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CS253 Order Of Evaluation

Basic Expressions

Consider the expression a+b, which parses as:

        			 ┌───┐
        			 │ + │
        			 └───┘
        			 ⠌   ⠡
        			⠌     ⠡
        		    ┌───┐     ┌───┐
        		    │ a │     │ b │
        		    └───┘     └───┘

Basic Expressions

How does a+b*c parse?

                  ┌───┐                       ┌───┐
                  │ * │                       │ + │
                  └───┘                       └───┘
                  ⠌   ⠡                       ⠌   ⠡
                 ⠌     ⠡                     ⠌     ⠡
             ┌───┐     ┌───┐             ┌───┐     ┌───┐
             │ + │     │ c │             │ a │     │ * │
             └───┘     └───┘             └───┘     └───┘
             ⠌   ⠡                                 ⠌   ⠡
            ⠌     ⠡                               ⠌     ⠡
        ┌───┐     ┌───┐                       ┌───┐     ┌───┐
        │ a │     │ b │                       │ b │     │ c │
        └───┘     └───┘                       └───┘     └───┘

The right-hand side, of course. * has higher precedence than +.

Basic Expressions

Let’s use parentheses. How does (a+b)*c parse?

                  ┌───┐                       ┌───┐
                  │ * │                       │ + │
                  └───┘                       └───┘
                  ⠌   ⠡                       ⠌   ⠡
                 ⠌     ⠡                     ⠌     ⠡
             ┌───┐     ┌───┐             ┌───┐     ┌───┐
             │ + │     │ c │             │ a │     │ * │
             └───┘     └───┘             └───┘     └───┘
             ⠌   ⠡                                 ⠌   ⠡
            ⠌     ⠡                               ⠌     ⠡
        ┌───┐     ┌───┐                       ┌───┐     ┌───┐
        │ a │     │ b │                       │ b │     │ c │
        └───┘     └───┘                       └───┘     └───┘

The left-hand side, of course. Parentheses mean “do this first”.

No

Really

              ┌───┐
              │ * │
              └───┘
              ⠌   ⠡
             ⠌     ⠡
         ┌───┐     ┌───┐
         │ + │     │ c │
         └───┘     └───┘
         ⠌   ⠡
        ⠌     ⠡
    ┌───┐     ┌───┐
    │ a │     │ b │
    └───┘     └───┘

• Parentheses do not mean “do this first”.
• Parentheses mean “group these together”.
• Parentheses determine the shape of the parse tree, not the order of evaluation.
• Of course, the shape of the tree determines the order of evaluation, to some extent.
• In this tree, the + node feeds to the * node, so + must execute before *.
• However, we can evaluate c before the addition, or after.

Really

              ┌───┐
              │ * │
              └───┘
              ⠌   ⠡
             ⠌     ⠡
         ┌───┐     ┌───┐
         │ + │     │ c │
         └───┘     └───┘
         ⠌   ⠡
        ⠌     ⠡
    ┌───┐     ┌───┐
    │ a │     │ b │
    └───┘     └───┘

Possible orders of evaluation:

1. a, b, c, +, *
2. a, b, +, c, *
3. a, c, b, +, *
4. b, a, c, +, *
5. b, a, +, c, *
6. b, c, a, +, *
7. c, a, b, +, *
8. c, b, a, +, *

Who Cares?

• So what? It doesn’t matter in which order a, b, and c are fetched.
  • If they’re simple variables, then, no, it doesn’t matter.
  • If they’re expressions with side effects, then it does matter:
    • increment/decrement
    • assignment
    • function calls
      • could change global variables
      • could generate output

Some Operators Are Different

• Some operators have order of evaluation specified:
  • && ||
  • , (in an expression, not as an argument separator)
  • ?:
• Most do not:
  • + - * / %
  • << >> & | ^
  • < > <= >= == !=
  • = += -= *= /= %= <<= >>= &= |= ^=

A user-defined operation (e.g., operator+) does not have order determined, because it’s a function called with two arguments. The order of evaluation of function arguments is unspecified.

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