Implementing Constructive Synchronous Programs on

POLIS CFSM Networks

G.BerryE.Sentovich

Ecole des Mines de Paris / INRIACadence Berkeley Labs

Concurrency :The Compositionality Principle

P

Q

R

P || Q

P

Q

R

td

t’

t’’

t’’ = t + d + t’t’’ ~ t ~ d ~ t’t ~ t + t

3 principal solutions :

• t arbitrary asynchrony

• t = 0 synchrony

• t fixed or bounded propagation

t arbitrary : Brownian Motion

Chemical reaction

H+

H+

Cl_ H+

Cl_

Cl_

HCL

HCL

HCL

H+

Internet RoutingH+ Cl

_HCL+

t = 0 : Perfect Synchrony

Synchronous = zero delay Communication by instantaneous broadcast Concurrency + determinism Reference: Newtonian Mechanics

T fixed or bounded : Vibration

Propagation of Sound Light Heat Wind

TRY PASS

REQ OK

GET_TOKEN PASS_TOKEN

Synchronous Digital Circuits

OK = REQ and GOPASS = not REQ and GOGO = TRY or GET_TOKENPASS_TOKEN = reg(GET_TOKEN)

GO

Synchronous view : magically solve equations 0-delay Vibration view : propagate voltages speed of light

Acyclic circuits : stabilization in predictable time

Wait long enough, same result as 0-delay !

module Sender :

type Messageinput MESSAGE : Message;output SEND : Message, SENT;input MS, ACK;

loop await MESSAGE ; abort every 100 MS do emit SEND (?MESSAGE) end every when ACK ; emit SENTend loopend module

POLIS : a GALS modelGlobally Asynchronous Locally Synchronous

CFSM

Input buffer

Input Buffer = presence + value

- A CFSM is runnable when an input comes in- Several inputs may come in before actual run- Presence / absence can be tested for each input- Value can be accessed for present signals- Transition in 0-delay- Output broadcast by the network, with delay- 1-place buffers can be overwritten

CFSM

• Synchronous programs- nice semantics / mathematics- concurrency + deterministic - optimization + verification feasible- limited in scope : compact systems

• CFSM networks- POLIS implementation model- good for hardware / software codesign- formal semantics, but can be wild- semantics purely operational (scheduler)

Can we implement synchronous languages on CFSM networks?

• Run large-scale synchronous programs on networks• Study classes of “well-behaved” CFSM networks• Study progressive relaxation of synchrony

Previous work : P. Caspi and A. Girault E,. Ledinot et.al., Dassault Aviation

Constructive Circuits

Esterel -> circuits, combinational cycles allowed

3 kinds of cyclic circuits:

- Well-behaved X = I and Y Y = not I and X

- Outlaws X = X X = not X

Y

X

I

ToBe = ToBe or not ToBe

ToBe

Strange Circuits

Unique Boolean solutionNo electrical stabilization for some delays

Electrons cannot reason by contradiction=> Constructive Boolean Logic

Fact : E=0 or E=1

E=0E and F = 0

F=0E and F = 0

E=1 F=1E and F = 1

E=0not E = 1

E=1not E = 0

X=E E=bX=b

Constructive Boolean Logic

E or not E = 1 not provable unless E=0 or E=1 FACTS! NO GUESS!

X

Y

I

J

X = I and not YY = J and not X

OK unless I = J = 1

Running Example

X = I and not YY = J and not X

(1) I=0(2) J=1(3) X=0 from (1)(4) not X=1 from (3)(5) Y=1 from (2) and (4)

(1) I=1(2) J=0(3) Y=0 from (2)(4) not Y=1 from (3)(5) X=1 from (2) and (4)

No proof of X and Y if I=J=1

Topological ordering : data independentProof ordering : data dependent

Proofs

Theorem (Berry-Shiple) : equivalence of 3 views

• Constructive semantics convergence = provability of a fact for each wire

• Delay-independent electrical behavior convergence = stabilization for any delay assignment

• Scott’s denotational semantics - 3-valued logic solve equation by least fixpoint in { , 0, 1} convergence = all wire values in {0,1} => compositionality

T

X = I and not YY = J and not X

I=0 . J=1 X : 2 Y : 2

I=0 . J=1 . X=0 X : 1 Y : 2

I=0 . J=1 . X=0 X : 1 Y : 1

I=0 . J=1 . X=0 . Y=1 X : 1 Y : 0

I=0 . J=1 . X=0 X : 1 Y : 0

I=0 . J=1 . X=0 . Y=1 X : 0 Y : 0

Esterel v5 Algorithm

X = I and not YY = J and not X

I=0 . J=0 X : 2 Y : 2

I=0 . J=0 . X=0 X : 1 Y : 2

I=0 . J=0 . X=0 . Y=0 X : 1 Y : 1

I=0 . J=0 . X=0 . Y=0 X : 0 Y : 0

I=0 . J=0 . X=0 . Y=0 X : 1 Y : 0

Esterel v5 Algo.

