diff options
Diffstat (limited to 'riscV/Op.v')
| -rw-r--r-- | riscV/Op.v | 296 |
1 files changed, 152 insertions, 144 deletions
@@ -38,6 +38,11 @@ Set Implicit Arguments. (** Conditions (boolean-valued operators). *) +(* Type to modelize the use of a special register in arith operations *) +Inductive oreg: Type := + | X0_L: oreg + | X0_R: oreg. + Inductive condition : Type := | Ccomp (c: comparison) (**r signed integer comparison *) | Ccompu (c: comparison) (**r unsigned integer comparison *) @@ -52,22 +57,22 @@ Inductive condition : Type := | Ccompfs (c: comparison) (**r 32-bit floating-point comparison *) | Cnotcompfs (c: comparison) (**r negation of a floating-point comparison *) (* Expansed branches *) - | CEbeqw (optR0: option bool) (**r branch-if-equal signed *) - | CEbnew (optR0: option bool) (**r branch-if-not-equal signed *) - | CEbequw (optR0: option bool) (**r branch-if-equal unsigned *) - | CEbneuw (optR0: option bool) (**r branch-if-not-equal unsigned *) - | CEbltw (optR0: option bool) (**r branch-if-less signed *) - | CEbltuw (optR0: option bool) (**r branch-if-less unsigned *) - | CEbgew (optR0: option bool) (**r branch-if-greater-or-equal signed *) - | CEbgeuw (optR0: option bool) (**r branch-if-greater-or-equal unsigned *) - | CEbeql (optR0: option bool) (**r branch-if-equal signed *) - | CEbnel (optR0: option bool) (**r branch-if-not-equal signed *) - | CEbequl (optR0: option bool) (**r branch-if-equal unsigned *) - | CEbneul (optR0: option bool) (**r branch-if-not-equal unsigned *) - | CEbltl (optR0: option bool) (**r branch-if-less signed *) - | CEbltul (optR0: option bool) (**r branch-if-less unsigned *) - | CEbgel (optR0: option bool) (**r branch-if-greater-or-equal signed *) - | CEbgeul (optR0: option bool). (**r branch-if-greater-or-equal unsigned *) + | CEbeqw (optR: option oreg) (**r branch-if-equal signed *) + | CEbnew (optR: option oreg) (**r branch-if-not-equal signed *) + | CEbequw (optR: option oreg) (**r branch-if-equal unsigned *) + | CEbneuw (optR: option oreg) (**r branch-if-not-equal unsigned *) + | CEbltw (optR: option oreg) (**r branch-if-less signed *) + | CEbltuw (optR: option oreg) (**r branch-if-less unsigned *) + | CEbgew (optR: option oreg) (**r branch-if-greater-or-equal signed *) + | CEbgeuw (optR: option oreg) (**r branch-if-greater-or-equal unsigned *) + | CEbeql (optR: option oreg) (**r branch-if-equal signed *) + | CEbnel (optR: option oreg) (**r branch-if-not-equal signed *) + | CEbequl (optR: option oreg) (**r branch-if-equal unsigned *) + | CEbneul (optR: option oreg) (**r branch-if-not-equal unsigned *) + | CEbltl (optR: option oreg) (**r branch-if-less signed *) + | CEbltul (optR: option oreg) (**r branch-if-less unsigned *) + | CEbgel (optR: option oreg) (**r branch-if-greater-or-equal signed *) + | CEbgeul (optR: option oreg). (**r branch-if-greater-or-equal unsigned *) (* This type will define the eval function of a OEmayundef operation. *) Inductive mayundef: Type := @@ -76,7 +81,7 @@ Inductive mayundef: Type := | MUshrx: int -> mayundef | MUshrxl: int -> mayundef. -(* This allow to have a single RTL constructor to perform an arith operation between an immediate and X0 *) +(* Type for allowing a single RTL constructor to perform an arith operation between an immediate and X0 *) Inductive opimm: Type := | OPimmADD: int -> opimm | OPimmADDL: int64 -> opimm. @@ -185,12 +190,12 @@ Inductive operation : Type := | Ocmp (cond: condition) (**r [rd = 1] if condition holds, [rd = 0] otherwise. *) (* Expansed conditions *) | OEimmR0 (opi: opimm) - | OEseqw (optR0: option bool) (**r [rd <- rs1 == rs2] signed *) - | OEsnew (optR0: option bool) (**r [rd <- rs1 != rs2] signed *) - | OEsequw (optR0: option bool) (**r [rd <- rs1 == rs2] unsigned *) - | OEsneuw (optR0: option bool) (**r [rd <- rs1 != rs2] unsigned *) - | OEsltw (optR0: option bool) (**r set-less-than *) - | OEsltuw (optR0: option bool) (**r set-less-than unsigned *) + | OEseqw (optR: option oreg) (**r [rd <- rs1 == rs2] signed *) + | OEsnew (optR: option oreg) (**r [rd <- rs1 != rs2] signed *) + | OEsequw (optR: option oreg) (**r [rd <- rs1 == rs2] unsigned *) + | OEsneuw (optR: option oreg) (**r [rd <- rs1 != rs2] unsigned *) + | OEsltw (optR: option oreg) (**r set-less-than *) + | OEsltuw (optR: option oreg) (**r set-less-than unsigned *) | OEsltiw (n: int) (**r set-less-than immediate *) | OEsltiuw (n: int) (**r set-less-than unsigned immediate *) | OEaddiw (n: int) (**r add immediate *) @@ -198,12 +203,12 @@ Inductive operation : Type := | OEoriw (n: int) (**r or immediate *) | OExoriw (n: int) (**r xor immediate *) | OEluiw (n: int) (**r load upper-immediate *) - | OEseql (optR0: option bool) (**r [rd <- rs1 == rs2] signed *) - | OEsnel (optR0: option bool) (**r [rd <- rs1 != rs2] signed *) - | OEsequl (optR0: option bool) (**r [rd <- rs1 == rs2] unsigned *) - | OEsneul (optR0: option bool) (**r [rd <- rs1 != rs2] unsigned *) - | OEsltl (optR0: option bool) (**r set-less-than *) - | OEsltul (optR0: option bool) (**r set-less-than unsigned *) + | OEseql (optR: option oreg) (**r [rd <- rs1 == rs2] signed *) + | OEsnel (optR: option oreg) (**r [rd <- rs1 != rs2] signed *) + | OEsequl (optR: option oreg) (**r [rd <- rs1 == rs2] unsigned *) + | OEsneul (optR: option oreg) (**r [rd <- rs1 != rs2] unsigned *) + | OEsltl (optR: option oreg) (**r set-less-than *) + | OEsltul (optR: option oreg) (**r set-less-than unsigned *) | OEsltil (n: int64) (**r set-less-than immediate *) | OEsltiul (n: int64) (**r set-less-than unsigned immediate *) | OEaddil (n: int64) (**r add immediate *) @@ -235,12 +240,15 @@ Inductive addressing: Type := (** Comparison functions (used in modules [CSE] and [Allocation]). *) +Definition oreg_eq: forall (x y: oreg), {x=y} + {x<>y}. +Proof. decide equality. Defined. + Definition eq_condition (x y: condition) : {x=y} + {x<>y}. Proof. - generalize Int.eq_dec Int64.eq_dec bool_dec; intros. + generalize Int.eq_dec Int64.eq_dec bool_dec oreg_eq; intros. assert (forall (x y: comparison), {x=y}+{x<>y}). decide equality. decide equality. - all: destruct optR0, optR1; decide equality. + all: destruct optR, optR0; decide equality. Defined. Definition eq_addressing (x y: addressing) : {x=y} + {x<>y}. @@ -251,9 +259,9 @@ Defined. Definition eq_operation: forall (x y: operation), {x=y} + {x<>y}. Proof. - generalize Int.eq_dec Int64.eq_dec Ptrofs.eq_dec Float.eq_dec Float32.eq_dec ident_eq eq_condition bool_dec Val.eq; intros. + generalize Int.eq_dec Int64.eq_dec Ptrofs.eq_dec Float.eq_dec Float32.eq_dec ident_eq eq_condition bool_dec Val.eq oreg_eq; intros. decide equality. - all: try destruct optR0, optR1; try decide equality. + all: try destruct optR, optR0; try decide equality. Defined. (* Alternate definition: @@ -273,11 +281,11 @@ Global Opaque eq_condition eq_addressing eq_operation. Definition zero32 := (Vint Int.zero). Definition zero64 := (Vlong Int64.zero). -Definition apply_bin_r0 {B} (optR0: option bool) (sem: val -> val -> B) (v1 v2 vz: val): B := - match optR0 with +Definition apply_bin_oreg {B} (optR: option oreg) (sem: val -> val -> B) (v1 v2 vz: val): B := + match optR with | None => sem v1 v2 - | Some true => sem vz v1 - | Some false => sem v1 vz + | Some X0_L => sem vz v1 + | Some X0_R => sem v1 vz end. Definition eval_may_undef (mu: mayundef) (v1 