Encode: Difference between revisions
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{{Built-in|Encode|⊤}}, also called '''Represent''' or '''Antibase''', is a [[dyadic]] [[primitive function]] which computes the representation of the right argument in the radix system defined by the left argument. Some implementations add [[monadic]] usage to this function, which computes the binary representation using as many bits as needed. Encode is the [[inverse]] of [[Decode]] <source lang=apl inline>⊥</ | {{Built-in|Encode|⊤}}, also called '''Represent''' or '''Antibase''', is a [[dyadic]] [[primitive function]] which computes the representation of the right argument in the radix system defined by the left argument. Some implementations add [[monadic]] usage to this function, which computes the binary representation using as many bits as needed. Encode is the [[inverse]] of [[Decode]] <source lang=apl inline>⊥</syntaxhighlight> with the same left argument X, when X is a [[vector]]. | ||
== Concept == | == Concept == | ||
Encode works by finding the "digits" one by one from the rightmost digit. Let's consider <source lang=apl inline>0 7 24 60⊤12345</ | Encode works by finding the "digits" one by one from the rightmost digit. Let's consider <source lang=apl inline>0 7 24 60⊤12345</syntaxhighlight> (convert 12345 minutes to weeks, days, hours, and minutes) as an example. | ||
<source lang=apl> | <source lang=apl> | ||
| Line 18: | Line 18: | ||
7÷⍨8-1 ⍝ 1 week remaining to convert | 7÷⍨8-1 ⍝ 1 week remaining to convert | ||
1 ⍝ No more conversion needed, since there is no limit for the highest digit | 1 ⍝ No more conversion needed, since there is no limit for the highest digit | ||
</ | </syntaxhighlight> | ||
Collecting all the digits gives the desired result. | Collecting all the digits gives the desired result. | ||
| Line 25: | Line 25: | ||
0 7 24 60⊤12345 | 0 7 24 60⊤12345 | ||
1 1 13 45 | 1 1 13 45 | ||
</ | </syntaxhighlight> | ||
If the left argument has high [[rank]], the vectors over the first [[axis]] act as independent radix systems. | If the left argument has high [[rank]], the vectors over the first [[axis]] act as independent radix systems. | ||
| Line 48: | Line 48: | ||
0 2 7 | 0 2 7 | ||
1 1 9 | 1 1 9 | ||
</ | </syntaxhighlight> | ||
== Examples == | == Examples == | ||
| Line 61: | Line 61: | ||
((1+⌊10⍟12345)⍴10)⊤12345 ⍝ Convert to decimal digits using just as many digits as needed | ((1+⌊10⍟12345)⍴10)⊤12345 ⍝ Convert to decimal digits using just as many digits as needed | ||
1 2 3 4 5 | 1 2 3 4 5 | ||
</ | </syntaxhighlight> | ||
Encode can be also used to convert a measure given in the smallest unit to a hierarchy of units. For example, given that 1 day = 24 hours, 1 hour = 60 minutes, and 1 minute = 60 seconds, how many days/hours/minutes/seconds is 210859 seconds? | Encode can be also used to convert a measure given in the smallest unit to a hierarchy of units. For example, given that 1 day = 24 hours, 1 hour = 60 minutes, and 1 minute = 60 seconds, how many days/hours/minutes/seconds is 210859 seconds? | ||
| Line 68: | Line 68: | ||
0 24 60 60⊤210859 | 0 24 60 60⊤210859 | ||
2 10 34 19 | 2 10 34 19 | ||
</ | </syntaxhighlight> | ||
Another common usage of Encode is to simulate "divmod": a function which, given two integers, computes the quotient and remainder at once. The construct can also be used to extract the integer part and fractional part of a real number. | Another common usage of Encode is to simulate "divmod": a function which, given two integers, computes the quotient and remainder at once. The construct can also be used to extract the integer part and fractional part of a real number. | ||
| Line 81: | Line 81: | ||
0 1⊤○1 ⍝ Integer and fractional parts of pi | 0 1⊤○1 ⍝ Integer and fractional parts of pi | ||
3 0.1415926536 | 3 0.1415926536 | ||
</ | </syntaxhighlight> | ||
Encode has an important property with array [[index]]: Given an arbitrary array A with [[shape]] S, encoding a [[ravel|raveled]] index by S gives the original index in A. This can be used to generate all indices of a given array or array shape. Note that [[index origin]] 0 (<source lang=apl inline>⎕IO←0</ | Encode has an important property with array [[index]]: Given an arbitrary array A with [[shape]] S, encoding a [[ravel|raveled]] index by S gives the original index in A. This can be used to generate all indices of a given array or array shape. Note that [[index origin]] 0 (<source lang=apl inline>⎕IO←0</syntaxhighlight>) is required for this to hold. | ||
<source lang=apl> | <source lang=apl> | ||
| Line 93: | Line 93: | ||
0 0 0 0 1 1 1 1 2 2 2 2 0 0 0 0 1 1 1 1 2 2 2 2 | 0 0 0 0 1 1 1 1 2 2 2 2 0 0 0 0 1 1 1 1 2 2 2 2 | ||
0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 | 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 | ||
</ | </syntaxhighlight> | ||
== External links == | == External links == | ||
| Line 105: | Line 105: | ||
* [https://help.dyalog.com/latest/#Language/Primitive%20Functions/Encode.htm Dyalog] | * [https://help.dyalog.com/latest/#Language/Primitive%20Functions/Encode.htm Dyalog] | ||
* [http://microapl.com/apl_help/ch_020_020_650.htm APLX] | * [http://microapl.com/apl_help/ch_020_020_650.htm APLX] | ||
* J [https://www.jsoftware.com/help/dictionary/d402.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/numberco#dyadic NuVoc] (as <source lang=j inline>#:</ | * J [https://www.jsoftware.com/help/dictionary/d402.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/numberco#dyadic NuVoc] (as <source lang=j inline>#:</syntaxhighlight>) | ||
{{APL built-ins}}[[Category:Primitive functions]] | {{APL built-ins}}[[Category:Primitive functions]] | ||
Revision as of 21:44, 10 September 2022
⊤
|
Encode (⊤), also called Represent or Antibase, is a dyadic primitive function which computes the representation of the right argument in the radix system defined by the left argument. Some implementations add monadic usage to this function, which computes the binary representation using as many bits as needed. Encode is the inverse of Decode <source lang=apl inline>⊥</syntaxhighlight> with the same left argument X, when X is a vector.
