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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="Returns information about a fixed point that is required by [`EccChip`]."><meta name="keywords" content="rust, rustlang, rust-lang, FixedPoint"><title>FixedPoint in halo2_gadgets::ecc::chip - 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" type="text/css" href="../../../normalize.css"><link rel="stylesheet" type="text/css" href="../../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../../../ayu.css" disabled><link rel="stylesheet" type="text/css" href="../../../dark.css" disabled><link rel="stylesheet" type="text/css" href="../../../light.css" id="themeStyle"><script id="default-settings" ></script><script src="../../../storage.js"></script><script src="../../../crates.js"></script><script defer src="../../../main.js"></script>
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</head><body class="rustdoc trait"><!--[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_gadgets/index.html"><div class="logo-container"><img class="rust-logo" src="../../../rust-logo.svg" alt="logo"></div>
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<nav class="sidebar"><a class="sidebar-logo" href="../../../halo2_gadgets/index.html"><div class="logo-container"><img class="rust-logo" src="../../../rust-logo.svg" alt="logo"></div>
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</a><h2 class="location"><a href="#">FixedPoint</a></h2><div class="sidebar-elems"><section><div class="block"><h3 class="sidebar-title"><a href="#required-associated-types">Required Associated Types</a></h3><ul><li><a href="#associatedtype.FixedScalarKind">FixedScalarKind</a></li></ul></div><div class="block"><h3 class="sidebar-title"><a href="#required-methods">Required Methods</a></h3><ul><li><a href="#tymethod.generator">generator</a></li><li><a href="#tymethod.u">u</a></li><li><a href="#tymethod.z">z</a></li></ul></div><div class="block"><h3 class="sidebar-title"><a href="#provided-methods">Provided Methods</a></h3><ul><li><a href="#method.lagrange_coeffs">lagrange_coeffs</a></li></ul></div><div class="block"><h3 class="sidebar-title"><a href="#implementors">Implementors</a></h3></div></section><h2 class="location"><a href="index.html">In halo2_gadgets::ecc::chip</a></h2><div id="sidebar-vars" data-name="FixedPoint" data-ty="trait" data-relpath=""></div><script defer src="sidebar-items.js"></script></div></nav><main><div class="width-limiter"><div class="sub-container"><a class="sub-logo-container" href="../../../halo2_gadgets/index.html"><img class="rust-logo" src="../../../rust-logo.svg" alt="logo"></a><nav class="sub"><div class="theme-picker hidden"><button id="theme-picker" aria-label="Pick another theme!" aria-haspopup="menu" title="themes"><img width="22" height="22" alt="Pick another theme!" src="../../../brush.svg"></button><div id="theme-choices" role="menu"></div></div><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"><button type="button" id="help-button" title="help">?</button><a id="settings-menu" href="../../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../../wheel.svg"></a></div></form></nav></div><section id="main-content" class="content"><div class="main-heading">
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<h1 class="fqn"><span class="in-band">Trait <a href="../../index.html">halo2_gadgets</a>::<wbr><a href="../index.html">ecc</a>::<wbr><a href="index.html">chip</a>::<wbr><a class="trait" href="#">FixedPoint</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_gadgets/ecc/chip.rs.html#205-222">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 trait"><code>pub trait FixedPoint<C: CurveAffine>: <a class="trait" href="https://doc.rust-lang.org/nightly/core/fmt/trait.Debug.html" title="trait core::fmt::Debug">Debug</a> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/cmp/trait.Eq.html" title="trait core::cmp::Eq">Eq</a> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/clone/trait.Clone.html" title="trait core::clone::Clone">Clone</a> {
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type <a href="#associatedtype.FixedScalarKind" class="associatedtype">FixedScalarKind</a>: <a class="trait" href="trait.FixedScalarKind.html" title="trait halo2_gadgets::ecc::chip::FixedScalarKind">FixedScalarKind</a>;
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fn <a href="#tymethod.generator" class="fnname">generator</a>(&self) -> C;
