Basic Linear Algebra Subprograms Routines Research Articles

BLAS Kütüphanelerinin GPU Mimarilerindeki Nicel Performans Analizi

Basic Linear Algebra Subprograms (BLAS) are a set of linear algebra routines commonly used by machine learning applications and scientific computing. BLAS libraries with optimized implementations of BLAS routines offer high performance by exploiting parallel execution units in target computing systems. With massively large number of cores, graphics processing units (GPUs) exhibit high performance for computationally-heavy workloads. Recent BLAS libraries utilize parallel cores of GPU architectures efficiently by employing inherent data parallelism. In this study, we analyze GPU-targeted functions from two BLAS libraries, cuBLAS and MAGMA, and evaluate their performance on a single-GPU NVIDIA architecture by considering architectural features and limitations. We collect architectural performance metrics and explore resource utilization characteristics. Our work aims to help researchers and programmers to understand the performance behavior and GPU resource utilization of the BLAS routines implemented by the libraries.

Parallel time integration using Batched BLAS (Basic Linear Algebra Subprograms) routines

We present an approach for integrating the time evolution of quantum systems. We leverage the computation power of graphics processing units (GPUs) to perform the integration of all time steps in parallel. The performance boost is especially prominent for small to medium-sized quantum systems. The devised algorithm can largely be implemented using the recently-specified batched versions of the BLAS routines, and can therefore be easily ported to a variety of platforms. Our PARAllelized Matrix Exponentiation for Numerical Time evolution (PARAMENT) implementation runs on CUDA-enabled graphics processing units. Program summaryProgram Title: PARAMENTCPC Library link to program files:https://doi.org/10.17632/zy5v4xs89d.1Developer's repository link:https://github.com/parament-integrator/paramentLicensing provisions: Apache 2.0Programming language: C / CUDA / PythonNature of problem: Time-integration of the Schrödinger equation with a time-dependent Hamiltonian for quantum systems with a small Hilbert space but many time-steps.Solution method: A 4th order Magnus integrator, highly parallelized on a GPU, implemented using a small subset of BLAS functions for improved portability.

Integration and exploitation of intra-routine malleability in BLIS

Malleability is a property of certain applications (or tasks) that, given an external request or autonomously, can accommodate a dynamic modification of the degree of parallelism being exploited at runtime. Malleability improves resource usage (core occupation) on modern multicore architectures for applications that exhibit irregular and divergent execution paths and heavily depend on the underlying library performance to attain high performance. The integration of malleability within high-performance instances of the Basic Linear Algebra Subprograms (BLAS) is nonexistent, and, in addition, it is difficult to attain given the rigidity of current application programming interfaces (APIs). In this paper, we overcome these issues presenting the integration of a malleability mechanism within BLIS, a high-performance and portable framework to implement BLAS-like operations. For this purpose, we leverage low-level (yet simple) APIs to integrate on-demand malleability across all Level-3 BLAS routines, and we demonstrate the performance benefits of this approach by means of a higher-level dense matrix operation: the LU factorization with partial pivoting and look-ahead.

Performance evaluation of kernel fusion BLAS routines on the GPU: iterative solvers as case study

Programmers usually implement iterative methods that solve partial differential equations by expressing them using a sequence of basic kernels from libraries optimized for the graphics processing unit (GPU). The global runtime of the resulting combination is often penalized by the smallest and most inefficient vector operations. To improve the GPU exploitation, we identify and analyze the potential kernels to be fused according to the data dependence, data type and size, and GPU resources. This paper provides an extensive analysis of the impact of fusing vector operations [level 1 of Basic Linear Algebra Subprograms (BLAS)] on the performance of the GPU. The experimental evaluation shows that this optimization provides noticeable improvement especially for kernels with lower memory requirements and on more modern GPUs. It is worth noting that the fused BLAS operations can be very useful to help programmers efficiently code iterative methods to solve large linear systems of equations for the GPU. Iterative methods such as biconjugate gradient method (BCG) are one of the examples that can benefit from this optimization strategy. Indeed, kernel fusion of vector routines makes the most efficient GPU implementation of BCG run between $$1.09\times $$ 1.09 × and $$1.27\times $$ 1.27 × faster on three GPUs of different characteristics.

High performance BLAS formulation of the adaptive Fast Multipole Method

In a previous work, we have presented a new formulation of the uniform version of the Fast Multipole Method (FMM) for the Laplace equation by using matrix products that can be efficiently computed thanks to the BLAS (Basic Linear Algebra Subprograms) routines. We propose here to extend this formulation to the adaptive version of the FMM: this requires the conception of a new data structure for the octree, namely the octree with indirections, which is efficient for both uniform and non-uniform distributions, as well as a detection mechanism of the available uniform areas in non-uniform distributions. In comparison with other M2L computation schemes (block FFT, rotations and plane wave expansions) in the case of non-uniform distributions of particles, our BLAS version appears to be the fastest for the common precisions used when one solves the Laplace equation.