â€œSoftwareâ€ Esterel Execution (work in progress)

“Software” Esterel Execution(work in progress) DumitruPOTOP-BUTUCARU Ecole des Mines de Paris tyshbe@math.tau.ac.il

loop emit S ; pause end

Start »loop emit S ; pause end

Start loop »emit S ; pause end

Start loop emit S ; »pause end

Start loop emit S ; pause end

Resume »loop emit S ; pause end

Resume loop emit S ; »pause end

Resume loop »emit S ; pause end

Resume loop emit S ; »pause end

Resume loop emit S ; pause end

Overview • Building an Intermediate Representation • Giving it a (proper) meaning, based on existing semantics • Some interesting classes of programs • Simulation and tentative optimization

What Esterel • Esterel v5 (with data) • In this paper, examples without data

signal S in emit S ; pause || present S then pause end end

signal S in emit S ; pause1 ||3 present S then pause2 end end

Organizing Actions in a Graph »signal S in emit S ; pause1 ||3 present S then pause2 end end start ·

Organizing Actions in a Graph · signal S in »emit S ; pause1 ||3 »present S then pause2 end end start enter 3 fork ·  

Organizing Actions in a Graph · signal S+ in emit S ; »pause1 ||3 »present S then pause2 end end S start enter 3 fork ·  

Organizing Actions in a Graph · signal S+ in emit S ; »pause1 ||3 present S then »pause2 end end S start enter 3 fork F S ·  T 

Organizing Actions in a Graph enter 1 · signal S+ in emit S ; pause1 ||3 present S then »pause2 end end S start enter 3 fork F S · T p 

Organizing Actions in a Graph enter 1 · signal S+ in emit S ; pause1 ||3 present S then pause2 end end S start enter 3 fork F S enter 2 · T p p

Organizing Actions in a Graph join enter 1 pause(1) signal S in emit S ; pause1 ||3 present S then pause2 end end S start enter 3 fork term(2) F pause S pause · enter 2 pause(2) T

Organizing Actions in a Graph join enter 1 pause(1) »signal S in emit S ; pause1 ||3 present S then pause2 end end S start enter 3 fork term(2) F pause S pause enter 2 pause(2) T join F inactive(1) active 1 exit 1 term(1) resume T fork · F inactive(2) active 2 term exit 3 term T exit 2 term(2)

Organizing Actions in a Graph join enter 1 pause(1) signal S- in emit S ; »pause1 ||3 present S then »pause2 end end S start enter 3 fork term(2) F pause S pause enter 2 pause(2)  T  join F F inactive(1) active 1 exit 1 term(1) · resume T fork F inactive(2) active 2 term exit 3 term T exit 2 · term(2)

Organizing Actions in a Graph join enter 1 pause(1) signal S- in emit S ; pause1 ||3 present Sthen »pause2 end end S start enter 3 fork term(2) F pause S pause enter 2 pause(2) T t  join F F inactive(1) active 1 exit 1 term(1) · resume T fork F inactive(2) active 2 term exit 3 term T exit 2 · term(2)

Organizing Actions in a Graph join enter 1 pause(1) signal S- in emit S ; pause1 ||3 present S then pause2 end end S start enter 3 fork term(2) F pause S pause enter 2 pause(2) T t t join F F inactive(1) active 1 exit 1 term(1) · resume T fork F inactive(2) active 2 term exit 3 term T exit 2 · term(2)

Organizing Actions in a Graph join enter 1 pause(1) signal S in emit S ; pause1 ||3 present S then pause2 end end S start enter 3 fork term(2) F pause S pause enter 2 pause(2) T join F inactive(1) active 1 exit 1 term(1) resume T fork F inactive(2) active 2 term exit 3 term · T exit 2 term(2)

Intermediate format • Vertices – represent computation • test • fork • join (parallel branch termination synchronizing) • emit • state/memory update action • Edges – control flow and signal dependencies S S

State representation issues • no state encoding decision yet • intuitive semantics: • one boolean variable per pause and composed statement • all false, in the beginning • enter sets it to 1, exit sets it to 0 • several possible encoding techniques • optimization issues

Semantics • SOS rules (using Cannot auxiliary functions) - dynamic • CCFG-like semantics on the intermediate graph • Translation to Constructive Circuits – fine grained, static

SOS rules k , E’ p’ p’’ E p’, p’’ are terms over statement p k  {} – completion code E:S v{0,1,} – input event E’ – emitted signal or  0 , E’ p’ p E  , E’ p’;q p;·q E

SOS rules ,S p’ p’’ E(S,) , signal S in p’end signal S+ in p’’ end E SCannot(p’) , signal S inp’end signal S- in p’ end E CONSTRUCTIVE

CCFG-based semantics • goal is sequential code generation • graph interpreted as a classical flowchart • limited class of programs • related to intermediate representation of Stephen Edwards and of the CNET group • graph acyclicity required • lesser grain • static

CCFG-based semantics ,S p’ p’’ E(S,) , signal S, in p’end signal S ,+ in p’’ end E SCannot’(p’) , signal S, + in p’end signal S+ in p’ end E SCannot’(p’) , signal S,  inp’end signal S- in p’ end E

S  Cannot(p’) • CCFG view • all the signal emission statements have been ruled out by executed tests • Constructive view • all the signal emission statements have been ruled out by either: • executed tests • not yet executed tests for which the test condition is already computed so that we can prune one of the test branches.

Acyclicity • Can be defined on both intermediate graph and associated circuit • Simple (cheap) correctness criteria for big programs • Basis of static scheduling • Problem: graph acyclicity is not the same as circuit acyclicity • what is a compilable program

Acyclicity discrepancy signal S in [ nothing || present I then nothing else present S then pause else pause end end present ]; emit S end signal term term(1) S start fork T term(2) pause I pause(2) T F S F

Acyclicity discrepancy signal S in [ nothing || present I then nothing else present S then pause else pause end end present ]; emit S end signal term S start T pause T F F

Acyclicity discrepancy • Possible solutions: • splitting the synchronizers with problems, and so borrow some expressive power from circuit semantics • duplicate cycle code based on the trigger or the problem test (improve the CCFG model)

Compilable Program Classes acyclic circuit acyclic CCFG

Static analysis • Graph arc removal in the circuit • Results hold in CCFG, if the result is acyclic • Problem: causality • Some particular simplifications proved, like erasing dependencies based on state incompatibility

Static analysis • What I would like to do term term(1) S start fork T term(2) pause I pause(2) T F S · F

Compilable Program Classes acyclic after simplif. acyclic circuit acyclic CCFG

Compilable Program Classes correct programs acyclic after simplif. acyclic circuit acyclic CCFG

Cyclic specifications • Proving correctness – not my goal • Execution (Simulation)

Cyclic specifications • 3-valued simulation • Resynthesis of cyclic parts

â€œSoftwareâ€ Esterel Execution (work in progress)