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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_proofs/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_proofs/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="#">FieldExt</a></h2><div class="sidebar-elems"><section><div class="block"><h3 class="sidebar-title"><a href="#required-associated-consts">Required Associated Constants</a></h3><ul><li><a href="#associatedconstant.DELTA">DELTA</a></li><li><a href="#associatedconstant.MODULUS">MODULUS</a></li><li><a href="#associatedconstant.ROOT_OF_UNITY_INV">ROOT_OF_UNITY_INV</a></li><li><a href="#associatedconstant.TWO_INV">TWO_INV</a></li><li><a href="#associatedconstant.ZETA">ZETA</a></li></ul></div><div class="block"><h3 class="sidebar-title"><a href="#required-methods">Required Methods</a></h3><ul><li><a href="#tymethod.from_bytes_wide">from_bytes_wide</a></li><li><a href="#tymethod.from_u128">from_u128</a></li><li><a href="#tymethod.get_lower_128">get_lower_128</a></li></ul></div><div class="block"><h3 class="sidebar-title"><a href="#provided-methods">Provided Methods</a></h3><ul><li><a href="#method.pow">pow</a></li></ul></div><div class="block"><h3 class="sidebar-title"><a href="#foreign-impls">Implementations on Foreign Types</a></h3><ul><li><a href="#impl-FieldExt-for-Fp">Fp</a></li><li><a href="#impl-FieldExt-for-Fq">Fq</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_proofs::arithmetic</a></h2><div id="sidebar-vars" data-name="FieldExt" 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_proofs/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_proofs</a>::<wbr><a href="index.html">arithmetic</a>::<wbr><a class="trait" href="#">FieldExt</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 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 FieldExt: <a class="trait" href="trait.SqrtRatio.html" title="trait halo2_proofs::arithmetic::SqrtRatio">SqrtRatio</a> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.From.html" title="trait core::convert::From">From</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a>> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/cmp/trait.Ord.html" title="trait core::cmp::Ord">Ord</a> + <a class="trait" href="trait.Group.html" title="trait halo2_proofs::arithmetic::Group">Group</a><Scalar = Self> {
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const <a href="#associatedconstant.MODULUS" class="constant">MODULUS</a>: &'static <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.str.html">str</a>;
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const <a href="#associatedconstant.ROOT_OF_UNITY_INV" class="constant">ROOT_OF_UNITY_INV</a>: Self;
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const <a href="#associatedconstant.DELTA" class="constant">DELTA</a>: Self;
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const <a href="#associatedconstant.TWO_INV" class="constant">TWO_INV</a>: Self;
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const <a href="#associatedconstant.ZETA" class="constant">ZETA</a>: Self;
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fn <a href="#tymethod.from_u128" class="fnname">from_u128</a>(v: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u128.html">u128</a>) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.from_bytes_wide" class="fnname">from_bytes_wide</a>(bytes: &<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">; 64]</a>) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.get_lower_128" class="fnname">get_lower_128</a>(&self) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u128.html">u128</a>;
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fn <a href="#method.pow" class="fnname">pow</a>(&self, by: &<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.u64.html">u64</a><a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.array.html">; 4]</a>) -> Self { ... }
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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>This trait is a common interface for dealing with elements of a finite
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field.</p>
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</div></details><h2 id="required-associated-consts" class="small-section-header">Required Associated Constants<a href="#required-associated-consts" class="anchor"></a></h2><div class="methods"><details class="rustdoc-toggle" open><summary><div id="associatedconstant.MODULUS" class="method has-srclink"><div class="rightside"></div><h4 class="code-header">const <a href="#associatedconstant.MODULUS" class="constant">MODULUS</a>: &'static <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.str.html">str</a></h4></div></summary><div class="docblock"><p>Modulus of the field written as a string for display purposes</p>
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</div></details><details class="rustdoc-toggle" open><summary><div id="associatedconstant.ROOT_OF_UNITY_INV" class="method has-srclink"><div class="rightside"></div><h4 class="code-header">const <a href="#associatedconstant.ROOT_OF_UNITY_INV" class="constant">ROOT_OF_UNITY_INV</a>: Self</h4></div></summary><div class="docblock"><p>Inverse of <code>PrimeField::root_of_unity()</code></p>
