VirtualGate2018-I-64

Question

Suppose a $32 K×8 K$ matrix A with $1$-byte elements is stored in row major order in virtual memory. Assume that only the program in question occupies space in physical memory.
Program $1$

for (i = 0; i < 32768; i++)
   for (j = 0; j < 8192; j++)
       A[i][j] = A[i][j] * A[i][j];

Program $2$

for (j = 0; j < 8192; j++)
 for (i = 0; i < 32768; i++)
      A[i][j] = A[i][j] * A[i][j];

If both program $1$ and program $2$ causes $8 K$ page faults, how many page faults would program $2$ experience if the physical memory can store only $1$ page?

$(A) 8M$
$(B) 16M$
$(C) 32M$
$(D) 64M$

Comments

Yes ma'am this row nd column majormajor I know.The question says how many page faults if " physical memory can store one page".meaning?

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I think it will be like this ,

j is page number for process P1 i.e. row major

and i is page number for P2 i.e. column major

Now, of course we can see P2  require more pages than P1

But, P1 and P2 has same page fault

That means P2 and P1 has same number of pages

So, we can say for loop executing more in P2 to visit 1 page than P1

As size of page in P2= size of page  in P1

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Finally understud to some extent😋

Thank you ma'am.

Answer 1

Given a matrix of size 32K*8K

also given that the page fault of both are equal, which is only possible if the whole matrix can be stored in memory.

Further its mentioned that the number of page fault is 8K which means the page size is 32K

Now we need to find out the number of page fault caused by program2 with page size 32K

Number of accesses in program2 for a single page = 4

for each iteration of for(i = 0; i < 32768; i++) loop there will be 32K/4 page faults = 8K page faults

This is repeated for(j = 0; j < 8192; j++) number of times.

Hence total number of page faults = 8K*8K = 64M

Option D is the correct answer

Comments

Number of page faults in program2 for a single page = 4

How?

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@Arjun

Sorry, I actually ment we can access 4 elements in a page without a page fault.

Answer 2

The correct answer is (D) 64M

 

Answer 3

64

Comments

Please do not copy paste answers