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Julia (programming language)

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</style><table class="infobox vevent"><tbody><tr><th colspan="2" class="infobox-above" style="background-color:#e0e0e0;">Julia</th></tr><tr><td colspan="2" class="infobox-image"></td></tr><tr><th scope="row" class="infobox-label"><a href="Programming_paradigm" title="Programming paradigm">Paradigm</a></th><td class="infobox-data"><a href="Multi-paradigm_programming_language" class="mw-redirect" title="Multi-paradigm programming language">Multi-paradigm</a>: <a href="Multiple_dispatch" title="Multiple dispatch">multiple dispatch</a> (primary paradigm), <a href="Functional_programming" title="Functional programming">functional</a>, <a href="Array_programming" title="Array programming">array</a>, <a href="Procedural_programming" title="Procedural programming">procedural</a> (<a href="Imperative_programming" title="Imperative programming">imperative</a>), <a href="Structured_programming" title="Structured programming">structured</a>, <a href="Reflective_programming" title="Reflective programming">reflective</a>, <a href="Metaprogramming" title="Metaprogramming">meta</a>, <a href="Multistaged_programming" class="mw-redirect" title="Multistaged programming">multistaged</a><a href="#cite_note-1">[1]</a></td></tr><tr><th scope="row" class="infobox-label"><a href="Software_design" title="Software design">Designed by</a></th><td class="infobox-data"><a href="Jeff_Bezanson_(programmer)" class="mw-redirect" title="Jeff Bezanson (programmer)">Jeff Bezanson</a>, <a href="Alan_Edelman" title="Alan Edelman">Alan Edelman</a>, <a href="Stefan_Karpinski" title="Stefan Karpinski">Stefan Karpinski</a>, <a href="Viral_B._Shah" title="Viral B. Shah">Viral B. Shah</a></td></tr><tr><th scope="row" class="infobox-label"><a href="Software_developer" class="mw-redirect" title="Software developer">Developer</a></th><td class="infobox-data organiser"><a href="Jeff_Bezanson_(programmer)" class="mw-redirect" title="Jeff Bezanson (programmer)">Jeff Bezanson</a>, <a href="Stefan_Karpinski" title="Stefan Karpinski">Stefan Karpinski</a>, <a href="Viral_B._Shah" title="Viral B. Shah">Viral B. Shah</a>, and other contributors<a href="#cite_note-license-2">[2]</a><a href="#cite_note-3">[3]</a></td></tr><tr><th scope="row" class="infobox-label">First appeared</th><td class="infobox-data">2012 (2012)<a href="#cite_note-announcement-4">[4]</a></td></tr><tr><td colspan="2" class="infobox-full-data"></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;"><a href="Software_release_life_cycle" title="Software release life cycle">Stable release</a></th><td class="infobox-data"><div style="margin:0px;">1.11.6<a href="#cite_note-wikidata-c682ff7e7ce6880b4155cd01b6d084f5159a754c-v20-5">[5]</a>

/ 10 July 2025 (10 July 2025) and 1.10.10<a href="#cite_note-9">[9]</a> (<a href="Long-term_support" title="Long-term support">LTS</a>) / 27 June 2025 (2025-06-27)</div></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;"><a href="Software_release_life_cycle#Beta" title="Software release life cycle">Preview release</a></th><td class="infobox-data"><div style="margin:0px;">1.12.0-rc1<a href="#cite_note-6">[6]</a><a href="#cite_note-7">[7]</a><a href="#cite_note-8">[8]</a>

/ 12 July 2025 (2025-07-12). Being worked on: 1.12.0-rc2<a href="#cite_note-10">[10]</a> and 1.13.0-DEV with daily updates</div></td></tr><tr style="display:none"><td colspan="2">

</td></tr><tr><th scope="row" class="infobox-label"><a href="Type_system" title="Type system">Typing discipline</a></th><td class="infobox-data"><a href="Dynamic_programming_language" title="Dynamic programming language">Dynamic</a>,<a href="#cite_note-Engheim-11">[11]</a> <a href="Type_inference" title="Type inference">inferred</a>, <a href="Optional_typing" class="mw-redirect" title="Optional typing">optional</a>, <a href="Nominal_type_system" title="Nominal type system">nominative</a>, <a href="Parametric_polymorphism" title="Parametric polymorphism">parametric</a>, <a href="Strong_and_weak_typing" title="Strong and weak typing">strong</a><a href="#cite_note-Engheim-11">[11]</a></td></tr><tr><th scope="row" class="infobox-label">Implementation language</th><td class="infobox-data">Julia, <a href="C_(programming_language)" title="C (programming language)">C</a>, <a href="C%2B%2B" title="C++">C++</a>, <a href="LLVM" title="LLVM">LLVM</a>,<a href="#cite_note-12">[12]</a> <a href="Scheme_(programming_language)" title="Scheme (programming language)">Scheme</a> (was used the parser; almost exclusively)</td></tr><tr><th scope="row" class="infobox-label"><a href="Computing_platform" title="Computing platform">Platform</a></th><td class="infobox-data">Tier 1: 64- and 32-bit <a href="Windows_10" title="Windows 10">Windows 10</a>+, <a href="Linux_distro" class="mw-redirect" title="Linux distro">Linux</a>, and 64-bit <a href="MacOS" title="MacOS">macOS</a>; <a href="IA-32" title="IA-32">IA-32</a>, <a href="X86-64" title="X86-64">x86-64</a>, <a href="Apple_silicon" title="Apple silicon">Apple silicon</a> (<a href="AArch64" title="AArch64">ARM64</a>) Macs; Nvidia GPUs/<a href="CUDA" title="CUDA">CUDA</a> 11.0+ (on Linux; tier 2 for Windows)<a href="#cite_note-13">[13]</a> Tier 2: 64-bit <a href="FreeBSD" title="FreeBSD">FreeBSD</a> 13.4+, Linux on <a href="Armv8" class="mw-redirect" title="Armv8">64-bit Arm</a>; Apple GPUs/Metal on macOS 13+, Intel GPUs/<a href="OneAPI_(compute_acceleration)" title="OneAPI (compute acceleration)">OneAPI</a> 6.2+ and Nvidia GPUs (on Windows) Tier 3: 64-bit <a href="RISC-V" title="RISC-V">RISC-V</a>, 64-bit <a href="Musl" title="Musl">musl</a> (e.g. <a href="Alpine_Linux" title="Alpine Linux">Alpine Linux</a>); and AMD GPUs/<a href="ROCm" title="ROCm">ROCm</a> 5.3+.</td></tr><tr><th scope="row" class="infobox-label"><a href="Operating_system" title="Operating system">OS</a></th><td class="infobox-data"><a href="Linux" title="Linux">Linux</a>, <a href="MacOS" title="MacOS">macOS</a>, <a href="Microsoft_Windows" title="Microsoft Windows">Windows</a> 10+ and <a href="FreeBSD" title="FreeBSD">FreeBSD</a></td></tr><tr><th scope="row" class="infobox-label"><a href="Software_license" title="Software license">License</a></th><td class="infobox-data"><a href="MIT_License" title="MIT License">MIT</a></td></tr><tr><th scope="row" class="infobox-label"><a href="Filename_extension" title="Filename extension">Filename extensions</a></th><td class="infobox-data">.jl</td></tr><tr><th scope="row" class="infobox-label">Website</th><td class="infobox-data"><a rel="nofollow" class="external text" href="https://JuliaLang.org">JuliaLang.org</a></td></tr><tr><th colspan="2" class="infobox-header" style="background-color: #EEEEEE;">Influenced by</th></tr><tr><td colspan="2" class="infobox-full-data"><style data-mw-deduplicate="TemplateStyles:r1129693374">

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<ul><li><a href="Dylan_(programming_language)" title="Dylan (programming language)">Dylan</a><a href="#cite_note-goldilocks-14">[14]</a></li>

<li><a href="Wolfram_Language" title="Wolfram Language">Mathematica</a><a href="#cite_note-17">[17]</a><a href="#cite_note-18">[18]</a></li>

<li><a href="MATLAB" title="MATLAB">MATLAB</a><a href="#cite_note-announcement-4">[4]</a></li>

<li><a href="Python_(programming_language)" title="Python (programming language)">Python</a><a href="#cite_note-Introduction-16">[16]</a></li>

<li><a href="Fortress_(programming_language)" title="Fortress (programming language)">Fortress</a></li></ul>

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Julia is a <a href="Dynamic_programming_language" title="Dynamic programming language">dynamic</a> <a href="General-purpose_programming_language" title="General-purpose programming language">general-purpose</a> <a href="Programming_language" title="Programming language">programming language</a>. As a <a href="High-level_programming_language" title="High-level programming language">high-level</a> language, distinctive aspects of Julia's design include a type system with <a href="Parametric_polymorphism" title="Parametric polymorphism">parametric polymorphism</a>, the use of <a href="Multiple_dispatch" title="Multiple dispatch">multiple dispatch</a> as a core <a href="Programming_paradigm" title="Programming paradigm">programming paradigm</a>, <a href="Just-in-time_compilation" title="Just-in-time compilation">just-in-time</a> (JIT) compilation and a parallel <a href="Tracing_garbage_collection" title="Tracing garbage collection">garbage collection</a> implementation. Notably Julia does not support <a href="Class_(computer_programming)" title="Class (computer programming)">classes</a> with <a href="Encapsulation_(computer_programming)" title="Encapsulation (computer programming)">encapsulated</a> methods but instead relies on the types of all of a function's arguments to determine which method will be called.

By default, Julia is run similarly to scripting languages, using its runtime, and allows for <a href="Read%E2%80%93eval%E2%80%93print_loop" title="Read–eval–print loop">interactions</a>,<a href="#cite_note-PackageCompiler.jl-19">[19]</a> but Julia programs/<a href="Source_code" title="Source code">source code</a> can also optionally be sent to users in one ready-to-install/run file, which can be made quickly, not needing anything preinstalled.<a href="#cite_note-AppBundler.jl-20">[20]</a>

Julia programs can reuse libraries from other languages (or itself be reused from other); Julia has a special no-boilerplate keyword allowing calling e.g. <a href="C_(programming_language)" title="C (programming language)">C</a>, <a href="Fortran" title="Fortran">Fortran</a> or <a href="Rust_(programming_language)" title="Rust (programming language)">Rust</a> libraries, and e.g. PythonCall.jl uses it indirectly for you, and Julia (libraries) can also be called from other languages, e.g. <a href="Python_(programming_language)" title="Python (programming language)">Python</a> and <a href="R_(programming_language)" title="R (programming language)">R</a>, and several Julia packages have been made easily available from those languages, in the form of Python and R <a href="Library_(computing)" title="Library (computing)">libraries</a> for corresponding Julia packages. Calling in either direction has been implemented for many languages, not just those and <a href="C%2B%2B" title="C++">C++</a>.

Julia is supported by programmer tools like IDEs (see below) and by notebooks like Pluto.jl, <a href="Project_Jupyter" title="Project Jupyter">Jupyter</a>, and since 2025 <a href="Google_Colab" title="Google Colab">Google Colab</a> officially supports Julia natively.

