## C++: abs() and its quirk with INT_MIN

If you use the `abs()`

function from `cmath`

, then you need to be aware of one little quirk. The `abs()`

function returns the absolute value of the signed integer passed as input. It is declared as:

int abs( int );

`abs()`

works as defined for all input integers, except for one integer: the `INT_MIN`

. For 32-bit integers, the value of `INT_MIN`

is `-2147483648`

. `abs( INT_MIN )`

returns `INT_MIN`

back!

To see why, consider the binary representation of any signed integral type (`char`

, `short`

, `int`

and `long`

). The range of the positive integer values that can be represented is one *less* than that of negative integer values.

For 32-bit integers, the largest representable integer (`INT_MAX`

) is `2147483647`

, whereas the smallest representable integer (`INT_MIN`

) is not `-2147483647`

, but it is `-2147483648`

. Though the number of values that can be represented by an integral type is even, integer value 0 steals one space and thus the positive integer values lose one space in their range.

Coming back to `abs()`

, since its return type is the same as the input type it simply cannot represent the positive value (`-INT_MIN`

) in an `int`

. Thus, it returns back `INT_MIN`

.

The binary representation of `0`

is `00000000000000000000000000000000`

and the binary representation of `INT_MIN`

is `10000000000000000000000000000000`

. That is, `INT_MIN`

is same as 0, with MSB set to 1. Quirks of integers, such as with abs(), could have been avoided if the int format had been defined with two zero values: a positive zero (`00000000000000000000000000000000`

) and a negative zero (`10000000000000000000000000000000`

).

Anyway, the reason you need to be careful about `abs()`

is because you might be using its return value to index into an array. Indexing an array using a negative value can be disastrous or result in a hard-to-replicate bug.