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Istituto di Tecnologie della Comunicazione dell’Informazione e della Percezione Explicit Preemption Point (EPP) placement for conditional code Marko Bertogna.

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Presentation on theme: "Istituto di Tecnologie della Comunicazione dell’Informazione e della Percezione Explicit Preemption Point (EPP) placement for conditional code Marko Bertogna."— Presentation transcript:

1 Istituto di Tecnologie della Comunicazione dell’Informazione e della Percezione Explicit Preemption Point (EPP) placement for conditional code Marko Bertogna and Nathan Fisher RTSOPS’11 July 5, 2011, Porto, Portugal

2 © 2011 Scuola Superiore Sant’Anna Deferred-preemption model Introduced by Burns in 1994 –a.k.a. Cooperative scheduling or Fixed Preemption Point (FPP) model Tasks are divided into a sequence of statically defined non-preemptive chunks Preemptions can take place only at chunk’s boundaries (Preemption Points) JHJH JLJL t

3 © 2011 Scuola Superiore Sant’Anna Selecting Preemption Points A task has a set of Possible Preemption Points (PPP), each with a corresponding preemption cost Only a subset of them is selected to become an Effective Preemption Point (EPP) Which EPPs have to be selected to minimize the WCET without affecting schedulability? Preemption cost PPP

4 © 2011 Scuola Superiore Sant’Anna Existing results Upper bound on the maximum non-preemptive region Q i allowed for each task  i Bertogna, Baruah TII’10: EDF case (tight) Yao et al. RTSJ’11: FP case Algorithm for the optimal selection of EPPs (ECRTS’11) –Conditional branches and loops assumed to be entirely contained inside a non-preemptive region (basic block)

5 © 2011 Scuola Superiore Sant’Anna Example Tasks composed of a sequence of Basic Blocks (BB) separated by a PPP 222123 12 331 Q=8 BB 1 BB 2 BB 3 BB 4 BB 5 BB 6 PPP 1 PPP 2 PPP 3 PPP 4 PPP 5 WCET of the BB Preemption cost of the PPP Constraint on the maximum distance between two consecutive EPPs

6 © 2011 Scuola Superiore Sant’Anna Example Which PPP to activate? 12 3 3 1 Q=8 222123 PPP 1 PPP 2 PPP 3 PPP 4 PPP 5 0

7 © 2011 Scuola Superiore Sant’Anna Example Which PPP to activate? If all PPPs are activated, the overall WCET is 22 2+1+2+2+2+3+1+3+2+1+3 = 22 12 3 3 1 Q=8 222123 PPP 1 PPP 2 PPP 3 PPP 4 PPP 5 0

8 © 2011 Scuola Superiore Sant’Anna Example Which PPP to activate? A possibility is to activate only one point (PPP 4 ) with a resulting WCET of 15 2+2+2+1+3+2+3 = 15 12 3 3 1 Q=8 222123 PPP 1 PPP 2 PPP 3 PPP 4 PPP 5 0

9 © 2011 Scuola Superiore Sant’Anna Example Which PPP to activate? The optimal strategy is to activate two points (PPP 1 and PPP 5 ) obtaining a WCET of 14 2+1+2+2+1+2+1+3 = 14 12 3 3 1 Q=8 222123 PPP 1 PPP 2 PPP 3 PPP 4 PPP 5 0

10 © 2011 Scuola Superiore Sant’Anna Considerations The EPP selection algorithm evaluates each PPP at most once Complexity linear in the number of PPPs –Memory requirement: O(N+Q) –Computational complexity: O(N) Does not work if a conditional branch spans more than one basic block

11 © 2011 Scuola Superiore Sant’Anna Problem Tasks include lots of conditional branches! A conditional branch might span a big share of the task code: In these cases the deferred preemption model shows its limits (degenerates to non-preemptive) if then else endif … … Start End

12 © 2011 Scuola Superiore Sant’Anna Open problem How to select which EPP to activate for a (DAG- based) task structure including conditional branches? Start End PPP … BB PPP … Q

13 © 2011 Scuola Superiore Sant’Anna Naïve idea Treating each branch separately does not work Example: 3 41 1 2 12 Start 33 End 13 1 1 3 5 5 1 1 3 1 Q = 8

14 © 2011 Scuola Superiore Sant’Anna Naïve idea Applying the linear method to the upper branch activates the red EPPs 3 41 1 2 12 Start 33 End 13 1 1 3 5 5 1 1 3 1 Q = 8

15 © 2011 Scuola Superiore Sant’Anna Naïve idea Applying the linear method to the upper branch activates the red EPPs Applying the linear method to the lower branch activates the green EPPs 3 41 1 2 12 Start 33 End 13 1 1 3 5 5 1 1 3 1 Q = 8

16 © 2011 Scuola Superiore Sant’Anna Naïve idea The optimal solution uses both red and green EPPs 3 41 1 2 12 Start 33 End 13 1 1 3 5 5 1 1 3 1 Q = 8

17 © 2011 Scuola Superiore Sant’Anna Open problem(s) Algorithm that optimally selects which EPP to activate in a task structure including conditional branches, such that –Distance between two consecutive EPPs is at most Q –Overall WCET is minimized How to consider loops? Which task structures have to be considered for strictly structured programming languages –i.e., those including only (see Böhm-Jacopini theorem) Sequential execution Conditional execution Iteration

18 © 2011 Scuola Superiore Sant’Anna thank you! marko@sssup.it

19 © 2011 Scuola Superiore Sant’Anna Example For the 5 th PPP, the beginning of the task cannot be the preceding EPP (2+2+2+1+2 > Q) 12 3 3 1 Q=8 222123 PPP 1 PPP 2 PPP 3 PPP 4 PPP 5 2 46 7 0 Min WCET What are the possible candidates?

