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Require Import Coqlib.
Require Import AST.
Require Import Integers.
Require Import Floats.
Require Import Values.
Require Import Memory.
Require Import Globalenvs.
Require Import Op.
Require Import ValueDomain.
Require Import RTL.
(** Value analysis for PowerPC operators *)
Definition eval_static_condition (cond: condition) (vl: list aval): abool :=
match cond, vl with
| Ccomp c, v1 :: v2 :: nil => cmp_bool c v1 v2
| Ccompu c, v1 :: v2 :: nil => cmpu_bool c v1 v2
| Ccompimm c n, v1 :: nil => cmp_bool c v1 (I n)
| Ccompuimm c n, v1 :: nil => cmpu_bool c v1 (I n)
| Ccompf c, v1 :: v2 :: nil => cmpf_bool c v1 v2
| Cnotcompf c, v1 :: v2 :: nil => cnot (cmpf_bool c v1 v2)
| Cmaskzero n, v1 :: nil => maskzero v1 n
| Cmasknotzero n, v1 :: nil => cnot (maskzero v1 n)
| _, _ => Bnone
end.
Definition eval_static_addressing (addr: addressing) (vl: list aval): aval :=
match addr, vl with
| Aindexed n, v1::nil => add v1 (I n)
| Aindexed2, v1::v2::nil => add v1 v2
| Aglobal s ofs, nil => Ptr (Gl s ofs)
| Abased s ofs, v1::nil => add (Ptr (Gl s ofs)) v1
| Ainstack ofs, nil => Ptr(Stk ofs)
| _, _ => Vbot
end.
Definition eval_static_operation (op: operation) (vl: list aval): aval :=
match op, vl with
| Omove, v1::nil => v1
| Ointconst n, nil => I n
| Ofloatconst n, nil => if propagate_float_constants tt then F n else ftop
| Oaddrsymbol id ofs, nil => Ptr (Gl id ofs)
| Oaddrstack ofs, nil => Ptr (Stk ofs)
| Ocast8signed, v1 :: nil => sign_ext 8 v1
| Ocast16signed, v1 :: nil => sign_ext 16 v1
| Oadd, v1::v2::nil => add v1 v2
| Oaddimm n, v1::nil => add v1 (I n)
| Oaddsymbol id ofs, v1::nil => add (Ptr (Gl id ofs)) v1
| Osub, v1::v2::nil => sub v1 v2
| Osubimm n, v1::nil => sub (I n) v1
| Omul, v1::v2::nil => mul v1 v2
| Omulimm n, v1::nil => mul v1 (I n)
| Omulhs, v1::v2::nil => mulhs v1 v2
| Omulhu, v1::v2::nil => mulhu v1 v2
| Odiv, v1::v2::nil => divs v1 v2
| Odivu, v1::v2::nil => divu v1 v2
| Oand, v1::v2::nil => and v1 v2
| Oandimm n, v1::nil => and v1 (I n)
| Oor, v1::v2::nil => or v1 v2
| Oorimm n, v1::nil => or v1 (I n)
| Oxor, v1::v2::nil => xor v1 v2
| Oxorimm n, v1::nil => xor v1 (I n)
| Onot, v1::nil => notint v1
| Onand, v1::v2::nil => notint(and v1 v2)
| Onor, v1::v2::nil => notint(or v1 v2)
| Onxor, v1::v2::nil => notint(xor v1 v2)
| Oandc, v1::v2::nil => and v1 (notint v2)
| Oorc, v1::v2::nil => or v1 (notint v2)
| Oshl, v1::v2::nil => shl v1 v2
| Oshr, v1::v2::nil => shr v1 v2
| Oshrimm n, v1::nil => shr v1 (I n)
| Oshrximm n, v1::nil => shrx v1 (I n)
| Oshru, v1::v2::nil => shru v1 v2
| Orolm amount mask, v1::nil => rolm v1 amount mask
| Oroli amount mask, v1::v2::nil => or (and v1 (I (Int.not mask))) (rolm v2 amount mask)
| Onegf, v1::nil => negf v1
| Oabsf, v1::nil => absf v1
| Oaddf, v1::v2::nil => addf v1 v2
| Osubf, v1::v2::nil => subf v1 v2
| Omulf, v1::v2::nil => mulf v1 v2
| Odivf, v1::v2::nil => divf v1 v2
| Osingleoffloat, v1::nil => singleoffloat v1
| Ointoffloat, v1::nil => intoffloat v1
| Ofloatofwords, v1::v2::nil => floatofwords v1 v2
| Omakelong, v1::v2::nil => longofwords v1 v2
| Olowlong, v1::nil => loword v1
| Ohighlong, v1::nil => hiword v1
| Ocmp c, _ => of_optbool (eval_static_condition c vl)
| _, _ => Vbot
end.
Section SOUNDNESS.
Variable bc: block_classification.
Variable ge: genv.
Hypothesis GENV: genv_match bc ge.
Variable sp: block.
Hypothesis STACK: bc sp = BCstack.
Theorem eval_static_condition_sound:
forall cond vargs m aargs,
list_forall2 (vmatch bc) vargs aargs ->
cmatch (eval_condition cond vargs m) (eval_static_condition cond aargs).
Proof.
intros until aargs; intros VM.
inv VM.
destruct cond; auto with va.
inv H0.
destruct cond; simpl; eauto with va.
inv H2.
destruct cond; simpl; eauto with va.
destruct cond; auto with va.
Qed.
Lemma symbol_address_sound:
forall id ofs,
vmatch bc (symbol_address ge id ofs) (Ptr (Gl id ofs)).
Proof.
intros; apply symbol_address_sound; apply GENV.
Qed.
Hint Resolve symbol_address_sound: va.
Ltac InvHyps :=
match goal with
| [H: None = Some _ |- _ ] => discriminate
| [H: Some _ = Some _ |- _] => inv H
| [H1: match ?vl with nil => _ | _ :: _ => _ end = Some _ ,
H2: list_forall2 _ ?vl _ |- _ ] => inv H2; InvHyps
| _ => idtac
end.
Theorem eval_static_addressing_sound:
forall addr vargs vres aargs,
eval_addressing ge (Vptr sp Int.zero) addr vargs = Some vres ->
list_forall2 (vmatch bc) vargs aargs ->
vmatch bc vres (eval_static_addressing addr aargs).
Proof.
unfold eval_addressing, eval_static_addressing; intros;
destruct addr; InvHyps; eauto with va.
rewrite Int.add_zero_l; auto with va.
Qed.
Theorem eval_static_operation_sound:
forall op vargs m vres aargs,
eval_operation ge (Vptr sp Int.zero) op vargs m = Some vres ->
list_forall2 (vmatch bc) vargs aargs ->
vmatch bc vres (eval_static_operation op aargs).
Proof.
unfold eval_operation, eval_static_operation; intros;
destruct op; InvHyps; eauto with va.
destruct (propagate_float_constants tt); constructor.
rewrite Int.add_zero_l; eauto with va.
fold (Val.sub (Vint i) a1). auto with va.
apply floatofwords_sound; auto.
apply of_optbool_sound. eapply eval_static_condition_sound; eauto.
Qed.
End SOUNDNESS.
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