**r Not All Bits Set in Mask *) - | ITany (**r Any Bits Set in Mask *) - | ITnone (**r Not Any Bits Set in Mask *) - . - -(** Offsets for load and store instructions. An offset is either an - immediate integer or the low part of a symbol. *) - -Inductive offset : Type := - | Ofsimm (ofs: ptrofs) - | Ofslow (id: ident) (ofs: ptrofs). - -(** We model a subset of the K1c instruction set. In particular, we do not - support floats yet. - - Although it is possible to use the 32-bits mode, for now we don't support it. - - We follow a design close to the one used for the Risc-V port: one set of - pseudo-instructions for 32-bit integer arithmetic, with suffix W, another - set for 64-bit integer arithmetic, with suffix L. - - When mapping to actual instructions, the OCaml code in TargetPrinter.ml - throws an error if we are not in 64-bits mode. -*) - -Definition label := positive. - -(** A note on immediates: there are various constraints on immediate - operands to K1c instructions. We do not attempt to capture these - restrictions in the abstract syntax nor in the semantics. The - assembler will emit an error if immediate operands exceed the - representable range. Of course, our K1c generator (file - [Asmgen]) is careful to respect this range. *) - -(** Instructions to be expanded *) -Inductive ex_instruction : Type := - (* Pseudo-instructions *) - | Pallocframe (sz: Z) (pos: ptrofs) (**r allocate new stack frame *) - | Pfreeframe (sz: Z) (pos: ptrofs) (**r deallocate stack frame and restore previous frame *) - | Plabel (lbl: label) (**r define a code label *) - | Ploadsymbol (rd: ireg) (id: ident) (ofs: ptrofs) (**r load the address of a symbol *) -(*| Ploadsymbol_high (rd: ireg) (id: ident) (ofs: ptrofs) (**r load the high part of the address of a symbol *) - | Ploadli (rd: ireg) (i: int64) (**r load an immediate int64 *) - | Ploadfi (rd: freg) (f: float) (**r load an immediate float *) - | Ploadsi (rd: freg) (f: float32) (**r load an immediate single *) - | Pbtbl (r: ireg) (tbl: list label) (**r N-way branch through a jump table *) *) - | Pbuiltin: external_function -> list (builtin_arg preg) - -> builtin_res preg -> ex_instruction (**r built-in function (pseudo) *) - (* Instructions not generated by Asmgen (most likely result of AsmExpand) *) - (* BCU *) - | Pawait - | Pbarrier - | Pdoze - | Pwfxl (rs1 rs2: ireg) - | Pwfxm (rs1 rs2: ireg) - | Pinvaldtlb - | Pinvalitlb - | Pprobetlb - | Preadtlb - | Psleep - | Pstop - | Psyncgroup (rs: ireg) - | Ptlbwrite - - (* LSU *) - | Pafda (rd rs1 rs2: ireg) - | Paldc (rd rs: ireg) - | Pdinval - | Pdinvall (rs: ireg) - | Pdtouchl (rs: ireg) - | Pdzerol (rs: ireg) - | Pfence - | Piinval - | Piinvals (rs: ireg) - | Pitouchl (rs: ireg) - | Plbsu (rd rs: ireg) - | Plbzu (rd rs: ireg) - | Pldu (rd rs: ireg) - | Plhsu (rd rs: ireg) - | Plhzu (rd rs: ireg) - | Plwzu (rd rs: ireg) - - (* ALU *) - | Paddhp (rd rs1 rs2: ireg) - | Padds (rd rs1 rs2: ireg) - | Pbwlu (rd rs1 rs2 rs3 rs4 rs5: ireg) - | Pbwluhp (rd rs1 rs2 rs3: ireg) - | Pbwluwp (rd rs1 rs2 rs3: ireg) - | Pcbs (rd rs: ireg) - | Pcbsdl (rd rs: ireg) - | Pclz (rd rs: ireg) - | Pclzw (rd rs: ireg) - | Pclzd (rd rs: ireg) - | Pclzdl (rd rs: ireg) - | Pcmove (rd rs1 rs2 rs3: ireg) - | Pctz (rd rs: ireg) - | Pctzw (rd rs: ireg) - | Pctzd (rd rs: ireg) - | Pctzdl (rd rs: ireg) - | Pextfz (rd rs1 rs2 rs3: ireg) - | Plandhp (rd rs1 rs2 rs3: ireg) - | Psat (rd rs1 rs2: ireg) - | Psatd (rd rs1 rs2: ireg) - | Psbfhp (rd rs1 rs2: ireg) - | Psbmm8 (rd rs1 rs2: ireg) - | Psbmmt8 (rd rs1 rs2: ireg) - | Psllhps (rd rs1 rs2: ireg) - | Psrahps (rd rs1 rs2: ireg) - | Pstsu (rd rs1 rs2: ireg) - | Pstsud (rd rs1 rs2: ireg) -. - -(** The pseudo-instructions are the following: - -- [Plabel]: define a code label at the current program point. - -- [Ploadsymbol]: load the address of a symbol in an integer register. - Expands to the [la] assembler pseudo-instruction, which does the right - thing even if we are in PIC mode. - -- [Ploadli rd ival]: load an immediate 64-bit integer into an integer - register rd. Expands to a load from an address in the constant data section, - using the integer register x31 as temporary: -<< - lui x31, %hi(lbl) - ld rd, %lo(lbl)(x31) -lbl: - .quad ival ->> - -- [Ploadfi rd fval]: similar to [Ploadli] but loads a double FP constant fval - into a float register rd. - -- [Ploadsi rd fval]: similar to [Ploadli] but loads a singe FP constant fval - into a float register rd. - -- [Pallocframe sz pos]: in the formal semantics, this - pseudo-instruction allocates a memory block with bounds [0] and - [sz], stores the value of the stack pointer at offset [pos] in this - block, and sets the stack pointer to the address of the bottom of - this block. - In the printed ASM assembly code, this allocation is: -<< - mv x30, sp - sub sp, sp, #sz - sw x30, #pos(sp) ->> - This cannot be expressed in our memory model, which does not reflect - the fact that stack frames are adjacent and allocated/freed - following a stack discipline. - -- [Pfreeframe sz pos]: in the formal semantics, this pseudo-instruction - reads the word at [pos] of the block pointed by the stack pointer, - frees this block, and sets the stack pointer to the value read. - In the printed ASM assembly code, this freeing is just an increment of [sp]: -<< - add sp, sp, #sz ->> - Again, our memory model cannot comprehend that this operation - frees (logically) the current stack frame. - -- [Pbtbl reg table]: this is a N-way branch, implemented via a jump table - as follows: -<< - la x31, table - add x31, x31, reg - jr x31 -table: .long table[0], table[1], ... ->> - Note that [reg] contains 4 times the index of the desired table entry. - -- [Pseq rd rs1 rs2]: since unsigned comparisons have particular - semantics for pointers, we cannot encode equality directly using - xor/sub etc, which have only integer semantics. -<< - xor rd, rs1, rs2 - sltiu rd, rd, 1 ->> - The [xor] is omitted if one of [rs1] and [rs2] is [x0]. - -- [Psne rd rs1 rs2]: similarly for unsigned inequality. -<< - xor rd, rs1, rs2 - sltu rd, x0, rd ->> -*) - -(** Control Flow instructions *) -Inductive cf_instruction : Type := - | Pget (rd: ireg) (rs: preg) (**r get system register *) - | Pset (rd: preg) (rs: ireg) (**r set system register *) - | Pret (**r return *) - | Pcall (l: label) (**r function call *) - (* Pgoto is for tailcalls, Pj_l is for jumping to a particular label *) - | Pgoto (l: label) (**r goto *) - | Pj_l (l: label) (**r jump to label *) - (* Conditional branches *) - | Pcb (bt: btest) (r: ireg) (l: label) (**r branch based on btest *) - | Pcbu (bt: btest) (r: ireg) (l: label) (**r branch based on btest with unsigned semantics *) -. - -(** Loads **) -Inductive ld_instruction : Type := - | Plb (rd: ireg) (ra: ireg) (ofs: offset) (**r load byte *) - | Plbu (rd: ireg) (ra: ireg) (ofs: offset) (**r load byte unsigned *) - | Plh (rd: ireg) (ra: ireg) (ofs: offset) (**r load half word *) - | Plhu (rd: ireg) (ra: ireg) (ofs: offset) (**r load half word unsigned *) - | Plw (rd: ireg) (ra: ireg) (ofs: offset) (**r load int32 *) - | Plw_a (rd: ireg) (ra: ireg) (ofs: offset) (**r load any32 *) - | Pld (rd: ireg) (ra: ireg) (ofs: offset) (**r load int64 *) - | Pld_a (rd: ireg) (ra: ireg) (ofs: offset) (**r load any64 *) - | Pfls (rd: freg) (ra: ireg) (ofs: offset) (**r load float *) - | Pfld (rd: freg) (ra: ireg) (ofs: offset) (**r load 64-bit float *) -. - -(** Stores **) -Inductive st_instruction : Type := - | Psb (rs: ireg) (ra: ireg) (ofs: offset) (**r store byte *) - | Psh (rs: ireg) (ra: ireg) (ofs: offset) (**r store half byte *) - | Psw (rs: ireg) (ra: ireg) (ofs: offset) (**r store int32 *) - | Psw_a (rs: ireg) (ra: ireg) (ofs: offset) (**r store any32 *) - | Psd (rs: ireg) (ra: ireg) (ofs: offset) (**r store int64 *) - | Psd_a (rs: ireg) (ra: ireg) (ofs: offset) (**r store any64 *) - | Pfss (rs: freg) (ra: ireg) (ofs: offset) (**r store float *) - | Pfsd (rd: freg) (ra: ireg) (ofs: offset) (**r store 64-bit float *) -. - -(** Arithmetic instructions **) -Inductive arith_name_r : Type := - | Pcvtw2l (**r Convert Word to Long *) -. - -Inductive arith_name_rr : Type := - | Pmv (**r register move *) - | Pnegw (**r negate word *) - | Pnegl (**r negate long *) - | Pfnegd (**r float negate double *) - | Pcvtl2w (**r Convert Long to Word *) - | Pmvw2l (**r Move Convert Word to Long *) -. - -Inductive arith_name_ri32 : Type := - | Pmake (**r load immediate *) -. - -Inductive arith_name_ri64 : Type := - | Pmakel (**r load immediate long *) -. - -Inductive arith_name_rrr : Type := - | Pcompw (it: itest) (**r comparison word *) - | Pcompl (it: itest) (**r comparison long *) - - | Paddw (**r add word *) - | Psubw (**r sub word *) - | Pmulw (**r mul word *) - | Pandw (**r and word *) - | Porw (**r or word *) - | Pxorw (**r xor word *) - | Psraw (**r shift right arithmetic word *) - | Psrlw (**r shift right logical word *) - | Psllw (**r shift left logical word *) - - | Paddl (**r add long *) - | Psubl (**r sub long *) - | Pandl (**r and long *) - | Porl (**r or long *) - | Pxorl (**r xor long *) - | Pmull (**r mul long (low part) *) - | Pslll (**r shift left logical long *) - | Psrll (**r shift right logical long *) - | Psral (**r shift right arithmetic long *) -. - -Inductive arith_name_rri32 : Type := - | Pcompiw (it: itest) (**r comparison imm word *) - - | Paddiw (**r add imm word *) - | Pandiw (**r and imm word *) - | Poriw (**r or imm word *) - | Pxoriw (**r xor imm word *) - | Psraiw (**r shift right arithmetic imm word *) - | Psrliw (**r shift right logical imm word *) - | Pslliw (**r shift left logical imm word *) - - | Psllil (**r shift left logical immediate long *) - | Psrlil (**r shift right logical immediate long *) - | Psrail (**r shift right arithmetic immediate long *) -. - -Inductive arith_name_rri64 : Type := - | Pcompil (it: itest) (**r comparison imm long *) - | Paddil (**r add immediate long *) - | Pandil (**r and immediate long *) - | Poril (**r or immediate long *) - | Pxoril (**r xor immediate long *) -. - -Inductive ar_instruction : Type := - | PArithR (i: arith_name_r) (rd: ireg) - | PArithRR (i: arith_name_rr) (rd rs: ireg) - | PArithRI32 (i: arith_name_ri32) (rd: ireg) (imm: int) - | PArithRI64 (i: arith_name_ri64) (rd: ireg) (imm: int64) - | PArithRRR (i: arith_name_rrr) (rd rs1 rs2: ireg) - | PArithRRI32 (i: arith_name_rri32) (rd rs: ireg) (imm: int) - | PArithRRI64 (i: arith_name_rri64) (rd rs: ireg) (imm: int64) -. - -Coercion PArithR: arith_name_r >-> Funclass. -Coercion PArithRR: arith_name_rr >-> Funclass. -Coercion PArithRI32: arith_name_ri32 >-> Funclass. -Coercion PArithRI64: arith_name_ri64 >-> Funclass. -Coercion PArithRRR: arith_name_rrr >-> Funclass. -Coercion PArithRRI32: arith_name_rri32 >-> Funclass. -Coercion PArithRRI64: arith_name_rri64 >-> Funclass. - -(*| Pfence (**r fence *) - - (* floating point register move *) - | Pfmv (rd: freg) (rs: freg) (**r move *) - | Pfmvxs (rd: ireg) (rs: freg) (**r move FP single to integer register *) - | Pfmvxd (rd: ireg) (rs: freg) (**r move FP double to integer register *) - -*)(* 32-bit (single-precision) floating point *) - -(*| Pfnegs (rd: freg) (rs: freg) (**r negation *) - | Pfabss (rd: freg) (rs: freg) (**r absolute value *) - - | Pfadds (rd: freg) (rs1 rs2: freg) (**r addition *) - | Pfsubs (rd: freg) (rs1 rs2: freg) (**r subtraction *) - | Pfmuls (rd: freg) (rs1 rs2: freg) (**r multiplication *) - | Pfdivs (rd: freg) (rs1 rs2: freg) (**r division *) - | Pfmins (rd: freg) (rs1 rs2: freg) (**r minimum *) - | Pfmaxs (rd: freg) (rs1 rs2: freg) (**r maximum *) - - | Pfeqs (rd: ireg) (rs1 rs2: freg) (**r compare equal *) - | Pflts (rd: ireg) (rs1 rs2: freg) (**r compare less-than *) - | Pfles (rd: ireg) (rs1 rs2: freg) (**r compare less-than/equal *) - - | Pfsqrts (rd: freg) (rs: freg) (**r square-root *) - - | Pfmadds (rd: freg) (rs1 rs2 rs3: freg) (**r fused multiply-add *) - | Pfmsubs (rd: freg) (rs1 rs2 rs3: freg) (**r fused multiply-sub *) - | Pfnmadds (rd: freg) (rs1 rs2 rs3: freg) (**r fused negated multiply-add *) - | Pfnmsubs (rd: freg) (rs1 rs2 rs3: freg) (**r fused negated multiply-sub *) - - | Pfcvtws (rd: ireg) (rs: freg) (**r float32 -> int32 conversion *) - | Pfcvtwus (rd: ireg) (rs: freg) (**r float32 -> unsigned int32 conversion *) - | Pfcvtsw (rd: freg) (rs: ireg) (**r int32 -> float32 conversion *) - | Pfcvtswu (rd: freg) (rs: ireg) (**r unsigned int32 -> float32 conversion *) - - | Pfcvtls (rd: ireg) (rs: freg) (**r float32 -> int64 conversion *) - | Pfcvtlus (rd: ireg) (rs: freg) (**r float32 -> unsigned int64 conversion *) - | Pfcvtsl (rd: freg) (rs: ireg) (**r int64 -> float32 conversion *) - | Pfcvtslu (rd: freg) (rs: ireg) (**r unsigned int 64-> float32 conversion *) - -*)(* 64-bit (double-precision) floating point *) -(*| Pfld_a (rd: freg) (ra: ireg) (ofs: offset) (**r load any64 *) - | Pfsd_a (rd: freg) (ra: ireg) (ofs: offset) (**r store any64 *) - - | Pfabsd (rd: freg) (rs: freg) (**r absolute value *) - - | Pfaddd (rd: freg) (rs1 rs2: freg) (**r addition *) - | Pfsubd (rd: freg) (rs1 rs2: freg) (**r subtraction *) - | Pfmuld (rd: freg) (rs1 rs2: freg) (**r multiplication *) - | Pfdivd (rd: freg) (rs1 rs2: freg) (**r division *) - | Pfmind (rd: freg) (rs1 rs2: freg) (**r minimum *) - | Pfmaxd (rd: freg) (rs1 rs2: freg) (**r maximum *) - - | Pfeqd (rd: ireg) (rs1 rs2: freg) (**r compare equal *) - | Pfltd (rd: ireg) (rs1 rs2: freg) (**r compare less-than *) - | Pfled (rd: ireg) (rs1 rs2: freg) (**r compare less-than/equal *) - - | Pfsqrtd (rd: freg) (rs: freg) (**r square-root *) - - | Pfmaddd (rd: freg) (rs1 rs2 rs3: freg) (**r fused multiply-add *) - | Pfmsubd (rd: freg) (rs1 rs2 rs3: freg) (**r fused multiply-sub *) - | Pfnmaddd (rd: freg) (rs1 rs2 rs3: freg) (**r fused negated multiply-add *) - | Pfnmsubd (rd: freg) (rs1 rs2 rs3: freg) (**r fused negated multiply-sub *) - - | Pfcvtwd (rd: ireg) (rs: freg) (**r float -> int32 conversion *) - | Pfcvtwud (rd: ireg) (rs: freg) (**r float -> unsigned int32 conversion *) - | Pfcvtdw (rd: freg) (rs: ireg) (**r int32 -> float conversion *) - | Pfcvtdwu (rd: freg) (rs: ireg) (**r unsigned int32 -> float conversion *) - - | Pfcvtld (rd: ireg) (rs: freg) (**r float -> int64 conversion *) - | Pfcvtlud (rd: ireg) (rs: freg) (**r float -> unsigned int64 conversion *) - | Pfcvtdl (rd: freg) (rs: ireg) (**r int64 -> float conversion *) - | Pfcvtdlu (rd: freg) (rs: ireg) (**r unsigned int64 -> float conversion *) - - | Pfcvtds (rd: freg) (rs: freg) (**r float32 -> float *) - | Pfcvtsd (rd: freg) (rs: freg) (**r float -> float32 *) -*) - -Inductive instruction : Type := - | PExpand (i: ex_instruction) - | PControlFlow (i: cf_instruction) - | PLoad (i: ld_instruction) - | PStore (i: st_instruction) - | PArith (i: ar_instruction) -. - -Coercion PExpand: ex_instruction >-> instruction. -Coercion PControlFlow: cf_instruction >-> instruction. -Coercion PLoad: ld_instruction >-> instruction. -Coercion PStore: st_instruction >-> instruction. -Coercion PArith: ar_instruction >-> instruction. - -Definition code := list instruction. -Record function : Type := mkfunction { fn_sig: signature; fn_code: code }. -Definition fundef := AST.fundef function. -Definition program := AST.program fundef unit. - -(** * Operational semantics *) - -(** The semantics operates over a single mapping from registers - (type [preg]) to values. We maintain - the convention that integer registers are mapped to values of - type [Tint] or [Tlong] (in 64 bit mode), - and float registers to values of type [Tsingle] or [Tfloat]. *) - -Definition regset := Pregmap.t val. -Definition genv := Genv.t fundef unit. - -Definition getw (rs: regset) (r: ireg) : val := - match r with - | _ => rs r - end. - -Definition getl (rs: regset) (r: ireg) : val := - match r with - | _ => rs r - end. - -Notation "a # b" := (a b) (at level 1, only parsing) : asm. -Notation "a ## b" := (getw a b) (at level 1) : asm. -Notation "a ### b" := (getl a b) (at level 1) : asm. -Notation "a # b <- c" := (Pregmap.set b c a) (at level 1, b at next level) : asm. - -Open Scope asm. - -(** Undefining some registers *) - -Fixpoint undef_regs (l: list preg) (rs: regset) : regset := - match l with - | nil => rs - | r :: l' => undef_regs l' (rs#r <- Vundef) - end. - -(** Assigning a register pair *) - -Definition set_pair (p: rpair preg) (v: val) (rs: regset) : regset := - match p with - | One r => rs#r <- v - | Twolong rhi rlo => rs#rhi <- (Val.hiword v) #rlo <- (Val.loword v) - end. - -(** Assigning multiple registers *) - -Fixpoint set_regs (rl: list preg) (vl: list val) (rs: regset) : regset := - match rl, vl with - | r1 :: rl', v1 :: vl' => set_regs rl' vl' (rs#r1 <- v1) - | _, _ => rs - end. - -(** Assigning the result of a builtin *) - -Fixpoint set_res (res: builtin_res preg) (v: val) (rs: regset) : regset := - match res with - | BR r => rs#r <- v - | BR_none => rs - | BR_splitlong hi lo => set_res lo (Val.loword v) (set_res hi (Val.hiword v) rs) - end. - -Section RELSEM. - -(** Looking up instructions in a code sequence by position. *) - -Fixpoint find_instr (pos: Z) (c: code) {struct c} : option instruction := - match c with - | nil => None - | i :: il => if zeq pos 0 then Some i else find_instr (pos - 1) il - end. - -(** Position corresponding to a label *) - -Definition is_label (lbl: label) (instr: instruction) : bool := - match instr with - | Plabel lbl' => if peq lbl lbl' then true else false - | _ => false - end. - -Lemma is_label_correct: - forall lbl instr, - if is_label lbl instr then instr = Plabel lbl else instr <> Plabel lbl. -Proof. - intros. destruct instr; simpl; try discriminate. - destruct i; simpl; try discriminate. - case (peq lbl lbl0); intro; congruence. -Qed. - -Fixpoint label_pos (lbl: label) (pos: Z) (c: code) {struct c} : option Z := - match c with - | nil => None - | instr :: c' => - if is_label lbl instr then Some (pos + 1) else label_pos lbl (pos + 1) c' - end. - -Variable ge: genv. - -(** The two functions below axiomatize how the linker processes - symbolic references [symbol + offset)] and splits their - actual values into a 20-bit high part [%hi(symbol + offset)] and - a 12-bit low part [%lo(symbol + offset)]. *) - -Parameter low_half: genv -> ident -> ptrofs -> ptrofs. -Parameter high_half: genv -> ident -> ptrofs -> val. - -(** The fundamental property of these operations is that, when applied - to the address of a symbol, their results can be recombined by - addition, rebuilding the original address. *) - -Axiom low_high_half: - forall id ofs, - Val.offset_ptr (high_half ge id ofs) (low_half ge id ofs) = Genv.symbol_address ge id ofs. - -(** The semantics is purely small-step and defined as a function - from the current state (a register set + a memory state) - to either [Next rs' m'] where [rs'] and [m'] are the updated register - set and memory state after execution of the instruction at [rs#PC], - or [Stuck] if the processor is stuck. *) - -Inductive outcome: Type := - | Next: regset -> mem -> outcome - | Stuck: outcome. - -(** Manipulations over the [PC] register: continuing with the next - instruction ([nextinstr]) or branching to a label ([goto_label]). *) - -Definition nextinstr (rs: regset) := - rs#PC <- (Val.offset_ptr rs#PC Ptrofs.one). - -Definition goto_label (f: function) (lbl: label) (rs: regset) (m: mem) := - match label_pos lbl 0 (fn_code f) with - | None => Stuck - | Some pos => - match rs#PC with - | Vptr b ofs => Next (rs#PC <- (Vptr b (Ptrofs.repr pos))) m - | _ => Stuck - end - end. - -(** Auxiliaries for memory accesses *) - -Definition eval_offset (ofs: offset) : ptrofs := - match ofs with - | Ofsimm n => n - | Ofslow id delta => low_half ge id delta - end. - -Definition exec_load (chunk: memory_chunk) (rs: regset) (m: mem) - (d: preg) (a: ireg) (ofs: offset) := - match Mem.loadv chunk m (Val.offset_ptr (rs a) (eval_offset ofs)) with - | None => Stuck - | Some v => Next (nextinstr (rs#d <- v)) m - end. - -Definition exec_store (chunk: memory_chunk) (rs: regset) (m: mem) - (s: preg) (a: ireg) (ofs: offset) := - match Mem.storev chunk m (Val.offset_ptr (rs a) (eval_offset ofs)) (rs s) with - | None => Stuck - | Some m' => Next (nextinstr rs) m' - end. - -(** Evaluating a branch *) - -Definition eval_branch (f: function) (l: label) (rs: regset) (m: mem) (res: option bool) : outcome := - match res with - | Some true => goto_label f l rs m - | Some false => Next (nextinstr rs) m - | None => Stuck - end. - -Inductive signedness: Type := Signed | Unsigned. - -Inductive intsize: Type := Int | Long. - -Definition itest_for_cmp (c: comparison) (s: signedness) := - match c, s with - | Cne, Signed => ITne - | Ceq, Signed => ITeq - | Clt, Signed => ITlt - | Cge, Signed => ITge - | Cle, Signed => ITle - | Cgt, Signed => ITgt - | Cne, Unsigned => ITneu - | Ceq, Unsigned => ITequ - | Clt, Unsigned => ITltu - | Cge, Unsigned => ITgeu - | Cle, Unsigned => ITleu - | Cgt, Unsigned => ITgtu - end. - -(* CoMPare Signed Words to Zero *) -Definition btest_for_cmpswz (c: comparison) := - match c with - | Cne => BTwnez - | Ceq => BTweqz - | Clt => BTwltz - | Cge => BTwgez - | Cle => BTwlez - | Cgt => BTwgtz - end. - -(* CoMPare Signed Doubles to Zero *) -Definition btest_for_cmpsdz (c: comparison) := - match c with - | Cne => BTdnez - | Ceq => BTdeqz - | Clt => BTdltz - | Cge => BTdgez - | Cle => BTdlez - | Cgt => BTdgtz - end. - -Definition cmp_for_btest (bt: btest) := - match bt with - | BTwnez => (Some Cne, Int) - | BTweqz => (Some Ceq, Int) - | BTwltz => (Some Clt, Int) - | BTwgez => (Some Cge, Int) - | BTwlez => (Some Cle, Int) - | BTwgtz => (Some Cgt, Int) - - | BTdnez => (Some Cne, Long) - | BTdeqz => (Some Ceq, Long) - | BTdltz => (Some Clt, Long) - | BTdgez => (Some Cge, Long) - | BTdlez => (Some Cle, Long) - | BTdgtz => (Some Cgt, Long) - end. - -Definition cmpu_for_btest (bt: btest) := - match bt with - | BTwnez => (Some Cne, Int) - | BTweqz => (Some Ceq, Int) - | BTdnez => (Some Cne, Long) - | BTdeqz => (Some Ceq, Long) - | _ => (None, Int) - end. - -(** Comparing integers *) -Definition compare_int (t: itest) (v1 v2: val) (m: mem): val := - match t with - | ITne => Val.cmp Cne v1 v2 - | ITeq => Val.cmp Ceq v1 v2 - | ITlt => Val.cmp Clt v1 v2 - | ITge => Val.cmp Cge v1 v2 - | ITle => Val.cmp Cle v1 v2 - | ITgt => Val.cmp Cgt v1 v2 - | ITneu => Val.cmpu (Mem.valid_pointer m) Cne v1 v2 - | ITequ => Val.cmpu (Mem.valid_pointer m) Ceq v1 v2 - | ITltu => Val.cmpu (Mem.valid_pointer m) Clt v1 v2 - | ITgeu => Val.cmpu (Mem.valid_pointer m) Cge v1 v2 - | ITleu => Val.cmpu (Mem.valid_pointer m) Cle v1 v2 - | ITgtu => Val.cmpu (Mem.valid_pointer m) Cgt v1 v2 - | ITall - | ITnall - | ITany - | ITnone => Vundef - end. - -Definition compare_long (t: itest) (v1 v2: val) (m: mem): val := - let res := match t with - | ITne => Val.cmpl Cne v1 v2 - | ITeq => Val.cmpl Ceq v1 v2 - | ITlt => Val.cmpl Clt v1 v2 - | ITge => Val.cmpl Cge v1 v2 - | ITle => Val.cmpl Cle v1 v2 - | ITgt => Val.cmpl Cgt v1 v2 - | ITneu => Val.cmplu (Mem.valid_pointer m) Cne v1 v2 - | ITequ => Val.cmplu (Mem.valid_pointer m) Ceq v1 v2 - | ITltu => Val.cmplu (Mem.valid_pointer m) Clt v1 v2 - | ITgeu => Val.cmplu (Mem.valid_pointer m) Cge v1 v2 - | ITleu => Val.cmplu (Mem.valid_pointer m) Cle v1 v2 - | ITgtu => Val.cmplu (Mem.valid_pointer m) Cgt v1 v2 - | ITall - | ITnall - | ITany - | ITnone => Some Vundef - end in - match res with - | Some v => v - | None => Vundef - end - . - -(** Execution of a single instruction [i] in initial state [rs] and - [m]. Return updated state. For instructions that correspond to - actual RISC-V instructions, the cases are straightforward - transliterations of the informal descriptions given in the RISC-V - user-mode specification. For pseudo-instructions, refer to the - informal descriptions given above. - - Note that we set to [Vundef] the registers used as temporaries by - the expansions of the pseudo-instructions, so that the RISC-V code - we generate cannot use those registers to hold values that must - survive the execution of the pseudo-instruction. *) - -Definition exec_instr (f: function) (i: instruction) (rs: regset) (m: mem) : outcome := -(** Get/Set system registers *) - match i with - | Pget rd ra => - match ra with - | RA => Next (nextinstr (rs#rd <- (rs#ra))) m - | _ => Stuck - end - | Pset ra rd => - match ra with - | RA => Next (nextinstr (rs#ra <- (rs#rd))) m - | _ => Stuck - end - -(** Branch Control Unit instructions *) - | Pret => - Next (rs#PC <- (rs#RA)) m - | Pcall s => - Next (rs#RA <- (Val.offset_ptr (rs#PC) Ptrofs.one)#PC <- (Genv.symbol_address ge s Ptrofs.zero)) m - | Pgoto s => - Next (rs#PC <- (Genv.symbol_address ge s Ptrofs.zero)) m - | Pj_l l => - goto_label f l rs m - | Pcb bt r l => - match cmp_for_btest bt with - | (Some c, Int) => eval_branch f l rs m (Val.cmp_bool c rs##r (Vint (Int.repr 0))) - | (Some c, Long) => eval_branch f l rs m (Val.cmpl_bool c rs###r (Vlong (Int64.repr 0))) - | (None, _) => Stuck - end - | Pcbu bt r l => - match cmpu_for_btest bt with - | (Some c, Int) => eval_branch f l rs m (Val.cmpu_bool (Mem.valid_pointer m) c rs##r (Vint (Int.repr 0))) - | (Some c, Long) => eval_branch f l rs m (Val.cmplu_bool (Mem.valid_pointer m) c rs###r (Vlong (Int64.repr 0))) - | (None, _) => Stuck - end - -(** Arithmetic Instructions *) - | PArithR n d => - match n with - | Pcvtw2l => Next (nextinstr (rs#d <- (Val.longofint rs#d))) m - end - - | PArithRR n d s => - match n with - | Pmv => Next (nextinstr (rs#d <- (rs#s))) m - | Pnegw => Next (nextinstr (rs#d <- (Val.neg rs###s))) m - | Pnegl => Next (nextinstr (rs#d <- (Val.negl rs###s))) m - | Pfnegd => Next (nextinstr (rs#d <- (Val.negf rs#s))) m - | Pcvtl2w => Next (nextinstr (rs#d <- (Val.loword rs###s))) m - | Pmvw2l => Next (nextinstr (rs#d <- (Val.longofint rs#s))) m - end - - | PArithRI32 n d i => - match n with - | Pmake => Next (nextinstr (rs#d <- (Vint i))) m - end - - | PArithRI64 n d i => - match n with - | Pmakel => Next (nextinstr (rs#d <- (Vlong i))) m - end - - | PArithRRR n d s1 s2 => - match n with - | Pcompw c => Next (nextinstr (rs#d <- (compare_int c rs##s1 rs##s2 m))) m - | Pcompl c => Next (nextinstr (rs#d <- (compare_long c rs###s1 rs###s2 m))) m - | Paddw => Next (nextinstr (rs#d <- (Val.add rs##s1 rs##s2))) m - | Psubw => Next (nextinstr (rs#d <- (Val.sub rs##s1 rs##s2))) m - | Pmulw => Next (nextinstr (rs#d <- (Val.mul rs##s1 rs##s2))) m - | Pandw => Next (nextinstr (rs#d <- (Val.and rs##s1 rs##s2))) m - | Porw => Next (nextinstr (rs#d <- (Val.or rs##s1 rs##s2))) m - | Pxorw => Next (nextinstr (rs#d <- (Val.xor rs##s1 rs##s2))) m - | Psrlw => Next (nextinstr (rs#d <- (Val.shru rs##s1 rs##s2))) m - | Psraw => Next (nextinstr (rs#d <- (Val.shr rs##s1 rs##s2))) m - | Psllw => Next (nextinstr (rs#d <- (Val.shl rs##s1 rs##s2))) m - - | Paddl => Next (nextinstr (rs#d <- (Val.addl rs###s1 rs###s2))) m - | Psubl => Next (nextinstr (rs#d <- (Val.subl rs###s1 rs###s2))) m - | Pandl => Next (nextinstr (rs#d <- (Val.andl rs###s1 rs###s2))) m - | Porl => Next (nextinstr (rs#d <- (Val.orl rs###s1 rs###s2))) m - | Pxorl => Next (nextinstr (rs#d <- (Val.xorl rs###s1 rs###s2))) m - | Pmull => Next (nextinstr (rs#d <- (Val.mull rs###s1 rs###s2))) m - | Pslll => Next (nextinstr (rs#d <- (Val.shll rs###s1 rs###s2))) m - | Psrll => Next (nextinstr (rs#d <- (Val.shrlu rs###s1 rs###s2))) m - | Psral => Next (nextinstr (rs#d <- (Val.shrl rs###s1 rs###s2))) m - end - - | PArithRRI32 n d s i => - match n with - | Pcompiw c => Next (nextinstr (rs#d <- (compare_int c rs##s (Vint i) m))) m - | Paddiw => Next (nextinstr (rs#d <- (Val.add rs##s (Vint i)))) m - | Pandiw => Next (nextinstr (rs#d <- (Val.and rs##s (Vint i)))) m - | Poriw => Next (nextinstr (rs#d <- (Val.or rs##s (Vint i)))) m - | Pxoriw => Next (nextinstr (rs#d <- (Val.xor rs##s (Vint i)))) m - | Psraiw => Next (nextinstr (rs#d <- (Val.shr rs##s (Vint i)))) m - | Psrliw => Next (nextinstr (rs#d <- (Val.shru rs##s (Vint i)))) m - | Pslliw => Next (nextinstr (rs#d <- (Val.shl rs##s (Vint i)))) m - - | Psllil => Next (nextinstr (rs#d <- (Val.shll rs###s (Vint i)))) m - | Psrlil => Next (nextinstr (rs#d <- (Val.shrlu rs###s (Vint i)))) m - | Psrail => Next (nextinstr (rs#d <- (Val.shrl rs###s (Vint i)))) m - end - - | PArithRRI64 n d s i => - match n with - | Pcompil c => Next (nextinstr (rs#d <- (compare_long c rs###s (Vlong i) m))) m - | Paddil => Next (nextinstr (rs#d <- (Val.addl rs###s (Vlong i)))) m - | Pandil => Next (nextinstr (rs#d <- (Val.andl rs###s (Vlong i)))) m - | Poril => Next (nextinstr (rs#d <- (Val.orl rs###s (Vlong i)))) m - | Pxoril => Next (nextinstr (rs#d <- (Val.xorl rs###s (Vlong i)))) m - end - -(** Loads and stores *) - | Plb d a ofs => - exec_load Mint8signed rs m d a ofs - | Plbu d a ofs => - exec_load Mint8unsigned rs m d a ofs - | Plh d a ofs => - exec_load Mint16signed rs m d a ofs - | Plhu d a ofs => - exec_load Mint16unsigned rs m d a ofs - | Plw d a ofs => - exec_load Mint32 rs m d a ofs - | Plw_a d a ofs => - exec_load Many32 rs m d a ofs - | Pld d a ofs => - exec_load Mint64 rs m d a ofs - | Pld_a d a ofs => - exec_load Many64 rs m d a ofs - | Psb s a ofs => - exec_store Mint8unsigned rs m s a ofs - | Psh s a ofs => - exec_store Mint16unsigned rs m s a ofs - | Psw s a ofs => - exec_store Mint32 rs m s a ofs - | Psw_a s a ofs => - exec_store Many32 rs m s a ofs - | Psd s a ofs => - exec_store Mint64 rs m s a ofs - | Psd_a s a ofs => - exec_store Many64 rs m s a ofs - -(** Floating point register move *) -(*| Pfmv d s => - Next (nextinstr (rs#d <- (rs#s))) m - -(** 32-bit (single-precision) floating point *) -*)| Pfls d a ofs => - exec_load Mfloat32 rs m d a ofs - | Pfss s a ofs => - exec_store Mfloat32 rs m s a ofs - -(*| Pfnegs d s => - Next (nextinstr (rs#d <- (Val.negfs rs#s))) m - | Pfabss d s => - Next (nextinstr (rs#d <- (Val.absfs rs#s))) m - - | Pfadds d s1 s2 => - Next (nextinstr (rs#d <- (Val.addfs rs#s1 rs#s2))) m - | Pfsubs d s1 s2 => - Next (nextinstr (rs#d <- (Val.subfs rs#s1 rs#s2))) m - | Pfmuls d s1 s2 => - Next (nextinstr (rs#d <- (Val.mulfs rs#s1 rs#s2))) m - | Pfdivs d s1 s2 => - Next (nextinstr (rs#d <- (Val.divfs rs#s1 rs#s2))) m - | Pfeqs d s1 s2 => - Next (nextinstr (rs#d <- (Val.cmpfs Ceq rs#s1 rs#s2))) m - | Pflts d s1 s2 => - Next (nextinstr (rs#d <- (Val.cmpfs Clt rs#s1 rs#s2))) m - | Pfles d s1 s2 => - Next (nextinstr (rs#d <- (Val.cmpfs Cle rs#s1 rs#s2))) m - - | Pfcvtws d s => - Next (nextinstr (rs#d <- (Val.maketotal (Val.intofsingle rs#s)))) m - | Pfcvtwus d s => - Next (nextinstr (rs#d <- (Val.maketotal (Val.intuofsingle rs#s)))) m - | Pfcvtsw d s => - Next (nextinstr (rs#d <- (Val.maketotal (Val.singleofint rs##s)))) m - | Pfcvtswu d s => - Next (nextinstr (rs#d <- (Val.maketotal (Val.singleofintu rs##s)))) m - - | Pfcvtls d s => - Next (nextinstr (rs#d <- (Val.maketotal (Val.longofsingle rs#s)))) m - | Pfcvtlus d s => - Next (nextinstr (rs#d <- (Val.maketotal (Val.longuofsingle rs#s)))) m - | Pfcvtsl d s => - Next (nextinstr (rs#d <- (Val.maketotal (Val.singleoflong rs###s)))) m - | Pfcvtslu d s => - Next (nextinstr (rs#d <- (Val.maketotal (Val.singleoflongu rs###s)))) m - -(** 64-bit (double-precision) floating point *) -*)| Pfld d a ofs => - exec_load Mfloat64 rs m d a ofs -(*| Pfld_a d a ofs => - exec_load Many64 rs m d a ofs -*)| Pfsd s a ofs => - exec_store Mfloat64 rs m s a ofs -(*| Pfsd_a s a ofs => - exec_store Many64 rs m s a ofs - - | Pfabsd d s => - Next (nextinstr (rs#d <- (Val.absf rs#s))) m - - | Pfaddd d s1 s2 => - Next (nextinstr (rs#d <- (Val.addf rs#s1 rs#s2))) m - | Pfsubd d s1 s2 => - Next (nextinstr (rs#d <- (Val.subf rs#s1 rs#s2))) m - | Pfmuld d s1 s2 => - Next (nextinstr (rs#d <- (Val.mulf rs#s1 rs#s2))) m - | Pfdivd d s1 s2 => - Next (nextinstr (rs#d <- (Val.divf rs#s1 rs#s2))) m - | Pfeqd d s1 s2 => - Next (nextinstr (rs#d <- (Val.cmpf Ceq rs#s1 rs#s2))) m - | Pfltd d s1 s2 => - Next (nextinstr (rs#d <- (Val.cmpf Clt rs#s1 rs#s2))) m - | Pfled d s1 s2 => - Next (nextinstr (rs#d <- (Val.cmpf Cle rs#s1 rs#s2))) m - - | Pfcvtwd d s => - Next (nextinstr (rs#d <- (Val.maketotal (Val.intoffloat rs#s)))) m - | Pfcvtwud d s => - Next (nextinstr (rs#d <- (Val.maketotal (Val.intuoffloat rs#s)))) m - | Pfcvtdw d s => - Next (nextinstr (rs#d <- (Val.maketotal (Val.floatofint rs##s)))) m - | Pfcvtdwu d s => - Next (nextinstr (rs#d <- (Val.maketotal (Val.floatofintu rs##s)))) m - - | Pfcvtld d s => - Next (nextinstr (rs#d <- (Val.maketotal (Val.longoffloat rs#s)))) m - | Pfcvtlud d s => - Next (nextinstr (rs#d <- (Val.maketotal (Val.longuoffloat rs#s)))) m - | Pfcvtdl d s => - Next (nextinstr (rs#d <- (Val.maketotal (Val.floatoflong rs###s)))) m - | Pfcvtdlu d s => - Next (nextinstr (rs#d <- (Val.maketotal (Val.floatoflongu rs###s)))) m - - | Pfcvtds d s => - Next (nextinstr (rs#d <- (Val.floatofsingle rs#s))) m - | Pfcvtsd d s => - Next (nextinstr (rs#d <- (Val.singleoffloat rs#s))) m - -(** Pseudo-instructions *) -*)| Pallocframe sz pos => - let (m1, stk) := Mem.alloc m 0 sz in - let sp := (Vptr stk Ptrofs.zero) in - match Mem.storev Mptr m1 (Val.offset_ptr sp pos) rs#SP with - | None => Stuck - | Some m2 => Next (nextinstr (rs #FP <- (rs SP) #SP <- sp #GPR31 <- Vundef)) m2 - end - | Pfreeframe sz pos => - match Mem.loadv Mptr m (Val.offset_ptr rs#SP pos) with - | None => Stuck - | Some v => - match rs SP with - | Vptr stk ofs => - match Mem.free m stk 0 sz with - | None => Stuck - | Some m' => Next (nextinstr (rs#SP <- v #GPR31 <- Vundef)) m' - end - | _ => Stuck - end - end - | Plabel lbl => - Next (nextinstr rs) m - | Ploadsymbol rd s ofs => - Next (nextinstr (rs#rd <- (Genv.symbol_address ge s ofs))) m -(*| Ploadsymbol_high rd s ofs => - Next (nextinstr (rs#rd <- (high_half ge s ofs))) m - | Ploadli rd i => - Next (nextinstr (rs#GPR31 <- Vundef #rd <- (Vlong i))) m - | Ploadfi rd f => - Next (nextinstr (rs#GPR31 <- Vundef #rd <- (Vfloat f))) m - | Ploadsi rd f => - Next (nextinstr (rs#GPR31 <- Vundef #rd <- (Vsingle f))) m - | Pbtbl r tbl => - match rs r with - | Vint n => - match list_nth_z tbl (Int.unsigned n) with - | None => Stuck - | Some lbl => goto_label f lbl (rs#GPR5 <- Vundef #GPR31 <- Vundef) m - end - | _ => Stuck - end -*)| Pbuiltin ef args res => - Stuck (**r treated specially below *) - - (** The following instructions and directives are not generated directly by Asmgen, - so we do not model them. *) - (* BCU *) - | Pawait - | Pbarrier - | Pdoze - | Pwfxl _ _ - | Pwfxm _ _ - | Pinvaldtlb - | Pinvalitlb - | Pprobetlb - | Preadtlb - | Psleep - | Pstop - | Psyncgroup _ - | Ptlbwrite - - (* LSU *) - | Pafda _ _ _ - | Paldc _ _ - | Pdinval - | Pdinvall _ - | Pdtouchl _ - | Pdzerol _ - | Pfence - | Piinval - | Piinvals _ - | Pitouchl _ - | Plbsu _ _ - | Plbzu _ _ - | Pldu _ _ - | Plhsu _ _ - | Plhzu _ _ - | Plwzu _ _ - - (* ALU *) - | Paddhp _ _ _ - | Padds _ _ _ - | Pbwlu _ _ _ _ _ _ - | Pbwluhp _ _ _ _ - | Pbwluwp _ _ _ _ - | Pcbs _ _ - | Pcbsdl _ _ - | Pclz _ _ - | Pclzw _ _ - | Pclzd _ _ - | Pclzdl _ _ - | Pcmove _ _ _ _ - | Pctz _ _ - | Pctzw _ _ - | Pctzd _ _ - | Pctzdl _ _ - | Pextfz _ _ _ _ - | Plandhp _ _ _ _ - | Psat _ _ _ - | Psatd _ _ _ - | Psbfhp _ _ _ - | Psbmm8 _ _ _ - | Psbmmt8 _ _ _ - | Psllhps _ _ _ - | Psrahps _ _ _ - | Pstsu _ _ _ - | Pstsud _ _ _ - - => Stuck - end. - -(** Translation of the LTL/Linear/Mach view of machine registers to - the RISC-V view. Note that no LTL register maps to [X31]. This - register is reserved as temporary, to be used by the generated RV32G - code. *) - - (* FIXME - R31 is not there *) -Definition preg_of (r: mreg) : preg := - match r with - | R0 => GPR0 | R1 => GPR1 | R2 => GPR2 | R3 => GPR3 | R4 => GPR4 - | R5 => GPR5 | R6 => GPR6 | R7 => GPR7 | R9 => GPR9 - | R10 => GPR10 (*| R11 => GPR11 | R12 => GPR12 | R13 => GPR13 | R14 => GPR14 *) - | R15 => GPR15 | R16 => GPR16 | R17 => GPR17 | R18 => GPR18 | R19 => GPR19 - | R20 => GPR20 | R21 => GPR21 | R22 => GPR22 | R23 => GPR23 | R24 => GPR24 - | R25 => GPR25 | R26 => GPR26 | R27 => GPR27 | R28 => GPR28 | R29 => GPR29 - | R30 => GPR30 | R32 => GPR32 | R33 => GPR33 | R34 => GPR34 - | R35 => GPR35 | R36 => GPR36 | R37 => GPR37 | R38 => GPR38 | R39 => GPR39 - | R40 => GPR40 | R41 => GPR41 | R42 => GPR42 | R43 => GPR43 | R44 => GPR44 - | R45 => GPR45 | R46 => GPR46 | R47 => GPR47 | R48 => GPR48 | R49 => GPR49 - | R50 => GPR50 | R51 => GPR51 | R52 => GPR52 | R53 => GPR53 | R54 => GPR54 - | R55 => GPR55 | R56 => GPR56 | R57 => GPR57 | R58 => GPR58 | R59 => GPR59 - | R60 => GPR60 | R61 => GPR61 | R62 => GPR62 | R63 => GPR63 - end. - -(** Extract the values of the arguments of an external call. - We exploit the calling conventions from module [Conventions], except that - we use RISC-V registers instead of locations. *) - -Inductive extcall_arg (rs: regset) (m: mem): loc -> val -> Prop := - | extcall_arg_reg: forall r, - extcall_arg rs m (R r) (rs (preg_of r)) - | extcall_arg_stack: forall ofs ty bofs v, - bofs = Stacklayout.fe_ofs_arg + 4 * ofs -> - Mem.loadv (chunk_of_type ty) m - (Val.offset_ptr rs#SP (Ptrofs.repr bofs)) = Some v -> - extcall_arg rs m (S Outgoing ofs ty) v. - -Inductive extcall_arg_pair (rs: regset) (m: mem): rpair loc -> val -> Prop := - | extcall_arg_one: forall l v, - extcall_arg rs m l v -> - extcall_arg_pair rs m (One l) v - | extcall_arg_twolong: forall hi lo vhi vlo, - extcall_arg rs m hi vhi -> - extcall_arg rs m lo vlo -> - extcall_arg_pair rs m (Twolong hi lo) (Val.longofwords vhi vlo). - -Definition extcall_arguments - (rs: regset) (m: mem) (sg: signature) (args: list val) : Prop := - list_forall2 (extcall_arg_pair rs m) (loc_arguments sg) args. - -Definition loc_external_result (sg: signature) : rpair preg := - map_rpair preg_of (loc_result sg). - -(** Execution of the instruction at [rs PC]. *) - -Inductive state: Type := - | State: regset -> mem -> state. - -Inductive step: state -> trace -> state -> Prop := - | exec_step_internal: - forall b ofs f i rs m rs' m', - rs PC = Vptr b ofs -> - Genv.find_funct_ptr ge b = Some (Internal f) -> - find_instr (Ptrofs.unsigned ofs) (fn_code f) = Some i -> - exec_instr f i rs m = Next rs' m' -> - step (State rs m) E0 (State rs' m') - | exec_step_builtin: - forall b ofs f ef args res rs m vargs t vres rs' m', - rs PC = Vptr b ofs -> - Genv.find_funct_ptr ge b = Some (Internal f) -> - find_instr (Ptrofs.unsigned ofs) f.(fn_code) = Some (A:=instruction) (Pbuiltin ef args res) -> - eval_builtin_args ge rs (rs SP) m args vargs -> - external_call ef ge vargs m t vres m' -> - rs' = nextinstr - (set_res res vres - (undef_regs (map preg_of (destroyed_by_builtin ef)) - (rs#GPR31 <- Vundef))) -> - step (State rs m) t (State rs' m') - | exec_step_external: - forall b ef args res rs m t rs' m', - rs PC = Vptr b Ptrofs.zero -> - Genv.find_funct_ptr ge b = Some (External ef) -> - external_call ef ge args m t res m' -> - extcall_arguments rs m (ef_sig ef) args -> - rs' = (set_pair (loc_external_result (ef_sig ef) ) res rs)#PC <- (rs RA) -> - step (State rs m) t (State rs' m'). - -End RELSEM. - -(** Execution of whole programs. *) - -Inductive initial_state (p: program): state -> Prop := - | initial_state_intro: forall m0, - let ge := Genv.globalenv p in - let rs0 := - (Pregmap.init Vundef) - # PC <- (Genv.symbol_address ge p.(prog_main) Ptrofs.zero) - # SP <- Vnullptr - # RA <- Vnullptr in - Genv.init_mem p = Some m0 -> - initial_state p (State rs0 m0). - -Inductive final_state: state -> int -> Prop := - | final_state_intro: forall rs m r, - rs PC = Vnullptr -> - rs GPR0 = Vint r -> - final_state (State rs m) r. - -Definition semantics (p: program) := - Semantics step (initial_state p) final_state (Genv.globalenv p). - -(** Determinacy of the [Asm] semantics. *) - -Remark extcall_arguments_determ: - forall rs m sg args1 args2, - extcall_arguments rs m sg args1 -> extcall_arguments rs m sg args2 -> args1 = args2. -Proof. - intros until m. - assert (A: forall l v1 v2, - extcall_arg rs m l v1 -> extcall_arg rs m l v2 -> v1 = v2). - { intros. inv H; inv H0; congruence. } - assert (B: forall p v1 v2, - extcall_arg_pair rs m p v1 -> extcall_arg_pair rs m p v2 -> v1 = v2). - { intros. inv H; inv H0. - eapply A; eauto. - f_equal; eapply A; eauto. } - assert (C: forall ll vl1, list_forall2 (extcall_arg_pair rs m) ll vl1 -> - forall vl2, list_forall2 (extcall_arg_pair rs m) ll vl2 -> vl1 = vl2). - { - induction 1; intros vl2 EA; inv EA. - auto. - f_equal; eauto. } - intros. eapply C; eauto. -Qed. - -Lemma semantics_determinate: forall p, determinate (semantics p). -Proof. -Ltac Equalities := - match goal with - | [ H1: ?a = ?b, H2: ?a = ?c |- _ ] => - rewrite H1 in H2; inv H2; Equalities - | _ => idtac - end. - intros; constructor; simpl; intros. -- (* determ *) - inv H; inv H0; Equalities. - split. constructor. auto. - discriminate. - discriminate. - assert (vargs0 = vargs) by (eapply eval_builtin_args_determ; eauto). subst vargs0. - exploit external_call_determ. eexact H5. eexact H11. intros [A B]. - split. auto. intros. destruct B; auto. subst. auto. - assert (args0 = args) by (eapply extcall_arguments_determ; eauto). subst args0. - exploit external_call_determ. eexact H3. eexact H8. intros [A B]. - split. auto. intros. destruct B; auto. subst. auto. -- (* trace length *) - red; intros. inv H; simpl. - omega. - eapply external_call_trace_length; eauto. - eapply external_call_trace_length; eauto. -- (* initial states *) - inv H; inv H0. f_equal. congruence. -- (* final no step *) - assert (NOTNULL: forall b ofs, Vnullptr <> Vptr b ofs). - { intros; unfold Vnullptr; destruct Archi.ptr64; congruence. } - inv H. unfold Vzero in H0. red; intros; red; intros. - inv H; rewrite H0 in *; eelim NOTNULL; eauto. -- (* final states *) - inv H; inv H0. congruence. -Qed. - -(** Classification functions for processor registers (used in Asmgenproof). *) - -Definition data_preg (r: preg) : bool := - match r with - | RA => false - | IR GPR31 => false - | IR GPR8 => false - | IR _ => true - | FR _ => true - | PC => false - end. +(* *********************************************************************)
+(* *)
+(* The Compcert verified compiler *)
+(* *)
+(* Xavier Leroy, INRIA Paris-Rocquencourt *)
+(* Prashanth Mundkur, SRI International *)
+(* *)
+(* Copyright Institut National de Recherche en Informatique et en *)
+(* Automatique. All rights reserved. This file is distributed *)
+(* under the terms of the INRIA Non-Commercial License Agreement. *)
+(* *)
+(* The contributions by Prashanth Mundkur are reused and adapted *)
+(* under the terms of a Contributor License Agreement between *)
+(* SRI International and INRIA. *)
+(* *)
+(* *********************************************************************)
+
+(** Abstract syntax and semantics for K1c assembly language. *)
+
+Require Import Coqlib.
+Require Import Maps.
+Require Import AST.
+Require Import Integers.
+Require Import Floats.
+Require Import Values.
+Require Import Memory.
+Require Import Events.
+Require Import Globalenvs.
+Require Import Smallstep.
+Require Import Locations.
+Require Stacklayout.
+Require Import Conventions.
+Require Import Asmblock.
+Require Import Linking.
+Require Import Errors.
+
+(** Definitions for OCaml code *)
+Definition label := positive.
+Definition preg := preg.
+
+(** Syntax *)
+Inductive instruction : Type :=
+ (** pseudo instructions *)
+ | Pallocframe (sz: Z) (pos: ptrofs) (**r allocate new stack frame *)
+ | Pfreeframe (sz: Z) (pos: ptrofs) (**r deallocate stack frame and restore previous frame *)
+ | Plabel (lbl: label) (**r define a code label *)
+ | Ploadsymbol (rd: ireg) (id: ident) (ofs: ptrofs) (**r load the address of a symbol *)
+ | Pbuiltin: external_function -> list (builtin_arg preg)
+ -> builtin_res preg -> instruction (**r built-in function (pseudo) *)
+ | Pnop (**r instruction that does nothing *)
+
+ (** builtins *)
+ | Pclzll (rd rs: ireg)
+ | Pstsud (rd rs1 rs2: ireg)
+
+ (** Control flow instructions *)
+ | Pget (rd: ireg) (rs: preg) (**r get system register *)
+ | Pset (rd: preg) (rs: ireg) (**r set system register *)
+ | Pret (**r return *)
+ | Pcall (l: label) (**r function call *)
+ (* Pgoto is for tailcalls, Pj_l is for jumping to a particular label *)
+ | Pgoto (l: label) (**r goto *)
+ | Pj_l (l: label) (**r jump to label *)
+ | Pcb (bt: btest) (r: ireg) (l: label) (**r branch based on btest *)
+ | Pcbu (bt: btest) (r: ireg) (l: label) (**r branch based on btest with unsigned semantics *)
+
+ (** Loads **)
+ | Plb (rd: ireg) (ra: ireg) (ofs: offset) (**r load byte *)
+ | Plbu (rd: ireg) (ra: ireg) (ofs: offset) (**r load byte unsigned *)
+ | Plh (rd: ireg) (ra: ireg) (ofs: offset) (**r load half word *)
+ | Plhu (rd: ireg) (ra: ireg) (ofs: offset) (**r load half word unsigned *)
+ | Plw (rd: ireg) (ra: ireg) (ofs: offset) (**r load int32 *)
+ | Plw_a (rd: ireg) (ra: ireg) (ofs: offset) (**r load any32 *)
+ | Pld (rd: ireg) (ra: ireg) (ofs: offset) (**r load int64 *)
+ | Pld_a (rd: ireg) (ra: ireg) (ofs: offset) (**r load any64 *)
+ | Pfls (rd: freg) (ra: ireg) (ofs: offset) (**r load float *)
+ | Pfld (rd: freg) (ra: ireg) (ofs: offset) (**r load 64-bit float *)
+
+ (** Stores **)
+ | Psb (rs: ireg) (ra: ireg) (ofs: offset) (**r store byte *)
+ | Psh (rs: ireg) (ra: ireg) (ofs: offset) (**r store half byte *)
+ | Psw (rs: ireg) (ra: ireg) (ofs: offset) (**r store int32 *)
+ | Psw_a (rs: ireg) (ra: ireg) (ofs: offset) (**r store any32 *)
+ | Psd (rs: ireg) (ra: ireg) (ofs: offset) (**r store int64 *)
+ | Psd_a (rs: ireg) (ra: ireg) (ofs: offset) (**r store any64 *)
+ | Pfss (rs: freg) (ra: ireg) (ofs: offset) (**r store float *)
+ | Pfsd (rd: freg) (ra: ireg) (ofs: offset) (**r store 64-bit float *)
+
+ (** Arith R *)
+ | Pcvtw2l (rd: ireg) (**r Convert Word to Long *)
+
+ (** Arith RR *)
+ | Pmv (rd rs: ireg) (**r register move *)
+ | Pnegw (rd rs: ireg) (**r negate word *)
+ | Pnegl (rd rs: ireg) (**r negate long *)
+ | Pfnegd (rd rs: ireg) (**r float negate double *)
+ | Pcvtl2w (rd rs: ireg) (**r Convert Long to Word *)
+ | Pmvw2l (rd rs: ireg) (**r Move Convert Word to Long *)
+
+ (** Arith RI32 *)
+ | Pmake (rd: ireg) (imm: int) (**r load immediate *)
+
+ (** Arith RI64 *)
+ | Pmakel (rd: ireg) (imm: int64) (**r load immediate long *)
+
+ (** Arith RRR *)
+ | Pcompw (it: itest) (rd rs1 rs2: ireg) (**r comparison word *)
+ | Pcompl (it: itest) (rd rs1 rs2: ireg) (**r comparison long *)
+
+ | Paddw (rd rs1 rs2: ireg) (**r add word *)
+ | Psubw (rd rs1 rs2: ireg) (**r sub word *)
+ | Pmulw (rd rs1 rs2: ireg) (**r mul word *)
+ | Pandw (rd rs1 rs2: ireg) (**r and word *)
+ | Porw (rd rs1 rs2: ireg) (**r or word *)
+ | Pxorw (rd rs1 rs2: ireg) (**r xor word *)
+ | Psraw (rd rs1 rs2: ireg) (**r shift right arithmetic word *)
+ | Psrlw (rd rs1 rs2: ireg) (**r shift right logical word *)
+ | Psllw (rd rs1 rs2: ireg) (**r shift left logical word *)
+
+ | Paddl (rd rs1 rs2: ireg) (**r add long *)
+ | Psubl (rd rs1 rs2: ireg) (**r sub long *)
+ | Pandl (rd rs1 rs2: ireg) (**r and long *)
+ | Porl (rd rs1 rs2: ireg) (**r or long *)
+ | Pxorl (rd rs1 rs2: ireg) (**r xor long *)
+ | Pmull (rd rs1 rs2: ireg) (**r mul long (low part) *)
+ | Pslll (rd rs1 rs2: ireg) (**r shift left logical long *)
+ | Psrll (rd rs1 rs2: ireg) (**r shift right logical long *)
+ | Psral (rd rs1 rs2: ireg) (**r shift right arithmetic long *)
+
+ (** Arith RRI32 *)
+ | Pcompiw (it: itest) (rd rs: ireg) (imm: int) (**r comparison imm word *)
+
+ | Paddiw (rd rs: ireg) (imm: int) (**r add imm word *)
+ | Pandiw (rd rs: ireg) (imm: int) (**r and imm word *)
+ | Poriw (rd rs: ireg) (imm: int) (**r or imm word *)
+ | Pxoriw (rd rs: ireg) (imm: int) (**r xor imm word *)
+ | Psraiw (rd rs: ireg) (imm: int) (**r shift right arithmetic imm word *)
+ | Psrliw (rd rs: ireg) (imm: int) (**r shift right logical imm word *)
+ | Pslliw (rd rs: ireg) (imm: int) (**r shift left logical imm word *)
+
+ | Psllil (rd rs: ireg) (imm: int) (**r shift left logical immediate long *)
+ | Psrlil (rd rs: ireg) (imm: int) (**r shift right logical immediate long *)
+ | Psrail (rd rs: ireg) (imm: int) (**r shift right arithmetic immediate long *)
+
+ (** Arith RRI64 *)
+ | Pcompil (it: itest) (rd rs: ireg) (imm: int64) (**r comparison imm long *)
+ | Paddil (rd rs: ireg) (imm: int64) (**r add immediate long *)
+ | Pandil (rd rs: ireg) (imm: int64) (**r and immediate long *)
+ | Poril (rd rs: ireg) (imm: int64) (**r or immediate long *)
+ | Pxoril (rd rs: ireg) (imm: int64) (**r xor immediate long *)
+ .
+
+(** Correspondance between Asmblock and Asm *)
+
+Definition control_to_instruction (c: control) :=
+ match c with
+ | PExpand (Asmblock.Pbuiltin ef args res) => Pbuiltin ef args res
+ | PCtlFlow Asmblock.Pret => Pret
+ | PCtlFlow (Asmblock.Pcall l) => Pcall l
+ | PCtlFlow (Asmblock.Pgoto l) => Pgoto l
+ | PCtlFlow (Asmblock.Pj_l l) => Pj_l l
+ | PCtlFlow (Asmblock.Pcb bt r l) => Pcb bt r l
+ | PCtlFlow (Asmblock.Pcbu bt r l) => Pcbu bt r l
+ end.
+
+Definition basic_to_instruction (b: basic) :=
+ match b with
+ (** Special basics *)
+ | Asmblock.Pget rd rs => Pget rd rs
+ | Asmblock.Pset rd rs => Pset rd rs
+ | Asmblock.Pnop => Pnop
+ | Asmblock.Pallocframe sz pos => Pallocframe sz pos
+ | Asmblock.Pfreeframe sz pos => Pfreeframe sz pos
+
+ (** PArith basics *)
+ (* R *)
+ | PArithR Asmblock.Pcvtw2l r => Pcvtw2l r
+ | PArithR (Asmblock.Ploadsymbol id ofs) r => Ploadsymbol r id ofs
+
+ (* RR *)
+ | PArithRR Asmblock.Pmv rd rs => Pmv rd rs
+ | PArithRR Asmblock.Pnegw rd rs => Pnegw rd rs
+ | PArithRR Asmblock.Pnegl rd rs => Pfnegd rd rs
+ | PArithRR Asmblock.Pcvtl2w rd rs => Pcvtl2w rd rs
+ | PArithRR Asmblock.Pmvw2l rd rs => Pmvw2l rd rs
+ | PArithRR Asmblock.Pfnegd rd rs => Pfnegd rd rs
+
+ (* RI32 *)
+ | PArithRI32 Asmblock.Pmake rd imm => Pmake rd imm
+
+ (* RI64 *)
+ | PArithRI64 Asmblock.Pmakel rd imm => Pmakel rd imm
+
+ (* RRR *)
+ | PArithRRR (Asmblock.Pcompw it) rd rs1 rs2 => Pcompw it rd rs1 rs2
+ | PArithRRR (Asmblock.Pcompl it) rd rs1 rs2 => Pcompl it rd rs1 rs2
+ | PArithRRR Asmblock.Paddw rd rs1 rs2 => Paddw rd rs1 rs2
+ | PArithRRR Asmblock.Psubw rd rs1 rs2 => Psubw rd rs1 rs2
+ | PArithRRR Asmblock.Pmulw rd rs1 rs2 => Pmulw rd rs1 rs2
+ | PArithRRR Asmblock.Pandw rd rs1 rs2 => Pandw rd rs1 rs2
+ | PArithRRR Asmblock.Porw rd rs1 rs2 => Porw rd rs1 rs2
+ | PArithRRR Asmblock.Pxorw rd rs1 rs2 => Pxorw rd rs1 rs2
+ | PArithRRR Asmblock.Psraw rd rs1 rs2 => Psraw rd rs1 rs2
+ | PArithRRR Asmblock.Psrlw rd rs1 rs2 => Psrlw rd rs1 rs2
+ | PArithRRR Asmblock.Psllw rd rs1 rs2 => Psllw rd rs1 rs2
+
+ | PArithRRR Asmblock.Paddl rd rs1 rs2 => Paddl rd rs1 rs2
+ | PArithRRR Asmblock.Psubl rd rs1 rs2 => Psubl rd rs1 rs2
+ | PArithRRR Asmblock.Pandl rd rs1 rs2 => Pandl rd rs1 rs2
+ | PArithRRR Asmblock.Porl rd rs1 rs2 => Porl rd rs1 rs2
+ | PArithRRR Asmblock.Pxorl rd rs1 rs2 => Pxorl rd rs1 rs2
+ | PArithRRR Asmblock.Pmull rd rs1 rs2 => Pmull rd rs1 rs2
+ | PArithRRR Asmblock.Pslll rd rs1 rs2 => Pslll rd rs1 rs2
+ | PArithRRR Asmblock.Psrll rd rs1 rs2 => Psrll rd rs1 rs2
+ | PArithRRR Asmblock.Psral rd rs1 rs2 => Psral rd rs1 rs2
+
+ (* RRI32 *)
+ | PArithRRI32 (Asmblock.Pcompiw it) rd rs imm => Pcompiw it rd rs imm
+ | PArithRRI32 Asmblock.Paddiw rd rs imm => Paddiw rd rs imm
+ | PArithRRI32 Asmblock.Pandiw rd rs imm => Pandiw rd rs imm
+ | PArithRRI32 Asmblock.Poriw rd rs imm => Poriw rd rs imm
+ | PArithRRI32 Asmblock.Pxoriw rd rs imm => Pxoriw rd rs imm
+ | PArithRRI32 Asmblock.Psraiw rd rs imm => Psraiw rd rs imm
+ | PArithRRI32 Asmblock.Psrliw rd rs imm => Psrliw rd rs imm
+ | PArithRRI32 Asmblock.Pslliw rd rs imm => Pslliw rd rs imm
+ | PArithRRI32 Asmblock.Psllil rd rs imm => Psllil rd rs imm
+ | PArithRRI32 Asmblock.Psrlil rd rs imm => Psrlil rd rs imm
+ | PArithRRI32 Asmblock.Psrail rd rs imm => Psrail rd rs imm
+
+ (* RRI64 *)
+ | PArithRRI64 (Asmblock.Pcompil it) rd rs imm => Pcompil it rd rs imm
+ | PArithRRI64 Asmblock.Paddil rd rs imm => Paddil rd rs imm
+ | PArithRRI64 Asmblock.Pandil rd rs imm => Pandil rd rs imm
+ | PArithRRI64 Asmblock.Poril rd rs imm => Poril rd rs imm
+ | PArithRRI64 Asmblock.Pxoril rd rs imm => Pxoril rd rs imm
+
+ (** Load *)
+ | PLoadRRO Asmblock.Plb rd ra ofs => Plb rd ra ofs
+ | PLoadRRO Asmblock.Plbu rd ra ofs => Plbu rd ra ofs
+ | PLoadRRO Asmblock.Plh rd ra ofs => Plh rd ra ofs
+ | PLoadRRO Asmblock.Plhu rd ra ofs => Plhu rd ra ofs
+ | PLoadRRO Asmblock.Plw rd ra ofs => Plw rd ra ofs
+ | PLoadRRO Asmblock.Plw_a rd ra ofs => Plw_a rd ra ofs
+ | PLoadRRO Asmblock.Pld rd ra ofs => Pld rd ra ofs
+ | PLoadRRO Asmblock.Pld_a rd ra ofs => Pld_a rd ra ofs
+ | PLoadRRO Asmblock.Pfls rd ra ofs => Pfls rd ra ofs
+ | PLoadRRO Asmblock.Pfld rd ra ofs => Pfld rd ra ofs
+
+ (** Store *)
+ | PStoreRRO Asmblock.Psb rd ra ofs => Psb rd ra ofs
+ | PStoreRRO Asmblock.Psh rd ra ofs => Psh rd ra ofs
+ | PStoreRRO Asmblock.Psw rd ra ofs => Psw rd ra ofs
+ | PStoreRRO Asmblock.Psw_a rd ra ofs => Psw_a rd ra ofs
+ | PStoreRRO Asmblock.Psd rd ra ofs => Psd rd ra ofs
+ | PStoreRRO Asmblock.Psd_a rd ra ofs => Psd_a rd ra ofs
+ | PStoreRRO Asmblock.Pfss rd ra ofs => Pfss rd ra ofs
+ | PStoreRRO Asmblock.Pfsd rd ra ofs => Pfss rd ra ofs
+
+ end.
+
+Section RELSEM.
+
+Definition code := list instruction.
+
+Fixpoint unfold_label (ll: list label) :=
+ match ll with
+ | nil => nil
+ | l :: ll => Plabel l :: unfold_label ll
+ end.
+
+Fixpoint unfold_body (lb: list basic) :=
+ match lb with
+ | nil => nil
+ | b :: lb => basic_to_instruction b :: unfold_body lb
+ end.
+
+Definition unfold_exit (oc: option control) :=
+ match oc with
+ | None => nil
+ | Some c => control_to_instruction c :: nil
+ end.
+
+Definition unfold_bblock (b: bblock) := unfold_label (header b) ++ unfold_body (body b) ++ unfold_exit (exit b).
+
+Fixpoint unfold (lb: bblocks) :=
+ match lb with
+ | nil => nil
+ | b :: lb => (unfold_bblock b) ++ unfold lb
+ end.
+
+Record function : Type := mkfunction { fn_sig: signature; fn_blocks: bblocks; fn_code: code;
+ correct: unfold fn_blocks = fn_code }.
+
+(* For OCaml code *)
+Program Definition dummy_function := {| fn_code := nil; fn_sig := signature_main; fn_blocks := nil |}.
+
+Definition fundef := AST.fundef function.
+Definition program := AST.program fundef unit.
+Definition genv := Genv.t fundef unit.
+
+Definition function_proj (f: function) := Asmblock.mkfunction (fn_sig f) (fn_blocks f).
+
+(*
+Definition fundef_proj (fu: fundef) : Asmblock.fundef := transf_fundef function_proj fu.
+
+Definition program_proj (p: program) : Asmblock.program := transform_program fundef_proj p.
+ *)
+
+Definition fundef_proj (fu: fundef) : Asmblock.fundef :=
+ match fu with
+ | Internal f => Internal (function_proj f)
+ | External ef => External ef
+ end.
+
+Definition globdef_proj (gd: globdef fundef unit) : globdef Asmblock.fundef unit :=
+ match gd with
+ | Gfun f => Gfun (fundef_proj f)
+ | Gvar gu => Gvar gu
+ end.
+
+Program Definition genv_trans (ge: genv) : Asmblock.genv :=
+ {| Genv.genv_public := Genv.genv_public ge;
+ Genv.genv_symb := Genv.genv_symb ge;
+ Genv.genv_defs := PTree.map1 globdef_proj (Genv.genv_defs ge);
+ Genv.genv_next := Genv.genv_next ge |}.
+Next Obligation.
+ destruct ge. simpl in *. eauto.
+Qed. Next Obligation.
+ destruct ge; simpl in *.
+ rewrite PTree.gmap1 in H.
+ destruct (genv_defs ! b) eqn:GEN.
+ - eauto.
+ - discriminate.
+Qed. Next Obligation.
+ destruct ge; simpl in *.
+ eauto.
+Qed.
+
+Fixpoint prog_defs_proj (l: list (ident * globdef fundef unit))
+ : list (ident * globdef Asmblock.fundef unit) :=
+ match l with
+ | nil => nil
+ | (i, gd) :: l => (i, globdef_proj gd) :: prog_defs_proj l
+ end.
+
+Definition program_proj (p: program) : Asmblock.program :=
+ {| prog_defs := prog_defs_proj (prog_defs p);
+ prog_public := prog_public p;
+ prog_main := prog_main p
+ |}.
+
+End RELSEM.
+
+Definition semantics (p: program) := Asmblock.semantics (program_proj p).
+
+(** Determinacy of the [Asm] semantics. *)
+
+Lemma semantics_determinate: forall p, determinate (semantics p).
+Proof.
+ intros. apply semantics_determinate.
+Qed.
+
+(** transf_program *)
+
+Program Definition transf_function (f: Asmblock.function) : function :=
+ {| fn_sig := Asmblock.fn_sig f; fn_blocks := Asmblock.fn_blocks f;
+ fn_code := unfold (Asmblock.fn_blocks f) |}.
+
+Lemma transf_function_proj: forall f, function_proj (transf_function f) = f.
+Proof.
+ intros f. destruct f as [sig blks]. unfold function_proj. simpl. auto.
+Qed.
+
+Definition transf_fundef : Asmblock.fundef -> fundef := AST.transf_fundef transf_function.
+
+Lemma transf_fundef_proj: forall f, fundef_proj (transf_fundef f) = f.
+Proof.
+ intros f. destruct f as [f|e]; simpl; auto.
+ rewrite transf_function_proj. auto.
+Qed.
+
+(* Definition transf_globdef (gd: globdef Asmblock.fundef unit) : globdef fundef unit :=
+ match gd with
+ | Gfun f => Gfun (transf_fundef f)
+ | Gvar gu => Gvar gu
+ end.
+
+Lemma transf_globdef_proj: forall gd, globdef_proj (transf_globdef gd) = gd.
+Proof.
+ intros gd. destruct gd as [f|v]; simpl; auto.
+ rewrite transf_fundef_proj; auto.
+Qed.
+
+Fixpoint transf_prog_defs (l: list (ident * globdef Asmblock.fundef unit))
+ : list (ident * globdef fundef unit) :=
+ match l with
+ | nil => nil
+ | (i, gd) :: l => (i, transf_globdef gd) :: transf_prog_defs l
+ end.
+
+Lemma transf_prog_proj: forall p, prog_defs p = prog_defs_proj (transf_prog_defs (prog_defs p)).
+Proof.
+ intros p. destruct p as [defs pub main]. simpl.
+ induction defs; simpl; auto.
+ destruct a as [i gd]. simpl.
+ rewrite transf_globdef_proj.
+ congruence.
+Qed.
+ *)
+
+Definition transf_program : Asmblock.program -> program := transform_program transf_fundef.
+
+Lemma program_equals {A B: Type} : forall (p1 p2: AST.program A B),
+ prog_defs p1 = prog_defs p2 ->
+ prog_public p1 = prog_public p2 ->
+ prog_main p1 = prog_main p2 ->
+ p1 = p2.
+Proof.
+ intros. destruct p1. destruct p2. simpl in *. subst. auto.
+Qed.
+
+Lemma transf_program_proj: forall p, program_proj (transf_program p) = p.
+Proof.
+ intros p. destruct p as [defs pub main]. unfold program_proj. simpl.
+ apply program_equals; simpl; auto.
+ induction defs.
+ - simpl; auto.
+ - simpl. rewrite IHdefs.
+ destruct a as [id gd]; simpl.
+ destruct gd as [f|v]; simpl; auto.
+ rewrite transf_fundef_proj. auto.
+Qed.
+
+Definition match_prog (p: Asmblock.program) (tp: program) :=
+ match_program (fun _ f tf => tf = transf_fundef f) eq p tp.
+
+Lemma transf_program_match:
+ forall p tp, transf_program p = tp -> match_prog p tp.
+Proof.
+ intros. rewrite <- H. eapply match_transform_program; eauto.
+Qed.
+
+Lemma cons_extract {A: Type} : forall (l: list A) a b, a = b -> a::l = b::l.
+Proof.
+ intros. congruence.
+Qed.
+
+(* I think it is a special case of Asmblock -> Asm. Very handy to have *)
+Lemma match_program_transf:
+ forall p tp, match_prog p tp -> transf_program p = tp.
+Proof.
+ intros p tp H. inversion_clear H. inv H1.
+ destruct p as [defs pub main]. destruct tp as [tdefs tpub tmain]. simpl in *.
+ subst. unfold transf_program. unfold transform_program. simpl.
+ apply program_equals; simpl; auto.
+ induction H0; simpl; auto.
+ rewrite IHlist_forall2. apply cons_extract.
+ destruct a1 as [ida gda]. destruct b1 as [idb gdb].
+ simpl in *.
+ inv H. inv H2.
+ - simpl in *. subst. auto.
+ - simpl in *. subst. inv H. auto.
+Qed.
+
+Section PRESERVATION.
+
+Variable prog: Asmblock.program.
+Variable tprog: program.
+Hypothesis TRANSF: match_prog prog tprog.
+Let ge := Genv.globalenv prog.
+Let tge := Genv.globalenv tprog.
+
+Definition match_states (s1 s2: state) := s1 = s2.
+
+Lemma symbols_preserved:
+ forall (s: ident), Genv.find_symbol tge s = Genv.find_symbol ge s.
+Proof (Genv.find_symbol_match TRANSF).
+
+Lemma senv_preserved:
+ Senv.equiv ge tge.
+Proof (Genv.senv_match TRANSF).
+
+
+Theorem transf_program_correct:
+ forward_simulation (Asmblock.semantics prog) (semantics tprog).
+Proof.
+ pose proof (match_program_transf prog tprog TRANSF) as TR.
+ subst. unfold semantics. rewrite transf_program_proj.
+
+ eapply forward_simulation_step with (match_states := match_states); simpl; auto.
+ - intros. exists s1. split; auto. congruence.
+ - intros. inv H. auto.
+ - intros. exists s1'. inv H0. split; auto. congruence.
+Qed.
