A Concurrent Matrix A Concurrent Matrix Transpose Algorithm, Transpose Algorithm, The The

VerificationVerification

PresentedPresented

byby

Pourya JafariPourya Jafari

Algorithm Review: Determine Algorithm Review: Determine preprocessingpreprocessing

Intra-process shift = row indexIntra-process shift = row index

After Intra-process; every column index is After Intra-process; every column index is equal to original row index equal to original row index j” = j + i’ = i j” = j + i’ = i i’: Row index after pre-processing i’ = i - Li’: Row index after pre-processing i’ = i - L i - L + j = i i - L + j = i

Now we can determine preprocess shift-up L = - j Now we can determine preprocess shift-up L = - j

Algorithm Review: Determine Post Algorithm Review: Determine Post ProcessingProcessing

Change of indices so farChange of indices so far (i - j, j) → (i - j, i - j + j) → (i - j, i) = (m, n)(i - j, j) → (i - j, i - j + j) → (i - j, i) = (m, n)

One operation to change row index to jOne operation to change row index to j n - m = (i - (i - j))= jn - m = (i - (i - j))= j

Algorithm Review: : All StepsAlgorithm Review: : All Steps

Pre-process inside Pre-process inside each threadeach thread Shift rowsShift rows

Intra-process/thread Intra-process/thread communicationcommunication Shift columnsShift columns

Post-process inside Post-process inside each threadeach thread Shift rows againShift rows again

0000 0101 0202 0303

1010 1111 1212 1313

2020 2121 2222 2323

3030 3131 3232 3333

0000 1010 2020 3030

0101 1111 2121 3131

0202 1212 2222 3232

0303 1313 2323 3333

0000 1111 2222 3333

0303 1010 2121 3232

0202 1313 2020 3131

0101 1212 2323 3030

0000 1111 2222 3333

1010 2121 3232 0303

2020 3131 0202 1313

3030 0101 1212 2323

0000 1111 2222 3333

1010 2121 3232 0303

2020 3131 0202 1313

3030 0101 1212 2323

UML DiagramUML Diagram

-PID : int-N : int-ch0 : One2OneChannel-ch1 : Any2OneChannel-ch2 : One2AnyChannel

CProcess

+run()

CSProcess

+In()+Out()

One2OneChannel

+In()+Out()

One2AnyChannel

+In()+Out()

Any2OneChannel

-N : int-ch1 : Any2OneChannel-ch2 : One2AnyChannel

MProcess -N : int-ch0 : One2OneChannel-ch1 : Any2OneChannel-ch2 : One2AnyChannel-CPs : CSProcess

Launcher

CProcess: Heart of ConcurrencyCProcess: Heart of Concurrency

Might send/receive multiple itemsMight send/receive multiple items Determines the indices that need to be shifted Determines the indices that need to be shifted Packs them in form of a messagePacks them in form of a message Sends the message to the next CProcess and Sends the message to the next CProcess and

receive from the previous process in the shift receive from the previous process in the shift chainchain

Unpack the received messageUnpack the received message Assign the items inside to the same indices Assign the items inside to the same indices

determined in the first stepdetermined in the first step

Running Launcher under JPFRunning Launcher under JPF

navy 310 % jpf -c ./jpf.properties Launcher | moreJavaPathfinder v4.1 - (C) 1999-2007 RIACS/NASA Ames Research Center

============================= system under testapplication: /cs/home/pourya/6490/Launcher.java

============== search started: 11/27/07 1:24 PMLauncher : start threadsCProcess 0: startsCProcess 1: startsMProcess : initate intraprocess stage

CProcess 0: finished step 0CProcess 0: 0 0CProcess 0: 1 1000000CProcess 0: done!CProcess 1: finished step 0CProcess 1: 0 1CProcess 1: 1 1000001

CProcess 1: done!MProcess : done!

Launcher : all threads done!

