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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, < | {{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 == | ||
< | <syntaxhighlight lang=apl> | ||
2⍟0.5 1 2 32 1024 | 2⍟0.5 1 2 32 1024 | ||
¯1 0 1 5 10 | ¯1 0 1 5 10 | ||
</ | </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: | ||
< | <syntaxhighlight lang=apl> | ||
Digits←{1+⌊⍺⍟⍵} | Digits←{1+⌊⍺⍟⍵} | ||
ToBase←⊥⍣¯1 | ToBase←⊥⍣¯1 | ||
| Line 23: | Line 23: | ||
│3│1 0 0│ | │3│1 0 0│ | ||
└─┴─────┘ | └─┴─────┘ | ||
</ | </syntaxhighlight>{{Works in|[[Dyalog APL]]}} | ||
== Properties == | == Properties == | ||
| Line 29: | Line 29: | ||
By definition, logarithm is the [[inverse]] of the [[power]] with the same base (left argument). | By definition, logarithm is the [[inverse]] of the [[power]] with the same base (left argument). | ||
< | <syntaxhighlight lang=apl> | ||
2*1 2 3 4 5 | 2*1 2 3 4 5 | ||
2 4 8 16 32 | 2 4 8 16 32 | ||
| Line 36: | Line 36: | ||
2 (*⍣¯1 ≡ ⍟) ⍳10 | 2 (*⍣¯1 ≡ ⍟) ⍳10 | ||
1 | 1 | ||
</ | </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. | ||
< | <syntaxhighlight lang=apl> | ||
2⍟÷2 4 8 16 32 | 2⍟÷2 4 8 16 32 | ||
¯1 ¯2 ¯3 ¯4 ¯5 | ¯1 ¯2 ¯3 ¯4 ¯5 | ||
(÷2)⍟2 4 8 16 32 | (÷2)⍟2 4 8 16 32 | ||
¯1 ¯2 ¯3 ¯4 ¯5 | ¯1 ¯2 ¯3 ¯4 ¯5 | ||
</ | </syntaxhighlight> | ||
== See also == | |||
* [[Root]] | |||
== External links == | == External links == | ||
| Line 51: | Line 54: | ||
=== Documentation === | === Documentation === | ||
* [ | * [https://help.dyalog.com/latest/#Language/Primitive%20Functions/Logarithm.htm Dyalog] | ||
* [http://microapl.com/apl_help/ch_020_020_220.htm APLX] | * [http://microapl.com/apl_help/ch_020_020_220.htm APLX] | ||
* J [https://www.jsoftware.com/help/dictionary/d201.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/hatdot#dyadic NuVoc] | * J [https://www.jsoftware.com/help/dictionary/d201.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/hatdot#dyadic NuVoc] | ||
{{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar | |||
== References == | |||
<references/> | |||
{{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar monadic functions]] | |||