Module Cminorgen

Translation from Csharpminor to Cminor.

Require Import FSets.
Require FSetAVL.
Require Import Coqlib.
Require Import Errors.
Require Import Maps.
Require Import Ordered.
Require Import Ast.
Require Import Integers.
Require Mem.
Require Import Csharpminor.
Import Csharpminor.
Require Import Op.
Require Import Cminorops.
Require Import Cminor.

Open Local Scope string_scope.
Open Local Scope error_monad_scope.

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 the insertion of truncation, zero- and sign-extension operations when assigning to a Csharpminor local variable of ``small'' type (e.g. Mfloat32 or Mint8signed). This is necessary to preserve the ``normalize at assignment-time'' semantics of Clight and Csharpminor. Finally, the Clight-like switch construct of Csharpminor is transformed into the simpler, lower-level switch construct of Cminor.

Translation of constants.

Definition transl_constant (cst: Csharpminor.constant): constant :=
  match cst with
  | Csharpminor.Ointconst n => Ointconst n
  | Csharpminor.Ofloatconst n => Ofloatconst n

make_cast chunk e returns a Cminor expression that normalizes the value of Cminor expression e as prescribed by the memory chunk chunk. For instance, 8-bit sign extension is performed if chunk is Mint8signed.

Definition make_cast (chunk: memory_chunk) (e: expr): expr :=
  match chunk with
  | Mint8signed => Eunop Ocast8signed e
  | Mint8unsigned => Eunop Ocast8unsigned e
  | Mint16signed => Eunop Ocast16signed e
  | Mint16unsigned => Eunop Ocast16unsigned e
  | Mint32 => e
  | Mfloat32 => Eunop Osingleoffloat e
  | Mfloat64 => e

When the translation of an expression is stored in memory, the normalization performed by make_cast can be redundant with that implicitly performed by the memory store. store_arg detects this case and strips away the redundant normalization.

Definition store_arg (chunk: memory_chunk) (e: expr) : expr :=
  match e with
  | Eunop Ocast8signed e1 =>
      match chunk with Mint8signed => e1 | _ => e end
  | Eunop Ocast8unsigned e1 =>
      match chunk with Mint8unsigned => e1 | _ => e end
  | Eunop Ocast16signed e1 =>
      match chunk with Mint16signed => e1 | _ => e end
  | Eunop Ocast16unsigned e1 =>
      match chunk with Mint16unsigned => e1 | _ => e end
  | Eunop Osingleoffloat e1 =>
      match chunk with Mfloat32 => e1 | _ => e end
  | _ => e

Definition make_store (chunk: memory_chunk) (e1 e2: expr): stmt :=
  Sstore chunk e1 (store_arg chunk e2).

Definition make_stackaddr (ofs: Z): expr :=
  Econst (Oaddrstack (Int.repr ofs)).

Definition make_globaladdr (id: ident): expr :=
  Econst (Oaddrsymbol id

Compile-time information attached to each Csharpminor variable: global variables, local variables, function parameters. Var_local denotes a scalar local variable whose address is not taken; it will be translated to a Cminor local variable of the same name. Var_stack_scalar and Var_stack_array denote local variables that are stored as sub-blocks of the Cminor stack data block. Var_global_scalar and Var_global_array denote global variables, stored in the global symbols with the same names.

Inductive var_info: Type :=
  | Var_local: memory_chunk -> var_info
  | Var_stack_scalar: memory_chunk -> Z -> var_info
  | Var_stack_array: Z -> var_info
  | Var_global_scalar: memory_chunk -> var_info
  | Var_global_array: var_info.

Definition compilenv := PMap.t var_info.

Generation of Cminor code corresponding to accesses to Csharpminor local variables: reads, assignments, and taking the address of.