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</div></details><details class="rustdoc-toggle" open><summary><div id="associatedconstant.DELTA" class="method has-srclink"><div class="rightside"></div><h4 class="code-header">const <a href="#associatedconstant.DELTA" class="constant">DELTA</a>: Self</h4></div></summary><div class="docblock"><p>Generator of the $t-order$ multiplicative subgroup</p>
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</div></details><details class="rustdoc-toggle" open><summary><div id="associatedconstant.TWO_INV" class="method has-srclink"><div class="rightside"></div><h4 class="code-header">const <a href="#associatedconstant.TWO_INV" class="constant">TWO_INV</a>: Self</h4></div></summary><div class="docblock"><p>Inverse of $2$ in the field.</p>
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</div></details><details class="rustdoc-toggle" open><summary><div id="associatedconstant.ZETA" class="method has-srclink"><div class="rightside"></div><h4 class="code-header">const <a href="#associatedconstant.ZETA" class="constant">ZETA</a>: Self</h4></div></summary><div class="docblock"><p>Element of multiplicative order $3$.</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.from_u128" class="method has-srclink"><div class="rightside"></div><h4 class="code-header">fn <a href="#tymethod.from_u128" class="fnname">from_u128</a>(v: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u128.html">u128</a>) -> Self</h4></div></summary><div class="docblock"><p>Obtains a field element congruent to the integer <code>v</code>.</p>
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</div></details><details class="rustdoc-toggle" open><summary><div id="tymethod.from_bytes_wide" class="method has-srclink"><div class="rightside"></div><h4 class="code-header">fn <a href="#tymethod.from_bytes_wide" class="fnname">from_bytes_wide</a>(bytes: &<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">; 64]</a>) -> Self</h4></div></summary><div class="docblock"><p>Obtains a field element that is congruent to the provided little endian
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byte representation of an integer.</p>
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</div></details><details class="rustdoc-toggle" open><summary><div id="tymethod.get_lower_128" class="method has-srclink"><div class="rightside"></div><h4 class="code-header">fn <a href="#tymethod.get_lower_128" class="fnname">get_lower_128</a>(&self) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u128.html">u128</a></h4></div></summary><div class="docblock"><p>Gets the lower 128 bits of this field element when expressed
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canonically.</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.pow" class="method has-srclink"><div class="rightside"></div><h4 class="code-header">fn <a href="#method.pow" class="fnname">pow</a>(&self, by: &<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.u64.html">u64</a><a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.array.html">; 4]</a>) -> Self</h4></div></summary><div class="docblock"><p>Exponentiates <code>self</code> by <code>by</code>, where <code>by</code> is a little-endian order
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integer exponent.</p>
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</div></details></div><h2 id="foreign-impls" class="small-section-header">Implementations on Foreign Types<a href="#foreign-impls" class="anchor"></a></h2><details class="rustdoc-toggle implementors-toggle"><summary><section id="impl-FieldExt-for-Fq" class="impl has-srclink"><a href="#impl-FieldExt-for-Fq" class="anchor"></a><h3 class="code-header in-band">impl <a class="trait" href="trait.FieldExt.html" title="trait halo2_proofs::arithmetic::FieldExt">FieldExt</a> for Fq</h3></section></summary><div class="impl-items"><details class="rustdoc-toggle method-toggle" open><summary><section id="method.from_bytes_wide" class="method trait-impl has-srclink"><a href="#method.from_bytes_wide" class="anchor"></a><h4 class="code-header">fn <a href="#tymethod.from_bytes_wide" class="fnname">from_bytes_wide</a>(bytes: &<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">; 64]</a>) -> Fq</h4></section></summary><div class="docblock"><p>Converts a 512-bit little endian integer into
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a <code>Fq</code> by reducing by the modulus.</p>
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</div></details><section id="associatedconstant.MODULUS-1" class="associatedconstant trait-impl has-srclink"><a href="#associatedconstant.MODULUS-1" class="anchor"></a><h4 class="code-header">const <a href="#associatedconstant.MODULUS" class="constant">MODULUS</a>: &'static <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.str.html">str</a> = "0x40000000000000000000000000000000224698fc0994a8dd8c46eb2100000001"</h4></section><section id="associatedconstant.ROOT_OF_UNITY_INV-1" class="associatedconstant trait-impl has-srclink"><a href="#associatedconstant.ROOT_OF_UNITY_INV-1" class="anchor"></a><h4 class="code-header">const <a href="#associatedconstant.ROOT_OF_UNITY_INV" class="constant">ROOT_OF_UNITY_INV</a>: Fq = Fq::from_raw([6336227815658842166, 5391806631710861324, 17638615478710601409,
