By Allen R, Kennedy K
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Additional resources for Optimizing compilers for modern architectures; a dependence based approach
In the early 1970's, Compass created a transformation tool for the Illiac IV known as the Parallelizer. The key papers describing the Parallelizer include theoretical technical reports by Lamport [13,14] and an elegant paper by Loveman espousing a philosophical approach toward optimization . The most influential ideas on automatic program transformations were pioneered at the University of Illinois under the direction of David Kuck. Illinois had been involved with parallelism at its very early stages via the Illiac series of computers; the direction of research turned toward automatic program transformations in the mid 1970's with the inception of the Parafrase project.
The compiler is free to transform a program in any way that makes sense, so long as the transformed program computes the same results as the original specification. While this viewpoint seems natural enough, it is often met with skepticism because of the radical transformations required to exploit parallelism. For instance, matrix multiplication required loop interchange, loop splitting, loop distribution, vectorization, and parallelization to achieve optimal results across various parallel architectures.
Since vector loops are executed “synchronously” by hardware, they must be the innermost loops in a given nest. Parallel loops, on the other hand, are executed asynchronously and therefore it is desirable to move them to the outermost position to ensure that there is enough computation to compensate for the start-up and synchronization overhead. 0 DO K = 1, N C(J,I) = C(J,I) + A(J,K) * B(K,I) ENDDO ENDDO ENDDO In this form, each processor can independently compute a column of the product matrix, with no need to synchronize with other processors until the product is complete.