Definition var_get (cenv: compilenv) (id: ident): res expr :=
  match PMap.get id cenv with
  | Var_local chunk =>
      OK(Evar id)
  | Var_stack_scalar chunk ofs =>
      OK(Eload chunk (make_stackaddr ofs))
  | Var_global_scalar chunk =>
      OK(Eload chunk (make_globaladdr id))
  | _ =>
      Error(msg "Cminorgen.var_get")

Definition var_set (cenv: compilenv) (id: ident) (rhs: expr): res stmt :=
  match PMap.get id cenv with
  | Var_local chunk =>
      OK(Sassign id (make_cast chunk rhs))
  | Var_stack_scalar chunk ofs =>
      OK(make_store chunk (make_stackaddr ofs) rhs)
  | Var_global_scalar chunk =>
      OK(make_store chunk (make_globaladdr id) rhs)
  | _ =>
      Error(msg "Cminorgen.var_set")

Definition var_addr (cenv: compilenv) (id: ident): res expr :=
  match PMap.get id cenv with
  | Var_local chunk => Error(msg "Cminorgen.var_addr")
  | Var_stack_scalar chunk ofs => OK (make_stackaddr ofs)
  | Var_stack_array ofs => OK (make_stackaddr ofs)
  | _ => OK (make_globaladdr id)

Translation of expressions. All the hard work is done by the make_* and var_* functions defined above.

Fixpoint transl_expr (cenv: compilenv) (e: Csharpminor.expr)
                     {struct e}: res expr :=
  match e with
  | Csharpminor.Evar id => var_get cenv id
  | Csharpminor.Eaddrof id => var_addr cenv id
  | Csharpminor.Econst cst =>
      OK (Econst (transl_constant cst))
  | Csharpminor.Eunop op e1 =>
      do te1 <- transl_expr cenv e1;
      OK (Eunop op te1)
  | Csharpminor.Ebinop op e1 e2 =>
      do te1 <- transl_expr cenv e1;
      do te2 <- transl_expr cenv e2;
      OK (Ebinop op te1 te2)
  | Csharpminor.Eload chunk e =>
      do te <- transl_expr cenv e;
      OK (Eload chunk te)
  | Csharpminor.Econdition e1 e2 e3 =>
      do te1 <- transl_expr cenv e1;
      do te2 <- transl_expr cenv e2;
      do te3 <- transl_expr cenv e3;
      OK (Econdition te1 te2 te3)

Fixpoint transl_exprlist (cenv: compilenv) (el: list Csharpminor.expr)
                     {struct el}: res (list expr) :=
  match el with
  | nil =>
      OK nil
  | e1 :: e2 =>
      do te1 <- transl_expr cenv e1;
      do te2 <- transl_exprlist cenv e2;
      OK (te1 :: te2)

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)

Fixpoint switch_table (ls: lbl_stmt) (k: nat) {struct ls} : list (int * nat) :=
  match ls with
  | LSdefault _ => nil
  | LScase ni _ rem => (ni, k) :: switch_table rem (S k)

Fixpoint switch_env (ls: lbl_stmt) (e: exit_env) {struct ls}: exit_env :=
  match ls with
  | LSdefault _ => e
  | LScase _ _ ls' => false :: switch_env ls' e

Translation of statements. The only nonobvious part is the translation of switch statements, outlined above.

