In this problem we compare cache replacement policies for a given trace of accesses to a set. A trace is made of consecutive block addresses…

 In this problem we compare cache replacement policies for a given trace of accesses to a set. A trace is made of consecutive block addresses dynamically accessed by a program. Take the following trace, where each letter is a block address:

aabcaadeffefefefabgcaef

(a) Assume that the fully associative cache of size 4 lines is cold at the beginning. What is the miss rate under the following replacement policies:

• LRU;

• FIFO;

• pseudo-LRU (you will know what this means from Exercise 4.4);

• LFU (least frequently used). In this policy, the replacement policy counts the number of accesses to each block. The block with the lowest number of references is replaced. In case of a tie, any one of the LFU blocks is picked at random. To make the solution uniform, pick the LRU block among the LFU blocks.

• Optimum.

(b) Calculate the number of conflict misses for each cache in the following cases:

• the number of capacity misses is counted for a FA cache with LRU;

• the number of capacity misses is counted for a FA cache with OPT.