Applicable course goals: Acquire and apply skills to analyze and quantify the effects of various system design criteria; further develop analytical skills and the ability to solve problems.
This assignment is based on the material in Chapter 2 & Appendix B – Memory Hierarchy.
In Part 1, average memory access time was presented as an indirect measure of memory performance. The basic formula for calculating AMAT is
AMAT = time for a hit + (miss rate x miss penalty).
In Part 2, we expanded the formula to encompass a level 1 and level 2 cache. The expanded formula for a 2-level cache is
AMAT = Hit timeL1 + (Miss rateL1 x (Hit timeL2 + (Miss rateL2 x Miss penaltyL2)))
1. Continue expanding the formula and derive the full calculation for a 3-level cache.
2. The following table defines the profile for a multilevel cache hierarchy.
Using the information in the table, calculate the average memory access time for this memory hierarchy. (10 points)
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3. The transpose of a matrix interchanges its rows and columns. The following diagram illustrates this concept.
123456789 Transpose 147258369
Here is a simple loop written in C that performs a matrix transpose on a 3 x 3 matrix:
for ( i = 0; i < 3; i++ )
for ( j = 0; j < 3; j++ )
Output[j][i] = input[i, j];
Assume all of the following:
The execution of the above code on the large matrix is not ideal for performance and applying loop interchange will not completely alleviate the performance issues. Therefore, blocking must be applied (Ch. 2/App. B – Part 3: Slide 13).
Rewrite the loop code above to perform the transpose with a block size parameter B that uses B x B blocks. (20 points)
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