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When Interchange Won't Work

Module by: Charles Severance, Kevin Dowd. E-mail the authors

In the matrix multiplication code, we encountered a non-unit stride and were able to eliminate it with a quick interchange of the loops. Unfortunately, life is rarely this simple. Often you find some mix of variables with unit and non-unit strides, in which case interchanging the loops moves the damage around, but doesn’t make it go away.

The loop to perform a matrix transpose represents a simple example of this dilemma:



      DO I=1,N                          DO 20 J=1,M
        DO J=1,M                          DO 10 I=1,N
          A(J,I) = B(I,J)                      A(J,I) = B(I,J) 
        ENDDO                             ENDDO
      ENDDO                             ENDDO

Whichever way you interchange them, you will break the memory access pattern for either A or B. Even more interesting, you have to make a choice between strided loads vs. strided stores: which will it be?1 We really need a general method for improving the memory access patterns for bothA and B, not one or the other. We’ll show you such a method in (Reference).

Footnotes

  1. I can’t tell you which is the better way to cast it; it depends on the brand of computer. Some perform better with the loops left as they are, sometimes by more than a factor of two. Others perform better with them interchanged. The difference is in the way the processor handles updates of main memory from cache.

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A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

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