Fix compile on ARM/x86 backends

2 files changed, 149 insertions, 434 deletions

diff --git a/aarch64/ExpansionOracle.ml b/aarch64/ExpansionOracle.ml
index 3b63b80d..0869007c 100644
--- a/aarch64/ExpansionOracle.ml
+++ b/aarch64/ExpansionOracle.ml
@@ -10,8 +10,6 @@
 (*                                                             *)
 (* *************************************************************)
 
-open RTLpathCommon
-
-let expanse (sb : superblock) code pm = (code, pm)
+let expanse n ibf btl = btl
 
 let find_last_node_reg c = ()
diff --git a/aarch64/PrepassSchedulingOracle.ml b/aarch64/PrepassSchedulingOracle.ml
index 2c3eb14f..0b3ba53a 100644
--- a/aarch64/PrepassSchedulingOracle.ml
+++ b/aarch64/PrepassSchedulingOracle.ml
@@ -6,472 +6,189 @@ open Registers
 open PrepassSchedulingOracleDeps
    
 let use_alias_analysis () = false
-                          
-let length_of_chunk = function
-| Mint8signed
-| Mint8unsigned -> 1
-| Mint16signed
-| Mint16unsigned -> 2
-| Mint32
-| Mfloat32
-| Many32 -> 4
-| Mint64
-| Mfloat64 
-| Many64 -> 8;;
 
-let get_simple_dependencies (opweights : opweights) (seqa : (instruction*Regset.t) array) =
+let build_constraints_and_resources (opweights : opweights) insts btl =
   let last_reg_reads : int list PTree.t ref = ref PTree.empty
-  and last_reg_write : (int*int) PTree.t ref = ref PTree.empty
+  and last_reg_write : (int * int) PTree.t ref = ref PTree.empty
   and last_mem_reads : int list ref = ref []
   and last_mem_write : int option ref = ref None
   and last_branch : int option ref = ref None
-  and last_non_pipelined_op : int array = Array.make
-                                        opweights.nr_non_pipelined_units ( -1 )
-  and latency_constraints : latency_constraint list ref = ref [] in
+  and last_non_pipelined_op : int array =
+    Array.make opweights.nr_non_pipelined_units (-1)
+  and latency_constraints : latency_constraint list ref = ref []
+  and resources = ref [] in
   let add_constraint instr_from instr_to latency =
     assert (instr_from <= instr_to);
     assert (latency >= 0);
-    if instr_from = instr_to
-    then (if latency = 0
-          then ()
-          else failwith "PrepassSchedulingOracle.get_dependencies: negative self-loop")
+    if instr_from = instr_to then
+      if latency = 0 then ()
+      else
+        failwith "PrepassSchedulingOracle.get_dependencies: negative self-loop"
     else
       latency_constraints :=
-        { instr_from = instr_from;
-          instr_to = instr_to;
-          latency = latency
-        }:: !latency_constraints
+        { instr_from; instr_to; latency } :: !latency_constraints
   and get_last_reads reg =
-    match PTree.get reg !last_reg_reads
-     with Some l -> l
-        | None -> [] in
+    match PTree.get reg !last_reg_reads with Some l -> l | None -> []
+  in
   let add_input_mem i =
-    if not (use_alias_analysis ())
-    then
-      begin
-        begin
-          (* Read after write *)
-          match !last_mem_write with
-          | None -> ()
-          | Some j -> add_constraint j i 1
-        end;
-        last_mem_reads := i :: !last_mem_reads
-      end
-  and add_output_mem i =
-    if not (use_alias_analysis ())
-    then
-      begin
-        begin
-          (* Write after write *)
-          match !last_mem_write with
-          | None -> ()
-          | Some j -> add_constraint j i 1
-        end;
-        (* Write after read *)
-        List.iter (fun j -> add_constraint j i 0) !last_mem_reads;
-        last_mem_write := Some i;
-        last_mem_reads := []
-      end
-  and add_input_reg i reg =
-    begin
+    if not (use_alias_analysis ()) then (
       (* Read after write *)
-      match PTree.get reg !last_reg_write with
-      | None -> ()
-      | Some (j, latency) -> add_constraint j i latency
-    end;
-    last_reg_reads := PTree.set reg
-                       (i :: get_last_reads reg)
-                       !last_reg_reads
