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(********************************************************************)
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(*                                                                  *)
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(*  The LustreC compiler toolset   /  The LustreC Development Team  *)
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(*  Copyright 2012 -    --   ONERA - CNRS - INPT - LIFL             *)
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(*                                                                  *)
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(*  LustreC is free software, distributed WITHOUT ANY WARRANTY      *)
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(*  under the terms of the GNU Lesser General Public License        *)
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(*  version 2.1.                                                    *)
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(*                                                                  *) 
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(*  This file was originally from the Prelude compiler              *)
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(*                                                                  *) 
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(********************************************************************)
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(** Simple modular syntactic causality analysis. Can reject correct
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    programs, especially if the program is not flattened first. *)
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open Utils
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open LustreSpec
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open Corelang
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open Graph
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open Format
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exception Cycle of ident list
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module IdentDepGraph = Graph.Imperative.Digraph.ConcreteBidirectional (IdentModule)
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(* Dependency of mem variables on mem variables is cut off 
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   by duplication of some mem vars into local node vars.
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   Thus, cylic dependency errors may only arise between no-mem vars.
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   non-mem variables are:
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   - inputs: not needed for causality/scheduling, needed only for detecting useless vars
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   - read mems (fake vars): same remark as above.
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   - outputs: decoupled from mems, if necessary
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   - locals
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   - instance vars (fake vars): simplify causality analysis
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   global constants are not part of the dependency graph.
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no_mem' = combinational(no_mem, mem);
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=> (mem -> no_mem' -> no_mem)
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mem' = pre(no_mem, mem);
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=> (mem' -> no_mem), (mem -> mem')
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   Global roadmap:
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   - compute two dep graphs g (non-mem/non-mem&mem) and g' (mem/mem)
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   - check cycles in g (a cycle means a dependency error)
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   - break cycles in g' (it's legal !):
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     - check cycles in g'
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     - if any, introduce aux var to break cycle, then start afresh
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   - insert g' into g
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   - return g
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*)
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(* Tests whether [v] is a root of graph [g], i.e. a source *)
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let is_graph_root v g =
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 IdentDepGraph.in_degree g v = 0
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(* Computes the set of graph roots, i.e. the sources of acyclic graph [g] *)
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let graph_roots g =
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 IdentDepGraph.fold_vertex
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   (fun v roots -> if is_graph_root v g then v::roots else roots)
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   g []
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let add_edges src tgt g =
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(*List.iter (fun s -> List.iter (fun t -> Format.eprintf "add %s -> %s@." s t) tgt) src;*)
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 List.iter
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   (fun s ->
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     List.iter
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       (fun t -> IdentDepGraph.add_edge g s t)
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       tgt)
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   src;
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  g
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let add_vertices vtc g =
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(*List.iter (fun t -> Format.eprintf "add %s@." t) vtc;*)
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 List.iter (fun v -> IdentDepGraph.add_vertex g v) vtc;
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  g
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let new_graph () =
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 IdentDepGraph.create ()
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module ExprDep = struct
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let instance_var_cpt = ref 0
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(* read vars represent input/mem read-only vars,
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   they are not part of the program/schedule,
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   as they are not assigned,
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   but used to compute useless inputs/mems.
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   a mem read var represents a mem at the beginning of a cycle  *)
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let mk_read_var id =
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 sprintf "#%s" id
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(* instance vars represent node instance calls,
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   they are not part of the program/schedule,
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   but used to simplify causality analysis
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    *)
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let mk_instance_var id =
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 incr instance_var_cpt; sprintf "!%s_%d" id !instance_var_cpt
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let is_read_var v = v.[0] = '#'
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let is_instance_var v = v.[0] = '!'
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let is_ghost_var v = is_instance_var v || is_read_var v
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let undo_read_var id =
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 assert (is_read_var id);
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 String.sub id 1 (String.length id - 1)
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let undo_instance_var id =
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 assert (is_instance_var id);
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 String.sub id 1 (String.length id - 1)
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let eq_memory_variables mems eq =
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  let rec match_mem lhs rhs mems =
