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 nonzero argument is always 1.
 × 3j4 ¯2j1 6j¯7
1 1 1
Zero divided by zero
The identity ×z
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.