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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="Source of the Rust file `/root/.cargo/registry/src/github.com-1ecc6299db9ec823/num-integer-0.1.45/src/lib.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>lib.rs - source</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="../../source-script.js"></script><script defer src="../../source-files.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"></head><body class="rustdoc source"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><a class="sidebar-logo" href="../../num_integer/index.html"><div class="logo-container"><img class="rust-logo" src="../../rust-logo.svg" alt="logo"></div></a></nav><main><div class="width-limiter"><nav class="sub"><a class="sub-logo-container" href="../../num_integer/index.html"><img class="rust-logo" src="../../rust-logo.svg" alt="logo"></a><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"><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="../../wheel.svg"></a></div></div></form></nav><section id="main-content" class="content"><div class="example-wrap"><pre class="src-line-numbers"><span id="1">1</span>
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 </pre><pre class="rust"><code><span class="comment">// Copyright 2013-2014 The Rust Project Developers. See the COPYRIGHT
 // file at the top-level directory of this distribution and at
 // http://rust-lang.org/COPYRIGHT.
 //
 // Licensed under the Apache License, Version 2.0 &lt;LICENSE-APACHE or
 // http://www.apache.org/licenses/LICENSE-2.0&gt; or the MIT license
 // &lt;LICENSE-MIT or http://opensource.org/licenses/MIT&gt;, at your
 // option. This file may not be copied, modified, or distributed
 // except according to those terms.

 </span><span class="doccomment">//! Integer trait and functions.
 //!
 //! ## Compatibility
 //!
 //! The `num-integer` crate is tested for rustc 1.8 and greater.

 </span><span class="attribute">#![doc(html_root_url = <span class="string">&quot;https://docs.rs/num-integer/0.1&quot;</span>)]
 #![no_std]
 #[cfg(feature = <span class="string">&quot;std&quot;</span>)]
 </span><span class="kw">extern crate </span>std;

 <span class="kw">extern crate </span>num_traits <span class="kw">as </span>traits;

 <span class="kw">use </span>core::mem;
 <span class="kw">use </span>core::ops::Add;

 <span class="kw">use </span>traits::{Num, Signed, Zero};

 <span class="kw">mod </span>roots;
 <span class="kw">pub use </span>roots::Roots;
 <span class="kw">pub use </span>roots::{cbrt, nth_root, sqrt};

 <span class="kw">mod </span>average;
 <span class="kw">pub use </span>average::Average;
 <span class="kw">pub use </span>average::{average_ceil, average_floor};

 <span class="kw">pub trait </span>Integer: Sized + Num + PartialOrd + Ord + Eq {
     <span class="doccomment">/// Floored integer division.
     ///
     /// # Examples
     ///
     /// ~~~
     /// # use num_integer::Integer;
     /// assert!(( 8).div_floor(&amp; 3) ==  2);
     /// assert!(( 8).div_floor(&amp;-3) == -3);
     /// assert!((-8).div_floor(&amp; 3) == -3);
     /// assert!((-8).div_floor(&amp;-3) ==  2);
     ///
     /// assert!(( 1).div_floor(&amp; 2) ==  0);
     /// assert!(( 1).div_floor(&amp;-2) == -1);
     /// assert!((-1).div_floor(&amp; 2) == -1);
     /// assert!((-1).div_floor(&amp;-2) ==  0);
     /// ~~~
     </span><span class="kw">fn </span>div_floor(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; <span class="self">Self</span>;

     <span class="doccomment">/// Floored integer modulo, satisfying:
     ///
     /// ~~~
     /// # use num_integer::Integer;
     /// # let n = 1; let d = 1;
     /// assert!(n.div_floor(&amp;d) * d + n.mod_floor(&amp;d) == n)
     /// ~~~
     ///
     /// # Examples
     ///
     /// ~~~
     /// # use num_integer::Integer;
     /// assert!(( 8).mod_floor(&amp; 3) ==  2);
     /// assert!(( 8).mod_floor(&amp;-3) == -1);
     /// assert!((-8).mod_floor(&amp; 3) ==  1);
     /// assert!((-8).mod_floor(&amp;-3) == -2);
     ///
     /// assert!(( 1).mod_floor(&amp; 2) ==  1);
     /// assert!(( 1).mod_floor(&amp;-2) == -1);
     /// assert!((-1).mod_floor(&amp; 2) ==  1);
     /// assert!((-1).mod_floor(&amp;-2) == -1);
     /// ~~~
     </span><span class="kw">fn </span>mod_floor(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; <span class="self">Self</span>;