Julia is sometimes used in <a href="Embedded_system" title="Embedded system">embedded systems</a> (e.g. has been used in a satellite in space on a <a href="Raspberry_Pi" title="Raspberry Pi">Raspberry Pi</a> Compute Module 4; 64-bit Pis work best with Julia, and Julia is supported in <a href="Raspbian" class="mw-redirect" title="Raspbian">Raspbian</a>).<a href="#cite_note-21">[21]</a>

<div class="mw-heading mw-heading2"><h2 id="History">History</h2></div>

Work on Julia began in 2009, when <a href="Jeff_Bezanson_(programmer)" class="mw-redirect" title="Jeff Bezanson (programmer)">Jeff Bezanson</a>, <a href="Stefan_Karpinski" title="Stefan Karpinski">Stefan Karpinski</a>, <a href="Viral_B._Shah" title="Viral B. Shah">Viral B. Shah</a>, and <a href="Alan_Edelman" title="Alan Edelman">Alan Edelman</a> set out to create a free language that was both high-level and fast. On 14 February 2012, the team launched a website with a blog post explaining the language's mission.<a href="#cite_note-announcement-4">[4]</a> In an interview with <a href="InfoWorld" title="InfoWorld">InfoWorld</a> in April 2012, Karpinski said of the name "Julia": "There's no good reason, really. It just seemed like a pretty name."<a href="#cite_note-infoworld-22">[22]</a> Bezanson said he chose the name on the recommendation of a friend,<a href="#cite_note-23">[23]</a> then years later wrote:

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</style><blockquote class="templatequote">Maybe julia stands for "<a href="Jeff_Bezanson_(programmer)" class="mw-redirect" title="Jeff Bezanson (programmer)">Jeff</a>'s <a href="MLisp" title="MLisp">uncommon lisp</a> is automated"?<a href="#cite_note-24">[24]</a></blockquote>

Julia's <a href="Syntax_(programming_languages)" title="Syntax (programming languages)">syntax</a> is now considered stable, since version 1.0 in 2018, and Julia has a <a href="Backward_compatibility" title="Backward compatibility">backward compatibility</a> guarantee for 1.x and also a stability promise for the documented (stable) <a href="Application_programming_interface" class="mw-redirect" title="Application programming interface">API</a>, while in the years before in the early development prior to 0.7 the syntax (and semantics) was changed in new versions. All of the (registered package) <a href="Ecosystem" title="Ecosystem">ecosystem</a> uses the new and improved syntax, and in most cases relies on new APIs that have been added regularly, and in some cases minor additional syntax added in a forward compatible way e.g. in Julia 1.7.

In the 10 years since the 2012 launch of pre-1.0 Julia, the community has grown. The Julia package ecosystem has over 11.8 million lines of code (including docs and tests).<a href="#cite_note-25">[25]</a> The JuliaCon <a href="Academic_conference" title="Academic conference">academic conference</a> for Julia users and developers has been held annually since 2014 with JuliaCon2020<a href="#cite_note-26">[26]</a> welcoming over 28,900 unique viewers,<a href="#cite_note-27">[27]</a> and then JuliaCon2021 breaking all previous records (with more than 300 JuliaCon2021 presentations available for free on YouTube, up from 162 the year before), and 43,000 unique viewers during the conference.<a href="#cite_note-28">[28]</a>

Three of the Julia co-creators are the recipients of the 2019 <a href="J._H._Wilkinson_Prize_for_Numerical_Software" title="J. H. Wilkinson Prize for Numerical Software">James H. Wilkinson Prize for Numerical Software</a> (awarded every four years) "for the creation of Julia, an innovative environment for the creation of high-performance tools that enable the analysis and solution of computational science problems."<a href="#cite_note-29">[29]</a> Also, Alan Edelman, professor of <a href="Applied_mathematics" title="Applied mathematics">applied mathematics</a> at <a href="Massachusetts_Institute_of_Technology" title="Massachusetts Institute of Technology">MIT</a>, has been selected to receive the 2019 <a href="Institute_of_Electrical_and_Electronics_Engineers" title="Institute of Electrical and Electronics Engineers">IEEE Computer Society</a> <a href="Sidney_Fernbach_Award" title="Sidney Fernbach Award">Sidney Fernbach Award</a> "for outstanding breakthroughs in high-performance computing, linear algebra, and computational science and for contributions to the Julia programming language."<a href="#cite_note-30">[30]</a>

Both Julia 0.7<a href="#cite_note-31">[31]</a> and version 1.0 were released on 8 August 2018. Work on Julia 0.7 was a "huge undertaking" (e.g., because of an "entirely new optimizer"), and some changes were made to semantics, e.g. the <a href="Iteration" title="Iteration">iteration</a> interface was simplified.<a href="#cite_note-32">[32]</a>

Julia 1.6 was the largest release since 1.0, and it was the <a href="Long-term_support" title="Long-term support">long-term support</a> (LTS) version for the longest time, faster on many fronts, e.g. introduced parallel precompilation and faster loading of packages, in some cases "50x speedup in load times for large trees of binary artifacts".<a href="#cite_note-33">[33]</a> Since 1.7 Julia development is back to <a href="Release_early%2C_release_often" title="Release early, release often">time-based releases</a>.<a href="#cite_note-34">[34]</a> Julia 1.7 was released in November 2021 with many changes, e.g. a new faster <a href="Random_number_generation" title="Random number generation">random-number generator</a> and Julia 1.7.3 fixed e.g. at least one security issue.<a href="#cite_note-35">[35]</a> Julia 1.8 was released in 2022 and 1.8.5 in January 2023,<a href="#cite_note-36">[36]</a> with 1.8.x improvements for distributing Julia programs without source code, and compiler speedup, in some cases by 25%,<a href="#cite_note-37">[37]</a> and more controllable <a href="Inline_expansion" title="Inline expansion">inlining</a> (i.e. now also allowing applying <code>@inline</code> at the call site, not just on the function itself). Julia 1.9 was released on 7 May 2023. It has many improvements, such as the ability to precompile packages to native machine code (older Julia versions also have precompilation for packages, but only partial, never fully to native code, so those earlier versions had a "first use" penalty, slowing down while waiting to fully compile). Precompiled packages, since version 1.9, can be up to hundreds of times faster on first use (e.g. for CSV.jl and DataFrames.jl), and to improve precompilation of packages a new package PrecompileTools.jl has been introduced. Julia 1.10 was released on 25 December 2023 with many new features, e.g. parallel garbage collection, and improved package load times and a new parser, i.e. it rewritten in Julia, with better error messages and improved stacktrace rendering.<a href="#cite_note-38">[38]</a>

Julia 1.11 was released on 7 October 2024 (and 1.11.6 on 9 July 2025), and with it 1.10.5 became the next <a href="Long-term_support" title="Long-term support">long-term support</a> (LTS) version (i.e. those are the only two supported versions), since replaced by 1.10.10 released on 27 June, and 1.6 is no longer an LTS version. Julia 1.11 adds e.g. parallel garbage collection and the new <code>public</code> keyword to signal safe public API (Julia users are advised to use such API, not internals, of Julia or packages, and package authors advised to use the keyword, generally indirectly, e.g. prefixed with the <code>@compat</code> macro, from Compat.jl, to also support older Julia versions, at least the LTS version). Julia 1.11.1 has much improved startup (over 1.11.0 that had a regression), and over 1.10, and this can be important for some benchmarks.

It's possible to compile very small binary executables using <code>juliac</code> which is available in the upcoming Julia 1.12 (now in beta3), and other compilers exist usable for older Julia versions, that also allows compiling though not to small binaries with the main one.

<div class="mw-heading mw-heading3"><h3 id="JuliaCon">JuliaCon</h3></div>

Since 2014,<a href="#cite_note-39">[39]</a> the Julia Community has hosted an annual Julia Conference focused on developers and users. The first JuliaCon took place in Chicago and kickstarted the annual occurrence of the conference. Since 2014, the conference has taken place across a number of locations including MIT<a href="#cite_note-40">[40]</a> and the University of Maryland, Baltimore.<a href="#cite_note-41">[41]</a> The event audience has grown from a few dozen people to over 28,900 unique attendees<a href="#cite_note-42">[42]</a> during JuliaCon 2020, which took place virtually. JuliaCon 2021 also took place virtually<a href="#cite_note-43">[43]</a> with keynote addresses from professors <a href="William_Kahan" title="William Kahan">William Kahan</a>, the primary architect of the <a href="IEEE_754-1985" title="IEEE 754-1985">IEEE 754</a> floating-point standard (which virtually all CPUs and languages, including Julia, use),<a href="#cite_note-44">[44]</a> Jan Vitek,<a href="#cite_note-45">[45]</a> Xiaoye <a href="Sherry_Li" title="Sherry Li">Sherry Li</a>, and Soumith Chintala, a co-creator of <a href="PyTorch" title="PyTorch">PyTorch</a>.<a href="#cite_note-46">[46]</a> JuliaCon grew to 43,000 unique attendees and more than 300 presentations (still freely accessible, plus for older years). JuliaCon 2022 will also be virtual held between July 27 and July 29, 2022, for the first time in several languages, not just in English.

<div class="mw-heading mw-heading3"><h3 id="Sponsors">Sponsors</h3></div>

The Julia language became a NumFOCUS fiscally sponsored project in 2014 in an effort to ensure the project's long-term sustainability.<a href="#cite_note-47">[47]</a> Jeremy Kepner at <a href="MIT_Lincoln_Laboratory" title="MIT Lincoln Laboratory">MIT Lincoln Laboratory</a> was the founding sponsor of the Julia project in its early days. In addition, funds from the <a href="Gordon_and_Betty_Moore_Foundation" title="Gordon and Betty Moore Foundation">Gordon and Betty Moore Foundation</a>, the <a href="Alfred_P._Sloan_Foundation" title="Alfred P. Sloan Foundation">Alfred P. Sloan Foundation</a>, <a href="Intel" title="Intel">Intel</a>, and agencies such as <a href="National_Science_Foundation" title="National Science Foundation">NSF</a>, <a href="DARPA" title="DARPA">DARPA</a>, <a href="National_Institutes_of_Health" title="National Institutes of Health">NIH</a>, <a href="NASA" title="NASA">NASA</a>, and <a href="Federal_Aviation_Administration" title="Federal Aviation Administration">FAA</a> have been essential to the development of Julia.<a href="#cite_note-48">[48]</a> <a href="Mozilla" title="Mozilla">Mozilla</a>, the maker of Firefox web browser, with its research grants for H1 2019, sponsored "a member of the official Julia team" for the project "Bringing Julia to the Browser",<a href="#cite_note-49">[49]</a> meaning to Firefox and other web browsers.<a href="#cite_note-50">[50]</a><a href="#cite_note-51">[51]</a><a href="#cite_note-52">[52]</a><a href="#cite_note-53">[53]</a> The Julia language is also supported by individual donors on GitHub.<a href="#cite_note-54">[54]</a>

<div class="mw-heading mw-heading3"><h3 id="The_Julia_company">The Julia company</h3></div>

JuliaHub, Inc. was founded in 2015 as Julia Computing, Inc. by <a href="Viral_B._Shah" title="Viral B. Shah">Viral B. Shah</a>, Deepak Vinchhi, <a href="Alan_Edelman" title="Alan Edelman">Alan Edelman</a>, <a href="Jeff_Bezanson" title="Jeff Bezanson">Jeff Bezanson</a>, <a href="Stefan_Karpinski" title="Stefan Karpinski">Stefan Karpinski</a> and <a href="Keno_Fischer" title="Keno Fischer">Keno Fischer</a>.<a href="#cite_note-55">[55]</a><a href="#cite_note-56">[56]</a>

In June 2017, Julia Computing raised US$4.6 million in seed funding from <a href="General_Catalyst" title="General Catalyst">General Catalyst</a> and Founder Collective,<a href="#cite_note-57">[57]</a> the same month was "granted $910,000 by the <a href="Alfred_P._Sloan_Foundation" title="Alfred P. Sloan Foundation">Alfred P. Sloan Foundation</a> to support <a href="Open-source_software" title="Open-source software">open-source</a> Julia development, including $160,000 to promote diversity in the Julia community",<a href="#cite_note-58">[58]</a> and in December 2019 the company got $1.1 million funding from the US government to "develop a neural component <a href="Machine_learning" title="Machine learning">machine learning</a> tool to reduce the total energy consumption of heating, ventilation, and air conditioning (HVAC) systems in buildings".<a href="#cite_note-59">[59]</a> In July 2021, Julia Computing announced they raised a $24 million <a href="Series_A_round" title="Series A round">Series A round</a> led by Dorilton Ventures,<a href="#cite_note-60">[60]</a> which also owns <a href="Formula_1" class="mw-redirect" title="Formula 1">Formula 1</a> team <a href="Williams_Grand_Prix_Engineering" class="mw-redirect" title="Williams Grand Prix Engineering">Williams Racing</a>, that partnered with Julia Computing. Williams' Commercial Director said: "Investing in companies building best-in-class cloud technology is a strategic focus for Dorilton and Julia's versatile platform, with revolutionary capabilities in simulation and modelling, is hugely relevant to our business. We look forward to embedding Julia Computing in the world's most technologically advanced sport".<a href="#cite_note-61">[61]</a> In June 2023, JuliaHub received (again, now under its new name) a $13 million strategic new investment led by AE Industrial Partners HorizonX ("AEI HorizonX"). AEI HorizonX is a venture capital investment platform formed in partnership with <a href="Boeing" title="Boeing">The Boeing Company</a>, which uses Julia.<a href="#cite_note-62">[62]</a> Tim Holy's work (at <a href="Washington_University_in_St._Louis" title="Washington University in St. Louis">Washington University in St. Louis</a>'s Holy Lab) on Julia 1.9 (improving responsiveness) was funded by the <a href="Chan_Zuckerberg_Initiative" title="Chan Zuckerberg Initiative">Chan Zuckerberg Initiative</a>.

