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|
(* *************************************************************)
(* *)
(* The Compcert verified compiler *)
(* *)
(* Sylvain Boulmé Grenoble-INP, VERIMAG *)
(* David Monniaux CNRS, VERIMAG *)
(* Cyril Six Kalray *)
(* *)
(* Copyright Kalray. Copyright VERIMAG. All rights reserved. *)
(* This file is distributed under the terms of the INRIA *)
(* Non-Commercial License Agreement. *)
(* *)
(* *************************************************************)
(** Schedule instructions on a synchronized pipeline
@author David Monniaux, CNRS, VERIMAG *)
type latency_constraint = {
instr_from : int;
instr_to : int;
latency : int };;
type problem = {
max_latency : int;
resource_bounds : int array;
instruction_usages : int array array;
latency_constraints : latency_constraint list;
};;
let print_problem channel problem =
(if problem.max_latency >= 0
then Printf.fprintf channel "max makespan: %d\n" problem.max_latency);
output_string channel "resource bounds:";
(Array.iter (fun b -> Printf.fprintf channel " %d" b) problem.resource_bounds);
output_string channel ";\n";
(Array.iteri (fun i v ->
Printf.fprintf channel "instr%d:" i;
(Array.iter (fun b -> Printf.fprintf channel " %d" b) v);
output_string channel ";\n") problem.instruction_usages);
List.iter (fun instr ->
Printf.printf "t%d - t%d >= %d;\n"
instr.instr_to instr.instr_from instr.latency)
problem.latency_constraints;;
let get_nr_instructions problem = Array.length problem.instruction_usages;;
let get_nr_resources problem = Array.length problem.resource_bounds;;
type solution = int array
type scheduler = problem -> solution option
(* DISABLED
(** Schedule the problem optimally by constraint solving using the Gecode solver. *)
external gecode_scheduler : problem -> solution option =
"caml_gecode_schedule_instr";;
*)
let maximum_slot_used times =
let maxi = ref (-1) in
for i=0 to (Array.length times)-2
do
maxi := max !maxi times.(i)
done;
!maxi;;
let check_schedule (problem : problem) (times : solution) =
let nr_instructions = get_nr_instructions problem in
(if Array.length times <> nr_instructions+1
then failwith
(Printf.sprintf "check_schedule: %d times expected, got %d"
(nr_instructions+1) (Array.length times)));
(if problem.max_latency >= 0 && times.(nr_instructions)> problem.max_latency
then failwith "check_schedule: max_latency exceeded");
(Array.iteri (fun i time ->
(if time < 0
then failwith (Printf.sprintf "time[%d] < 0" i))) times);
let slot_resources = Array.init ((maximum_slot_used times)+1)
(fun _ -> Array.copy problem.resource_bounds) in
for i=0 to nr_instructions -1
do
let remaining_resources = slot_resources.(times.(i))
and used_resources = problem.instruction_usages.(i) in
for resource=0 to (Array.length used_resources)-1
do
let after = remaining_resources.(resource) - used_resources.(resource) in
(if after < 0
then failwith (Printf.sprintf "check_schedule: instruction %d exceeds resource %d at slot %d" i resource times.(i)));
remaining_resources.(resource) <- after
done
done;
List.iter (fun ctr ->
if times.(ctr.instr_to) - times.(ctr.instr_from) < ctr.latency
then failwith (Printf.sprintf "check_schedule: time[%d]=%d - time[%d]=%d < %d"
ctr.instr_to times.(ctr.instr_to)
ctr.instr_from times.(ctr.instr_from)
ctr.latency)
) problem.latency_constraints;;
let bound_max_time problem =
let total = ref(Array.length problem.instruction_usages) in
List.iter (fun ctr -> total := !total + ctr.latency) problem.latency_constraints;
!total;;
let vector_less_equal a b =
try
Array.iter2 (fun x y ->
if x>y
then raise Exit) a b;
true
with Exit -> false;;
let vector_subtract a b =
assert ((Array.length a) = (Array.length b));
for i=0 to (Array.length a)-1
do
b.(i) <- b.(i) - a.(i)
done;;
(* The version with critical path ordering is much better! *)
type list_scheduler_order =
| INSTRUCTION_ORDER
| CRITICAL_PATH_ORDER;;
let int_max (x : int) (y : int) =
if x > y then x else y;;
let int_min (x : int) (y : int) =
if x < y then x else y;;
let get_predecessors problem =
let nr_instructions = get_nr_instructions problem in
let predecessors = Array.make (nr_instructions+1) [] in
List.iter (fun ctr ->
predecessors.(ctr.instr_to) <-
(ctr.instr_from, ctr.latency)::predecessors.(ctr.instr_to))
problem.latency_constraints;
predecessors;;
let get_successors problem =
let nr_instructions = get_nr_instructions problem in
let successors = Array.make nr_instructions [] in
List.iter (fun ctr ->
