1) Visualize the data distributions resulting from the following statements:

!HPF PROCESSORS  p (6), q (2,3)
     REAL A1(10), A2(10,10)

a) !HPF DISTRIBUTE  A1(BLOCK)     ONTO  p
b) !HPF DISTRIBUTE  A1(CYCLIC)    ONTO  p
c) !HPF DISTRIBUTE  A1(CYCLIC(2)) ONTO  p
d) !HPF DISTRIBUTE  A2(BLOCK,*)   ONTO  p
e) !HPF DISTRIBUTE  A2(*,BLOCK)   ONTO  p
f) !HPF DISTRIBUTE  A2(BLOCK,CYCLIC) ONTO  q

(10 points)


2) Visualize the data alignments resulting from the following statements:

REAL s, A1(5), B1(5), A2(5,5), B2(5,5)

a) !HPF ALIGN A1(*)   WITH  s
b) !HPF ALIGN s       WITH  A1(*)  
c) !HPF ALIGN A2(:,*) WITH  A1(:)
d) !HPF ALIGN A1(:)   WITH  A2(:,*)  
e) !HPF ALIGN A1(:)   WITH  A2(:,2)  
f) !HPF ALIGN A2(I,J) WITH  B2(J,I)
g) !HPF ALIGN A1(*)   WITH  B1(*)  
h) !HPF ALIGN A2(:,*) WITH  B2(*,:)  

(15 points)


3)  Consider the following nested FORALL construct:

   FORALL I=1,5
      A2(I,I) = I
      FORALL  J=I-1,I+1 , J\=I .AND. J>=1 .AND. J<=5
         A2(I,J) = A2(I,I)*A2(J,J)
      END FORALL
   END FORALL

a) Detemine the valid and active index sets
b) What is the resulting matrix A2

(10 points)


4) Parallelize the following piece of code in OpenMP (pencil and paper):

   READ *,n
   w = 1/n
   sum = 0
   DO i=1,n
      x = w * (i-0.5)
      sum = sum + 4/(1+x*x)
   ENDDO

(15 points)