Amdahl’s law

تمرين 7 از فصل1 كتاب پردازش موازي پرهامي

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Question 1 (20 PT)
Amdahl’s law can be applied in contexts other than parallel processing. Suppose that a
numerical application consists of 20% floating point and 80% integer/control operations
– these are based on operation counts rather than their execution times. The execution
time of a floating-point operation is three times as long as other operations. We are
considering redesigning of the floating-point unit in a microprocessor to make it faster.
a. Formulate a more general version of Amdahl’s law in terms of selective
speed of a portion of a computation rather than in terms of parallel
processing.
b. How much faster should the new floating-point unit be for 25% overall
speed improvement?
c. What is the maximum speed-up that we can hope to achieve by only
modifying the floating-point unit?
Question 2 (20 PT)
Consider two versions of the task graph in Fig. 1.13. Version U corresponds to each node
requiring unit computation time. Version E/O corresponds to each odd-numbered node
taking unit time and each even-numbered node taking twice as long.
a. Convert the E/O version to an equivalent V version where each node is unit-time.
b. Find the maximum attainable speed-up for each of the U and V versions.
c. What is the minimum number of processors needed to achieve the speed-ups of
part (b)?
d. What is the maximum attainable speed-up in each case with three processors?
e. Which of the U and V versions of the task graph would you say is “more parallel”
and why?
Question 3 (10 PT)
Determine the following properties of a k-ary tree:
a. Node degree
b. Diameter
c. Number of nodes
d. Number of links
Question 4 (10 PT)
Determine the following properties of a r X j mesh and torus:
a. Node degree
b. Diameter
c. Number of nodes
d. Number of links 
 


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