Thesis /

ROMDOC-THESIS-2017-1141

Linear algebra on connex parallel architecture

Calfa, Ana-Maria
2012-09-06

Abstract: In the past 20 years due to the challenges of various fields of science, led to the development of applications that require high computing power, which can not be offered by current sequential architectures von Neumann type. Building a sequential architecture to meet the needs of the modern world in terms of processing large volumes of data is difficult due to limitations of miniaturization imposed that affect the transmission speed but also because of high material resources. Also considering that the world around us, from the formation of the universe, the movement of planets and to the human body are parallel systems, parallel computation show that the evolution was somehow natural. In this thesis we propose the study of an parallel architecture , Connex, which is a linear array of 1024 execution units, each of which is a 16 bit machine with 1 KB of memory to store local data of 512 vectors, with 1024 parts each. Connex Architecture has specific features imposed in order to improve GIPS/Watt and GIPS/mm2 and was designed for embedded computation in systems on chip design. Validation supposes exploring by turn different application domains to see how the specific architectural and design assumptions affected the actual performance. For this we have considered the 13 compuational motifs issued by Berkeley’s University. Of these, the first two reasons: dense linear algebra and sparse linear algebra were investigated in this thesis. The algoritms implemented in the domain of dense linear algebra were transpose a matrix, a matrix with a matrix multiplication and inverse of a matrix, using both Gauss-Jordan elimination method and Cramer's rule. To get the best possible performance, some of these algortmi were implemented, exploring both spatial and temporal dimensions of Connex Array. In the sparse linear algebra algorithms for both random sparse matrices and band type, were implemented: transpose of a matrix, multiplication of a matrix with a vector and a matrix with a matrix multiplication. To emphasize better Connex’s architecture performances, simulation results using VectorC, were compared with results available in literature both for other parallel architectures on the market and sequential architecture, demonstrating that Connex brings an improvement in performance in both cases, but as any parallel system has its own limitations and increasing parallelism is not always the answer to the problem.

Keyword(s): Arhitectura calculatoarelor -- Prelucrare în paralel (Calculatoare) -- Teză de doctorat
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