Fixpoint transl_stmt (cenv: compilenv) (xenv: exit_env) (s: Csharpminor.stmt)
                     {struct s}: res stmt :=
  match s with
  | Csharpminor.Sskip =>
      OK Sskip
  | Csharpminor.Sassign id e =>
      do te <- transl_expr cenv e; var_set cenv id te
  | Csharpminor.Sstore chunk e1 e2 =>
      do te1 <- transl_expr cenv e1;
      do te2 <- transl_expr cenv e2;
      OK (make_store chunk te1 te2)
  | Csharpminor.Scall None sig e el =>
      do te <- transl_expr cenv e;
      do tel <- transl_exprlist cenv el;
      OK (Scall None sig te tel)
  | Csharpminor.Scall (Some id) sig e el =>
      do te <- transl_expr cenv e;
      do tel <- transl_exprlist cenv el;
      do s <- var_set cenv id (Evar id);
      OK (Sseq (Scall (Some id) sig te tel) s)
  | Csharpminor.Sseq s1 s2 =>
      do ts1 <- transl_stmt cenv xenv s1;
      do ts2 <- transl_stmt cenv xenv s2;
      OK (Sseq ts1 ts2)
  | Csharpminor.Sifthenelse e s1 s2 =>
      do te <- transl_expr cenv e;
      do ts1 <- transl_stmt cenv xenv s1;
      do ts2 <- transl_stmt cenv xenv s2;
      OK (Sifthenelse te ts1 ts2)
  | Csharpminor.Sloop s =>
      do ts <- transl_stmt cenv xenv s;
      OK (Sloop ts)
  | Csharpminor.Sblock s =>
      do ts <- transl_stmt cenv (true :: xenv) s;
      OK (Sblock ts)
  | Csharpminor.Sexit n =>
      OK (Sexit (shift_exit xenv n))
  | Csharpminor.Sswitch e ls =>
      let cases := switch_table ls O in
      let default := length cases in
      do te <- transl_expr cenv e;
      transl_lblstmt cenv (switch_env ls xenv) ls (Sswitch te cases default)
  | Csharpminor.Sreturn None =>
      OK (Sreturn None)
  | Csharpminor.Sreturn (Some e) =>
      do te <- transl_expr cenv e; OK (Sreturn (Some te))
  | Csharpminor.Slabel lbl s =>
      do ts <- transl_stmt cenv xenv s; OK (Slabel lbl ts)
  | Csharpminor.Sgoto lbl =>
      OK (Sgoto lbl)
  | Csharpminor.Sthread_create e1 e2 =>
      do te1 <- transl_expr cenv e1;
      do te2 <- transl_expr cenv e2;
      OK (Sthread_create te1 te2)
  | Csharpminor.Satomic None op el =>
      do tel <- transl_exprlist cenv el;
      OK (Satomic None op tel)
  | Csharpminor.Satomic (Some id) op el =>
      do tel <- transl_exprlist cenv el;
      do s <- var_set cenv id (Evar id);
      OK (Sseq (Satomic (Some id) op tel) s)
  | Csharpminor.Smfence =>
      OK Smfence

with transl_lblstmt (cenv: compilenv) (xenv: exit_env)
                    (ls: Csharpminor.lbl_stmt) (body: stmt)
                    {struct ls}: res stmt :=
  match ls with
  | Csharpminor.LSdefault s =>
      do ts <- transl_stmt cenv xenv s;
      OK (Sseq (Sblock body) ts)
  | Csharpminor.LScase _ s ls' =>
      do ts <- transl_stmt cenv xenv s;
      transl_lblstmt cenv (List.tail xenv) ls' (Sseq (Sblock body) ts)

Computation of the set of variables whose address is taken in a piece of Csharpminor code.

Module Identset := FSetAVL.Make(OrderedPositive).

Fixpoint addr_taken_expr (e: Csharpminor.expr): Identset.t :=
  match e with
  | Csharpminor.Evar id => Identset.empty
  | Csharpminor.Eaddrof id => Identset.add id Identset.empty
  | Csharpminor.Econst cst => Identset.empty
  | Csharpminor.Eunop op e1 => addr_taken_expr e1
  | Csharpminor.Ebinop op e1 e2 =>
      Identset.union (addr_taken_expr e1) (addr_taken_expr e2)
  | Csharpminor.Eload chunk e => addr_taken_expr e
  | Csharpminor.Econdition e1 e2 e3 =>
      Identset.union (addr_taken_expr e1)
        (Identset.union (addr_taken_expr e2) (addr_taken_expr e3))

