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   bash    ( 1 )

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ARITHMETIC EVALUATION

The shell allows arithmetic expressions to be evaluated, under
       certain circumstances (see the let and declare builtin commands,
       the (( compound command, and Arithmetic Expansion).  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
       - +    unary minus and plus
       ++id --id
              variable pre-increment and pre-decrement
       ! ~    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 operator
       = *= /= %= += -= <<= >>= &= ^= |=
              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.  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.