= Bash Arithmetic =

`bash(1)` is capable of doing integer arithmetic.

<<TableOfContents>>

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== Integer Literals ==

Literals follow the C language definition.

A leading `0` indicates an octal number.

A leading `0x` or `0X` indicates hexadecimal.

Otherwise, numbers take the form `[base#]n`, where `base` is a decimal number between 2 and 64 representing the arithmetic base. If `base#` is omitted, the default of base 10 applies. When specifying `n`, if a non-digit is required, the digits greater than 9 are represented by lowercase letters, uppercase letters, `@`, and `_`, in that order. If `base` is less than or equal to 36, lowercase and uppercase letters are interchange.

To force evaluation as a ''positive'' base 10 integer, try:

{{{
a=$(( 10#$a ))
}}}

Note that this will not work if `$a` is signed (i.e. `+1`, `-1`).

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== Usage ==

`bash(1)` parses tokens as arithmetic in any of the following contexts:

 * the `let` [[Bash/BuiltinCommands#Let|builtin]]
 * `$(( ... ))`
 * [[Bash/Expansion#Arithmetic_Expansion|Arithmetic expansions]] (i.e. `(( ... ))`)
 * [[Bash/Looping#For_Loops|C-style for loops]] (i.e. `for ((i=0; i<10; i++)); do ... done`)
 * [[Bash/Array|Array indexing]] (i.e. `args[i+1]`)

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== Unary Operators ==

Unary operators have the highest priority.

||'''Operator'''||'''Meaning'''      ||
||`a++`         ||post-increment `$a`||
||`a--`         ||post-decrement `$a`||
||`++a`         ||pre-increment `$a` ||
||`--a`         ||pre-decrement `$a` ||
||`+`           ||positive           ||
||`-` 	        ||negative           ||
||`!`           ||negation           ||

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== Binary Operators ==

The binary operators include arithmetic and logic operations.

||'''Operator'''||'''Meaning'''        ||
||`*`           ||multiplication       ||
||`/`           ||division             ||
||`%`           ||remainder            ||
||`+`           ||addition             ||
||`-`           ||subtraction          ||
||`**`          ||exponentiation       ||
||`<`           ||less than            ||
||`>`           ||greater than         ||
||`<=`          ||less than or equal   ||
||`>=`          ||greater than or equal||
||`=` or `==`   ||equality             ||
||`!=`          ||inequality           ||

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== Ternary Operators ==

There is just one ternary operator:

{{{
a ? b : c
}}}

`a` is the test, `b` is the value if true, and `c` is the value if false.

Note that ternary operators follow [[Bash/Logic#Conditional_Commands|logic operators]] as well.
 
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== Assignment ==

||'''Operator'''||'''Meaning''' ||
||`a = b`       ||assignment    ||
||`a *= b`      ||`a = a * b`   ||
||`a /= b`      ||`a = a / b`   ||
||`a %= b`      ||`a = a % b`   ||
||`a += b`      ||`a = a + b`   ||
||`a -= b`      ||`a = a - b`   ||

Note that assignment operators follow [[Bash/Logic#Conditional_Commands|logic operators]] as well.

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== Bit-wise Operators ==

||'''Operator'''||'''Meaning''' ||
||`~`           ||negation      ||
||`<<`          ||bitshift left ||
||`>>`          ||bitshift right||
||`&`           ||AND           ||
||`^`           ||XOR           ||
||`|`           ||OR            ||
||`a <<= b`     ||`a = a << b`  ||
||`a >>= b`     ||`a = a >> b`  ||
||`a &= b`      ||`a = a & b`   ||
||`a ^= b`      ||`a = a ^ b`   ||
||`a |= b`      ||`a = a | b`   ||

Note that negation has equal precedence to other unary operators; bitshifts (such as `<<`) follow arithmetic operators; bit-wise logic (such as `&`) come after all other binary operators; and bit-wise assignment operators (such as `<<=`) have equal precedence to other assignment operators.



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