lustrec / src / causality.ml @ 307aba8d
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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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|
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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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|
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exception Cycle of ident list |
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|
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module IdentDepGraph = Graph.Imperative.Digraph.ConcreteBidirectional (IdentModule) |
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|
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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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|
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global constants are not part of the dependency graph. |
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|
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no_mem' = combinational(no_mem, mem); |
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=> (mem -> no_mem' -> no_mem) |
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|
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mem' = pre(no_mem, mem); |
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=> (mem' -> no_mem), (mem -> mem') |
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|
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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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|
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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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|
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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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|
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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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|
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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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|
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let new_graph () = |
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IdentDepGraph.create () |
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|
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module ExprDep = struct |
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|
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let instance_var_cpt = ref 0 |
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|
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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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|
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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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|
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let is_read_var v = v.[0] = '#' |
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|
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let is_instance_var v = v.[0] = '!' |
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|
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let is_ghost_var v = is_instance_var v || is_read_var v |
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|
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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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|
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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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|
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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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|
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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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|
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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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|
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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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|
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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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|
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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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|
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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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|
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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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|
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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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|
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|
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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 (add_edges lhs [mk_read_var x] g, g') (* x is a global constant, treated as a read var *) 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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|
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|
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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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|
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end |
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|
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module NodeDep = struct |
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|
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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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|
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module ESet = Set.Make(ExprModule) |
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|
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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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|
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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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|
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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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|
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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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|
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) prog g in |
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g |
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|
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let rec filter_static_inputs inputs args = |
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match inputs, args with |
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| [] , [] -> [] |
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| 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 |
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| _ -> assert false |
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|
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let compute_generic_calls prog = |
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List.iter |
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(fun td -> |
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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) |
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| _ -> () |
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|
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) prog |
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|
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end |
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|
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module CycleDetection = struct |
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|
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(* ---- Look for cycles in a dependency graph *) |
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module Cycles = Graph.Components.Make (IdentDepGraph) |
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|
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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) |
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|| (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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|
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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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|
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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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|
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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 *) |
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let check_cycles g = |
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let scc_l = Cycles.scc_list g in |
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List.iter (fun partition -> |
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if wrong_partition g partition then |
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raise (Cycle partition) |
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else () |
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) scc_l |
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|
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(* Creates the sub-graph of [g] restricted to vertices and edges in partition *) |
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let copy_partition g partition = |
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let copy_g = IdentDepGraph.create () in |
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IdentDepGraph.iter_edges |
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(fun src tgt -> |
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if List.mem src partition && List.mem tgt partition |
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then IdentDepGraph.add_edge copy_g src tgt) |
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g |
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|
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|
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(* Breaks dependency cycles in a graph [g] by inserting aux variables. |
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[head] is a head of a non-trivial scc of [g]. |
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In Lustre, this is legal only for mem/mem cycles *) |
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let break_cycle head cp_head g = |
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let succs = IdentDepGraph.succ g head in |
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IdentDepGraph.add_edge g head cp_head; |
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IdentDepGraph.add_edge g cp_head (ExprDep.mk_read_var head); |
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List.iter |
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(fun s -> |
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IdentDepGraph.remove_edge g head s; |
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IdentDepGraph.add_edge g s cp_head) |
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succs |
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|
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(* Breaks cycles of the dependency graph [g] of memory variables [mems] |
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belonging in node [node]. Returns: |
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- a list of new auxiliary variable declarations |
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- a list of new equations |
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- a modified acyclic version of [g] |
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*) |
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let break_cycles node mems g = |
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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 |
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let rec break vdecls mem_eqs g = |
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let scc_l = Cycles.scc_list g in |
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let wrong = List.filter (wrong_partition g) scc_l in |
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match wrong with |
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| [] -> (vdecls, non_mem_eqs@mem_eqs, g) |
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| [head]::_ -> |
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begin |
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IdentDepGraph.remove_edge g head head; |
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break vdecls mem_eqs g |
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end |
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| (head::part)::_ -> |
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begin |
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let vdecl_cp_head, cp_eq = mk_copy_eq node head in |
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let pvar v = List.mem v part in |
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let fvar v = if v = head then vdecl_cp_head.var_id else v in |
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let mem_eqs' = List.map (eq_replace_rhs_var pvar fvar) mem_eqs in |
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break_cycle head vdecl_cp_head.var_id g; |
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break (vdecl_cp_head::vdecls) (cp_eq::mem_eqs') g |
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end |
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| _ -> assert false |
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in break [] mem_eqs g |
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|
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end |
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|
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(* Module used to compute static disjunction of variables based upon their clocks. *) |
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module Disjunction = |
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struct |
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module ClockedIdentModule = |
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struct |
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type t = var_decl |
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let root_branch vdecl = Clocks.root vdecl.var_clock, Clocks.branch vdecl.var_clock |
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let compare v1 v2 = compare (root_branch v2, v2.var_id) (root_branch v1, v1.var_id) |
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end |
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|
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module CISet = Set.Make(ClockedIdentModule) |
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|
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(* map: var |-> list of disjoint vars, sorted in increasing branch length order, |
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maybe removing shorter branches *) |
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type disjoint_map = (ident, CISet.t) Hashtbl.t |
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|
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let pp_ciset fmt t = |
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begin |
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Format.fprintf fmt "{@ "; |
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CISet.iter (fun s -> Format.fprintf fmt "%a@ " Printers.pp_var_name s) t; |
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Format.fprintf fmt "}@." |
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end |
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|
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let clock_disjoint_map vdecls = |
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let map = Hashtbl.create 23 in |
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begin |
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List.iter |
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(fun v1 -> let disj_v1 = |
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List.fold_left |
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(fun res v2 -> if Clocks.disjoint v1.var_clock v2.var_clock then CISet.add v2 res else res) |
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CISet.empty |
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vdecls in |
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(* 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; |
474 |
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: *) |