# Signum

(Redirected from Direction)
 `×`

Signum (`×`), Sign, Sign of, or Direction is a monadic scalar function which returns the sign of a real or complex number. That is, it returns 0 when given an argument of 0, and otherwise returns a number with magnitude 1 given by dividing the argument by its own magnitude.

## Examples

The three possible results of Signum on a real argument are `0`, `1`, and `¯1`.

```      × ¯3 0 5
¯1 0 1
```

In dialects with complex numbers, Signum is a somewhat more complicated function, and may return any unit complex number.

```      × 3j4
0.6J0.8
```

The result is still equal to the original number divided by its magnitude:

```      | 3j4
5
3j4 ÷ | 3j4
0.6J0.8
```

The magnitude of the result for a non-zero argument is always 1.

```      | × 3j4 ¯2j1 6j¯7
1 1 1
```

## Zero divided by zero

The identity `×z` ${\displaystyle \Leftrightarrow }$ `z÷|z` holds only when `z` is not zero in most APLs. In "Zero Divided by Zero"[1], Eugene McDonnell gave this identity as a reason to define `0÷0` to be equal to `0`. In J, which took McDonnell's suggestion, the identity always holds. Dyalog APL and NARS2000 allow choosing division method though the default remains 1.