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(* *********************************************************************)
(* *)
(* The Compcert verified compiler *)
(* *)
(* Xavier Leroy, INRIA Paris *)
(* *)
(* 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. *)
(* *)
(* *********************************************************************)
Require Import Coqlib Compopts.
Require Import AST Integers Floats Values Memory Globalenvs.
Require Import Op RTL ValueDomain.
(** Value analysis for x86_64 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)
| Ccompl c, v1 :: v2 :: nil => cmpl_bool c v1 v2
| Ccomplu c, v1 :: v2 :: nil => cmplu_bool c v1 v2
| Ccomplimm c n, v1 :: nil => cmpl_bool c v1 (L n)
| Ccompluimm c n, v1 :: nil => cmplu_bool c v1 (L n)
| Ccompf c, v1 :: v2 :: nil => cmpf_bool c v1 v2
| Cnotcompf c, v1 :: v2 :: nil => cnot (cmpf_bool c v1 v2)
| Ccompfs c, v1 :: v2 :: nil => cmpfs_bool c v1 v2
| Cnotcompfs c, v1 :: v2 :: nil => cnot (cmpfs_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_32 (addr: addressing) (vl: list aval): aval :=
match addr, vl with
| Aindexed n, v1::nil => add v1 (I (Int.repr n))
| Aindexed2 n, v1::v2::nil => add (add v1 v2) (I (Int.repr n))
| Ascaled sc ofs, v1::nil => add (mul v1 (I (Int.repr sc))) (I (Int.repr ofs))
| Aindexed2scaled sc ofs, v1::v2::nil => add v1 (add (mul v2 (I (Int.repr sc))) (I (Int.repr ofs)))
| Aglobal s ofs, nil => Ptr (Gl s ofs)
| Abased s ofs, v1::nil => add (Ptr (Gl s ofs)) v1
| Abasedscaled sc s ofs, v1::nil => add (Ptr (Gl s ofs)) (mul v1 (I (Int.repr sc)))
| Ainstack ofs, nil => Ptr(Stk ofs)
| _, _ => Vbot
end.
Definition eval_static_addressing_64 (addr: addressing) (vl: list aval): aval :=
match addr, vl with
| Aindexed n, v1::nil => addl v1 (L (Int64.repr n))
| Aindexed2 n, v1::v2::nil => addl (addl v1 v2) (L (Int64.repr n))
| Ascaled sc ofs, v1::nil => addl (mull v1 (L (Int64.repr sc))) (L (Int64.repr ofs))
| Aindexed2scaled sc ofs, v1::v2::nil => addl v1 (addl (mull v2 (L (Int64.repr sc))) (L (Int64.repr ofs)))
| Aglobal s ofs, nil => Ptr (Gl s ofs)
| Abased s ofs, v1::nil => addl (Ptr (Gl s ofs)) v1
| Abasedscaled sc s ofs, v1::nil => addl (Ptr (Gl s ofs)) (mull v1 (L (Int64.repr sc)))
| Ainstack ofs, nil => Ptr(Stk ofs)
| _, _ => Vbot
end.
Definition eval_static_addressing (addr: addressing) (vl: list aval): aval :=
if Archi.ptr64
then eval_static_addressing_64 addr vl
else eval_static_addressing_32 addr vl.
Definition eval_static_operation (op: operation) (vl: list aval): aval :=
match op, vl with
| Omove, v1::nil => v1
| Ointconst n, nil => I n
| Olongconst n, nil => L n
| Ofloatconst n, nil => if propagate_float_constants tt then F n else ntop
| Osingleconst n, nil => if propagate_float_constants tt then FS n else ntop
| Oindirectsymbol id, nil => Ifptr (Gl id Ptrofs.zero)
| Ocast8signed, v1 :: nil => sign_ext 8 v1
| Ocast8unsigned, v1 :: nil => zero_ext 8 v1
| Ocast16signed, v1 :: nil => sign_ext 16 v1
| Ocast16unsigned, v1 :: nil => zero_ext 16 v1
| Oneg, v1::nil => neg v1
| Osub, v1::v2::nil => sub v1 v2
| 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
| Omod, v1::v2::nil => mods v1 v2
| Omodu, v1::v2::nil => modu 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
| Oshl, v1::v2::nil => shl v1 v2
| Oshlimm n, v1::nil => shl v1 (I n)
| 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
| Oshruimm n, v1::nil => shru v1 (I n)
| Ororimm n, v1::nil => ror v1 (I n)
| Oshldimm n, v1::v2::nil => or (shl v1 (I n)) (shru v2 (I (Int.sub Int.iwordsize n)))
| Olea addr, _ => eval_static_addressing_32 addr vl
| Omakelong, v1::v2::nil => longofwords v1 v2
| Olowlong, v1::nil => loword v1
| Ohighlong, v1::nil => hiword v1
| Ocast32signed, v1::nil => longofint v1
| Ocast32unsigned, v1::nil => longofintu v1
| Onegl, v1::nil => negl v1
| Oaddlimm n, v1::nil => addl v1 (L n)
| Osubl, v1::v2::nil => subl v1 v2
| Omull, v1::v2::nil => mull v1 v2
| Omullimm n, v1::nil => mull v1 (L n)
| Omullhs, v1::v2::nil => mullhs v1 v2
