Ministerio de Economía, Industria y Competitividad TIN2017-89842-P (MABICAP)Ministerio de Economía y Competitividad TIN2015-71562-RED

Martínez del Amor, Miguel Ángel

Orellana Martín, David

Pérez Hurtado de Mendoza, Ignacio

Pérez Jiménez, Mario de Jesús

Riscos Núñez, Agustín

Valencia Cabrera, Luis

English

idUS. Depósito de Investigación Universidad de Sevilla

Simulation of Computing P Systems:A GPU Design for the Factorization ProblemMiguel Á. Martínez-del-Amor, David Orellana-MartínIgnacio Pérez-Hurtado, Luis Valencia-CabreraAgustín Riscos-Núñez, Mario J. Pérez-JiménezResearch Group on Natural ComputingDept. Computer Science and Artificial IntelligenceUniversidad de SevillaCMC19, 4-7 September 2018, Dresden (Germany)M.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 1 / 37Contents1 GPU computing fundamentals2 GPU simulators for P systemsStructure of a GPU simulatorState of the artOther P system models3 Concepts for specific simulators4 Future research linesM.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 2 / 37GPU computing fundamentalsOutline1 GPU computing fundamentals2 GPU simulators for P systemsStructure of a GPU simulatorState of the artOther P system models3 Concepts for specific simulators4 Future research linesM.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 3 / 37GPU computing fundamentalsGPU computingGraphics Processor Unit (GPU)Data-parallel computing model:SPMD programming model (Same Program for Multiple Data)Shared memory systemNew programming languages: CUDA, OpenCL, DirectComputeA GPU features thousand of coresM.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 4 / 37GPU computing fundamentalsNVIDIA’s technologyCUDA programming model1Heterogeneous model: CPU (host) + GPU (device).All threads execute the same code (kernel) in parallel.Three-level hierarchy of threads (grid, blocks, threads).Memory hierarchy (global, shared within block).1W.-M. Hwu, D. Kirk. Programming massively parallel processors, Morgan Kaufmann, 2010.M.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 5 / 37GPU computing fundamentalsWhy is the GPU interesting for simulating P systems?Desired properties:High level of parallelism (up to 4000 cores)Shared memory system (easily synchronized)Scalability and portabilityKnown languages: C/C++, Python, Fortran...Cheap technology everywhere (cost andmaintenance)Undesired properties:Best performance requires lot of research.Programming model imposes many restrictionsM.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 6 / 37GPU simulators for P systems Structure of a GPU simulatorOutline1 GPU computing fundamentals2 GPU simulators for P systemsStructure of a GPU simulatorState of the artOther P system models3 Concepts for specific simulators4 Future research linesM.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 7 / 37GPU simulators for P systems Structure of a GPU simulatorGPU simulator workflow - Initialization (I)CPU (serial code) GPU (serial code)Read P system information:+ P system model description+ Initial configurationAllocate memory in GPUGPU memoryP system info (rules, alphabet)P system configuration(incl. all possible membranes to be generated during computation)Copy P system information to GPUCopy P system initial config to GPUAuxiliary(rule selection)M.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 8 / 37GPU simulators for P systems Structure of a GPU simulatorGPU simulator workflow - Simulation - Selection (II)CPU (serial code) GPU (serial code)Read P system information:+ P system model description+ Initial configurationAllocate memory in GPUCopy P system information to GPUCopy P system initial config to GPUCall to Selection Kernel(s)GPU gridGPU memoryP system infoP system configuration AuxiliaryM.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 9 / 37GPU simulators for P systems Structure of a GPU simulatorGPU simulator workflow - Simulation - Execution (III)CPU (serial code) GPU (serial code)Read P system information:+ P system model description+ Initial configurationAllocate memory in GPUCopy P system information to GPUCopy P system initial config to GPUCall to Execution Kernel(s) GPU gridGPU memoryP system infoP system configuration AuxiliaryCall to Selection Kernel(s)     REPEATM.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 10 / 37GPU simulators for P systems Structure of a GPU simulatorGPU simulator workflow - Wrap up (IV)CPU (serial code) GPU (serial code)Read P system information:+ P system model description+ Initial configurationAllocate memory in GPUCopy P system information to GPUCopy P system initial config to GPUCall to Execution Kernel(s)GPU memoryP system infoP system configuration(incl. all possible membrane to be generated during computation)AuxiliaryCall to Selection Kernel(s)Copy P system configuration(s) back to CPU memoryReport outcome of simulationM.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 11 / 37GPU simulators for P systems State of the artOutline1 GPU computing fundamentals2 GPU simulators for P systemsStructure of a GPU simulatorState of the artOther P system models3 Concepts for specific simulators4 Future research linesM.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 12 / 37GPU simulators for P systems State of the artSimulation approachesGeneric approach: simulator for a variant / class (under restrictions).Specific approach: simulator for a certain family / model.M.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 13 / 37GPU simulators for P systems State of the artSimulating models (“generic” approach)P systems with active membranesRooted tree of membranes.Polarization and no cooperation (only one object in LHS).Rules: Evolution, send-in, send-out, division and dissolution.Assumptions to simplify the simulator:Confluent modelsOnly two-level trees (skin and elementary membranes)M.