CristalCaveGem » LustreC

(********************************************************************)

(*                                                                  *)

(*  The LustreC compiler toolset   /  The LustreC Development Team  *)

(*  Copyright 2012 -    --   ONERA - CNRS - INPT                    *)

(*                                                                  *)

(*  LustreC is free software, distributed WITHOUT ANY WARRANTY      *)

(*  under the terms of the GNU Lesser General Public License        *)

(*  version 2.1.                                                    *)

(*                                                                  *)

(********************************************************************)

open Utils

open Lustre_types 

open Machine_code_types

open Corelang

open Causality

open Machine_code_common

open Dimension

module Mpfr = Lustrec_mpfr

let pp_elim m fmt elim =

  begin

    Format.fprintf fmt "@[{ /* elim table: */@ ";

    IMap.iter (fun v expr -> Format.fprintf fmt "%s |-> %a@ " v (pp_val m) expr) elim;

    Format.fprintf fmt "}@ @]";

  end

let rec eliminate m elim instr =

  let e_expr = eliminate_expr m elim in

  match get_instr_desc instr with

  | MSpec _ | MComment _         -> instr

  | MLocalAssign (i,v) -> update_instr_desc instr (MLocalAssign (i, e_expr v))

  | MStateAssign (i,v) -> update_instr_desc instr (MStateAssign (i, e_expr v))

  | MReset i           -> instr

  | MNoReset i         -> instr

  | MStep (il, i, vl)  -> update_instr_desc instr (MStep(il, i, List.map e_expr vl))

  | MBranch (g,hl)     -> 

     update_instr_desc instr (

       MBranch

	 (e_expr g, 

	  (List.map 

	     (fun (l, il) -> l, List.map (eliminate m elim) il) 

	     hl

	  )

	 )

     )

and eliminate_expr m elim expr =

  let eliminate_expr = eliminate_expr m in

  match expr.value_desc with

  | Var v -> if is_memory m v then

               expr

             else

               (try IMap.find v.var_id elim with Not_found -> expr)

  | Fun (id, vl) -> {expr with value_desc = Fun (id, List.map (eliminate_expr elim) vl)}

  | Array(vl) -> {expr with value_desc = Array(List.map (eliminate_expr elim) vl)}

  | Access(v1, v2) -> { expr with value_desc = Access(eliminate_expr elim v1, eliminate_expr elim v2)}

  | Power(v1, v2) -> { expr with value_desc = Power(eliminate_expr elim v1, eliminate_expr elim v2)}

  | Cst _ -> expr

let eliminate_dim elim dim =

  Dimension.expr_replace_expr 

    (fun v -> try

		dimension_of_value (IMap.find v elim) 

      with Not_found -> mkdim_ident dim.dim_loc v) 

    dim

(* 8th Jan 2016: issues when merging salsa with horn_encoding: The following

   functions seem unsused. They have to be adapted to the new type for expr

*)

let unfold_expr_offset m offset expr =

  List.fold_left

    (fun res -> (function | Index i -> mk_val (Access (res, value_of_dimension m i))

					      (Types.array_element_type res.value_type)

                          | Field f -> Format.eprintf "internal error: not yet implemented !"; assert false))

    expr offset

let rec simplify_cst_expr m offset typ cst =

    match offset, cst with

    | []          , _

      -> mk_val (Cst cst) typ

    | Index i :: q, Const_array cl when Dimension.is_dimension_const i

      -> let elt_typ = Types.array_element_type typ in

         simplify_cst_expr m q elt_typ (List.nth cl (Dimension.size_const_dimension i))

    | Index i :: q, Const_array cl

      -> let elt_typ = Types.array_element_type typ in

         unfold_expr_offset m [Index i] (mk_val (Array (List.map (simplify_cst_expr m q elt_typ) cl)) typ)

    | Field f :: q, Const_struct fl

      -> let fld_typ = Types.struct_field_type typ f in

         simplify_cst_expr m q fld_typ (List.assoc f fl)

    | _ -> (Format.eprintf "internal error: Optimize_machine.simplify_cst_expr %a@." Printers.pp_const cst; assert false)

let simplify_expr_offset m expr =

  let rec simplify offset expr =

    match offset, expr.value_desc with

    | Field f ::q , _                -> failwith "not yet implemented"

