6.5 Shell Arithmetic
The shell allows arithmetic expressions to be evaluated, as one of
the shell expansions or by 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 and associativity are the same
as in the C language.
The following list of operators is grouped into levels of
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.
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
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 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