Re: Theory on loop transformations

assmann@karlsruhe.gmd.de (Uwe Assmann) writes:
>I remember that M. Wolfe (and probably others) have tried to develop a
>theory on loop transformations ...
>In general, I am interested in a general theory on loop transformations.


Actually, it was M. E. Wolf, not M. Wolfe (confusing, isn't it?).
Here are a couple of references on the subject.


Bill Pugh
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U. Banerjee.
  Unimodular transformations of double loops.
  In {\em Proc. of the 3rd Workshop on Programming Languages and
    Compilers for Parallel Computing}, Irvine, CA, August 1990.


Paul Feautrier.
  Some efficient solutions to the affine scheduling problem, part i,
    one-dimensional time.
  Technical Report 92.28, IBP/MASI, April 1992.


Paul Feautrier.
  Some efficient solutions to the affine scheduling problem, part ii,
    multi-dimensional time.
  Technical Report 92.78, IBP/MASI, Oct 1992.


Wayne Kelly and William Pugh,
  Generating Schedules and Code within a
Unified Reordering Transformation Framework,
    Technical Report CS-TR-2995,
    Dept. of Computer Science, University of Maryland, College Park,
    November, 1992




K. G. Kumar, D. Kulkarni, and A. Basu.
  Deriving good transformations for mapping nested loops on hieracical
    parallel machines in polynomial time.
  In {\em Proc. of the 1992 International Conference on
    Supercomputing}, July 1992.


Wei Li and Keshav Pingali.
  A singular loop transformation framework based on non-singular
    matrices.
  In {\em 5th Workshop on Languages and Compilers for Parallel
    Computing}, Yale University, August 1992.


Lee-Chung Lu.
  A unified framework for systematic loop transformations.
  In {\em Proceedings of Third ACM SIGPLAN Symp. on the Principles \&
    Practice of Parallel Programming}, April 1991.


William Pugh.
  Uniform techniques for loop optimization.
  In {\em 1991 International Conference on Supercomputing}, pages
    341--352, Cologne, Germany, June 1991.


J. Ramanujam.
  Non-unimodular transformations of nested loops.
  In {\em Supercomputing `92}, November 1992.


Vivek Sarkar and Radhika Thekkath.
  A general framework for iteration-reordering loop transformations.
  In {\em ACM SIGPLAN'92 Conference on Programming Language Design and
    Implementation}, San Francisco, California, Jun 1992.


Michael E. Wolf and Monica S. Lam.
  A data locality optimizing algorithm.
  In {\em ACM SIGPLAN'91 Conference on Programming Language Design and
    Implementation}, 1991.


Michael E. Wolf and Monica S. Lam.
  A loop transformation theory and an algorithm to maximize
    parallelism.
  In {\em IEEE Transactions on Parallel and Distributed Systems}, July
    1991.






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