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    match rhs.expr_desc with
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    | Expr_fby _
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    | Expr_pre _    -> List.fold_right ISet.add lhs mems
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    | Expr_tuple tl -> 
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      let lhs' = (transpose_list [lhs]) in
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      List.fold_right2 match_mem lhs' tl mems
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    | _             -> mems in
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  match_mem eq.eq_lhs eq.eq_rhs mems
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let node_memory_variables nd =
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 List.fold_left eq_memory_variables ISet.empty (get_node_eqs nd)
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let node_input_variables nd =
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 List.fold_left (fun inputs v -> ISet.add v.var_id inputs) ISet.empty nd.node_inputs
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let node_local_variables nd =
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 List.fold_left (fun locals v -> ISet.add v.var_id locals) ISet.empty nd.node_locals
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let node_output_variables nd =
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 List.fold_left (fun outputs v -> ISet.add v.var_id outputs) ISet.empty nd.node_outputs
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let node_auxiliary_variables nd =
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 ISet.diff (node_local_variables nd) (node_memory_variables nd)
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let node_variables nd =
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  let inputs = node_input_variables nd in
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  let inoutputs = List.fold_left (fun inoutputs v -> ISet.add v.var_id inoutputs) inputs nd.node_outputs in
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  List.fold_left (fun vars v -> ISet.add v.var_id vars) inoutputs nd.node_locals
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(* computes the equivalence relation relating variables 
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   in the same equation lhs, under the form of a table 
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   of class representatives *)
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let node_eq_equiv nd =
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  let eq_equiv = Hashtbl.create 23 in
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  List.iter (fun eq ->
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    let first = List.hd eq.eq_lhs in
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    List.iter (fun v -> Hashtbl.add eq_equiv v first) eq.eq_lhs
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  )
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    (get_node_eqs nd);
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  eq_equiv
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(* Create a tuple of right dimension, according to [expr] type, *)
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(* filled with variable [v] *)
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let adjust_tuple v expr =
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 match expr.expr_type.Types.tdesc with
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 | Types.Ttuple tl -> duplicate v (List.length tl)
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 | _         -> [v]
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(* Add dependencies from lhs to rhs in [g, g'], *)
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(* no-mem/no-mem and mem/no-mem in g            *)
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(* mem/mem in g'                                *)
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(*     match (lhs_is_mem, ISet.mem x mems) with
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      | (false, true ) -> (add_edges [x] lhs g,
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			   g')
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      | (false, false) -> (add_edges lhs [x] g,
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			   g')
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      | (true , false) -> (add_edges lhs [x] g,
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			   g')
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      | (true , true ) -> (g,
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			   add_edges [x] lhs g')
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*)
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let add_eq_dependencies mems inputs node_vars eq (g, g') =
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  let add_var lhs_is_mem lhs x (g, g') =
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    if is_instance_var x || ISet.mem x node_vars then
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      if ISet.mem x mems
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      then
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	let g = add_edges lhs [mk_read_var x] g in
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	if lhs_is_mem
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	then
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	  (g, add_edges [x] lhs g')
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	else
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	  (add_edges [x] lhs g, g')
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      else
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	let x = if ISet.mem x inputs then mk_read_var x else x in
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	(add_edges lhs [x] g, g')
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    else (g, g') in
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(* Add dependencies from [lhs] to rhs clock [ck]. *)
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  let rec add_clock lhs_is_mem lhs ck g =
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    (*Format.eprintf "add_clock %a@." Clocks.print_ck ck;*)
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    match (Clocks.repr ck).Clocks.cdesc with
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    | Clocks.Con (ck', cr, _)   -> add_var lhs_is_mem lhs (Clocks.const_of_carrier cr) (add_clock lhs_is_mem lhs ck' g)
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    | Clocks.Ccarrying (_, ck') -> add_clock lhs_is_mem lhs ck' g
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    | _                         -> g 
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  in
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  let rec add_dep lhs_is_mem lhs rhs g =
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    (* Add mashup dependencies for a user-defined node instance [lhs] = [f]([e]) *)
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    (* i.e every input is connected to every output, through a ghost var *)
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    let mashup_appl_dependencies f e g =
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      let f_var = mk_instance_var (sprintf "%s_%d" f eq.eq_loc.Location.loc_start.Lexing.pos_lnum) in
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      List.fold_right (fun rhs -> add_dep lhs_is_mem (adjust_tuple f_var rhs) rhs)
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	(expr_list_of_expr e) (add_var lhs_is_mem lhs f_var g) 
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    in
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    match rhs.expr_desc with
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    | Expr_const _    -> g
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    | Expr_fby (e1, e2)  -> add_dep true lhs e2 (add_dep false lhs e1 g)
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    | Expr_pre e      -> add_dep true lhs e g
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    | Expr_ident x -> add_var lhs_is_mem lhs x (add_clock lhs_is_mem lhs rhs.expr_clock g)
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    | Expr_access (e1, _)
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    | Expr_power (e1, _) -> add_dep lhs_is_mem lhs e1 g
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    | Expr_array a -> List.fold_right (add_dep lhs_is_mem lhs) a g
