Consider the following program fragment that deals with a table $\mathrm{T}$ with $17$ rows and $1024$ columns, computing an average for each column and printing it to screen ( $\mathrm{i}$ is row index and $\mathrm{j}$ is column index):
for j = 0 . .1023]{
temp $=0$;
for $\mathrm{i}=[0 \ldots 16]$;
temp $=$ temp $+T[i][i]$
print $($ temp $/ 17.0) ;\}$
$\mathrm{T}$ [i] [i] and temp are $32$ bit floating point values and memory is word addressable. The temporary variable temp is kept in a processor register so access to temp does not involve a memory reference. The main memory is page and holds $16$ pages of size $1024$ words, the page replacement policy is "least recently used ", If $\mathrm{T}$ is stored in the virtual address space in row major format.
Consider that $\mathrm{T}$ is stored in column major format, how many page faults will be encountered?
- $14$
- $15$
- $16$
- $17$