successors.(ctr.instr_from) <-
(ctr.instr_to, ctr.latency)::successors.(ctr.instr_from))
problem.latency_constraints;
successors;;
let critical_paths successors =
let nr_instructions = Array.length successors in
let path_lengths = Array.make nr_instructions (-1) in
let rec compute i =
if i=nr_instructions then 0 else
match path_lengths.(i) with
| -2 -> failwith "InstructionScheduler: the dependency graph has cycles"
| -1 -> path_lengths.(i) <- -2;
let x = List.fold_left
(fun cur (j, latency)-> int_max cur (latency+(compute j)))
1 successors.(i)
in path_lengths.(i) <- x; x
| x -> x
in for i = nr_instructions-1 downto 0
do
ignore (compute i)
done;
path_lengths;;
let maximum_critical_path problem =
let paths = critical_paths (get_successors problem) in
Array.fold_left int_max 0 paths;;
let get_earliest_dates predecessors =
let nr_instructions = (Array.length predecessors)-1 in
let path_lengths = Array.make (nr_instructions+1) (-1) in
let rec compute i =
match path_lengths.(i) with
| -2 -> failwith "InstructionScheduler: the dependency graph has cycles"
| -1 -> path_lengths.(i) <- -2;
let x = List.fold_left
(fun cur (j, latency)-> int_max cur (latency+(compute j)))
0 predecessors.(i)
in path_lengths.(i) <- x; x
| x -> x
in for i = 0 to nr_instructions
do
ignore (compute i)
done;
for i = 0 to nr_instructions - 1
do
path_lengths.(nr_instructions) <- int_max
path_lengths.(nr_instructions) (1 + path_lengths.(i))
done;
path_lengths;;
exception Unschedulable
let get_latest_dates deadline successors =
let nr_instructions = Array.length successors
and path_lengths = critical_paths successors in
Array.init (nr_instructions + 1)
(fun i ->
if i < nr_instructions then
let path_length = path_lengths.(i) in
assert (path_length >= 1);
(if path_length > deadline
then raise Unschedulable);
deadline - path_length
else deadline);;
let priority_list_scheduler (order : list_scheduler_order)
(problem : problem) :
solution option =
let nr_instructions = get_nr_instructions problem in
let successors = get_successors problem
and predecessors = get_predecessors problem
and times = Array.make (nr_instructions+1) (-1) in
let priorities = match order with
| INSTRUCTION_ORDER -> None
| CRITICAL_PATH_ORDER -> Some (critical_paths successors) in
let module InstrSet =
Set.Make (struct type t=int
let compare = match priorities with
| None -> (fun x y -> x - y)
| Some p -> (fun x y ->
(match p.(y)-p.(x) with
| 0 -> x - y
| z -> z))
end) in
let max_time = bound_max_time problem in
let ready = Array.make max_time InstrSet.empty in
Array.iteri (fun i preds ->
if i<nr_instructions && preds=[]
then ready.(0) <- InstrSet.add i ready.(0)) predecessors;
let current_time = ref 0
and current_resources = Array.copy problem.resource_bounds
and earliest_time i =
try
let time = ref (-1) in
List.iter (fun (j, latency) ->
if times.(j) < 0
then raise Exit
else let t = times.(j) + latency in
if t > !time
then time := t) predecessors.(i);
assert(!time >= 0);
!time
with Exit -> -1
in
let advance_time() =
begin
(if !current_time < max_time-1
then
begin
Array.blit problem.resource_bounds 0 current_resources 0
(Array.length current_resources);
ready.(!current_time + 1) <-
InstrSet.union (ready.(!current_time)) (ready.(!current_time + 1));
ready.(!current_time) <- InstrSet.empty;
end);
incr current_time
end in
let attempt_scheduling ready usages =
let result = ref (-1) in
try
InstrSet.iter (fun i ->
(* Printf.printf "trying scheduling %d\n" i;
pr int_vector usages.(i);
print _vector current_resources; *)
if vector_less_equal usages.(i) current_resources
then
begin
vector_subtract usages.(i) current_resources;
result := i;
raise Exit
end) ready;
-1
with Exit -> !result in
while !current_time < max_time
do
if (InstrSet.is_empty ready.(!current_time))
then advance_time()
else
match attempt_scheduling ready.(!current_time)
problem.instruction_usages with
| -1 -> advance_time()
| i ->
begin
assert(times.(i) < 0);
times.(i) <- !current_time;
ready.(!current_time) <- InstrSet.remove i (ready.(!current_time));
List.iter (fun (instr_to, latency) ->
if instr_to < nr_instructions then
match earliest_time instr_to with
| -1 -> ()
| to_time ->
ready.(to_time) <- InstrSet.add instr_to ready.(to_time))
successors.(i);
successors.(i) <- []
end
done;
try
let final_time = ref (-1) in
for i=0 to nr_instructions-1
do
(if times.(i) < 0 then raise Exit);
(if !final_time < times.(i)+1 then final_time := times.(i)+1)
done;
List.iter (fun (i, latency) ->