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2465124479527549238])</h4></section><section id="associatedconstant.DELTA-1" class="associatedconstant trait-impl has-srclink"><a href="#associatedconstant.DELTA-1" class="anchor"></a><h4 class="code-header">const <a href="#associatedconstant.DELTA" class="constant">DELTA</a>: Fq = DELTA</h4></section><section id="associatedconstant.TWO_INV-1" class="associatedconstant trait-impl has-srclink"><a href="#associatedconstant.TWO_INV-1" class="anchor"></a><h4 class="code-header">const <a href="#associatedconstant.TWO_INV" class="constant">TWO_INV</a>: Fq = Fq::from_raw([14277384507177828353, 1234914826959606894, 0,
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2305843009213693952])</h4></section><section id="associatedconstant.ZETA-1" class="associatedconstant trait-impl has-srclink"><a href="#associatedconstant.ZETA-1" class="anchor"></a><h4 class="code-header">const <a href="#associatedconstant.ZETA" class="constant">ZETA</a>: Fq = Fq::from_raw([3074220081524903503, 1147650983937979311, 5845026731688660826,
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468825539646214798])</h4></section><section id="method.from_u128" class="method trait-impl has-srclink"><a href="#method.from_u128" class="anchor"></a><h4 class="code-header">fn <a href="#tymethod.from_u128" class="fnname">from_u128</a>(v: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u128.html">u128</a>) -> Fq</h4></section><section id="method.get_lower_128" class="method trait-impl has-srclink"><a href="#method.get_lower_128" class="anchor"></a><h4 class="code-header">fn <a href="#tymethod.get_lower_128" class="fnname">get_lower_128</a>(&self) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u128.html">u128</a></h4></section></div></details><details class="rustdoc-toggle implementors-toggle"><summary><section id="impl-FieldExt-for-Fp" class="impl has-srclink"><a href="#impl-FieldExt-for-Fp" class="anchor"></a><h3 class="code-header in-band">impl <a class="trait" href="trait.FieldExt.html" title="trait halo2_proofs::arithmetic::FieldExt">FieldExt</a> for Fp</h3></section></summary><div class="impl-items"><details class="rustdoc-toggle method-toggle" open><summary><section id="method.from_bytes_wide-1" class="method trait-impl has-srclink"><a href="#method.from_bytes_wide-1" class="anchor"></a><h4 class="code-header">fn <a href="#tymethod.from_bytes_wide" class="fnname">from_bytes_wide</a>(bytes: &<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">; 64]</a>) -> Fp</h4></section></summary><div class="docblock"><p>Converts a 512-bit little endian integer into
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a <code>Fp</code> by reducing by the modulus.</p>
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</div></details><section id="associatedconstant.MODULUS-2" class="associatedconstant trait-impl has-srclink"><a href="#associatedconstant.MODULUS-2" class="anchor"></a><h4 class="code-header">const <a href="#associatedconstant.MODULUS" class="constant">MODULUS</a>: &'static <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.str.html">str</a> = "0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001"</h4></section><section id="associatedconstant.ROOT_OF_UNITY_INV-2" class="associatedconstant trait-impl has-srclink"><a href="#associatedconstant.ROOT_OF_UNITY_INV-2" class="anchor"></a><h4 class="code-header">const <a href="#associatedconstant.ROOT_OF_UNITY_INV" class="constant">ROOT_OF_UNITY_INV</a>: Fp = Fp::from_raw([17345750844130103798, 9556816360606991983, 13037233058361039569,
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3230532478545521500])</h4></section><section id="associatedconstant.DELTA-2" class="associatedconstant trait-impl has-srclink"><a href="#associatedconstant.DELTA-2" class="anchor"></a><h4 class="code-header">const <a href="#associatedconstant.DELTA" class="constant">DELTA</a>: Fp = DELTA</h4></section><section id="associatedconstant.TWO_INV-2" class="associatedconstant trait-impl has-srclink"><a href="#associatedconstant.TWO_INV-2" class="anchor"></a><h4 class="code-header">const <a href="#associatedconstant.TWO_INV" class="constant">TWO_INV</a>: Fp = Fp::from_raw([14742138064964943873, 1234914826957257869, 0,
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2305843009213693952])</h4></section><section id="associatedconstant.ZETA-2" class="associatedconstant trait-impl has-srclink"><a href="#associatedconstant.ZETA-2" class="anchor"></a><h4 class="code-header">const <a href="#associatedconstant.ZETA" class="constant">ZETA</a>: Fp = Fp::from_raw([2138469568173984441, 2098549686371430729, 3218620026049966512,
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1354680253176199793])</h4></section><section id="method.from_u128-1" class="method trait-impl has-srclink"><a href="#method.from_u128-1" class="anchor"></a><h4 class="code-header">fn <a href="#tymethod.from_u128" class="fnname">from_u128</a>(v: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u128.html">u128</a>) -> Fp</h4></section><section id="method.get_lower_128-1" class="method trait-impl has-srclink"><a href="#method.get_lower_128-1" class="anchor"></a><h4 class="code-header">fn <a href="#tymethod.get_lower_128" class="fnname">get_lower_128</a>(&self) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u128.html">u128</a></h4></section></div></details><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/pasta_curves/arithmetic/fields/trait.FieldExt.js" async></script></section></div></main><div id="rustdoc-vars" data-root-path="../../" data-current-crate="halo2_proofs" data-themes="ayu,dark,light" data-resource-suffix="" data-rustdoc-version="1.62.0-nightly (30f386087 2022-05-05)" ></div>
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