COMS W4115
Programming Languages and Translators
Lecture 19: Arrays, Boolean Expressions, Flow of Control
April 7, 2008

Lecture Outline

1. Review
2. Assignment statements
3. Arrays
4. Boolean expressions
5. Flow-of-control statements

1. Review

• Types
• Type equivalence
• Type inference
• Type conversions
• Run-time storage organization

2. Assignment Statements

• Example assignment: a = b * -c + b * -c;
• AST
• DAG
• Three-address code
• Stack code

3. Arrays

• Referencing a one-dimensional array
• In C and Java, array elements are numbered 0, 1,..., n-1 for an array A with n elements.
• Element A[i] begins in location (base + i × w) where base is the relative address of the storage allocated for A and w is the width of each element.
• Row-major order
• Column-major order
• See Fig. 6.21, p. 382.

4. Boolean Expressions

• Boolean expressions are composed of boolean operators (&&, ||, !) applied to boolean variables, relational expressions, and other boolean expressions.
• Short-circuit evaluation: Some languages, such as C and Java, do not require an entire boolean expression to be evaluated.
• Given x && y, if x is false, then we can conclude the entire expression is false without evaluating y.
• Given x || y, if x is true, then we can conclude the entire expression is true without evaluating y.
• Numerical encoding
• In C, the numerical value 0 represents false; a nonzero value represents true.
• Positional encoding
• The value of a boolean expression can be represented by a position in three-address code, and the boolean operators can be translated into jumps.
• The expression

       if (x < 100) || x > 200 && x != y)
         x = 0;
       

can be translated into the following three-address instructions:

           if x < 100 goto L2
           ifFalse x > 200 goto L1
           ifFalse x != y goto L1
       L2: x = 0
       L1:
       

5. Flow-of-Control Statements

• Boolean expressions often appear in the context of flow-of-control statements such as:
• If statements
• If-else statement
• While statements
• See Figs. 6.35 and 6.36 for an SDD for the translation of these statements.
• For the expression

       if (x < 100) || x > 200 && x != y)
         x = 0;
       

this SDD produces the following three-address instructions:

           if x < 100 goto L2
           goto L3
       L3: if x > 200 goto L4
           goto L1
       L4: if x != y goto L2
           goto L1
       L2: x = 0
       L1:
       

The code above can be obtained by optimizing this three-address code.

6. Reading

• ALSU, Sections 6.4, 6.6