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| index origin            = 0 or 1
| index origin            = 0 or 1
| function styles          = [[tradfn]], [[dfn]], [[tacit]]
| function styles          = [[tradfn]], [[dfn]], [[tacit]]
| numeric types            = complex floats, decimal float
| numeric types            = [[complex]] floats, [[decimal float]]s
| unicode support          = full
| unicode support          = full
| released                = 1983
| released                = 1983
Line 16: Line 16:
| file ext                = .dws, .dse, .dcf, .dyalog, .dyapp, .apl, .apla, .aplf, .aplo, .apln, .aplc, .apli
| file ext                = .dws, .dse, .dcf, .dyalog, .dyapp, .apl, .apla, .aplf, .aplo, .apln, .aplc, .apli
| documentation            = [https://docs.dyalog.com/ Documentation Centre]
| documentation            = [https://docs.dyalog.com/ Documentation Centre]
| influenced by            = [[APL2]], [[J]], [[SHARP APL]], [[wikipedia:Scheme (programming language)|Scheme]], [[wikipedia:C-Sharp_|C#]]
| influenced by            = [[APL2]], [[J]], [[SHARP APL]], [[wikipedia:Scheme (programming language)|Scheme]], [[wikipedia:C_Sharp_(programming_language)|C#]]
| influenced              = [[NARS2000]], [[GNU APL]], [[ngn/apl]], [[dzaima/APL]], [[APL\iv]]
| influenced              = [[NARS2000]], [[GNU APL]], [[ngn/apl]], [[dzaima/APL]], [[APL\iv]]
| run online              = [https://tryapl.org/ TryAPL]
}}
}}
'''Dyalog APL''', or simply '''Dyalog''', is a modern APL in the [[APL2]] tradition, first released by British company [[Dyalog Ltd.|Dyadic Systems Ltd.]] (now Dyalog Ltd.) in 1983 for the Zylog Z80 processor (the name ''Dyalog'' is a portmanteau of ''Dyadic'' and ''Zylog''). Dyalog supports several platforms and interfaces with many languages and runtimes including native [[wikipedia:Shared library|shared libraries]], [[.NET]], the [[wikipedia:Java virtual machine|JVM]], [[wikipedia:R (programming language)|R]], and [[wikipedia:Python (programming language)|Python]]. It is actively developed and has introduced many new primitives and concepts to array programming. Major categories of features introduced to APL by Dyalog are [[tacit]] programming by allowing named [[derived function]]s and later [[train]]s, lexically-scoped functional programming using [[dfns]], [[namespace]]s and [[object-oriented programming]], and the addition of [[leading axis theory]] and the [[Rank operator]] to the [[nested array model|nested array]] paradigm.
:''For the chat bot, see [[APL Orchard#Chat bot]].''
'''Dyalog APL''', or simply '''Dyalog''', is a modern APL in the [[APL2]] tradition, first released by British company [[Dyalog Ltd.|Dyadic Systems Ltd.]] (now Dyalog Ltd.) in 1983 for the Zylog Z80 processor (the name ''Dyalog'' is a portmanteau of ''Dyadic'' and ''Zylog''). Dyalog supports several platforms and interfaces with many languages and runtimes including native [[wikipedia:Shared library|shared libraries]], [[.NET]], the [[wikipedia:Java virtual machine|JVM]], [[wikipedia:R (programming language)|R]], and [[wikipedia:Python (programming language)|Python]]. It is actively developed and has introduced many new primitives and concepts to array programming. Major categories of features introduced to APL by Dyalog are [[tacit]] programming by allowing named [[derived function]]s and later [[train]]s, lexically-scoped functional programming using [[dfn]]s, [[namespace]]s and [[object-oriented programming]], and the addition of [[leading axis theory]] and the [[Rank operator]] to the [[nested array model|nested array]] paradigm.


In 1995, two Dyalog developers—[[John Scholes]] and [[Peter Donnelly]]—were awarded the [[Iverson Award]] for their work on the interpreter. [[Gitte Christensen]] and [[Morten Kromberg]] were joint recipients of the Iverson Award in 2016.
In 1995, two Dyalog developers—[[John Scholes]] and [[Peter Donnelly]]—were awarded the [[Iverson Award]] for their work on the interpreter. [[Gitte Christensen]] and [[Morten Kromberg]] were joint recipients of the Iverson Award in 2016.
