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Cache Miss Rate Computations

This text explores the cache miss rates for a simple array cache using different scenarios and access patterns. It covers topics such as array fits in cache, reusing blocks, accessing blocks in order, and 2D array accesses.

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Cache Miss Rate Computations

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  1. Cache Miss Rate Computations Topics • Simple examples

  2. Assumed Simple Cache • 2 ints per block • 2-way set associative • 2 blocks total • 1 set • i.e., same thing as fully associative • Replacement policy: Least Recently Used (LRU) Cache Block 0 Block 1

  3. Array Access: Key Questions • How many array elements are there per block? • Does the data structure fit in the cache? • Do I re-use blocks over time? • In what order am I accessing blocks?

  4. Simple Array Cache for (i=0;i<N;i++){ … = A[i]; } A Miss rate = #misses / #accesses

  5. Simple Array Cache for (i=0;i<N;i++){ … = A[i]; } A Miss rate = #misses / #accesses = (N//2) / N = ½ = 50%

  6. Simple Array w outer loop Cache for (k=0;k<P;k++){ for (i=0;i<N;i++){ … = A[i]; } } A Assume A[] fits in the cache: Miss rate = #misses / #accesses =

  7. Simple Array w outer loop Cache for (k=0;k<P;k++){ for (i=0;i<N;i++){ … = A[i]; } } A Assume A[] fits in the cache: First Visit Miss rate = #misses / #accesses = (N//2) / N = ½ = 50%

  8. Simple Array w outer loop Cache for (k=0;k<P;k++){ for (i=0;i<N;i++){ … = A[i]; } } A Assume A[] fits in the cache: Miss rate = #misses / #accesses  0% if P  infinity Lesson: for sequential accesses with re-use, If fits in the cache, first visit suffers all the misses

  9. Simple Array Cache for (i=0;i<N;i++){ … = A[i]; } A Assume A[] does not fit in the cache: Miss rate = #misses / #accesses

  10. Simple Array Cache for (i=0;i<N;i++){ … = A[i]; } A Assume A[] does not fit in the cache: Miss rate = #misses / #accesses = (N/2) / N = ½ = 50% Lesson: for sequential accesses, if no-reuse it doesn’t matter whether data structure fits

  11. Simple Array with outer loop Cache for (k=0;k<P;k++){ for (i=0;i<N;i++){ … = A[i]; } } A Assume A[] does not fit in the cache: Miss rate = #misses / #accesses = (N/2) / N = ½ = 50% Lesson: for sequential accesses with re-use, If the data structure doesn’t fit, same miss rate as no-reuse

  12. 2D array Cache for (i=0;i<N;i++){ for (j=0;j<N;j++){ … = A[i][j]; } } A Assume A[] fits in the cache: Miss rate = #misses / #accesses = (N*N/2) / (N*N) = ½ = 50%

  13. 2D array Cache A for (i=0;i<N;i++){ for (j=0;j<N;j++){ … = A[i][j]; } } Assume A[] does not fit in the cache: Miss rate = #misses / #accesses = 50% Lesson: for 2D accesses, if row order and no-reuse, same hit rate as sequential, whether fits or not

  14. 2D array Cache for (j=0;j<N;j++){ for (i=0;i<N;i++){ … = A[i][j]; } } A Assume A[] fits in the cache: Miss rate = #misses / #accesses = (N*N/2) / N*N = ½ = 50% Lesson: for 2D accesses, if column order and no-reuse, same hit rate as sequential if entire column fits in the cache

  15. 2D array Cache A for (j=0;j<N;j++){ for (i=0;i<N;i++){ … = A[i][j]; } } Assume A[] does not fit in the cache: Miss rate = #misses / #accesses = 100% Lesson: for 2D accesses, if column order, if entire column doesn’t fit, then 100% miss rate (block (1,2) is gone after access to element 9).

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