By Utpal Banerjee
Dependence research might be thought of to be the second one variation of the author's 1988 booklet, Dependence research for Supercomputing. it really is, besides the fact that, a totally new paintings that subsumes the cloth of the 1988 e-book. This publication is the 3rd quantity in the sequence Loop differences for Restructuring Compilers. This sequence has been designed to supply a whole mathematical conception of differences that may be used to immediately switch a sequential application containing FORTRAN-like do loops into an identical parallel shape. In Dependence research, the writer extends the version to a application which includes do loops and task statements, the place the loops don't need to be sequentially nested and are allowed to have arbitrary strides. within the context of this sort of software, the writer experiences, intimately, dependence among statements of this system attributable to application variables which are components of arrays. Dependence research is directed towards graduate and undergraduate scholars, writers of restructuring compilers. The prerequisite for the e-book comprises a few wisdom of programming languages, and familiarity with calculus and graph idea. No wisdom of linear programming is needed.
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Additional resources for Dependence Analysis (Loop Transformation for Restructuring Compilers)
First, note that the sets YI, ~ - 1, Y0 r e p r e s e n t the following three d e p e n d e n c e s , respectively: 1. loop-carried d e p e n d e n c e of T on S, 2. loop-carried d e p e n d e n c e of S o n T, 3. l o o p - i n d e p e n d e n t d e p e n d e n c e of T on S (provided S < T). We cannot have a l o o p - i n d e p e n d e n t d e p e n d e n c e of S on T, since S < T by hypothesis. A s s u m e n o w that a, b are n o t b o t h zero. The values of t defining a n o n e m p t y Y-set f o r m a finite sequence of c o n t i g u o u s integers (steps 8, 12, 13).
The iteration p o i n t s are c o n t i g u o u s while the index p o i n t s generally are not. The iteration variable [ always increases f r o m zero in steps of one as the loop is e x e c u t e d sequentially. The index variable I, on the o t h e r hand, m a y increase or decrease d e p e n d i n g on the sign of 0, a n d will n o t c h a n g e in s t e p s of one if 101 > 1. For this reason, it is easier to w o r k with ~ rather t h a n with I. 5) where ~ is an integer. Also, I m u s t lie b e t w e e n 120 and 10.
12(a) become /~(7, - 3 , 0, 38, 0) < c < v ( 7 , - 3 , 0 , 3 8 , 0 ) . 21), and get the inequalities - 1 1 4 < - 5 < 152 which obviously hold. 12, a d e p e n d e n c e of T on S m a y exist. 5 that this is indeed the case. Next, s t u d y the possible d e p e n d e n c e of S on T.