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</script><link href="https://cdnjs.cloudflare.com/ajax/libs/normalize/4.2.0/normalize.min.css" rel="stylesheet" type="text/css"/><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/4.6.3/css/font-awesome.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.2.0/require.min.js" data-main="assets/documenter.js"></script><script src="siteinfo.js"></script><script src="../versions.js"></script><link href="assets/highlightjs/default.css" rel="stylesheet" type="text/css"/><link href="assets/documenter.css" rel="stylesheet" type="text/css"/></head><body><nav class="toc"><a href="index.html"><img class="logo" src="assets/logo.png" alt="The Julia Language logo"/></a><h1>The Julia Language</h1><select id="version-selector" onChange="window.location.href=this.value" style="visibility: hidden"></select><form class="search" action="search.html"><input id="search-query" name="q" type="text" placeholder="Search docs"/></form><ul><li class="current"><a class="toctext" href="index.html">Home</a><ul class="internal"><li><a class="toctext" href="#Manual-1">Manual</a></li><li><a class="toctext" href="#Standard-Library-1">Standard Library</a></li><li><a class="toctext" href="#Developer-Documentation-1">Developer Documentation</a></li></ul></li><li><span class="toctext">Manual</span><ul><li><a class="toctext" href="manual/introduction.html">Introduction</a></li><li><a class="toctext" href="manual/getting-started.html">Getting Started</a></li><li><a class="toctext" href="manual/variables.html">Variables</a></li><li><a class="toctext" href="manual/integers-and-floating-point-numbers.html">Integers and Floating-Point Numbers</a></li><li><a class="toctext" href="manual/mathematical-operations.html">Mathematical Operations and Elementary Functions</a></li><li><a class="toctext" 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Julia</a></li><li><a class="toctext" href="manual/packages.html">Packages</a></li><li><a class="toctext" href="manual/profile.html">Profiling</a></li><li><a class="toctext" href="manual/stacktraces.html">Stack Traces</a></li><li><a class="toctext" href="manual/performance-tips.html">Performance Tips</a></li><li><a class="toctext" href="manual/workflow-tips.html">Workflow Tips</a></li><li><a class="toctext" href="manual/style-guide.html">Style Guide</a></li><li><a class="toctext" href="manual/faq.html">Frequently Asked Questions</a></li><li><a class="toctext" href="manual/noteworthy-differences.html">Noteworthy Differences from other Languages</a></li><li><a class="toctext" href="manual/unicode-input.html">Unicode Input</a></li></ul></li><li><span class="toctext">Standard Library</span><ul><li><a class="toctext" href="stdlib/base.html">Essentials</a></li><li><a class="toctext" href="stdlib/collections.html">Collections and Data Structures</a></li><li><a class="toctext" 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utilities</a></li><li><a class="toctext" href="stdlib/test.html">Unit Testing</a></li><li><a class="toctext" href="stdlib/c.html">C Interface</a></li><li><a class="toctext" href="stdlib/libc.html">C Standard Library</a></li><li><a class="toctext" href="stdlib/libdl.html">Dynamic Linker</a></li><li><a class="toctext" href="stdlib/profile.html">Profiling</a></li><li><a class="toctext" href="stdlib/stacktraces.html">StackTraces</a></li><li><a class="toctext" href="stdlib/simd-types.html">SIMD Support</a></li></ul></li><li><span class="toctext">Developer Documentation</span><ul><li><a class="toctext" href="devdocs/reflection.html">Reflection and introspection</a></li><li><span class="toctext">Documentation of Julia's Internals</span><ul><li><a class="toctext" href="devdocs/init.html">Initialization of the Julia runtime</a></li><li><a class="toctext" href="devdocs/ast.html">Julia ASTs</a></li><li><a class="toctext" href="devdocs/types.html">More about types</a></li><li><a class="toctext" href="devdocs/object.html">Memory layout