Question

For the given code snippets, predict the cache hit rate. The cache is 256KB, direct mapped,

and has 64-byte cache lines. There are two implementations for the for loops (v1 and v2) which
are executed separately in isolation. Assume that the:
a. long variables total_sum and array arr are doublewords
b. the cache is empty before the loops start executing.

Answer 1

The cache hit rate for the given code snippets is 100% for v2 implementation and a calculation is provided to determine the cache lines needed for v1 implementation.

Step-by-step explanation:

In a direct mapped cache, each cache line can only store one block of memory. In this case, the cache has a total size of 256KB, which is equivalent to 256 * 1024 bytes. Each cache line is 64 bytes. To calculate the number of cache lines, we divide the total cache size by the cache line size: 256 * 1024 / 64 = 4096 cache lines.

For v1 implementation, assume that the array arr is 1024 longs (doublewords). Each long (doubleword) is 8 bytes. So, the total size of the array is 1024 * 8 = 8192 bytes. Since the cache is direct mapped, each cache line can only hold one block of memory, which means it can only hold one doubleword. Therefore, we divide the size of the array by the size of each cache line: 8192 / 64 = 128 cache lines are needed to store the array.

For v2 implementation, assume the array arr is 4096 longs (doublewords), which is exactly the number of cache lines. In this case, each doubleword will have a unique cache line assigned to it, resulting in a **100% cache hit rate** for v2 implementation.