+
+End PRESERVATION.
diff --git a/mppa_k1c/Asmblock.v b/mppa_k1c/Asmblock.v new file mode 100644 index 00000000..557ab788 --- /dev/null +++ b/mppa_k1c/Asmblock.v @@ -0,0 +1,1361 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, INRIA Paris-Rocquencourt *) +(* Prashanth Mundkur, SRI International *) +(* *) +(* Copyright Institut National de Recherche en Informatique et en *) +(* Automatique. All rights reserved. This file is distributed *) +(* under the terms of the INRIA Non-Commercial License Agreement. *) +(* *) +(* The contributions by Prashanth Mundkur are reused and adapted *) +(* under the terms of a Contributor License Agreement between *) +(* SRI International and INRIA. *) +(* *) +(* *********************************************************************) + +(** Abstract syntax and semantics for K1c assembly language. *) + +Require Import Coqlib. +Require Import Maps. +Require Import AST. +Require Import Integers. +Require Import Floats. +Require Import Values. +Require Import Memory. +Require Import Events. +Require Import Globalenvs. +Require Import Smallstep. +Require Import Locations. +Require Stacklayout. +Require Import Conventions. + +(** * Abstract syntax *) + +(** General Purpose registers. +*) + +Inductive gpreg: Type := + | GPR0: gpreg | GPR1: gpreg | GPR2: gpreg | GPR3: gpreg | GPR4: gpreg + | GPR5: gpreg | GPR6: gpreg | GPR7: gpreg | GPR8: gpreg | GPR9: gpreg + | GPR10: gpreg | GPR11: gpreg | GPR12: gpreg | GPR13: gpreg | GPR14: gpreg + | GPR15: gpreg | GPR16: gpreg | GPR17: gpreg | GPR18: gpreg | GPR19: gpreg + | GPR20: gpreg | GPR21: gpreg | GPR22: gpreg | GPR23: gpreg | GPR24: gpreg + | GPR25: gpreg | GPR26: gpreg | GPR27: gpreg | GPR28: gpreg | GPR29: gpreg + | GPR30: gpreg | GPR31: gpreg | GPR32: gpreg | GPR33: gpreg | GPR34: gpreg + | GPR35: gpreg | GPR36: gpreg | GPR37: gpreg | GPR38: gpreg | GPR39: gpreg + | GPR40: gpreg | GPR41: gpreg | GPR42: gpreg | GPR43: gpreg | GPR44: gpreg + | GPR45: gpreg | GPR46: gpreg | GPR47: gpreg | GPR48: gpreg | GPR49: gpreg + | GPR50: gpreg | GPR51: gpreg | GPR52: gpreg | GPR53: gpreg | GPR54: gpreg + | GPR55: gpreg | GPR56: gpreg | GPR57: gpreg | GPR58: gpreg | GPR59: gpreg + | GPR60: gpreg | GPR61: gpreg | GPR62: gpreg | GPR63: gpreg. + +Definition ireg := gpreg. +Definition freg := gpreg. + +Lemma ireg_eq: forall (x y: ireg), {x=y} + {x<>y}. +Proof. decide equality. Defined. + +Lemma freg_eq: forall (x y: freg), {x=y} + {x<>y}. +Proof. decide equality. Defined. + +(** We model the following registers of the RISC-V architecture. *) + +(** basic register *) +Inductive preg: Type := + | IR: gpreg -> preg (**r integer registers *) + | FR: gpreg -> preg (**r float registers *) + | RA: preg + | PC: preg + . + +Coercion IR: gpreg >-> preg. +Coercion FR: gpreg >-> preg. + +Lemma preg_eq: forall (x y: preg), {x=y} + {x<>y}. +Proof. decide equality. apply ireg_eq. apply freg_eq. Defined. + +Module PregEq. + Definition t := preg. + Definition eq := preg_eq. +End PregEq. + +Module Pregmap := EMap(PregEq). + +(** Conventional names for stack pointer ([SP]) and return address ([RA]). *) + +Notation "'SP'" := GPR12 (only parsing) : asm. +Notation "'FP'" := GPR10 (only parsing) : asm. +Notation "'RTMP'" := GPR31 (only parsing) : asm. + +Inductive btest: Type := + | BTdnez (**r Double Not Equal to Zero *) + | BTdeqz (**r Double Equal to Zero *) + | BTdltz (**r Double Less Than Zero *) + | BTdgez (**r Double Greater Than or Equal to Zero *) + | BTdlez (**r Double Less Than or Equal to Zero *) + | BTdgtz (**r Double Greater Than Zero *) +(*| BTodd (**r Odd (LSB Set) *) + | BTeven (**r Even (LSB Clear) *) +*)| BTwnez (**r Word Not Equal to Zero *) + | BTweqz (**r Word Equal to Zero *) + | BTwltz (**r Word Less Than Zero *) + | BTwgez (**r Word Greater Than or Equal to Zero *) + | BTwlez (**r Word Less Than or Equal to Zero *) + | BTwgtz (**r Word Greater Than Zero *) + . + +Inductive itest: Type := + | ITne (**r Not Equal *) + | ITeq (**r Equal *) + | ITlt (**r Less Than *) + | ITge (**r Greater Than or Equal *) + | ITle (**r Less Than or Equal *) + | ITgt (**r Greater Than *) + | ITneu (**r Unsigned Not Equal *) + | ITequ (**r Unsigned Equal *) + | ITltu (**r Less Than Unsigned *) + | ITgeu (**r Greater Than or Equal Unsigned *) + | ITleu (**r Less Than or Equal Unsigned *) + | ITgtu (**r Greater Than Unsigned *) + (* Not used yet *) + | ITall (**r All Bits Set in Mask *) + | ITnall (**r Not All Bits Set in Mask *) + | ITany (**r Any Bits Set in Mask *) + | ITnone (**r Not Any Bits Set in Mask *) + . + +(** Offsets for load and store instructions. An offset is either an + immediate integer or the low part of a symbol. *) + +Inductive offset : Type := + | Ofsimm (ofs: ptrofs) + | Ofslow (id: ident) (ofs: ptrofs). + +(** We model a subset of the K1c instruction set. In particular, we do not + support floats yet. + + Although it is possible to use the 32-bits mode, for now we don't support it. + + We follow a design close to the one used for the Risc-V port: one set of + pseudo-instructions for 32-bit integer arithmetic, with suffix W, another + set for 64-bit integer arithmetic, with suffix L. + + When mapping to actual instructions, the OCaml code in TargetPrinter.ml + throws an error if we are not in 64-bits mode. +*) + +(** * Instructions *) + +Definition label := positive. + +(* FIXME - rewrite the comment *) +(** A note on immediates: there are various constraints on immediate + operands to K1c instructions. We do not attempt to capture these + restrictions in the abstract syntax nor in the semantics. The + assembler will emit an error if immediate operands exceed the + representable range. Of course, our K1c generator (file + [Asmgen]) is careful to respect this range. *) + +(** Instructions to be expanded in control-flow +*) +Inductive ex_instruction : Type := + (* Pseudo-instructions *) +(*| Ploadsymbol_high (rd: ireg) (id: ident) (ofs: ptrofs) (**r load the high part of the address of a symbol *) + | Pbtbl (r: ireg) (tbl: list label) (**r N-way branch through a jump table *) *) + + | Pbuiltin: external_function -> list (builtin_arg preg) + -> builtin_res preg -> ex_instruction (**r built-in function (pseudo) *) +. + +(** FIXME: comment not up to date ! + + + The pseudo-instructions are the following: + +- [Ploadsymbol]: load the address of a symbol in an integer register. + Expands to the [la] assembler pseudo-instruction, which does the right + thing even if we are in PIC mode. + +- [Pallocframe sz pos]: in the formal semantics, this + pseudo-instruction allocates a memory block with bounds [0] and + [sz], stores the value of the stack pointer at offset [pos] in this + block, and sets the stack pointer to the address of the bottom of + this block. + In the printed ASM assembly code, this allocation is: +<< + mv x30, sp + sub sp, sp, #sz + sw x30, #pos(sp) +>> + This cannot be expressed in our memory model, which does not reflect + the fact that stack frames are adjacent and allocated/freed + following a stack discipline. + +- [Pfreeframe sz pos]: in the formal semantics, this pseudo-instruction + reads the word at [pos] of the block pointed by the stack pointer, + frees this block, and sets the stack pointer to the value read. + In the printed ASM assembly code, this freeing is just an increment of [sp]: +<< + add sp, sp, #sz +>> + Again, our memory model cannot comprehend that this operation + frees (logically) the current stack frame. + +- [Pbtbl reg table]: this is a N-way branch, implemented via a jump table + as follows: +<< + la x31, table + add x31, x31, reg + jr x31 +table: .long table[0], table[1], ... +>> + Note that [reg] contains 4 times the index of the desired table entry. +*) + +(** Control Flow instructions *) +Inductive cf_instruction : Type := + | Pret (**r return *) + | Pcall (l: label) (**r function call *) + + (* Pgoto is for tailcalls, Pj_l is for jumping to a particular label *) + | Pgoto (l: label) (**r goto *) + | Pj_l (l: label) (**r jump to label *) + + (* Conditional branches *) + | Pcb (bt: btest) (r: ireg) (l: label) (**r branch based on btest *) + | Pcbu (bt: btest) (r: ireg) (l: label) (**r branch based on btest with unsigned semantics *) +. + +(** Loads **) +Inductive load_name_rro : Type := + | Plb (**r load byte *) + | Plbu (**r load byte unsigned *) + | Plh (**r load half word *) + | Plhu (**r load half word unsigned *) + | Plw (**r load int32 *) + | Plw_a (**r load any32 *) + | Pld (**r load int64 *) + | Pld_a (**r load any64 *) + | Pfls (**r load float *) + | Pfld (**r load 64-bit float *) +. + +Inductive ld_instruction : Type := + | PLoadRRO (i: load_name_rro) (rd: ireg) (ra: ireg) (ofs: offset) +. + +Coercion PLoadRRO: load_name_rro >-> Funclass. + +(** Stores **) +Inductive store_name_rro : Type := + | Psb (**r store byte *) + | Psh (**r store half byte *) + | Psw (**r store int32 *) + | Psw_a (**r store any32 *) + | Psd (**r store int64 *) + | Psd_a (**r store any64 *) + | Pfss (**r store float *) + | Pfsd (**r store 64-bit float *) +. + +Inductive st_instruction : Type := + | PStoreRRO (i: store_name_rro) (rs: ireg) (ra: ireg) (ofs: offset) +. + +Coercion PStoreRRO: store_name_rro >-> Funclass. + +(** Arithmetic instructions **) +Inductive arith_name_r : Type := + | Pcvtw2l (**r Convert Word to Long *) + | Ploadsymbol (id: ident) (ofs: ptrofs) (**r load the address of a symbol *) +. + +Inductive arith_name_rr : Type := + | Pmv (**r register move *) + | Pnegw (**r negate word *) + | Pnegl (**r negate long *) + | Pfnegd (**r float negate double *) + | Pcvtl2w (**r Convert Long to Word *) + | Pmvw2l (**r Move Convert Word to Long *) +. + +Inductive arith_name_ri32 : Type := + | Pmake (**r load immediate *) +. + +Inductive arith_name_ri64 : Type := + | Pmakel (**r load immediate long *) +. + +Inductive arith_name_rrr : Type := + | Pcompw (it: itest) (**r comparison word *) + | Pcompl (it: itest) (**r comparison long *) + + | Paddw (**r add word *) + | Psubw (**r sub word *) + | Pmulw (**r mul word *) + | Pandw (**r and word *) + | Porw (**r or word *) + | Pxorw (**r xor word *) + | Psraw (**r shift right arithmetic word *) + | Psrlw (**r shift right logical word *) + | Psllw (**r shift left logical word *) + + | Paddl (**r add long *) + | Psubl (**r sub long *) + | Pandl (**r and long *) + | Porl (**r or long *) + | Pxorl (**r xor long *) + | Pmull (**r mul long (low part) *) + | Pslll (**r shift left logical long *) + | Psrll (**r shift right logical long *) + | Psral (**r shift right arithmetic long *) +. + +Inductive arith_name_rri32 : Type := + | Pcompiw (it: itest) (**r comparison imm word *) + + | Paddiw (**r add imm word *) + | Pandiw (**r and imm word *) + | Poriw (**r or imm word *) + | Pxoriw (**r xor imm word *) + | Psraiw (**r shift right arithmetic imm word *) + | Psrliw (**r shift right logical imm word *) + | Pslliw (**r shift left logical imm word *) + + | Psllil (**r shift left logical immediate long *) + | Psrlil (**r shift right logical immediate long *) + | Psrail (**r shift right arithmetic immediate long *) +. + +Inductive arith_name_rri64 : Type := + | Pcompil (it: itest) (**r comparison imm long *) + | Paddil (**r add immediate long *) + | Pandil (**r and immediate long *) + | Poril (**r or immediate long *) + | Pxoril (**r xor immediate long *) +. + +Inductive ar_instruction : Type := + | PArithR (i: arith_name_r) (rd: ireg) + | PArithRR (i: arith_name_rr) (rd rs: ireg) + | PArithRI32 (i: arith_name_ri32) (rd: ireg) (imm: int) + | PArithRI64 (i: arith_name_ri64) (rd: ireg) (imm: int64) + | PArithRRR (i: arith_name_rrr) (rd rs1 rs2: ireg) + | PArithRRI32 (i: arith_name_rri32) (rd rs: ireg) (imm: int) + | PArithRRI64 (i: arith_name_rri64) (rd rs: ireg) (imm: int64) +. + +Coercion PArithR: arith_name_r >-> Funclass. +Coercion PArithRR: arith_name_rr >-> Funclass. +Coercion PArithRI32: arith_name_ri32 >-> Funclass. +Coercion PArithRI64: arith_name_ri64 >-> Funclass. +Coercion PArithRRR: arith_name_rrr >-> Funclass. +Coercion PArithRRI32: arith_name_rri32 >-> Funclass. +Coercion PArithRRI64: arith_name_rri64 >-> Funclass. + +Inductive basic : Type := + | PArith (i: ar_instruction) + | PLoad (i: ld_instruction) + | PStore (i: st_instruction) + | Pallocframe (sz: Z) (pos: ptrofs) (**r allocate new stack frame *) + | Pfreeframe (sz: Z) (pos: ptrofs) (**r deallocate stack frame and restore previous frame *) + | Pget (rd: ireg) (rs: preg) (**r get system register *) + | Pset (rd: preg) (rs: ireg) (**r set system register *) + | Pnop (**r virtual instruction that does nothing *) +. + +Coercion PLoad: ld_instruction >-> basic. +Coercion PStore: st_instruction >-> basic. +Coercion PArith: ar_instruction >-> basic. + + +Inductive control : Type := + | PExpand (i: ex_instruction) + | PCtlFlow (i: cf_instruction) +. + +Coercion PExpand: ex_instruction >-> control. +Coercion PCtlFlow: cf_instruction >-> control. + + +(** * Definition of a bblock *) + +Definition non_empty_bblock (body: list basic) (exit: option control): Prop + := body <> nil \/ exit <> None. + +Definition non_empty_body (body: list basic): bool := + match body with + | nil => false + | _ => true + end. + +Definition non_empty_exit (exit: option control): bool := + match exit with + | None => false + | _ => true + end. + +Definition non_empty_bblockb (body: list basic) (exit: option control): bool := non_empty_body body || non_empty_exit exit. + +Lemma non_empty_bblock_refl: + forall body exit, + non_empty_bblock body exit -> + Is_true (non_empty_bblockb body exit). +Proof. + intros. destruct body; destruct exit. + all: simpl; auto. + inv H; contradiction. +Qed. + +(* Definition builtin_alone (body: list basic) (exit: option control) := forall ef args res, + exit = Some (PExpand (Pbuiltin ef args res)) -> body = nil. + *) + +(* Definition wf_bblock (header: list label) (body: list basic) (exit: option control) := + non_empty_bblock body exit (* /\ builtin_alone body exit *). *) + +(** A bblock is well-formed if he contains at least one instruction, + and if there is a builtin then it must be alone in this bblock. *) + +Record bblock := mk_bblock { + header: list label; + body: list basic; + exit: option control; + correct: Is_true (non_empty_bblockb body exit) +}. + +Ltac bblock_auto_correct := (apply non_empty_bblock_refl; try discriminate; try (left; discriminate); try (right; discriminate)). +(* Local Obligation Tactic := bblock_auto_correct. *) + +Lemma Istrue_proof_irrelevant (b: bool): forall (p1 p2:Is_true b), p1=p2. +Proof. + destruct b; simpl; auto. + - destruct p1, p2; auto. + - destruct p1. +Qed. + +Lemma bblock_equality bb1 bb2: header bb1=header bb2 -> body bb1 = body bb2 -> exit bb1 = exit bb2 -> bb1 = bb2. +Proof. + destruct bb1 as [h1 b1 e1 c1], bb2 as [h2 b2 e2 c2]; simpl. + intros; subst. + rewrite (Istrue_proof_irrelevant _ c1 c2). + auto. +Qed. + + +(* FIXME: redundant with definition in Machblock *) +Definition length_opt {A} (o: option A) : nat := + match o with + | Some o => 1 + | None => 0 + end. + +(* WARNING: the notion of size is not the same than in Machblock ! + We ignore labels here... + The result is in Z to be compatible with operations on PC +*) +Definition size (b:bblock): Z := Z.of_nat (length (body b) + length_opt (exit b)). +(* match (body b, exit b) with + | (nil, None) => 1 + | _ => + end. + *) + +Lemma length_nonil {A: Type} : forall l:(list A), l <> nil -> (length l > 0)%nat. +Proof. + intros. destruct l; try (contradict H; auto; fail). + simpl. omega. +Qed. + +Lemma to_nat_pos : forall z:Z, (Z.to_nat z > 0)%nat -> z > 0. +Proof. + intros. destruct z; auto. + - contradict H. simpl. apply gt_irrefl. + - apply Zgt_pos_0. + - contradict H. simpl. apply gt_irrefl. +Qed. + +Lemma size_positive (b:bblock): size b > 0. +Proof. + unfold size. destruct b as [hd bdy ex cor]. simpl. + destruct ex; destruct bdy; try (apply to_nat_pos; rewrite Nat2Z.id; simpl; omega). + inversion cor; contradict H; simpl; auto. +(* rewrite eq. (* inversion COR. *) (* inversion H. *) + - assert ((length b > 0)%nat). apply length_nonil. auto. + omega. + - destruct e; simpl; try omega. contradict H; simpl; auto. + *)Qed. + +Definition bblocks := list bblock. + +Record function : Type := mkfunction { fn_sig: signature; fn_blocks: bblocks }. +Definition fundef := AST.fundef function. +Definition program := AST.program fundef unit. + +Inductive instruction : Type := + | PBasic (i: basic) + | PControl (i: control) +. + +Coercion PBasic: basic >-> instruction. +Coercion PControl: control >-> instruction. + +Definition code := list instruction. +Definition bcode := list basic. + +Fixpoint basics_to_code (l: list basic) := + match l with + | nil => nil + | bi::l => (PBasic bi)::(basics_to_code l) + end. + +Fixpoint code_to_basics (c: code) := + match c with + | (PBasic i)::c => + match code_to_basics c with + | None => None + | Some l => Some (i::l) + end + | _::c => None + | nil => Some nil + end. + +Lemma code_to_basics_id: forall c, code_to_basics (basics_to_code c) = Some c. +Proof. + intros. induction c as [|i c]; simpl; auto. + rewrite IHc. auto. +Qed. + +Lemma code_to_basics_dist: + forall c c' l l', + code_to_basics c = Some l -> + code_to_basics c' = Some l' -> + code_to_basics (c ++ c') = Some (l ++ l'). +Proof. + induction c as [|i c]; simpl; auto. + - intros. inv H. simpl. auto. + - intros. destruct i; try discriminate. destruct (code_to_basics c) eqn:CTB; try discriminate. + inv H. erewrite IHc; eauto. auto. +Qed. + +(** + Asmblockgen will have to translate a Mach control into a list of instructions of the form + i1 :: i2 :: i3 :: ctl :: nil ; where i1..i3 are basic instructions, ctl is a control instruction + These functions provide way to extract the basic / control instructions +*) + +Fixpoint extract_basic (c: code) := + match c with + | nil => nil + | PBasic i :: c => i :: (extract_basic c) + | PControl i :: c => nil + end. + +Fixpoint extract_ctl (c: code) := + match c with + | nil => None + | PBasic i :: c => extract_ctl c + | PControl i :: nil => Some i + | PControl i :: _ => None (* if the first found control instruction isn't the last *) + end. + +(** * Utility for Asmblockgen *) + +Program Definition bblock_single_inst (i: instruction) := + match i with + | PBasic b => {| header:=nil; body:=(b::nil); exit:=None |} + | PControl ctl => {| header:=nil; body:=nil; exit:=(Some ctl) |} + end. + +Program Definition bblock_basic_ctl (c: list basic) (i: option control) := + match i with + | Some i => {| header:=nil; body:=c; exit:=Some i |} + | None => + match c with + | _::_ => {| header:=nil; body:=c; exit:=None |} + | nil => {| header:=nil; body:=Pnop::nil; exit:=None |} + end + end. +Next Obligation. + bblock_auto_correct. +Qed. Next Obligation. + bblock_auto_correct. +Qed. + + +(** * Operational semantics *) + +(** The semantics operates over a single mapping from registers + (type [preg]) to values. We maintain + the convention that integer registers are mapped to values of + type [Tint] or [Tlong] (in 64 bit mode), + and float registers to values of type [Tsingle] or [Tfloat]. *) + +Definition regset := Pregmap.t val. + +Definition genv := Genv.t fundef unit. + +Notation "a # b" := (a b) (at level 1, only parsing) : asm. +Notation "a # b <- c" := (Pregmap.set b c a) (at level 1, b at next level) : asm. + +Open Scope asm. + +(** Undefining some registers *) + +Fixpoint undef_regs (l: list preg) (rs: regset) : regset := + match l with + | nil => rs + | r :: l' => undef_regs l' (rs#r <- Vundef) + end. + + +(** Assigning a register pair *) +Definition set_pair (p: rpair preg) (v: val) (rs: regset) : regset := + match p with + | One r => rs#r <- v + | Twolong rhi rlo => rs#rhi <- (Val.hiword v) #rlo <- (Val.loword v) + end. + +(* TODO: Is it still useful ?? *) + + +(** Assigning multiple registers *) + +(* Fixpoint set_regs (rl: list preg) (vl: list val) (rs: regset) : regset := + match rl, vl with + | r1 :: rl', v1 :: vl' => set_regs rl' vl' (rs#r1 <- v1) + | _, _ => rs + end. + *) +(** Assigning the result of a builtin *) + +Fixpoint set_res (res: builtin_res preg) (v: val) (rs: regset) : regset := + match res with + | BR r => rs#r <- v + | BR_none => rs + | BR_splitlong hi lo => set_res lo (Val.loword v) (set_res hi (Val.hiword v) rs) + end. + +Section RELSEM. + + +(** The semantics is purely small-step and defined as a function + from the current state (a register set + a memory state) + to either [Next rs' m'] where [rs'] and [m'] are the updated register + set and memory state after execution of the instruction at [rs#PC], + or [Stuck] if the processor is stuck. *) + +Inductive outcome {rgset}: Type := + | Next (rs:rgset) (m:mem) + | Stuck. +Arguments outcome: clear implicits. + + +(** ** Arithmetic Expressions (including comparisons) *) + +Inductive signedness: Type := Signed | Unsigned. + +Inductive intsize: Type := Int | Long. + +Definition itest_for_cmp (c: comparison) (s: signedness) := + match c, s with + | Cne, Signed => ITne + | Ceq, Signed => ITeq + | Clt, Signed => ITlt + | Cge, Signed => ITge + | Cle, Signed => ITle + | Cgt, Signed => ITgt + | Cne, Unsigned => ITneu + | Ceq, Unsigned => ITequ + | Clt, Unsigned => ITltu + | Cge, Unsigned => ITgeu + | Cle, Unsigned => ITleu + | Cgt, Unsigned => ITgtu + end. + +(* CoMPare Signed Words to Zero *) +Definition btest_for_cmpswz (c: comparison) := + match c with + | Cne => BTwnez + | Ceq => BTweqz + | Clt => BTwltz + | Cge => BTwgez + | Cle => BTwlez + | Cgt => BTwgtz + end. + +(* CoMPare Signed Doubles to Zero *) +Definition btest_for_cmpsdz (c: comparison) := + match c with + | Cne => BTdnez + | Ceq => BTdeqz + | Clt => BTdltz + | Cge => BTdgez + | Cle => BTdlez + | Cgt => BTdgtz + end. + +Definition cmp_for_btest (bt: btest) := + match bt with + | BTwnez => (Some Cne, Int) + | BTweqz => (Some Ceq, Int) + | BTwltz => (Some Clt, Int) + | BTwgez => (Some Cge, Int) + | BTwlez => (Some Cle, Int) + | BTwgtz => (Some Cgt, Int) + + | BTdnez => (Some Cne, Long) + | BTdeqz => (Some Ceq, Long) + | BTdltz => (Some Clt, Long) + | BTdgez => (Some Cge, Long) + | BTdlez => (Some Cle, Long) + | BTdgtz => (Some Cgt, Long) + end. + +Definition cmpu_for_btest (bt: btest) := + match bt with + | BTwnez => (Some Cne, Int) + | BTweqz => (Some Ceq, Int) + | BTdnez => (Some Cne, Long) + | BTdeqz => (Some Ceq, Long) + | _ => (None, Int) + end. + +(** Comparing integers *) +Definition compare_int (t: itest) (v1 v2: val) (m: mem): val := + match t with + | ITne => Val.cmp Cne v1 v2 + | ITeq => Val.cmp Ceq v1 v2 + | ITlt => Val.cmp Clt v1 v2 + | ITge => Val.cmp Cge v1 v2 + | ITle => Val.cmp Cle v1 v2 + | ITgt => Val.cmp Cgt v1 v2 + | ITneu => Val.cmpu (Mem.valid_pointer m) Cne v1 v2 + | ITequ => Val.cmpu (Mem.valid_pointer m) Ceq v1 v2 + | ITltu => Val.cmpu (Mem.valid_pointer m) Clt v1 v2 + | ITgeu => Val.cmpu (Mem.valid_pointer m) Cge v1 v2 + | ITleu => Val.cmpu (Mem.valid_pointer m) Cle v1 v2 + | ITgtu => Val.cmpu (Mem.valid_pointer m) Cgt v1 v2 + | ITall + | ITnall + | ITany + | ITnone => Vundef + end. + +Definition compare_long (t: itest) (v1 v2: val) (m: mem): val := + let res := match t with + | ITne => Val.cmpl Cne v1 v2 + | ITeq => Val.cmpl Ceq v1 v2 + | ITlt => Val.cmpl Clt v1 v2 + | ITge => Val.cmpl Cge v1 v2 + | ITle => Val.cmpl Cle v1 v2 + | ITgt => Val.cmpl Cgt v1 v2 + | ITneu => Val.cmplu (Mem.valid_pointer m) Cne v1 v2 + | ITequ => Val.cmplu (Mem.valid_pointer m) Ceq v1 v2 + | ITltu => Val.cmplu (Mem.valid_pointer m) Clt v1 v2 + | ITgeu => Val.cmplu (Mem.valid_pointer m) Cge v1 v2 + | ITleu => Val.cmplu (Mem.valid_pointer m) Cle v1 v2 + | ITgtu => Val.cmplu (Mem.valid_pointer m) Cgt v1 v2 + | ITall + | ITnall + | ITany + | ITnone => Some Vundef + end in + match res with + | Some v => v + | None => Vundef + end + . +(** Execution of arith instructions + +TODO: subsplitting by instruction type ? Could be useful for expressing auxiliary lemma... + +FIXME: replace parameter "m" by a function corresponding to the resul of "(Mem.valid_pointer m)" + +*) + +Variable ge: genv. + + +Definition exec_arith_instr (ai: ar_instruction) (rs: regset) (m: mem) : regset := + match ai with + | PArithR n d => + match n with + | Pcvtw2l => rs#d <- (Val.longofint rs#d) + | Ploadsymbol s ofs => rs#d <- (Genv.symbol_address ge s ofs) + end + + | PArithRR n d s => + match n with + | Pmv => rs#d <- (rs#s) + | Pnegw => rs#d <- (Val.neg rs#s) + | Pnegl => rs#d <- (Val.negl rs#s) + | Pfnegd => rs#d <- (Val.negf rs#s) + | Pcvtl2w => rs#d <- (Val.loword rs#s) + | Pmvw2l => rs#d <- (Val.longofint rs#s) + end + + | PArithRI32 n d i => + match n with + | Pmake => rs#d <- (Vint i) + end + + | PArithRI64 n d i => + match n with + | Pmakel => rs#d <- (Vlong i) + end + + | PArithRRR n d s1 s2 => + match n with + | Pcompw c => rs#d <- (compare_int c rs#s1 rs#s2 m) + | Pcompl c => rs#d <- (compare_long c rs#s1 rs#s2 m) + | Paddw => rs#d <- (Val.add rs#s1 rs#s2) + | Psubw => rs#d <- (Val.sub rs#s1 rs#s2) + | Pmulw => rs#d <- (Val.mul rs#s1 rs#s2) + | Pandw => rs#d <- (Val.and rs#s1 rs#s2) + | Porw => rs#d <- (Val.or rs#s1 rs#s2) + | Pxorw => rs#d <- (Val.xor rs#s1 rs#s2) + | Psrlw => rs#d <- (Val.shru rs#s1 rs#s2) + | Psraw => rs#d <- (Val.shr rs#s1 rs#s2) + | Psllw => rs#d <- (Val.shl rs#s1 rs#s2) + + | Paddl => rs#d <- (Val.addl rs#s1 rs#s2) + | Psubl => rs#d <- (Val.subl rs#s1 rs#s2) + | Pandl => rs#d <- (Val.andl rs#s1 rs#s2) + | Porl => rs#d <- (Val.orl rs#s1 rs#s2) + | Pxorl => rs#d <- (Val.xorl rs#s1 rs#s2) + | Pmull => rs#d <- (Val.mull rs#s1 rs#s2) + | Pslll => rs#d <- (Val.shll rs#s1 rs#s2) + | Psrll => rs#d <- (Val.shrlu rs#s1 rs#s2) + | Psral => rs#d <- (Val.shrl rs#s1 rs#s2) + end + + | PArithRRI32 n d s i => + match n with + | Pcompiw c => rs#d <- (compare_int c rs#s (Vint i) m) + | Paddiw => rs#d <- (Val.add rs#s (Vint i)) + | Pandiw => rs#d <- (Val.and rs#s (Vint i)) + | Poriw => rs#d <- (Val.or rs#s (Vint i)) + | Pxoriw => rs#d <- (Val.xor rs#s (Vint i)) + | Psraiw => rs#d <- (Val.shr rs#s (Vint i)) + | Psrliw => rs#d <- (Val.shru rs#s (Vint i)) + | Pslliw => rs#d <- (Val.shl rs#s (Vint i)) + | Psllil => rs#d <- (Val.shll rs#s (Vint i)) + | Psrlil => rs#d <- (Val.shrlu rs#s (Vint i)) + | Psrail => rs#d <- (Val.shrl rs#s (Vint i)) + end + + | PArithRRI64 n d s i => + match n with + | Pcompil c => rs#d <- (compare_long c rs#s (Vlong i) m) + | Paddil => rs#d <- (Val.addl rs#s (Vlong i)) + | Pandil => rs#d <- (Val.andl rs#s (Vlong i)) + | Poril => rs#d <- (Val.orl rs#s (Vlong i)) + | Pxoril => rs#d <- (Val.xorl rs#s (Vlong i)) + end + end. + +(** * load/store *) + +(** The two functions below axiomatize how the linker processes + symbolic references [symbol + offset)] and splits their + actual values into a 20-bit high part [%hi(symbol + offset)] and + a 12-bit low part [%lo(symbol + offset)]. *) + +Parameter low_half: genv -> ident -> ptrofs -> ptrofs. +Parameter high_half: genv -> ident -> ptrofs -> val. + +(** The fundamental property of these operations is that, when applied + to the address of a symbol, their results can be recombined by + addition, rebuilding the original address. *) + +Axiom low_high_half: + forall id ofs, + Val.offset_ptr (high_half ge id ofs) (low_half ge id ofs) = Genv.symbol_address ge id ofs. + +(** Auxiliaries for memory accesses *) + +Definition eval_offset (ofs: offset) : ptrofs := + match ofs with + | Ofsimm n => n + | Ofslow id delta => low_half ge id delta + end. + +Definition exec_load (chunk: memory_chunk) (rs: regset) (m: mem) + (d: preg) (a: ireg) (ofs: offset) := + match Mem.loadv chunk m (Val.offset_ptr (rs a) (eval_offset ofs)) with + | None => Stuck + | Some v => Next (rs#d <- v) m + end. + +Definition exec_store (chunk: memory_chunk) (rs: regset) (m: mem) + (s: preg) (a: ireg) (ofs: offset) := + match Mem.storev chunk m (Val.offset_ptr (rs a) (eval_offset ofs)) (rs s) with + | None => Stuck + | Some m' => Next rs m' + end. + +(** * basic instructions *) + +Definition exec_basic_instr (bi: basic) (rs: regset) (m: mem) : outcome regset := + match bi with + | PArith ai => Next (exec_arith_instr ai rs m) m + + | PLoadRRO n d a ofs => + match n with + | Plb => exec_load Mint8signed rs m d a ofs + | Plbu => exec_load Mint8unsigned rs m d a ofs + | Plh => exec_load Mint16signed rs m d a ofs + | Plhu => exec_load Mint16unsigned rs m d a ofs + | Plw => exec_load Mint32 rs m d a ofs + | Plw_a => exec_load Many32 rs m d a ofs + | Pld => exec_load Mint64 rs m d a ofs + | Pld_a => exec_load Many64 rs m d a ofs + | Pfls => exec_load Mfloat32 rs m d a ofs + | Pfld => exec_load Mfloat64 rs m d a ofs + end + + | PStoreRRO n s a ofs => + match n with + | Psb => exec_store Mint8unsigned rs m s a ofs + | Psh => exec_store Mint16unsigned rs m s a ofs + | Psw => exec_store Mint32 rs m s a ofs + | Psw_a => exec_store Many32 rs m s a ofs + | Psd => exec_store Mint64 rs m s a ofs + | Psd_a => exec_store Many64 rs m s a ofs + | Pfss => exec_store Mfloat32 rs m s a ofs + | Pfsd => exec_store Mfloat64 rs m s a ofs + end + + | Pallocframe sz pos => + let (m1, stk) := Mem.alloc m 0 sz in + let sp := (Vptr stk Ptrofs.zero) in + match Mem.storev Mptr m1 (Val.offset_ptr sp pos) rs#SP with + | None => Stuck + | Some m2 => Next (rs #FP <- (rs SP) #SP <- sp #GPR31 <- Vundef) m2 + end + + | Pfreeframe sz pos => + match Mem.loadv Mptr m (Val.offset_ptr rs#SP pos) with + | None => Stuck + | Some v => + match rs SP with + | Vptr stk ofs => + match Mem.free m stk 0 sz with + | None => Stuck + | Some m' => Next (rs#SP <- v #GPR31 <- Vundef) m' + end + | _ => Stuck + end + end + | Pget rd ra => + match ra with + | RA => Next (rs#rd <- (rs#ra)) m + | _ => Stuck + end + | Pset ra rd => + match ra with + | RA => Next (rs#ra <- (rs#rd)) m + | _ => Stuck + end + | Pnop => Next rs m +end. + +Fixpoint exec_body (body: list basic) (rs: regset) (m: mem): outcome regset := + match body with + | nil => Next rs m + | bi::body' => + match exec_basic_instr bi rs m with + | Next rs' m' => exec_body body' rs' m' + | Stuck => Stuck + end + end. + +(** Manipulations over the [PC] register: continuing with the next + instruction ([nextblock]) or branching to a label ([goto_label]). *) + +Definition nextblock (b:bblock) (rs: regset) := + rs#PC <- (Val.offset_ptr rs#PC (Ptrofs.repr (size b))). + +(** Looking up bblocks in a code sequence by position. *) +Fixpoint find_bblock (pos: Z) (lb: bblocks) {struct lb} : option bblock := + match lb with + | nil => None + | b :: il => + if zlt pos 0 then None (* NOTE: It is impossible to branch inside a block *) + else if zeq pos 0 then Some b + else find_bblock (pos - (size b)) il + end. + + +(** Position corresponding to a label *) + +(** TODO: redundant w.r.t Machblock *) +Lemma in_dec (lbl: label) (l: list label): { List.In lbl l } + { ~(List.In lbl l) }. +Proof. + apply List.in_dec. + apply Pos.eq_dec. +Qed. + + +(** Note: copy-paste from Machblock *) +Definition is_label (lbl: label) (bb: bblock) : bool := + if in_dec lbl (header bb) then true else false. + +Lemma is_label_correct_true lbl bb: + List.In lbl (header bb) <-> is_label lbl bb = true. +Proof. + unfold is_label; destruct (in_dec lbl (header bb)); simpl; intuition. +Qed. + +Lemma is_label_correct_false lbl bb: + ~(List.In lbl (header bb)) <-> is_label lbl bb = false. +Proof. + unfold is_label; destruct (in_dec lbl (header bb)); simpl; intuition. +Qed. + +(** convert a label into a position in the code *) +Fixpoint label_pos (lbl: label) (pos: Z) (lb: bblocks) {struct lb} : option Z := + match lb with + | nil => None + | b :: lb' => if is_label lbl b then Some pos else label_pos lbl (pos + (size b)) lb' + end. + +Definition goto_label (f: function) (lbl: label) (rs: regset) (m: mem) : outcome regset := + match label_pos lbl 0 (fn_blocks f) with + | None => Stuck + | Some pos => + match rs#PC with + | Vptr b ofs => Next (rs#PC <- (Vptr b (Ptrofs.repr pos))) m + | _ => Stuck + end + end. + +(** Evaluating a branch + +Warning: in m PC is assumed to be already pointing on the next instruction ! + +*) +Definition eval_branch (f: function) (l: label) (rs: regset) (m: mem) (res: option bool) : outcome regset := + match res with + | Some true => goto_label f l rs m + | Some false => Next rs m + | None => Stuck + end. + + +(** Execution of a single control-flow instruction [i] in initial state [rs] and + [m]. Return updated state. + + As above: PC is assumed to be incremented on the next block before the control-flow instruction + + For instructions that correspond tobuiltin + actual RISC-V instructions, the cases are straightforward + transliterations of the informal descriptions given in the RISC-V + user-mode specification. For pseudo-instructions, refer to the + informal descriptions given above. + + Note that we set to [Vundef] the registers used as temporaries by + the expansions of the pseudo-instructions, so that the RISC-V code + we generate cannot use those registers to hold values that must + survive the execution of the pseudo-instruction. *) + +Definition exec_control (f: function) (oc: option control) (rs: regset) (m: mem) : outcome regset := + match oc with + | Some ic => +(** Get/Set system registers *) + match ic with + + +(** Branch Control Unit instructions *) + | Pret => + Next (rs#PC <- (rs#RA)) m + | Pcall s => + Next (rs#RA <- (rs#PC) #PC <- (Genv.symbol_address ge s Ptrofs.zero)) m + | Pgoto s => + Next (rs#PC <- (Genv.symbol_address ge s Ptrofs.zero)) m + | Pj_l l => + goto_label f l rs m + | Pcb bt r l => + match cmp_for_btest bt with + | (Some c, Int) => eval_branch f l rs m (Val.cmp_bool c rs#r (Vint (Int.repr 0))) + | (Some c, Long) => eval_branch f l rs m (Val.cmpl_bool c rs#r (Vlong (Int64.repr 0))) + | (None, _) => Stuck + end + | Pcbu bt r l => + match cmpu_for_btest bt with + | (Some c, Int) => eval_branch f l rs m (Val.cmpu_bool (Mem.valid_pointer m) c rs#r (Vint (Int.repr 0))) + | (Some c, Long) => eval_branch f l rs m (Val.cmplu_bool (Mem.valid_pointer m) c rs#r (Vlong (Int64.repr 0))) + | (None, _) => Stuck + end + + +(** Pseudo-instructions *) + | Pbuiltin ef args res => + Stuck (**r treated specially below *) + end + | None => Next rs m +end. + +Definition exec_bblock (f: function) (b: bblock) (rs0: regset) (m: mem) : outcome regset := + match exec_body (body b) rs0 m with + | Next rs' m' => + let rs1 := nextblock b rs' in exec_control f (exit b) rs1 m' + | Stuck => Stuck + end. + +(** Translation of the LTL/Linear/Mach view of machine registers to + the RISC-V view. Note that no LTL register maps to [X31]. This + register is reserved as temporary, to be used by the generated RV32G + code. *) + + (* FIXME - R31 is not there *) +Definition preg_of (r: mreg) : preg := + match r with + | R0 => GPR0 | R1 => GPR1 | R2 => GPR2 | R3 => GPR3 | R4 => GPR4 + | R5 => GPR5 | R6 => GPR6 | R7 => GPR7 | R9 => GPR9 + | R10 => GPR10 (*| R11 => GPR11 | R12 => GPR12 | R13 => GPR13 | R14 => GPR14 *) + | R15 => GPR15 | R16 => GPR16 | R17 => GPR17 | R18 => GPR18 | R19 => GPR19 + | R20 => GPR20 | R21 => GPR21 | R22 => GPR22 | R23 => GPR23 | R24 => GPR24 + | R25 => GPR25 | R26 => GPR26 | R27 => GPR27 | R28 => GPR28 | R29 => GPR29 + | R30 => GPR30 | R32 => GPR32 | R33 => GPR33 | R34 => GPR34 + | R35 => GPR35 | R36 => GPR36 | R37 => GPR37 | R38 => GPR38 | R39 => GPR39 + | R40 => GPR40 | R41 => GPR41 | R42 => GPR42 | R43 => GPR43 | R44 => GPR44 + | R45 => GPR45 | R46 => GPR46 | R47 => GPR47 | R48 => GPR48 | R49 => GPR49 + | R50 => GPR50 | R51 => GPR51 | R52 => GPR52 | R53 => GPR53 | R54 => GPR54 + | R55 => GPR55 | R56 => GPR56 | R57 => GPR57 | R58 => GPR58 | R59 => GPR59 + | R60 => GPR60 | R61 => GPR61 | R62 => GPR62 | R63 => GPR63 + end. + +(** Extract the values of the arguments of an external call. + We exploit the calling conventions from module [Conventions], except that + we use RISC-V registers instead of locations. *) + +Inductive extcall_arg (rs: regset) (m: mem): loc -> val -> Prop := + | extcall_arg_reg: forall r, + extcall_arg rs m (R r) (rs (preg_of r)) + | extcall_arg_stack: forall ofs ty bofs v, + bofs = Stacklayout.fe_ofs_arg + 4 * ofs -> + Mem.loadv (chunk_of_type ty) m + (Val.offset_ptr rs#SP (Ptrofs.repr bofs)) = Some v -> + extcall_arg rs m (S Outgoing ofs ty) v. + +Inductive extcall_arg_pair (rs: regset) (m: mem): rpair loc -> val -> Prop := + | extcall_arg_one: forall l v, + extcall_arg rs m l v -> + extcall_arg_pair rs m (One l) v + | extcall_arg_twolong: forall hi lo vhi vlo, + extcall_arg rs m hi vhi -> + extcall_arg rs m lo vlo -> + extcall_arg_pair rs m (Twolong hi lo) (Val.longofwords vhi vlo). + +Definition extcall_arguments + (rs: regset) (m: mem) (sg: signature) (args: list val) : Prop := + list_forall2 (extcall_arg_pair rs m) (loc_arguments sg) args. + +Definition loc_external_result (sg: signature) : rpair preg := + map_rpair preg_of (loc_result sg). + +(** Execution of the instruction at [rs PC]. *) + +Inductive state: Type := + | State: regset -> mem -> state. + + +(** TODO + * For now, we consider a builtin is alone in a basic block. + * Perhaps there is a way to avoid that ? + *) + +Inductive step: state -> trace -> state -> Prop := + | exec_step_internal: + forall b ofs f bi rs m rs' m', + rs PC = Vptr b ofs -> + Genv.find_funct_ptr ge b = Some (Internal f) -> + find_bblock (Ptrofs.unsigned ofs) (fn_blocks f) = Some bi -> + exec_bblock f bi rs m = Next rs' m' -> + step (State rs m) E0 (State rs' m') + | exec_step_builtin: + forall b ofs f ef args res rs m vargs t vres rs' m' bi, + rs PC = Vptr b ofs -> + Genv.find_funct_ptr ge b = Some (Internal f) -> + find_bblock (Ptrofs.unsigned ofs) f.(fn_blocks) = Some bi -> + exit bi = Some (PExpand (Pbuiltin ef args res)) -> + eval_builtin_args ge rs (rs SP) m args vargs -> + external_call ef ge vargs m t vres m' -> + rs' = nextblock bi + (set_res res vres + (undef_regs (map preg_of (destroyed_by_builtin ef)) + (rs#GPR31 <- Vundef))) -> + step (State rs m) t (State rs' m') + | exec_step_external: + forall b ef args res rs m t rs' m', + rs PC = Vptr b Ptrofs.zero -> + Genv.find_funct_ptr ge b = Some (External ef) -> + external_call ef ge args m t res m' -> + extcall_arguments rs m (ef_sig ef) args -> + rs' = (set_pair (loc_external_result (ef_sig ef) ) res rs)#PC <- (rs RA) -> + step (State rs m) t (State rs' m') + . + + + +End RELSEM. + +(** Execution of whole programs. *) + +Inductive initial_state (p: program): state -> Prop := + | initial_state_intro: forall m0, + let ge := Genv.globalenv p in + let rs0 := + (Pregmap.init Vundef) + # PC <- (Genv.symbol_address ge p.(prog_main) Ptrofs.zero) + # SP <- Vnullptr + # RA <- Vnullptr in + Genv.init_mem p = Some m0 -> + initial_state p (State rs0 m0). + +Inductive final_state: state -> int -> Prop := + | final_state_intro: forall rs m r, + rs PC = Vnullptr -> + rs GPR0 = Vint r -> + final_state (State rs m) r. + +Definition semantics (p: program) := + Semantics step (initial_state p) final_state (Genv.globalenv p). + +Remark extcall_arguments_determ: + forall rs m sg args1 args2, + extcall_arguments rs m sg args1 -> extcall_arguments rs m sg args2 -> args1 = args2. +Proof. + intros until m. + assert (A: forall l v1 v2, + extcall_arg rs m l v1 -> extcall_arg rs m l v2 -> v1 = v2). + { intros. inv H; inv H0; congruence. } + assert (B: forall p v1 v2, + extcall_arg_pair rs m p v1 -> extcall_arg_pair rs m p v2 -> v1 = v2). + { intros. inv H; inv H0. + eapply A; eauto. + f_equal; eapply A; eauto. } + assert (C: forall ll vl1, list_forall2 (extcall_arg_pair rs m) ll vl1 -> + forall vl2, list_forall2 (extcall_arg_pair rs m) ll vl2 -> vl1 = vl2). + { + induction 1; intros vl2 EA; inv EA. + auto. + f_equal; eauto. } + intros. eapply C; eauto. +Qed. + +Lemma semantics_determinate: forall p, determinate (semantics p). +Proof. +Ltac Equalities := + match goal with + | [ H1: ?a = ?b, H2: ?a = ?c |- _ ] => + rewrite H1 in H2; inv H2; Equalities + | _ => idtac + end. + intros; constructor; simpl; intros. +- (* determ *) + inv H; inv H0; Equalities. + + split. constructor. auto. + + unfold exec_bblock in H4. destruct (exec_body _ _ _ _); try discriminate. + rewrite H9 in H4. discriminate. + + unfold exec_bblock in H13. destruct (exec_body _ _ _ _); try discriminate. + rewrite H4 in H13. discriminate. + + assert (vargs0 = vargs) by (eapply eval_builtin_args_determ; eauto). subst vargs0. + exploit external_call_determ. eexact H6. eexact H13. intros [A B]. + split. auto. intros. destruct B; auto. subst. auto. + + assert (args0 = args) by (eapply extcall_arguments_determ; eauto). subst args0. + exploit external_call_determ. eexact H3. eexact H8. intros [A B]. + split. auto. intros. destruct B; auto. subst. auto. +- (* trace length *) + red; intros. inv H; simpl. + omega. + eapply external_call_trace_length; eauto. + eapply external_call_trace_length; eauto. +- (* initial states *) + inv H; inv H0. f_equal. congruence. +- (* final no step *) + assert (NOTNULL: forall b ofs, Vnullptr <> Vptr b ofs). + { intros; unfold Vnullptr; destruct Archi.ptr64; congruence. } + inv H. unfold Vzero in H0. red; intros; red; intros. + inv H; rewrite H0 in *; eelim NOTNULL; eauto. +- (* final states *) + inv H; inv H0. congruence. +Qed. + +Definition data_preg (r: preg) : bool :=
+ match r with
+ | RA => false
+ | IR GPR31 => false
+ | IR GPR8 => false
+ | IR _ => true
+ | FR _ => true
+ | PC => false
+ end.
+
+(** Determinacy of the [Asm] semantics. *)
+
+(* TODO.
+
+Remark extcall_arguments_determ:
+ forall rs m sg args1 args2,
+ extcall_arguments rs m sg args1 -> extcall_arguments rs m sg args2 -> args1 = args2.
+Proof.
+ intros until m.
+ assert (A: forall l v1 v2,
+ extcall_arg rs m l v1 -> extcall_arg rs m l v2 -> v1 = v2).
+ { intros. inv H; inv H0; congruence. }
+ assert (B: forall p v1 v2,
+ extcall_arg_pair rs m p v1 -> extcall_arg_pair rs m p v2 -> v1 = v2).
+ { intros. inv H; inv H0.
+ eapply A; eauto.
+ f_equal; eapply A; eauto. }
+ assert (C: forall ll vl1, list_forall2 (extcall_arg_pair rs m) ll vl1 ->
+ forall vl2, list_forall2 (extcall_arg_pair rs m) ll vl2 -> vl1 = vl2).
+ {
+ induction 1; intros vl2 EA; inv EA.
+ auto.
+ f_equal; eauto. }
+ intros. eapply C; eauto.
+Qed.
+
+Lemma semantics_determinate: forall p, determinate (semantics p).
+Proof.
+Ltac Equalities :=
+ match goal with
+ | [ H1: ?a = ?b, H2: ?a = ?c |- _ ] =>
+ rewrite H1 in H2; inv H2; Equalities
+ | _ => idtac
+ end.
+ intros; constructor; simpl; intros.
+- (* determ *)
+ inv H; inv H0; Equalities.
+ split. constructor. auto.
+ discriminate.
+ discriminate.
+ assert (vargs0 = vargs) by (eapply eval_builtin_args_determ; eauto). subst vargs0.
+ exploit external_call_determ. eexact H5. eexact H11. intros [A B].
+ split. auto. intros. destruct B; auto. subst. auto.
+ assert (args0 = args) by (eapply extcall_arguments_determ; eauto). subst args0.
+ exploit external_call_determ. eexact H3. eexact H8. intros [A B].
+ split. auto. intros. destruct B; auto. subst. auto.
+- (* trace length *)
+ red; intros. inv H; simpl.
+ omega.
+ eapply external_call_trace_length; eauto.
+ eapply external_call_trace_length; eauto.
+- (* initial states *)
+ inv H; inv H0. f_equal. congruence.
+- (* final no step *)
+ assert (NOTNULL: forall b ofs, Vnullptr <> Vptr b ofs).
+ { intros; unfold Vnullptr; destruct Archi.ptr64; congruence. }
+ inv H. unfold Vzero in H0. red; intros; red; intros.
+ inv H; rewrite H0 in *; eelim NOTNULL; eauto.
+- (* final states *)
+ inv H; inv H0. congruence.
+Qed.
+*)
diff --git a/mppa_k1c/Asmblockgen.v b/mppa_k1c/Asmblockgen.v new file mode 100644 index 00000000..e16c701f --- /dev/null +++ b/mppa_k1c/Asmblockgen.v @@ -0,0 +1,943 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, INRIA Paris-Rocquencourt *) +(* Prashanth Mundkur, SRI International *) +(* *) +(* Copyright Institut National de Recherche en Informatique et en *) +(* Automatique. All rights reserved. This file is distributed *) +(* under the terms of the INRIA Non-Commercial License Agreement. *) +(* *) +(* The contributions by Prashanth Mundkur are reused and adapted *) +(* under the terms of a Contributor License Agreement between *) +(* SRI International and INRIA. *) +(* *) +(* *********************************************************************) + +(** Translation from Machblock to K1c assembly language (Asmblock) *) + +Require Archi. +Require Import Coqlib Errors. +Require Import AST Integers Floats Memdata. +Require Import Op Locations Machblock Asmblock. + +Local Open Scope string_scope. +Local Open Scope error_monad_scope. + +(** The code generation functions take advantage of several + characteristics of the [Mach] code generated by earlier passes of the + compiler, mostly that argument and result registers are of the correct + types. These properties are true by construction, but it's easier to + recheck them during code generation and fail if they do not hold. *) + +(** Extracting integer or float registers. *) + +Definition ireg_of (r: mreg) : res ireg := + match preg_of r with IR mr => OK mr | _ => Error(msg "Asmgen.ireg_of") end. + +Definition freg_of (r: mreg) : res freg := + match preg_of r with IR mr => OK mr | _ => Error(msg "Asmgen.freg_of") end. + +(* +(** Decomposition of 32-bit integer constants. They are split into either + small signed immediates that fit in 12-bits, or, if they do not fit, + into a (20-bit hi, 12-bit lo) pair where lo is sign-extended. *) + +*) +Inductive immed32 : Type := + | Imm32_single (imm: int). + +Definition make_immed32 (val: int) := Imm32_single val. + +(** Likewise, for 64-bit integer constants. *) +Inductive immed64 : Type := + | Imm64_single (imm: int64) +. + +(* For now, let's suppose all instructions of K1c can handle 64-bits immediate *) +Definition make_immed64 (val: int64) := Imm64_single val. + +Notation "a ::g b" := (cons (A:=instruction) a b) (at level 49, right associativity). +Notation "a ::i b" := (cons (A:=basic) a b) (at level 49, right associativity). +Notation "a ::b lb" := ((bblock_single_inst a) :: lb) (at level 49, right associativity). +Notation "a ++g b" := (app (A:=instruction) a b) (at level 49, right associativity). + +(** Smart constructors for arithmetic operations involving + a 32-bit or 64-bit integer constant. Depending on whether the + constant fits in 12 bits or not, one or several instructions + are generated as required to perform the operation + and prepended to the given instruction sequence [k]. *) + +Definition loadimm32 (r: ireg) (n: int) := + match make_immed32 n with + | Imm32_single imm => Pmake r imm + end. + +Definition opimm32 (op: arith_name_rrr) + (opimm: arith_name_rri32) + (rd rs: ireg) (n: int) := + match make_immed32 n with + | Imm32_single imm => opimm rd rs imm + end. + +Definition addimm32 := opimm32 Paddw Paddiw. +Definition andimm32 := opimm32 Pandw Pandiw. +Definition orimm32 := opimm32 Porw Poriw. +Definition xorimm32 := opimm32 Pxorw Pxoriw. +(* +Definition sltimm32 := opimm32 Psltw Psltiw. +Definition sltuimm32 := opimm32 Psltuw Psltiuw. +*) + +Definition loadimm64 (r: ireg) (n: int64) := + match make_immed64 n with + | Imm64_single imm => Pmakel r imm + end. + +Definition opimm64 (op: arith_name_rrr) + (opimm: arith_name_rri64) + (rd rs: ireg) (n: int64) := + match make_immed64 n with + | Imm64_single imm => opimm rd rs imm +end. + +Definition addimm64 := opimm64 Paddl Paddil. +Definition orimm64 := opimm64 Porl Poril. +Definition andimm64 := opimm64 Pandl Pandil. +Definition xorimm64 := opimm64 Pxorl Pxoril. + +(* +Definition sltimm64 := opimm64 Psltl Psltil. +Definition sltuimm64 := opimm64 Psltul Psltiul. +*) + +Definition cast32signed (rd rs: ireg) := + if (ireg_eq rd rs) + then Pcvtw2l rd + else Pmvw2l rd rs + . + +Definition addptrofs (rd rs: ireg) (n: ptrofs) := + if Ptrofs.eq_dec n Ptrofs.zero then + Pmv rd rs + else + addimm64 rd rs (Ptrofs.to_int64 n). + +(** Translation of conditional branches. *) + +Definition transl_comp + (c: comparison) (s: signedness) (r1 r2: ireg) (lbl: label) (k: code) : list instruction := + Pcompw (itest_for_cmp c s) RTMP r1 r2 ::g Pcb BTwnez RTMP lbl ::g k. + +Definition transl_compl + (c: comparison) (s: signedness) (r1 r2: ireg) (lbl: label) (k: code) : list instruction := + Pcompl (itest_for_cmp c s) RTMP r1 r2 ::g Pcb BTwnez RTMP lbl ::g k. + +Definition select_comp (n: int) (c: comparison) : option comparison := + if Int.eq n Int.zero then + match c with + | Ceq => Some Ceq + | Cne => Some Cne + | _ => None + end + else + None + . + +Definition transl_opt_compuimm + (n: int) (c: comparison) (r1: ireg) (lbl: label) (k: code) : list instruction := + if Int.eq n Int.zero then + match c with + | Ceq => Pcbu BTweqz r1 lbl ::g k + | Cne => Pcbu BTwnez r1 lbl ::g k + | _ => loadimm32 RTMP n ::g (transl_comp c Unsigned r1 RTMP lbl k) + end + else + loadimm32 RTMP n ::g (transl_comp c Unsigned r1 RTMP lbl k) + . + +(* Definition transl_opt_compuimm + (n: int) (c: comparison) (r1: ireg) (lbl: label) (k: code) : list instruction := + loadimm32 RTMP n ::g (transl_comp c Unsigned r1 RTMP lbl k). *) + +(* match select_comp n c with + | Some Ceq => Pcbu BTweqz r1 lbl ::g k + | Some Cne => Pcbu BTwnez r1 lbl ::g k + | Some _ => nil (* Never happens *) + | None => loadimm32 RTMP n ::g (transl_comp c Unsigned r1 RTMP lbl k) + end + . + *) + +Definition select_compl (n: int64) (c: comparison) : option comparison := + if Int64.eq n Int64.zero then + match c with + | Ceq => Some Ceq + | Cne => Some Cne + | _ => None + end + else + None + . + +Definition transl_opt_compluimm + (n: int64) (c: comparison) (r1: ireg) (lbl: label) (k: code) : list instruction := + if Int64.eq n Int64.zero then + match c with + | Ceq => Pcbu BTdeqz r1 lbl ::g k + | Cne => Pcbu BTdnez r1 lbl ::g k + | _ => loadimm64 RTMP n ::g (transl_compl c Unsigned r1 RTMP lbl k) + end + else + loadimm64 RTMP n ::g (transl_compl c Unsigned r1 RTMP lbl k) + . + +(* match select_compl n c with + | Some Ceq => Pcbu BTdeqz r1 lbl ::g k + | Some Cne => Pcbu BTdnez r1 lbl ::g k + | Some _ => nil (* Never happens *) + | None => loadimm64 RTMP n ::g (transl_compl c Unsigned r1 RTMP lbl k) + end + . + *) + +Definition transl_cbranch + (cond: condition) (args: list mreg) (lbl: label) (k: code) : res (list instruction ) := + match cond, args with + | Ccompuimm c n, a1 :: nil => + do r1 <- ireg_of a1; + OK (transl_opt_compuimm n c r1 lbl k) + | Ccomp c, a1 :: a2 :: nil => + do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (transl_comp c Signed r1 r2 lbl k) + | Ccompu c, a1 :: a2 :: nil => + do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (transl_comp c Unsigned r1 r2 lbl k) + | Ccompimm c n, a1 :: nil => + do r1 <- ireg_of a1; + OK (if Int.eq n Int.zero then + Pcb (btest_for_cmpswz c) r1 lbl ::g k + else + loadimm32 RTMP n ::g (transl_comp c Signed r1 RTMP lbl k) + ) + | Ccompluimm c n, a1 :: nil => + do r1 <- ireg_of a1; + OK (transl_opt_compluimm n c r1 lbl k) + | Ccompl c, a1 :: a2 :: nil => + do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (transl_compl c Signed r1 r2 lbl k) + | Ccomplu c, a1 :: a2 :: nil => + do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (transl_compl c Unsigned r1 r2 lbl k) + | Ccomplimm c n, a1 :: nil => + do r1 <- ireg_of a1; + OK (if Int64.eq n Int64.zero then + Pcb (btest_for_cmpsdz c) r1 lbl ::g k + else + loadimm64 RTMP n ::g (transl_compl c Signed r1 RTMP lbl k) + ) +(*| Ccompf c, f1 :: f2 :: nil => + do r1 <- freg_of f1; do r2 <- freg_of f2; + let (insn, normal) := transl_cond_float c rd r1 r2 in + OK (insn :: if normal then k else Pxoriw rd rd Int.one :: k) + | Cnotcompf c, f1 :: f2 :: nil => + do r1 <- freg_of f1; do r2 <- freg_of f2; + let (insn, normal) := transl_cond_float c rd r1 r2 in + OK (insn :: if normal then Pxoriw rd rd Int.one :: k else k) + | Ccompfs c, f1 :: f2 :: nil => + do r1 <- freg_of f1; do r2 <- freg_of f2; + let (insn, normal) := transl_cond_single c rd r1 r2 in + OK (insn :: if normal then k else Pxoriw rd rd Int.one :: k) + | Cnotcompfs c, f1 :: f2 :: nil => + do r1 <- freg_of f1; do r2 <- freg_of f2; + let (insn, normal) := transl_cond_single c rd r1 r2 in + OK (insn :: if normal then Pxoriw rd rd Int.one :: k else k) +*)| _, _ => + Error(msg "Asmgen.transl_cbranch") + end. + +(** Translation of a condition operator. The generated code sets the + [rd] target register to 0 or 1 depending on the truth value of the + condition. *) + +Definition transl_cond_int32s (cmp: comparison) (rd r1 r2: ireg) (k: bcode) := + Pcompw (itest_for_cmp cmp Signed) rd r1 r2 ::i k. + +Definition transl_cond_int32u (cmp: comparison) (rd r1 r2: ireg) (k: bcode) := + Pcompw (itest_for_cmp cmp Unsigned) rd r1 r2 ::i k. + +Definition transl_cond_int64s (cmp: comparison) (rd r1 r2: ireg) (k: bcode) := + Pcompl (itest_for_cmp cmp Signed) rd r1 r2 ::i k. + +Definition transl_cond_int64u (cmp: comparison) (rd r1 r2: ireg) (k: bcode) := + Pcompl (itest_for_cmp cmp Unsigned) rd r1 r2 ::i k. + +Definition transl_condimm_int32s (cmp: comparison) (rd r1: ireg) (n: int) (k: bcode) := + Pcompiw (itest_for_cmp cmp Signed) rd r1 n ::i k. + +Definition transl_condimm_int32u (cmp: comparison) (rd r1: ireg) (n: int) (k: bcode) := + Pcompiw (itest_for_cmp cmp Unsigned) rd r1 n ::i k. + +Definition transl_condimm_int64s (cmp: comparison) (rd r1: ireg) (n: int64) (k: bcode) := + Pcompil (itest_for_cmp cmp Signed) rd r1 n ::i k. + +Definition transl_condimm_int64u (cmp: comparison) (rd r1: ireg) (n: int64) (k: bcode) := + Pcompil (itest_for_cmp cmp Unsigned) rd r1 n ::i k. + +Definition transl_cond_op + (cond: condition) (rd: ireg) (args: list mreg) (k: bcode) := + match cond, args with + | Ccomp c, a1 :: a2 :: nil => + do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (transl_cond_int32s c rd r1 r2 k) + | Ccompu c, a1 :: a2 :: nil => + do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (transl_cond_int32u c rd r1 r2 k) + | Ccompimm c n, a1 :: nil => + do r1 <- ireg_of a1; + OK (transl_condimm_int32s c rd r1 n k) + | Ccompuimm c n, a1 :: nil => + do r1 <- ireg_of a1; + OK (transl_condimm_int32u c rd r1 n k) + | Ccompl c, a1 :: a2 :: nil => + do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (transl_cond_int64s c rd r1 r2 k) + | Ccomplu c, a1 :: a2 :: nil => + do r1 <- ireg_of a1; do r2 <- ireg_of a2; + OK (transl_cond_int64u c rd r1 r2 k) + | Ccomplimm c n, a1 :: nil => + do r1 <- ireg_of a1; + OK (transl_condimm_int64s c rd r1 n k) + | Ccompluimm c n, a1 :: nil => + do r1 <- ireg_of a1; + OK (transl_condimm_int64u c rd r1 n k) +(*| Ccompf c, f1 :: f2 :: nil => + do r1 <- freg_of f1; do r2 <- freg_of f2; + let (insn, normal) := transl_cond_float c rd r1 r2 in + OK (insn :: if normal then k else Pxoriw rd rd Int.one :: k) + | Cnotcompf c, f1 :: f2 :: nil => + do r1 <- freg_of f1; do r2 <- freg_of f2; + let (insn, normal) := transl_cond_float c rd r1 r2 in + OK (insn :: if normal then Pxoriw rd rd Int.one :: k else k) + | Ccompfs c, f1 :: f2 :: nil => + do r1 <- freg_of f1; do r2 <- freg_of f2; + let (insn, normal) := transl_cond_single c rd r1 r2 in + OK (insn :: if normal then k else Pxoriw rd rd Int.one :: k) + | Cnotcompfs c, f1 :: f2 :: nil => + do r1 <- freg_of f1; do r2 <- freg_of f2; + let (insn, normal) := transl_cond_single c rd r1 r2 in + OK (insn :: if normal then Pxoriw rd rd Int.one :: k else k) +*)| _, _ => + Error(msg "Asmgen.transl_cond_op") +end. + +(** Translation of the arithmetic operation [r <- op(args)]. + The corresponding instructions are prepended to [k]. *) + +Definition transl_op + (op: operation) (args: list mreg) (res: mreg) (k: bcode) := + match op, args with + | Omove, a1 :: nil => + match preg_of res, preg_of a1 with + | IR r, IR a => OK (Pmv r a ::i k) + | _ , _ => Error(msg "Asmgen.Omove") + end + | Ointconst n, nil => + do rd <- ireg_of res; + OK (loadimm32 rd n ::i k) + | Olongconst n, nil => + do rd <- ireg_of res; + OK (loadimm64 rd n ::i k) +(*| Ofloatconst f, nil => + do rd <- freg_of res; + OK (if Float.eq_dec f Float.zero + then Pfcvtdw rd GPR0 :: k + else Ploadfi rd f :: k) + | Osingleconst f, nil => + do rd <- freg_of res; + OK (if Float32.eq_dec f Float32.zero + then Pfcvtsw rd GPR0 :: k + else Ploadsi rd f :: k) +*)| Oaddrsymbol s ofs, nil => + do rd <- ireg_of res; + OK (if Archi.pic_code tt && negb (Ptrofs.eq ofs Ptrofs.zero) + then Ploadsymbol s Ptrofs.zero rd ::i addptrofs rd rd ofs ::i k + else Ploadsymbol s ofs rd ::i k) + | Oaddrstack n, nil => + do rd <- ireg_of res; + OK (addptrofs rd SP n ::i k) + + | Ocast8signed, a1 :: nil => + do rd <- ireg_of res; do rs <- ireg_of a1; + OK (Pslliw rd rs (Int.repr 24) ::i Psraiw rd rd (Int.repr 24) ::i k) + | Ocast16signed, a1 :: nil => + do rd <- ireg_of res; do rs <- ireg_of a1; + OK (Pslliw rd rs (Int.repr 16) ::i Psraiw rd rd (Int.repr 16) ::i k) + | Oadd, a1 :: a2 :: nil => + do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; + OK (Paddw rd rs1 rs2 ::i k) + | Oaddimm n, a1 :: nil => + do rd <- ireg_of res; do rs <- ireg_of a1; + OK (addimm32 rd rs n ::i k) + | Oneg, a1 :: nil => + do rd <- ireg_of res; do rs <- ireg_of a1; + OK (Pnegw rd rs ::i k) + | Osub, a1 :: a2 :: nil => + do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; + OK (Psubw rd rs1 rs2 ::i k) + | Omul, a1 :: a2 :: nil => + do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; + OK (Pmulw rd rs1 rs2 ::i k) +(*| Omulhs, a1 :: a2 :: nil => + do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; + OK (Pmulhw rd rs1 rs2 :: k) + | Omulhu, a1 :: a2 :: nil => + do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; + OK (Pmulhuw rd rs1 rs2 :: k) + | Odiv, a1 :: a2 :: nil => + do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; + OK (Pdivw rd rs1 rs2 :: k) + | Odivu, a1 :: a2 :: nil => + do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; + OK (Pdivuw rd rs1 rs2 :: k) + | Omod, a1 :: a2 :: nil => + do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; + OK (Premw rd rs1 rs2 :: k) + | Omodu, a1 :: a2 :: nil => + do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; + OK (Premuw rd rs1 rs2 :: k) +*)| Oand, a1 :: a2 :: nil => + do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; + OK (Pandw rd rs1 rs2 ::i k) + | Oandimm n, a1 :: nil => + do rd <- ireg_of res; do rs <- ireg_of a1; + OK (andimm32 rd rs n ::i k) + | Oor, a1 :: a2 :: nil => + do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; + OK (Porw rd rs1 rs2 ::i k) + | Oorimm n, a1 :: nil => + do rd <- ireg_of res; do rs <- ireg_of a1; + OK (orimm32 rd rs n ::i k) + | Oxor, a1 :: a2 :: nil => + do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; + OK (Pxorw rd rs1 rs2 ::i k) + | Oxorimm n, a1 :: nil => + do rd <- ireg_of res; do rs <- ireg_of a1; + OK (xorimm32 rd rs n ::i k) + | Oshl, a1 :: a2 :: nil => + do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; + OK (Psllw rd rs1 rs2 ::i k) + | Oshlimm n, a1 :: nil => + do rd <- ireg_of res; do rs <- ireg_of a1; + OK (Pslliw rd rs n ::i k) + | Oshr, a1 :: a2 :: nil => + do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; + OK (Psraw rd rs1 rs2 ::i k) + | Oshrimm n, a1 :: nil => + do rd <- ireg_of res; do rs <- ireg_of a1; + OK (Psraiw rd rs n ::i k) + | Oshru, a1 :: a2 :: nil => + do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; + OK (Psrlw rd rs1 rs2 ::i k) + | Oshruimm n, a1 :: nil => + do rd <- ireg_of res; do rs <- ireg_of a1; + OK (Psrliw rd rs n ::i k) + | Oshrximm n, a1 :: nil => + do rd <- ireg_of res; do rs <- ireg_of a1; + OK (if Int.eq n Int.zero then Pmv rd rs ::i k else + Psraiw GPR31 rs (Int.repr 31) ::i + Psrliw GPR31 GPR31 (Int.sub Int.iwordsize n) ::i + Paddw GPR31 rs GPR31 ::i + Psraiw rd GPR31 n ::i k) + + (* [Omakelong], [Ohighlong] should not occur *) + | Olowlong, a1 :: nil => + do rd <- ireg_of res; do rs <- ireg_of a1; + OK (Pcvtl2w rd rs ::i k) + | Ocast32signed, a1 :: nil => + do rd <- ireg_of res; do rs <- ireg_of a1; + OK (cast32signed rd rs ::i k) + | Ocast32unsigned, a1 :: nil => + do rd <- ireg_of res; do rs <- ireg_of a1; + assertion (ireg_eq rd rs); + OK (Pcvtw2l rd ::i Psllil rd rd (Int.repr 32) ::i Psrlil rd rd (Int.repr 32) ::i k) + | Oaddl, a1 :: a2 :: nil => + do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; + OK (Paddl rd rs1 rs2 ::i k) + | Oaddlimm n, a1 :: nil => + do rd <- ireg_of res; do rs <- ireg_of a1; + OK (addimm64 rd rs n ::i k) + | Onegl, a1 :: nil => + do rd <- ireg_of res; do rs <- ireg_of a1; + OK (Pnegl rd rs ::i k) + | Osubl, a1 :: a2 :: nil => + do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; + OK (Psubl rd rs1 rs2 ::i k) + | Omull, a1 :: a2 :: nil => + do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; + OK (Pmull rd rs1 rs2 ::i k) +(*| Omullhs, a1 :: a2 :: nil => + do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; + OK (Pmulhl rd rs1 rs2 :: k) + | Omullhu, a1 :: a2 :: nil => + do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; + OK (Pmulhul rd rs1 rs2 :: k) + | Odivl, a1 :: a2 :: nil => + do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; + OK (Pdivl rd rs1 rs2 :: k) + | Odivlu, a1 :: a2 :: nil => + do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; + OK (Pdivul rd rs1 rs2 :: k) + | Omodl, a1 :: a2 :: nil => + do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; + OK (Preml rd rs1 rs2 :: k) + | Omodlu, a1 :: a2 :: nil => + do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; + OK (Premul rd rs1 rs2 :: k) +*)| Oandl, a1 :: a2 :: nil => + do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; + OK (Pandl rd rs1 rs2 ::i k) + | Oandlimm n, a1 :: nil => + do rd <- ireg_of res; do rs <- ireg_of a1; + OK (andimm64 rd rs n ::i k) + | Oorl, a1 :: a2 :: nil => + do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; + OK (Porl rd rs1 rs2 ::i k) + | Oorlimm n, a1 :: nil => + do rd <- ireg_of res; do rs <- ireg_of a1; + OK (orimm64 rd rs n ::i k) + | Oxorl, a1 :: a2 :: nil => + do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; + OK (Pxorl rd rs1 rs2 ::i k) + | Oxorlimm n, a1 :: nil => + do rd <- ireg_of res; do rs <- ireg_of a1; + OK (xorimm64 rd rs n ::i k) + | Oshll, a1 :: a2 :: nil => + do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; + OK (Pslll rd rs1 rs2 ::i k) + | Oshllimm n, a1 :: nil => + do rd <- ireg_of res; do rs <- ireg_of a1; + OK (Psllil rd rs n ::i k) + | Oshrl, a1 :: a2 :: nil => + do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; + OK (Psral rd rs1 rs2 ::i k) + | Oshrlimm n, a1 :: nil => + do rd <- ireg_of res; do rs <- ireg_of a1; + OK (Psrail rd rs n ::i k) + | Oshrlu, a1 :: a2 :: nil => + do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; + OK (Psrll rd rs1 rs2 ::i k) + | Oshrluimm n, a1 :: nil => + do rd <- ireg_of res; do rs <- ireg_of a1; + OK (Psrlil rd rs n ::i k) +(*| Oshrxlimm n, a1 :: nil => + do rd <- ireg_of res; do rs <- ireg_of a1; + OK (if Int.eq n Int.zero then Pmv rd rs :: k else + Psrail GPR31 rs (Int.repr 63) :: + Psrlil GPR31 GPR31 (Int.sub Int64.iwordsize' n) :: + Paddl GPR31 rs GPR31 :: + Psrail rd GPR31 n :: k) + +*)| Onegf, a1 :: nil => + do rd <- freg_of res; do rs <- freg_of a1; + OK (Pfnegd rd rs ::i k) +(*| Oabsf, a1 :: nil => + do rd <- freg_of res; do rs <- freg_of a1; + OK (Pfabsd rd rs :: k) + | Oaddf, a1 :: a2 :: nil => + do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2; + OK (Pfaddd rd rs1 rs2 :: k) + | Osubf, a1 :: a2 :: nil => + do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2; + OK (Pfsubd rd rs1 rs2 :: k) + | Omulf, a1 :: a2 :: nil => + do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2; + OK (Pfmuld rd rs1 rs2 :: k) + | Odivf, a1 :: a2 :: nil => + do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2; + OK (Pfdivd rd rs1 rs2 :: k) + + | Onegfs, a1 :: nil => + do rd <- freg_of res; do rs <- freg_of a1; + OK (Pfnegs rd rs :: k) + | Oabsfs, a1 :: nil => + do rd <- freg_of res; do rs <- freg_of a1; + OK (Pfabss rd rs :: k) + | Oaddfs, a1 :: a2 :: nil => + do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2; + OK (Pfadds rd rs1 rs2 :: k) + | Osubfs, a1 :: a2 :: nil => + do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2; + OK (Pfsubs rd rs1 rs2 :: k) + | Omulfs, a1 :: a2 :: nil => + do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2; + OK (Pfmuls rd rs1 rs2 :: k) + | Odivfs, a1 :: a2 :: nil => + do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2; + OK (Pfdivs rd rs1 rs2 :: k) + + | Osingleoffloat, a1 :: nil => + do rd <- freg_of res; do rs <- freg_of a1; + OK (Pfcvtsd rd rs :: k) + | Ofloatofsingle, a1 :: nil => + do rd <- freg_of res; do rs <- freg_of a1; + OK (Pfcvtds rd rs :: k) + + | Ointoffloat, a1 :: nil => + do rd <- ireg_of res; do rs <- freg_of a1; + OK (Pfcvtwd rd rs :: k) + | Ointuoffloat, a1 :: nil => + do rd <- ireg_of res; do rs <- freg_of a1; + OK (Pfcvtwud rd rs :: k) + | Ofloatofint, a1 :: nil => + do rd <- freg_of res; do rs <- ireg_of a1; + OK (Pfcvtdw rd rs :: k) + | Ofloatofintu, a1 :: nil => + do rd <- freg_of res; do rs <- ireg_of a1; + OK (Pfcvtdwu rd rs :: k) + | Ointofsingle, a1 :: nil => + do rd <- ireg_of res; do rs <- freg_of a1; + OK (Pfcvtws rd rs :: k) + | Ointuofsingle, a1 :: nil => + do rd <- ireg_of res; do rs <- freg_of a1; + OK (Pfcvtwus rd rs :: k) + | Osingleofint, a1 :: nil => + do rd <- freg_of res; do rs <- ireg_of a1; + OK (Pfcvtsw rd rs :: k) + | Osingleofintu, a1 :: nil => + do rd <- freg_of res; do rs <- ireg_of a1; + OK (Pfcvtswu rd rs :: k) + + | Olongoffloat, a1 :: nil => + do rd <- ireg_of res; do rs <- freg_of a1; + OK (Pfcvtld rd rs :: k) + | Olonguoffloat, a1 :: nil => + do rd <- ireg_of res; do rs <- freg_of a1; + OK (Pfcvtlud rd rs :: k) + | Ofloatoflong, a1 :: nil => + do rd <- freg_of res; do rs <- ireg_of a1; + OK (Pfcvtdl rd rs :: k) + | Ofloatoflongu, a1 :: nil => + do rd <- freg_of res; do rs <- ireg_of a1; + OK (Pfcvtdlu rd rs :: k) + | Olongofsingle, a1 :: nil => + do rd <- ireg_of res; do rs <- freg_of a1; + OK (Pfcvtls rd rs :: k) + | Olonguofsingle, a1 :: nil => + do rd <- ireg_of res; do rs <- freg_of a1; + OK (Pfcvtlus rd rs :: k) + | Osingleoflong, a1 :: nil => + do rd <- freg_of res; do rs <- ireg_of a1; + OK (Pfcvtsl rd rs :: k) + | Osingleoflongu, a1 :: nil => + do rd <- freg_of res; do rs <- ireg_of a1; + OK (Pfcvtslu rd rs :: k) + +*)| Ocmp cmp, _ => + do rd <- ireg_of res; + transl_cond_op cmp rd args k + + | _, _ => + Error(msg "Asmgen.transl_op") + end. + +(** Accessing data in the stack frame. *) + +Definition indexed_memory_access + (mk_instr: ireg -> offset -> basic) + (base: ireg) (ofs: ptrofs) := + match make_immed64 (Ptrofs.to_int64 ofs) with + | Imm64_single imm => + mk_instr base (Ofsimm (Ptrofs.of_int64 imm)) +(*| Imm64_pair hi lo => + Pluil GPR31 hi :: Paddl GPR31 base GPR31 :: mk_instr GPR31 (Ofsimm (Ptrofs.of_int64 lo)) :: k + | Imm64_large imm => + Pmake GPR31 imm :: Paddl GPR31 base GPR31 :: mk_instr GPR31 (Ofsimm Ptrofs.zero) :: k +*)end. + +Definition loadind (base: ireg) (ofs: ptrofs) (ty: typ) (dst: mreg) (k: bcode) := + match ty, preg_of dst with + | Tint, IR rd => OK (indexed_memory_access (Plw rd) base ofs ::i k) + | Tlong, IR rd => OK (indexed_memory_access (Pld rd) base ofs ::i k) + | Tsingle, IR rd => OK (indexed_memory_access (Pfls rd) base ofs ::i k) + | Tfloat, IR rd => OK (indexed_memory_access (Pfld rd) base ofs ::i k) + | Tany32, IR rd => OK (indexed_memory_access (Plw_a rd) base ofs ::i k) + | Tany64, IR rd => OK (indexed_memory_access (Pld_a rd) base ofs ::i k) + | _, _ => Error (msg "Asmgen.loadind") + end. + +Definition storeind (src: mreg) (base: ireg) (ofs: ptrofs) (ty: typ) (k: bcode) := + match ty, preg_of src with + | Tint, IR rd => OK (indexed_memory_access (Psw rd) base ofs ::i k) + | Tlong, IR rd => OK (indexed_memory_access (Psd rd) base ofs ::i k) + | Tsingle, IR rd => OK (indexed_memory_access (Pfss rd) base ofs ::i k) + | Tfloat, IR rd => OK (indexed_memory_access (Pfsd rd) base ofs ::i k) + | Tany32, IR rd => OK (indexed_memory_access (Psw_a rd) base ofs ::i k) + | Tany64, IR rd => OK (indexed_memory_access (Psd_a rd) base ofs ::i k) + | _, _ => Error (msg "Asmgen.storeind") + end. + +Definition loadind_ptr (base: ireg) (ofs: ptrofs) (dst: ireg) := + indexed_memory_access (Pld dst) base ofs. + +Definition storeind_ptr (src: ireg) (base: ireg) (ofs: ptrofs) := + indexed_memory_access (Psd src) base ofs. + +(** Translation of memory accesses: loads, and stores. *) + +Definition transl_memory_access + (mk_instr: ireg -> offset -> basic) + (addr: addressing) (args: list mreg) (k: bcode) : res bcode := + match addr, args with + | Aindexed ofs, a1 :: nil => + do rs <- ireg_of a1; + OK (indexed_memory_access mk_instr rs ofs ::i k) + | Aglobal id ofs, nil => + OK (Ploadsymbol id ofs GPR31 ::i (mk_instr GPR31 (Ofsimm Ptrofs.zero) ::i k)) + | Ainstack ofs, nil => + OK (indexed_memory_access mk_instr SP ofs ::i k) + | _, _ => + Error(msg "Asmgen.transl_memory_access") + end. + +Definition transl_load (chunk: memory_chunk) (addr: addressing) + (args: list mreg) (dst: mreg) (k: bcode) : res bcode := + match chunk with + | Mint8signed => + do r <- ireg_of dst; + transl_memory_access (Plb r) addr args k + | Mint8unsigned => + do r <- ireg_of dst; + transl_memory_access (Plbu r) addr args k + | Mint16signed => + do r <- ireg_of dst; + transl_memory_access (Plh r) addr args k + | Mint16unsigned => + do r <- ireg_of dst; + transl_memory_access (Plhu r) addr args k + | Mint32 => + do r <- ireg_of dst; + transl_memory_access (Plw r) addr args k + | Mint64 => + do r <- ireg_of dst; + transl_memory_access (Pld r) addr args k + | Mfloat32 => + do r <- freg_of dst; + transl_memory_access (Pfls r) addr args k + | Mfloat64 => + do r <- freg_of dst; + transl_memory_access (Pfld r) addr args k + | _ => + Error (msg "Asmgen.transl_load") + end. + +Definition transl_store (chunk: memory_chunk) (addr: addressing) + (args: list mreg) (src: mreg) (k: bcode) : res bcode := + match chunk with + | Mint8signed | Mint8unsigned => + do r <- ireg_of src; + transl_memory_access (Psb r) addr args k + | Mint16signed | Mint16unsigned => + do r <- ireg_of src; + transl_memory_access (Psh r) addr args k + | Mint32 => + do r <- ireg_of src; + transl_memory_access (Psw r) addr args k + | Mint64 => + do r <- ireg_of src; + transl_memory_access (Psd r) addr args k + | Mfloat32 => + do r <- freg_of src; + transl_memory_access (Pfss r) addr args k + | Mfloat64 => + do r <- freg_of src; + transl_memory_access (Pfsd r) addr args k + | _ => + Error (msg "Asmgen.transl_store") + end. + +(** Function epilogue *) + +Definition make_epilogue (f: Machblock.function) (k: code) := + (loadind_ptr SP f.(fn_retaddr_ofs) GPR8) + ::g Pset RA GPR8 ::g Pfreeframe f.(fn_stacksize) f.(fn_link_ofs) ::g k. + +(** Translation of a Mach instruction. *) + +Definition transl_instr_basic (f: Machblock.function) (i: Machblock.basic_inst) + (ep: bool) (k: bcode) := + match i with + | MBgetstack ofs ty dst => + loadind SP ofs ty dst k + | MBsetstack src ofs ty => + storeind src SP ofs ty k + | MBgetparam ofs ty dst => + (* load via the frame pointer if it is valid *) + do c <- loadind FP ofs ty dst k; + OK (if ep then c + else (loadind_ptr SP f.(fn_link_ofs) FP) ::i c) + | MBop op args res => + transl_op op args res k + | MBload chunk addr args dst => + transl_load chunk addr args dst k + | MBstore chunk addr args src => + transl_store chunk addr args src k + end. + +Definition transl_instr_control (f: Machblock.function) (oi: option Machblock.control_flow_inst) + : res code := + match oi with + | None => OK nil + | Some i => + match i with +(*| Mcall sig (inl r) => + do r1 <- ireg_of r; OK (Pjal_r r1 sig :: k) +*) | MBcall sig (inr symb) => + OK ((Pcall symb) ::g nil) +(*| Mtailcall sig (inl r) => + do r1 <- ireg_of r; + OK (make_epilogue f (Pcall :: k)) +*) | MBtailcall sig (inr symb) => + OK (make_epilogue f ((Pgoto symb) ::g nil)) + | MBbuiltin ef args res => + OK (Pbuiltin ef (List.map (map_builtin_arg preg_of) args) (map_builtin_res preg_of res) ::g nil) +(* | Mlabel lbl => + OK (Plabel lbl ::i k) *) + | MBgoto lbl => + OK (Pj_l lbl ::g nil) + | MBcond cond args lbl => + transl_cbranch cond args lbl nil +(*| Mjumptable arg tbl => do r <- ireg_of arg; OK (Pbtbl r tbl :: k) +*) | MBreturn => + OK (make_epilogue f (Pret ::g nil)) + (*OK (make_epilogue f (Pj_r RA f.(Mach.fn_sig) :: k))*) + | _ => + Error (msg "Asmgen.transl_instr") + end + end. + +(* TODO - dans l'idée, transl_instr_control renvoie une liste d'instructions sous la forme : + * transl_instr_control _ _ _ = lb ++ (ctl :: nil), où lb est une liste de basics, ctl est un control_inst + + Il faut arriver à exprimer cet aspect là ; extraire le lb, le rajouter dans le body ; et extraire le ctl + qu'on met dans le exit +*) + +(** Translation of a code sequence *) + +Definition fp_is_parent (before: bool) (i: Machblock.basic_inst) : bool := + match i with + | MBsetstack src ofs ty => before + | MBgetparam ofs ty dst => negb (mreg_eq dst R10) + | MBop op args res => before && negb (mreg_eq res R10) + | _ => false + end. + +(** This is the naive definition that we no longer use because it + is not tail-recursive. It is kept as specification. *) + +Fixpoint transl_basic_code (f: Machblock.function) (il: list Machblock.basic_inst) (it1p: bool) := + match il with + | nil => OK nil + | i1 :: il' => + do k <- transl_basic_code f il' (fp_is_parent it1p i1); + transl_instr_basic f i1 it1p k + end. + +(* (** This is an equivalent definition in continuation-passing style + that runs in constant stack space. *) + +Fixpoint transl_basic_rec (f: Machblock.function) (il: list Machblock.basic_inst) + (it1p: bool) (k: bcode -> res bcode) := + match il with + | nil => k nil + | i1 :: il' => + transl_basic_rec f il' (fp_is_parent it1p i1) + (fun c1 => do c2 <- transl_instr_basic f i1 it1p c1; k c2) + end. + +Definition transl_basic_code' (f: Machblock.function) (il: list Machblock.basic_inst) (it1p: bool) := + transl_basic_rec f il it1p (fun c => OK c). *) + +(** Translation of a whole function. Note that we must check + that the generated code contains less than [2^32] instructions, + otherwise the offset part of the [PC] code pointer could wrap + around, leading to incorrect executions. *) + +(* Local Obligation Tactic := bblock_auto_correct. *) + +(* Program Definition gen_bblock_noctl (hd: list label) (c: list basic) := + match c with + | nil => {| header := hd; body := Pnop::nil; exit := None |} + | i::c => {| header := hd; body := i::c; exit := None |} + end. + *) + +(** Can generate two bblocks if the ctl is a PExpand (since the PExpand must be alone in its block) *) +Program Definition gen_bblocks (hd: list label) (c: list basic) (ctl: list instruction) := + match (extract_ctl ctl) with + | None => + match c with + | nil => {| header := hd; body := Pnop::nil; exit := None |} :: nil + | i::c => {| header := hd; body := ((i::c) ++ extract_basic ctl); exit := None |} :: nil + end +(* gen_bblock_noctl hd (c ++ (extract_basic ctl)) :: nil *) + | Some (PExpand (Pbuiltin ef args res)) => + match c with + | nil => {| header := hd; body := nil; exit := Some (PExpand (Pbuiltin ef args res)) |} :: nil + | _ => {| header := hd; body := c; exit := None |} + :: {| header := nil; body := nil; exit := Some (PExpand (Pbuiltin ef args res)) |} :: nil + end + | Some (PCtlFlow i) => {| header := hd; body := (c ++ extract_basic ctl); exit := Some (PCtlFlow i) |} :: nil + end +. +Next Obligation. + bblock_auto_correct. intros. constructor. apply not_eq_sym. auto. +Qed. Next Obligation. + bblock_auto_correct. +Qed. + +Definition transl_block (f: Machblock.function) (fb: Machblock.bblock) (ep: bool) : res (list bblock) := + do c <- transl_basic_code f fb.(Machblock.body) ep; + do ctl <- transl_instr_control f fb.(Machblock.exit); + OK (gen_bblocks fb.(Machblock.header) c ctl) +. + +Fixpoint transl_blocks (f: Machblock.function) (lmb: list Machblock.bblock) (ep: bool) := + match lmb with + | nil => OK nil + | mb :: lmb => + do lb <- transl_block f mb (if Machblock.header mb then ep else false); + do lb' <- transl_blocks f lmb false; + OK (lb ++ lb') + end +. + +Definition transl_function (f: Machblock.function) := + do lb <- transl_blocks f f.(Machblock.fn_code) true; + OK (mkfunction f.(Machblock.fn_sig) + (Pallocframe f.(fn_stacksize) f.(fn_link_ofs) ::b + Pget GPR8 RA ::b + storeind_ptr GPR8 SP f.(fn_retaddr_ofs) ::b lb)). + +Fixpoint size_blocks (l: bblocks): Z := + match l with + | nil => 0 + | b :: l => + (size b) + (size_blocks l) + end + . + +Definition transf_function (f: Machblock.function) : res Asmblock.function := + do tf <- transl_function f; + if zlt Ptrofs.max_unsigned (size_blocks tf.(fn_blocks)) + then Error (msg "code size exceeded") + else OK tf. + + +Definition transf_fundef (f: Machblock.fundef) : res Asmblock.fundef := + transf_partial_fundef transf_function f. + +Definition transf_program (p: Machblock.program) : res Asmblock.program := + transform_partial_program transf_fundef p. diff --git a/mppa_k1c/Asmblockgenproof.v b/mppa_k1c/Asmblockgenproof.v new file mode 100644 index 00000000..ee18e5e3 --- /dev/null +++ b/mppa_k1c/Asmblockgenproof.v @@ -0,0 +1,2143 @@ +(* *********************************************************************)
+(* *)
+(* The Compcert verified compiler *)
+(* *)
+(* Xavier Leroy, INRIA Paris-Rocquencourt *)
+(* *)
+(* Copyright Institut National de Recherche en Informatique et en *)
+(* Automatique. All rights reserved. This file is distributed *)
+(* under the terms of the INRIA Non-Commercial License Agreement. *)
+(* *)
+(* *********************************************************************)
+
+(** Correctness proof for RISC-V generation: main proof. *)
+
+Require Import Coqlib Errors.
