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...

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).

Figure 8.10

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 Vi 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).

Figure 8.11