== Platforms ==
Besides for working out-of-the-box on Windows, macOS, and AIX, Dyalog APL runs on many Linuxes. However, to function, some require additional action beyond simple installation. As of 2019-05-15, the necessary actions for versions 16.0, 17.0, and 17.1 are:
{| class=wikitable
! Distribution    !! Action
|-
|Debian 8.2, 9.8, 9.9 || no pre-reqs
|-
|Fedora 29, 30        || <code>dnf install ncurses-compat-libs</code>
|-
|Linux Mint 18.0, 19.0|| no pre-reqs
|-
|openSUSE 15.0        || <code>zypper install libncurses5</code>
|-
|CentOS/RedHat 6      || not supported for 17.1 as glibc is at too low a level
|-
|CentOS/RedHat 7      || no pre-reqs
|-
|RedHat 8            || <code>rpm -Uvh ncurses-compat-libs</code>  (note: RH8 would not install in a VM)
|-
|Ubuntu 16.04, 18.04  || no pre-reqs
|-
|Ubuntu 19.04        || <code>apt-get install libtinfo5</code>
|}


== Versions ==
== Versions ==


Dyalog lists historical versions, along with release notes since 14.0, on [https://www.dyalog.com/dyalog/dyalog-versions.htm its website].
{{Main|Dyalog APL versions}}
 
Dyalog lists historical versions, along with release notes since 14.0, on [https://www.dyalog.com/dyalog/dyalog-versions.htm its website]. Its early history is recounted in more detail by [[Pete Donnelly]] in [https://www.dyalog.com/uploads/files/apl50/Dyalog%20APL%20A%20Personal%20History.pdf Dyalog APL: A Personal History (pdf)].


{|class=wikitable
{|class=wikitable
! Number   !! Year !! Month    !! Features
! Number                             !! Year !! Month    !! Features
|-
|-
| '''1'''  || 1983 || April    || [[Assignment]] for [[derived function]]s
|                             1       || 1983 || April    || (Zilog S8000 only)
|-
|-
| '''2'''  || 1984 ||          ||
|                             2       || 1984 ||          || (Many more platforms)
|-
|-
| '''3.0''' || 1985 ||          ||
|                             3.0     || 1985 ||          || (More platforms) Rectangular display of arrays
|-
|-
| '''4.0''' || 1986 || October  ||
|                             4.0     || 1986 || October  || User-defined operators, [[Assignment]] for functions (including [[derived function]]s), <source lang=apl inline>⎕MONITOR</source>
|-
|-
| '''5.0''' || 1987 || April    ||
|                             5.0     || 1987 || April    || Nested array editor
|-
|-
|     5.1   || 1988 || April    ||
|                             5.1     || 1988 || April    || (first version for DOS) User-defined input/output tables, <source lang=apl inline>⎕SM</source> and <source lang=apl inline>⎕SR</source>, windowed editor/tracer, interface to GSS/CGI
|-
|-
|     5.2   || 1990 || January  ||
|                             5.2     || 1990 || January  || Naked trace
|-
|-
| '''6.0''' || 1990 || April    || [[Namespaces]]
|                             6.0     || 1990 || April    || GUI IDE
|-
|-
|     6.1   || 1990 || October  ||
|                             6.1     || 1990 || October  || <source lang=apl inline>⎕ED</source>
|-
|-
|     6.2   || 1993 || April    ||
|                             6.2.1  || 1992 || July      || (first version for Windows) <source lang=apl inline>⎕WC</source>, <source lang=apl inline>⎕DQ</source>, etc.
