Non-uniformly Communicating Non-contiguous Data: A Case Study with PETSc and MPI P. Balaji, D. Buntinas, S. Balay, B. Smith, R. Thakur and W. Gropp Mathematics and Computer Science Argonne National Laboratory

Numerical Libraries in HEC Developing parallel applications is a complex task –Discretizing physical equations to numerical forms –Representing the domain of interest as data points Libraries allow developers to abstract low-level details –E.g., Numerical Analysis, Communication, I/O Numerical libraries (e.g., PETSc, ScaLAPACK, PESSL) –Parallel data layout and processing –Tools for distributed data layout (matrix, vector) –Tools for data processing (SLES, SNES)

Overview of PETSc Portable, Extensible Toolkit for Scientific Computing Software tools for solving PDEs –Suite of routines to create vectors, matrices and distributed arrays –Sequential/parallel data layout –Linear and nonlinear numerical solvers Widely used in Nanosimulations, Molecular dynamics, etc. Uses MPI for communication BLASLAPACKMPI MatricesVectorsIndex Sets KSP (Krylov subspace Methods) PC (Preconditioners) Draw SNES (Nonlinear Equation Solvers) SLES (Linear Equation Solvers) TS (Time Stepping) PDE Solvers Application Codes Level of Abstraction

Handling Parallel Data Layouts in PETSc Grid layout exposed to the application –Structured or Unstructured (1D, 2D, 3D) –Internally managed as a single vector of data elements –Representation often suited to optimize its operations Impact on communication: –Data representation and communication pattern might not be ideal for MPI communication operations –Non-uniformity and Non-contiguity in communication are the primary culprits

Presentation Layout Introduction Impact of PETSc Data Layout and Processing on MPI MPI Enhancements and Optimizations Experimental Evaluation Concluding Remarks and Future Work

Local Data Point Data Layout and Processing in PETSc Grid layouts: data is divided among processes –Ghost data points shared Non-contiguous Data Communication –2 nd dimension of the grid Non-uniform communication –Structure of the grid –Stencil type used –Sides larger than corners Process Boundary Ghost Data Point Proc 1Proc 0 Box-type stencil Proc 1Proc 0 Star-type stencil

MPI Derived Datatypes –Application describes noncontiguous data layout to MPI –Data is either packed to contiguous buffers and pipelined (sparse layouts) or sent individually (dense layouts) Good for simple algorithms, but very restrictive –Lookup upcoming content to predecide algorithm to use –Multiple parses on the datatype loses context! Non-contiguous Communication in MPI Non-contiguous Data layout Save Context Send Data Save Context Packing Buffer

Issues with Lost Datatype Context Rollback of context not possible –Datatypes could be recursive Duplication of context not possible –Context information might be large –When datatype elements are small, context could be larger than the datatype itself Search of context possible, but very expensive –Quadratically increasing search time with increasing datatype size –Currently used mechanism!

Non-uniform Collective Communication Non-uniform communication algorithms are optimized for “uniform” communication Case Studies –Allgatherv uses a ring algorithm Causes idleness if data volumes are very different –Alltoallw sends data to nodes in round-robin manner MPI processing is sequential Large Message Small Message

Presentation Layout Introduction Impact of PETSc Data Layout and Processing on MPI MPI Enhancements and Optimizations Experimental Evaluation Concluding Remarks and Future Work

Dual-context Approach for Non-contiguous Communication Previous approaches are in-efficient in complex designs –E.g., if a look-ahead is performed to understand the structure of the upcoming data, the saved context is lost Dual-context approach retains the data context –Look-aheads are performed using a separate context –Completely eliminates the search time Non-contiguous Data layout Save Context Send Data Save Context Look-ahead Packing Buffer

Non-Uniform Communication: AllGatherv Single point of distribution is the primary bottleneck Identify if a small fraction of messages are very large –Floyd and Rivest Algorithm –Linear time detection of outliers Binomial Algorithms –Recursive doubling or Dissemination –Logarithmic time Large Message Small Message

