1. Processor Pipelines and Their Properties for Static WCET Analysis Jakob Engblom and Bengt Jonsson Presented by Kiran Seth

3. Goals of paper Define mathematical model of pipeline behavior, to study Long Timing Effects (LTE). Examples of LTE. Conditions for LTE to occur.

4. Timing Model Program is set of Nodes connected by Edges. A Node can be one or more instructions. Hardware is deterministic (so same sequence of instructions gives same execution time). Multiple nodes are used to model variability.

7. Negative timing effects – potential savings in execution time. Ignoring means WCET less tight. Positive timing effects – add to the execution time. Ignoring means underestimating WCET. BAD NEWS!!! Long timing effects (LTE) – When effects of instruction can be seen further into the pipeline. Positive LTE must be accounted for.

9. Paper concentrates on explaining cause and effect of LTE. Many theorems to the effect. A pipeline model is also given to explain and create better examples of the LTE.

10. Pipeline Model Pipeline model captures timing behavior by temporal constraints. Each instruction I i is seen as a sequence r 1 i …r n i of resource requirements. r j i time instruction i wants in stage j. p j i is time when instruction i enters stage j.

11. Pipeline Model Constraints For sequence of m instructions in a n-stage pipeline - (1<= i <=m, 1<=j <=n) Instruction cannot enter next stage before current stage is done. Next instruction cannot enter pipeline till previous instruction is done. Other Constraints-

12. Graphical Representation of Pipeline Model Use a weighted directed acyclic graph. Execution time T(I 1..I m ) is maximal distance from p 1 1 to some end point in constraint system.

13. Theorem 1 For a single in-order pipeline, a timing effect  I1...Im <>0 can occur for a sequence of instructions I 1...I m, m >= 3 only if I 1 stalls the execution of some instruction in I 2...I m. Means that if first instruction stalls one of its successors OR first instruction reaches past I 2...I m-1, we will have a LTE over I 1...I m.

14. Theorem 2 For a sequence of instructions I 1... I m,m>=2, executing on a pipeline with the CCP property,  I 1...I m <= 0. Crossing Critical Path (CCP) implies that pipeline is without positive LTE.

15. Theorem 3 A single in-order pipeline has the CCP property if each constraint introduced by branches and data dependences either - a) occurs between adjacent instructions, or b)is subsumed by the basic constraints. This theorem characterizes the pipelines with CCP properties.

16. Theorem 4-5 For in-order pipelines, no timing anomalies can appear when we increase the execution time of an instruction. For in-order pipelines, no timing anomalies can appear when we decrease the execution time of an instruction.

17. More about LTE’s Parallel pipelines cause positive LTE. In general it is not possible to provide a bound on the length of sequences of instructions that can exhibit LTE.

18. Results - Safety of WCET Analysis Safely ignore negative LTEs. Make sure no positive LTEs are missed. Even simple pipelines can exhibit LTEs across arbitrary numbers of instructions. In-order single-issue processors don’t have any timing anamolies.