|-
|-
|     6.3   || 1993 || October  ||
|                             6.3.1  || 1993 || April    || <source lang=apl inline>⎕NA</source>, graphical, clipboard and printer objects
|-
|-
| '''7.0''' || 1994 || August    ||
|                             7.0.1  || 1994 || August    || Namespaces, additional GUI objects
|-
|-
|     7.1   || 1995 || May      || [[Control structures|Keywords]] (If/Then/Else, Repeat/Until, exception handling, and so on)
|                             7.1     || 1995 || May      || <source lang=apl inline>⎕CS</source>, GUI objects as namespaces, greater [[APL2]] compatibility
|-
|-
| '''8.0''' || 1996 || May      || [[dfns]] with [[lexical scope]]
|                             8.0     || 1996 || May      || [[Control structure|Keywords]] (<source lang=apl inline>:If</source>/<source lang=apl inline>:Else</source>, <source lang=apl inline>:Repeat</source>/<source lang=apl inline>:Until</source>, <source lang=apl inline>:Trap</source>, and so on), <source lang=apl inline>⎕PATH</source>, additional GUI objects, OLE
|-
|-
|     8.1   || 1997 || March    ||
|                             8.1     || 1997 || March    || [[dfn]]s with [[lexical scope]], syntax colouring, TCPSocket object, OLE client/server, automatic file tie numbers
|-
|-
|     8.2   || 1999 || January  || Threading with [[Spawn]] (<source lang=apl inline>&</source>)
|                             8.2     || 1999 || January  || [[Windowed Reduction]] and [[scalar function]]s with [[Function axis|axis]] (from [[APL2]]), Threading with [[Spawn]] (<source lang=apl inline>&</source>), ActiveX, <source lang=apl inline>:With</source>, additional GUI objects
|-
|-
| '''9.0''' || 2000 || September || [[Namespace]] [[reference]]s (instead of [[string]] names) and dot syntax, context-sensitive help (F1)
|                             9.0     || 2000 || September || [[Namespace]] [[reference]]s (instead of [[string]] names) and dot syntax, context-sensitive help (F1), aditional GUI objects with animation
|-
|-
|     9.0.1 || 2001 || January  ||
|                             9.0.1   || 2001 || January  || (Windows CE) Pocket APL
|-
|-
|     9.0.2 || 2002 || January  ||
|                             9.0.2   || 2002 || January  || [[.NET]] support
|-
|-
|     9.5   || 2002 || September ||
|                             9.5     || 2002 || September ||
|-
|-
| '''10.0''' || 2003 || March    || <source lang=apl inline>⎕NULL</source>
|                           10.0     || 2003 || March    || <source lang=apl inline>⎕NULL</source>, <source lang=apl inline>⎕MAP</source>, [[idiom recognition]] (mapped files), retained hash tables, [[.NET]] support built-in, run-time workspace as .exe, auto-completion, mapped
|-
|-
|   10.1   || 2004 || July      ||
|                           10.1     || 2004 || July      || Multiple arguments in [[tradfn]] headers, thread tokens, 64-bit component files, value tips
|-
|-
| '''11.0''' || 2006 || October  || [[Object oriented programming]] (classes, objects, interfaces) modelled after [[wikipedia:C-Sharp_|C#]], [[Squad indexing|Index]] (<source lang=apl inline>⌷</source>), [[Power operator]] (<source lang=apl inline>⍣</source>), [[GCD]] (<source lang=apl inline>∨</source>), [[LCM]] (<source lang=apl inline>∧</source>)
| [[Dyalog_APL_versions#11.0|11.0]]  || 2006 || October  || [[Object-oriented programming]] (classes, objects, interfaces) modelled after [[wikipedia:C-Sharp_|C#]], [[Squad indexing|Index]] (<source lang=apl inline>⌷</source>), [[Power operator]] (<source lang=apl inline>⍣</source>), [[GCD]] (<source lang=apl inline>∨</source>), [[LCM]] (<source lang=apl inline>∧</source>)
|-
|-
| '''12.0''' || 2008 || August    || [[Unicode]] support (<source lang=apl inline>⎕AVU</source>, <source lang=apl inline>⎕UCS</source>), <source lang=apl inline>⎕FCOPY</source>, <source lang=apl inline>⎕FPROPS</source>
| [[Dyalog_APL_versions#12.0|12.0]]  || 2008 || August    || [[Unicode]] support (<source lang=apl inline>⎕AVU</source>, <source lang=apl inline>⎕UCS</source>), <source lang=apl inline>⎕FCOPY</source>, <source lang=apl inline>⎕FPROPS</source>