<div class="mw-heading mw-heading2"><h2 id="Language_features">Language features</h2></div>

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<div class="side-box-text plainlist">Wikibooks has a book on the topic of: <a href="https://en.wikibooks.org/wiki/Introducing_Julia" class="extiw external" title="wikibooks:Introducing Julia">Introducing Julia</a></div></div>

</div>

Julia is a <a href="General-purpose_programming_language" title="General-purpose programming language">general-purpose programming language</a>,<a href="#cite_note-63">[63]</a> while also originally designed for numerical/technical computing. It is also useful for low-level <a href="System_programming" class="mw-redirect" title="System programming">systems programming</a>,<a href="#cite_note-LowLevelSystemsProgrammingInJulia-64">[64]</a> as a <a href="Specification_language" title="Specification language">specification language</a>,<a href="#cite_note-spec-65">[65]</a> high-level synthesis (HLS) tool (for hardware, e.g. <a href="Field-programmable_gate_array" title="Field-programmable gate array">FPGAs</a>),<a href="#cite_note-HLS/FPGA-66">[66]</a> and for web programming<a href="#cite_note-67">[67]</a> at both server<a href="#cite_note-68">[68]</a><a href="#cite_note-69">[69]</a> and client<a href="#cite_note-JSExpr-70">[70]</a><a href="#cite_note-WebAssembly-71">[71]</a> side.

The main features of the language are:

<ul><li>Multiple dispatch: providing ability to define function behavior across combinations of argument types</li>

<li><a href="Dynamic_type" class="mw-redirect" title="Dynamic type">Dynamic type</a> system: types for documentation, optimization, and dispatch</li>

<li>Performance approaching that of <a href="Type_system" title="Type system">statically-typed</a> languages like C</li>

<li>A built-in <a href="Package_manager" title="Package manager">package manager</a></li>

<li><a href="Lisp_(programming_language)" title="Lisp (programming language)">Lisp</a>-like macros and other <a href="Metaprogramming" title="Metaprogramming">metaprogramming</a> facilities</li>

<li>Designed for <a href="Parallel_computing" title="Parallel computing">parallel</a> and <a href="Distributed_computing" title="Distributed computing">distributed computing</a></li>

<li><a href="Coroutine" title="Coroutine">Coroutines</a>: lightweight <a href="Green_thread" title="Green thread">green threading</a></li>

<li>Automatic generation of code for different argument types</li>

<li>Extensible conversions and promotions for numeric and other types</li></ul>

Multiple dispatch (also termed <a href="Multimethod" class="mw-redirect" title="Multimethod">multimethods</a> in Lisp) is a <a href="Generalization" title="Generalization">generalization</a> of <a href="Single_dispatch" class="mw-redirect" title="Single dispatch">single dispatch</a> – the <a href="Polymorphism_(computer_science)" title="Polymorphism (computer science)">polymorphic mechanism</a> used in common <a href="Object-oriented_programming" title="Object-oriented programming">object-oriented programming</a> (OOP) languages, such as <a href="Python_(programming_language)" title="Python (programming language)">Python</a>, <a href="C%2B%2B" title="C++">C++</a>, <a href="Java_(programming_language)" title="Java (programming language)">Java</a>, <a href="JavaScript" title="JavaScript">JavaScript</a>, and <a href="Smalltalk" title="Smalltalk">Smalltalk</a> – that use <a href="Inheritance_(object-oriented_programming)" title="Inheritance (object-oriented programming)">inheritance</a>.

In Julia, all concrete types are <a href="Subtyping" title="Subtyping">subtypes</a> of abstract types, directly or indirectly subtypes of the <code>Any</code> type, which is the top of the type hierarchy. Concrete types cannot themselves be subtyped the way they can in other languages; composition is used instead (see also <a href="Inheritance_(object-oriented_programming)#Inheritance_vs_subtyping" title="Inheritance (object-oriented programming)">inheritance vs subtyping</a>).

By default, the Julia runtime must be pre-installed as user-provided source code is run. Alternatively, Julia (GUI) apps can be quickly bundled up into a single file with AppBundler.jl<a href="#cite_note-AppBundler.jl-20">[20]</a> for "building Julia GUI applications in modern desktop application installer formats. It uses Snap for Linux, <a href=".msix" class="mw-redirect" title=".msix">MSIX</a> for Windows, and DMG for MacOS as targets. It bundles full Julia within the app".<a href="#cite_note-72">[72]</a> PackageCompiler.jl can build standalone <a href="Executable" title="Executable">executables</a> that need no Julia source code to run.<a href="#cite_note-PackageCompiler.jl-19">[19]</a>

In Julia, everything is an object, much like object-oriented languages; however, unlike most object-oriented languages, all functions use <a href="Multiple_dispatch" title="Multiple dispatch">multiple dispatch</a> to select methods, rather than single dispatch.

Most programming paradigms can be implemented using Julia's <a href="Homoiconicity" title="Homoiconicity">homoiconic</a> macros and packages. Julia's <a href="Macro_(computer_science)#Syntactic_macros" title="Macro (computer science)">syntactic macros</a> (used for <a href="Metaprogramming" title="Metaprogramming">metaprogramming</a>), like Lisp macros, are more powerful than <a href="Macro_(computer_science)#Text-substitution_macros" title="Macro (computer science)">text-substitution macros</a> used in the <a href="Preprocessor" title="Preprocessor">preprocessor</a> of some other languages such as C, because they work at the level of <a href="Abstract_syntax_tree" title="Abstract syntax tree">abstract syntax trees</a> (ASTs). Julia's macro system is <a href="Hygienic_macro" title="Hygienic macro">hygienic</a>, but also supports deliberate capture when desired (like for <a href="Anaphoric_macro" title="Anaphoric macro">anaphoric macros</a>) using the <code>esc</code> construct.

Julia draws inspiration from various dialects of Lisp, including <a href="Scheme_(programming_language)" title="Scheme (programming language)">Scheme</a> and <a href="Common_Lisp" title="Common Lisp">Common Lisp</a>, and it shares many features with <a href="Dylan_(programming_language)" title="Dylan (programming language)">Dylan</a>, also a multiple-dispatch-oriented dynamic language (which features an <a href="Infix_notation" title="Infix notation">infix</a> syntax rather than a Lisp-like prefix syntax, while in Julia "everything"<a href="#cite_note-Learn_Julia_in_Y-73">[73]</a> is an <a href="Expression_(computer_science)" title="Expression (computer science)">expression</a>), and with <a href="Fortress_(programming_language)" title="Fortress (programming language)">Fortress</a>, another numerical programming language (which features multiple dispatch and a sophisticated parametric type system). While <a href="Common_Lisp_Object_System" title="Common Lisp Object System">Common Lisp Object System</a> (CLOS) adds multiple dispatch to Common Lisp, not all functions are generic functions.

In Julia, Dylan, and Fortress, extensibility is the default, and the system's built-in functions are all generic and extensible. In Dylan, multiple dispatch is as fundamental as it is in Julia: all user-defined functions and even basic built-in operations like <code>+</code> are generic. Dylan's type system, however, does not fully support parametric types, which are more typical of the <a href="Generational_list_of_programming_languages#ML_based" title="Generational list of programming languages">ML lineage of languages</a>. By default, CLOS does not allow for dispatch on Common Lisp's parametric types; such extended dispatch semantics can only be added as an extension through the <a href="Common_Lisp_Object_System#Metaobject_Protocol" title="Common Lisp Object System">CLOS Metaobject Protocol</a>. By convergent design, Fortress also features multiple dispatch on parametric types; unlike Julia, however, Fortress is statically rather than dynamically typed, with separate compiling and executing phases. The language features are summarized in the following table:

<th><a href="Programming_language" title="Programming language">Language</a></th>

<th><a href="Type_system" title="Type system">Type system</a></th>

<th><a href="Generic_function" title="Generic function">Generic functions</a></th>

<th><a href="Parametric_polymorphism" title="Parametric polymorphism">Parametric types</a>

</th></tr>

<tr>

<td>Julia</td>

<td>Dynamic</td>

<td>Default</td>

<td style="background:#9EFF9E;color:black;vertical-align:middle;text-align:center;" class="table-yes">Yes

</td></tr>

<tr>

<td><a href="Common_Lisp" title="Common Lisp">Common Lisp</a></td>

<td>Dynamic</td>

<td style="background:#bfd; color:black; vertical-align:middle; text-align:center;" class="table-yes2">Yes (but no dispatch)

</td></tr>

<tr>

<td><a href="Dylan_(programming_language)" title="Dylan (programming language)">Dylan</a></td>

<td>Dynamic</td>

<td>Default</td>

<td style="background:#FFB; color:black;vertical-align:middle;text-align:center;" class="table-partial">Partial (no dispatch)

</td></tr>

<tr>

<td><a href="Fortress_(programming_language)" title="Fortress (programming language)">Fortress</a></td>

<td>Static</td>

<td>Default</td>

<td style="background:#9EFF9E;color:black;vertical-align:middle;text-align:center;" class="table-yes">Yes

</td></tr></tbody></table>

An example of the extensibility of Julia, the Unitful.jl package adds support for physical <a href="Unit_of_measurement" title="Unit of measurement">units of measurement</a> to the language.

<div class="mw-heading mw-heading3"><h3 id="Interoperability">Interoperability</h3></div>

Julia has built-in support for calling <a href="C_(programming_language)" title="C (programming language)">C</a> or <a href="Fortran" title="Fortran">Fortran</a> language libraries using the <code class="mw-highlight mw-highlight-lang-julia mw-content-ltr" dir="ltr">@ccall</code> macro. Additional libraries allow users to call to or from other languages such as <a href="Python_(programming_language)" title="Python (programming language)">Python</a>,<a href="#cite_note-74">[74]</a> <a href="C%2B%2B" title="C++">C++</a>,<a href="#cite_note-75">[75]</a><a href="#cite_note-76">[76]</a> <a href="Rust_(programming_language)" title="Rust (programming language)">Rust</a>, <a href="R_(programming_language)" title="R (programming language)">R</a>,<a href="#cite_note-77">[77]</a> <a href="Java_(programming_language)" title="Java (programming language)">Java</a><a href="#cite_note-78">[78]</a> and to use with <a href="SQL" title="SQL">SQL</a>.<a href="#cite_note-79">[79]</a><a href="#cite_note-80">[80]</a><a href="#cite_note-81">[81]</a><a href="#cite_note-82">[82]</a>

<div class="mw-heading mw-heading3"><h3 id="Separately-compiled_executables_option">Separately-compiled executables option</h3></div>

Julia can be compiled to binary <a href="Executable" title="Executable">executables</a> with PackageCompiler.jl.<a href="#cite_note-PackageCompiler.jl-19">[19]</a> Smaller executables can also be written using a static subset of the language provided by StaticCompiler.jl that does not support <a href="Runtime_dispatch" class="mw-redirect" title="Runtime dispatch">runtime dispatch</a> (nor garbage collection, since excludes the runtime that provides it).<a href="#cite_note-83">[83]</a>

<div class="mw-heading mw-heading2"><h2 id="Interaction">Interaction</h2></div>

The Julia official distribution includes an interactive command-line <a href="Read%E2%80%93eval%E2%80%93print_loop" title="Read–eval–print loop">read–eval–print loop</a> (REPL),<a href="#cite_note-84">[84]</a> with a searchable history, <a href="Command-line_completion" title="Command-line completion">tab completion</a>, and dedicated help and <a href="Shell_(computing)" title="Shell (computing)">shell</a> modes,<a href="#cite_note-85">[85]</a> which can be used to experiment and test code quickly.<a href="#cite_note-86">[86]</a> The following fragment represents a sample session example where strings are concatenated automatically by <code>println</code>:<a href="#cite_note-87">[87]</a>

<div class="mw-highlight mw-highlight-lang-jlcon mw-content-ltr" dir="ltr"><pre>julia> p(x) = 2x^2 + 1; f(x, y) = 1 + 2p(x)y

julia> println("Hello world!", " I'm on cloud ", f(0, 4), " as Julia supports recognizable syntax!")