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<span class="item-spacer"></span> fn <a href="#tymethod.u" class="fnname">u</a>(&self) -> <a class="struct" href="https://doc.rust-lang.org/nightly/alloc/vec/struct.Vec.html" title="struct alloc::vec::Vec">Vec</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.array.html">[</a><a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.array.html">[</a><a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u8.html">u8</a><a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.array.html">; 32]</a><a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.array.html">; 8]</a>><span class="notable-traits"><span class="notable-traits-tooltip">ⓘ<span class="notable-traits-tooltiptext"><span class="docblock"><span class="notable">Notable traits for <a class="struct" href="https://doc.rust-lang.org/nightly/alloc/vec/struct.Vec.html" title="struct alloc::vec::Vec">Vec</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u8.html">u8</a>, A></span><code class="content"><span class="where fmt-newline">impl<A> <a class="trait" href="https://doc.rust-lang.org/nightly/std/io/trait.Write.html" title="trait std::io::Write">Write</a> for <a class="struct" href="https://doc.rust-lang.org/nightly/alloc/vec/struct.Vec.html" title="struct alloc::vec::Vec">Vec</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u8.html">u8</a>, A> <span class="where fmt-newline">where<br> A: <a class="trait" href="https://doc.rust-lang.org/nightly/core/alloc/trait.Allocator.html" title="trait core::alloc::Allocator">Allocator</a>, </span></span></code></span></span></span></span>;
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<span class="item-spacer"></span> fn <a href="#tymethod.z" class="fnname">z</a>(&self) -> <a class="struct" href="https://doc.rust-lang.org/nightly/alloc/vec/struct.Vec.html" title="struct alloc::vec::Vec">Vec</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u64.html">u64</a>><span class="notable-traits"><span class="notable-traits-tooltip">ⓘ<span class="notable-traits-tooltiptext"><span class="docblock"><span class="notable">Notable traits for <a class="struct" href="https://doc.rust-lang.org/nightly/alloc/vec/struct.Vec.html" title="struct alloc::vec::Vec">Vec</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u8.html">u8</a>, A></span><code class="content"><span class="where fmt-newline">impl<A> <a class="trait" href="https://doc.rust-lang.org/nightly/std/io/trait.Write.html" title="trait std::io::Write">Write</a> for <a class="struct" href="https://doc.rust-lang.org/nightly/alloc/vec/struct.Vec.html" title="struct alloc::vec::Vec">Vec</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u8.html">u8</a>, A> <span class="where fmt-newline">where<br> A: <a class="trait" href="https://doc.rust-lang.org/nightly/core/alloc/trait.Allocator.html" title="trait core::alloc::Allocator">Allocator</a>, </span></span></code></span></span></span></span>;
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fn <a href="#method.lagrange_coeffs" class="fnname">lagrange_coeffs</a>(&self) -> <a class="struct" href="https://doc.rust-lang.org/nightly/alloc/vec/struct.Vec.html" title="struct alloc::vec::Vec">Vec</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.array.html">[</a>C::Base<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.array.html">; 8]</a>><span class="notable-traits"><span class="notable-traits-tooltip">ⓘ<span class="notable-traits-tooltiptext"><span class="docblock"><span class="notable">Notable traits for <a class="struct" href="https://doc.rust-lang.org/nightly/alloc/vec/struct.Vec.html" title="struct alloc::vec::Vec">Vec</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u8.html">u8</a>, A></span><code class="content"><span class="where fmt-newline">impl<A> <a class="trait" href="https://doc.rust-lang.org/nightly/std/io/trait.Write.html" title="trait std::io::Write">Write</a> for <a class="struct" href="https://doc.rust-lang.org/nightly/alloc/vec/struct.Vec.html" title="struct alloc::vec::Vec">Vec</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u8.html">u8</a>, A> <span class="where fmt-newline">where<br> A: <a class="trait" href="https://doc.rust-lang.org/nightly/core/alloc/trait.Allocator.html" title="trait core::alloc::Allocator">Allocator</a>, </span></span></code></span></span></span></span> { ... }