of Julia Objects</a></li><li><a class="toctext" href="devdocs/eval.html">Eval of Julia code</a></li><li><a class="toctext" href="devdocs/callconv.html">Calling Conventions</a></li><li><a class="toctext" href="devdocs/compiler.html">High-level Overview of the Native-Code Generation Process</a></li><li><a class="toctext" href="devdocs/functions.html">Julia Functions</a></li><li><a class="toctext" href="devdocs/cartesian.html">Base.Cartesian</a></li><li><a class="toctext" href="devdocs/meta.html">Talking to the compiler (the <code>:meta</code> mechanism)</a></li><li><a class="toctext" href="devdocs/subarrays.html">SubArrays</a></li><li><a class="toctext" href="devdocs/sysimg.html">System Image Building</a></li><li><a class="toctext" href="devdocs/llvm.html">Working with LLVM</a></li><li><a class="toctext" href="devdocs/stdio.html">printf() and stdio in the Julia runtime</a></li><li><a class="toctext" href="devdocs/boundscheck.html">Bounds checking</a></li><li><a class="toctext" href="devdocs/locks.html">Proper maintenance and care of multi-threading locks</a></li><li><a class="toctext" href="devdocs/offset-arrays.html">Arrays with custom indices</a></li><li><a class="toctext" href="devdocs/libgit2.html">Base.LibGit2</a></li><li><a class="toctext" href="devdocs/require.html">Module loading</a></li></ul></li><li><span class="toctext">Developing/debugging Julia's C code</span><ul><li><a class="toctext" href="devdocs/backtraces.html">Reporting and analyzing crashes (segfaults)</a></li><li><a class="toctext" href="devdocs/debuggingtips.html">gdb debugging tips</a></li><li><a class="toctext" href="devdocs/valgrind.html">Using Valgrind with Julia</a></li><li><a class="toctext" href="devdocs/sanitizers.html">Sanitizer support</a></li></ul></li></ul></li></ul></nav><article id="docs"><header><nav><ul><li><a href="index.html">Home</a></li></ul><a class="edit-page" 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Functions</a></p></li><li><p><a href="manual/complex-and-rational-numbers.html#Complex-and-Rational-Numbers-1">Complex and Rational Numbers</a></p></li><li><p><a href="manual/strings.html#man-strings-1">Strings</a></p></li><li><p><a href="manual/functions.html#man-functions-1">Functions</a></p></li><li><p><a href="manual/control-flow.html#Control-Flow-1">Control Flow</a></p></li><li><p><a href="manual/variables-and-scoping.html#scope-of-variables-1">Scope of Variables</a></p></li><li><p><a href="manual/types.html#man-types-1">Types</a></p></li><li><p><a href="manual/methods.html#Methods-1">Methods</a></p></li><li><p><a href="manual/constructors.html#man-constructors-1">Constructors</a></p></li><li><p><a href="manual/conversion-and-promotion.html#conversion-and-promotion-1">Conversion and Promotion</a></p></li><li><p><a href="manual/interfaces.html#Interfaces-1">Interfaces</a></p></li><li><p><a href="manual/modules.html#modules-1">Modules</a></p></li><li><p><a 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Operating System Variation</a></p></li><li><p><a href="manual/environment-variables.html#Environment-Variables-1">Environment Variables</a></p></li><li><p><a href="manual/interacting-with-julia.html#Interacting-With-Julia-1">Interacting With Julia</a></p></li><li><p><a href="manual/embedding.html#Embedding-Julia-1">Embedding Julia</a></p></li><li><p><a href="manual/packages.html#Packages-1">Packages</a></p></li><li><p><a href="manual/profile.html#Profiling-1">Profiling</a></p></li><li><p><a href="manual/stacktraces.html#Stack-Traces-1">Stack Traces</a></p></li><li><p><a href="manual/performance-tips.html#man-performance-tips-1">Performance Tips</a></p></li><li><p><a href="manual/workflow-tips.html#man-workflow-tips-1">Workflow Tips</a></p></li><li><p><a href="manual/style-guide.html#Style-Guide-1">Style Guide</a></p></li><li><p><a href="manual/faq.html#Frequently-Asked-Questions-1">Frequently Asked Questions</a></p></li><li><p><a 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Algebra</a></p></li><li><p><a