Concept
Encode works by finding the "digits" one by one from the rightmost digit. Let's consider <source lang=apl inline>0 7 24 60⊤12345</syntaxhighlight> (convert 12345 minutes to weeks, days, hours, and minutes) as an example.
<source lang=apl>
60|12345 ⍝ Minute's digit; 45 minutes
45
60÷⍨12345-45 ⍝ 205 hours remaining to convert
205
24|205 ⍝ Hour's digit; 13 hours
13
24÷⍨205-13 ⍝ 8 days remaining to convert
8
7|8 ⍝ Day's digit; 1 day
1
7÷⍨8-1 ⍝ 1 week remaining to convert
1 ⍝ No more conversion needed, since there is no limit for the highest digit </syntaxhighlight>
Collecting all the digits gives the desired result.
<source lang=apl>
0 7 24 60⊤12345
1 1 13 45 </syntaxhighlight>
If the left argument has high rank, the vectors over the first axis act as independent radix systems.
<source lang=apl>
⎕←mat←8 3⍴2 10 16 ⍝ Base 2, 10, and 16, being able to represent at most 8 digits
2 10 16 2 10 16 2 10 16 2 10 16 2 10 16 2 10 16 2 10 16 2 10 16
mat⊤121 ⍝ 121 is 1111001 in binary, 121 in decimal, 79 in hexadecimal
0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 2 7 1 1 9 </syntaxhighlight>
Examples
A common use case is to convert an integer to base N, usually base 2 or 10. However, Encode does not know how many digits to produce, so it needs to be supplied as the shape of the left argument.
<source lang=apl>
10⊤12345 ⍝ This does not work
5
(10⍴10)⊤12345 ⍝ Convert to ten decimal digits, giving leading zeros if too small
0 0 0 0 0 1 2 3 4 5
((1+⌊10⍟12345)⍴10)⊤12345 ⍝ Convert to decimal digits using just as many digits as needed
1 2 3 4 5 </syntaxhighlight>
Encode can be also used to convert a measure given in the smallest unit to a hierarchy of units. For example, given that 1 day = 24 hours, 1 hour = 60 minutes, and 1 minute = 60 seconds, how many days/hours/minutes/seconds is 210859 seconds?
<source lang=apl>
0 24 60 60⊤210859
2 10 34 19 </syntaxhighlight>
Another common usage of Encode is to simulate "divmod": a function which, given two integers, computes the quotient and remainder at once. The construct can also be used to extract the integer part and fractional part of a real number.
<source lang=apl>
⌊7÷3 ⍝ Quotient
2
3|7 ⍝ Remainder
1
0 3⊤7 ⍝ Quotient and remainder at once
2 1
0 1⊤○1 ⍝ Integer and fractional parts of pi
3 0.1415926536 </syntaxhighlight>
Encode has an important property with array index: Given an arbitrary array A with shape S, encoding a raveled index by S gives the original index in A. This can be used to generate all indices of a given array or array shape. Note that index origin 0 (<source lang=apl inline>⎕IO←0</syntaxhighlight>) is required for this to hold.
<source lang=apl>
⎕IO←0
⎕A[17]=(2 3 4⊤17)⌷2 3 4⍴⎕A
1
2 3 4⊤⍳×/2 3 4 ⍝ Generating all indices of a 2×3×4 array as columns
0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 2 2 2 2 0 0 0 0 1 1 1 1 2 2 2 2 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 </syntaxhighlight>
External links
Lesson
Documentation
- Dyalog
- APLX
- J Dictionary, NuVoc (as <source lang=j inline>#:</syntaxhighlight>)