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Diffstat (limited to 'verilog/ValueAOp.v')
| -rw-r--r-- | verilog/ValueAOp.v | 266 |
1 files changed, 266 insertions, 0 deletions
diff --git a/verilog/ValueAOp.v b/verilog/ValueAOp.v new file mode 100644 index 00000000..d0b8427a --- /dev/null +++ b/verilog/ValueAOp.v @@ -0,0 +1,266 @@ +(* *********************************************************************) +(* *) +(* 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 + | 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 of_optbool_sound. eapply eval_static_condition_sound; eauto. + apply select_sound; auto. eapply eval_static_condition_sound; eauto. +Qed. + +End SOUNDNESS. + |