diff options
Diffstat (limited to 'riscV/ValueAOp.v')
| -rw-r--r-- | riscV/ValueAOp.v | 329 |
1 files changed, 312 insertions, 17 deletions
diff --git a/riscV/ValueAOp.v b/riscV/ValueAOp.v index 5670b5fe..d29180e4 100644 --- a/riscV/ValueAOp.v +++ b/riscV/ValueAOp.v @@ -13,9 +13,46 @@ Require Import Coqlib Compopts. Require Import AST Integers Floats Values Memory Globalenvs. Require Import Op RTL ValueDomain. +Require Import Zbits. (** Value analysis for RISC V operators *) +Definition zero32 := (I Int.zero). +Definition zero64 := (L Int64.zero). + +(** Functions to select a special register (see Op.v) *) + +Definition apply_bin_oreg {B} (optR: option oreg) (sem: aval -> aval -> B) (v1 v2 vz: aval): B := + match optR with + | None => sem v1 v2 + | Some X0_L => sem vz v1 + | Some X0_R => sem v1 vz + end. + +Definition eval_may_undef (mu: mayundef) (v1 v2: aval): aval := + match mu with + | MUint => match v1, v2 with + | I _, I _ => v2 + | _, _ => Ifptr Ptop + end + | MUlong => match v1, v2 with + | L _, I _ => v2 + | _, _ => Ifptr Ptop + end + | MUshrx i => + match v1, v2 with + | I _, I _ => + if Int.ltu i (Int.repr 31) then v2 else Ifptr Ptop + | _, _ => Ifptr Ptop + end + | MUshrxl i => + match v1, v2 with + | L _, L _ => + if Int.ltu i (Int.repr 63) then v2 else Ifptr Ptop + | _, _ => Ifptr Ptop + end + end. + Definition eval_static_condition (cond: condition) (vl: list aval): abool := match cond, vl with | Ccomp c, v1 :: v2 :: nil => cmp_bool c v1 v2 @@ -30,6 +67,22 @@ Definition eval_static_condition (cond: condition) (vl: list aval): abool := | 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) + | CEbeqw optR, v1 :: v2 :: nil => apply_bin_oreg optR (cmp_bool Ceq) v1 v2 zero32 + | CEbnew optR, v1 :: v2 :: nil => apply_bin_oreg optR (cmp_bool Cne) v1 v2 zero32 + | CEbequw optR, v1 :: v2 :: nil => apply_bin_oreg optR (cmpu_bool Ceq) v1 v2 zero32 + | CEbneuw optR, v1 :: v2 :: nil => apply_bin_oreg optR (cmpu_bool Cne) v1 v2 zero32 + | CEbltw optR, v1 :: v2 :: nil => apply_bin_oreg optR (cmp_bool Clt) v1 v2 zero32 + | CEbltuw optR, v1 :: v2 :: nil => apply_bin_oreg optR (cmpu_bool Clt) v1 v2 zero32 + | CEbgew optR, v1 :: v2 :: nil => apply_bin_oreg optR (cmp_bool Cge) v1 v2 zero32 + | CEbgeuw optR, v1 :: v2 :: nil => apply_bin_oreg optR (cmpu_bool Cge) v1 v2 zero32 + | CEbeql optR, v1 :: v2 :: nil => apply_bin_oreg optR (cmpl_bool Ceq) v1 v2 zero64 + | CEbnel optR, v1 :: v2 :: nil => apply_bin_oreg optR (cmpl_bool Cne) v1 v2 zero64 + | CEbequl optR, v1 :: v2 :: nil => apply_bin_oreg optR (cmplu_bool Ceq) v1 v2 zero64 + | CEbneul optR, v1 :: v2 :: nil => apply_bin_oreg optR (cmplu_bool Cne) v1 v2 zero64 + | CEbltl optR, v1 :: v2 :: nil => apply_bin_oreg optR (cmpl_bool Clt) v1 v2 zero64 + | CEbltul optR, v1 :: v2 :: nil => apply_bin_oreg optR (cmplu_bool Clt) v1 v2 zero64 + | CEbgel optR, v1 :: v2 :: nil => apply_bin_oreg optR (cmpl_bool Cge) v1 v2 zero64 + | CEbgeul optR, v1 :: v2 :: nil => apply_bin_oreg optR (cmplu_bool Cge) v1 v2 zero64 | _, _ => Bnone end. @@ -41,6 +94,39 @@ Definition eval_static_addressing (addr: addressing) (vl: list aval): aval := | _, _ => Vbot end. +Definition