20 © 2011 Scuola Superiore Sant’Anna Example What are the possible candidates for the preceding EPP of the 5 th PPP? 12 3 3 1 Q=8 222123 PPP 1 PPP 2 PPP 3 PPP 4 PPP 5 2 46 7 0 Min WCET Possible candidates: PPP 0 : 2+2+2+1+2=8 ≤ Q  NO PPP 1 : 1+2+2+1+2=8 ≤ Q  OK

21 © 2011 Scuola Superiore Sant’Anna Example What are the possible candidates for the preceding EPP of the 5 th PPP? 12 3 3 1 Q=8 222123 PPP 1 PPP 2 PPP 3 PPP 4 PPP 5 2 46 7 0 Min WCET Possible candidates: PPP 0 : 2+2+2+1+2=8 ≤ Q  NO PPP 1 : 1+2+2+1+2=8 ≤ Q  OK PPP 2 : 2+2+1+2=7 ≤ Q  OK

22 © 2011 Scuola Superiore Sant’Anna Example What are the possible candidates for the preceding EPP of the 5 th PPP? 12 3 3 1 Q=8 222123 PPP 1 PPP 2 PPP 3 PPP 4 PPP 5 2 46 7 0 Min WCET Possible candidates: PPP 0 : 2+2+2+1+2=8 ≤ Q  NO PPP 1 : 1+2+2+1+2=8 ≤ Q  OK PPP 2 : 2+2+1+2=7 ≤ Q  OK PPP 3 : 3+1+2=6 ≤ Q  OK

23 © 2011 Scuola Superiore Sant’Anna Example What are the possible candidates for the preceding EPP of the 5 th PPP? 12 3 3 1 Q=8 222123 PPP 1 PPP 2 PPP 3 PPP 4 PPP 5 2 46 7 0 Min WCET Possible candidates: PPP 0 : 2+2+2+1+2=8 ≤ Q  NO PPP 1 : 1+2+2+1+2=8 ≤ Q  OK PPP 2 : 2+2+1+2=7 ≤ Q  OK PPP 3 : 3+1+2=6 ≤ Q  OK PPP 4 : 3+2=5 ≤ Q  OK

24 © 2011 Scuola Superiore Sant’Anna Example Which one minimizes the WCET up to PPP 5 ? 12 3 3 1 Q=8 222123 PPP 1 PPP 2 PPP 3 PPP 4 PPP 5 2 46 7 0 Min WCET Potential WCET of [0, PPP 5 ]: PPP 1 : 2+1+2+2+1+2=10 PPP 2 : 4+2+2+1+2=11 PPP 3 : 6+3+1+2=12 PPP 4 : 7+3+2=12 X

25 © 2011 Scuola Superiore Sant’Anna Example Which one minimizes the WCET up to PPP 5 ? 12 3 3 1 Q=8 222123 PPP 1 PPP 2 PPP 3 PPP 4 PPP 5 2 46 7 0 Min WCET Potential WCET of [0, PPP 5 ]: PPP 1 : 2+1+2+2+1+2=10 PPP 2 : 4+2+2+1+2=11 PPP 3 : 6+3+1+2=12 PPP 4 : 7+3+2=12 X

26 © 2011 Scuola Superiore Sant’Anna Example PPP 1 is the best preceding EPP for PPP 5 12 3 3 1 Q=8 222123 PPP 1 PPP 2 PPP 3 PPP 4 PPP 5 2 46 7 0 Min WCET 10

27 © 2011 Scuola Superiore Sant’Anna Example Reaching the end of the task 12 3 3 1 Q=8 222123 PPP 1 PPP 2 PPP 3 PPP 4 PPP 5 2 46 7 0 Min WCET 10 Only two potential candidates: PPP 4 : 7+3+2+3=15 PPP 5 : 10+1+3=14 End

28 © 2011 Scuola Superiore Sant’Anna Example PPP 5 is the best preceding EPP of the End point, i.e., it is the last one to be activated 12 3 3 1 Q=8 222123 PPP 1 PPP 2 PPP 3 PPP 4 PPP 5 2 46 7 0 Min WCET 10 End 14

29 © 2011 Scuola Superiore Sant’Anna Example PPP 1 is the best preceding EPP of PPP 5 12 3 3 1 Q=8 222123 PPP 1 PPP 2 PPP 3 PPP 4 PPP 5 2 46 7 0 Min WCET 10 End 14

30 © 2011 Scuola Superiore Sant’Anna Example The start of the task is the best preceding EPP of PPP 1 12 3 3 1 Q=8 222123 PPP 1 PPP 2 PPP 3 PPP 4 PPP 5 2 46 7 0 Min WCET 10 End 14

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