let target_time = latency + times.(i) in
if target_time > !final_time
then final_time := target_time
) predecessors.(nr_instructions);
times.(nr_instructions) <- !final_time;
Some times
with Exit -> None;;
let list_scheduler = priority_list_scheduler CRITICAL_PATH_ORDER;;
(* dummy code for placating ocaml's warnings *)
let _ = fun x -> priority_list_scheduler INSTRUCTION_ORDER x;;
type bundle = int list;;
let rec extract_deps_to index = function
| [] -> []
| dep :: deps -> let extracts = extract_deps_to index deps in
if (dep.instr_to == index) then
dep :: extracts
else
extracts
exception InvalidBundle;;
let dependency_check problem bundle index =
let index_deps = extract_deps_to index problem.latency_constraints in
List.iter (fun i ->
List.iter (fun dep ->
if (dep.instr_from == i) then raise InvalidBundle
) index_deps
) bundle;;
let rec make_bundle problem resources bundle index =
let resources_copy = Array.copy resources in
let nr_instructions = get_nr_instructions problem in
if (index >= nr_instructions) then (bundle, index+1) else
let inst_usage = problem.instruction_usages.(index) in
try match vector_less_equal inst_usage resources with
| false -> raise InvalidBundle
| true -> (
dependency_check problem bundle index;
vector_subtract problem.instruction_usages.(index) resources_copy;
make_bundle problem resources_copy (index::bundle) (index+1)
)
with InvalidBundle -> (bundle, index);;
let rec make_bundles problem index : bundle list =
if index >= get_nr_instructions problem then
[]
else
let (bundle, new_index) = make_bundle problem problem.resource_bounds [] index in
bundle :: (make_bundles problem new_index);;
let bundles_to_schedule problem bundles : solution =
let nr_instructions = get_nr_instructions problem in
let schedule = Array.make (nr_instructions+1) (nr_instructions+4) in
let time = ref 0 in
List.iter (fun bundle ->
begin
List.iter (fun i ->
schedule.(i) <- !time
) bundle;
time := !time + 1
end
) bundles; schedule;;
let greedy_scheduler (problem : problem) : solution option =
let bundles = make_bundles problem 0 in
Some (bundles_to_schedule problem bundles);;
(* alternate implementation
let swap_array_elements a i j =
let x = a.(i) in
a.(i) <- a.(j);
a.(j) <- x;;
let array_reverse_slice a first last =
let i = ref first and j = ref last in
while i < j
do
swap_array_elements a !i !j;
incr i;
decr j
done;;
let array_reverse a =
let a' = Array.copy a in
array_reverse_slice a' 0 ((Array.length a)-1);
a';;
*)
(* unneeded
let array_reverse a =
let n=Array.length a in
Array.init n (fun i -> a.(n-1-i));;
*)
let reverse_constraint nr_instructions ctr =
{ instr_to = nr_instructions -ctr.instr_from;
instr_from = nr_instructions - ctr.instr_to;
latency = ctr.latency };;
(* unneeded
let rec list_map_filter f = function
| [] -> []
| h::t ->
(match f h with
| None -> list_map_filter f t
| Some x -> x :: (list_map_filter f t));;
*)
let reverse_problem problem =
let nr_instructions = get_nr_instructions problem in
{
max_latency = problem.max_latency;
resource_bounds = problem.resource_bounds;
instruction_usages = Array.init (nr_instructions + 1)
(fun i ->
if i=0
then Array.map (fun _ -> 0) problem.resource_bounds else problem.instruction_usages.(nr_instructions - i));
latency_constraints = List.map (reverse_constraint nr_instructions)
problem.latency_constraints
};;
let max_scheduled_time solution =
let time = ref (-1) in
for i = 0 to ((Array.length solution) - 2)
do
time := max !time solution.(i)
done;
!time;;
(*
let recompute_makespan problem solution =
let n = (Array.length solution) - 1 and ms = ref 0 in
List.iter (fun cstr ->
if cstr.instr_to = n
then ms := max !ms (solution.(cstr.instr_from) + cstr.latency)
) problem.latency_constraints;
!ms;;
*)
let schedule_reversed (scheduler : problem -> solution option)
(problem : problem) =
match scheduler (reverse_problem problem) with
| None -> None
| Some solution ->
let nr_instructions = get_nr_instructions problem in
let makespan = max_scheduled_time solution in
let ret = Array.init (nr_instructions + 1)
(fun i -> makespan-solution.(nr_instructions-i)) in
ret.(nr_instructions) <- max ((max_scheduled_time ret) + 1)
(ret.(nr_instructions));
Some ret;;
(** Schedule the problem using a greedy list scheduling algorithm, from the end. *)
let reverse_list_scheduler = schedule_reversed list_scheduler;;
let check_problem problem =
(if (Array.length problem.instruction_usages) < 1
then failwith "length(problem.instruction_usages) < 1");;
