Question

q4.1: we add a 1 kib cache which has a hit time of 5 clock cycles; our miss penalty is still the 100 clock cycles needed to access main memory. to test this cache, we then run a program that accesses random memory addresses. to the nearest clock cycle, what does the amat converge to as the program runs indefinitely? hint: if the memory accesses are purely random, are you exploiting the spatial/temporal locality offered by caches? what happens to your miss rate?

Answer 1

The AMAT will converge towards the miss penalty of 100 clock cycles as the program runs indefinitely.

Step-by-step explanation:

The AMAT (Average Memory Access Time) is the average time it takes to access a memory location in a computer system, taking into account both cache hits and cache misses. In this case, the cache has a hit time of 5 clock cycles and a miss penalty of 100 clock cycles to access main memory.

If the memory accesses are purely random, it means that there is no spatial or temporal locality being exploited. Spatial locality refers to accessing nearby memory locations, while temporal locality refers to accessing the same memory location multiple times.

As the program runs indefinitely, the AMAT will converge towards the weighted average of the hit time and miss penalty, based on the cache hit rate and miss rate. In this case, since the memory accesses are random, the cache hit rate will be low and the miss rate will be high. Therefore, the AMAT will be closer to the miss penalty of 100 clock cycles.

Answer 2

As the program runs indefinitely and memory accesses are purely random, the AMAT converges to approximately 105 clock cycles.

How to solve

Average Memory Access Time (AMAT) Analysis

Cache Parameters:

Cache size: 1 KiB (1024 bytes)

Hit time: 5 clock cycles

Miss penalty: 100 clock cycles

Memory Access Pattern:

Random memory accesses do not exploit spatial or temporal locality, leading to a high miss rate.

Calculating AMAT:

AMAT = Hit rate * Hit time + Miss rate * Miss penalty

Step 1: Calculate Miss Rate

As the memory accesses are random, the miss rate is equal to the probability that the accessed address is not present in the cache.

Since the cache is very small (1 KiB) compared to the total address space, the probability of a miss is very high, approaching 1.

Therefore, Miss rate ≈ 1

Step 2: Calculate AMAT

AMAT ≈ (1) * 5 + (1) * 100

AMAT ≈ 5 + 100

AMAT ≈ 105 clock cycles

As the program runs indefinitely and memory accesses are purely random, the AMAT converges to approximately 105 clock cycles. This is because the high miss rate due to the small cache size and random access pattern overshadows the benefits of the fast hit time.