diff options
author | Sylvain Boulmé <sylvain.boulme@univ-grenoble-alpes.fr> | 2021-02-11 08:23:46 +0100 |
---|---|---|
committer | Sylvain Boulmé <sylvain.boulme@univ-grenoble-alpes.fr> | 2021-02-11 08:23:46 +0100 |
commit | c98683ff46b50620fda6c4b2c40e0b71aa99dbbb (patch) | |
tree | 5b50158e3b4b684995170f5287206ca8f3e3eb59 /scheduling | |
parent | aaaa8f529716876a61f9405f4f696fc09505370a (diff) | |
download | compcert-kvx-c98683ff46b50620fda6c4b2c40e0b71aa99dbbb.tar.gz compcert-kvx-c98683ff46b50620fda6c4b2c40e0b71aa99dbbb.zip |
specification of pre_output_regs for the simulation checker
Diffstat (limited to 'scheduling')
-rw-r--r-- | scheduling/RTLpath.v | 1 | ||||
-rw-r--r-- | scheduling/RTLpathLivegenaux.ml | 4 | ||||
-rw-r--r-- | scheduling/RTLpathSE_impl.v | 46 | ||||
-rw-r--r-- | scheduling/RTLpathSE_simu_specs.v | 121 | ||||
-rw-r--r-- | scheduling/RTLpathSE_theory.v | 21 | ||||
-rw-r--r-- | scheduling/RTLpathSchedulerproof.v | 39 |
6 files changed, 107 insertions, 125 deletions
diff --git a/scheduling/RTLpath.v b/scheduling/RTLpath.v index cccc8147..5b34dc16 100644 --- a/scheduling/RTLpath.v +++ b/scheduling/RTLpath.v @@ -85,6 +85,7 @@ Record path_info := { psize: nat; (* number minus 1 of instructions in the path *) input_regs: Regset.t; (** Registers that are used (as input_regs) by the "fallthrough successors" of the path *) + pre_output_regs: Regset.t; (** This field is not used by the verificator, but is helpful for the superblock scheduler *) output_regs: Regset.t }. diff --git a/scheduling/RTLpathLivegenaux.ml b/scheduling/RTLpathLivegenaux.ml index ab921954..3d14a393 100644 --- a/scheduling/RTLpathLivegenaux.ml +++ b/scheduling/RTLpathLivegenaux.ml @@ -99,7 +99,7 @@ let get_path_map code entry join_points = dig_path_rec n' end | None -> Some ({ psize = (Camlcoq.Nat.of_int !psize); - input_regs = Regset.empty; output_regs = Regset.empty }, + input_regs = Regset.empty; pre_output_regs = Regset.empty; output_regs = Regset.empty }, !path_successors @ successors_inst inst) end else None @@ -240,7 +240,7 @@ let set_pathmap_liveness f pm = let inputs = get_some @@ PTree.get n liveness in let outputs = get_outputs liveness code n pi in new_pm := PTree.set n - {psize=pi.psize; input_regs=inputs; output_regs=outputs} !new_pm + {psize=pi.psize; input_regs=inputs; pre_output_regs=outputs; output_regs=outputs} !new_pm (* FIXME: STUB *) ) (PTree.elements pm); !new_pm end diff --git a/scheduling/RTLpathSE_impl.v b/scheduling/RTLpathSE_impl.v index 38930a75..bd26171d 100644 --- a/scheduling/RTLpathSE_impl.v +++ b/scheduling/RTLpathSE_impl.v @@ -1149,22 +1149,6 @@ Qed. Global Opaque PTree_frame_eq_check. Local Hint Resolve PTree_frame_eq_check_correct: wlp. -Definition hsilocal_simu_check hst1 hst2 : ?? unit := - DEBUG("? last check");; - phys_check (hsi_smem hst2) (hsi_smem hst1) "hsilocal_simu_check: hsi_smem sets aren't equiv";; - PTree_eq_check (hsi_sreg hst1) (hsi_sreg hst2);; - Sets.assert_list_incl mk_hash_params (hsi_ok_lsval hst2) (hsi_ok_lsval hst1);; - DEBUG("=> last check: OK"). - -Lemma hsilocal_simu_check_correct hst1 hst2: - WHEN hsilocal_simu_check hst1 hst2 ~> _ THEN - hsilocal_simu_spec None hst1 hst2. -Proof. - unfold hsilocal_simu_spec; wlp_simplify. -Qed. -Hint Resolve hsilocal_simu_check_correct: wlp. -Global Opaque hsilocal_simu_check. - Definition hsilocal_frame_simu_check frame hst1 hst2 : ?? unit := DEBUG("? frame check");; phys_check (hsi_smem hst2) (hsi_smem hst1) "hsilocal_frame_simu_check: hsi_smem sets aren't equiv";; @@ -1192,7 +1176,7 @@ Local Hint Resolve regset_elements_in: core. Lemma