# Signum

 ×

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 the choosing division method though the default remains 1.