Natural Logarithm

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Natural Logarithm (⍟), or Natural Log, is a monadic scalar function which computes the natural logarithm of the argument. Logarithm shares the glyph <source lang=apl inline>⍟</syntaxhighlight> with the dyadic arithmetic function Logarithm. The glyph, a composition of the glyphs for Circular (<source lang=apl inline>○</syntaxhighlight>) and Exponential (<source lang=apl inline>*</syntaxhighlight>) to indicate its close mathematical ties with these two functions, is a stylised tree log.[1]

A natural log
This page describes the monadic arithmetic function. For the dyadic logarithm function, see Logarithm.

Examples

<source lang=apl> 

     ⍟1 2 (*1) (*10)

0 0.6931471806 1 10 </syntaxhighlight>

Properties

Natural logarithm is a special case of Logarithm with the default left argument of e (<source lang=apl inline>*1</syntaxhighlight>).

<source lang=apl> 

     ((*1)∘⍟ ≡ ⍟) 1 ¯1 0J1

1

</syntaxhighlight>

Works in: Dyalog APL

Natural logarithm and exponential <source lang=apl inline>*</syntaxhighlight> are inverses of each other, except where the natural log is undefined.

<source lang=apl> 

     (⊢ ≡ ⍟∘*) 0 1 ¯1 0J1

1 

     (⊢ ≡ *∘⍟) 1 ¯1 0J1 ⍝ natural log of zero is undefined

1

</syntaxhighlight>

Works in: Dyalog APL

External links

Documentation

References

  1. ↑ McDonnell, E. E.. Recreational APL: The Story of <source lang=apl inline>○</syntaxhighlight>. APL Quote-Quad, Volume 8, Number 2, 1977-12.
APL built-ins [edit]
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