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 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] a) How many 32-bit integers can be stored in a 16-byte cache line? b) References to which variables exhibit temporal locality? c) References to which variables exhibit spatial locality?

Locality is affected by both the 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 : 8 for j = 1 : 8000 A( i , j ) = B( i , 1 ) + A( j , i ); end end d) References to which variables exhibit temporal locality? e) References to which variables exhibit spatial locality?