     <span class="doccomment">/// Ceiled integer division.
     ///
     /// # Examples
     ///
     /// ~~~
     /// # use num_integer::Integer;
     /// assert_eq!(( 8).div_ceil( &amp;3),  3);
     /// assert_eq!(( 8).div_ceil(&amp;-3), -2);
     /// assert_eq!((-8).div_ceil( &amp;3), -2);
     /// assert_eq!((-8).div_ceil(&amp;-3),  3);
     ///
     /// assert_eq!(( 1).div_ceil( &amp;2), 1);
     /// assert_eq!(( 1).div_ceil(&amp;-2), 0);
     /// assert_eq!((-1).div_ceil( &amp;2), 0);
     /// assert_eq!((-1).div_ceil(&amp;-2), 1);
     /// ~~~
     </span><span class="kw">fn </span>div_ceil(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; <span class="self">Self </span>{
         <span class="kw">let </span>(q, r) = <span class="self">self</span>.div_mod_floor(other);
         <span class="kw">if </span>r.is_zero() {
             q
         } <span class="kw">else </span>{
             q + <span class="self">Self</span>::one()
         }
     }

     <span class="doccomment">/// Greatest Common Divisor (GCD).
     ///
     /// # Examples
     ///
     /// ~~~
     /// # use num_integer::Integer;
     /// assert_eq!(6.gcd(&amp;8), 2);
     /// assert_eq!(7.gcd(&amp;3), 1);
     /// ~~~
     </span><span class="kw">fn </span>gcd(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; <span class="self">Self</span>;

     <span class="doccomment">/// Lowest Common Multiple (LCM).
     ///
     /// # Examples
     ///
     /// ~~~
     /// # use num_integer::Integer;
     /// assert_eq!(7.lcm(&amp;3), 21);
     /// assert_eq!(2.lcm(&amp;4), 4);
     /// assert_eq!(0.lcm(&amp;0), 0);
     /// ~~~
     </span><span class="kw">fn </span>lcm(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; <span class="self">Self</span>;

     <span class="doccomment">/// Greatest Common Divisor (GCD) and
     /// Lowest Common Multiple (LCM) together.
     ///
     /// Potentially more efficient than calling `gcd` and `lcm`
     /// individually for identical inputs.
     ///
     /// # Examples
     ///
     /// ~~~
     /// # use num_integer::Integer;
     /// assert_eq!(10.gcd_lcm(&amp;4), (2, 20));
     /// assert_eq!(8.gcd_lcm(&amp;9), (1, 72));
     /// ~~~
     </span><span class="attribute">#[inline]
     </span><span class="kw">fn </span>gcd_lcm(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; (<span class="self">Self</span>, <span class="self">Self</span>) {
         (<span class="self">self</span>.gcd(other), <span class="self">self</span>.lcm(other))
     }

     <span class="doccomment">/// Greatest common divisor and Bézout coefficients.
     ///
     /// # Examples
     ///
     /// ~~~
     /// # extern crate num_integer;
     /// # extern crate num_traits;
     /// # fn main() {
     /// # use num_integer::{ExtendedGcd, Integer};
     /// # use num_traits::NumAssign;
     /// fn check&lt;A: Copy + Integer + NumAssign&gt;(a: A, b: A) -&gt; bool {
     ///     let ExtendedGcd { gcd, x, y, .. } = a.extended_gcd(&amp;b);
     ///     gcd == x * a + y * b
     /// }
     /// assert!(check(10isize, 4isize));
     /// assert!(check(8isize,  9isize));
     /// # }
     /// ~~~
     </span><span class="attribute">#[inline]
     </span><span class="kw">fn </span>extended_gcd(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; ExtendedGcd&lt;<span class="self">Self</span>&gt;
     <span class="kw">where
         </span><span class="self">Self</span>: Clone,
     {
         <span class="kw">let </span><span class="kw-2">mut </span>s = (<span class="self">Self</span>::zero(), <span class="self">Self</span>::one());
         <span class="kw">let </span><span class="kw-2">mut </span>t = (<span class="self">Self</span>::one(), <span class="self">Self</span>::zero());
         <span class="kw">let </span><span class="kw-2">mut </span>r = (other.clone(), <span class="self">self</span>.clone());

