A novel algorithm for computing the incomplete-LU and Cholesky factorization with 0 fill-in on a graphics processing unit (GPU) is proposed. It implements the incomplete factorization of the given matrix in two phases. First, the symbolic analysis phase builds a dependency graph based on the matrix sparsity pattern and groups the independent rows into levels. Second, the numerical factorization phase obtains the resulting lower and upper sparse triangular factors by iterating sequentially across the constructed levels. The Gaussian elimination of the elements below the main diagonal in the rows corresponding to each single level is performed in parallel. The numerical experiments are also presented and it is shown that the numerical factorization phase can achieve on average more than 2.8x speedup over MKL, while the incomplete-LU and Cholesky preconditioned iterative methods can achieve an average of 2x speedup on GPU over their CPU implementation.
(Maxim Naumov. Parallel Incomplete-LU and Cholesky Factorization in the Preconditioned Iterative Methods on the GPU, NVIDIA Technical Report NVR-2012-003. May 2012.)
Register today up now for a webinar series on how to use the Intel® SDK for OpenCL Applications to best utilize the CPU and Intel® HD Graphics of 3rd Gen Intel® Core™ processors for developing OpenCL applications:
This publication describes efficient low level algorithms for performing relational queries on parallel processors, such as NVIDIA Fermi or Kepler. Relations are stored in GPU memory as sorted arrays of tuples, and manipulated by relational operators that preserve the sorted property. Most significantly, this work introduces algorithms for JOIN and SET INTERSECTION/UNION/DIFFERENCE that can process data at over 50 GB/s.
Relational databases remain an important application domain for organizing and analyzing the massive volume of data generated as sensor technology, retail and inventory transactions, social media, computer vision, and new fields continue to evolve. At the same time, processor architectures are beginning to shift towards hierarchical and parallel architectures employing throughput-optimized memory systems, lightweight multi-threading, and Single-Instruction Multiple-Data (SIMD) core organizations. Examples include general purpose graphics processing units (GPUs) such as NVIDIA’s Fermi, Intels Sandy Bridge, and AMD’s Fusion processors. This paper explores the mapping of primitive relational algebra operations onto GPUs. In particular, we focus on algorithms and data structure design identifying a fundamental conflict between the structure of algorithms with good computational complexity and that of algorithms with memory access patterns and instruction schedules that achieve peak machine utilization. To reconcile this conflict, our design space exploration converges on a hybrid multi-stage algorithm that devotes a small amount of the total runtime to prune input data sets using an irregular algorithm with good computational complexity. The partial results are then fed into a regular algorithm that achieves near peak machine utilization. The design process leading to the most efficient algorithm for each stage is described, detailing alternative implementations, their performance characteristics, and an explanation of why they were ultimately abandoned. The least efficient algorithm (JOIN) achieves 57% − 72% of peak machine performance depending on the density of the input. The most efficient algorithms (PRODUCT, PROJECT, and SELECT) achieve 86% − 92% of peak machine performance across all input data sets. To the best of our knowledge, these represent the best known published results to date for any implementations. This work lays the foundation for the development of a relational database system that achieves good scalability on a Multi-Bulk-Synchronous-Parallel (M-BSP) processor architecture. Additionally, the algorithm design may offer insights into the design of parallel and distributed relational database systems. It leaves the problems of query planning, operator→query synthesis, corner case optimization, and system/OS interaction as future work that would be necessary for commercial deployment.
(Gregory Diamos, Ashwin Lele, Jin Wang, Sudhakar Yalamanchili: “Relational Algorithms for Multi-Bulk-Synchronous Processors “, NVIDIA Tech Report, June 2012. [WWW])
Together with EuroPar-12, the 5th Workshop on UnConventional High Performance Computing 2012 (UCHPC 2012) will take place on August 27/28 at Rhodes Island, Greece. The workshop tries to capture solutions for HPC which are unconventional today but could become conventional and significant tomorrow. While GPGPU is already used a lot in HPC, there still are all kind of issues around best exploitation and productivity for the programmer. Submission deadline: June 6, 2012. For more details, see
http://www.lrr.in.tum.de/~weidendo/uchpc12. UPDATE: Submission deadline extended to June 11.
VexCL is vector expression template library for OpenCL developed by the Supercomputer Center of Russian academy of sciences. It has been created for ease of C++ based OpenCL development. Multi-device (and multi-platform) computations are supported. The code is publicly available under MIT license.
- Selection and initialization of compute devices according to extensible set of device filters.
- Transparent allocation of device vectors spanning multiple devices.
- Convenient notation for vector arithmetic, sparse matrix-vector multiplication, reductions. All computations are performed in parallel on all selected devices.
- Appropriate kernels for vector expressions are generated automatically first time an expression is used.
Doxygen-generated documentation is available at http://ddemidov.github.com/vexcl/index.html.
C++ Accelerated Massive Parallelism (C++ AMP) is a new open specification heterogeneous programming model, which builds on the established C++ language. Developed for heterogeneous platforms C++ AMP is designed to accelerate the execution of C++ code by taking advantage of the data-parallel hardware that is commonly present as a GPU. These courses are aimed at programmers who are looking to develop comprehensive skills in writing and optimizing applications using C++ AMP. Read the rest of this entry »
SpeedIT provides a set of accelerated solvers for sparse linear systems of equations. The library supports C/C++ and Fortran, and it can be used with OpenFOAM to accelerate CFD simulations. SpeedIT 2.1 contains two new preconditioners:
• Algebraic Multigrid with Smoothed Aggregation (AMG)
• Approximate Inverse (AINV)
OpenFOAM simulations on the GPU can be up to 3.5x faster compared to CG and DIC/DILU preconditioners on the CPU and up to 1.6x faster if you run GAMG.
See the SpeedIT website and blog for more details.
Traditional CPU-based computing environments offer a variety of binary instrumentation frameworks. Instrumentation and analysis tools for GPU environments to date have been more limited. Panoptes is a binary instrumentation framework for CUDA that targets the GPU. By exploiting the GPU to run modified kernels, computationally-intensive programs can be run at the native parallelism of the device during analysis. To demonstrate its instrumentation capabilities, we currently implement a memory addressability and validity checker that targets CUDA programs.
Panoptes traces targeted programs by library interposition at runtime. Read the rest of this entry »
NVIDIA Kepler GK110 Die Shot
This white paper describes the new Kepler GK110 Architecture from NVIDIA.
Comprising 7.1 billion transistors, Kepler GK110 is not only the fastest, but also the most architecturally complex microprocessor ever built. Adding many new innovative features focused on compute performance, GK110 was designed to be a parallel processing powerhouse for Tesla® and the HPC market.
Kepler GK110 will provide over 1 TFlop of double precision throughput with greater than 80% DGEMM efficiency versus 60‐65% on the prior Fermi architecture.
In addition to greatly improved performance, the Kepler architecture offers a huge leap forward in power efficiency, delivering up to 3x the performance per watt of Fermi.
The paper describes features of the Kepler GK110 architecture, including
- Dynamic Parallelism;
- Grid Management Unit;
- NVIDIA GPUDirect™;
- New SHFL instruction and atomic instruction enhancements;
- New read-only data cache previously only accessible to texture;
- Bindless Textures;
- and much more.
This report describes advantages of using GPUs for analytical queries. It compares performance of the Alenka database engine using a GPU with the performance of Oracle on a SPARC server. More information on Alenka including source code: https://github.com/antonmks/Alenka