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{"documenter":{"julia_version":"1.10.0","generation_timestamp":"2024-02-02T12:29:18","documenter_version":"1.2.1"}}
{"documenter":{"julia_version":"1.10.0","generation_timestamp":"2024-02-02T13:38:15","documenter_version":"1.2.1"}}
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<!DOCTYPE html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Julia Set · OhMyThreads.jl</title><meta name="title" content="Julia Set · OhMyThreads.jl"/><meta property="og:title" content="Julia Set · OhMyThreads.jl"/><meta property="twitter:title" content="Julia Set · OhMyThreads.jl"/><meta name="description" content="Documentation for OhMyThreads.jl."/><meta property="og:description" content="Documentation for OhMyThreads.jl."/><meta property="twitter:description" content="Documentation for OhMyThreads.jl."/><script data-outdated-warner src="../../../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" 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data-theme-name="documenter-light" data-theme-primary/><script src="../../../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../../../">OhMyThreads.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><a class="tocitem" href="../../../">OhMyThreads</a></li><li><input class="collapse-toggle" id="menuitem-2" type="checkbox" checked/><label class="tocitem" for="menuitem-2"><span class="docs-label">Examples</span><i class="docs-chevron"></i></label><ul class="collapsed"><li><a class="tocitem" href="../../mc/mc/">Parallel Monte Carlo</a></li><li class="is-active"><a class="tocitem" href>Julia Set</a><ul class="internal"><li><a class="tocitem" href="#Sequential-computation"><span>Sequential computation</span></a></li><li><a class="tocitem" href="#Parallelization"><span>Parallelization</span></a></li><li><a class="tocitem" href="#Benchmark"><span>Benchmark</span></a></li></ul></li></ul></li><li><input class="collapse-toggle" id="menuitem-3" type="checkbox"/><label class="tocitem" for="menuitem-3"><span class="docs-label">References</span><i class="docs-chevron"></i></label><ul class="collapsed"><li><a class="tocitem" href="../../../refs/api/">Public API</a></li><li><a class="tocitem" href="../../../refs/internal/">Internal</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Examples</a></li><li class="is-active"><a href>Julia Set</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Julia Set</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/JuliaFolds2/OhMyThreads.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/JuliaFolds2/OhMyThreads.jl/blob/master/docs/src/examples/juliaset/juliaset.jl#" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Julia-Set"><a class="docs-heading-anchor" href="#Julia-Set">Julia Set</a><a id="Julia-Set-1"></a><a class="docs-heading-anchor-permalink" href="#Julia-Set" title="Permalink"></a></h1><p>In this example, we will compute an image of the <a href="https://en.wikipedia.org/wiki/Julia_set">Julia set</a> in parallel. We will explore the <code>schedule</code> and <code>nchunks</code> options that can be used to get load balancing.</p><p>The value of a single pixel of the Julia set, which corresponds to a point in the complex number plane, can be computed by the following iteration procedure.</p><pre><code class="language-julia hljs">function _compute_pixel(i, j, n; max_iter = 255, c = -0.79 + 0.15 * im)
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Julia Set · OhMyThreads.jl</title><meta name="title" content="Julia Set · OhMyThreads.jl"/><meta property="og:title" content="Julia Set · OhMyThreads.jl"/><meta property="twitter:title" content="Julia Set · OhMyThreads.jl"/><meta name="description" content="Documentation for OhMyThreads.jl."/><meta property="og:description" content="Documentation for OhMyThreads.jl."/><meta property="twitter:description" content="Documentation for OhMyThreads.jl."/><script data-outdated-warner src="../../../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="../../.."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../../../assets/documenter.js"></script><script src="../../../search_index.js"></script><script src="../../../siteinfo.js"></script><script src="../../../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../../../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../../../">OhMyThreads.