         <span class="kw">while </span>!r.<span class="number">0</span>.is_zero() {
             <span class="kw">let </span>q = r.<span class="number">1</span>.clone() / r.<span class="number">0</span>.clone();
             <span class="kw">let </span>f = |<span class="kw-2">mut </span>r: (<span class="self">Self</span>, <span class="self">Self</span>)| {
                 mem::swap(<span class="kw-2">&amp;mut </span>r.<span class="number">0</span>, <span class="kw-2">&amp;mut </span>r.<span class="number">1</span>);
                 r.<span class="number">0 </span>= r.<span class="number">0 </span>- q.clone() * r.<span class="number">1</span>.clone();
                 r
             };
             r = f(r);
             s = f(s);
             t = f(t);
         }

         <span class="kw">if </span>r.<span class="number">1 </span>&gt;= <span class="self">Self</span>::zero() {
             ExtendedGcd {
                 gcd: r.<span class="number">1</span>,
                 x: s.<span class="number">1</span>,
                 y: t.<span class="number">1</span>,
             }
         } <span class="kw">else </span>{
             ExtendedGcd {
                 gcd: <span class="self">Self</span>::zero() - r.<span class="number">1</span>,
                 x: <span class="self">Self</span>::zero() - s.<span class="number">1</span>,
                 y: <span class="self">Self</span>::zero() - t.<span class="number">1</span>,
             }
         }
     }

     <span class="doccomment">/// Greatest common divisor, least common multiple, and Bézout coefficients.
     </span><span class="attribute">#[inline]
     </span><span class="kw">fn </span>extended_gcd_lcm(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; (ExtendedGcd&lt;<span class="self">Self</span>&gt;, <span class="self">Self</span>)
     <span class="kw">where
         </span><span class="self">Self</span>: Clone + Signed,
     {
         (<span class="self">self</span>.extended_gcd(other), <span class="self">self</span>.lcm(other))
     }

     <span class="doccomment">/// Deprecated, use `is_multiple_of` instead.
     </span><span class="kw">fn </span>divides(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; bool;

     <span class="doccomment">/// Returns `true` if `self` is a multiple of `other`.
     ///
     /// # Examples
     ///
     /// ~~~
     /// # use num_integer::Integer;
     /// assert_eq!(9.is_multiple_of(&amp;3), true);
     /// assert_eq!(3.is_multiple_of(&amp;9), false);
     /// ~~~
     </span><span class="kw">fn </span>is_multiple_of(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; bool;

     <span class="doccomment">/// Returns `true` if the number is even.
     ///
     /// # Examples
     ///
     /// ~~~
     /// # use num_integer::Integer;
     /// assert_eq!(3.is_even(), false);
     /// assert_eq!(4.is_even(), true);
     /// ~~~
     </span><span class="kw">fn </span>is_even(<span class="kw-2">&amp;</span><span class="self">self</span>) -&gt; bool;

     <span class="doccomment">/// Returns `true` if the number is odd.
     ///
     /// # Examples
     ///
     /// ~~~
     /// # use num_integer::Integer;
     /// assert_eq!(3.is_odd(), true);
     /// assert_eq!(4.is_odd(), false);
     /// ~~~
     </span><span class="kw">fn </span>is_odd(<span class="kw-2">&amp;</span><span class="self">self</span>) -&gt; bool;

     <span class="doccomment">/// Simultaneous truncated integer division and modulus.
     /// Returns `(quotient, remainder)`.
     ///
     /// # Examples
     ///
     /// ~~~
     /// # use num_integer::Integer;
     /// assert_eq!(( 8).div_rem( &amp;3), ( 2,  2));
     /// assert_eq!(( 8).div_rem(&amp;-3), (-2,  2));
     /// assert_eq!((-8).div_rem( &amp;3), (-2, -2));
     /// assert_eq!((-8).div_rem(&amp;-3), ( 2, -2));
     ///
     /// assert_eq!(( 1).div_rem( &amp;2), ( 0,  1));
     /// assert_eq!(( 1).div_rem(&amp;-2), ( 0,  1));
     /// assert_eq!((-1).div_rem( &amp;2), ( 0, -1));
     /// assert_eq!((-1).div_rem(&amp;-2), ( 0, -1));
     /// ~~~
     </span><span class="kw">fn </span>div_rem(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; (<span class="self">Self</span>, <span class="self">Self</span>);

