Data parallel computers and the FORALL statement

An Axiomatic Semantics for Data-Parallel Computation

“…The precondition of the for loop, I [1], is shown to be consistent with the precondition and statements 1 -4:…”

“…Data parallel computation is attractive because (i) many scientific applications can be conveniently described and efficiently implemented in the framework; and (ii) it is conceptually simpler than many alternative models (for example, CSP [11] and BSP [15]). Its significance is reflected by the adoption of the array assignment construct in FORTRAN 90 [6] and the FORALL statement [1] in HPF [9]. The goals of this paper are to (i) provide an axiomatic definition of data parallel assignment and (ii) illustrate how the resulting formal rules may be used in correctness proofs.…”

A novel compiler support for automatic parallelization on multicore systems

“…For each pixel of the original image (see loop nest in lines 8-9), the program computes a convolution sumX of the 3 × 3 matrix GX and the intensity of the pixel and its eight neighbors (lines [19][20][21][22][23][24]. A similar convolution sumY with the 3 × 3 matrix GY is also computed (lines 25-30).…”

“…Our approach is based on the existence of parallelizing transformations designed for each type of diKernel. The procedure is as follows: (1) scalar reduction diKernels are executed as parallel reduction operations (using the reduction OpenMP clause); (2) regular assignment and regular reduction diKernels are converted into forall parallel loops [19]; (3) irregular assignment and irregular reduction diKernels are transformed via an array expansion technique [20,21]; (4) in general, recurrence diKernels cannot be transformed in parallel code, but there exist parallelizing transformations for particular cases [22] (examples will be shown in Section 4). Thus, the critical path is the longest path that only contains diKernel-level flow dependences and parallelizable diKernels.…”