Stanislav G. Sedukhin

Blocked All-Pairs Shortest Paths Algorithm for Hybrid CPU-GPU System

This paper presents a blocked algorithm for the all-pairs shortest paths (APSP) problem for a hybrid CPU-GPU system. In the blocked APSP algorithm, the amount of data communication between CPU (host) memory and GPU memory is minimized. When a problem size (the number of vertices in a graph) is large enough compared with a blocking factor, the blocked algorithm virtually requires CPU

Implementing a Code Generator for Fast Matrix Multiplication in OpenCL on the GPU

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Performance Tuning of Matrix Multiplication in OpenCL on Different GPUs and CPUs

GPU exchanging of two block matrices for a block computation on the GPU. We also estimate a required memory/communication bandwidth to utilize the GPU efficiently. On a system containing an Intel West mere CPU (Core i7 970) and an AMD Cypress GPU (Radeon HD 5870), our implementation of the blocked APSP algorithm achieves the performance up to 1 TFlop/s in single precision.

Parallel algorithm and architecture for two-step division-free Gaussian elimination

This paper presents results of an implementation of code generator for fast general matrix multiply (GEMM) kernels. When a set of parameters is given, the code generator produces the corresponding GEMM kernel written in OpenCL. The produced kernels are optimized for high-performance implementation on GPUs from AMD. Access latencies to GPU global memory is the main drawback for high performance. This study shows that storing matrix data in a block-major layout increases the performance and stability of GEMM kernels. On the Tahiti GPU (Radeon HD 7970), our DGEMM (double-precision GEMM) and SGEMM (single-precisionGEMM) kernels achieve the performance up to 848 GFlop/s (90% of the peak) and 2646 GFlop/s (70%), respectively.

Multi-level Optimization of Matrix Multiplication for GPU-equipped Systems

OpenCL (Open Computing Language) is a framework for general-purpose parallel programming. Programs written in OpenCL are functionally portable across multiple processors including CPUs, GPUs, and also FPGAs. Using an auto-tuning technique makes performance of OpenCL programs also portable on different processors. We have developed an auto-tuning system with a code generator for fast matrix multiply kernels in OpenCL. This paper presents results of performance evaluation of DGEMM (double-precision general matrix multiply) and SGEMM (single-precision GEMM) implementations by using the auto-tuning system. Performance evaluations are conducted on two AMD GPUs (Tahiti and Cayman), two NVIDIA GPUs (Kepler and Fermi), and two CPUs (Intel Sandy Bridge and AMD Bulldozer). Our GEMM implementations on the AMD GPUs show higher performance than the highly tuned vendor library while the implementations on the NVIDIA GPUs are comparable.

Image scrambling based on a new linear transform

The design of parallel algorithms and architectures for solving linear systems using two-step division-free Gaussian elimination method is considered. The two-step method circumvents the ordinary single-step division-free method by its greater numerical stability. In spite of the rather complicated computations needed at each iteration of the two-step method, we develop first an innovative regular iterative algorithm, then a two-dimensional array processor by deriving a localized dependency graph of the algorithm and adopting a systematic approach to investigate the set of all admissible solutions and obtain the optimal architecture under linear scheduling. The optimal array processor improves the previous systolic designs based on the widely used Gaussian elimination in term of numerical stability and the time-space complexity for VLSI implementation because of the absence of division operations.

Orbital Algorithms and Unified Array Processor for Computing 2D Separable Transforms

This paper presents results of our study on double-precision general matrix-matrix multiplication (DGEMM) for GPU-equipped systems. We applied further optimization to utilize the DGEMM stream kernel previously implemented for a Cypress GPU from AMD. We have examined the effects of different memory access patterns to the performance of the DGEMM kernel by changing its layout function. The experimental results show that the GEMM kernel with X-Morton layout function superiors to the one with any other functions in terms of performance and cache hit rate. Moreover, we have implemented a DGEMM routine for large matrices, where all data cannot be allocated in a GPU memory. Our DGEMM performance achieves up to 472 GFlop/s and 921 GFlop/s on a system, using one GPU and two GPUs, respectively.

Mesh-of-Tori: A Novel Interconnection Network for Frontal Plane Cellular Processors

A new linear transform for scrambling images is proposed in this paper. The forward transform scrambles the image and the inverse transform unscrambles the image. We define transformation matrices for both scalar and blocked cases. Recursive and non-recursive algorithms based on the new transform are also proposed. The degree of scrambling or unscrambling can be determined by the user. The experimental results show that the positions of the pixels are strongly irregularized using the proposed transform. Unscrambling using a wrong key fails and results in an unintelligible image which cannot be recognized. We also show that the new transform provides a high level of image scrambling and is robust under common attacks and noise. The proposed linear transform is very simple and its implementation as triple-matrix multiplication is straightforward.

A new systolic architecture for pipeline prime factor DFT-algorithm

The two-dimensional (2D) forward/inverse discrete Fourier transform (DFT), discrete cosine transform (DCT), discrete sine transform (DST), discrete Hartley transform (DHT), discrete Walsh-Hadamard transform (DWHT), play a fundamental role in many practical applications. Due to the separability property, all these transforms can be uniquely defined as a triple matrix product with one matrix transposition. Based on a systematic approach to represent and schedule different forms of the

The general matrix multiply-add operation on 2D torus

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