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    | Expr_tuple t -> List.fold_right2 (fun l r -> add_dep lhs_is_mem [l] r) lhs t g
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    | Expr_merge (c, hl) -> add_var lhs_is_mem lhs c (List.fold_right (fun (_, h) -> add_dep lhs_is_mem lhs h) hl g)
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    | Expr_ite   (c, t, e) -> add_dep lhs_is_mem lhs c (add_dep lhs_is_mem lhs t (add_dep lhs_is_mem lhs e g))
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    | Expr_arrow (e1, e2)  -> add_dep lhs_is_mem lhs e2 (add_dep lhs_is_mem lhs e1 g)
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    | Expr_when  (e, c, _)  -> add_dep lhs_is_mem lhs e (add_var lhs_is_mem lhs c g)
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    | Expr_appl (f, e, None) ->
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      if Basic_library.is_internal_fun f
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      (* tuple component-wise dependency for internal operators *)
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      then
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	List.fold_right (add_dep lhs_is_mem lhs) (expr_list_of_expr e) g
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      (* mashed up dependency for user-defined operators *)
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      else
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	mashup_appl_dependencies f e g
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    | Expr_appl (f, e, Some c) ->
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      mashup_appl_dependencies f e (add_dep lhs_is_mem lhs c g)
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  in
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  let g =
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    List.fold_left
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      (fun g lhs -> if ISet.mem lhs mems then add_vertices [lhs; mk_read_var lhs] g else add_vertices [lhs] g) g eq.eq_lhs in
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  add_dep false eq.eq_lhs eq.eq_rhs (g, g')
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(* Returns the dependence graph for node [n] *)
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let dependence_graph mems inputs node_vars n =
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  instance_var_cpt := 0;
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  let g = new_graph (), new_graph () in
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  (* Basic dependencies *)
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  let g = List.fold_right (add_eq_dependencies mems inputs node_vars) (get_node_eqs n) g in
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  g
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end
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module NodeDep = struct
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  module ExprModule =
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  struct
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    type t = expr
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    let compare = compare
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    let hash n = Hashtbl.hash n
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    let equal n1 n2 = n1 = n2
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  end
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  module ESet = Set.Make(ExprModule)
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  let rec get_expr_calls prednode expr = 
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    match expr.expr_desc with
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      | Expr_const _ 
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      | Expr_ident _ -> ESet.empty
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      | Expr_access (e, _)
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      | Expr_power (e, _) -> get_expr_calls prednode e
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      | Expr_array t
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      | Expr_tuple t -> List.fold_right (fun x set -> ESet.union (get_expr_calls prednode x) set) t ESet.empty
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      | Expr_merge (_,hl) -> List.fold_right (fun (_,h) set -> ESet.union (get_expr_calls prednode h) set) hl ESet.empty
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      | Expr_fby (e1,e2)
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      | Expr_arrow (e1,e2) -> ESet.union (get_expr_calls prednode e1) (get_expr_calls prednode e2)
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      | Expr_ite   (c, t, e) -> ESet.union (get_expr_calls prednode c) (ESet.union (get_expr_calls prednode t) (get_expr_calls prednode e))
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      | Expr_pre e 
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      | Expr_when (e,_,_) -> get_expr_calls prednode e
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      | Expr_appl (id,e, _) ->
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	if not (Basic_library.is_internal_fun id) && prednode id
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	then ESet.add expr (get_expr_calls prednode e)
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	else (get_expr_calls prednode e)
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282
  let get_callee expr =
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    match expr.expr_desc with
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    | Expr_appl (id, args, _) -> Some (id, expr_list_of_expr args)
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    | _ -> None
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287
  let get_calls prednode eqs =
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    let deps =
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      List.fold_left 
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	(fun accu eq -> ESet.union accu (get_expr_calls prednode eq.eq_rhs))
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	ESet.empty
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	eqs in
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    ESet.elements deps
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295
  let dependence_graph prog =
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  let g = new_graph () in
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  let g = List.fold_right 
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    (fun td accu -> (* for each node we add its dependencies *)
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      match td.top_decl_desc with 
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	| Node nd ->
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	  (*Format.eprintf "Computing deps of node %s@.@?" nd.node_id; *)
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	  let accu = add_vertices [nd.node_id] accu in
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	  let deps = List.map (fun e -> fst (desome (get_callee e))) (get_calls (fun _ -> true) (get_node_eqs nd)) in
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	   (*Format.eprintf "%a@.@?" (Utils.fprintf_list ~sep:"@." Format.pp_print_string) deps; *)
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	  add_edges [nd.node_id] deps accu
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	| _ -> assert false (* should not happen *)
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308
    ) prog g in
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  g   
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311
  let rec filter_static_inputs inputs args =
312
   match inputs, args with
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   | []   , [] -> []
314
   | v::vq, a::aq -> if v.var_dec_const then (dimension_of_expr a) :: filter_static_inputs vq aq else filter_static_inputs vq aq
315
   | _ -> assert false
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317
  let compute_generic_calls prog =
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    List.iter
319
      (fun td ->
320
	match td.top_decl_desc with 
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	| Node nd ->
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	  let prednode n = is_generic_node (Hashtbl.find node_table n) in
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	  nd.node_gencalls <- get_calls prednode (get_node_eqs nd)
324
	| _ -> ()
325
      