hsilocal_frame_simu_check_correct hst1 hst2 alive: WHEN hsilocal_frame_simu_check (Regset.elements alive) hst1 hst2 ~> _ THEN - hsilocal_simu_spec (Some alive) hst1 hst2. + hsilocal_simu_spec alive hst1 hst2. Proof. unfold hsilocal_simu_spec; wlp_simplify. symmetry; eauto. Qed. @@ -1246,13 +1230,13 @@ Qed. Hint Resolve hsiexits_simu_check_correct: wlp. Global Opaque hsiexits_simu_check. -Definition hsistate_simu_check (dm: PTree.t node) (f: RTLpath.function) (hst1 hst2: hsistate) := +Definition hsistate_simu_check (dm: PTree.t node) (f: RTLpath.function) outframe (hst1 hst2: hsistate) := hsiexits_simu_check dm f (hsi_exits hst1) (hsi_exits hst2);; - hsilocal_simu_check (hsi_local hst1) (hsi_local hst2). + hsilocal_frame_simu_check (Regset.elements outframe) (hsi_local hst1) (hsi_local hst2). -Lemma hsistate_simu_check_correct dm f hst1 hst2: - WHEN hsistate_simu_check dm f hst1 hst2 ~> _ THEN - hsistate_simu_spec dm f hst1 hst2. +Lemma hsistate_simu_check_correct dm f outframe hst1 hst2: + WHEN hsistate_simu_check dm f outframe hst1 hst2 ~> _ THEN + hsistate_simu_spec dm f outframe hst1 hst2. Proof. unfold hsistate_simu_spec; wlp_simplify. Qed. @@ -1386,18 +1370,18 @@ Qed. Hint Resolve sfval_simu_check_correct: wlp. Global Opaque sfval_simu_check. -Definition hsstate_simu_check (dm: PTree.t node) (f: RTLpath.function) (hst1 hst2: hsstate) := - hsistate_simu_check dm f (hinternal hst1) (hinternal hst2);; +Definition hsstate_simu_check (dm: PTree.t node) (f: RTLpath.function) outframe (hst1 hst2: hsstate) := + hsistate_simu_check dm f outframe (hinternal hst1) (hinternal hst2);; sfval_simu_check dm f (hsi_pc hst1) (hsi_pc hst2) (hfinal hst1) (hfinal hst2). -Lemma hsstate_simu_check_correct dm f hst1 hst2: - WHEN hsstate_simu_check dm f hst1 hst2 ~> _ THEN - hsstate_simu_spec dm f hst1 hst2. +Lemma hsstate_simu_check_correct dm f outframe hst1 hst2: + WHEN hsstate_simu_check dm f outframe hst1 hst2 ~> _ THEN + hsstate_simu_spec dm f outframe hst1 hst2. Proof. unfold hsstate_simu_spec; wlp_simplify. Qed. Hint Resolve hsstate_simu_check_correct: wlp. -Global Opaque hsstate_simu_check. +Global Opaque hsstate_simu_check. Definition simu_check_single (dm: PTree.t node) (f: RTLpath.function) (tf: RTLpath.function) (m: node * node): ?? unit := let (pc2, pc1) := m in @@ -1411,8 +1395,10 @@ Definition simu_check_single (dm: PTree.t node) (f: RTLpath.function) (tf: RTLpa DO hst1 <~ hsexec f pc1;; XDEBUG pc2 (fun pc => DO name_pc <~ string_of_Z (Zpos pc);; RET ("entry-point of output superblock: " +; name_pc)%string);; DO hst2 <~ hsexec tf pc2;; + DO path <~ some_or_fail ((fn_path f)!pc1) "simu_check_single.internal_error.1";; + let outframe := path.(pre_output_regs) in (* comparing the executions *) - hsstate_simu_check dm f hst1 hst2. + hsstate_simu_check dm f outframe hst1 hst2. Lemma simu_check_single_correct dm tf f pc1 pc2: WHEN simu_check_single dm f tf (pc2, pc1) ~> _ THEN @@ -1423,7 +1409,7 @@ Proof. intros (st2 & SEXEC2 & REF2). try_simplify_someHyps. exploit H3; clear H3. 1-3: wlp_simplify. intros (st3 & SEXEC3 & REF3). try_simplify_someHyps. - eexists. split; eauto. + eexists. eexists. split; eauto. split; eauto. intros ctx. eapply hsstate_simu_spec_correct; eauto. Qed. diff --git a/scheduling/RTLpathSE_simu_specs.v b/scheduling/RTLpathSE_simu_specs.v index c9e272c0..03329651 100644 --- a/scheduling/RTLpathSE_simu_specs.v +++ b/scheduling/RTLpathSE_simu_specs.v @@ -18,10 +18,10 @@ Local Open Scope list_scope. (** * Auxilary notions on simulation tests *) -Definition silocal_simu (dm: PTree.t node) (f: RTLpath.function) (sl1 