Download Architecture of High Performance Computers Volume II: Array by R. N. & Topham, N. P. Ibbett PDF

By R. N. & Topham, N. P. Ibbett

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Hence, East may be connected to West and North may be connected to South. 10. 3. Both machines support the FORTRAN DO loop in their respective instruction sets to varying degrees of sophistication. The TI ASC provides support for triple-nested loops wh ich are iterated sequentially. In comparison the DAP has a single-nested loop which evaluates all iterations of a double-nested 64 x 64 loop (in the x and y dimensions) in parallel. 5 Performance In this section we look at the performance of the DAP in several ways.

The binary k-cube A binary k-cube, often referred to simply as a 'hypercube', connects N = 2k network nodes in the form of a cube constructed in k-dimensional space. The corners of this cube represent the nodes, and the edges represent the inter-nodal connections. More formally, if the nodes are numbered from o to 2 k - 1, no des whose binary numbering differs in exactly one position have connections between them. 9 shows how binary k-cubes are constructed far k in the range 0 to 4. 9 Constructing binary k-cubes The binary k-cube therefore has k routing functions, Ci {O ::; i ::; k-1}, one routing within each dimension, defined thus Informally, for each dimension either an exchange permutation (Ei) or an identity permutation (I) is applied to x in order to establish a route from any sour ce to any destination node.

N, and as m is normally similar in magnitude to n this equates to approximately n 2 . This makes such interconnection structures impractical for highly parallel systems, where n and mare typically in the range 28 to 2 16 . Designers must forgo the luxury of full connectivity, and accept more restricted, or slower, communication structures. In an SIMD system the movement of data through the interconnection structure takes place under explicit program contro!. Therefore, datamovement instructions must define source-to-destination mappings, known 22 Interconnection Networks 23 as routing functions, from which network control signals can be generated.

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