326
      ) prog
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328
end
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module CycleDetection = struct
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(* ---- Look for cycles in a dependency graph *)
333
  module Cycles = Graph.Components.Make (IdentDepGraph)
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  let mk_copy_var n id =
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    let used name =
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         (List.exists (fun v -> v.var_id = name) n.node_locals)
338
      || (List.exists (fun v -> v.var_id = name) n.node_inputs)
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      || (List.exists (fun v -> v.var_id = name) n.node_outputs)
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    in mk_new_name used id
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  let mk_copy_eq n var =
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    let var_decl = get_node_var var n in
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    let cp_var = mk_copy_var n var in
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    let expr =
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      { expr_tag = Utils.new_tag ();
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	expr_desc = Expr_ident var;
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	expr_type = var_decl.var_type;
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	expr_clock = var_decl.var_clock;
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	expr_delay = Delay.new_var ();
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	expr_annot = None;
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	expr_loc = var_decl.var_loc } in
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    { var_decl with var_id = cp_var; var_orig = false },
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    mkeq var_decl.var_loc ([cp_var], expr)
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356
  let wrong_partition g partition =
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    match partition with
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    | [id]    -> IdentDepGraph.mem_edge g id id
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    | _::_::_ -> true
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    | []      -> assert false
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(* Checks that the dependency graph [g] does not contain a cycle. Raises
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   [Cycle partition] if the succession of dependencies [partition] forms a cycle *)
364
  let check_cycles g =
365
    let scc_l = Cycles.scc_list g in
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    List.iter (fun partition ->
367
      if wrong_partition g partition then
368
	raise (Cycle partition)
369
      else ()
370
    ) scc_l
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(* Creates the sub-graph of [g] restricted to vertices and edges in partition *)
373
  let copy_partition g partition =
374
    let copy_g = IdentDepGraph.create () in
375
    IdentDepGraph.iter_edges
376
      (fun src tgt ->
377
	if List.mem src partition && List.mem tgt partition
378
	then IdentDepGraph.add_edge copy_g src tgt)
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      g
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(* Breaks dependency cycles in a graph [g] by inserting aux variables.
383
  [head] is a head of a non-trivial scc of [g]. 
384
   In Lustre, this is legal only for mem/mem cycles *)
385
  let break_cycle head cp_head g =
386
    let succs = IdentDepGraph.succ g head in
387
    IdentDepGraph.add_edge g head cp_head;
388
    IdentDepGraph.add_edge g cp_head (ExprDep.mk_read_var head);
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    List.iter
390
      (fun s ->
391
	IdentDepGraph.remove_edge g head s;
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	IdentDepGraph.add_edge    g s cp_head)
393
      succs
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(* Breaks cycles of the dependency graph [g] of memory variables [mems]
396
   belonging in node [node]. Returns:
397
   - a list of new auxiliary variable declarations
398
   - a list of new equations
399
   - a modified acyclic version of [g]
400
*)
401
  let break_cycles node mems g =
402
    let (mem_eqs, non_mem_eqs) = List.partition (fun eq -> List.exists (fun v -> ISet.mem v mems) eq.eq_lhs) (get_node_eqs node) in
403
    let rec break vdecls mem_eqs g =
404
      let scc_l = Cycles.scc_list g in
405
      let wrong = List.filter (wrong_partition g) scc_l in
406
      match wrong with
407
      | []              -> (vdecls, non_mem_eqs@mem_eqs, g)
408
      | [head]::_       ->
409
	begin
410
	  IdentDepGraph.remove_edge g head head;
411
	  break vdecls mem_eqs g
412
	end
413
      | (head::part)::_ -> 
414
	begin
415
	  let vdecl_cp_head, cp_eq = mk_copy_eq node head in
416
	  let pvar v = List.mem v part in
417
	  let fvar v = if v = head then vdecl_cp_head.var_id else v in
418
	  let mem_eqs' = List.map (eq_replace_rhs_var pvar fvar) mem_eqs in
419
	  break_cycle head vdecl_cp_head.var_id g;
420
	  break (vdecl_cp_head::vdecls) (cp_eq::mem_eqs') g
421
	end
422
      | _               -> assert false
423
    in break [] mem_eqs g
424

