Cyclic Reduction Tridiagonal Solvers on GPUs Applied to Mixed Precision Multigrid

March 3rd, 2010

Abstract:

We have previously suggested mixed precision iterative solvers specifically tailored to the iterative solution of sparse linear equation systems as they typically arise in the finite element discretization of partial differential equations. These schemes have been evaluated for a number of hardware platforms, in particular single precision GPUs as accelerators to the general purpose CPU. This paper reevaluates the situation with new mixed precision solvers that run entirely on the GPU: We demonstrate that mixed precision schemes constitute a significant performance gain over native double precision. Moreover, we present a new implementation of cyclic reduction for the parallel solution of tridiagonal systems and employ this scheme as a line relaxation smoother in our GPU-based multigrid solver. With an alternating direction implicit variant of this advanced smoother we can extend the applicability of the GPU multigrid solvers to very ill-conditioned systems arising from the discretization on anisotropic meshes, that previously had to be solved on the CPU. The resulting mixed precision schemes are always faster than double precision alone, and outperform tuned CPU solvers consistently by almost an order of magnitude.

(Dominik Göddeke and Robert Strzodka: “Cyclic Reduction Tridiagonal Solvers on GPUs Applied to Mixed Precision Multigrid” , accepted in: IEEE Transactions on Parallel and Distributed Systems, Special Issue: High Performance Computing with Accelerators, Mar. 2010. Link.)

Easy GPU programming with GMAC

March 1st, 2010

GMAC (Global Memory for ACcelerators) is a user-level library that implements an Asymmetric Distributed Shared Memory model to be used by CUDA programs. An ADSM model allows CPU code to access data hosted in accelerator (GPU) memory. In this model, a single pointer is used for data structures accessed both in the CPU and the GPU and the coherency of the data is transparently handled by the library. Moreover, the data allocated with GMAC can be accessed by all the host threads of the program. That makes your code simpler and cleaner. GMAC currently supports programs programmed with CUDA, but OpenCL support is planned.

A paper describing the Asymmetric Distributed Shared Memory model and its implementation in GMAC has been accepted in the ASPLOS XV conference. GMAC is being developed by the Operating System Group at the Universitat Politecnica de Catalunya and the IMPACT Research Group at the University of Illinois. Binary pre-compiled packages, the source code, documentation and examples are available at the project website.

(Isaac Gelado, Javier Cabezas, John Stone, Sanjay Patel, Nacho Navarro and Wen-mei Hwu,  “An Asymmetric Distributed Shared Memory Model for Heterogeneous Parallel Systems”, accepted in: Fifteenth International Conference on Architectural Support for Programming Languages and Operating Systems (ASPLOS 2010), March 2010.)

Lattice-Boltzmann Simulation of the Shallow-Water Equations with Fluid-Structure Interaction on Multi- and Manycore Processors

February 28th, 2010

Abstract:

We present an efficient method for the simulation of laminar fluid flows with free surfaces including their interaction with moving rigid bodies, based on the two-dimensional shallow water equations and the Lattice-Boltzmann method. Our implementation targets multiple fundamentally different architectures such as commodity multicore CPUs with SSE, GPUs, the Cell BE and clusters. We show that our code scales well on an MPI-based cluster; that an eightfold speedup can be achieved using modern GPUs in contrast to multithreaded CPU code and, finally, that it is possible to solve fluid-structure interaction scenarios with high resolution at interactive rates.

(Markus Geveler, Dirk Ribbrock, Dominik Göddeke and Stefan Turek: “Lattice-Boltzmann Simulation of the Shallow-Water Equations with Fluid-Structure Interaction on Multi- and Manycore Processors”, Accepted in: Facing the Multicore Challenge, Heidelberg, Germany, Mar. 2010. Link.)

OpenNL 3.0: CUDA sparse linear solvers

February 14th, 2010

OpenNL (Open Numerical Library) is a library for solving sparse linear systems, especially designed for the Computer Graphics community. The goal of OpenNL is to be as small as possible, while offering the subset of functionalities required by this application field. The Makefiles of OpenNL can generate a single .c and .h file that make it very easy to integrate into other projects. The distribution includes an implementation of a Least Squares Conformal Maps parameterization method.  The new version 3.0 of OpenNL includes support for CUDA (with Concurrent Number Cruncher and CUSP ELL formats).

