diff options
author | David Monniaux <david.monniaux@univ-grenoble-alpes.fr> | 2020-03-03 16:57:52 +0100 |
---|---|---|
committer | David Monniaux <david.monniaux@univ-grenoble-alpes.fr> | 2020-03-03 16:57:52 +0100 |
commit | fe0862b9bb1c9deeb1ea1393889c294fc2cc2ebe (patch) | |
tree | 50a6ecbb87438cfc21461b4f5066edcf28f8b14e /x86 | |
parent | 1ab7b51c30e1b10ac45b0bd64cefdc01da0f7f68 (diff) | |
parent | 3b640f041be480b82f1b3a1f695ed8a57193bf28 (diff) | |
download | compcert-kvx-fe0862b9bb1c9deeb1ea1393889c294fc2cc2ebe.tar.gz compcert-kvx-fe0862b9bb1c9deeb1ea1393889c294fc2cc2ebe.zip |
fixed CSE2 for mppa_k1c
Merge branch 'dm-cse2-naive' of https://github.com/monniaux/CompCert into mppa-cse2
Diffstat (limited to 'x86')
-rw-r--r-- | x86/CSE2deps.v | 24 | ||||
-rw-r--r-- | x86/CSE2depsproof.v | 262 |
2 files changed, 286 insertions, 0 deletions
diff --git a/x86/CSE2deps.v b/x86/CSE2deps.v new file mode 100644 index 00000000..f4d9e254 --- /dev/null +++ b/x86/CSE2deps.v @@ -0,0 +1,24 @@ +Require Import BoolEqual Coqlib. +Require Import AST Integers Floats. +Require Import Values Memory Globalenvs Events. +Require Import Op. + +Definition can_swap_accesses_ofs ofsr chunkr ofsw chunkw := + (0 <=? ofsw) && (ofsw <=? (Ptrofs.modulus - largest_size_chunk)) + && (0 <=? ofsr) && (ofsr <=? (Ptrofs.modulus - largest_size_chunk)) + && ((ofsw + size_chunk chunkw <=? ofsr) || + (ofsr + size_chunk chunkr <=? ofsw)). + +Definition may_overlap chunk addr args chunk' addr' args' := + match addr, addr', args, args' with + | (Aindexed ofs), (Aindexed ofs'), + (base :: nil), (base' :: nil) => + if peq base base' + then negb (can_swap_accesses_ofs ofs' chunk' ofs chunk) + else true + | (Aglobal symb ofs), (Aglobal symb' ofs'), nil, nil => + if peq symb symb' + then negb (can_swap_accesses_ofs (Ptrofs.unsigned ofs') chunk' (Ptrofs.unsigned ofs) chunk) + else false + | _, _, _, _ => true + end. diff --git a/x86/CSE2depsproof.v b/x86/CSE2depsproof.v new file mode 100644 index 00000000..37e16dfe --- /dev/null +++ b/x86/CSE2depsproof.v @@ -0,0 +1,262 @@ +Require Import Coqlib Maps Errors Integers Floats Lattice Kildall. +Require Import AST Linking. +Require Import Memory Registers Op RTL Maps. + +Require Import Globalenvs Values. +Require Import Linking Values Memory Globalenvs Events Smallstep. +Require Import Registers Op RTL. +Require Import CSE2 CSE2deps. +Require Import Lia. + +Section SOUNDNESS. + Variable F V : Type. + Variable genv: Genv.t F V. + Variable sp : val. + +Section MEMORY_WRITE. + Variable m m2 : mem. + Variable chunkw chunkr : memory_chunk. + Variable base : val. + + Variable addrw addrr valw valr : val. + Hypothesis STORE : Mem.storev chunkw m addrw valw = Some m2. + Hypothesis READ : Mem.loadv chunkr m addrr = Some valr. + + Section INDEXED_AWAY. + Variable ofsw ofsr : Z. + Hypothesis ADDRW : eval_addressing genv sp + (Aindexed ofsw) (base :: nil) = Some addrw. + Hypothesis ADDRR : eval_addressing genv sp + (Aindexed ofsr) (base :: nil) = Some addrr. + + Lemma load_store_away1 : + forall RANGEW : 0 <= ofsw <= Ptrofs.modulus - largest_size_chunk, + forall RANGER : 0 <= ofsr <= Ptrofs.modulus - largest_size_chunk, + forall SWAPPABLE : ofsw + size_chunk chunkw <= ofsr + \/ ofsr + size_chunk chunkr <= ofsw, + Mem.loadv chunkr m2 addrr = Some valr. + Proof. + intros. + + pose proof (max_size_chunk chunkr) as