let validated_scheduler (scheduler : problem -> solution option)
(problem : problem) =
check_problem problem;
match scheduler problem with
| None -> None
| (Some solution) as ret -> check_schedule problem solution; ret;;
let get_max_latency solution =
solution.((Array.length solution)-1);;
let show_date_ranges problem =
let deadline = problem.max_latency in
assert(deadline >= 0);
let successors = get_successors problem
and predecessors = get_predecessors problem in
let earliest_dates : int array = get_earliest_dates predecessors
and latest_dates : int array = get_latest_dates deadline successors in
assert ((Array.length earliest_dates) =
(Array.length latest_dates));
Array.iteri (fun i early ->
let late = latest_dates.(i) in
Printf.printf "t[%d] in %d..%d\n" i early late)
earliest_dates;;
type pseudo_boolean_problem_type =
| SATISFIABILITY
| OPTIMIZATION;;
type pseudo_boolean_mapper = {
mapper_pb_type : pseudo_boolean_problem_type;
mapper_nr_instructions : int;
mapper_nr_pb_variables : int;
mapper_earliest_dates : int array;
mapper_latest_dates : int array;
mapper_var_offsets : int array;
mapper_final_predecessors : (int * int) list
};;
(* Latency constraints are:
presence of instr-to at each t <= sum of presences of instr-from at compatible times
if reverse_encoding
presence of instr-from at each t <= sum of presences of instr-to at compatible times *)
(* Experiments show reverse_encoding=true multiplies time by 2 in sat4j
without making hard instances easier *)
let direct_encoding = false
and reverse_encoding = false
and delta_encoding = true
let pseudo_boolean_print_problem channel problem pb_type =
let deadline = problem.max_latency in
assert (deadline > 0);
let nr_instructions = get_nr_instructions problem
and nr_resources = get_nr_resources problem
and successors = get_successors problem
and predecessors = get_predecessors problem in
let earliest_dates = get_earliest_dates predecessors
and latest_dates = get_latest_dates deadline successors in
let var_offsets = Array.make
(match pb_type with
| OPTIMIZATION -> nr_instructions+1
| SATISFIABILITY -> nr_instructions) 0 in
let nr_pb_variables =
(let nr = ref 0 in
for i=0 to (match pb_type with
| OPTIMIZATION -> nr_instructions
| SATISFIABILITY -> nr_instructions-1)
do
var_offsets.(i) <- !nr;
nr := !nr + latest_dates.(i) - earliest_dates.(i) + 1
done;
!nr)
and nr_pb_constraints =
(match pb_type with
| OPTIMIZATION -> nr_instructions+1
| SATISFIABILITY -> nr_instructions) +
(let count = ref 0 in
for t=0 to deadline-1
do
for j=0 to nr_resources-1
do
try
for i=0 to nr_instructions-1
do
let usage = problem.instruction_usages.(i).(j) in
if t >= earliest_dates.(i) && t <= latest_dates.(i)
&& usage > 0 then raise Exit
done
with Exit -> incr count
done
done;
!count) +
(let count=ref 0 in
List.iter
(fun ctr ->
if ctr.instr_to < nr_instructions
then count := !count + 1 + latest_dates.(ctr.instr_to)
- earliest_dates.(ctr.instr_to)
+ (if reverse_encoding
then 1 + latest_dates.(ctr.instr_from)
- earliest_dates.(ctr.instr_from)
else 0)
)
problem.latency_constraints;
!count) +
(match pb_type with
| OPTIMIZATION -> (1 + deadline - earliest_dates.(nr_instructions)) * nr_instructions
| SATISFIABILITY -> 0)
and measured_nr_constraints = ref 0 in
let pb_var i t =
assert(t >= earliest_dates.(i));
assert(t <= latest_dates.(i));
let v = 1+var_offsets.(i)+t-earliest_dates.(i) in
assert(v <= nr_pb_variables);
Printf.sprintf "x%d" v in
let end_constraint () =
begin
output_string channel ";\n";
incr measured_nr_constraints
end in
let gen_latency_constraint i_to i_from latency t_to =
Printf.fprintf channel "* t[%d] - t[%d] >= %d when t[%d]=%d\n"
i_to i_from latency i_to t_to;
for t_from=earliest_dates.(i_from) to
int_min latest_dates.(i_from) (t_to - latency)
do
Printf.fprintf channel "+1 %s " (pb_var i_from t_from)
done;
Printf.fprintf channel "-1 %s " (pb_var i_to t_to);
Printf.fprintf channel ">= 0";
end_constraint()
and gen_dual_latency_constraint i_to i_from latency t_from =
Printf.fprintf channel "* t[%d] - t[%d] >= %d when t[%d]=%d\n"
i_to i_from latency i_to t_from;
for t_to=int_max earliest_dates.(i_to) (t_from + latency)
to latest_dates.(i_to)
do
Printf.fprintf channel "+1 %s " (pb_var i_to t_to)
done;
Printf.fprintf channel "-1 %s " (pb_var i_from t_from);
Printf.fprintf channel ">= 0";
end_constraint()
in
Printf.fprintf channel "* #variable= %d #constraint= %d\n" nr_pb_variables nr_pb_constraints;