Hello world! I'm on cloud 9 as Julia supports recognizable syntax!

</pre></div>

The REPL gives user access to the system shell and to help mode, by pressing <code>;</code> or <code>?</code> after the prompt (preceding each command), respectively. It also keeps the history of commands, including between sessions.<a href="#cite_note-88">[88]</a> Code can be tested inside Julia's interactive session or saved into a file with a <code>.jl</code> extension and run from the command line by typing:<a href="#cite_note-Learn_Julia_in_Y-73">[73]</a>

<div class="mw-highlight mw-highlight-lang-console mw-content-ltr" dir="ltr"><pre>$ julia <filename>

</pre></div>

Julia uses <a href="UTF-8" title="UTF-8">UTF-8</a> and <a href="LaTeX" title="LaTeX">LaTeX</a> codes, allowing it to support common math symbols for many operators, such as ∈ for the <code>in</code> operator, typable with <code>\in</code> then pressing <style data-mw-deduplicate="TemplateStyles:r1249182868">

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</style><kbd class="keyboard-key nowrap">Tab ↹</kbd> (i.e. uses <a href="LaTeX" title="LaTeX">LaTeX</a> codes, or also possible by simply copy-pasting, e.g. √ and ∛ possible for <a href="Square_root" title="Square root">sqrt</a> and <a href="Cube_root" title="Cube root">cbrt</a> functions). Julia has support for <a href="Unicode" title="Unicode">Unicode</a> 15.1 (Julia 1.12.0-rc1 supports latest 16.0 release<a href="#cite_note-89">[89]</a>) for the languages of the world, even for source code, e.g. variable names (while it's recommended to use English for public code, and e.g. package names).

Julia is supported by <a href="Project_Jupyter" title="Project Jupyter">Jupyter</a>, an online interactive "notebooks" environment,<a href="#cite_note-90">[90]</a> and <a rel="nofollow" class="external text" href="https://github.com/fonsp/Pluto.jl">Pluto.jl</a>, a "reactive notebook" (where notebooks are saved as pure Julia files), a possible replacement for the former kind.<a href="#cite_note-91">[91]</a> In addition Posit's (formerly <a href="RStudio" title="RStudio">RStudio</a> Inc's) Quarto publishing system supports Julia, Python, R and Observable <a href="JavaScript" title="JavaScript">JavaScript</a> (those languages have official support by the company, and can even be weaved together in the same notebook document, more languages are unofficially supported).<a href="#cite_note-92">[92]</a><a href="#cite_note-93">[93]</a>

The REPL can be extended with additional modes, and has been with packages, e.g. with an <a href="SQL" title="SQL">SQL</a> mode,<a href="#cite_note-94">[94]</a> for database access, and RCall.jl adds an R mode, to work with the <a href="R_(programming_language)" title="R (programming language)">R language</a>.<a href="#cite_note-95">[95]</a>

Julia's <a href="Visual_Studio_Code" title="Visual Studio Code">Visual Studio Code</a> extension provides a fully featured <a href="Integrated_development_environment" title="Integrated development environment">integrated development environment</a> with "built-in dynamic autocompletion, inline results, plot pane, integrated REPL, variable view, code navigation, and many other advanced language features"<a href="#cite_note-96">[96]</a> e.g. debugging is possible, <a href="Lint_(software)" title="Lint (software)">linting</a>, and <a href="Profiling_(computer_programming)" title="Profiling (computer programming)">profiling</a>.<a href="#cite_note-97">[97]</a><a href="#cite_note-98">[98]</a><a href="#cite_note-99">[99]</a><a href="#cite_note-100">[100]</a>

<div class="mw-heading mw-heading3"><h3 id="Use_with_other_languages">Use with other languages</h3></div>

Julia is in practice <a href="Interoperability" title="Interoperability">interoperable</a> with other languages, in fact the majority of the top 20 languages in popular use. Julia can be used to call shared library functions individually, such as those written in C or Fortran, and packages are available to allow calling other languages (which do not provide C-exported functions directly), e.g. Python (with PythonCall.jl), R,<a href="#cite_note-101">[101]</a> MATLAB, C# (and other .NET languages with DotNET.jl, from them with JdotNET), JavaScript, Java (and other JVM languages, such as <a href="Scala_(programming_language)" title="Scala (programming language)">Scala</a> with JavaCall.jl). And packages for other languages allow to call to Julia, e.g. from Python, R (to Julia 1.10.x currently possible<a href="#cite_note-102">[102]</a>), <a href="Rust_(programming_language)" title="Rust (programming language)">Rust</a>, Ruby, or C#. Such as with juliacall (part of PythonCall.jl) to call from Python and a different JuliaCall package for calling, Julia up to 1.10.x, from R. Julia has also been used for hardware, i.e. to compile to <a href="VHDL" title="VHDL">VHDL</a>, as a <a href="High-level_synthesis" title="High-level synthesis">high-level synthesis</a> tool, for example <a href="Field-programmable_gate_array" title="Field-programmable gate array">FPGAs</a>.<a href="#cite_note-HLS/FPGA-66">[66]</a>

Julia has packages supporting markup languages such as <a href="HTML" title="HTML">HTML</a> (and also for <a href="HTTP" title="HTTP">HTTP</a>), <a href="XML" title="XML">XML</a>, <a href="JSON" title="JSON">JSON</a> and <a href="BSON" title="BSON">BSON</a>, and for <a href="Database" title="Database">databases</a> (such as PostgreSQL,<a href="#cite_note-103">[103]</a> Mongo,<a href="#cite_note-FunSQL-104">[104]</a> Oracle, including for <a href="TimesTen" title="TimesTen">TimesTen</a>,<a href="#cite_note-105">[105]</a> MySQL, SQLite, Microsoft SQL Server,<a href="#cite_note-FunSQL-104">[104]</a> Amazon Redshift, Vertica, ODBC) and web use in general.<a href="#cite_note-106">[106]</a><a href="#cite_note-107">[107]</a>

<div class="mw-heading mw-heading2"><h2 id="Package_system">Package system</h2></div>

Julia has a built-in <a href="Package_manager" title="Package manager">package manager</a> and includes a default registry system.<a href="#cite_note-108">[108]</a> Packages are most often distributed as source code hosted on <a href="GitHub" title="GitHub">GitHub</a>, though alternatives can also be used just as well. Packages can also be installed as binaries, using artifacts.<a href="#cite_note-109">[109]</a> Julia's package manager is used to query and compile packages, as well as managing environments. Federated package registries are supported, allowing registries other than the official to be added locally.<a href="#cite_note-110">[110]</a>

<div class="mw-heading mw-heading2"><h2 id="Implementation">Implementation</h2></div>

Julia's core is implemented in Julia and <a href="C_(programming_language)" title="C (programming language)">C</a>, together with <a href="C%2B%2B" title="C++">C++</a> for the <a href="LLVM" title="LLVM">LLVM</a> dependency. The code parsing, code-lowering, and bootstrapping were implemented in FemtoLisp, a <a href="Scheme_(programming_language)" title="Scheme (programming language)">Scheme</a> dialect, up to version 1.10.<a href="#cite_note-JeffBezanson_2019-111">[111]</a> Since that version the new pure-Julia stdlib package JuliaSyntax.jl is used for the parsing (while the old one can still be chosen)<a href="#cite_note-112">[112]</a> which improves speed and "greatly improves parser error messages in various cases".<a href="#cite_note-113">[113]</a> The LLVM compiler infrastructure project is used as the <a href="Compiler#Back_end" title="Compiler">back end</a> for generating optimized <a href="Machine_code" title="Machine code">machine code</a> for all commonly used platforms. With some exceptions, the <a href="Standard_library" title="Standard library">standard library</a> is implemented in Julia.

<div class="mw-heading mw-heading3"><h3 id="Current_and_future_platforms">Current and future platforms</h3></div>

Julia has tier 1 <a href="MacOS" title="MacOS">macOS</a> support, for 64-bit <a href="Apple_Silicon" class="mw-redirect" title="Apple Silicon">Apple Silicon</a> Macs, natively (previously such <a href="Apple_M1" title="Apple M1">Apple M1</a>-based Macs were only supported by running in <a href="Rosetta_2" class="mw-redirect" title="Rosetta 2">Rosetta 2</a> emulation<a href="#cite_note-Apple_Silicon-114">[114]</a><a href="#cite_note-115">[115]</a>), and also fully supports Intel-based Macs. <a href="Windows_10" title="Windows 10">Windows on ARM</a> has no official support yet. OpenBSD has received "initial support" and is under active development.

Julia has four support tiers.<a href="#cite_note-116">[116]</a> All <a href="IA-32" title="IA-32">IA-32</a> processors completely implementing the <a href="P6_(microarchitecture)" title="P6 (microarchitecture)">i686</a> subarchitecture are supported and all 64-bit <a href="X86-64" title="X86-64">x86-64</a> (aka <a href="Amd64" class="mw-redirect" title="Amd64">amd64</a>), i.e. all less than about a decade old are supported. 64-bit <a href="Armv8" class="mw-redirect" title="Armv8">Armv8</a> (and later; i.e. <a href="AArch64" title="AArch64">AArch64</a>) processors are supported on first tier (for macOS); otherwise second tier on Linux, and ARMv7 (AArch32) on third tier.<a href="#cite_note-117">[117]</a> Hundreds of packages are <a href="General-purpose_computing_on_graphics_processing_units" title="General-purpose computing on graphics processing units">GPU-accelerated</a>:<a href="#cite_note-118">[118]</a> Nvidia GPUs have support with <a href="CUDA" title="CUDA">CUDA</a>.jl (tier 1 on 64-bit Linux and tier 2 on 64-bit Windows, the package implementing <a href="Parallel_Thread_Execution" title="Parallel Thread Execution">PTX</a>, for compute capability 3.5 (Kepler) or higher; both require CUDA 11+, older package versions work down to CUDA 9). There are also additionally packages supporting other accelerators, such as Google's <a href="Tensor_processing_unit" class="mw-redirect" title="Tensor processing unit">TPUs</a>,<a href="#cite_note-119">[119]</a> and some Intel (integrated) GPUs, through <a href="OneAPI_(compute_acceleration)" title="OneAPI (compute acceleration)">oneAPI.jl</a>,<a href="#cite_note-120">[120]</a> and AMD's GPUs have support with e.g. <a href="OpenCL" title="OpenCL">OpenCL</a>; and experimental support for the AMD <a href="ROCm" title="ROCm">ROCm</a> stack.<a href="#cite_note-121">[121]</a>

for several ARM platforms, from small Raspberry Pis to the world's fastest (at one point, until recently) supercomputer <a href="Fugaku_(supercomputer)" title="Fugaku (supercomputer)">Fugaku</a>'s ARM-based <a href="Fujitsu_A64FX" title="Fujitsu A64FX">A64FX</a>.<a href="#cite_note-122">[122]</a> <a href="Power_Architecture" class="mw-redirect" title="Power Architecture">PowerPC</a> <a href="Little_endian" class="mw-redirect" title="Little endian">LE</a> (64-bit) has tier 3 support, meaning it "may or may not build", and its tier will lower to 4 for 1.12, i.e. then no longer builds/works.<a href="#cite_note-123">[123]</a>

