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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"><meta name="generator" content="rustdoc"><meta name="description" content="Performs a radix-$2$ Fast-Fourier Transformation (FFT) on a vector of size $n = 2^k$, when provided `log_n` = $k$ and an element of multiplicative order $n$ called `omega` ($\omega$). The result is that the vector `a`, when interpreted as the coefficients of a polynomial of degree $n - 1$, is transformed into the evaluations of this polynomial at each of the $n$ distinct powers of $\omega$. This transformation is invertible by providing $\omega^{-1}$ in place of $\omega$ and dividing each resulting field element by $n$."><meta name="keywords" content="rust, rustlang, rust-lang, best_fft"><title>best_fft in halo2_proofs::arithmetic - Rust</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceSerif4-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../FiraSans-Regular.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../FiraSans-Medium.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceCodePro-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceSerif4-Bold.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceCodePro-Semibold.ttf.woff2"><link rel="stylesheet" href="../../normalize.css"><link rel="stylesheet" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" href="../../ayu.css" disabled><link rel="stylesheet" href="../../dark.css" disabled><link rel="stylesheet" href="../../light.css" id="themeStyle"><script id="default-settings" ></script><script src="../../storage.js"></script><script defer src="sidebar-items.js"></script><script defer src="../../main.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="alternate icon" type="image/png" href="../../favicon-16x16.png"><link rel="alternate icon" type="image/png" href="../../favicon-32x32.png"><link rel="icon" type="image/svg+xml" href="../../favicon.svg"><link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.10.0/dist/katex.min.css" integrity="sha384-9eLZqc9ds8eNjO3TmqPeYcDj8n+Qfa4nuSiGYa6DjLNcv9BtN69ZIulL9+8CqC9Y" crossorigin="anonymous">
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</head><body class="rustdoc fn"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="mobile-topbar"><button class="sidebar-menu-toggle">☰</button><a class="sidebar-logo" href="../../halo2_proofs/index.html"><div class="logo-container"><img class="rust-logo" src="../../rust-logo.svg" alt="logo"></div></a><h2 class="location"></h2></nav><nav class="sidebar"><a class="sidebar-logo" href="../../halo2_proofs/index.html"><div class="logo-container"><img class="rust-logo" src="../../rust-logo.svg" alt="logo"></div></a><div class="sidebar-elems"><h2 class="location"><a href="index.html">In halo2_proofs::arithmetic</a></h2></div></nav><main><div class="width-limiter"><div class="sub-container"><a class="sub-logo-container" href="../../halo2_proofs/index.html"><img class="rust-logo" src="../../rust-logo.svg" alt="logo"></a><nav class="sub"><form class="search-form"><div class="search-container"><span></span><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" title="help" tabindex="-1"><button type="button">?</button></div><div id="settings-menu" tabindex="-1"><a href="../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../wheel.svg"></a></div></div></form></nav></div><section id="main-content" class="content"><div class="main-heading"><h1 class="fqn"><span class="in-band">Function <a href="../index.html">halo2_proofs</a>::<wbr><a href="index.html">arithmetic</a>::<wbr><a class="fn" href="#">best_fft</a><button id="copy-path" onclick="copy_path(this)" title="Copy item path to clipboard"><img src="../../clipboard.svg" width="19" height="18" alt="Copy item path"></button></span></h1><span class="out-of-band"><a class="srclink" href="../../src/halo2_proofs/arithmetic.rs.html#171-234">source</a> · <a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class="inner">−</span>]</a></span></div><div class="docblock item-decl"><pre class="rust fn"><code>pub fn best_fft<G: <a class="trait" href="trait.Group.html" title="trait halo2_proofs::arithmetic::Group">Group</a>>(a: &mut <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.slice.html">[G]</a>, omega: G::<a class="associatedtype" href="trait.Group.html#associatedtype.Scalar" title="type halo2_proofs::arithmetic::Group::Scalar">Scalar</a>, log_n: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u32.html">u32</a>)</code></pre></div><details class="rustdoc-toggle top-doc" open><summary class="hideme"><span>Expand description</span></summary><div class="docblock"><p>Performs a radix-$2$ Fast-Fourier Transformation (FFT) on a vector of size
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$n = 2^k$, when provided <code>log_n</code> = $k$ and an element of multiplicative
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order $n$ called <code>omega</code> ($\omega$). The result is that the vector <code>a</code>, when
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interpreted as the coefficients of a polynomial of degree $n - 1$, is
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transformed into the evaluations of this polynomial at each of the $n$
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distinct powers of $\omega$. This transformation is invertible by providing
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$\omega^{-1}$ in place of $\omega$ and dividing each resulting field element
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by $n$.</p>
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<p>This will use multithreading if beneficial.</p>
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