    | _           , Fun (id, vl) when Basic_library.is_value_internal_fun expr

                                     -> mk_val (Fun (id, List.map (simplify offset) vl)) expr.value_type

    | _           , Fun _

    | _           , Var _            -> unfold_expr_offset m offset expr

    | _           , Cst cst          -> simplify_cst_expr m offset expr.value_type cst

    | _           , Access (expr, i) -> simplify (Index (dimension_of_value i) :: offset) expr

    | []          , _                -> expr

    | Index _ :: q, Power (expr, _)  -> simplify q expr

    | Index i :: q, Array vl when Dimension.is_dimension_const i

                                     -> simplify q (List.nth vl (Dimension.size_const_dimension i))

    | Index i :: q, Array vl         -> unfold_expr_offset m [Index i] (mk_val (Array (List.map (simplify q) vl)) expr.value_type)

    (*Format.eprintf "simplify_expr %a %a = %a@." pp_val expr (Utils.fprintf_list ~sep:"" Printers.pp_offset) offset pp_val res; res)

     with e -> (Format.eprintf "simplify_expr %a %a = <FAIL>@." pp_val expr (Utils.fprintf_list ~sep:"" Printers.pp_offset) offset; raise e*)

  in simplify [] expr

let rec simplify_instr_offset m instr =

  match get_instr_desc instr with

  | MLocalAssign (v, expr) -> update_instr_desc instr (MLocalAssign (v, simplify_expr_offset m expr))

  | MStateAssign (v, expr) -> update_instr_desc instr (MStateAssign (v, simplify_expr_offset m expr))

  | MReset id              -> instr

  | MNoReset id            -> instr

  | MStep (outputs, id, inputs) -> update_instr_desc instr (MStep (outputs, id, List.map (simplify_expr_offset m) inputs))

  | MBranch (cond, brl)

    -> update_instr_desc instr (

      MBranch(simplify_expr_offset m cond, List.map (fun (l, il) -> l, simplify_instrs_offset m il) brl)

    )

  | MSpec _ | MComment _             -> instr

and simplify_instrs_offset m instrs =

  List.map (simplify_instr_offset m) instrs

let is_scalar_const c =

  match c with

  | Const_real _

  | Const_int _

  | Const_tag _   -> true

  | _             -> false

(* An instruction v = expr may (and will) be unfolded iff:

   - either expr is atomic

     (no complex expressions, only const, vars and array/struct accesses)

   - or v has a fanin <= 1 (used at most once)

*)

let is_unfoldable_expr fanin expr =

  let rec unfold_const offset cst =

    match offset, cst with

    | _           , Const_int _

    | _           , Const_real _

    | _           , Const_tag _     -> true

    | Field f :: q, Const_struct fl -> unfold_const q (List.assoc f fl)

    | []          , Const_struct _  -> false

    | Index i :: q, Const_array cl when Dimension.is_dimension_const i

                                    -> unfold_const q (List.nth cl (Dimension.size_const_dimension i))

    | _           , Const_array _   -> false

    | _                             -> assert false in

  let rec unfold offset expr =

    match offset, expr.value_desc with

    | _           , Cst cst                      -> unfold_const offset cst

    | _           , Var _                        -> true

    | []          , Power _

    | []          , Array _                      -> false

    | Index i :: q, Power (v, _)                 -> unfold q v

    | Index i :: q, Array vl when Dimension.is_dimension_const i

                                                 -> unfold q (List.nth vl (Dimension.size_const_dimension i))

    | _           , Array _                      -> false

    | _           , Access (v, i)                -> unfold (Index (dimension_of_value i) :: offset) v

    | _           , Fun (id, vl) when fanin < 2 && Basic_library.is_value_internal_fun expr

                                                 -> List.for_all (unfold offset) vl

    | _           , Fun _                        -> false

    | _                                          -> assert false

  in unfold [] expr

let basic_unfoldable_assign fanin v expr =

  try

    let d = Hashtbl.find fanin v.var_id

    in is_unfoldable_expr d expr

  with Not_found -> false

let unfoldable_assign fanin v expr =

   (if !Options.mpfr then Mpfr.unfoldable_value expr else true)

