February 22, 2017

A Systolic Array Parallelizing Compiler by Ping-Sheng Tseng

By Ping-Sheng Tseng

Widespread use of parallel processing becomes a truth provided that the method of porting functions to parallel pcs could be mostly computerized. often it's trouble-free for a consumer to figure out how an software may be mapped onto a parallel computing device; even though, the particular improvement of parallel code, if performed by means of hand, is usually tough and time eating. Parallelizing compilers, which may gen­ erate parallel code instantly, are hence a key expertise for parallel processing. during this publication, Ping-Sheng Tseng describes a parallelizing compiler for systolic arrays, referred to as AL. even though parallelizing compilers are very common for shared-memory parallel machines, the AL compiler is without doubt one of the first operating parallelizing compilers for allotted­ reminiscence machines, of which systolic arrays are a distinct case. The AL compiler takes good thing about the effective grain and excessive bandwidth interprocessor communique functions in a systolic structure to generate effective parallel code. xii Foreword whereas in a position to dealing with a massive classification of functions, AL isn't really meant to be a general-purpose parallelizing compiler.

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We assume that the systolic array has as many cells as data compatibility classes in the DO* loop so that we can simply assign data compatibility class C i to reside on cell i and loop iteration i to execute on cell i. We assume cells are fully interconnected so that any cell can communicate with any other cell directly. We call such a loop distribution model the simple loop distribution model. In the simple loop distribution model, each cell has a copy of the Loop Distribution 39 normal variables and a single data compatibility class.

3 shows an AL compiler generated W2 matrix factorization program for the lO-celi Warp machine. For this particular example, the compiler distributes data slices by assigning slice A[ i] to cell (i modulo 10). Systolic array programming 17 float a [50] [500], row[500]; int k, i, fe, fi, ee, ei, lj; for k := 0 to n do { if (eellid = (k 1. 10» then { for i := k+l to n do { a[k/l0] [i] := - a[k/l0] [i] /a[k/l0] [k]; } } for i := k+l to n do { if (eellid = (k 1. 10» then { row[i] := a[k/l0] [i] ; send(l, row[i]); sendeR, row[i]); } else { if (eellid < (k 1.

1 fB 3 For such a case, we have to dynamically distribute some DARRAYs for each DO'" loop, which will be discussed in the next section. 3 Scope of data compatibility classes The default scope of a set of data compatibility classes is the DO'" loop which defines them. However, by constructing joint data compatibility classes, we may extend its scope to the entire program. IT a program only has a single set or multiple unrelated sets of data compatibility classes, the scope of all its data compatibility classes is the entire program.

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