    
425
end
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427
(* Module used to compute static disjunction of variables based upon their clocks. *)
428
module Disjunction =
429
struct
430
  module ClockedIdentModule =
431
  struct
432
    type t = var_decl
433
    let root_branch vdecl = Clocks.root vdecl.var_clock, Clocks.branch vdecl.var_clock
434
    let compare v1 v2 = compare (root_branch v2, v2.var_id) (root_branch v1, v1.var_id)
435
  end
436

    
437
  module CISet = Set.Make(ClockedIdentModule)
438

    
439
  (* map: var |-> list of disjoint vars, sorted in increasing branch length order,
440
     maybe removing shorter branches *)
441
  type disjoint_map = (ident, CISet.t) Hashtbl.t
442

    
443
  let pp_ciset fmt t =
444
    begin
445
      Format.fprintf fmt "{@ ";
446
      CISet.iter (fun s -> Format.fprintf fmt "%a@ " Printers.pp_var_name s) t;
447
      Format.fprintf fmt "}@."
448
    end
449

    
450
  let clock_disjoint_map vdecls =
451
    let map = Hashtbl.create 23 in
452
    begin
453
      List.iter
454
	(fun v1 -> let disj_v1 =
455
		     List.fold_left
456
		       (fun res v2 -> if Clocks.disjoint v1.var_clock v2.var_clock then CISet.add v2 res else res)
457
		       CISet.empty
458
		       vdecls in
459
		   (* disjoint vdecls are stored in increasing branch length order *)
460
		   Hashtbl.add map v1.var_id disj_v1)
461
	vdecls;
462
      (map : disjoint_map)
463
    end
464

    
465
  (* merge variables [v] and [v'] in disjunction [map]. Then:
466
      - the mapping v' becomes v' |-> (map v) inter (map v')
467
      - the mapping v |-> ... then disappears
468
      - other mappings become x |-> (map x) \ (if v in x then v else v')
469
  *)
470
  let merge_in_disjoint_map map v v' =
471
    begin
472
      Hashtbl.replace map v'.var_id (CISet.inter (Hashtbl.find map v.var_id) (Hashtbl.find map v'.var_id));
473
      Hashtbl.remove map v.var_id;
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      Hashtbl.iter (fun x map_x -> Hashtbl.replace map x (CISet.remove (if CISet.mem v map_x then v else v') map_x)) map;
475
    end
476

