In this exercise, we look at memory locality properties of matrix computation. The following code is written in C, where elements within the same row are stored contiguously. Assume each word is 32-bit integer, and A and B are 16x16 integer arrays. For (I = 0; I < 15; I++) For (J = 0; J < 15; J++) A[I] [J] = B[J][I] + A[J][0]; a) How many 32-bit integers can be stored in a 16-byte cache block?
b) References to which variables exhibit temporal locality?
c) References to which variables exhibit spatial locality?
d) Assume that starting address of matrix A is 0 times 1000, and the starting address of matrix B is 0 times 1800. Given a 512Byte 2-way set associative data cache with write allocate. Assume each cache block is 16 Byte. Estimate the cache hit ratio.
Locality is affected by both reference order and data layout. The same computation can also be written below in Matlab, which differs from C by storing matrix elements within the same column contiguously in memory.
For I = 1:15
For J =1:15
A(l, J) = B(J, I) + A(J, 0);
End
a) How many 16-byte cache blocks are needed to store both matrix A and B?
b) References to which variables exhibit temporal locality?
c) References to which variables exhibit spatial locality?
d) Assume that starting address of matrix A is 0 times 1000, and the starting address of matrix B is 0 times 1800. Given a 512Byte 2-way set associative data cache with write allocate. Assume each cache block is 16 Byte. Estimate the cache hit ratio.