-  and add_output_reg i latency reg =
-    begin
+      (match !last_mem_write with None -> () | Some j -> add_constraint j i 1);
+      last_mem_reads := i :: !last_mem_reads)
+  and add_output_mem i =
+    if not (use_alias_analysis ()) then (
       (* Write after write *)
-      match PTree.get reg !last_reg_write with
-      | None -> ()
-      | Some (j, _) -> add_constraint j i 1
-    end;
-    begin
+      (match !last_mem_write with None -> () | Some j -> add_constraint j i 1);
       (* Write after read *)
-      List.iter (fun j -> add_constraint j i 0) (get_last_reads reg)
-    end;
+      List.iter (fun j -> add_constraint j i 0) !last_mem_reads;
+      last_mem_write := Some i;
+      last_mem_reads := [])
+  and add_input_reg i reg =
+    (* Read after write *)
+    (match PTree.get reg !last_reg_write with
+    | None -> ()
+    | Some (j, latency) -> add_constraint j i latency);
+    last_reg_reads := PTree.set reg (i :: get_last_reads reg) !last_reg_reads
+  and add_output_reg i latency reg =
+    (* Write after write *)
+    (match PTree.get reg !last_reg_write with
+    | None -> ()
+    | Some (j, _) -> add_constraint j i 1);
+    (* Write after read *)
+    List.iter (fun j -> add_constraint j i 0) (get_last_reads reg);
     last_reg_write := PTree.set reg (i, latency) !last_reg_write;
     last_reg_reads := PTree.remove reg !last_reg_reads
-    in
-  let add_input_regs i regs = List.iter (add_input_reg i) regs in
-  let rec add_builtin_res i (res : reg builtin_res) =
-    match res with
-    | BR r -> add_output_reg i 10 r
-    | BR_none -> ()
-    | BR_splitlong (hi, lo) -> add_builtin_res i hi;
-                               add_builtin_res i lo in
-  let rec add_builtin_arg i (ba : reg builtin_arg) =
-    match ba with
-    | BA r -> add_input_reg i r
-    | BA_int _ | BA_long _ | BA_float _ | BA_single _ -> ()
-    | BA_loadstack(_,_) -> add_input_mem i
-    | BA_addrstack _ -> ()
-    | BA_loadglobal(_, _, _) -> add_input_mem i
-    | BA_addrglobal _ -> ()
-    | BA_splitlong(hi, lo) -> add_builtin_arg i hi;
-                              add_builtin_arg i lo
-    | BA_addptr(a1, a2) -> add_builtin_arg i a1;
-                           add_builtin_arg i a2 in
-  let irreversible_action i =
-    match !last_branch with
-    | None -> ()
-    | Some j -> add_constraint j i 1 in
+  in
+  let add_input_regs i regs = List.iter (add_input_reg i) regs
+  and irreversible_action i =
+    match !last_branch with None -> () | Some j -> add_constraint j i 1
+  in
   let set_branch i =
     irreversible_action i;
-    last_branch := Some i in
-  let add_non_pipelined_resources i resources =
+    last_branch := Some i
+  and add_non_pipelined_resources i resources =
     Array.iter2
       (fun latency last ->
         if latency >= 0 && last >= 0 then add_constraint last i latency)
       resources last_non_pipelined_op;
-    Array.iteri (fun rsc latency ->
-        if latency >= 0
-        then last_non_pipelined_op.(rsc) <- i) resources
+    Array.iteri
+      (fun rsc latency -> if latency >= 0 then last_non_pipelined_op.(rsc) <- i)
+      resources
   in
   Array.iteri
-    begin
-      fun i (insn, other_uses) ->
-      List.iter (fun use ->
-          add_input_reg i use)
-        (Regset.elements other_uses);
-      
-      match insn with
-      | Inop _ -> ()
-      | Iop(op, inputs, output, _) ->
-         add_non_pipelined_resources i
-           (opweights.non_pipelined_resources_of_op op (List.length inputs));
-         (if Op.is_trapping_op op then irreversible_action i);
-         add_input_regs i inputs;
-         add_output_reg i (opweights.latency_of_op op (List.length inputs)) output
-      | Iload(trap, chunk, addressing, addr_regs, output, _) ->
-         (if trap=TRAP then irreversible_action i);
-         add_input_mem i;
-         add_input_regs i addr_regs;
-         add_output_reg i (opweights.latency_of_load trap chunk addressing (List.length addr_regs)) output
