By R. C. Calinescu DPhil, MSc (auth.)
Architecture-independent programming and automated parallelisation have lengthy been considered as diversified technique of assuaging the prohibitive expenditures of parallel software program improvement. construction on fresh advances in either parts, Architecture-Independent Loop Parallelisation proposes a unified method of the parallelisation of clinical computing code. This novel method is predicated at the bulk-synchronous parallel version of computation, and succeeds in instantly producing parallel code that's architecture-independent, scalable, and of analytically predictable functionality.
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4), and computes the size ofa data footprint by case analysis on the matrix G. e. Idet GI = I), when G is invertible, when the rows of G are dependent and its columns are independent, and when the columns of G are dependent. Their framework is then able to provide solutions to the first three cases. These solutions are exact for single references and close approximations for multiple references. Our footprint size computation framework extends and significantly simplifies the one proposed by Agarwal et al.
Nevertheless, for the dense computations whose automatic parallelisation is addressed in this book, the initial data are typically distributed uniformly across the processors of the parallel machine. Furthermore, the execution of the parallel schedules we consider always leaves the data uniformly distributed. Hence, the amount of data received by a processor during the preliminary superstep is also a good measure for the amount of data sent by a processor, and we shall use it to quantify the size of the h-relation.
K XklXk2 .. 7) det[~1 '~2,oo·,gkml#O Rule 2: If the k-th column ofG, 1 ::; k::; K, is zero, F(IKI, G) = F(IK-I [XI ,X2, ... ,Xk-I ,Xk+I, ... ,XK]T, [gl ,g2, .. · ,~-I ,~+I, ... 8) 4. Communication Overheads in Loop Nest Scheduling 30 Rule 3: /fgj,k, 1 $ j $ m, 1 $ k $ K, is the only non-zero element in the j-th row of G, F(IKx,G) =XkF(IK-J[XI,X2, ... ,Xk_I,Xk+I, ... ,XK]T, [gl,~, ... 9) Rule 4: Let gj,I. gj,2, ... , gj,K be the elements of the j-th row of G, 1 $ j $ m, and a = gcd(gj,l,gj,2, ...
Architecture-Independence Loop Parallelisation by R. C. Calinescu DPhil, MSc (auth.)