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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`."><title>FixedPoint in halo2_gadgets::ecc::chip - Rust</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceSerif4-Regular-46f98efaafac5295.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/FiraSans-Regular-018c141bf0843ffd.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/FiraSans-Medium-8f9a781e4970d388.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceCodePro-Regular-562dcc5011b6de7d.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceSerif4-Bold-a2c9cd1067f8b328.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceCodePro-Semibold-d899c5a5c4aeb14a.ttf.woff2"><link rel="stylesheet" href="../../../static.files/normalize-76eba96aa4d2e634.css"><link rel="stylesheet" href="../../../static.files/rustdoc-fa3bb1812debf86c.css"><meta name="rustdoc-vars" data-root-path="../../../" data-static-root-path="../../../static.files/" data-current-crate="halo2_gadgets" data-themes="" data-resource-suffix="" data-rustdoc-version="1.75.0-nightly (2bbb61989 2023-10-04)" data-channel="nightly" data-search-js="search-8be46b629f5f14a8.js" data-settings-js="settings-74424d7eec62a23e.js" ><script src="../../../static.files/storage-fec3eaa3851e447d.js"></script><script defer src="sidebar-items.js"></script><script defer src="../../../static.files/main-c5bd66d33317d69f.js"></script><noscript><link rel="stylesheet" href="../../../static.files/noscript-5d8b3c7633ad77ba.css"></noscript><link rel="alternate icon" type="image/png" href="../../../static.files/favicon-16x16-8b506e7a72182f1c.png"><link rel="alternate icon" type="image/png" href="../../../static.files/favicon-32x32-422f7d1d52889060.png"><link rel="icon" type="image/svg+xml" href="../../../static.files/favicon-2c020d218678b618.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 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="logo-container" href="../../../halo2_gadgets/index.html"><img class="rust-logo" src="../../../static.files/rust-logo-151179464ae7ed46.svg" alt="logo"></a></nav><nav class="sidebar"><a class="logo-container" href="../../../halo2_gadgets/index.html"><img class="rust-logo" src="../../../static.files/rust-logo-151179464ae7ed46.svg" alt="logo"></a><h2 class="location"><a href="#">FixedPoint</a></h2><div class="sidebar-elems"><section><h3><a href="#required-associated-types">Required Associated Types</a></h3><ul class="block"><li><a href="#associatedtype.FixedScalarKind">FixedScalarKind</a></li></ul><h3><a href="#required-methods">Required Methods</a></h3><ul class="block"><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><h3><a href="#provided-methods">Provided Methods</a></h3><ul class="block"><li><a href="#method.lagrange_coeffs">lagrange_coeffs</a></li></ul><h3><a href="#implementors">Implementors</a></h3></section><h2><a href="index.html">In halo2_gadgets::ecc::chip</a></h2></div></nav><main><div class="width-limiter"><nav class="sub"><form class="search-form"><span></span><input class="search-input" name="search" aria-label="Run search in the documentation" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" title="help" tabindex="-1"><a href="../../../help.html">?</a></div><div id="settings-menu" tabindex="-1"><a href="../../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../../static.files/wheel-7b819b6101059cd0.svg"></a></div></form></nav><section id="main-content" class="content"><div class="main-heading"><h1>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" title="Copy item path to clipboard"><img src="../../../static.files/clipboard-7571035ce49a181d.svg" width="19" height="18" alt="Copy item path"></button></h1><span class="out-of-band"><a class="src" href="../../../src/halo2_gadgets/ecc/chip.rs.html#209-226">source</a> · <button id="toggle-all-docs" title="collapse all docs">[<span>−</span>]</button></span></div><pre class="rust item-decl"><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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// Required methods
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fn <a href="#tymethod.generator" class="fn">generator</a>(&self) -> C;
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<span class="item-spacer"></span> fn <a href="#tymethod.u" class="fn">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><[<C::Base as PrimeField>::Repr; <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.array.html">8</a>]>;
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<span class="item-spacer"></span> fn <a href="#tymethod.z" class="fn">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>>;
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// Provided method
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fn <a href="#method.lagrange_coeffs" class="fn">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><[C::Base; <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.array.html">8</a>]> { ... }
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}</code></pre><details class="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="struct halo2_gadgets::ecc::chip::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="toggle" open><summary><section id="associatedtype.FixedScalarKind" class="method"><a class="src rightside" href="../../../src/halo2_gadgets/ecc/chip.rs.html#211">source</a><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></section></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="toggle method-toggle" open><summary><section id="tymethod.generator" class="method"><a class="src rightside" href="../../../src/halo2_gadgets/ecc/chip.rs.html#214">source</a><h4 class="code-header">fn <a href="#tymethod.generator" class="fn">generator</a>(&self) -> C</h4></section></summary><div class="docblock"><p>Returns the generator for this fixed point.</p>
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</div></details><details class="toggle method-toggle" open><summary><section id="tymethod.u" class="method"><a class="src rightside" href="../../../src/halo2_gadgets/ecc/chip.rs.html#217">source</a><h4 class="code-header">fn <a href="#tymethod.u" class="fn">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><[<C::Base as PrimeField>::Repr; <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.array.html">8</a>]></h4></section></summary><div class="docblock"><p>Returns the $u$ values for this fixed point.</p>
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</div></details><details class="toggle method-toggle" open><summary><section id="tymethod.z" class="method"><a class="src rightside" href="../../../src/halo2_gadgets/ecc/chip.rs.html#220">source</a><h4 class="code-header">fn <a href="#tymethod.z" class="fn">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>></h4></section></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="toggle method-toggle" open><summary><section id="method.lagrange_coeffs" class="method"><a class="src rightside" href="../../../src/halo2_gadgets/ecc/chip.rs.html#223-225">source</a><h4 class="code-header">fn <a href="#method.lagrange_coeffs" class="fn">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><[C::Base; <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.array.html">8</a>]></h4></section></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 id="implementors-list"></div><script src="../../../implementors/halo2_gadgets/ecc/chip/trait.FixedPoint.js" async></script></section></div></main></body></html> |