-      | Istore(chunk, addressing, addr_regs, input, _) ->
-         irreversible_action i;
-         add_input_regs i addr_regs;
-         add_input_reg i input;
-         add_output_mem i
-      | Icall(signature, ef, inputs, output, _) ->
-         set_branch i;
-         (match ef with
-          | Datatypes.Coq_inl r -> add_input_reg i r
-          | Datatypes.Coq_inr symbol -> ()
-         );
-         add_input_mem i;
-         add_input_regs i inputs;
-         add_output_reg i (opweights.latency_of_call signature ef) output;
-         add_output_mem i;
-         failwith "Icall"
-      | Itailcall(signature, ef, inputs) ->
-         set_branch i;
-        (match ef with
-          | Datatypes.Coq_inl r -> add_input_reg i r
-          | Datatypes.Coq_inr symbol -> ()
-         );
-         add_input_mem i;
-         add_input_regs i inputs;
-         failwith "Itailcall"
-      | Ibuiltin(ef, builtin_inputs, builtin_output, _) ->
-         set_branch i;
-         add_input_mem i;
-         List.iter (add_builtin_arg i) builtin_inputs;
-         add_builtin_res i builtin_output;
-         add_output_mem i;
-         failwith "Ibuiltin"
-      | Icond(cond, inputs, _, _, _) ->
-         set_branch i;
-         add_input_mem i;
-         add_input_regs i inputs
-      | Ijumptable(input, _) ->
-         set_branch i;
-         add_input_reg i input;
-         failwith "Ijumptable"
-      | Ireturn(Some input) ->
-         set_branch i;
-         add_input_reg i input;
-         failwith "Ireturn"
-      | Ireturn(None) ->
-         set_branch i;
-         failwith "Ireturn none"
-    end seqa;
-  !latency_constraints;;
-
-let resources_of_instruction (opweights : opweights) = function
-  | Inop _ -> Array.map (fun _ -> 0) opweights.pipelined_resource_bounds
-  | Iop(op, inputs, output, _) ->
-     opweights.resources_of_op op (List.length inputs)
-  | Iload(trap, chunk, addressing, addr_regs, output, _) ->
-     opweights.resources_of_load trap chunk addressing (List.length addr_regs)
-  | Istore(chunk, addressing, addr_regs, input, _) ->
-     opweights.resources_of_store chunk addressing (List.length addr_regs)
-  | Icall(signature, ef, inputs, output, _) ->
-     opweights.resources_of_call signature ef
-  | Ibuiltin(ef, builtin_inputs, builtin_output, _) ->
-     opweights.resources_of_builtin ef
-  | Icond(cond, args, _, _ , _) ->
-     opweights.resources_of_cond cond (List.length args)
-  | Itailcall _ | Ijumptable _ | Ireturn _ -> opweights.pipelined_resource_bounds
-    
-let print_sequence pp (seqa : instruction array) =
-  Array.iteri (
-      fun i (insn : instruction) ->
-      PrintRTL.print_instruction pp (i, insn)) seqa;;
-
-type unique_id = int
-               
-type 'a symbolic_term_node =
-  | STop of Op.operation * 'a list
-  | STinitial_reg of int
-  | STother of int;;
-
-type symbolic_term = {
-    hash_id : unique_id;
-    hash_ct : symbolic_term symbolic_term_node
-  };;
-
-let rec print_term channel term =
-  match term.hash_ct with
-  | STop(op, args) ->
-     PrintOp.print_operation print_term channel (op, args)
-  | STinitial_reg n -> Printf.fprintf channel "x%d" n
-  | STother n -> Printf.fprintf channel "y%d" n;;
-
-type symbolic_term_table = {
-    st_table : (unique_id symbolic_term_node, symbolic_term) Hashtbl.t;
-    mutable st_next_id : unique_id };;
-
-let hash_init () = {
-    st_table = Hashtbl.create 20;
-    st_next_id = 0
-  };;
-
-let ground_to_id = function
-  | STop(op, l) -> STop(op, List.map (fun t -> t.hash_id) l)
-  | STinitial_reg r -> STinitial_reg r
-  | STother i -> STother i;;
-
-let hash_node (table : symbolic_term_table) (term : symbolic_term symbolic_term_node) : symbolic_term =
-  let grounded = ground_to_id term in
-  match Hashtbl.find_opt table.st_table grounded with
-  | Some x -> x
-  | None ->
-     let term' = { hash_id = table.st_next_id;
