Compile-time Loop Splitting for Distributed Memory ... - Stanford AI Lab

List of Tables
2.1 A 1-D loop nest before and after partitioning. The processor identifier, ranging
from 0 to 3, is denoted by pid. XXXXXXXXXXXXXXXXXXXXXXXXXXXXX 16
2.2 Two examples of task partitioning for a 2-D loop nest: the programmer’s orig-
inal code, the code after blocking, and the code after striping. XXXXXXXXXX 17
2.3 Reduction in operations for array references by an optimizing compiler. XXXX 26
3.1 Transformation of a 1-D loop nest into two different code sequences illustrating
arbitrary loop splitting. The loop body is a function of the index variable �. X X 29
3.2 Ten separate loops of equal iteration length can be reduced in code to two
nested loops. XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 30
3.3 The original loop with a prologue and epilogue both peeled away and grouped
into loops themselves. XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 30
3.4 A loop before and after code hoisting. XXXXXXXXXXXXXXXXXXXXXXXXX 31
3.5 The same code after strength reduction on the multiplication and the modulo
function. XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 32
3.6 Eight code sequences showing various forms of optimization; the right column
is generalization of the example on the left, where — and ˜ are positive integer
constants. XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 33
3.7 A one-dimensional loop erroneously transformed by loop splitting. XXXXXXXX 35
3.8 The previous example with correct loop splitting, showing peeled iterations;
the general loop splitting transformation. XXXXXXXXXXXXXXXXXXXXXXX 36
3.9 The optimized general 1-D array reference. XXXXXXXXXXXXXXXXXXXXX 38
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