Julia has official (tier 2) support for 64-bit ARMv8 meaning e.g. newer 64-bit (ARMv8-A) <a href="Raspberry_Pi" title="Raspberry Pi">Raspberry Pi</a> computers work with Julia (e.g. the Pi Compute Module 4 has been used in space running Julia code).<a href="#cite_note-space_GPS-124">[124]</a> For many Pis, especially older 32-bit ones, it helps to cross-compile the user's Julia code for them. The older 32-bit ARMv7 Pis worked in older Julia versions (still do, but for latest Julia version(s), note downgraded from tier 3 to its current tier 4: "Julia built at some point in the past, but is known not to build currently."). The original <a href="Raspberry_Pi" title="Raspberry Pi">Raspberry Pi</a> 1 has no official support (since it uses <a href="ARMv6" class="mw-redirect" title="ARMv6">ARMv6</a> which has newer had a support tier; though some cut-down Julia has been known to run on that Pi).<a href="#cite_note-125">[125]</a><a href="#cite_note-126">[126]</a>

Pico versions of the Pi are known to no work (since using the M-profile Arm, not running under Linux; not yet supported). Julia is now supported in <a href="Raspbian" class="mw-redirect" title="Raspbian">Raspbian</a><a href="#cite_note-127">[127]</a> while support is better for newer Pis, e.g., those with Armv7 or newer; the Julia support is promoted by the <a href="Raspberry_Pi_Foundation" title="Raspberry Pi Foundation">Raspberry Pi Foundation</a>.<a href="#cite_note-128">[128]</a>

On some platforms, Julia may need to be compiled from source code (e.g., the original <a href="Raspberry_Pi" title="Raspberry Pi">Raspberry Pi</a>), with specific build options, which has been done and unofficial pre-built binaries (and build instructions) are available.<a href="#cite_note-129">[129]</a><a href="#cite_note-130">[130]</a>

Julia has also been built for 64-bit <a href="RISC-V" title="RISC-V">RISC-V</a> (has tier 3 support),<a href="#cite_note-131">[131]</a><a href="#cite_note-132">[132]</a> i.e. has some supporting code in core Julia.

While Julia requires an <a href="Operating_system" title="Operating system">operating system</a> by default, and has no official support to run without, or on <a href="Embedded_system" title="Embedded system">embedded system</a> platforms such as <a href="Arduino" title="Arduino">Arduino</a>, Julia code has still been run on it, with some limitations, i.e. on a baremetal 16 <a href="Hertz#Computers" title="Hertz">MHz</a> <a href="8-bit_computing" title="8-bit computing">8-bit</a> (<a href="ATmega328P" class="mw-redirect" title="ATmega328P">ATmega328P</a>) <a href="AVR_microcontrollers" title="AVR microcontrollers">AVR-microcontroller</a> Arduino with 2 KB RAM (plus 32 KB of flash memory).<a href="#cite_note-133">[133]</a><a href="#cite_note-134">[134]</a>

<div class="mw-heading mw-heading2"><h2 id="Adoption">Adoption</h2></div>

Julia has been adopted at many universities including <a href="MIT" class="mw-redirect" title="MIT">MIT</a>, <a href="Stanford_University" title="Stanford University">Stanford</a>, <a href="UC_Berkeley" class="mw-redirect" title="UC Berkeley">UC Berkeley</a>, <a href="Ferdowsi_University_of_Mashhad" title="Ferdowsi University of Mashhad">Ferdowsi University of Mashhad</a> and the <a href="University_of_Cape_Town" title="University of Cape Town">University of Cape Town</a>. Large private firms across many sectors have adopted the language including <a href="Amazon_(company)" title="Amazon (company)">Amazon</a>, <a href="IBM" title="IBM">IBM</a>, <a href="JP_Morgan" class="mw-redirect" title="JP Morgan">JP Morgan</a> AI Research,<a href="#cite_note-135">[135]</a> and <a href="ASML_Holding" title="ASML Holding">ASML</a>. Julia has also been used by government agencies including <a href="NASA" title="NASA">NASA</a> and the <a href="Federal_Aviation_Administration" title="Federal Aviation Administration">FAA</a>, as well as every US national energy laboratory.<a href="#cite_note-Fastest-136">[136]</a><a href="#cite_note-137">[137]</a>

<div class="mw-heading mw-heading3"><h3 id="Scientific_computing_and_engineering">Scientific computing and engineering</h3></div>

<ul><li><a href="Amazon_(company)" title="Amazon (company)">Amazon</a>, for <a href="Quantum_computing" title="Quantum computing">quantum computing</a><a href="#cite_note-138">[138]</a> and <a href="Machine_learning" title="Machine learning">machine learning</a> through <a href="Amazon_SageMaker" title="Amazon SageMaker">Amazon SageMaker</a><a href="#cite_note-139">[139]</a></li>

<li><a href="ASML_Holding" title="ASML Holding">ASML</a>, for <a href="Hard_real-time" class="mw-redirect" title="Hard real-time">hard real-time</a> programming with their machines<a href="#cite_note-140">[140]</a></li>

<li>The Climate Modeling Alliance<a href="#cite_note-141">[141]</a> for climate change modeling<a href="#cite_note-Julia_Nvidia-142">[142]</a></li>

<li><a href="CERN" title="CERN">CERN</a>, to analyze data from the <a href="Large_Hadron_Collider" title="Large Hadron Collider">Large Hadron Collider</a> (<a href="LHCb_experiment" title="LHCb experiment">LHCb experiment</a>)<a href="#cite_note-143">[143]</a><a href="#cite_note-144">[144]</a><a href="#cite_note-145">[145]</a><a href="#cite_note-146">[146]</a><a href="#cite_note-147">[147]</a><a href="#cite_note-148">[148]</a></li>

<li>NASA and the <a href="Jet_Propulsion_Laboratory" title="Jet Propulsion Laboratory">Jet Propulsion Laboratory</a> use Julia to model spacecraft separation dynamics,<a href="#cite_note-149">[149]</a><a href="#cite_note-150">[150]</a><a href="#cite_note-151">[151]</a> analyze <a href="TRAPPIST" title="TRAPPIST">TRAPPIST</a> <a href="Exoplanet" title="Exoplanet">exoplanet</a> datasets,<a href="#cite_note-152">[152]</a><a href="#cite_note-153">[153]</a> and analyze <a href="Cosmic_microwave_background" title="Cosmic microwave background">cosmic microwave background</a> data from the <a href="Big_Bang" title="Big Bang">Big Bang</a><a href="#cite_note-154">[154]</a></li>

<li>The Brazilian <a href="National_Institute_for_Space_Research" title="National Institute for Space Research">INPE</a>, for space missions and <a href="Satellite" title="Satellite">satellite</a> simulations<a href="#cite_note-155">[155]</a></li>

<li>Julia has also flown in space, on a small satellite,<a href="#cite_note-space_GPS-124">[124]</a> used for a GPS module. And Julia has also been used to design <a href="Satellite_constellation" title="Satellite constellation"> satellite constellations</a>.<a href="#cite_note-156">[156]</a></li>

<li><a href="Embedded_system" title="Embedded system">Embedded</a> hardware to plan and execute flight of autonomous U.S. <a href="Air_Force_Research_Laboratory" title="Air Force Research Laboratory">Air Force Research Laboratory</a> <a href="VTOL" title="VTOL">VTOL</a> <a href="Unmanned_aircraft_system" class="mw-redirect" title="Unmanned aircraft system">drones</a><a href="#cite_note-157">[157]</a></li></ul>

<div class="mw-heading mw-heading4"><h4 id="Pharmaceuticals_and_drug_development">Pharmaceuticals and drug development</h4></div>

Julia is widely used for drug development in the pharmaceutical industry, having been adopted by <a href="Moderna" title="Moderna">Moderna</a>, <a href="Pfizer" title="Pfizer">Pfizer</a>, <a href="AstraZeneca" title="AstraZeneca">AstraZeneca</a>, <a href="Procter_%26_Gamble" title="Procter & Gamble">Procter & Gamble</a>, and <a href="United_Therapeutics" title="United Therapeutics">United Therapeutics</a>.<a href="#cite_note-158">[158]</a><a href="#cite_note-159">[159]</a>

<div class="mw-heading mw-heading3"><h3 id="Economics,_finance,_and_political_science">Economics, finance, and political science</h3></div>

<ul><li>The <a href="Federal_Reserve_Bank_of_New_York" title="Federal Reserve Bank of New York">Federal Reserve Bank of New York</a>, for macroeconomic modeling in Julia since 2015, including estimates of <a href="COVID-19" title="COVID-19">COVID-19</a> shocks in 2021<a href="#cite_note-160">[160]</a></li>

<li>Also the <a href="Bank_of_Canada" title="Bank of Canada">Bank of Canada</a>, <a href="Central_bank" title="Central bank">central bank</a>, for macroeconomic modeling<a href="#cite_note-161">[161]</a></li>

<li><a href="BlackRock" title="BlackRock">BlackRock</a>, the world's largest asset manager, for <a href="Financial_time-series_analysis" class="mw-redirect" title="Financial time-series analysis">financial time-series analysis</a><a href="#cite_note-:0-162">[162]</a></li>

<li><a href="Aviva" title="Aviva">Aviva</a>, the <a href="United_Kingdom" title="United Kingdom">UK</a>'s largest general insurer, for actuarial calculations<a href="#cite_note-:0-162">[162]</a></li>

<li><a href="Mitre_Corporation" title="Mitre Corporation">Mitre Corporation</a>, for verification of published election results<a href="#cite_note-163">[163]</a></li>

<li>Nobel laureate <a href="Thomas_J._Sargent" title="Thomas J. Sargent">Thomas J. Sargent</a>, for <a href="Macroeconometrics" class="mw-redirect" title="Macroeconometrics">macroeconometric modeling</a><a href="#cite_note-164">[164]</a></li></ul>

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<ul><li><a href="Comparison_of_numerical-analysis_software" title="Comparison of numerical-analysis software">Comparison of numerical-analysis software</a></li>

<li><a href="Comparison_of_statistical_packages" title="Comparison of statistical packages">Comparison of statistical packages</a></li>

<li><a href="Differentiable_programming" title="Differentiable programming">Differentiable programming</a></li>

<li><a href="JuMP" title="JuMP">JuMP</a> – an algebraic modeling language for mathematical optimization embedded in Julia</li>

<li><a href="Python_(programming_language)" title="Python (programming language)">Python</a></li>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://medium.com/@acidflask/smoothing-data-with-julia-s-generated-functions-c80e240e05f3#.615wk3dle">"Smoothing data with Julia's @generated functions"</a>. 5 November 2015. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160304105339/https://medium.com/@acidflask/smoothing-data-with-julia-s-generated-functions-c80e240e05f3#.615wk3dle">Archived</a> from the original on 4 March 2016. Retrieved 9 December 2015. <q>Julia's generated functions are closely related to the multistaged programming (MSP) paradigm popularized by Taha and Sheard, which generalizes the compile time/run time stages of program execution by allowing for multiple stages of delayed code execution.</q></cite>