-                   hash_ct = term } in
-     (if table.st_next_id = max_int then failwith "hash: max_int");
-     table.st_next_id <- table.st_next_id + 1;
-     Hashtbl.add table.st_table grounded term';
-     term';;
-
-type access = {
-    base : symbolic_term;
-    offset : int64;
-    length : int
-  };;
-
-let term_equal a b = (a.hash_id = b.hash_id);;
-
-let access_of_addressing get_reg chunk addressing args =
-  match addressing, args with
-  | (Op.Aindexed ofs), [reg] -> Some
-     { base = get_reg reg;
-       offset = Camlcoq.camlint64_of_ptrofs ofs;
-       length = length_of_chunk chunk
-     }
-  | _, _ -> None ;;
-(* TODO: global *)
-
-let symbolic_execution (seqa : instruction array) =
-  let regs = ref PTree.empty
-  and table = hash_init() in
-  let assign reg term = regs := PTree.set reg term !regs
-  and hash term = hash_node table term in
-  let get_reg reg =
-    match PTree.get reg !regs with
-    | None -> hash (STinitial_reg (Camlcoq.P.to_int reg))
-    | Some x -> x in
-  let targets = Array.make (Array.length seqa) None in
-  Array.iteri
-    begin
-      fun i insn ->
-      match insn with
-      | Iop(Op.Omove, [input], output, _) ->
-         assign output (get_reg input)
-      | Iop(op, inputs, output, _) ->
-         assign output (hash (STop(op, List.map get_reg inputs)))
-
-      | Iload(trap, chunk, addressing, args, output, _) ->
-         let access = access_of_addressing get_reg chunk addressing args in
-         targets.(i) <- access;
-         assign output (hash (STother(i)))
-        
-      | Icall(_, _, _, output, _)
-      | Ibuiltin(_, _, BR output, _) -> 
-         assign output (hash (STother(i)))
-        
-      | Istore(chunk, addressing, args, va, _) ->
-         let access = access_of_addressing get_reg chunk addressing args in
-         targets.(i) <- access
-                                          
-      | Inop _ -> ()
-      | Ibuiltin(_, _, BR_none, _) -> ()
-      | Ibuiltin(_, _, BR_splitlong _, _) -> failwith "BR_splitlong"
-
-      | Itailcall (_, _, _)
-      |Icond (_, _, _, _, _)
-      |Ijumptable (_, _)
-      |Ireturn _ -> ()
-    end seqa;
-  targets;;
-
-let print_access channel = function
-  | None -> Printf.fprintf channel "any"
-  | Some x -> Printf.fprintf channel "%a + %Ld" print_term x.base x.offset;;
-
-let print_targets channel seqa =
-  let targets = symbolic_execution seqa in
-  Array.iteri
-    (fun i insn ->
-      match insn with
-      | Iload _ -> Printf.fprintf channel "%d: load %a\n"
-                      i print_access targets.(i) 
-      | Istore _ -> Printf.fprintf channel "%d: store %a\n"
-                       i print_access targets.(i)
-      | _ -> ()
-    ) seqa;;
-
-let may_overlap a0 b0 =
-  match a0, b0 with
-  | (None, _)  | (_ , None) -> true
-  | (Some a), (Some b) ->
-     if term_equal a.base b.base
-     then (max a.offset b.offset) <
-          (min (Int64.add (Int64.of_int a.length) a.offset)
-               (Int64.add (Int64.of_int b.length) b.offset))
-     else match a.base.hash_ct, b.base.hash_ct with
-          | STop(Op.Oaddrsymbol(ida, ofsa),[]),
-            STop(Op.Oaddrsymbol(idb, ofsb),[]) ->
-             (ida=idb) &&
-               let ao = Int64.add a.offset (Camlcoq.camlint64_of_ptrofs ofsa)
-               and bo = Int64.add b.offset (Camlcoq.camlint64_of_ptrofs ofsb) in
-               (max ao bo) <
-               (min (Int64.add (Int64.of_int a.length) ao)
-                  (Int64.add (Int64.of_int b.length) bo))
-          | STop(Op.Oaddrstack _, []),
-            STop(Op.Oaddrsymbol _, [])
-          | STop(Op.Oaddrsymbol _, []),
-            STop(Op.Oaddrstack _, []) -> false
-          | STop(Op.Oaddrstack(ofsa),[]),
-            STop(Op.Oaddrstack(ofsb),[]) ->
-               let ao = Int64.add a.offset (Camlcoq.camlint64_of_ptrofs ofsa)
-               and bo = Int64.add b.offset (Camlcoq.camlint64_of_ptrofs ofsb) in
-               (max ao bo) <