bits_of_single (v : aval) : aval := + match v with + | FS f => I (Float32.to_bits f) + | _ => ntop1 v + end. + +Definition bits_of_float (v : aval) : aval := + match v with + | F f => L (Float.to_bits f) + | _ => ntop1 v + end. + +Definition single_of_bits (v : aval) : aval := + match v with + | I f => FS (Float32.of_bits f) + | _ => ntop1 v + end. + +Definition float_of_bits (v : aval) : aval := + match v with + | L f => F (Float.of_bits f) + | _ => ntop1 v + end. + +Definition select01_long (vb : aval) (vt : aval) (vf : aval) := + match vb with + | I b => + if Int.eq b Int.one then add_undef vt + else if Int.eq b Int.zero then add_undef vf + else add_undef (vlub vt vf) + | _ => add_undef (vlub vt vf) + end. + Definition eval_static_operation (op: operation) (vl: list aval): aval := match op, vl with | Omove, v1::nil => v1 @@ -59,10 +145,10 @@ Definition eval_static_operation (op: operation) (vl: list aval): aval := | Omul, v1::v2::nil => mul v1 v2 | 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 + | Odiv, v1::v2::nil => divs_total v1 v2 + | Odivu, v1::v2::nil => divu_total v1 v2 + | Omod, v1::v2::nil => mods_total v1 v2 + | Omodu, v1::v2::nil => modu_total v1 v2 | Oand, v1::v2::nil => and v1 v2 | Oandimm n, v1::nil => and v1 (I n) | Oor, v1::v2::nil => or v1 v2 @@ -88,10 +174,10 @@ Definition eval_static_operation (op: operation) (vl: list aval): aval := | Omull, v1::v2::nil => mull v1 v2 | 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 + | Odivl, v1::v2::nil => divls_total v1 v2 + | Odivlu, v1::v2::nil => divlu_total v1 v2 + | Omodl, v1::v2::nil => modls_total v1 v2 + | Omodlu, v1::v2::nil => modlu_total v1 v2 | Oandl, v1::v2::nil => andl v1 v2 | Oandlimm n, v1::nil => andl v1 (L n) | Oorl, v1::v2::nil => orl v1 v2 @@ -119,23 +205,64 @@ Definition eval_static_operation (op: operation) (vl: list aval): aval := | Odivfs, v1::v2::nil => divfs v1 v2 | Osingleoffloat, v1::nil => singleoffloat v1 | Ofloatofsingle, v1::nil => floatofsingle v1 - | Ointoffloat, v1::nil => intoffloat v1 - | Ointuoffloat, v1::nil => intuoffloat v1 + | Ointoffloat, v1::nil => intoffloat_total v1 + | Ointuoffloat, v1::nil => intuoffloat_total v1 | Ofloatofint, v1::nil => floatofint v1 | Ofloatofintu, v1::nil => floatofintu v1 - | Ointofsingle, v1::nil => intofsingle v1 - | Ointuofsingle, v1::nil => intuofsingle v1 + | Ointofsingle, v1::nil => intofsingle_total v1 + | Ointuofsingle, v1::nil => intuofsingle_total v1 | Osingleofint, v1::nil => singleofint v1 | Osingleofintu, v1::nil => singleofintu v1 - | Olongoffloat, v1::nil => longoffloat v1 - | Olonguoffloat, v1::nil => longuoffloat v1 + | Olongoffloat, v1::nil => longoffloat_total v1 + | Olonguoffloat, v1::nil => longuoffloat_total v1 | Ofloatoflong, v1::nil => floatoflong v1 | Ofloatoflongu, v1::nil => floatoflongu v1 - | Olongofsingle, v1::nil => longofsingle v1 - | Olonguofsingle, v1::nil => longuofsingle v1 + | Olongofsingle, v1::nil => longofsingle_total v1 + | Olonguofsingle, v1::nil => longuofsingle_total v1 | Osingleoflong, v1::nil => singleoflong v1 | Osingleoflongu, v1::nil => singleoflongu v1 | Ocmp c, _ => of_optbool (eval_static_condition c