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|
Require Export String List NPeano NArith.
Require Export Bedrock.Word.
(* A formalization of x86 qhasm *)
Definition Label := nat.
Definition Index (limit: nat) := {x: nat | (x < limit)%nat}.
Definition Invert := bool.
(* Sugar and Tactics *)
Definition convert {A B: Type} (x: A) (H: A = B): B :=
eq_rect A (fun B0 : Type => B0) x B H.
Notation "'always' A" := (fun _ => A) (at level 90) : state_scope.
Notation "'cast' e" := (convert e _) (at level 20) : state_scope.
Notation "'lift' e" := (exist _ e _) (at level 20) : state_scope.
Notation "'contra'" := (False_rec _ _) : state_scope.
Obligation Tactic := abstract intuition.
(* Float Datatype *)
Record Float (floatBits: nat) (fractionBits: nat) := mkFloat {
validFloat: word floatBits -> Prop;
wordToFloat: word fractionBits -> {w: word floatBits | validFloat w};
floatToWord: {w: word floatBits | validFloat w} -> word fractionBits;
wordToFloat_spec : forall x, floatToWord (wordToFloat x) = x;
serialize: {w: word floatBits | validFloat w} -> N;
deserialize: N -> {w: word floatBits | validFloat w};
serialize_spec1 : forall x, serialize (deserialize x) = x;
serialize_spec2 : forall x, deserialize (serialize x) = x;
floatPlus: {w: word floatBits | validFloat w}
-> {w: word floatBits | validFloat w}
-> {w: word floatBits | validFloat w};
floatPlus_wordToFloat : forall n m,
(wordToN n < (Npow2 (fractionBits - 1)))%N ->
(wordToN m < (Npow2 (fractionBits - 1)))%N ->
floatPlus (wordToFloat n) (wordToFloat m)
= wordToFloat (wplus n m);
floatMult: {w: word floatBits | validFloat w}
-> {w: word floatBits | validFloat w}
-> {w: word floatBits | validFloat w};
floatMult_wordToFloat : forall n m,
(wordToN n < (Npow2 (fractionBits / 2)%nat))%N ->
(wordToN m < (Npow2 (fractionBits / 2)%nat))%N ->
floatMult (wordToFloat n) (wordToFloat m)
= wordToFloat (wmult n m);
floatAnd: {w: word floatBits | validFloat w}
-> {w: word floatBits | validFloat w}
-> {w: word floatBits | validFloat w};
floatAnd_wordToFloat : forall n m,
floatAnd (wordToFloat n) (wordToFloat m) = wordToFloat (wand n m)
}.
Parameter Float32: Float 32 23.
Parameter Float64: Float 64 52.
(* Asm Types *)
Inductive IConst: nat -> Type :=
| constInt32: word 32 -> IConst 32.
Inductive FConst: nat -> Type :=
| constFloat32: word 32 -> FConst 32
| constFloat64: word 64 -> FConst 64.
Inductive IReg: nat -> Type :=
| regInt32: nat -> IReg 32.
Inductive FReg: nat -> Type :=
| regFloat32: nat -> FReg 32
| regFloat64: nat -> FReg 64.
Inductive Stack: nat -> Type :=
| stack32: nat -> Stack 32
| stack64: nat -> Stack 64
| stack128: nat -> Stack 128.
Definition CarryState := option bool.
(* Assignments *)
Inductive Assignment : Type :=
| ARegStackInt: forall n, IReg n -> Stack n -> Assignment
| ARegStackFloat: forall n, FReg n -> Stack n -> Assignment
| AStackRegInt: forall n, Stack n -> IReg n -> Assignment
| AStackRegFloat: forall n, Stack n -> FReg n -> Assignment
| ARegRegInt: forall n, IReg n -> IReg n -> Assignment
| ARegRegFloat: forall n, FReg n -> FReg n -> Assignment
| AConstInt: forall n, IReg n -> IConst n -> Assignment
| AConstFloat: forall n, FReg n -> FConst n -> Assignment
| AIndex: forall n m, IReg n -> IReg m -> Index (n/m)%nat -> Assignment
| APtr: forall n, IReg 32 -> Stack n -> Assignment.
Hint Constructors Assignment.
(* Operations *)
Inductive IntOp :=
| IPlus: IntOp | IMinus: IntOp
| IXor: IntOp | IAnd: IntOp | IOr: IntOp.
Inductive FloatOp :=
| FPlus: FloatOp | FMult: FloatOp | FAnd: FloatOp.
Inductive RotOp :=
| Shl: RotOp | Shr: RotOp.
Inductive Operation :=
| IOpConst: IntOp -> IReg 32 -> IConst 32 -> Operation
| IOpReg: IntOp -> IReg 32 -> IReg 32 -> Operation
| FOpConst32: FloatOp -> FReg 32 -> FConst 32 -> Operation
| FOpReg32: FloatOp -> FReg 32 -> FReg 32 -> Operation
| FOpConst64: FloatOp -> FReg 64 -> FConst 64 -> Operation
| FOpReg64: FloatOp -> FReg 64 -> FReg 64 -> Operation
| OpRot: RotOp -> IReg 32 -> Index 32 -> Operation.
Hint Constructors Operation.
(* Control Flow *)
Inductive TestOp :=
| TEq: TestOp | TLt: TestOp | TLe: TestOp
| TGt: TestOp | TGe: TestOp.
Inductive Conditional :=
| TestTrue: Conditional
| TestFalse: Conditional
| TestInt: forall n, TestOp -> IReg n -> IReg n -> Conditional
| TestFloat: forall n, TestOp -> FReg n -> FReg n -> Conditional.
Hint Constructors Conditional.
(* Reg, Stack, Const Utilities *)
Definition getIRegWords {n} (x: IReg n) :=
match x with
| regInt32 loc => 1
end.
Definition getFRegWords {n} (x: FReg n) :=
match x with
| regFloat32 loc => 1
| regFloat64 loc => 2
end.
Definition getStackWords {n} (x: Stack n) :=
match x with
| stack32 loc => 1
| stack64 loc => 2
| stack128 loc => 4
end.
Definition getIRegIndex {n} (x: IReg n): nat :=
match x with
| regInt32 loc => loc
end.
Definition getFRegIndex {n} (x: FReg n): nat :=
match x with
| regFloat32 loc => loc
| regFloat64 loc => loc
end.
Definition getStackIndex {n} (x: Stack n): nat :=
match x with
| stack32 loc => loc
| stack64 loc => loc
| stack128 loc => loc
end.
(* For register allocation checking *)
Definition intRegCount (base: nat): nat :=
match base with
| 32 => 7
| _ => 0
end.
Definition floatRegCount (base: nat): nat :=
match base with
| 32 => 8
| 64 => 8
| _ => 0
end.
|