+Require Import Integers Floats AST Linking.
+Require Import Values Memory Events Globalenvs Smallstep.
+Require Import Op Locations Machblock Conventions Asmblock.
+(* Require Import Asmgen Asmgenproof0 Asmgenproof1. *)
+Require Import Asmblockgen Asmblockgenproof0 Asmblockgenproof1.
+
+Module MB := Machblock.
+Module AB := Asmblock.
+
+Definition match_prog (p: Machblock.program) (tp: Asmblock.program) :=
+ match_program (fun _ f tf => transf_fundef f = OK tf) eq p tp.
+
+Lemma transf_program_match:
+ forall p tp, transf_program p = OK tp -> match_prog p tp.
+Proof.
+ intros. eapply match_transform_partial_program; eauto.
+Qed.
+
+Section PRESERVATION.
+
+Variable prog: Machblock.program.
+Variable tprog: Asmblock.program.
+Hypothesis TRANSF: match_prog prog tprog.
+Let ge := Genv.globalenv prog.
+Let tge := Genv.globalenv tprog.
+
+Lemma symbols_preserved:
+ forall (s: ident), Genv.find_symbol tge s = Genv.find_symbol ge s.
+Proof (Genv.find_symbol_match TRANSF).
+
+Lemma senv_preserved:
+ Senv.equiv ge tge.
+Proof (Genv.senv_match TRANSF).
+
+
+Lemma functions_translated:
+ forall b f,
+ Genv.find_funct_ptr ge b = Some f ->
+ exists tf,
+ Genv.find_funct_ptr tge b = Some tf /\ transf_fundef f = OK tf.
+Proof (Genv.find_funct_ptr_transf_partial TRANSF).
+
+Lemma functions_transl:
+ forall fb f tf,
+ Genv.find_funct_ptr ge fb = Some (Internal f) ->
+ transf_function f = OK tf ->
+ Genv.find_funct_ptr tge fb = Some (Internal tf).
+Proof.
+ intros. exploit functions_translated; eauto. intros [tf' [A B]].
+ monadInv B. rewrite H0 in EQ; inv EQ; auto.
+Qed.
+
+(** * Properties of control flow *)
+
+Lemma transf_function_no_overflow:
+ forall f tf,
+ transf_function f = OK tf -> size_blocks tf.(fn_blocks) <= Ptrofs.max_unsigned.
+Proof.
+ intros. monadInv H. destruct (zlt Ptrofs.max_unsigned (size_blocks x.(fn_blocks))); inv EQ0.
+ omega.
+Qed.
+
+(*
+Lemma exec_straight_exec:
+ forall fb f c ep tf tc c' rs m rs' m',
+ transl_code_at_pc ge (rs PC) fb f c ep tf tc ->
+ exec_straight tge tf tc rs m c' rs' m' ->
+ plus step tge (State rs m) E0 (State rs' m').
+Proof.
+ intros. inv H.
+ eapply exec_straight_steps_1; eauto.
+ eapply transf_function_no_overflow; eauto.
+ eapply functions_transl; eauto.
+Qed.
+
+Lemma exec_straight_at:
+ forall fb f c ep tf tc c' ep' tc' rs m rs' m',
+ transl_code_at_pc ge (rs PC) fb f c ep tf tc ->
+ transl_code f c' ep' = OK tc' ->
+ exec_straight tge tf tc rs m tc' rs' m' ->
+ transl_code_at_pc ge (rs' PC) fb f c' ep' tf tc'.
+Proof.
+ intros. inv H.
+ exploit exec_straight_steps_2; eauto.
+ eapply transf_function_no_overflow; eauto.
+ eapply functions_transl; eauto.
+ intros [ofs' [PC' CT']].
+ rewrite PC'. constructor; auto.
+Qed.
+ *)
+(** The following lemmas show that the translation from Mach to Asm
+ preserves labels, in the sense that the following diagram commutes:
+<<
+ translation
+ Mach code ------------------------ Asm instr sequence
+ | |
+ | Mach.find_label lbl find_label lbl |
+ | |
+ v v
+ Mach code tail ------------------- Asm instr seq tail
+ translation
+>>
+ The proof demands many boring lemmas showing that Asm constructor
+ functions do not introduce new labels.
+*)
+
+Section TRANSL_LABEL.
+
+(* Remark loadimm32_label:
+ forall r n k, tail_nolabel k (loadimm32 r n k).
+Proof.
+ intros; unfold loadimm32. destruct (make_immed32 n); TailNoLabel.
+(*unfold load_hilo32. destruct (Int.eq lo Int.zero); TailNoLabel.*)
+Qed.
+Hint Resolve loadimm32_label: labels.
+
+Remark opimm32_label:
+ forall (op: arith_name_rrr) (opimm: arith_name_rri32) r1 r2 n k,
+ (forall r1 r2 r3, nolabel (op r1 r2 r3)) ->
+ (forall r1 r2 n, nolabel (opimm r1 r2 n)) ->
+ tail_nolabel k (opimm32 op opimm r1 r2 n k).
+Proof.
+ intros; unfold opimm32. destruct (make_immed32 n); TailNoLabel.
+(*unfold load_hilo32. destruct (Int.eq lo Int.zero); TailNoLabel.*)
+Qed.
+Hint Resolve opimm32_label: labels.
+
+Remark loadimm64_label:
+ forall r n k, tail_nolabel k (loadimm64 r n k).
+Proof.
+ intros; unfold loadimm64. destruct (make_immed64 n); TailNoLabel.
+(*unfold load_hilo64. destruct (Int64.eq lo Int64.zero); TailNoLabel.*)
+Qed.
+Hint Resolve loadimm64_label: labels.
+
+Remark cast32signed_label:
+ forall rd rs k, tail_nolabel k (cast32signed rd rs k).
+Proof.
+ intros; unfold cast32signed. destruct (ireg_eq rd rs); TailNoLabel.
+Qed.
+Hint Resolve cast32signed_label: labels.
+
+Remark opimm64_label:
+ forall (op: arith_name_rrr) (opimm: arith_name_rri64) r1 r2 n k,
+ (forall r1 r2 r3, nolabel (op r1 r2 r3)) ->
+ (forall r1 r2 n, nolabel (opimm r1 r2 n)) ->
+ tail_nolabel k (opimm64 op opimm r1 r2 n k).
+Proof.
+ intros; unfold opimm64. destruct (make_immed64 n); TailNoLabel.
+(*unfold load_hilo64. destruct (Int64.eq lo Int64.zero); TailNoLabel.*)
+Qed.
+Hint Resolve opimm64_label: labels.
+
+Remark addptrofs_label:
+ forall r1 r2 n k, tail_nolabel k (addptrofs r1 r2 n k).
+Proof.
+ unfold addptrofs; intros. destruct (Ptrofs.eq_dec n Ptrofs.zero). TailNoLabel.
+ apply opimm64_label; TailNoLabel.
+Qed.
+Hint Resolve addptrofs_label: labels.
+(*
+Remark transl_cond_float_nolabel:
+ forall c r1 r2 r3 insn normal,
+ transl_cond_float c r1 r2 r3 = (insn, normal) -> nolabel insn.
+Proof.
+ unfold transl_cond_float; intros. destruct c; inv H; exact I.
+Qed.
+
+Remark transl_cond_single_nolabel:
+ forall c r1 r2 r3 insn normal,
+ transl_cond_single c r1 r2 r3 = (insn, normal) -> nolabel insn.
+Proof.
+ unfold transl_cond_single; intros. destruct c; inv H; exact I.
+Qed.
+*)
+Remark transl_cbranch_label:
+ forall cond args lbl k c,
+ transl_cbranch cond args lbl k = OK c -> tail_nolabel k c.
+Proof.
+ intros. unfold transl_cbranch in H. destruct cond; TailNoLabel.
+(* Ccomp *)
+ - unfold transl_comp; TailNoLabel.
+(* Ccompu *)
+ - unfold transl_comp; TailNoLabel.
+(* Ccompimm *)
+ - destruct (Int.eq n Int.zero); TailNoLabel.
+ unfold loadimm32. destruct (make_immed32 n); TailNoLabel. unfold transl_comp; TailNoLabel.
+(* Ccompuimm *)
+ - unfold transl_opt_compuimm.
+ remember (select_comp n c0) as selcomp; destruct selcomp.
+ + destruct c; TailNoLabel; contradict Heqselcomp; unfold select_comp;
+ destruct (Int.eq n Int.zero); destruct c0; discriminate.
+ + unfold loadimm32;
+ destruct (make_immed32 n); TailNoLabel; unfold transl_comp; TailNoLabel.
+(* Ccompl *)
+ - unfold transl_compl; TailNoLabel.
+(* Ccomplu *)
+ - unfold transl_compl; TailNoLabel.
+(* Ccomplimm *)
+ - destruct (Int64.eq n Int64.zero); TailNoLabel.
+ unfold loadimm64. destruct (make_immed64 n); TailNoLabel. unfold transl_compl; TailNoLabel.
+(* Ccompluimm *)
+ - unfold transl_opt_compluimm.
+ remember (select_compl n c0) as selcomp; destruct selcomp.
+ + destruct c; TailNoLabel; contradict Heqselcomp; unfold select_compl;
+ destruct (Int64.eq n Int64.zero); destruct c0; discriminate.
+ + unfold loadimm64;
+ destruct (make_immed64 n); TailNoLabel; unfold transl_compl; TailNoLabel.
+Qed.
+
+(*
+- destruct c0; simpl; TailNoLabel.
+- destruct c0; simpl; TailNoLabel.
+- destruct (Int.eq n Int.zero).
+ destruct c0; simpl; TailNoLabel.
+ apply tail_nolabel_trans with (transl_cbranch_int32s c0 x X31 lbl :: k).
+ auto with labels. destruct c0; simpl; TailNoLabel.
+- destruct (Int.eq n Int.zero).
+ destruct c0; simpl; TailNoLabel.
+ apply tail_nolabel_trans with (transl_cbranch_int32u c0 x X31 lbl :: k).
+ auto with labels. destruct c0; simpl; TailNoLabel.
+- destruct c0; simpl; TailNoLabel.
+- destruct c0; simpl; TailNoLabel.
+- destruct (Int64.eq n Int64.zero).
+ destruct c0; simpl; TailNoLabel.
+ apply tail_nolabel_trans with (transl_cbranch_int64s c0 x X31 lbl :: k).
+ auto with labels. destruct c0; simpl; TailNoLabel.
+- destruct (Int64.eq n Int64.zero).
+ destruct c0; simpl; TailNoLabel.
+ apply tail_nolabel_trans with (transl_cbranch_int64u c0 x X31 lbl :: k).
+ auto with labels. destruct c0; simpl; TailNoLabel.
+- destruct (transl_cond_float c0 X31 x x0) as [insn normal] eqn:F; inv EQ2.
+ apply tail_nolabel_cons. eapply transl_cond_float_nolabel; eauto.
+ destruct normal; TailNoLabel.
+- destruct (transl_cond_float c0 X31 x x0) as [insn normal] eqn:F; inv EQ2.
+ apply tail_nolabel_cons. eapply transl_cond_float_nolabel; eauto.
+ destruct normal; TailNoLabel.
+- destruct (transl_cond_single c0 X31 x x0) as [insn normal] eqn:F; inv EQ2.
+ apply tail_nolabel_cons. eapply transl_cond_single_nolabel; eauto.
+ destruct normal; TailNoLabel.
+- destruct (transl_cond_single c0 X31 x x0) as [insn normal] eqn:F; inv EQ2.
+ apply tail_nolabel_cons. eapply transl_cond_single_nolabel; eauto.
+ destruct normal; TailNoLabel.
+*)
+
+Remark transl_cond_op_label:
+ forall cond args r k c,
+ transl_cond_op cond r args k = OK c -> tail_nolabel k c.
+Proof.
+ intros. unfold transl_cond_op in H; destruct cond; TailNoLabel.
+- unfold transl_cond_int32s; destruct c0; simpl; TailNoLabel.
+- unfold transl_cond_int32u; destruct c0; simpl; TailNoLabel.
+- unfold transl_condimm_int32s; destruct c0; simpl; TailNoLabel.
+- unfold transl_condimm_int32u; destruct c0; simpl; TailNoLabel.
+- unfold transl_cond_int64s; destruct c0; simpl; TailNoLabel.
+- unfold transl_cond_int64u; destruct c0; simpl; TailNoLabel.
+- unfold transl_condimm_int64s; destruct c0; simpl; TailNoLabel.
+- unfold transl_condimm_int64u; destruct c0; simpl; TailNoLabel.
+Qed.
+
+Remark transl_op_label:
+ forall op args r k c,
+ transl_op op args r k = OK c -> tail_nolabel k c.
+Proof.
+Opaque Int.eq.
+ unfold transl_op; intros; destruct op; TailNoLabel.
+(* Omove *)
+- destruct (preg_of r); try discriminate; destruct (preg_of m); inv H; TailNoLabel.
+(* Oaddrsymbol *)
+- destruct (Archi.pic_code tt && negb (Ptrofs.eq ofs Ptrofs.zero)); TailNoLabel.
+(* Oaddimm32 *)
+- apply opimm32_label; intros; exact I.
+(* Oandimm32 *)
+- apply opimm32_label; intros; exact I.
+(* Oorimm32 *)
+- apply opimm32_label; intros; exact I.
+(* Oxorimm32 *)
+- apply opimm32_label; intros; exact I.
+(* Oshrximm *)
+- destruct (Int.eq n Int.zero); TailNoLabel.
+(* Oaddimm64 *)
+- apply opimm64_label; intros; exact I.
+(* Oandimm64 *)
+- apply opimm64_label; intros; exact I.
+(* Oorimm64 *)
+- apply opimm64_label; intros; exact I.
+(* Oxorimm64 *)
+- apply opimm64_label; intros; exact I.
+(* Ocmp *)
+- eapply transl_cond_op_label; eauto.
+Qed.
+
+(*
+- destruct (preg_of r); try discriminate; destruct (preg_of m); inv H; TailNoLabel.
+- destruct (Float.eq_dec n Float.zero); TailNoLabel.
+- destruct (Float32.eq_dec n Float32.zero); TailNoLabel.
+- destruct (Archi.pic_code tt && negb (Ptrofs.eq ofs Ptrofs.zero)).
++ eapply tail_nolabel_trans; [|apply addptrofs_label]. TailNoLabel.
++ TailNoLabel.
+- apply opimm32_label; intros; exact I.
+- apply opimm32_label; intros; exact I.
+- apply opimm32_label; intros; exact I.
+- apply opimm32_label; intros; exact I.
+- destruct (Int.eq n Int.zero); TailNoLabel.
+- apply opimm64_label; intros; exact I.
+- apply opimm64_label; intros; exact I.
+- apply opimm64_label; intros; exact I.
+- apply opimm64_label; intros; exact I.
+- destruct (Int.eq n Int.zero); TailNoLabel.
+- eapply transl_cond_op_label; eauto.
+*)
+*)
+
+(* Remark indexed_memory_access_label:
+ forall (mk_instr: ireg -> offset -> instruction) base ofs k,
+ (forall r o, nolabel (mk_instr r o)) ->
+ tail_nolabel k (indexed_memory_access mk_instr base ofs k).
+Proof.
+ unfold indexed_memory_access; intros.
+ (* destruct Archi.ptr64. *)
+ destruct (make_immed64 (Ptrofs.to_int64 ofs)); TailNoLabel.
+ (* destruct (make_immed32 (Ptrofs.to_int ofs)); TailNoLabel. *)
+Qed. *)
+
+(*
+Remark loadind_label:
+ forall base ofs ty dst k c,
+ loadind base ofs ty dst k = OK c -> tail_nolabel k c.
+Proof.
+ unfold loadind; intros.
+ destruct ty, (preg_of dst); inv H; apply indexed_memory_access_label; intros; exact I.
+Qed.
+
+Remark storeind_label:
+ forall src base ofs ty k c,
+ storeind src base ofs ty k = OK c -> tail_nolabel k c.
+Proof.
+ unfold storeind; intros.
+ destruct ty, (preg_of src); inv H; apply indexed_memory_access_label; intros; exact I.
+Qed.
+
+Remark loadind_ptr_label:
+ forall base ofs dst k, tail_nolabel k (loadind_ptr base ofs dst k).
+Proof.
+ intros. apply indexed_memory_access_label. intros; destruct Archi.ptr64; exact I.
+Qed.
+*)
+
+(* Remark storeind_ptr_label:
+ forall src base ofs k, tail_nolabel k (storeind_ptr src base ofs k).
+Proof.
+ intros. apply indexed_memory_access_label. intros; destruct Archi.ptr64; exact I.
+Qed. *)
+
+(*
+Remark transl_memory_access_label:
+ forall (mk_instr: ireg -> offset -> instruction) addr args k c,
+ (forall r o, nolabel (mk_instr r o)) ->
+ transl_memory_access mk_instr addr args k = OK c ->
+ tail_nolabel k c.
+Proof.
+ unfold transl_memory_access; intros; destruct addr; TailNoLabel; apply indexed_memory_access_label; auto.
+Qed.
+
+Remark make_epilogue_label:
+ forall f k, tail_nolabel k (make_epilogue f k).
+Proof.
+ unfold make_epilogue; intros. eapply tail_nolabel_trans. apply loadind_ptr_label. TailNoLabel.
+Qed.
+
+Lemma transl_instr_label:
+ forall f i ep k c,
+ transl_instr f i ep k = OK c ->
+ match i with Mlabel lbl => c = Plabel lbl ::i k | _ => tail_nolabel k c end.
+Proof.
+ unfold transl_instr; intros; destruct i; TailNoLabel.
+(* loadind *)
+- eapply loadind_label; eauto.
+(* storeind *)
+- eapply storeind_label; eauto.
+(* Mgetparam *)
+- destruct ep. eapply loadind_label; eauto.
+ eapply tail_nolabel_trans. apply loadind_ptr_label. eapply loadind_label; eauto.
+(* transl_op *)
+- eapply transl_op_label; eauto.
+(* transl_load *)
+- destruct m; monadInv H; eapply transl_memory_access_label; eauto; intros; exact I.
+(* transl store *)
+- destruct m; monadInv H; eapply transl_memory_access_label; eauto; intros; exact I.
+- destruct s0; monadInv H; TailNoLabel.
+- destruct s0; monadInv H; eapply tail_nolabel_trans
+ ; [eapply make_epilogue_label|TailNoLabel].
+- eapply transl_cbranch_label; eauto.
+- eapply tail_nolabel_trans; [eapply make_epilogue_label|TailNoLabel].
+Qed.
+(*
+
+
+- eapply transl_op_label; eauto.
+- destruct m; monadInv H; eapply transl_memory_access_label; eauto; intros; exact I.
+- destruct m; monadInv H; eapply transl_memory_access_label; eauto; intros; exact I.
+- destruct s0; monadInv H; (eapply tail_nolabel_trans; [eapply make_epilogue_label|TailNoLabel]).
+- eapply tail_nolabel_trans; [eapply make_epilogue_label|TailNoLabel].
+*)
+
+Lemma transl_instr_label':
+ forall lbl f i ep k c,
+ transl_instr f i ep k = OK c ->
+ find_label lbl c = if Mach.is_label lbl i then Some k else find_label lbl k.
+Proof.
+ intros. exploit transl_instr_label; eauto.
+ destruct i; try (intros [A B]; apply B).
+ intros. subst c. simpl. auto.
+Qed.
+*)
+
+Lemma gen_bblocks_label:
+ forall hd bdy ex tbb tc,
+ gen_bblocks hd bdy ex = tbb::tc ->
+ header tbb = hd.
+Proof.
+ intros until tc. intros GENB. unfold gen_bblocks in GENB.
+ destruct (extract_ctl ex); try destruct c; try destruct i; try destruct bdy.
+ all: inv GENB; simpl; auto.
+Qed.
+
+Lemma gen_bblocks_label2:
+ forall hd bdy ex tbb1 tbb2,
+ gen_bblocks hd bdy ex = tbb1::tbb2::nil ->
+ header tbb2 = nil.
+Proof.
+ intros until tbb2. intros GENB. unfold gen_bblocks in GENB.
+ destruct (extract_ctl ex); try destruct c; try destruct i; try destruct bdy.
+ all: inv GENB; simpl; auto.
+Qed.
+
+Lemma in_dec_transl:
+ forall lbl hd,
+ (if in_dec lbl hd then true else false) = (if MB.in_dec lbl hd then true else false).
+Proof.
+ intros. destruct (in_dec lbl hd), (MB.in_dec lbl hd). all: tauto.
+Qed.
+
+Lemma transl_is_label:
+ forall lbl bb tbb f ep tc,
+ transl_block f bb ep = OK (tbb::tc) ->
+ is_label lbl tbb = MB.is_label lbl bb.
+Proof.
+ intros until tc. intros TLB.
+ destruct tbb as [thd tbdy tex]; simpl in *.
+ monadInv TLB.
+ unfold is_label. simpl.
+ apply gen_bblocks_label in H0. simpl in H0. subst.
+ rewrite in_dec_transl. auto.
+Qed.
+
+Lemma transl_is_label_false2:
+ forall lbl bb f ep tbb1 tbb2,
+ transl_block f bb ep = OK (tbb1::tbb2::nil) ->
+ is_label lbl tbb2 = false.
+Proof.
+ intros until tbb2. intros TLB.
+ destruct tbb2 as [thd tbdy tex]; simpl in *.
+ monadInv TLB. apply gen_bblocks_label2 in H0. simpl in H0. subst.
+ apply is_label_correct_false. simpl. auto.
+Qed.
+
+Lemma transl_is_label2:
+ forall f bb ep tbb1 tbb2 lbl,
+ transl_block f bb ep = OK (tbb1::tbb2::nil) ->
+ is_label lbl tbb1 = MB.is_label lbl bb
+ /\ is_label lbl tbb2 = false.
+Proof.
+ intros. split. eapply transl_is_label; eauto. eapply transl_is_label_false2; eauto.
+Qed.
+
+Lemma transl_block_nonil:
+ forall f c ep tc,
+ transl_block f c ep = OK tc ->
+ tc <> nil.
+Proof.
+ intros. monadInv H. unfold gen_bblocks.
+ destruct (extract_ctl x0); try destruct c0; try destruct x; try destruct i.
+ all: discriminate.
+Qed.
+
+Lemma transl_block_limit: forall f bb ep tbb1 tbb2 tbb3 tc,
+ ~transl_block f bb ep = OK (tbb1 :: tbb2 :: tbb3 :: tc).
+Proof.
+ intros. intro. monadInv H.
+ unfold gen_bblocks in H0.
+ destruct (extract_ctl x0); try destruct x; try destruct c; try destruct i.
+ all: discriminate.
+Qed.
+
+Lemma find_label_transl_false:
+ forall x f lbl bb ep x',
+ transl_block f bb ep = OK x ->
+ MB.is_label lbl bb = false ->
+ find_label lbl (x++x') = find_label lbl x'.
+Proof.
+ intros until x'. intros TLB MBis; simpl; auto.
+ destruct x as [|x0 x1]; simpl; auto.
+ destruct x1 as [|x1 x2]; simpl; auto.
+ - erewrite <- transl_is_label in MBis; eauto. rewrite MBis. auto.
+ - destruct x2 as [|x2 x3]; simpl; auto.
+ + erewrite <- transl_is_label in MBis; eauto. rewrite MBis.
+ erewrite transl_is_label_false2; eauto.
+ + apply transl_block_limit in TLB. destruct TLB.
+Qed.
+
+Lemma transl_blocks_label:
+ forall lbl f c tc ep,
+ transl_blocks f c ep = OK tc ->
+ match MB.find_label lbl c with
+ | None => find_label lbl tc = None
+ | Some c' => exists tc', find_label lbl tc = Some tc' /\ transl_blocks f c' false = OK tc'
+ end.
+Proof.
+ induction c; simpl; intros.
+ inv H. auto.
+ monadInv H.
+ destruct (MB.is_label lbl a) eqn:MBis.
+ - destruct x as [|tbb tc]. { apply transl_block_nonil in EQ. contradiction. }
+ simpl find_label. exploit transl_is_label; eauto. intros ABis. rewrite MBis in ABis.
+ rewrite ABis.
+ eexists. eexists. split; eauto. simpl transl_blocks.
+ assert (MB.header a <> nil).
+ { apply MB.is_label_correct_true in MBis.
+ destruct (MB.header a). contradiction. discriminate. }
+ destruct (MB.header a); try contradiction.
+ rewrite EQ. simpl. rewrite EQ1. simpl. auto.
+ - apply IHc in EQ1. destruct (MB.find_label lbl c).
+ + destruct EQ1 as (tc' & FIND & TLBS). exists tc'; eexists; auto.
+ erewrite find_label_transl_false; eauto.
+ + erewrite find_label_transl_false; eauto.
+Qed.
+
+Lemma find_label_nil:
+ forall bb lbl c,
+ header bb = nil ->
+ find_label lbl (bb::c) = find_label lbl c.
+Proof.
+ intros. destruct bb as [hd bdy ex]; simpl in *. subst.
+ assert (is_label lbl {| AB.header := nil; AB.body := bdy; AB.exit := ex; AB.correct := correct |} = false).
+ { erewrite <- is_label_correct_false. simpl. auto. }
+ rewrite H. auto.
+Qed.
+
+Lemma transl_find_label:
+ forall lbl f tf,
+ transf_function f = OK tf ->
+ match MB.find_label lbl f.(MB.fn_code) with
+ | None => find_label lbl tf.(fn_blocks) = None
+ | Some c => exists tc, find_label lbl tf.(fn_blocks) = Some tc /\ transl_blocks f c false = OK tc
+ end.
+Proof.
+ intros. monadInv H. destruct (zlt Ptrofs.max_unsigned (size_blocks (fn_blocks x))); inv EQ0. clear g.
+ monadInv EQ. simpl fn_blocks. repeat (rewrite find_label_nil); simpl; auto.
+ eapply transl_blocks_label; eauto.
+Qed.
+
+End TRANSL_LABEL.
+
+(** A valid branch in a piece of Mach code translates to a valid ``go to''
+ transition in the generated Asm code. *)
+
+Lemma find_label_goto_label:
+ forall f tf lbl rs m c' b ofs,
+ Genv.find_funct_ptr ge b = Some (Internal f) ->
+ transf_function f = OK tf ->
+ rs PC = Vptr b ofs ->
+ MB.find_label lbl f.(MB.fn_code) = Some c' ->
+ exists tc', exists rs',
+ goto_label tf lbl rs m = Next rs' m
+ /\ transl_code_at_pc ge (rs' PC) b f c' false tf tc'
+ /\ forall r, r <> PC -> rs'#r = rs#r.
+Proof.
+ intros. exploit (transl_find_label lbl f tf); eauto. rewrite H2.
+ intros (tc & A & B).
+ exploit label_pos_code_tail; eauto. instantiate (1 := 0).
+ intros [pos' [P [Q R]]].
+ exists tc; exists (rs#PC <- (Vptr b (Ptrofs.repr pos'))).
+ split. unfold goto_label. rewrite P. rewrite H1. auto.
+ split. rewrite Pregmap.gss. constructor; auto.
+ rewrite Ptrofs.unsigned_repr. replace (pos' - 0) with pos' in Q.
+ auto. omega.
+ generalize (transf_function_no_overflow _ _ H0). omega.
+ intros. apply Pregmap.gso; auto.
+Qed.
+
+(** Existence of return addresses *)
+
+(* NB: the hypothesis in comment on [b] is not needed in the proof !
+*)
+Lemma return_address_exists:
+ forall b f (* sg ros *) c, (* b.(MB.exit) = Some (MBcall sg ros) -> *) is_tail (b :: c) f.(MB.fn_code) ->
+ exists ra, return_address_offset f c ra.
+Proof.
+ intros. eapply Asmblockgenproof0.return_address_exists; eauto.
+
+- intros. monadInv H0.
+ destruct (zlt Ptrofs.max_unsigned (size_blocks x.(fn_blocks))); inv EQ0. monadInv EQ. simpl.
+(* rewrite transl_code'_transl_code in EQ0. *)
+ exists x; exists true; split; auto. (* unfold fn_code. *)
+ repeat constructor.
+ - exact transf_function_no_overflow.
+Qed.
+
+(** * Proof of semantic preservation *)
+
+(** Semantic preservation is proved using simulation diagrams
+ of the following form.
+<<
+ st1 --------------- st2
+ | |
+ t| *|t
+ | |
+ v v
+ st1'--------------- st2'
+>>
+ The invariant is the [match_states] predicate below, which includes:
+- The Asm code pointed by the PC register is the translation of
+ the current Mach code sequence.
+- Mach register values and Asm register values agree.
+*)
+
+(*
+Lemma exec_straight_steps:
+ forall s fb f rs1 i c ep tf tc m1' m2 m2' sp ms2,
+ match_stack ge s ->
+ Mem.extends m2 m2' ->
+ Genv.find_funct_ptr ge fb = Some (Internal f) ->
+ transl_code_at_pc ge (rs1 PC) fb f (i :: c) ep tf tc ->
+ (forall k c (TR: transl_instr f i ep k = OK c),
+ exists rs2,
+ exec_straight tge tf c rs1 m1' k rs2 m2'
+ /\ agree ms2 sp rs2
+ /\ (fp_is_parent ep i = true -> rs2#FP = parent_sp s)) ->
+ exists st',
+ plus step tge (State rs1 m1') E0 st' /\
+ match_states (Mach.State s fb sp c ms2 m2) st'.
+Proof.
+ intros. inversion H2. subst. monadInv H7.
+ exploit H3; eauto. intros [rs2 [A [B C]]].
+ exists (State rs2 m2'); split.
+ eapply exec_straight_exec; eauto.
+ econstructor; eauto. eapply exec_straight_at; eauto.
+Qed.
+*)
+
+(*
+Lemma exec_straight_steps_goto:
+ forall s fb f rs1 i c ep tf tc m1' m2 m2' sp ms2 lbl c',
+ match_stack ge s ->
+ Mem.extends m2 m2' ->
+ Genv.find_funct_ptr ge fb = Some (Internal f) ->
+ Mach.find_label lbl f.(Mach.fn_code) = Some c' ->
+ transl_code_at_pc ge (rs1 PC) fb f (i :: c) ep tf tc ->
+ fp_is_parent ep i = false ->
+ (forall k c (TR: transl_instr f i ep k = OK c),
+ exists jmp, exists k', exists rs2,
+ exec_straight tge tf c rs1 m1' (jmp :: k') rs2 m2'
+ /\ agree ms2 sp rs2
+ /\ exec_instr tge tf jmp rs2 m2' = goto_label tf lbl rs2 m2') ->
+ exists st',
+ plus step tge (State rs1 m1') E0 st' /\
+ match_states (Mach.State s fb sp c' ms2 m2) st'.
+Proof.
+ intros. inversion H3. subst. monadInv H9.
+ exploit H5; eauto. intros [jmp [k' [rs2 [A [B C]]]]].
+ generalize (functions_transl _ _ _ H7 H8); intro FN.
+ generalize (transf_function_no_overflow _ _ H8); intro NOOV.
+ exploit exec_straight_steps_2; eauto.
+ intros [ofs' [PC2 CT2]].
+ exploit find_label_goto_label; eauto.
+ intros [tc' [rs3 [GOTO [AT' OTH]]]].
+ exists (State rs3 m2'); split.
+ eapply plus_right'.
+ eapply exec_straight_steps_1; eauto.
+ econstructor; eauto.
+ eapply find_instr_tail. eauto.
+ rewrite C. eexact GOTO.
+ traceEq.
+ econstructor; eauto.
+ apply agree_exten with rs2; auto with asmgen.
+ congruence.
+Qed.
+
+Lemma exec_straight_opt_steps_goto:
+ forall s fb f rs1 i c ep tf tc m1' m2 m2' sp ms2 lbl c',
+ match_stack ge s ->
+ Mem.extends m2 m2' ->
+ Genv.find_funct_ptr ge fb = Some (Internal f) ->
+ Mach.find_label lbl f.(Mach.fn_code) = Some c' ->
+ transl_code_at_pc ge (rs1 PC) fb f (i :: c) ep tf tc ->
+ fp_is_parent ep i = false ->
+ (forall k c (TR: transl_instr f i ep k = OK c),
+ exists jmp, exists k', exists rs2,
+ exec_straight_opt tge tf c rs1 m1' (jmp :: k') rs2 m2'
+ /\ agree ms2 sp rs2
+ /\ exec_instr tge tf jmp rs2 m2' = goto_label tf lbl rs2 m2') ->
+ exists st',
+ plus step tge (State rs1 m1') E0 st' /\
+ match_states (Mach.State s fb sp c' ms2 m2) st'.
+Proof.
+ intros. inversion H3. subst. monadInv H9.
+ exploit H5; eauto. intros [jmp [k' [rs2 [A [B C]]]]].
+ generalize (functions_transl _ _ _ H7 H8); intro FN.
+ generalize (transf_function_no_overflow _ _ H8); intro NOOV.
+ inv A.
+- exploit find_label_goto_label; eauto.
+ intros [tc' [rs3 [GOTO [AT' OTH]]]].
+ exists (State rs3 m2'); split.
+ apply plus_one. econstructor; eauto.
+ eapply find_instr_tail. eauto.
+ rewrite C. eexact GOTO.
+ econstructor; eauto.
+ apply agree_exten with rs2; auto with asmgen.
+ congruence.
+- exploit exec_straight_steps_2; eauto.
+ intros [ofs' [PC2 CT2]].
+ exploit find_label_goto_label; eauto.
+ intros [tc' [rs3 [GOTO [AT' OTH]]]].
+ exists (State rs3 m2'); split.
+ eapply plus_right'.
+ eapply exec_straight_steps_1; eauto.
+ econstructor; eauto.
+ eapply find_instr_tail. eauto.
+ rewrite C. eexact GOTO.
+ traceEq.
+ econstructor; eauto.
+ apply agree_exten with rs2; auto with asmgen.
+ congruence.
+Qed. *)
+
+(** We need to show that, in the simulation diagram, we cannot
+ take infinitely many Mach transitions that correspond to zero
+ transitions on the Asm side. Actually, all Mach transitions
+ correspond to at least one Asm transition, except the
+ transition from [Machsem.Returnstate] to [Machsem.State].
+ So, the following integer measure will suffice to rule out
+ the unwanted behaviour. *)
+
+
+Remark preg_of_not_FP: forall r, negb (mreg_eq r R10) = true -> IR FP <> preg_of r.
+Proof.
+ intros. change (IR FP) with (preg_of R10). red; intros.
+ exploit preg_of_injective; eauto. intros; subst r; discriminate.
+Qed.
+
+Inductive match_states: Machblock.state -> Asmblock.state -> Prop :=
+ | match_states_intro:
+ forall s fb sp c ep ms m m' rs f tf tc
+ (STACKS: match_stack ge s)
+ (FIND: Genv.find_funct_ptr ge fb = Some (Internal f))
+ (MEXT: Mem.extends m m')
+ (AT: transl_code_at_pc ge (rs PC) fb f c ep tf tc)
+ (AG: agree ms sp rs)
+ (DXP: ep = true -> rs#FP = parent_sp s),
+ match_states (Machblock.State s fb sp c ms m)
+ (Asmblock.State rs m')
+ | match_states_call:
+ forall s fb ms m m' rs
+ (STACKS: match_stack ge s)
+ (MEXT: Mem.extends m m')
+ (AG: agree ms (parent_sp s) rs)
+ (ATPC: rs PC = Vptr fb Ptrofs.zero)
+ (ATLR: rs RA = parent_ra s),
+ match_states (Machblock.Callstate s fb ms m)
+ (Asmblock.State rs m')
+ | match_states_return:
+ forall s ms m m' rs
+ (STACKS: match_stack ge s)
+ (MEXT: Mem.extends m m')
+ (AG: agree ms (parent_sp s) rs)
+ (ATPC: rs PC = parent_ra s),
+ match_states (Machblock.Returnstate s ms m)
+ (Asmblock.State rs m').
+
+Record codestate :=
+ Codestate { pstate: state;
+ pheader: list label;
+ pbody1: list basic;
+ pbody2: list basic;
+ pctl: option control;
+ fpok: bool;
+ rem: list AB.bblock;
+ cur: option bblock }.
+
+(* | Codestate: state -> list AB.bblock -> option bblock -> codestate. *)
+
+Inductive match_codestate fb: Machblock.state -> codestate -> Prop :=
+ | match_codestate_intro:
+ forall s sp ms m rs0 m0 f tc ep c bb tbb tbc tbi
+ (STACKS: match_stack ge s)
+ (FIND: Genv.find_funct_ptr ge fb = Some (Internal f))
+ (MEXT: Mem.extends m m0)
+ (TBC: transl_basic_code f (MB.body bb) (if MB.header bb then ep else false) = OK tbc)
+ (TIC: transl_instr_control f (MB.exit bb) = OK tbi)
+ (TBLS: transl_blocks f c false = OK tc)
+(* (TRANS: transl_blocks f (bb::c) ep = OK (tbb::tc)) *)
+ (AG: agree ms sp rs0)
+ (DXP: (if MB.header bb then ep else false) = true -> rs0#FP = parent_sp s)
+ ,
+ match_codestate fb (Machblock.State s fb sp (bb::c) ms m)
+ {| pstate := (Asmblock.State rs0 m0);
+ pheader := (MB.header bb);
+ pbody1 := tbc;
+ pbody2 := (extract_basic tbi);
+ pctl := extract_ctl tbi;
+ fpok := ep;
+ rem := tc;
+ cur := Some tbb
+ |}
+.
+
+Inductive match_asmstate fb: codestate -> Asmblock.state -> Prop :=
+ | match_asmstate_some:
+ forall rs f tf tc m tbb ofs ep tbdy tex lhd
+ (FIND: Genv.find_funct_ptr ge fb = Some (Internal f))
+ (TRANSF: transf_function f = OK tf)
+ (PCeq: rs PC = Vptr fb ofs)
+ (TAIL: code_tail (Ptrofs.unsigned ofs) (fn_blocks tf) (tbb::tc))
+(* (HDROK: header tbb = lhd) *)
+ ,
+ match_asmstate fb
+ {| pstate := (Asmblock.State rs m);
+ pheader := lhd;
+ pbody1 := tbdy;
+ pbody2 := extract_basic tex;
+ pctl := extract_ctl tex;
+ fpok := ep;
+ rem := tc;
+ cur := Some tbb |}
+ (Asmblock.State rs m)
+.
+
+Ltac exploreInst :=
+ repeat match goal with
+ | [ H : match ?var with | _ => _ end = _ |- _ ] => destruct var
+ | [ H : OK _ = OK _ |- _ ] => monadInv H
+ | [ |- context[if ?b then _ else _] ] => destruct b
+ | [ |- context[match ?m with | _ => _ end] ] => destruct m
+ | [ |- context[match ?m as _ return _ with | _ => _ end]] => destruct m
+ | [ H : bind _ _ = OK _ |- _ ] => monadInv H
+ | [ H : Error _ = OK _ |- _ ] => inversion H
+ end.
+
+Lemma transl_blocks_nonil:
+ forall f bb c tc ep,
+ transl_blocks f (bb::c) ep = OK tc ->
+ exists tbb tc', tc = tbb :: tc'.
+Proof.
+ intros until ep. intros TLBS. monadInv TLBS. monadInv EQ. unfold gen_bblocks.
+ destruct (extract_ctl x2).
+ - destruct c0; destruct i; simpl; eauto. destruct x1; simpl; eauto.
+ - destruct x1; simpl; eauto.
+Qed.
+
+Lemma no_builtin_preserved:
+ forall f ex x2,
+ (forall ef args res, ex <> Some (MBbuiltin ef args res)) ->
+ transl_instr_control f ex = OK x2 ->
+ (exists i, extract_ctl x2 = Some (PCtlFlow i))
+ \/ extract_ctl x2 = None.
+Proof.
+ intros until x2. intros Hbuiltin TIC.
+ destruct ex.
+ - destruct c.
+ + simpl in TIC. exploreInst; simpl; eauto.
+ + simpl in TIC. exploreInst; simpl; eauto.
+ + assert (H: Some (MBbuiltin e l b) <> Some (MBbuiltin e l b)).
+ apply Hbuiltin. contradict H; auto.
+ + simpl in TIC. exploreInst; simpl; eauto.
+ + simpl in TIC. unfold transl_cbranch in TIC. exploreInst; simpl; eauto.
+ * unfold transl_opt_compuimm. exploreInst; simpl; eauto.
+ * unfold transl_opt_compluimm. exploreInst; simpl; eauto.
+ + simpl in TIC. inv TIC.
+ + simpl in TIC. monadInv TIC. simpl. eauto.
+ - monadInv TIC. simpl; auto.
+Qed.
+
+Lemma transl_blocks_distrib:
+ forall c f bb tbb tc ep,
+ transl_blocks f (bb::c) ep = OK (tbb::tc)
+ -> (forall ef args res, MB.exit bb <> Some (MBbuiltin ef args res))
+ -> transl_block f bb (if MB.header bb then ep else false) = OK (tbb :: nil)
+ /\ transl_blocks f c false = OK tc.
+Proof.
+ intros until ep. intros TLBS Hbuiltin.
+ destruct bb as [hd bdy ex].
+ monadInv TLBS. monadInv EQ.
+ exploit no_builtin_preserved; eauto. intros Hectl. destruct Hectl.
+ - destruct H as [i Hectl].
+ unfold gen_bblocks in H0. rewrite Hectl in H0. inv H0.
+ simpl in *. unfold transl_block; simpl. rewrite EQ0. rewrite EQ. simpl.
+ unfold gen_bblocks. rewrite Hectl. auto.
+ - unfold gen_bblocks in H0. rewrite H in H0.
+ destruct x1 as [|bi x1].
+ + simpl in H0. inv H0. simpl in *. unfold transl_block; simpl. rewrite EQ0. rewrite EQ. simpl.
+ unfold gen_bblocks. rewrite H. auto.
+ + simpl in H0. inv H0. simpl in *. unfold transl_block; simpl. rewrite EQ0. rewrite EQ. simpl.
+ unfold gen_bblocks. rewrite H. auto.
+Qed.
+
+Lemma gen_bblocks_nobuiltin:
+ forall thd tbdy tex tbb,
+ (tbdy <> nil \/ extract_ctl tex <> None) ->
+ (forall ef args res, extract_ctl tex <> Some (PExpand (Pbuiltin ef args res))) ->
+ gen_bblocks thd tbdy tex = tbb :: nil ->
+ header tbb = thd
+ /\ body tbb = tbdy ++ extract_basic tex
+ /\ exit tbb = extract_ctl tex.
+Proof.
+ intros until tbb. intros Hnonil Hnobuiltin GENB. unfold gen_bblocks in GENB.
+ destruct (extract_ctl tex) eqn:ECTL.
+ - destruct c.
+ + destruct i. assert False. eapply Hnobuiltin. eauto. destruct H.
+ + inv GENB. simpl. auto.
+ - inversion Hnonil.
+ + destruct tbdy as [|bi tbdy]; try (contradict H; simpl; auto; fail). inv GENB. auto.
+ + contradict H; simpl; auto.
+Qed.
+
+Lemma transl_instr_basic_nonil:
+ forall k f bi ep x,
+ transl_instr_basic f bi ep k = OK x ->
+ x <> nil.
+Proof.
+ intros until x. intros TIB.
+ destruct bi.
+ - simpl in TIB. unfold loadind in TIB. exploreInst; try discriminate.
+ - simpl in TIB. unfold storeind in TIB. exploreInst; try discriminate.
+ - simpl in TIB. monadInv TIB. unfold loadind in EQ. exploreInst; try discriminate.
+ - simpl in TIB. unfold transl_op in TIB. exploreInst; try discriminate.
+ unfold transl_cond_op in EQ0. exploreInst; try discriminate.
+ - simpl in TIB. unfold transl_load in TIB. exploreInst; try discriminate.
+ all: unfold transl_memory_access in EQ0; exploreInst; try discriminate.
+ - simpl in TIB. unfold transl_store in TIB. exploreInst; try discriminate.
+ all: unfold transl_memory_access in EQ0; exploreInst; try discriminate.
+Qed.
+
+Lemma transl_basic_code_nonil:
+ forall bdy f x ep,
+ bdy <> nil ->
+ transl_basic_code f bdy ep = OK x ->
+ x <> nil.
+Proof.
+ induction bdy as [|bi bdy].
+ intros. contradict H0; auto.
+ destruct bdy as [|bi2 bdy].
+ - clear IHbdy. intros f x b _ TBC. simpl in TBC. eapply transl_instr_basic_nonil; eauto.
+ - intros f x b Hnonil TBC. remember (bi2 :: bdy) as bdy'.
+ monadInv TBC.
+ assert (x0 <> nil).
+ eapply IHbdy; eauto. subst bdy'. discriminate.
+ eapply transl_instr_basic_nonil; eauto.
+Qed.
+
+Lemma transl_instr_control_nonil:
+ forall ex f x,
+ ex <> None ->
+ transl_instr_control f ex = OK x ->
+ extract_ctl x <> None.
+Proof.
+ intros ex f x Hnonil TIC.
+ destruct ex as [ex|].
+ - clear Hnonil. destruct ex.
+ all: try (simpl in TIC; exploreInst; discriminate).
+ + simpl in TIC. unfold transl_cbranch in TIC. exploreInst; try discriminate.
+ * unfold transl_opt_compuimm. exploreInst; try discriminate.
+ * unfold transl_opt_compluimm. exploreInst; try discriminate.
+ - contradict Hnonil; auto.
+Qed.
+
+Lemma transl_instr_control_nobuiltin:
+ forall f ex x,
+ (forall ef args res, ex <> Some (MBbuiltin ef args res)) ->
+ transl_instr_control f ex = OK x ->
+ (forall ef args res, extract_ctl x <> Some (PExpand (Pbuiltin ef args res))).
+Proof.
+ intros until x. intros Hnobuiltin TIC. intros until res.
+ unfold transl_instr_control in TIC. exploreInst.
+ all: try discriminate.
+ - assert False. eapply Hnobuiltin; eauto. destruct H.
+ - unfold transl_cbranch in TIC. exploreInst.
+ all: try discriminate.
+ + unfold transl_opt_compuimm. exploreInst. all: try discriminate.
+ + unfold transl_opt_compluimm. exploreInst. all: try discriminate.
+Qed.
+
+Theorem match_state_codestate:
+ forall mbs abs s fb sp bb c ms m,
+ (forall ef args res, MB.exit bb <> Some (MBbuiltin ef args res)) ->
+ (MB.body bb <> nil \/ MB.exit bb <> None) ->
+ mbs = (Machblock.State s fb sp (bb::c) ms m) ->
+ match_states mbs abs ->
+ exists cs fb f tbb tc ep,
+ match_codestate fb mbs cs /\ match_asmstate fb cs abs
+ /\ Genv.find_funct_ptr ge fb = Some (Internal f)
+ /\ transl_blocks f (bb::c) ep = OK (tbb::tc)
+ /\ body tbb = pbody1 cs ++ pbody2 cs
+ /\ exit tbb = pctl cs
+ /\ cur cs = Some tbb /\ rem cs = tc
+ /\ pstate cs = abs.
+Proof.
+ intros until m. intros Hnobuiltin Hnotempty Hmbs MS. subst. inv MS.
+ inv AT. clear H0. exploit transl_blocks_nonil; eauto. intros (tbb & tc' & Htc). subst.
+ exploit transl_blocks_distrib; eauto. intros (TLB & TLBS). clear H2.
+ monadInv TLB. exploit gen_bblocks_nobuiltin; eauto.
+ { inversion Hnotempty.
+ - destruct (MB.body bb) as [|bi bdy]; try (contradict H0; simpl; auto; fail).
+ left. eapply transl_basic_code_nonil; eauto.
+ - destruct (MB.exit bb) as [ei|]; try (contradict H0; simpl; auto; fail).
+ right. eapply transl_instr_control_nonil; eauto. }
+ eapply transl_instr_control_nobuiltin; eauto.
+ intros (Hth & Htbdy & Htexit).
+ exists {| pstate := (State rs m'); pheader := (Machblock.header bb); pbody1 := x; pbody2 := extract_basic x0;
+ pctl := extract_ctl x0; fpok := ep; rem := tc'; cur := Some tbb |}, fb, f, tbb, tc', ep.
+ repeat split. 1-2: econstructor; eauto.
+ { destruct (MB.header bb). eauto. discriminate. } eauto.
+ unfold transl_blocks. fold transl_blocks. unfold transl_block. rewrite EQ. simpl. rewrite EQ1; simpl.
+ rewrite TLBS. simpl. rewrite H2.
+ all: simpl; auto.
+Qed.
+
+Definition mb_remove_body (bb: MB.bblock) :=
+ {| MB.header := MB.header bb; MB.body := nil; MB.exit := MB.exit bb |}.
+
+Lemma exec_straight_pnil:
+ forall c rs1 m1 rs2 m2,
+ exec_straight tge c rs1 m1 (Pnop::gnil) rs2 m2 ->
+ exec_straight tge c rs1 m1 nil rs2 m2.
+Proof.
+ intros. eapply exec_straight_trans. eapply H. econstructor; eauto.
+Qed.
+
+Lemma transl_block_nobuiltin:
+ forall f bb ep tbb,
+ (MB.body bb <> nil \/ MB.exit bb <> None) ->
+ (forall ef args res, MB.exit bb <> Some (MBbuiltin ef args res)) ->
+ transl_block f bb ep = OK (tbb :: nil) ->
+ exists c c',
+ transl_basic_code f (MB.body bb) ep = OK c
+ /\ transl_instr_control f (MB.exit bb) = OK c'
+ /\ body tbb = c ++ extract_basic c'
+ /\ exit tbb = extract_ctl c'.
+Proof.
+ intros until tbb. intros Hnonil Hnobuiltin TLB. monadInv TLB. destruct Hnonil.
+ - eexists. eexists. split; eauto. split; eauto. eapply gen_bblocks_nobuiltin; eauto.
+ left. eapply transl_basic_code_nonil; eauto. eapply transl_instr_control_nobuiltin; eauto.
+ - eexists. eexists. split; eauto. split; eauto. eapply gen_bblocks_nobuiltin; eauto.
+ right. eapply transl_instr_control_nonil; eauto. eapply transl_instr_control_nobuiltin; eauto.
+Qed.
+
+Lemma nextblock_preserves:
+ forall rs rs' bb r,
+ rs' = nextblock bb rs ->
+ data_preg r = true ->
+ rs r = rs' r.
+Proof.
+ intros. destruct r; try discriminate.
+ - subst. Simpl.
+ - subst. Simpl.
+Qed.
+
+Lemma cons3_app {A: Type}:
+ forall a b c (l: list A),
+ a :: b :: c :: l = (a :: b :: c :: nil) ++ l.
+Proof.
+ intros. simpl. auto.
+Qed.
+
+Lemma exec_straight_opt_body2:
+ forall c rs1 m1 c' rs2 m2,
+ exec_straight_opt tge c rs1 m1 c' rs2 m2 ->
+ exists body,
+ exec_body tge body rs1 m1 = Next rs2 m2
+ /\ (basics_to_code body) ++g c' = c.
+Proof.
+ intros until m2. intros EXES.
+ inv EXES.
+ - exists nil. split; auto.
+ - eapply exec_straight_body2. auto.
+Qed.
+
+Lemma extract_basics_to_code:
+ forall lb c,
+ extract_basic (basics_to_code lb ++ c) = lb ++ extract_basic c.
+Proof.
+ induction lb; intros; simpl; congruence.
+Qed.
+
+Lemma extract_ctl_basics_to_code:
+ forall lb c,
+ extract_ctl (basics_to_code lb ++ c) = extract_ctl c.
+Proof.
+ induction lb; intros; simpl; congruence.
+Qed.
+
+(* Lemma goto_label_inv:
+ forall fn tbb l rs m b ofs,
+ rs PC = Vptr b ofs ->
+ goto_label fn l rs m = goto_label fn l (nextblock tbb rs) m.
+Proof.
+ intros.
+ unfold goto_label. rewrite nextblock_pc. unfold Val.offset_ptr. rewrite H.
+ exploreInst; auto.
+ unfold nextblock. rewrite Pregmap.gss.
+
+Qed.
+
+
+Lemma exec_control_goto_label_inv:
+ exec_control tge fn (Some ctl) rs m = goto_label fn l rs m ->
+ exec_control tge fn (Some ctl) (nextblock tbb rs) m = goto_label fn l (nextblock tbb rs) m.
+Proof.
+Qed. *)
+
+Theorem step_simu_control:
+ forall bb' fb fn s sp c ms' m' rs2 m2 E0 S'' rs1 m1 tbb tbdy2 tex cs2,
+ MB.body bb' = nil ->
+ (forall ef args res, MB.exit bb' <> Some (MBbuiltin ef args res)) ->
+ Genv.find_funct_ptr tge fb = Some (Internal fn) ->
+ pstate cs2 = (Asmblock.State rs2 m2) ->
+ pbody1 cs2 = nil -> pbody2 cs2 = tbdy2 -> pctl cs2 = tex ->
+ cur cs2 = Some tbb ->
+ match_codestate fb (MB.State s fb sp (bb'::c) ms' m') cs2 ->
+ match_asmstate fb cs2 (Asmblock.State rs1 m1) ->
+ exit_step return_address_offset ge (MB.exit bb') (MB.State s fb sp (bb'::c) ms' m') E0 S'' ->
+ (exists rs3 m3 rs4 m4,
+ exec_body tge tbdy2 rs2 m2 = Next rs3 m3
+ /\ exec_control_rel tge fn tex tbb rs3 m3 rs4 m4
+ /\ match_states S'' (State rs4 m4)).
+Proof.
+ intros until cs2. intros Hbody Hbuiltin FIND Hpstate Hpbody1 Hpbody2 Hpctl Hcur MCS MAS ESTEP.
+ inv ESTEP.
+ - inv MCS. inv MAS. simpl in *.
+ inv Hcur. inv Hpstate.
+ destruct ctl.
+ + (* MBcall *)
+ destruct bb' as [mhd' mbdy' mex']; simpl in *. subst.
+ inv TBC. inv TIC. inv H0.
+
+ assert (f0 = f) by congruence. subst f0.
+ assert (NOOV: size_blocks tf.(fn_blocks) <= Ptrofs.max_unsigned).
+ eapply transf_function_no_overflow; eauto.
+ destruct s1 as [rf|fid]; simpl in H7.
+ * (* Indirect call *) inv H1.
+ * (* Direct call *)
+ monadInv H1.
+ generalize (code_tail_next_int _ _ _ _ NOOV TAIL). intro CT1.
+ remember (Ptrofs.add _ _) as ofs'.
+ assert (TCA: transl_code_at_pc ge (Vptr fb ofs') fb f c false tf tc).
+ econstructor; eauto.
+ assert (f1 = f) by congruence. subst f1.
+ exploit return_address_offset_correct; eauto. intros; subst ra.
+ repeat eexists.
+ rewrite H6. econstructor; eauto.
+ rewrite H7. econstructor; eauto.
+ econstructor; eauto.
+ econstructor; eauto. eapply agree_sp_def; eauto. simpl. eapply agree_exten; eauto. intros. Simpl.
+ Simpl. unfold Genv.symbol_address. rewrite symbols_preserved. simpl in H14. rewrite H14. auto.
+ Simpl. simpl. subst. Simpl. simpl. unfold Val.offset_ptr. rewrite PCeq. auto.
+ + (* MBtailcall *)
+ destruct bb' as [mhd' mbdy' mex']; simpl in *. subst.
+ inv TBC. inv TIC. inv H0.
+
+ assert (f0 = f) by congruence. subst f0.
+ assert (NOOV: size_blocks tf.(fn_blocks) <= Ptrofs.max_unsigned).
+ eapply transf_function_no_overflow; eauto.
+ exploit Mem.loadv_extends. eauto. eexact H15. auto. simpl. intros [parent' [A B]].
+ destruct s1 as [rf|fid]; simpl in H13.
+ * inv H1.
+ * monadInv H1. assert (f = f1) by congruence. subst f1. clear FIND1. clear H14.
+ exploit make_epilogue_correct; eauto. intros (rs1 & m1 & U & V & W & X & Y & Z).
+ exploit exec_straight_body; eauto.
+ simpl. eauto.
+ intros EXEB.
+ repeat eexists.
+ rewrite H6. simpl extract_basic. eauto.
+ rewrite H7. simpl extract_ctl. simpl. reflexivity.
+ econstructor; eauto.
+ { apply agree_set_other.
+ - econstructor; auto with asmgen.
+ + apply V.
+ + intro r. destruct r; apply V; auto.
+ - eauto with asmgen. }
+ { Simpl. unfold Genv.symbol_address. rewrite symbols_preserved. rewrite H13. auto. }
+ + (* MBbuiltin (contradiction) *)
+ assert (MB.exit bb' <> Some (MBbuiltin e l b)) by (apply Hbuiltin).
+ rewrite <- H in H1. contradict H1; auto.
+ + (* MBgoto *)
+ destruct bb' as [mhd' mbdy' mex']; simpl in *. subst.
+ inv TBC. inv TIC. inv H0.
+
+ assert (f0 = f) by congruence. subst f0. assert (f1 = f) by congruence. subst f1. clear H11.
+ remember (nextblock tbb rs2) as rs2'.
+ (* inv AT. monadInv H4. *)
+ exploit functions_transl. eapply FIND0. eapply TRANSF0. intros FIND'.
+ assert (tf = fn) by congruence. subst tf.
+ exploit find_label_goto_label.
+ eauto. eauto.
+ instantiate (2 := rs2').
+ { subst. unfold nextblock. Simpl. unfold Val.offset_ptr. rewrite PCeq. eauto. }
+ eauto.
+ intros (tc' & rs' & GOTO & AT2 & INV).
+
+ eexists. eexists. repeat eexists. repeat split.
+ rewrite H6. simpl extract_basic. simpl. eauto.
+ rewrite H7. simpl extract_ctl. simpl. rewrite <- Heqrs2'. eauto.
+ econstructor; eauto.
+ rewrite Heqrs2' in INV. unfold nextblock in INV.
+ eapply agree_exten; eauto with asmgen.
+ assert (forall r : preg, r <> PC -> rs' r = rs2 r).
+ { intros. destruct r.
+ - destruct g. all: rewrite INV; Simpl; auto.
+ - destruct g. all: rewrite INV; Simpl; auto.
+ - rewrite INV; Simpl; auto.
+ - contradiction. }
+ eauto with asmgen.
+ congruence.
+ + (* MBcond *)
+ destruct bb' as [mhd' mbdy' mex']; simpl in *. subst.
+ inv TBC. inv TIC. inv H0.
+
+ * (* MBcond true *)
+ assert (f0 = f) by congruence. subst f0.
+ exploit eval_condition_lessdef.
+ eapply preg_vals; eauto.
+ all: eauto.
+ intros EC.
+ exploit transl_cbranch_correct_true; eauto. intros (rs' & jmp & A & B & C).
+ exploit exec_straight_opt_body2. eauto. intros (bdy & EXEB & BTC).
+ assert (PCeq': rs2 PC = rs' PC). { inv A; auto. erewrite <- exec_straight_pc. 2: eapply H. eauto. }
+ rewrite PCeq' in PCeq.
+ assert (f1 = f) by congruence. subst f1.
+ exploit find_label_goto_label.
+ 4: eapply H16. 1-2: eauto. instantiate (2 := (nextblock tbb rs')). rewrite nextblock_pc.
+ unfold Val.offset_ptr. rewrite PCeq. eauto.
+ intros (tc' & rs3 & GOTOL & TLPC & Hrs3).
+ exploit functions_transl. eapply FIND1. eapply TRANSF0. intros FIND'.
+ assert (tf = fn) by congruence. subst tf.
+
+ repeat eexists.
+ rewrite H6. rewrite <- BTC. rewrite extract_basics_to_code. simpl. rewrite app_nil_r. eauto.
+ rewrite H7. rewrite <- BTC. rewrite extract_ctl_basics_to_code. simpl extract_ctl. rewrite B. eauto.
+
+ econstructor; eauto.
+ eapply agree_exten with rs2; eauto with asmgen.
+ { intros. destruct r; try destruct g; try discriminate.
+ all: rewrite Hrs3; try discriminate; unfold nextblock; Simpl. }
+ intros. discriminate.
+
+ * (* MBcond false *)
+ assert (f0 = f) by congruence. subst f0.
+ exploit eval_condition_lessdef.
+ eapply preg_vals; eauto.
+ all: eauto.
+ intros EC.
+
+ exploit transl_cbranch_correct_false; eauto. intros (rs' & jmp & A & B & C).
+ exploit exec_straight_opt_body2. eauto. intros (bdy & EXEB & BTC).
+ assert (PCeq': rs2 PC = rs' PC). { inv A; auto. erewrite <- exec_straight_pc. 2: eapply H. eauto. }
+ rewrite PCeq' in PCeq.
+ exploit functions_transl. eapply FIND1. eapply TRANSF0. intros FIND'.
+ assert (tf = fn) by congruence. subst tf.
+
+ assert (NOOV: size_blocks fn.(fn_blocks) <= Ptrofs.max_unsigned).
+ eapply transf_function_no_overflow; eauto.
+ generalize (code_tail_next_int _ _ _ _ NOOV TAIL). intro CT1.
+
+ repeat eexists.
+ rewrite H6. rewrite <- BTC. rewrite extract_basics_to_code. simpl. rewrite app_nil_r. eauto.
+ rewrite H7. rewrite <- BTC. rewrite extract_ctl_basics_to_code. simpl extract_ctl. rewrite B. eauto.
+
+ econstructor; eauto.
+ unfold nextblock. Simpl. unfold Val.offset_ptr. rewrite PCeq. econstructor; eauto.
+ eapply agree_exten with rs2; eauto with asmgen.
+ { intros. destruct r; try destruct g; try discriminate.
+ all: rewrite <- C; try discriminate; unfold nextblock; Simpl. }
+ intros. discriminate.
+ + (* MBjumptable *)
+ destruct bb' as [mhd' mbdy' mex']; simpl in *. subst.
+ inv TBC. inv TIC.
+ + (* MBreturn *)
+ destruct bb' as [mhd' mbdy' mex']; simpl in *. subst.
+ inv TBC. inv TIC. inv H0.
+
+ assert (f0 = f) by congruence. subst f0.
+ assert (NOOV: size_blocks tf.(fn_blocks) <= Ptrofs.max_unsigned).
+ eapply transf_function_no_overflow; eauto.
+ exploit make_epilogue_correct; eauto. intros (rs1 & m1 & U & V & W & X & Y & Z).
+ exploit exec_straight_body; eauto.
+ simpl. eauto.
+ intros EXEB.
+ assert (f1 = f) by congruence. subst f1.
+
+ repeat eexists.
+ rewrite H6. simpl extract_basic. eauto.
+ rewrite H7. simpl extract_ctl. simpl. reflexivity.
+ econstructor; eauto.
+ unfold nextblock. repeat apply agree_set_other; auto with asmgen.
+
+ - inv MCS. inv MAS. simpl in *. subst. inv Hpstate. inv Hcur.
+(* exploit transl_blocks_distrib; eauto. (* rewrite <- H2. discriminate. *)
+ intros (TLB & TLBS).
+ *) destruct bb' as [hd' bdy' ex']; simpl in *. subst.
+(* unfold transl_block in TLB. simpl in TLB. unfold gen_bblocks in TLB; simpl in TLB. inv TLB. *)
+ monadInv TBC. monadInv TIC. simpl in *. rewrite H5. rewrite H6.
+ simpl. repeat eexists.
+ econstructor. 4: instantiate (3 := false). all:eauto.
+ unfold nextblock. Simpl. unfold Val.offset_ptr. rewrite PCeq.
+ assert (NOOV: size_blocks tf.(fn_blocks) <= Ptrofs.max_unsigned).
+ eapply transf_function_no_overflow; eauto.
+ assert (f = f0) by congruence. subst f0. econstructor; eauto.
+ generalize (code_tail_next_int _ _ _ _ NOOV TAIL). intro CT1. eauto.
+ eapply agree_exten; eauto. intros. Simpl.
+ discriminate.
+Qed.
+
+Definition mb_remove_first (bb: MB.bblock) :=
+ {| MB.header := MB.header bb; MB.body := tail (MB.body bb); MB.exit := MB.exit bb |}.
+
+Lemma exec_straight_body:
+ forall c c' lc rs1 m1 rs2 m2,
+ exec_straight tge c rs1 m1 c' rs2 m2 ->
+ code_to_basics c = Some lc ->
+ exists l ll,
+ c = l ++ c'
+ /\ code_to_basics l = Some ll
+ /\ exec_body tge ll rs1 m1 = Next rs2 m2.
+Proof.
+ induction c; try (intros; inv H; fail).
+ intros until m2. intros EXES CTB. inv EXES.
+ - exists (i1 ::g nil),(i1::nil). repeat (split; simpl; auto). rewrite H6. auto.
+ - inv CTB. destruct (code_to_basics c); try discriminate. inv H0.
+ eapply IHc in H7; eauto. destruct H7 as (l' & ll & Hc & CTB & EXECB). subst.
+ exists (i ::g l'),(i::ll). repeat (split; simpl; auto).
+ rewrite CTB. auto.
+ rewrite H1. auto.
+Qed.
+
+Lemma basics_to_code_app:
+ forall c l x ll,
+ basics_to_code c = l ++ basics_to_code x ->
+ code_to_basics l = Some ll ->
+ c = ll ++ x.
+Proof.
+ intros. apply (f_equal code_to_basics) in H.
+ erewrite code_to_basics_dist in H; eauto. 2: eapply code_to_basics_id.
+ rewrite code_to_basics_id in H. inv H. auto.
+Qed.
+
+Lemma basics_to_code_app2:
+ forall i c l x ll,
+ (PBasic i) :: basics_to_code c = l ++ basics_to_code x ->
+ code_to_basics l = Some ll ->
+ i :: c = ll ++ x.
+Proof.
+ intros until ll. intros.
+ exploit basics_to_code_app. instantiate (3 := (i::c)). simpl.
+ all: eauto.
+Qed.
+
+Lemma step_simu_basic:
+ forall bb bb' s fb sp c ms m rs1 m1 ms' m' bi cs1 tbdy bdy,
+ MB.header bb = nil -> MB.body bb = bi::(bdy) -> (forall ef args res, MB.exit bb <> Some (MBbuiltin ef args res)) ->
+ bb' = {| MB.header := nil; MB.body := bdy; MB.exit := MB.exit bb |} ->
+ basic_step ge s fb sp ms m bi ms' m' ->
+ pstate cs1 = (State rs1 m1) -> pbody1 cs1 = tbdy ->
+ match_codestate fb (MB.State s fb sp (bb::c) ms m) cs1 ->
+ (exists rs2 m2 l cs2 tbdy',
+ cs2 = {| pstate := (State rs2 m2); pheader := nil; pbody1 := tbdy'; pbody2 := pbody2 cs1;
+ pctl := pctl cs1; fpok := fp_is_parent (fpok cs1) bi; rem := rem cs1; cur := cur cs1 |}
+ /\ tbdy = l ++ tbdy'
+ /\ exec_body tge l rs1 m1 = Next rs2 m2
+ /\ match_codestate fb (MB.State s fb sp (bb'::c) ms' m') cs2).
+Proof.
+ intros until bdy. intros Hheader Hbody Hnobuiltin (* Hnotempty *) Hbb' BSTEP Hpstate Hpbody1 MCS. inv MCS.
+ simpl in *. inv Hpstate.
+ rewrite Hbody in TBC. monadInv TBC.
+ inv BSTEP.
+ - (* MBgetstack *)
+ simpl in EQ0.
+ unfold Mach.load_stack in H.
+ exploit Mem.loadv_extends; eauto. intros [v' [A B]].
+ rewrite (sp_val _ _ _ AG) in A.
+ exploit loadind_correct; eauto with asmgen.
+ intros (rs2 & EXECS & Hrs'1 & Hrs'2).
+ eapply exec_straight_body in EXECS.
+ 2: eapply code_to_basics_id; eauto.
+ destruct EXECS as (l & Hlbi & BTC & CTB & EXECB).
+ exists rs2, m1, Hlbi.
+ eexists. eexists. split. instantiate (1 := x). eauto.
+ repeat (split; auto).
+ eapply basics_to_code_app; eauto.
+ remember {| MB.header := _; MB.body := _; MB.exit := _ |} as bb'.
+(* assert (Hheadereq: MB.header bb' = MB.header bb). { subst. simpl. auto. }
+ rewrite <- Hheadereq. *) subst.
+
+ eapply match_codestate_intro; eauto. simpl. simpl in EQ. (* { destruct (MB.header bb); auto. } *)
+ eapply agree_set_mreg; eauto with asmgen.
+ intro Hep. simpl in Hep. inv Hep.
+ - (* MBsetstack *)
+ simpl in EQ0.
+ unfold Mach.store_stack in H.
+ assert (Val.lessdef (ms src) (rs1 (preg_of src))). { eapply preg_val; eauto. }
+ exploit Mem.storev_extends; eauto. intros [m2' [A B]].
+ exploit storeind_correct; eauto with asmgen.
+ rewrite (sp_val _ _ _ AG) in A. eauto. intros [rs' [P Q]].
+
+ eapply exec_straight_body in P.
+ 2: eapply code_to_basics_id; eauto.
+ destruct P as (l & ll & TBC & CTB & EXECB).
+ exists rs', m2', ll.
+ eexists. eexists. split. instantiate (1 := x). eauto.
+ repeat (split; auto).
+ eapply basics_to_code_app; eauto.
+ remember {| MB.header := _; MB.body := _; MB.exit := _ |} as bb'.
+(* assert (Hheadereq: MB.header bb' = MB.header bb). { subst. auto. }
+ rewrite <- Hheadereq. *) subst.
+ eapply match_codestate_intro; eauto. simpl. simpl in EQ. rewrite Hheader in EQ. auto.
+
+ eapply agree_undef_regs; eauto with asmgen.
+ simpl; intros. rewrite Q; auto with asmgen. rewrite Hheader in DXP. auto.
+ - (* MBgetparam *)
+ simpl in EQ0.
+
+ assert (f0 = f) by congruence; subst f0.
+ unfold Mach.load_stack in *.
+ exploit Mem.loadv_extends. eauto. eexact H0. auto.
+ intros [parent' [A B]]. rewrite (sp_val _ _ _ AG) in A.
+ exploit lessdef_parent_sp; eauto. clear B; intros B; subst parent'.
+ exploit Mem.loadv_extends. eauto. eexact H1. auto.
+ intros [v' [C D]].
+
+ (* Opaque loadind. *)
+(* left; eapply exec_straight_steps; eauto; intros. monadInv TR. *)
+ monadInv EQ0. rewrite Hheader. rewrite Hheader in DXP.
+ destruct ep eqn:EPeq.
+ (* GPR31 contains parent *)
+ + exploit loadind_correct. eexact EQ1.
+ instantiate (2 := rs1). rewrite DXP; eauto. congruence.
+ intros [rs2 [P [Q R]]].
+
+ eapply exec_straight_body in P.
+ 2: eapply code_to_basics_id; eauto.
+ destruct P as (l & ll & BTC & CTB & EXECB).