&& basic_unfoldable_assign fanin v expr

let merge_elim elim1 elim2 =

  let merge k e1 e2 =

    match e1, e2 with

    | Some e1, Some e2 -> if e1 = e2 then Some e1 else None

    | _      , Some e2 -> Some e2

    | Some e1, _       -> Some e1

    | _                -> None

  in IMap.merge merge elim1 elim2

(* see if elim has to take in account the provided instr:

   if so, update elim and return the remove flag,

   otherwise, the expression should be kept and elim is left untouched *)

let rec instrs_unfold m fanin elim instrs =

  let elim, rev_instrs = 

    List.fold_left (fun (elim, instrs) instr ->

      (* each subexpression in instr that could be rewritten by the elim set is

	 rewritten *)

      let instr = eliminate m (IMap.map fst elim) instr in

      (* if instr is a simple local assign, then (a) elim is simplified with it (b) it

	 is stored as the elim set *)

      instr_unfold m fanin instrs elim instr

    ) (elim, []) instrs

  in elim, List.rev rev_instrs

and instr_unfold m fanin instrs (elim:(value_t * eq) IMap.t) instr =

(*  Format.eprintf "SHOULD WE STORE THE EXPRESSION IN INSTR %a TO ELIMINATE IT@." pp_instr instr;*)

  match get_instr_desc instr with

  (* Simple cases*)

  | MStep([v], id, vl) when Basic_library.is_value_internal_fun (mk_val (Fun (id, vl)) v.var_type)

    -> instr_unfold m fanin instrs elim (update_instr_desc instr (MLocalAssign (v, mk_val (Fun (id, vl)) v.var_type)))

  | MLocalAssign(v, expr) when not (is_clock_dec_type v.var_dec_type.ty_dec_desc) && unfoldable_assign fanin v expr

    -> (* we don't eliminate clock definitions *)

     let new_eq =

       Corelang.mkeq

         (desome instr.lustre_eq).eq_loc

         ([v.var_id], (desome instr.lustre_eq).eq_rhs)

     in

     (IMap.add v.var_id (expr, new_eq )  elim, instrs)

  | MBranch(g, hl) when false

    -> let elim_branches = List.map (fun (h, l) -> (h, instrs_unfold m fanin elim l)) hl in

       let (elim, branches) =

	 List.fold_right

	   (fun (h, (e, l)) (elim, branches) -> (merge_elim elim e, (h, l)::branches))

	   elim_branches (elim, [])

       in elim, ((update_instr_desc instr (MBranch (g, branches))) :: instrs)

  | _

    -> (elim, instr :: instrs)

    (* default case, we keep the instruction and do not modify elim *)

(** We iterate in the order, recording simple local assigns in an accumulator

    1. each expression is rewritten according to the accumulator

    2. local assigns then rewrite occurrences of the lhs in the computed accumulator

*)

let static_call_unfold elim (inst, (n, args)) =

  let replace v =

    try

      dimension_of_value (IMap.find v elim)

    with Not_found -> Dimension.mkdim_ident Location.dummy_loc v

  in (inst, (n, List.map (Dimension.expr_replace_expr replace) args))

(** Perform optimization on machine code:

    - iterate through step instructions and remove simple local assigns

*)

let machine_unfold fanin elim machine =

  Log.report ~level:3 (fun fmt -> Format.fprintf fmt "machine_unfold %s %a@." machine.mname.node_id (pp_elim machine) (IMap.map fst elim)); 

  let elim_consts, mconst = instrs_unfold machine fanin elim machine.mconst in

  let elim_vars, instrs = instrs_unfold machine fanin elim_consts machine.mstep.step_instrs in

  let instrs = simplify_instrs_offset machine instrs in

  let checks = List.map

                 (fun (loc, check) ->

                   loc,

                   eliminate_expr machine (IMap.map fst elim_vars) check

                 ) machine.mstep.step_checks

  in

  let locals = List.filter (fun v -> not (IMap.mem v.var_id elim_vars)) machine.mstep.step_locals in

  let elim_consts = IMap.map fst elim_consts in

  let minstances = List.map (static_call_unfold elim_consts) machine.minstances in

  let mcalls = List.map (static_call_unfold elim_consts) machine.mcalls

  in

  {

    machine with

      mstep = { 

	machine.mstep with 

	  step_locals = locals;

	  step_instrs = instrs;

	  step_checks = checks

      };

      mconst = mconst;

      minstances = minstances;

      mcalls = mcalls;