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<li id="cite_note-157"><a href="#cite_ref-157">^</a> <cite id="CITEREFHobbs2022" class="citation web cs1">Hobbs, Kerianne (December 2022). <a rel="nofollow" class="external text" href="https://digitaleditions.walsworth.com/publication/?m=7270&i=769555&p=48">"Year of Autonomy in Alaskan Glaciers, Flight, Earth Orbit, Cislunar Space and Mars"</a>. Aerospace America Year in Review. p. 48. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20240619193142/https://digitaleditions.walsworth.com/publication/?m=7270&i=769555&p=48">Archived</a> from the original on 19 June 2024. Retrieved 26 January 2023. <q>The flight test team was able to demonstrate … a vertical takeoff and landing vehicle with both electric and conventional fuel propulsion systems onboard. The <a href="Unmanned_aircraft_system" class="mw-redirect" title="Unmanned aircraft system">[uncrewed aerial system]</a> was able to plan and execute these missions autonomously using onboard hardware. It was the first time the Julia programming language was flown on the embedded hardware - algorithms were precompiled ahead of time.</q></cite>

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</li>

</ol></div>

<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>

<ul><li><cite id="CITEREFNagar2017" class="citation book cs1">Nagar, Sandeep (2017). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=KmRADwAAQBAJ&pg=PR1">Beginning Julia Programming: For Engineers and Scientists</a>. Springer. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-4842-3171-5</bdi>.</cite></li>

<li><cite id="CITEREFBezansonEdelmanKarpinskiShah2017" class="citation journal cs1">Bezanson, J; Edelman, A; Karpinski, S; Shah, V. B (2017). "Julia: A fresh approach to numerical computing". SIAM Review. 59 (1): 65–98. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/1411.1607">1411.1607</a>. <a href="CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.760.8894">10.1.1.760.8894</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1137%2F141000671">10.1137/141000671</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:13026838">13026838</a>.</cite></li>

<li><cite id="CITEREFJoshi2016" class="citation book cs1">Joshi, Anshul (2016). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Bn9cDgAAQBAJ&pg=PP2">Julia for Data Science － Explore the world of data science from scratch with Julia by your side</a>. Packt. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-78355-386-0</bdi>.</cite></li>

<li>Tobin A Driscoll and Richard J. Braun (Aug. 2022). Fundamentals of Numerical Computation: Julia Edition. SIAM. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-611977-00-4</bdi>.</li>

<li>C. T. Kelley (2022). Solving Nonlinear Equations with Iterative Methods: Solvers and Examples in Julia, SIAM. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-611977-26-4</bdi>.</li>

<li><cite id="CITEREFKalicharan2021" class="citation book cs1">Kalicharan, Noel (2021). <a rel="nofollow" class="external text" href="https://link.springer.com/book/10.1007/978-3-030-73936-2">Julia - Bit by Bit</a>. Undergraduate Topics in Computer Science. Springer. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-030-73936-2">10.1007/978-3-030-73936-2</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-030-73936-2</bdi>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:235917112">235917112</a>.</cite></li>

<li>Clemens Heitzinger (2022): Algorithms with Julia, Springer, ISBN 978-3-031-16559-7.</li>

<li>Kenneth Lange (Jun. 2025): Algorithms from THE BOOK (2nd Ed.), SIAM, ISBN 978-1-61197-838-4.</li></ul>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

</div>

<ul><li><a rel="nofollow" class="external text" href="https://julialang.org">Official website</a></li>

<li><a rel="nofollow" class="external text" href="https://github.com/JuliaLang/Julia">Julia</a> on <a href="GitHub" title="GitHub">GitHub</a></li></ul>

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</style><div id="Programming_languages625" style="font-size:114%;margin:0 4em"><a href="Programming_language" title="Programming language">Programming languages</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div>

<ul><li><a href="Comparison_of_programming_languages" title="Comparison of programming languages">Comparison</a></li>

<li><a href="Timeline_of_programming_languages" title="Timeline of programming languages">Timeline</a></li>

<li><a href="History_of_programming_languages" title="History of programming languages">History</a></li></ul>

</div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="ALGOL" title="ALGOL">ALGOL</a>

<ul><li><a href="Simula" title="Simula">Simula</a></li></ul></li>

<li><a href="Assembly_language" title="Assembly language">Assembly</a></li>

<li><a href="BASIC" title="BASIC">BASIC</a>

<ul><li><a href="Visual_Basic" title="Visual Basic">Visual Basic</a>

<ul><li><a href="Visual_Basic_(classic)" title="Visual Basic (classic)">classic</a></li>

<li><a href="COBOL" title="COBOL">COBOL</a></li>

<li><a href="Erlang_(programming_language)" title="Erlang (programming language)">Erlang</a>

<ul><li><a href="Elixir_(programming_language)" title="Elixir (programming language)">Elixir</a></li></ul></li>

<li><a href="Forth_(programming_language)" title="Forth (programming language)">Forth</a></li>

<li><a href="Fortran" title="Fortran">Fortran</a></li>

<li><a href="Haskell" title="Haskell">Haskell</a></li>

<li><a href="JavaScript" title="JavaScript">JavaScript</a></li>

<li><a href="Kotlin_(programming_language)" title="Kotlin (programming language)">Kotlin</a></li>

<li><a href="MATLAB" title="MATLAB">MATLAB</a></li>

<ul><li><a href="OCaml" title="OCaml">OCaml</a></li></ul></li></ul></li>

<li><a href="Pascal_(programming_language)" title="Pascal (programming language)">Pascal</a>

<ul><li><a href="Object_Pascal" title="Object Pascal">Object Pascal</a></li></ul></li>

<li><a href="Prolog" title="Prolog">Prolog</a></li>

<li><a href="Python_(programming_language)" title="Python (programming language)">Python</a></li>

<li><a href="Scratch_(programming_language)" title="Scratch (programming language)">Scratch</a></li>

<li><a href="Shell_script" title="Shell script">Shell</a></li>

<li><a href="Smalltalk" title="Smalltalk">Smalltalk</a></li>

<li><a href="Swift_(programming_language)" title="Swift (programming language)">Swift</a></li>

</div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div>

<ul><li> Lists: <a href="List_of_programming_languages" title="List of programming languages">Alphabetical</a></li>

<li><a href="List_of_programming_languages_by_type" title="List of programming languages by type">Categorical</a></li>

<li><a href="Generational_list_of_programming_languages" title="Generational list of programming languages">Generational</a></li>

<li><a href="Non-English-based_programming_languages" title="Non-English-based programming languages">Non-English-based</a></li>

<li> Category</li></ul>

</div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Free_and_open-source_software510" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Free_and_open-source_software510" style="font-size:114%;margin:0 4em"><a href="Free_and_open-source_software" title="Free and open-source software">Free and open-source software</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">General</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Alternative_terms_for_free_software" title="Alternative terms for free software">Alternative terms for free software</a></li>

<li><a href="Comparison_of_open-source_and_closed-source_software" title="Comparison of open-source and closed-source software">Comparison of open-source and closed-source software</a></li>

<li><a href="Comparison_of_source-code-hosting_facilities" title="Comparison of source-code-hosting facilities">Comparison of source-code-hosting facilities</a></li>

<li><a href="Free_software" title="Free software">Free software</a></li>

<li><a href="List_of_free_software_project_directories" title="List of free software project directories">Free software project directories</a></li>

<li><a href="Gratis_versus_libre" title="Gratis versus libre">Gratis versus libre</a></li>

<li><a href="Long-term_support" title="Long-term support">Long-term support</a></li>

<li><a href="Open-source_software" title="Open-source software">Open-source software</a></li>

<li><a href="Open-source_software_development" title="Open-source software development">Open-source software development</a></li>

<li><a href="Outline_of_free_software" title="Outline of free software">Outline</a></li>

<li><a href="Timeline_of_free_and_open-source_software" title="Timeline of free and open-source software">Timeline</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="List_of_free_and_open-source_software_packages" title="List of free and open-source software packages">Software packages</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Comparison_of_free_software_for_audio" title="Comparison of free software for audio">Audio</a></li>

<li><a href="List_of_open-source_bioinformatics_software" title="List of open-source bioinformatics software">Bioinformatics</a></li>

<li><a href="List_of_open-source_codecs" title="List of open-source codecs">Codecs</a></li>

<li><a href="Comparison_of_open-source_configuration_management_software" title="Comparison of open-source configuration management software">Configuration management</a></li>

<li><a href="Device_driver" title="Device driver">Drivers</a>

<ul><li><a href="Free_and_open-source_graphics_device_driver" title="Free and open-source graphics device driver">Graphics</a></li>

<li><a href="Comparison_of_open-source_wireless_drivers" title="Comparison of open-source wireless drivers">Wireless</a></li></ul></li>

<li><a href="List_of_open-source_health_software" title="List of open-source health software">Health</a></li>

<li><a href="List_of_open-source_software_for_mathematics" title="List of open-source software for mathematics">Mathematics</a></li>

<li><a href="List_of_office_suites" title="List of office suites">Office suites</a></li>

<li><a href="Comparison_of_open-source_operating_systems" title="Comparison of open-source operating systems">Operating systems</a></li>

<li><a href="List_of_open-source_routing_platforms" title="List of open-source routing platforms">Routing</a></li>

<li><a href="List_of_free_television_software" title="List of free television software">Television</a></li>

<li><a href="List_of_open-source_video_games" title="List of open-source video games">Video games</a></li>

<li><a href="List_of_free_and_open-source_web_applications" title="List of free and open-source web applications">Web applications</a>

<ul><li><a href="Comparison_of_shopping_cart_software" title="Comparison of shopping cart software">E-commerce</a></li></ul></li>

<li><a href="List_of_free_and_open-source_Android_applications" title="List of free and open-source Android applications">Android apps</a></li>

<li><a href="List_of_commercial_open-source_applications_and_services" title="List of commercial open-source applications and services">Commercial</a></li>

<li><a href="List_of_formerly_proprietary_software" title="List of formerly proprietary software">Formerly proprietary</a></li>

<li><a href="List_of_formerly_free_and_open-source_software" class="mw-redirect" title="List of formerly free and open-source software">Formerly open-source</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Community_of_practice" title="Community of practice">Community</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Free_software_movement" title="Free software movement">Free software movement</a></li>

<li><a href="History_of_free_and_open-source_software" title="History of free and open-source software">History</a></li>

<li><a href="Open-source-software_movement" class="mw-redirect" title="Open-source-software movement">Open-source-software movement</a></li>

<li><a href="List_of_free-software_events" title="List of free-software events">Events</a></li>

<li><a href="Open-source_software_advocacy" title="Open-source software advocacy">Advocacy</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="List_of_free_and_open-source_software_organizations" title="List of free and open-source software organizations">Organisations</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Free_Software_Movement_of_India" title="Free Software Movement of India">Free Software Movement of India</a></li>

<li><a href="Free_Software_Foundation" title="Free Software Foundation">Free Software Foundation</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Free-software_license" title="Free-software license">Licenses</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="Apache_License" title="Apache License">Apache</a></li>

<li><a href="Artistic_License" title="Artistic License">Artistic</a></li>

<li><a href="Beerware" title="Beerware">Beerware</a></li>

<li><a href="Creative_Commons_license" title="Creative Commons license">Creative Commons</a></li>

<li><a href="Free_Software_Foundation" title="Free Software Foundation">Free Software Foundation</a>

<li><a href="Python_License" title="Python License">Python</a></li>

<li><a href="Python_Software_Foundation_License" title="Python Software Foundation License">Python Software Foundation License</a></li>

<li><a href="Shared_Source_Initiative" title="Shared Source Initiative">Shared Source Initiative</a></li>

<li><a href="Sleepycat_License" class="mw-redirect" title="Sleepycat License">Sleepycat</a></li>

<li><a href="Unlicense" title="Unlicense">Unlicense</a></li>

<li><a href="WTFPL" title="WTFPL">WTFPL</a></li>

</div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Types_and_standards23" scope="row" class="navbox-group" style="width:1%">Types and standards</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Comparison_of_free_and_open-source_software_licenses" title="Comparison of free and open-source software licenses">Comparison of licenses</a></li>

<li><a href="Contributor_License_Agreement" title="Contributor License Agreement">Contributor License Agreement</a></li>

<li><a href="Copyleft" title="Copyleft">Copyleft</a></li>

<li><a href="Debian_Free_Software_Guidelines" class="mw-redirect" title="Debian Free Software Guidelines">Debian Free Software Guidelines</a></li>