+ exists rs2, m1, ll. eexists.
+ eexists. split. instantiate (1 := x). eauto.
+ repeat (split; auto).
+ { eapply basics_to_code_app; eauto. }
+ remember {| MB.header := _; MB.body := _; MB.exit := _ |} as bb'.
+ assert (Hheadereq: MB.header bb' = MB.header bb). { subst. simpl. auto. }
+ (* rewrite <- Hheadereq. *)subst.
+ eapply match_codestate_intro; eauto.
+
+ eapply agree_set_mreg. eapply agree_set_mreg; eauto. congruence. auto with asmgen.
+ simpl; intros. rewrite R; auto with asmgen.
+ apply preg_of_not_FP; auto.
+
+ (* GPR11 does not contain parent *)
+ + rewrite chunk_of_Tptr in A.
+ exploit loadind_ptr_correct. eexact A. congruence. intros [rs2 [P [Q R]]].
+ exploit loadind_correct. eexact EQ1. instantiate (2 := rs2). rewrite Q. eauto. congruence.
+ intros [rs3 [S [T U]]].
+
+ exploit exec_straight_trans.
+ eapply P.
+ eapply S.
+ intros EXES.
+
+ eapply exec_straight_body in EXES.
+ 2: simpl. 2: erewrite code_to_basics_id; eauto.
+ destruct EXES as (l & ll & BTC & CTB & EXECB).
+ exists rs3, m1, ll.
+ eexists. eexists. split. instantiate (1 := x). eauto.
+ repeat (split; auto).
+ eapply basics_to_code_app2; eauto.
+ remember {| MB.header := _; MB.body := _; MB.exit := _ |} as bb'.
+ assert (Hheadereq: MB.header bb' = MB.header bb). { subst. auto. }
+ subst.
+ eapply match_codestate_intro; eauto.
+ eapply agree_set_mreg. eapply agree_set_mreg. eauto. eauto.
+ instantiate (1 := rs2#FP <- (rs3#FP)). intros.
+ rewrite Pregmap.gso; auto with asmgen.
+ congruence.
+ intros. unfold Pregmap.set. destruct (PregEq.eq r' FP). congruence. auto with asmgen.
+ simpl; intros. rewrite U; auto with asmgen.
+ apply preg_of_not_FP; auto.
+ - (* MBop *)
+ simpl in EQ0. rewrite Hheader in DXP.
+
+ assert (eval_operation tge sp op (map ms args) m' = Some v).
+ rewrite <- H. apply eval_operation_preserved. exact symbols_preserved.
+ exploit eval_operation_lessdef.
+ eapply preg_vals; eauto.
+ 2: eexact H0.
+ all: eauto.
+ intros [v' [A B]]. rewrite (sp_val _ _ _ AG) in A.
+ exploit transl_op_correct; eauto. intros [rs2 [P [Q R]]].
+
+ eapply exec_straight_body in P.
+ 2: eapply code_to_basics_id; eauto.
+ destruct P as (l & ll & TBC & CTB & EXECB).
+ exists rs2, m1, ll.
+ eexists. eexists. split. instantiate (1 := x). eauto.
+ repeat (split; auto).
+ eapply basics_to_code_app; eauto.
+ remember {| MB.header := _; MB.body := _; MB.exit := _ |} as bb'.
+(* assert (Hheadereq: MB.header bb' = MB.header bb). { subst. auto. }
+ rewrite <- Hheadereq. *) subst.
+ eapply match_codestate_intro; eauto. simpl. simpl in EQ. rewrite Hheader in EQ. auto.
+ apply agree_set_undef_mreg with rs1; auto.
+ apply Val.lessdef_trans with v'; auto.
+ simpl; intros. destruct (andb_prop _ _ H1); clear H1.
+ rewrite R; auto. apply preg_of_not_FP; auto.
+Local Transparent destroyed_by_op.
+ destruct op; simpl; auto; congruence.
+ - (* MBload *)
+ simpl in EQ0. rewrite Hheader in DXP.
+
+ assert (eval_addressing tge sp addr (map ms args) = Some a).
+ rewrite <- H. apply eval_addressing_preserved. exact symbols_preserved.
+ exploit eval_addressing_lessdef. eapply preg_vals; eauto. eexact H1.
+ intros [a' [A B]]. rewrite (sp_val _ _ _ AG) in A.
+ exploit Mem.loadv_extends; eauto. intros [v' [C D]].
+ exploit transl_load_correct; eauto.
+ intros [rs2 [P [Q R]]].
+
+ eapply exec_straight_body in P.
+ 2: eapply code_to_basics_id; eauto.
+ destruct P as (l & ll & TBC & CTB & EXECB).
+ exists rs2, m1, ll.
+ eexists. eexists. split. instantiate (1 := x). eauto.
+ repeat (split; auto).
+ eapply basics_to_code_app; eauto.
+ remember {| MB.header := _; MB.body := _; MB.exit := _ |} as bb'.
+(* assert (Hheadereq: MB.header bb' = MB.header bb). { subst. auto. }
+ rewrite <- Hheadereq. *) subst.
+ eapply match_codestate_intro; eauto. simpl. simpl in EQ.
+
+ eapply agree_set_undef_mreg; eauto. intros; auto with asmgen.
+ simpl; congruence.
+
+ - (* MBstore *)
+ simpl in EQ0. rewrite Hheader in DXP.
+
+ assert (eval_addressing tge sp addr (map ms args) = Some a).
+ rewrite <- H. apply eval_addressing_preserved. exact symbols_preserved.
+ exploit eval_addressing_lessdef. eapply preg_vals; eauto. eexact H1.
+ intros [a' [A B]]. rewrite (sp_val _ _ _ AG) in A.
+ assert (Val.lessdef (ms src) (rs1 (preg_of src))). eapply preg_val; eauto.
+ exploit Mem.storev_extends; eauto. intros [m2' [C D]].
+ exploit transl_store_correct; eauto. intros [rs2 [P Q]].
+
+ eapply exec_straight_body in P.
+ 2: eapply code_to_basics_id; eauto.
+ destruct P as (l & ll & TBC & CTB & EXECB).
+ exists rs2, m2', ll.
+ eexists. eexists. split. instantiate (1 := x). eauto.
+ repeat (split; auto).
+ eapply basics_to_code_app; eauto.
+ remember {| MB.header := _; MB.body := _; MB.exit := _ |} as bb'.
+ subst.
+ eapply match_codestate_intro; eauto. simpl. simpl in EQ.
+
+ eapply agree_undef_regs; eauto with asmgen.
+ simpl; congruence.
+Qed.
+
+Lemma exec_body_trans:
+ forall l l' rs0 m0 rs1 m1 rs2 m2,
+ exec_body tge l rs0 m0 = Next rs1 m1 ->
+ exec_body tge l' rs1 m1 = Next rs2 m2 ->
+ exec_body tge (l++l') rs0 m0 = Next rs2 m2.
+Proof.
+ induction l.
+ - simpl. congruence.
+ - intros until m2. intros EXEB1 EXEB2.
+ inv EXEB1. destruct (exec_basic_instr _) eqn:EBI; try discriminate.
+ simpl. rewrite EBI. eapply IHl; eauto.
+Qed.
+
+Definition mb_remove_header bb := {| MB.header := nil; MB.body := MB.body bb; MB.exit := MB.exit bb |}.
+
+Program Definition remove_header tbb := {| header := nil; body := body tbb; exit := exit tbb |}.
+Next Obligation.
+ destruct tbb. simpl. auto.
+Qed.
+
+Inductive exec_header: codestate -> codestate -> Prop :=
+ | exec_header_cons: forall cs1,
+ exec_header cs1 {| pstate := pstate cs1; pheader := nil; pbody1 := pbody1 cs1; pbody2 := pbody2 cs1;
+ pctl := pctl cs1; fpok := (if pheader cs1 then fpok cs1 else false); rem := rem cs1;
+ (* cur := match cur cs1 with None => None | Some bcur => Some (remove_header bcur) end *)
+ cur := cur cs1 |}.
+
+Lemma step_simu_header:
+ forall bb s fb sp c ms m rs1 m1 cs1,
+(* (forall ef args res, MB.exit bb <> Some (MBbuiltin ef args res)) -> *)
+ pstate cs1 = (State rs1 m1) ->
+ match_codestate fb (MB.State s fb sp (bb::c) ms m) cs1 ->
+ (exists cs1',
+ exec_header cs1 cs1'
+ /\ match_codestate fb (MB.State s fb sp (mb_remove_header bb::c) ms m) cs1').
+Proof.
+ intros until cs1. intros Hpstate MCS.
+ eexists. split; eauto.
+ econstructor; eauto.
+ inv MCS. simpl in *. inv Hpstate.
+ econstructor; eauto.
+Qed.
+
+Lemma step_matchasm_header:
+ forall fb cs1 cs1' s1,
+ match_asmstate fb cs1 s1 ->
+ exec_header cs1 cs1' ->
+ match_asmstate fb cs1' s1.
+Proof.
+ intros until s1. intros MAS EXH.
+ inv MAS. inv EXH.
+ simpl. econstructor; eauto.
+Qed.
+
+Lemma step_simu_body:
+ forall bb s fb sp c ms m rs1 m1 ms' cs1 m',
+ MB.header bb = nil ->
+ (forall ef args res, MB.exit bb <> Some (MBbuiltin ef args res)) ->
+ body_step ge s fb sp (MB.body bb) ms m ms' m' ->
+ pstate cs1 = (State rs1 m1) ->
+ match_codestate fb (MB.State s fb sp (bb::c) ms m) cs1 ->
+ (exists rs2 m2 cs2 ep,
+ cs2 = {| pstate := (State rs2 m2); pheader := nil; pbody1 := nil; pbody2 := pbody2 cs1;
+ pctl := pctl cs1; fpok := ep; rem := rem cs1; cur := cur cs1 |}
+ /\ exec_body tge (pbody1 cs1) rs1 m1 = Next rs2 m2
+ /\ match_codestate fb (MB.State s fb sp ({| MB.header := nil; MB.body := nil; MB.exit := MB.exit bb |}::c) ms' m') cs2).
+Proof.
+ intros bb. destruct bb as [hd bdy ex]; simpl; auto. induction bdy as [|bi bdy].
+ - intros until m'. intros Hheader Hnobuiltin BSTEP Hpstate MCS.
+ inv BSTEP.
+ exists rs1, m1, cs1, (fpok cs1).
+ inv MCS. inv Hpstate. simpl in *. monadInv TBC. repeat (split; simpl; auto).
+ econstructor; eauto.
+ - intros until m'. intros Hheader Hnobuiltin BSTEP Hpstate MCS. inv BSTEP.
+ rename ms' into ms''. rename m' into m''. rename rs' into ms'. rename m'0 into m'.
+ exploit (step_simu_basic); eauto. simpl. eauto. simpl; auto. simpl; auto.
+ intros (rs2 & m2 & l & cs2 & tbdy' & Hcs2 & Happ & EXEB & MCS').
+ simpl in *.
+ exploit IHbdy. auto. 2: eapply H6. 3: eapply MCS'. all: eauto. subst; eauto. simpl; auto.
+ intros (rs3 & m3 & cs3 & ep & Hcs3 & EXEB' & MCS'').
+ exists rs3, m3, cs3, ep.
+ repeat (split; simpl; auto). subst. simpl in *. auto.
+ rewrite Happ. eapply exec_body_trans; eauto. rewrite Hcs2 in EXEB'; simpl in EXEB'. auto.
+Qed.
+
+(* Lemma exec_body_straight:
+ forall l rs0 m0 rs1 m1,
+ l <> nil ->
+ exec_body tge l rs0 m0 = Next rs1 m1 ->
+ exec_straight tge l rs0 m0 nil rs1 m1.
+Proof.
+ induction l as [|i1 l].
+ intros. contradict H; auto.
+ destruct l as [|i2 l].
+ - intros until m1. intros _ EXEB. simpl in EXEB.
+ destruct (exec_basic_instr _ _ _) eqn:EBI; try discriminate.
+ inv EXEB. econstructor; eauto.
+ - intros until m1. intros _ EXEB. simpl in EXEB. simpl in IHl.
+ destruct (exec_basic_instr tge i1 rs0 m0) eqn:EBI; try discriminate.
+ econstructor; eauto. eapply IHl; eauto. discriminate.
+Qed. *)
+
+Lemma exec_body_pc:
+ forall l rs1 m1 rs2 m2,
+ exec_body tge l rs1 m1 = Next rs2 m2 ->
+ rs2 PC = rs1 PC.
+Proof.
+ induction l.
+ - intros. inv H. auto.
+ - intros until m2. intro EXEB.
+ inv EXEB. destruct (exec_basic_instr _ _ _) eqn:EBI; try discriminate.
+ eapply IHl in H0. rewrite H0.
+ erewrite exec_basic_instr_pc; eauto.
+Qed.
+
+Lemma exec_body_control:
+ forall b rs1 m1 rs2 m2 rs3 m3 fn,
+ exec_body tge (body b) rs1 m1 = Next rs2 m2 ->
+ exec_control_rel tge fn (exit b) b rs2 m2 rs3 m3 ->
+ exec_bblock_rel tge fn b rs1 m1 rs3 m3.
+Proof.
+ intros until fn. intros EXEB EXECTL.
+ econstructor; eauto. inv EXECTL.
+ unfold exec_bblock. rewrite EXEB. auto.
+Qed.
+
+Definition mbsize (bb: MB.bblock) := (length (MB.body bb) + length_opt (MB.exit bb))%nat.
+
+Lemma mbsize_eqz:
+ forall bb, mbsize bb = 0%nat -> MB.body bb = nil /\ MB.exit bb = None.
+Proof.
+ intros. destruct bb as [hd bdy ex]; simpl in *. unfold mbsize in H.
+ remember (length _) as a. remember (length_opt _) as b.
+ assert (a = 0%nat) by omega. assert (b = 0%nat) by omega. subst. clear H.
+ inv H0. inv H1. destruct bdy; destruct ex; auto.
+ all: try discriminate.
+Qed.
+
+Lemma mbsize_neqz:
+ forall bb, mbsize bb <> 0%nat -> (MB.body bb <> nil \/ MB.exit bb <> None).
+Proof.
+ intros. destruct bb as [hd bdy ex]; simpl in *.
+ destruct bdy; destruct ex; try (right; discriminate); try (left; discriminate).
+ contradict H. unfold mbsize. simpl. auto.
+Qed.
+
+(* Alternative form of step_simulation_bblock, easier to prove *)
+Lemma step_simulation_bblock':
+ forall sf f sp bb bb' bb'' rs m rs' m' s'' c S1,
+ bb' = mb_remove_header bb ->
+ body_step ge sf f sp (Machblock.body bb') rs m rs' m' ->
+ bb'' = mb_remove_body bb' ->
+ (forall ef args res, MB.exit bb'' <> Some (MBbuiltin ef args res)) ->
+ exit_step return_address_offset ge (Machblock.exit bb'') (Machblock.State sf f sp (bb'' :: c) rs' m') E0 s'' ->
+ match_states (Machblock.State sf f sp (bb :: c) rs m) S1 ->
+ exists S2 : state, plus step tge S1 E0 S2 /\ match_states s'' S2.
+Proof.
+ intros until S1. intros Hbb' BSTEP Hbb'' Hbuiltin ESTEP MS.
+ destruct (mbsize bb) eqn:SIZE.
+ - apply mbsize_eqz in SIZE. destruct SIZE as (Hbody & Hexit).
+ destruct bb as [hd bdy ex]; simpl in *; subst.
+ inv MS. inv AT. exploit transl_blocks_nonil; eauto. intros (tbb & tc' & Htc). subst. rename tc' into tc.
+ monadInv H2. simpl in *. inv ESTEP. inv BSTEP.
+ eexists. split. eapply plus_one.
+ exploit functions_translated; eauto. intros (tf0 & FIND' & TRANSF'). monadInv TRANSF'.
+ assert (x = tf) by congruence. subst x.
+ eapply exec_step_internal; eauto. eapply find_bblock_tail; eauto.
+ unfold exec_bblock. simpl. eauto.
+ econstructor. eauto. eauto. eauto.
+ unfold nextblock. Simpl. unfold Val.offset_ptr. rewrite <- H.
+ assert (NOOV: size_blocks tf.(fn_blocks) <= Ptrofs.max_unsigned).
+ eapply transf_function_no_overflow; eauto.
+ econstructor; eauto.
+ generalize (code_tail_next_int _ _ _ _ NOOV H3). intro CT1. eauto.
+ eapply agree_exten; eauto. intros. Simpl.
+ intros. discriminate.
+ - subst. exploit mbsize_neqz. { instantiate (1 := bb). rewrite SIZE. discriminate. }
+ intros Hnotempty.
+
+ (* initial setting *)
+ exploit match_state_codestate.
+ 2: eapply Hnotempty.
+ all: eauto.
+ intros (cs1 & fb & f0 & tbb & tc & ep & MCS & MAS & FIND & TLBS & Hbody & Hexit & Hcur & Hrem & Hpstate).
+
+ (* step_simu_header part *)
+ assert (exists rs1 m1, pstate cs1 = State rs1 m1). { inv MAS. simpl. eauto. }
+ destruct H as (rs1 & m1 & Hpstate2). subst.
+ assert (f = fb). { inv MCS. auto. } subst fb.
+ exploit step_simu_header.
+ 2: eapply MCS.
+ all: eauto.
+ intros (cs1' & EXEH & MCS2).
+
+ (* step_simu_body part *)
+(* assert (MB.body bb = MB.body (mb_remove_header bb)). { destruct bb; simpl; auto. }
+ rewrite H in BSTEP. clear H. *)
+ assert (Hpstate': pstate cs1' = pstate cs1). { inv EXEH; auto. }
+ exploit step_simu_body.
+ 3: eapply BSTEP.
+ 4: eapply MCS2.
+ all: eauto. rewrite Hpstate'. eauto.
+ intros (rs2 & m2 & cs2 & ep' & Hcs2 & EXEB & MCS').
+
+ (* step_simu_control part *)
+ assert (exists tf, Genv.find_funct_ptr tge f = Some (Internal tf)).
+ { exploit functions_translated; eauto. intros (tf & FIND' & TRANSF'). monadInv TRANSF'. eauto. }
+ destruct H as (tf & FIND').
+ assert (exists tex, pbody2 cs1 = extract_basic tex /\ pctl cs1 = extract_ctl tex).
+ { inv MAS. simpl in *. eauto. }
+ destruct H as (tex & Hpbody2 & Hpctl).
+ inv EXEH. simpl in *.
+ subst. exploit step_simu_control.
+ 9: eapply MCS'. all: simpl.
+ 10: eapply ESTEP.
+ all: simpl; eauto.
+ rewrite Hpbody2. rewrite Hpctl. rewrite Hcur.
+ { inv MAS; simpl in *. inv Hcur. inv Hpstate2. eapply match_asmstate_some; eauto.
+ erewrite exec_body_pc; eauto. }
+ intros (rs3 & m3 & rs4 & m4 & EXEB' & EXECTL' & MS').
+
+ (* bringing the pieces together *)
+ exploit exec_body_trans.
+ eapply EXEB.
+ eauto.
+ intros EXEB2.
+ exploit exec_body_control; eauto.
+ rewrite <- Hpbody2 in EXEB2. rewrite <- Hbody in EXEB2. eauto.
+ rewrite Hexit. rewrite Hpctl. eauto.
+ intros EXECB. inv EXECB.
+ exists (State rs4 m4).
+ split; auto. eapply plus_one. rewrite Hpstate2.
+ assert (exists ofs, rs1 PC = Vptr f ofs).
+ { rewrite Hpstate2 in MAS. inv MAS. simpl in *. eauto. }
+ destruct H0 as (ofs & Hrs1pc).
+ eapply exec_step_internal; eauto.
+
+ (* proving the initial find_bblock *)
+ rewrite Hpstate2 in MAS. inv MAS. simpl in *.
+ assert (f1 = f0) by congruence. subst f0.
+ rewrite PCeq in Hrs1pc. inv Hrs1pc.
+ exploit functions_translated; eauto. intros (tf1 & FIND'' & TRANS''). rewrite FIND' in FIND''.
+ inv FIND''. monadInv TRANS''. rewrite TRANSF0 in EQ. inv EQ. inv Hcur.
+ eapply find_bblock_tail; eauto.
+Qed.
+
+Lemma step_simulation_bblock:
+ forall sf f sp bb ms m ms' m' S2 c,
+ body_step ge sf f sp (Machblock.body bb) ms m ms' m' ->
+ (forall ef args res, MB.exit bb <> Some (MBbuiltin ef args res)) ->
+ exit_step return_address_offset ge (Machblock.exit bb) (Machblock.State sf f sp (bb :: c) ms' m') E0 S2 ->
+ forall S1', match_states (Machblock.State sf f sp (bb :: c) ms m) S1' ->
+ exists S2' : state, plus step tge S1' E0 S2' /\ match_states S2 S2'.
+Proof.
+ intros until c. intros BSTEP Hbuiltin ESTEP S1' MS.
+ eapply step_simulation_bblock'; eauto.
+ all: destruct bb as [hd bdy ex]; simpl in *; eauto.
+ inv ESTEP.
+ - econstructor. inv H; try (econstructor; eauto; fail).
+ - econstructor.
+Qed.
+
+Definition measure (s: MB.state) : nat :=
+ match s with
+ | MB.State _ _ _ _ _ _ => 0%nat
+ | MB.Callstate _ _ _ _ => 0%nat
+ | MB.Returnstate _ _ _ => 1%nat
+ end.
+
+Definition split (c: MB.code) :=
+ match c with
+ | nil => nil
+ | bb::c => {| MB.header := MB.header bb; MB.body := MB.body bb; MB.exit := None |}
+ :: {| MB.header := nil; MB.body := nil; MB.exit := MB.exit bb |} :: c
+ end.
+
+Lemma cons_ok_eq3 {A: Type} :
+ forall (x:A) y z x' y' z',
+ x = x' -> y = y' -> z = z' ->
+ OK (x::y::z) = OK (x'::y'::z').
+Proof.
+ intros. subst. auto.
+Qed.
+
+Lemma transl_blocks_split_builtin:
+ forall bb c ep f ef args res,
+ MB.exit bb = Some (MBbuiltin ef args res) -> MB.body bb <> nil ->
+ transl_blocks f (split (bb::c)) ep = transl_blocks f (bb::c) ep.
+Proof.
+ intros until res. intros Hexit Hbody. simpl split.
+ unfold transl_blocks. fold transl_blocks. unfold transl_block.
+ simpl. remember (transl_basic_code _ _ _) as tbc. remember (transl_instr_control _ _) as tbi.
+ remember (transl_blocks _ _ _) as tlbs.
+ destruct tbc; destruct tbi; destruct tlbs.
+ all: try simpl; auto.
+ - simpl. rewrite Hexit in Heqtbi. simpl in Heqtbi. monadInv Heqtbi. simpl.
+ unfold gen_bblocks. simpl. destruct l.
+ + exploit transl_basic_code_nonil; eauto. intro. destruct H.
+ + simpl. rewrite app_nil_r. apply cons_ok_eq3. all: try eapply bblock_equality. all: simpl; auto.
+Qed.
+
+Lemma transl_code_at_pc_split_builtin:
+ forall rs f f0 bb c ep tf tc ef args res,
+ MB.body bb <> nil -> MB.exit bb = Some (MBbuiltin ef args res) ->
+ transl_code_at_pc ge (rs PC) f f0 (bb :: c) ep tf tc ->
+ transl_code_at_pc ge (rs PC) f f0 (split (bb :: c)) ep tf tc.
+Proof.
+ intros until res. intros Hbody Hexit AT. inv AT.
+ econstructor; eauto. erewrite transl_blocks_split_builtin; eauto.
+Qed.
+
+Theorem match_states_split_builtin:
+ forall sf f sp bb c rs m ef args res S1,
+ MB.body bb <> nil -> MB.exit bb = Some (MBbuiltin ef args res) ->
+ match_states (Machblock.State sf f sp (bb :: c) rs m) S1 ->
+ match_states (Machblock.State sf f sp (split (bb::c)) rs m) S1.
+Proof.
+ intros until S1. intros Hbody Hexit MS.
+ inv MS.
+ econstructor; eauto.
+ eapply transl_code_at_pc_split_builtin; eauto.
+Qed.
+
+Lemma step_simulation_builtin:
+ forall ef args res bb sf f sp c ms m t S2,
+ MB.body bb = nil -> MB.exit bb = Some (MBbuiltin ef args res) ->
+ exit_step return_address_offset ge (MB.exit bb) (Machblock.State sf f sp (bb :: c) ms m) t S2 ->
+ forall S1', match_states (Machblock.State sf f sp (bb :: c) ms m) S1' ->
+ exists S2' : state, plus step tge S1' t S2' /\ match_states S2 S2'.
+Proof.
+ intros until S2. intros Hbody Hexit ESTEP S1' MS.
+ inv MS. inv AT. monadInv H2. monadInv EQ.
+ rewrite Hbody in EQ0. monadInv EQ0.
+ rewrite Hexit in EQ. monadInv EQ.
+ rewrite Hexit in ESTEP. inv ESTEP. inv H4.
+
+ exploit functions_transl; eauto. intro FN.
+ generalize (transf_function_no_overflow _ _ H1); intro NOOV.
+ exploit builtin_args_match; eauto. intros [vargs' [P Q]].
+ exploit external_call_mem_extends; eauto.
+ intros [vres' [m2' [A [B [C D]]]]].
+ econstructor; split. apply plus_one.
+ simpl in H3.
+ eapply exec_step_builtin. eauto. eauto.
+ eapply find_bblock_tail; eauto.
+ simpl. eauto.
+ erewrite <- sp_val by eauto.
+ eapply eval_builtin_args_preserved with (ge1 := ge); eauto. exact symbols_preserved.
+ eapply external_call_symbols_preserved; eauto. apply senv_preserved.
+ eauto.
+ econstructor; eauto.
+ instantiate (2 := tf); instantiate (1 := x0).
+ unfold nextblock. rewrite Pregmap.gss.
+ rewrite set_res_other. rewrite undef_regs_other_2. rewrite Pregmap.gso by congruence.
+ rewrite <- H. simpl. econstructor; eauto.
+ eapply code_tail_next_int; eauto.
+ rewrite preg_notin_charact. intros. auto with asmgen.
+ auto with asmgen.
+ apply agree_nextblock. eapply agree_set_res; auto.
+ eapply agree_undef_regs; eauto. intros. rewrite undef_regs_other_2; auto.
+ apply Pregmap.gso; auto with asmgen.
+ congruence.
+Qed.
+
+Theorem step_simulation:
+ forall S1 t S2, MB.step return_address_offset ge S1 t S2 ->
+ forall S1' (MS: match_states S1 S1'),
+ (exists S2', plus step tge S1' t S2' /\ match_states S2 S2')
+ \/ (measure S2 < measure S1 /\ t = E0 /\ match_states S2 S1')%nat.
+Proof.
+ induction 1; intros.
+
+- (* bblock *)
+ left. destruct (Machblock.exit bb) eqn:MBE; try destruct c0.
+ all: try(inversion H0; subst; inv H2; eapply step_simulation_bblock;
+ try (rewrite MBE; try discriminate); eauto).
+ + (* MBbuiltin *)
+ destruct (MB.body bb) eqn:MBB.
+ * inv H. eapply step_simulation_builtin; eauto. rewrite MBE. eauto.
+ * eapply match_states_split_builtin in MS; eauto.
+ 2: rewrite MBB; discriminate.
+ simpl split in MS.
+ rewrite <- MBB in H.
+ remember {| MB.header := _; MB.body := _; MB.exit := _ |} as bb1.
+ assert (MB.body bb = MB.body bb1). { subst. simpl. auto. }
+ rewrite H1 in H. subst.
+ exploit step_simulation_bblock. eapply H.
+ discriminate.
+ simpl. constructor.
+ eauto.
+ intros (S2' & PLUS1 & MS').
+ rewrite MBE in MS'.
+ assert (exit_step return_address_offset ge (Some (MBbuiltin e l b))
+ (MB.State sf f sp ({| MB.header := nil; MB.body := nil; MB.exit := Some (MBbuiltin e l b) |}::c)
+ rs' m') t s').
+ { inv H0. inv H3. econstructor. econstructor; eauto. }
+ exploit step_simulation_builtin.
+ 4: eapply MS'.
+ all: simpl; eauto.
+ intros (S3' & PLUS'' & MS'').
+ exists S3'. split; eauto.
+ eapply plus_trans. eapply PLUS1. eapply PLUS''. eauto.
+ + inversion H0. subst. eapply step_simulation_bblock; try (rewrite MBE; try discriminate); eauto.
+
+- (* internal function *)
+ inv MS.
+ exploit functions_translated; eauto. intros [tf [A B]]. monadInv B.
+ generalize EQ; intros EQ'. monadInv EQ'.
+ destruct (zlt Ptrofs.max_unsigned (size_blocks x0.(fn_blocks))); inversion EQ1. clear EQ1. subst x0.
+ unfold Mach.store_stack in *.
+ exploit Mem.alloc_extends. eauto. eauto. apply Z.le_refl. apply Z.le_refl.
+ intros [m1' [C D]].
+ exploit Mem.storev_extends. eexact D. eexact H1. eauto. eauto.
+ intros [m2' [F G]].
+ simpl chunk_of_type in F.
+ exploit Mem.storev_extends. eexact G. eexact H2. eauto. eauto.
+ intros [m3' [P Q]].
+ (* Execution of function prologue *)
+ monadInv EQ0. (* rewrite transl_code'_transl_code in EQ1. *)
+ set (tfbody := Pallocframe (fn_stacksize f) (fn_link_ofs f) ::b
+ Pget GPR8 RA ::b
+ storeind_ptr GPR8 SP (fn_retaddr_ofs f) ::b x0) in *.
+ set (tf := {| fn_sig := MB.fn_sig f; fn_blocks := tfbody |}) in *.
+ set (rs2 := nextblock (bblock_single_inst (Pallocframe (fn_stacksize f) (fn_link_ofs f)))
+ (rs0#FP <- (parent_sp s) #SP <- sp #GPR31 <- Vundef)).
+ exploit (Pget_correct tge GPR8 RA nil rs2 m2'); auto.
+ intros (rs' & U' & V').
+ exploit (exec_straight_through_singleinst); eauto.
+ intro W'. remember (nextblock _ rs') as rs''.
+ exploit (storeind_ptr_correct tge SP (fn_retaddr_ofs f) GPR8 nil rs'' m2').
+ rewrite chunk_of_Tptr in P.
+ assert (rs' GPR8 = rs0 RA). { apply V'. }
+ assert (rs'' GPR8 = rs' GPR8). { subst. Simpl. }
+ assert (rs' GPR12 = rs2 GPR12). { apply V'; discriminate. }
+ assert (rs'' GPR12 = rs' GPR12). { subst. Simpl. }
+ rewrite H4. rewrite H3. rewrite H6. rewrite H5.
+ (* change (rs' GPR8) with (rs0 RA). *)
+ rewrite ATLR.
+ change (rs2 GPR12) with sp. eexact P.
+ congruence. congruence.
+ intros (rs3 & U & V).
+ exploit (exec_straight_through_singleinst); eauto.
+ intro W.
+ remember (nextblock _ rs3) as rs3'.
+ assert (EXEC_PROLOGUE:
+ exec_straight_blocks tge tf
+ tf.(fn_blocks) rs0 m'
+ x0 rs3' m3').
+ { change (fn_blocks tf) with tfbody; unfold tfbody.
+ apply exec_straight_blocks_step with rs2 m2'.
+ unfold exec_bblock. simpl exec_body. rewrite C. fold sp. simpl exec_control.
+ rewrite <- (sp_val _ _ _ AG). rewrite chunk_of_Tptr in F. simpl in F. rewrite F. reflexivity.
+ reflexivity.
+ eapply exec_straight_blocks_trans.
+ - eexact W'.
+ - eexact W. }
+ exploit exec_straight_steps_2; eauto using functions_transl.
+ simpl fn_blocks. simpl fn_blocks in g. unfold tfbody. simpl bblock_single_inst. omega. constructor.
+ intros (ofs' & X & Y).
+ left; exists (State rs3' m3'); split.
+ eapply exec_straight_steps_1; eauto.
+ simpl fn_blocks. simpl fn_blocks in g. unfold tfbody. simpl bblock_single_inst. omega.
+ constructor.
+ econstructor; eauto.
+ rewrite X; econstructor; eauto.
+ apply agree_exten with rs2; eauto with asmgen.
+ unfold rs2.
+ apply agree_nextblock. apply agree_set_other; auto with asmgen.
+ apply agree_change_sp with (parent_sp s).
+ apply agree_undef_regs with rs0. auto.
+Local Transparent destroyed_at_function_entry.
+ simpl; intros; Simpl.
+ unfold sp; congruence.
+
+ intros.
+ assert (r <> GPR31). { contradict H3; rewrite H3; unfold data_preg; auto. }
+ rewrite Heqrs3'. Simpl. rewrite V. rewrite Heqrs''. Simpl. inversion V'. rewrite H6. auto.
+ assert (r <> GPR8). { contradict H3; rewrite H3; unfold data_preg; auto. }
+ assert (forall r : preg, r <> PC -> r <> GPR8 -> rs' r = rs2 r). { apply V'. }
+ (* rewrite H8; auto. *)
+ contradict H3; rewrite H3; unfold data_preg; auto.
+ contradict H3; rewrite H3; unfold data_preg; auto.
+ contradict H3; rewrite H3; unfold data_preg; auto.
+ auto. intros. rewrite Heqrs3'. Simpl. rewrite V by auto with asmgen.
+ assert (forall r : preg, r <> PC -> r <> GPR8 -> rs' r = rs2 r). { apply V'. }
+ rewrite Heqrs''. Simpl.
+ rewrite H4 by auto with asmgen. reflexivity.
+- (* external function *)
+ inv MS.
+ exploit functions_translated; eauto.
+ intros [tf [A B]]. simpl in B. inv B.
+ exploit extcall_arguments_match; eauto.
+ intros [args' [C D]].
+ exploit external_call_mem_extends; eauto.
+ intros [res' [m2' [P [Q [R S]]]]].
+ left; econstructor; split.
+ apply plus_one. eapply exec_step_external; eauto.
+ eapply external_call_symbols_preserved; eauto. apply senv_preserved.
+ econstructor; eauto.
+ unfold loc_external_result.
+ apply agree_set_other; auto.
+ apply agree_set_pair; auto.
+
+- (* return *)
+ inv MS.
+ inv STACKS. simpl in *.
+ right. split. omega. split. auto.
+ rewrite <- ATPC in H5.
+ econstructor; eauto. congruence.
+Qed.
+
+Lemma transf_initial_states:
+ forall st1, MB.initial_state prog st1 ->
+ exists st2, AB.initial_state tprog st2 /\ match_states st1 st2.
+Proof.
+ intros. inversion H. unfold ge0 in *.
+ econstructor; split.
+ econstructor.
+ eapply (Genv.init_mem_transf_partial TRANSF); eauto.
+ replace (Genv.symbol_address (Genv.globalenv tprog) (prog_main tprog) Ptrofs.zero)
+ with (Vptr fb Ptrofs.zero).
+ econstructor; eauto.
+ constructor.
+ apply Mem.extends_refl.
+ split. auto. simpl. unfold Vnullptr; destruct Archi.ptr64; congruence.
+ intros. rewrite Mach.Regmap.gi. auto.
+ unfold Genv.symbol_address.
+ rewrite (match_program_main TRANSF).
+ rewrite symbols_preserved.
+ unfold ge; rewrite H1. auto.
+Qed.
+
+Lemma transf_final_states:
+ forall st1 st2 r,
+ match_states st1 st2 -> MB.final_state st1 r -> AB.final_state st2 r.
+Proof.
+ intros. inv H0. inv H. constructor. assumption.
+ compute in H1. inv H1.
+ generalize (preg_val _ _ _ R0 AG). rewrite H2. intros LD; inv LD. auto.
+Qed.
+
+Definition return_address_offset : Machblock.function -> Machblock.code -> ptrofs -> Prop :=
+ Asmblockgenproof0.return_address_offset.
+
+Theorem transf_program_correct:
+ forward_simulation (MB.semantics return_address_offset prog) (AB.semantics tprog).
+Proof.
+ eapply forward_simulation_star with (measure := measure).
+ - apply senv_preserved.
+ - eexact transf_initial_states.
+ - eexact transf_final_states.
+ - exact step_simulation.
+Qed.
+
+End PRESERVATION.
diff --git a/mppa_k1c/Asmblockgenproof0.v b/mppa_k1c/Asmblockgenproof0.v new file mode 100644 index 00000000..e2b72295 --- /dev/null +++ b/mppa_k1c/Asmblockgenproof0.v @@ -0,0 +1,1081 @@ +Require Import Coqlib. +Require Intv. +Require Import AST. +Require Import Errors. +Require Import Integers. +Require Import Floats. +Require Import Values. +Require Import Memory. +Require Import Globalenvs. +Require Import Events. +Require Import Smallstep. +Require Import Locations. +Require Import Machblock. +Require Import Asmblock. +Require Import Asmblockgen. + +Module MB:=Machblock. +Module AB:=Asmblock. + +Hint Extern 2 (_ <> _) => congruence: asmgen. + +Lemma ireg_of_eq: + forall r r', ireg_of r = OK r' -> preg_of r = IR r'. +Proof. + unfold ireg_of; intros. destruct (preg_of r); inv H; auto. +(* destruct b. all: try discriminate. + inv H1. auto. + *)Qed. + +(* FIXME - Replaced FR by IR for MPPA *) +Lemma freg_of_eq: + forall r r', freg_of r = OK r' -> preg_of r = IR r'. +Proof. + unfold freg_of; intros. destruct (preg_of r); inv H; auto. +(* destruct b. all: try discriminate. + inv H1. auto. + *)Qed. + + +Lemma preg_of_injective: + forall r1 r2, preg_of r1 = preg_of r2 -> r1 = r2. +Proof. + destruct r1; destruct r2; simpl; intros; reflexivity || discriminate. +Qed. + +Lemma preg_of_data: + forall r, data_preg (preg_of r) = true. +Proof. + intros. destruct r; reflexivity. +Qed. +Hint Resolve preg_of_data: asmgen. + +Lemma data_diff: + forall r r', + data_preg r = true -> data_preg r' = false -> r <> r'. +Proof. + congruence. +Qed. +Hint Resolve data_diff: asmgen. + +Lemma preg_of_not_SP: + forall r, preg_of r <> SP. +Proof. + intros. unfold preg_of; destruct r; simpl; congruence. +Qed. + +Lemma preg_of_not_PC: + forall r, preg_of r <> PC. +Proof. + intros. apply data_diff; auto with asmgen. +Qed. + +Hint Resolve preg_of_not_SP preg_of_not_PC: asmgen. + +Lemma nextblock_pc: + forall b rs, (nextblock b rs)#PC = Val.offset_ptr rs#PC (Ptrofs.repr (size b)). +Proof. + intros. apply Pregmap.gss. +Qed. + +Lemma nextblock_inv: + forall b r rs, r <> PC -> (nextblock b rs)#r = rs#r. +Proof. + intros. unfold nextblock. apply Pregmap.gso. red; intro; subst. auto. +Qed. + +Lemma nextblock_inv1: + forall b r rs, data_preg r = true -> (nextblock b rs)#r = rs#r. +Proof. + intros. apply nextblock_inv. red; intro; subst; discriminate. +Qed. + +Lemma undef_regs_other: + forall r rl rs, + (forall r', In r' rl -> r <> r') -> + undef_regs rl rs r = rs r. +Proof. + induction rl; simpl; intros. auto. + rewrite IHrl by auto. rewrite Pregmap.gso; auto. +Qed. + +Fixpoint preg_notin (r: preg) (rl: list mreg) : Prop := + match rl with + | nil => True + | r1 :: nil => r <> preg_of r1 + | r1 :: rl => r <> preg_of r1 /\ preg_notin r rl + end. + +Remark preg_notin_charact: + forall r rl, + preg_notin r rl <-> (forall mr, In mr rl -> r <> preg_of mr). +Proof. + induction rl; simpl; intros. + tauto. + destruct rl. + simpl. split. intros. intuition congruence. auto. + rewrite IHrl. split. + intros [A B]. intros. destruct H. congruence. auto. + auto. +Qed. + +Lemma undef_regs_other_2: + forall r rl rs, + preg_notin r rl -> + undef_regs (map preg_of rl) rs r = rs r. +Proof. + intros. apply undef_regs_other. intros. + exploit list_in_map_inv; eauto. intros [mr [A B]]. subst. + rewrite preg_notin_charact in H. auto. +Qed. + +(** * Agreement between Mach registers and processor registers *) + +Record agree (ms: Mach.regset) (sp: val) (rs: AB.regset) : Prop := mkagree { + agree_sp: rs#SP = sp; + agree_sp_def: sp <> Vundef; + agree_mregs: forall r: mreg, Val.lessdef (ms r) (rs#(preg_of r)) +}. + +Lemma preg_val: + forall ms sp rs r, agree ms sp rs -> Val.lessdef (ms r) rs#(preg_of r). +Proof. + intros. destruct H. auto. +Qed. + +Lemma preg_vals: + forall ms sp rs, agree ms sp rs -> + forall l, Val.lessdef_list (map ms l) (map rs (map preg_of l)). +Proof. + induction l; simpl. constructor. constructor. eapply preg_val; eauto. auto. +Qed. + +Lemma sp_val: + forall ms sp rs, agree ms sp rs -> sp = rs#SP. +Proof. + intros. destruct H; auto. +Qed. + +Lemma ireg_val: + forall ms sp rs r r', + agree ms sp rs -> + ireg_of r = OK r' -> + Val.lessdef (ms r) rs#r'. +Proof. + intros. rewrite <- (ireg_of_eq _ _ H0). eapply preg_val; eauto. +Qed. + +Lemma freg_val: + forall ms sp rs r r', + agree ms sp rs -> + freg_of r = OK r' -> + Val.lessdef (ms r) (rs#r'). +Proof. + intros. rewrite <- (freg_of_eq _ _ H0). eapply preg_val; eauto. +Qed. + +Lemma agree_exten: + forall ms sp rs rs', + agree ms sp rs -> + (forall r, data_preg r = true -> rs'#r = rs#r) -> + agree ms sp rs'. +Proof. + intros. destruct H. split; auto. + rewrite H0; auto. auto. + intros. rewrite H0; auto. apply preg_of_data. +Qed. + +(** Preservation of register agreement under various assignments. *) + +Lemma agree_set_mreg: + forall ms sp rs r v rs', + agree ms sp rs -> + Val.lessdef v (rs'#(preg_of r)) -> + (forall r', data_preg r' = true -> r' <> preg_of r -> rs'#r' = rs#r') -> + agree (Mach.Regmap.set r v ms) sp rs'. +Proof. + intros. destruct H. split; auto. + rewrite H1; auto. apply not_eq_sym. apply preg_of_not_SP. + intros. unfold Mach.Regmap.set. destruct (Mach.RegEq.eq r0 r). congruence. + rewrite H1. auto. apply preg_of_data. + red; intros; elim n. eapply preg_of_injective; eauto. +Qed. + +Corollary agree_set_mreg_parallel: + forall ms sp rs r v v', + agree ms sp rs -> + Val.lessdef v v' -> + agree (Mach.Regmap.set r v ms) sp (Pregmap.set (preg_of r) v' rs). +Proof. + intros. eapply agree_set_mreg; eauto. rewrite Pregmap.gss; auto. intros; apply Pregmap.gso; auto. +Qed. + +Lemma agree_set_other: + forall ms sp rs r v, + agree ms sp rs -> + data_preg r = false -> + agree ms sp (rs#r <- v). +Proof. + intros. apply agree_exten with rs. auto. + intros. apply Pregmap.gso. congruence. +Qed. + +Lemma agree_nextblock: + forall ms sp rs b, + agree ms sp rs -> agree ms sp (nextblock b rs). +Proof. + intros. unfold nextblock. apply agree_set_other. auto. auto. +Qed. + +Lemma agree_set_pair: + forall sp p v v' ms rs, + agree ms sp rs -> + Val.lessdef v v' -> + agree (Mach.set_pair p v ms) sp (set_pair (map_rpair preg_of p) v' rs). +Proof. + intros. destruct p; simpl. +- apply agree_set_mreg_parallel; auto. +- apply agree_set_mreg_parallel. apply agree_set_mreg_parallel; auto. + apply Val.hiword_lessdef; auto. apply Val.loword_lessdef; auto. +Qed. + +Lemma agree_undef_nondata_regs: + forall ms sp rl rs, + agree ms sp rs -> + (forall r, In r rl -> data_preg r = false) -> + agree ms sp (undef_regs rl rs). +Proof. + induction rl; simpl; intros. auto. + apply IHrl. apply agree_exten with rs; auto. + intros. apply Pregmap.gso. red; intros; subst. + assert (data_preg a = false) by auto. congruence. + intros. apply H0; auto. +Qed. + +Lemma agree_undef_regs: + forall ms sp rl rs rs', + agree ms sp rs -> + (forall r', data_preg r' = true -> preg_notin r' rl -> rs'#r' = rs#r') -> + agree (Mach.undef_regs rl ms) sp rs'. +Proof. + intros. destruct H. split; auto. + rewrite <- agree_sp0. apply H0; auto. + rewrite preg_notin_charact. intros. apply not_eq_sym. apply preg_of_not_SP. + intros. destruct (In_dec mreg_eq r rl). + rewrite Mach.undef_regs_same; auto. + rewrite Mach.undef_regs_other; auto. rewrite H0; auto. + apply preg_of_data. + rewrite preg_notin_charact. intros; red; intros. elim n. + exploit preg_of_injective; eauto. congruence. +Qed. + +(* Lemma agree_undef_regs2: + forall ms sp rl rs rs', + agree (Mach.undef_regs rl ms) sp rs -> + (forall r', data_preg r' = true -> preg_notin r' rl -> rs'#r' = rs#r') -> + agree (Mach.undef_regs rl ms) sp rs'. +Proof. + intros. destruct H. split; auto. + rewrite <- agree_sp0. apply H0; auto. + rewrite preg_notin_charact. intros. apply not_eq_sym. apply preg_of_not_SP. + intros. destruct (In_dec mreg_eq r rl). + rewrite Mach.undef_regs_same; auto. + rewrite H0; auto. + apply preg_of_data. + rewrite preg_notin_charact. intros; red; intros. elim n. + exploit preg_of_injective; eauto. congruence. +Qed. + *) + +Lemma agree_set_undef_mreg: + forall ms sp rs r v rl rs', + agree ms sp rs -> + Val.lessdef v (rs'#(preg_of r)) -> + (forall r', data_preg r' = true -> r' <> preg_of r -> preg_notin r' rl -> rs'#r' = rs#r') -> + agree (Mach.Regmap.set r v (Mach.undef_regs rl ms)) sp rs'. +Proof. + intros. apply agree_set_mreg with (rs'#(preg_of r) <- (rs#(preg_of r))); auto. + apply agree_undef_regs with rs; auto. + intros. unfold Pregmap.set. destruct (PregEq.eq r' (preg_of r)). + congruence. auto. + intros. rewrite Pregmap.gso; auto. +Qed. + +Lemma agree_change_sp: + forall ms sp rs sp', + agree ms sp rs -> sp' <> Vundef -> + agree ms sp' (rs#SP <- sp'). +Proof. + intros. inv H. split; auto. + intros. rewrite Pregmap.gso; auto with asmgen. +Qed. + +(** Connection between Mach and Asm calling conventions for external + functions. *) + +Lemma extcall_arg_match: + forall ms sp rs m m' l v, + agree ms sp rs -> + Mem.extends m m' -> + Mach.extcall_arg ms m sp l v -> + exists v', AB.extcall_arg rs m' l v' /\ Val.lessdef v v'. +Proof. + intros. inv H1. + exists (rs#(preg_of r)); split. constructor. eapply preg_val; eauto. + unfold Mach.load_stack in H2. + exploit Mem.loadv_extends; eauto. intros [v' [A B]]. + rewrite (sp_val _ _ _ H) in A. + exists v'; split; auto. + econstructor. eauto. assumption. +Qed. + +Lemma extcall_arg_pair_match: + forall ms sp rs m m' p v, + agree ms sp rs -> + Mem.extends m m' -> + Mach.extcall_arg_pair ms m sp p v -> + exists v', AB.extcall_arg_pair rs m' p v' /\ Val.lessdef v v'. +Proof. + intros. inv H1. +- exploit extcall_arg_match; eauto. intros (v' & A & B). exists v'; split; auto. constructor; auto. +- exploit extcall_arg_match. eauto. eauto. eexact H2. intros (v1 & A1 & B1). + exploit extcall_arg_match. eauto. eauto. eexact H3. intros (v2 & A2 & B2). + exists (Val.longofwords v1 v2); split. constructor; auto. apply Val.longofwords_lessdef; auto. +Qed. + + +Lemma extcall_args_match: + forall ms sp rs m m', agree ms sp rs -> Mem.extends m m' -> + forall ll vl, + list_forall2 (Mach.extcall_arg_pair ms m sp) ll vl -> + exists vl', list_forall2 (AB.extcall_arg_pair rs m') ll vl' /\ Val.lessdef_list vl vl'. +Proof. + induction 3; intros. + exists (@nil val); split. constructor. constructor. + exploit extcall_arg_pair_match; eauto. intros [v1' [A B]]. + destruct IHlist_forall2 as [vl' [C D]]. + exists (v1' :: vl'); split; constructor; auto. +Qed. + +Lemma extcall_arguments_match: + forall ms m m' sp rs sg args, + agree ms sp rs -> Mem.extends m m' -> + Mach.extcall_arguments ms m sp sg args -> + exists args', AB.extcall_arguments rs m' sg args' /\ Val.lessdef_list args args'. +Proof. + unfold Mach.extcall_arguments, AB.extcall_arguments; intros. + eapply extcall_args_match; eauto. +Qed. + +Remark builtin_arg_match: + forall ge (rs: regset) sp m a v, + eval_builtin_arg ge (fun r => rs (preg_of r)) sp m a v -> + eval_builtin_arg ge rs sp m (map_builtin_arg preg_of a) v. +Proof. + induction 1; simpl; eauto with barg. +Qed. + +Lemma builtin_args_match: + forall ge ms sp rs m m', agree ms sp rs -> Mem.extends m m' -> + forall al vl, eval_builtin_args ge ms sp m al vl -> + exists vl', eval_builtin_args ge rs sp m' (map (map_builtin_arg preg_of) al) vl' + /\ Val.lessdef_list vl vl'. +Proof. + induction 3; intros; simpl. + exists (@nil val); split; constructor. + exploit (@eval_builtin_arg_lessdef _ ge ms (fun r => rs (preg_of r))); eauto. + intros; eapply preg_val; eauto. + intros (v1' & A & B). + destruct IHlist_forall2 as [vl' [C D]]. + exists (v1' :: vl'); split; constructor; auto. apply builtin_arg_match; auto. +Qed. + +Lemma agree_set_res: + forall res ms sp rs v v', + agree ms sp rs -> + Val.lessdef v v' -> + agree (Mach.set_res res v ms) sp (AB.set_res (map_builtin_res preg_of res) v' rs). +Proof. + induction res; simpl; intros. +- eapply agree_set_mreg; eauto. rewrite Pregmap.gss. auto. + intros. apply Pregmap.gso; auto. +- auto. +- apply IHres2. apply IHres1. auto. + apply Val.hiword_lessdef; auto. + apply Val.loword_lessdef; auto. +Qed. + +Lemma set_res_other: + forall r res v rs, + data_preg r = false -> + set_res (map_builtin_res preg_of res) v rs r = rs r. +Proof. + induction res; simpl; intros. +- apply Pregmap.gso. red; intros; subst r. rewrite preg_of_data in H; discriminate. +- auto. +- rewrite IHres2, IHres1; auto. +Qed. + +(* inspired from Mach *) + +Lemma find_label_tail: + forall lbl c c', MB.find_label lbl c = Some c' -> is_tail c' c. +Proof. + induction c; simpl; intros. discriminate. + destruct (MB.is_label lbl a). inv H. auto with coqlib. eauto with coqlib. +Qed. + +(* inspired from Asmgenproof0 *) + +(* ... skip ... *) + +(** The ``code tail'' of an instruction list [c] is the list of instructions + starting at PC [pos]. *) + +Inductive code_tail: Z -> bblocks -> bblocks -> Prop := + | code_tail_0: forall c, + code_tail 0 c c + | code_tail_S: forall pos bi c1 c2, + code_tail pos c1 c2 -> + code_tail (pos + (size bi)) (bi :: c1) c2. + +Lemma code_tail_pos: + forall pos c1 c2, code_tail pos c1 c2 -> pos >= 0. +Proof. + induction 1. omega. generalize (size_positive bi); intros; omega. +Qed. + +Lemma find_bblock_tail: + forall c1 bi c2 pos, + code_tail pos c1 (bi :: c2) -> + find_bblock pos c1 = Some bi. +Proof. + induction c1; simpl; intros. + inversion H. + destruct (zlt pos 0). generalize (code_tail_pos _ _ _ H); intro; omega. + destruct (zeq pos 0). subst pos. + inv H. auto. generalize (size_positive a) (code_tail_pos _ _ _ H4). intro; omega. + inv H. congruence. replace (pos0 + size a - size a) with pos0 by omega. + eauto. +Qed. + + +Local Hint Resolve code_tail_0 code_tail_S. + +Lemma code_tail_next: + forall fn ofs c0, + code_tail ofs fn c0 -> + forall bi c1, c0 = bi :: c1 -> code_tail (ofs + (size bi)) fn c1. +Proof. + induction 1; intros. + - subst; eauto. + - replace (pos + size bi + size bi0) with ((pos + size bi0) + size bi); eauto. + omega. +Qed. + +Lemma size_blocks_pos c: 0 <= size_blocks c. +Proof. + induction c as [| a l ]; simpl; try omega. + generalize (size_positive a); omega. +Qed. + +Remark code_tail_positive: + forall fn ofs c, + code_tail ofs fn c -> 0 <= ofs. +Proof. + induction 1; intros; simpl. + - omega. + - generalize (size_positive bi). omega. +Qed. + +Remark code_tail_size: + forall fn ofs c, + code_tail ofs fn c -> size_blocks fn = ofs + size_blocks c. +Proof. + induction 1; intros; simpl; try omega. +Qed. + +Remark code_tail_bounds fn ofs c: + code_tail ofs fn c -> 0 <= ofs <= size_blocks fn. +Proof. + intro H; + exploit code_tail_size; eauto. + generalize (code_tail_positive _ _ _ H), (size_blocks_pos c). + omega. +Qed. + +Local Hint Resolve code_tail_next. + +Lemma code_tail_next_int: + forall fn ofs bi c, + size_blocks fn <= Ptrofs.max_unsigned -> + code_tail (Ptrofs.unsigned ofs) fn (bi :: c) -> + code_tail (Ptrofs.unsigned (Ptrofs.add ofs (Ptrofs.repr (size bi)))) fn c. +Proof. + intros. + exploit code_tail_size; eauto. + simpl; generalize (code_tail_positive _ _ _ H0), (size_positive bi), (size_blocks_pos c). + intros. + rewrite Ptrofs.add_unsigned, Ptrofs.unsigned_repr. + - rewrite Ptrofs.unsigned_repr; eauto. + omega. + - rewrite Ptrofs.unsigned_repr; omega. +Qed. + +(** Predictor for return addresses in generated Asm code. + + The [return_address_offset] predicate defined here is used in the + semantics for Mach to determine the return addresses that are + stored in activation records. *) + +(** Consider a Mach function [f] and a sequence [c] of Mach instructions + representing the Mach code that remains to be executed after a + function call returns. The predicate [return_address_offset f c ofs] + holds if [ofs] is the integer offset of the PPC instruction + following the call in the Asm code obtained by translating the + code of [f]. Graphically: +<< + Mach function f |--------- Mcall ---------| + Mach code c | |--------| + | \ \ + | \ \ + | \ \ + Asm code | |--------| + Asm function |------------- Pcall ---------| + + <-------- ofs -------> +>> +*) + +Definition return_address_offset (f: MB.function) (c: MB.code) (ofs: ptrofs) : Prop := + forall tf tc, + transf_function f = OK tf -> + transl_blocks f c false = OK tc -> + code_tail (Ptrofs.unsigned ofs) (fn_blocks tf) tc. + +(* NB: these two lemma should go into [Coqlib.v] *) +Lemma is_tail_app A (l1: list A): forall l2, is_tail l2 (l1 ++ l2). +Proof. + induction l1; simpl; auto with coqlib. +Qed. +Hint Resolve is_tail_app: coqlib. + +Lemma is_tail_app_inv A (l1: list A): forall l2 l3, is_tail (l1 ++ l2) l3 -> is_tail l2 l3. +Proof. + induction l1; simpl; auto with coqlib. + intros l2 l3 H; inversion H; eauto with coqlib. +Qed. +Hint Resolve is_tail_app_inv: coqlib. + + +Lemma transl_blocks_tail: + forall f c1 c2, is_tail c1 c2 -> + forall tc2 ep2, transl_blocks f c2 ep2 = OK tc2 -> + exists tc1, exists ep1, transl_blocks f c1 ep1 = OK tc1 /\ is_tail tc1 tc2. +Proof. + induction 1; simpl; intros. + exists tc2; exists ep2; split; auto with coqlib. + monadInv H0. exploit IHis_tail; eauto. intros (tc1 & ep1 & A & B). + exists tc1; exists ep1; split. auto. + eapply is_tail_trans with x0; eauto with coqlib. +Qed. + +Lemma is_tail_code_tail: + forall c1 c2, is_tail c1 c2 -> exists ofs, code_tail ofs c2 c1. +Proof. + induction 1; eauto. + destruct IHis_tail; eauto. +Qed. + +Section RETADDR_EXISTS. + +Hypothesis transf_function_inv: + forall f tf, transf_function f = OK tf -> + exists tc ep, transl_blocks f (Machblock.fn_code f) ep = OK tc /\ is_tail tc (fn_blocks tf). + +Hypothesis transf_function_len: + forall f tf, transf_function f = OK tf -> size_blocks (fn_blocks tf) <= Ptrofs.max_unsigned. + + +(* NB: the hypothesis in comment on [b] is not needed in the proof ! *) +Lemma return_address_exists: + forall b f (* sg ros *) c, (* b.(MB.exit) = Some (MBcall sg ros) -> *) is_tail (b :: c) f.(MB.fn_code) -> + exists ra, return_address_offset f c ra. +Proof. + intros. destruct (transf_function f) as [tf|] eqn:TF. + + exploit transf_function_inv; eauto. intros (tc1 & ep1 & TR1 & TL1). + exploit transl_blocks_tail; eauto. intros (tc2 & ep2 & TR2 & TL2). +(* unfold return_address_offset. *) + monadInv TR2. + assert (TL3: is_tail x0 (fn_blocks tf)). + { apply is_tail_trans with tc1; auto. + apply is_tail_trans with (x++x0); auto. eapply is_tail_app. + } + exploit is_tail_code_tail. eexact TL3. intros [ofs CT]. + exists (Ptrofs.repr ofs). red; intros. + rewrite Ptrofs.unsigned_repr. congruence. + exploit code_tail_bounds; eauto. + intros; apply transf_function_len in TF. omega. + + exists Ptrofs.zero; red; intros. congruence. +Qed. + +End RETADDR_EXISTS. + +(** [transl_code_at_pc pc fb f c ep tf tc] holds if the code pointer [pc] points + within the Asm code generated by translating Mach function [f], + and [tc] is the tail of the generated code at the position corresponding + to the code pointer [pc]. *) + +Inductive transl_code_at_pc (ge: MB.genv): + val -> block -> MB.function -> MB.code -> bool -> AB.function -> AB.bblocks -> Prop := + transl_code_at_pc_intro: + forall b ofs f c ep tf tc, + Genv.find_funct_ptr ge b = Some(Internal f) -> + transf_function f = Errors.OK tf -> + transl_blocks f c ep = OK tc -> + code_tail (Ptrofs.unsigned ofs) (fn_blocks tf) tc -> + transl_code_at_pc ge (Vptr b ofs) b f c ep tf tc. + +Remark code_tail_no_bigger: + forall pos c1 c2, code_tail pos c1 c2 -> (length c2 <= length c1)%nat. +Proof. + induction 1; simpl; omega. +Qed. + +Remark code_tail_unique: + forall fn c pos pos', + code_tail pos fn c -> code_tail pos' fn c -> pos = pos'. +Proof. + induction fn; intros until pos'; intros ITA CT; inv ITA; inv CT; auto. + generalize (code_tail_no_bigger _ _ _ H3); simpl; intro; omega. + generalize (code_tail_no_bigger _ _ _ H3); simpl; intro; omega. + f_equal. eauto. +Qed. + +Lemma return_address_offset_correct: + forall ge b ofs fb f c tf tc ofs', + transl_code_at_pc ge (Vptr b ofs) fb f c false tf tc -> + return_address_offset f c ofs' -> + ofs' = ofs. +Proof. + intros. inv H. red in H0. + exploit code_tail_unique. eexact H12. eapply H0; eauto. intro. + rewrite <- (Ptrofs.repr_unsigned ofs). + rewrite <- (Ptrofs.repr_unsigned ofs'). + congruence. +Qed. + +(** The [find_label] function returns the code tail starting at the + given label. A connection with [code_tail] is then established. *) + +Fixpoint find_label (lbl: label) (c: bblocks) {struct c} : option bblocks := + match c with + | nil => None + | bb1 :: bbl => if is_label lbl bb1 then Some c else find_label lbl bbl + end. + +Lemma label_pos_code_tail: + forall lbl c pos c', + find_label lbl c = Some c' -> + exists pos', + label_pos lbl pos c = Some pos' + /\ code_tail (pos' - pos) c c' + /\ pos <= pos' <= pos + size_blocks c. +Proof. + induction c. + simpl; intros. discriminate. + simpl; intros until c'. + case (is_label lbl a). + - intros. inv H. exists pos. split; auto. split. + replace (pos - pos) with 0 by omega. constructor. constructor; try omega. + generalize (size_blocks_pos c). generalize (size_positive a). omega. + - intros. generalize (IHc (pos+size a) c' H). intros [pos' [A [B C]]]. + exists pos'. split. auto. split. + replace (pos' - pos) with ((pos' - (pos + (size a))) + (size a)) by omega. + constructor. auto. generalize (size_positive a). omega. +Qed. + +(** Helper lemmas to reason about +- the "code is tail of" property +- correct translation of labels. *) + +Definition tail_nolabel (k c: bblocks) : Prop := + is_tail k c /\ forall lbl, find_label lbl c = find_label lbl k. + +Lemma tail_nolabel_refl: + forall c, tail_nolabel c c. +Proof. + intros; split. apply is_tail_refl. auto. +Qed. + +Lemma tail_nolabel_trans: + forall c1 c2 c3, tail_nolabel c2 c3 -> tail_nolabel c1 c2 -> tail_nolabel c1 c3. +Proof. + intros. destruct H; destruct H0; split. + eapply is_tail_trans; eauto. + intros. rewrite H1; auto. +Qed. + +Definition nolabel (b: bblock) := + match (header b) with nil => True | _ => False end. + +Hint Extern 1 (nolabel _) => exact I : labels. + +Lemma tail_nolabel_cons: + forall b c k, + nolabel b -> tail_nolabel k c -> tail_nolabel k (b :: c). +Proof. + intros. destruct H0. split. + constructor; auto. + intros. simpl. rewrite <- H1. destruct b as [hd bdy ex]; simpl in *. + destruct hd as [|l hd]; simpl in *. + - assert (is_label lbl {| AB.header := nil; AB.body := bdy; AB.exit := ex; AB.correct := correct |} = false). + { apply is_label_correct_false. simpl header. apply in_nil. } + rewrite H2. auto. + - contradiction. +Qed. + +Hint Resolve tail_nolabel_refl: labels. + +Ltac TailNoLabel := + eauto with labels; + match goal with + | [ |- tail_nolabel _ (_ :: _) ] => apply tail_nolabel_cons; [auto; exact I | TailNoLabel] + | [ H: Error _ = OK _ |- _ ] => discriminate + | [ H: assertion_failed = OK _ |- _ ] => discriminate + | [ H: OK _ = OK _ |- _ ] => inv H; TailNoLabel + | [ H: bind _ _ = OK _ |- _ ] => monadInv H; TailNoLabel + | [ H: (if ?x then _ else _) = OK _ |- _ ] => destruct x; TailNoLabel + | [ H: match ?x with nil => _ | _ :: _ => _ end = OK _ |- _ ] => destruct x; TailNoLabel + | _ => idtac + end. + +Remark tail_nolabel_find_label: + forall lbl k c, tail_nolabel k c -> find_label lbl c = find_label lbl k. +Proof. + intros. destruct H. auto. +Qed. + +Remark tail_nolabel_is_tail: + forall k c, tail_nolabel k c -> is_tail k c. +Proof. + intros. destruct H. auto. +Qed. + +Section STRAIGHTLINE. + +Variable ge: genv. +Variable fn: function. + +(** Straight-line code is composed of processor instructions that execute + in sequence (no branches, no function calls and returns). + The following inductive predicate relates the machine states + before and after executing a straight-line sequence of instructions. + Instructions are taken from the first list instead of being fetched + from memory. *) + +Inductive exec_straight: list instruction -> regset -> mem -> + list instruction -> regset -> mem -> Prop := + | exec_straight_one: + forall i1 c rs1 m1 rs2 m2, + exec_basic_instr ge i1 rs1 m1 = Next rs2 m2 -> + exec_straight ((PBasic i1) ::g c) rs1 m1 c rs2 m2 + | exec_straight_step: + forall i c rs1 m1 rs2 m2 c' rs3 m3, + exec_basic_instr ge i rs1 m1 = Next rs2 m2 -> + exec_straight c rs2 m2 c' rs3 m3 -> + exec_straight ((PBasic i) :: c) rs1 m1 c' rs3 m3. + +Inductive exec_control_rel: option control -> bblock -> regset -> mem -> + regset -> mem -> Prop := + | exec_control_rel_intro: + forall rs1 m1 b rs1' ctl rs2 m2, + rs1' = nextblock b rs1 -> + exec_control ge fn ctl rs1' m1 = Next rs2 m2 -> + exec_control_rel ctl b rs1 m1 rs2 m2. + +Inductive exec_bblock_rel: bblock -> regset -> mem -> regset -> mem -> Prop := + | exec_bblock_rel_intro: + forall rs1 m1 b rs2 m2, + exec_bblock ge fn b rs1 m1 = Next rs2 m2 -> + exec_bblock_rel b rs1 m1 rs2 m2. + +Lemma exec_straight_body: + forall c l rs1 m1 rs2 m2, + exec_straight c rs1 m1 nil rs2 m2 -> + code_to_basics c = Some l -> + exec_body ge l rs1 m1 = Next rs2 m2. +Proof. + induction c as [|i c]. + - intros until m2. intros EXES CTB. inv EXES. + - intros until m2. intros EXES CTB. inv EXES. + + inv CTB. simpl. rewrite H6. auto. + + inv CTB. destruct (code_to_basics c); try discriminate. inv H0. eapply IHc in H7; eauto. + rewrite <- H7. simpl. rewrite H1. auto. +Qed. + +Lemma exec_straight_body2: + forall c rs1 m1 c' rs2 m2, + exec_straight c rs1 m1 c' rs2 m2 -> + exists body, + exec_body ge body rs1 m1 = Next rs2 m2 + /\ (basics_to_code body) ++g c' = c. +Proof. + intros until m2. induction 1. + - exists (i1::nil). split; auto. simpl. rewrite H. auto. + - destruct IHexec_straight as (bdy & EXEB & BTC). + exists (i:: bdy). split; simpl. + + rewrite H. auto. + + congruence. +Qed. + +Lemma exec_straight_trans: + forall c1 rs1 m1 c2 rs2 m2 c3 rs3 m3, + exec_straight c1 rs1 m1 c2 rs2 m2 -> + exec_straight c2 rs2 m2 c3 rs3 m3 -> + exec_straight c1 rs1 m1 c3 rs3 m3. +Proof. + induction 1; intros. + apply exec_straight_step with rs2 m2; auto. + apply exec_straight_step with rs2 m2; auto. +Qed. + +(* Theorem exec_straight_bblock: + forall rs1 m1 rs2 m2 rs3 m3 b, + exec_straight (body b) rs1 m1 nil rs2 m2 -> + exec_control_rel (exit b) b rs2 m2 rs3 m3 -> + exec_bblock_rel b rs1 m1 rs3 m3. +Proof. + intros. + econstructor; eauto. unfold exec_bblock. erewrite exec_straight_body; eauto. + inv H0. auto. +Qed. *) + + +Lemma exec_straight_two: + forall i1 i2 c rs1 m1 rs2 m2 rs3 m3, + exec_basic_instr ge i1 rs1 m1 = Next rs2 m2 -> + exec_basic_instr ge i2 rs2 m2 = Next rs3 m3 -> + exec_straight (i1 ::g i2 ::g c) rs1 m1 c rs3 m3. +Proof. + intros. apply exec_straight_step with rs2 m2; auto. + apply exec_straight_one; auto. +Qed. + +Lemma exec_straight_three: + forall i1 i2 i3 c rs1 m1 rs2 m2 rs3 m3 rs4 m4, + exec_basic_instr ge i1 rs1 m1 = Next rs2 m2 -> + exec_basic_instr ge i2 rs2 m2 = Next rs3 m3 -> + exec_basic_instr ge i3 rs3 m3 = Next rs4 m4 -> + exec_straight (i1 ::g i2 ::g i3 ::g c) rs1 m1 c rs4 m4. +Proof. + intros. apply exec_straight_step with rs2 m2; auto. + eapply exec_straight_two; eauto. +Qed. + +(** Like exec_straight predicate, but on blocks *) + +Inductive exec_straight_blocks: bblocks -> regset -> mem -> + bblocks -> regset -> mem -> Prop := + | exec_straight_blocks_one: + forall b1 c rs1 m1 rs2 m2, + exec_bblock ge fn b1 rs1 m1 = Next rs2 m2 -> + rs2#PC = Val.offset_ptr rs1#PC (Ptrofs.repr (size b1)) -> + exec_straight_blocks (b1 :: c) rs1 m1 c rs2 m2 + | exec_straight_blocks_step: + forall b c rs1 m1 rs2 m2 c' rs3 m3, + exec_bblock ge fn b rs1 m1 = Next rs2 m2 -> + rs2#PC = Val.offset_ptr rs1#PC (Ptrofs.repr (size b)) -> + exec_straight_blocks c rs2 m2 c' rs3 m3 -> + exec_straight_blocks (b :: c) rs1 m1 c' rs3 m3. + +Lemma exec_straight_blocks_trans: + forall c1 rs1 m1 c2 rs2 m2 c3 rs3 m3, + exec_straight_blocks c1 rs1 m1 c2 rs2 m2 -> + exec_straight_blocks c2 rs2 m2 c3 rs3 m3 -> + exec_straight_blocks c1 rs1 m1 c3 rs3 m3. +Proof. + induction 1; intros. + apply exec_straight_blocks_step with rs2 m2; auto. + apply exec_straight_blocks_step with rs2 m2; auto. +Qed. + +(** Linking exec_straight with exec_straight_blocks *) + +Ltac Simplif := + ((rewrite nextblock_inv by eauto with asmgen) + || (rewrite nextblock_inv1 by eauto with asmgen) + || (rewrite Pregmap.gss) + || (rewrite nextblock_pc) + || (rewrite Pregmap.gso by eauto with asmgen) + ); auto with asmgen. + +Ltac Simpl := repeat Simplif. + +Lemma exec_basic_instr_pc: + forall b rs1 m1 rs2 m2, + exec_basic_instr ge b rs1 m1 = Next rs2 m2 -> + rs2 PC = rs1 PC. +Proof. + intros. destruct b; try destruct i; try destruct i. + all: try (inv H; Simpl). + all: try (unfold exec_load in H1; destruct (Mem.loadv _ _ _); [inv H1; Simpl | discriminate]). + all: try (unfold exec_store in H1; destruct (Mem.storev _ _ _); [inv H1; auto | discriminate]). + destruct (Mem.alloc _ _ _). destruct (Mem.store _ _ _ _ _). inv H1. Simpl. discriminate. + destruct (rs1 _); try discriminate. + destruct (Mem.free _ _ _ _). inv H0. Simpl. discriminate. + destruct rs; try discriminate. inv H1. Simpl. + destruct rd; try discriminate. inv H1; Simpl. + auto. +Qed. + +(* Lemma exec_straight_pc': + forall c rs1 m1 rs2 m2, + exec_straight c rs1 m1 nil rs2 m2 -> + rs2 PC = rs1 PC. +Proof. + induction c; intros; try (inv H; fail). + inv H. + - erewrite exec_basic_instr_pc; eauto. + - rewrite (IHc rs3 m3 rs2 m2); auto. + erewrite exec_basic_instr_pc; eauto. +Qed. *) + +Lemma exec_straight_pc: + forall c c' rs1 m1 rs2 m2, + exec_straight c rs1 m1 c' rs2 m2 -> + rs2 PC = rs1 PC. +Proof. + induction c; intros; try (inv H; fail). + inv H. + - eapply exec_basic_instr_pc; eauto. + - rewrite (IHc c' rs3 m3 rs2 m2); auto. + erewrite exec_basic_instr_pc; eauto. +Qed. + +(* Lemma exec_straight_through: + forall c i b lb rs1 m1 rs2 m2 rs2' m2', + bblock_basic_ctl c i = b -> + exec_straight c rs1 m1 nil rs2 m2 -> + nextblock b rs2 = rs2' -> m2 = m2' -> + exec_control ge fn i rs2' m2' = Next rs2' m2' -> (* if the control does not jump *) + exec_straight_blocks (b::lb) rs1 m1 lb rs2' m2'. +Proof. + intros. subst. destruct i. + - constructor 1. + + unfold exec_bblock. simpl body. erewrite exec_straight_body; eauto. + + rewrite <- (exec_straight_pc c nil rs1 m1 rs2 m2'); auto. + - destruct c as [|i c]; try (inv H0; fail). + constructor 1. + + unfold exec_bblock. simpl body. erewrite exec_straight_body; eauto. + + rewrite <- (exec_straight_pc (i ::i c) nil rs1 m1 rs2 m2'); auto. +Qed. + *) +Lemma exec_straight_through_singleinst: + forall a b rs1 m1 rs2 m2 rs2' m2' lb, + bblock_single_inst (PBasic a) = b -> + exec_straight (a ::g nil) rs1 m1 nil rs2 m2 -> + nextblock b rs2 = rs2' -> m2 = m2' -> + exec_straight_blocks (b::lb) rs1 m1 lb rs2' m2'. +Proof. + intros. subst. constructor 1. unfold exec_bblock. simpl body. erewrite exec_straight_body; eauto. + simpl. auto. + simpl; auto. unfold nextblock; simpl. Simpl. erewrite exec_straight_pc; eauto. +Qed. + +(** The following lemmas show that straight-line executions + (predicate [exec_straight_blocks]) correspond to correct Asm executions. *) + +Lemma exec_straight_steps_1: + forall c rs m c' rs' m', + exec_straight_blocks c rs m c' rs' m' -> + size_blocks (fn_blocks fn) <= Ptrofs.max_unsigned -> + forall b ofs, + rs#PC = Vptr b ofs -> + Genv.find_funct_ptr ge b = Some (Internal fn) -> + code_tail (Ptrofs.unsigned ofs) (fn_blocks fn) c -> + plus step ge (State rs m) E0 (State rs' m'). +Proof. + induction 1; intros. + apply plus_one. + econstructor; eauto. + eapply find_bblock_tail. eauto. + eapply plus_left'. + econstructor; eauto. + eapply find_bblock_tail. eauto. + apply IHexec_straight_blocks with b0 (Ptrofs.add ofs (Ptrofs.repr (size b))). + auto. rewrite H0. rewrite H3. reflexivity. + auto. + apply code_tail_next_int; auto. + traceEq. +Qed. + +Lemma exec_straight_steps_2: + forall c rs m c' rs' m', + exec_straight_blocks c rs m c' rs' m' -> + size_blocks (fn_blocks fn) <= Ptrofs.max_unsigned -> + forall b ofs, + rs#PC = Vptr b ofs -> + Genv.find_funct_ptr ge b = Some (Internal fn) -> + code_tail (Ptrofs.unsigned ofs) (fn_blocks fn) c -> + exists ofs', + rs'#PC = Vptr b ofs' + /\ code_tail (Ptrofs.unsigned ofs') (fn_blocks fn) c'. +Proof. + induction 1; intros. + exists (Ptrofs.add ofs (Ptrofs.repr (size b1))). split. + rewrite H0. rewrite H2. auto. + apply code_tail_next_int; auto. + apply IHexec_straight_blocks with (Ptrofs.add ofs (Ptrofs.repr (size b))). + auto. rewrite H0. rewrite H3. reflexivity. auto. + apply code_tail_next_int; auto. +Qed. + +End STRAIGHTLINE. + + +(** * Properties of the Machblock call stack *) + +Section MATCH_STACK. + +Variable ge: MB.genv. + +Inductive match_stack: list MB.stackframe -> Prop := + | match_stack_nil: + match_stack nil + | match_stack_cons: forall fb sp ra c s f tf tc, + Genv.find_funct_ptr ge fb = Some (Internal f) -> + transl_code_at_pc ge ra fb f c false tf tc -> + sp <> Vundef -> + match_stack s -> + match_stack (Stackframe fb sp ra c :: s). + +Lemma parent_sp_def: forall s, match_stack s -> parent_sp s <> Vundef. +Proof. + induction 1; simpl. + unfold Vnullptr; destruct Archi.ptr64; congruence. + auto. +Qed. + +Lemma parent_ra_def: forall s, match_stack s -> parent_ra s <> Vundef. +Proof. + induction 1; simpl. + unfold Vnullptr; destruct Archi.ptr64; congruence. + inv H0. congruence. +Qed. + +Lemma lessdef_parent_sp: + forall s v, + match_stack s -> Val.lessdef (parent_sp s) v -> v = parent_sp s. +Proof. + intros. inv H0. auto. exploit parent_sp_def; eauto. tauto. +Qed. + +Lemma lessdef_parent_ra: + forall s v, + match_stack s -> Val.lessdef (parent_ra s) v -> v = parent_ra s. +Proof. + intros. inv H0. auto. exploit parent_ra_def; eauto. tauto. +Qed. + +End MATCH_STACK.