|-
|-
|   12.1   || 2009 || November  || [[I-Beam]] (<source lang=apl inline>⌶</source>), [[Table]] (<source lang=apl inline>⍪</source>), <source lang=apl inline>⎕XML</source>, <source lang=apl inline>⎕FCHK</source>, [[User commands]]
| [[Dyalog_APL_versions#12.1|12.1]]  || 2009 || November  || [[I-Beam]] (<source lang=apl inline>⌶</source>), [[Table]] (<source lang=apl inline>⍪</source>), <source lang=apl inline>⎕XML</source>, <source lang=apl inline>⎕FCHK</source>, [[User command]]s
|-
|-
| '''13.0''' || 2011 || April    || [[Left]] (<source lang=apl inline>⊣</source>), [[Right]] (<source lang=apl inline>⊢</source>), [[Variant]] (<source lang=apl inline>⍠</source>), <source lang=apl inline>⎕OPT</source>, <source lang=apl inline>⎕R</source>, <source lang=apl inline>⎕S</source>, <source lang=apl inline>⎕PROFILE</source>, <source lang=apl inline>⎕RSI</source>, [[complex number]] and [[decimal float]] support, short arguments for [[Take]], [[Drop]], and [[Squad indexing|Index]] (<source lang=apl inline>↑</source>, <source lang=apl inline>↓</source>, <source lang=apl inline>⌷</source>)
| [[Dyalog_APL_versions#13.0|13.0]]  || 2011 || April    || [[Left]] (<source lang=apl inline>⊣</source>), [[Right]] (<source lang=apl inline>⊢</source>), [[Variant]] (<source lang=apl inline>⍠</source>), <source lang=apl inline>⎕OPT</source>, <source lang=apl inline>⎕R</source>, <source lang=apl inline>⎕S</source>, <source lang=apl inline>⎕PROFILE</source>, <source lang=apl inline>⎕RSI</source>, [[complex number]] and [[decimal float]] support, short arguments for [[Take]], [[Drop]], and [[Squad indexing|Index]] (<source lang=apl inline>↑</source>, <source lang=apl inline>↓</source>, <source lang=apl inline>⌷</source>)
|-
|-
|   13.1   || 2012 || April    || <source lang=apl inline>⎕DMX</source>, <source lang=apl inline>⎕FHIST</source>
| [[Dyalog_APL_versions#13.1|13.1]]  || 2012 || April    || <source lang=apl inline>⎕DMX</source>, <source lang=apl inline>⎕FHIST</source>
|-
|-
|   13.2   || 2013 || January  || Array [[Editor]]
| [[Dyalog_APL_versions#13.2|13.2]]  || 2013 || January  || Array [[Editor]]
|-
|-
| '''14.0''' || 2014 || June      || [[Trains]], [[Tally]] (<source lang=apl inline>≢</source>), [[Key]] (<source lang=apl inline>⌸</source>), [[Rank operator]] (<source lang=apl inline>⍤</source>), multi-threading with [[futures]] and [[isolates]]
| [[Dyalog_APL_versions#14.0|14.0]]  || 2014 || June      || [[Train]]s, [[Tally]] (<source lang=apl inline>≢</source>), [[Key]] (<source lang=apl inline>⌸</source>), [[Rank operator]] (<source lang=apl inline>⍤</source>), [[High-rank set functions|high-rank]] [[Index Of]], multi-threading with [[future]]s and [[isolate]]s
|-
|-
|   14.1   || 2015 || June      ||
| [[Dyalog_APL_versions#14.1|14.1]]  || 2015 || June      || <source lang=apl inline>:Disposable</source> [[.NET]] objects and resources, gesture support, many new I-beams
|-
|-
| '''15.0''' || 2016 || June      || <source lang=apl inline>⎕MKDIR</source>, <source lang=apl inline>⎕NDELETE</source>, <source lang=apl inline>⎕NEXISTS</source>, <source lang=apl inline>⎕NGET</source>, <source lang=apl inline>⎕NINFO</source>, <source lang=apl inline>⎕NPARTS</source>, <source lang=apl inline>⎕NPUT</source>
| [[Dyalog_APL_versions#15.0|15.0]]  || 2016 || June      || <source lang=apl inline>⎕MKDIR</source>, <source lang=apl inline>⎕NDELETE</source>, <source lang=apl inline>⎕NEXISTS</source>, <source lang=apl inline>⎕NGET</source>, <source lang=apl inline>⎕NINFO</source>, <source lang=apl inline>⎕NPARTS</source>, <source lang=apl inline>⎕NPUT</source>
|-
|-
| '''16.0''' || 2017 || June      || [[At]] (<source lang=apl inline>@</source>), [[Interval Index]] (<source lang=apl inline>⍸</source>), [[Where]] (<source lang=apl inline>⍸</source>), [[Nest]] (<source lang=apl inline>⊆</source>), [[Partition]] (<source lang=apl inline>⊆</source>), [[Stencil]] (<source lang=apl inline>⌺</source>), <source lang=apl inline>⎕JSON</source>, <source lang=apl inline>⎕CSV</source>