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}</code></pre></div><details class="rustdoc-toggle top-doc" open><summary class="hideme"><span>Expand description</span></summary><div class="docblock"><p>Returns information about a fixed point that is required by <a href="struct.EccChip.html" title="EccChip"><code>EccChip</code></a>.</p>
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<p>For each window required by <code>Self::FixedScalarKind</code>, $z$ is a field element such that for
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each point $(x, y)$ in the window:</p>
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<ul>
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<li>$z + y = u^2$ (some square in the field); and</li>
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<li>$z - y$ is not a square.</li>
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</ul>
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<p>TODO: When associated consts can be used as const generics, introduce a
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<code>const NUM_WINDOWS: usize</code> associated const, and return <code>NUM_WINDOWS</code>-sized
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arrays instead of <code>Vec</code>s.</p>
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</div></details><h2 id="required-associated-types" class="small-section-header">Required Associated Types<a href="#required-associated-types" class="anchor"></a></h2><div class="methods"><details class="rustdoc-toggle" open><summary><div id="associatedtype.FixedScalarKind" class="method has-srclink"><div class="rightside"><a class="srclink" href="../../../src/halo2_gadgets/ecc/chip.rs.html#207">source</a></div><h4 class="code-header">type <a href="#associatedtype.FixedScalarKind" class="associatedtype">FixedScalarKind</a>: <a class="trait" href="trait.FixedScalarKind.html" title="trait halo2_gadgets::ecc::chip::FixedScalarKind">FixedScalarKind</a></h4></div></summary><div class="docblock"><p>The kind of scalar that this fixed point can be multiplied by.</p>
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</div></details></div><h2 id="required-methods" class="small-section-header">Required Methods<a href="#required-methods" class="anchor"></a></h2><div class="methods"><details class="rustdoc-toggle" open><summary><div id="tymethod.generator" class="method has-srclink"><div class="rightside"><a class="srclink" href="../../../src/halo2_gadgets/ecc/chip.rs.html#210">source</a></div><h4 class="code-header">fn <a href="#tymethod.generator" class="fnname">generator</a>(&self) -> C</h4></div></summary><div class="docblock"><p>Returns the generator for this fixed point.</p>
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</div></details><details class="rustdoc-toggle" open><summary><div id="tymethod.u" class="method has-srclink"><div class="rightside"><a class="srclink" href="../../../src/halo2_gadgets/ecc/chip.rs.html#213">source</a></div><h4 class="code-header">fn <a href="#tymethod.u" class="fnname">u</a>(&self) -> <a class="struct" href="https://doc.rust-lang.org/nightly/alloc/vec/struct.Vec.html" title="struct alloc::vec::Vec">Vec</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.array.html">[</a><a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.array.html">[</a><a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u8.html">u8</a><a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.array.html">; 32]</a><a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.array.html">; 8]</a>><span class="notable-traits"><span class="notable-traits-tooltip">ⓘ<span class="notable-traits-tooltiptext"><span class="docblock"><span class="notable">Notable traits for <a class="struct" href="https://doc.rust-lang.org/nightly/alloc/vec/struct.Vec.html" title="struct alloc::vec::Vec">Vec</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u8.html">u8</a>, A></span><code class="content"><span class="where fmt-newline">impl<A> <a class="trait" href="https://doc.rust-lang.org/nightly/std/io/trait.Write.html" title="trait std::io::Write">Write</a> for <a class="struct" href="https://doc.rust-lang.org/nightly/alloc/vec/struct.Vec.html" title="struct alloc::vec::Vec">Vec</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u8.html">u8</a>, A> <span class="where fmt-newline">where<br> A: <a class="trait" href="https://doc.rust-lang.org/nightly/core/alloc/trait.Allocator.html" title="trait core::alloc::Allocator">Allocator</a>, </span></span></code></span></span></span></span></h4></div></summary><div class="docblock"><p>Returns the $u$ values for this fixed point.</p>
