Advaned Computer Architecture

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Problem 1: Loop Optimization 

For the following code fragments; first list all the data dependencies and then rearrange the code to reduce the dependencies and identify regions of parallelism.

1.

for i=1:n

for j=1:m

A(i,j)=A(j-1,i+1)+S

end

end

2.

for i=1:n

for j=1:m

A(i+1,j+1)=A(i,j)+A(i+1,j)

end

end

3.

for i=1:n

for j=1:m

A(i,j)=A(i-1,j)+A(i+1,j)+A(i,j+1)+A(i,j-1)

end

end

Problem 2: Branch Prediction 

Diagram is attached below 

The Figure represents a 2-bit predictor, that predicts whether a branch will be taken or not depending on the state. A (m; n) predictor is one where we consider the outcome of the last m branches to on an n-bit predictor to predict the next branch. Assume we are using a (1,2) predictor. We have two 2-bit predictors. Predictor 1 is used when the previous branch was executed and Predictor 2 is used when the previous branch is not executed. Based on this; what will be the accuracy of prediction for the following codes. Assume in the first step we start from state “predict taken”. Show all steps.

1.

a=T; 

b=F; 

for i=1:5

if(a==T) {a=T;}

 {b=!b;}

if(a==b) {a=F; b=T;} 

end

2.

a=T;

b=F;

for i=1:5

if(a==T) {a=F;} 

if(b==T){b=F;}

if(a==b) {a=T; b=F;} 

end

Problem 3: Parallel Algorithm Design

Design and implement a parallel algorithm for finding the (i) maximum, (ii) standard deviation and (iii) mode of a given set of positive numbers. Submit the code and a table/graph listing the running time changes for 2,4,8,16,32 processors for set size 5K 10K and 20K.

Show the steps for applying the parallel algorithms on this sequence: 8,24,4,32,128,64,12, 56, 48, 4

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