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 14 / 37GPU simulators for P systems State of the artSimulating models (“generic” approach)Mapping double parallelism:Membranes to Thread BlocksObjects to Threads: thanks to no-cooperative rules, it is enough tocheck the existence of one object to trigger a rule.M.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 15 / 37GPU simulators for P systems State of the artSimulating models (“generic” approach)Performance analysisTwo benchmarks (on a C1060 with 240 cores):A. A simple test P system2Max speedup: 5.8xB. An efficient solution to SATMax speedup: 1.5x (n = 18, 218 membranes)Density of objects per membrane:RealityWorstCase=#ObjectsAlphabetSizeTest A: 100%Test B: ∼ 15%2One division rule: [d]2 → [d]2 [d]2, Many evolution rules: [oi → oi ]2, 0≤ i ≤ NM.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 16 / 37GPU simulators for P systems State of the artSimulating models (“generic” approach)Performance analysisTwo benchmarks (on a C1060 with 240 cores):A. A simple test P system2Max speedup: 5.8xB. An efficient solution to SATMax speedup: 1.5x (n = 18, 218 membranes)Density of objects per membrane:RealityWorstCase=#ObjectsAlphabetSizeTest A: 100%Test B: ∼ 15%2One division rule: [d]2 → [d]2 [d]2, Many evolution rules: [oi → oi ]2, 0≤ i ≤ NM.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 16 / 37GPU simulators for P systems State of the artSimulating models (“generic” approach)Foreseen performance by Sevilla Carpets: D. Orellana-Martín etal. Sevilla Carpets revisited: Enriching theMembrane Computing toolbox. FundamentaInformaticae, 134 (2014), 153-166.The flatter the carpet, the higher the parallel degree in the system (and so, inthe simulation).M.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 17 / 37GPU simulators for P systems State of the artSimulating models (“specific” approach)Cell-like solution to SATP systems with active membranesA specific linear time solution to SAT, with exponential workspaceEncoding:Objects: literals of the formula and auxiliary (counters, etc.)Membranes: truth assignmentsA 4-staged solution:1 Generation2 Synchronization3 Check out4 OutputM.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 18 / 37GPU simulators for P systems State of the artSimulating models (“specific” approach)Cell-like solution to SAT - parallel designMembranes to Thread BlocksObjects in initial multiset to Threads: we have constrained the numberof threads to the amount of different objects in the initial multiset.M.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 19 / 37GPU simulators for P systems State of the artSimulating models (“specific” approach)Tissue-like solution to SATTissue P systems with cell divisionDirected graph of cells.No polarization and cooperation (multisets in LHS)Communication (symport/antiport) and division rules.Active environment.A specific linear time solution to SAT, with exponential workspaceEncoding:Objects: literals of the formula and auxiliary (counters, etc.)Cell: truth assignmentA 5-staged solution:1 Generation2 Exchange3 Synchronization4 Checking5 OutputM.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 20 / 37GPU simulators for P systems State of the artSimulating models (“specific” approach)Tissue-like solution to SATTissue P systems with cell divisionDirected graph of cells.No polarization and cooperation (multisets in LHS)Communication (symport/antiport) and division rules.Active environment.A specific linear time solution to SAT, with exponential workspaceEncoding:Objects: literals of the formula and auxiliary (counters, etc.)Cell: truth assignmentA 5-staged solution:1 Generation2 Exchange3 Synchronization4 Checking5 OutputM.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 20 / 37GPU simulators for P systems State of the artSimulating models (“specific” approach)Tissue-like solution to SAT - parallel designCells to Thread BlocksObjects in initial multiset, objects for truth assignation, and auxiliaryobjects to Threads: selection of rules is not direct given that there iscooperation.M.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 21 / 37GPU simulators for P systems State of the artSimulating models (“specific” approach)Performance analysisCell-like approach:Max speedup: 63x (n = 21)Tissue-like approach:Max speedup: 10x (n = 21)Conclusion:Charges save space, and help to increase object densityNo-cooperation avoids synchronization issuesShallow P systems (no more than skin and elementary membranes)M.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 22 / 37GPU simulators for P systems State of the artSimulating models (“specific” approach)Performance analysisCell-like approach:Max speedup: 63x (n = 21)Tissue-like approach:Max speedup: 10x (n = 21)Conclusion:Charges save space, and help to increase object densityNo-cooperation avoids synchronization issuesShallow P systems (no more than skin and elementary membranes)M.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 22 / 37GPU simulators for P systems Other P system modelsOutline1 GPU computing fundamentals2 GPU simulators for P systemsStructure of a GPU simulatorState of the artOther P system models3 Concepts for specific simulators4 Future research linesM.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 23 / 37GPU simulators for P systems Other P system modelsPMCGPU project:http://sourceforge.net/projects/pmcgpuM.