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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="Constants required for the ECC chip."><meta name="keywords" content="rust, rustlang, rust-lang, constants"><title>halo2_gadgets::ecc::chip::constants - 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 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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</a><h2 class="location"><a href="#">Module constants</a></h2><div class="sidebar-elems"><section><div class="block"><ul><li><a href="#constants">Constants</a></li><li><a href="#functions">Functions</a></li></ul></div></section></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"><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><div id="settings-menu" tabindex="-1">
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<h1 class="fqn"><span class="in-band">Module <a href="../../../index.html">halo2_gadgets</a>::<wbr><a href="../../index.html">ecc</a>::<wbr><a href="../index.html">chip</a>::<wbr><a class="mod" href="#">constants</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/constants.rs.html#1-282">source</a> · <a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class="inner">−</span>]</a></span></div><details class="rustdoc-toggle top-doc" open><summary class="hideme"><span>Expand description</span></summary><div class="docblock"><p>Constants required for the ECC chip.</p>
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</div></details><h2 id="constants" class="small-section-header"><a href="#constants">Constants</a></h2>
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<div class="item-table"><div class="item-row"><div class="item-left module-item"><a class="constant" href="constant.FIXED_BASE_WINDOW_SIZE.html" title="halo2_gadgets::ecc::chip::constants::FIXED_BASE_WINDOW_SIZE constant">FIXED_BASE_WINDOW_SIZE</a></div><div class="item-right docblock-short"><p>Window size for fixed-base scalar multiplication</p>
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</div></div><div class="item-row"><div class="item-left module-item"><a class="constant" href="constant.H.html" title="halo2_gadgets::ecc::chip::constants::H constant">H</a></div><div class="item-right docblock-short"><p>$2^{<code>FIXED_BASE_WINDOW_SIZE</code>}$</p>
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</div></div><div class="item-row"><div class="item-left module-item"><a class="constant" href="constant.NUM_WINDOWS.html" title="halo2_gadgets::ecc::chip::constants::NUM_WINDOWS constant">NUM_WINDOWS</a></div><div class="item-right docblock-short"><p>Number of windows for a full-width scalar</p>
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</div></div><div class="item-row"><div class="item-left module-item"><a class="constant" href="constant.NUM_WINDOWS_SHORT.html" title="halo2_gadgets::ecc::chip::constants::NUM_WINDOWS_SHORT constant">NUM_WINDOWS_SHORT</a></div><div class="item-right docblock-short"><p>Number of windows for a short signed scalar</p>
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</div></div></div><h2 id="functions" class="small-section-header"><a href="#functions">Functions</a></h2>
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<div class="item-table"><div class="item-row"><div class="item-left module-item"><a class="fn" href="fn.compute_lagrange_coeffs.html" title="halo2_gadgets::ecc::chip::constants::compute_lagrange_coeffs fn">compute_lagrange_coeffs</a></div><div class="item-right docblock-short"><p>For each window, we interpolate the $x$-coordinate.
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Here, we pre-compute and store the coefficients of the interpolation polynomial.</p>
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</div></div><div class="item-row"><div class="item-left module-item"><a class="fn" href="fn.find_zs_and_us.html" title="halo2_gadgets::ecc::chip::constants::find_zs_and_us fn">find_zs_and_us</a></div><div class="item-right docblock-short"><p>For each window, $z$ is a field element such that for each point $(x, y)$ in the window:</p>
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</div></div><div class="item-row"><div class="item-left module-item"><a class="fn" href="fn.test_lagrange_coeffs.html" title="halo2_gadgets::ecc::chip::constants::test_lagrange_coeffs fn">test_lagrange_coeffs</a><span class="stab portability" title="Available on crate feature `test-dependencies` only"><code>test-dependencies</code></span></div><div class="item-right docblock-short"><p>Test that Lagrange interpolation coefficients reproduce the correct x-coordinate
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for each fixed-base multiple in each window.</p>
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</div></div><div class="item-row"><div class="item-left module-item"><a class="fn" href="fn.test_zs_and_us.html" title="halo2_gadgets::ecc::chip::constants::test_zs_and_us fn">test_zs_and_us</a><span class="stab portability" title="Available on crate feature `test-dependencies` only"><code>test-dependencies</code></span></div><div class="item-right docblock-short"><p>Test that the z-values and u-values satisfy the conditions:
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1. z + y = u^2,
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2. z - y is not a square
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for the y-coordinate of each fixed-base multiple in each window.</p>
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