Arithmetic expressions

The shell allows arithmetic expressions to be evaluated, as one of the shell expansions or by the let builtin.

Evaluation is done in long integers with no check for overflow, though division by 0 is trapped and flagged as an error. The operators and their precedence and associativity are the same as in the C language.

The following list of operators is grouped into levels of equal-precedence operators. The levels are listed in order of decreasing precedence.

id++ id--
variable post-increment and post-decrement
++id --id
variable pre-increment and pre-decrement
- +
unary minus and plus
! ~
logical and bitwise negation
**
exponentiation
* / %
multiplication, division, remainder
+ -
addition, subtraction
<< >>
left and right bitwise shifts
<= >= < >
comparison
== !=
equality and inequality
&
bitwise AND
^
bitwise exclusive OR
|
bitwise OR
&&
logical AND
||
logical OR
expr ? expr : expr
conditional evaluation
= *= /= %= += -= <<= >>= &= ^= |=
assignment
expr1 , expr2
comma

Shell variables are allowed as operands; parameter expansion is performed before the expression is evaluated. Within an expression, shell variables may also be referenced by name without using the parameter expansion syntax. The value of a variable is evaluated as an arithmetic expression when it is referenced. A shell variable need not have its integer attribute turned on to be used in an expression.

Constants with a leading 0 are interpreted as octal numbers.
A leading `0x' or `0X' denotes hexadecimal.
Otherwise, numbers take the form [base#]n, where base is a decimal number between 2 and 64 representing the arithmetic base, and n is a number in that base. If base# is omitted, then base 10 is used. The digits greater than 9 are represented by the lowercase letters, the uppercase letters, `_', and `@', in that order. If base is less than or equal to 36, lowercase and uppercase letters may be used interchangably to represent numbers between 10 and 35.

Operators are evaluated in order of precedence. Sub-expressions in parentheses are evaluated first and may override the precedence rules above.

Related:

Bash Syntax
NIST Digital Library of Mathematical Functions
Windows equivalent command: SET /A - Display, set, or remove Windows environment variables


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