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</div></details><details class="rustdoc-toggle" open><summary><div id="tymethod.z" class="method has-srclink"><div class="rightside"><a class="srclink" href="../../../src/halo2_gadgets/ecc/chip.rs.html#216">source</a></div><h4 class="code-header">fn <a href="#tymethod.z" class="fnname">z</a>(&self) -> <a class="struct" href="https://doc.rust-lang.org/nightly/alloc/vec/struct.Vec.html" title="struct alloc::vec::Vec">Vec</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u64.html">u64</a>><span class="notable-traits"><span class="notable-traits-tooltip">ⓘ<span class="notable-traits-tooltiptext"><span class="docblock"><span class="notable">Notable traits for <a class="struct" href="https://doc.rust-lang.org/nightly/alloc/vec/struct.Vec.html" title="struct alloc::vec::Vec">Vec</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u8.html">u8</a>, A></span><code class="content"><span class="where fmt-newline">impl<A> <a class="trait" href="https://doc.rust-lang.org/nightly/std/io/trait.Write.html" title="trait std::io::Write">Write</a> for <a class="struct" href="https://doc.rust-lang.org/nightly/alloc/vec/struct.Vec.html" title="struct alloc::vec::Vec">Vec</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u8.html">u8</a>, A> <span class="where fmt-newline">where<br> A: <a class="trait" href="https://doc.rust-lang.org/nightly/core/alloc/trait.Allocator.html" title="trait core::alloc::Allocator">Allocator</a>, </span></span></code></span></span></span></span></h4></div></summary><div class="docblock"><p>Returns the $z$ value for this fixed point.</p>
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</div></details></div><h2 id="provided-methods" class="small-section-header">Provided Methods<a href="#provided-methods" class="anchor"></a></h2><div class="methods"><details class="rustdoc-toggle" open><summary><div id="method.lagrange_coeffs" class="method has-srclink"><div class="rightside"><a class="srclink" href="../../../src/halo2_gadgets/ecc/chip.rs.html#219-221">source</a></div><h4 class="code-header">fn <a href="#method.lagrange_coeffs" class="fnname">lagrange_coeffs</a>(&self) -> <a class="struct" href="https://doc.rust-lang.org/nightly/alloc/vec/struct.Vec.html" title="struct alloc::vec::Vec">Vec</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.array.html">[</a>C::Base<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.array.html">; 8]</a>><span class="notable-traits"><span class="notable-traits-tooltip">ⓘ<span class="notable-traits-tooltiptext"><span class="docblock"><span class="notable">Notable traits for <a class="struct" href="https://doc.rust-lang.org/nightly/alloc/vec/struct.Vec.html" title="struct alloc::vec::Vec">Vec</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u8.html">u8</a>, A></span><code class="content"><span class="where fmt-newline">impl<A> <a class="trait" href="https://doc.rust-lang.org/nightly/std/io/trait.Write.html" title="trait std::io::Write">Write</a> for <a class="struct" href="https://doc.rust-lang.org/nightly/alloc/vec/struct.Vec.html" title="struct alloc::vec::Vec">Vec</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u8.html">u8</a>, A> <span class="where fmt-newline">where<br> A: <a class="trait" href="https://doc.rust-lang.org/nightly/core/alloc/trait.Allocator.html" title="trait core::alloc::Allocator">Allocator</a>, </span></span></code></span></span></span></span></h4></div></summary><div class="docblock"><p>Returns the Lagrange coefficients for this fixed point.</p>
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</div></details></div><h2 id="implementors" class="small-section-header">Implementors<a href="#implementors" class="anchor"></a></h2><div class="item-list" id="implementors-list"></div><script type="text/javascript" src="../../../implementors/halo2_gadgets/ecc/chip/trait.FixedPoint.js" data-ignore-extern-crates="" async></script></section></div></main><div id="rustdoc-vars" data-root-path="../../../" data-current-crate="halo2_gadgets" data-themes="ayu,dark,light" data-resource-suffix="" data-rustdoc-version="1.62.0-nightly (88860d547 2022-05-09)" ></div>
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