  },

  elim_vars

let instr_of_const top_const =

  let const = const_of_top top_const in

  let loc = const.const_loc in

  let id = const.const_id in

  let vdecl = mkvar_decl loc (id, mktyp Location.dummy_loc Tydec_any, mkclock loc Ckdec_any, true, None, None) in

  let vdecl = { vdecl with var_type = const.const_type } in

  let lustre_eq = mkeq loc ([const.const_id], mkexpr loc (Expr_const const.const_value)) in

  mkinstr

    ~lustre_eq:lustre_eq 

    (MLocalAssign (vdecl, mk_val (Cst const.const_value) vdecl.var_type))

(* We do not perform this optimization on contract nodes since there

   is not explicit dependence btw variables and their use in

   contracts. *)

let machines_unfold consts node_schs machines =

  List.fold_right (fun m (machines, removed) ->

      let is_contract = match m.mspec with Some (Contract _) -> true | _ -> false in

      if is_contract then

        m::machines, removed

      else 

        let fanin = (IMap.find m.mname.node_id node_schs).Scheduling_type.fanin_table in

        let elim_consts, _ = instrs_unfold m fanin IMap.empty (List.map instr_of_const consts) in

        let (m, removed_m) =  machine_unfold fanin elim_consts m in

        (m::machines, IMap.add m.mname.node_id removed_m removed)

    )

    machines

    ([], IMap.empty)

let get_assign_lhs instr =

  match get_instr_desc instr with

  | MLocalAssign(v, e) -> mk_val (Var v) e.value_type

  | MStateAssign(v, e) -> mk_val (Var v) e.value_type

  | _                  -> assert false

let get_assign_rhs instr =

  match get_instr_desc instr with

  | MLocalAssign(_, e)

  | MStateAssign(_, e) -> e

  | _                  -> assert false

let is_assign instr =

  match get_instr_desc instr with

  | MLocalAssign _

  | MStateAssign _ -> true

  | _              -> false

let mk_assign m v e =

 match v.value_desc with

 | Var v -> if is_memory m v then MStateAssign(v, e) else MLocalAssign(v, e)

 | _          -> assert false

let rec assigns_instr instr assign =

  match get_instr_desc instr with  

  | MLocalAssign (i,_)

  | MStateAssign (i,_) -> VSet.add i assign

  | MStep (ol, _, _)   -> List.fold_right VSet.add ol assign

  | MBranch (_,hl)     -> List.fold_right (fun (_, il) -> assigns_instrs il) hl assign

  | _                  -> assign

and assigns_instrs instrs assign =

  List.fold_left (fun assign instr -> assigns_instr instr assign) assign instrs

(*    

and substitute_expr subst expr =

  match expr with

  | Var v -> (try IMap.find expr subst with Not_found -> expr)

  | Fun (id, vl) -> Fun (id, List.map (substitute_expr subst) vl)

  | Array(vl) -> Array(List.map (substitute_expr subst) vl)

  | Access(v1, v2) -> Access(substitute_expr subst v1, substitute_expr subst v2)

  | Power(v1, v2) -> Power(substitute_expr subst v1, substitute_expr subst v2)

  | Cst _  -> expr

*)

(** Finds a substitute for [instr] in [instrs], 

   i.e. another instr' with the same rhs expression.

   Then substitute this expression with the first assigned var

*)

let subst_instr m subst instrs instr =

  (* Format.eprintf "subst instr: %a@." (pp_instr m) instr; *)

  let instr = eliminate m subst instr in

  let instr_v = get_assign_lhs instr in  

  let instr_e = get_assign_rhs instr in

  try

    (* Searching for equivalent asssign *)

    let instr' = List.find (fun instr' -> is_assign instr' &&

                                            get_assign_rhs instr' = instr_e) instrs in

    (* Registering the instr_v as instr'_v while replacing *)

    match instr_v.value_desc with

    | Var v ->

       let instr'_v = get_assign_lhs instr' in

         if not (is_memory m v) then

         (* The current instruction defines a local variables, ie not

            memory, we can just record the relationship and continue

          *)

         IMap.add v.var_id instr'_v subst, instrs

       else  (

         (* The current instruction defines a memory. We need to keep

            the definition, simplified *)

         (match instr'_v.value_desc with

          | Var v' ->

             if not (is_memory m v') then

               (* We define v' = v. Don't need to update the records. *)

               let instr = eliminate m subst (update_instr_desc instr (mk_assign m instr_v instr'_v)) in

	       subst, instr :: instrs

             else ( (* Last case, v', the lhs of the previous similar

                       definition is, itself, a memory *)

               (* TODO regarder avec X. Il me semble qu'on peut faire plus simple: *)

               (* Filtering out the list of instructions: 

                  - we copy in the same order the list of instr in instrs (fold_right)

                  - if the current instr is this instr' then apply 

                    the elimination with v' -> v on instr' before recording it as an instruction.  