v2: val): val := @@ -332,22 +340,22 @@ Definition eval_condition (cond: condition) (vl: list val) (m: mem): option bool | Ccompfs c, v1 :: v2 :: nil => Val.cmpfs_bool c v1 v2 | Cnotcompfs c, v1 :: v2 :: nil => option_map negb (Val.cmpfs_bool c v1 v2) (* Expansed branches *) - | CEbeqw optR0, v1 :: v2 :: nil => apply_bin_r0 optR0 (Val.cmp_bool Ceq) v1 v2 zero32 - | CEbnew optR0, v1 :: v2 :: nil => apply_bin_r0 optR0 (Val.cmp_bool Cne) v1 v2 zero32 - | CEbequw optR0, v1 :: v2 :: nil => apply_bin_r0 optR0 (Val.cmpu_bool (Mem.valid_pointer m) Ceq) v1 v2 zero32 - | CEbneuw optR0, v1 :: v2 :: nil => apply_bin_r0 optR0 (Val.cmpu_bool (Mem.valid_pointer m) Cne) v1 v2 zero32 - | CEbltw optR0, v1 :: v2 :: nil => apply_bin_r0 optR0 (Val.cmp_bool Clt) v1 v2 zero32 - | CEbltuw optR0, v1 :: v2 :: nil => apply_bin_r0 optR0 (Val.cmpu_bool (Mem.valid_pointer m) Clt) v1 v2 zero32 - | CEbgew optR0, v1 :: v2 :: nil => apply_bin_r0 optR0 (Val.cmp_bool Cge) v1 v2 zero32 - | CEbgeuw optR0, v1 :: v2 :: nil => apply_bin_r0 optR0 (Val.cmpu_bool (Mem.valid_pointer m) Cge) v1 v2 zero32 - | CEbeql optR0, v1 :: v2 :: nil => apply_bin_r0 optR0 (Val.cmpl_bool Ceq) v1 v2 zero64 - | CEbnel optR0, v1 :: v2 :: nil => apply_bin_r0 optR0 (Val.cmpl_bool Cne) v1 v2 zero64 - | CEbequl optR0, v1 :: v2 :: nil => apply_bin_r0 optR0 (Val.cmplu_bool (Mem.valid_pointer m) Ceq) v1 v2 zero64 - | CEbneul optR0, v1 :: v2 :: nil => apply_bin_r0 optR0 (Val.cmplu_bool (Mem.valid_pointer m) Cne) v1 v2 zero64 - | CEbltl optR0, v1 :: v2 :: nil => apply_bin_r0 optR0 (Val.cmpl_bool Clt) v1 v2 zero64 - | CEbltul optR0, v1 :: v2 :: nil => apply_bin_r0 optR0 (Val.cmplu_bool (Mem.valid_pointer m) Clt) v1 v2 zero64 - | CEbgel optR0, v1 :: v2 :: nil => apply_bin_r0 optR0 (Val.cmpl_bool Cge) v1 v2 zero64 - | CEbgeul optR0, v1 :: v2 :: nil => apply_bin_r0 optR0 (Val.cmplu_bool (Mem.valid_pointer m) Cge) v1 v2 zero64 + | CEbeqw optR, v1 :: v2 :: nil => apply_bin_oreg optR (Val.cmp_bool Ceq) v1 v2 zero32 + | CEbnew optR, v1 :: v2 :: nil => apply_bin_oreg optR (Val.cmp_bool Cne) v1 v2 zero32 + | CEbequw optR, v1 :: v2 :: nil => apply_bin_oreg optR (Val.cmpu_bool (Mem.valid_pointer m) Ceq) v1 v2 zero32 + | CEbneuw optR, v1 :: v2 :: nil => apply_bin_oreg optR (Val.cmpu_bool (Mem.valid_pointer m) Cne) v1 v2 zero32 + | CEbltw optR, v1 :: v2 :: nil => apply_bin_oreg optR (Val.cmp_bool Clt) v1 v2 zero32 + | CEbltuw optR, v1 :: v2 :: nil => apply_bin_oreg optR (Val.cmpu_bool (Mem.valid_pointer m) Clt) v1 v2 zero32 + | CEbgew optR, v1 :: v2 :: nil => apply_bin_oreg optR (Val.cmp_bool Cge) v1 v2 zero32 + | CEbgeuw optR, v1 :: v2 :: nil => apply_bin_oreg optR (Val.cmpu_bool (Mem.valid_pointer m) Cge) v1 v2 zero32 + | CEbeql optR, v1 :: v2 :: nil => apply_bin_oreg optR (Val.cmpl_bool Ceq) v1 v2 zero64 + | CEbnel optR, v1 :: v2 :: nil => apply_bin_oreg optR (Val.cmpl_bool Cne) v1 v2 zero64 + | CEbequl optR, v1 :: v2 :: nil => apply_bin_oreg optR (Val.cmplu_bool (Mem.valid_pointer m) Ceq) v1 v2 zero64 + | CEbneul optR, v1 :: v2 :: nil => apply_bin_oreg optR (Val.cmplu_bool (Mem.valid_pointer m) Cne) v1 v2 zero64 + | CEbltl optR, v1 :: v2 :: nil => apply_bin_oreg optR (Val.cmpl_bool Clt) v1 v2 zero64 + | CEbltul optR, v1 :: v2 :: nil => apply_bin_oreg optR (Val.cmplu_bool (Mem.valid_pointer m) Clt) v1 v2 zero64 + | CEbgel optR, v1 :: v2 :: nil => apply_bin_oreg optR (Val.cmpl_bool Cge) v1 v2 zero64 + | CEbgeul optR, v1 :: v2 :: nil => apply_bin_oreg optR (Val.cmplu_bool (Mem.valid_pointer m) Cge) v1 v2 zero64 | _, _ => None end. @@ -454,12 +462,12 @@ Definition eval_operation | Ocmp c, _ => Some (Val.of_optbool (eval_condition c vl m)) (* Expansed conditions *) | OEimmR0 