\ No newline at end of file diff --git a/mppa_k1c/Asmblockgenproof1.v b/mppa_k1c/Asmblockgenproof1.v new file mode 100644 index 00000000..d0c205cd --- /dev/null +++ b/mppa_k1c/Asmblockgenproof1.v @@ -0,0 +1,1633 @@ +(* *********************************************************************) +(* *) +(* The Compcert verified compiler *) +(* *) +(* Xavier Leroy, INRIA Paris-Rocquencourt *) +(* Prashanth Mundkur, SRI International *) +(* *) +(* Copyright Institut National de Recherche en Informatique et en *) +(* Automatique. All rights reserved. This file is distributed *) +(* under the terms of the INRIA Non-Commercial License Agreement. *) +(* *) +(* The contributions by Prashanth Mundkur are reused and adapted *) +(* under the terms of a Contributor License Agreement between *) +(* SRI International and INRIA. *) +(* *) +(* *********************************************************************) + +Require Import Coqlib Errors Maps. +Require Import AST Integers Floats Values Memory Globalenvs. +Require Import Op Locations Machblock Conventions. +Require Import Asmblock Asmblockgen Asmblockgenproof0. + +(** Decomposition of integer constants. *) + +Lemma make_immed32_sound: + forall n, + match make_immed32 n with + | Imm32_single imm => n = imm + end. +Proof. + intros; unfold make_immed32. set (lo := Int.sign_ext 12 n). + predSpec Int.eq Int.eq_spec n lo; auto. +(* +- auto. +- set (m := Int.sub n lo). + assert (A: Int.eqmod (two_p 12) (Int.unsigned lo) (Int.unsigned n)) by (apply Int.eqmod_sign_ext'; compute; auto). + assert (B: Int.eqmod (two_p 12) (Int.unsigned n - Int.unsigned lo) 0). + { replace 0 with (Int.unsigned n - Int.unsigned n) by omega. + auto using Int.eqmod_sub, Int.eqmod_refl. } + assert (C: Int.eqmod (two_p 12) (Int.unsigned m) 0). + { apply Int.eqmod_trans with (Int.unsigned n - Int.unsigned lo); auto. + apply Int.eqmod_divides with Int.modulus. apply Int.eqm_sym; apply Int.eqm_unsigned_repr. + exists (two_p (32-12)); auto. } + assert (D: Int.modu m (Int.repr 4096) = Int.zero). + { apply Int.eqmod_mod_eq in C. unfold Int.modu. + change (Int.unsigned (Int.repr 4096)) with (two_p 12). rewrite C. + reflexivity. + apply two_p_gt_ZERO; omega. } + rewrite <- (Int.divu_pow2 m (Int.repr 4096) (Int.repr 12)) by auto. + rewrite Int.shl_mul_two_p. + change (two_p (Int.unsigned (Int.repr 12))) with 4096. + replace (Int.mul (Int.divu m (Int.repr 4096)) (Int.repr 4096)) with m. + unfold m. rewrite Int.sub_add_opp. rewrite Int.add_assoc. rewrite <- (Int.add_commut lo). + rewrite Int.add_neg_zero. rewrite Int.add_zero. auto. + rewrite (Int.modu_divu_Euclid m (Int.repr 4096)) at 1 by (vm_compute; congruence). + rewrite D. apply Int.add_zero. +*) +Qed. + +Lemma make_immed64_sound: + forall n, + match make_immed64 n with + | Imm64_single imm => n = imm +(*| Imm64_pair hi lo => n = Int64.add (Int64.sign_ext 32 (Int64.shl hi (Int64.repr 12))) lo + | Imm64_large imm => n = imm +*)end. +Proof. + intros; unfold make_immed64. set (lo := Int64.sign_ext 12 n). + predSpec Int64.eq Int64.eq_spec n lo. +- auto. +- set (m := Int64.sub n lo). + set (p := Int64.zero_ext 20 (Int64.shru m (Int64.repr 12))). + predSpec Int64.eq Int64.eq_spec n (Int64.add (Int64.sign_ext 32 (Int64.shl p (Int64.repr 12))) lo). + auto. + auto. +Qed. + + + +(** Properties of registers *) + +Lemma ireg_of_not_GPR31: + forall m r, ireg_of m = OK r -> IR r <> IR GPR31. +Proof. + intros. erewrite <- ireg_of_eq; eauto with asmgen. +Qed. + +Lemma ireg_of_not_GPR31': + forall m r, ireg_of m = OK r -> r <> GPR31. +Proof. + intros. apply ireg_of_not_GPR31 in H. congruence. +Qed. + +Hint Resolve ireg_of_not_GPR31 ireg_of_not_GPR31': asmgen. + + +(** Useful simplification tactic *) + +Ltac Simplif := + ((rewrite nextblock_inv by eauto with asmgen) + || (rewrite nextblock_inv1 by eauto with asmgen) + || (rewrite Pregmap.gss) + || (rewrite nextblock_pc) + || (rewrite Pregmap.gso by eauto with asmgen) + ); auto with asmgen. + +Ltac Simpl := repeat Simplif. + +(** * Correctness of RISC-V constructor functions *) + +Section CONSTRUCTORS. + +Variable ge: genv. +Variable fn: function. + +(* +(** 32-bit integer constants and arithmetic *) +(* +Lemma load_hilo32_correct: + forall rd hi lo k rs m, + exists rs', + exec_straight ge fn (load_hilo32 rd hi lo k) rs m k rs' m + /\ rs'#rd = Vint (Int.add (Int.shl hi (Int.repr 12)) lo) + /\ forall r, r <> PC -> r <> rd -> rs'#r = rs#r. +Proof. + unfold load_hilo32; intros. + predSpec Int.eq Int.eq_spec lo Int.zero. +- subst lo. econstructor; split. + apply exec_straight_one. simpl; eauto. auto. + split. rewrite Int.add_zero. Simpl. + intros; Simpl. +- econstructor; split. + eapply exec_straight_two. simpl; eauto. simpl; eauto. auto. auto. + split. Simpl. + intros; Simpl. +Qed. +*) + +*) + +Lemma loadimm32_correct: + forall rd n k rs m, + exists rs', + exec_straight ge (loadimm32 rd n ::g k) rs m k rs' m + /\ rs'#rd = Vint n + /\ forall r, r <> PC -> r <> rd -> rs'#r = rs#r. +Proof. + unfold loadimm32; intros. generalize (make_immed32_sound n); intros E. + destruct (make_immed32 n). +- subst imm. econstructor; split. + apply exec_straight_one. simpl; eauto. auto. + split. Simpl. + intros; Simpl. +Qed. + +Lemma loadimm64_correct: + forall rd n k rs m, + exists rs', + exec_straight ge (loadimm64 rd n ::g k) rs m k rs' m + /\ rs'#rd = Vlong n + /\ forall r, r <> PC -> r <> rd -> r <> GPR31 -> rs'#r = rs#r. +Proof. + unfold loadimm64; intros. generalize (make_immed64_sound n); intros E. + destruct (make_immed64 n). +- subst imm. econstructor; split. + apply exec_straight_one. simpl; eauto. auto. + split. Simpl. + intros; Simpl. +Qed. + +(* +(* +Lemma opimm32_correct: + forall (op: ireg -> ireg0 -> ireg0 -> instruction) + (opi: ireg -> ireg0 -> int -> instruction) + (sem: val -> val -> val) m, + (forall d s1 s2 rs, + exec_instr ge fn (op d s1 s2) rs m = Next (nextinstr (rs#d <- (sem rs##s1 rs##s2))) m) -> + (forall d s n rs, + exec_instr ge fn (opi d s n) rs m = Next (nextinstr (rs#d <- (sem rs##s (Vint n)))) m) -> + forall rd r1 n k rs, + r1 <> GPR31 -> + exists rs', + exec_straight ge fn (opimm32 op opi rd r1 n k) rs m k rs' m + /\ rs'#rd = sem rs##r1 (Vint n) + /\ forall r, r <> PC -> r <> rd -> r <> GPR31 -> rs'#r = rs#r. +Proof. + intros. unfold opimm32. generalize (make_immed32_sound n); intros E. + destruct (make_immed32 n). +- subst imm. econstructor; split. + apply exec_straight_one. rewrite H0. simpl; eauto. auto. + split. Simpl. intros; Simpl. +- destruct (load_hilo32_correct GPR31 hi lo (op rd r1 GPR31 :: k) rs m) + as (rs' & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. apply exec_straight_one. + rewrite H; eauto. auto. + split. Simpl. simpl. rewrite B, C, E. auto. congruence. congruence. + intros; Simpl. +Qed. + +(** 64-bit integer constants and arithmetic *) + +Lemma load_hilo64_correct: + forall rd hi lo k rs m, + exists rs', + exec_straight ge fn (load_hilo64 rd hi lo k) rs m k rs' m + /\ rs'#rd = Vlong (Int64.add (Int64.sign_ext 32 (Int64.shl hi (Int64.repr 12))) lo) + /\ forall r, r <> PC -> r <> rd -> rs'#r = rs#r. +Proof. + unfold load_hilo64; intros. + predSpec Int64.eq Int64.eq_spec lo Int64.zero. +- subst lo. econstructor; split. + apply exec_straight_one. simpl; eauto. auto. + split. rewrite Int64.add_zero. Simpl. + intros; Simpl. +- econstructor; split. + eapply exec_straight_two. simpl; eauto. simpl; eauto. auto. auto. + split. Simpl. + intros; Simpl. +Qed. +*) +*) + +Definition yolo := 4. + +Lemma opimm64_correct: + forall (op: arith_name_rrr) + (opi: arith_name_rri64) + (sem: val -> val -> val) m, + (forall d s1 s2 rs, + exec_basic_instr ge (op d s1 s2) rs m = Next ((rs#d <- (sem rs#s1 rs#s2))) m) -> + (forall d s n rs, + exec_basic_instr ge (opi d s n) rs m = Next ((rs#d <- (sem rs#s (Vlong n)))) m) -> + forall rd r1 n k rs, + r1 <> GPR31 -> + exists rs', + exec_straight ge (opimm64 op opi rd r1 n ::g k) rs m k rs' m + /\ rs'#rd = sem rs#r1 (Vlong n) + /\ forall r, r <> PC -> r <> rd -> r <> GPR31 -> rs'#r = rs#r. +Proof. + intros. unfold opimm64. generalize (make_immed64_sound n); intros E. + destruct (make_immed64 n). +- subst imm. econstructor; split. + apply exec_straight_one. rewrite H0. simpl; eauto. auto. + split. Simpl. intros; Simpl. +(* +- destruct (load_hilo64_correct GPR31 hi lo (op rd r1 GPR31 :: k) rs m) + as (rs' & A & B & C). + econstructor; split. + eapply exec_straight_trans. eexact A. apply exec_straight_one. + rewrite H; eauto. auto. + split. Simpl. simpl. rewrite B, C, E. auto. congruence. congruence. + intros; Simpl. +- subst imm. econstructor; split. + eapply exec_straight_two. simpl; eauto. rewrite H. simpl; eauto. auto. auto. + split. Simpl. intros; Simpl. +*) +Qed. + +(** Add offset to pointer *) + +Lemma addptrofs_correct: + forall rd r1 n k rs m, + r1 <> GPR31 -> + exists rs', + exec_straight ge (addptrofs rd r1 n ::g k) rs m k rs' m + /\ Val.lessdef (Val.offset_ptr rs#r1 n) rs'#rd + /\ forall r, r <> PC -> r <> rd -> r <> GPR31 -> rs'#r = rs#r. +Proof. + unfold addptrofs; intros. + destruct (Ptrofs.eq_dec n Ptrofs.zero). +- subst n. econstructor; split. + apply exec_straight_one. simpl; eauto. auto. + split. Simpl. destruct (rs r1); simpl; auto. rewrite Ptrofs.add_zero; auto. + intros; Simpl. +- unfold addimm64. + exploit (opimm64_correct Paddl Paddil Val.addl); eauto. intros (rs' & A & B & C). + exists rs'; split. eexact A. split; auto. + rewrite B. destruct (rs r1); simpl; auto. + rewrite Ptrofs.of_int64_to_int64 by auto. auto. +Qed. + +(* +(* +Lemma addptrofs_correct_2: + forall rd r1 n k (rs: regset) m b ofs, + r1 <> GPR31 -> rs#r1 = Vptr b of +s -> + exists rs', + exec_straight ge fn (addptrofs rd r1 n k) rs m k rs' m + /\ rs'#rd = Vptr b (Ptrofs.add ofs n) + /\ forall r, r <> PC -> r <> rd -> r <> GPR31 -> rs'#r = rs#r. +Proof. + intros. exploit (addptrofs_correct rd r1 n); eauto. intros (rs' & A & B & C). + exists rs'; intuition eauto. + rewrite H0 in B. inv B. auto. +Qed. + +(** Translation of conditional branches *) + +Remark branch_on_GPR31: + forall normal lbl (rs: regset) m b, + rs#GPR31 = Val.of_bool (eqb normal b) -> + exec_instr ge fn (if normal then Pbnew GPR31 X0 lbl else Pbeqw GPR31 X0 lbl) rs m = + eval_branch fn lbl rs m (Some b). +Proof. + intros. destruct normal; simpl; rewrite H; simpl; destruct b; reflexivity. +Qed. +*) +*) + +Ltac ArgsInv := + repeat (match goal with + | [ H: Error _ = OK _ |- _ ] => discriminate + | [ H: match ?args with nil => _ | _ :: _ => _ end = OK _ |- _ ] => destruct args + | [ H: bind _ _ = OK _ |- _ ] => monadInv H + | [ H: match _ with left _ => _ | right _ => assertion_failed end = OK _ |- _ ] => monadInv H; ArgsInv + | [ H: match _ with true => _ | false => assertion_failed end = OK _ |- _ ] => monadInv H; ArgsInv + end); + subst; + repeat (match goal with + | [ H: ireg_of _ = OK _ |- _ ] => simpl in *; rewrite (ireg_of_eq _ _ H) in * + | [ H: freg_of _ = OK _ |- _ ] => simpl in *; rewrite (freg_of_eq _ _ H) in * + end). + +Inductive exec_straight_opt: list instruction -> regset -> mem -> list instruction -> regset -> mem -> Prop := + | exec_straight_opt_refl: forall c rs m, + exec_straight_opt c rs m c rs m + | exec_straight_opt_intro: forall c1 rs1 m1 c2 rs2 m2, + exec_straight ge c1 rs1 m1 c2 rs2 m2 -> + exec_straight_opt c1 rs1 m1 c2 rs2 m2. + +Remark exec_straight_opt_right: + forall c3 rs3 m3 c1 rs1 m1 c2 rs2 m2, + exec_straight_opt c1 rs1 m1 c2 rs2 m2 -> + exec_straight ge c2 rs2 m2 c3 rs3 m3 -> + exec_straight ge c1 rs1 m1 c3 rs3 m3. +Proof. + destruct 1; intros. auto. eapply exec_straight_trans; eauto. +Qed. + +Lemma transl_comp_correct: + forall cmp r1 r2 lbl k rs m tbb b, + exists rs', + exec_straight ge (transl_comp cmp Signed r1 r2 lbl k) rs m (Pcb BTwnez GPR31 lbl ::g k) rs' m + /\ (forall r : preg, r <> PC -> r <> RTMP -> rs' r = rs r) + /\ ( Val.cmp_bool cmp rs#r1 rs#r2 = Some b -> + exec_control ge fn (Some (PCtlFlow (Pcb BTwnez GPR31 lbl))) (nextblock tbb rs') m + = eval_branch fn lbl (nextblock tbb rs') m (Some b)) + . +Proof. + intros. esplit. split. +- unfold transl_comp. apply exec_straight_one; simpl; eauto. +- split. + + intros; Simpl. + + intros. + remember (rs # GPR31 <- (compare_int (itest_for_cmp cmp Signed) rs # r1 rs # r2 m)) as rs'. + simpl. assert (Val.cmp_bool Cne (nextblock tbb rs') # GPR31 (Vint (Int.repr 0)) = Some b). + { + assert ((nextblock tbb rs') # GPR31 = (compare_int (itest_for_cmp cmp Signed) rs # r1 rs # r2 m)). + { rewrite Heqrs'. auto. } + rewrite H0. rewrite <- H. + remember (Val.cmp_bool cmp rs#r1 rs#r2) as cmpbool. + destruct cmp; simpl; + unfold Val.cmp; rewrite <- Heqcmpbool; destruct cmpbool; simpl; auto; + destruct b0; simpl; auto. + } + rewrite H0. simpl; auto. +Qed. + +Lemma transl_compu_correct: + forall cmp r1 r2 lbl k rs m tbb b, + exists rs', + exec_straight ge (transl_comp cmp Unsigned r1 r2 lbl k) rs m (Pcb BTwnez GPR31 lbl ::g k) rs' m + /\ (forall r : preg, r <> PC -> r <> RTMP -> rs' r = rs r) + /\ ( Val.cmpu_bool (Mem.valid_pointer m) cmp rs#r1 rs#r2 = Some b -> + exec_control ge fn (Some (PCtlFlow ((Pcb BTwnez GPR31 lbl)))) (nextblock tbb rs') m + = eval_branch fn lbl (nextblock tbb rs') m (Some b)) + . +Proof. + intros. esplit. split. +- unfold transl_comp. apply exec_straight_one; simpl; eauto. +- split. + + intros; Simpl. + + intros. + remember (rs # GPR31 <- (compare_int (itest_for_cmp cmp Unsigned) rs # r1 rs # r2 m)) as rs'. + simpl. assert (Val.cmp_bool Cne (nextblock tbb rs') # GPR31 (Vint (Int.repr 0)) = Some b). + { + assert ((nextblock tbb rs') # GPR31 = (compare_int (itest_for_cmp cmp Unsigned) rs # r1 rs # r2 m)). + { rewrite Heqrs'. auto. } + rewrite H0. rewrite <- H. + remember (Val.cmpu_bool (Mem.valid_pointer m) cmp rs#r1 rs#r2) as cmpubool. + destruct cmp; simpl; unfold Val.cmpu; rewrite <- Heqcmpubool; destruct cmpubool; simpl; auto; + destruct b0; simpl; auto. + } + rewrite H0. simpl; auto. +Qed. + +Lemma transl_compl_correct: + forall cmp r1 r2 lbl k rs m tbb b, + exists rs', + exec_straight ge (transl_compl cmp Signed r1 r2 lbl k) rs m (Pcb BTwnez GPR31 lbl ::g k) rs' m + /\ (forall r : preg, r <> PC -> r <> RTMP -> rs' r = rs r) + /\ ( Val.cmpl_bool cmp rs#r1 rs#r2 = Some b -> + exec_control ge fn (Some (PCtlFlow (Pcb BTwnez GPR31 lbl))) (nextblock tbb rs') m + = eval_branch fn lbl (nextblock tbb rs') m (Some b)) + . +Proof. + intros. esplit. split. +- unfold transl_compl. apply exec_straight_one; simpl; eauto. +- split. + + intros; Simpl. + + intros. + remember (rs # GPR31 <- (compare_long (itest_for_cmp cmp Signed) rs # r1 rs # r2 m)) as rs'. + simpl. assert (Val.cmp_bool Cne (nextblock tbb rs') # GPR31 (Vint (Int.repr 0)) = Some b). + { + assert ((nextblock tbb rs') # GPR31 = (compare_long (itest_for_cmp cmp Signed) rs # r1 rs # r2 m)). + { rewrite Heqrs'. auto. } + rewrite H0. rewrite <- H. + remember (Val.cmpl_bool cmp rs#r1 rs#r2) as cmpbool. + destruct cmp; simpl; + unfold compare_long; + unfold Val.cmpl; rewrite <- Heqcmpbool; destruct cmpbool; simpl; auto; + destruct b0; simpl; auto. + } + rewrite H0. simpl; auto. +Qed. + +Lemma transl_complu_correct: + forall cmp r1 r2 lbl k rs m tbb b, + exists rs', + exec_straight ge (transl_compl cmp Unsigned r1 r2 lbl k) rs m (Pcb BTwnez GPR31 lbl ::g k) rs' m + /\ (forall r : preg, r <> PC -> r <> RTMP -> rs' r = rs r) + /\ ( Val.cmplu_bool (Mem.valid_pointer m) cmp rs#r1 rs#r2 = Some b -> + exec_control ge fn (Some (PCtlFlow (Pcb BTwnez GPR31 lbl))) (nextblock tbb rs') m + = eval_branch fn lbl (nextblock tbb rs') m (Some b)) + . +Proof. + intros. esplit. split. +- unfold transl_compl. apply exec_straight_one; simpl; eauto. +- split. + + intros; Simpl. + + intros. + remember (rs # GPR31 <- (compare_long (itest_for_cmp cmp Unsigned) rs # r1 rs # r2 m)) as rs'. + simpl. assert (Val.cmp_bool Cne (nextblock tbb rs') # GPR31 (Vint (Int.repr 0)) = Some b). + { + assert ((nextblock tbb rs') # GPR31 = (compare_long (itest_for_cmp cmp Unsigned) rs # r1 rs # r2 m)). + { rewrite Heqrs'. auto. } + rewrite H0. rewrite <- H. + remember (Val.cmplu_bool (Mem.valid_pointer m) cmp rs#r1 rs#r2) as cmpbool. + destruct cmp; simpl; + unfold compare_long; + unfold Val.cmplu; rewrite <- Heqcmpbool; destruct cmpbool; simpl; auto; + destruct b0; simpl; auto. + } + rewrite H0. simpl; auto. +Qed. + +Lemma transl_opt_compuimm_correct: + forall n cmp r1 lbl k rs m b tbb c, + select_comp n cmp = Some c -> + exists rs', exists insn, + exec_straight_opt (transl_opt_compuimm n cmp r1 lbl k) rs m ((PControl insn) ::g k) rs' m + /\ (forall r : preg, r <> PC -> r <> RTMP -> rs' r = rs r) + /\ ( Val.cmpu_bool (Mem.valid_pointer m) cmp rs#r1 (Vint n) = Some b -> + exec_control ge fn (Some insn) (nextblock tbb rs') m = eval_branch fn lbl (nextblock tbb rs') m (Some b)) + . +Proof. + intros. +(* unfold transl_opt_compuimm. unfold select_comp in H. rewrite H; simpl. *) + remember c as c'. + destruct c'. + - (* c = Ceq *) + assert (Int.eq n Int.zero = true) as H'. + { remember (Int.eq n Int.zero) as termz. destruct termz; auto. + generalize H. unfold select_comp; rewrite <- Heqtermz; simpl. + discriminate. } + assert (n = (Int.repr 0)) as H0. { + destruct (Int.eq_dec n (Int.repr 0)) as [Ha|Ha]; auto. + generalize (Int.eq_false _ _ Ha). unfold Int.zero in H'. + rewrite H'. discriminate. + } + assert (Ceq = cmp). { + remember cmp as c0'. destruct c0'; auto; generalize H; unfold select_comp; + rewrite H'; simpl; auto; + intros; contradict H; discriminate. + } + unfold transl_opt_compuimm. subst. rewrite H'. + + exists rs, (Pcbu BTweqz r1 lbl). + split. + * constructor. + * split; auto. simpl. intros. + assert (rs r1 = (nextblock tbb rs) r1). + unfold nextblock. Simpl. rewrite H1 in H0. + (*assert (Val.cmp_bool Ceq (rs r1) (Vint (Int.repr 0)) = Some b) as EVAL'S. + { rewrite <- H2. rewrite <- H0. rewrite <- H1. auto. }*) + auto; + unfold eval_branch. rewrite H0; auto. + - (* c = Cne *) + assert (Int.eq n Int.zero = true) as H'. + { remember (Int.eq n Int.zero) as termz. destruct termz; auto. + generalize H. unfold select_comp; rewrite <- Heqtermz; simpl. + discriminate. } + assert (n = (Int.repr 0)) as H0. { + destruct (Int.eq_dec n (Int.repr 0)) as [Ha|Ha]; auto. + generalize (Int.eq_false _ _ Ha). unfold Int.zero in H'. + rewrite H'. discriminate. + } + assert (Cne = cmp). { + remember cmp as c0'. destruct c0'; auto; generalize H; unfold select_comp; + rewrite H'; simpl; auto; + intros; contradict H; discriminate. + } + unfold transl_opt_compuimm. subst. rewrite H'. + + exists rs, (Pcbu BTwnez r1 lbl). + split. + * constructor. + * split; auto. simpl. intros. + assert (rs r1 = (nextblock tbb rs) r1). + unfold nextblock. Simpl. rewrite H1 in H0. + auto; + unfold eval_branch. rewrite H0. auto. + - (* c = Clt *) contradict H; unfold select_comp; destruct (Int.eq n Int.zero); + destruct cmp; discriminate. + - (* c = Cle *) contradict H; unfold select_comp; destruct (Int.eq n Int.zero); + destruct cmp; discriminate. + - (* c = Cgt *) contradict H; unfold select_comp; destruct (Int.eq n Int.zero); + destruct cmp; discriminate. + - (* c = Cge *) contradict H; unfold select_comp; destruct (Int.eq n Int.zero); + destruct cmp; discriminate. +Qed. + +Lemma transl_opt_compluimm_correct: + forall n cmp r1 lbl k rs m b tbb c, + select_compl n cmp = Some c -> + exists rs', exists insn, + exec_straight_opt (transl_opt_compluimm n cmp r1 lbl k) rs m ((PControl insn) ::g k) rs' m + /\ (forall r : preg, r <> PC -> r <> RTMP -> rs' r = rs r) + /\ ( Val.cmplu_bool (Mem.valid_pointer m) cmp rs#r1 (Vlong n) = Some b -> + exec_control ge fn (Some insn) (nextblock tbb rs') m = eval_branch fn lbl (nextblock tbb rs') m (Some b)) + . +Proof. + intros. +(* unfold transl_opt_compluimm; rewrite H; simpl. *) + remember c as c'. + destruct c'. + - (* c = Ceq *) + assert (Int64.eq n Int64.zero = true) as H'. + { remember (Int64.eq n Int64.zero) as termz. destruct termz; auto. + generalize H. unfold select_compl; rewrite <- Heqtermz; simpl. + discriminate. } + assert (n = (Int64.repr 0)) as H0. { + destruct (Int64.eq_dec n (Int64.repr 0)) as [Ha|Ha]; auto. + generalize (Int64.eq_false _ _ Ha). unfold Int64.zero in H'. + rewrite H'. discriminate. + } + assert (Ceq = cmp). { + remember cmp as c0'. destruct c0'; auto; generalize H; unfold select_compl; + rewrite H'; simpl; auto; + intros; contradict H; discriminate. + } + unfold transl_opt_compluimm; subst; rewrite H'. + + exists rs, (Pcbu BTdeqz r1 lbl). + split. + * constructor. + * split; auto. simpl. intros. + assert (rs r1 = (nextblock tbb rs) r1). + unfold nextblock. Simpl. rewrite H1 in H0. + auto; + unfold eval_branch. rewrite H0; auto. + - (* c = Cne *) + assert (Int64.eq n Int64.zero = true) as H'. + { remember (Int64.eq n Int64.zero) as termz. destruct termz; auto. + generalize H. unfold select_compl; rewrite <- Heqtermz; simpl. + discriminate. } + assert (n = (Int64.repr 0)) as H0. { + destruct (Int64.eq_dec n (Int64.repr 0)) as [Ha|Ha]; auto. + generalize (Int64.eq_false _ _ Ha). unfold Int64.zero in H'. + rewrite H'. discriminate. + } + assert (Cne = cmp). { + remember cmp as c0'. destruct c0'; auto; generalize H; unfold select_compl; + rewrite H'; simpl; auto; + intros; contradict H; discriminate. + } + unfold transl_opt_compluimm; subst; rewrite H'. + + exists rs, (Pcbu BTdnez r1 lbl). + split. + * constructor. + * split; auto. simpl. intros. + assert (rs r1 = (nextblock tbb rs) r1). + unfold nextblock. Simpl. rewrite H1 in H0. + auto; + unfold eval_branch. rewrite H0; auto. + - (* c = Clt *) contradict H; unfold select_compl; destruct (Int64.eq n Int64.zero); + destruct cmp; discriminate. + - (* c = Cle *) contradict H; unfold select_compl; destruct (Int64.eq n Int64.zero); + destruct cmp; discriminate. + - (* c = Cgt *) contradict H; unfold select_compl; destruct (Int64.eq n Int64.zero); + destruct cmp; discriminate. + - (* c = Cge *) contradict H; unfold select_compl; destruct (Int64.eq n Int64.zero); + destruct cmp; discriminate. +Qed. + +Lemma transl_cbranch_correct_1: + forall cond args lbl k c m ms b sp rs m' tbb, + transl_cbranch cond args lbl k = OK c -> + eval_condition cond (List.map ms args) m = Some b -> + agree ms sp rs -> + Mem.extends m m' -> + exists rs', exists insn, + exec_straight_opt c rs m' ((PControl insn) ::g k) rs' m' + /\ exec_control ge fn (Some insn) (nextblock tbb rs') m' = eval_branch fn lbl (nextblock tbb rs') m' (Some b) + /\ forall r, r <> PC -> r <> RTMP -> rs'#r = rs#r. +Proof. + intros until tbb; intros TRANSL EVAL AG MEXT. + set (vl' := map rs (map preg_of args)). + assert (EVAL': eval_condition cond vl' m' = Some b). + { apply eval_condition_lessdef with (map ms args) m; auto. eapply preg_vals; eauto. } + clear EVAL MEXT AG. + destruct cond; simpl in TRANSL; ArgsInv. +(* Ccomp *) +- exploit (transl_comp_correct c0 x x0 lbl); eauto. intros (rs' & A & B & C). + exists rs', (Pcb BTwnez GPR31 lbl). + split. + + constructor. eexact A. + + split; auto. apply C; auto. +(* Ccompu *) +- exploit (transl_compu_correct c0 x x0 lbl); eauto. intros (rs' & A & B & C). + exists rs', (Pcb BTwnez GPR31 lbl). + split. + + constructor. eexact A. + + split; auto. apply C; auto. +(* Ccompimm *) +- remember (Int.eq n Int.zero) as eqz. + destruct eqz. + + assert (n = (Int.repr 0)). { + destruct (Int.eq_dec n (Int.repr 0)) as [H|H]; auto. + generalize (Int.eq_false _ _ H). unfold Int.zero in Heqeqz. + rewrite <- Heqeqz. discriminate. + } + exists rs, (Pcb (btest_for_cmpswz c0) x lbl). + split. + * constructor. + * split; auto. + assert (rs x = (nextblock tbb rs) x). + unfold nextblock. Simpl. rewrite H0 in EVAL'. clear H0. + destruct c0; simpl; auto; + unfold eval_branch; rewrite <- H; rewrite EVAL'; auto. + + exploit (loadimm32_correct GPR31 n); eauto. intros (rs' & A & B & C). + exploit (transl_comp_correct c0 x GPR31 lbl); eauto. intros (rs'2 & A' & B' & C'). + exists rs'2, (Pcb BTwnez GPR31 lbl). + split. + * constructor. apply exec_straight_trans + with (c2 := (transl_comp c0 Signed x GPR31 lbl k)) (rs2 := rs') (m2 := m'). + eexact A. eexact A'. + * split; auto. + { apply C'; auto. rewrite B, C; eauto with asmgen. } + { intros. rewrite B'; eauto with asmgen. } +(* Ccompuimm *) +- remember (select_comp n c0) as selcomp. + destruct selcomp. + + exploit (transl_opt_compuimm_correct n c0 x lbl k). apply eq_sym. apply Heqselcomp. + intros (rs' & i & A & B & C). + exists rs', i. + split. + * apply A. + * split; auto. apply C. apply EVAL'. + + assert (transl_opt_compuimm n c0 x lbl k = loadimm32 GPR31 n ::g transl_comp c0 Unsigned x GPR31 lbl k). + { unfold transl_opt_compuimm. + destruct (Int.eq n Int.zero) eqn:EQN. + all: unfold select_comp in Heqselcomp; rewrite EQN in Heqselcomp; destruct c0; simpl in *; auto. + all: discriminate. } + rewrite H. clear H. + exploit (loadimm32_correct GPR31 n); eauto. intros (rs' & A & B & C). + exploit (transl_compu_correct c0 x GPR31 lbl); eauto. intros (rs'2 & A' & B' & C'). + exists rs'2, (Pcb BTwnez GPR31 lbl). + split. + * constructor. apply exec_straight_trans + with (c2 := (transl_comp c0 Unsigned x GPR31 lbl k)) (rs2 := rs') (m2 := m'). + eexact A. eexact A'. + * split; auto. + { apply C'; auto. rewrite B, C; eauto with asmgen. } + { intros. rewrite B'; eauto with asmgen. } +(* Ccompl *) +- exploit (transl_compl_correct c0 x x0 lbl); eauto. intros (rs' & A & B & C). + exists rs', (Pcb BTwnez GPR31 lbl). + split. + + constructor. eexact A. + + split; auto. apply C; auto. +(* Ccomplu *) +- exploit (transl_complu_correct c0 x x0 lbl); eauto. intros (rs' & A & B & C). + exists rs', (Pcb BTwnez GPR31 lbl). + split. + + constructor. eexact A. + + split; auto. apply C; auto. +(* Ccomplimm *) +- remember (Int64.eq n Int64.zero) as eqz. + destruct eqz. + + assert (n = (Int64.repr 0)). { + destruct (Int64.eq_dec n (Int64.repr 0)) as [H|H]; auto. + generalize (Int64.eq_false _ _ H). unfold Int64.zero in Heqeqz. + rewrite <- Heqeqz. discriminate. + } + exists rs, (Pcb (btest_for_cmpsdz c0) x lbl). + split. + * constructor. + * split; auto. + assert (rs x = (nextblock tbb rs) x). + unfold nextblock. Simpl. rewrite H0 in EVAL'. clear H0. + destruct c0; simpl; auto; + unfold eval_branch; rewrite <- H; rewrite EVAL'; auto. + + exploit (loadimm64_correct GPR31 n); eauto. intros (rs' & A & B & C). + exploit (transl_compl_correct c0 x GPR31 lbl); eauto. intros (rs'2 & A' & B' & C'). + exists rs'2, (Pcb BTwnez GPR31 lbl). + split. + * constructor. apply exec_straight_trans + with (c2 := (transl_compl c0 Signed x GPR31 lbl k)) (rs2 := rs') (m2 := m'). + eexact A. eexact A'. + * split; auto. + { apply C'; auto. rewrite B, C; eauto with asmgen. } + { intros. rewrite B'; eauto with asmgen. } + +(* Ccompluimm *) +- remember (select_compl n c0) as selcomp. + destruct selcomp. + + exploit (transl_opt_compluimm_correct n c0 x lbl k). apply eq_sym. apply Heqselcomp. + intros (rs' & i & A & B & C). + exists rs', i. + split. + * apply A. + * split; auto. apply C. apply EVAL'. + + assert (transl_opt_compluimm n c0 x lbl k = loadimm64 GPR31 n ::g transl_compl c0 Unsigned x GPR31 lbl k). + { unfold transl_opt_compluimm. + destruct (Int64.eq n Int64.zero) eqn:EQN. + all: unfold select_compl in Heqselcomp; rewrite EQN in Heqselcomp; destruct c0; simpl in *; auto. + all: discriminate. } + rewrite H. clear H. + exploit (loadimm64_correct GPR31 n); eauto. intros (rs' & A & B & C). + exploit (transl_complu_correct c0 x GPR31 lbl); eauto. intros (rs'2 & A' & B' & C'). + exists rs'2, (Pcb BTwnez GPR31 lbl). + split. + * constructor. apply exec_straight_trans + with (c2 := (transl_compl c0 Unsigned x GPR31 lbl k)) (rs2 := rs') (m2 := m'). + eexact A. eexact A'. + * split; auto. + { apply C'; auto. rewrite B, C; eauto with asmgen. } + { intros. rewrite B'; eauto with asmgen. } +Qed. + +Lemma transl_cbranch_correct_true: + forall cond args lbl k c m ms sp rs m' tbb, + transl_cbranch cond args lbl k = OK c -> + eval_condition cond (List.map ms args) m = Some true -> + agree ms sp rs -> + Mem.extends m m' -> + exists rs', exists insn, + exec_straight_opt c rs m' ((PControl insn) ::g k) rs' m' + /\ exec_control ge fn (Some insn) (nextblock tbb rs') m' = goto_label fn lbl (nextblock tbb rs') m' + /\ forall r, r <> PC -> r <> GPR31 -> rs'#r = rs#r. +Proof. + intros. eapply transl_cbranch_correct_1 with (b := true); eauto. +Qed. + +Lemma transl_cbranch_correct_false: + forall cond args lbl k c m ms sp rs tbb m', + transl_cbranch cond args lbl k = OK c -> + eval_condition cond (List.map ms args) m = Some false -> + agree ms sp rs -> + Mem.extends m m' -> + exists rs', exists insn, + exec_straight_opt c rs m' ((PControl insn) ::g k) rs' m' + /\ exec_control ge fn (Some insn) (nextblock tbb rs') m' = Next (nextblock tbb rs') m' + /\ forall r, r <> PC -> r <> GPR31 -> rs'#r = rs#r. +Proof. + intros. exploit transl_cbranch_correct_1; eauto. +Qed. +(* intros (rs' & insn & A & B & C). + exists rs'. + split. eapply exec_straight_opt_right; eauto. apply exec_straight_one; auto. + intros; Simpl. + *) + +(** Translation of condition operators *) + +Lemma transl_cond_int32s_correct: + forall cmp rd r1 r2 k rs m, + exists rs', + exec_straight ge (basics_to_code (transl_cond_int32s cmp rd r1 r2 k)) rs m (basics_to_code k) rs' m + /\ Val.lessdef (Val.cmp cmp rs#r1 rs#r2) rs'#rd + /\ forall r, r <> PC -> r <> rd -> rs'#r = rs#r. +Proof. + intros. destruct cmp; simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +Qed. + +Lemma transl_cond_int32u_correct: + forall cmp rd r1 r2 k rs m, + exists rs', + exec_straight ge (basics_to_code (transl_cond_int32u cmp rd r1 r2 k)) rs m (basics_to_code k) rs' m + /\ rs'#rd = Val.cmpu (Mem.valid_pointer m) cmp rs#r1 rs#r2 + /\ forall r, r <> PC -> r <> rd -> rs'#r = rs#r. +Proof. + intros. destruct cmp; simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +Qed. + +Lemma transl_cond_int64s_correct: + forall cmp rd r1 r2 k rs m, + exists rs', + exec_straight ge (basics_to_code (transl_cond_int64s cmp rd r1 r2 k)) rs m (basics_to_code k) rs' m + /\ Val.lessdef (Val.maketotal (Val.cmpl cmp rs#r1 rs#r2)) rs'#rd + /\ forall r, r <> PC -> r <> rd -> rs'#r = rs#r. +Proof. + intros. destruct cmp; simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +Qed. + +Lemma transl_cond_int64u_correct: + forall cmp rd r1 r2 k rs m, + exists rs', + exec_straight ge (basics_to_code (transl_cond_int64u cmp rd r1 r2 k)) rs m (basics_to_code k) rs' m + /\ rs'#rd = Val.maketotal (Val.cmplu (Mem.valid_pointer m) cmp rs#r1 rs#r2) + /\ forall r, r <> PC -> r <> rd -> rs'#r = rs#r. +Proof. + intros. destruct cmp; simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +Qed. + +Lemma transl_condimm_int32s_correct: + forall cmp rd r1 n k rs m, + r1 <> GPR31 -> + exists rs', + exec_straight ge (basics_to_code (transl_condimm_int32s cmp rd r1 n k)) rs m (basics_to_code k) rs' m + /\ Val.lessdef (Val.cmp cmp rs#r1 (Vint n)) rs'#rd + /\ forall r, r <> PC -> r <> rd -> r <> GPR31 -> rs'#r = rs#r. +Proof. + intros. destruct cmp; simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +Qed. + +Lemma transl_condimm_int32u_correct: + forall cmp rd r1 n k rs m, + r1 <> GPR31 -> + exists rs', + exec_straight ge (basics_to_code (transl_condimm_int32u cmp rd r1 n k)) rs m (basics_to_code k) rs' m + /\ Val.lessdef (Val.cmpu (Mem.valid_pointer m) cmp rs#r1 (Vint n)) rs'#rd + /\ forall r, r <> PC -> r <> rd -> r <> GPR31 -> rs'#r = rs#r. +Proof. + intros. destruct cmp; simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +Qed. + +Lemma transl_condimm_int64s_correct: + forall cmp rd r1 n k rs m, + r1 <> GPR31 -> + exists rs', + exec_straight ge (basics_to_code (transl_condimm_int64s cmp rd r1 n k)) rs m (basics_to_code k) rs' m + /\ Val.lessdef (Val.maketotal (Val.cmpl cmp rs#r1 (Vlong n))) rs'#rd + /\ forall r, r <> PC -> r <> rd -> r <> GPR31 -> rs'#r = rs#r. +Proof. + intros. destruct cmp; simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +Qed. + +Lemma transl_condimm_int64u_correct: + forall cmp rd r1 n k rs m, + r1 <> GPR31 -> + exists rs', + exec_straight ge (basics_to_code (transl_condimm_int64u cmp rd r1 n k)) rs m (basics_to_code k) rs' m + /\ Val.lessdef (Val.maketotal (Val.cmplu (Mem.valid_pointer m) cmp rs#r1 (Vlong n))) rs'#rd + /\ forall r, r <> PC -> r <> rd -> r <> GPR31 -> rs'#r = rs#r. +Proof. + intros. destruct cmp; simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +- econstructor; split. apply exec_straight_one; [simpl; eauto]. + split; intros; Simpl. +Qed. + +Lemma transl_cond_op_correct: + forall cond rd args k c rs m, + transl_cond_op cond rd args k = OK c -> + exists rs', + exec_straight ge (basics_to_code c) rs m (basics_to_code k) rs' m + /\ Val.lessdef (Val.of_optbool (eval_condition cond (map rs (map preg_of args)) m)) rs'#rd + /\ forall r, r <> PC -> r <> rd -> r <> GPR31 -> rs'#r = rs#r. +Proof. + assert (MKTOT: forall ob, Val.of_optbool ob = Val.maketotal (option_map Val.of_bool ob)). + { destruct ob as [[]|]; reflexivity. } + intros until m; intros TR. + destruct cond; simpl in TR; ArgsInv. ++ (* cmp *) + exploit transl_cond_int32s_correct; eauto. simpl. intros (rs' & A & B & C). exists rs'; eauto. ++ (* cmpu *) + exploit transl_cond_int32u_correct; eauto. simpl. intros (rs' & A & B & C). + exists rs'; repeat split; eauto. rewrite B; auto. ++ (* cmpimm *) + apply transl_condimm_int32s_correct; eauto with asmgen. ++ (* cmpuimm *) + apply transl_condimm_int32u_correct; eauto with asmgen. ++ (* cmpl *) + exploit transl_cond_int64s_correct; eauto. simpl. intros (rs' & A & B & C). + exists rs'; repeat split; eauto. rewrite MKTOT; eauto. ++ (* cmplu *) + exploit transl_cond_int64u_correct; eauto. simpl. intros (rs' & A & B & C). + exists rs'; repeat split; eauto. rewrite B, MKTOT; eauto. ++ (* cmplimm *) + exploit transl_condimm_int64s_correct; eauto. instantiate (1 := x); eauto with asmgen. simpl. + intros (rs' & A & B & C). + exists rs'; repeat split; eauto. rewrite MKTOT; eauto. ++ (* cmpluimm *) + exploit transl_condimm_int64u_correct; eauto. instantiate (1 := x); eauto with asmgen. simpl. + intros (rs' & A & B & C). + exists rs'; repeat split; eauto. rewrite MKTOT; eauto. +Qed. + +(* +(* ++ (* cmpf *) + destruct (transl_cond_float c0 rd x x0) as [insn normal] eqn:TR. + fold (Val.cmpf c0 (rs x) (rs x0)). + set (v := Val.cmpf c0 (rs x) (rs x0)). + destruct normal; inv EQ2. +* econstructor; split. + apply exec_straight_one. eapply transl_cond_float_correct with (v := v); eauto. auto. + split; intros; Simpl. +* econstructor; split. + eapply exec_straight_two. + eapply transl_cond_float_correct with (v := Val.notbool v); eauto. + simpl; reflexivity. + auto. auto. + split; intros; Simpl. unfold v, Val.cmpf. destruct (Val.cmpf_bool c0 (rs x) (rs x0)) as [[]|]; auto. ++ (* notcmpf *) + destruct (transl_cond_float c0 rd x x0) as [insn normal] eqn:TR. + rewrite Val.notbool_negb_3. fold (Val.cmpf c0 (rs x) (rs x0)). + set (v := Val.cmpf c0 (rs x) (rs x0)). + destruct normal; inv EQ2. +* econstructor; split. + eapply exec_straight_two. + eapply transl_cond_float_correct with (v := v); eauto. + simpl; reflexivity. + auto. auto. + split; intros; Simpl. unfold v, Val.cmpf. destruct (Val.cmpf_bool c0 (rs x) (rs x0)) as [[]|]; auto. +* econstructor; split. + apply exec_straight_one. eapply transl_cond_float_correct with (v := Val.notbool v); eauto. auto. + split; intros; Simpl. ++ (* cmpfs *) + destruct (transl_cond_single c0 rd x x0) as [insn normal] eqn:TR. + fold (Val.cmpfs c0 (rs x) (rs x0)). + set (v := Val.cmpfs c0 (rs x) (rs x0)). + destruct normal; inv EQ2. +* econstructor; split. + apply exec_straight_one. eapply transl_cond_single_correct with (v := v); eauto. auto. + split; intros; Simpl. +* econstructor; split. + eapply exec_straight_two. + eapply transl_cond_single_correct with (v := Val.notbool v); eauto. + simpl; reflexivity. + auto. auto. + split; intros; Simpl. unfold v, Val.cmpfs. destruct (Val.cmpfs_bool c0 (rs x) (rs x0)) as [[]|]; auto. ++ (* notcmpfs *) + destruct (transl_cond_single c0 rd x x0) as [insn normal] eqn:TR. + rewrite Val.notbool_negb_3. fold (Val.cmpfs c0 (rs x) (rs x0)). + set (v := Val.cmpfs c0 (rs x) (rs x0)). + destruct normal; inv EQ2. +* econstructor; split. + eapply exec_straight_two. + eapply transl_cond_single_correct with (v := v); eauto. + simpl; reflexivity. + auto. auto. + split; intros; Simpl. unfold v, Val.cmpfs. destruct (Val.cmpfs_bool c0 (rs x) (rs x0)) as [[]|]; auto. +* econstructor; split. + apply exec_straight_one. eapply transl_cond_single_correct with (v := Val.notbool v); eauto. auto. + split; intros; Simpl. +*) +*) + +(** Some arithmetic properties. *) + +Remark cast32unsigned_from_cast32signed: + forall i, Int64.repr (Int.unsigned i) = Int64.zero_ext 32 (Int64.repr (Int.signed i)). +Proof. + intros. apply Int64.same_bits_eq; intros. + rewrite Int64.bits_zero_ext, !Int64.testbit_repr by tauto. + rewrite Int.bits_signed by tauto. fold (Int.testbit i i0). + change Int.zwordsize with 32. + destruct (zlt i0 32). auto. apply Int.bits_above. auto. +Qed. + +Lemma cast32signed_correct: + forall (d s: ireg) (k: code) (rs: regset) (m: mem), + exists rs': regset, + exec_straight ge (cast32signed d s ::g k) rs m k rs' m + /\ Val.lessdef (Val.longofint (rs s)) (rs' d) + /\ (forall r: preg, r <> PC -> r <> d -> rs' r = rs r). +Proof. + intros. unfold cast32signed. destruct (ireg_eq d s). +- econstructor; split. + + apply exec_straight_one. simpl. eauto with asmgen. + + split. + * rewrite e. Simpl. + * intros. destruct r; Simpl. +- econstructor; split. + + apply exec_straight_one. simpl. eauto with asmgen. + + split. + * Simpl. + * intros. destruct r; Simpl. +Qed. + +(* Translation of arithmetic operations *) + +Ltac SimplEval H := + match type of H with + | Some _ = None _ => discriminate + | Some _ = Some _ => inv H + | ?a = Some ?b => let A := fresh in assert (A: Val.maketotal a = b) by (rewrite H; reflexivity) +end. + +Ltac TranslOpSimpl := + econstructor; split; + [ apply exec_straight_one; reflexivity + | split; [ apply Val.lessdef_same; simpl; Simpl; fail | intros; simpl; Simpl; fail ] ]. + +Lemma transl_op_correct: + forall op args res k (rs: regset) m v c, + transl_op op args res k = OK c -> + eval_operation ge (rs#SP) op (map rs (map preg_of args)) m = Some v -> + exists rs', + exec_straight ge (basics_to_code c) rs m (basics_to_code k) rs' m + /\ Val.lessdef v rs'#(preg_of res) + /\ forall r, data_preg r = true -> r <> preg_of res -> preg_notin r (destroyed_by_op op) -> rs' r = rs r. +Proof. + assert (SAME: forall v1 v2, v1 = v2 -> Val.lessdef v2 v1). { intros; subst; auto. } +Opaque Int.eq. + intros until c; intros TR EV. + unfold transl_op in TR; destruct op; ArgsInv; simpl in EV; SimplEval EV; try TranslOpSimpl. +- (* Omove *) + destruct (preg_of res), (preg_of m0); inv TR; TranslOpSimpl. +- (* Oaddrsymbol *) + destruct (Archi.pic_code tt && negb (Ptrofs.eq ofs Ptrofs.zero)). ++ set (rs1 := (rs#x <- (Genv.symbol_address ge id Ptrofs.zero))). + exploit (addptrofs_correct x x ofs (basics_to_code k) rs1 m); eauto with asmgen. + intros (rs2 & A & B & C). + exists rs2; split. + apply exec_straight_step with rs1 m; auto. + split. replace ofs with (Ptrofs.add Ptrofs.zero ofs) by (apply Ptrofs.add_zero_l). + rewrite Genv.shift_symbol_address. + replace (rs1 x) with (Genv.symbol_address ge id Ptrofs.zero) in B by (unfold rs1; Simpl). + exact B. + intros. rewrite C by eauto with asmgen. unfold rs1; Simpl. ++ TranslOpSimpl. +- (* Oaddrstack *) + exploit addptrofs_correct. instantiate (1 := GPR12); auto with asmgen. intros (rs' & A & B & C). + exists rs'; split; eauto. auto with asmgen. +- (* Ocast8signed *) + econstructor; split. + eapply exec_straight_two. simpl;eauto. simpl;eauto. + split; intros; simpl; Simpl. + assert (A: Int.ltu (Int.repr 24) Int.iwordsize = true) by auto. + destruct (rs x0); auto; simpl. rewrite A; simpl. Simpl. unfold Val.shr. rewrite A. + apply Val.lessdef_same. f_equal. apply Int.sign_ext_shr_shl. split; reflexivity. +- (* Ocast16signed *) + econstructor; split. + eapply exec_straight_two. simpl;eauto. simpl;eauto. + split; intros; Simpl. + assert (A: Int.ltu (Int.repr 16) Int.iwordsize = true) by auto. + destruct (rs x0); auto; simpl. rewrite A; simpl. Simpl. unfold Val.shr. rewrite A. + apply Val.lessdef_same. f_equal. apply Int.sign_ext_shr_shl. split; reflexivity. +- (* Oshrximm *) + clear H. exploit Val.shrx_shr_2; eauto. intros E; subst v; clear EV. + destruct (Int.eq n Int.zero). ++ econstructor; split. apply exec_straight_one. simpl; eauto. + split; intros; Simpl. ++ change (Int.repr 32) with Int.iwordsize. set (n' := Int.sub Int.iwordsize n). + econstructor; split. + eapply exec_straight_step. simpl; reflexivity. auto. + eapply exec_straight_step. simpl; reflexivity. auto. + eapply exec_straight_step. simpl; reflexivity. auto. + apply exec_straight_one. simpl; reflexivity. auto. + split; intros; Simpl. +- (* Ocast32signed *) + exploit cast32signed_correct; eauto. intros (rs' & A & B & C). + exists rs'; split; eauto. split. apply B. + intros. assert (r <> PC). { destruct r; auto; contradict H; discriminate. } + apply C; auto. +- (* longofintu *) + econstructor; split. + eapply exec_straight_three. simpl; eauto. simpl; eauto. simpl; eauto. + split; intros; Simpl. (* unfold Pregmap.set; Simpl. *) destruct (PregEq.eq x0 x0). + + destruct (rs x0); auto. simpl. + assert (A: Int.ltu (Int.repr 32) Int64.iwordsize' = true) by auto. + rewrite A; simpl. rewrite A. apply Val.lessdef_same. f_equal. + rewrite cast32unsigned_from_cast32signed. apply Int64.zero_ext_shru_shl. compute; auto. + + contradict n. auto. +- (* Ocmp *) + exploit transl_cond_op_correct; eauto. intros (rs' & A & B & C). + exists rs'; split. eexact A. eauto with asmgen. +(* +- (* intconst *) + exploit loadimm32_correct; eauto. intros (rs' & A & B & C). + exists rs'; split; eauto. rewrite B; auto with asmgen. +- (* longconst *) + exploit loadimm64_correct; eauto. intros (rs' & A & B & C). + exists rs'; split; eauto. rewrite B; auto with asmgen. +- (* floatconst *) + destruct (Float.eq_dec n Float.zero). ++ subst n. econstructor; split. + apply exec_straight_one. simpl; eauto. auto. + split; intros; Simpl. ++ econstructor; split. + apply exec_straight_one. simpl; eauto. auto. + split; intros; Simpl. +- (* singleconst *) + destruct (Float32.eq_dec n Float32.zero). ++ subst n. econstructor; split. + apply exec_straight_one. simpl; eauto. auto. + split; intros; Simpl. ++ econstructor; split. + apply exec_straight_one. simpl; eauto. auto. + split; intros; Simpl. +- (* stackoffset *) + exploit addptrofs_correct. instantiate (1 := X2); auto with asmgen. intros (rs' & A & B & C). + exists rs'; split; eauto. auto with asmgen. +- (* addimm *) + exploit (opimm32_correct Paddw Paddiw Val.add); auto. instantiate (1 := x0); eauto with asmgen. + intros (rs' & A & B & C). + exists rs'; split; eauto. rewrite B; auto with asmgen. +- (* andimm *) + exploit (opimm32_correct Pandw Pandiw Val.and); auto. instantiate (1 := x0); eauto with asmgen. + intros (rs' & A & B & C). + exists rs'; split; eauto. rewrite B; auto with asmgen. +- (* orimm *) + exploit (opimm32_correct Porw Poriw Val.or); auto. instantiate (1 := x0); eauto with asmgen. + intros (rs' & A & B & C). + exists rs'; split; eauto. rewrite B; auto with asmgen. +- (* xorimm *) + exploit (opimm32_correct Pxorw Pxoriw Val.xor); auto. instantiate (1 := x0); eauto with asmgen. + intros (rs' & A & B & C). + exists rs'; split; eauto. rewrite B; auto with asmgen. + + + +- (* addlimm *) + exploit (opimm64_correct Paddl Paddil Val.addl); auto. instantiate (1 := x0); eauto with asmgen. + intros (rs' & A & B & C). + exists rs'; split; eauto. rewrite B; auto with asmgen. + +- (* andimm *) + exploit (opimm64_correct Pandl Pandil Val.andl); auto. instantiate (1 := x0); eauto with asmgen. + intros (rs' & A & B & C). + exists rs'; split; eauto. rewrite B; auto with asmgen. +- (* orimm *) + exploit (opimm64_correct Porl Poril Val.orl); auto. instantiate (1 := x0); eauto with asmgen. + intros (rs' & A & B & C). + exists rs'; split; eauto. rewrite B; auto with asmgen. +- (* xorimm *) + exploit (opimm64_correct Pxorl Pxoril Val.xorl); auto. instantiate (1 := x0); eauto with asmgen. + intros (rs' & A & B & C). + exists rs'; split; eauto. rewrite B; auto with asmgen. +- (* shrxlimm *) + clear H. exploit Val.shrxl_shrl_2; eauto. intros E; subst v; clear EV. + destruct (Int.eq n Int.zero). ++ econstructor; split. apply exec_straight_one. simpl; eauto. auto. + split; intros; Simpl. ++ change (Int.repr 64) with Int64.iwordsize'. set (n' := Int.sub Int64.iwordsize' n). + econstructor; split. + eapply exec_straight_step. simpl; reflexivity. auto. + eapply exec_straight_step. simpl; reflexivity. auto. + eapply exec_straight_step. simpl; reflexivity. auto. + apply exec_straight_one. simpl; reflexivity. auto. + split; intros; Simpl. +*) +Qed. + +(** Memory accesses *) + +Lemma indexed_memory_access_correct: + forall mk_instr base ofs k rs m, + base <> GPR31 -> + exists base' ofs' rs', + exec_straight_opt (indexed_memory_access mk_instr base ofs ::g k) rs m + (mk_instr base' ofs' ::g k) rs' m + /\ Val.offset_ptr rs'#base' (eval_offset ge ofs') = Val.offset_ptr rs#base ofs + /\ forall r, r <> PC -> r <> GPR31 -> rs'#r = rs#r. +Proof. + unfold indexed_memory_access; intros. + (* destruct Archi.ptr64 eqn:SF. *) + assert (Archi.ptr64 = true) as SF; auto. +- generalize (make_immed64_sound (Ptrofs.to_int64 ofs)); intros EQ. + destruct (make_immed64 (Ptrofs.to_int64 ofs)). ++ econstructor; econstructor; econstructor; split. + apply exec_straight_opt_refl. + split; auto. simpl. subst imm. rewrite Ptrofs.of_int64_to_int64 by auto. auto. +(* ++ econstructor; econstructor; econstructor; split. + constructor. eapply exec_straight_two. + simpl; eauto. simpl; eauto. auto. auto. + split; intros; Simpl. destruct (rs base); auto; simpl. rewrite SF. simpl. + rewrite Ptrofs.add_assoc. f_equal. f_equal. + rewrite <- (Ptrofs.of_int64_to_int64 SF ofs). rewrite EQ. + symmetry; auto with ptrofs. ++ econstructor; econstructor; econstructor; split. + constructor. eapply exec_straight_two. + simpl; eauto. simpl; eauto. auto. auto. + split; intros; Simpl. unfold eval_offset. destruct (rs base); auto; simpl. rewrite SF. simpl. + rewrite Ptrofs.add_zero. subst imm. rewrite Ptrofs.of_int64_to_int64 by auto. auto. +(* 32 bits part, irrelevant for us +- generalize (make_immed32_sound (Ptrofs.to_int ofs)); intros EQ. + destruct (make_immed32 (Ptrofs.to_int ofs)). ++ econstructor; econstructor; econstructor; split. + apply exec_straight_opt_refl. + split; auto. simpl. subst imm. rewrite Ptrofs.of_int_to_int by auto. auto. ++ econstructor; econstructor; econstructor; split. + constructor. eapply exec_straight_two. + simpl; eauto. simpl; eauto. auto. auto. + split; intros; Simpl. destruct (rs base); auto; simpl. rewrite SF. simpl. + rewrite Ptrofs.add_assoc. f_equal. f_equal. + rewrite <- (Ptrofs.of_int_to_int SF ofs). rewrite EQ. + symmetry; auto with ptrofs. +*)*) +Qed. + + +Lemma indexed_load_access_correct: + forall chunk (mk_instr: ireg -> offset -> basic) rd m, + (forall base ofs rs, + exec_basic_instr ge (mk_instr base ofs) rs m = exec_load ge chunk rs m rd base ofs) -> + forall (base: ireg) ofs k (rs: regset) v, + Mem.loadv chunk m (Val.offset_ptr rs#base ofs) = Some v -> + base <> GPR31 -> rd <> PC -> + exists rs', + exec_straight ge (indexed_memory_access mk_instr base ofs ::g k) rs m k rs' m + /\ rs'#rd = v + /\ forall r, r <> PC -> r <> GPR31 -> r <> rd -> rs'#r = rs#r. +Proof. + intros until m; intros EXEC; intros until v; intros LOAD NOT31 NOTPC. + exploit indexed_memory_access_correct; eauto. + intros (base' & ofs' & rs' & A & B & C). + econstructor; split. + eapply exec_straight_opt_right. eexact A. apply exec_straight_one. rewrite EXEC. + unfold exec_load. rewrite B, LOAD. eauto. Simpl. + split; intros; Simpl. auto. +Qed. + +Lemma indexed_store_access_correct: + forall chunk (mk_instr: ireg -> offset -> basic) r1 m, + (forall base ofs rs, + exec_basic_instr ge (mk_instr base ofs) rs m = exec_store ge chunk rs m r1 base ofs) -> + forall (base: ireg) ofs k (rs: regset) m', + Mem.storev chunk m (Val.offset_ptr rs#base ofs) (rs#r1) = Some m' -> + base <> GPR31 -> r1 <> GPR31 -> r1 <> PC -> + exists rs', + exec_straight ge (indexed_memory_access mk_instr base ofs ::g k) rs m k rs' m' + /\ forall r, r <> PC -> r <> GPR31 -> rs'#r = rs#r. +Proof. + intros until m; intros EXEC; intros until m'; intros STORE NOT31 NOT31' NOTPC. + exploit indexed_memory_access_correct. instantiate (1 := base). eauto. + intros (base' & ofs' & rs' & A & B & C). + econstructor; split. + eapply exec_straight_opt_right. eapply A. apply exec_straight_one. rewrite EXEC. + unfold exec_store. rewrite B, C, STORE. eauto. eauto. auto. + intros; Simpl. rewrite C; auto. +Qed. + +Lemma loadind_correct: + forall (base: ireg) ofs ty dst k c (rs: regset) m v, + loadind base ofs ty dst k = OK c -> + Mem.loadv (chunk_of_type ty) m (Val.offset_ptr rs#base ofs) = Some v -> + base <> GPR31 -> + exists rs', + exec_straight ge (basics_to_code c) rs m (basics_to_code k) rs' m + /\ rs'#(preg_of dst) = v + /\ forall r, r <> PC -> r <> GPR31 -> r <> preg_of dst -> rs'#r = rs#r. +Proof. + intros until v; intros TR LOAD NOT31. + assert (A: exists mk_instr, + c = indexed_memory_access mk_instr base ofs :: k + /\ forall base' ofs' rs', + exec_basic_instr ge (mk_instr base' ofs') rs' m = + exec_load ge (chunk_of_type ty) rs' m (preg_of dst) base' ofs'). + { unfold loadind in TR. + destruct ty, (preg_of dst); inv TR; econstructor; split; eauto. } + destruct A as (mk_instr & B & C). subst c. + eapply indexed_load_access_correct; eauto with asmgen. +Qed. + +Lemma storeind_correct: + forall (base: ireg) ofs ty src k c (rs: regset) m m', + storeind src base ofs ty k = OK c -> + Mem.storev (chunk_of_type ty) m (Val.offset_ptr rs#base ofs) rs#(preg_of src) = Some m' -> + base <> GPR31 -> + exists rs', + exec_straight ge (basics_to_code c) rs m (basics_to_code k) rs' m' + /\ forall r, r <> PC -> r <> GPR31 -> rs'#r = rs#r. +Proof. + intros until m'; intros TR STORE NOT31. + assert (A: exists mk_instr, + c = indexed_memory_access mk_instr base ofs :: k + /\ forall base' ofs' rs', + exec_basic_instr ge (mk_instr base' ofs') rs' m = + exec_store ge (chunk_of_type ty) rs' m (preg_of src) base' ofs'). + { unfold storeind in TR. destruct ty, (preg_of src); inv TR; econstructor; split; eauto. } + destruct A as (mk_instr & B & C). subst c. + eapply indexed_store_access_correct; eauto with asmgen. +Qed. + +Ltac bsimpl := unfold exec_bblock; simpl. + +Lemma Pget_correct: + forall (dst: gpreg) (src: preg) k (rs: regset) m, + src = RA -> + exists rs', + exec_straight ge (Pget dst src ::g k) rs m k rs' m + /\ rs'#dst = rs#src + /\ forall r, r <> PC -> r <> dst -> rs'#r = rs#r. +Proof. + intros. econstructor; econstructor; econstructor. +- rewrite H. bsimpl. auto. +- Simpl. +- intros. Simpl. +Qed. + +Lemma Pset_correct: + forall (dst: preg) (src: gpreg) k (rs: regset) m, + dst = RA -> + exists rs', + exec_straight ge (Pset dst src ::g k) rs m k rs' m + /\ rs'#dst = rs#src + /\ forall r, r <> PC -> r <> dst -> rs'#r = rs#r. +Proof. + intros. econstructor; econstructor; econstructor; simpl. + rewrite H. auto. + Simpl. + Simpl. + intros. rewrite H. Simpl. +Qed. + +Lemma loadind_ptr_correct: + forall (base: ireg) ofs (dst: ireg) k (rs: regset) m v, + Mem.loadv Mptr m (Val.offset_ptr rs#base ofs) = Some v -> + base <> GPR31 -> + exists rs', + exec_straight ge (loadind_ptr base ofs dst ::g k) rs m k rs' m + /\ rs'#dst = v + /\ forall r, r <> PC -> r <> GPR31 -> r <> dst -> rs'#r = rs#r. +Proof. + intros. eapply indexed_load_access_correct; eauto with asmgen. + intros. unfold Mptr. assert (Archi.ptr64 = true). auto. rewrite H1. auto. +Qed. + +Lemma storeind_ptr_correct: + forall (base: ireg) ofs (src: ireg) k (rs: regset) m m', + Mem.storev Mptr m (Val.offset_ptr rs#base ofs) rs#src = Some m' -> + base <> GPR31 -> src <> GPR31 -> + exists rs', + exec_straight ge (storeind_ptr src base ofs ::g k) rs m k rs' m' + /\ forall r, r <> PC -> r <> GPR31 -> rs'#r = rs#r. +Proof. + intros. eapply indexed_store_access_correct with (r1 := src); eauto with asmgen. + intros. unfold Mptr. assert (Archi.ptr64 = true); auto. +Qed. + +Lemma transl_memory_access_correct: + forall mk_instr addr args k c (rs: regset) m v, + transl_memory_access mk_instr addr args k = OK c -> + eval_addressing ge rs#SP addr (map rs (map preg_of args)) = Some v -> + exists base ofs rs', + exec_straight_opt (basics_to_code c) rs m (mk_instr base ofs ::g (basics_to_code k)) rs' m + /\ Val.offset_ptr rs'#base (eval_offset ge ofs) = v + /\ forall r, r <> PC -> r <> GPR31 -> rs'#r = rs#r. +Proof. + intros until v; intros TR EV. + unfold transl_memory_access in TR; destruct addr; ArgsInv. +- (* indexed *) + inv EV. apply indexed_memory_access_correct; eauto with asmgen. +- (* global *) + simpl in EV. inv EV. inv TR. econstructor; econstructor; econstructor; split. + constructor. apply exec_straight_one. simpl; eauto. auto. + split; intros; Simpl. unfold eval_offset. + assert (Val.lessdef (Val.offset_ptr (Genv.symbol_address ge i i0) Ptrofs.zero) (Genv.symbol_address ge i i0)). + { apply Val.offset_ptr_zero. } + remember (Genv.symbol_address ge i i0) as symbol. + destruct symbol; auto. + + contradict Heqsymbol; unfold Genv.symbol_address; + destruct (Genv.find_symbol ge i); discriminate. + + contradict Heqsymbol; unfold Genv.symbol_address; + destruct (Genv.find_symbol ge i); discriminate. + + contradict Heqsymbol; unfold Genv.symbol_address; + destruct (Genv.find_symbol ge i); discriminate. + + contradict Heqsymbol; unfold Genv.symbol_address; + destruct (Genv.find_symbol ge i); discriminate. + + simpl. rewrite Ptrofs.add_zero; auto. +- (* stack *) + inv TR. inv EV. apply indexed_memory_access_correct; eauto with asmgen. +Qed. + +Lemma transl_load_access_correct: + forall chunk (mk_instr: ireg -> offset -> basic) addr args k c rd (rs: regset) m v v', + (forall base ofs rs, + exec_basic_instr ge (mk_instr base ofs) rs m = exec_load ge chunk rs m rd base ofs) -> + transl_memory_access mk_instr addr args k = OK c -> + eval_addressing ge rs#SP addr (map rs (map preg_of args)) = Some v -> + Mem.loadv chunk m v = Some v' -> + rd <> PC -> + exists rs', + exec_straight ge (basics_to_code c) rs m (basics_to_code k) rs' m + /\ rs'#rd = v' + /\ forall r, r <> PC -> r <> GPR31 -> r <> rd -> rs'#r = rs#r. +Proof. + intros until v'; intros INSTR TR EV LOAD NOTPC. + exploit transl_memory_access_correct; eauto. + intros (base & ofs & rs' & A & B & C). + econstructor; split. + eapply exec_straight_opt_right. eexact A. apply exec_straight_one. + rewrite INSTR. unfold exec_load. rewrite B, LOAD. reflexivity. Simpl. + split; intros; Simpl. auto. +Qed. + +Lemma transl_store_access_correct: + forall chunk (mk_instr: ireg -> offset -> basic) addr args k c r1 (rs: regset) m v m', + (forall base ofs rs, + exec_basic_instr ge (mk_instr base ofs) rs m = exec_store ge chunk rs m r1 base ofs) -> + transl_memory_access mk_instr addr args k = OK c -> + eval_addressing ge rs#SP addr (map rs (map preg_of args)) = Some v -> + Mem.storev chunk m v rs#r1 = Some m' -> + r1 <> PC -> r1 <> GPR31 -> + exists rs', + exec_straight ge (basics_to_code c) rs m (basics_to_code k) rs' m' + /\ forall r, r <> PC -> r <> GPR31 -> rs'#r = rs#r. +Proof. + intros until m'; intros INSTR TR EV STORE NOTPC NOT31. + exploit transl_memory_access_correct; eauto. + intros (base & ofs & rs' & A & B & C). + econstructor; split. + eapply exec_straight_opt_right. eexact A. apply exec_straight_one. + rewrite INSTR. unfold exec_store. rewrite B, C, STORE by auto. reflexivity. auto. +Qed. + +Lemma transl_load_correct: + forall chunk addr args dst k c (rs: regset) m a v, + transl_load chunk addr args dst k = OK c -> + eval_addressing ge rs#SP addr (map rs (map preg_of args)) = Some a -> + Mem.loadv chunk m a = Some v -> + exists rs', + exec_straight ge (basics_to_code c) rs m (basics_to_code k) rs' m + /\ rs'#(preg_of dst) = v + /\ forall r, r <> PC -> r <> GPR31 -> r <> preg_of dst -> rs'#r = rs#r. +Proof. + intros until v; intros TR EV LOAD. + assert (A: exists mk_instr, + transl_memory_access mk_instr addr args k = OK c + /\ forall base ofs rs, + exec_basic_instr ge (mk_instr base ofs) rs m = exec_load ge chunk rs m (preg_of dst) base ofs). + { unfold transl_load in TR; destruct chunk; ArgsInv; econstructor; (split; [eassumption|auto]). } + destruct A as (mk_instr & B & C). + eapply transl_load_access_correct; eauto with asmgen. +Qed. + +Lemma transl_store_correct: + forall chunk addr args src k c (rs: regset) m a m', + transl_store chunk addr args src k = OK c -> + eval_addressing ge rs#SP addr (map rs (map preg_of args)) = Some a -> + Mem.storev chunk m a rs#(preg_of src) = Some m' -> + exists rs', + exec_straight ge (basics_to_code c) rs m (basics_to_code k) rs' m' + /\ forall r, r <> PC -> r <> GPR31 -> rs'#r = rs#r. +Proof. + intros until m'; intros TR EV STORE. + assert (A: exists mk_instr chunk', + transl_memory_access mk_instr addr args k = OK c + /\ (forall base ofs rs, + exec_basic_instr ge (mk_instr base ofs) rs m = exec_store ge chunk' rs m (preg_of src) base ofs) + /\ Mem.storev chunk m a rs#(preg_of src) = Mem.storev chunk' m a rs#(preg_of src)). + { unfold transl_store in TR; destruct chunk; ArgsInv; + (econstructor; econstructor; split; [eassumption | split; [ intros; simpl; reflexivity | auto]]). + destruct a; auto. apply Mem.store_signed_unsigned_8. + destruct a; auto. apply Mem.store_signed_unsigned_16. + } + destruct A as (mk_instr & chunk' & B & C & D). + rewrite D in STORE; clear D. + eapply transl_store_access_correct; eauto with asmgen. +Qed. + +Lemma make_epilogue_correct: + forall ge0 f m stk soff cs m' ms rs k tm, + Mach.load_stack m (Vptr stk soff) Tptr f.(fn_link_ofs) = Some (parent_sp cs) -> + Mach.load_stack m (Vptr stk soff) Tptr f.(fn_retaddr_ofs) = Some (parent_ra cs) -> + Mem.free m stk 0 f.(fn_stacksize) = Some m' -> + agree ms (Vptr stk soff) rs -> + Mem.extends m tm -> + match_stack ge0 cs -> + exists rs', exists tm', + exec_straight ge (make_epilogue f k) rs tm k rs' tm' + /\ agree ms (parent_sp cs) rs' + /\ Mem.extends m' tm' + /\ rs'#RA = parent_ra cs + /\ rs'#SP = parent_sp cs + /\ (forall r, r <> PC -> r <> RA -> r <> SP -> r <> GPR31 -> r <> GPR8 -> rs'#r = rs#r). +Proof. + intros until tm; intros LP LRA FREE AG MEXT MCS. + exploit Mem.loadv_extends. eauto. eexact LP. auto. simpl. intros (parent' & LP' & LDP'). + exploit Mem.loadv_extends. eauto. eexact LRA. auto. simpl. intros (ra' & LRA' & LDRA'). + exploit lessdef_parent_sp; eauto. intros EQ; subst parent'; clear LDP'. + exploit lessdef_parent_ra; eauto. intros EQ; subst ra'; clear LDRA'. + exploit Mem.free_parallel_extends; eauto. intros (tm' & FREE' & MEXT'). + unfold make_epilogue. + rewrite chunk_of_Tptr in *. + + exploit ((loadind_ptr_correct SP (fn_retaddr_ofs f) GPR8 (Pset RA GPR8 ::g Pfreeframe (fn_stacksize f) (fn_link_ofs f) ::g k)) + rs tm). + - rewrite <- (sp_val _ _ rs AG). simpl. eexact LRA'. + - congruence. + - intros (rs1 & A1 & B1 & C1). + assert (agree ms (Vptr stk soff) rs1) as AG1. + + destruct AG. + apply mkagree; auto. + rewrite C1; discriminate || auto. + intro. rewrite C1; auto; destruct r; simpl; try discriminate. + + exploit (Pset_correct RA GPR8 (Pfreeframe (fn_stacksize f) (fn_link_ofs f) ::g k) rs1 tm). auto. + intros (rs2 & A2 & B2 & C2). + econstructor; econstructor; split. + * eapply exec_straight_trans. + { eexact A1. } + { eapply exec_straight_trans. + { eapply A2. } + { apply exec_straight_one. simpl. + rewrite (C2 GPR12) by auto with asmgen. rewrite <- (sp_val _ _ rs1 AG1). simpl; rewrite LP'. + rewrite FREE'; eauto. (* auto. *) } } + * split. (* apply agree_nextinstr. *)apply agree_set_other; auto with asmgen. + apply agree_change_sp with (Vptr stk soff). + apply agree_exten with rs; auto. intros; rewrite C2; auto with asmgen. + eapply parent_sp_def; eauto. + split. auto. + split. Simpl. rewrite B2. auto. + split. Simpl. + intros. Simpl. + rewrite C2; auto. +Qed. + +End CONSTRUCTORS. + + diff --git a/mppa_k1c/Asmexpand.ml b/mppa_k1c/Asmexpand.ml index 951a7511..13869268 100644 --- a/mppa_k1c/Asmexpand.ml +++ b/mppa_k1c/Asmexpand.ml @@ -20,6 +20,7 @@ of the RISC-V assembly code. *) open Asm +open Asmgen open Asmexpandaux open AST open Camlcoq @@ -47,9 +48,9 @@ let align n a = (n + a - 1) land (-a) List.iter emit (Asmgen.loadimm32 dst n []) *) let expand_addptrofs dst src n = - List.iter emit (Asmgen.addptrofs dst src n []) + List.iter emit (addptrofs dst src n :: []) let expand_storeind_ptr src base ofs = - List.iter emit (Asmgen.storeind_ptr src base ofs []) + List.iter emit (storeind_ptr src base ofs :: []) (* Built-ins. They come in two flavors: - annotation statements: take their arguments in registers or stack @@ -61,7 +62,7 @@ let expand_storeind_ptr src base ofs = (* Fix-up code around calls to variadic functions. Floating-point arguments residing in FP registers need to be moved to integer registers. *) -let int_param_regs = [| GPR0; GPR1; GPR2; GPR3; GPR4; GPR5; GPR6; GPR7 |] +let int_param_regs = let open Asmblock in [| GPR0; GPR1; GPR2; GPR3; GPR4; GPR5; GPR6; GPR7 |] (* let float_param_regs = [| F10; F11; F12; F13; F14; F15; F16; F17 |] *) let float_param_regs = [| |] @@ -330,7 +331,7 @@ let rec args_size sz = function let arguments_size sg = args_size 0 sg.sig_args -let save_arguments first_reg base_ofs = +let save_arguments first_reg base_ofs = let open Asmblock in for i = first_reg to 7 do expand_storeind_ptr int_param_regs.