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Why is an unrolling amount of three or four iterations generally sufficient for simple vector loops on a RISC processor? What relationship does the unrolling amount have to floating-point pipeline depths?
On a processor that can execute one floating-point multiply, one floating-point addition/subtraction, and one memory reference per cycle, what’s the best performance you could expect from the following loop?
DO I = 1,10000
A(I) = B(I) * C(I) - D(I) * E(I)ENDDO Try unrolling, interchanging, or blocking the loop in subroutine
BAZFAZ to increase the performance. What method or combination of methods works best? Look at the assembly language created by the compiler to see what its approach is at the highest level of optimization.
BAZFAZ separately; adjust
NTIMES so that the untuned run takes about one minute; and use the compiler’s default optimization level.
PROGRAM MAIN
IMPLICIT NONEINTEGER M,N,I,J
PARAMETER (N = 512, M = 640, NTIMES = 500)DOUBLE PRECISION Q(N,M), R(M,N)
CDO I=1,M
DO J=1,NQ(J,I) = 1.0D0
R(I,J) = 1.0D0ENDDO
ENDDOC
DO I=1,NTIMESCALL BAZFAZ (Q,R,N,M)
ENDDOENDSUBROUTINE BAZFAZ (Q,R,N,M)
IMPLICIT NONEINTEGER M,N,I,J
DOUBLE PRECISION Q(N,M), R(N,M)C
DO I=1,NDO J=1,M
R(I,J) = Q(I,J) * R(J,I)ENDDO
ENDDOC
END Code the matrix multiplication algorithm in the “straightforward” manner and compile it with various optimization levels. See if the compiler performs any type of loop interchange.
Try the same experiment with the following code:
DO I=1,N
DO J=1,NA(I,J) = A(I,J) + 1.3
ENDDOENDDO
Do you see a difference in the compiler’s ability to optimize these two loops? If you see a difference, explain it.
Code the matrix multiplication algorithm both the ways shown in this chapter. Execute the program for a range of values for N. Graph the execution time divided by N3 for values of N ranging from 50×50 to 500×500. Explain the performance you see.
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