sl2: sistate_local) (ctx: simu_proof_context f): Prop := +Definition silocal_simu (dm: PTree.t node) (f: RTLpath.function) outframe (sl1 sl2: sistate_local) (ctx: simu_proof_context f): Prop := forall is1, ssem_local (the_ge1 ctx) (the_sp ctx) sl1 (the_rs0 ctx) (the_m0 ctx) (irs is1) (imem is1) -> exists is2, ssem_local (the_ge2 ctx) (the_sp ctx) sl2 (the_rs0 ctx) (the_m0 ctx) (irs is2) (imem is2) - /\ istate_simu f dm is1 is2. + /\ istate_simu f dm outframe is1 is2. (* a kind of negation of sabort_local *) Definition sok_local (ge: RTL.genv) (sp:val) (rs0: regset) (m0: mem) (st: sistate_local): Prop := @@ -36,7 +36,7 @@ Proof. intuition congruence. Qed. -Definition siexit_simu (dm: PTree.t node) (f: RTLpath.function) (ctx: simu_proof_context f) (se1 se2: sistate_exit) := +Definition siexit_simu (dm: PTree.t node) (f: RTLpath.function) outframe (ctx: simu_proof_context f) (se1 se2: sistate_exit) := (sok_local (the_ge1 ctx) (the_sp ctx) (the_rs0 ctx) (the_m0 ctx) (si_elocal se1) -> (seval_condition (the_ge1 ctx) (the_sp ctx) (si_cond se1) (si_scondargs se1) (si_smem (si_elocal se1)) (the_rs0 ctx) (the_m0 ctx)) = @@ -47,10 +47,10 @@ Definition siexit_simu (dm: PTree.t node) (f: RTLpath.function) (ctx: simu_proof ssem_exit (the_ge1 ctx) (the_sp ctx) se1 (the_rs0 ctx) (the_m0 ctx) (irs is1) (imem is1) (ipc is1) -> exists is2, ssem_exit (the_ge2 ctx) (the_sp ctx) se2 (the_rs0 ctx) (the_m0 ctx) (irs is2) (imem is2) (ipc is2) - /\ istate_simu f dm is1 is2. + /\ istate_simu f dm outframe is1 is2. -Definition siexits_simu (dm: PTree.t node) (f: RTLpath.function) (lse1 lse2: list sistate_exit) (ctx: simu_proof_context f) := - list_forall2 (siexit_simu dm f ctx) lse1 lse2. +Definition siexits_simu (dm: PTree.t node) (f: RTLpath.function) outframe (lse1 lse2: list sistate_exit) (ctx: simu_proof_context f) := + list_forall2 (siexit_simu dm f outframe ctx) lse1 lse2. (** * Implementation of Data-structure use in Hash-consing *) @@ -318,9 +318,9 @@ Definition hsstate_refines (hst: hsstate) (st:sstate): Prop := (** ** Specification of the simulation test on [hsistate_local]. It is motivated by [hsilocal_simu_spec_correct theorem] below *) -Definition hsilocal_simu_spec (oalive: option Regset.t) (hst1 hst2: hsistate_local) := +Definition hsilocal_simu_spec (alive: Regset.t) (hst1 hst2: hsistate_local) := List.incl (hsi_ok_lsval hst2) (hsi_ok_lsval hst1) - /\ (forall r, (match oalive with Some alive => Regset.In r alive | _ => True end) -> PTree.get r hst2 = PTree.get r hst1) + /\ (forall r, Regset.In r alive -> PTree.get r hst2 = PTree.get r hst1) /\ hsi_smem hst1 = hsi_smem hst2. Definition seval_sval_partial ge sp rs0 m0 hsv := @@ -368,18 +368,14 @@ Proof. - erewrite MEMOK in OKM. erewrite smem_eval_preserved; eauto. Qed. -Theorem hsilocal_simu_spec_correct hst1 hst2 of ge1 ge2 sp rs0 m0 rs m st1 st2: - hsilocal_simu_spec of hst1 hst2 -> +Theorem hsilocal_simu_spec_correct hst1 hst2 alive ge1 ge2 sp rs0 m0 rs m st1 st2: + hsilocal_simu_spec alive hst1 hst2 -> hsilocal_refines ge1 sp rs0 m0 hst1 st1 -> hsilocal_refines ge2 sp rs0 m0 hst2 st2 -> (forall s, Genv.find_symbol ge1 s = Genv.find_symbol ge2 s) -> ssem_local ge1 sp st1 rs0 m0 rs m -> - match of with - | None => ssem_local ge2 sp st2 rs0 m0 rs m - | Some alive => - let rs' := seval_partial_regset ge2 sp rs0 m0 (hsi_sreg hst2) - in ssem_local ge2 sp st2 rs0 m0 rs' m /\ eqlive_reg (fun r => Regset.In r alive) rs rs' - end. + let rs' := seval_partial_regset ge2 sp rs0 m0 (hsi_sreg hst2) + in ssem_local ge2 sp st2 rs0 m0 rs' m /\ eqlive_reg (fun r => Regset.In r alive) rs rs'. Proof. intros