The shell allows arithmetic expressions to be evaluated, as one of
the shell expansions or by using the
(( compound command, the
let builtin, or the
-i option to the
Evaluation is done in fixed-width integers with no check for overflow, though division by 0 is trapped and flagged as an error. The operators and their precedence, associativity, and values 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.
* / %
<= >= < >
expr ? expr : expr
= *= /= %= += -= <<= >>= &= ^= |=
expr1 , expr2
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.
A shell variable that is null or unset evaluates to 0 when referenced
by name without using the parameter expansion syntax.
The value of a variable is evaluated as an arithmetic expression
when it is referenced, or when a variable which has been given the
integer attribute using ‘
declare -i’ is assigned a value.
A null value evaluates to 0.
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 [
n, where the optional
is a decimal number between 2 and 64 representing the arithmetic
n is a number in that 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.
base is less than or equal to 36, lowercase and uppercase
letters may be used interchangeably to represent numbers between 10
Operators are evaluated in order of precedence. Sub-expressions in parentheses are evaluated first and may override the precedence rules above.