-               (min (Int64.add (Int64.of_int a.length) ao)
-                  (Int64.add (Int64.of_int b.length) bo))
-          | _ -> true;;
-
-(*
-(* TODO suboptimal quadratic algorithm *)
-let get_alias_dependencies seqa =
-  let targets = symbolic_execution seqa
-  and deps = ref [] in
-  let add_constraint instr_from instr_to latency =
-    deps := { instr_from = instr_from;
-              instr_to = instr_to;
-              latency = latency
-            }:: !deps in
-  for i=0 to (Array.length seqa)-1
-  do
-    for j=0 to i-1
-    do
-      match seqa.(j), seqa.(i) with
-      | (Istore _), ((Iload _) | (Istore _)) ->
-         if may_overlap targets.(j) targets.(i)
-         then add_constraint j i 1
-      | (Iload _), (Istore _) ->
-         if may_overlap targets.(j) targets.(i)
-         then add_constraint j i 0
-      | (Istore _ | Iload _), (Icall _ | Ibuiltin _)
-      | (Icall _ | Ibuiltin _), (Icall _ | Ibuiltin _ | Iload _ | Istore _) ->
-         add_constraint j i 1
-      | (Inop _ | Iop _), _
-      | _, (Inop _ | Iop _)
-      | (Iload _), (Iload _) -> ()
-    done
-  done;
-  !deps;;
- *)
-
-let define_problem (opweights : opweights) seqa =
-  let simple_deps = get_simple_dependencies opweights seqa in
-  { max_latency = -1;
+    (fun i inst ->
+      match inst with
+      | Bnop _ ->
+          let rs = Array.map (fun _ -> 0) opweights.pipelined_resource_bounds in
+          resources := rs :: !resources
+      | Bop (op, lr, rd, _) ->
+          add_non_pipelined_resources i
+            (opweights.non_pipelined_resources_of_op op (List.length lr));
+          if Op.is_trapping_op op then irreversible_action i;
+          add_input_regs i lr;
+          add_output_reg i (opweights.latency_of_op op (List.length lr)) rd;
+          let rs = opweights.resources_of_op op (List.length lr) in
+          resources := rs :: !resources
+      | Bload (trap, chk, addr, lr, rd, _) ->
+          if trap = TRAP then irreversible_action i;
+          add_input_mem i;
+          add_input_regs i lr;
+          add_output_reg i
+            (opweights.latency_of_load trap chk addr (List.length lr))
+            rd;
+          let rs = opweights.resources_of_load trap chk addr (List.length lr) in
+          resources := rs :: !resources
+      | Bstore (chk, addr, lr, src, _) ->
+          irreversible_action i;
+          add_input_regs i lr;
+          add_input_reg i src;
+          add_output_mem i;
+          let rs = opweights.resources_of_store chk addr (List.length lr) in
+          resources := rs :: !resources
+      | Bcond (cond, lr, BF (Bgoto s, _), ibnot, _) ->
+          (* TODO gourdinl test with/out this line *)
+          let live = (get_some @@ PTree.get s btl).input_regs in
+          add_input_regs i (Regset.elements live);
+          set_branch i;
+          add_input_mem i;
+          add_input_regs i lr;
+          let rs = opweights.resources_of_cond cond (List.length lr) in
+          resources := rs :: !resources
+      | Bcond (_, _, _, _, _) ->
+          failwith "get_simple_dependencies: invalid Bcond"
+      | BF (_, _) -> failwith "get_simple_dependencies: BF"
+      | Bseq (_, _) -> failwith "get_simple_dependencies: Bseq")
+    insts;
+  (!latency_constraints, Array.of_list (List.rev !resources))
+
+let define_problem (opweights : opweights) ibf btl =
+  let simple_deps, resources =
+    build_constraints_and_resources opweights ibf btl
+  in
+  {
+    max_latency = -1;
     resource_bounds = opweights.pipelined_resource_bounds;
-    instruction_usages = Array.map (resources_of_instruction opweights) (Array.map fst seqa);
-    latency_constraints =
-      (* if (use_alias_analysis ())
-      then (get_alias_dependencies seqa) @ simple_deps
-      else *) simple_deps };;
+    instruction_usages = resources;
+    latency_constraints = simple_deps;
+  }
 
 let zigzag_scheduler problem early_ones =