Non-uniform Communication: Alltoallw Distributing messages to be sent out as bins (based on message size) allows differential treatment to nodes Send out small messages first –Nodes waiting for small messages have to wait lesser –Ratio of increase in time for nodes waiting for larger messages is much smaller –No skew for zero-byte data with lesser synchronization Most helpful for non-contiguous messages –MPI processing (e.g., packing) is sequential for non- contiguous messages

Presentation Layout Introduction Impact of PETSc Data Layout and Processing on MPI MPI Enhancements and Optimizations Experimental Evaluation Concluding Remarks and Future Work

Experimental Testbed 64-node Cluster –32 nodes with dual Intel EM64T 3.6GHz processors 2MB L2 Cache, 2GB DDR2 400MHz SDRAM Intel E7520 (Lindenhurst) Chipset –32 nodes with dual Opteron 2.8GHz processors 1MB L2 Cache, 4GB DDR 400MHz SDRAM NVidia 2200/2050 Chipset RedHat AS4 with kernel.org kernel InfiniBand DDR (16Gbps) Network: –MT25208 adapters connected through a 144-port switch MVAPICH MPI implementation

Non-uniform Communication Evaluation Search time can dominate performance if the working context is lost!

AllGatherv Evaluation

Alltoallw Evaluation Our algorithm reduces the skew introduced due to the Alltoallw operations by sending out smaller messages first and allowing the corresponding applications to progress

PETSc Vector Scatter

3-D Laplacian Multigrid Solver

Presentation Layout Introduction Impact of PETSc Data Layout and Processing on MPI MPI Enhancements and Optimizations Experimental Evaluation Concluding Remarks and Future Work

Non-uniform and Non-contiguous communication is inherent in several libraries and applications Current algorithms deal with non-uniform communication in a same way as uniform communication Demonstrated that more sophisticated algorithms can give close to 10x improvements in performance Designs are a part of MPICH and –To be picked up by MPICH2 derivatives in later releases Future Work: –Skew tolerance in non-uniform communication –Other libraries and applications

Thank You Group Web-page: Home-page:

Backup Slides

Noncontiguous Communication in PETSc Copy Buffer vector (count = 8, stride = 8) contiguous (count = 3) double | double | double contiguous (count = 3) Data might not always be contiguously laid out in memory –E.g., Second dimension of a structured grid Communication is performed by packing data Pipelining copy and communication is important for performance

Hand-tuning vs. Automated optimization Nonuniformity and noncontiguity in data communication is inherent in several applications –Communicating unequal amounts of data to the different peer processes –Communication data from noncontiguous memory locations Previous research has primarily focused on uniform and contiguous data communication Accordingly applications and libraries tried hand-tuning attempts to convert communication formats –Manually packing noncontiguous data –Re-implementing collective operations in the application

Non-contiguous Communication in MPI MPI Derived Datatypes –Common approach for non-contiguous communication –Application describes noncontiguous data layout to MPI –Data is either packed into contiguous memory (sparse layouts) or sent as independent segments (dense layouts) Pipelining of packing and communication improves performance, but requires context information! Non-contiguous Data layout Save Context Send Data Save Context Packing Buffer

Issues with Non-contiguous Communication Current approach is simple and works as long as there is a single parse on the noncontiguous data More intelligent algorithms might suffer: –E.g., lookup upcoming datatype content to predecide algorithm to use –Multiple parses on the datatype lose the context ! –Searching for the lost context every time requires quadratically increasing time with datatype size PETSc non-contiguous communication suffers with such high search times

MPI-level Evaluation

Experimental Results MPI-level Micro-benchmarks –Non-contiguous data communication time –Non-uniform collective communication Allgatherv Operation Alltoallw Operation PETSc Vector Scatter Benchmark –Performs communication only 3-D Laplacian Multigrid Solver Application –Partial differential equation solver –Utilizes PETSc numerical solver operations