(i) @@ -412,82 +413,18 @@ let expand_bswap64 d s = assert false (* Handling of compiler-inlined builtins *) -let expand_builtin_inline name args res = +let expand_builtin_inline name args res = let open Asmblock in match name, args, res with (* Synchronization *) | "__builtin_membar", [], _ -> () - (* BCU *) - | "__builtin_k1_await", [], BR(IR _) -> emit (PExpand (Pawait)) - | "__builtin_k1_barrier", [], BR(IR _) -> emit (PExpand (Pbarrier)) - | "__builtin_k1_doze", [], BR(IR _) -> emit (PExpand (Pdoze)) - | "__builtin_k1_wfxl", [BA(IR a1); BA(IR a2)], BR(IR _) -> emit (PExpand (Pwfxl(a1, a2))) - | "__builtin_k1_wfxm", [BA(IR a1); BA(IR a2)], BR(IR _) -> emit (PExpand (Pwfxm(a1, a2))) - | "__builtin_k1_invaldtlb", [], BR(IR _) -> emit (PExpand (Pinvaldtlb)) - | "__builtin_k1_invalitlb", [], BR(IR _) -> emit (PExpand (Pinvalitlb)) - | "__builtin_k1_probetlb", [], BR(IR _) -> emit (PExpand (Pprobetlb)) - | "__builtin_k1_readtlb", [], BR(IR _) -> emit (PExpand (Preadtlb)) - | "__builtin_k1_sleep", [], BR(IR _) -> emit (PExpand (Psleep)) - | "__builtin_k1_stop", [], BR(IR _) -> emit (PExpand (Pstop)) - | "__builtin_k1_syncgroup", [BA(IR a1)], BR(IR _) -> emit (PExpand (Psyncgroup(a1))) - | "__builtin_k1_tlbwrite", [], BR(IR _) -> emit (PExpand (Ptlbwrite)) - - (* LSU *) - | "__builtin_k1_afda", [BA(IR a1); BA(IR a2)], BR(IR r) -> emit (PExpand (Pafda(r, a1, a2))) - | "__builtin_k1_aldc", [BA(IR a1)], BR(IR r) -> emit (PExpand (Paldc(r, a1))) - | "__builtin_k1_dinval", [], BR(IR _) -> emit (PExpand (Pdinval)) - | "__builtin_k1_dinvall", [BA(IR a1)], BR(IR _) -> emit (PExpand (Pdinvall(a1))) - | "__builtin_k1_dtouchl", [BA(IR a1)], BR(IR _) -> emit (PExpand (Pdtouchl(a1))) - | "__builtin_k1_dzerol", [BA(IR a1)], BR(IR _) -> emit (PExpand (Pdzerol(a1))) - | "__builtin_k1_fence", [], BR(IR _) -> emit (PExpand (Pfence)) - | "__builtin_k1_iinval", [], BR(IR _) -> emit (PExpand (Piinval)) - | "__builtin_k1_iinvals", [BA(IR a1)], BR(IR _) -> emit (PExpand (Piinvals(a1))) - | "__builtin_k1_itouchl", [BA(IR a1)], BR(IR _) -> emit (PExpand (Pitouchl(a1))) - | "__builtin_k1_lbsu", [BA(IR a1)], BR(IR r) -> emit (PExpand (Plbsu(r, a1))) - | "__builtin_k1_lbzu", [BA(IR a1)], BR(IR r) -> emit (PExpand (Plbzu(r, a1))) - | "__builtin_k1_ldu", [BA(IR a1)], BR(IR r) -> emit (PExpand (Pldu(r, a1))) - | "__builtin_k1_lhsu", [BA(IR a1)], BR(IR r) -> emit (PExpand (Plhsu(r, a1))) - | "__builtin_k1_lhzu", [BA(IR a1)], BR(IR r) -> emit (PExpand (Plhzu(r, a1))) - | "__builtin_k1_lwzu", [BA(IR a1)], BR(IR r) -> emit (PExpand (Plwzu(r, a1))) - - (* ALU *) - | "__builtin_k1_addhp", [BA(IR a1); BA(IR a2)], BR(IR r) -> emit (PExpand (Paddhp(r, a1, a2))) - | "__builtin_k1_adds", [BA(IR a1); BA(IR a2)], BR(IR r) -> emit (PExpand (Padds(r, a1, a2))) - | "__builtin_k1_bwlu", [BA(IR a1); BA(IR a2); BA(IR a3); BA(IR a4); BA(IR a5)], BR(IR r) -> - emit (PExpand (Pbwlu(r, a1, a2, a3, a4, a5))) - | "__builtin_k1_bwluhp", [BA(IR a1); BA(IR a2); BA(IR a3);], BR(IR r) -> - emit (PExpand (Pbwluhp(r, a1, a2, a3))) - | "__builtin_k1_bwluwp", [BA(IR a1); BA(IR a2); BA(IR a3);], BR(IR r) -> - emit (PExpand (Pbwluwp(r, a1, a2, a3))) - | "__builtin_k1_cbs", [BA(IR a1)], BR(IR r) -> emit (PExpand (Pcbs(r, a1))) - | "__builtin_k1_cbsdl", [BA(IR a1)], BR(IR r) -> emit (PExpand (Pcbsdl(r, a1))) - | "__builtin_k1_clz", [BA(IR a1)], BR(IR r) -> emit (PExpand (Pclz(r, a1))) - | "__builtin_k1_clzw", [BA(IR a1)], BR(IR r) -> emit (PExpand (Pclzw(r, a1))) - | "__builtin_k1_clzd", [BA(IR a1)], BR(IR r) -> emit (PExpand (Pclzd(r, a1))) - | "__builtin_k1_clzdl", [BA(IR a1)], BR(IR r) -> emit (PExpand (Pclzdl(r, a1))) - | "__builtin_k1_cmove", [BA(IR a1); BA(IR a2); BA(IR a3);], BR(IR r) -> - emit (PExpand (Pcmove(r, a1, a2, a3))) - | "__builtin_k1_ctz", [BA(IR a1)], BR(IR r) -> emit (PExpand (Pctz(r, a1))) - | "__builtin_k1_ctzw", [BA(IR a1)], BR(IR r) -> emit (PExpand (Pctzw(r, a1))) - | "__builtin_k1_ctzd", [BA(IR a1)], BR(IR r) -> emit (PExpand (Pctzd(r, a1))) - | "__builtin_k1_ctzdl", [BA(IR a1)], BR(IR r) -> emit (PExpand (Pctzdl(r, a1))) - | "__builtin_k1_extfz", [BA(IR a1); BA(IR a2); BA(IR a3);], BR(IR r) -> - emit (PExpand (Pextfz(r, a1, a2, a3))) - | "__builtin_k1_landhp", [BA(IR a1); BA(IR a2); BA(IR a3);], BR(IR r) -> - emit (PExpand (Plandhp(r, a1, a2, a3))) - | "__builtin_k1_sat", [BA(IR a1); BA(IR a2)], BR(IR r) -> emit (PExpand (Psat(r, a1, a2))) - | "__builtin_k1_satd", [BA(IR a1); BA(IR a2)], BR(IR r) -> emit (PExpand (Psatd(r, a1, a2))) - | "__builtin_k1_sbfhp", [BA(IR a1); BA(IR a2)], BR(IR r) -> emit (PExpand (Psbfhp(r, a1, a2))) - | "__builtin_k1_sbmm8", [BA(IR a1); BA(IR a2)], BR(IR r) -> emit (PExpand (Psbmm8(r, a1, a2))) - | "__builtin_k1_sbmmt8", [BA(IR a1); BA(IR a2)], BR(IR r) -> emit (PExpand (Psbmmt8(r, a1, a2))) - | "__builtin_k1_sllhps", [BA(IR a1); BA(IR a2)], BR(IR r) -> emit (PExpand (Psllhps(r, a1, a2))) - | "__builtin_k1_srahps", [BA(IR a1); BA(IR a2)], BR(IR r) -> emit (PExpand (Psrahps(r, a1, a2))) - | "__builtin_k1_stsu", [BA(IR a1); BA(IR a2)], BR(IR r) -> emit (PExpand (Pstsu(r, a1, a2))) - | "__builtin_k1_stsud", [BA(IR a1); BA(IR a2)], BR(IR r) -> emit (PExpand (Pstsud(r, a1, a2))) - (* Vararg stuff *) | "__builtin_va_start", [BA(IR a)], _ -> expand_builtin_va_start a + | "__builtin_clzll", [BA(IR a)], BR(IR res) -> + emit (Pclzll(res, a)) + | "__builtin_k1_stsud", [BA(IR a1); BA(IR a2)], BR(IR res) -> + emit (Pstsud(res, a1, a2)) (* Byte swaps *) (*| "__builtin_bswap16", [BA(IR a1)], BR(IR res) -> expand_bswap16 res a1 @@ -502,32 +439,32 @@ let expand_builtin_inline name args res = let expand_instruction instr = match instr with - | PExpand Pallocframe (sz, ofs) -> + | Pallocframe (sz, ofs) -> let sg = get_current_function_sig() in - emit (PArith (PArithRR (Pmv, GPR10, GPR12))); + emit (Pmv (Asmblock.GPR10, Asmblock.GPR12)); if sg.sig_cc.cc_vararg then begin let n = arguments_size sg in let extra_sz = if n >= 8 then 0 else align 16 ((8 - n) * wordsize) in let full_sz = Z.add sz (Z.of_uint extra_sz) in - expand_addptrofs GPR12 GPR12 (Ptrofs.repr (Z.neg full_sz)); - expand_storeind_ptr GPR10 GPR12 ofs; + expand_addptrofs Asmblock.GPR12 Asmblock.GPR12 (Ptrofs.repr (Z.neg full_sz)); + expand_storeind_ptr Asmblock.GPR10 Asmblock.GPR12 ofs; let va_ofs = Z.add full_sz (Z.of_sint ((n - 8) * wordsize)) in vararg_start_ofs := Some va_ofs; save_arguments n va_ofs end else begin - expand_addptrofs GPR12 GPR12 (Ptrofs.repr (Z.neg sz)); - expand_storeind_ptr GPR10 GPR12 ofs; + expand_addptrofs Asmblock.GPR12 Asmblock.GPR12 (Ptrofs.repr (Z.neg sz)); + expand_storeind_ptr Asmblock.GPR10 Asmblock.GPR12 ofs; vararg_start_ofs := None end - | PExpand Pfreeframe (sz, ofs) -> + | Pfreeframe (sz, ofs) -> let sg = get_current_function_sig() in let extra_sz = if sg.sig_cc.cc_vararg then begin let n = arguments_size sg in if n >= 8 then 0 else align 16 ((8 - n) * wordsize) end else 0 in - expand_addptrofs GPR12 GPR12 (Ptrofs.repr (Z.add sz (Z.of_uint extra_sz))) + expand_addptrofs Asmblock.GPR12 Asmblock.GPR12 (Ptrofs.repr (Z.add sz (Z.of_uint extra_sz))) (*| Pseqw(rd, rs1, rs2) -> (* emulate based on the fact that x == 0 iff x <u 1 (unsigned cmp) *) @@ -557,10 +494,10 @@ let expand_instruction instr = end else begin emit (Pxorl(rd, rs1, rs2)); emit (Psltul(rd, X0, X rd)) end -*)| PArith PArithRR (Pcvtl2w,rd, rs) -> +*)| Pcvtl2w (rd, rs) -> assert Archi.ptr64; - emit (PArith (PArithRRI32 (Paddiw,rd, rs, Int.zero))) (* 32-bit sign extension *) - | PArith PArithR r -> (* Pcvtw2l *) + emit (Paddiw (rd, rs, Int.zero)) (* 32-bit sign extension *) + | Pcvtw2l (r) -> (* Pcvtw2l *) assert Archi.ptr64 (* no-operation because the 32-bit integer was kept sign extended already *) (* FIXME - is it really the case on the MPPA ? *) @@ -574,7 +511,7 @@ let expand_instruction instr = | Pj_s(symb, sg) -> fixup_call sg; emit instr -*)| PExpand Pbuiltin (ef,args,res) -> +*)| Pbuiltin (ef,args,res) -> begin match ef with | EF_builtin (name,sg) -> expand_builtin_inline (camlstring_of_coqstring name) args res @@ -596,7 +533,7 @@ let expand_instruction instr = (* NOTE: Dwarf register maps for RV32G are not yet specified officially. This is just a placeholder. *) -let int_reg_to_dwarf = function +let int_reg_to_dwarf = let open Asmblock in function | GPR0 -> 1 | GPR1 -> 2 | GPR2 -> 3 | GPR3 -> 4 | GPR4 -> 5 | GPR5 -> 6 | GPR6 -> 7 | GPR7 -> 8 | GPR8 -> 9 | GPR9 -> 10 | GPR10 -> 11 | GPR11 -> 12 | GPR12 -> 13 | GPR13 -> 14 | GPR14 -> 15 @@ -611,7 +548,7 @@ let int_reg_to_dwarf = function | GPR55 -> 56 | GPR56 -> 57 | GPR57 -> 58 | GPR58 -> 59 | GPR59 -> 60 | GPR60 -> 61 | GPR61 -> 62 | GPR62 -> 63 | GPR63 -> 64 -let preg_to_dwarf = function +let preg_to_dwarf = let open Asmblock in function | IR r -> int_reg_to_dwarf r | FR r -> int_reg_to_dwarf r | RA -> 65 (* FIXME - No idea what is $ra DWARF number in k1-gdb *) diff --git a/mppa_k1c/Asmgen.v b/mppa_k1c/Asmgen.v index 6b6531c3..9b9e6272 100644 --- a/mppa_k1c/Asmgen.v +++ b/mppa_k1c/Asmgen.v @@ -15,826 +15,29 @@ (* *) (* *********************************************************************) -(** Translation from Mach to RISC-V assembly language *) +Require Import Integers. +Require Import Mach Asm Asmblock Asmblockgen Machblockgen. +Require Import Errors. -Require Archi. -Require Import Coqlib Errors. -Require Import AST Integers Floats Memdata. -Require Import Op Locations Mach Asm. - -Local Open Scope string_scope. Local Open Scope error_monad_scope. -(** The code generation functions take advantage of several - characteristics of the [Mach] code generated by earlier passes of the - compiler, mostly that argument and result registers are of the correct - types. These properties are true by construction, but it's easier to - recheck them during code generation and fail if they do not hold. *) - -(** Extracting integer or float registers. *) - -Definition ireg_of (r: mreg) : res ireg := - match preg_of r with IR mr => OK mr | _ => Error(msg "Asmgen.ireg_of") end. - -Definition freg_of (r: mreg) : res freg := - match preg_of r with IR mr => OK mr | _ => Error(msg "Asmgen.freg_of") end. - -(* -(** Decomposition of 32-bit integer constants. They are split into either - small signed immediates that fit in 12-bits, or, if they do not fit, - into a (20-bit hi, 12-bit lo) pair where lo is sign-extended. *) - -*) -Inductive immed32 : Type := - | Imm32_single (imm: int). - -Definition make_immed32 (val: int) := Imm32_single val. - -(** Likewise, for 64-bit integer constants. *) -Inductive immed64 : Type := - | Imm64_single (imm: int64) -. - -(* For now, let's suppose all instructions of K1c can handle 64-bits immediate *) -Definition make_immed64 (val: int64) := Imm64_single val. - -Notation "a ::i b" := (cons (A:=instruction) a b) (at level 49, right associativity). - -(** Smart constructors for arithmetic operations involving - a 32-bit or 64-bit integer constant. Depending on whether the - constant fits in 12 bits or not, one or several instructions - are generated as required to perform the operation - and prepended to the given instruction sequence [k]. *) - -Definition loadimm32 (r: ireg) (n: int) (k: code) := - match make_immed32 n with - | Imm32_single imm => Pmake r imm ::i k - end. - -Definition opimm32 (op: arith_name_rrr) - (opimm: arith_name_rri32) - (rd rs: ireg) (n: int) (k: code) := - match make_immed32 n with - | Imm32_single imm => opimm rd rs imm ::i k - end. - -Definition addimm32 := opimm32 Paddw Paddiw. -Definition andimm32 := opimm32 Pandw Pandiw. -Definition orimm32 := opimm32 Porw Poriw. -Definition xorimm32 := opimm32 Pxorw Pxoriw. -(* -Definition sltimm32 := opimm32 Psltw Psltiw. -Definition sltuimm32 := opimm32 Psltuw Psltiuw. -*) - -Definition loadimm64 (r: ireg) (n: int64) (k: code) := - match make_immed64 n with - | Imm64_single imm => Pmakel r imm ::i k - end. - -Definition opimm64 (op: arith_name_rrr) - (opimm: arith_name_rri64) - (rd rs: ireg) (n: int64) (k: code) := - match make_immed64 n with - | Imm64_single imm => opimm rd rs imm ::i k -end. - -Definition addimm64 := opimm64 Paddl Paddil. -Definition orimm64 := opimm64 Porl Poril. -Definition andimm64 := opimm64 Pandl Pandil. -Definition xorimm64 := opimm64 Pxorl Pxoril. - -(* -Definition sltimm64 := opimm64 Psltl Psltil. -Definition sltuimm64 := opimm64 Psltul Psltiul. -*) - -Definition cast32signed (rd rs: ireg) (k: code) := - if (ireg_eq rd rs) - then Pcvtw2l rd ::i k - else Pmvw2l rd rs ::i k - . - -Definition addptrofs (rd rs: ireg) (n: ptrofs) (k: code) := - if Ptrofs.eq_dec n Ptrofs.zero then - Pmv rd rs ::i k - else - addimm64 rd rs (Ptrofs.to_int64 n) k. - -(** Translation of conditional branches. *) - -Definition transl_comp - (c: comparison) (s: signedness) (r1 r2: ireg) (lbl: label) (k: code) : list instruction := - Pcompw (itest_for_cmp c s) RTMP r1 r2 ::i Pcb BTwnez RTMP lbl ::i k. - -Definition transl_compl - (c: comparison) (s: signedness) (r1 r2: ireg) (lbl: label) (k: code) : list instruction := - Pcompl (itest_for_cmp c s) RTMP r1 r2 ::i Pcb BTwnez RTMP lbl ::i k. - -Definition select_comp (n: int) (c: comparison) : option comparison := - if Int.eq n Int.zero then - match c with - | Ceq => Some Ceq - | Cne => Some Cne - | _ => None - end - else - None - . - -Definition transl_opt_compuimm - (n: int) (c: comparison) (r1: ireg) (lbl: label) (k: code) : list instruction := - match select_comp n c with - | Some Ceq => Pcbu BTweqz r1 lbl ::i k - | Some Cne => Pcbu BTwnez r1 lbl ::i k - | Some _ => nil (* Never happens *) - | None => loadimm32 RTMP n (transl_comp c Unsigned r1 RTMP lbl k) - end - . - -Definition select_compl (n: int64) (c: comparison) : option comparison := - if Int64.eq n Int64.zero then - match c with - | Ceq => Some Ceq - | Cne => Some Cne - | _ => None - end - else - None - . - -Definition transl_opt_compluimm - (n: int64) (c: comparison) (r1: ireg) (lbl: label) (k: code) : list instruction := - match select_compl n c with - | Some Ceq => Pcbu BTdeqz r1 lbl ::i k - | Some Cne => Pcbu BTdnez r1 lbl ::i k - | Some _ => nil (* Never happens *) - | None => loadimm64 RTMP n (transl_compl c Unsigned r1 RTMP lbl k) - end - . - -Definition transl_cbranch - (cond: condition) (args: list mreg) (lbl: label) (k: code) : res (list instruction ) := - match cond, args with - | Ccompuimm c n, a1 :: nil => - do r1 <- ireg_of a1; - OK (transl_opt_compuimm n c r1 lbl k) - | Ccomp c, a1 :: a2 :: nil => - do r1 <- ireg_of a1; do r2 <- ireg_of a2; - OK (transl_comp c Signed r1 r2 lbl k) - | Ccompu c, a1 :: a2 :: nil => - do r1 <- ireg_of a1; do r2 <- ireg_of a2; - OK (transl_comp c Unsigned r1 r2 lbl k) - | Ccompimm c n, a1 :: nil => - do r1 <- ireg_of a1; - OK (if Int.eq n Int.zero then - Pcb (btest_for_cmpswz c) r1 lbl ::i k - else - loadimm32 RTMP n (transl_comp c Signed r1 RTMP lbl k) - ) - | Ccompluimm c n, a1 :: nil => - do r1 <- ireg_of a1; - OK (transl_opt_compluimm n c r1 lbl k) - | Ccompl c, a1 :: a2 :: nil => - do r1 <- ireg_of a1; do r2 <- ireg_of a2; - OK (transl_compl c Signed r1 r2 lbl k) - | Ccomplu c, a1 :: a2 :: nil => - do r1 <- ireg_of a1; do r2 <- ireg_of a2; - OK (transl_compl c Unsigned r1 r2 lbl k) - | Ccomplimm c n, a1 :: nil => - do r1 <- ireg_of a1; - OK (if Int64.eq n Int64.zero then - Pcb (btest_for_cmpsdz c) r1 lbl ::i k - else - loadimm64 RTMP n (transl_compl c Signed r1 RTMP lbl k) - ) -(*| Ccompf c, f1 :: f2 :: nil => - do r1 <- freg_of f1; do r2 <- freg_of f2; - let (insn, normal) := transl_cond_float c rd r1 r2 in - OK (insn :: if normal then k else Pxoriw rd rd Int.one :: k) - | Cnotcompf c, f1 :: f2 :: nil => - do r1 <- freg_of f1; do r2 <- freg_of f2; - let (insn, normal) := transl_cond_float c rd r1 r2 in - OK (insn :: if normal then Pxoriw rd rd Int.one :: k else k) - | Ccompfs c, f1 :: f2 :: nil => - do r1 <- freg_of f1; do r2 <- freg_of f2; - let (insn, normal) := transl_cond_single c rd r1 r2 in - OK (insn :: if normal then k else Pxoriw rd rd Int.one :: k) - | Cnotcompfs c, f1 :: f2 :: nil => - do r1 <- freg_of f1; do r2 <- freg_of f2; - let (insn, normal) := transl_cond_single c rd r1 r2 in - OK (insn :: if normal then Pxoriw rd rd Int.one :: k else k) -*)| _, _ => - Error(msg "Asmgen.transl_cbranch") - end. - -(** Translation of a condition operator. The generated code sets the - [rd] target register to 0 or 1 depending on the truth value of the - condition. *) - -Definition transl_cond_int32s (cmp: comparison) (rd r1 r2: ireg) (k: code) := - Pcompw (itest_for_cmp cmp Signed) rd r1 r2 ::i k. - -Definition transl_cond_int32u (cmp: comparison) (rd r1 r2: ireg) (k: code) := - Pcompw (itest_for_cmp cmp Unsigned) rd r1 r2 ::i k. - -Definition transl_cond_int64s (cmp: comparison) (rd r1 r2: ireg) (k: code) := - Pcompl (itest_for_cmp cmp Signed) rd r1 r2 ::i k. - -Definition transl_cond_int64u (cmp: comparison) (rd r1 r2: ireg) (k: code) := - Pcompl (itest_for_cmp cmp Unsigned) rd r1 r2 ::i k. - -Definition transl_condimm_int32s (cmp: comparison) (rd r1: ireg) (n: int) (k: code) := - Pcompiw (itest_for_cmp cmp Signed) rd r1 n ::i k. - -Definition transl_condimm_int32u (cmp: comparison) (rd r1: ireg) (n: int) (k: code) := - Pcompiw (itest_for_cmp cmp Unsigned) rd r1 n ::i k. - -Definition transl_condimm_int64s (cmp: comparison) (rd r1: ireg) (n: int64) (k: code) := - Pcompil (itest_for_cmp cmp Signed) rd r1 n ::i k. - -Definition transl_condimm_int64u (cmp: comparison) (rd r1: ireg) (n: int64) (k: code) := - Pcompil (itest_for_cmp cmp Unsigned) rd r1 n ::i k. +(** For OCaml code *) +Definition addptrofs (rd rs: ireg) (n: ptrofs) := basic_to_instruction (addptrofs rd rs n). +Definition storeind_ptr (src: ireg) (base: ireg) (ofs: ptrofs) := + basic_to_instruction (storeind_ptr src base ofs). -Definition transl_cond_op - (cond: condition) (rd: ireg) (args: list mreg) (k: code) := - match cond, args with - | Ccomp c, a1 :: a2 :: nil => - do r1 <- ireg_of a1; do r2 <- ireg_of a2; - OK (transl_cond_int32s c rd r1 r2 k) - | Ccompu c, a1 :: a2 :: nil => - do r1 <- ireg_of a1; do r2 <- ireg_of a2; - OK (transl_cond_int32u c rd r1 r2 k) - | Ccompimm c n, a1 :: nil => - do r1 <- ireg_of a1; - OK (transl_condimm_int32s c rd r1 n k) - | Ccompuimm c n, a1 :: nil => - do r1 <- ireg_of a1; - OK (transl_condimm_int32u c rd r1 n k) - | Ccompl c, a1 :: a2 :: nil => - do r1 <- ireg_of a1; do r2 <- ireg_of a2; - OK (transl_cond_int64s c rd r1 r2 k) - | Ccomplu c, a1 :: a2 :: nil => - do r1 <- ireg_of a1; do r2 <- ireg_of a2; - OK (transl_cond_int64u c rd r1 r2 k) - | Ccomplimm c n, a1 :: nil => - do r1 <- ireg_of a1; - OK (transl_condimm_int64s c rd r1 n k) - | Ccompluimm c n, a1 :: nil => - do r1 <- ireg_of a1; - OK (transl_condimm_int64u c rd r1 n k) -(*| Ccompf c, f1 :: f2 :: nil => - do r1 <- freg_of f1; do r2 <- freg_of f2; - let (insn, normal) := transl_cond_float c rd r1 r2 in - OK (insn :: if normal then k else Pxoriw rd rd Int.one :: k) - | Cnotcompf c, f1 :: f2 :: nil => - do r1 <- freg_of f1; do r2 <- freg_of f2; - let (insn, normal) := transl_cond_float c rd r1 r2 in - OK (insn :: if normal then Pxoriw rd rd Int.one :: k else k) - | Ccompfs c, f1 :: f2 :: nil => - do r1 <- freg_of f1; do r2 <- freg_of f2; - let (insn, normal) := transl_cond_single c rd r1 r2 in - OK (insn :: if normal then k else Pxoriw rd rd Int.one :: k) - | Cnotcompfs c, f1 :: f2 :: nil => - do r1 <- freg_of f1; do r2 <- freg_of f2; - let (insn, normal) := transl_cond_single c rd r1 r2 in - OK (insn :: if normal then Pxoriw rd rd Int.one :: k else k) -*)| _, _ => - Error(msg "Asmgen.transl_cond_op") -end. - -(** Translation of the arithmetic operation [r <- op(args)]. - The corresponding instructions are prepended to [k]. *) - -Definition transl_op - (op: operation) (args: list mreg) (res: mreg) (k: code) := - match op, args with - | Omove, a1 :: nil => - match preg_of res, preg_of a1 with - | IR r, IR a => OK (Pmv r a ::i k) - | _ , _ => Error(msg "Asmgen.Omove") - end - | Ointconst n, nil => - do rd <- ireg_of res; - OK (loadimm32 rd n k) - | Olongconst n, nil => - do rd <- ireg_of res; - OK (loadimm64 rd n k) -(*| Ofloatconst f, nil => - do rd <- freg_of res; - OK (if Float.eq_dec f Float.zero - then Pfcvtdw rd GPR0 :: k - else Ploadfi rd f :: k) - | Osingleconst f, nil => - do rd <- freg_of res; - OK (if Float32.eq_dec f Float32.zero - then Pfcvtsw rd GPR0 :: k - else Ploadsi rd f :: k) -*)| Oaddrsymbol s ofs, nil => - do rd <- ireg_of res; - OK (if Archi.pic_code tt && negb (Ptrofs.eq ofs Ptrofs.zero) - then Ploadsymbol rd s Ptrofs.zero ::i addptrofs rd rd ofs k - else Ploadsymbol rd s ofs ::i k) - | Oaddrstack n, nil => - do rd <- ireg_of res; - OK (addptrofs rd SP n k) - - | Ocast8signed, a1 :: nil => - do rd <- ireg_of res; do rs <- ireg_of a1; - OK (Pslliw rd rs (Int.repr 24) ::i Psraiw rd rd (Int.repr 24) ::i k) - | Ocast16signed, a1 :: nil => - do rd <- ireg_of res; do rs <- ireg_of a1; - OK (Pslliw rd rs (Int.repr 16) ::i Psraiw rd rd (Int.repr 16) ::i k) - | Oadd, a1 :: a2 :: nil => - do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; - OK (Paddw rd rs1 rs2 ::i k) - | Oaddimm n, a1 :: nil => - do rd <- ireg_of res; do rs <- ireg_of a1; - OK (addimm32 rd rs n k) - | Oneg, a1 :: nil => - do rd <- ireg_of res; do rs <- ireg_of a1; - OK (Pnegw rd rs ::i k) - | Osub, a1 :: a2 :: nil => - do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; - OK (Psubw rd rs1 rs2 ::i k) - | Omul, a1 :: a2 :: nil => - do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; - OK (Pmulw rd rs1 rs2 ::i k) -(*| Omulhs, a1 :: a2 :: nil => - do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; - OK (Pmulhw rd rs1 rs2 :: k) - | Omulhu, a1 :: a2 :: nil => - do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; - OK (Pmulhuw rd rs1 rs2 :: k) - | Odiv, a1 :: a2 :: nil => - do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; - OK (Pdivw rd rs1 rs2 :: k) - | Odivu, a1 :: a2 :: nil => - do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; - OK (Pdivuw rd rs1 rs2 :: k) - | Omod, a1 :: a2 :: nil => - do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; - OK (Premw rd rs1 rs2 :: k) - | Omodu, a1 :: a2 :: nil => - do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; - OK (Premuw rd rs1 rs2 :: k) -*)| Oand, a1 :: a2 :: nil => - do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; - OK (Pandw rd rs1 rs2 ::i k) - | Oandimm n, a1 :: nil => - do rd <- ireg_of res; do rs <- ireg_of a1; - OK (andimm32 rd rs n k) - | Oor, a1 :: a2 :: nil => - do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; - OK (Porw rd rs1 rs2 ::i k) - | Oorimm n, a1 :: nil => - do rd <- ireg_of res; do rs <- ireg_of a1; - OK (orimm32 rd rs n k) - | Oxor, a1 :: a2 :: nil => - do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; - OK (Pxorw rd rs1 rs2 ::i k) - | Oxorimm n, a1 :: nil => - do rd <- ireg_of res; do rs <- ireg_of a1; - OK (xorimm32 rd rs n k) - | Oshl, a1 :: a2 :: nil => - do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; - OK (Psllw rd rs1 rs2 ::i k) - | Oshlimm n, a1 :: nil => - do rd <- ireg_of res; do rs <- ireg_of a1; - OK (Pslliw rd rs n ::i k) - | Oshr, a1 :: a2 :: nil => - do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; - OK (Psraw rd rs1 rs2 ::i k) - | Oshrimm n, a1 :: nil => - do rd <- ireg_of res; do rs <- ireg_of a1; - OK (Psraiw rd rs n ::i k) - | Oshru, a1 :: a2 :: nil => - do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; - OK (Psrlw rd rs1 rs2 ::i k) - | Oshruimm n, a1 :: nil => - do rd <- ireg_of res; do rs <- ireg_of a1; - OK (Psrliw rd rs n ::i k) - | Oshrximm n, a1 :: nil => - do rd <- ireg_of res; do rs <- ireg_of a1; - OK (if Int.eq n Int.zero then Pmv rd rs ::i k else - Psraiw GPR31 rs (Int.repr 31) ::i - Psrliw GPR31 GPR31 (Int.sub Int.iwordsize n) ::i - Paddw GPR31 rs GPR31 ::i - Psraiw rd GPR31 n ::i k) - - (* [Omakelong], [Ohighlong] should not occur *) - | Olowlong, a1 :: nil => - do rd <- ireg_of res; do rs <- ireg_of a1; - OK (Pcvtl2w rd rs ::i k) - | Ocast32signed, a1 :: nil => - do rd <- ireg_of res; do rs <- ireg_of a1; - OK (cast32signed rd rs k) - | Ocast32unsigned, a1 :: nil => - do rd <- ireg_of res; do rs <- ireg_of a1; - assertion (ireg_eq rd rs); - OK (Pcvtw2l rd ::i Psllil rd rd (Int.repr 32) ::i Psrlil rd rd (Int.repr 32) ::i k) - | Oaddl, a1 :: a2 :: nil => - do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; - OK (Paddl rd rs1 rs2 ::i k) - | Oaddlimm n, a1 :: nil => - do rd <- ireg_of res; do rs <- ireg_of a1; - OK (addimm64 rd rs n k) - | Onegl, a1 :: nil => - do rd <- ireg_of res; do rs <- ireg_of a1; - OK (Pnegl rd rs ::i k) - | Osubl, a1 :: a2 :: nil => - do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; - OK (Psubl rd rs1 rs2 ::i k) - | Omull, a1 :: a2 :: nil => - do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; - OK (Pmull rd rs1 rs2 ::i k) -(*| Omullhs, a1 :: a2 :: nil => - do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; - OK (Pmulhl rd rs1 rs2 :: k) - | Omullhu, a1 :: a2 :: nil => - do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; - OK (Pmulhul rd rs1 rs2 :: k) - | Odivl, a1 :: a2 :: nil => - do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; - OK (Pdivl rd rs1 rs2 :: k) - | Odivlu, a1 :: a2 :: nil => - do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; - OK (Pdivul rd rs1 rs2 :: k) - | Omodl, a1 :: a2 :: nil => - do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; - OK (Preml rd rs1 rs2 :: k) - | Omodlu, a1 :: a2 :: nil => - do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; - OK (Premul rd rs1 rs2 :: k) -*)| Oandl, a1 :: a2 :: nil => - do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; - OK (Pandl rd rs1 rs2 ::i k) - | Oandlimm n, a1 :: nil => - do rd <- ireg_of res; do rs <- ireg_of a1; - OK (andimm64 rd rs n k) - | Oorl, a1 :: a2 :: nil => - do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; - OK (Porl rd rs1 rs2 ::i k) - | Oorlimm n, a1 :: nil => - do rd <- ireg_of res; do rs <- ireg_of a1; - OK (orimm64 rd rs n k) - | Oxorl, a1 :: a2 :: nil => - do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; - OK (Pxorl rd rs1 rs2 ::i k) - | Oxorlimm n, a1 :: nil => - do rd <- ireg_of res; do rs <- ireg_of a1; - OK (xorimm64 rd rs n k) - | Oshll, a1 :: a2 :: nil => - do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; - OK (Pslll rd rs1 rs2 ::i k) - | Oshllimm n, a1 :: nil => - do rd <- ireg_of res; do rs <- ireg_of a1; - OK (Psllil rd rs n ::i k) - | Oshrl, a1 :: a2 :: nil => - do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; - OK (Psral rd rs1 rs2 ::i k) - | Oshrlimm n, a1 :: nil => - do rd <- ireg_of res; do rs <- ireg_of a1; - OK (Psrail rd rs n ::i k) - | Oshrlu, a1 :: a2 :: nil => - do rd <- ireg_of res; do rs1 <- ireg_of a1; do rs2 <- ireg_of a2; - OK (Psrll rd rs1 rs2 ::i k) - | Oshrluimm n, a1 :: nil => - do rd <- ireg_of res; do rs <- ireg_of a1; - OK (Psrlil rd rs n ::i k) -(*| Oshrxlimm n, a1 :: nil => - do rd <- ireg_of res; do rs <- ireg_of a1; - OK (if Int.eq n Int.zero then Pmv rd rs :: k else - Psrail GPR31 rs (Int.repr 63) :: - Psrlil GPR31 GPR31 (Int.sub Int64.iwordsize' n) :: - Paddl GPR31 rs GPR31 :: - Psrail rd GPR31 n :: k) - -*)| Onegf, a1 :: nil => - do rd <- freg_of res; do rs <- freg_of a1; - OK (Pfnegd rd rs ::i k) -(*| Oabsf, a1 :: nil => - do rd <- freg_of res; do rs <- freg_of a1; - OK (Pfabsd rd rs :: k) - | Oaddf, a1 :: a2 :: nil => - do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2; - OK (Pfaddd rd rs1 rs2 :: k) - | Osubf, a1 :: a2 :: nil => - do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2; - OK (Pfsubd rd rs1 rs2 :: k) - | Omulf, a1 :: a2 :: nil => - do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2; - OK (Pfmuld rd rs1 rs2 :: k) - | Odivf, a1 :: a2 :: nil => - do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2; - OK (Pfdivd rd rs1 rs2 :: k) - - | Onegfs, a1 :: nil => - do rd <- freg_of res; do rs <- freg_of a1; - OK (Pfnegs rd rs :: k) - | Oabsfs, a1 :: nil => - do rd <- freg_of res; do rs <- freg_of a1; - OK (Pfabss rd rs :: k) - | Oaddfs, a1 :: a2 :: nil => - do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2; - OK (Pfadds rd rs1 rs2 :: k) - | Osubfs, a1 :: a2 :: nil => - do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2; - OK (Pfsubs rd rs1 rs2 :: k) - | Omulfs, a1 :: a2 :: nil => - do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2; - OK (Pfmuls rd rs1 rs2 :: k) - | Odivfs, a1 :: a2 :: nil => - do rd <- freg_of res; do rs1 <- freg_of a1; do rs2 <- freg_of a2; - OK (Pfdivs rd rs1 rs2 :: k) - - | Osingleoffloat, a1 :: nil => - do rd <- freg_of res; do rs <- freg_of a1; - OK (Pfcvtsd rd rs :: k) - | Ofloatofsingle, a1 :: nil => - do rd <- freg_of res; do rs <- freg_of a1; - OK (Pfcvtds rd rs :: k) - - | Ointoffloat, a1 :: nil => - do rd <- ireg_of res; do rs <- freg_of a1; - OK (Pfcvtwd rd rs :: k) - | Ointuoffloat, a1 :: nil => - do rd <- ireg_of res; do rs <- freg_of a1; - OK (Pfcvtwud rd rs :: k) - | Ofloatofint, a1 :: nil => - do rd <- freg_of res; do rs <- ireg_of a1; - OK (Pfcvtdw rd rs :: k) - | Ofloatofintu, a1 :: nil => - do rd <- freg_of res; do rs <- ireg_of a1; - OK (Pfcvtdwu rd rs :: k) - | Ointofsingle, a1 :: nil => - do rd <- ireg_of res; do rs <- freg_of a1; - OK (Pfcvtws rd rs :: k) - | Ointuofsingle, a1 :: nil => - do rd <- ireg_of res; do rs <- freg_of a1; - OK (Pfcvtwus rd rs :: k) - | Osingleofint, a1 :: nil => - do rd <- freg_of res; do rs <- ireg_of a1; - OK (Pfcvtsw rd rs :: k) - | Osingleofintu, a1 :: nil => - do rd <- freg_of res; do rs <- ireg_of a1; - OK (Pfcvtswu rd rs :: k) - - | Olongoffloat, a1 :: nil => - do rd <- ireg_of res; do rs <- freg_of a1; - OK (Pfcvtld rd rs :: k) - | Olonguoffloat, a1 :: nil => - do rd <- ireg_of res; do rs <- freg_of a1; - OK (Pfcvtlud rd rs :: k) - | Ofloatoflong, a1 :: nil => - do rd <- freg_of res; do rs <- ireg_of a1; - OK (Pfcvtdl rd rs :: k) - | Ofloatoflongu, a1 :: nil => - do rd <- freg_of res; do rs <- ireg_of a1; - OK (Pfcvtdlu rd rs :: k) - | Olongofsingle, a1 :: nil => - do rd <- ireg_of res; do rs <- freg_of a1; - OK (Pfcvtls rd rs :: k) - | Olonguofsingle, a1 :: nil => - do rd <- ireg_of res; do rs <- freg_of a1; - OK (Pfcvtlus rd rs :: k) - | Osingleoflong, a1 :: nil => - do rd <- freg_of res; do rs <- ireg_of a1; - OK (Pfcvtsl rd rs :: k) - | Osingleoflongu, a1 :: nil => - do rd <- freg_of res; do rs <- ireg_of a1; - OK (Pfcvtslu rd rs :: k) - -*)| Ocmp cmp, _ => - do rd <- ireg_of res; - transl_cond_op cmp rd args k - - | _, _ => - Error(msg "Asmgen.transl_op") - end. - -(** Accessing data in the stack frame. *) - -Definition indexed_memory_access - (mk_instr: ireg -> offset -> instruction) - (base: ireg) (ofs: ptrofs) (k: code) := - match make_immed64 (Ptrofs.to_int64 ofs) with - | Imm64_single imm => - mk_instr base (Ofsimm (Ptrofs.of_int64 imm)) ::i k -(*| Imm64_pair hi lo => - Pluil GPR31 hi :: Paddl GPR31 base GPR31 :: mk_instr GPR31 (Ofsimm (Ptrofs.of_int64 lo)) :: k - | Imm64_large imm => - Pmake GPR31 imm :: Paddl GPR31 base GPR31 :: mk_instr GPR31 (Ofsimm Ptrofs.zero) :: k -*)end. - -Definition loadind (base: ireg) (ofs: ptrofs) (ty: typ) (dst: mreg) (k: code) := - match ty, preg_of dst with - | Tint, IR rd => OK (indexed_memory_access (Plw rd) base ofs k) - | Tlong, IR rd => OK (indexed_memory_access (Pld rd) base ofs k) - | Tsingle, IR rd => OK (indexed_memory_access (Pfls rd) base ofs k) - | Tfloat, IR rd => OK (indexed_memory_access (Pfld rd) base ofs k) - | Tany32, IR rd => OK (indexed_memory_access (Plw_a rd) base ofs k) - | Tany64, IR rd => OK (indexed_memory_access (Pld_a rd) base ofs k) - | _, _ => Error (msg "Asmgen.loadind") - end. - -Definition storeind (src: mreg) (base: ireg) (ofs: ptrofs) (ty: typ) (k: code) := - match ty, preg_of src with - | Tint, IR rd => OK (indexed_memory_access (Psw rd) base ofs k) - | Tlong, IR rd => OK (indexed_memory_access (Psd rd) base ofs k) - | Tsingle, IR rd => OK (indexed_memory_access (Pfss rd) base ofs k) - | Tfloat, IR rd => OK (indexed_memory_access (Pfsd rd) base ofs k) - | Tany32, IR rd => OK (indexed_memory_access (Psw_a rd) base ofs k) - | Tany64, IR rd => OK (indexed_memory_access (Psd_a rd) base ofs k) - | _, _ => Error (msg "Asmgen.storeind") - end. - -Definition loadind_ptr (base: ireg) (ofs: ptrofs) (dst: ireg) (k: code) := - indexed_memory_access (Pld dst) base ofs k. - -Definition storeind_ptr (src: ireg) (base: ireg) (ofs: ptrofs) (k: code) := - indexed_memory_access (Psd src) base ofs k. - -(** Translation of memory accesses: loads, and stores. *) - -Definition transl_memory_access - (mk_instr: ireg -> offset -> instruction) - (addr: addressing) (args: list mreg) (k: code) : res (list instruction) := - match addr, args with - | Aindexed ofs, a1 :: nil => - do rs <- ireg_of a1; - OK (indexed_memory_access mk_instr rs ofs k) - | Aglobal id ofs, nil => - OK (Ploadsymbol GPR31 id ofs ::i (mk_instr GPR31 (Ofsimm Ptrofs.zero) ::i k)) - | Ainstack ofs, nil => - OK (indexed_memory_access mk_instr SP ofs k) - | _, _ => - Error(msg "Asmgen.transl_memory_access") - end. - -Definition transl_load (chunk: memory_chunk) (addr: addressing) - (args: list mreg) (dst: mreg) (k: code) : res (list instruction) := - match chunk with - | Mint8signed => - do r <- ireg_of dst; - transl_memory_access (Plb r) addr args k - | Mint8unsigned => - do r <- ireg_of dst; - transl_memory_access (Plbu r) addr args k - | Mint16signed => - do r <- ireg_of dst; - transl_memory_access (Plh r) addr args k - | Mint16unsigned => - do r <- ireg_of dst; - transl_memory_access (Plhu r) addr args k - | Mint32 => - do r <- ireg_of dst; - transl_memory_access (Plw r) addr args k - | Mint64 => - do r <- ireg_of dst; - transl_memory_access (Pld r) addr args k - | Mfloat32 => - do r <- freg_of dst; - transl_memory_access (Pfls r) addr args k - | Mfloat64 => - do r <- freg_of dst; - transl_memory_access (Pfld r) addr args k - | _ => - Error (msg "Asmgen.transl_load") - end. - -Definition transl_store (chunk: memory_chunk) (addr: addressing) - (args: list mreg) (src: mreg) (k: code) : res (list instruction) := - match chunk with - | Mint8signed | Mint8unsigned => - do r <- ireg_of src; - transl_memory_access (Psb r) addr args k - | Mint16signed | Mint16unsigned => - do r <- ireg_of src; - transl_memory_access (Psh r) addr args k - | Mint32 => - do r <- ireg_of src; - transl_memory_access (Psw r) addr args k - | Mint64 => - do r <- ireg_of src; - transl_memory_access (Psd r) addr args k - | Mfloat32 => - do r <- freg_of src; - transl_memory_access (Pfss r) addr args k - | Mfloat64 => - do r <- freg_of src; - transl_memory_access (Pfsd r) addr args k - | _ => - Error (msg "Asmgen.transl_store") - end. - -(** Function epilogue *) - -Definition make_epilogue (f: Mach.function) (k: code) := - loadind_ptr SP f.(fn_retaddr_ofs) GPR8 - (Pset RA GPR8 ::i Pfreeframe f.(fn_stacksize) f.(fn_link_ofs) ::i k). - -(** Translation of a Mach instruction. *) - -Definition transl_instr (f: Mach.function) (i: Mach.instruction) - (ep: bool) (k: code) := - match i with - | Mgetstack ofs ty dst => - loadind SP ofs ty dst k - | Msetstack src ofs ty => - storeind src SP ofs ty k - | Mgetparam ofs ty dst => - (* load via the frame pointer if it is valid *) - do c <- loadind FP ofs ty dst k; - OK (if ep then c - else loadind_ptr SP f.(fn_link_ofs) FP c) - | Mop op args res => - transl_op op args res k - | Mload chunk addr args dst => - transl_load chunk addr args dst k - | Mstore chunk addr args src => - transl_store chunk addr args src k -(*| Mcall sig (inl r) => - do r1 <- ireg_of r; OK (Pjal_r r1 sig :: k) -*)| Mcall sig (inr symb) => - OK ((Pcall symb) ::i k) -(*| Mtailcall sig (inl r) => - do r1 <- ireg_of r; - OK (make_epilogue f (Pcall :: k)) -*)| Mtailcall sig (inr symb) => - OK (make_epilogue f ((Pgoto symb) ::i k)) - | Mbuiltin ef args res => - OK (Pbuiltin ef (List.map (map_builtin_arg preg_of) args) (map_builtin_res preg_of res) ::i k) - | Mlabel lbl => - OK (Plabel lbl ::i k) - | Mgoto lbl => - OK (Pj_l lbl ::i k) - | Mcond cond args lbl => - transl_cbranch cond args lbl k -(*| Mjumptable arg tbl => do r <- ireg_of arg; OK (Pbtbl r tbl :: k) -*)| Mreturn => - OK (make_epilogue f (Pret ::i k)) - (*OK (make_epilogue f (Pj_r RA f.(Mach.fn_sig) :: k))*) - | _ => - Error (msg "Asmgen.transl_instr") - end. - -(** Translation of a code sequence *) - -Definition it1_is_parent (before: bool) (i: Mach.instruction) : bool := - match i with - | Msetstack src ofs ty => before - | Mgetparam ofs ty dst => negb (mreg_eq dst R10) - | Mop op args res => before && negb (mreg_eq res R10) - | _ => false - end. - -(** This is the naive definition that we no longer use because it - is not tail-recursive. It is kept as specification. *) - -Fixpoint transl_code (f: Mach.function) (il: list Mach.instruction) (it1p: bool) := - match il with - | nil => OK nil - | i1 :: il' => - do k <- transl_code f il' (it1_is_parent it1p i1); - transl_instr f i1 it1p k - end. - -(** This is an equivalent definition in continuation-passing style - that runs in constant stack space. *) - -Fixpoint transl_code_rec (f: Mach.function) (il: list Mach.instruction) - (it1p: bool) (k: code -> res code) := - match il with - | nil => k nil - | i1 :: il' => - transl_code_rec f il' (it1_is_parent it1p i1) - (fun c1 => do c2 <- transl_instr f i1 it1p c1; k c2) - end. - -Definition transl_code' (f: Mach.function) (il: list Mach.instruction) (it1p: bool) := - transl_code_rec f il it1p (fun c => OK c). - -(** Translation of a whole function. Note that we must check - that the generated code contains less than [2^32] instructions, - otherwise the offset part of the [PC] code pointer could wrap - around, leading to incorrect executions. *) - -Definition transl_function (f: Mach.function) := - do c <- transl_code' f f.(Mach.fn_code) true; - OK (mkfunction f.(Mach.fn_sig) - (Pallocframe f.(fn_stacksize) f.(fn_link_ofs) ::i - Pget GPR8 RA ::i - storeind_ptr GPR8 SP f.(fn_retaddr_ofs) c)). +Definition transf_program (p: Mach.program) : res Asm.program := + let mbp := Machblockgen.transf_program p in + do abp <- Asmblockgen.transf_program mbp; + OK (Asm.transf_program abp). Definition transf_function (f: Mach.function) : res Asm.function := - do tf <- transl_function f; - if zlt Ptrofs.max_unsigned (list_length_z tf.(fn_code)) - then Error (msg "code size exceeded") - else OK tf. - -Definition transf_fundef (f: Mach.fundef) : res Asm.fundef := - transf_partial_fundef transf_function f. - -Definition transf_program (p: Mach.program) : res Asm.program := - transform_partial_program transf_fundef p. + let mbf := Machblockgen.transf_function f in + do abf <- Asmblockgen.transf_function mbf; + OK (Asm.transf_function abf). + +Definition transl_code (f: Mach.function) (l: Mach.code) : res (list Asm.instruction) := + let mbf := Machblockgen.transf_function f in + let mbc := Machblockgen.trans_code l in + do abc <- transl_blocks mbf mbc true; + OK (unfold abc).
\ No newline at end of file diff --git a/mppa_k1c/Asmgenproof.v b/mppa_k1c/Asmgenproof.v index 896e9ce9..74be571d 100644 --- a/mppa_k1c/Asmgenproof.v +++ b/mppa_k1c/Asmgenproof.v @@ -15,1092 +15,148 @@ Require Import Coqlib Errors. Require Import Integers Floats AST Linking. Require Import Values Memory Events Globalenvs Smallstep. -Require Import Op Locations Mach Conventions Asm. -Require Import Asmgen Asmgenproof0 Asmgenproof1. +Require Import Op Locations Mach Conventions Asm Asmgen Machblockgen Asmblockgen. +Require Import Machblockgenproof Asmblockgenproof. -Definition match_prog (p: Mach.program) (tp: Asm.program) := - match_program (fun _ f tf => transf_fundef f = OK tf) eq p tp. +Local Open Scope linking_scope. -Lemma transf_program_match: - forall p tp, transf_program p = OK tp -> match_prog p tp. -Proof. - intros. eapply match_transform_partial_program; eauto. -Qed. - -Section PRESERVATION. - -Variable prog: Mach.program. -Variable tprog: Asm.program. -Hypothesis TRANSF: match_prog prog tprog. -Let ge := Genv.globalenv prog. -Let tge := Genv.globalenv tprog. - -Lemma symbols_preserved: - forall (s: ident), Genv.find_symbol tge s = Genv.find_symbol ge s. -Proof (Genv.find_symbol_match TRANSF). - -Lemma senv_preserved: - Senv.equiv ge tge. -Proof (Genv.senv_match TRANSF). - -Lemma functions_translated: - forall b f, - Genv.find_funct_ptr ge b = Some f -> - exists tf, - Genv.find_funct_ptr tge b = Some tf /\ transf_fundef f = OK tf. -Proof (Genv.find_funct_ptr_transf_partial TRANSF). - -Lemma functions_transl: - forall fb f tf, - Genv.find_funct_ptr ge fb = Some (Internal f) -> - transf_function f = OK tf -> - Genv.find_funct_ptr tge fb = Some (Internal tf). -Proof. - intros. exploit functions_translated; eauto. intros [tf' [A B]]. - monadInv B. rewrite H0 in EQ; inv EQ; auto. -Qed. - -(** * Properties of control flow *) - -Lemma transf_function_no_overflow: - forall f tf, - transf_function f = OK tf -> list_length_z tf.(fn_code) <= Ptrofs.max_unsigned. -Proof. - intros. monadInv H. destruct (zlt Ptrofs.max_unsigned (list_length_z x.(fn_code))); inv EQ0. - omega. -Qed. - -Lemma exec_straight_exec: - forall fb f c ep tf tc c' rs m rs' m', - transl_code_at_pc ge (rs PC) fb f c ep tf tc -> - exec_straight tge tf tc rs m c' rs' m' -> - plus step tge (State rs m) E0 (State rs' m'). -Proof. - intros. inv H. - eapply exec_straight_steps_1; eauto. - eapply transf_function_no_overflow; eauto. - eapply functions_transl; eauto. -Qed. - -Lemma exec_straight_at: - forall fb f c ep tf tc c' ep' tc' rs m rs' m', - transl_code_at_pc ge (rs PC) fb f c ep tf tc -> - transl_code f c' ep' = OK tc' -> - exec_straight tge tf tc rs m tc' rs' m' -> - transl_code_at_pc ge (rs' PC) fb f c' ep' tf tc'. -Proof. - intros. inv H. - exploit exec_straight_steps_2; eauto. - eapply transf_function_no_overflow; eauto. - eapply functions_transl; eauto. - intros [ofs' [PC' CT']]. - rewrite PC'. constructor; auto. -Qed. - -(** The following lemmas show that the translation from Mach to Asm - preserves labels, in the sense that the following diagram commutes: -<< - translation - Mach code ------------------------ Asm instr sequence - | | - | Mach.find_label lbl find_label lbl | - | | - v v - Mach code tail ------------------- Asm instr seq tail - translation ->> - The proof demands many boring lemmas showing that Asm constructor - functions do not introduce new labels. -*) +Definition block_passes := + mkpass Machblockgenproof.match_prog + ::: mkpass Asmblockgenproof.match_prog + ::: mkpass Asm.match_prog + ::: pass_nil _. -Section TRANSL_LABEL. - -Remark loadimm32_label: - forall r n k, tail_nolabel k (loadimm32 r n k). -Proof. - intros; unfold loadimm32. destruct (make_immed32 n); TailNoLabel. -(*unfold load_hilo32. destruct (Int.eq lo Int.zero); TailNoLabel.*) -Qed. -Hint Resolve loadimm32_label: labels. - -Remark opimm32_label: - forall (op: arith_name_rrr) (opimm: arith_name_rri32) r1 r2 n k, - (forall r1 r2 r3, nolabel (op r1 r2 r3)) -> - (forall r1 r2 n, nolabel (opimm r1 r2 n)) -> - tail_nolabel k (opimm32 op opimm r1 r2 n k). -Proof. - intros; unfold opimm32. destruct (make_immed32 n); TailNoLabel. -(*unfold load_hilo32. destruct (Int.eq lo Int.zero); TailNoLabel.*) -Qed. -Hint Resolve opimm32_label: labels. - -Remark loadimm64_label: - forall r n k, tail_nolabel k (loadimm64 r n k). -Proof. - intros; unfold loadimm64. destruct (make_immed64 n); TailNoLabel. -(*unfold load_hilo64. destruct (Int64.eq lo Int64.zero); TailNoLabel.*) -Qed. -Hint Resolve loadimm64_label: labels. - -Remark cast32signed_label: - forall rd rs k, tail_nolabel k (cast32signed rd rs k). -Proof. - intros; unfold cast32signed. destruct (ireg_eq rd rs); TailNoLabel. -Qed. -Hint Resolve cast32signed_label: labels. - -Remark opimm64_label: - forall (op: arith_name_rrr) (opimm: arith_name_rri64) r1 r2 n k, - (forall r1 r2 r3, nolabel (op r1 r2 r3)) -> - (forall r1 r2 n, nolabel (opimm r1 r2 n)) -> - tail_nolabel k (opimm64 op opimm r1 r2 n k). -Proof. - intros; unfold opimm64. destruct (make_immed64 n); TailNoLabel. -(*unfold load_hilo64. destruct (Int64.eq lo Int64.zero); TailNoLabel.*) -Qed. -Hint Resolve opimm64_label: labels. - -Remark addptrofs_label: - forall r1 r2 n k, tail_nolabel k (addptrofs r1 r2 n k). -Proof. - unfold addptrofs; intros. destruct (Ptrofs.eq_dec n Ptrofs.zero). TailNoLabel. - apply opimm64_label; TailNoLabel. -Qed. -Hint Resolve addptrofs_label: labels. -(* -Remark transl_cond_float_nolabel: - forall c r1 r2 r3 insn normal, - transl_cond_float c r1 r2 r3 = (insn, normal) -> nolabel insn. -Proof. - unfold transl_cond_float; intros. destruct c; inv H; exact I. -Qed. - -Remark transl_cond_single_nolabel: - forall c r1 r2 r3 insn normal, - transl_cond_single c r1 r2 r3 = (insn, normal) -> nolabel insn. -Proof. - unfold transl_cond_single; intros. destruct c; inv H; exact I. -Qed. -*) -Remark transl_cbranch_label: - forall cond args lbl k c, - transl_cbranch cond args lbl k = OK c -> tail_nolabel k c. -Proof. - intros. unfold transl_cbranch in H. destruct cond; TailNoLabel. -(* Ccomp *) - - unfold transl_comp; TailNoLabel. -(* Ccompu *) - - unfold transl_comp; TailNoLabel. -(* Ccompimm *) - - destruct (Int.eq n Int.zero); TailNoLabel. - unfold loadimm32. destruct (make_immed32 n); TailNoLabel. unfold transl_comp; TailNoLabel. -(* Ccompuimm *) - - unfold transl_opt_compuimm. - remember (select_comp n c0) as selcomp; destruct selcomp. - + destruct c; TailNoLabel; contradict Heqselcomp; unfold select_comp; - destruct (Int.eq n Int.zero); destruct c0; discriminate. - + unfold loadimm32; - destruct (make_immed32 n); TailNoLabel; unfold transl_comp; TailNoLabel. -(* Ccompl *) - - unfold transl_compl; TailNoLabel. -(* Ccomplu *) - - unfold transl_compl; TailNoLabel. -(* Ccomplimm *) - - destruct (Int64.eq n Int64.zero); TailNoLabel. - unfold loadimm64. destruct (make_immed64 n); TailNoLabel. unfold transl_compl; TailNoLabel. -(* Ccompluimm *) - - unfold transl_opt_compluimm. - remember (select_compl n c0) as selcomp; destruct selcomp. - + destruct c; TailNoLabel; contradict Heqselcomp; unfold select_compl; - destruct (Int64.eq n Int64.zero); destruct c0; discriminate. - + unfold loadimm64; - destruct (make_immed64 n); TailNoLabel; unfold transl_compl; TailNoLabel. -Qed. - -(* -- destruct c0; simpl; TailNoLabel. -- destruct c0; simpl; TailNoLabel. -- destruct (Int.eq n Int.zero). - destruct c0; simpl; TailNoLabel. - apply tail_nolabel_trans with (transl_cbranch_int32s c0 x X31 lbl :: k). - auto with labels. destruct c0; simpl; TailNoLabel. -- destruct (Int.eq n Int.zero). - destruct c0; simpl; TailNoLabel. - apply tail_nolabel_trans with (transl_cbranch_int32u c0 x X31 lbl :: k). - auto with labels. destruct c0; simpl; TailNoLabel. -- destruct c0; simpl; TailNoLabel. -- destruct c0; simpl; TailNoLabel. -- destruct (Int64.eq n Int64.zero). - destruct c0; simpl; TailNoLabel. - apply tail_nolabel_trans with (transl_cbranch_int64s c0 x X31 lbl :: k). - auto with labels. destruct c0; simpl; TailNoLabel. -- destruct (Int64.eq n Int64.zero). - destruct c0; simpl; TailNoLabel. - apply tail_nolabel_trans with (transl_cbranch_int64u c0 x X31 lbl :: k). - auto with labels. destruct c0; simpl; TailNoLabel. -- destruct (transl_cond_float c0 X31 x x0) as [insn normal] eqn:F; inv EQ2. - apply tail_nolabel_cons. eapply transl_cond_float_nolabel; eauto. - destruct normal; TailNoLabel. -- destruct (transl_cond_float c0 X31 x x0) as [insn normal] eqn:F; inv EQ2. - apply tail_nolabel_cons. eapply transl_cond_float_nolabel; eauto. - destruct normal; TailNoLabel. -- destruct (transl_cond_single c0 X31 x x0) as [insn normal] eqn:F; inv EQ2. - apply tail_nolabel_cons. eapply transl_cond_single_nolabel; eauto. - destruct normal; TailNoLabel. -- destruct (transl_cond_single c0 X31 x x0) as [insn normal] eqn:F; inv EQ2. - apply tail_nolabel_cons. eapply transl_cond_single_nolabel; eauto. - destruct normal; TailNoLabel. -*) - -Remark transl_cond_op_label: - forall cond args r k c, - transl_cond_op cond r args k = OK c -> tail_nolabel k c. -Proof. - intros. unfold transl_cond_op in H; destruct cond; TailNoLabel. -- unfold transl_cond_int32s; destruct c0; simpl; TailNoLabel. -- unfold transl_cond_int32u; destruct c0; simpl; TailNoLabel. -- unfold transl_condimm_int32s; destruct c0; simpl; TailNoLabel. -- unfold transl_condimm_int32u; destruct c0; simpl; TailNoLabel. -- unfold transl_cond_int64s; destruct c0; simpl; TailNoLabel. -- unfold transl_cond_int64u; destruct c0; simpl; TailNoLabel. -- unfold transl_condimm_int64s; destruct c0; simpl; TailNoLabel. -- unfold transl_condimm_int64u; destruct c0; simpl; TailNoLabel. -Qed. - -Remark transl_op_label: - forall op args r k c, - transl_op op args r k = OK c -> tail_nolabel k c. -Proof. -Opaque Int.eq. - unfold transl_op; intros; destruct op; TailNoLabel. -(* Omove *) -- destruct (preg_of r); try discriminate; destruct (preg_of m); inv H; TailNoLabel. -(* Oaddrsymbol *) -- destruct (Archi.pic_code tt && negb (Ptrofs.eq ofs Ptrofs.zero)); TailNoLabel. -(* Oaddimm32 *) -- apply opimm32_label; intros; exact I. -(* Oandimm32 *) -- apply opimm32_label; intros; exact I. -(* Oorimm32 *) -- apply opimm32_label; intros; exact I. -(* Oxorimm32 *) -- apply opimm32_label; intros; exact I. -(* Oshrximm *) -- destruct (Int.eq n Int.zero); TailNoLabel. -(* Oaddimm64 *) -- apply opimm64_label; intros; exact I. -(* Oandimm64 *) -- apply opimm64_label; intros; exact I. -(* Oorimm64 *) -- apply opimm64_label; intros; exact I. -(* Oxorimm64 *) -- apply opimm64_label; intros; exact I. -(* Ocmp *) -- eapply transl_cond_op_label; eauto. -Qed. - -(* -- destruct (preg_of r); try discriminate; destruct (preg_of m); inv H; TailNoLabel. -- destruct (Float.eq_dec n Float.zero); TailNoLabel. -- destruct (Float32.eq_dec n Float32.zero); TailNoLabel. -- destruct (Archi.pic_code tt && negb (Ptrofs.eq ofs Ptrofs.zero)). -+ eapply tail_nolabel_trans; [|apply addptrofs_label]. TailNoLabel. -+ TailNoLabel. -- apply opimm32_label; intros; exact I. -- apply opimm32_label; intros; exact I. -- apply opimm32_label; intros; exact I. -- apply opimm32_label; intros; exact I. -- destruct (Int.eq n Int.zero); TailNoLabel. -- apply opimm64_label; intros; exact I. -- apply opimm64_label; intros; exact I. -- apply opimm64_label; intros; exact I. -- apply opimm64_label; intros; exact I. -- destruct (Int.eq n Int.zero); TailNoLabel. -- eapply transl_cond_op_label; eauto. -*) - -Remark indexed_memory_access_label: - forall (mk_instr: ireg -> offset -> instruction) base ofs k, - (forall r o, nolabel (mk_instr r o)) -> - tail_nolabel k (indexed_memory_access mk_instr base ofs k). -Proof. - unfold indexed_memory_access; intros. - (* destruct Archi.ptr64. *) - destruct (make_immed64 (Ptrofs.to_int64 ofs)); TailNoLabel. - (* destruct (make_immed32 (Ptrofs.to_int ofs)); TailNoLabel. *) -Qed. - -Remark loadind_label: - forall base ofs ty dst k c, - loadind base ofs ty dst k = OK c -> tail_nolabel k c. -Proof. - unfold loadind; intros. - destruct ty, (preg_of dst); inv H; apply indexed_memory_access_label; intros; exact I. -Qed. - -Remark storeind_label: - forall src base ofs ty k c, - storeind src base ofs ty k = OK c -> tail_nolabel k c. -Proof. - unfold storeind; intros. - destruct ty, (preg_of src); inv H; apply indexed_memory_access_label; intros; exact I. -Qed. - -Remark loadind_ptr_label: - forall base ofs dst k, tail_nolabel k (loadind_ptr base ofs dst k). -Proof. - intros. apply indexed_memory_access_label. intros; destruct Archi.ptr64; exact I. -Qed. - -Remark storeind_ptr_label: - forall src base ofs k, tail_nolabel k (storeind_ptr src base ofs k). -Proof. - intros. apply indexed_memory_access_label. intros; destruct Archi.ptr64; exact I. -Qed. +Definition match_prog := pass_match (compose_passes block_passes). -Remark transl_memory_access_label: - forall (mk_instr: ireg -> offset -> instruction) addr args k c, - (forall r o, nolabel (mk_instr r o)) -> - transl_memory_access mk_instr addr args k = OK c -> - tail_nolabel k c. -Proof. - unfold transl_memory_access; intros; destruct addr; TailNoLabel; apply indexed_memory_access_label; auto. -Qed. - -Remark make_epilogue_label: - forall f k, tail_nolabel k (make_epilogue f k). -Proof. - unfold make_epilogue; intros. eapply tail_nolabel_trans. apply loadind_ptr_label. TailNoLabel. -Qed. - -Lemma transl_instr_label: - forall f i ep k c, - transl_instr f i ep k = OK c -> - match i with Mlabel lbl => c = Plabel lbl ::i k | _ => tail_nolabel k c end. -Proof. - unfold transl_instr; intros; destruct i; TailNoLabel. -(* loadind *) -- eapply loadind_label; eauto. -(* storeind *) -- eapply storeind_label; eauto. -(* Mgetparam *) -- destruct ep. eapply loadind_label; eauto. - eapply tail_nolabel_trans. apply loadind_ptr_label. eapply loadind_label; eauto. -(* transl_op *) -- eapply transl_op_label; eauto. -(* transl_load *) -- destruct m; monadInv H; eapply transl_memory_access_label; eauto; intros; exact I. -(* transl store *) -- destruct m; monadInv H; eapply transl_memory_access_label; eauto; intros; exact I. -- destruct s0; monadInv H; TailNoLabel. -- destruct s0; monadInv H; eapply tail_nolabel_trans - ; [eapply make_epilogue_label|TailNoLabel]. -- eapply transl_cbranch_label; eauto. -- eapply tail_nolabel_trans; [eapply make_epilogue_label|TailNoLabel]. -Qed. -(* - - -- eapply transl_op_label; eauto. -- destruct m; monadInv H; eapply transl_memory_access_label; eauto; intros; exact I. -- destruct m; monadInv H; eapply transl_memory_access_label; eauto; intros; exact I. -- destruct s0; monadInv H; (eapply tail_nolabel_trans; [eapply make_epilogue_label|TailNoLabel]). -- eapply tail_nolabel_trans; [eapply make_epilogue_label|TailNoLabel]. -*) - -Lemma transl_instr_label': - forall lbl f i ep k c, - transl_instr f i ep k = OK c -> - find_label lbl c = if Mach.is_label lbl i then Some k else find_label lbl k. -Proof. - intros. exploit transl_instr_label; eauto. - destruct i; try (intros [A B]; apply B). - intros. subst c. simpl. auto. -Qed. - -Lemma transl_code_label: - forall lbl f c ep tc, - transl_code f c ep = OK tc -> - match Mach.find_label lbl c with - | None => find_label lbl tc = None - | Some c' => exists tc', find_label lbl tc = Some tc' /\ transl_code f c' false = OK tc' - end. -Proof. - induction c; simpl; intros. - inv H. auto. - monadInv H. rewrite (transl_instr_label' lbl _ _ _ _ _ EQ0). - generalize (Mach.is_label_correct lbl a). - destruct (Mach.is_label lbl a); intros. - subst a. simpl in EQ. exists x; auto. - eapply IHc; eauto. -Qed. - -Lemma transl_find_label: - forall lbl f tf, - transf_function f = OK tf -> - match Mach.find_label lbl f.(Mach.fn_code) with - | None => find_label lbl tf.(fn_code) = None - | Some c => exists tc, find_label lbl tf.(fn_code) = Some tc /\ transl_code f c false = OK tc - end. -Proof. - intros. monadInv H. destruct (zlt Ptrofs.max_unsigned (list_length_z x.(fn_code))); inv EQ0. - monadInv EQ. rewrite transl_code'_transl_code in EQ0. unfold fn_code. - simpl. destruct (storeind_ptr_label GPR8 GPR12 (fn_retaddr_ofs f) x) as [A B]. - (* destruct B. *) - eapply transl_code_label; eauto. -Qed. - -End TRANSL_LABEL. - -(** A valid branch in a piece of Mach code translates to a valid ``go to'' - transition in the generated Asm code. *) - -Lemma find_label_goto_label: - forall f tf lbl rs m c' b ofs, - Genv.find_funct_ptr ge b = Some (Internal f) -> - transf_function f = OK tf -> - rs PC = Vptr b ofs -> - Mach.find_label lbl f.(Mach.fn_code) = Some c' -> - exists tc', exists rs', - goto_label tf lbl rs m = Next rs' m - /\ transl_code_at_pc ge (rs' PC) b f c' false tf tc' - /\ forall r, r <> PC -> rs'#r = rs#r. -Proof. - intros. exploit (transl_find_label lbl f tf); eauto. rewrite H2. - intros [tc [A B]]. - exploit label_pos_code_tail; eauto. instantiate (1 := 0). - intros [pos' [P [Q R]]]. - exists tc; exists (rs#PC <- (Vptr b (Ptrofs.repr pos'))). - split. unfold goto_label. rewrite P. rewrite H1. auto. - split. rewrite Pregmap.gss. constructor; auto. - rewrite Ptrofs.unsigned_repr. replace (pos' - 0) with pos' in Q. - auto. omega. - generalize (transf_function_no_overflow _ _ H0). omega. - intros. apply Pregmap.gso; auto. +Lemma transf_program_match: + forall p tp, Asmgen.transf_program p = OK tp -> match_prog p tp. +Proof. + intros p tp H. + unfold Asmgen.transf_program in H. apply bind_inversion in H. destruct H. + inversion_clear H. inversion H1. remember (Machblockgen.transf_program p) as mbp. + unfold match_prog; simpl. + exists mbp; split. apply Machblockgenproof.transf_program_match; auto. + exists x; split. apply Asmblockgenproof.transf_program_match; auto. + exists tp; split. apply Asm.transf_program_match; auto. auto. +Qed. + +(** Return Address Offset *) + +Definition return_address_offset (f: Mach.function) (c: Mach.code) (ofs: ptrofs) : Prop := + Asmblockgenproof.return_address_offset (Machblockgen.transf_function f) (Machblockgen.trans_code c) ofs. + + +(* TODO: put this proof in Machblocgen ? (it is specific to Machblocgen) *) +Lemma trans_code_monotonic c i b l: + trans_code c = b::l -> + exists l', exists b', trans_code (i::c) = l' ++ (b'::l). +Proof. + destruct c as [|i' c]. { rewrite trans_code_equation; intros; congruence. } + destruct (get_code_nature (i :: i':: c)) eqn:GCNIC. + - apply get_code_nature_empty in GCNIC. discriminate. + - (* i=label *) + destruct i; try discriminate. + rewrite! trans_code_equation; + remember (to_bblock (Mlabel l0 :: i' :: c)) as b0. + destruct b0 as [b0 c0]. + exploit to_bblock_label; eauto. + intros (H1 & H2). rewrite H2; simpl; clear H2. + intros H2; inversion H2; subst. + exists nil; simpl; eauto. + - (*i=basic *) + rewrite! trans_code_equation; destruct (to_basic_inst i) eqn:TBI; [| destruct i; discriminate]. + destruct (cn_eqdec (get_code_nature (i':: c)) IsLabel). + + (* i'=label *) remember (to_bblock (i :: i' :: c)) as b1. + destruct b1 as [b1 c1]. + assert (X: c1 = i'::c). + { generalize Heqb1; clear Heqb1. + unfold to_bblock. + erewrite to_bblock_header_noLabel; try congruence. + destruct i'; try discriminate. + destruct i; try discriminate; simpl; + intro X; inversion X; auto. + } + subst c1. + rewrite !trans_code_equation. intro H1; rewrite H1. + exists (b1 :: nil). simpl; eauto. + + (* i'<>label *) remember (to_bblock (i :: i' :: c)) as b1. + destruct b1 as [b1 c1]. + remember (to_bblock (i' :: c)) as b2. + destruct b2 as [b2 c2]. + intro H1; assert (X: c1=c2). + { generalize Heqb1, Heqb2; clear Heqb1 Heqb2. + unfold to_bblock. + erewrite to_bblock_header_noLabel; try congruence. + destruct i'; simpl in * |- ; try congruence; + destruct i; try discriminate; simpl; + try (destruct (to_bblock_body c) as [xx yy], (to_bblock_exit yy); + intros X1 X2; inversion X1; inversion X2; auto). + } + subst; inversion H1. + exists nil; simpl; eauto. + - (* i=cfi *) + remember (to_cfi i) as cfi. + intros H. destruct cfi. + + erewrite trans_code_cfi; eauto. + rewrite H. + refine (ex_intro _ (_::nil) _). simpl; eauto. + + destruct i; simpl in * |-; try congruence. +Qed. + +Lemma Mach_Machblock_tail sg ros c c1 c2: c1=(Mcall sg ros :: c) -> is_tail c1 c2 -> + exists b, (* Machblock.exit b = Some (Machblock.MBcall sg ros) /\ *) + is_tail (b :: trans_code c) (trans_code c2). +Proof. + intro H; induction 1. + - intros; subst. + rewrite (trans_code_equation (Mcall sg ros :: c)). + simpl. + eapply ex_intro; eauto with coqlib. + - intros; exploit IHis_tail; eauto. clear IHis_tail. + intros (b & Hb). + + inversion Hb; clear Hb. + * exploit (trans_code_monotonic c2 i); eauto. + intros (l' & b' & Hl'); rewrite Hl'. + simpl; eauto with coqlib. + * exploit (trans_code_monotonic c2 i); eauto. + intros (l' & b' & Hl'); rewrite Hl'. + simpl; eapply ex_intro. + eapply is_tail_trans; eauto with coqlib. Qed. -(** Existence of return addresses *) - Lemma return_address_exists: forall f sg ros c, is_tail (Mcall sg ros :: c) f.(Mach.fn_code) -> exists ra, return_address_offset f c ra. Proof. - intros. eapply Asmgenproof0.return_address_exists; eauto. -- intros. exploit transl_instr_label; eauto. - destruct i; try (intros [A B]; apply A). intros. subst c0. repeat constructor. -- intros. monadInv H0. - destruct (zlt Ptrofs.max_unsigned (list_length_z x.(fn_code))); inv EQ0. monadInv EQ. - rewrite transl_code'_transl_code in EQ0. - exists x; exists true; split; auto. unfold fn_code. - constructor. apply is_tail_cons. apply (storeind_ptr_label GPR8 GPR12 (fn_retaddr_ofs f0) x). -- exact transf_function_no_overflow. -Qed. - -(** * Proof of semantic preservation *) - -(** Semantic preservation is proved using simulation diagrams - of the following form. -<< - st1 --------------- st2 - | | - t| *|t - | | - v v - st1'--------------- st2' ->> - The invariant is the [match_states] predicate below, which includes: -- The Asm code pointed by the PC register is the translation of - the current Mach code sequence. -- Mach register values and Asm register values agree. -*) - -Inductive match_states: Mach.state -> Asm.state -> Prop := - | match_states_intro: - forall s fb sp c ep ms m m' rs f tf tc - (STACKS: match_stack ge s) - (FIND: Genv.find_funct_ptr ge fb = Some (Internal f)) - (MEXT: Mem.extends m m') - (AT: transl_code_at_pc ge (rs PC) fb f c ep tf tc) - (AG: agree ms sp rs) - (DXP: ep = true -> rs#FP = parent_sp s), - match_states (Mach.State s fb sp c ms m) - (Asm.State rs m') - | match_states_call: - forall s fb ms m m' rs - (STACKS: match_stack ge s) - (MEXT: Mem.extends m m') - (AG: agree ms (parent_sp s) rs) - (ATPC: rs PC = Vptr fb Ptrofs.zero) - (ATLR: rs RA = parent_ra s), - match_states (Mach.Callstate s fb ms m) - (Asm.State rs m') - | match_states_return: - forall s ms m m' rs - (STACKS: match_stack ge s) - (MEXT: Mem.extends m m') - (AG: agree ms (parent_sp s) rs) - (ATPC: rs PC = parent_ra s), - match_states (Mach.Returnstate s ms m) - (Asm.State rs m'). - -Lemma exec_straight_steps: - forall s fb f rs1 i c ep tf tc m1' m2 m2' sp ms2, - match_stack ge s -> - Mem.extends m2 m2' -> - Genv.find_funct_ptr ge fb = Some (Internal f) -> - transl_code_at_pc ge (rs1 PC) fb f (i :: c) ep tf tc -> - (forall k c (TR: transl_instr f i ep k = OK c), - exists rs2, - exec_straight tge tf c rs1 m1' k rs2 m2' - /\ agree ms2 sp rs2 - /\ (it1_is_parent ep i = true -> rs2#FP = parent_sp s)) -> - exists st', - plus step tge (State rs1 m1') E0 st' /\ - match_states (Mach.State s fb sp c ms2 m2) st'. -Proof. - intros. inversion H2. subst. monadInv H7. - exploit H3; eauto. intros [rs2 [A [B C]]]. - exists (State rs2 m2'); split. - eapply exec_straight_exec; eauto. - econstructor; eauto. eapply exec_straight_at; eauto. -Qed. - -Lemma exec_straight_steps_goto: - forall s fb f rs1 i c ep tf tc m1' m2 m2' sp ms2 lbl c', - match_stack ge s -> - Mem.extends m2 m2' -> - Genv.find_funct_ptr ge fb = Some (Internal f) -> - Mach.find_label lbl f.(Mach.fn_code) = Some c' -> - transl_code_at_pc ge (rs1 PC) fb f (i :: c) ep tf tc -> - it1_is_parent ep i = false -> - (forall k c (TR: transl_instr f i ep k = OK c), - exists jmp, exists k', exists rs2, - exec_straight tge tf c rs1 m1' (jmp :: k') rs2 m2' - /\ agree ms2 sp rs2 - /\ exec_instr tge tf jmp rs2 m2' = goto_label tf lbl rs2 m2') -> - exists st', - plus step tge (State rs1 m1') E0 st' /\ - match_states (Mach.State s fb sp c' ms2 m2) st'. -Proof. - intros. inversion H3. subst. monadInv H9. - exploit H5; eauto. intros [jmp [k' [rs2 [A [B C]]]]]. - generalize (functions_transl _ _ _ H7 H8); intro FN. - generalize (transf_function_no_overflow _ _ H8); intro NOOV. - exploit exec_straight_steps_2; eauto. - intros [ofs' [PC2 CT2]]. - exploit find_label_goto_label; eauto. - intros [tc' [rs3 [GOTO [AT' OTH]]]]. - exists (State rs3 m2'); split. - eapply plus_right'. - eapply exec_straight_steps_1; eauto. - econstructor; eauto. - eapply find_instr_tail. eauto. - rewrite C. eexact GOTO. - traceEq. - econstructor; eauto. - apply agree_exten with rs2; auto with asmgen. - congruence. -Qed. - -Lemma exec_straight_opt_steps_goto: - forall s fb f rs1 i c ep tf tc m1' m2 m2' sp ms2 lbl c', - match_stack ge s -> - Mem.extends m2 m2' -> - Genv.find_funct_ptr ge fb = Some (Internal f) -> - Mach.find_label lbl f.