opi, nil => Some (eval_opimmR0 opi) - | OEseqw optR0, v1::v2::nil => Some (apply_bin_r0 optR0 (Val.cmp Ceq) v1 v2 zero32) - | OEsnew optR0, v1::v2::nil => Some (apply_bin_r0 optR0 (Val.cmp Cne) v1 v2 zero32) - | OEsequw optR0, v1::v2::nil => Some (apply_bin_r0 optR0 (Val.cmpu (Mem.valid_pointer m) Ceq) v1 v2 zero32) - | OEsneuw optR0, v1::v2::nil => Some (apply_bin_r0 optR0 (Val.cmpu (Mem.valid_pointer m) Cne) v1 v2 zero32) - | OEsltw optR0, v1::v2::nil => Some (apply_bin_r0 optR0 (Val.cmp Clt) v1 v2 zero32) - | OEsltuw optR0, v1::v2::nil => Some (apply_bin_r0 optR0 (Val.cmpu (Mem.valid_pointer m) Clt) v1 v2 zero32) + | OEseqw optR, v1::v2::nil => Some (apply_bin_oreg optR (Val.cmp Ceq) v1 v2 zero32) + | OEsnew optR, v1::v2::nil => Some (apply_bin_oreg optR (Val.cmp Cne) v1 v2 zero32) + | OEsequw optR, v1::v2::nil => Some (apply_bin_oreg optR (Val.cmpu (Mem.valid_pointer m) Ceq) v1 v2 zero32) + | OEsneuw optR, v1::v2::nil => Some (apply_bin_oreg optR (Val.cmpu (Mem.valid_pointer m) Cne) v1 v2 zero32) + | OEsltw optR, v1::v2::nil => Some (apply_bin_oreg optR (Val.cmp Clt) v1 v2 zero32) + | OEsltuw optR, v1::v2::nil => Some (apply_bin_oreg optR (Val.cmpu (Mem.valid_pointer m) Clt) v1 v2 zero32) | OEsltiw n, v1::nil => Some (Val.cmp Clt v1 (Vint n)) | OEsltiuw n, v1::nil => Some (Val.cmpu (Mem.valid_pointer m) Clt v1 (Vint n)) | OExoriw n, v1::nil => Some (Val.xor v1 (Vint n)) @@ -467,12 +475,12 @@ Definition eval_operation | OEaddiw n, v1::nil => Some (Val.add (Vint n) v1) | OEandiw n, v1::nil => Some (Val.and (Vint n) v1) | OEoriw n, v1::nil => Some (Val.or (Vint n) v1) - | OEseql optR0, v1::v2::nil => Some (Val.maketotal (apply_bin_r0 optR0 (Val.cmpl Ceq) v1 v2 zero64)) - | OEsnel optR0, v1::v2::nil => Some (Val.maketotal (apply_bin_r0 optR0 (Val.cmpl Cne) v1 v2 zero64)) - | OEsequl optR0, v1::v2::nil => Some (Val.maketotal (apply_bin_r0 optR0 (Val.cmplu (Mem.valid_pointer m) Ceq) v1 v2 zero64)) - | OEsneul optR0, v1::v2::nil => Some (Val.maketotal (apply_bin_r0 optR0 (Val.cmplu (Mem.valid_pointer m) Cne) v1 v2 zero64)) - | OEsltl optR0, v1::v2::nil => Some (Val.maketotal (apply_bin_r0 optR0 (Val.cmpl Clt) v1 v2 zero64)) - | OEsltul optR0, v1::v2::nil => Some (Val.maketotal (apply_bin_r0 optR0 (Val.cmplu (Mem.valid_pointer m) Clt) v1 v2 zero64)) + | OEseql optR, v1::v2::nil => Some (Val.maketotal (apply_bin_oreg optR (Val.cmpl Ceq) v1 v2 zero64)) + | OEsnel optR, v1::v2::nil => Some (Val.maketotal (apply_bin_oreg optR (Val.cmpl Cne) v1 v2 zero64)) + | OEsequl optR, v1::v2::nil => Some (Val.maketotal (apply_bin_oreg optR (Val.cmplu (Mem.valid_pointer m) Ceq) v1 v2 zero64)) + | OEsneul optR, v1::v2::nil => Some (Val.maketotal (apply_bin_oreg optR (Val.cmplu (Mem.valid_pointer m) Cne) v1 v2 zero64)) + | OEsltl optR, v1::v2::nil => Some (Val.maketotal (apply_bin_oreg optR (Val.cmpl Clt) v1 v2 zero64)) + | OEsltul optR, v1::v2::nil => Some (Val.maketotal (apply_bin_oreg optR (Val.cmplu (Mem.valid_pointer m) Clt) v1 v2 zero64)) | OEsltil n, v1::nil => Some (Val.maketotal (Val.cmpl Clt v1 (Vlong n))) | OEsltiul n, v1::nil => Some (Val.maketotal (Val.cmplu (Mem.valid_pointer m) Clt v1 (Vlong n))) | OExoril n, v1::nil => Some (Val.xorl v1 (Vlong n)) @@ -924,22 +932,22 @@ Proof with (try exact I; try reflexivity; auto using Val.Vptr_has_type). (* OEimmR0 *) - destruct opi; unfold eval_opimmR0; simpl; auto. (* OEseqw *) - - destruct optR0 as [[]|]; simpl; unfold Val.cmp; + - destruct optR as [[]|]; simpl; unfold Val.cmp; destruct Val.cmp_bool... all: destruct b... (* OEsnew *) - - destruct optR0 as [[]|]; simpl; unfold Val.cmp; + - destruct optR as [[]|]; simpl; unfold Val.cmp; destruct Val.cmp_bool... all: destruct b... (* OEsequw *) - - destruct optR0 as [[]|]; simpl; unfold Val.cmpu; + - destruct optR as [[]|]; simpl; unfold Val.cmpu; destruct Val.cmpu_bool... all: destruct b... (* OEsneuw *) - - destruct optR0 as [[]|]; simpl; unfold Val.cmpu; + - destruct optR as [[]|]; simpl; unfold Val.cmpu; destruct Val.cmpu_bool... all: destruct b... (* OEsltw *) - - destruct optR0 as [[]|]; simpl; unfold Val.cmp; + - destruct optR as [[]|]; simpl; unfold Val.cmp; destruct Val.cmp_bool... all: destruct b... (* OEsltuw *) - - destruct optR0 as [[]|]; simpl; unfold Val.cmpu; + - destruct optR as [[]|]; simpl; unfold Val.cmpu; destruct Val.cmpu_bool... all: destruct b... (* OEsltiw *) - unfold Val.cmp; destruct Val.cmp_bool... @@ -957,22 +965,22 @@ Proof with (try exact I; try reflexivity; auto using Val.Vptr_has_type). (* OEluiw *) - destruct (Int.ltu _ _); cbn; trivial. (* OEseql *) - - destruct optR0 as [[]|]; simpl; unfold Val.cmpl; + - destruct optR as [[]|]; simpl; unfold Val.cmpl; destruct Val.cmpl_bool... all: destruct b... (* OEsnel *) - - destruct optR0 as [[]|]; simpl; unfold Val.cmpl; + - destruct optR as [[]|]; simpl; unfold Val.cmpl; destruct Val.cmpl_bool... all: destruct b... (* OEsequl *) - - destruct optR0 as [[]|]; simpl; unfold Val.cmplu; + - destruct optR as [[]|]; simpl; unfold Val.cmplu; destruct Val.cmplu_bool... all: destruct b... (* OEsneul *) - - destruct optR0 as [[]|]; simpl; unfold Val.cmplu; + - destruct optR as [[]|]; simpl; unfold Val.cmplu; destruct Val.cmplu_bool... all: destruct b... (* OEsltl *) - - destruct optR0 as [[]|]; simpl; unfold Val.cmpl; + - destruct optR as [[]|]; simpl; unfold Val.cmpl; destruct Val.cmpl_bool... all: destruct b... (* OEsltul *) - - destruct optR0 as [[]|]; simpl; unfold Val.cmplu; + - destruct optR as [[]|]; simpl; unfold Val.cmplu; destruct Val.cmplu_bool... all: destruct b... (* OEsltil *) - unfold Val.cmpl; destruct Val.cmpl_bool... @@ -1092,22 +1100,22 @@ Definition negate_condition (cond: condition): condition := | Cnotcompf c => Ccompf c | Ccompfs c => Cnotcompfs c | Cnotcompfs c => Ccompfs c - | CEbeqw optR0 => CEbnew optR0 - | CEbnew optR0 => CEbeqw optR0 - | CEbequw optR0 => CEbneuw optR0 - | CEbneuw optR0 => CEbequw optR0 - | CEbltw optR0 => CEbgew optR0 - | CEbltuw optR0 => CEbgeuw optR0 - | CEbgew optR0 => CEbltw optR0 - | CEbgeuw optR0 => CEbltuw optR0 - | CEbeql optR0 => CEbnel optR0 - | CEbnel optR0 => CEbeql optR0 - | CEbequl optR0 => CEbneul optR0 - | CEbneul optR0 => CEbequl optR0 - | CEbltl optR0 => CEbgel optR0 - | CEbltul optR0 => CEbgeul optR0 - | CEbgel optR0 => CEbltl optR0 - | CEbgeul optR0 => CEbltul optR0 + | CEbeqw optR => CEbnew optR + | CEbnew optR => CEbeqw optR + | CEbequw optR => CEbneuw optR + | CEbneuw optR => CEbequw optR + | CEbltw optR => CEbgew optR + | CEbltuw optR => CEbgeuw optR + | CEbgew optR => CEbltw optR + | CEbgeuw optR => CEbltuw optR + | CEbeql optR => CEbnel optR + | CEbnel optR => CEbeql optR + | CEbequl optR => CEbneul optR + | CEbneul optR => CEbequl optR + | CEbltl optR => CEbgel optR + | CEbltul optR => CEbgeul optR + | CEbgel optR => CEbltl optR + | CEbgeul optR => CEbltul optR end. Lemma eval_negate_condition: @@ -1128,37 +1136,37 @@ Proof. repeat (destruct vl; auto). repeat (destruct vl; auto). destruct (Val.cmpfs_bool c v v0) as [[]|]; auto. - repeat (destruct vl; auto); replace (Cne) with (negate_comparison Ceq) by auto; destruct optR0 as [[]|]; + repeat (destruct vl; auto); replace (Cne) with (negate_comparison Ceq) by auto; destruct optR as [[]|]; apply Val.negate_cmp_bool. - repeat (destruct vl; auto); replace (Ceq) with (negate_comparison Cne) by auto; destruct optR0 as [[]|]; + repeat (destruct vl; auto); replace (Ceq) with (negate_comparison Cne) by auto; destruct optR as [[]|]; apply Val.negate_cmp_bool. - repeat (destruct vl; auto); replace (Cne) with (negate_comparison Ceq) by auto; destruct optR0 as [[]|]; + repeat (destruct vl; auto); replace (Cne) with (negate_comparison Ceq) by auto; destruct optR as [[]|]; apply Val.negate_cmpu_bool. - repeat (destruct vl; auto); replace (Ceq) with (negate_comparison Cne) by auto; destruct optR0 as [[]|]; + repeat (destruct vl; auto); replace (Ceq) with (negate_comparison Cne) by auto; destruct optR as [[]|]; apply Val.negate_cmpu_bool. - repeat (destruct vl; auto); replace (Cge) with (negate_comparison Clt) by auto; destruct optR0 as [[]|]; + repeat (destruct vl; auto); replace (Cge) with (negate_comparison Clt) by auto; destruct optR as [[]|]; apply Val.negate_cmp_bool. - repeat (destruct vl; auto); replace (Cge) with (negate_comparison Clt) by auto; destruct optR0 as [[]|]; + repeat (destruct vl; auto); replace (Cge) with (negate_comparison Clt) by auto; destruct optR as [[]|]; apply Val.negate_cmpu_bool. - repeat (destruct vl; auto); replace (Clt) with (negate_comparison Cge) by auto; destruct optR0 as [[]|]; + repeat (destruct vl; auto); replace (Clt) with (negate_comparison Cge) by auto; destruct optR as [[]|]; apply Val.negate_cmp_bool. - repeat (destruct vl; auto); replace (Clt) with (negate_comparison Cge) by auto; destruct optR0 as [[]|]; + repeat (destruct vl; auto); replace (Clt) with (negate_comparison Cge) by auto; destruct optR as [[]|]; apply Val.negate_cmpu_bool. - repeat (destruct vl; auto); replace (Cne) with (negate_comparison Ceq) by auto; destruct optR0 as [[]|]; + repeat (destruct vl; auto); replace (Cne) with (negate_comparison Ceq) by auto; destruct optR as [[]|]; apply Val.negate_cmpl_bool. - repeat (destruct vl; auto); replace (Ceq) with (negate_comparison Cne) by auto; destruct optR0 as [[]|]; + repeat (destruct vl; auto); replace (Ceq) with (negate_comparison Cne) by auto; destruct optR as [[]|]; apply Val.negate_cmpl_bool. - repeat (destruct vl; auto); replace (Cne) with (negate_comparison Ceq) by auto; destruct optR0 as [[]|]; + repeat (destruct vl; auto); replace (Cne) with (negate_comparison Ceq) by auto; destruct optR as [[]|]; apply Val.negate_cmplu_bool. - repeat (destruct vl; auto); replace (Ceq) with (negate_comparison Cne) by auto; destruct optR0 as [[]|]; + repeat (destruct vl; auto); replace (Ceq) with (negate_comparison Cne) by auto; destruct optR as [[]|]; apply Val.negate_cmplu_bool. - repeat (destruct vl; auto); replace (Cge) with (negate_comparison Clt) by auto; destruct optR0 as [[]|]; + repeat (destruct vl; auto); replace (Cge) with (negate_comparison Clt) by auto; destruct optR as [[]|]; apply Val.negate_cmpl_bool. - repeat (destruct vl; auto); replace (Cge) with (negate_comparison Clt) by auto; destruct optR0 as [[]|]; + repeat (destruct vl; auto); replace (Cge) with (negate_comparison Clt) by auto; destruct optR as [[]|]; apply Val.negate_cmplu_bool. - repeat (destruct vl; auto); replace (Clt) with (negate_comparison Cge) by auto; destruct optR0 as [[]|]; + repeat (destruct vl; auto); replace (Clt) with (negate_comparison Cge) by auto; destruct optR as [[]|]; apply Val.negate_cmpl_bool. - repeat (destruct vl; auto); replace (Clt) with (negate_comparison Cge) by auto; destruct optR0 as [[]|]; + repeat (destruct vl; auto); replace (Clt) with (negate_comparison Cge) by auto; destruct optR as [[]|]; apply Val.negate_cmplu_bool. Qed. @@ -1303,7 +1311,7 @@ Proof. f_equal. f_equal. apply cond_depends_on_memory_correct; trivial. all: intros; repeat (destruct args; auto); unfold