                *)

               let subst_v' = IMap.add v'.var_id instr_v IMap.empty in

	       let instrs' =

                 snd

                   (List.fold_right

                      (fun instr (ok, instrs) ->

                        (ok || instr = instr',

                         if ok then

                           instr :: instrs

                         else

                           if instr = instr' then

                             instrs

                           else

                             eliminate m subst_v' instr :: instrs))

                      instrs (false, []))

               in

	       IMap.add v'.var_id instr_v subst, instr :: instrs'

             )

          | _           -> assert false)

       )

    | _          -> assert false

  with Not_found ->

    (* No such equivalent expr: keeping the definition *)

    subst, instr :: instrs

(** Common sub-expression elimination for machine instructions *)

(* - [subst] : hashtable from ident to (simple) definition

               it is an equivalence table

   - [elim]   : set of eliminated variables

   - [instrs] : previous instructions, which [instr] is compared against

   - [instr] : current instruction, normalized by [subst]

*)

let rec instr_cse m (subst, instrs) instr =

  match get_instr_desc instr with

  (* Simple cases*)

  | MStep([v], id, vl) when Basic_library.is_internal_fun id (List.map (fun v -> v.value_type) vl)

      -> instr_cse m (subst, instrs) (update_instr_desc instr (MLocalAssign (v, mk_val (Fun (id, vl)) v.var_type)))

  | MLocalAssign(v, expr) when is_unfoldable_expr 2 expr

      -> (IMap.add v.var_id expr subst, instr :: instrs)

  | _ when is_assign instr

      -> subst_instr m subst instrs instr

  | _ -> (subst, instr :: instrs)

(** Apply common sub-expression elimination to a sequence of instrs

*)

let instrs_cse m subst instrs =

  let subst, rev_instrs = 

    List.fold_left (instr_cse m) (subst, []) instrs

  in subst, List.rev rev_instrs

(** Apply common sub-expression elimination to a machine

    - iterate through step instructions and remove simple local assigns

*)

let machine_cse subst machine =

  (*Log.report ~level:1 (fun fmt -> Format.fprintf fmt "machine_cse %a@." pp_elim subst);*)

  let subst, instrs = instrs_cse machine subst machine.mstep.step_instrs in

  let assigned = assigns_instrs instrs VSet.empty

  in

  {

    machine with

      mmemory = List.filter (fun vdecl -> VSet.mem vdecl assigned) machine.mmemory;

      mstep = { 

	machine.mstep with 

	  step_locals = List.filter (fun vdecl -> VSet.mem vdecl assigned) machine.mstep.step_locals;

	  step_instrs = instrs

      }

  }

let machines_cse machines =

  List.map

    (machine_cse IMap.empty)

    machines

(* variable substitution for optimizing purposes *)

(* checks whether an [instr] is skip and can be removed from program *)

let rec instr_is_skip instr =

  match get_instr_desc instr with

  | MLocalAssign (i, { value_desc = (Var v) ; _}) when i = v -> true

  | MStateAssign (i, { value_desc = Var v; _}) when i = v -> true

  | MBranch (g, hl) -> List.for_all (fun (_, il) -> instrs_are_skip il) hl

  | _               -> false

and instrs_are_skip instrs =

  List.for_all instr_is_skip instrs

let instr_cons instr cont =

 if instr_is_skip instr then cont else instr::cont

let rec instr_remove_skip instr cont =

  match get_instr_desc instr with

  | MLocalAssign (i, { value_desc = Var v; _ }) when i = v -> cont

  | MStateAssign (i, { value_desc = Var v; _ }) when i = v -> cont

  | MBranch (g, hl) -> update_instr_desc instr (MBranch (g, List.map (fun (h, il) -> (h, instrs_remove_skip il [])) hl)) :: cont