Printf.fprintf channel "* nr_instructions=%d deadline=%d\n" nr_instructions deadline;
begin
match pb_type with
| SATISFIABILITY -> ()
| OPTIMIZATION ->
output_string channel "min:";
for t=earliest_dates.(nr_instructions) to deadline
do
Printf.fprintf channel " %+d %s" t (pb_var nr_instructions t)
done;
output_string channel ";\n";
end;
for i=0 to (match pb_type with
| OPTIMIZATION -> nr_instructions
| SATISFIABILITY -> nr_instructions-1)
do
let early = earliest_dates.(i) and late= latest_dates.(i) in
Printf.fprintf channel "* t[%d] in %d..%d\n" i early late;
for t=early to late
do
Printf.fprintf channel "+1 %s " (pb_var i t)
done;
Printf.fprintf channel "= 1";
end_constraint()
done;
for t=0 to deadline-1
do
for j=0 to nr_resources-1
do
let bound = problem.resource_bounds.(j)
and coeffs = ref [] in
for i=0 to nr_instructions-1
do
let usage = problem.instruction_usages.(i).(j) in
if t >= earliest_dates.(i) && t <= latest_dates.(i)
&& usage > 0
then coeffs := (i, usage) :: !coeffs
done;
if !coeffs <> [] then
begin
Printf.fprintf channel "* resource #%d at t=%d <= %d\n" j t bound;
List.iter (fun (i, usage) ->
Printf.fprintf channel "%+d %s " (-usage) (pb_var i t)) !coeffs;
Printf.fprintf channel ">= %d" (-bound);
end_constraint();
end
done
done;
List.iter
(fun ctr ->
if ctr.instr_to < nr_instructions then
begin
for t_to=earliest_dates.(ctr.instr_to) to latest_dates.(ctr.instr_to)
do
gen_latency_constraint ctr.instr_to ctr.instr_from ctr.latency t_to
done;
if reverse_encoding
then
for t_from=earliest_dates.(ctr.instr_from) to latest_dates.(ctr.instr_from)
do
gen_dual_latency_constraint ctr.instr_to ctr.instr_from ctr.latency t_from
done
end
) problem.latency_constraints;
begin
match pb_type with
| SATISFIABILITY -> ()
| OPTIMIZATION ->
let final_latencies = Array.make nr_instructions 1 in
List.iter (fun (i, latency) ->
final_latencies.(i) <- int_max final_latencies.(i) latency)
predecessors.(nr_instructions);
for t_to=earliest_dates.(nr_instructions) to deadline
do
for i_from = 0 to nr_instructions -1
do
gen_latency_constraint nr_instructions i_from final_latencies.(i_from) t_to
done
done
end;
assert (!measured_nr_constraints = nr_pb_constraints);
{
mapper_pb_type = pb_type;
mapper_nr_instructions = nr_instructions;
mapper_nr_pb_variables = nr_pb_variables;
mapper_earliest_dates = earliest_dates;
mapper_latest_dates = latest_dates;
mapper_var_offsets = var_offsets;
mapper_final_predecessors = predecessors.(nr_instructions)
};;
type pb_answer =
| Positive
| Negative
| Unknown
let line_to_pb_solution sol line nr_pb_variables =
let assign s v =
begin
let i = int_of_string s in
sol.(i-1) <- v
end in
List.iter
begin
function "" -> ()
| item ->
(match String.get item 0 with
| '+' ->
assert ((String.length item) >= 3);
assert ((String.get item 1) = 'x');
assign (String.sub item 2 ((String.length item)-2)) Positive
| '-' ->
assert ((String.length item) >= 3);
assert ((String.get item 1) = 'x');
assign (String.sub item 2 ((String.length item)-2)) Negative
| 'x' ->
assert ((String.length item) >= 2);
assign (String.sub item 1 ((String.length item)-1)) Positive
| _ -> failwith "syntax error in pseudo Boolean solution: epected + - or x"
)
end
(String.split_on_char ' ' (String.sub line 2 ((String.length line)-2)));;
let pb_solution_to_schedule mapper pb_solution =
Array.mapi (fun i offset ->
let first = mapper.mapper_earliest_dates.(i)
and last = mapper.mapper_latest_dates.(i)
and time = ref (-1) in
for t=first to last
do
match pb_solution.(t - first + offset) with
| Positive ->
(if !time = -1
then time:=t
else failwith "duplicate time in pseudo boolean solution")
| Negative -> ()
| Unknown -> failwith "unknown value in pseudo boolean solution"
done;
(if !time = -1
then failwith "no time in pseudo boolean solution");
!time
) mapper.mapper_var_offsets;;
let pseudo_boolean_read_solution mapper channel =
let optimum = ref (-1)
and optimum_found = ref false
and solution = Array.make mapper.mapper_nr_pb_variables Unknown in
try
while true do
match input_line channel with
| "" -> ()
| line ->
begin
match String.get line 0 with
| 'c' -> ()
| 'o' ->
assert ((String.length line) >= 2);
assert ((String.get line 1) = ' ');
optimum := int_of_string (String.sub line 2 ((String.length line)-2))
| 's' -> (match line with
| "s OPTIMUM FOUND" -> optimum_found := true
| "s SATISFIABLE" -> ()
| "s UNSATISFIABLE" -> close_in channel;
raise Unschedulable
| _ -> failwith line)
| 'v' -> line_to_pb_solution solution line mapper.mapper_nr_pb_variables