CUDPP Users: Please Complete This Survey!

February 11th, 2010

The developers of the CUDPP (CUDA Data-Parallel Primitives) Library request that users (past and current) of the CUDPP Library fill out the CUDPP Survey.  This survey will help the CUDPP Team prioritize new development and support for existing and new features.

Harnessing Graphics Processors for the Fast Computation of Acoustic Likelihoods in Speech Recognition

February 10th, 2010

Abstract:

In large vocabulary continuous speech recognition (LVCSR) the acoustic model computations often account for the largest processing overhead. Our weighted finite state transducer (WFST) based decoding engine can utilize a commodity graphics processing unit (GPU) to perform the acoustic computations to move this burden off the main processor. In this paper we describe our new GPU scheme that can achieve a very substantial improvement in recognition speed whilst incurring no reduction in recognition accuracy. We evaluate the GPU technique on a large vocabulary spontaneous speech recognition task using a set of acoustic models with varying complexity and the results consistently show by using the GPU it is possible to reduce the recognition time with largest improvements occurring in systems with large numbers of Gaussians. For the systems which achieve the best accuracy we obtained between 2.5 and 3 times speed-ups. The faster decoding times translate to reductions in space, power and hardware costs by only requiring standard hardware that is already widely installed.

(Paul R. Dixon, Tasuku Oonishi, Sadaoki Furui, “Harnessing graphics processors for the fast computation of acoustic likelihoods in speech recognition”, Computer Speech & Language, Volume 23, Issue 4, October 2009, Pages 510-526, ISSN 0885-2308, DOI: 10.1016/j.csl.2009.03.005)

Programming Massively Parallel Processors: A Hands-on Approach

February 9th, 2010

Programming Massively Parallel Processors Cover ImageThe first textbook of its kind, Programming Massively Parallel Processors: A Hands-on Approach launches today, authored by Dr. David B. Kirk, NVIDIA Fellow and former chief scientist, and Dr. Wen-mei Hwu, who serves at the University of Illinois at Urbana-Champaign as Chair of Electrical and Computer Engineering in the Coordinated Science Laboratory, co-director of the Universal Parallel Computing Research Center and principal investigator of the CUDA Center of Excellence. The textbook, which is 256 pages, is the first aimed at teaching advanced students and professionals the basic concepts of parallel programming and GPU architectures. Published by Morgan-Kauffman, it explores various techniques for constructing parallel programs and reviews numerous case studies.

With conventional CPU-based computing no longer scaling in performance and the world’s computational challenges increasing in complexity, the need for massively parallel processing has never been greater. GPUs have hundreds of cores capable of delivering transformative performance increases across a wide range of computational challenges. The rise of these multi-core architectures has raised the need to teach advanced programmers a new and essential skill: how to program massively parallel processors.

Among the book’s key features:

  • First and only text that teaches how to program within a massively parallel environment
  • Portions of the NVIDIA-provided content have been part of the curriculum at 300 universities worldwide
  • Drafts of sections of the book have been tested and taught by Kirk at the University of Illinois
  • Book utilizes OpenCL and CUDA C, the NVIDIA parallel computing language developed specifically for massively parallel environments

Programming Massively Parallel Processors: A Hands-on Approach is available to purchase from Amazon or directly from Elsevier.

Triangular matrix inversion on Graphics Processing Unit

February 6th, 2010

Abstract:

Dense matrix inversion is a basic procedure in many linear algebra algorithms. A computationally arduous step in most dense matrix inversion methods is the inversion of triangular matrices as produced by factorization methods such as LU decomposition. In this paper, we demonstrate how triangular matrix inversion (TMI) can be accelerated considerably by using commercial Graphics Processing Units (GPU) in a standard PC. Our implementation is based on a divide and conquer type recursive TMI algorithm, efficiently adapted to the GPU architecture. Our implementation obtains a speedup of 34x versus a CPU-based LAPACK reference routine, and runs at up to 54 gigaflops/s on a GTX 280 in double precision. Limitations of the algorithm are discussed, and strategies to cope with them are introduced. In addition, we show how inversion of an L- and U-matrix can be performed concurrently on a GTX 295 based dual-GPU system at up to 90 gigaflops/s.