| [[Dyalog_APL_versions#16.0|16.0]]  || 2017 || June      || [[At]] (<source lang=apl inline>@</source>), [[Interval Index]] (<source lang=apl inline>⍸</source>), [[Where]] (<source lang=apl inline>⍸</source>), [[Nest]] (<source lang=apl inline>⊆</source>), [[Partition]] (<source lang=apl inline>⊆</source>), [[Stencil]] (<source lang=apl inline>⌺</source>), <source lang=apl inline>⎕JSON</source>, <source lang=apl inline>⎕CSV</source>
|-
|-
| '''17.0''' || 2018 || July      || <source lang=apl inline>⎕NCOPY</source>, <source lang=apl inline>⎕NMOVE</source>
| [[Dyalog_APL_versions#17.0|17.0]]  || 2018 || July      || <source lang=apl inline>⎕NCOPY</source>, <source lang=apl inline>⎕NMOVE</source>
|-
|-
|   17.1   || 2019 || October  || Duplicates in [[Interval Index]] (<source lang=apl inline>⍸</source>) look-up array
| [[Dyalog_APL_versions#17.1|17.1]]  || 2019 || October  || Duplicates in [[Interval Index]] (<source lang=apl inline>⍸</source>) look-up array
|-
|-
| '''18.0''' ||colspan=2| Unreleased || [[Atop]] (<source lang=apl inline>⍤</source>), [[Over]] (<source lang=apl inline>⍥</source>), [[Constant]] (<source lang=apl inline>⍨</source>), [[Unique Mask]] (<source lang=apl inline>≠</source>), duplicates from [[Where]] (<source lang=apl inline>⍸</source>), empty partitions from partitioned enclose (<source lang=apl inline>⊂</source>), multi-line session input, date-time conversion, case folding/mapping (<source lang=apl inline>⎕C</source>), initial cross-platform support for .NET Core,
| [[Dyalog_APL_versions#18.0|18.0]]  ||colspan=2| Unreleased || [[Atop]] (<source lang=apl inline>⍤</source>), [[Over]] (<source lang=apl inline>⍥</source>), [[Constant]] (<source lang=apl inline>⍨</source>), [[Unique Mask]] (<source lang=apl inline>≠</source>), duplicates from [[Where]] (<source lang=apl inline>⍸</source>), empty partitions from [[Partitioned Enclose]] (<source lang=apl inline>⊂</source>), multi-line session input, date-time conversion, case folding/mapping (<source lang=apl inline>⎕C</source>)
|}
|}


Line 252: Line 280:
| <source lang=apl inline>f∘g</source>  ||colspan=2| [[Beside]]
| <source lang=apl inline>f∘g</source>  ||colspan=2| [[Beside]]
|-
|-
| <source lang=apl inline>f⍤B</source>  ||colspan=2| [[Rank]]
| <source lang=apl inline>f⍤B</source>  ||colspan=2| [[Rank operator|Rank]]
|-
|-
| <source lang=apl inline>f⍤g</source>  ||colspan=2| [[Atop]]
| <source lang=apl inline>f⍤g</source>  ||colspan=2| [[Atop]]
Line 272: Line 300:
| <source lang=apl inline>f[B]</source> ||colspan=2| [[Function axis|Axis]]
| <source lang=apl inline>f[B]</source> ||colspan=2| [[Function axis|Axis]]
|}
|}
== Implementation ==
Dyalog APL is implemented primarily in [[wikipedia:C (programming language)|C]] with some parts implemented in [[wikipedia:C++|C++]] in order to use [[wikipedia:C++#Templates|templates]]. C [[wikipedia:Intrinsic function|intrinsics]] are used to access instruction set extensions. Some architecture-specific [[wikipedia:Assembly language|assembly]], both compiled separately and inline from C, is used for functionality like [[wikipedia:Status register|exception flags]] which is not easily accessible in C. Prior to [[Dyalog APL versions#17.0|version 17.0]], assembly was also used for vectorized arithmetic. In 17.0, this code was replaced by a new C++ implementation.
=== Internal types ===
Dyalog uses the following [[numeric]] types:
* 1-bit packed [[Boolean]]
* 1-byte integer
* 2-byte integer
* 4-byte integer
* 8-byte [[wikipedia:IEEE 754|double]]
* 16-byte [[complex]] (one double for each component)
* 16-byte decimal float "decf" ([[wikipedia:Binary integer decimal|BID]] or [[wikipedia:Densely packed decimal|DPD]])
[[Character]] encodings differ for classic and unicode interpreters: classic interpreters use a custom 1-byte encoding for all characters, and are limited to a 256-character set, while characters in unicode interpreters are 1-, 2-, or 4-byte unsigned unicode [[wikipedia:code point|code point]] values.