    
477
  (* replace variable [v] by [v'] in disjunction [map].
478
    [v'] is a dead variable. Then:
479
      - the mapping v' becomes v' |-> (map v)
480
      - the mapping v |-> ... then disappears
481
      - all mappings become x |-> ((map x) \ { v}) union ({v'} if v in map x)
482
  *)
483
  let replace_in_disjoint_map map v v' =
484
    begin
485
      Hashtbl.replace map v'.var_id (Hashtbl.find map v.var_id);
486
      Hashtbl.remove  map v.var_id;
487
      Hashtbl.iter (fun x mapx -> Hashtbl.replace map x (if CISet.mem v mapx then CISet.add v' (CISet.remove v mapx) else CISet.remove v' mapx)) map;
488
    end
489

    
490
  (* remove variable [v] in disjunction [map]. Then:
491
      - the mapping v |-> ... then disappears
492
      - all mappings become x |-> (map x) \ { v}
493
  *)
494
  let remove_in_disjoint_map map v =
495
    begin
496
      Hashtbl.remove map v.var_id;
497
      Hashtbl.iter (fun x mapx -> Hashtbl.replace map x (CISet.remove v mapx)) map;
498
    end
499

    
500
  let pp_disjoint_map fmt map =
501
    begin
502
      Format.fprintf fmt "{ /* disjoint map */@.";
503
      Hashtbl.iter (fun k v -> Format.fprintf fmt "%s # { %a }@." k (Utils.fprintf_list ~sep:", " Printers.pp_var_name) (CISet.elements v)) map;
504
      Format.fprintf fmt "}@."
505
    end
506
end
507

    
508
let pp_dep_graph fmt g =
509
  begin
510
    Format.fprintf fmt "{ /* graph */@.";
511
    IdentDepGraph.iter_edges (fun s t -> Format.fprintf fmt "%s -> %s@." s t) g;
512
    Format.fprintf fmt "}@."
513
  end
514

    
515
let pp_error fmt trace =
516
  fprintf fmt "@.Causality error, cyclic data dependencies: %a@."
517
    (fprintf_list ~sep:", " pp_print_string) trace
518

    
519
(* Merges elements of graph [g2] into graph [g1] *)
520
let merge_with g1 g2 =
521
  begin
522
    IdentDepGraph.iter_vertex (fun v -> IdentDepGraph.add_vertex g1 v) g2;
523
    IdentDepGraph.iter_edges (fun s t -> IdentDepGraph.add_edge g1 s t) g2
524
  end
525

    
526
let add_external_dependency outputs mems g =
527
  let caller ="!!_world" in
528
  begin
529
    IdentDepGraph.add_vertex g caller;
530
    ISet.iter (fun o -> IdentDepGraph.add_edge g caller o) outputs;
531
    ISet.iter (fun m -> IdentDepGraph.add_edge g caller m) mems;
532
  end
533

    
534
let global_dependency node =
535
  let mems = ExprDep.node_memory_variables node in
536
  let inputs = ExprDep.node_input_variables node in
537
  let outputs = ExprDep.node_output_variables node in
538
  let node_vars = ExprDep.node_variables node in
539
  let (g_non_mems, g_mems) = ExprDep.dependence_graph mems inputs node_vars node in
540
  (*Format.eprintf "g_non_mems: %a" pp_dep_graph g_non_mems;
541
  Format.eprintf "g_mems: %a" pp_dep_graph g_mems;*)
542
  CycleDetection.check_cycles g_non_mems;
543
  let (vdecls', eqs', g_mems') = CycleDetection.break_cycles node mems g_mems in
544
  (*Format.eprintf "g_mems': %a" pp_dep_graph g_mems';*)
545
  begin
546
    merge_with g_non_mems g_mems';
547
    add_external_dependency outputs mems g_non_mems;
548
    { node with node_stmts = List.map (fun eq -> Eq eq) eqs'; node_locals = vdecls'@node.node_locals }, 
549
    g_non_mems
550
  end
551

    
552
(* Local Variables: *)
553
(* compile-command:"make -C .." *)
554
(* End: *)