   let nr_instructions = get_nr_instructions problem in
-  assert(nr_instructions = (Array.length early_ones));
+  assert (nr_instructions = Array.length early_ones);
   match list_scheduler problem with
   | Some fwd_schedule ->
-     let fwd_makespan = fwd_schedule.((Array.length fwd_schedule) - 1) in
-     let constraints' = ref problem.latency_constraints in
-     Array.iteri (fun i is_early ->
-         if is_early then
-           constraints' :=  {
-             instr_from = i;
-             instr_to = nr_instructions ;
-             latency = fwd_makespan - fwd_schedule.(i) } ::!constraints' )
-       early_ones;
-     validated_scheduler reverse_list_scheduler
-       { problem with latency_constraints = !constraints' }
-  | None -> None;;
-  
-let prepass_scheduler_by_name name problem early_ones =
+      let fwd_makespan = fwd_schedule.(Array.length fwd_schedule - 1) in
+      let constraints' = ref problem.latency_constraints in
+      Array.iteri
+        (fun i is_early ->
+          if is_early then
+            constraints' :=
+              {
+                instr_from = i;
+                instr_to = nr_instructions;
+                latency = fwd_makespan - fwd_schedule.(i);
+              }
+              :: !constraints')
+        early_ones;
+      validated_scheduler reverse_list_scheduler
+        { problem with latency_constraints = !constraints' }
+  | None -> None
+
+let prepass_scheduler_by_name name problem insts =
   match name with
-  | "zigzag" -> zigzag_scheduler problem early_ones
+  | "zigzag" ->
+      let early_ones =
+        Array.map
+          (fun inst ->
+            match inst with Bcond (_, _, _, _, _) -> true | _ -> false)
+          insts
+      in
+      zigzag_scheduler problem early_ones
   | _ -> scheduler_by_name name problem
-  
-let schedule_sequence (seqa : (instruction*Regset.t) array) =
+
+let schedule_sequence insts btl =
   let opweights = OpWeights.get_opweights () in
   try
-    if (Array.length seqa) <= 1
-    then None
+    if Array.length insts <= 1 then None
     else
-      begin
-      let nr_instructions = Array.length seqa in
-      (if !Clflags.option_debug_compcert > 6
-       then Printf.printf "prepass scheduling length = %d\n" (Array.length seqa));
-      let problem = define_problem opweights seqa in
-      (if !Clflags.option_debug_compcert > 7
-       then (print_sequence stdout (Array.map fst seqa);
-             print_problem stdout problem));
-      match prepass_scheduler_by_name
-              (!Clflags.option_fprepass_sched)
-              problem
-              (Array.map (fun (ins, _) ->
-                   match ins with
-                   | Icond _ -> true
-                   | _ -> false) seqa) with
-      | None -> Printf.printf "no solution in prepass scheduling\n";
-                None
+      let nr_instructions = Array.length insts in
+      let problem = define_problem opweights insts btl in
+      match
+        prepass_scheduler_by_name !Clflags.option_fprepass_sched problem insts
+      with
+      | None ->
+          Printf.printf "no solution in prepass scheduling\n";
+          None
       | Some solution ->
-         let positions = Array.init nr_instructions (fun i -> i) in
-         Array.sort (fun i j ->
-             let si = solution.(i) and sj = solution.(j) in
-             if si < sj then -1
-             else if si > sj then 1
-             else i - j) positions;
-         Some positions
-    end
-  with (Failure s) ->
+          let positions = Array.init nr_instructions (fun i -> i) in
+          Array.sort
+            (fun i j ->
+              let si = solution.(i) and sj = solution.(j) in
+              if si < sj then -1 else if si > sj then 1 else i - j)
+            positions;
+          Some positions
+  with Failure s ->
     Printf.printf "failure in prepass scheduling: %s\n" s;
-    None;;
-                                                            
+    None
+
+