| x -> Printf.printf "unknown: %s\n" line
end
done;
assert false
with End_of_file ->
close_in channel;
begin
let sol = pb_solution_to_schedule mapper solution in
sol
end;;
let recompute_max_latency mapper solution =
let maxi = ref (-1) in
for i=0 to (mapper.mapper_nr_instructions-1)
do
maxi := int_max !maxi (1+solution.(i))
done;
List.iter (fun (i, latency) ->
maxi := int_max !maxi (solution.(i) + latency)) mapper.mapper_final_predecessors;
!maxi;;
let adjust_check_solution mapper solution =
match mapper.mapper_pb_type with
| OPTIMIZATION ->
let max_latency = recompute_max_latency mapper solution in
assert (max_latency = solution.(mapper.mapper_nr_instructions));
solution
| SATISFIABILITY ->
let max_latency = recompute_max_latency mapper solution in
Array.init (mapper.mapper_nr_instructions+1)
(fun i -> if i < mapper.mapper_nr_instructions
then solution.(i)
else max_latency);;
(* let pseudo_boolean_solver = ref "/local/monniaux/progs/naps/naps" *)
(* let pseudo_boolean_solver = ref "/local/monniaux/packages/sat4j/org.sat4j.pb.jar CuttingPlanes" *)
(* let pseudo_boolean_solver = ref "java -jar /usr/share/java/org.sat4j.pb.jar CuttingPlanes" *)
(* let pseudo_boolean_solver = ref "java -jar /usr/share/java/org.sat4j.pb.jar" *)
(* let pseudo_boolean_solver = ref "clasp" *)
(* let pseudo_boolean_solver = ref "/home/monniaux/progs/CP/open-wbo/open-wbo_static -formula=1" *)
(* let pseudo_boolean_solver = ref "/home/monniaux/progs/CP/naps/naps" *)
(* let pseudo_boolean_solver = ref "/home/monniaux/progs/CP/minisatp/build/release/bin/minisatp" *)
(* let pseudo_boolean_solver = ref "java -jar sat4j-pb.jar CuttingPlanesStar" *)
let pseudo_boolean_solver = ref "pb_solver"
let pseudo_boolean_scheduler pb_type problem =
try
let filename_in = "problem.opb"
(* needed only if not using stdout and filename_out = "problem.sol" *) in
let opb_problem = open_out filename_in in
let mapper = pseudo_boolean_print_problem opb_problem problem pb_type in
close_out opb_problem;
let opb_solution = Unix.open_process_in (!pseudo_boolean_solver ^ " " ^ filename_in) in
let ret = adjust_check_solution mapper (pseudo_boolean_read_solution mapper opb_solution) in
close_in opb_solution;
Some ret
with
| Unschedulable -> None;;
let rec reoptimizing_scheduler (scheduler : scheduler) (previous_solution : solution) (problem : problem) =
if (get_max_latency previous_solution)>1 then
begin
Printf.printf "reoptimizing < %d\n" (get_max_latency previous_solution);
flush stdout;
match scheduler
{ problem with max_latency = (get_max_latency previous_solution)-1 }
with
| None -> previous_solution
| Some solution -> reoptimizing_scheduler scheduler solution problem
end
else previous_solution;;
let smt_var i = Printf.sprintf "t%d" i
let is_resource_used problem j =
try
Array.iter (fun usages ->
if usages.(j) > 0
then raise Exit) problem.instruction_usages;
false
with Exit -> true;;
let smt_use_quantifiers = false
let smt_print_problem channel problem =
let nr_instructions = get_nr_instructions problem in
let gen_smt_resource_constraint time j =
output_string channel "(<= (+";
Array.iteri
(fun i usages ->
let usage=usages.(j) in
if usage > 0
then Printf.fprintf channel " (ite (= %s %s) %d 0)"
time (smt_var i) usage)
problem.instruction_usages;
Printf.fprintf channel ") %d)" problem.resource_bounds.(j)
in
output_string channel "(set-option :produce-models true)\n";
for i=0 to nr_instructions
do
Printf.fprintf channel "(declare-const %s Int)\n" (smt_var i);
Printf.fprintf channel "(assert (>= %s 0))\n" (smt_var i)
done;
for i=0 to nr_instructions-1
do
Printf.fprintf channel "(assert (< %s %s))\n"
(smt_var i) (smt_var nr_instructions)
done;
(if problem.max_latency > 0
then Printf.fprintf channel "(assert (<= %s %d))\n"
(smt_var nr_instructions) problem.max_latency);
List.iter (fun ctr ->
Printf.fprintf channel "(assert (>= (- %s %s) %d))\n"
(smt_var ctr.instr_to)
(smt_var ctr.instr_from)
ctr.latency) problem.latency_constraints;
for j=0 to (Array.length problem.resource_bounds)-1
do
if is_resource_used problem j
then
begin
if smt_use_quantifiers
then
begin
Printf.fprintf channel
"; resource #%d <= %d\n(assert (forall ((t Int)) "
j problem.resource_bounds.(j);
gen_smt_resource_constraint "t" j;
output_string channel "))\n"
end
else
begin
(if problem.max_latency < 0
then failwith "quantifier explosion needs max latency");
for t=0 to problem.max_latency
do
Printf.fprintf channel
"; resource #%d <= %d at t=%d\n(assert "