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><a class="tocitem" href="../../../">OhMyThreads</a></li><li><input class="collapse-toggle" id="menuitem-2" type="checkbox" checked/><label class="tocitem" for="menuitem-2"><span class="docs-label">Examples</span><i class="docs-chevron"></i></label><ul class="collapsed"><li><a class="tocitem" href="../../mc/mc/">Parallel Monte Carlo</a></li><li class="is-active"><a class="tocitem" href>Julia Set</a><ul class="internal"><li><a class="tocitem" href="#Sequential-computation"><span>Sequential computation</span></a></li><li><a class="tocitem" href="#Parallelization"><span>Parallelization</span></a></li><li><a class="tocitem" href="#Benchmark"><span>Benchmark</span></a></li></ul></li></ul></li><li><a class="tocitem" href="../../../translation/">Translation Guide</a></li><li><input class="collapse-toggle" id="menuitem-4" type="checkbox"/><label class="tocitem" for="menuitem-4"><span class="docs-label">References</span><i class="docs-chevron"></i></label><ul class="collapsed"><li><a class="tocitem" href="../../../refs/api/">Public API</a></li><li><a class="tocitem" href="../../../refs/internal/">Internal</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Examples</a></li><li class="is-active"><a href>Julia Set</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Julia Set</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/JuliaFolds2/OhMyThreads.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/JuliaFolds2/OhMyThreads.jl/blob/master/docs/src/examples/juliaset/juliaset.jl#" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Julia-Set"><a class="docs-heading-anchor" href="#Julia-Set">Julia Set</a><a id="Julia-Set-1"></a><a class="docs-heading-anchor-permalink" href="#Julia-Set" title="Permalink"></a></h1><p>In this example, we will compute an image of the <a href="https://en.wikipedia.org/wiki/Julia_set">Julia set</a> in parallel. We will explore the <code>schedule</code> and <code>nchunks</code> options that can be used to get load balancing.</p><p>The value of a single pixel of the Julia set, which corresponds to a point in the complex number plane, can be computed by the following iteration procedure.</p><pre><code class="language-julia hljs">function _compute_pixel(i, j, n; max_iter = 255, c = -0.79 + 0.15 * im)
x = -2.0 + (j - 1) * 4.0 / (n - 1)
y = -2.0 + (i - 1) * 4.0 / (n - 1)

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63.707 ms (39 allocations: 3.30 KiB)
</code></pre><p>As hoped, the parallel implementation is faster. But can we improve the performance further?</p><h3 id="Tuning-nchunks"><a class="docs-heading-anchor" href="#Tuning-nchunks">Tuning <code>nchunks</code></a><a id="Tuning-nchunks-1"></a><a class="docs-heading-anchor-permalink" href="#Tuning-nchunks" title="Permalink"></a></h3><p>As stated above, the per-pixel computation is non-uniform. Hence, we might benefit from load balancing. The simplest way to get it is to increase <code>nchunks</code> to a value larger than <code>nthreads</code>. This divides the overall workload into smaller tasks than can be dynamically distributed among threads (by Julia&#39;s scheduler) to balance the per-thread load.</p><pre><code class="language-julia hljs">@btime compute_juliaset_parallel!($img; schedule=:dynamic, nchunks=N) samples=10 evals=3;</code></pre><pre><code class="nohighlight hljs"> 32.000 ms (12013 allocations: 1.14 MiB)
</code></pre><p>Note that if we opt out of dynamic scheduling and set <code>schedule=:static</code>, this strategy doesn&#39;t help anymore (because chunks are naively distributed up front).</p><pre><code class="language-julia hljs">@btime compute_juliaset_parallel!($img; schedule=:static, nchunks=N) samples=10 evals=3;</code></pre><pre><code class="nohighlight hljs"> 63.439 ms (42 allocations: 3.37 KiB)
</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../mc/mc/">« Parallel Monte Carlo</a><a class="docs-footer-nextpage" href="../../../refs/api/">Public API »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Friday 2 February 2024 12:29">Friday 2 February 2024</span>. Using Julia version 1.10.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../mc/mc/">« Parallel Monte Carlo</a><a class="docs-footer-nextpage" href="../../../translation/">Translation Guide »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Friday 2 February 2024 13:38">Friday 2 February 2024</span>. Using Julia version 1.10.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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