Apply the transformations of this section to your flow graphs from (a) Exercise 

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Apply the transformations of this section to your flow graphs from (a) Exercise 8.4.1; (b) Exercise 8.4.2.

Exercise 8.4.1 : Figure 8.10 is a simple matrix-multiplication program.

a) Translate the program into three-address statements of the type we have been using in this section. Assume the matrix entries are numbers that require 8 bytes, and that matrices are stored in row-major order.

b) Construct the flow graph for your code from (a).

c) Identify the loops in your flow graph from (b).

Exercise 8.4.2 : Figure 8.11 is code to count the number of primes from 2 to n, using the sieve method on a suitably large array a. That is, a[i] is TRUE at the end only if there is no prime √i or less that evenly divides i. We initialize all a[i] to TRUE and then set a[j] to FALSE if we find a divisor of j.

a) Translate the program into three-address statements of the type we have been using in this section. Assume integers require 4 bytes.

b) Construct the flow graph for your code from (a).

c) Identify the loops in your flow graph from (b).