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Commit 6083f8e5 authored by Felipe Cerqueira's avatar Felipe Cerqueira
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Fix comments in EDF comp

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bertogna_edf_comp.v
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......@@ -10,7 +10,7 @@ Module ResponseTimeIterationEDF.
ResponseTimeAnalysisEDF.
(* In this section, we define the algorithm of Bertogna and Cirinei's
response-time analysis for FP scheduling. *)
response-time analysis for EDF scheduling. *)
Section Analysis.
Context {sporadic_task: eqType}.
......@@ -36,8 +36,8 @@ Module ResponseTimeIterationEDF.
total_interference_bound_edf task_cost task_period task_deadline tsk rt_bounds delta.
(* ..., which yields the following response-time bound. *)
Let response_time_bound (rt_bounds: seq task_with_response_time)
(tsk: sporadic_task) (delta: time) :=
Definition edf_response_time_bound (rt_bounds: seq task_with_response_time)
(tsk: sporadic_task) (delta: time) :=
task_cost tsk + div_floor (I rt_bounds tsk delta) num_cpus.
(* Also note that a response-time is only valid if it is no larger
......@@ -55,7 +55,7 @@ Module ResponseTimeIterationEDF.
Definition update_bound (rt_bounds: seq task_with_response_time)
(pair : task_with_response_time) :=
let (tsk, R) := pair in
(tsk, response_time_bound rt_bounds tsk R).
(tsk, edf_response_time_bound rt_bounds tsk R).
(* To compute the response-time bounds of the entire task set,
We start the iteration with a sequence of tasks and costs:
......@@ -149,7 +149,7 @@ Module ResponseTimeIterationEDF.
rewrite iterS in IN.
move: IN => /mapP IN; destruct IN as [x IN EQ].
unfold update_bound in EQ; destruct x; inversion EQ.
by unfold response_time_bound; apply leq_addr.
by unfold edf_response_time_bound; apply leq_addr.
}
Qed.
......@@ -195,7 +195,7 @@ Module ResponseTimeIterationEDF.
set prev_state := iter step edf_rta_iteration (initial_state ts).
fold prev_state in IN, IHstep.
specialize (IHstep tsk IN); des.
exists (response_time_bound prev_state tsk R).
exists (edf_response_time_bound prev_state tsk R).
by apply/mapP; exists (tsk, R); [by done | by f_equal].
}
Qed.
......@@ -253,7 +253,10 @@ Module ResponseTimeIterationEDF.
End MonotonicityOfInterferenceBound.
(* In this section, we prove the convergence of the RTA procedure. *)
(* In this section, we prove the convergence of the RTA procedure.
Since we define the RTA procedure as the application of a function
a fixed number of times, this translates into proving that the value
of the iteration at (max_steps ts) is equal to the value at (max_steps ts) + 1. *)
Section Convergence.
(* Consider any valid task set. *)
......@@ -408,7 +411,7 @@ Module ResponseTimeIterationEDF.
last by rewrite size_zip 2!size_map -SIZE minnn in LTi.
rewrite (nth_map p0);
last by rewrite size_zip 2!size_map SIZE minnn in LTi.
unfold update_bound, response_time_bound; desf; simpl.
unfold update_bound, edf_response_time_bound; desf; simpl.
rename s into tsk_i, s0 into tsk_i', n into R_i, n0 into R_i', Heq into EQ, Heq0 into EQ'.
assert (EQtsk: tsk_i = tsk_i').
{
......@@ -567,7 +570,8 @@ Module ResponseTimeIterationEDF.
by unfold edf_rta_iteration.
Qed.
(* Otherwise, if the iteration converged at an earlier step, then it remains stable. *)
(* Otherwise, if the iteration reached a fixed point before (max_steps ts), then
the value at (max_steps ts) is still at a fixed point. *)
Lemma bertogna_edf_comp_f_converges_early :
(exists k, k <= max_steps ts /\ f k = f k.+1) ->
f (max_steps ts) = f (max_steps ts).+1.
......@@ -757,14 +761,13 @@ Module ResponseTimeIterationEDF.
End DerivingContradiction.
(* Using the lemmas above, we prove that edf_rta_iteration remains stable
(* Using the lemmas above, we prove that edf_rta_iteration reaches a fixed point
after (max_steps ts) iterations, ... *)
Lemma edf_claimed_bounds_converges_helper :
forall rt_bounds,
edf_claimed_bounds ts = Some rt_bounds ->
valid_sporadic_taskset task_cost task_period task_deadline ts ->
iter (max_steps ts) edf_rta_iteration (initial_state ts)
= iter (max_steps ts).+1 edf_rta_iteration (initial_state ts).
f (max_steps ts) = f (max_steps ts).+1.
Proof.
intros rt_bounds SOME VALID.
unfold valid_sporadic_taskset, is_valid_sporadic_task in *.
......@@ -856,6 +859,7 @@ Module ResponseTimeIterationEDF.
have CONV := edf_claimed_bounds_converges_helper rt_bounds.
unfold edf_claimed_bounds in *; desf.
exploit (CONV); [by done | by done | intro ITER; clear CONV].
unfold f in ITER.
cut (update_bound (iter (max_steps ts)
edf_rta_iteration (initial_state ts)) (tsk,R) = (tsk, R)).
......@@ -953,7 +957,7 @@ Module ResponseTimeIterationEDF.
job_misses_no_deadline job_cost job_deadline rate sched.
(* In the following theorem, we prove that any response-time bound contained
in fp_claimed_bounds is safe. The proof follows by direct application of
in edf_claimed_bounds is safe. The proof follows by direct application of
the main Theorem from bertogna_edf_theory.v. *)
Theorem edf_analysis_yields_response_time_bounds :
forall tsk R,
......@@ -979,7 +983,7 @@ Module ResponseTimeIterationEDF.
Hypothesis H_test_succeeds: edf_schedulable ts.
(*... no task misses its deadline. *)
Theorem taskset_schedulable_by_fp_rta :
Theorem taskset_schedulable_by_edf_rta :
forall tsk, tsk \in ts -> no_deadline_missed_by_task tsk.
Proof.
unfold no_deadline_missed_by_task, task_misses_no_deadline,
......@@ -1021,11 +1025,11 @@ Module ResponseTimeIterationEDF.
(* For completeness, since all jobs of the arrival sequence
are spawned by the task set, we conclude that no job misses
its deadline. *)
Theorem jobs_schedulable_by_fp_rta :
Theorem jobs_schedulable_by_edf_rta :
forall (j: JobIn arr_seq), no_deadline_missed_by_job j.
Proof.
intros j.
have SCHED := taskset_schedulable_by_fp_rta.
have SCHED := taskset_schedulable_by_edf_rta.
unfold no_deadline_missed_by_task, task_misses_no_deadline in *.
apply SCHED with (tsk := job_task j); last by done.
by apply H_all_jobs_from_taskset.
......
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