j problem.resource_bounds.(j) t;
gen_smt_resource_constraint (string_of_int t) j;
output_string channel ")\n"
done
end
end
done;
output_string channel "(check-sat)(get-model)\n";;
let ilp_print_problem channel problem pb_type =
let deadline = problem.max_latency in
assert (deadline > 0);
let nr_instructions = get_nr_instructions problem
and nr_resources = get_nr_resources problem
and successors = get_successors problem
and predecessors = get_predecessors problem in
let earliest_dates = get_earliest_dates predecessors
and latest_dates = get_latest_dates deadline successors in
let pb_var i t =
Printf.sprintf "x%d_%d" i t in
let gen_latency_constraint i_to i_from latency t_to =
Printf.fprintf channel "\\ t[%d] - t[%d] >= %d when t[%d]=%d\n"
i_to i_from latency i_to t_to;
Printf.fprintf channel "c_%d_%d_%d_%d: "
i_to i_from latency t_to;
for t_from=earliest_dates.(i_from) to
int_min latest_dates.(i_from) (t_to - latency)
do
Printf.fprintf channel "+1 %s " (pb_var i_from t_from)
done;
Printf.fprintf channel "-1 %s " (pb_var i_to t_to);
output_string channel ">= 0\n"
and gen_dual_latency_constraint i_to i_from latency t_from =
Printf.fprintf channel "\\ t[%d] - t[%d] >= %d when t[%d]=%d\n"
i_to i_from latency i_to t_from;
Printf.fprintf channel "d_%d_%d_%d_%d: "
i_to i_from latency t_from;
for t_to=int_max earliest_dates.(i_to) (t_from + latency)
to latest_dates.(i_to)
do
Printf.fprintf channel "+1 %s " (pb_var i_to t_to)
done;
Printf.fprintf channel "-1 %s " (pb_var i_from t_from);
Printf.fprintf channel ">= 0\n"
and gen_delta_constraint i_from i_to latency =
if delta_encoding
then Printf.fprintf channel "l_%d_%d_%d: +1 t%d -1 t%d >= %d\n"
i_from i_to latency i_to i_from latency
in
Printf.fprintf channel "\\ nr_instructions=%d deadline=%d\n" nr_instructions deadline;
begin
match pb_type with
| SATISFIABILITY -> output_string channel "Minimize dummy: 0\n"
| OPTIMIZATION ->
Printf.fprintf channel "Minimize\nmakespan: t%d\n" nr_instructions
end;
output_string channel "Subject To\n";
for i=0 to (match pb_type with
| OPTIMIZATION -> nr_instructions
| SATISFIABILITY -> nr_instructions-1)
do
let early = earliest_dates.(i) and late= latest_dates.(i) in
Printf.fprintf channel "\\ t[%d] in %d..%d\ntimes%d: " i early late i;
for t=early to late
do
Printf.fprintf channel "+1 %s " (pb_var i t)
done;
Printf.fprintf channel "= 1\n"
done;
for t=0 to deadline-1
do
for j=0 to nr_resources-1
do
let bound = problem.resource_bounds.(j)
and coeffs = ref [] in
for i=0 to nr_instructions-1
do
let usage = problem.instruction_usages.(i).(j) in
if t >= earliest_dates.(i) && t <= latest_dates.(i)
&& usage > 0
then coeffs := (i, usage) :: !coeffs
done;
if !coeffs <> [] then
begin
Printf.fprintf channel "\\ resource #%d at t=%d <= %d\nr%d_%d: " j t bound j t;
List.iter (fun (i, usage) ->
Printf.fprintf channel "%+d %s " (-usage) (pb_var i t)) !coeffs;
Printf.fprintf channel ">= %d\n" (-bound)
end
done
done;
List.iter
(fun ctr ->
if ctr.instr_to < nr_instructions then
begin
gen_delta_constraint ctr.instr_from ctr.instr_to ctr.latency;
begin
if direct_encoding
then
for t_to=earliest_dates.(ctr.instr_to) to latest_dates.(ctr.instr_to)
do
gen_latency_constraint ctr.instr_to ctr.instr_from ctr.latency t_to
done
end;
begin
if reverse_encoding
then
for t_from=earliest_dates.(ctr.instr_from) to latest_dates.(ctr.instr_from)
do
gen_dual_latency_constraint ctr.instr_to ctr.instr_from ctr.latency t_from
done
end
end
) problem.latency_constraints;
begin
match pb_type with
| SATISFIABILITY -> ()
| OPTIMIZATION ->
let final_latencies = Array.make nr_instructions 1 in
List.iter (fun (i, latency) ->
final_latencies.(i) <- int_max final_latencies.(i) latency)
predecessors.(nr_instructions);
for i_from = 0 to nr_instructions -1
do
gen_delta_constraint i_from nr_instructions final_latencies.(i_from)
done;
for t_to=earliest_dates.(nr_instructions) to deadline
do
for i_from = 0 to nr_instructions -1
do
gen_latency_constraint nr_instructions i_from final_latencies.(i_from) t_to
done
done
end;
for i=0 to (match pb_type with
| OPTIMIZATION -> nr_instructions
| SATISFIABILITY -> nr_instructions-1)
do
Printf.fprintf channel "ct%d : -1 t%d" i i;
let early = earliest_dates.(i) and late= latest_dates.(i) in
for t=early to late do
Printf.fprintf channel " +%d %s" t (pb_var i t)
done;
output_string channel " = 0\n"
done;
output_string channel "Bounds\n";
for i=0 to (match pb_type with
| OPTIMIZATION -> nr_instructions
