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6.5 Shell Arithmetic

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 declare builtin.

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.

id++ id--

variable post-increment and post-decrement

++id --id

variable pre-increment and pre-decrement

- +

unary minus and plus

! ~

logical and bitwise negation



* / %

multiplication, division, remainder

+ -

addition, subtraction

<< >>

left and right bitwise shifts

<= >= < >


== !=

equality and inequality


bitwise AND


bitwise exclusive OR


bitwise OR


logical AND


logical OR

expr ? expr : expr

conditional operator

= *= /= %= += -= <<= >>= &= ^= |=


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 character constants. 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. If 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 and 35.

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

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