a framework to quantify the overestimations of static wcet … · 2016. 9. 30. · a framework to...

A Framework to Quantify the Overestimations of Static WCET Analysis Hugues Cassé, Haluk Ozaktas, Christine Rochange

15th Workshop on WCET Analysis – July 7, 2015

Static WCET analysis

source code binary code compiler

B

C D

E

A

CFG building

flow analysis

low-‐level analysis

WCET computa@on WCET

Static WCET analysis Quantifying pessimism

Example: cache analysis Future work

feasible paths

local WCETs

Static WCET analysis Static WCET analysis Quantifying pessimism


source code binary code compiler

B

C D

E

A

CFG building

flow analysis

WCET computa@on WCET

linear p

rogram

max T=xA.wA + xB.wB+ xC.wC + xD.wD + xE.wE xA = 1 xA = xAB xB = xAB + xEB xB = xBC + xBD xC = xBC xC = xCE xD = xBD xD = xDE xE = xCE + xDE xE = 1 + xEB

xEB ≤ 255; xBC ≤ 0.5 xB;


wA = …; wB = …; wC = …; wD = …; wE = …;

Implicit Path Enumeration Technique (IPET)

"Static analysis overestimates WCET" Static WCET analysis Quantifying pessimism


distribution

execution time

real WCET static WCET estimation

pessimism

observed execution times

pessimism ?



flow analysis low-‐level analysis

WCET computa@on



flow analysis

WCET computa@on

P T = all the CFG paths

B

C D

E

A

source code

binary code user annotations

P + = P T – known-to-be-infeasible paths

P r = really-feasible paths

longest paths



flow analysis low-‐level analysis

WCET computa@on




WCET computa@on

initial hardware state

H T = all the theoretically-possible states H + = H T – known-to-be-infeasible states

H r = really-feasible states





WCET computa@on

C T = all the theoretically-possible scenarios C + = C T – known-to-be-infeasible scenarios

C r = really-feasible scenarios

B

C D

E

A

Static analysis determines local WCETs (basic blocks) -  abstracts (over-approximates) hardware states -  considers all "maybe-possible" scenarios

Quantifying the pessimism of WCET estimates

Real WCET Static WCET estimation

§  upper bound on the WCET:

§  lower bound on the WCET:

Static WCET analysis Quantifying pessimism Example: cache analysis

Future work

U = WCET+ - WCET-



Future work

flow analysis

WCET computa@on

P T = all the CFG paths

source code

binary code user annotations

P + = P T – known-to-be-infeasible paths

P r = really-feasible paths

P - = known-to-be-feasible paths



Future work


WCET computa@on

initial hardware state

H T = all the theoretically-possible states H + = H T – known-to-be-infeasible states

H r = really-feasible states

H - = known-to-be-feasible states




Future work


WCET computa@on

C T = all the theoreticaly-possible scenarios C + = C T – known-to-be-infeasible scenarios

C r = really-feasible scenarios

B

C D

E

A

C - = known-to-be-feasible scenarios or scenarios that cannot produce an execution time that is longer than WCET r


Real WCET Static WCET estimation

§  upper bound on the WCET:

§  lower bound on the WCET:


Future work

U = WCET+ - WCET-

Example: pessimism of cache analysis

Background on static cache analysis



B

C D

E

A

§  abstract interpretation §  cache state = ages of cache blocks (0..A)

S

S’ Update()

S’’ S’’’ Join() §  May and Must analyses

§  categories assigned to cache accesses -  AlwaysHit -  AlwaysMiss -  Persistent -  NotClassified

D


Low-level analysis scenarios §  C T = {mmm, mmh,mhm, mhh,

hmm, hmh, hhm, hhh}

§  C + = {hmm, hmh, hhm, hhh}

§  C r = {hmh, hhm, hhh}

§  C - = {hhh}



a1 a2 a3

AlwaysHit

NotClassified

basic block

NotClassified


Experimental methodology §  hardware platform (model):

²  MPC5554-like pipeline ²  4 KB, 4-way associative LRU instruction & data caches

–  infinite write buffer §  benchmarks from the TACLeBench collection (MediaBench)




Experimental methodology §  hardware platform (model):

²  MPC5554-like pipeline ²  4 KB, 4-way associative LRU instruction & data caches

–  infinite write buffer §  benchmarks from the TACLeBench collection (MediaBench) §  WCET analysis with the OTAWA toolset (WCET +)

²  we added the computation of WCET -




Global results (instruction + data caches)




Uncertainty of instruction cache analysis §  with pessimistic data cache analysis




Uncertainty of data cache analysis §  with pessimistic instruction cache analysis



Summary

Framework §  static analysis provides a guaranteed WCET upper bound (WCET+) §  we can compute a lower bound on the WCET (WCET-) §  the real WCET must be between WCET- and WCET+

²  uncertainty U = WCET+ - WCET-

Possible interpretations of U §  is my WCET estimation tight?

²  if not, it might be due to a poor analysis or to a poorly coded application

§  how do two analyses of the same component compare? §  which parts of the application would deserve a more precise analysis?

a framework to quantify the overestimations of static wcet … · 2016. 9. 30. · a framework to...

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