vl) + | OEseqw optR, v1::v2::nil => of_optbool (apply_bin_oreg optR (cmp_bool Ceq) v1 v2 zero32) + | OEsnew optR, v1::v2::nil => of_optbool (apply_bin_oreg optR (cmp_bool Cne) v1 v2 zero32) + | OEsequw optR, v1::v2::nil => of_optbool (apply_bin_oreg optR (cmpu_bool Ceq) v1 v2 zero32) + | OEsneuw optR, v1::v2::nil => of_optbool (apply_bin_oreg optR (cmpu_bool Cne) v1 v2 zero32) + | OEsltw optR, v1::v2::nil => of_optbool (apply_bin_oreg optR (cmp_bool Clt) v1 v2 zero32) + | OEsltuw optR, v1::v2::nil => of_optbool (apply_bin_oreg optR (cmpu_bool Clt) v1 v2 zero32) + | OEsltiw n, v1::nil => of_optbool (cmp_bool Clt v1 (I n)) + | OEsltiuw n, v1::nil => of_optbool (cmpu_bool Clt v1 (I n)) + | OExoriw n, v1::nil => xor v1 (I n) + | OEluiw n, nil => shl (I n) (I (Int.repr 12)) + | OEaddiw optR n, nil => apply_bin_oreg optR add (I n) (Ifptr Ptop) zero32 + | OEaddiw optR n, v1::nil => apply_bin_oreg optR add v1 (I n) (Ifptr Ptop) + | OEandiw n, v1::nil => and (I n) v1 + | OEoriw n, v1::nil => or (I n) v1 + | OEseql optR, v1::v2::nil => of_optbool (apply_bin_oreg optR (cmpl_bool Ceq) v1 v2 zero64) + | OEsnel optR, v1::v2::nil => of_optbool (apply_bin_oreg optR (cmpl_bool Cne) v1 v2 zero64) + | OEsequl optR, v1::v2::nil => of_optbool (apply_bin_oreg optR (cmplu_bool Ceq) v1 v2 zero64) + | OEsneul optR, v1::v2::nil => of_optbool (apply_bin_oreg optR (cmplu_bool Cne) v1 v2 zero64) + | OEsltl optR, v1::v2::nil => of_optbool (apply_bin_oreg optR (cmpl_bool Clt) v1 v2 zero64) + | OEsltul optR, v1::v2::nil => of_optbool (apply_bin_oreg optR (cmplu_bool Clt) v1 v2 zero64) + | OEsltil n, v1::nil => of_optbool (cmpl_bool Clt v1 (L n)) + | OEsltiul n, v1::nil => of_optbool (cmplu_bool Clt v1 (L n)) + | OEandil n, v1::nil => andl (L n) v1 + | OEoril n, v1::nil => orl (L n) v1 + | OExoril n, v1::nil => xorl v1 (L n) + | OEluil n, nil => sign_ext 32 (shll (L n) (L (Int64.repr 12))) + | OEaddil optR n, nil => apply_bin_oreg optR addl (L n) (Ifptr Ptop) zero64 + | OEaddil optR n, v1::nil => apply_bin_oreg optR addl v1 (L n) (Ifptr Ptop) + | OEloadli n, nil => L (n) + | OEmayundef mu, v1 :: v2 :: nil => eval_may_undef mu v1 v2 + | OEfeqd, v1::v2::nil => of_optbool (cmpf_bool Ceq v1 v2) + | OEfltd, v1::v2::nil => of_optbool (cmpf_bool Clt v1 v2) + | OEfled, v1::v2::nil => of_optbool (cmpf_bool Cle v1 v2) + | OEfeqs, v1::v2::nil => of_optbool (cmpfs_bool Ceq v1 v2) + | OEflts, v1::v2::nil => of_optbool (cmpfs_bool Clt v1 v2) + | OEfles, v1::v2::nil => of_optbool (cmpfs_bool Cle v1 v2) + | Obits_of_single, v1::nil => bits_of_single v1 + | Obits_of_float, v1::nil => bits_of_float v1 + | Osingle_of_bits, v1::nil => single_of_bits v1 + | Ofloat_of_bits, v1::nil => float_of_bits v1 + | Oselectl, vb::vt::vf::nil => select01_long vb vt vf | _, _ => Vbot end. @@ -147,6 +274,75 @@ Hypothesis GENV: genv_match bc ge. Variable sp: block. Hypothesis STACK: bc sp = BCstack. +Lemma bits_of_single_sound: + forall v x, vmatch bc v x -> vmatch bc (ExtValues.bits_of_single v) (bits_of_single x). +Proof. + unfold ExtValues.bits_of_single; intros. inv H; cbn; constructor. +Qed. + +Lemma bits_of_float_sound: + forall v x, vmatch bc v x -> vmatch