Val.cmpu, Val.cmpu_bool, Val.cmplu, Val.cmplu_bool; - try destruct optR0 as [[]|]; simpl; + try destruct optR as [[]|]; simpl; destruct v; try destruct v0; simpl; auto; try apply negb_false_iff in H; try rewrite H; auto. Qed. @@ -1315,7 +1323,7 @@ Lemma cond_valid_pointer_eq: Proof. intros until m2. intro MEM. destruct cond eqn:COND; simpl; try congruence. all: repeat (destruct args; simpl; try congruence); - try destruct optR0 as [[]|]; simpl; + try destruct optR as [[]|]; simpl; try destruct v, v0; try rewrite !MEM; auto; try erewrite cmpu_bool_valid_pointer_eq || erewrite cmplu_bool_valid_pointer_eq; eauto. Qed. @@ -1328,7 +1336,7 @@ Proof. intros until m2. destruct op; simpl; try congruence. intro MEM; erewrite cond_valid_pointer_eq; eauto. all: intros MEM; repeat (destruct args; simpl; try congruence); - try destruct optR0 as [[]|]; simpl; try destruct v, v0; try rewrite !MEM; auto; + try destruct optR as [[]|]; simpl; try destruct v, v0; try rewrite !MEM; auto; unfold Val.cmpu, Val.cmplu; erewrite cmpu_bool_valid_pointer_eq || erewrite cmplu_bool_valid_pointer_eq; eauto. Qed. @@ -1460,14 +1468,14 @@ Proof. intros EQ; rewrite EQ; destruct b; simpl; constructor; eauto. Qed. -Lemma eval_cmpu_bool_inj_opt: forall c v v' v0 v'0 optR0, +Lemma eval_cmpu_bool_inj_opt: forall c v v' v0 v'0 optR, Val.inject f v v' -> Val.inject f v0 v'0 -> - Val.inject f (apply_bin_r0 optR0 (Val.cmpu (Mem.valid_pointer m1) c) v v0 zero32) - (apply_bin_r0 optR0 (Val.cmpu (Mem.valid_pointer m2) c) v' v'0 zero32). + Val.inject f (apply_bin_oreg optR (Val.cmpu (Mem.valid_pointer m1) c) v v0 zero32) + (apply_bin_oreg optR (Val.cmpu (Mem.valid_pointer m2) c) v' v'0 zero32). Proof. - intros until optR0. intros HV1 HV2. - destruct optR0 as [[]|]; simpl; unfold zero32, Val.cmpu; + intros until optR. intros HV1 HV2. + destruct optR as [[]|]; simpl; unfold zero32, Val.cmpu; destruct (Val.cmpu_bool (Mem.valid_pointer m1) c _ _) eqn:?; eauto; assert (HVI: Val.inject f (Vint Int.zero) (Vint Int.zero)) by apply Val.inject_int. + exploit eval_cmpu_bool_inj'. eapply HVI. eapply HV1. eapply Heqo. @@ -1501,14 +1509,14 @@ Proof. intros EQ; rewrite EQ; destruct b; simpl; constructor; eauto. Qed. -Lemma eval_cmplu_bool_inj_opt: forall c v v' v0 v'0 optR0, +Lemma eval_cmplu_bool_inj_opt: forall c v v' v0 v'0 optR, Val.inject f v v' -> Val.inject f v0 v'0 -> - Val.inject f (Val.maketotal (apply_bin_r0 optR0 (Val.cmplu (Mem.valid_pointer m1) c) v v0 zero64)) - (Val.maketotal (apply_bin_r0 optR0 (Val.cmplu (Mem.valid_pointer m2) c) v' v'0 zero64)). + Val.inject f (Val.maketotal (apply_bin_oreg optR (Val.cmplu (Mem.valid_pointer m1) c) v v0 zero64)) + (Val.maketotal (apply_bin_oreg optR (Val.cmplu (Mem.valid_pointer m2) c) v' v'0 zero64)). Proof. - intros until optR0. intros HV1 HV2. - destruct optR0 as [[]|]; simpl; unfold zero64, Val.cmplu; + intros until optR. intros HV1 HV2. + destruct optR as [[]|]; simpl; unfold zero64, Val.cmplu; destruct (Val.cmplu_bool (Mem.valid_pointer m1) c _ _) eqn:?; eauto; assert (HVI: Val.inject f (Vlong Int64.zero) (Vlong Int64.zero)) by apply Val.inject_long. + exploit eval_cmplu_bool_inj'. eapply HVI. eapply HV1. eapply Heqo. @@ -1541,37 +1549,37 @@ Proof. - inv H3; inv H2; simpl in H0; inv H0; auto. - inv H3; inv H2; simpl in H0; inv H0; auto. - inv H3; inv H2; simpl in H0; inv H0; auto. -- destruct optR0 as [[]|]; unfold apply_bin_r0 in *; +- destruct optR as [[]|]; unfold apply_bin_oreg in *; inv H3; inv H2; simpl in H0; inv H0; auto. -- destruct optR0 as [[]|]; unfold apply_bin_r0 in *; +- destruct optR as [[]|]; unfold apply_bin_oreg in *; inv H3; inv H2; simpl in H0; inv H0; auto. -- destruct