• Encode facts in CFSM events• Use one CFSM per gate• Use the network to propagate the facts

POLIS Implementation

Combinational gates -> sequential CFSMsSynchronous cycle -> full network execution

Constructive and not gate as a CFSM - v1

AB

C

input A: boolean, B : boolean;output C : boolean;[ await A; if not ?A then emit C(false) end|| await B; if ?B then emit C(false) end];if ?A and not ?B then emit C(true) end

signal Caux : combine boolean with and in [ await A; if not ?A then emit Caux(false) end || await B; if ?B then emit Caux(false) end ]; if ?A and not ?B then emit Caux(true) end|| await Caux; emit C(?Caux)end signal

V2 : protecting double emission

Given an input assignment, the network builds a proof

• Each gate buffer is written at most once - no buffer overwriting - bounded time (linear)

• Termination when no more runnable CFSM - #events = #fanins -> constructive - else non-constructive

• Any scheduling gives the right answer!

But works only for one global tick!

Macro-cycles - give synchronous events successively - logical timing by stream ordering

a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 c0 c1 c2 c3 c4

Four basic solutions :

1. Wait long enough (as for circuits)

2. Compute explicit termination signal

3. Let the scheduler report termination

4. Use a flow control protocol

-> pipelining

Flow Control

AB

C

A_Free

B_FreeC_Free

loop signal Caux : combine boolean with and in [ await A; emit A_Free; if not ?A then emit Caux(false) end || await B; emit B_Free; if ?B then emit Caux(false) end ]; if ?A and not ?B then emit Caux(true) end || [ await Caux || await C_Free ] ; emit C(?Caux) end signalend loop

V3 : flow control

A gate resets for next tick when it has received all its input. No additional protocol needed!

A=0 A_FreeC_Free C=0B=1 B_Free loop

A=1 A_FreeC_Free B=1 B_Free C=1 loop

Automatic Gate Reset

Pipelining

Problem : out-of-order data for next cycle

A(0) -> A_FreeC_Free -> C(0)A(1) ->B(1) -> B_Free

3. Tell the scheduler that only arrival of B matters => sensitivity lists

1. Memorize A(1) in the CFSM - heavy!

2. Write back 1 in the A buffer but gate immediately made runnable again!

module AndNot :

% Boolean IOinput A : boolean, B : boolean;output X : boolean;

% Flow control IOoutput A_Free, B_Free;input C_Free;

% Scheduling IOoutput A_Wait, B_Wait;output C_Free_Wait;

loop signal Caux : combine boolean with and in < handle A and B > || < handle C > end signalend loop

[ abort sustain A_Wait when A; emit A_Free; if not ?A then emit Caux(false) end|| abort sustain B_Wait when B; emit B_Free; if ?B then emit Caux(false) end];if ?A and not ?B then emit Caux(true)

[ await Caux|| abort sustain C_Free_Wait when C_Free];emit C(?Caux)

Temporary Summary

• One can implement a constructive circuit in POLIS by translating each gate into a CFSM

• Therefore, on can implement Esterel by first translating Esterel programs into gates

• Of course, this is inefficient : too fine grain

• But, we did not use compositionality yet!

Using Compositionality

• Any network of gates acts just as a gate• Group gates either synchronously, using v5 algo., or asynchronously, in the network• Adjust grouping according to geographical and performance requirements

Optimisation

• Group messages going from A to B• Precompute the transitive effect of messages

X=0

Y=1

X=0

Y=1

Summary

• Constructive logic semantics facts as information quanta• Propagate facts synchronously in CFSM nodes asynchronously in the network• Correct by construction• Applicable to (some) real problems• A step to mixed 0-delay / vibration language design

Termination signal

X

Y

I

J

DONE

Too expensiveNon-local