Fixpoint addr_taken_exprlist (e: list Csharpminor.expr): Identset.t :=
  match e with
  | nil => Identset.empty
  | e1 :: e2 =>
      Identset.union (addr_taken_expr e1) (addr_taken_exprlist e2)

Fixpoint addr_taken_stmt (s: Csharpminor.stmt): Identset.t :=
  match s with
  | Csharpminor.Sskip => Identset.empty
  | Csharpminor.Sassign id e => addr_taken_expr e
  | Csharpminor.Sstore chunk e1 e2 =>
      Identset.union (addr_taken_expr e1) (addr_taken_expr e2)
  | Csharpminor.Scall optid sig e el =>
      Identset.union (addr_taken_expr e) (addr_taken_exprlist el)
  | Csharpminor.Sseq s1 s2 =>
      Identset.union (addr_taken_stmt s1) (addr_taken_stmt s2)
  | Csharpminor.Sifthenelse e s1 s2 =>
      Identset.union (addr_taken_expr e)
        (Identset.union (addr_taken_stmt s1) (addr_taken_stmt s2))
  | Csharpminor.Sloop s => addr_taken_stmt s
  | Csharpminor.Sblock s => addr_taken_stmt s
  | Csharpminor.Sexit n => Identset.empty
  | Csharpminor.Sswitch e ls =>
      Identset.union (addr_taken_expr e) (addr_taken_lblstmt ls)
  | Csharpminor.Sreturn None => Identset.empty
  | Csharpminor.Sreturn (Some e) => addr_taken_expr e
  | Csharpminor.Slabel lbl s => addr_taken_stmt s
  | Csharpminor.Sgoto lbl => Identset.empty
  | Csharpminor.Sthread_create id e =>
      Identset.union (addr_taken_expr id) (addr_taken_expr e)
  | Csharpminor.Satomic optid op el => addr_taken_exprlist el
  | Csharpminor.Smfence => Identset.empty

with addr_taken_lblstmt (ls: Csharpminor.lbl_stmt): Identset.t :=
  match ls with
  | Csharpminor.LSdefault s => addr_taken_stmt s
  | Csharpminor.LScase _ s ls' => Identset.union (addr_taken_stmt s) (addr_taken_lblstmt ls')

Layout of the Cminor stack data block and construction of the compilation environment. Csharpminor local variables that are arrays or whose address is taken are allocated a slot in the Cminor stack data. Sufficient padding is inserted to ensure adequate alignment of addresses.

Definition array_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
    (atk: Identset.t)
    (id_lv: ident * var_kind)
    (cenv_stacksize: compilenv * Z) : compilenv * Z :=
  let (cenv, stacksize) := cenv_stacksize in
  match id_lv with
  | (id, Varray sz) =>
      let ofs := align stacksize (array_alignment sz) in
      (PMap.set id (Var_stack_array ofs) cenv, ofs + Zmax 1 sz)
  | (id, Vscalar chunk) =>
      if Identset.mem id atk then
        let sz := size_chunk chunk in
        let ofs := align stacksize sz in
        (PMap.set id (Var_stack_scalar chunk ofs) cenv, ofs + sz)
        (PMap.set id (Var_local chunk) cenv, stacksize)

Fixpoint assign_variables
    (atk: Identset.t)
    (id_lv_list: list (ident * var_kind))
    (cenv_stacksize: compilenv * Z)
    {struct id_lv_list}: compilenv * Z :=
  match id_lv_list with
  | nil => cenv_stacksize
  | id_lv :: rem =>
      assign_variables atk rem (assign_variable atk id_lv cenv_stacksize)

Definition build_compilenv
          (globenv: compilenv) (f: Csharpminor.function) : compilenv * Z :=
    (addr_taken_stmt f.(Csharpminor.fn_body))
    (fn_variables f)
    (globenv, 0).

