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.
variable post-increment and post-decrement
variable pre-increment and pre-decrement
unary minus and plus
logical and bitwise negation
* / %
multiplication, division, remainder
left and right bitwise shifts
<= >= < >
equality and inequality
bitwise exclusive OR
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.
Integer constants follow the C language definition, without suffixes or
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 the optional base
is a decimal number between 2 and 64 representing the arithmetic
base, and n is a number in that base.
# is omitted, then base 10 is used.
When specifying n,
if a non-digit is required,
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 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.