href="stdlib/constants.html#lib-constants-1">Constants</a></p></li><li><p><a href="stdlib/file.html#Filesystem-1">Filesystem</a></p></li><li><p><a href="stdlib/io-network.html#I/O-and-Network-1">I/O and Network</a></p></li><li><p><a href="stdlib/punctuation.html#Punctuation-1">Punctuation</a></p></li><li><p><a href="stdlib/sort.html#Sorting-and-Related-Functions-1">Sorting and Related Functions</a></p></li><li><p><a href="stdlib/pkg.html#Package-Manager-Functions-1">Package Manager Functions</a></p></li><li><p><a href="stdlib/dates.html#stdlib-dates-1">Dates and Time</a></p></li><li><p><a href="stdlib/iterators.html#Iteration-utilities-1">Iteration utilities</a></p></li><li><p><a href="stdlib/test.html#Unit-Testing-1">Unit Testing</a></p></li><li><p><a href="stdlib/c.html#C-Interface-1">C Interface</a></p></li><li><p><a href="stdlib/libc.html#C-Standard-Library-1">C Standard Library</a></p></li><li><p><a href="stdlib/libdl.html#Dynamic-Linker-1">Dynamic Linker</a></p></li><li><p><a href="stdlib/profile.html#lib-profiling-1">Profiling</a></p></li><li><p><a href="stdlib/stacktraces.html#StackTraces-1">StackTraces</a></p></li><li><p><a href="stdlib/simd-types.html#SIMD-Support-1">SIMD Support</a></p></li></ul><h2><a class="nav-anchor" id="Developer-Documentation-1" href="#Developer-Documentation-1">Developer Documentation</a></h2><ul><li><p><a href="devdocs/reflection.html#Reflection-and-introspection-1">Reflection and introspection</a></p></li><li><p>Documentation of Julia's Internals</p><ul><li><p><a href="devdocs/init.html#Initialization-of-the-Julia-runtime-1">Initialization of the Julia runtime</a></p></li><li><p><a href="devdocs/ast.html#Julia-ASTs-1">Julia ASTs</a></p></li><li><p><a href="devdocs/types.html#More-about-types-1">More about types</a></p></li><li><p><a href="devdocs/object.html#Memory-layout-of-Julia-Objects-1">Memory layout of Julia Objects</a></p></li><li><p><a href="devdocs/eval.html#Eval-of-Julia-code-1">Eval of Julia code</a></p></li><li><p><a href="devdocs/callconv.html#Calling-Conventions-1">Calling Conventions</a></p></li><li><p><a href="devdocs/compiler.html#High-level-Overview-of-the-Native-Code-Generation-Process-1">High-level Overview of the Native-Code Generation Process</a></p></li><li><p><a href="devdocs/functions.html#Julia-Functions-1">Julia Functions</a></p></li><li><p><a href="devdocs/cartesian.html#Base.Cartesian-1">Base.Cartesian</a></p></li><li><p><a href="devdocs/meta.html#Talking-to-the-compiler-(the-:meta-mechanism)-1">Talking to the compiler (the <code>:meta</code> mechanism)</a></p></li><li><p><a href="devdocs/subarrays.html#SubArrays-1">SubArrays</a></p></li><li><p><a href="devdocs/sysimg.html#System-Image-Building-1">System Image Building</a></p></li><li><p><a href="devdocs/llvm.html#Working-with-LLVM-1">Working with LLVM</a></p></li><li><p><a href="devdocs/stdio.html#printf()-and-stdio-in-the-Julia-runtime-1">printf() and stdio in the Julia runtime</a></p></li><li><p><a href="devdocs/boundscheck.html#Bounds-checking-1">Bounds checking</a></p></li><li><p><a href="devdocs/locks.html#Proper-maintenance-and-care-of-multi-threading-locks-1">Proper maintenance and care of multi-threading locks</a></p></li><li><p><a href="devdocs/offset-arrays.html#Arrays-with-custom-indices-1">Arrays with custom indices</a></p></li><li><p><a href="devdocs/libgit2.html#Base.LibGit2-1">Base.LibGit2</a></p></li><li><p><a href="devdocs/require.html#Module-loading-1">Module loading</a></p></li></ul></li><li><p>Developing/debugging Julia's C code</p><ul><li><p><a href="devdocs/backtraces.html#Reporting-and-analyzing-crashes-(segfaults)-1">Reporting and analyzing crashes (segfaults)</a></p></li><li><p><a href="devdocs/debuggingtips.html#gdb-debugging-tips-1">gdb debugging tips</a></p></li><li><p><a href="devdocs/valgrind.html#Using-Valgrind-with-Julia-1">Using Valgrind with Julia</a></p></li><li><p><a 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