optR0 as [[]|]; unfold apply_bin_r0 in *; +- destruct optR as [[]|]; unfold apply_bin_oreg in *; eapply eval_cmpu_bool_inj'; eauto. -- destruct optR0 as [[]|]; unfold apply_bin_r0 in *; +- destruct optR as [[]|]; unfold apply_bin_oreg in *; eapply eval_cmpu_bool_inj'; eauto. -- destruct optR0 as [[]|]; simpl; +- destruct optR as [[]|]; simpl; inv H3; inv H2; simpl in H0; inv H0; auto. -- destruct optR0 as [[]|]; unfold apply_bin_r0 in *; +- destruct optR as [[]|]; unfold apply_bin_oreg in *; eapply eval_cmpu_bool_inj'; eauto. -- destruct optR0 as [[]|]; simpl; +- destruct optR as [[]|]; simpl; inv H3; inv H2; simpl in H0; inv H0; auto. -- destruct optR0 as [[]|]; unfold apply_bin_r0 in *; +- destruct optR as [[]|]; unfold apply_bin_oreg in *; eapply eval_cmpu_bool_inj'; eauto. -- destruct optR0 as [[]|]; unfold apply_bin_r0 in *; +- destruct optR as [[]|]; unfold apply_bin_oreg in *; inv H3; inv H2; simpl in H0; inv H0; auto. -- destruct optR0 as [[]|]; unfold apply_bin_r0 in *; +- destruct optR as [[]|]; unfold apply_bin_oreg in *; inv H3; inv H2; simpl in H0; inv H0; auto. -- destruct optR0 as [[]|]; unfold apply_bin_r0 in *; +- destruct optR as [[]|]; unfold apply_bin_oreg in *; eapply eval_cmplu_bool_inj'; eauto. -- destruct optR0 as [[]|]; unfold apply_bin_r0 in *; +- destruct optR as [[]|]; unfold apply_bin_oreg in *; eapply eval_cmplu_bool_inj'; eauto. -- destruct optR0 as [[]|]; simpl; +- destruct optR as [[]|]; simpl; inv H3; inv H2; simpl in H0; inv H0; auto. -- destruct optR0 as [[]|]; unfold apply_bin_r0 in *; +- destruct optR as [[]|]; unfold apply_bin_oreg in *; eapply eval_cmplu_bool_inj'; eauto. -- destruct optR0 as [[]|]; simpl; +- destruct optR as [[]|]; simpl; inv H3; inv H2; simpl in H0; inv H0; auto. -- destruct optR0 as [[]|]; unfold apply_bin_r0 in *; +- destruct optR as [[]|]; unfold apply_bin_oreg in *; eapply eval_cmplu_bool_inj'; eauto. Qed. @@ -1784,11 +1792,11 @@ Proof. (* OEimmR0 *) - destruct opi; unfold eval_opimmR0; simpl; auto. (* OEseqw *) - - destruct optR0 as [[]|]; simpl; unfold zero32, Val.cmp; + - destruct optR as [[]|]; simpl; unfold zero32, Val.cmp; inv H4; inv H2; simpl; try destruct (Int.eq _ _); simpl; cbn; auto; try apply Val.inject_int. (* OEsnew *) - - destruct optR0 as [[]|]; simpl; unfold zero32, Val.cmp; + - destruct optR as [[]|]; simpl; unfold zero32, Val.cmp; inv H4; inv H2; simpl; try destruct (Int.eq _ _); simpl; cbn; auto; try apply Val.inject_int. (* OEsequw *) @@ -1796,7 +1804,7 @@ Proof. (* OEsneuw *) - apply eval_cmpu_bool_inj_opt; auto. (* OEsltw *) - - destruct optR0 as [[]|]; simpl; unfold zero32, Val.cmp; + - destruct optR as [[]|]; simpl; unfold zero32, Val.cmp; inv H4; inv H2; simpl; try destruct (Int.lt _ _); simpl; cbn; auto; try apply Val.inject_int. (* OEsltuw *) @@ -1818,11 +1826,11 @@ Proof. (* OEluiw *) - destruct (Int.ltu _ _); auto. (* OEseql *) - - destruct optR0 as [[]|]; simpl; unfold zero64, Val.cmpl; + - destruct optR as [[]|]; simpl; unfold zero64, Val.cmpl; inv H4; inv H2; simpl; try destruct (Int64.eq _ _); simpl; cbn; auto; try apply Val.inject_int. (* OEsnel *) - - destruct optR0 as [[]|]; simpl; unfold zero64, Val.cmpl; + - destruct optR as [[]|]; simpl; unfold zero64, Val.cmpl; inv H4; inv H2; simpl; try destruct (Int64.eq _ _); simpl; cbn; auto; try apply Val.inject_int. (* OEsequl *) @@ -1830,7 +1838,7 @@ Proof. (* OEsneul *) - apply eval_cmplu_bool_inj_opt; auto. (* OEsltl *) - - destruct optR0 as [[]|]; simpl; unfold zero64, Val.cmpl; + - destruct optR as [[]|]; simpl; unfold zero64, Val.cmpl; inv H4; inv H2; simpl; try destruct (Int64.lt _ _); simpl; cbn; auto; try apply Val.inject_int. (* OEsltul *) |