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 24 / 37Concepts for specific simulatorsContents1 GPU computing fundamentals2 GPU simulators for P systemsStructure of a GPU simulatorState of the artOther P system models3 Concepts for specific simulators4 Future research linesM.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 25 / 37Concepts for specific simulatorsCase study: FACTORIZATION problemGiven a natural number which is the product of two prime numbers, findits decomposition.Partial function FACT from N to N2: FACT (x) = (y ,z)Solution presented in WMC/UCNC 2018:a family {Π(n)|n ∈ N} of (binary) computing polarizationless P systemswith active membranesmakes use of minimal cooperation and minimal productionno dissolution rulesno division rules for non-elementary membranesM.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 26 / 37Concepts for specific simulatorsCase study: FACTORIZATION problemStages in the computation of Π(n):1 Generation2 Multiplication3 Equality checking4 Trivial solution check5 First delete6 Second delete7 Output 18 Output 2M.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 27 / 37Concepts for specific simulatorsCase study: FACTORIZATION problemMore features:After generation, Π(n) contains 22n+2, where n = kx , being x an instanceof the problem (x has n + 1 digits in its binary representation).The computation takes at most 19n + 28 steps.Some rules:M.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 28 / 37Concepts for specific simulatorsDesign of specific simulatorsConsiderations:No need to do selection - execution (we know the rules)No need to do per-transition simulation (we can take short paths)No need to store rules in memory (we know the rules!!)Under control: we should be able to know, looking into the simulator, thestate of the P system at every transitionCommon designs:Models are normally designed by staged computationsEach one with different behaviour (generation, checking, ...)A kernel per stageM.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 29 / 37Concepts for specific simulatorsDesign of specific simulatorsConsiderations:No need to do selection - execution (we know the rules)No need to do per-transition simulation (we can take short paths)No need to store rules in memory (we know the rules!!)Under control: we should be able to know, looking into the simulator, thestate of the P system at every transitionCommon designs:Models are normally designed by staged computationsEach one with different behaviour (generation, checking, ...)A kernel per stageM.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 29 / 37Concepts for specific simulatorsDesign of specific simulatorsIncreasing density of objects: from sparse to dense representation a         b        c         d        e        f         o1      o2      o3      o4     o5     o6      o7       o8a b c d e f oiInitial Multiset Objects acting as countersM.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 30 / 37Concepts for specific simulatorsDesign of specific simulatorsDesign decisions:Objects acting as counters, variable or in memory?Are we able to set an upper-bound of objects appearing in membranes?Minimal production helps!!Do we know the maximum amount of membranes?A kernel or several kernels per stage?Fusing kernels for simple stages?M.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 31 / 37Future research linesOutline1 GPU computing fundamentals2 GPU simulators for P systemsStructure of a GPU simulatorState of the artOther P system models3 Concepts for specific simulators4 Future research linesM.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 32 / 37Future research linesGPU-oriented P systemsMABICAP: Bio-inspired machines over high performance platforms.Seeking P system models well-suited for GPU deployments.Selection of best ingredients, while keeping computing power andexpressibility:ChargesMinimal productionMinimal (almost no-) cooperationShallow structure (horizontal parallelism)Towards efficient simulation of Spiking Neural P systems (sparserepresentation)M.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 33 / 37Future research linesNew GPU featuresKernel compilation in runtime (customizable to the model)Cooperative Groups (for deeper P systems)Tensor cores (matrix representations for SNP systems)Dynamic Parallelism (to be seen...)Faster memoryCloudM.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 34 / 37Future research linesComing CallsBICAS 2019: Biologically Inspired Parallel and Distributed Computing,Algorithms and SolutionsPart of HPCS 2019 (a CORE B conference)Dublin (Ireland), July 15 – 19, 2019Deadline: TBD (around March)Proceedings in IEEE XploreSpecial issues in ISI journals (FGCS, CCPE, ...)http://hpcs2019.cisedu.infoM.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 35 / 37Future research linesComing CallsBWMC 2019: Brainstorming Week on Membrane ComputingSevilla (Spain)Dates: 5-8 FebruaryAnnouncements at RGNC website: http://www.gcn.us.esM.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 36 / 37Future research linesThank you for your attention!Vielen Dank für Ihre Beachtung!The authors acknowledge support of the R&D project MABICAP TIN2017-89842-P and REDBIOCOM TIN2015-71562-REDT, funded by theSpanish government and EU FEDER funds.M.Á. Martínez-del-Amor et al. (RGNC) Simulation of Computing P Systems CMC19, Dresden (Germany) 37 / 37

Simulation of Computing P Systems: A GPU Design for the Factorization Problem

https://idus.us.es/bitstream/11441/106210/1/Simulation%20of%20computing%20P%20systems%20A%20GPU%20design%20for%20the%20factorization%20problem.pdf

Simulation of Computing P Systems: A GPU Design for the Factorization Problem

Abstract

Similar works

Full text

Available Versions

idUS. Depósito de Investigación Universidad de Sevilla