     <span class="doccomment">/// Simultaneous floored integer division and modulus.
     /// Returns `(quotient, remainder)`.
     ///
     /// # Examples
     ///
     /// ~~~
     /// # use num_integer::Integer;
     /// assert_eq!(( 8).div_mod_floor( &amp;3), ( 2,  2));
     /// assert_eq!(( 8).div_mod_floor(&amp;-3), (-3, -1));
     /// assert_eq!((-8).div_mod_floor( &amp;3), (-3,  1));
     /// assert_eq!((-8).div_mod_floor(&amp;-3), ( 2, -2));
     ///
     /// assert_eq!(( 1).div_mod_floor( &amp;2), ( 0,  1));
     /// assert_eq!(( 1).div_mod_floor(&amp;-2), (-1, -1));
     /// assert_eq!((-1).div_mod_floor( &amp;2), (-1,  1));
     /// assert_eq!((-1).div_mod_floor(&amp;-2), ( 0, -1));
     /// ~~~
     </span><span class="kw">fn </span>div_mod_floor(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; (<span class="self">Self</span>, <span class="self">Self</span>) {
         (<span class="self">self</span>.div_floor(other), <span class="self">self</span>.mod_floor(other))
     }

     <span class="doccomment">/// Rounds up to nearest multiple of argument.
     ///
     /// # Notes
     ///
     /// For signed types, `a.next_multiple_of(b) = a.prev_multiple_of(b.neg())`.
     ///
     /// # Examples
     ///
     /// ~~~
     /// # use num_integer::Integer;
     /// assert_eq!(( 16).next_multiple_of(&amp; 8),  16);
     /// assert_eq!(( 23).next_multiple_of(&amp; 8),  24);
     /// assert_eq!(( 16).next_multiple_of(&amp;-8),  16);
     /// assert_eq!(( 23).next_multiple_of(&amp;-8),  16);
     /// assert_eq!((-16).next_multiple_of(&amp; 8), -16);
     /// assert_eq!((-23).next_multiple_of(&amp; 8), -16);
     /// assert_eq!((-16).next_multiple_of(&amp;-8), -16);
     /// assert_eq!((-23).next_multiple_of(&amp;-8), -24);
     /// ~~~
     </span><span class="attribute">#[inline]
     </span><span class="kw">fn </span>next_multiple_of(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; <span class="self">Self
     </span><span class="kw">where
         </span><span class="self">Self</span>: Clone,
     {
         <span class="kw">let </span>m = <span class="self">self</span>.mod_floor(other);
         <span class="self">self</span>.clone()
             + <span class="kw">if </span>m.is_zero() {
                 <span class="self">Self</span>::zero()
             } <span class="kw">else </span>{
                 other.clone() - m
             }
     }

     <span class="doccomment">/// Rounds down to nearest multiple of argument.
     ///
     /// # Notes
     ///
     /// For signed types, `a.prev_multiple_of(b) = a.next_multiple_of(b.neg())`.
     ///
     /// # Examples
     ///
     /// ~~~
     /// # use num_integer::Integer;
     /// assert_eq!(( 16).prev_multiple_of(&amp; 8),  16);
     /// assert_eq!(( 23).prev_multiple_of(&amp; 8),  16);
     /// assert_eq!(( 16).prev_multiple_of(&amp;-8),  16);
     /// assert_eq!(( 23).prev_multiple_of(&amp;-8),  24);
     /// assert_eq!((-16).prev_multiple_of(&amp; 8), -16);
     /// assert_eq!((-23).prev_multiple_of(&amp; 8), -24);
     /// assert_eq!((-16).prev_multiple_of(&amp;-8), -16);
     /// assert_eq!((-23).prev_multiple_of(&amp;-8), -16);
     /// ~~~
     </span><span class="attribute">#[inline]
     </span><span class="kw">fn </span>prev_multiple_of(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; <span class="self">Self
     </span><span class="kw">where
         </span><span class="self">Self</span>: Clone,
     {
         <span class="self">self</span>.clone() - <span class="self">self</span>.mod_floor(other)
     }
 }