| SATISFIABILITY -> nr_instructions-1)
do
let early = earliest_dates.(i) and late= latest_dates.(i) in
begin
Printf.fprintf channel "%d <= t%d <= %d\n" early i late;
if true then
for t=early to late do
Printf.fprintf channel "0 <= %s <= 1\n" (pb_var i t)
done
end
done;
output_string channel "Integer\n";
for i=0 to (match pb_type with
| OPTIMIZATION -> nr_instructions
| SATISFIABILITY -> nr_instructions-1)
do
Printf.fprintf channel "t%d " i
done;
output_string channel "\nBinary\n";
for i=0 to (match pb_type with
| OPTIMIZATION -> nr_instructions
| SATISFIABILITY -> nr_instructions-1)
do
let early = earliest_dates.(i) and late= latest_dates.(i) in
for t=early to late do
output_string channel (pb_var i t);
output_string channel " "
done;
output_string channel "\n"
done;
output_string channel "End\n";
{
mapper_pb_type = pb_type;
mapper_nr_instructions = nr_instructions;
mapper_nr_pb_variables = 0;
mapper_earliest_dates = earliest_dates;
mapper_latest_dates = latest_dates;
mapper_var_offsets = [| |];
mapper_final_predecessors = predecessors.(nr_instructions)
};;
(* Guess what? Cplex sometimes outputs 11.000000004 instead of integer 11 *)
let positive_float_round x = truncate (x +. 0.5)
let float_round (x : float) : int =
if x > 0.0
then positive_float_round x
else - (positive_float_round (-. x))
let rounded_int_of_string x = float_round (float_of_string x)
let ilp_read_solution mapper channel =
let times = Array.make
(match mapper.mapper_pb_type with
| OPTIMIZATION -> 1+mapper.mapper_nr_instructions
| SATISFIABILITY -> mapper.mapper_nr_instructions) (-1) in
try
while true do
let line = input_line channel in
( if (String.length line) < 3
then failwith (Printf.sprintf "bad ilp output: length(line) < 3: %s" line));
match String.get line 0 with
| 'x' -> ()
| 't' -> let space =
try String.index line ' '
with Not_found ->
failwith "bad ilp output: no t variable number"
in
let tnumber =
try int_of_string (String.sub line 1 (space-1))
with Failure _ ->
failwith "bad ilp output: not a variable number"
in
(if tnumber < 0 || tnumber >= (Array.length times)
then failwith (Printf.sprintf "bad ilp output: not a correct variable number: %d (%d)" tnumber (Array.length times)));
let value =
let s = String.sub line (space+1) ((String.length line)-space-1) in
try rounded_int_of_string s
with Failure _ ->
failwith (Printf.sprintf "bad ilp output: not a time number (%s)" s)
in
(if value < 0
then failwith "bad ilp output: negative time");
times.(tnumber) <- value
| '#' -> ()
| '0' -> ()
| _ -> failwith (Printf.sprintf "bad ilp output: bad variable initial, line = %s" line)
done;
assert false
with End_of_file ->
Array.iteri (fun i x ->
if i<(Array.length times)-1
&& x<0 then raise Unschedulable) times;
times;;
let ilp_solver = ref "ilp_solver"
let problem_nr = ref 0
let ilp_scheduler pb_type problem =
try
let filename_in = Printf.sprintf "problem%05d.lp" !problem_nr
and filename_out = Printf.sprintf "problem%05d.sol" !problem_nr in
incr problem_nr;
let opb_problem = open_out filename_in in
let mapper = ilp_print_problem opb_problem problem pb_type in
close_out opb_problem;
begin
match Unix.system (!ilp_solver ^ " " ^ filename_in ^ " " ^ filename_out) with
| Unix.WEXITED 0 ->
let opb_solution = open_in filename_out in
let ret = adjust_check_solution mapper (ilp_read_solution mapper opb_solution) in
close_in opb_solution;
Some ret
| Unix.WEXITED _ -> failwith "failed to start ilp solver"
| _ -> None
end
with
| Unschedulable -> None;;
let current_utime_all () =
let t = Unix.times() in
t.Unix.tms_cutime +. t.Unix.tms_utime;;
let utime_all_fn fn arg =
let utime_start = current_utime_all () in
let output = fn arg in
let utime_end = current_utime_all () in
(output, utime_end -. utime_start);;
let cascaded_scheduler (problem : problem) =
let (some_initial_solution, list_scheduler_time) =
utime_all_fn (validated_scheduler list_scheduler) problem in
match some_initial_solution with
| None -> None
| Some initial_solution ->
let (solution, reoptimizing_time) = utime_all_fn (reoptimizing_scheduler (validated_scheduler (ilp_scheduler SATISFIABILITY)) initial_solution) problem in
begin
let latency2 = get_max_latency solution
and latency1 = get_max_latency initial_solution in
Printf.printf "postpass %s: %d, %d, %d, %g, %g\n"
(if latency2 < latency1 then "REOPTIMIZED" else "unchanged")
(get_nr_instructions problem)
latency1 latency2
list_scheduler_time reoptimizing_time;
flush stdout
end;
Some solution;;
|