<li><a href="Definition_of_Free_Cultural_Works" title="Definition of Free Cultural Works">Definition of Free Cultural Works</a></li>

<li><a href="Free_license" title="Free license">Free license</a></li>

<li><a href="The_Free_Software_Definition" title="The Free Software Definition">The Free Software Definition</a></li>

<li><a href="The_Open_Source_Definition" title="The Open Source Definition">The Open Source Definition</a></li>

<li><a href="Open-source_license" title="Open-source license">Open-source license</a></li>

<li><a href="Permissive_software_license" title="Permissive software license">Permissive software license</a></li>

<li><a href="Public_domain" title="Public domain">Public domain</a></li></ul>

</div></td></tr></tbody></table><div>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Challenges</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Digital_rights_management" title="Digital rights management">Digital rights management</a></li>

<li><a href="License_proliferation" title="License proliferation">License proliferation</a></li>

<li><a href="Mozilla_software_rebranded_by_Debian" class="mw-redirect" title="Mozilla software rebranded by Debian">Mozilla software rebranding</a></li>

<li><a href="Proprietary_device_driver" class="mw-redirect" title="Proprietary device driver">Proprietary device drivers</a></li>

<li><a href="Proprietary_firmware" title="Proprietary firmware">Proprietary firmware</a></li>

<li><a href="Proprietary_software" title="Proprietary software">Proprietary software</a></li>

<li><a href="SCO%E2%80%93Linux_disputes" title="SCO–Linux disputes">SCO/Linux controversies</a></li>

<li><a href="Software_patents_and_free_software" title="Software patents and free software">Software patents</a></li>

<li><a href="Open-source_software_security" title="Open-source software security">Software security</a></li>

<li><a href="Tivoization" title="Tivoization">Tivoization</a></li>

<li><a href="Trusted_Computing" title="Trusted Computing">Trusted Computing</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related topics</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Fork_(software_development)" title="Fork (software development)">Forking</a></li>

<li><a href="GNU_Manifesto" title="GNU Manifesto">GNU Manifesto</a></li>

<li><a href="Microsoft_Open_Specification_Promise" title="Microsoft Open Specification Promise">Microsoft Open Specification Promise</a></li>

<li><a href="Open-core_model" title="Open-core model">Open-core model</a></li>

<li><a href="Open-source_hardware" title="Open-source hardware">Open-source hardware</a></li>

<li><a href="Shared_Source_Initiative" title="Shared Source Initiative">Shared Source Initiative</a></li>

<li><a href="Source-available_software" title="Source-available software">Source-available software</a></li>

<li><a href="The_Cathedral_and_the_Bazaar" title="The Cathedral and the Bazaar">The Cathedral and the Bazaar</a></li>

<li><a href="Revolution_OS" title="Revolution OS">Revolution OS</a></li></ul>

</div></td></tr><tr><td class="navbox-abovebelow" colspan="2" style="font-weight:bold"><div>

<ul><li> <a href="Portal%3AFree_and_open-source_software" title="Portal:Free and open-source software">Portal</a></li>

<li> Category</li></ul>

</div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Numerical-analysis_software146" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Numerical-analysis_software146" style="font-size:114%;margin:0 4em"><a href="List_of_numerical-analysis_software" title="List of numerical-analysis software">Numerical-analysis software</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Free</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Advanced_Simulation_Library" title="Advanced Simulation Library">Advanced Simulation Library</a></li>

<li><a href="Chapel_(programming_language)" title="Chapel (programming language)">Chapel</a></li>

<li><a href="Euler_Mathematical_Toolbox" title="Euler Mathematical Toolbox">Euler Mathematical Toolbox</a></li>

<li><a href="FreeFem%2B%2B" title="FreeFem++">FreeFem++</a></li>

<li><a href="FreeMat" title="FreeMat">FreeMat</a></li>

<li><a href="Genius_(mathematics_software)" title="Genius (mathematics software)">Genius</a></li>

<li><a href="GNU_Octave" title="GNU Octave">GNU Octave</a></li>

<li><a href="Gretl" title="Gretl">gretl</a></li>

<li><a href="Project_Jupyter" title="Project Jupyter">Jupyter</a> (Julia, Python, R; <a href="IPython" title="IPython">IPython</a>)</li>

<li><a href="OpenFOAM" title="OpenFOAM">OpenFOAM</a></li>

<li><a href="Python_(programming_language)" title="Python (programming language)">Python</a></li>

<li><a href="SageMath" title="SageMath">SageMath</a></li>

<li><a href="Salome_(software)" title="Salome (software)">Salome</a></li>

<li><a href="ScicosLab" title="ScicosLab">ScicosLab</a></li>

<li><a href="Scilab" title="Scilab">Scilab</a></li>

</div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Discontinued12" scope="row" class="navbox-group" style="width:1%">Discontinued</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Fortress_(programming_language)" title="Fortress (programming language)">Fortress</a></li></ul>

</div></td></tr></tbody></table><div>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Proprietary</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="DADiSP" title="DADiSP">DADiSP</a></li>

<li><a href="FEATool_Multiphysics" title="FEATool Multiphysics">FEATool Multiphysics</a></li>

<li><a href="GAUSS_(software)" title="GAUSS (software)">GAUSS</a></li>

<li><a href="LabVIEW" title="LabVIEW">LabVIEW</a></li>

<li><a href="Maple_(software)" title="Maple (software)">Maple</a></li>

<li><a href="Mathcad" title="Mathcad">Mathcad</a></li>

<li><a href="Wolfram_Mathematica" class="mw-redirect" title="Wolfram Mathematica">Mathematica</a></li>

<li><a href="MATLAB" title="MATLAB">MATLAB</a></li>

<li><a href="MWorks" title="MWorks">MWorks</a></li>

<li><a href="Speakeasy_(computational_environment)" title="Speakeasy (computational environment)">Speakeasy</a></li>

<li><a href="VisSim" title="VisSim">VisSim</a></li></ul>

</div></td></tr><tr><td class="navbox-abovebelow hlist" colspan="2"><div>

<ul><li><a href="Comparison_of_numerical-analysis_software" title="Comparison of numerical-analysis software">Comparison</a></li></ul>

</div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Mathematical_optimization_software220" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Mathematical_optimization_software220" style="font-size:114%;margin:0 4em"><a href="List_of_optimization_software" title="List of optimization software">Mathematical optimization software</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;">Data formats</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;"><a href="Mathematical_modeling" class="mw-redirect" title="Mathematical modeling">Modeling</a> tools</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="AIMMS" title="AIMMS">AIMMS</a></li>

<li><a href="APMonitor" title="APMonitor">APMonitor</a></li>

<li><a href="ECLiPSe" title="ECLiPSe">ECLiPSe</a>-CLP</li>

<li><a href="Gekko_(optimization_software)" title="Gekko (optimization software)">Gekko</a></li>

<li><a href="GNU_Linear_Programming_Kit" title="GNU Linear Programming Kit">GNU MathProg</a></li>

<li><a href="LINDO" title="LINDO">LINDO</a></li>

<li><a href="Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a></li>

<li><a href="MiniZinc" title="MiniZinc">MiniZinc</a></li>

<li><a href="OptimJ" title="OptimJ">OptimJ</a></li>

<li><a href="Pyomo" title="Pyomo">Pyomo</a></li>

<li><a href="TOMLAB" title="TOMLAB">TOMLAB</a></li>

<li><a href="FICO_Xpress" title="FICO Xpress">Xpress Mosel</a></li>

<li><a href="SCIP_(optimization_software)" class="mw-redirect" title="SCIP (optimization software)">ZIMPL</a></li>

<li><a href="CasADi" title="CasADi">CasADi</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;"><a href="Solver" title="Solver">Solvers</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Linear_programming" title="Linear programming">LP</a>, <a href="Linear_programming#Integer_unknowns" title="Linear programming">MILP</a>∗</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="APOPT" title="APOPT">APOPT</a>∗</li>

<li><a href="ANTIGONE" title="ANTIGONE">ANTIGONE</a>∗</li>

<li><a href="Artelys_Knitro" title="Artelys Knitro">Artelys Knitro</a>∗</li>

<li><a href="CPLEX" title="CPLEX">CPLEX</a>∗</li>

<li><a href="FortMP" title="FortMP">FortMP</a>∗</li>

<li><a href="GNU_Linear_Programming_Kit" title="GNU Linear Programming Kit">GLPK/GLPSOL</a>∗</li>

<li><a href="Gurobi_Optimizer" title="Gurobi Optimizer">Gurobi Optimizer</a>∗</li>

<li><a href="HiGHS_optimization_solver" title="HiGHS optimization solver">HiGHS</a>∗</li>

<li><a href="LINDO" title="LINDO">LINDO</a>∗</li>

<li><a href="Lp_solve" title="Lp solve">Lp_solve</a></li>

<li><a href="Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a></li>

<li><a href="MINOS_(optimization_software)" title="MINOS (optimization software)">MINOS</a></li>

<li><a href="MINTO" title="MINTO">MINTO</a>∗</li>

<li><a href="MOSEK" title="MOSEK">MOSEK</a>∗</li>

<li><a href="SCIP_(optimization_software)" class="mw-redirect" title="SCIP (optimization software)">SoPlex</a></li>

<li><a href="Octeract_Engine" title="Octeract Engine">Octeract Engine</a>∗</li>

<li><a href="COIN-OR#SYMPHONY" title="COIN-OR">SYMPHONY</a>∗</li>

<li><a href="FICO_Xpress" title="FICO Xpress">Xpress Optimizer</a>∗</li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Quadratic_programming" title="Quadratic programming">QP</a>, MIQP∗</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="APOPT" title="APOPT">APOPT</a>∗</li>

<li><a href="ANTIGONE" title="ANTIGONE">ANTIGONE</a>∗</li>

<li><a href="Artelys_Knitro" title="Artelys Knitro">Artelys Knitro</a>∗</li>

<li><a href="CPLEX" title="CPLEX">CPLEX</a>∗</li>

<li><a href="FortMP" title="FortMP">FortMP</a>∗</li>

<li><a href="HiGHS_optimization_solver" title="HiGHS optimization solver">HiGHS</a></li>

<li><a href="Gurobi_Optimizer" title="Gurobi Optimizer">Gurobi Optimizer</a>∗</li>

<li><a href="IPOPT" title="IPOPT">IPOPT</a></li>

<li><a href="LINDO" title="LINDO">LINDO</a>∗</li>

<li><a href="Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a></li>

<li><a href="MINOS_(optimization_software)" title="MINOS (optimization software)">MINOS</a></li>

<li><a href="MOSEK" title="MOSEK">MOSEK</a>∗</li>

<li><a href="Octeract_Engine" title="Octeract Engine">Octeract Engine</a>∗</li>

<li><a href="FICO_Xpress" title="FICO Xpress">Xpress Optimizer</a>∗</li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Quadratically_constrained_quadratic_program" title="Quadratically constrained quadratic program">QCP</a>, MIQCP∗</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="APOPT" title="APOPT">APOPT</a>∗</li>

<li><a href="ANTIGONE" title="ANTIGONE">ANTIGONE</a>∗</li>

<li><a href="Artelys_Knitro" title="Artelys Knitro">Artelys Knitro</a>∗</li>

<li><a href="CPLEX" title="CPLEX">CPLEX</a>∗</li>

<li><a href="Gurobi_Optimizer" title="Gurobi Optimizer">Gurobi Optimizer</a>∗</li>

<li><a href="IPOPT" title="IPOPT">IPOPT</a></li>

<li><a href="LINDO" title="LINDO">LINDO</a>∗</li>

<li><a href="Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a></li>

<li><a href="MINOS_(optimization_software)" title="MINOS (optimization software)">MINOS</a></li>

