By Constantine D. Polychronopoulos (auth.)
The moment 1/2 the Nineteen Seventies was once marked with notable advances in array/vector architectures and vectorization concepts and compilers. This growth endured with a specific specialize in vector machines till the center of the Nineteen Eighties. the key ity of supercomputers in this interval have been register-to-register (Cray 1) or memory-to-memory (CDC Cyber 205) vector (pipelined) machines. although, the expanding call for for greater computational premiums lead certainly to parallel comput ers and software program. in the course of the replication of self sustaining processors in a coordinated process, you possibly can bypass over functionality boundaries due know-how barriers. In princi ple, parallelism bargains limitless functionality strength. however, it's very tricky to gain this functionality power in perform. up to now, we've seen merely the top of the iceberg known as "parallel machines and parallel programming". Parallel programming specifically is a swiftly evolving paintings and, at this time, hugely empirical. during this ebook we talk about numerous points of parallel programming and parallelizing compilers. rather than attempting to increase parallel programming methodologies and paradigms, we regularly concentrate on extra complex subject matters assuming that the reader has an enough heritage in parallel processing. The booklet is equipped in 3 major components. within the first half (Chapters 1 and a couple of) we set the level and concentrate on application differences and parallelizing compilers. the second one a part of this publication (Chapters three and four) discusses scheduling for parallel machines from the sensible viewpoint macro and microtasking and aiding environments). ultimately, the final half (Le.
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Obviously, (3k (*) = U (3k (i). We will first consider 1=1 the transformation for two loops in sequence. Let B1 and B2 be two serial loops in 48 Parallel Programming and Compilers sequence and let /31 (j) denote the j -th iteration of B1 • The transformation will produce a new serial loop such that each iteration of the new loop will execute one iteration of B1 (say /31 (i») and one iteration of B2 (say /32 (i-k») in parallel. Thus the two following loops DO 1=1, N1 /31 (I) ENDO DO 1=1, N2 /32 (I) ENDO will be transformed to DO 1=1, N1 COBEGIN /31 (I) ; IF I>K THEN /32(I-K); COEND ENDO DO I=N 1 - K + 1 , N2 /32 (I) ENDO Since the original iterations of B1 (B 2) are still executed in sequence, violations may arise from loop across depend€nces only.
However, for our purpose we can assume a worst-case overhead of /. For simplicity, let us also assume that our baseunit is the execution time of a program "statement". 9=k. For serial loops of the type discussed so far, the compiler must compute A and g and make the appropriate selection between cycle shrinking, parI i I ioning, or none of Restrueturlng for Parallel Exeeutlon 45 the above (in which case the loop remains serial). Two cases are of interest: >->g=l and >-k>g>1. In this case cycle shrinking is the only alternative for parallelizing the loop.
DO I = 1, N A(aI+b) A(eI+d) ENDO For a flow dependence to exist we must have values i and j oC index I such that 1 ~ i ~ j ~ Nand ai+b = ej+d or ai-ej = d-b. , the greatest common divisor oC a, e), divides d - b. 0+ gcd (a, e) ta j = j 0 + --:--=-""'-- gcd (a, e) Acceptable solutions are those Cor which 1~1~j~. In [Bane79j it is shown how to compute the set S={ (1. j) I (1. j) asolutionand1~1~j~}. From the set S we can then obtain the distance vector as < (j-1) I (1. j) ES>. The procedure Cor multiply nested loops and index expressions with more than one variable is similar.