Question

The following code is written in C, where elements within the same row are stored contiguously. Assume each word is a 32-bit integer.
for (I = 0; I < 8; I++)

for (J = 0; J < 8000; J++)

A[I][J] = B[I][0] + A[J][I];

5.1.1 How many 32-bit integers can be stored in a 16-byte cache block?

5.1.2 References to which variables exhibit temporal locality?

5.1.3 References to which variables exhibit spatial locality?

Answer 1

5.1.1 How many 32-bit integers can be stored in a 16-byte cache block?

Ans :-

5.1.2 References to which variables exhibit temporal locality?

Ans:-

5.1.3 References to which variables exhibit spatial locality?

Ans:-

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Answer 2

5.1.1 How many 32-bit integers can be stored in a 16-byte cache block?

To determine how many 32-bit integers can be stored in a 16-byte cache block, we need to consider the size of each 32-bit integer and the total size of the cache block.

A 32-bit integer takes 4 bytes (32 bits / 8 bits per byte). A 16-byte cache block can store:

Number of 32-bit integers = Cache block size / Size of each 32-bit integer Number of 32-bit integers = 16 bytes / 4 bytes per 32-bit integer Number of 32-bit integers = 4

So, a 16-byte cache block can store 4 32-bit integers.

5.1.2 References to which variables exhibit temporal locality?

Temporal locality refers to the tendency of a program to access the same memory location repeatedly over a short period of time. In the given code snippet, references to variable A exhibit temporal locality. This is because the inner loop iterates over J from 0 to 7999, and in each iteration, the element A[J][I] is accessed repeatedly for different values of I. As a result, there is a high probability that the same memory location in array A will be accessed multiple times within a short time span.

5.1.3 References to which variables exhibit spatial locality?

Spatial locality refers to the tendency of a program to access memory locations that are close to each other in memory. In the given code snippet, references to variable B exhibit spatial locality. This is because the expression B[I][0] accesses elements within the same row (i.e., row I) of array B. The consecutive elements in a row are stored contiguously in memory, and as the outer loop iterates over I from 0 to 7, there is a high likelihood that the memory locations containing elements of the same row will be accessed successively, demonstrating spatial locality.