Cache Miss Rate Computations

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Cache Miss Rate Computations

• Topics
• Simple examples

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Assumed Simple Cache
Cache


Block 0
Block 1

• 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)

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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?

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Simple Array
Cache
for (i0iltNi) Ai


1 2 3 4
A
Miss rate misses / accesses
5
Simple Array
Cache
for (i0iltNi) Ai


1 2 3 4
A
Miss rate misses / accesses
(N//2) / N ½ 50
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Simple Array w outer loop
Cache
for (k0kltPk) for (i0iltNi)
Ai


1 2 3 4
A
Assume A fits in the cache Miss rate
misses / accesses
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Simple Array w outer loop
Cache
for (k0kltPk) for (i0iltNi)
Ai


1 2 3 4
A
Assume A fits in the cache First Visit Miss
rate misses / accesses
(N//2) / N ½ 50
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Simple Array w outer loop
Cache
for (k0kltPk) for (i0iltNi)
Ai


1 2 3 4
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
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Simple Array
Cache
for (i0iltNi) Ai


1 2 3 4 5 6 7 8
A
Assume A does not fit in the cache Miss rate
misses / accesses
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Simple Array
Cache
for (i0iltNi) Ai
5 6
7 8
1 2 3 4 5 6 7 8
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
doesnt matter whether data structure fits
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Simple Array with outer loop
Cache
for (k0kltPk) for (i0iltNi)
Ai


1 2 3 4 5 6 7 8
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 doesnt fit, same miss rate as
no-reuse
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2D array
Cache
for (i0iltNi) for (j0jltNj)
Aij
A


1 2
3 4
Assume A fits in the cache Miss rate
misses / accesses
(NN/2) / (NN) ½ 50
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2D array
Cache
A
for (i0iltNi) for (j0jltNj)
Aij
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16


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
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2D array
Cache
for (j0jltNj) for (i0iltNi)
Aij
A


1 2
3 4
Assume A fits in the cache Miss rate
misses / accesses (NN/2) / NN ½ 50
Lesson for 2D accesses, if column order and
no-reuse, same hit rate as sequential if entire
column fits in the cache
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2D array
Cache
A
for (j0jltNj) for (i0iltNi)
Aij
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16


Assume A does not fit in the cache Miss rate
misses / accesses
100
Lesson for 2D accesses, if column order, if
entire column doesnt fit, then 100 miss rate
(block (1,2) is gone after access to element 9).
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