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Require Import QhasmEvalCommon QhasmUtil State.
Require Import Language.
Require Import List.
Module Pseudo <: Language.
Import EvalUtil ListState Util.
Inductive Pseudo {w: nat} {s: Width w}: nat -> nat -> Type :=
| PVar: forall n, option bool -> Index n -> Pseudo n 1
| PMem: forall n m , Index n -> Index m -> Pseudo n 1
| PConst: forall n, word w -> Pseudo n 1
| PBin: forall n, IntOp -> Pseudo n 2 -> Pseudo n 1
| PDual: forall n, DualOp -> Pseudo n 2 -> Pseudo n 2
| PCarry: forall n, CarryOp -> Pseudo n 2 -> Pseudo n 1
| PShift: forall n, RotOp -> Index w -> Pseudo n 1 -> Pseudo n 1
| PFunExp: forall n, Pseudo n n -> nat -> Pseudo n n
| PLet: forall n k m, Pseudo n k -> Pseudo (n + k) m -> Pseudo n m
| PComb: forall n a b, Pseudo n a -> Pseudo n b -> Pseudo n (a + b)
| PCall: forall n m, Label -> Pseudo n m -> Pseudo n m
| PIf: forall n m, TestOp -> Index n -> Index n ->
Pseudo n m -> Pseudo n m -> Pseudo n m.
Hint Constructors Pseudo.
Record Params': Type := mkParams {
width: nat;
spec: Width width;
inputs: nat;
outputs: nat
}.
Definition Params := Params'.
Definition State (p: Params): Type := ListState (width p).
Definition Program (p: Params): Type :=
@Pseudo (width p) (spec p) (inputs p) (outputs p).
Definition Unary32: Params := mkParams 32 W32 1 1.
Definition Unary64: Params := mkParams 64 W64 1 1.
(* Evaluation *)
Fixpoint pseudoEval {n m w s} (prog: @Pseudo w s n m) (st: ListState w): option (ListState w) :=
match prog with
| PVar n _ i => omap (getVar i st) (fun x => Some (setList [x] st))
| PMem n m v i => omap (getMem v i st) (fun x => Some (setList [x] st))
| PConst n c => Some (setList [c] st)
| PBin n o p =>
omap (pseudoEval p st) (fun sp =>
match (getList sp) with
| [wa; wb] =>
let (v, c) := evalIntOp o wa wb in
Some (setList [v] (setCarryOpt c sp))
| _ => None
end)
| PCarry n o p =>
omap (pseudoEval p st) (fun sp =>
match (getList sp, getCarry sp) with
| ([wa; wb], Some c) =>
let (v, c') := evalCarryOp o wa wb c in
Some (setList [v] (setCarry c' sp))
| _ => None
end)
| PDual n o p =>
omap (pseudoEval p st) (fun sp =>
match (getList sp) with
| [wa; wb] =>
let (low, high) := evalDualOp o wa wb in
Some (setList [low; high] sp)
| _ => None
end)
| PShift n o a x =>
omap (pseudoEval x st) (fun sx =>
match (getList sx) with
| [wx] => Some (setList [evalRotOp o wx a] sx)
| _ => None
end)
| PLet n k m f g =>
omap (pseudoEval f st) (fun sf =>
omap (pseudoEval g (setList ((getList st) ++ (getList sf)) sf))
(fun sg => Some sg))
| PComb n a b f g =>
omap (pseudoEval f st) (fun sf =>
omap (pseudoEval g st) (fun sg =>
Some (setList ((getList sf) ++ (getList sg)) sg)))
| PIf n m t i0 i1 l r =>
omap (getVar i0 st) (fun v0 =>
omap (getVar i1 st) (fun v1 =>
if (evalTest t v0 v1)
then pseudoEval l st
else pseudoEval r st ))
| PFunExp n p e =>
(fix funexpseudo (e': nat) (st': ListState w) :=
match e' with
| O => Some st'
| S e'' =>
omap (pseudoEval p st') (fun st'' =>
funexpseudo e'' st'')
end) e st
| PCall n m _ p => pseudoEval p st
end.
Definition evaluatesTo (p: Params) (prog: Program p) (st st': State p) :=
pseudoEval prog st = Some st'.
Delimit Scope pseudo_notations with p.
Definition indexize (n: nat) (p: (n > 0)%nat) (x: nat): Index n.
intros; exists (x mod n);
abstract (pose proof (mod_bound_pos x n); omega).
Defined.
Notation "% A" := (PVar _ (Some false) (indexize _ _ A))
(at level 20, right associativity) : pseudo_notations.
Notation "$ A" := (PVar _ (Some true) (indexize _ _ A))
(at level 20, right associativity) : pseudo_notations.
Notation "A :[ B ]:" := (PMem _ _ (indexize _ _ A) (indexize _ _ B))
(at level 20, right associativity) : pseudo_notations.
Notation "# A" := (PConst _ (natToWord _ A))
(at level 20, right associativity) : pseudo_notations.
Notation "A :+: B" := (PBin _ Add (PComb _ _ _ A B))
(at level 60, right associativity) : pseudo_notations.
Notation "A :+c: B" := (PCarry _ AddWithCarry (PComb _ _ _ A B))
(at level 60, right associativity) : pseudo_notations.
Notation "A :-: B" := (PBin _ Sub (PComb _ _ _ A B))
(at level 60, right associativity) : pseudo_notations.
Notation "A :&: B" := (PBin _ And (PComb _ _ _ A B))
(at level 45, right associativity) : pseudo_notations.
Notation "A :^: B" := (PBin _ Xor (PComb _ _ _ A B))
(at level 45, right associativity) : pseudo_notations.
Notation "A :>>: B" := (PShift _ Shr (indexize _ _ B) A)
(at level 60, right associativity) : pseudo_notations.
Notation "A :<<: B" := (PShift _ Shl (indexize _ _ B) A)
(at level 60, right associativity) : pseudo_notations.
Notation "A :*: B" := (PDual _ Mult (PComb _ _ _ A B))
(at level 55, right associativity) : pseudo_notations.
Notation "O :( A , B ): :?: L ::: R" :=
(PIf _ _ O (indexize _ _ A) (indexize _ _ B) L R)
(at level 70, right associativity) : pseudo_notations.
Notation "F :**: e" :=
(PFunExp _ F e)
(at level 70, right associativity) : pseudo_notations.
Notation "E :->: F" :=
(PLet _ _ _ E F)
(at level 70, right associativity) : pseudo_notations.
Notation "A :|: B" :=
(PComb _ _ _ A B)
(at level 65, left associativity) : pseudo_notations.
Notation "n ::: A :():" :=
(PCall _ _ n A)
(at level 65, left associativity) : pseudo_notations.
End Pseudo.
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