Question 65

Expression: $q + r / 3 + s - t * 5 + u * v / w$.

In Static Single Assignment (SSA) form, every temporary variable is defined exactly once.
Evaluating operations adhering to standard operator precedence and left-to-right associativity:

1. Multiplications and Divisions (higher precedence):

   • $t_1 = r / 3$
   • $t_2 = t * 5$
   • $t_3 = u * v$
   • $t_4 = t_3 / w$

2. Additions and Subtractions (evaluated left-to-right):

   • $t_5 = q + t_1$
   • $t_6 = t_5 + s$
   • $t_7 = t_6 - t_2$
   • $t_8 = t_7 + t_4$

There are 8 distinct binary operations in the expression: two divisions, two multiplications, three additions, and one subtraction.
Each three-address code instruction computes one binary operator, requiring a distinct temporary variable under SSA rules ($t_1, t_2, t_3, t_4, t_5, t_6, t_7, t_8$).

Therefore, the least number of temporary variables required is $8$.