Replicate: Difference between revisions

Outside of APL, [[wikipedia:filter (higher-order function)|filter]] typically provides the functionality of Compress, while Replicate has no common equivalent.

       1 1 0 1 0 1 0 0 / 'compress'

cope

If the right argument is an array of [[indices]] generated by [[Iota]], Replicate resembles the function [[Indices]].

<source lang=apl>

       1 1 0 0 1 / ⍳5

1 2 5

With an array of non-negative integers, Replicate copies each element of the right argument the corresponding number of times. As with Compress, these copies retain their original ordering, and the length of the result is the sum of the control array.

<source lang=apl>

       ⍴ 0 3 0 0 2 0 1 0 2 / 'replicate'

8

Replicate usually allows [[scalar extension]] of the left argument, which results in every element being copied a fixed number of times.

<source lang=apl>

       3 / 'replicate'

rrreeepppllliiicccaaattteee

=== Negative numbers ===

       0 2 ¯3 1 / ⍳4

2 2 0 0 0 4

<source lang=apl>

       0 2 ¯3 1 / ⍳3

2 2 0 0 0 3

<source lang=apl>

       1 ¯2 3 / 'a'

a  aaa

=== High-rank arrays ===

<source lang=apl>

       ⎕←A ← 4 6⍴⎕A

MNOPQR

STUVWX

[[APL2]] further extends the [[singleton extension]] of the right argument, allowing it to have length 1 along the replication axis even if other axes have lengths not equal to 1.

<source lang=apl>

b  bbb

c  ccc

=== Operator or function? ===

{{Main|Function-operator overloading}}

<source lang=apl>

       1 3 /¨ 'ab' 'cd'   

       (1 3/)¨ 'ab' 'cd'

  abbb  cddd

If Replicate is a function, then Each will apply to Replicate only, and the resulting derived function will be invoked monadically.

<source lang=apl>

       1 3 (/¨) 'ab' 'cd'

  ab  cccddd

In early APLs such as [[APL\360]], applying an operator to Compress will always result in a [[SYNTAX ERROR]], because Compress is not an allowed operand of any operator. This is also the case in [[ngn/apl]]: although operators can apply to any function, Replicate cannot be used unless both arguments are immediately available. In both cases there is no way to determine whether Replicate "acts like a function" or "acts like an operator".

== History ==

In 1980, [[Bob Bernecky]] introduced the extension Replicate to [[SHARP APL]]: he allowed an operand (since SHARP's Replicate is an operator) consisting of non-negative integers rather than just [[Boolean]]s to indicate the number of times to copy.<ref>[[Bob Bernecky|Bernecky, Bob]]. SATN-34: Replication. [[IPSA]]. 1980-08-15.</ref> This extension was rapidly and widely adopted, starting with [[NARS]] in 1981, and is now a feature of the [[ISO/IEC 13751:2001]] standard.

Two extensions to allow negative numbers in the left argument have been introduced, in each case specifying that the negative of a number indicates that many [[fill element]]s should appear in the result. In 1981 [[NARS]] specified that these fill elements replace the corresponding right argument element, so that the lengths of the left and right arguments are always equal, and extended [[Expand]] similarly. [[APL2]], in 1984, made the opposite choice, so that the length of the right argument along the specified axis is equal to the number of non-negative elements on the left. [[APL2]] also loosened the [[conformability]] requirements further than simply allowing [[singleton extension]]: it allowed a right argument with length 1 along the replication axis to be extended. [[Dyalog APL]], created before APL2, adopted the [[NARS]] definition for negative elements but added APL2 conformability extension in [[Dyalog APL 13.1|version 13.1]]. Later [[APLX]] took advantage of the fact that the two negative number extensions can be distinguished by the length of the left argument, and implemented every NARS and APL2 extension.

== Extension support ==

| [[APL2]]                                            || Operator  || {{Yes}} || {{No}}  || {{Yes}} || {{Yes|APL2}}        || {{Yes}} ||

|-

|-

|-

| [[ISO/IEC 13751:2001]]                              || Function  || {{Yes}} ||colspan=2 {{No}}    || {{Maybe|Scalar}}      || {{Yes}} ||

| [[GNU APL]]                                        || Function  || {{Yes}} || {{No}}  || {{Yes}} || {{Yes|APL2}}        || {{Yes}} ||

|-

|-

|}

== Outside of APL ==

While filter is similar to Compress, some extensions to the [[wikipedia:x86|x86]] instruction set are exactly equivalent to Compress on particular data types. In [[wikipedia:BMI2|BMI2]], the PEXT and PDEP instructions (parallel bit extract and deposit) are identical to Compress and [[Expand]] on the bits of a register argument. Indeed, [[Dyalog APL]] uses these instructions to implement those primitives (see [[Dyalog APL#Instruction set usage]]). The [[wikipedia:AVX-512|AVX-512]] instructions VPCOMPRESSQ and VPEXPANDQ (and variations) are not only equivalent to Compress and Expand using a mask register for the [[Boolean]] argument and a vector register for the other argument, but are named after the APL functions. These instructions allow compression of 4-byte and 8-byte elements, and with AVX-512_VBMI2 support was added for 1-byte and 2-byte elements as well.