  | _               -> instr::cont

and instrs_remove_skip instrs cont =

  List.fold_right instr_remove_skip instrs cont

let rec value_replace_var fvar value =

  match value.value_desc with

  | Cst c -> value

  | Var v -> { value with value_desc = Var (fvar v) }

  | Fun (id, args) -> { value with value_desc = Fun (id, List.map (value_replace_var fvar) args) }

  | Array vl -> { value with value_desc = Array (List.map (value_replace_var fvar) vl)}

  | Access (t, i) -> { value with value_desc = Access(value_replace_var fvar t, i)}

  | Power (v, n) -> { value with value_desc = Power(value_replace_var fvar v, n)}

let rec instr_replace_var fvar instr cont =

  match get_instr_desc instr with

  | MSpec _ | MComment _          -> instr_cons instr cont

  | MLocalAssign (i, v) -> instr_cons (update_instr_desc instr (MLocalAssign (fvar i, value_replace_var fvar v))) cont

  | MStateAssign (i, v) -> instr_cons (update_instr_desc instr (MStateAssign (i, value_replace_var fvar v))) cont

  | MReset i            -> instr_cons instr cont

  | MNoReset i          -> instr_cons instr cont

  | MStep (il, i, vl)   -> instr_cons (update_instr_desc instr (MStep (List.map fvar il, i, List.map (value_replace_var fvar) vl))) cont

  | MBranch (g, hl)     -> instr_cons (update_instr_desc instr (MBranch (value_replace_var fvar g, List.map (fun (h, il) -> (h, instrs_replace_var fvar il [])) hl))) cont

and instrs_replace_var fvar instrs cont =

  List.fold_right (instr_replace_var fvar) instrs cont

let step_replace_var fvar step =

  (* Some outputs may have been replaced by locals.

     We then need to rename those outputs

     without changing their clocks, etc *)

  let outputs' =

    List.map (fun o -> { o with var_id = (fvar o).var_id }) step.step_outputs in

  let locals'  =

    List.fold_left (fun res l ->

      let l' = fvar l in

      if List.exists (fun o -> o.var_id = l'.var_id) outputs'

      then res

      else Utils.add_cons l' res)

      [] step.step_locals in

  { step with

    step_checks = List.map (fun (l, v) -> (l, value_replace_var fvar v)) step.step_checks;

    step_outputs = outputs';

    step_locals = locals';

    step_instrs = instrs_replace_var fvar step.step_instrs [];

}

let rec machine_replace_variables fvar m =

  { m with

    mstep = step_replace_var fvar m.mstep

  }

let machine_reuse_variables m reuse =

  let fvar v =

    try

      Hashtbl.find reuse v.var_id

    with Not_found -> v in

  machine_replace_variables fvar m

let machines_reuse_variables prog reuse_tables =

  List.map 

    (fun m -> 

      machine_reuse_variables m (Utils.IMap.find m.mname.node_id reuse_tables)

    ) prog

let rec instr_assign res instr =

  match get_instr_desc instr with

  | MLocalAssign (i, _) -> Disjunction.CISet.add i res

  | MStateAssign (i, _) -> Disjunction.CISet.add i res

  | MBranch (g, hl)     -> List.fold_left (fun res (h, b) -> instrs_assign res b) res hl

  | MStep (il, _, _)    -> List.fold_right Disjunction.CISet.add il res

  | _                   -> res

and instrs_assign res instrs =

  List.fold_left instr_assign res instrs

let rec instr_constant_assign var instr =

  match get_instr_desc instr with

  | MLocalAssign (i, { value_desc = Cst (Const_tag _); _ })

  | MStateAssign (i, { value_desc = Cst (Const_tag _); _ }) -> i = var

  | MBranch (g, hl)                     -> List.for_all (fun (h, b) -> instrs_constant_assign var b) hl

  | _                                   -> false

and instrs_constant_assign var instrs =

  List.fold_left (fun res i -> if Disjunction.CISet.mem var (instr_assign Disjunction.CISet.empty i) then instr_constant_assign var i else res) false instrs

let rec instr_reduce branches instr1 cont =

  match get_instr_desc instr1 with

  | MLocalAssign (_, { value_desc = Cst (Const_tag c); _}) -> instr1 :: (List.assoc c branches @ cont)

  | MStateAssign (_, { value_desc = Cst (Const_tag c); _}) -> instr1 :: (List.assoc c branches @ cont)