| Omullhu, v1::v2::nil => mullhu v1 v2
| Odivl, v1::v2::nil => divls v1 v2
| Odivlu, v1::v2::nil => divlu v1 v2
| Omodl, v1::v2::nil => modls v1 v2
| Omodlu, v1::v2::nil => modlu v1 v2
| Oandl, v1::v2::nil => andl v1 v2
| Oandlimm n, v1::nil => andl v1 (L n)
| Oorl, v1::v2::nil => orl v1 v2
| Oorlimm n, v1::nil => orl v1 (L n)
| Oxorl, v1::v2::nil => xorl v1 v2
| Oxorlimm n, v1::nil => xorl v1 (L n)
| Onotl, v1::nil => notl v1
| Oshll, v1::v2::nil => shll v1 v2
| Oshllimm n, v1::nil => shll v1 (I n)
| Oshrl, v1::v2::nil => shrl v1 v2
| Oshrlimm n, v1::nil => shrl v1 (I n)
| Oshrxlimm n, v1::nil => shrxl v1 (I n)
| Oshrlu, v1::v2::nil => shrlu v1 v2
| Oshrluimm n, v1::nil => shrlu v1 (I n)
| Ororlimm n, v1::nil => rorl v1 (I n)
| Oleal addr, _ => eval_static_addressing_64 addr vl
| 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
| Omaxf, v1::v2::nil => binop_float float_max v1 v2
| Ominf, v1::v2::nil => binop_float float_min v1 v2
| Onegfs, v1::nil => negfs v1
| Oabsfs, v1::nil => absfs v1
| Oaddfs, v1::v2::nil => addfs v1 v2
| Osubfs, v1::v2::nil => subfs v1 v2
| Omulfs, v1::v2::nil => mulfs v1 v2
| Odivfs, v1::v2::nil => divfs v1 v2
| Osingleoffloat, v1::nil => singleoffloat v1
| Ofloatofsingle, v1::nil => floatofsingle v1
| Ointoffloat, v1::nil => intoffloat v1
| Ofloatofint, v1::nil => floatofint v1
| Ointofsingle, v1::nil => intofsingle v1
| Osingleofint, v1::nil => singleofint v1
| Olongoffloat, v1::nil => longoffloat v1
| Ofloatoflong, v1::nil => floatoflong v1
| Olongofsingle, v1::nil => longofsingle v1
| Osingleoflong, v1::nil => singleoflong v1
| Ocmp c, _ => of_optbool (eval_static_condition c vl)
| Osel c ty, v1::v2::vl => select (eval_static_condition c vl) v1 v2
| _, _ => 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 (Genv.symbol_address ge id ofs) (Ptr (Gl id ofs)).
Proof.
intros; apply symbol_address_sound; apply GENV.
Qed.
Lemma symbol_address_sound_2:
forall id ofs,
vmatch bc (Genv.symbol_address ge id ofs) (Ifptr (Gl id ofs)).
Proof.
intros. unfold Genv.symbol_address. destruct (Genv.find_symbol ge id) as [b|] eqn:F.
constructor. constructor. apply GENV; auto.
constructor.
Qed.
Hint Resolve symbol_address_sound symbol_address_sound_2: 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
| [H: (if Archi.ptr64 then _ else _) = Some _ |- _] => destruct Archi.ptr64 eqn:?; InvHyps
| _ => idtac
end.
Theorem eval_static_addressing_32_sound:
forall addr vargs vres aargs,
eval_addressing32 ge (Vptr sp Ptrofs.zero) addr vargs = Some vres ->
list_forall2 (vmatch bc) vargs aargs ->
vmatch bc vres (eval_static_addressing_32 addr aargs).
Proof.
unfold eval_addressing32, eval_static_addressing_32; intros;
destruct addr; InvHyps; eauto with va.
rewrite Ptrofs.add_zero_l; eauto with va.
Qed.
Theorem eval_static_addressing_64_sound:
forall addr vargs vres aargs,
eval_addressing64 ge (Vptr sp Ptrofs.zero) addr vargs = Some vres ->
list_forall2 (vmatch bc) vargs aargs ->
vmatch bc vres (eval_static_addressing_64 addr aargs).
Proof.
unfold eval_addressing64, eval_static_addressing_64; intros;
destruct addr; InvHyps; eauto with va.
rewrite Ptrofs.add_zero_l; eauto with va.
Qed.
Theorem eval_static_addressing_sound:
forall addr vargs vres aargs,
eval_addressing ge (Vptr sp Ptrofs.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 Archi.ptr64; eauto using eval_static_addressing_32_sound, eval_static_addressing_64_sound.
Qed.
Theorem eval_static_operation_sound:
forall op vargs m vres aargs,
eval_operation ge (Vptr sp Ptrofs.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.
destruct (propagate_float_constants tt); constructor.
eapply eval_static_addressing_32_sound; eauto.
eapply eval_static_addressing_64_sound; eauto.
apply binop_float_sound; auto.
apply binop_float_sound; auto.
apply of_optbool_sound. eapply eval_static_condition_sound; eauto.
apply select_sound; auto. eapply eval_static_condition_sound; eauto.
Qed.
End SOUNDNESS.
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