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(bashref.info)Shell Arithmetic

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Shell Arithmetic
================

   The shell allows arithmetic expressions to be evaluated, as one of
the shell expansions or by the `let' builtin.

   Evaluation is done in long 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
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

`**'
     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 evaluation

`= *= /= %= += -= <<= >>= &= ^= |='
     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.  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`#' 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.  If BASE is less than or equal to 36, lowercase
and uppercase letters may be used interchangably 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.