[[Nested]] and [[mixed array]]s (that is, [[pointer array]]s) are always stored as arrays of pointers, while [[simple array|simple]] numeric or character arrays are always stored using one of the above types. For both numbers and characters, an array may be represented using any type that can contain all the values. The interpreter may reduce the type of an array to the minimum possible ("squeeze" the array) during execution.
Because there is no [[complex]] representation using decimal floats for the components, arrays containing both decimal floats and complex numbers have no common representation. Dyalog converts such arrays to complex numbers, resulting in a loss of precision for decf elements.
=== Instruction set usage ===
Dyalog makes heavy use of [[vector instructions]] on all platforms, as well as other special instruction sets primarily on x86. Instruction set availability is checked at runtime, so that the minimum required instruction set remains low:
* For 32-bit x86, only [[wikipedia:SSE2|SSE2]] is required.
* For x86_64, there is no minimum requirement as every processor supports SSE2. SSE4.1 is required on macOS as all x86 Apple machines support this instruction set.
* For ARM32, there is no minimum requirement.
* As of version 17.1, POWER7 and above are supported. Support for older systems is dropped because Dyalog compiles separate binaries for each POWER architecture.
In Dyalog 17.0, the code for vectorized [[scalar function]]s was unified and extended to allow Intel [[wikipedia:AVX2|AVX2]] and ARM NEON in addition to Intel [[wikipedia:SSE2|SSE2]] and [[wikipedia:SSE4.1|SSE4.1]], and AltiVec VMX for IBM POWER. This code is also used for operations involving the scalar dyadics [[Plus]], [[Minus]], [[Times]], [[Divide]], [[Maximum]], [[Minimum]], and [[comparison function]]s, as well as some functions derived from operators applied to these functions, such as the [[Outer Product]] and [[Inner Product]].
Dyalog also uses many other x86 extensions:
* Since at least [[Dyalog APL versions#12.1|12.1]], [[wikipedia:SSE2|SSE2]] is used for [[scalar dyadic]]s.
* Since [[Dyalog APL versions#17.0|17.0]], [[wikipedia:AVX2|AVX2]] is used for scalar dyadics if available.
* Since [[Dyalog APL versions#14.1|14.1]], [[wikipedia:SSE4.1|SSE4.1]] is used for [[Minimum]] and [[Maximum]], and finding the range of an array. [[wikipedia:AVX2|AVX2]] can also be used for these purposes in [[Dyalog APL versions#18.0|18.0]].
* Since [[Dyalog APL versions#17.0|17.0]], [[wikipedia:SSSE3|SSSE3]] is used primarily for the shuffle instruction for permuting arrays and searching small lookup tables.
* Since [[Dyalog APL versions#14.0|14.0]], [[wikipedia:SSE4.2|SSE4.2]] POPCNT is used to sum Boolean arrays.
* Since [[Dyalog APL versions#14.0|14.0]], [[wikipedia:SSE4.2|SSE4.2]] CRC32 is used to compute fast hash functions.
* Since [[Dyalog APL versions#15.0|15.0]], [[wikipedia:BMI2|BMI2]] is used for Boolean matrix transpose. Since [[Dyalog APL versions#16.0|16.0]], it is used for Boolean [[Compress]] and [[Expand]], and several [[structural function]]s on Boolean arrays.
* Since [[Dyalog APL versions#18.0|18.0]], [[wikipedia:CLMUL instruction set|CLMUL]] is used for [[xor]] [[reduction]]s and [[scan]]s.
* Since [[Dyalog APL versions#18.0|18.0]], [[wikipedia:FMA instruction set|FMA3]] is used to implement [[Divide|division]] by a [[singleton]].
It also uses the POWER8 [https://www.ibm.com/support/knowledgecenter/SSGH2K_13.1.3/com.ibm.xlc1313.aix.doc/compiler_ref/vec_gbb.html gather-bits-by-bytes] instruction, which is equivalent to transposing an 8x8 bit matrix for [[Boolean]] [[Transpose]] since version 15.0 (expanded in applicability in 16.0) and the fused multiply-add instruction for division like x86 FMA3 in 18.0.


== External links ==
== External links ==
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* [https://dyalog.com Download]
* [https://dyalog.com Download]


{{APL programming language}}
{{APL dialects}}
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