bc (ExtValues.bits_of_float v) (bits_of_float x). +Proof. + unfold ExtValues.bits_of_float; intros. inv H; cbn; constructor. +Qed. + +Lemma single_of_bits_sound: + forall v x, vmatch bc v x -> vmatch bc (ExtValues.single_of_bits v) (single_of_bits x). +Proof. + unfold ExtValues.bits_of_single; intros. inv H; cbn; constructor. +Qed. + +Lemma float_of_bits_sound: + forall v x, vmatch bc v x -> vmatch bc (ExtValues.float_of_bits v) (float_of_bits x). +Proof. + unfold ExtValues.bits_of_float; intros. inv H; cbn; constructor. +Qed. + + +Lemma select01_long_sound: + forall vb xb vt xt vf xf + (MATCH_b : vmatch bc vb xb) + (MATCH_t : vmatch bc vt xt) + (MATCH_f : vmatch bc vf xf), + vmatch bc (Val.normalize (ExtValues.select01_long vb vt vf) Tlong) + (select01_long xb xt xf). +Proof. + intros. + inv MATCH_b; cbn; try apply add_undef_undef. + - destruct (Int.eq i Int.one). { apply add_undef_normalize; trivial. } + destruct (Int.eq i Int.zero). { apply add_undef_normalize; trivial. } + cbn. apply add_undef_undef. + - destruct (Int.eq i Int.one). + { apply add_undef_normalize. + apply vmatch_lub_l. + trivial. } + destruct (Int.eq i Int.zero). + { apply add_undef_normalize. + apply vmatch_lub_r. + trivial. } + cbn. apply add_undef_undef. + - destruct (Int.eq i Int.one). + { apply add_undef_normalize. + apply vmatch_lub_l. + trivial. } + destruct (Int.eq i Int.zero). + { apply add_undef_normalize. + apply vmatch_lub_r. + trivial. } + cbn. apply add_undef_undef. + - destruct (Int.eq i Int.one). + { apply add_undef_normalize. + apply vmatch_lub_l. + trivial. } + destruct (Int.eq i Int.zero). + { apply add_undef_normalize. + apply vmatch_lub_r. + trivial. } + cbn. apply add_undef_undef. +Qed. + +Hint Resolve bits_of_single_sound bits_of_float_sound single_of_bits_sound float_of_bits_sound select01_long_sound : va. + Theorem eval_static_condition_sound: forall cond vargs m aargs, list_forall2 (vmatch bc) vargs aargs -> @@ -158,7 +354,9 @@ Proof. destruct cond; simpl; eauto with va. inv H2. destruct cond; simpl; eauto with va. - destruct cond; auto with va. + 17: destruct cond; simpl; eauto with va. + all: destruct optR as [[]|]; unfold apply_bin_oreg, Op.apply_bin_oreg; + unfold zero32, Op.zero32, zero64, Op.zero64; eauto with va. Qed. Lemma symbol_address_sound: @@ -200,6 +398,70 @@ Proof. rewrite Ptrofs.add_zero_l; eauto with va. Qed. +Lemma of_optbool_maketotal_sound: + forall ob ab, cmatch ob ab -> vmatch bc (Val.maketotal (option_map Val.of_bool ob)) (of_optbool ab). +Proof. + intros. + assert (DEFAULT: vmatch bc (Val.maketotal (option_map Val.of_bool ob)) (Uns Pbot 1)). + { + destruct ob; simpl; auto with va. + destruct b; constructor; try omega. + change 1 with (usize Int.one). apply is_uns_usize. + red; intros. apply Int.bits_zero. + } + inv H; auto. simpl. destruct b; constructor. +Qed. + +Lemma eval_cmpu_sound c: forall a1 b1 a0 b0 optR m, + c = Ceq \/ c = Cne \/ c = Clt-> + vmatch bc a1 b1 -> + vmatch bc a0 b0 -> + vmatch bc (Op.apply_bin_oreg optR (Val.cmpu (Mem.valid_pointer m) c) a1 a0 Op.zero32) + (of_optbool (apply_bin_oreg optR (cmpu_bool c) b1 b0 zero32)). +Proof. + intros. + destruct optR