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{{Built-in|Decode|⊥}}, also called '''Base''', is a [[dyadic]] [[primitive function]] which evaluates the right [[argument]] in terms of the radix system defined by the left argument. Some implementations add [[monadic]] usage to this function, where the left argument defaults to the [[scalar]] 2. Decode is the [[inverse]] of [[Encode]] <source lang=apl inline>⊤</source> with the same left argument X, when X is a | {{Built-in|Decode|⊥}}, also called '''Base''', is a [[dyadic]] [[primitive function]] which evaluates the right [[argument]] in terms of the radix system defined by the left argument. Some implementations add [[monadic]] usage to this function, where the left argument defaults to the [[scalar]] 2. Decode is the [[inverse]] of [[Encode]] <source lang=apl inline>⊤</source> with the same left argument X, when X is a [[vector]] and the right argument is a valid representation of a number in the radix system defined by X. | ||
== APL model == | == APL model == | ||
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</source> | </source> | ||
Decode has an important property with array [[index]]: Given an arbitrary array A with [[shape]] S, the index of an [[element]] in A can be decoded with S to obtain the corresponding index in the [[ravel]] of A. Decoding all indices given by [[Index Generator]] shows the ravel order of the elements of an array with the given shape. Note that <source lang=apl inline>⎕IO←0</source> is required for this to hold. | Decode has an important property with array [[index]]: Given an arbitrary array A with [[shape]] S, the index of an [[element]] in A can be decoded with S to obtain the corresponding index in the [[ravel]] of A. Decoding all indices given by [[Index Generator]] shows the ravel order of the elements of an array with the given shape. Note that [[index origin]] 0 (<source lang=apl inline>⎕IO←0</source>) is required for this to hold. | ||
<source lang=apl> | <source lang=apl> | ||
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* [https://help.dyalog.com/latest/#Language/Primitive%20Functions/Decode.htm Dyalog] | * [https://help.dyalog.com/latest/#Language/Primitive%20Functions/Decode.htm Dyalog] | ||
* [http://microapl.com/apl_help/ch_020_020_660.htm APLX] | * [http://microapl.com/apl_help/ch_020_020_660.htm APLX] | ||
* J [https://www.jsoftware.com/help/dictionary/d401.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/numberdot NuVoc] (as <source lang=j inline>#.</source>) | * J [https://www.jsoftware.com/help/dictionary/d401.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/numberdot#dyadic NuVoc] (as <source lang=j inline>#.</source>) | ||
{{APL built-ins}}[[Category:Primitive functions]] | {{APL built-ins}}[[Category:Primitive functions]] | ||