Question

In this exercise, we will look at the different ways capacity affects overall performance. In general, cache access time is proportional to capacity. Assume that main memory accesses take 70 ns and that memory accesses are 36% of all instructions. The following table shows data for L1 caches attached to each of two processors, P1 and P2.

	L1 Size	L1 Miss Rate	L1 Hit Time
P1	2 KiB	8.0%	0.66 ns
P2	4 KiB	6.0%	0.90 ns

(5.6.1) Assuming that the L1 hit time determines the cycle times for P1 and P2, what are their respective clock rates?

(5.6.2) What is the Average Memory Access Time for P1 and P2?

(5.6.3) Assuming a base CPI of 1.0 without any memory stalls, what is the total Cpi for P1 and P2? Which processor is faster?

For the next three problems, we will consider the addition of an L2 cache to P1 to presumably make up for its limited L1 cache capacity. Use the L1 cache capacities and hit times from the previous table when solving these problems. The L2 miss rate indicated is its local miss rate.

L2 Size	L2 Miss Rate	L2 Hit Time
1 MiB	95%	5.62 ns

(5.6.4) What is the AMAT for P1 with the addition of an L2 cache? Is the AMAT better or worse with the L2 cache?

(5.6.5) Assuming a base CPI of 1.0 without any memory stalls, what is the total CPI for P1 with the addition of an L2 cache?

(5.6.6) Which processor is faster, now that P1 has an L2 cache? If P1 is faster, what miss rate would P2 need in its L1 cache to match P1’s performance? If P2 is faster, what miss rate would P1 need in its L1 cache to match P2’s performance?

Short answer

(5.6.1)

The clock rate for P1 is 1.515 GHz and P2 is 1.111 GHz.

(5.6.2)

The average memory access time for P1 is 6.26 and for P2 is 5.1.

(5.6.3)

The total CPI for P1 is 12.53 and for P2 is 7.33.

(5.6.4)

The average access time for processor P1 with both L1 and L2 cache is 6.42. The average memory access time is worse than processor P1 with only one cache.

(5.6.5)

The value of CPI is 8.317.

(5.6.6)

The processor P2 is fast. The miss rate is 0.0635

Step-by-step solution

Formula for calculating clock rate

(5.6.1)

The clock rate of the processor is the number of cycles per second it can execute. If the hit time determines the clock rate of the processor, the following formula gives the clock rate:

Calculation of clock rate for processors P1 and P2

For processor P1, the hit time is 0.66. Thus, the clock rate is:

For processor P2, the hit time is 0.90. Thus, the clock rate is:

Formula to calculate average memory access time

(5.6.2)

Average memory access time (AMAT) is a metric used to measure the performance of the memory system. The formula to calculate average memory access time is:

Calculation of average memory access time for processors P1 and P2

The average memory access time for P1 is calculated below:

The average memory access time for P2 is calculated below:

Formula to calculate CPI

(5.6.3)

The CPI is the number of cycles per instruction. The formula to calculate total CPI is given as

Calculation of CPI for processors P1 and P2

For processor P1, the total CPI is:

For processor P2, the total CPI is:

Calculation of the average access time for a processor with both L1 and L2 cache

(5.6.4)

The average access time for a processor with both L1 and L2 cache is given as:

Using the values given in the question, the average access time for processor P1 is:

The average memory access time of processor P1 with L1 and L2 cache is more than the time with lone L1 cache. So, the average memory access time is worse.

Calculation of CPI for processor P1 with L1 and L2 cache

(5.6.5)

To calculate the CPI with two L1 and L2 caches, the following formula can be used:

AMAT is calculated in the last step. Using that value, CPI can be calculated as:

Calculation of miss rate for a slower processor to match the performance of a faster processor

(5.6.6)

The average access for processor P1 is 6.42. The average access for processor P2 is 5.11. The processor P2 is fast. For P1 to match P2’s performance

5.11 = 0.66 + miss rate * 70

Miss rate = 0.0635