Question

1) i 2 for (i2; i<=n; i++) 2) if i>n goto7) 3) t1 i 4 ali TRUE; count = 0; 4) alt1]= TRUE 5) i = i+ 1 (u)9 for (i-2; i<=s;i++) 6) goto (2) if (alil) //i has been found to be a prime 7 count = 0 count++; 8) s sqrt(n) for (j-2'i; i<=n; j = i+i) ail =FALSE; // no multiple of i is a prime 10) ifi>s goto (22) Fig 4.0 Figure 4 .0 is the code to count the number of primes from 2 to n, using 11) t2 i4 12) ifFalse alt2] goto (20) the sieve method on a suitably large array a. That is, ali] is TRUE at the 13) count= count + 1 end only if there is no prime i 0.5 or less that evenly divides i. We initialize 14) i 2 *i 15) if j> n goto (20) 16) t3 i 4 all ali] to TRUE and then set ail to FALSE if we find a divisor of j. The equivalent three-address code (TAC) is presented in fig 4.1 17) alt3) = FALSE c. Construct the flow graph for the TAC (6 points) 18) j-i+i d. Identify the loops in your flow graph from (a). (3 points) Perform local and global optimization as much as you can 19) goto (15) e. 20) i i+ 1 21) goto (10) (6 points) Fig 4.1

Answer 1

n i-2 Loop 1 B1 B2 11-ititisi //onerator strength reduction ati] TRUE +1 count C B3 s sqrt(n) i2 Loop 2 B4 B5 iti>s GOTO END END j- it1 t2 +i copy propaqation +operator strenqth reduction if alt2] false GOTO B5 B6 Count count +1 Loop3 B7 if j n GOTO B5 alt31 False j+1