(Mach.fn_code) = Some c' -> - transl_code_at_pc ge (rs1 PC) fb f (i :: c) ep tf tc -> - it1_is_parent ep i = false -> - (forall k c (TR: transl_instr f i ep k = OK c), - exists jmp, exists k', exists rs2, - exec_straight_opt tge tf c rs1 m1' (jmp :: k') rs2 m2' - /\ agree ms2 sp rs2 - /\ exec_instr tge tf jmp rs2 m2' = goto_label tf lbl rs2 m2') -> - exists st', - plus step tge (State rs1 m1') E0 st' /\ - match_states (Mach.State s fb sp c' ms2 m2) st'. -Proof. - intros. inversion H3. subst. monadInv H9. - exploit H5; eauto. intros [jmp [k' [rs2 [A [B C]]]]]. - generalize (functions_transl _ _ _ H7 H8); intro FN. - generalize (transf_function_no_overflow _ _ H8); intro NOOV. - inv A. -- exploit find_label_goto_label; eauto. - intros [tc' [rs3 [GOTO [AT' OTH]]]]. - exists (State rs3 m2'); split. - apply plus_one. econstructor; eauto. - eapply find_instr_tail. eauto. - rewrite C. eexact GOTO. - econstructor; eauto. - apply agree_exten with rs2; auto with asmgen. - congruence. -- exploit exec_straight_steps_2; eauto. - intros [ofs' [PC2 CT2]]. - exploit find_label_goto_label; eauto. - intros [tc' [rs3 [GOTO [AT' OTH]]]]. - exists (State rs3 m2'); split. - eapply plus_right'. - eapply exec_straight_steps_1; eauto. - econstructor; eauto. - eapply find_instr_tail. eauto. - rewrite C. eexact GOTO. - traceEq. - econstructor; eauto. - apply agree_exten with rs2; auto with asmgen. - congruence. -Qed. - -(** We need to show that, in the simulation diagram, we cannot - take infinitely many Mach transitions that correspond to zero - transitions on the Asm side. Actually, all Mach transitions - correspond to at least one Asm transition, except the - transition from [Machsem.Returnstate] to [Machsem.State]. - So, the following integer measure will suffice to rule out - the unwanted behaviour. *) - -Definition measure (s: Mach.state) : nat := - match s with - | Mach.State _ _ _ _ _ _ => 0%nat - | Mach.Callstate _ _ _ _ => 0%nat - | Mach.Returnstate _ _ _ => 1%nat - end. - -Remark preg_of_not_FP: forall r, negb (mreg_eq r R10) = true -> IR FP <> preg_of r. -Proof. - intros. change (IR FP) with (preg_of R10). red; intros. - exploit preg_of_injective; eauto. intros; subst r; discriminate. -Qed. - -(** This is the simulation diagram. We prove it by case analysis on the Mach transition. *) - -Theorem step_simulation: - forall S1 t S2, Mach.step return_address_offset ge S1 t S2 -> - forall S1' (MS: match_states S1 S1'), - (exists S2', plus step tge S1' t S2' /\ match_states S2 S2') - \/ (measure S2 < measure S1 /\ t = E0 /\ match_states S2 S1')%nat. -Proof. - induction 1; intros; inv MS. - -- (* Mlabel *) - left; eapply exec_straight_steps; eauto; intros. - monadInv TR. econstructor; split. apply exec_straight_one. simpl; eauto. auto. - split. apply agree_nextinstr; auto. simpl; congruence. - -- (* Mgetstack *) - unfold load_stack in H. - exploit Mem.loadv_extends; eauto. intros [v' [A B]]. - rewrite (sp_val _ _ _ AG) in A. - left; eapply exec_straight_steps; eauto. intros. simpl in TR. - exploit loadind_correct; eauto with asmgen. intros [rs' [P [Q R]]]. - exists rs'; split. eauto. - split. eapply agree_set_mreg; eauto with asmgen. congruence. - simpl; congruence. - - -- (* Msetstack *) - unfold store_stack in H. - assert (Val.lessdef (rs src) (rs0 (preg_of src))). eapply preg_val; eauto. - exploit Mem.storev_extends; eauto. intros [m2' [A B]]. - left; eapply exec_straight_steps; eauto. - rewrite (sp_val _ _ _ AG) in A. intros. simpl in TR. - inversion TR. - exploit storeind_correct; eauto with asmgen. intros [rs' [P Q]]. - exists rs'; split. eauto. - split. eapply agree_undef_regs; eauto with asmgen. - simpl; intros. rewrite Q; auto with asmgen. - -- (* Mgetparam *) - assert (f0 = f) by congruence; subst f0. - unfold load_stack in *. - exploit Mem.loadv_extends. eauto. eexact H0. auto. - intros [parent' [A B]]. rewrite (sp_val _ _ _ AG) in A. - exploit lessdef_parent_sp; eauto. clear B; intros B; subst parent'. - exploit Mem.loadv_extends. eauto. eexact H1. auto. - intros [v' [C D]]. -(* Opaque loadind. *) - left; eapply exec_straight_steps; eauto; intros. monadInv TR. - destruct ep. -(* GPR31 contains parent *) - exploit loadind_correct. eexact EQ. - instantiate (2 := rs0). rewrite DXP; eauto. congruence. - intros [rs1 [P [Q R]]]. - exists rs1; split. eauto. - split. eapply agree_set_mreg. eapply agree_set_mreg; eauto. congruence. auto with asmgen. - simpl; intros. rewrite R; auto with asmgen. - apply preg_of_not_FP; auto. -(* GPR11 does not contain parent *) - rewrite chunk_of_Tptr in A. - exploit loadind_ptr_correct. eexact A. congruence. intros [rs1 [P [Q R]]]. - exploit loadind_correct. eexact EQ. instantiate (2 := rs1). rewrite Q. eauto. congruence. - intros [rs2 [S [T U]]]. - exists rs2; split. eapply exec_straight_trans; eauto. - split. eapply agree_set_mreg. eapply agree_set_mreg. eauto. eauto. - instantiate (1 := rs1#FP <- (rs2#FP)). intros. - rewrite Pregmap.gso; auto with asmgen. - congruence. - intros. unfold Pregmap.set. destruct (PregEq.eq r' FP). congruence. auto with asmgen. - simpl; intros. rewrite U; auto with asmgen. - apply preg_of_not_FP; auto. -- (* Mop *) - assert (eval_operation tge sp op (map rs args) m = Some v). - rewrite <- H. apply eval_operation_preserved. exact symbols_preserved. - exploit eval_operation_lessdef. eapply preg_vals; eauto. eauto. eexact H0. - intros [v' [A B]]. rewrite (sp_val _ _ _ AG) in A. - left; eapply exec_straight_steps; eauto; intros. simpl in TR. - exploit transl_op_correct; eauto. intros [rs2 [P [Q R]]]. - exists rs2; split. eauto. split. auto. - apply agree_set_undef_mreg with rs0; auto. - apply Val.lessdef_trans with v'; auto. - simpl; intros. destruct (andb_prop _ _ H1); clear H1. - rewrite R; auto. apply preg_of_not_FP; auto. -Local Transparent destroyed_by_op. - destruct op; simpl; auto; congruence. - -- (* Mload *) - assert (eval_addressing tge sp addr (map rs args) = Some a). - rewrite <- H. apply eval_addressing_preserved. exact symbols_preserved. - exploit eval_addressing_lessdef. eapply preg_vals; eauto. eexact H1. - intros [a' [A B]]. rewrite (sp_val _ _ _ AG) in A. - exploit Mem.loadv_extends; eauto. intros [v' [C D]]. - left; eapply exec_straight_steps; eauto; intros. simpl in TR. - inversion TR. - exploit transl_load_correct; eauto. - intros [rs2 [P [Q R]]]. - exists rs2; split. eauto. - split. eapply agree_set_undef_mreg; eauto. congruence. - intros; auto with asmgen. - simpl; congruence. - - -- (* Mstore *) - assert (eval_addressing tge sp addr (map rs args) = Some a). - rewrite <- H. apply eval_addressing_preserved. exact symbols_preserved. - exploit eval_addressing_lessdef. eapply preg_vals; eauto. eexact H1. - intros [a' [A B]]. rewrite (sp_val _ _ _ AG) in A. - assert (Val.lessdef (rs src) (rs0 (preg_of src))). eapply preg_val; eauto. - exploit Mem.storev_extends; eauto. intros [m2' [C D]]. - left; eapply exec_straight_steps; eauto. - intros. simpl in TR. - inversion TR. - exploit transl_store_correct; eauto. intros [rs2 [P Q]]. - exists rs2; split. eauto. - split. eapply agree_undef_regs; eauto with asmgen. - simpl; congruence. - -- (* Mcall *) - assert (f0 = f) by congruence. subst f0. - inv AT. - assert (NOOV: list_length_z tf.(fn_code) <= Ptrofs.max_unsigned). - eapply transf_function_no_overflow; eauto. - destruct ros as [rf|fid]; simpl in H; monadInv H5. -(* -+ (* Indirect call *) - assert (rs rf = Vptr f' Ptrofs.zero). - destruct (rs rf); try discriminate. - revert H; predSpec Ptrofs.eq Ptrofs.eq_spec i Ptrofs.zero; intros; congruence. - assert (rs0 x0 = Vptr f' Ptrofs.zero). - exploit ireg_val; eauto. rewrite H5; intros LD; inv LD; auto. - generalize (code_tail_next_int _ _ _ _ NOOV H6). intro CT1. - assert (TCA: transl_code_at_pc ge (Vptr fb (Ptrofs.add ofs Ptrofs.one)) fb f c false tf x). - econstructor; eauto. - exploit return_address_offset_correct; eauto. intros; subst ra. - left; econstructor; split. - apply plus_one. eapply exec_step_internal. Simpl. rewrite <- H2; simpl; eauto. - eapply functions_transl; eauto. eapply find_instr_tail; eauto. - simpl. eauto. - econstructor; eauto. - econstructor; eauto. - eapply agree_sp_def; eauto. - simpl. eapply agree_exten; eauto. intros. Simpl. - Simpl. rewrite <- H2. auto. -*) -+ (* Direct call *) - generalize (code_tail_next_int _ _ _ _ NOOV H6). intro CT1. - assert (TCA: transl_code_at_pc ge (Vptr fb (Ptrofs.add ofs Ptrofs.one)) fb f c false tf x). - econstructor; eauto. - exploit return_address_offset_correct; eauto. intros; subst ra. - left; econstructor; split. - apply plus_one. eapply exec_step_internal. eauto. - eapply functions_transl; eauto. eapply find_instr_tail; eauto. - simpl. unfold Genv.symbol_address. rewrite symbols_preserved. rewrite H. eauto. - econstructor; eauto. - econstructor; eauto. - eapply agree_sp_def; eauto. - simpl. eapply agree_exten; eauto. intros. Simpl. - Simpl. rewrite <- H2. auto. - -- (* Mtailcall *) - assert (f0 = f) by congruence. subst f0. - inversion AT; subst. - assert (NOOV: list_length_z tf.(fn_code) <= Ptrofs.max_unsigned). - eapply transf_function_no_overflow; eauto. exploit Mem.loadv_extends. eauto. eexact H1. auto. simpl. intros [parent' [A B]]. - destruct ros as [rf|fid]; simpl in H; monadInv H7. -(* -+ (* Indirect call *) - assert (rs rf = Vptr f' Ptrofs.zero). - destruct (rs rf); try discriminate. - revert H; predSpec Ptrofs.eq Ptrofs.eq_spec i Ptrofs.zero; intros; congruence. - assert (rs0 x0 = Vptr f' Ptrofs.zero). - exploit ireg_val; eauto. rewrite H7; intros LD; inv LD; auto. - exploit make_epilogue_correct; eauto. intros (rs1 & m1 & U & V & W & X & Y & Z). - exploit exec_straight_steps_2; eauto using functions_transl. - intros (ofs' & P & Q). - left; econstructor; split. - (* execution *) - eapply plus_right'. eapply exec_straight_exec; eauto. - econstructor. eexact P. eapply functions_transl; eauto. eapply find_instr_tail. eexact Q. - simpl. reflexivity. - traceEq. - (* match states *) - econstructor; eauto. - apply agree_set_other; auto with asmgen. - Simpl. rewrite Z by (rewrite <- (ireg_of_eq _ _ EQ1); eauto with asmgen). assumption. -*) -+ (* Direct call *) - exploit make_epilogue_correct; eauto. intros (rs1 & m1 & U & V & W & X & Y & Z). - exploit exec_straight_steps_2; eauto using functions_transl. - intros (ofs' & P & Q). - left; econstructor; split. - (* execution *) - eapply plus_right'. eapply exec_straight_exec; eauto. - econstructor. eexact P. eapply functions_transl; eauto. eapply find_instr_tail. eexact Q. - simpl. reflexivity. - traceEq. - (* match states *) - econstructor; eauto. - { apply agree_set_other. - - econstructor; auto with asmgen. - + apply V. - + intro r. destruct r; apply V; auto. - - eauto with asmgen. } - { Simpl. unfold Genv.symbol_address. rewrite symbols_preserved. rewrite H. auto. } - -- (* Mbuiltin *) - inv AT. monadInv H4. - exploit functions_transl; eauto. intro FN. - generalize (transf_function_no_overflow _ _ H3); intro NOOV. - exploit builtin_args_match; eauto. intros [vargs' [P Q]]. - exploit external_call_mem_extends; eauto. - intros [vres' [m2' [A [B [C D]]]]]. - left. econstructor; split. apply plus_one. - eapply exec_step_builtin. eauto. eauto. - eapply find_instr_tail; eauto. - erewrite <- sp_val by eauto. - eapply eval_builtin_args_preserved with (ge1 := ge); eauto. exact symbols_preserved. - eapply external_call_symbols_preserved; eauto. apply senv_preserved. - eauto. - econstructor; eauto. - instantiate (2 := tf); instantiate (1 := x). - unfold nextinstr. rewrite Pregmap.gss. - rewrite set_res_other. rewrite undef_regs_other_2. rewrite Pregmap.gso by congruence. - rewrite <- H1. simpl. econstructor; eauto. - eapply code_tail_next_int; eauto. - rewrite preg_notin_charact. intros. auto with asmgen. - auto with asmgen. - apply agree_nextinstr. eapply agree_set_res; auto. - eapply agree_undef_regs; eauto. intros. rewrite undef_regs_other_2; auto. apply Pregmap.gso; auto with asmgen. - congruence. - -- (* Mgoto *) - assert (f0 = f) by congruence. subst f0. - inv AT. monadInv H4. - exploit find_label_goto_label; eauto. intros [tc' [rs' [GOTO [AT2 INV]]]]. - left; exists (State rs' m'); split. - apply plus_one. econstructor; eauto. - eapply functions_transl; eauto. - eapply find_instr_tail; eauto. - simpl; eauto. - econstructor; eauto. - eapply agree_exten; eauto with asmgen. - congruence. -- (* Mcond true *) - assert (f0 = f) by congruence. subst f0. - exploit eval_condition_lessdef. eapply preg_vals; eauto. eauto. eauto. intros EC. - left; eapply exec_straight_opt_steps_goto; eauto. - intros. simpl in TR. - inversion TR. - exploit transl_cbranch_correct_true; eauto. intros (rs' & jmp & A & B & C). - exists jmp; exists k; exists rs'. - split. eexact A. - split. apply agree_exten with rs0; auto with asmgen. - exact B. -- (* Mcond false *) - exploit eval_condition_lessdef. eapply preg_vals; eauto. eauto. eauto. intros EC. - left; eapply exec_straight_steps; eauto. intros. simpl in TR. - inversion TR. - exploit transl_cbranch_correct_false; eauto. intros (rs' & A & B). - exists rs'. - split. eexact A. - split. apply agree_exten with rs0; auto with asmgen. - simpl. congruence. -- (* Mjumptable *) - assert (f0 = f) by congruence. subst f0. - inv AT. monadInv H6. -(* - exploit functions_transl; eauto. intro FN. - generalize (transf_function_no_overflow _ _ H5); intro NOOV. - exploit find_label_goto_label. eauto. eauto. - instantiate (2 := rs0#X5 <- Vundef #X31 <- Vundef). - Simpl. eauto. - eauto. - intros [tc' [rs' [A [B C]]]]. - exploit ireg_val; eauto. rewrite H. intros LD; inv LD. - left; econstructor; split. - apply plus_one. econstructor; eauto. - eapply find_instr_tail; eauto. - simpl. rewrite <- H9. unfold Mach.label in H0; unfold label; rewrite H0. eexact A. - econstructor; eauto. - eapply agree_undef_regs; eauto. - simpl. intros. rewrite C; auto with asmgen. Simpl. - congruence. -*) -- (* Mreturn *) - assert (f0 = f) by congruence. subst f0. - inversion AT; subst. simpl in H6; monadInv H6. - assert (NOOV: list_length_z tf.(fn_code) <= Ptrofs.max_unsigned). - eapply transf_function_no_overflow; eauto. - exploit make_epilogue_correct; eauto. intros (rs1 & m1 & U & V & W & X & Y & Z). - exploit exec_straight_steps_2; eauto using functions_transl. - intros (ofs' & P & Q). - left; econstructor; split. - (* execution *) - eapply plus_right'. eapply exec_straight_exec; eauto. - econstructor. eexact P. eapply functions_transl; eauto. eapply find_instr_tail. eexact Q. - simpl. reflexivity. - traceEq. - (* match states *) - econstructor; eauto. - apply agree_set_other; auto with asmgen. - -- (* internal function *) - exploit functions_translated; eauto. intros [tf [A B]]. monadInv B. - generalize EQ; intros EQ'. monadInv EQ'. - destruct (zlt Ptrofs.max_unsigned (list_length_z x0.(fn_code))); inversion EQ1. clear EQ1. subst x0. - unfold store_stack in *. - exploit Mem.alloc_extends. eauto. eauto. apply Z.le_refl. apply Z.le_refl. - intros [m1' [C D]]. - exploit Mem.storev_extends. eexact D. eexact H1. eauto. eauto. - intros [m2' [F G]]. - simpl chunk_of_type in F. - exploit Mem.storev_extends. eexact G. eexact H2. eauto. eauto. - intros [m3' [P Q]]. - (* Execution of function prologue *) - monadInv EQ0. rewrite transl_code'_transl_code in EQ1. - set (tfbody := Pallocframe (fn_stacksize f) (fn_link_ofs f) ::i - Pget GPR8 RA ::i - storeind_ptr GPR8 SP (fn_retaddr_ofs f) x0) in *. - set (tf := {| fn_sig := Mach.fn_sig f; fn_code := tfbody |}) in *. - set (rs2 := nextinstr (rs0#FP <- (parent_sp s) #SP <- sp #GPR31 <- Vundef)). - exploit (Pget_correct tge tf GPR8 RA (storeind_ptr GPR8 SP (fn_retaddr_ofs f) x0) rs2 m2'); auto. - intros (rs' & U' & V'). - exploit (storeind_ptr_correct tge tf SP (fn_retaddr_ofs f) GPR8 x0 rs' m2'). - rewrite chunk_of_Tptr in P. - assert (rs' GPR8 = rs0 RA). { apply V'. } - assert (rs' GPR12 = rs2 GPR12). { apply V'; discriminate. } - rewrite H3. rewrite H4. - (* change (rs' GPR8) with (rs0 RA). *) - rewrite ATLR. - change (rs2 GPR12) with sp. eexact P. - congruence. congruence. - intros (rs3 & U & V). - assert (EXEC_PROLOGUE: - exec_straight tge tf - tf.(fn_code) rs0 m' - x0 rs3 m3'). - { change (fn_code tf) with tfbody; unfold tfbody. - apply exec_straight_step with rs2 m2'. - unfold exec_instr. rewrite C. fold sp. - rewrite <- (sp_val _ _ _ AG). rewrite chunk_of_Tptr in F. rewrite F. reflexivity. - reflexivity. - eapply exec_straight_trans. - - eexact U'. - - eexact U. } - exploit exec_straight_steps_2; eauto using functions_transl. omega. constructor. - intros (ofs' & X & Y). - left; exists (State rs3 m3'); split. - eapply exec_straight_steps_1; eauto. omega. constructor. - econstructor; eauto. - rewrite X; econstructor; eauto. - apply agree_exten with rs2; eauto with asmgen. - unfold rs2. - apply agree_nextinstr. apply agree_set_other; auto with asmgen. - apply agree_change_sp with (parent_sp s). - apply agree_undef_regs with rs0. auto. -Local Transparent destroyed_at_function_entry. - simpl; intros; Simpl. - unfold sp; congruence. - intros. - assert (r <> GPR31). { contradict H3; rewrite H3; unfold data_preg; auto. } - rewrite V. - assert (r <> GPR8). { contradict H3; rewrite H3; unfold data_preg; auto. } - assert (forall r : preg, r <> PC -> r <> GPR8 -> rs' r = rs2 r). { apply V'. } - rewrite H6; auto. - contradict H3; rewrite H3; unfold data_preg; auto. - contradict H3; rewrite H3; unfold data_preg; auto. - contradict H3; rewrite H3; unfold data_preg; auto. - intros. rewrite V by auto with asmgen. - assert (forall r : preg, r <> PC -> r <> GPR8 -> rs' r = rs2 r). { apply V'. } - rewrite H4 by auto with asmgen. reflexivity. - -- (* external function *) - exploit functions_translated; eauto. - intros [tf [A B]]. simpl in B. inv B. - exploit extcall_arguments_match; eauto. - intros [args' [C D]]. - exploit external_call_mem_extends; eauto. - intros [res' [m2' [P [Q [R S]]]]]. - left; econstructor; split. - apply plus_one. eapply exec_step_external; eauto. - eapply external_call_symbols_preserved; eauto. apply senv_preserved. - econstructor; eauto. - unfold loc_external_result. - apply agree_set_other; auto. apply agree_set_pair; auto. - -- (* return *) - inv STACKS. simpl in *. - right. split. omega. split. auto. - rewrite <- ATPC in H5. - econstructor; eauto. congruence. + exploit Mach_Machblock_tail; eauto. + destruct 1. + eapply Asmblockgenproof.return_address_exists; eauto. Qed. -Lemma transf_initial_states: - forall st1, Mach.initial_state prog st1 -> - exists st2, Asm.initial_state tprog st2 /\ match_states st1 st2. -Proof. - intros. inversion H. unfold ge0 in *. - econstructor; split. - econstructor. - eapply (Genv.init_mem_transf_partial TRANSF); eauto. - replace (Genv.symbol_address (Genv.globalenv tprog) (prog_main tprog) Ptrofs.zero) - with (Vptr fb Ptrofs.zero). - econstructor; eauto. - constructor. - apply Mem.extends_refl. - split. auto. simpl. unfold Vnullptr; destruct Archi.ptr64; congruence. - intros. rewrite Regmap.gi. auto. - unfold Genv.symbol_address. - rewrite (match_program_main TRANSF). - rewrite symbols_preserved. - unfold ge; rewrite H1. auto. -Qed. -Lemma transf_final_states: - forall st1 st2 r, - match_states st1 st2 -> Mach.final_state st1 r -> Asm.final_state st2 r. -Proof. - intros. inv H0. inv H. constructor. assumption. - compute in H1. inv H1. - generalize (preg_val _ _ _ R0 AG). rewrite H2. intros LD; inv LD. auto. -Qed. +Section PRESERVATION. + +Variable prog: Mach.program. +Variable tprog: program. +Hypothesis TRANSF: match_prog prog tprog. +Let ge := Genv.globalenv prog. +Let tge := Genv.globalenv tprog. Theorem transf_program_correct: forward_simulation (Mach.semantics return_address_offset prog) (Asm.semantics tprog). Proof. - eapply forward_simulation_star with (measure := measure). - apply senv_preserved. - eexact transf_initial_states. - eexact transf_final_states. - exact step_simulation. + unfold match_prog in TRANSF. simpl in TRANSF. + inv TRANSF. inv H. inv H1. inv H. inv H2. inv H. + eapply compose_forward_simulations. + exploit Machblockgenproof.transf_program_correct; eauto. + unfold Machblockgenproof.inv_trans_rao. + intros X; apply X. + eapply compose_forward_simulations. apply Asmblockgenproof.transf_program_correct; eauto. + apply Asm.transf_program_correct. eauto. Qed. End PRESERVATION. + +Instance TransfAsm: TransfLink match_prog := pass_match_link (compose_passes block_passes). + diff --git a/mppa_k1c/Machblock.v b/mppa_k1c/Machblock.v new file mode 100644 index 00000000..44cec642 --- /dev/null +++ b/mppa_k1c/Machblock.v @@ -0,0 +1,355 @@ +Require Import Coqlib. +Require Import Maps. +Require Import AST. +Require Import Integers. +Require Import Values. +Require Import Memory. +Require Import Globalenvs. +Require Import Events. +Require Import Smallstep. +Require Import Op. +Require Import Locations. +Require Import Conventions. +Require Stacklayout. +Require Import Mach. +Require Import Linking. + +(** instructions "basiques" (ie non control-flow) *) +Inductive basic_inst: Type := + | MBgetstack: ptrofs -> typ -> mreg -> basic_inst + | MBsetstack: mreg -> ptrofs -> typ -> basic_inst + | MBgetparam: ptrofs -> typ -> mreg -> basic_inst + | MBop: operation -> list mreg -> mreg -> basic_inst + | MBload: memory_chunk -> addressing -> list mreg -> mreg -> basic_inst + | MBstore: memory_chunk -> addressing -> list mreg -> mreg -> basic_inst + . + +Definition bblock_body := list basic_inst. + +(** instructions de control flow *) +Inductive control_flow_inst: Type := + | MBcall: signature -> mreg + ident -> control_flow_inst + | MBtailcall: signature -> mreg + ident -> control_flow_inst + | MBbuiltin: external_function -> list (builtin_arg mreg) -> builtin_res mreg -> control_flow_inst + | MBgoto: label -> control_flow_inst + | MBcond: condition -> list mreg -> label -> control_flow_inst + | MBjumptable: mreg -> list label -> control_flow_inst + | MBreturn: control_flow_inst + . + +Record bblock := mk_bblock { + header: list label; + body: bblock_body; + exit: option control_flow_inst +}. + +Lemma bblock_eq: + forall b1 b2, + header b1 = header b2 -> + body b1 = body b2 -> + exit b1 = exit b2 -> + b1 = b2. +Proof. + intros. destruct b1. destruct b2. + simpl in *. subst. auto. +Qed. + +Definition length_opt {A} (o: option A) : nat := + match o with + | Some o => 1 + | None => 0 + end. + +Definition size (b:bblock): nat := (length (header b))+(length (body b))+(length_opt (exit b)). + +Lemma size_null b: + size b = 0%nat -> + header b = nil /\ body b = nil /\ exit b = None. +Proof. + destruct b as [h b e]. simpl. unfold size. simpl. + intros H. + assert (length h = 0%nat) as Hh; [ omega |]. + assert (length b = 0%nat) as Hb; [ omega |]. + assert (length_opt e = 0%nat) as He; [ omega|]. + repeat split. + destruct h; try (simpl in Hh; discriminate); auto. + destruct b; try (simpl in Hb; discriminate); auto. + destruct e; try (simpl in He; discriminate); auto. +Qed. + +Definition code := list bblock. + +Record function: Type := mkfunction + { fn_sig: signature; + fn_code: code; + fn_stacksize: Z; + fn_link_ofs: ptrofs; + fn_retaddr_ofs: ptrofs }. + +Definition fundef := AST.fundef function. + +Definition program := AST.program fundef unit. + +Definition genv := Genv.t fundef unit. + +(*** sémantique ***) + +Lemma in_dec (lbl: label) (l: list label): { List.In lbl l } + { ~(List.In lbl l) }. +Proof. + apply List.in_dec. + apply Pos.eq_dec. +Qed. + +Definition is_label (lbl: label) (bb: bblock) : bool := + if in_dec lbl (header bb) then true else false. + +Lemma is_label_correct_true lbl bb: + List.In lbl (header bb) <-> is_label lbl bb = true. +Proof. + unfold is_label; destruct (in_dec lbl (header bb)); simpl; intuition. +Qed. + +Lemma is_label_correct_false lbl bb: + ~(List.In lbl (header bb)) <-> is_label lbl bb = false. +Proof. + unfold is_label; destruct (in_dec lbl (header bb)); simpl; intuition. +Qed. + + +Local Open Scope nat_scope. + +Fixpoint find_label (lbl: label) (c: code) {struct c} : option code := + match c with + | nil => None + | bb1 :: bbl => if is_label lbl bb1 then Some c else find_label lbl bbl + end. + +Section RELSEM. + +Variable rao:function -> code -> ptrofs -> Prop. +Variable ge:genv. + +Definition find_function_ptr + (ge: genv) (ros: mreg + ident) (rs: regset) : option block := + match ros with + | inl r => + match rs r with + | Vptr b ofs => if Ptrofs.eq ofs Ptrofs.zero then Some b else None + | _ => None + end + | inr symb => + Genv.find_symbol ge symb + end. + +(** Machblock execution states. *) + +Inductive stackframe: Type := + | Stackframe: + forall (f: block) (**r pointer to calling function *) + (sp: val) (**r stack pointer in calling function *) + (retaddr: val) (**r Asm return address in calling function *) + (c: code), (**r program point in calling function *) + stackframe. + +Inductive state: Type := + | State: + forall (stack: list stackframe) (**r call stack *) + (f: block) (**r pointer to current function *) + (sp: val) (**r stack pointer *) + (c: code) (**r current program point *) + (rs: regset) (**r register state *) + (m: mem), (**r memory state *) + state + | Callstate: + forall (stack: list stackframe) (**r call stack *) + (f: block) (**r pointer to function to call *) + (rs: regset) (**r register state *) + (m: mem), (**r memory state *) + state + | Returnstate: + forall (stack: list stackframe) (**r call stack *) + (rs: regset) (**r register state *) + (m: mem), (**r memory state *) + state. + +Definition parent_sp (s: list stackframe) : val := + match s with + | nil => Vnullptr + | Stackframe f sp ra c :: s' => sp + end. + +Definition parent_ra (s: list stackframe) : val := + match s with + | nil => Vnullptr + | Stackframe f sp ra c :: s' => ra + end. + +Inductive basic_step (s: list stackframe) (fb: block) (sp: val) (rs: regset) (m:mem): basic_inst -> regset -> mem -> Prop := + | exec_MBgetstack: + forall ofs ty dst v, + load_stack m sp ty ofs = Some v -> + basic_step s fb sp rs m (MBgetstack ofs ty dst) (rs#dst <- v) m + | exec_MBsetstack: + forall src ofs ty m' rs', + store_stack m sp ty ofs (rs src) = Some m' -> + rs' = undef_regs (destroyed_by_setstack ty) rs -> + basic_step s fb sp rs m (MBsetstack src ofs ty) rs' m' + | exec_MBgetparam: + forall ofs ty dst v rs' f, + Genv.find_funct_ptr ge fb = Some (Internal f) -> + load_stack m sp Tptr f.(fn_link_ofs) = Some (parent_sp s) -> + load_stack m (parent_sp s) ty ofs = Some v -> + rs' = (rs # temp_for_parent_frame <- Vundef # dst <- v) -> + basic_step s fb sp rs m (MBgetparam ofs ty dst) rs' m + | exec_MBop: + forall op args v rs' res, + eval_operation ge sp op rs##args m = Some v -> + rs' = ((undef_regs (destroyed_by_op op) rs)#res <- v) -> + basic_step s fb sp rs m (MBop op args res) rs' m + | exec_MBload: + forall addr args a v rs' chunk dst, + eval_addressing ge sp addr rs##args = Some a -> + Mem.loadv chunk m a = Some v -> + rs' = ((undef_regs (destroyed_by_load chunk addr) rs)#dst <- v) -> + basic_step s fb sp rs m (MBload chunk addr args dst) rs' m + | exec_MBstore: + forall chunk addr args src m' a rs', + eval_addressing ge sp addr rs##args = Some a -> + Mem.storev chunk m a (rs src) = Some m' -> + rs' = undef_regs (destroyed_by_store chunk addr) rs -> + basic_step s fb sp rs m (MBstore chunk addr args src) rs' m' + . + + +Inductive body_step (s: list stackframe) (f: block) (sp: val): bblock_body -> regset -> mem -> regset -> mem -> Prop := + | exec_nil_body: + forall rs m, + body_step s f sp nil rs m rs m + | exec_cons_body: + forall rs m bi p rs' m' rs'' m'', + basic_step s f sp rs m bi rs' m' -> + body_step s f sp p rs' m' rs'' m'' -> + body_step s f sp (bi::p) rs m rs'' m'' + . + +Inductive cfi_step: control_flow_inst -> state -> trace -> state -> Prop := + | exec_MBcall: + forall s fb sp sig ros c b rs m f f' ra, + find_function_ptr ge ros rs = Some f' -> + Genv.find_funct_ptr ge fb = Some (Internal f) -> + rao f c ra -> + cfi_step (MBcall sig ros) (State s fb sp (b::c) rs m) + E0 (Callstate (Stackframe fb sp (Vptr fb ra) c :: s) + f' rs m) + | exec_MBtailcall: + forall s fb stk soff sig ros c rs m f f' m', + find_function_ptr ge ros rs = Some f' -> + Genv.find_funct_ptr ge fb = Some (Internal f) -> + load_stack m (Vptr stk soff) Tptr f.(fn_link_ofs) = Some (parent_sp s) -> + load_stack m (Vptr stk soff) Tptr f.(fn_retaddr_ofs) = Some (parent_ra s) -> + Mem.free m stk 0 f.(fn_stacksize) = Some m' -> + cfi_step (MBtailcall sig ros) (State s fb (Vptr stk soff) c rs m) + E0 (Callstate s f' rs m') + | exec_MBbuiltin: + forall s f sp rs m ef args res b c vargs t vres rs' m', + eval_builtin_args ge rs sp m args vargs -> + external_call ef ge vargs m t vres m' -> + rs' = set_res res vres (undef_regs (destroyed_by_builtin ef) rs) -> + cfi_step (MBbuiltin ef args res) (State s f sp (b :: c) rs m) + t (State s f sp c rs' m') + | exec_MBgoto: + forall s fb f sp lbl c rs m c', + Genv.find_funct_ptr ge fb = Some (Internal f) -> + find_label lbl f.(fn_code) = Some c' -> + cfi_step (MBgoto lbl) (State s fb sp c rs m) + E0 (State s fb sp c' rs m) + | exec_MBcond_true: + forall s fb f sp cond args lbl c rs m c' rs', + eval_condition cond rs##args m = Some true -> + Genv.find_funct_ptr ge fb = Some (Internal f) -> + find_label lbl f.(fn_code) = Some c' -> + rs' = undef_regs (destroyed_by_cond cond) rs -> + cfi_step (MBcond cond args lbl) (State s fb sp c rs m) + E0 (State s fb sp c' rs' m) + | exec_MBcond_false: + forall s f sp cond args lbl b c rs m rs', + eval_condition cond rs##args m = Some false -> + rs' = undef_regs (destroyed_by_cond cond) rs -> + cfi_step (MBcond cond args lbl) (State s f sp (b :: c) rs m) + E0 (State s f sp c rs' m) + | exec_MBjumptable: + forall s fb f sp arg tbl c rs m n lbl c' rs', + rs arg = Vint n -> + list_nth_z tbl (Int.unsigned n) = Some lbl -> + Genv.find_funct_ptr ge fb = Some (Internal f) -> + find_label lbl f.(fn_code) = Some c' -> + rs' = undef_regs destroyed_by_jumptable rs -> + cfi_step (MBjumptable arg tbl) (State s fb sp c rs m) + E0 (State s fb sp c' rs' m) + | exec_MBreturn: + forall s fb stk soff c rs m f m', + Genv.find_funct_ptr ge fb = Some (Internal f) -> + load_stack m (Vptr stk soff) Tptr f.(fn_link_ofs) = Some (parent_sp s) -> + load_stack m (Vptr stk soff) Tptr f.(fn_retaddr_ofs) = Some (parent_ra s) -> + Mem.free m stk 0 f.(fn_stacksize) = Some m' -> + cfi_step MBreturn (State s fb (Vptr stk soff) c rs m) + E0 (Returnstate s rs m') + . + +Inductive exit_step: option control_flow_inst -> state -> trace -> state -> Prop := + | exec_Some_exit: + forall ctl s t s', + cfi_step ctl s t s' -> + exit_step (Some ctl) s t s' + | exec_None_exit: + forall stk f sp b lb rs m, + exit_step None (State stk f sp (b::lb) rs m) E0 (State stk f sp lb rs m) + . + +Inductive step: state -> trace -> state -> Prop := + | exec_bblock: + forall sf f sp bb c rs m rs' m' t s', + body_step sf f sp (body bb) rs m rs' m' -> + exit_step (exit bb) (State sf f sp (bb::c) rs' m') t s' -> + step (State sf f sp (bb::c) rs m) t s' + | exec_function_internal: + forall s fb rs m f m1 m2 m3 stk rs', + Genv.find_funct_ptr ge fb = Some (Internal f) -> + Mem.alloc m 0 f.(fn_stacksize) = (m1, stk) -> + let sp := Vptr stk Ptrofs.zero in + store_stack m1 sp Tptr f.(fn_link_ofs) (parent_sp s) = Some m2 -> + store_stack m2 sp Tptr f.(fn_retaddr_ofs) (parent_ra s) = Some m3 -> + rs' = undef_regs destroyed_at_function_entry rs -> + step (Callstate s fb rs m) + E0 (State s fb sp f.(fn_code) rs' m3) + | exec_function_external: + forall s fb rs m t rs' ef args res m', + Genv.find_funct_ptr ge fb = Some (External ef) -> + extcall_arguments rs m (parent_sp s) (ef_sig ef) args -> + external_call ef ge args m t res m' -> + rs' = set_pair (loc_result (ef_sig ef)) res rs -> + step (Callstate s fb rs m) + t (Returnstate s rs' m') + | exec_return: + forall s f sp ra c rs m, + step (Returnstate (Stackframe f sp ra c :: s) rs m) + E0 (State s f sp c rs m) + . + +End RELSEM. + +Inductive initial_state (p: program): state -> Prop := + | initial_state_intro: forall fb m0, + let ge := Genv.globalenv p in + Genv.init_mem p = Some m0 -> + Genv.find_symbol ge p.(prog_main) = Some fb -> + initial_state p (Callstate nil fb (Regmap.init Vundef) m0). + +Inductive final_state: state -> int -> Prop := + | final_state_intro: forall rs m r retcode, + loc_result signature_main = One r -> + rs r = Vint retcode -> + final_state (Returnstate nil rs m) retcode. + +Definition semantics (rao: function -> code -> ptrofs -> Prop) (p: program) := + Semantics (step rao) (initial_state p) final_state (Genv.globalenv p). diff --git a/mppa_k1c/Machblockgen.v b/mppa_k1c/Machblockgen.v new file mode 100644 index 00000000..1d5555df --- /dev/null +++ b/mppa_k1c/Machblockgen.v @@ -0,0 +1,578 @@ +Require Import Coqlib. +Require Import Maps. +Require Import AST. +Require Import Integers. +Require Import Values. +Require Import Memory. +Require Import Globalenvs. +Require Import Events. +Require Import Smallstep. +Require Import Op. +Require Import Locations. +Require Import Conventions. +Require Stacklayout. +Require Import Mach. +Require Import Linking. +Require Import Machblock. + + +Fixpoint to_bblock_header (c: Mach.code): list label * Mach.code := + match c with + | (Mlabel l)::c' => + let (h, c'') := to_bblock_header c' in + (l::h, c'') + | _ => (nil, c) + end. + +Definition to_basic_inst(i: Mach.instruction): option basic_inst := + match i with + | Mgetstack ofs ty dst => Some (MBgetstack ofs ty dst) + | Msetstack src ofs ty => Some (MBsetstack src ofs ty) + | Mgetparam ofs ty dst => Some (MBgetparam ofs ty dst) + | Mop op args res => Some (MBop op args res) + | Mload chunk addr args dst => Some (MBload chunk addr args dst) + | Mstore chunk addr args src => Some (MBstore chunk addr args src) + | _ => None + end. + +Fixpoint to_bblock_body(c: Mach.code): bblock_body * Mach.code := + match c with + | nil => (nil,nil) + | i::c' => + match to_basic_inst i with + | Some bi => + let (p,c'') := to_bblock_body c' in + (bi::p, c'') + | None => (nil, c) + end + end. + + +Definition to_cfi (i: Mach.instruction): option control_flow_inst := + match i with + | Mcall sig ros => Some (MBcall sig ros) + | Mtailcall sig ros => Some (MBtailcall sig ros) + | Mbuiltin ef args res => Some (MBbuiltin ef args res) + | Mgoto lbl => Some (MBgoto lbl) + | Mcond cond args lbl => Some (MBcond cond args lbl) + | Mjumptable arg tbl => Some (MBjumptable arg tbl) + | Mreturn => Some (MBreturn) + | _ => None + end. + +Definition to_bblock_exit (c: Mach.code): option control_flow_inst * Mach.code := + match c with + | nil => (None,nil) + | i::c' => + match to_cfi i with + | Some bi as o => (o, c') + | None => (None, c) + end + end. + +Inductive code_nature: Set := IsEmpty | IsLabel | IsBasicInst | IsCFI. + +Definition get_code_nature (c: Mach.code): code_nature := + match c with + | nil => IsEmpty + | (Mlabel _)::_ => IsLabel + | i::_ => match to_basic_inst i with + | Some _ => IsBasicInst + | None => IsCFI + end + end. + +Lemma cn_eqdec (cn1 cn2: code_nature): { cn1=cn2 } + {cn1 <> cn2}. +Proof. + decide equality. +Qed. + +Lemma get_code_nature_nil c: c<>nil -> get_code_nature c <> IsEmpty. +Proof. + intros H. unfold get_code_nature. + destruct c; try (contradict H; auto; fail). + destruct i; discriminate. +Qed. + +Lemma get_code_nature_empty c: get_code_nature c = IsEmpty -> c = nil. +Proof. + intros H. destruct c; auto. exploit (get_code_nature_nil (i::c)); discriminate || auto. + intro F. contradict F. +Qed. + +Lemma to_bblock_header_noLabel c: + get_code_nature c <> IsLabel -> + to_bblock_header c = (nil, c). +Proof. + intros H. destruct c as [|i c]; auto. + destruct i; simpl; auto. + contradict H; simpl; auto. +Qed. + +Lemma to_bblock_header_wfe c: + forall h c0, + to_bblock_header c = (h, c0) -> + (length c >= length c0)%nat. +Proof. + induction c as [ |i c]; simpl; intros h c' H. + - inversion H; subst; clear H; simpl; auto. + - destruct i; try (inversion H; subst; simpl; auto; fail). + remember (to_bblock_header c) as bhc; destruct bhc as [h0 c0]. + inversion H; subst. + lapply (IHc h0 c'); auto. +Qed. + +Lemma to_bblock_header_wf c b c0: + get_code_nature c = IsLabel -> + to_bblock_header c = (b, c0) -> + (length c > length c0)%nat. +Proof. + intros H1 H2; destruct c; [ contradict H1; simpl; discriminate | ]. + destruct i; try discriminate. + simpl in H2. + remember (to_bblock_header c) as bh; destruct bh as [h c'']. + inversion H2; subst. + exploit to_bblock_header_wfe; eauto. + simpl; omega. +Qed. + +Lemma to_bblock_body_noBasic c: + get_code_nature c <> IsBasicInst -> + to_bblock_body c = (nil, c). +Proof. + intros H. destruct c as [|i c]; simpl; auto. + destruct i; simpl; auto. + all: contradict H; simpl; auto. +Qed. + +Lemma to_bblock_body_wfe c b c0: + to_bblock_body c = (b, c0) -> + (length c >= length c0)%nat. +Proof. + generalize b c0; clear b c0. + induction c as [|i c]. + - intros b c0 H. simpl in H. inversion H; subst; auto. + - intros b c0 H. simpl in H. destruct (to_basic_inst i). + + remember (to_bblock_body c) as tbbc; destruct tbbc as [p c'']. + exploit (IHc p c''); auto. inversion H; subst; simpl; omega. + + inversion H; subst; auto. +Qed. + +(** Attempt to eliminate cons_to_bblock_body *) +(* +Lemma to_bblock_body_basic c: + get_code_nature c = IsBasicInst -> + exists i bi b c', + to_basic_inst i = Some bi + /\ c = i :: c' + /\ to_bblock_body c = (bi::b, snd (to_bblock_body c')). +Proof. + intros H. + destruct c as [|i c]; try (contradict H; simpl; discriminate). + destruct i eqn:I; try (contradict H; simpl; discriminate). + all: simpl; destruct (to_bblock_body c) as [p c''] eqn:TBBC; repeat (eapply ex_intro); (repeat split); + simpl; eauto; rewrite TBBC; simpl; eauto. +Qed. + +Lemma to_bblock_body_wf c b c0: + get_code_nature c = IsBasicInst -> + to_bblock_body c = (b, c0) -> + (length c > length c0)%nat. +Proof. + intros H1 H2; exploit to_bblock_body_basic; eauto. + intros X. destruct X as (i & bi & b' & c' & X1 & X2 & X3). + exploit to_bblock_body_wfe. eauto. subst. simpl. + rewrite X3 in H2. inversion H2; clear H2; subst. + simpl; omega. +Qed. +*) + +Inductive cons_to_bblock_body c0: Mach.code -> bblock_body -> Prop := + Cons_to_bbloc_body i bi c' b': + to_basic_inst i = Some bi + -> to_bblock_body c' = (b', c0) + -> cons_to_bblock_body c0 (i::c') (bi::b'). + +Lemma to_bblock_body_IsBasicInst c b c0: + get_code_nature c = IsBasicInst -> + to_bblock_body c = (b, c0) -> + cons_to_bblock_body c0 c b. +Proof. + intros H1 H2. destruct c; [ contradict H1; simpl; discriminate | ]. + remember (to_basic_inst i) as tbii. destruct tbii. + - simpl in H2. rewrite <- Heqtbii in H2. + remember (to_bblock_body c) as tbbc. destruct tbbc as [p1 c1]. + inversion H2. subst. eapply Cons_to_bbloc_body; eauto. + - destruct i; try discriminate. +Qed. + +Lemma to_bblock_body_wf c b c0: + get_code_nature c = IsBasicInst -> + to_bblock_body c = (b, c0) -> + (length c > length c0)%nat. +Proof. + intros H1 H2; exploit to_bblock_body_IsBasicInst; eauto. + intros X. destruct X. + exploit to_bblock_body_wfe; eauto. subst. simpl. + simpl; omega. +Qed. + +Lemma to_bblock_exit_noCFI c: + get_code_nature c <> IsCFI -> + to_bblock_exit c = (None, c). +Proof. + intros H. destruct c as [|i c]; simpl; auto. + destruct i; simpl; auto. + all: contradict H; simpl; auto. +Qed. + +Lemma to_bblock_exit_wf c b c0: + get_code_nature c = IsCFI -> + to_bblock_exit c = (b, c0) -> + (length c > length c0)%nat. +Proof. + intros H1 H2. destruct c as [|i c]; try discriminate. + destruct i; try discriminate; + unfold to_bblock_header in H2; inversion H2; auto. +Qed. + +Lemma to_bblock_exit_wfe c b c0: + to_bblock_exit c = (b, c0) -> + (length c >= length c0)%nat. +Proof. + intros H. destruct c as [|i c]. + - simpl in H. inversion H; subst; clear H; auto. + - destruct i; try ( simpl in H; inversion H; subst; clear H; auto ). + all: simpl; auto. +Qed. + +Definition to_bblock(c: Mach.code): bblock * Mach.code := + let (h,c0) := to_bblock_header c in + let (bdy, c1) := to_bblock_body c0 in + let (ext, c2) := to_bblock_exit c1 in + ({| header := h; body := bdy; exit := ext |}, c2) + . + +Lemma to_bblock_acc_label c l b c': + to_bblock c = (b, c') -> + to_bblock (Mlabel l :: c) = ({| header := l::(header b); body := (body b); exit := (exit b) |}, c'). +Proof. + unfold to_bblock; simpl. + remember (to_bblock_header c) as bhc; destruct bhc as [h c0]. + remember (to_bblock_body c0) as bbc; destruct bbc as [bdy c1]. + remember (to_bblock_exit c1) as bbc; destruct bbc as [ext c2]. + intros H; inversion H; subst; clear H; simpl; auto. +Qed. + +Lemma to_bblock_basic_then_label i c bi: + get_code_nature (i::c) = IsBasicInst -> + get_code_nature c = IsLabel -> + to_basic_inst i = Some bi -> + fst (to_bblock (i::c)) = {| header := nil; body := bi::nil; exit := None |}. +Proof. + intros H1 H2 H3. + destruct c as [|i' c]; try (contradict H1; simpl; discriminate). + destruct i'; try (contradict H1; simpl; discriminate). + destruct i; simpl in *; inversion H3; subst; auto. +Qed. + +Lemma to_bblock_CFI i c cfi: + get_code_nature (i::c) = IsCFI -> + to_cfi i = Some cfi -> + fst (to_bblock (i::c)) = {| header := nil; body := nil; exit := Some cfi |}. +Proof. + intros H1 H2. + destruct i; try discriminate. + all: subst; rewrite <- H2; simpl; auto. +Qed. + +Lemma to_bblock_noLabel c: + get_code_nature c <> IsLabel -> + fst (to_bblock c) = {| + header := nil; + body := body (fst (to_bblock c)); + exit := exit (fst (to_bblock c)) + |}. +Proof. + intros H. + destruct c as [|i c]; simpl; auto. + apply bblock_eq; simpl; + destruct i; ( + try ( + remember (to_bblock _) as bb; + unfold to_bblock in *; + remember (to_bblock_header _) as tbh; + destruct tbh; + destruct (to_bblock_body _); + destruct (to_bblock_exit _); + subst; simpl; inversion Heqtbh; auto; fail + ) + || contradict H; simpl; auto ). +Qed. + +Lemma to_bblock_body_nil c c': + to_bblock_body c = (nil, c') -> + c = c'. +Proof. + intros H. + destruct c as [|i c]; [ simpl in *; inversion H; auto |]. + destruct i; try ( simpl in *; remember (to_bblock_body c) as tbc; destruct tbc as [p c'']; inversion H ). + all: auto. +Qed. + +Lemma to_bblock_exit_nil c c': + to_bblock_exit c = (None, c') -> + c = c'. +Proof. + intros H. + destruct c as [|i c]; [ simpl in *; inversion H; auto |]. + destruct i; try ( simpl in *; remember (to_bblock_exit c) as tbe; destruct tbe as [p c'']; inversion H ). + all: auto. +Qed. + +Lemma to_bblock_label b l c c': + to_bblock (Mlabel l :: c) = (b, c') -> + (header b) = l::(tail (header b)) /\ to_bblock c = ({| header:=tail (header b); body := body b; exit := exit b |}, c'). +Proof. + unfold to_bblock; simpl. + remember (to_bblock_header c) as bhc; destruct bhc as [h c0]. + remember (to_bblock_body c0) as bbc; destruct bbc as [bdy c1]. + remember (to_bblock_exit c1) as bbc; destruct bbc as [ext c2]. + intros H; inversion H; subst; clear H; simpl; auto. +Qed. + +Lemma to_bblock_basic c i bi: + get_code_nature (i::c) = IsBasicInst -> + to_basic_inst i = Some bi -> + get_code_nature c <> IsLabel -> + fst (to_bblock (i::c)) = {| + header := nil; + body := bi :: body (fst (to_bblock c)); + exit := exit (fst (to_bblock c)) + |}. +Proof. + intros. + destruct c; try (destruct i; inversion H0; subst; simpl; auto; fail). + apply bblock_eq; simpl. +(* header *) + + destruct i; simpl; auto; ( + exploit to_bblock_noLabel; [rewrite H; discriminate | intro; rewrite H2; simpl; auto]). +(* body *) +(* FIXME - the proof takes some time to prove.. N² complexity :( *) + + unfold to_bblock. + remember (to_bblock_header _) as tbh; destruct tbh. + remember (to_bblock_body _) as tbb; destruct tbb. + remember (to_bblock_exit _) as tbe; destruct tbe. + simpl. + destruct i; destruct i0. + all: try (simpl in H1; contradiction). + all: try discriminate. + all: try ( + simpl in Heqtbh; inversion Heqtbh; clear Heqtbh; subst; + simpl in Heqtbb; remember (to_bblock_body c) as tbbc; destruct tbbc; + inversion Heqtbb; clear Heqtbb; subst; simpl in *; clear H H1; + inversion H0; clear H0; subst; destruct (to_bblock_body c); + inversion Heqtbbc; clear Heqtbbc; subst; + destruct (to_bblock_exit c1); simpl; auto; fail). +(* exit *) + + unfold to_bblock. + remember (to_bblock_header _) as tbh; destruct tbh. + remember (to_bblock_body _) as tbb; destruct tbb. + remember (to_bblock_exit _) as tbe; destruct tbe. + simpl. + destruct i; destruct i0. + all: try (simpl in H1; contradiction). + all: try discriminate. + all: try ( + simpl in Heqtbh; inversion Heqtbh; clear Heqtbh; subst; + simpl in Heqtbb; remember (to_bblock_body c) as tbbc; destruct tbbc; + inversion Heqtbb; clear Heqtbb; subst; simpl in *; clear H H1; + inversion H0; clear H0; subst; destruct (to_bblock_body c) eqn:TBBC; + inversion Heqtbbc; clear Heqtbbc; subst; + destruct (to_bblock_exit c1) eqn:TBBE; simpl; + inversion Heqtbe; clear Heqtbe; subst; auto; fail). +Qed. + +Lemma to_bblock_size_single_label c i: + get_code_nature (i::c) = IsLabel -> + size (fst (to_bblock (i::c))) = Datatypes.S (size (fst (to_bblock c))). +Proof. + intros H. + destruct i; try discriminate. + remember (to_bblock c) as bl. destruct bl as [b c']. + erewrite to_bblock_acc_label; eauto. + unfold size; simpl. + auto. +Qed. + +Lemma to_bblock_size_label_neqz c: + get_code_nature c = IsLabel -> + size (fst (to_bblock c)) <> 0%nat. +Proof. + destruct c as [ |i c]; try discriminate. + intros; rewrite to_bblock_size_single_label; auto. +Qed. + +Lemma to_bblock_size_basic_neqz c: + get_code_nature c = IsBasicInst -> + size (fst (to_bblock c)) <> 0%nat. +Proof. + intros H. destruct c as [|i c]; try (contradict H; auto; simpl; discriminate). + destruct i; try (contradict H; simpl; discriminate); + ( + destruct (get_code_nature c) eqn:gcnc; + (* Case gcnc is not IsLabel *) + try (erewrite to_bblock_basic; eauto; [ + unfold size; simpl; auto + | simpl; auto + | rewrite gcnc; discriminate + ]); + erewrite to_bblock_basic_then_label; eauto; [ + unfold size; simpl; auto + | simpl; auto + ] + ). +Qed. + +Lemma to_bblock_size_cfi_neqz c: + get_code_nature c = IsCFI -> + size (fst (to_bblock c)) <> 0%nat. +Proof. + intros H. destruct c as [|i c]; try (contradict H; auto; simpl; discriminate). + destruct i; discriminate. +Qed. + +Lemma to_bblock_size_single_basic c i: + get_code_nature (i::c) = IsBasicInst -> + get_code_nature c <> IsLabel -> + size (fst (to_bblock (i::c))) = Datatypes.S (size (fst (to_bblock c))). +Proof. + intros. + destruct i; try (contradict H; simpl; discriminate); try ( + (exploit to_bblock_basic; eauto); + [remember (to_basic_inst _) as tbi; destruct tbi; eauto |]; + intro; rewrite H1; unfold size; simpl; + assert ((length (header (fst (to_bblock c)))) = 0%nat); + exploit to_bblock_noLabel; eauto; intro; rewrite H2; simpl; auto; + rewrite H2; auto + ). +Qed. + +Lemma to_bblock_wf c b c0: + c <> nil -> + to_bblock c = (b, c0) -> + (length c > length c0)%nat. +Proof. + intro H; lapply (get_code_nature_nil c); eauto. + intro H'; remember (get_code_nature c) as gcn. + unfold to_bblock. + remember (to_bblock_header c) as p1; eauto. + destruct p1 as [h c1]. + intro H0. + destruct gcn. + - contradict H'; auto. + - exploit to_bblock_header_wf; eauto. + remember (to_bblock_body c1) as p2; eauto. + destruct p2 as [h2 c2]. + exploit to_bblock_body_wfe; eauto. + remember (to_bblock_exit c2) as p3; eauto. + destruct p3 as [h3 c3]. + exploit to_bblock_exit_wfe; eauto. + inversion H0. omega. + - exploit to_bblock_header_noLabel; eauto. rewrite <- Heqgcn. discriminate. + intro. rewrite H1 in Heqp1. inversion Heqp1. clear Heqp1. subst. + remember (to_bblock_body c) as p2; eauto. + destruct p2 as [h2 c2]. + exploit to_bblock_body_wf; eauto. + remember (to_bblock_exit c2) as p3; eauto. + destruct p3 as [h3 c3]. + exploit to_bblock_exit_wfe; eauto. + inversion H0. omega. + - exploit to_bblock_header_noLabel; eauto. rewrite <- Heqgcn. discriminate. + intro. rewrite H1 in Heqp1. inversion Heqp1; clear Heqp1; subst. + remember (to_bblock_body c) as p2; eauto. + destruct p2 as [h2 c2]. + exploit (to_bblock_body_noBasic c); eauto. rewrite <- Heqgcn. discriminate. + intros H2; rewrite H2 in Heqp2; inversion Heqp2; clear Heqp2; subst. + remember (to_bblock_exit c) as p3; eauto. + destruct p3 as [h3 c3]. + exploit (to_bblock_exit_wf c h3 c3); eauto. + inversion H0. omega. +Qed. + +Lemma to_bblock_nonil i c0: + size (fst (to_bblock (i :: c0))) <> 0%nat. +Proof. + intros H. remember (i::c0) as c. remember (get_code_nature c) as gcnc. destruct gcnc. + - contradict Heqgcnc. subst. simpl. destruct i; discriminate. + - eapply to_bblock_size_label_neqz; eauto. + - eapply to_bblock_size_basic_neqz; eauto. + - eapply to_bblock_size_cfi_neqz; eauto. +Qed. + +Function trans_code (c: Mach.code) { measure length c }: code := + match c with + | nil => nil + | _ => + let (b, c0) := to_bblock c in + b::(trans_code c0) + end. +Proof. + intros; eapply to_bblock_wf; eauto. discriminate. +Qed. + +Lemma trans_code_nonil c: + c <> nil -> trans_code c <> nil. +Proof. + intros H. + induction c, (trans_code c) using trans_code_ind; simpl; auto. discriminate. +Qed. + +Lemma trans_code_step c b lb0 hb c1 bb c2 eb c3: + trans_code c = b :: lb0 -> + to_bblock_header c = (hb, c1) -> + to_bblock_body c1 = (bb, c2) -> + to_bblock_exit c2 = (eb, c3) -> + hb = header b /\ bb = body b /\ eb = exit b /\ trans_code c3 = lb0. +Proof. + intros. + induction c, (trans_code c) using trans_code_ind. discriminate. clear IHc0. + subst. destruct _x as [|i c]; try (contradict y; auto; fail). + inversion H; subst. clear H. unfold to_bblock in e0. + remember (to_bblock_header (i::c)) as hd. destruct hd as [hb' c1']. + remember (to_bblock_body c1') as bd. destruct bd as [bb' c2']. + remember (to_bblock_exit c2') as be. destruct be as [eb' c3']. + inversion e0. simpl. + inversion H0. subst. + rewrite <- Heqbd in H1. inversion H1. subst. + rewrite <- Heqbe in H2. inversion H2. subst. + auto. +Qed. + +Lemma trans_code_cfi i c cfi: + to_cfi i = Some cfi -> + trans_code (i :: c) = {| header := nil ; body := nil ; exit := Some cfi |} :: trans_code c. +Proof. + intros. rewrite trans_code_equation. remember (to_bblock _) as tb; destruct tb as [b c0]. + destruct i; try (contradict H; discriminate). + all: unfold to_bblock in Heqtb; remember (to_bblock_header _) as tbh; destruct tbh as [h c0']; + remember (to_bblock_body c0') as tbb; destruct tbb as [bdy c1']; + remember (to_bblock_exit c1') as tbe; destruct tbe as [ext c2]; simpl in *; + inversion Heqtbh; subst; inversion Heqtbb; subst; inversion Heqtbe; subst; + inversion Heqtb; subst; rewrite H; auto. +Qed. + +(* à finir pour passer des Mach.function au function, etc. *) +Definition transf_function (f: Mach.function) : function := + {| fn_sig:=Mach.fn_sig f; + fn_code:=trans_code (Mach.fn_code f); + fn_stacksize := Mach.fn_stacksize f; + fn_link_ofs := Mach.fn_link_ofs f; + fn_retaddr_ofs := Mach.fn_retaddr_ofs f + |}. + +Definition transf_fundef (f: Mach.fundef) : fundef := + transf_fundef transf_function f. + +Definition transf_program (src: Mach.program) : program := + transform_program transf_fundef src. diff --git a/mppa_k1c/Machblockgenproof.v b/mppa_k1c/Machblockgenproof.v new file mode 100644 index 00000000..62c1e0ed --- /dev/null +++ b/mppa_k1c/Machblockgenproof.v @@ -0,0 +1,629 @@ +Require Import Coqlib. +Require Import Maps. +Require Import AST. +Require Import Integers. +Require Import Values. +Require Import Memory. +Require Import Globalenvs. +Require Import Events. +Require Import Smallstep. +Require Import Op. +Require Import Locations. +Require Import Conventions. +Require Stacklayout. +Require Import Mach. +Require Import Linking. +Require Import Machblock. +Require Import Machblockgen. +Require Import ForwardSimulationBlock. + +Definition inv_trans_rao (rao: function -> code -> ptrofs -> Prop) (f: Mach.function) (c: Mach.code) := + rao (transf_function f) (trans_code c). + +Definition match_prog (p: Mach.program) (tp: Machblock.program) := + match_program (fun _ f tf => tf = transf_fundef f) eq p tp. + +Lemma transf_program_match: forall p tp, transf_program p = tp -> match_prog p tp. +Proof. + intros. rewrite <- H. eapply match_transform_program; eauto. +Qed. + +Definition trans_stackframe (msf: Mach.stackframe) : stackframe := + match msf with + | Mach.Stackframe f sp retaddr c => Stackframe f sp retaddr (trans_code c) + end. + +Fixpoint trans_stack (mst: list Mach.stackframe) : list stackframe := + match mst with + | nil => nil + | msf :: mst0 => (trans_stackframe msf) :: (trans_stack mst0) + end. + +Definition trans_state (ms: Mach.state) : state := + match ms with + | Mach.State s f sp c rs m => State (trans_stack s) f sp (trans_code c) rs m + | Mach.Callstate s f rs m => Callstate (trans_stack s) f rs m + | Mach.Returnstate s rs m => Returnstate (trans_stack s) rs m + end. + +Section PRESERVATION. + +Local Open Scope nat_scope. + +Variable prog: Mach.program. +Variable tprog: Machblock.program. +Hypothesis TRANSF: match_prog prog tprog. +Let ge := Genv.globalenv prog. +Let tge := Genv.globalenv tprog. + + +Variable rao: function -> code -> ptrofs -> Prop. + +Definition match_states: Mach.state -> state -> Prop + := ForwardSimulationBlock.match_states (Mach.semantics (inv_trans_rao rao) prog) (Machblock.semantics rao tprog) trans_state. + +Lemma match_states_trans_state s1: match_states s1 (trans_state s1). +Proof. + apply match_states_trans_state. +Qed. + +Local Hint Resolve match_states_trans_state. + +Lemma symbols_preserved: + forall (s: ident), Genv.find_symbol tge s = Genv.find_symbol ge s. +Proof (Genv.find_symbol_match TRANSF). + +Lemma senv_preserved: + Senv.equiv ge tge. +Proof (Genv.senv_match TRANSF). + +Lemma init_mem_preserved: + forall m, + Genv.init_mem prog = Some m -> + Genv.init_mem tprog = Some m. +Proof (Genv.init_mem_transf TRANSF). + +Lemma prog_main_preserved: + prog_main tprog = prog_main prog. +Proof (match_program_main TRANSF). + +Lemma functions_translated: + forall b f, + Genv.find_funct_ptr ge b = Some f -> + exists tf, Genv.find_funct_ptr tge b = Some tf /\ transf_fundef f = tf. +Proof. + intros. + exploit (Genv.find_funct_ptr_match TRANSF); eauto. intro. + destruct H0 as (cunit & tf & A & B & C). + eapply ex_intro. intuition; eauto. subst. eapply A. +Qed. + +Lemma find_function_ptr_same: + forall s rs, + Mach.find_function_ptr ge s rs = find_function_ptr tge s rs. +Proof. + intros. unfold Mach.find_function_ptr. unfold find_function_ptr. + destruct s; auto. + rewrite symbols_preserved; auto. +Qed. + +Lemma find_funct_ptr_same: + forall f f0, + Genv.find_funct_ptr ge f = Some (Internal f0) -> + Genv.find_funct_ptr tge f = Some (Internal (transf_function f0)). +Proof. + intros. exploit (Genv.find_funct_ptr_transf TRANSF); eauto. +Qed. + +Lemma find_funct_ptr_same_external: + forall f f0, + Genv.find_funct_ptr ge f = Some (External f0) -> + Genv.find_funct_ptr tge f = Some (External f0). +Proof. + intros. exploit (Genv.find_funct_ptr_transf TRANSF); eauto. +Qed. + +Lemma parent_sp_preserved: + forall s, + Mach.parent_sp s = parent_sp (trans_stack s). +Proof. + unfold parent_sp. unfold Mach.parent_sp. destruct s; simpl; auto. + unfold trans_stackframe. destruct s; simpl; auto. +Qed. + +Lemma parent_ra_preserved: + forall s, + Mach.parent_ra s = parent_ra (trans_stack s). +Proof. + unfold parent_ra. unfold Mach.parent_ra. destruct s; simpl; auto. + unfold trans_stackframe. destruct s; simpl; auto. +Qed. + +Lemma external_call_preserved: + forall ef args m t res m', + external_call ef ge args m t res m' -> + external_call ef tge args m t res m'. +Proof. + intros. eapply external_call_symbols_preserved; eauto. + apply senv_preserved. +Qed. + +Lemma Mach_find_label_split l i c c': + Mach.find_label l (i :: c) = Some c' -> + (i=Mlabel l /\ c' = c) \/ (i <> Mlabel l /\ Mach.find_label l c = Some c'). +Proof. + intros H. + destruct i; try (constructor 2; split; auto; discriminate ). + destruct (peq l0 l) as [P|P]. + - constructor. subst l0; split; auto. + revert H. unfold Mach.find_label. simpl. rewrite peq_true. + intros H; injection H; auto. + - constructor 2. split. + + intro F. injection F. intros. contradict P; auto. + + revert H. unfold Mach.find_label. simpl. rewrite peq_false; auto. +Qed. + + +Definition concat (h: list label) (c: code): code := + match c with + | nil => {| header := h; body := nil; exit := None |}::nil + | b::c' => {| header := h ++ (header b); body := body b; exit := exit b |}::c' + end. + +Lemma to_bblock_start_label i c l b c0: + (b, c0) = to_bblock (i :: c) + -> In l (header b) + -> i <> Mlabel l + -> exists l2, i=Mlabel l2. +Proof. + unfold to_bblock. + remember (to_bblock_header _) as bh; destruct bh as [h c1]. + remember (to_bblock_body _) as bb; destruct bb as [bdy c2]. + remember (to_bblock_exit _) as be; destruct be as [ext c3]. + intros H; inversion H; subst; clear H; simpl. + destruct i; try (simpl in Heqbh; inversion Heqbh; subst; clear Heqbh; simpl; intuition eauto). +Qed. + +Lemma find_label_stop c: + forall l b c0 c', + (b, c0) = to_bblock c + -> Mach.find_label l c = Some c' + -> In l (header b) + -> exists h, In l h /\ Some (b :: trans_code c0) = Some (concat h (trans_code c')). +Proof. + induction c as [ |i c]. + - simpl; intros; discriminate. + - intros l b c0 c' H H1 H2. + exploit Mach_find_label_split; eauto; clear H1. + intros [(X1 & X2) | (X1 & X2)]. + * subst. exploit to_bblock_label; eauto. clear H. + intros (H3 & H4). constructor 1 with (x:=l::nil); simpl; intuition auto. + symmetry. + rewrite trans_code_equation. + destruct c as [ |i c]. + + unfold to_bblock in H4; simpl in H4. + injection H4. clear H4; intros H4 H H0 H1; subst. simpl. + rewrite trans_code_equation; simpl. + rewrite <- H1 in H3; clear H1. + destruct b as [h b e]; simpl in * |- *; subst; auto. + + rewrite H4; clear H4; simpl. rewrite <- H3; clear H3. + destruct b; simpl; auto. + * exploit to_bblock_start_label; eauto. + intros (l' & H'). subst. + assert (X: l' <> l). { intro Z; subst; destruct X1; auto. } + clear X1. + exploit to_bblock_label; eauto. clear H. + intros (H3 & H4). + exploit IHc; eauto. { simpl. rewrite H3 in H2; simpl in H2. destruct H2; subst; tauto. } + intros (h' & H5 & H6). + constructor 1 with (x:=l'::h'); simpl; intuition auto. + destruct b as [h b e]; simpl in * |- *; subst. + remember (tl h) as th. subst h. + remember (trans_code c') as tcc'. + rewrite trans_code_equation in Heqtcc'. + destruct c'; subst; simpl in * |- *. + + inversion H6; subst; auto. + + destruct (to_bblock (i :: c')) as [b1 c1]. simpl in * |- *. + inversion H6; subst; auto. +Qed. + +Lemma to_bblock_header_find_label c l: forall c1 h c', + to_bblock_header c = (h, c1) + -> Mach.find_label l c = Some c' + -> ~ In l h + -> Mach.find_label l c = Mach.find_label l c1. +Proof. + induction c as [|i c]; simpl; auto. + - intros; discriminate. + - destruct i; + try (simpl; intros c1 h c' H1 H2; inversion H1; subst; clear H1; intros; apply refl_equal). + remember (to_bblock_header c) as tbhc. destruct tbhc as [h2 c2]. + intros h c1 c' H1; inversion H1; subst; clear H1. + simpl. destruct (peq _ _). + + subst; tauto. + + intros H1 H2; erewrite IHc; eauto. +Qed. + +Lemma to_bblock_body_find_label c1 l: forall c2 bdy, + (bdy, c2) = to_bblock_body c1 -> + Mach.find_label l c1 = Mach.find_label l c2. +Proof. + induction c1 as [|i c1]. + - intros bdy0 c0 H. simpl in H. inversion H; subst; clear H. auto. + - intros bdy' c2' H. simpl in H. destruct i; try ( + simpl in H; remember (to_bblock_body c1) as tbb; destruct tbb as [p c'']; + inversion H; subst; clear H; simpl; erewrite IHc1; eauto; fail). +Qed. + +Lemma to_bblock_exit_find_label c1 l c2 ext: + (ext, c2) = to_bblock_exit c1 + -> Mach.find_label l c1 = Mach.find_label l c2. +Proof. + intros H. destruct c1 as [|i c1]. + - simpl in H. inversion H; subst; clear H. auto. + - destruct i; try ( + simpl in H; inversion H; subst; clear H; auto; fail). +Qed. + +Lemma find_label_transcode_preserved: + forall l c c', + Mach.find_label l c = Some c' -> + exists h, In l h /\ find_label l (trans_code c) = Some (concat h (trans_code c')). +Proof. + intros l c; induction c, (trans_code c) using trans_code_ind. + - intros c' H; inversion H. + - intros c' H. subst _x. destruct c as [| i c]; try tauto. + unfold to_bblock in * |-. + remember (to_bblock_header _) as bh; destruct bh as [h c1]. + remember (to_bblock_body _) as bb; destruct bb as [bdy c2]. + remember (to_bblock_exit _) as be; destruct be as [ext c3]. + simpl; injection e0; intros; subst; clear e0. + unfold is_label; simpl; destruct (in_dec l h) as [Y|Y]. + + clear IHc0. + eapply find_label_stop; eauto. + unfold to_bblock. + rewrite <- Heqbh, <- Heqbb, <- Heqbe. + auto. + + exploit IHc0; eauto. clear IHc0. + rewrite <- H. + erewrite (to_bblock_header_find_label (i::c) l c1); eauto. + erewrite (to_bblock_body_find_label c1 l c2); eauto. + erewrite (to_bblock_exit_find_label c2 l c0); eauto. +Qed. + + +Lemma find_label_preserved: + forall l f c, + Mach.find_label l (Mach.fn_code f) = Some c -> + exists h, In l h /\ find_label l (fn_code (transf_function f)) = Some (concat h (trans_code c)). +Proof. + intros. cutrewrite ((fn_code (transf_function f)) = trans_code (Mach.fn_code f)); eauto. + apply find_label_transcode_preserved; auto. +Qed. + +Lemma mem_free_preserved: + forall m stk f, + Mem.free m stk 0 (Mach.fn_stacksize f) = Mem.free m stk 0 (fn_stacksize (transf_function f)). +Proof. + intros. auto. +Qed. + +Local Hint Resolve symbols_preserved senv_preserved init_mem_preserved prog_main_preserved functions_translated + parent_sp_preserved. + +Definition dist_end_block_code (c: Mach.code) := (size (fst (to_bblock c))-1)%nat. + + +Definition dist_end_block (s: Mach.state): nat := + match s with + | Mach.State _ _ _ c _ _ => dist_end_block_code c + | _ => 0 + end. + +Local Hint Resolve exec_nil_body exec_cons_body. +Local Hint Resolve exec_MBgetstack exec_MBsetstack exec_MBgetparam exec_MBop exec_MBload exec_MBstore. + +Ltac ExploitDistEndBlockCode := + match goal with + | [ H : dist_end_block_code (Mlabel ?l :: ?c) <> 0%nat |- _ ] => + exploit (to_bblock_size_single_label c (Mlabel l)); eauto + | [ H : dist_end_block_code (?i0 :: ?c) <> 0%nat |- _ ] => + exploit (to_bblock_size_single_basic c i0); eauto + | _ => idtac + end. + +Ltac totologize H := + match type of H with + | ( ?id = _ ) => + let Hassert := fresh "Htoto" in ( + assert (id = id) as Hassert; auto; rewrite H in Hassert at 2; simpl in Hassert; rewrite H in Hassert) + end. + +Lemma dist_end_block_code_simu_mid_block i c: + dist_end_block_code (i::c) <> 0 -> + (dist_end_block_code (i::c) = Datatypes.S (dist_end_block_code c)). +Proof. + intros H. + unfold dist_end_block_code. + destruct (get_code_nature (i::c)) eqn:GCNIC. + - apply get_code_nature_empty in GCNIC. discriminate. + - rewrite to_bblock_size_single_label; auto. + destruct c as [|i' c]. + + contradict H. destruct i; simpl; auto. + + assert (size (fst (to_bblock (i'::c))) <> 0). apply to_bblock_nonil. omega. + - destruct (get_code_nature c) eqn:GCNC. + + apply get_code_nature_empty in GCNC. subst. contradict H. destruct i; simpl; auto. + + contradict H. destruct c as [|i' c]; try discriminate. + destruct i'; try discriminate. + destruct i; try discriminate. all: simpl; auto. + + destruct (to_basic_inst i) eqn:TBI; [| destruct i; discriminate]. + erewrite to_bblock_basic; eauto; [| rewrite GCNC; discriminate ]. + simpl. destruct c as [|i' c]; try discriminate. + assert (size (fst (to_bblock (i'::c))) <> 0). apply to_bblock_nonil. + cutrewrite (Datatypes.S (size (fst (to_bblock (i'::c))) - 1) = size (fst (to_bblock (i'::c)))). + unfold size. cutrewrite (length (header (fst (to_bblock (i' :: c)))) = 0). simpl. omega. + rewrite to_bblock_noLabel. simpl; auto. + rewrite GCNC. discriminate. + omega. + + destruct (to_basic_inst i) eqn:TBI; [| destruct i; discriminate]. + erewrite to_bblock_basic; eauto; [| rewrite GCNC; discriminate ]. + simpl. destruct c as [|i' c]; try discriminate. + assert (size (fst (to_bblock (i'::c))) <> 0). apply to_bblock_nonil. + cutrewrite (Datatypes.S (size (fst (to_bblock (i'::c))) - 1) = size (fst (to_bblock (i'::c)))). + unfold size. cutrewrite (length (header (fst (to_bblock (i' :: c)))) = 0). simpl. omega. + rewrite to_bblock_noLabel. simpl; auto. + rewrite GCNC. discriminate. + omega. + - contradict H. destruct i; try discriminate. + all: unfold dist_end_block_code; erewrite to_bblock_CFI; eauto; simpl; eauto. +Qed. + +Local Hint Resolve dist_end_block_code_simu_mid_block. + +Lemma step_simu_basic_step (i: Mach.instruction) (bi: basic_inst) (c: Mach.code) s f sp rs m (t:trace) (s':Mach.state): + to_basic_inst i = Some bi -> + Mach.step (inv_trans_rao rao) ge (Mach.State s f sp (i::c) rs m) t s' -> + exists rs' m', s'=Mach.State s f sp c rs' m' /\ t=E0 /\ basic_step tge (trans_stack s) f sp rs m bi rs' m'. +Proof. + destruct i; simpl in * |-; + (discriminate + || (intro H; inversion_clear H; intro X; inversion_clear X; eapply ex_intro; eapply ex_intro; intuition eauto)). + - eapply exec_MBgetparam; eauto. exploit (functions_translated); eauto. intro. + destruct H3 as (tf & A & B). subst. eapply A. + all: simpl; rewrite <- parent_sp_preserved; auto. + - eapply exec_MBop; eauto. rewrite <- H. destruct o; simpl; auto. destruct (rs ## l); simpl; auto. + unfold Genv.symbol_address; rewrite symbols_preserved; auto. + - eapply exec_MBload; eauto; rewrite <- H; destruct a; simpl; auto; destruct (rs ## l); simpl; auto; + unfold Genv.symbol_address; rewrite symbols_preserved; auto. + - eapply exec_MBstore; eauto; rewrite <- H; destruct a; simpl; auto; destruct (rs ## l); simpl; auto; + unfold Genv.symbol_address; rewrite symbols_preserved; auto. +Qed. + + +Lemma star_step_simu_body_step s f sp c: + forall (p:bblock_body) c' rs m t s', + to_bblock_body c = (p, c') -> + starN (Mach.step (inv_trans_rao rao)) ge (length p) (Mach.State s f sp c rs m) t s' -> + exists rs' m', s'=Mach.State s f sp c' rs' m' /\ t=E0 /\ body_step tge (trans_stack s) f sp p rs m rs' m'. +Proof. + induction c as [ | i0 c0 Hc0]; simpl; intros p c' rs m t s' H. + * (* nil *) + inversion_clear H; simpl; intros X; inversion_clear X. + eapply ex_intro; eapply ex_intro; intuition eauto. + * (* cons *) + remember (to_basic_inst i0) as o eqn:Ho. + destruct o as [bi |]. + + (* to_basic_inst i0 = Some bi *) + remember (to_bblock_body c0) as r eqn:Hr. + destruct r as [p1 c1]; inversion H; simpl; subst; clear H. + intros X; inversion_clear X. + exploit step_simu_basic_step; eauto. + intros [rs' [m' [H2 [H3 H4]]]]; subst. + exploit Hc0; eauto. + intros [rs'' [m'' [H5 [H6 H7]]]]; subst. + refine (ex_intro _ rs'' (ex_intro _ m'' _)); intuition eauto. + + (* to_basic_inst i0 = None *) + inversion_clear H; simpl. + intros X; inversion_clear X. intuition eauto. +Qed. + +Local Hint Resolve exec_MBcall exec_MBtailcall exec_MBbuiltin exec_MBgoto exec_MBcond_true exec_MBcond_false exec_MBjumptable exec_MBreturn exec_Some_exit exec_None_exit. +Local Hint Resolve eval_builtin_args_preserved external_call_symbols_preserved