size_chunkr_bounded. + pose proof (max_size_chunk chunkw) as size_chunkw_bounded. + try change (Ptrofs.modulus - largest_size_chunk) with 4294967288 in *. + try change (Ptrofs.modulus - largest_size_chunk) with 18446744073709551608 in *. + destruct addrr ; simpl in * ; try discriminate. + unfold eval_addressing in *. + destruct Archi.ptr64 eqn:PTR64; destruct base; simpl in *; try discriminate. + rewrite PTR64 in *. + + inv ADDRR. + inv ADDRW. + rewrite <- READ. + eapply Mem.load_store_other with (chunk := chunkw) (v := valw) (b := b). + exact STORE. + right. + + all: try (destruct (Ptrofs.unsigned_add_either i0 + (Ptrofs.of_int (Int.repr ofsr))) as [OFSR | OFSR]; + rewrite OFSR). + all: try (destruct (Ptrofs.unsigned_add_either i0 + (Ptrofs.of_int64 (Int64.repr ofsr))) as [OFSR | OFSR]; + rewrite OFSR). + all: try (destruct (Ptrofs.unsigned_add_either i0 + (Ptrofs.of_int (Int.repr ofsw))) as [OFSW | OFSW]; + rewrite OFSW). + all: try (destruct (Ptrofs.unsigned_add_either i0 + (Ptrofs.of_int64 (Int64.repr ofsw))) as [OFSW | OFSW]; + rewrite OFSW). + + all: unfold Ptrofs.of_int64. + all: unfold Ptrofs.of_int. + + + all: repeat rewrite Int.unsigned_repr by (change Int.max_unsigned with 4294967295; lia). + all: repeat rewrite Ptrofs.unsigned_repr by (change Ptrofs.max_unsigned with 4294967295; lia). + all: repeat rewrite Int64.unsigned_repr by (change Int64.max_unsigned with 18446744073709551615; lia). + all: repeat rewrite Ptrofs.unsigned_repr by (change Ptrofs.max_unsigned with 18446744073709551615; lia). + + all: try change Ptrofs.modulus with 4294967296. + all: try change Ptrofs.modulus with 18446744073709551616. + + all: intuition lia. + Qed. + + Theorem load_store_away : + can_swap_accesses_ofs ofsr chunkr ofsw chunkw = true -> + Mem.loadv chunkr m2 addrr = Some valr. + Proof. + intro SWAP. + unfold can_swap_accesses_ofs in SWAP. + repeat rewrite andb_true_iff in SWAP. + repeat rewrite orb_true_iff in SWAP. + repeat rewrite Z.leb_le in SWAP. + apply load_store_away1. + all: tauto. + Qed. + End INDEXED_AWAY. + + Section DIFFERENT_GLOBALS. + Variable ofsw ofsr : ptrofs. + Hypothesis symw symr : ident. + Hypothesis ADDRW : eval_addressing genv sp + (Aglobal symw ofsw) nil = Some addrw. + Hypothesis ADDRR : eval_addressing genv sp + (Aglobal symr ofsr) nil = Some addrr. + + Lemma ptr64_cases: + forall {T : Type}, + forall b : bool, + forall x y : T, + (if b then (if b then x else y) else (if b then y else x)) = x. + Proof. + destruct b; reflexivity. + Qed. + + Lemma load_store_diff_globals : + symw <> symr -> + Mem.loadv chunkr m2 addrr = Some valr. + Proof. + intros. + unfold eval_addressing in *. + simpl in *. + rewrite ptr64_cases in ADDRR. + rewrite ptr64_cases in ADDRW. + unfold Genv.symbol_address in *. + unfold Genv.find_symbol in *. + destruct ((Genv.genv_symb genv) ! symw) as [bw |] eqn:SYMW; inv ADDRW. + 2: simpl in STORE; discriminate. + destruct ((Genv.genv_symb genv) ! symr) as [br |] eqn:SYMR; inv ADDRR. + 2: simpl in READ; discriminate. + assert (br <> bw). + { + intro EQ. + subst br. + assert (symr = symw). + { + eapply Genv.genv_vars_inj; eauto. + } + congruence. + } + rewrite <- READ. + eapply Mem.load_store_other with (chunk := chunkw) (v := valw) (b := bw). + - exact STORE. + - left. assumption. + Qed. + End DIFFERENT_GLOBALS. + + Section SAME_GLOBALS. + Variable ofsw ofsr : ptrofs. + Hypothesis sym : ident. + Hypothesis ADDRW : eval_addressing genv sp + (Aglobal sym ofsw) nil = Some addrw. + Hypothesis ADDRR : eval_addressing genv sp + (Aglobal sym ofsr) nil = Some addrr. + + Lemma load_store_glob_away1 : + forall RANGEW : 0 <= (Ptrofs.unsigned ofsw) <= Ptrofs.modulus - largest_size_chunk, + forall RANGER : 0 <= (Ptrofs.unsigned ofsr) <= Ptrofs.modulus - largest_size_chunk, + forall SWAPPABLE : (Ptrofs.unsigned ofsw) + size_chunk chunkw <= (Ptrofs.unsigned ofsr) + \/ (Ptrofs.unsigned ofsr) + size_chunk chunkr <= (Ptrofs.unsigned ofsw), + Mem.loadv chunkr m2 addrr = Some valr. + Proof. + intros. + + pose proof (max_size_chunk chunkr) as size_chunkr_bounded. + pose proof (max_size_chunk chunkw) as size_chunkw_bounded. + unfold largest_size_chunk in size_chunkr_bounded, size_chunkw_bounded. + try change (Ptrofs.modulus - largest_size_chunk) with 4294967288 in *. + try change (Ptrofs.modulus - largest_size_chunk) with 18446744073709551608 in *. + unfold eval_addressing, eval_addressing32, eval_addressing64 in *. + destruct Archi.ptr64 eqn:PTR64. + + { + unfold Genv.symbol_address in *. + inv ADDRR. + inv ADDRW. + destruct (Genv.find_symbol genv sym). + 2: discriminate. + + rewrite <- READ. + eapply Mem.load_store_other with (chunk := chunkw) (v := valw) (b := b). + exact STORE. + right. + tauto. + } + + { + unfold Genv.symbol_address in *. + inv ADDRR. + inv ADDRW. + destruct (Genv.find_symbol genv sym). + 2: discriminate. + + rewrite <- READ. + eapply Mem.load_store_other with (chunk := chunkw) (v := valw) (b := b). + exact STORE. + right. + tauto. + } + Qed. + + Lemma load_store_glob_away : + (can_swap_accesses_ofs (Ptrofs.unsigned ofsr) chunkr (Ptrofs.unsigned ofsw) chunkw) = true -> + Mem.loadv chunkr m2 addrr = Some valr. + Proof. + intro SWAP. + unfold can_swap_accesses_ofs in SWAP. + repeat rewrite andb_true_iff in SWAP. + repeat rewrite orb_true_iff in SWAP. + repeat rewrite Z.leb_le in SWAP. + apply load_store_glob_away1. + all: tauto. + Qed. + End SAME_GLOBALS. +End MEMORY_WRITE. +End SOUNDNESS. + + +Section SOUNDNESS. + Variable F V : Type. + Variable genv: Genv.t F V. + Variable sp : val. + +Lemma may_overlap_sound: + forall m m' : mem, + forall chunk addr args chunk' addr' args' v a a' vl rs, + (eval_addressing genv sp addr (rs ## args)) = Some a -> + (eval_addressing genv sp addr' (rs ## args')) = Some a' -> + (may_overlap chunk addr args chunk' addr' args') = false -> + (Mem.storev chunk m a v) = Some m' -> + (Mem.loadv chunk' m a') = Some vl -> + (Mem.loadv chunk' m' a') = Some vl. +Proof. + intros until rs. + intros ADDR ADDR' OVERLAP STORE LOAD. + destruct addr; destruct addr'; try discriminate. + { (* Aindexed / Aindexed *) + destruct args as [ | base [ | ]]. 1,3: discriminate. + destruct args' as [ | base' [ | ]]. 1,3: discriminate. + simpl in OVERLAP. + destruct (peq base base'). 2: discriminate. + subst base'. + destruct (can_swap_accesses_ofs z0 chunk' z chunk) eqn:SWAP. + 2: discriminate. + simpl in *. + eapply load_store_away; eassumption. + } + { (* Aglobal / Aglobal *) + destruct args. 2: discriminate. + destruct args'. 2: discriminate. + simpl in *. + destruct (peq i i1). + { + subst i1. + rewrite negb_false_iff in OVERLAP. + eapply load_store_glob_away; eassumption. + } + eapply load_store_diff_globals; eassumption. + } +Qed. + +End SOUNDNESS. |