(** The main task in translating Csharpminor to Cminor is to explicitly
  stack-allocate local variables whose address is taken: these local
  variables become sub-blocks of the Cminor stack data block for the
  current function.  Taking the address of such a variable becomes
  a [Oaddrstack] operation with the corresponding offset.  Accessing
  or assigning such a variable becomes a load or store operation at
  that address.  Only scalar local variables whose address is never
  taken in the Csharpminor code can be mapped to Cminor local
  variable, since the latter do not reside in memory.

  Another task performed during the translation to Cminor is to
  transform the Clight-like [switch] construct of Csharpminor
  into the simpler, lower-level [switch] constructs of Cminor.
*)

(** * Handling of variables *)

(** To every Csharpminor variable, the compiler associates its offset
  in the Cminor stack data block. *)

Definition compilenv := PTree.t Z.(** Generation of a Cminor expression for taking the address of
  a Csharpminor variable. *)

Definition var_addr (cenv: compilenv) (id: ident): expr :=
  match PTree.get id cenv with
  | Some ofs => Econst (Oaddrstack (Ptrofs.repr ofs))
  | None     => Econst (Oaddrsymbol id Ptrofs.zero)
  end.(** * Translation of expressions and statements. *)

(** Translation of constants. *)

Definition transl_constant (cst: Csharpminor.constant): constant :=
  match cst with
  | Csharpminor.Ointconst n =>
      Ointconst n
  | Csharpminor.Ofloatconst n =>
      Ofloatconst n
  | Csharpminor.Osingleconst n =>
      Osingleconst n
  | Csharpminor.Olongconst n =>
      Olongconst n
  end.(** To translate [switch] statements, we wrap the statements associated with
  the various cases in a cascade of nested Cminor blocks.
  The multi-way branch is performed by a Cminor [switch]
  statement that exits to the appropriate case.  For instance:
<<
switch (e) {        --->    block { block { block {
  case N1: s1;                switch (e) { N1: exit 0; N2: exit 1; default: exit 2; }
  case N2: s2;                } ; s1  // with exits shifted by 2
  default: s;                 } ; s2  // with exits shifted by 1
}                             } ; s   // with exits unchanged
>>
  To shift [exit] statements appropriately, we use a second
  compile-time environment, of type [exit_env], which
  records the blocks inserted during the translation.
  A [true] element means the block was present in the original code;
  a [false] element, that it was inserted during translation.
*)

Definition exit_env := list bool.Fixpoint shift_exit (e: exit_env) (n: nat) {struct e} : nat :=
  match e, n with
  | nil, _ => n
  | false :: e', _ => S (shift_exit e' n)
  | true :: e', O => O
  | true :: e', S m => S (shift_exit e' m)
  end.Fixpoint switch_table (ls: lbl_stmt) (k: nat) {struct ls} : list (Z * nat) * nat :=
  match ls with
  | LSnil =>
      (nil, k)
  | LScons None _ rem =>
      let (tbl, dfl) := switch_table rem (S k) in (tbl, k)
  | LScons (Some ni) _ rem =>
      let (tbl, dfl) := switch_table rem (S k) in ((ni, k) :: tbl, dfl)
  end.Fixpoint switch_env (ls: lbl_stmt) (e: exit_env) {struct ls}: exit_env :=
  match ls with
  | LSnil => e
  | LScons _ _ ls' => false :: switch_env ls' e
  end.(** * Stack layout *)

(** Layout of the Cminor stack data block and construction of the
  compilation environment.  Every Csharpminor local variable is
  allocated a slot in the Cminor stack data.  Sufficient padding is
  inserted to ensure adequate alignment of addresses. *)

Definition block_alignment (sz: Z) : Z :=
  if zlt sz 2 then 1
  else if zlt sz 4 then 2
  else if zlt sz 8 then 4 else 8.Definition assign_variable
    (cenv_stacksize: compilenv * Z) (id_sz: ident * Z) : compilenv * Z :=
  let (id, sz) := id_sz in
  let (cenv, stacksize) := cenv_stacksize in
  let ofs := align stacksize (block_alignment sz) in
  (PTree.set id ofs cenv, ofs + Z.max 0 sz).Definition assign_variables (cenv_stacksize: compilenv * Z) (vars: list (ident * Z)) : compilenv * Z :=
  List.fold_left assign_variable vars cenv_stacksize.Definition t := (ident * Z)%type.Definition leb (v1 v2: t) : bool := zle (snd v1) (snd v2).

(* Specifications: *)
Theorem leb_total: forall v1 v2, leb v1 v2 = true \/ leb v2 v1 = true.