find_funct_ptr_same. + +Lemma match_states_concat_trans_code st f sp c rs m h: + match_states (Mach.State st f sp c rs m) (State (trans_stack st) f sp (concat h (trans_code c)) rs m). +Proof. + constructor 1; simpl. + + intros (t0 & s1' & H0) t s'. + rewrite! trans_code_equation. + destruct c as [| i c]. { inversion H0. } + remember (to_bblock (i :: c)) as bic. destruct bic as [b c0]. + simpl. + constructor 1; intros H; inversion H; subst; simpl in * |- *; + eapply exec_bblock; eauto. + - inversion H11; subst; eauto. + inversion H2; subst; eauto. + - inversion H11; subst; simpl; eauto. + inversion H2; subst; simpl; eauto. + + intros H r; constructor 1; intro X; inversion X. +Qed. + +Lemma step_simu_cfi_step: + forall c e c' stk f sp rs m t s' b lb', + to_bblock_exit c = (Some e, c') -> + trans_code c' = lb' -> + Mach.step (inv_trans_rao rao) ge (Mach.State stk f sp c rs m) t s' -> + exists s2, cfi_step rao tge e (State (trans_stack stk) f sp (b::lb') rs m) t s2 /\ match_states s' s2. +Proof. + intros c e c' stk f sp rs m t s' b lb'. + intros Hexit Htc Hstep. + destruct c as [|ei c]; try (contradict Hexit; discriminate). + destruct ei; (contradict Hexit; discriminate) || ( + inversion Hexit; subst; inversion Hstep; subst; simpl + ). + * eapply ex_intro; constructor 1; [ idtac | eapply match_states_trans_state ]; eauto. + apply exec_MBcall with (f := (transf_function f0)); auto. + rewrite find_function_ptr_same in H9; auto. + * eapply ex_intro; constructor 1; [ idtac | eapply match_states_trans_state ]; eauto. + apply exec_MBtailcall with (f := (transf_function f0)); auto. + rewrite find_function_ptr_same in H9; auto. + rewrite parent_sp_preserved in H11; subst; auto. + rewrite parent_ra_preserved in H12; subst; auto. + * eapply ex_intro; constructor 1; [ idtac | eapply match_states_trans_state ]; eauto. + eapply exec_MBbuiltin; eauto. + * exploit find_label_transcode_preserved; eauto. intros (h & X1 & X2). + eapply ex_intro; constructor 1; [ idtac | eapply match_states_concat_trans_code ]; eauto. + * exploit find_label_transcode_preserved; eauto. intros (h & X1 & X2). + eapply ex_intro; constructor 1; [ idtac | eapply match_states_concat_trans_code ]; eauto. + * eapply ex_intro; constructor 1; [ idtac | eapply match_states_trans_state ]; eauto. + eapply exec_MBcond_false; eauto. + * exploit find_label_transcode_preserved; eauto. intros (h & X1 & X2). + eapply ex_intro; constructor 1; [ idtac | eapply match_states_concat_trans_code ]; eauto. + * eapply ex_intro; constructor 1; [ idtac | eapply match_states_trans_state ]; eauto. + eapply exec_MBreturn; eauto. + rewrite parent_sp_preserved in H8; subst; auto. + rewrite parent_ra_preserved in H9; subst; auto. +Qed. + + + +Lemma step_simu_exit_step c e c' stk f sp rs m t s' b: + to_bblock_exit c = (e, c') -> + starN (Mach.step (inv_trans_rao rao)) (Genv.globalenv prog) (length_opt e) (Mach.State stk f sp c rs m) t s' -> + exists s2, exit_step rao tge e (State (trans_stack stk) f sp (b::trans_code c') rs m) t s2 /\ match_states s' s2. +Proof. + intros H1 H2; destruct e as [ e |]; inversion_clear H2. + + (* Some *) inversion H0; clear H0; subst. autorewrite with trace_rewrite. + exploit step_simu_cfi_step; eauto. + intros (s2' & H2 & H3); eapply ex_intro; intuition eauto. + + (* None *) + destruct c as [ |i c]; simpl in H1; inversion H1. + - eapply ex_intro; intuition eauto; try eapply match_states_trans_state. + - remember to_cfi as o. destruct o; try discriminate. + inversion_clear H1. + eapply ex_intro; intuition eauto; try eapply match_states_trans_state. +Qed. + +Lemma step_simu_header st f sp rs m s c: forall h c' t, + (h, c') = to_bblock_header c -> + starN (Mach.step (inv_trans_rao rao)) (Genv.globalenv prog) (length h) (Mach.State st f sp c rs m) t s -> s = Mach.State st f sp c' rs m /\ t = E0. +Proof. + induction c as [ | i c]; simpl; intros h c' t H. + - inversion_clear H. simpl; intros H; inversion H; auto. + - destruct i; try (injection H; clear H; intros H H2; subst; simpl; intros H; inversion H; subst; auto). + remember (to_bblock_header c) as bhc. destruct bhc as [h0 c0]. + injection H; clear H; intros H H2; subst; simpl; intros H; inversion H; subst. + inversion H1; clear H1; subst; auto. autorewrite with trace_rewrite. + exploit IHc; eauto. +Qed. + +Lemma simu_end_block: + forall s1 t s1', + starN (Mach.step (inv_trans_rao rao)) ge (Datatypes.S (dist_end_block s1)) s1 t s1' -> + exists s2', step rao tge (trans_state s1) t s2' /\ match_states s1' s2'. +Proof. + destruct s1; simpl. + + (* State *) + (* c cannot be nil *) + destruct c as [|i c]; simpl; try ( (* nil => absurd *) + unfold dist_end_block_code; simpl; + intros t s1' H; inversion_clear H; + inversion_clear H0; fail + ). + + intros t s1' H. + remember (_::_) as c0. remember (trans_code c0) as tc0. + + (* tc0 cannot be nil *) + destruct tc0; try + ( exploit (trans_code_nonil c0); subst; auto; try discriminate; intro H0; contradict H0 ). + + assert (X: Datatypes.S (dist_end_block_code c0) = (size (fst (to_bblock c0)))). + { + unfold dist_end_block_code. remember (size _) as siz. + assert (siz <> 0%nat). rewrite Heqsiz; subst; apply to_bblock_nonil with (c0 := c) (i := i); auto. + omega. + } + + (* decomposition of starN in 3 parts: header + body + exit *) + rewrite X in H; unfold size in H. + destruct (starN_split (Mach.semantics (inv_trans_rao rao) prog) _ _ _ _ H _ _ refl_equal) as [t3 [t4 [s1 [H0 [H3 H4]]]]]. + subst t; clear X H. + destruct (starN_split (Mach.semantics (inv_trans_rao rao) prog) _ _ _ _ H0 _ _ refl_equal) as [t1 [t2 [s0 [H [H1 H2]]]]]. + subst t3; clear H0. + + unfold to_bblock in * |- *. + (* naming parts of block "b" *) + remember (to_bblock_header c0) as hd. destruct hd as [hb c1]. + remember (to_bblock_body c1) as bb. destruct bb as [bb c2]. + remember (to_bblock_exit c2) as exb. destruct exb as [exb c3]. + simpl in * |- *. + + exploit trans_code_step; eauto. intro EQ. destruct EQ as (EQH & EQB & EQE & EQTB0). + subst hb bb exb. + + (* header opt step *) + exploit step_simu_header; eauto. + intros [X1 X2]; subst s0 t1. + autorewrite with trace_rewrite. + (* body steps *) + exploit (star_step_simu_body_step); eauto. + clear H1; intros [rs' [m' [H0 [H1 H2]]]]. + subst s1 t2. autorewrite with trace_rewrite. + (* exit step *) + subst tc0. + exploit step_simu_exit_step; eauto. clear H3. + intros (s2' & H3 & H4). + eapply ex_intro; intuition eauto. + eapply exec_bblock; eauto. + + (* Callstate *) + intros t s1' H; inversion_clear H. + eapply ex_intro; constructor 1; eauto. + inversion H1; subst; clear H1. + inversion_clear H0; simpl. + - (* function_internal*) + cutrewrite (trans_code (Mach.fn_code f0) = fn_code (transf_function f0)); eauto. + eapply exec_function_internal; eauto. + rewrite <- parent_sp_preserved; eauto. + rewrite <- parent_ra_preserved; eauto. + - (* function_external *) + autorewrite with trace_rewrite. + eapply exec_function_external; eauto. + apply find_funct_ptr_same_external; auto. + rewrite <- parent_sp_preserved; eauto. + + (* Returnstate *) + intros t s1' H; inversion_clear H. + eapply ex_intro; constructor 1; eauto. + inversion H1; subst; clear H1. + inversion_clear H0; simpl. + eapply exec_return. +Qed. + +Theorem transf_program_correct: + forward_simulation (Mach.semantics (inv_trans_rao rao) prog) (Machblock.semantics rao tprog). +Proof. + apply forward_simulation_block_trans with (dist_end_block := dist_end_block) (trans_state := trans_state). +(* simu_mid_block *) + - intros s1 t s1' H1. + destruct H1; simpl; omega || (intuition auto). +(* public_preserved *) + - apply senv_preserved. +(* match_initial_states *) + - intros. simpl. + eapply ex_intro; constructor 1. + eapply match_states_trans_state. + destruct H. split. + apply init_mem_preserved; auto. + rewrite prog_main_preserved. rewrite <- H0. apply symbols_preserved. +(* match_final_states *) + - intros. simpl. destruct H. split with (r := r); auto. +(* final_states_end_block *) + - intros. simpl in H0. inversion H0. + inversion H; simpl; auto. + (* the remaining instructions cannot lead to a Returnstate *) + all: subst; discriminate. +(* simu_end_block *) + - apply simu_end_block. +Qed. + +End PRESERVATION. diff --git a/mppa_k1c/SelectLong.vp b/mppa_k1c/SelectLong.vp index b3e07bf5..26735c99 100644 --- a/mppa_k1c/SelectLong.vp +++ b/mppa_k1c/SelectLong.vp @@ -292,14 +292,10 @@ Definition notl (e: expr) := (** ** Integer division and modulus *) -Definition divlu_base (e1: expr) (e2: expr) := - if Archi.splitlong then SplitLong.divlu_base e1 e2 else Eop Odivlu (e1:::e2:::Enil). -Definition modlu_base (e1: expr) (e2: expr) := - if Archi.splitlong then SplitLong.modlu_base e1 e2 else Eop Omodlu (e1:::e2:::Enil). -Definition divls_base (e1: expr) (e2: expr) := - if Archi.splitlong then SplitLong.divls_base e1 e2 else Eop Odivl (e1:::e2:::Enil). -Definition modls_base (e1: expr) (e2: expr) := - if Archi.splitlong then SplitLong.modls_base e1 e2 else Eop Omodl (e1:::e2:::Enil). +Definition divlu_base (e1: expr) (e2: expr) := SplitLong.divlu_base e1 e2. +Definition modlu_base (e1: expr) (e2: expr) := SplitLong.modlu_base e1 e2. +Definition divls_base (e1: expr) (e2: expr) := SplitLong.divls_base e1 e2. +Definition modls_base (e1: expr) (e2: expr) := SplitLong.modls_base e1 e2. Definition shrxlimm (e: expr) (n: int) := if Archi.splitlong then SplitLong.shrxlimm e n else diff --git a/mppa_k1c/TargetPrinter.ml b/mppa_k1c/TargetPrinter.ml index f3babcd6..143b7622 100644 --- a/mppa_k1c/TargetPrinter.ml +++ b/mppa_k1c/TargetPrinter.ml @@ -40,7 +40,7 @@ module Target : TARGET = let print_label oc lbl = label oc (transl_label lbl) - let int_reg_name = function + let int_reg_name = let open Asmblock in function | GPR0 -> "$r0" | GPR1 -> "$r1" | GPR2 -> "$r2" | GPR3 -> "$r3" | GPR4 -> "$r4" | GPR5 -> "$r5" | GPR6 -> "$r6" | GPR7 -> "$r7" | GPR8 -> "$r8" | GPR9 -> "$r9" | GPR10 -> "$r10" | GPR11 -> "$r11" @@ -62,13 +62,13 @@ module Target : TARGET = let ireg = ireg - let preg oc = function + let preg oc = let open Asmblock in function | IR r -> ireg oc r | FR r -> ireg oc r | RA -> output_string oc "$ra" - | _ -> assert false + | _ -> assert false - let preg_annot = function + let preg_annot = let open Asmblock in function | IR r -> int_reg_name r | FR r -> int_reg_name r | RA -> "$ra" @@ -149,11 +149,11 @@ module Target : TARGET = *) (* Offset part of a load or store *) - let offset oc = function + let offset oc = let open Asmblock in function | Ofsimm n -> ptrofs oc n | Ofslow(id, ofs) -> fprintf oc "%%lo(%a)" symbol_offset (id, ofs) - let icond_name = function + let icond_name = let open Asmblock in function | ITne | ITneu -> "ne" | ITeq | ITequ -> "eq" | ITlt -> "lt" @@ -171,7 +171,7 @@ module Target : TARGET = let icond oc c = fprintf oc "%s" (icond_name c) - let bcond_name = function + let bcond_name = let open Asmblock in function | BTwnez -> "wnez" | BTweqz -> "weqz" | BTwltz -> "wltz" @@ -188,7 +188,7 @@ module Target : TARGET = let bcond oc c = fprintf oc "%s" (bcond_name c) (* Printing of instructions *) - let print_ex_instruction oc = function + let print_instruction oc = function (* Pseudo-instructions expanded in Asmexpand *) | Pallocframe(sz, ofs) -> assert false @@ -221,127 +221,13 @@ module Target : TARGET = | _ -> assert false end + | Pnop -> fprintf oc " nop\n;;\n" + + | Pclzll (rd, rs) -> fprintf oc " clzd %a = %a\n;;\n" ireg rd ireg rs + | Pstsud (rd, rs1, rs2) -> fprintf oc " stsud %a = %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 - (* Pseudo-instructions not generated by Asmgen *) - (* BCU instructions *) - | Pawait -> - fprintf oc " await \n;;\n" - | Pbarrier -> - fprintf oc " barrier \n;;\n" - | Pdoze -> - fprintf oc " doze \n;;\n" - | Pwfxl(rs1, rs2) -> - fprintf oc " wfxl %a, %a\n;;\n" ireg rs1 ireg rs2 - | Pwfxm(rs1, rs2) -> - fprintf oc " wfxm %a, %a\n;;\n" ireg rs1 ireg rs2 - | Pinvaldtlb -> - fprintf oc " invaldtlb \n;;\n" - | Pinvalitlb -> - fprintf oc " invalitlb \n;;\n" - | Pprobetlb -> - fprintf oc " probetlb \n;;\n" - | Preadtlb -> - fprintf oc " readtlb \n;;\n" - | Psleep -> - fprintf oc " sleep \n;;\n" - | Pstop -> - fprintf oc " stop \n;;\n" - | Psyncgroup(rs) -> - fprintf oc " syncgroup %a\n;;\n" ireg rs - | Ptlbwrite -> - fprintf oc " tlbwrite \n;;\n" - - (* LSU instructions *) - | Pafda(rd, rs1, rs2) -> - fprintf oc " afda %a = %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 - | Paldc(rd, rs1) -> - fprintf oc " aldc %a = %a\n;;\n" ireg rd ireg rs1 - | Pdinval -> - fprintf oc " dinval \n;;\n" - | Pdinvall (rs) -> - fprintf oc " dinvall %a\n;;\n" ireg rs - | Pdtouchl (rs) -> - fprintf oc " dtouchl %a\n;;\n" ireg rs - | Pdzerol (rs) -> - fprintf oc " dzerol %a\n;;\n" ireg rs - | Pfence -> - fprintf oc " fence \n;;\n" - | Piinval -> - fprintf oc " iinval \n;;\n" - | Piinvals (rs) -> - fprintf oc " iinvals %a\n;;\n" ireg rs - | Pitouchl (rs) -> - fprintf oc " itouchl %a\n;;\n" ireg rs - | Plbsu(rd, rs1) -> - fprintf oc " lbsu %a = %a\n;;\n" ireg rd ireg rs1 - | Plbzu(rd, rs1) -> - fprintf oc " lbzu %a = %a\n;;\n" ireg rd ireg rs1 - | Pldu(rd, rs1) -> - fprintf oc " ldu %a = %a\n;;\n" ireg rd ireg rs1 - | Plhsu(rd, rs1) -> - fprintf oc " lhsu %a = %a\n;;\n" ireg rd ireg rs1 - | Plhzu(rd, rs1) -> - fprintf oc " lhzu %a = %a\n;;\n" ireg rd ireg rs1 - | Plwzu(rd, rs1) -> - fprintf oc " lwzu %a = %a\n;;\n" ireg rd ireg rs1 - - (* ALU instructions *) - | Paddhp(rd, rs1, rs2) -> - fprintf oc " addhp %a = %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 - | Padds(rd, rs1, rs2) -> - fprintf oc " adds %a = %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 - | Pbwlu(rd, rs1, rs2, rs3, rs4, rs5) -> - fprintf oc " bwlu %a = %a, %a, %a, %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 ireg rs3 ireg rs4 ireg rs5 - | Pbwluhp(rd, rs1, rs2, rs3) -> - fprintf oc " bwluhp %a = %a, %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 ireg rs3 - | Pbwluwp(rd, rs1, rs2, rs3) -> - fprintf oc " bwluwp %a = %a, %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 ireg rs3 - | Pcbs(rd, rs) -> - fprintf oc " cbs %a = %a\n;;\n" ireg rd ireg rs - | Pcbsdl(rd, rs) -> - fprintf oc " cbsdl %a = %a\n;;\n" ireg rd ireg rs - | Pclz(rd, rs) -> - fprintf oc " clz %a = %a\n;;\n" ireg rd ireg rs - | Pclzw(rd, rs) -> - fprintf oc " clzw %a = %a\n;;\n" ireg rd ireg rs - | Pclzd(rd, rs) -> - fprintf oc " clzd %a = %a\n;;\n" ireg rd ireg rs - | Pclzdl(rd, rs) -> - fprintf oc " clzdl %a = %a\n;;\n" ireg rd ireg rs - | Pcmove(rd, rs1, rs2, rs3) -> - fprintf oc " cmove %a = %a, %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 ireg rs3 - | Pctz(rd, rs) -> - fprintf oc " ctz %a = %a\n;;\n" ireg rd ireg rs - | Pctzw(rd, rs) -> - fprintf oc " ctzw %a = %a\n;;\n" ireg rd ireg rs - | Pctzd(rd, rs) -> - fprintf oc " ctzd %a = %a\n;;\n" ireg rd ireg rs - | Pctzdl(rd, rs) -> - fprintf oc " ctzdl %a = %a\n;;\n" ireg rd ireg rs - | Pextfz(rd, rs1, rs2, rs3) -> - fprintf oc " extfz %a = %a, %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 ireg rs3 - | Plandhp(rd, rs1, rs2, rs3) -> - fprintf oc " landhp %a = %a, %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 ireg rs3 - | Psat(rd, rs1, rs2) -> - fprintf oc " sat %a = %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 - | Psatd(rd, rs1, rs2) -> - fprintf oc " satd %a = %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 - | Psbfhp(rd, rs1, rs2) -> - fprintf oc " sbfhp %a = %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 - | Psbmm8(rd, rs1, rs2) -> - fprintf oc " sbmm8 %a = %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 - | Psbmmt8(rd, rs1, rs2) -> - fprintf oc " sbmmt8 %a = %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 - | Psllhps(rd, rs1, rs2) -> - fprintf oc " sllhps %a = %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 - | Psrahps(rd, rs1, rs2) -> - fprintf oc " srahps %a = %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 - | Pstsu(rd, rs1, rs2) -> - fprintf oc " stsu %a = %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 - | Pstsud(rd, rs1, rs2) -> - fprintf oc " stsud %a = %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 - - let print_cf_instruction oc = function + + (* Control flow instructions *) | Pget (rd, rs) -> fprintf oc " get %a = %a\n;;\n" ireg rd preg rs | Pset (rd, rs) -> @@ -357,7 +243,7 @@ module Target : TARGET = | Pcb (bt, r, lbl) | Pcbu (bt, r, lbl) -> fprintf oc " cb.%a %a?%a\n;;\n" bcond bt ireg r print_label lbl - let print_ld_instruction oc = function + (* Load/Store instructions *) | Plb(rd, ra, ofs) -> fprintf oc " lbs %a = %a[%a]\n;;\n" ireg rd offset ofs ireg ra | Plbu(rd, ra, ofs) -> @@ -370,8 +256,7 @@ module Target : TARGET = fprintf oc " lws %a = %a[%a]\n;;\n" ireg rd offset ofs ireg ra | Pld(rd, ra, ofs) | Pfld(rd, ra, ofs) | Pld_a(rd, ra, ofs) -> assert Archi.ptr64; fprintf oc " ld %a = %a[%a]\n;;\n" ireg rd offset ofs ireg ra - - let print_st_instruction oc = function + | Psb(rd, ra, ofs) -> fprintf oc " sb %a[%a] = %a\n;;\n" offset ofs ireg ra ireg rd | Psh(rd, ra, ofs) -> @@ -381,124 +266,108 @@ module Target : TARGET = | Psd(rd, ra, ofs) | Psd_a(rd, ra, ofs) | Pfsd(rd, ra, ofs) -> assert Archi.ptr64; fprintf oc " sd %a[%a] = %a\n;;\n" offset ofs ireg ra ireg rd - let print_ar_r_instruction oc rd = (* function - | Pcvtw2l ->*) assert false + (* Arith R instructions *) + | Pcvtw2l(rd) -> assert false - let print_ar_rr_instruction oc rd rs = function - | Pmv | Pmvw2l -> + (* Arith RR instructions *) + | Pmv(rd, rs) | Pmvw2l(rd, rs) -> fprintf oc " addd %a = %a, 0\n;;\n" ireg rd ireg rs - | Pcvtl2w -> assert false - | Pnegl -> assert Archi.ptr64; + | Pcvtl2w(rd, rs) -> assert false + | Pnegl(rd, rs) -> assert Archi.ptr64; fprintf oc " negd %a = %a\n;;\n" ireg rd ireg rs - | Pnegw -> + | Pnegw(rd, rs) -> fprintf oc " negw %a = %a\n;;\n" ireg rd ireg rs - | Pfnegd -> + | Pfnegd(rd, rs) -> fprintf oc " fnegd %a = %a\n;;\n" ireg rs ireg rd - let print_ar_ri32_instruction oc rd imm = (* function - | Pmake (rd, imm) -> *) + (* Arith RI32 instructions *) + | Pmake (rd, imm) -> fprintf oc " make %a, %a\n;;\n" ireg rd coqint imm - let print_ar_ri64_instruction oc rd imm = (* function - | Pmakel (rd, imm) -> *) + (* Arith RI64 instructions *) + | Pmakel (rd, imm) -> fprintf oc " make %a, %a\n;;\n" ireg rd coqint64 imm - let print_ar_rrr_instruction oc rd rs1 rs2 = function - | Pcompw (it) -> + (* Arith RRR instructions *) + | Pcompw (it, rd, rs1, rs2) -> fprintf oc " compw.%a %a = %a, %a\n;;\n" icond it ireg rd ireg rs1 ireg rs2 - | Pcompl (it) -> + | Pcompl (it, rd, rs1, rs2) -> fprintf oc " compd.%a %a = %a, %a\n;;\n" icond it ireg rd ireg rs1 ireg rs2 - | Paddw -> + | Paddw (rd, rs1, rs2) -> fprintf oc " addw %a = %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 - | Psubw -> + | Psubw (rd, rs1, rs2) -> fprintf oc " sbfw %a = %a, %a\n;;\n" ireg rd ireg rs2 ireg rs1 - | Pmulw -> + | Pmulw (rd, rs1, rs2) -> fprintf oc " mulw %a = %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 - | Pandw -> + | Pandw (rd, rs1, rs2) -> fprintf oc " andw %a = %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 - | Porw -> + | Porw (rd, rs1, rs2) -> fprintf oc " orw %a = %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 - | Pxorw -> + | Pxorw (rd, rs1, rs2) -> fprintf oc " xorw %a = %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 - | Psraw -> + | Psraw (rd, rs1, rs2) -> fprintf oc " sraw %a = %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 - | Psrlw -> + | Psrlw (rd, rs1, rs2) -> fprintf oc " srlw %a = %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 - | Psllw -> + | Psllw (rd, rs1, rs2) -> fprintf oc " sllw %a = %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 - | Paddl -> assert Archi.ptr64; + | Paddl (rd, rs1, rs2) -> assert Archi.ptr64; fprintf oc " addd %a = %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 - | Psubl -> + | Psubl (rd, rs1, rs2) -> fprintf oc " sbfd %a = %a, %a\n;;\n" ireg rd ireg rs2 ireg rs1 - | Pandl -> assert Archi.ptr64; + | Pandl (rd, rs1, rs2) -> assert Archi.ptr64; fprintf oc " andd %a = %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 - | Porl -> assert Archi.ptr64; + | Porl (rd, rs1, rs2) -> assert Archi.ptr64; fprintf oc " ord %a = %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 - | Pxorl -> assert Archi.ptr64; + | Pxorl (rd, rs1, rs2) -> assert Archi.ptr64; fprintf oc " xord %a = %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 - | Pmull -> + | Pmull (rd, rs1, rs2) -> fprintf oc " muld %a = %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 - | Pslll -> + | Pslll (rd, rs1, rs2) -> fprintf oc " slld %a = %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 - | Psrll -> + | Psrll (rd, rs1, rs2) -> fprintf oc " srld %a = %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 - | Psral -> + | Psral (rd, rs1, rs2) -> fprintf oc " srad %a = %a, %a\n;;\n" ireg rd ireg rs1 ireg rs2 - let print_ar_rri32_instruction oc rd rs imm = function - | Pcompiw (it) -> + (* Arith RRI32 instructions *) + | Pcompiw (it, rd, rs, imm) -> fprintf oc " compw.%a %a = %a, %a\n;;\n" icond it ireg rd ireg rs coqint64 imm - | Paddiw -> + | Paddiw (rd, rs, imm) -> fprintf oc " addw %a = %a, %a\n;;\n" ireg rd ireg rs coqint64 imm - | Pandiw -> + | Pandiw (rd, rs, imm) -> fprintf oc " andw %a = %a, %a\n;;\n" ireg rd ireg rs coqint64 imm - | Poriw -> + | Poriw (rd, rs, imm) -> fprintf oc " orw %a = %a, %a\n;;\n" ireg rd ireg rs coqint64 imm - | Pxoriw -> + | Pxoriw (rd, rs, imm) -> fprintf oc " xorw %a = %a, %a\n;;\n" ireg rd ireg rs coqint64 imm - | Psraiw -> + | Psraiw (rd, rs, imm) -> fprintf oc " sraw %a = %a, %a\n;;\n" ireg rd ireg rs coqint64 imm - | Psrliw -> + | Psrliw (rd, rs, imm) -> fprintf oc " srlw %a = %a, %a\n;;\n" ireg rd ireg rs coqint64 imm - | Pslliw -> + | Pslliw (rd, rs, imm) -> fprintf oc " sllw %a = %a, %a\n;;\n" ireg rd ireg rs coqint64 imm - | Psllil -> + | Psllil (rd, rs, imm) -> fprintf oc " slld %a = %a, %a\n;;\n" ireg rd ireg rs coqint64 imm - | Psrlil -> + | Psrlil (rd, rs, imm) -> fprintf oc " srld %a = %a, %a\n;;\n" ireg rd ireg rs coqint64 imm - | Psrail -> + | Psrail (rd, rs, imm) -> fprintf oc " srad %a = %a, %a\n;;\n" ireg rd ireg rs coqint64 imm - let print_ar_rri64_instruction oc rd rs imm = function - | Pcompil (it) -> + (* Arith RRI64 instructions *) + | Pcompil (it, rd, rs, imm) -> fprintf oc " compd.%a %a = %a, %a\n;;\n" icond it ireg rd ireg rs coqint64 imm - | Paddil -> assert Archi.ptr64; + | Paddil (rd, rs, imm) -> assert Archi.ptr64; fprintf oc " addd %a = %a, %a\n;;\n" ireg rd ireg rs coqint64 imm - | Pandil -> assert Archi.ptr64; + | Pandil (rd, rs, imm) -> assert Archi.ptr64; fprintf oc " andd %a = %a, %a\n;;\n" ireg rd ireg rs coqint64 imm - | Poril -> assert Archi.ptr64; + | Poril (rd, rs, imm) -> assert Archi.ptr64; fprintf oc " ord %a = %a, %a\n;;\n" ireg rd ireg rs coqint64 imm - | Pxoril -> assert Archi.ptr64; + | Pxoril (rd, rs, imm) -> assert Archi.ptr64; fprintf oc " xord %a = %a, %a\n;;\n" ireg rd ireg rs coqint64 imm - let print_ar_instruction oc = function - | PArithR(d) -> print_ar_r_instruction oc d - | PArithRR(ins, d, s) -> print_ar_rr_instruction oc d s ins - | PArithRI32(d, i) -> print_ar_ri32_instruction oc d i - | PArithRI64(d, i) -> print_ar_ri64_instruction oc d i - | PArithRRR(ins, d, s1, s2) -> print_ar_rrr_instruction oc d s1 s2 ins - | PArithRRI32(ins, d, s, i) -> print_ar_rri32_instruction oc d s i ins - | PArithRRI64(ins, d, s, i) -> print_ar_rri64_instruction oc d s i ins - - let print_instruction oc = function - | PExpand(i) -> print_ex_instruction oc i - | PControlFlow(i) -> print_cf_instruction oc i - | PLoad(i) -> print_ld_instruction oc i - | PStore(i) -> print_st_instruction oc i - | PArith(i) -> print_ar_instruction oc i - let get_section_names name = let (text, lit) = match C2C.atom_sections name with diff --git a/mppa_k1c/extractionMachdep.v b/mppa_k1c/extractionMachdep.v index c9a1040a..e70f51de 100644 --- a/mppa_k1c/extractionMachdep.v +++ b/mppa_k1c/extractionMachdep.v @@ -23,5 +23,7 @@ Extract Constant Archi.ptr64 => " Configuration.model = ""64"" ". Extract Constant Archi.pic_code => "fun () -> false". (* for the time being *) (* Asm *) +(* Extract Constant Asm.low_half => "fun _ _ _ -> assert false". Extract Constant Asm.high_half => "fun _ _ _ -> assert false". +*) diff --git a/test/mppa/.gitignore b/test/mppa/.gitignore index f03fc12c..e8ebeff8 100644 --- a/test/mppa/.gitignore +++ b/test/mppa/.gitignore @@ -1 +1,20 @@ check +asm_coverage +instr/Makefile +mmult/Makefile +prng/Makefile +sort/Makefile +prng/.zero +sort/.zero +sort/insertion-ccomp-k1c +sort/insertion-gcc-k1c +sort/insertion-gcc-x86 +sort/main-ccomp-k1c +sort/main-gcc-k1c +sort/main-gcc-x86 +sort/merge-ccomp-k1c +sort/merge-gcc-k1c +sort/merge-gcc-x86 +sort/selection-ccomp-k1c +sort/selection-gcc-k1c +sort/selection-gcc-x86 diff --git a/test/mppa/Makefile b/test/mppa/Makefile deleted file mode 100644 index 22f22945..00000000 --- a/test/mppa/Makefile +++ /dev/null @@ -1,90 +0,0 @@ -DIR=general -BINDIR=bin -ASMDIR=asm -TESTNAMES=$(notdir $(subst .c,,$(wildcard $(DIR)/*.c))) - -CCOMP=../../ccomp -ELF=$(addprefix $(DIR)/$(BINDIR)/,$(addsuffix .bin,$(TESTNAMES))) -TOK=$(addprefix $(DIR)/$(BINDIR)/,$(addsuffix .tok,$(TESTNAMES))) -ASM=$(addprefix $(DIR)/$(ASMDIR)/,$(addsuffix .s,$(TESTNAMES))) -DEBUG:=$(if $(DEBUG),"-dall",) - -.PHONY: all -all: $(ELF) - -nobin: $(ASM) - -## -# Assembling CompCert's assembly file -## -$(DIR)/$(BINDIR)/%.bin: $(DIR)/$(ASMDIR)/%.s - @mkdir -p $(@D) - ccomp $< -o $@ - -## -# Compiling the C file with CompCert -## -.SECONDARY: -$(DIR)/$(ASMDIR)/%.s: $(DIR)/%.c $(CCOMP) - @mkdir -p $(@D) - ccomp $(DEBUG) -O0 -v -S $< -o $@ - -## -# A token (.tok) is created if the .bin (created by CompCert) yields the same -# result as the .bin.exp (created by executing the binary compiled with gcc) -## -$(DIR)/$(BINDIR)/%.tok: $(DIR)/$(BINDIR)/%.bin $(DIR)/output/%.bin.exp - @mkdir -p $(@D) - @bash check.sh $< $@ - -## -# Generate .bin.exp : compile with gcc, execute, store the result in .bin.exp -## -$(DIR)/output/%.bin.exp: $(DIR)/%.c - @bash generate.sh $< $@ - -.PHONY: FORCE -FORCE: - -.PHONY: check -check: $(TOK) sort mmult - -## -# A utility displaying which of the pseudo-instructions are covered in the tests -## -.PHONY: coverage -coverage: $(ASM) - bash coverage.sh $(DIR)/$(ASMDIR) - -## -# Different versions of a sorting algorithm -## -.PHONY: sort -sort: FORCE - (cd sort && make compc-check) - -## -# Different versions of a matrix multiply -## -.PHONY: mmult -mmult: FORCE - (cd mmult && make compc-check) - -.PHONY: clean -clean: - rm -f $(DIR)/*.alloctrace - rm -f $(DIR)/*.cm - rm -f $(DIR)/*.compcert.c - rm -f $(DIR)/*.i - rm -f $(DIR)/*.light.c - rm -f $(DIR)/*.ltl - rm -f $(DIR)/*.mach - rm -f $(DIR)/*.parsed.c - rm -f $(DIR)/*.rtl.? - rm -f $(DIR)/$(ASMDIR)/*.s - rm -f $(DIR)/$(BINDIR)/*.bin - rm -f $(DIR)/$(BINDIR)/*.tok - rm -f $(DIR)/output/*.out - rm -f $(DIR)/output/*.exp - rm -rf $(DIR)/profile/ - rm -f $(ELF) diff --git a/test/mppa/builtins/clzll.c b/test/mppa/builtins/clzll.c new file mode 100644 index 00000000..13905cba --- /dev/null +++ b/test/mppa/builtins/clzll.c @@ -0,0 +1,7 @@ +#include "framework.h" + +BEGIN_TEST(long long) +{ + c = __builtin_clzll(a); +} +END_TEST() diff --git a/test/mppa/general/stsud.c b/test/mppa/builtins/stsud.c index fb07b94f..fb07b94f 100644 --- a/test/mppa/general/stsud.c +++ b/test/mppa/builtins/stsud.c diff --git a/test/mppa/check.sh b/test/mppa/check.sh index dd9691be..8db50f1b 100644..100755 --- a/test/mppa/check.sh +++ b/test/mppa/check.sh @@ -1,32 +1,6 @@ -# $1: binary file to check -# $2: output check token +#!/bin/bash +# Tests the execution of the binaries produced by CompCert -elffile="$1" -token="$2" +source do_test.sh -if [ ! -f $elffile ]; then - >&2 echo "ERROR: $elffile not found" - shift; continue -fi - -dir="$(dirname $elffile)" -elf="$(basename $elffile)" - -exp="$dir/../output/$elf.exp" -out="$dir/../output/$elf.out" -if [ ! -f $exp ]; then - >&2 echo "ERROR: $exp not found" - exit -fi - -k1-cluster -- $elffile > $out -echo $? >> $out - -if ! diff $exp $out; then - >&2 echo "ERROR: $exp and $out differ" - exit -fi - -echo "PASSED: $elf" -touch $token -#shift +do_test check diff --git a/test/mppa/do_test.sh b/test/mppa/do_test.sh new file mode 100644 index 00000000..ee7cbcf7 --- /dev/null +++ b/test/mppa/do_test.sh @@ -0,0 +1,33 @@ +do_test () { +cat << EOF + +## +# PRNG tests +## +EOF +(cd prng && make $1 -j8) + +cat << EOF + +## +# Matrix Multiplication tests +## +EOF +(cd mmult && make $1 -j8) + +cat << EOF + +## +# List sort tests +## +EOF +(cd sort && make $1 -j8) + +cat << EOF + +## +# Instruction unit tests +## +EOF +(cd instr && make $1 -j8) +} diff --git a/test/mppa/generate.sh b/test/mppa/generate.sh deleted file mode 100644 index ea633724..00000000 --- a/test/mppa/generate.sh +++ /dev/null @@ -1,21 +0,0 @@ -# $1: c file to examine -# $2: write file - -cfile="$1" -writefile="$2" - -dirwritefile=$(dirname $writefile) -asmdir=$dirwritefile/../asm/gcc - -if [ ! -f $cfile ]; then - >&2 echo "ERROR: $cfile not found" - shift; continue -fi - -mkdir -p $dirwritefile -mkdir -p $asmdir - -tmpbin=/tmp/k1-$(basename $1)-bin -k1-gcc -O0 $1 -S -o $asmdir/$(basename $1).s -k1-gcc -O0 $1 -o $tmpbin -(k1-cluster -- $tmpbin; echo $? > $2) diff --git a/test/mppa/general/.gitignore b/test/mppa/instr/.gitignore index ea1472ec..ea1472ec 100644 --- a/test/mppa/general/.gitignore +++ b/test/mppa/instr/.gitignore diff --git a/test/mppa/instr/Makefile b/test/mppa/instr/Makefile new file mode 100644 index 00000000..89ff9a73 --- /dev/null +++ b/test/mppa/instr/Makefile @@ -0,0 +1,111 @@ +K1CC ?= k1-mbr-gcc +CC ?= gcc +CCOMP ?= ccomp +CFLAGS ?= -O2 +SIMU ?= k1-cluster +TIMEOUT ?= 10s + +DIR=./ +SRCDIR=$(DIR) +OUTDIR=$(DIR)/out +BINDIR=$(DIR)/bin +ASMDIR=$(DIR)/asm + +## +# Intended flow : .c -> .gcc.s -> .gcc.bin -> .gcc.out +# -> .ccomp.s -> .ccomp.bin -> .ccomp.out +## + +K1CCPATH=$(shell which $(K1CC)) +CCPATH=$(shell which $(CC)) +CCOMPPATH=$(shell which $(CCOMP)) +SIMUPATH=$(shell which $(SIMU)) + +TESTNAMES=$(notdir $(subst .c,,$(wildcard $(DIR)/*.c))) +X86_GCC_OUT=$(addprefix $(OUTDIR)/,$(addsuffix .x86-gcc.out,$(TESTNAMES))) +GCC_OUT=$(addprefix $(OUTDIR)/,$(addsuffix .gcc.out,$(TESTNAMES))) +CCOMP_OUT=$(addprefix $(OUTDIR)/,$(addsuffix .ccomp.out,$(TESTNAMES))) + +OUT=$(X86_GCC_OUT) $(GCC_OUT) $(CCOMP_OUT) +BIN=$(addprefix $(BINDIR)/,$(addsuffix .x86-gcc.bin,$(TESTNAMES)))\ + $(addprefix $(BINDIR)/,$(addsuffix .gcc.bin,$(TESTNAMES)))\ + $(addprefix $(BINDIR)/,$(addsuffix .ccomp.bin,$(TESTNAMES))) + +## +# Targets +## + +all: $(BIN) + +.PHONY: +test: $(X86_GCC_OUT) $(GCC_OUT) + @echo "Comparing x86 gcc output to k1 gcc.." + @for test in $(TESTNAMES); do\ + x86out=$(OUTDIR)/$$test.x86-gcc.out;\ + gccout=$(OUTDIR)/$$test.gcc.out;\ + if ! diff $$x86out $$gccout; then\ + >&2 echo "ERROR: $$x86out and $$gccout differ";\ + else\ + echo "GOOD: $$x86out and $$gccout concur";\ + fi;\ + done + +.PHONY: +check: $(GCC_OUT) $(CCOMP_OUT) + @echo "Comparing k1 gcc output to ccomp.." + @for test in $(TESTNAMES); do\ + gccout=$(OUTDIR)/$$test.gcc.out;\ + ccompout=$(OUTDIR)/$$test.ccomp.out;\ + if ! diff $$ccompout $$gccout; then\ + >&2 echo "ERROR: $$ccompout and $$gccout differ";\ + else\ + echo "GOOD: $$ccompout and $$gccout concur";\ + fi;\ + done + +## +# Rules +## + +.SECONDARY: +# Generating output + +$(OUTDIR)/%.x86-gcc.out: $(BINDIR)/%.x86-gcc.bin + @mkdir -p $(@D) + ret=0; timeout $(TIMEOUT) ./$< > $@ || { ret=$$?; }; echo $$ret >> $@ + +$(OUTDIR)/%.gcc.out: $(BINDIR)/%.gcc.bin $(SIMUPATH) + @mkdir -p $(@D) + ret=0; timeout $(TIMEOUT) $(SIMU) -- $< > $@ || { ret=$$?; }; echo $$ret >> $@ + +$(OUTDIR)/%.ccomp.out: $(BINDIR)/%.ccomp.bin $(SIMUPATH) + @mkdir -p $(@D) + ret=0; timeout $(TIMEOUT) $(SIMU) -- $< > $@ || { ret=$$?; }; echo $$ret >> $@ + +# Assembly to binary + +$(BINDIR)/%.x86-gcc.bin: $(ASMDIR)/%.x86-gcc.s $(CCPATH) + @mkdir -p $(@D) + $(CC) $(CFLAGS) $< -o $@ + +$(BINDIR)/%.gcc.bin: $(ASMDIR)/%.gcc.s $(K1CCPATH) + @mkdir -p $(@D) + $(K1CC) $(CFLAGS) $< -o $@ + +$(BINDIR)/%.ccomp.bin: $(ASMDIR)/%.ccomp.s $(CCOMPPATH) + @mkdir -p $(@D) + $(CCOMP) $(CFLAGS) $< -o $@ + +# Source to assembly + +$(ASMDIR)/%.x86-gcc.s: $(SRCDIR)/%.c $(CCPATH) + @mkdir -p $(@D) + $(CC) $(CFLAGS) -S $< -o $@ + +$(ASMDIR)/%.gcc.s: $(SRCDIR)/%.c $(K1CCPATH) + @mkdir -p $(@D) + $(K1CC) $(CFLAGS) -S $< -o $@ + +$(ASMDIR)/%.ccomp.s: $(SRCDIR)/%.c $(CCOMPPATH) + @mkdir -p $(@D) + $(CCOMP) $(CFLAGS) -S $< -o $@ diff --git a/test/mppa/general/addw.c b/test/mppa/instr/addw.c index be8afc67..be8afc67 100644 --- a/test/mppa/general/addw.c +++ b/test/mppa/instr/addw.c diff --git a/test/mppa/general/andd.c b/test/mppa/instr/andd.c index 4f503764..4f503764 100644 --- a/test/mppa/general/andd.c +++ b/test/mppa/instr/andd.c diff --git a/test/mppa/general/andw.c b/test/mppa/instr/andw.c index 99de0049..99de0049 100644 --- a/test/mppa/general/andw.c +++ b/test/mppa/instr/andw.c diff --git a/test/mppa/general/branch.c b/test/mppa/instr/branch.c index 72e7e20e..72e7e20e 100644 --- a/test/mppa/general/branch.c +++ b/test/mppa/instr/branch.c diff --git a/test/mppa/general/branchz.c b/test/mppa/instr/branchz.c index fb86d357..fb86d357 100644 --- a/test/mppa/general/branchz.c +++ b/test/mppa/instr/branchz.c diff --git a/test/mppa/general/branchzu.c b/test/mppa/instr/branchzu.c index 97adb605..97adb605 100644 --- a/test/mppa/general/branchzu.c +++ b/test/mppa/instr/branchzu.c diff --git a/test/mppa/general/call.c b/test/mppa/instr/call.c index 727cef63..727cef63 100644 --- a/test/mppa/general/call.c +++ b/test/mppa/instr/call.c diff --git a/test/mppa/general/cb.deqz.c b/test/mppa/instr/cb.deqz.c index c56733f0..c56733f0 100644 --- a/test/mppa/general/cb.deqz.c +++ b/test/mppa/instr/cb.deqz.c diff --git a/test/mppa/general/cb.dgez.c b/test/mppa/instr/cb.dgez.c index abb6ec57..abb6ec57 100644 --- a/test/mppa/general/cb.dgez.c +++ b/test/mppa/instr/cb.dgez.c diff --git a/test/mppa/general/cb.dgtz.c b/test/mppa/instr/cb.dgtz.c index d4271845..d4271845 100644 --- a/test/mppa/general/cb.dgtz.c +++ b/test/mppa/instr/cb.dgtz.c diff --git a/test/mppa/general/cb.dlez.c b/test/mppa/instr/cb.dlez.c index 18e67f06..18e67f06 100644 --- a/test/mppa/general/cb.dlez.c +++ b/test/mppa/instr/cb.dlez.c diff --git a/test/mppa/general/cb.dltz.c b/test/mppa/instr/cb.dltz.c index 366aea49..366aea49 100644 --- a/test/mppa/general/cb.dltz.c +++ b/test/mppa/instr/cb.dltz.c diff --git a/test/mppa/general/cb.dnez.c b/test/mppa/instr/cb.dnez.c index 81c2cd29..81c2cd29 100644 --- a/test/mppa/general/cb.dnez.c +++ b/test/mppa/instr/cb.dnez.c diff --git a/test/mppa/general/cb.wgez.c b/test/mppa/instr/cb.wgez.c index 477f4bc6..477f4bc6 100644 --- a/test/mppa/general/cb.wgez.c +++ b/test/mppa/instr/cb.wgez.c diff --git a/test/mppa/general/cb.wgtz.c b/test/mppa/instr/cb.wgtz.c index c9ab9a06..c9ab9a06 100644 --- a/test/mppa/general/cb.wgtz.c +++ b/test/mppa/instr/cb.wgtz.c diff --git a/test/mppa/general/cb.wlez.c b/test/mppa/instr/cb.wlez.c index c3069fda..c3069fda 100644 --- a/test/mppa/general/cb.wlez.c +++ b/test/mppa/instr/cb.wlez.c diff --git a/test/mppa/general/cb.wltz.c b/test/mppa/instr/cb.wltz.c index 6cf5fcf0..6cf5fcf0 100644 --- a/test/mppa/general/cb.wltz.c +++ b/test/mppa/instr/cb.wltz.c diff --git a/test/mppa/general/compd.eq.c b/test/mppa/instr/compd.eq.c index d19a4d20..d19a4d20 100644 --- a/test/mppa/general/compd.eq.c +++ b/test/mppa/instr/compd.eq.c diff --git a/test/mppa/general/compd.geu.c b/test/mppa/instr/compd.geu.c index edc31183..edc31183 100644 --- a/test/mppa/general/compd.geu.c +++ b/test/mppa/instr/compd.geu.c diff --git a/test/mppa/general/compd.gt.c b/test/mppa/instr/compd.gt.c index 24147779..24147779 100644 --- a/test/mppa/general/compd.gt.c +++ b/test/mppa/instr/compd.gt.c diff --git a/test/mppa/general/compd.gtu.c b/test/mppa/instr/compd.gtu.c index 5ce82569..5ce82569 100644 --- a/test/mppa/general/compd.gtu.c +++ b/test/mppa/instr/compd.gtu.c diff --git a/test/mppa/general/compd.le.c b/test/mppa/instr/compd.le.c index a84aad97..a84aad97 100644 --- a/test/mppa/general/compd.le.c +++ b/test/mppa/instr/compd.le.c diff --git a/test/mppa/general/compd.leu.c b/test/mppa/instr/compd.leu.c index e386bc27..e386bc27 100644 --- a/test/mppa/general/compd.leu.c +++ b/test/mppa/instr/compd.leu.c diff --git a/test/mppa/general/compd.lt.c b/test/mppa/instr/compd.lt.c index df07a708..df07a708 100644 --- a/test/mppa/general/compd.lt.c +++ b/test/mppa/instr/compd.lt.c diff --git a/test/mppa/general/compd.ltu.c b/test/mppa/instr/compd.ltu.c index dfaa8921..dfaa8921 100644 --- a/test/mppa/general/compd.ltu.c +++ b/test/mppa/instr/compd.ltu.c diff --git a/test/mppa/general/compd.ne.c b/test/mppa/instr/compd.ne.c index 19ce0a69..19ce0a69 100644 --- a/test/mppa/general/compd.ne.c +++ b/test/mppa/instr/compd.ne.c diff --git a/test/mppa/general/compw.eq.c b/test/mppa/instr/compw.eq.c index dc7a3ab1..dc7a3ab1 100644 --- a/test/mppa/general/compw.eq.c +++ b/test/mppa/instr/compw.eq.c diff --git a/test/mppa/general/compw.geu.c b/test/mppa/instr/compw.geu.c index d72ca56c..d72ca56c 100644 --- a/test/mppa/general/compw.geu.c +++ b/test/mppa/instr/compw.geu.c diff --git a/test/mppa/general/compw.gt.c b/test/mppa/instr/compw.gt.c index 9ad02610..9ad02610 100644 --- a/test/mppa/general/compw.gt.c +++ b/test/mppa/instr/compw.gt.c diff --git a/test/mppa/general/compw.gtu.c b/test/mppa/instr/compw.gtu.c index 77f04989..77f04989 100644 --- a/test/mppa/general/compw.gtu.c +++ b/test/mppa/instr/compw.gtu.c diff --git a/test/mppa/general/compw.le.c b/test/mppa/instr/compw.le.c index b7a7a432..b7a7a432 100644 --- a/test/mppa/general/compw.le.c +++ b/test/mppa/instr/compw.le.c diff --git a/test/mppa/general/compw.leu.c b/test/mppa/instr/compw.leu.c index 4892f06c..4892f06c 100644 --- a/test/mppa/general/compw.leu.c +++ b/test/mppa/instr/compw.leu.c diff --git a/test/mppa/general/compw.lt.c b/test/mppa/instr/compw.lt.c index 2cc151bf..2cc151bf 100644 --- a/test/mppa/general/compw.lt.c +++ b/test/mppa/instr/compw.lt.c diff --git a/test/mppa/general/compw.ltu.c b/test/mppa/instr/compw.ltu.c index b524127f..b524127f 100644 --- a/test/mppa/general/compw.ltu.c +++ b/test/mppa/instr/compw.ltu.c diff --git a/test/mppa/general/compw.ne.c b/test/mppa/instr/compw.ne.c index 433b0b86..433b0b86 100644 --- a/test/mppa/general/compw.ne.c +++ b/test/mppa/instr/compw.ne.c diff --git a/test/mppa/general/div2.c b/test/mppa/instr/div2.c index 01a4b575..01a4b575 100644 --- a/test/mppa/general/div2.c +++ b/test/mppa/instr/div2.c diff --git a/test/mppa/general/for.c b/test/mppa/instr/for.c index d6870afb..d6870afb 100644 --- a/test/mppa/general/for.c +++ b/test/mppa/instr/for.c diff --git a/test/mppa/general/forvar.c b/test/mppa/instr/forvar.c index 57548274..57548274 100644 --- a/test/mppa/general/forvar.c +++ b/test/mppa/instr/forvar.c diff --git a/test/mppa/general/forvarl.c b/test/mppa/instr/forvarl.c index 30717a51..30717a51 100644 --- a/test/mppa/general/forvarl.c +++ b/test/mppa/instr/forvarl.c diff --git a/test/mppa/general/framework.h b/test/mppa/instr/framework.h index b7dc4933..52ba97bc 100644 --- a/test/mppa/general/framework.h +++ b/test/mppa/instr/framework.h @@ -1,7 +1,7 @@ #ifndef __FRAMEWORK_H__ #define __FRAMEWORK_H__ -#include "../lib/prng.c" +#include "../prng/prng.c" #define BEGIN_TEST_N(type, N)\ int main(void){\ diff --git a/test/mppa/general/lbs.c b/test/mppa/instr/lbs.c index f104d62b..f104d62b 100644 --- a/test/mppa/general/lbs.c +++ b/test/mppa/instr/lbs.c diff --git a/test/mppa/general/lbz.c b/test/mppa/instr/lbz.c index 2deeaebe..2deeaebe 100644 --- a/test/mppa/general/lbz.c +++ b/test/mppa/instr/lbz.c diff --git a/test/mppa/general/muld.c b/test/mppa/instr/muld.c index 9a40f389..9a40f389 100644 --- a/test/mppa/general/muld.c +++ b/test/mppa/instr/muld.c diff --git a/test/mppa/general/mulw.c b/test/mppa/instr/mulw.c index bf517ce8..bf517ce8 100644 --- a/test/mppa/general/mulw.c +++ b/test/mppa/instr/mulw.c diff --git a/test/mppa/general/negd.c b/test/mppa/instr/negd.c index a8e8ff45..a8e8ff45 100644 --- a/test/mppa/general/negd.c +++ b/test/mppa/instr/negd.c diff --git a/test/mppa/general/ord.c b/test/mppa/instr/ord.c index eaedcb28..eaedcb28 100644 --- a/test/mppa/general/ord.c +++ b/test/mppa/instr/ord.c diff --git a/test/mppa/general/sbfd.c b/test/mppa/instr/sbfd.c index 912f1fdb..912f1fdb 100644 --- a/test/mppa/general/sbfd.c +++ b/test/mppa/instr/sbfd.c diff --git a/test/mppa/general/sbfw.c b/test/mppa/instr/sbfw.c index feffd497..feffd497 100644 --- a/test/mppa/general/sbfw.c +++ b/test/mppa/instr/sbfw.c diff --git a/test/mppa/general/simple.c b/test/mppa/instr/simple.c index 89bba27e..89bba27e 100644 --- a/test/mppa/general/simple.c +++ b/test/mppa/instr/simple.c diff --git a/test/mppa/general/sllw.c b/test/mppa/instr/sllw.c index df55c9e8..df55c9e8 100644 --- a/test/mppa/general/sllw.c +++ b/test/mppa/instr/sllw.c diff --git a/test/mppa/general/srad.c b/test/mppa/instr/srad.c index b4047bc7..b4047bc7 100644 --- a/test/mppa/general/srad.c +++ b/test/mppa/instr/srad.c diff --git a/test/mppa/general/srld.c b/test/mppa/instr/srld.c index 71e82b2a..71e82b2a 100644 --- a/test/mppa/general/srld.c +++ b/test/mppa/instr/srld.c diff --git a/test/mppa/general/udivd.c b/test/mppa/instr/udivd.c index 52e0d412..52e0d412 100644 --- a/test/mppa/general/udivd.c +++ b/test/mppa/instr/udivd.c diff --git a/test/mppa/general/umodd.c b/test/mppa/instr/umodd.c index e7dd506f..e7dd506f 100644 --- a/test/mppa/general/umodd.c +++ b/test/mppa/instr/umodd.c diff --git a/test/mppa/general/xord.c b/test/mppa/instr/xord.c index b9d86f06..b9d86f06 100644 --- a/test/mppa/general/xord.c +++ b/test/mppa/instr/xord.c diff --git a/test/mppa/lib/.gitignore b/test/mppa/lib/.gitignore deleted file mode 100644 index 1879eaee..00000000 --- a/test/mppa/lib/.gitignore +++ /dev/null @@ -1,2 +0,0 @@ -prng-test-k1c -prng-test-x86 diff --git a/test/mppa/lib/Makefile b/test/mppa/lib/Makefile deleted file mode 100644 index 7aeab9f3..00000000 --- a/test/mppa/lib/Makefile +++ /dev/null @@ -1,30 +0,0 @@ -prng-test-x86: prng.c - gcc -D__UNIT_TEST_PRNG__ -O2 -std=c99 $< -o $@ - -prng-test-k1c: prng.c - k1-gcc -D__UNIT_TEST_PRNG__ -O2 -std=c99 $< -o $@ - -.PHONY: -test: test-x86 test-k1c - -.PHONY: -test-x86: prng-test-x86 - @if ! ./$<; then\ - >&2 echo "ERROR: $< failed";\ - exit;\ - else\ - echo "x86: Test Succeeded";\ - fi - -.PHONY: -test-k1c: prng-test-k1c - @if ! k1-cluster -- ./$<; then\ - >&2 echo "ERROR: $< failed";\ - exit;\ - else\ - echo "k1c: Test Succeeded";\ - fi - -.PHONY: -clean: - rm -f prng-test-x86 prng-test-k1c diff --git a/test/mppa/mmult/.gitignore b/test/mppa/mmult/.gitignore index 5883d367..c9cd4c65 100644 --- a/test/mppa/mmult/.gitignore +++ b/test/mppa/mmult/.gitignore @@ -1,3 +1,4 @@ -mmult-test-k1c -mmult-test-x86 -test-ccomp +mmult-test-ccomp-k1c +mmult-test-gcc-k1c +mmult-test-gcc-x86 +.zero diff --git a/test/mppa/mmult/Makefile b/test/mppa/mmult/Makefile index 23b31d49..cf82e359 100644 --- a/test/mppa/mmult/Makefile +++ b/test/mppa/mmult/Makefile @@ -1,78 +1,67 @@ -PRNG=../lib/prng.c -CCOMP=../../../ccomp - -ALL= mmult-test-x86 mmult-test-k1c\ +K1CC ?= k1-mbr-gcc +CC ?= gcc +CCOMP ?= ccomp +CFLAGS ?= -O2 +SIMU ?= k1-cluster +TIMEOUT ?= 10s + +K1CCPATH=$(shell which $(K1CC)) +CCPATH=$(shell which $(CC)) +CCOMPPATH=$(shell which $(CCOMP)) +SIMUPATH=$(shell which $(SIMU)) + +PRNG=../prng/prng.c + +ALL= mmult-test-gcc-x86 mmult-test-gcc-k1c mmult-test-ccomp-k1c +CCOMP_OUT= mmult-test-ccomp-k1c.out +GCC_OUT= mmult-test-gcc-k1c.out +X86_GCC_OUT= mmult-test-gcc-x86.out +STUB_OUT=.zero all: $(ALL) -%-test-x86: %.c $(PRNG) - gcc -D__UNIT_TEST_$$(echo $(basename $<) | tr a-z A-Z)__ -O2 -std=c99 $^ -o $@ - -%-test-k1c: %.c $(PRNG) - k1-gcc -D__UNIT_TEST_$$(echo $(basename $<) | tr a-z A-Z)__ -O2 -std=c99 $^ -o $@ +mmult-test-gcc-x86: mmult.c $(PRNG) $(CCPATH) + $(CC) $(CFLAGS) $(filter-out $(CCPATH),$^) -o $@ -test-x86: mmult.c $(PRNG) - gcc -O2 -std=c99 $^ -o $@ +mmult-test-gcc-k1c: mmult.c $(PRNG) $(K1CCPATH) + $(K1CC) $(CFLAGS) $(filter-out $(K1CCPATH),$^) -o $@ -test-k1c: mmult.c $(PRNG) - k1-gcc -O2 -std=c99 $^ -o $@ +mmult-test-ccomp-k1c: mmult.c $(PRNG) $(CCOMPPATH) + $(CCOMP) $(CFLAGS) $(filter-out $(CCOMPPATH),$^) -o $@ -%.s: %.c $(CCOMP) - ccomp -O2 -S $< -o $@ +.SECONDARY: +%k1c.out: %k1c $(SIMUPATH) + ret=0; timeout $(TIMEOUT) $(SIMU) -- $< > $@ || { ret=$$?; }; echo $$ret >> $@ -test-ccomp: mmult.s $(subst .c,.s,$(PRNG)) - k1-gcc $^ -o $@ +%x86.out: %x86 + ret=0; timeout $(TIMEOUT) ./$< > $@ || { ret=$$?; }; echo $$ret >> $@ -.PHONY: -unittest: unittest-x86 unittest-k1c +.zero: + @echo "0" > $@ .PHONY: -check: check-x86 check-k1c +test: test-x86 test-k1c .PHONY: -compc-check: test-ccomp - @if ! k1-cluster -- ./$<; then\ - >&2 echo "ERROR k1c: mmult $< failed";\ +test-x86: $(X86_GCC_OUT) $(STUB_OUT) + @if ! diff $< $(STUB_OUT); then\ + >&2 echo "ERROR x86: $< failed";\ else\ - echo "k1c: Test mmult $< succeeded";\ + echo "GOOD x86: $< succeeded";\ fi .PHONY: -check-x86: test-x86 - @if ! ./$<; then\ - >&2 echo "ERROR x86: $< failed";\ +test-k1c: $(GCC_OUT) $(STUB_OUT) + @if ! diff $< $(STUB_OUT); then\ + >&2 echo "ERROR k1c: $< failed";\ else\ - echo "x86: Test $< succeeded";\ + echo "GOOD k1c: $< succeeded";\ fi .PHONY: -check-k1c: test-k1c - @if ! k1-cluster -- ./$<; then\ +check: $(CCOMP_OUT) $(STUB_OUT) + @if ! diff $< $(STUB_OUT); then\ >&2 echo "ERROR k1c: $< failed";\ else\ - echo "k1c: Test $< succeeded";\ + echo "GOOD k1c: $< succeeded";\ fi - -.PHONY: -unittest-x86: mmult-test-x86 - @for test in $^; do\ - if ! ./$$test; then\ - >&2 echo "ERROR x86: $$test failed";\ - else\ - echo "x86: Test $$test Succeeded";\ - fi;\ - done - -.PHONY: -unittest-k1c: mmult-test-k1c - @for test in $^; do\ - if ! k1-cluster -- ./$$test; then\ - >&2 echo "ERROR k1c: $$test failed";\ - else\ - echo "k1c: Test $$test Succeeded";\ - fi;\ - done - -.PHONY: -clean: - rm -f $(ALL) diff --git a/test/mppa/mmult/README.md b/test/mppa/mmult/README.md new file mode 100644 index 00000000..ef2bff7e --- /dev/null +++ b/test/mppa/mmult/README.md @@ -0,0 +1,17 @@ +MMULT +===== + +Examples of matrix multiplication using different methods. + +We compute matrix multiplication using column-based matrix multiplication, then row-based, and finally block based. + +The test verifies that the result is the same on the three methods. If it is the same, 0 will be returned. + +The following commands can be run inside the folder: + +- `make`: produces the unitary test binaries + - `mmult-test-gcc-x86` : binary from gcc on x86 + - `mmult-test-k1c-x86` : binary from gcc on k1c + - `mmult-test-ccomp-x86` : binary from ccomp on k1c +- `make test`: tests the return value of the binaries produced by gcc. +- `make check`: tests the return value of the binary produced by CompCert. diff --git a/test/mppa/mmult/mmult.c b/test/mppa/mmult/mmult.c index b674ca80..aeb91d48 100644 --- a/test/mppa/mmult/mmult.c +++ b/test/mppa/mmult/mmult.c @@ -1,5 +1,5 @@ -#include "../lib/types.h" -#include "../lib/prng.h" +#include "../prng/types.h" +#include "../prng/prng.h" #define __UNIT_TEST_MMULT__ @@ -10,24 +10,28 @@ #endif void mmult_row(uint64_t C[][SIZE], uint64_t A[][SIZE], uint64_t B[][SIZE]){ - for (int i = 0 ; i < SIZE ; i++) - for (int j = 0 ; j < SIZE ; j++) + int i, j, k; + + for (i = 0 ; i < SIZE ; i++) + for (j = 0 ; j < SIZE ; j++) C[i][j] = 0; - for (int i = 0 ; i < SIZE ; i++) - for (int j = 0 ; j < SIZE ; j++) - for (int k = 0 ; k < SIZE ; k++) + for (i = 0 ; i < SIZE ; i++) + for (j = 0 ; j < SIZE ; j++) + for (k = 0 ; k < SIZE ; k++) C[i][j] += A[i][k] * B[k][j]; } void mmult_col(uint64_t C[][SIZE], uint64_t A[][SIZE], uint64_t B[][SIZE]){ - for (int i = 0 ; i < SIZE ; i++) - for (int j = 0 ; j < SIZE ; j++) + int i, j, k; + + for (i = 0 ; i < SIZE ; i++) + for (j = 0 ; j < SIZE ; j++) C[i][j] = 0; - for (int k = 0 ; k < SIZE ; k++) - for (int i = 0 ; i < SIZE ; i++) - for (int j = 0 ; j < SIZE ; j++) + for (k = 0 ; k < SIZE ; k++) + for (i = 0 ; i < SIZE ; i++) + for (j = 0 ; j < SIZE ; j++) C[i][j] += A[i][k] * B[k][j]; } @@ -41,10 +45,11 @@ typedef struct mblock { void divac_mul(mblock *C, const mblock *A, const mblock *B){ const int size = C->imax - C->imin; + int i, j, k; - for (int i = 0 ; i < size ; i++) - for (int j = 0 ; j < size ; j++) - for (int k = 0 ; k < size ; k++) + for (i = 0 ; i < size ; i++) + for (j = 0 ; j < size ; j++) + for (k = 0 ; k < size ; k++) MAT_IJ(C, i, j) += MAT_IJ(A, i, k) * MAT_IJ(B, k, j); } @@ -119,9 +124,10 @@ static uint64_t A[SIZE][SIZE], B[SIZE][SIZE]; int main(void){ srand(42); + int i, j; - for (int i = 0 ; i < SIZE ; i++) - for (int j = 0 ; j < SIZE ; j++){ + for (i = 0 ; i < SIZE ; i++) + for (j = 0 ; j < SIZE ; j++){ A[i][j] = randlong(); B[i][j] = randlong(); } @@ -130,8 +136,8 @@ int main(void){ mmult_col(C2, A, B); mmult_divac(C3, A, B); - for (int i = 0 ; i < SIZE ; i++) - for (int j = 0 ; j < SIZE ; j++) + for (i = 0 ; i < SIZE ; i++) + for (j = 0 ; j < SIZE ; j++) if (!(C1[i][j] == C2[i][j] && C1[i][j] == C3[i][j])) return -1; diff --git a/test/mppa/prng/.gitignore b/test/mppa/prng/.gitignore new file mode 100644 index 00000000..0792a78b --- /dev/null +++ b/test/mppa/prng/.gitignore @@ -0,0 +1,3 @@ +prng-test-ccomp-k1c +prng-test-gcc-x86 +prng-test-gcc-k1c diff --git a/test/mppa/prng/Makefile b/test/mppa/prng/Makefile new file mode 100644 index 00000000..5580cd8e --- /dev/null +++ b/test/mppa/prng/Makefile @@ -0,0 +1,69 @@ +K1CC ?= k1-mbr-gcc +CC ?= gcc +CCOMP ?= ccomp +CFLAGS ?= -O2 +SIMU ?= k1-cluster +TIMEOUT ?= 10s + +K1CCPATH=$(shell which $(K1CC)) +CCPATH=$(shell which $(CC)) +CCOMPPATH=$(shell which $(CCOMP)) +SIMUPATH=$(shell which $(SIMU)) + +ALL= prng-test-gcc-x86 prng-test-gcc-k1c prng-test-ccomp-k1c +CCOMP_OUT= prng-test-ccomp-k1c.out +GCC_OUT= prng-test-gcc-k1c.out +X86_GCC_OUT= prng-test-gcc-x86.out +STUB_OUT=.zero + +all: $(ALL) + +prng-test-gcc-x86: prng.c $(CCPATH) + $(CC) -D__UNIT_TEST_PRNG__ $(CFLAGS) $< -o $@ + +prng-test-gcc-k1c: prng.c $(K1CCPATH) + $(K1CC) -D__UNIT_TEST_PRNG__ $(CFLAGS) $< -o $@ + +prng-test-ccomp-k1c: prng.c $(CCOMPPATH) + $(CCOMP) -D__UNIT_TEST_PRNG__ $(CFLAGS) $< -o $@ + +.SECONDARY: +%k1c.out: %k1c $(SIMUPATH) + ret=0; timeout $(TIMEOUT) $(SIMU) -- $< > $@ || { ret=$$?; }; echo $$ret >> $@ + +%x86.out: %x86 + ret=0; timeout $(TIMEOUT) ./$< > $@ || { ret=$$?; }; echo $$ret >> $@ + +.zero: + @echo "0" > $@ + +.PHONY: +test: test-x86 test-k1c + +.PHONY: +test-x86: $(X86_GCC_OUT) $(STUB_OUT) + @if ! diff $< $(STUB_OUT); then\ + >&2 echo "ERROR x86: $< failed";\ + else\ + echo "GOOD x86: $< succeeded";\ + fi + +.PHONY: +test-k1c: $(GCC_OUT) $(STUB_OUT) + @if ! diff $< $(STUB_OUT); then\ + >&2 echo "ERROR k1c: $< failed";\ + else\ + echo "GOOD k1c: $< succeeded";\ + fi + +.PHONY: +check: $(CCOMP_OUT) $(STUB_OUT) + @if ! diff $< $(STUB_OUT); then\ + >&2 echo "ERROR k1c: $< failed";\ + else\ + echo "GOOD k1c: $< succeeded";\ + fi + +.PHONY: +clean: + rm -f prng-test-gcc-x86 prng-test-gcc-k1c prng-test-ccomp-k1c diff --git a/test/mppa/prng/README.md b/test/mppa/prng/README.md new file mode 100644 index 00000000..b4c2279b --- /dev/null +++ b/test/mppa/prng/README.md @@ -0,0 +1,17 @@ +PRNG +==== + +This is a simple Pseudo Random Number Generator. + +`prng.c` contains a simple unitary test that compares the sum of the "bytewise sum" +of 1000 generated numbers to a hardcoded result, that is the one obtained with +`gcc -O2` on a x86 processor, and returns 0 if the result is correct. + +The following commands can be run inside that folder: + +- `make`: produces the unitary test binaries + - `prng-test-gcc-x86` : binary from gcc on x86 + - `prng-test-k1c-x86` : binary from gcc on k1c + - `prng-test-ccomp-x86` : binary from ccomp on k1c +- `make test`: tests the return value of the binaries produced by gcc. +- `make check`: tests the return value of the binary produced by CompCert. diff --git a/test/mppa/lib/prng.c b/test/mppa/prng/prng.c index 59ec7ca6..71de1dc3 100644 --- a/test/mppa/lib/prng.c +++ b/test/mppa/prng/prng.c @@ -19,8 +19,9 @@ uint64_t randlong(void){ #ifdef __UNIT_TEST_PRNG__ char bytewise_sum(uint64_t to_check){ char sum = 0; + int i; - for (int i = 0 ; i < 8 ; i++) + for (i = 0 ; i < 8 ; i++) sum += (to_check & (uint64_t)(0xFFULL << i*8)) >> i*8; return sum; @@ -28,15 +29,13 @@ char bytewise_sum(uint64_t to_check){ int main(void){ srand(42); + int i; - if (bytewise_sum(0xdeadbeefb00b1355ULL) != 91) - return 1; - - for (int i = 0 ; i < 1000 ; i++) + for (i = 0 ; i < 1000 ; i++) randlong(); uint64_t last = randlong(); - return !((unsigned char)bytewise_sum(last) == 251); + return !((unsigned char)bytewise_sum(last) == 155); } #endif // __UNIT_TEST_PRNG__ diff --git a/test/mppa/lib/prng.h b/test/mppa/prng/prng.h index 6abdb45a..6abdb45a 100644 --- a/test/mppa/lib/prng.h +++ b/test/mppa/prng/prng.h diff --git a/test/mppa/lib/types.h b/test/mppa/prng/types.h index 584023e3..584023e3 100644 --- a/test/mppa/lib/types.h +++ b/test/mppa/prng/types.h diff --git a/test/mppa/sort/.gitignore b/test/mppa/sort/.gitignore index c8f4f4e5..a8d6921c 100644 --- a/test/mppa/sort/.gitignore +++ b/test/mppa/sort/.gitignore @@ -1,9 +1,9 @@ -insertion-test-k1c -insertion-test-x86 -merge-test-k1c -selection-test-k1c -test-k1c -merge-test-x86 -selection-test-x86 -test-x86 -test-ccomp +main-test-ccomp-k1c +main-test-gcc-k1c +main-test-gcc-x86 +merge-test-gcc-k1c +merge-test-gcc-x86 +selection-test-gcc-k1c +selection-test-gcc-x86 +insertion-test-gcc-k1c +insertion-test-gcc-x86 diff --git a/test/mppa/sort/Makefile b/test/mppa/sort/Makefile index f94fe6b8..ebbad5b5 100644 --- a/test/mppa/sort/Makefile +++ b/test/mppa/sort/Makefile @@ -1,82 +1,91 @@ -PRNG=../lib/prng.c -CCOMP=../../../ccomp - -ALL= insertion-test-x86 insertion-test-k1c\ - selection-test-x86 selection-test-k1c\ - merge-test-x86 merge-test-k1c\ - test-x86 test-k1c\ - test-ccomp +K1CC ?= k1-mbr-gcc +CC ?= gcc +CCOMP ?= ccomp +CFLAGS ?= -O2 +SIMU ?= k1-cluster +TIMEOUT ?= 10s + +K1CCPATH=$(shell which $(K1CC)) +CCPATH=$(shell which $(CC)) +CCOMPPATH=$(shell which $(CCOMP)) +SIMUPATH=$(shell which $(SIMU)) + +PRNG=../prng/prng.c + +CFILES=insertion.c merge.c selection.c main.c + +ALL= insertion-gcc-x86 insertion-gcc-k1c insertion-ccomp-k1c\ + selection-gcc-x86 selection-gcc-k1c selection-ccomp-k1c\ + merge-gcc-x86 merge-gcc-k1c merge-ccomp-k1c\ + main-gcc-x86 main-gcc-k1c main-ccomp-k1c + +CCOMP_OUT= insertion-ccomp-k1c.out selection-ccomp-k1c.out merge-ccomp-k1c.out\ + main-ccomp-k1c.out +GCC_OUT= insertion-gcc-k1c.out selection-gcc-k1c.out merge-gcc-k1c.out\ + main-gcc-k1c.out +X86_GCC_OUT= insertion-gcc-x86.out selection-gcc-x86.out merge-gcc-x86.out\ + main-gcc-x86.out +STUB_OUT= .zero all: $(ALL) -%-test-x86: %.c $(PRNG) - gcc -g -D__UNIT_TEST_$$(echo $(basename $<) | tr a-z A-Z)__ -O2 -std=c99 $^ -o $@ - -%-test-k1c: %.c $(PRNG) - k1-gcc -g -D__UNIT_TEST_$$(echo $(basename $<) | tr a-z A-Z)__ -O2 -std=c99 $^ -o $@ +main-gcc-x86: $(CFILES) $(PRNG) $(CCPATH) + $(CC) $(CFLAGS) $(filter-out $(CCPATH),$^) -o $@ -test-x86: selection.c merge.c insertion.c test.c $(PRNG) - gcc -g -O2 -std=c99 $^ -o $@ +%-gcc-x86: %.c $(PRNG) $(CCPATH) + $(CC) -D__UNIT_TEST_$$(echo $(basename $<) | tr a-z A-Z)__ $(CFLAGS) $(filter-out $(CCPATH),$^) -o $@ -test-k1c: selection.c merge.c insertion.c test.c $(PRNG) - k1-gcc -g -O2 -std=c99 $^ -o $@ +main-gcc-k1c: $(CFILES) $(PRNG) $(CCPATH) + $(K1CC) $(CFLAGS) $(filter-out $(CCPATH),$^) -o $@ -%.s: %.c $(CCOMP) - ccomp -O2 -S $< -o $@ +%-gcc-k1c: %.c $(PRNG) $(K1CCPATH) + $(K1CC) -D__UNIT_TEST_$$(echo $(basename $<) | tr a-z A-Z)__ $(CFLAGS) $(filter-out $(K1CCPATH),$^) -o $@ -test-ccomp: selection.s merge.s insertion.s test.s $(subst .c,.s,$(PRNG)) - k1-gcc $^ -o $@ +main-ccomp-k1c: $(CFILES) $(PRNG) $(CCOMPPATH) + $(CCOMP) $(CFLAGS) $(filter-out $(CCOMPPATH),$^) -o $@ -.PHONY: -unittest: unittest-x86 unittest-k1c +%-ccomp-k1c: %.c $(PRNG) $(CCOMPPATH) + $(CCOMP) -D__UNIT_TEST_$$(echo $(basename $<) | tr a-z A-Z)__ $(CFLAGS) $(filter-out $(CCOMPPATH),$^) -o $@ -.PHONY: -check: check-x86 check-k1c +.SECONDARY: +%x86.out: %x86 + ret=0; timeout $(TIMEOUT) ./$< > $@ || { ret=$$?; }; echo $$ret >> $@ -.PHONY: -compc-check: test-ccomp - @if ! k1-cluster -- ./$<; then\ - >&2 echo "ERROR k1c: sort $< failed";\ - else\ - echo "k1c: Test sort $< succeeded";\ - fi - -.PHONY: -check-x86: test-x86 - @if ! ./$<; then\ - >&2 echo "ERROR x86: $< failed";\ - else\ - echo "x86: Test $< succeeded";\ - fi +%k1c.out: %k1c $(SIMUPATH) + ret=0; timeout $(TIMEOUT) $(SIMU) -- $< > $@ || { ret=$$?; }; echo $$ret >> $@ -.PHONY: -check-k1c: test-k1c - @if ! k1-cluster -- ./$<; then\ - >&2 echo "ERROR k1c: $< failed";\ - else\ - echo "k1c: Test $< succeeded";\ - fi +.zero: + @echo "0" > $@ .PHONY: -unittest-x86: insertion-test-x86 selection-test-x86 merge-test-x86 - @for test in $^; do\ - if ! ./$$test; then\ +test-x86: $(STUB_OUT) $(X86_GCC_OUT) + @for test in $(wordlist 2,100,$^); do\ + if ! diff $$test $(STUB_OUT); then\ >&2 echo "ERROR x86: $$test failed";\ else\ - echo "x86: Test $$test Succeeded";\ + echo "GOOD x86: $$test succeeded";\ fi;\ done .PHONY: -unittest-k1c: insertion-test-k1c selection-test-k1c merge-test-k1c - @for test in $^; do\ - if ! k1-cluster -- ./$$test; then\ +test-k1c: $(STUB_OUT) $(GCC_OUT) + @for test in $(wordlist 2,100,$^); do\ + if ! diff $$test $(STUB_OUT); then\ >&2 echo "ERROR k1c: $$test failed";\ else\ - echo "k1c: Test $$test Succeeded";\ + echo "GOOD k1c: $$test succeeded";\ fi;\ done .PHONY: -clean: - rm -f $(ALL) +test: test-x86 test-k1c + +.PHONY: +check: $(STUB_OUT) $(CCOMP_OUT) + @for test in $(wordlist 2,100,$^); do\ + if ! diff $$test $(STUB_OUT); then\ + >&2 echo "ERROR k1c: $$test failed";\ + else\ + echo "GOOD k1c: $$test succeeded";\ + fi;\ + done diff --git a/test/mppa/sort/README.md b/test/mppa/sort/README.md new file mode 100644 index 00000000..b4c2279b --- /dev/null +++ b/test/mppa/sort/README.md @@ -0,0 +1,17 @@ +PRNG +==== + +This is a simple Pseudo Random Number Generator. + +`prng.c` contains a simple unitary test that compares the sum of the "bytewise sum" +of 1000 generated numbers to a hardcoded result, that is the one obtained with +`gcc -O2` on a x86 processor, and returns 0 if the result is correct. + +The following commands can be run inside that folder: + +- `make`: produces the unitary test binaries + - `prng-test-gcc-x86` : binary from gcc on x86 + - `prng-test-k1c-x86` : binary from gcc on k1c + - `prng-test-ccomp-x86` : binary from ccomp on k1c +- `make test`: tests the return value of the binaries produced by gcc. +- `make check`: tests the return value of the binary produced by CompCert. diff --git a/test/mppa/sort/insertion.c b/test/mppa/sort/insertion.c index 88093b64..bca09599 100644 --- a/test/mppa/sort/insertion.c +++ b/test/mppa/sort/insertion.c @@ -1,5 +1,5 @@ -#include "../lib/prng.h" -#include "../lib/types.h" +#include "../prng/prng.h" +#include "../prng/types.h" #ifdef __UNIT_TEST_INSERTION__ #define SIZE 100 @@ -14,16 +14,18 @@ void swap_ins(uint64_t *a, uint64_t *b){ } int insert_sort(uint64_t *res, const uint64_t *T){ + int i, j; + if (SIZE <= 0) return -1; - for (int i = 0 ; i < SIZE ; i++) + for (i = 0 ; i < SIZE ; i++) res[i] = T[i]; - for (int i = 0 ; i < SIZE-1 ; i++){ + for (i = 0 ; i < SIZE-1 ; i++){ if (res[i] > res[i+1]){ swap_ins(&res[i], &res[i+1]); - for (int j = i ; j > 0 ; j--) + for (j = i ; j > 0 ; j--) if (res[j-1] > res[j]) swap_ins(&res[j-1], &res[j]); } @@ -36,9 +38,10 @@ int insert_sort(uint64_t *res, const uint64_t *T){ int main(void){ uint64_t T[SIZE]; uint64_t res[SIZE]; + int i; srand(42); - for (int i = 0 ; i < SIZE ; i++) + for (i = 0 ; i < SIZE ; i++) T[i] = randlong(); /* Sorting the table */ @@ -46,7 +49,7 @@ int main(void){ /* Computing max(T) */ uint64_t max = T[0]; - for (int i = 1 ; i < SIZE ; i++) + for (i = 1 ; i < SIZE ; i++) if (T[i] > max) max = T[i]; diff --git a/test/mppa/sort/test.c b/test/mppa/sort/main.c index e5e14fef..aef419aa 100644 --- a/test/mppa/sort/test.c +++ b/test/mppa/sort/main.c @@ -1,5 +1,5 @@ -#include "../lib/prng.h" -#include "../lib/types.h" +#include "../prng/prng.h" +#include "../prng/types.h" #include "test.h" #include "insertion.h" @@ -9,9 +9,10 @@ int main(void){ uint64_t T[SIZE]; uint64_t res1[SIZE], res2[SIZE], res3[SIZE]; + int i; srand(42); - for (int i = 0 ; i < SIZE ; i++) + for (i = 0 ; i < SIZE ; i++) T[i] = randlong(); /* insertion sort */ @@ -24,7 +25,7 @@ int main(void){ if (merge_sort(res3, T) < 0) return -3; /* We should have: res1[i] == res2[i] == res3[i] */ - for (int i = 0 ; i < SIZE ; i++){ + for (i = 0 ; i < SIZE ; i++){ if (!(res1[i] == res2[i] && res2[i] == res3[i])) return -4; } diff --git a/test/mppa/sort/merge.c b/test/mppa/sort/merge.c index b2d41ce3..99f8ba85 100644 --- a/test/mppa/sort/merge.c +++ b/test/mppa/sort/merge.c @@ -1,5 +1,5 @@ -#include "../lib/prng.h" -#include "../lib/types.h" +#include "../prng/prng.h" +#include "../prng/types.h" //https://en.wikipedia.org/wiki/Merge_sort @@ -15,8 +15,8 @@ int min(int a, int b){ void BottomUpMerge(const uint64_t *A, int iLeft, int iRight, int iEnd, uint64_t *B) { - int i = iLeft, j = iRight; - for (int k = iLeft; k < iEnd; k++) { + int i = iLeft, j = iRight, k; + for (k = iLeft; k < iEnd; k++) { if (i < iRight && (j >= iEnd || A[i] <= A[j])) { B[k] = A[i]; i = i + 1; @@ -30,18 +30,20 @@ void BottomUpMerge(const uint64_t *A, int iLeft, int iRight, int iEnd, uint64_t void CopyArray(uint64_t *to, const uint64_t *from) { const int n = SIZE; + int i; - for(int i = 0; i < n; i++) + for(i = 0; i < n; i++) to[i] = from[i]; } void BottomUpMergeSort(uint64_t *A, uint64_t *B) { const int n = SIZE; + int width, i; - for (int width = 1; width < n; width = 2 * width) + for (width = 1; width < n; width = 2 * width) { - for (int i = 0; i < n; i = i + 2 * width) + for (i = 0; i < n; i = i + 2 * width) { BottomUpMerge(A, i, min(i+width, n), min(i+2*width, n), B); } @@ -50,12 +52,14 @@ void BottomUpMergeSort(uint64_t *A, uint64_t *B) } int merge_sort(uint64_t *res, const uint64_t *T){ + int i; + if (SIZE <= 0) return -1; uint64_t B[SIZE]; uint64_t *A = res; - for (int i = 0 ; i < SIZE ; i++) + for (i = 0 ; i < SIZE ; i++) A[i] = T[i]; BottomUpMergeSort(A, B); @@ -67,9 +71,10 @@ int merge_sort(uint64_t *res, const uint64_t *T){ int main(void){ uint64_t T[SIZE]; uint64_t res[SIZE]; + int i; srand(42); - for (int i = 0 ; i < SIZE ; i++) + for (i = 0 ; i < SIZE ; i++) T[i] = randlong(); /* Sorting the table */ @@ -77,7 +82,7 @@ int main(void){ /* Computing max(T) */ uint64_t max = T[0]; - for (int i = 1 ; i < SIZE ; i++) + for (i = 1 ; i < SIZE ; i++) if (T[i] > max) max = T[i]; diff --git a/test/mppa/sort/selection.c b/test/mppa/sort/selection.c index 89bc2c65..df4be04f 100644 --- a/test/mppa/sort/selection.c +++ b/test/mppa/sort/selection.c @@ -1,5 +1,5 @@ -#include "../lib/prng.h" -#include "../lib/types.h" +#include "../prng/prng.h" +#include "../prng/types.h" #ifdef __UNIT_TEST_SELECTION__ #define SIZE 100 @@ -14,15 +14,16 @@ void swap_sel(uint64_t *a, uint64_t *b){ } int select_sort(uint64_t *res, const uint64_t *T){ + int i, j, iMin; + if (SIZE <= 0) return -1; - for (int i = 0 ; i < SIZE ; i++) + for (i = 0 ; i < SIZE ; i++) res[i] = T[i]; - for (int j = 0 ; j < SIZE ; j++){ - int i; - int iMin = j; + for (j = 0 ; j < SIZE ; j++){ + iMin = j; for (i = j+1 ; i < SIZE ; i++) if (res[i] < res[iMin]) iMin = i; @@ -38,17 +39,19 @@ int select_sort(uint64_t *res, const uint64_t *T){ int main(void){ uint64_t T[SIZE]; uint64_t res[SIZE]; + uint64_t max; + int i; srand(42); - for (int i = 0 ; i < SIZE ; i++) + for (i = 0 ; i < SIZE ; i++) T[i] = randlong(); /* Sorting the table */ if (select_sort(res, T) < 0) return -1; /* Computing max(T) */ - uint64_t max = T[0]; - for (int i = 1 ; i < SIZE ; i++) + max = T[0]; + for (i = 1 ; i < SIZE ; i++) if (T[i] > max) max = T[i]; diff --git a/test/mppa/test.sh b/test/mppa/test.sh new file mode 100755 index 00000000..dfeb153a --- /dev/null +++ b/test/mppa/test.sh @@ -0,0 +1,6 @@ +#!/bin/bash +# Tests the validity of the tests + +source do_test.sh + +do_test test |