CORE HREF1 HREF2 GFS SEML. refine (modusponens _ _ (ssem_local_refines_hok _ _ _ _ _ _ _ _ _ _) _); eauto. @@ -394,9 +390,8 @@ Proof. rewrite <- MEMEQ2; auto. rewrite <- MEMEQ3. erewrite smem_eval_preserved; [| eapply GFS]. rewrite MEMEQ1; auto. } - destruct of as [alive |]. - - constructor. - + constructor; [assumption | constructor; [assumption|]]. + constructor. + + constructor; [assumption | constructor; [assumption|]]. destruct HREF2 as (B & _ & A & _). (** B is used for the auto below. *) assert (forall r : positive, hsi_sreg_eval ge2 sp hst2 r rs0 m0 = seval_sval ge2 sp (si_sreg st2 r) rs0 m0) by auto. @@ -420,17 +415,6 @@ Proof. unfold hsi_sreg_eval, hsi_sreg_proj in B; rewrite B; [|assumption]. rewrite RSEQ. reflexivity. ++ rewrite <- RSEQ. rewrite <- B; [|assumption]. unfold hsi_sreg_eval, hsi_sreg_proj. rewrite <- C; [|assumption]. rewrite HST2. reflexivity. - - constructor; [|constructor]. - + destruct HREF2 as (OKEQ & _ & _). rewrite <- OKEQ in HOK2. apply HOK2. - + destruct HREF2 as (_ & MEMEQ2 & _). destruct HREF1 as (_ & MEMEQ1 & _). - destruct CORE as (_ & _ & MEMEQ3). - rewrite <- MEMEQ2; auto. rewrite <- MEMEQ3. - erewrite smem_eval_preserved; [| eapply GFS]. - rewrite MEMEQ1; auto. - + intro r. destruct HREF2 as (_ & _ & A & _). destruct HREF1 as (_ & _ & B & _). - destruct CORE as (_ & C & _). rewrite <- A; auto. unfold hsi_sreg_eval, hsi_sreg_proj. - rewrite C; [|auto]. erewrite seval_preserved; [| eapply GFS]. - unfold hsi_sreg_eval, hsi_sreg_proj in B; rewrite B; auto. Qed. (** ** Specification of the simulation test on [hsistate_exit]. @@ -438,17 +422,17 @@ Qed. *) Definition hsiexit_simu_spec dm f (hse1 hse2: hsistate_exit) := (exists path, (fn_path f) ! (hsi_ifso hse1) = Some path - /\ hsilocal_simu_spec (Some path.(input_regs)) (hsi_elocal hse1) (hsi_elocal hse2)) + /\ hsilocal_simu_spec path.(input_regs) (hsi_elocal hse1) (hsi_elocal hse2)) /\ dm ! (hsi_ifso hse2) = Some (hsi_ifso hse1) /\ hsi_cond hse1 = hsi_cond hse2 /\ hsi_scondargs hse1 = hsi_scondargs hse2. -Definition hsiexit_simu dm f (ctx: simu_proof_context f) hse1 hse2: Prop := forall se1 se2, +Definition hsiexit_simu dm f outframe (ctx: simu_proof_context f) hse1 hse2: Prop := forall se1 se2, hsiexit_refines_stat hse1 se1 -> hsiexit_refines_stat hse2 se2 -> hsiexit_refines_dyn (the_ge1 ctx) (the_sp ctx) (the_rs0 ctx) (the_m0 ctx) hse1 se1 -> hsiexit_refines_dyn (the_ge2 ctx) (the_sp ctx) (the_rs0 ctx) (the_m0 ctx) hse2 se2 -> - siexit_simu dm f ctx se1 se2. + siexit_simu dm f outframe ctx se1 se2. Lemma hsiexit_simu_spec_nofail dm f hse1 hse2 ge1 ge2 sp rs m: hsiexit_simu_spec dm f hse1 hse2 -> @@ -461,9 +445,9 @@ Proof. eapply hsilocal_simu_spec_nofail; eauto. Qed. -Theorem hsiexit_simu_spec_correct dm f hse1 hse2 ctx: +Theorem hsiexit_simu_spec_correct dm f outframe hse1 hse2 ctx: hsiexit_simu_spec dm f hse1 hse2 -> - hsiexit_simu dm f ctx hse1 hse2. + hsiexit_simu dm f outframe ctx hse1 hse2. Proof. intros SIMUC st1 st2 HREF1 HREF2 HDYN1 HDYN2. assert (SEVALC: @@ -498,13 +482,13 @@ Proof. constructor; [|constructor]; simpl; auto. Qed. -Remark hsiexit_simu_siexit dm f ctx hse1 hse2 se1 se2: - hsiexit_simu dm f ctx hse1 hse2 -> +Remark hsiexit_simu_siexit dm f outframe ctx hse1 hse2 se1 se2: + hsiexit_simu dm f outframe ctx hse1 hse2 -> hsiexit_refines_stat hse1 se1 -> hsiexit_refines_stat hse2 se2 -> hsiexit_refines_dyn (the_ge1 ctx) (the_sp ctx) (the_rs0 ctx) (the_m0 ctx) hse1 se1 -> hsiexit_refines_dyn (the_ge2 ctx) (the_sp ctx) (the_rs0 ctx) (the_m0 ctx) hse2 se2 -> - siexit_simu dm f ctx se1 se2. + siexit_simu dm f outframe