  | MBranch (g, hl)                     -> (update_instr_desc instr1 (MBranch (g, List.map (fun (h, b) -> (h, instrs_reduce branches b [])) hl))) :: cont

  | _                                   -> instr1 :: cont

and instrs_reduce branches instrs cont =

 match instrs with

 | []        -> cont

 | [i]       -> instr_reduce branches i cont

 | i1::i2::q -> i1 :: instrs_reduce branches (i2::q) cont

let rec instrs_fusion instrs =

  match instrs, List.map get_instr_desc instrs with

  | [], []

  | [_], [_]                                                               ->

    instrs

  | i1::i2::q, i1_desc::(MBranch ({ value_desc = Var v; _}, hl))::q_desc when instr_constant_assign v i1 ->

    instr_reduce (List.map (fun (h, b) -> h, instrs_fusion b) hl) i1 (instrs_fusion q)

  | i1::i2::q, _                                                         ->

    i1 :: instrs_fusion (i2::q)

  | _ -> assert false (* Other cases should not happen since both lists are of same size *)

let step_fusion step =

  { step with

    step_instrs = instrs_fusion step.step_instrs;

  }

let rec machine_fusion m =

  { m with

    mstep = step_fusion m.mstep

  }

let machines_fusion prog =

  List.map machine_fusion prog

(* Additional function to modify the prog according to removed variables map *)

let elim_prog_variables prog removed_table =

  List.map (

      fun t ->

      match t.top_decl_desc with

        Node nd ->

         if IMap.mem nd.node_id removed_table then

           let nd_elim_map = IMap.find nd.node_id removed_table in

           (* Iterating through the elim map to compute

              - the list of variables to remove

              - the associated list of lustre definitions x = expr to

                be used when removing these variables *)

           let vars_to_replace, defs = (* Recovering vid from node locals *)

             IMap.fold (fun v (_,eq) (accu_locals, accu_defs) ->

                 let locals =

                   try

                     (List.find (fun v' -> v'.var_id = v) nd.node_locals)::accu_locals

                   with Not_found -> accu_locals (* Variable v shall

                                                    be a global

                                                    constant, we do no

                                                    need to eliminate

                                                    it from the locals

                                                    *)

                 in

                 (* xxx let new_eq = { eq_lhs = [v]; eq_rhs = e; eq_loc = e.expr_loc } in *)

                 let defs = eq::accu_defs in

                 locals, defs

               ) nd_elim_map ([], [])

           in

           let new_locals, new_stmts =

             List.fold_right (fun stmt (locals, res_stmts) ->

                 match stmt with

                   Aut _ -> assert false (* should be processed by now *)

                 | Eq eq -> (

                   match eq.eq_lhs with

                   | [] -> assert false (* shall not happen *)

                   | _::_::_ ->

                      (* When more than one lhs we just keep the

                         equation and do not delete it *)

                      let eq_rhs' = substitute_expr vars_to_replace defs eq.eq_rhs in

                      locals, (Eq { eq with eq_rhs = eq_rhs' })::res_stmts

                   | [lhs] -> 

                      if List.exists (fun v -> v.var_id = lhs) vars_to_replace then 

                        (* We remove the def *)

                        List.filter (fun l -> l.var_id != lhs) locals,

                        res_stmts

                      else (* We keep it but modify any use of an eliminatend var *)

                        let eq_rhs' = substitute_expr vars_to_replace defs eq.eq_rhs in 

                        locals,

                        (Eq { eq with eq_rhs = eq_rhs' })::res_stmts

                 )

               ) nd.node_stmts (nd.node_locals,[])

           in

           let nd' = { nd with

                       node_locals = new_locals;

                       node_stmts = new_stmts;

                     }

           in

           { t with top_decl_desc = Node nd' }

         else

           t

      | _ -> t

    ) prog

(*** Main function ***)

(* 

This functions produces an optimzed prog * machines

It 

1- eliminates common sub-expressions (TODO how is this different from normalization?)

2- inline constants and eliminate duplicated variables 

3- try to reuse variables whenever possible

When item (2) identified eliminated variables, the initial prog is modified, its normalized recomputed, as well as its scheduling, before regenerating the machines.

The function returns both the (possibly updated) prog as well as the machines 

*)

let optimize params prog node_schs machine_code =