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Question: Linear loop transformations are useful in reductions of cache misses and increase possible parall...

Linear loop transformations are useful in reductions of cache misses and increase possible parallelization. Consider the following two loops. Which of these loops would yield better performance? Why?

For I = 1, 1000

For J= 1, 1000

c(J) = c(J) + a(I,J)*b(J)

For J=1, 1000

For J=1, 1000

c(J) = c(J) + a(I,J)*b(J)

Answer 1

LINEAR LOOP TRANSFORMATION: -

For I = 1, 1000

For J= 1, 1000

c(J) = c(J) + a(I,J)*b(J)

For J=1, 1000

For J=1, 1000

c(J) = c(J) + a(I,J)*b(J)

*May be it may missing of the loop part B by the inner loop must be " For I = 1,1000" Then the those two loops of J doesn't have mean.
*So let's make this correction and answer the question. Here first loop would yield better performance than second loop.
*The causes of the array in memory is mannaged in a row-major order.
*Their by the array element a(I,J) and a(I,J+1) will be adjacent in memory location but the array element a(I,J) and a(I+1,J) will not be adjacent .
*Since the first loop have adjacent memory location access in successive iteration of loop and hence locality of reference will be followed and hence there will be better cache hit in first loop than second loop.
*Hence the first design will yield better performance in terms of cache access hit rate.
Please comment for any clarification.

Answer 2