ctx se1 se2. Proof. auto. Qed. @@ -513,15 +497,15 @@ Qed. It is motivated by [hsiexit_simu_spec_correct theorem] below *) -Definition hsiexits_simu dm f (ctx: simu_proof_context f) (lhse1 lhse2: list hsistate_exit): Prop := - list_forall2 (hsiexit_simu dm f ctx) lhse1 lhse2. +Definition hsiexits_simu dm f outframe (ctx: simu_proof_context f) (lhse1 lhse2: list hsistate_exit): Prop := + list_forall2 (hsiexit_simu dm f outframe ctx) lhse1 lhse2. Definition hsiexits_simu_spec dm f lhse1 lhse2: Prop := list_forall2 (hsiexit_simu_spec dm f) lhse1 lhse2. -Theorem hsiexits_simu_spec_correct dm f lhse1 lhse2 ctx: +Theorem hsiexits_simu_spec_correct dm f outframe lhse1 lhse2 ctx: hsiexits_simu_spec dm f lhse1 lhse2 -> - hsiexits_simu dm f ctx lhse1 lhse2. + hsiexits_simu dm f outframe ctx lhse1 lhse2. Proof. induction 1; [constructor|]. constructor; [|apply IHlist_forall2; assumption]. @@ -529,8 +513,8 @@ Proof. Qed. -Lemma siexits_simu_all_fallthrough dm f ctx: forall lse1 lse2, - siexits_simu dm f lse1 lse2 ctx -> +Lemma siexits_simu_all_fallthrough dm f outframe ctx: forall lse1 lse2, + siexits_simu dm f outframe lse1 lse2 ctx -> all_fallthrough (the_ge1 ctx) (the_sp ctx) lse1 (the_rs0 ctx) (the_m0 ctx) -> (forall se1, In se1 lse1 -> sok_local (the_ge1 ctx) (the_sp ctx) (the_rs0 ctx) (the_m0 ctx) (si_elocal se1)) -> all_fallthrough (the_ge2 ctx) (the_sp ctx) lse2 (the_rs0 ctx) (the_m0 ctx). @@ -545,8 +529,8 @@ Proof. Qed. -Lemma siexits_simu_all_fallthrough_upto dm f ctx lse1 lse2: - siexits_simu dm f lse1 lse2 ctx -> +Lemma siexits_simu_all_fallthrough_upto dm f outframe ctx lse1 lse2: + siexits_simu dm f outframe lse1 lse2 ctx -> forall ext1 lx1, (forall se1, In se1 lx1 -> sok_local (the_ge1 ctx) (the_sp ctx) (the_rs0 ctx) (the_m0 ctx) (si_elocal se1)) -> all_fallthrough_upto_exit (the_ge1 ctx) (the_sp ctx) ext1 lx1 lse1 (the_rs0 ctx) (the_m0 ctx) -> @@ -570,14 +554,14 @@ Proof. Qed. -Lemma hsiexits_simu_siexits dm f ctx lhse1 lhse2: - hsiexits_simu dm f ctx lhse1 lhse2 -> +Lemma hsiexits_simu_siexits dm f outframe ctx lhse1 lhse2: + hsiexits_simu dm f outframe ctx lhse1 lhse2 -> forall lse1 lse2, hsiexits_refines_stat lhse1 lse1 -> hsiexits_refines_stat lhse2 lse2 -> hsiexits_refines_dyn (the_ge1 ctx) (the_sp ctx) (the_rs0 ctx) (the_m0 ctx) lhse1 lse1 -> hsiexits_refines_dyn (the_ge2 ctx) (the_sp ctx) (the_rs0 ctx) (the_m0 ctx) lhse2 lse2 -> - siexits_simu dm f lse1 lse2 ctx. + siexits_simu dm f outframe lse1 lse2 ctx. Proof. induction 1. - intros. inv H. inv H0. constructor. @@ -591,16 +575,16 @@ Qed. It is motivated by [hsistate_simu_spec_correct theorem] below *) -Definition hsistate_simu_spec dm f (hse1 hse2: hsistate) := +Definition hsistate_simu_spec dm f outframe (hse1 hse2: hsistate) := list_forall2 (hsiexit_simu_spec dm f) (hsi_exits hse1) (hsi_exits hse2) - /\ hsilocal_simu_spec None (hsi_local hse1) (hsi_local hse2). + /\ hsilocal_simu_spec outframe (hsi_local hse1) (hsi_local hse2). -Definition hsistate_simu dm f (hst1 hst2: hsistate) (ctx: simu_proof_context f): Prop := forall st1 st2, +Definition hsistate_simu dm f outframe (hst1 hst2: hsistate) (ctx: simu_proof_context f): Prop := forall st1 st2, hsistate_refines_stat hst1 st1 -> hsistate_refines_stat hst2 st2 -> hsistate_refines_dyn (the_ge1 ctx) (the_sp ctx) (the_rs0 ctx) (the_m0 ctx) hst1 st1 -> hsistate_refines_dyn (the_ge2 ctx) (the_sp ctx) (the_rs0 ctx) (the_m0 ctx) hst2 st2 -> - sistate_simu dm f st1 st2 ctx. + sistate_simu dm f outframe st1 st2 ctx. Lemma list_forall2_nth_error {A} (l1 l2: list A) P: list_forall2 P l1 l2 -> @@ -644,9 +628,9 @@ Proof. rewrite H0; auto. Qed. -Theorem hsistate_simu_spec_correct dm f hst1 hst2 ctx: - hsistate_simu_spec dm f hst1 hst2 -> - hsistate_simu dm f hst1 hst2 ctx. +Theorem hsistate_simu_spec_correct dm f outframe hst1 hst2 ctx: + hsistate_simu_spec dm f outframe hst1 hst2 -> + hsistate_simu dm f outframe hst1 hst2 ctx. Proof. intros (ESIMU & LSIMU) st1 st2 (PCREF1 & EREF1) (PCREF2 & EREF2) DREF1 DREF2 is1 SEMI. destruct DREF1 as (DEREF1 & LREF1 & NESTED). destruct DREF2 as (DEREF2 & LREF2 & _). @@ -655,22 +639,23 @@ Proof. - destruct SEMI as (SSEML & PCEQ & ALLFU). exploit hsilocal_simu_spec_correct; eauto; [apply ctx|]. simpl. intro SSEML2. exists (mk_istate (icontinue is1) (si_pc st2) (irs is1) (imem is1)). constructor. - + unfold ssem_internal. simpl. rewrite ICONT. constructor; [assumption | constructor; [reflexivity |]]. + + unfold ssem_internal. simpl. rewrite ICONT. admit. + (* constructor; [assumption | constructor; [reflexivity |]]. eapply siexits_simu_all_fallthrough; eauto. * eapply hsiexits_simu_siexits; eauto. * eapply nested_sok_prop; eauto. - eapply ssem_local_sok; eauto. + eapply ssem_local_sok; eauto. *) + unfold istate_simu. rewrite ICONT. constructor; [simpl; assumption | constructor; [| reflexivity]]. constructor. - destruct SEMI as (ext & lx & SSEME & ALLFU). - assert (SESIMU: siexits_simu dm f (si_exits st1) (si_exits st2) ctx) by (eapply hsiexits_simu_siexits; eauto). + assert (SESIMU: siexits_simu dm f outframe (si_exits st1) (si_exits st2) ctx) by (eapply hsiexits_simu_siexits; eauto). exploit siexits_simu_all_fallthrough_upto; eauto. * destruct ALLFU as (ITAIL & ALLF). exploit nested_sok_tail; eauto. intros NESTED2. inv NESTED2. destruct SSEME as (_ & SSEML & _). eapply ssem_local_sok in SSEML. eapply nested_sok_prop; eauto. * intros (ext2 & lx2 & ALLFU2 & LENEQ). - assert (EXTSIMU: siexit_simu dm f ctx ext ext2). { + assert (EXTSIMU: siexit_simu dm f outframe ctx ext ext2). { eapply list_forall2_nth_error; eauto. - destruct ALLFU as (ITAIL & _). eapply is_tail_nth_error; eauto. - destruct ALLFU2 as (ITAIL & _). eapply is_tail_nth_error in ITAIL. @@ -683,7 +668,7 @@ Proof. + unfold istate_simu in *. rewrite ICONT in *. destruct ISIMU as (path & PATHEQ & ISIMULIVE & DMEQ). destruct ISIMULIVE as (CONTEQ & REGEQ & MEMEQ). exists path. repeat (constructor; auto). -Qed. +Admitted. (** ** Specification of the simulation test on [sfval]. @@ -858,18 +843,18 @@ Qed. It is motivated by [hsstate_simu_spec_correct theorem] below *) -Definition hsstate_simu_spec (dm: PTree.t node) (f: RTLpath.function) (hst1 hst2: hsstate) := - hsistate_simu_spec dm f (hinternal hst1) (hinternal hst2) +Definition hsstate_simu_spec (dm: PTree.t node) (f: RTLpath.function) outframe (hst1 hst2: hsstate) := + hsistate_simu_spec dm f outframe (hinternal hst1) (hinternal hst2) /\ hfinal_simu_spec dm f (hsi_pc (hinternal hst1)) (hsi_pc (hinternal hst2)) (hfinal hst1) (hfinal hst2). -Definition hsstate_simu dm f (hst1 hst2: hsstate) ctx: Prop := +Definition hsstate_simu dm f outframe (hst1 hst2: hsstate) ctx: Prop := forall st1 st2, hsstate_refines hst1 st1 -> - hsstate_refines hst2 st2 -> sstate_simu dm f st1 st2 ctx. + hsstate_refines hst2 st2 -> sstate_simu dm f outframe st1 st2 ctx. -Theorem hsstate_simu_spec_correct dm f ctx hst1 hst2: - hsstate_simu_spec dm f hst1 hst2 -> - hsstate_simu dm f hst1 hst2 ctx. +Theorem hsstate_simu_spec_correct dm f outframe ctx hst1 hst2: + hsstate_simu_spec dm f outframe hst1 hst2 -> + hsstate_simu dm f outframe hst1 hst2 ctx. Proof. intros (SCORE & FSIMU) st1 st2 (SREF1 & DREF1 & FREF1) (SREF2 & DREF2 & FREF2). generalize SCORE. intro SIMU; eapply hsistate_simu_spec_correct in SIMU; eauto. diff --git a/scheduling/RTLpathSE_theory.v b/scheduling/RTLpathSE_theory.v index 4c492ecd..eec0bc51 100644 --- a/scheduling/RTLpathSE_theory.v +++ b/scheduling/RTLpathSE_theory.v @@ -1627,13 +1627,9 @@ Definition istate_simulive alive (srce: PTree.t node) (is1 is2: istate): Prop := /\ eqlive_reg alive is1.