(Florian Ries, Tommaso De Marco, Matteo Zivieri and Roberto Guerrieri, Triangular Matrix Inversion on Graphics Processing Units, Supercomputing 2009, DOI 10.1145/1654059.1654069)

HONEI: A collection of libraries for numerical computations targeting multiple processor architectures

February 2nd, 2010

Abstract:

We present HONEI, an open-source collection of libraries offering a hardware oriented approach to numerical calculations. HONEI abstracts the hardware, and applications written on top of HONEI can be executed on a wide range of computer architectures such as CPUs, GPUs and the Cell processor. We demonstrate the flexibility and performance of our approach with two test applications, a Finite Element multigrid solver for the Poisson problem and a robust and fast simulation of shallow water waves. By linking against HONEI’s libraries, we achieve a two-fold speedup over straight forward C++ code using HONEI’s SSE backend, and additional 3–4 and 4–16 times faster execution on the Cell and a GPU. A second important aspect of our approach is that the full performance capabilities of the hardware under consideration can be exploited by adding optimised application-specific operations to the HONEI libraries. HONEI provides all necessary infrastructure for development and evaluation of such kernels, significantly simplifying their development.

(Danny van Dyk, Markus Geveler, Sven Mallach, Dirk Ribbrock, Dominik Göddeke and Carsten Gutwenger: HONEI: A collection of libraries for numerical computations targeting multiple processor architectures. Computer Physics Communications 180(12), pp. 2534-2543, December 2009. DOI 10.1016/j.cpc.2009.04.018)

FCUDA: Enabling efficient compilation of CUDA kernels onto FPGAs

February 2nd, 2010

Abstract:

As growing power dissipation and thermal effects disrupted the rising clock frequency trend and threatened to annul Moore’s law, the computing industry has switched its route to higher performance through parallel processing. The rise of multi-core systems in all domains of computing has opened the door to heterogeneous multi-processors, where processors of different compute characteristics can be combined to effectively boost the performance per watt of different application kernels. GPUs and FPGAs are becoming very popular in PC-based heterogeneous systems for speeding up compute intensive kernels of scientific, imaging and simulation applications. GPUs can execute hundreds of concurrent threads, while FPGAs provide customized concurrency for highly parallel kernels. However, exploiting the parallelism available in these applications is currently not a push-button task. Often the programmer has to expose the application’s fine and coarse grained parallelism by using special APIs. CUDA is such a parallel-computing API that is driven by the GPU industry and is gaining significant popularity. In this work, we adapt the CUDA programming model into a new FPGA design flow called FCUDA, which efficiently maps the coarse and fine grained parallelism exposed in CUDA onto the reconfigurable fabric. Our CUDA-to-FPGA flow employs AutoPilot, an advanced high-level synthesis tool which enables high-abstraction FPGA programming. FCUDA is based on a source-to-source compilation that transforms the SPMD CUDA thread blocks into parallel C code for AutoPilot. We describe the details of our CUDA-to-FPGA flow and demonstrate the highly competitive performance of the resulting customized FPGA multi-core accelerators. To the best of our knowledge, this is the first CUDA-to-FPGA flow to demonstrate the applicability and potential advantage of using the CUDA programming model for high-performance computing in FPGAs.

(Alexandros Papakonstantinou, Karthik Gururaj, John A. Stratton, Deming Chen, Jason Cong and Wen-Mei W. Hwu, FCUDA: Enabling efficient compilation of CUDA kernels onto FPGAs, Proceedings of the 7th Symposium on Application Specific Processors, pp.35-42, July 2009. DOI: 10.1109/SASP.2009.5226333)

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