Name: cs598dhp Parallel Processing Midterm Exam Due in ... - Polaris

cs598dhpParallel ProcessingMidterm ExamDue in class Tuesday, May 4, 2008(11 pages / 8 questions total)Name:____________________________1. Short questions [5 pts.](a) A way to characterize locality of a program is the space-time product. Find the definitionof space time product and state it. How is it related to the notion of efficiency for parallelprograms? In other words, what figure of merit tends to improve when space-time product isminimized or efficiency is maximized?1

(b) List the essential features of the Von Neumann computational model2

2. Paging [5 pts.] Consider the loop below where array A is assumed stored bycolumns. Assume a computer with n page frames available in main memory. Eachpage is 512 bytes long. Assume also that the replacement strategy is Least RecentlyUsed (LRU). Finally, assume that no page from A or B is in main memory when theloop starts executing. If n = 1, 2 and 3, state how many page faults will take place?For what value of n will the number of page faults will be lower than the number ofpage faults when n=3? For the purposes of this problem, you can ignore all referencesother than those to A and B.real A(128,128),B(128,128)do i=1,128do j=1,128A(i,j)=B(i,j) + A(i,j)B(i,j)=A(i,j)+1end doend do3

3. Locality enhancement [5 pts.] Consider the loop below.(a) How would you transform it to enhance locality?(b) For large values of n, what fraction of cache misses do your improved versionsaves relative to the original version?do i=1,ndo j=1,nB(i,j)=A(i,j+1)+A(i-1,j)+A(i,j-1)+A(i+1,j)end doend do4

4. SIMD programs [5 pts.] Consider the programdo i=1,na(i) = b(i) + c(i)s = s + a(i)end do(a) Translate this program into a vector version. Use only triplet notation. Do not useintrinsic functions to represent operations.(b) Compute the speedup, efficiency, and redundancy on an array machine assumingn/4 PEs. Assume all floating point operations take one unit of time and ignore allother operations including those to control the loop and those needed forcommunication.5

5. SIMD programming [10 pts.]Transform the following program into vector form.Vectorize as much as possiblek=ip=d(i)do j=i+1,nif (d(j)>=p) thenk=jp=d(j)end ifend doif (k /= i) thend(k)=d(i)d(i)=pdo j=1,np=v(j,i)v(j,i)=v(j,k)v(j,k)=pend doend if6

6. OpenMP [5 pts.] Parallelize (as much as possible) the following loop and present thesolution in OpenMPdo i=1,ndo j=1,nk=k+px = a(k,j) + b(j,i)c(i,j)= x + x ** 2 + a(k,j) + 1end doend do7

7. OpenMP [5 pts.] For each of the following three loop nests, specify whether or notthe outermost loop can be transformed into parallel form without changing the loopbody. If the answer is no, state the reason(a) do i=1,ndo j=1,na(i,j) = a(i,j-1) + 1b(i,j) = a(i,j) + a(i,j)end doend do(b) do i=1,ndo j=1,na(i,j) = a(i-1,j-1) + 1end doend do(c) do i=1,ndo j=1,na(i,j) = a(i-1,n+1) + 1b(i,j) = a(i-1,j) + a(i,j)end doend do8

8. Race conditions [5 pts.] In the following four code segments, identify whether ornot there are race conditions. In each case, explain why or why not and list all raceconditions you can detect. Also, indicate what directives need to be inserted in eachcase to get rid of the race conditions.(a)c$ompc$ompc$ompc$ompc$ompc$ompparallel private(i)pdodo i=1,nx(i)=x(i)+1end doend pdo nowaitpdodo i=1,ny(i)=x(i) + 1end doend pdo nowaitend parallel9

(b)c$ompc$ompc$ompc$ompparallel private(i)pdodo i=1,nx(i)=x(i)+1end doend pdo waitx(5) = x(5) + 1end parallel10

(c)c$ompparallel dodo i=1,na(i)=b(i+1)+b(i-1)+a(i)end do(d)c$ompc$ompc$ompparallel private(i,j,k,t)k=some_function()t=y+x(k)barrierj=omp_get_thread_num()x(j)=tend parallel11