(irs) is2.(irs) /\ is1.(imem) = is2.(imem). -Definition istate_simu f (srce: PTree.t node) is1 is2: Prop := +Definition istate_simu f (srce: PTree.t node) outframe is1 is2: Prop := if is1.(icontinue) then - (* TODO: il faudra raffiner le (fun _ => True) si on veut autoriser l'oracle à - ajouter du "code mort" sur des registres non utilisés (loop invariant code motion à la David) - Typiquement, pour connaître la frame des registres vivants, il faudra faire une propagation en arrière - sur la dernière instruction du superblock. *) - istate_simulive (fun _ => True) srce is1 is2 + istate_simulive (fun r => Regset.In r outframe) srce is1 is2 else exists path, f.(fn_path)!(is1.(ipc)) = Some path /\ istate_simulive (fun r => Regset.In r path.(input_regs)) srce is1 is2 @@ -1651,10 +1647,10 @@ Record simu_proof_context {f1: RTLpath.function} := { Arguments simu_proof_context: clear implicits. (* NOTE: a pure semantic definition on [sistate], for a total freedom in refinements *) -Definition sistate_simu (dm: PTree.t node) (f: RTLpath.function) (st1 st2: sistate) (ctx: simu_proof_context f): Prop := +Definition sistate_simu (dm: PTree.t node) (f: RTLpath.function) outframe (st1 st2: sistate) (ctx: simu_proof_context f): Prop := forall is1, ssem_internal (the_ge1 ctx) (the_sp ctx) st1 (the_rs0 ctx) (the_m0 ctx) is1 -> exists is2, ssem_internal (the_ge2 ctx) (the_sp ctx) st2 (the_rs0 ctx) (the_m0 ctx) is2 - /\ istate_simu f dm is1 is2. + /\ istate_simu f dm outframe is1 is2. Inductive svident_simu (f: RTLpath.function) (ctx: simu_proof_context f): (sval + ident) -> (sval + ident) -> Prop := | Sleft_simu sv1 sv2: @@ -1885,13 +1881,14 @@ Inductive sfval_simu (dm: PTree.t node) (f: RTLpath.function) (opc1 opc2: node) = (seval_sval (the_ge2 ctx) (the_sp ctx) sv2 (the_rs0 ctx) (the_m0 ctx)) -> sfval_simu dm f opc1 opc2 ctx (Sreturn (Some sv1)) (Sreturn (Some sv2)). -Definition sstate_simu dm f (s1 s2: sstate) (ctx: simu_proof_context f): Prop := - sistate_simu dm f s1.(internal) s2.(internal) ctx - /\ forall is1, +Definition sstate_simu dm f outframe (s1 s2: sstate) (ctx: simu_proof_context f): Prop := + sistate_simu dm f outframe s1.(internal) s2.(internal) ctx + /\ forall is1, ssem_internal (the_ge1 ctx) (the_sp ctx) s1 (the_rs0 ctx) (the_m0 ctx) is1 -> is1.(icontinue) = true -> sfval_simu dm f s1.(si_pc) s2.(si_pc) ctx s1.(final) s2.(final). Definition sexec_simu dm (f1 f2: RTLpath.function) pc1 pc2: Prop := forall st1, sexec f1 pc1 = Some st1 -> - exists st2, sexec f2 pc2 = Some st2 /\ forall ctx, sstate_simu dm f1 st1 st2 ctx. + exists path st2, (fn_path f1)!pc1 = Some path /\ sexec f2 pc2 = Some st2 + /\ forall ctx, sstate_simu dm f1 path.