Consider a machine with a $2$-way set associative data cache of size $64$ $Kbytes$ and block size $16$ $bytes$. The cache is managed using $32$ $bit$ virtual addresses and the page size is $4$ $Kbytes$. A program to be run on this machine begins as follows:
int i, j;
/*Initialize array ARR to 0.0 */
for(i = 0; i < 1024; i++)
for(j = 0; j < 1024; j++)
ARR[i][j] = 0.0;
The size of double is 8 bytes. Array $ARR$ is located in memory starting at the beginning of virtual page $0xFF000$ and stored in row major order. The cache is initially empty and no pre-fetching is done. The only data memory references made by the program are those to array $ARR$.
The cache hit ratio for this initialization loop is: