Signum

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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 <source lang=apl inline>0</syntaxhighlight>, <source lang=apl inline>1</syntaxhighlight>, and <source lang=apl inline>¯1</syntaxhighlight>. <source lang=apl> 

     × ¯3 0 5

¯1 0 1 </syntaxhighlight> In dialects with complex numbers, Signum is a somewhat more complicated function, and may return any unit complex number. <source lang=apl> 

     × 3j4

0.6J0.8 </syntaxhighlight> The result is still equal to the original number divided by its magnitude: <source lang=apl> 

     | 3j4

5 

     3j4 ÷ | 3j4

0.6J0.8 </syntaxhighlight> The magnitude of the result for a non-zero argument is always 1. <source lang=apl> 

     | × 3j4 ¯2j1 6j¯7

1 1 1 </syntaxhighlight>

Zero divided by zero

The identity <source lang=apl inline>×z</syntaxhighlight> <source lang=apl inline>z÷|z</syntaxhighlight> holds only when <source lang=apl inline>z</syntaxhighlight> is not zero in most APLs. In "Zero Divided by Zero"[1], Eugene McDonnell gave this identity as a reason to define <source lang=apl inline>0÷0</syntaxhighlight> to be equal to <source lang=apl inline>0</syntaxhighlight>. In J, which took McDonnell's suggestion, the identity always holds. Dyalog APL and NARS2000 allow choosing division method though the default remains 1.

See also

External links

Documentation

References

  1. ↑ McDonnell, Eugene. "Zero Divided by Zero". APL76.
APL built-ins [edit]
Primitives (Timeline) Functions
Scalar
Monadic Conjugate ∙ Negate ∙ Signum ∙ Reciprocal ∙ Magnitude ∙ Exponential ∙ Natural Logarithm ∙ Floor ∙ Ceiling ∙ Factorial ∙ Not ∙ Pi Times ∙ Roll ∙ Type ∙ Imaginary ∙ Square Root ∙ Round
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Non-Scalar
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Quad names Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector
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