What happens when an expression contains two operators of equal priority? the tie between them is settled using the associativity of the operators. Operator precedence determines which operator will be performed first in a group of operators with different precedence’s. For instance
The order of operations (or operator precedence) is a collection of rules that define which procedures to perform first in order to evaluate a given mathematical expression.
The associativity (or fixity) of an operator is a property that determines how operators of the same precedence are grouped in the absence of parentheses.
The operator associativity rules define the order in which adjacent operators with the same precedence level are evaluated. For instance the expression
Associativity can be of two types—Left to Right or Right to Left. Left to Right associativity means that the left operand must be unambiguous. Unambiguous in what sense? It must not be involved in evaluation of any other sub-expression. Similarly, in case of Right to Left associativity the right operand must be unambiguous.
Consider the expression
Since both / and * have L to R associativity and only / has unambiguous left operand it is performed earlier.
Consider the expression
Since both = have R to L associativity and only the second = has unambiguous right operand the second = is performed earlier.
Consider the expression
Here since left operands for both operators are unambiguous Compiler is free to perform * or / operation as per its convenience.
Hierarchy of Operators in C:
All operators in C are ranked according to their precedence. A statement may have two or more arithmetic operators. The priority or precedence in which the operations in an arithmetic statement are performed is called the hierarchy of operations.
Within parentheses the same hierarchy as mentioned in table above is operative. Also, if there are more than one set of parentheses, the operations within the innermost parentheses would be performed first, followed by the operations within the second innermost pair and so on.
Stepwise evaluation of this expression is shown below:
5 + 3 * 2 is calculated as 5 + (3 * 2), giving 11, and not as (5 + 3) * 2, giving 16. The order of operations (or operator precedence) is a collection of rules that define which procedures to perform first in order to evaluate a given mathematical expression.
The associativity (or fixity) of an operator is a property that determines how operators of the same precedence are grouped in the absence of parentheses.
The operator associativity rules define the order in which adjacent operators with the same precedence level are evaluated. For instance the expression
8 - 3 - 2 is calculated as (8 - 3) - 2, giving 3, and not as 8 - (3 - 2), giving 7. In this case we say that subtraction is left associative meaning that the left most subtraction must be done first.Associativity can be of two types—Left to Right or Right to Left. Left to Right associativity means that the left operand must be unambiguous. Unambiguous in what sense? It must not be involved in evaluation of any other sub-expression. Similarly, in case of Right to Left associativity the right operand must be unambiguous.
Consider the expression
a = 3 / 2 * 5 ;
| Operator | Left | Right |
|---|---|---|
| / | 3 | 2 *5 |
| * | 3/2 | 5 |
Consider the expression
a = b = 3 ;
| Operator | Left | Right |
|---|---|---|
| = | a | b = 3 |
| = | a = b | 3 |
Consider the expression
z = a * b + c / d ;
| Operator | Left | Right |
|---|---|---|
| * | a | b |
| / | c | d |
| Precedence | Description | Operator | Associativity |
|---|---|---|---|
| 2 highest | Postfix increment | ++ | Left to Right |
| Postfix decrement | -- | Left to Right | |
| Function call | () | Left to Right | |
| Array subscripting | [] | Left to Right | |
| Element selection by reference | -> | Left to Right | |
| Element selection through pointer | . | Left to Right | |
| 3 | Prefix increment | ++ | Right to Left |
| Prefix decrement | -- | Right to Left | |
| Unary plus | + | Right to Left | |
| Unary minus | - | Right to Left | |
| Logical NOT | ! | Right to Left | |
| Bitwise NOT | ~ | Right to Left | |
| Type cast | (type) | Right to Left | |
| Indirection | * | Right to Left | |
| Address of | & | Right to Left | |
| Size-of | sizeof | Right to Left | |
| 5 | Multiplication | * | Left to Right |
| Division | / | Left to Right | |
| Modulus | % | Left to Right | |
| 6 | Addition | + | Left to Right |
| Subtraction | - | Left to Right | |
| 7 | Bitwise Left Shift | << | Left to Right |
| Bitwise Right Shift | >> | Left to Right | |
| 8 | Less than | < | Left to Right |
| Less than or equal to | <= | Left to Right | |
| Greater than | > | Left to Right | |
| Greater than or equal to | >= | Left to Right | |
| 9 | Equal to | == | Left to Right |
| Not equal to | != | Left to Right | |
| 10 | Bitwise AND | & | Left to Right |
| 11 | Bitwise exclusive OR | ^ | Left to Right |
| 12 | Bitwise OR | | | Left to Right |
| 13 | Logical AND | && | Left to Right |
| 14 | Logical OR | || | Left to Right |
| 15 | Conditional | ? : | Right to Left |
| 16 | Direct assignment | = | Right to Left |
| Addition assignment | += | Right to Left | |
| Subtraction assignment | -= | Right to Left | |
| Multiplication assignment | *= | Right to Left | |
| Division assignment | /= | Right to Left | |
| Modulo assignment | %= | Right to Left | |
| Bitwise left shift assignment | <<= | Right to Left | |
| Bitwise right shift assignment | >>= | Right to Left | |
| Bitwise AND assignment | &= | Right to Left | |
| Bitwise XOR assignment | ^= | Right to Left | |
| Bitwise OR assignment | |= | Right to Left | |
| 18 lowest | Comma | , | Right to Left |
Hierarchy of Operators in C:
All operators in C are ranked according to their precedence. A statement may have two or more arithmetic operators. The priority or precedence in which the operations in an arithmetic statement are performed is called the hierarchy of operations.
| Priority | Operators | Description |
|---|---|---|
| 1st | */ % | Multiplication, division, modular division |
| 2nd | + - | Addition, subtraction |
| 3rd | = | Assignment |
Stepwise evaluation of this expression is shown below:
i = 2 * 3 / 4 + 4 / 4 + 8 - 2 + 5 / 8
i = 6 / 4 + 4 / 4 + 8 - 2 + 5 / 8 operation: *
i = 1 + 4 / 4 + 8 - 2 + 5 / 8 operation: /
i = 1 + 1+ 8 - 2 + 5 / 8 operation: /
i = 1 + 1 + 8 - 2 + 0 operation: /
i = 2 + 8 - 2 + 0 operation: +
i = 10 - 2 + 0 operation: +
i = 8 + 0 operation : -
i = 8 operation: +
Related topics:
Overview of Operators in C | Arithmetic Operators in C | Relational Operators in C | Logical Operators in C | Bitwise Operators in C | Compound Assignment Operators in C | Conditional Operators in C | Miscellaneous Operators in C
List of topics: C Programming
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