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Consider the following program fragment that deals with a table T with 17 rows and 1024 columns, computing an average for each column and printing it to screen, where i is row index and j is column index:

for j = [0.....1023] {

temp = 0;

for i = [0.....16]:

temp = temp + T[i][j];

print(temp/17.0);

}

T[i][j] 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 paged and holds 16 pages of size 1024 words, the page replacement policy is least recently used.

Consider that T is stored in column major format, how many page faults will be encountered?





Solution

Total elements in table T:

$17 \times 1024 = 17408$

Page size:

$1024$ words

Number of pages required:

$\frac{17408}{1024}=17$

In column major format, the program accesses elements column by column, so memory access is sequential.

Each page will cause one page fault.

Therefore,

Total page faults = $17$


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