as [[]|]; unfold Op.apply_bin_oreg, apply_bin_oreg; + apply of_optbool_sound; unfold Op.zero32, zero32; eauto with va. +Qed. + +Lemma eval_cmplu_sound c: forall a1 b1 a0 b0 optR m, + c = Ceq \/ c = Cne \/ c = Clt-> + vmatch bc a1 b1 -> + vmatch bc a0 b0 -> + vmatch bc + (Val.maketotal + (Op.apply_bin_oreg optR (Val.cmplu (Mem.valid_pointer m) c) a1 a0 + Op.zero64)) + (of_optbool (apply_bin_oreg optR (cmplu_bool c) b1 b0 zero64)). +Proof. + intros. + destruct optR as [[]|]; unfold Op.apply_bin_oreg, apply_bin_oreg; + apply of_optbool_maketotal_sound; unfold Op.zero64, zero64; eauto with va. +Qed. + +Lemma eval_cmp_sound: forall a1 b1 a0 b0 optR cmp, + vmatch bc a1 b1 -> + vmatch bc a0 b0 -> + vmatch bc (Op.apply_bin_oreg optR (Val.cmp cmp) a1 a0 Op.zero32) + (of_optbool (apply_bin_oreg optR (cmp_bool cmp) b1 b0 zero32)). +Proof. + intros. + destruct optR as [[]|]; unfold Op.apply_bin_oreg, apply_bin_oreg; + apply of_optbool_sound; unfold Op.zero32, zero32; eauto with va. +Qed. + +Lemma eval_cmpl_sound: forall a1 b1 a0 b0 optR cmp, + vmatch bc a1 b1 -> + vmatch bc a0 b0 -> + vmatch bc + (Val.maketotal (Op.apply_bin_oreg optR (Val.cmpl cmp) a1 a0 Op.zero64)) + (of_optbool (apply_bin_oreg optR (cmpl_bool cmp) b1 b0 zero64)). +Proof. + intros. + destruct optR as [[]|]; unfold Op.apply_bin_oreg, apply_bin_oreg; + apply of_optbool_maketotal_sound; unfold Op.zero64, zero64; eauto with va. +Qed. + Theorem eval_static_operation_sound: forall op vargs m vres aargs, eval_operation ge (Vptr sp Ptrofs.zero) op vargs m = Some vres -> @@ -212,6 +474,39 @@ Proof. destruct (propagate_float_constants tt); constructor. rewrite Ptrofs.add_zero_l; eauto with va. apply of_optbool_sound. eapply eval_static_condition_sound; eauto. + + 3,4,6: apply eval_cmpu_sound; auto. + 1,2,3: apply eval_cmp_sound; auto. + unfold Val.cmp; apply of_optbool_sound; eauto with va. + unfold Val.cmpu; apply of_optbool_sound; eauto with va. + + { destruct optR as [[]|]; simpl; eauto with va. } + { destruct optR as [[]|]; + unfold apply_bin_oreg, Op.apply_bin_oreg; eauto with va. } + { fold (Val.and (Vint n) a1); eauto with va. } + { fold (Val.or (Vint n) a1); eauto with va. } + { simpl; try destruct (Int.ltu _ _); eauto with va; unfold ntop1; + try apply vmatch_ifptr_undef. } + 9: { destruct optR as [[]|]; simpl; eauto with va. } + 9: { destruct optR as [[]|]; + unfold apply_bin_oreg, Op.apply_bin_oreg; eauto with va. } + 9: { fold (Val.andl (Vlong n) a1); eauto with va. } + 9: { fold (Val.orl (Vlong n) a1); eauto with va. } + 9: { simpl; unfold ntop1, sign_ext, Int64.sign_ext, sgn; simpl; + apply vmatch_ifptr_l. } + + 1,10: simpl; eauto with va. + 10: + unfold Op.eval_may_undef, eval_may_undef; destruct mu; + inv H1; inv H0; eauto with va; + try destruct (Int.ltu _ _); simpl; + try eapply vmatch_ifptr_p, pmatch_top'; eauto with va. + + 4,5,7: apply eval_cmplu_sound; auto. + 1,3,4: apply eval_cmpl_sound; auto. + 2: { unfold Val.cmpl; apply of_optbool_maketotal_sound; eauto with va. } + 2: { unfold Val.cmplu; apply of_optbool_maketotal_sound; eauto with va. } + all: unfold Val.cmpf; apply of_optbool_sound; eauto with va. Qed. End SOUNDNESS. |