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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,NA(J,I) = B(I,J) A(J,I) = B(I,J)
ENDDO ENDDOENDDO 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?
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. We really need a general method for improving the memory access patterns for
both
A and
B , not one or the other. We’ll show you such a method in
[link] .
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