<li><a href="MOSEK" title="MOSEK">MOSEK</a>∗</li>

<li><a href="Octeract_Engine" title="Octeract Engine">Octeract Engine</a>∗</li>

<li><a href="FICO_Xpress" title="FICO Xpress">Xpress Optimizer</a>∗</li>

<li><a href="FICO_Xpress" title="FICO Xpress">Xpress NonLinear</a>∗</li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Second-order_cone_programming" title="Second-order cone programming">SOCP</a>, MISOCP∗</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Artelys_Knitro" title="Artelys Knitro">Artelys Knitro</a>∗</li>

<li><a href="CPLEX" title="CPLEX">CPLEX</a>∗</li>

<li><a href="Gurobi_Optimizer" title="Gurobi Optimizer">Gurobi Optimizer</a>∗</li>

<li><a href="LINDO" title="LINDO">LINDO</a>∗</li>

<li><a href="Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a></li>

<li><a href="MOSEK" title="MOSEK">MOSEK</a>∗</li>

<li><a href="FICO_Xpress" title="FICO Xpress">Xpress Optimizer</a>∗</li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Semidefinite_programming" title="Semidefinite programming">SDP</a>, MISDP∗</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a></li>

<li><a href="MOSEK" title="MOSEK">MOSEK</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Nonlinear_programming" title="Nonlinear programming">NLP</a>, MINLP∗</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="APOPT" title="APOPT">APOPT</a>∗</li>

<li><a href="ANTIGONE" title="ANTIGONE">ANTIGONE</a>∗</li>

<li><a href="Artelys_Knitro" title="Artelys Knitro">Artelys Knitro</a>∗</li>

<li><a href="BARON" title="BARON">BARON</a>∗</li>

<li><a href="Couenne" title="Couenne">Couenne</a>∗</li>

<li><a href="Galahad_library" title="Galahad library">Galahad library</a></li>

<li><a href="Gurobi_Optimizer" title="Gurobi Optimizer">Gurobi Optimizer</a>∗</li>

<li><a href="IPOPT" title="IPOPT">IPOPT</a></li>

<li><a href="LINDO" title="LINDO">LINDO</a>∗</li>

<li><a href="MIDACO" title="MIDACO">MIDACO</a>∗</li>

<li><a href="MINOS_(optimization_software)" title="MINOS (optimization software)">MINOS</a></li>

<li><a href="NLPQLP" title="NLPQLP">NLPQLP</a></li>

<li><a href="NPSOL" title="NPSOL">NPSOL</a></li>

<li><a href="SNOPT" title="SNOPT">SNOPT</a>∗</li>

<li><a href="Octeract_Engine" title="Octeract Engine">Octeract Engine</a>∗</li>

<li><a href="WORHP" title="WORHP">WORHP</a></li>

<li><a href="FICO_Xpress" title="FICO Xpress">Xpress NonLinear</a>∗</li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Global_optimization" title="Global optimization">GO</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="ANTIGONE" title="ANTIGONE">ANTIGONE</a>∗</li>

<li><a href="BARON" title="BARON">BARON</a></li>

<li><a href="Couenne" title="Couenne">Couenne</a>∗</li>

<li><a href="FICO_Xpress" title="FICO Xpress">Xpress Global</a></li>

<li><a href="Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a></li>

<li><a href="LINDO" title="LINDO">LINDO</a></li>

<li><a href="Octeract_Engine" title="Octeract Engine">Octeract Engine</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Constraint_programming" title="Constraint programming">CP</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li>Artelys Kalis</li>

<li>Comet</li>

<li><a href="CPLEX" title="CPLEX">CPLEX</a> CP Optimizer</li>

<li><a href="Gecode" title="Gecode">Gecode</a></li>

<li><a href="Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a></li>

<li><a href="JaCoP_(solver)" title="JaCoP (solver)">JaCoP</a></li>

<li><a href="FICO_Xpress" title="FICO Xpress">Xpress Kalis</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div>

<ul><li><a href="List_of_optimization_software" title="List of optimization software">List of optimization software</a></li>

<li><a href="Comparison_of_optimization_software" title="Comparison of optimization software">Comparison of optimization software</a></li></ul>

</div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Statistical_software284" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Statistical_software284" style="font-size:114%;margin:0 4em"><a href="List_of_statistical_software" title="List of statistical software">Statistical software</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Public-domain_software" title="Public-domain software">Public domain</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Dataplot" title="Dataplot">Dataplot</a></li>

<li><a href="CSPro" title="CSPro">CSPro</a></li>

<li><a href="X-12-ARIMA" class="mw-redirect" title="X-12-ARIMA">X-12-ARIMA</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Open-source_software" title="Open-source software">Open-source</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="Gretl" title="Gretl">gretl</a></li>

<li><a href="Jamovi" title="Jamovi">jamovi</a></li>

<li><a href="JMulTi" title="JMulTi">JMulTi</a></li>

<li><a href="Project_Jupyter" title="Project Jupyter">Jupyter</a> (Julia, Python, R)</li>

<li><a href="GNU_Octave" title="GNU Octave">GNU Octave</a></li>

<li><a href="OpenBUGS" title="OpenBUGS">OpenBUGS</a></li>

<li><a href="Orange_(software)" title="Orange (software)">Orange</a></li>

<li><a href="Python_(programming_language)" title="Python (programming language)">Python</a> (statsmodels, <a href="PyMC3" class="mw-redirect" title="PyMC3">PyMC3</a>, <a href="IPython" title="IPython">IPython</a>, <a href="IDLE" title="IDLE">IDLE</a>)</li>

<li><a href="R_(programming_language)" title="R (programming language)">R</a> (<a href="RStudio" title="RStudio">RStudio</a>)</li>

<li><a href="SageMath" title="SageMath">SageMath</a></li>

<li><a href="SimFiT" title="SimFiT">SimFiT</a></li>

<li><a href="SOFA_Statistics" title="SOFA Statistics">SOFA Statistics</a></li>

<li><a href="XLispStat" title="XLispStat">XLispStat</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Freeware" title="Freeware">Freeware</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="CumFreq" title="CumFreq">CumFreq</a></li>

<li><a href="SegReg" title="SegReg">SegReg</a></li>

<li><a href="XploRe" title="XploRe">XploRe</a></li>

<li><a href="WinBUGS" title="WinBUGS">WinBUGS</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Commercial_software" title="Commercial software">Commercial</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Cross-platform_software" title="Cross-platform software">Cross-platform</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="GAUSS_(software)" title="GAUSS (software)">GAUSS</a></li>

<li><a href="GraphPad_InStat" class="mw-redirect" title="GraphPad InStat">GraphPad InStat</a></li>

<li><a href="GraphPad_Prism" class="mw-redirect" title="GraphPad Prism">GraphPad Prism</a></li>

<li>IBM <a href="SPSS" title="SPSS">SPSS</a> Statistics</li>

<li>IBM <a href="SPSS_Modeler" title="SPSS Modeler">SPSS Modeler</a></li>

<li><a href="Maple_(software)" title="Maple (software)">Maple</a></li>

<li><a href="Mathcad" title="Mathcad">Mathcad</a></li>

<li><a href="Wolfram_Mathematica" class="mw-redirect" title="Wolfram Mathematica">Mathematica</a></li>

<li><a href="MATLAB" title="MATLAB">MATLAB</a></li>

<li><a href="OxMetrics" title="OxMetrics">OxMetrics</a></li>

<li><a href="Revolution_Analytics" title="Revolution Analytics">Revolution Analytics</a></li>

<li><a href="SmartPLS" title="SmartPLS">SmartPLS</a></li>

<li><a href="Stata" title="Stata">Stata</a></li>

<li><a href="StatView" title="StatView">StatView</a></li>

<li><a href="SUDAAN" title="SUDAAN">SUDAAN</a></li>

<li><a href="World_Programming_System" title="World Programming System">World Programming System</a> (WPS)</li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Microsoft_Windows" title="Microsoft Windows">Windows</a> only</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="EViews" title="EViews">EViews</a></li>

<li><a href="Genstat" title="Genstat">GenStat</a></li>

<li><a href="LIMDEP" title="LIMDEP">LIMDEP</a></li>

<li><a href="LISREL" title="LISREL">LISREL</a></li>

<li><a href="MedCalc" title="MedCalc">MedCalc</a></li>

<li><a href="Microfit" title="Microfit">Microfit</a></li>

<li><a href="Minitab" title="Minitab">Minitab</a></li>

<li><a href="MLwiN" title="MLwiN">MLwiN</a></li>

<li><a href="Shazam_(econometrics_software)" title="Shazam (econometrics software)">Shazam</a></li>

<li><a href="SigmaStat" title="SigmaStat">SigmaStat</a></li>

<li><a href="Statistica" title="Statistica">Statistica</a></li>

<li><a href="StatsDirect" title="StatsDirect">StatsDirect</a></li>

<li><a href="StatXact" title="StatXact">StatXact</a></li>

<li><a href="SYSTAT_(statistics_package)" title="SYSTAT (statistics package)">SYSTAT</a></li>

<li><a href="The_Unscrambler" title="The Unscrambler">The Unscrambler</a></li>

<li>Unistat</li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Microsoft_Excel" title="Microsoft Excel">Excel</a> add-ons</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Analyse-it" title="Analyse-it">Analyse-it</a></li>

<li>Unistat for Excel</li>

<li><a href="XLfit" title="XLfit">XLfit</a></li>

<li><a href="RExcel" title="RExcel">RExcel</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><a href="Comparison_of_statistical_packages" title="Comparison of statistical packages">Comparison</a> • Category</div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Differentiable_computing254" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Differentiable_computing254" style="font-size:114%;margin:0 4em">Differentiable computing</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Differentiable_function" title="Differentiable function">General</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Differentiable_programming" title="Differentiable programming">Differentiable programming</a></li>

<li><a href="Information_geometry" title="Information geometry">Information geometry</a></li>

<li><a href="Statistical_manifold" title="Statistical manifold">Statistical manifold</a></li>

<li><a href="Automatic_differentiation" title="Automatic differentiation">Automatic differentiation</a></li>

<li><a href="Neuromorphic_computing" title="Neuromorphic computing">Neuromorphic computing</a></li>

<li><a href="Pattern_recognition" title="Pattern recognition">Pattern recognition</a></li>

<li><a href="Ricci_calculus" title="Ricci calculus">Ricci calculus</a></li>

<li><a href="Computational_learning_theory" title="Computational learning theory">Computational learning theory</a></li>

<li><a href="Inductive_bias" title="Inductive bias">Inductive bias</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Hardware</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="Memristor" title="Memristor">Memristor</a></li>

<li><a href="SpiNNaker" title="SpiNNaker">SpiNNaker</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Software libraries</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="TensorFlow" title="TensorFlow">TensorFlow</a></li>

<li><a href="PyTorch" title="PyTorch">PyTorch</a></li>

<li><a href="Keras" title="Keras">Keras</a></li>

<li><a href="Scikit-learn" title="Scikit-learn">scikit-learn</a></li>

<li><a href="Theano_(software)" title="Theano (software)">Theano</a></li>

<li><a href="MindSpore" title="MindSpore">MindSpore</a></li></ul>

</div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div>

<ul><li> Portals

<ul><li><a href="Portal%3AComputer_programming" title="Portal:Computer programming">Computer programming</a></li>

<li><a href="Portal%3ATechnology" title="Portal:Technology">Technology</a></li></ul></li></ul>

</div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox authority-control" aria-labelledby="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q2613697#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata923" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q2613697#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata923" style="font-size:114%;margin:0 4em">Authority control databases </div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">International</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><a rel="nofollow" class="external text" href="https://id.worldcat.org/fast/1938397">FAST</a></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">National</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh2016000127">United States</a></li><li><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb18069381b">France</a></li><li><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb18069381b">BnF data</a></li><li><a rel="nofollow" class="external text" href="https://www.nli.org.il/en/authorities/987007417317505171">Israel</a></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><a rel="nofollow" class="external text" href="https://lux.collections.yale.edu/view/concept/15598042-daa6-4c91-a775-3bbaf144c518">Yale LUX</a></li></ul></div></td></tr></tbody></table></div> </div><div><div class="zim-footer">

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