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Compiler Optimizations

This document discusses loop interchange and various data transformation techniques that can enhance the performance of programs. It highlights how these methods can improve data locality, reduce cache misses, and optimize memory access patterns. Key concepts like reuse within loops, strip-mining, array alignment, and merging are explored to illustrate their impact on execution efficiency. The importance of understanding reuse distance, cache behavior, and legal transformations in maintaining program correctness is emphasized, providing insights into optimizing compiler performance.

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Compiler Optimizations

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  1. Compiler Optimizations

  2. Loop interchange Do j=1,n do i=1,m b(i,j)=5.0 enddo enddo Do i=1,n do j=1,m b(i,j)=5.0 enddo enddo

  3. Reuse • Programs exhibit reuse • Within loop • Across loops DO I = 2, N-1 B[I] = (A[I-1]+A[I+1]) / 2 END DO DO I = 2, N-1 A[I] = B[I] END DO Reuse within loop Reuse across loops

  4. Locality • Reuse can lead to cache hits if • Cache capacity is large enough (reuse distance) • No cache conflicts occur.

  5. Reuse distance • Definition (reference and memory access) • A reference is a read or a write in the source code, while a memory access is one particular execution of that read or write. • Definition (reuse pair and reuse distance) • A reuse pair (r1; r2) is a pair of memory accesses in a memory access stream, which touch the same memory location, without intermediate accesses to that location. The reuse distance of a reuse pair (r1; r2) is the number of unique memory locations accessed between references r1and r2.

  6. Strip-mining do i=1,n do j=1,n ... = a(i,j) enddo enddo do i=1,n do jj=1,n,B do j=jj,min(jj+B-1,n) ... = a(i,j) enddo enddo enddo

  7. Tiling (Strip-mining & loop interchange) do jj=1,N,B do ii=1,N,B do t=1,T do j=jj,min(jj+B-1,N) do i=ii,min(ii+B-1,N) ... = a[i,j] end do end do end do end do end do do t=1,T do j=1,N do i=1,N ... = a[i,j] end do end do end do

  8. Data transformations • Alignment • Array padding • Array element reordering • Array merging

  9. Alignment • Align a data structure such that it begins at a cache line boundary. • Useful for cache-line-sized data structures. • May also help to reduce false sharing.

  10. Array Padding • Increases size of inner array dimension. integer a[256,256] do j=1,N do i=1,N ... = a[i,j]+ a[i,j+1] end do end do integer a[260,256] .... j i Assumption: 64 lines á 4 words

  11. Array Element Reordering • Modifies storage order for elements integer A[256,512] DO I = 1, 256 DO J = 1, 512 ...=A[I,J] ... END DO END DO integer A[512,256] DO I = 1, 256 DO J = 1, 512 ...=A[J,I] ... END DO END DO

  12. Array Merging • Interleaves data from multiple arrays integer B[200], A[200] DO I = 2, N-1 ... B[I]=... A[I]... ... END DO integer C[400] DO I = 2, N-1 ... C[2*I-1]=... C[2*I]... ... END DO

  13. Summary • Loop transformations and data transformations can improve locality. • Elimination of conflicts and reduction of reuse distance. • Legality of loop transformations depends on dependences. • Data transformations are always legal as long as all references can be adapted. • Profitability of transformation is extremely difficult to predict.

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