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order of precedence
summary
This subchapter looks at order of precedence.
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This subchapter looks at order of precedence.
free computer programming text book projecttable of contents
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This subchapter looks at order of precedence.
Every programming language needs to have some system for determining the order of evaluation of expressions.
x := 5 + 6 * 7;
or
x = 5 + 6 * 7
Is x 47 or 77?
(5 + 6) = 11; followed by 11 * 7 = 77
(6 * 7) = 42; 5 + 42 = 47
The normal rules of elementary algebra call for multiplication (and division) to have a higher priority than addition (or subtraction), which would make x = 42.
| elementary algebra |
|---|
| parenthesis |
| exponentiation |
| multiplication |
| division |
| addition |
| subtraction |
A strict left to right evaluation would make the answer x = 77.
A strict right to left evaluation would make the answer x = 42.
The use of a reverse Polish notation (RPN, such as is used in Forth) avoids the question.
The two most common approaches used in computer programming languages are either (1) some order of precendence) or (2) directional evaluation (left-to-right or right-to-left).
The use of parenthesis can be used to change the normal order of evaluation.
Parenthesis can also be used to make complicated expressions more clear to a human reader. This makes the program easier to udnerstand and easier to maintain over years or decades of use.
The order of precedence in the following charts are from highest to lowest (top to bottom). Items on the same level are of equal order of precendence.
| Primary-expression operators | |
|---|---|
| 15 | ( ) [ ] . -> |
| Unary operators | |
| 14 | * & - ! ~ ++ -- sizeof (type) |
| 13 | * / % |
| 12 | + - |
| 11 | >> << |
| 10 | < > <= >= |
| 9 | == != |
| 8 | & |
| 7 | ^ |
| 6 | | |
| 5 | && |
| 4 | || |
| 3 | ?: |
| Assignment operators | |
| 2 | = += -= *= /= %=
>> =< <= &= ^= |= |
| Sequence operator | |
| 1 | , (comma) |
| unary + unary - not |
| * / div mod and |
| + - or |
| = <> < <= > >= in |
| 1 | all subexpressions in parenthesis from innermost to outermost |
| 2 | all exponentiations from right to left |
| 3 | all multiplications and divisions from left to right |
| 4 | all additions and subtractions from left to right |
| 1 | parenthesis |
| 2 | ↑ (exponentiation) |
| 3 | × / ÷ (multiplication and division) |
| 4 | + - (addition and subtraction) |
| 5 | < ≤ = ≠ ≥ > (relational operators) |
| 6 | ¬ (not) |
| 7 | ∧ (and) |
| 8 | ∨ (or) |
| 9 | ⊃ (implies) |
| 10 | ≡ (is equivalent to) |
Note that the actual ALGOL symbol for is not greater than has the less than symbol over the equals symbol rather than ≤ and the ALGOL symbol for not less than has the greater than symbol over the equals symbol rather than ≥.
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