By Constantine D. Polychronopoulos (auth.)
The moment half the Nineteen Seventies used to be marked with notable advances in array/vector architectures and vectorization thoughts and compilers. This growth endured with a specific specialize in vector machines until eventually the center of the Nineteen Eighties. the main ity of supercomputers in this interval have been register-to-register (Cray 1) or memory-to-memory (CDC Cyber 205) vector (pipelined) machines. notwithstanding, the expanding call for for greater computational premiums lead clearly to parallel comput ers and software program. in the course of the replication of independent processors in a coordinated approach, you'll be able to pass over functionality obstacles due know-how boundaries. In princi ple, parallelism deals limitless functionality power. however, it's very tough to gain this functionality capability in perform. to this point, we've seen in simple terms the end of the iceberg referred to as "parallel machines and parallel programming". Parallel programming specifically is a quickly evolving paintings and, at the moment, hugely empirical. during this ebook we speak about a number of features of parallel programming and parallelizing compilers. rather than attempting to advance parallel programming methodologies and paradigms, we regularly specialise in extra complex subject matters assuming that the reader has an enough heritage in parallel processing. The publication is geared up in 3 major components. within the first half (Chapters 1 and a couple of) we set the degree and concentrate on software differences and parallelizing compilers. the second one a part of this booklet (Chapters three and four) discusses scheduling for parallel machines from the sensible standpoint macro and microtasking and assisting environments). ultimately, the final half (Le.
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Moreover let (3, T 1 , Ts, and Tp be the execution time of a single loop iteration, the serial execution time of a loop, and the execution time of the transformed loops after shrinking and partitioning respectively. In general, the overhead associated with barrier synchronization in multiprocessor systems is not constant. 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).
If either a or e is equal to zero then the process of checking dependence and computing the value of k is trivial. In what follows, we assume that neither a nor e is zero. d. test. If that is passed then we can do the following to obtain the value of k. The problem has been reduced to choosing the value of k such that for all 1,1 ~ i ~ N, if f(i)=g(i-k+1) then 1>0. Substituting we get f (i) =g (1-k+1), or a1+b=ci-ek+e1+d, or finally = 1 (a-c) 1+ (b-d) e + k. Since we must have 1 >0, we get k > (e-a) i+ (d-b) e Ie Also, since 1 ~ 1 ~ N, we know that the maximum value of «e-a) i+ (d-b» must occur at 1=1 or 1=N depending on the sign of (e-a) In either case we see that the following must hold.
N -1. It is obvious however that J is an arithmetic progression shifted (with wrap around) once to the right. 2. Index Recurrences As is the case with induction variables, some times (less often) some loopdefined index variables are used to index array elements. Their values do not form progressions but they give for example, the sum of the first I terms of a progression, where I is the loop index. An example of a simple index recurrence is shown in the following loop. J =0 DO I = 1, N J = J + I A(I} = A(I} + B(J} ENDO 1 In this case J is the sum ~ k for each iteration I of the loop.