Definition assign_global_variable
     (ce: compilenv) (info: ident * list init_data * var_kind) : compilenv :=
  match info with
  | (id, _, Vscalar chunk) => PMap.set id (Var_global_scalar chunk) ce
  | (id, _, Varray _) => PMap.set id Var_global_array ce

Definition build_global_compilenv (p: Csharpminor.program) : compilenv :=
  List.fold_left assign_global_variable
                 p.(prog_vars) (PMap.init Var_global_array).

Function parameters whose address is taken must be stored in their stack slots at function entry. (Cminor passes these parameters in local variables.)

Fixpoint store_parameters
       (cenv: compilenv) (params: list (ident * memory_chunk))
       {struct params} : res stmt :=
  match params with
  | nil => OK Sskip
  | (id, chunk) :: rem =>
      do s1 <- var_set cenv id (Evar id);
      do s2 <- store_parameters cenv rem;
      OK (Sseq s1 s2)

The local variables of the generated Cminor function must include all local variables of the C#minor function (to help the proof in Cminorgenproof go through). We must also add the destinations x of calls x = f(args), because some of these x can be global variables and therefore not part of the C#minor local variables.

Fixpoint call_dest (s: stmt) : Identset.t :=
  match s with
  | Sskip => Identset.empty
  | Sassign x e => Identset.empty
  | Sstore chunk e1 e2 => Identset.empty
  | Scall None sg e el => Identset.empty
  | Scall (Some x) sg e el => Identset.singleton x
  | Sseq s1 s2 => Identset.union (call_dest s1) (call_dest s2)
  | Sifthenelse e s1 s2 => Identset.union (call_dest s1) (call_dest s2)
  | Sloop s1 => call_dest s1
  | Sblock s1 => call_dest s1
  | Sexit n => Identset.empty
  | Sswitch e cases dfl => Identset.empty
  | Sreturn opte => Identset.empty
  | Slabel lbl s1 => call_dest s1
  | Sgoto lbl => Identset.empty
  | Sthread_create id e => Identset.empty
  | Satomic None op el => Identset.empty
  | Satomic (Some x) op el => Identset.singleton x
  | Smfence => Identset.empty

Definition identset_removelist (l: list ident) (s: Identset.t) : Identset.t :=
  List.fold_right Identset.remove s l.

Definition make_vars (params: list ident) (vars: list ident)
                     (body: Cminor.stmt) : list ident :=
  vars ++
  Identset.elements (identset_removelist (params ++ vars) (call_dest body)).

Translation of a Csharpminor function. We must check that the required Cminor stack block is no bigger than Int.max_signed, otherwise address computations within the stack block could overflow machine arithmetic and lead to incorrect code.

Definition transl_funbody
  (cenv: compilenv) (stacksize: Z) (f: Csharpminor.function): res function :=
    do tbody <- transl_stmt cenv nil f.(Csharpminor.fn_body);
    do sparams <- store_parameters cenv f.(Csharpminor.fn_params);
       OK (mkfunction
              (Csharpminor.fn_sig f)
              (Csharpminor.fn_params_names f)
              (make_vars (Csharpminor.fn_params_names f)
                         (Csharpminor.fn_vars_names f)
                         (Sseq sparams tbody))
              (Sseq sparams tbody)).

Definition transl_function
         (gce: compilenv) (f: Csharpminor.function): res function :=
  let (cenv, stacksize) := build_compilenv gce f in
  if zle stacksize Int.max_signed
  then transl_funbody cenv stacksize f
  else Error(msg "Cminorgen: too many local variables, stack size exceeded").

Definition transl_fundef (gce: compilenv) (f: Csharpminor.fundef): res fundef :=
  transf_partial_fundef (transl_function gce) f.

Definition transl_globvar (vk: var_kind) := OK tt.

Definition transl_program (p: Csharpminor.program) : res program :=
  let gce := build_global_compilenv p in
  transform_partial_program2 (transl_fundef gce) transl_globvar p.