========================== error #1gov.nasa.jpf.jvm.NotDeadlockedPropertydeadlock encountered: thread index=0,name=main,status=TERMINATED,this=null,target=null,priority=5,lockCount=0 thread index=1,name=CProcess@ab6b,status=WAITING,this=org.jcsp.lang.ParThread@518,priority=5,lockCount=1 thread index=2,name=CProcess@aa76,status=WAITING,this=org.jcsp.lang.ParThread@550,priority=5,lockCount=1

========================= trace #1

Simple JCSP testSimple JCSP test

import org.jcsp.lang.*;

Public class test{ public static void main(String[] args) {

new Parallel {

new CSProcess[]{ new TCSP(), new TCSP()}

).run(); System.out.print("Test done!\n"); }}

import org.jcsp.lang.*;

public class TCSP implements CSProcess { public TCSP(){ }

//@Override public void run() { System.out.printf("TCSP done!\n"); }}

Simple JCSP test under JPFSimple JCSP test under JPF

navy 313 % jpf -c ./jpf.properties test | moreJavaPathfinder v4.1 - (C) 1999-2007 RIACS/NASA Ames Research Center

====================================================== system under testapplication: /cs/home/pourya/6490/test.java====================================================== search started: 11/27/07 1:43 PMTCSP done!

TCSP done!

Test done!

====================================================== error #1gov.nasa.jpf.jvm.NotDeadlockedPropertydeadlock encountered: thread index=0,name=main,status=TERMINATED,this=null,target=null,priority=5,lockCount=0 thread index=1,name=TCSP@ab6c,status=WAITING,this=org.jcsp.lang.ParThread@177,priority=5,lockCount=1====================================================== trace #1

Deadlock causeDeadlock cause

Threads are still alive at least under JPF Threads are still alive at least under JPF environmentenvironment

We should force thread termination the We should force thread termination the end of runend of run

Two solutionsTwo solutions System.exit(0) in the end of MProcessSystem.exit(0) in the end of MProcess Use release mechanism in Parallel under Use release mechanism in Parallel under

JCSP: releaseAllThreads();JCSP: releaseAllThreads();

Modification to test and ResultsModification to test and Results

import org.jcsp.lang.*;

class test{ public static void main(String[] args) { Parallel P = new Parallel (

new CSProcess[]{ new TCSP(), new TCSP()}

); P.run(); System.out.print("Test done!\n"); P.releaseAllThreads(); }}

navy 317 % jpf -c ./jpf.properties test JavaPathfinder v4.1 - (C) 1999-2007 RIACS/NASA Ames Research Center

===================== system under testapplication: /cs/home/pourya/6490/test.java======== search started: 11/27/07 1:06 PMTCSP done!

TCSP done!

Test done!Test done!...TCSP done!

Test done!

================================== resultsno errors detected=================inished: 11/27/07 1:06 PM

Verifying LauncherVerifying Launcher

No deadlocks after the releaseThread fixNo deadlocks after the releaseThread fix

Precision Racing TestPrecision Racing Test No racing warning or errorsNo racing warning or errors

Underlying mechanisms in JCSP use synchronized Underlying mechanisms in JCSP use synchronized blocksblocks

Functional verification?Functional verification?

Functional verificationFunctional verification

Each thread initially generate values using Each thread initially generate values using following line of codefollowing line of code

After transpose the first and last digit will After transpose the first and last digit will be swappedbe swapped

for(int i=0; i<N; i++)column[i] = PID*1000000 + i;

We use a for-loop which sets a Boolean We use a for-loop which sets a Boolean value and, then a assertion to verify value and, then a assertion to verify resultsresults

Boolean correctSoFar = true;

for(i=0; i<N && correctSoFar; i++){

if (column[i] != i*1000000 + PID)correctSoFar = false;

}assert (correctSoFar) : "CProcess value incorrect”);

Final ResultsFinal Results

navy 310 % jpf -c ./jpf.properties Launcher | moreJavaPathfinder v4.1 - (C) 1999-2007 RIACS/NASA Ames Research Center

============================= system under testapplication: /cs/home/pourya/6490/Launcher.java

============== search started: 11/27/07 1:35 PMLauncher : start threadsCProcess 0: startsCProcess 1: startsMProcess : initate intraprocess stage

CProcess 0: finished step 0CProcess 0: 0 0CProcess 1: startsCProcess 1: startsCProcess 1: startsCProcess 0: startsCProcess 0: starts

CProcess 1: done!MProcess : done!

Launcher : all threads done!..CProcess 1: startsCProcess 1: startsCProcess 1: startsCProcess 1: startsCProcess 0: startsCProcess 0: startsCProcess 0: startsCProcess 0: startsCProcess 0: starts

============================================ resultsno errors detected

================== search finished: 11/27/07 1:37 PM

Future workFuture work

We could break the cycle on a first-come We could break the cycle on a first-come first-served basisfirst-served basis

Locking mechanism neededLocking mechanism needed Racing might rise with a faulty lockRacing might rise with a faulty lock

Racing verification requiredRacing verification required

76543210 8