(pre_output_regs) st1 st2 ctx. diff --git a/scheduling/RTLpathSchedulerproof.v b/scheduling/RTLpathSchedulerproof.v index 4ba197b0..23f7fa8a 100644 --- a/scheduling/RTLpathSchedulerproof.v +++ b/scheduling/RTLpathSchedulerproof.v @@ -167,12 +167,12 @@ Proof. (* intros. eapply all_fundef_liveness_ok; eauto. *) Qed. -Lemma sistate_simu f dupmap sp st st' rs m is +Lemma sistate_simu f dupmap outframe sp st st' rs m is (LIVE: liveness_ok_function f): ssem_internal ge sp st rs m is -> - sistate_simu dupmap f st st' (mkctx sp rs m LIVE)-> + sistate_simu dupmap f outframe st st' (mkctx sp rs m LIVE)-> exists is', - ssem_internal tge sp st' rs m is' /\ istate_simu f dupmap is is'. + ssem_internal tge sp st' rs m is' /\ istate_simu f dupmap outframe is is'. Proof. intros SEM X; eapply X; eauto. Qed. @@ -198,13 +198,12 @@ Lemma ssem_final_simu dm f f' stk stk' sp st st' rs0 m0 sv sv' rs m t s (LIVE: liveness_ok_function f): match_function dm f f' -> list_forall2 match_stackframes stk stk' -> - (* s_istate_simu f dupmap st st' -> *) sfval_simu dm f st.(si_pc) st'.(si_pc) (mkctx sp rs0 m0 LIVE) sv sv' -> ssem_final pge ge sp st.(si_pc) stk f rs0 m0 sv rs m t s -> exists s', ssem_final tpge tge sp st'.(si_pc) stk' f' rs0 m0 sv' rs m t s' /\ match_states s s'. Proof. Local Hint Resolve transf_fundef_correct: core. - intros FUN STK (* SIS *) SFV. destruct SFV; intros SEM; inv SEM; simpl in *. + intros FUN STK SFV. destruct SFV; intros SEM; inv SEM; simpl in *. - (* Snone *) exploit initialize_path. { eapply dupmap_path_entry1; eauto. } intros (path & PATH). @@ -253,18 +252,29 @@ Proof. + rewrite <- H. erewrite <- seval_preserved; eauto. Qed. +Lemma pre_output_regs_correct f pc0 path0 stk sp (st:sstate) rs0 m0 t s' rs m rs': + (liveness_ok_function f) -> + (fn_path f) ! pc0 = Some path0 -> + path_step ge pge (psize path0) stk f sp rs0 m0 pc0 t s' -> + ssem_final pge ge sp (si_pc st) stk f rs0 m0 (final st) rs m t s' -> + eqlive_reg (fun r : Regset.elt => Regset.In r (pre_output_regs path0)) rs rs' -> + ssem_final pge ge sp (si_pc st) stk f rs0 m0 (final st) rs' m t s'. +Admitted. + (* The main theorem on simulation of symbolic states ! *) -Theorem ssem_sstate_simu dm f f' stk stk' sp st st' rs m t s: +Theorem ssem_sstate_simu dm f f' pc0 path0 stk stk' sp st st' rs m t s: + (fn_path f) ! pc0 = Some path0 -> + path_step ge pge (psize path0) stk f sp rs m pc0 t s -> match_function dm f f' -> liveness_ok_function f -> list_forall2 match_stackframes stk stk' -> ssem pge ge sp st stk f rs m t s -> - (forall ctx: simu_proof_context f, sstate_simu dm f st st' ctx) -> + (forall ctx: simu_proof_context f, sstate_simu dm f (pre_output_regs path0) st st' ctx) -> exists s', ssem tpge tge sp st' stk' f' rs m t s' /\ match_states s s'. Proof. - intros MFUNC LIVE STACKS SEM SIMU. + intros PATH0 STEP MFUNC LIVE STACKS SEM SIMU. destruct (SIMU (mkctx sp rs m LIVE)) as (SIMU1 & SIMU2); clear SIMU. - destruct SEM as [is CONT SEM|is t s' CONT SEM1 SEM2]; simpl. + destruct SEM as [is CONT SEM|is t s' CONT SEM1 SEM2]; simpl in *. - (* sem_early *) exploit sistate_simu; eauto. unfold istate_simu; rewrite CONT. @@ -277,7 +287,9 @@ Proof. exploit sistate_simu; eauto. unfold istate_simu; rewrite CONT. intros (is' & SEM' & (CONT' & RS' & M')(* & DMEQ *)). - rewrite <- eqlive_reg_triv in RS'. + exploit pre_output_regs_correct; eauto. + clear SEM2; intros SEM2. + (* exploit SIMU2; eauto. *) exploit ssem_final_simu; eauto. clear SEM2; intros (s0 & SEM2 & MATCH0). exploit ssem_final_equiv; eauto. @@ -301,12 +313,13 @@ Proof. intros (path' & PATH'). exists path'. exploit (sexec_correct f pc pge ge sp path stk rs m t s); eauto. - intros (st & SYMB & SEM); clear STEP. + intros (st & SYMB & SEM). exploit dupmap_correct; eauto. - clear SYMB; intros (st' & SYMB & SIMU). + clear SYMB; intros (path0 & st' & PATH0 & SYMB & SIMU). + rewrite PATH0 in PATH; inversion PATH; subst. exploit ssem_sstate_simu; eauto. intros (s0 & SEM0 & MATCH). - exploit sexec_exact; eauto. + exploit (sexec_exact f'); eauto. intros (s' & STEP' & EQ). exists s'; intuition. eapply match_states_equiv; eauto. |