Logarithm: Difference between revisions

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:''This page describes the dyadic arithmetic function. For the monadic natural logarithm function, see [[Natural Logarithm]].''
:''This page describes the dyadic arithmetic function. For the monadic natural logarithm function, see [[Natural Logarithm]].''


{{Built-in|Logarithm|⍟}}, or '''Log''', is a [[dyadic]] [[scalar function]] which computes the [[wikipedia:logarithm|logarithm]] of the two [[argument|arguments]]. More precisely, <syntaxhighlight lang=apl inline>X⍟Y</source> computes how much [[power]] of X equals Y, i.e. the value of R that satisfies <syntaxhighlight lang=apl inline>Y=X*R</source>. Logarithm shares the [[glyph]] <syntaxhighlight lang=apl inline>⍟</source> with the monadic arithmetic function [[Natural Logarithm]]. The [[glyph]], a composition of the glyphs for [[Circular]] (<syntaxhighlight lang=apl inline>○</source>) and [[Power]] (<syntaxhighlight lang=apl inline>*</source>) to indicate its close mathematical ties with these two functions, is a stylised tree log.<ref>[[E. E. McDonnell|McDonnell, E. E.]]. [https://www.jsoftware.com/papers/eem/storyofo.htm Recreational APL: The Story of <syntaxhighlight lang=apl inline>○</source>]. [[APL Quote-Quad]], Volume 8, Number 2, 1977-12.</ref>
{{Built-in|Logarithm|⍟}}, or '''Log''', is a [[dyadic]] [[scalar function]] which computes the [[wikipedia:logarithm|logarithm]] of the two [[argument|arguments]]. More precisely, <syntaxhighlight lang=apl inline>X⍟Y</syntaxhighlight> computes how much [[power]] of X equals Y, i.e. the value of R that satisfies <syntaxhighlight lang=apl inline>Y=X*R</syntaxhighlight>. Logarithm shares the [[glyph]] <syntaxhighlight lang=apl inline>⍟</syntaxhighlight> with the monadic arithmetic function [[Natural Logarithm]]. The [[glyph]], a composition of the glyphs for [[Circular]] (<syntaxhighlight lang=apl inline>○</syntaxhighlight>) and [[Power]] (<syntaxhighlight lang=apl inline>*</syntaxhighlight>) to indicate its close mathematical ties with these two functions, is a stylised tree log.<ref>[[E. E. McDonnell|McDonnell, E. E.]]. [https://www.jsoftware.com/papers/eem/storyofo.htm Recreational APL: The Story of <syntaxhighlight lang=apl inline>○</syntaxhighlight>]. [[APL Quote-Quad]], Volume 8, Number 2, 1977-12.</ref>


== Examples ==
== Examples ==
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       2⍟0.5 1 2 32 1024
       2⍟0.5 1 2 32 1024
¯1 0 1 5 10
¯1 0 1 5 10
</source>
</syntaxhighlight>


Logarithm can be used to determine how many digits are needed to write a positive integer Y in base X:
Logarithm can be used to determine how many digits are needed to write a positive integer Y in base X:
Line 23: Line 23:
│3│1 0 0│
│3│1 0 0│
└─┴─────┘
└─┴─────┘
</source>{{Works in|[[Dyalog APL]]}}
</syntaxhighlight>{{Works in|[[Dyalog APL]]}}


== Properties ==
== Properties ==
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       2 (*⍣¯1 ≡ ⍟) ⍳10
       2 (*⍣¯1 ≡ ⍟) ⍳10
1
1
</source>{{Works in|[[Dyalog APL]]}}
</syntaxhighlight>{{Works in|[[Dyalog APL]]}}


[[Reciprocal]] on the left or right argument gives the [[negate|negated]] result.
[[Reciprocal]] on the left or right argument gives the [[negate|negated]] result.
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       (÷2)⍟2 4 8 16 32
       (÷2)⍟2 4 8 16 32
¯1 ¯2 ¯3 ¯4 ¯5
¯1 ¯2 ¯3 ¯4 ¯5
</source>
</syntaxhighlight>


== See also ==
== See also ==

Latest revision as of 22:06, 10 September 2022

This page describes the dyadic arithmetic function. For the monadic natural logarithm function, see Natural Logarithm.
⍟

Logarithm (⍟), or Log, is a dyadic scalar function which computes the logarithm of the two arguments. More precisely, X⍟Y computes how much power of X equals Y, i.e. the value of R that satisfies Y=X*R. Logarithm shares the glyph ⍟ with the monadic arithmetic function Natural Logarithm. The glyph, a composition of the glyphs for Circular (○) and Power (*) to indicate its close mathematical ties with these two functions, is a stylised tree log.[1]

Examples

      2⍟0.5 1 2 32 1024
¯1 0 1 5 10

Logarithm can be used to determine how many digits are needed to write a positive integer Y in base X: 

      Digits←{1+⌊⍺⍟⍵}
      ToBase←⊥⍣¯1
      (2 Digits 100) (2 ToBase 100)
┌─┬─────────────┐
│7│1 1 0 0 1 0 0│
└─┴─────────────┘
      (10 Digits 100) (10 ToBase 100)
┌─┬─────┐
│3│1 0 0│
└─┴─────┘
Works in: Dyalog APL

Properties

By definition, logarithm is the inverse of the power with the same base (left argument). 

      2*1 2 3 4 5
2 4 8 16 32
      2⍟2 4 8 16 32
1 2 3 4 5
      2 (*⍣¯1 ≡ ⍟) ⍳10
1
Works in: Dyalog APL

Reciprocal on the left or right argument gives the negated result. 

      2⍟÷2 4 8 16 32
¯1 ¯2 ¯3 ¯4 ¯5
      (÷2)⍟2 4 8 16 32
¯1 ¯2 ¯3 ¯4 ¯5

See also

External links

Documentation

References

  1. ↑ McDonnell, E. E.. Recreational APL: The Story of ○. APL Quote-Quad, Volume 8, Number 2, 1977-12.
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