 <span class="doccomment">/// Greatest common divisor and Bézout coefficients
 ///
 /// ```no_build
 /// let e = isize::extended_gcd(a, b);
 /// assert_eq!(e.gcd, e.x*a + e.y*b);
 /// ```
 </span><span class="attribute">#[derive(Debug, Clone, Copy, PartialEq, Eq)]
 </span><span class="kw">pub struct </span>ExtendedGcd&lt;A&gt; {
     <span class="kw">pub </span>gcd: A,
     <span class="kw">pub </span>x: A,
     <span class="kw">pub </span>y: A,
 }

 <span class="doccomment">/// Simultaneous integer division and modulus
 </span><span class="attribute">#[inline]
 </span><span class="kw">pub fn </span>div_rem&lt;T: Integer&gt;(x: T, y: T) -&gt; (T, T) {
     x.div_rem(<span class="kw-2">&amp;</span>y)
 }
 <span class="doccomment">/// Floored integer division
 </span><span class="attribute">#[inline]
 </span><span class="kw">pub fn </span>div_floor&lt;T: Integer&gt;(x: T, y: T) -&gt; T {
     x.div_floor(<span class="kw-2">&amp;</span>y)
 }
 <span class="doccomment">/// Floored integer modulus
 </span><span class="attribute">#[inline]
 </span><span class="kw">pub fn </span>mod_floor&lt;T: Integer&gt;(x: T, y: T) -&gt; T {
     x.mod_floor(<span class="kw-2">&amp;</span>y)
 }
 <span class="doccomment">/// Simultaneous floored integer division and modulus
 </span><span class="attribute">#[inline]
 </span><span class="kw">pub fn </span>div_mod_floor&lt;T: Integer&gt;(x: T, y: T) -&gt; (T, T) {
     x.div_mod_floor(<span class="kw-2">&amp;</span>y)
 }
 <span class="doccomment">/// Ceiled integer division
 </span><span class="attribute">#[inline]
 </span><span class="kw">pub fn </span>div_ceil&lt;T: Integer&gt;(x: T, y: T) -&gt; T {
     x.div_ceil(<span class="kw-2">&amp;</span>y)
 }

 <span class="doccomment">/// Calculates the Greatest Common Divisor (GCD) of the number and `other`. The
 /// result is always non-negative.
 </span><span class="attribute">#[inline(always)]
 </span><span class="kw">pub fn </span>gcd&lt;T: Integer&gt;(x: T, y: T) -&gt; T {
     x.gcd(<span class="kw-2">&amp;</span>y)
 }
 <span class="doccomment">/// Calculates the Lowest Common Multiple (LCM) of the number and `other`.
 </span><span class="attribute">#[inline(always)]
 </span><span class="kw">pub fn </span>lcm&lt;T: Integer&gt;(x: T, y: T) -&gt; T {
     x.lcm(<span class="kw-2">&amp;</span>y)
 }

 <span class="doccomment">/// Calculates the Greatest Common Divisor (GCD) and
 /// Lowest Common Multiple (LCM) of the number and `other`.
 </span><span class="attribute">#[inline(always)]
 </span><span class="kw">pub fn </span>gcd_lcm&lt;T: Integer&gt;(x: T, y: T) -&gt; (T, T) {
     x.gcd_lcm(<span class="kw-2">&amp;</span>y)
 }

 <span class="macro">macro_rules! </span>impl_integer_for_isize {
     (<span class="macro-nonterminal">$T</span>:ty, <span class="macro-nonterminal">$test_mod</span>:ident) =&gt; {
         <span class="kw">impl </span>Integer <span class="kw">for </span><span class="macro-nonterminal">$T </span>{
             <span class="doccomment">/// Floored integer division
             </span><span class="attribute">#[inline]
             </span><span class="kw">fn </span>div_floor(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; <span class="self">Self </span>{
                 <span class="comment">// Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,
                 // December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)
                 </span><span class="kw">let </span>(d, r) = <span class="self">self</span>.div_rem(other);
                 <span class="kw">if </span>(r &gt; <span class="number">0 </span>&amp;&amp; <span class="kw-2">*</span>other &lt; <span class="number">0</span>) || (r &lt; <span class="number">0 </span>&amp;&amp; <span class="kw-2">*</span>other &gt; <span class="number">0</span>) {
                     d - <span class="number">1
                 </span>} <span class="kw">else </span>{
                     d
                 }
             }

             <span class="doccomment">/// Floored integer modulo
             </span><span class="attribute">#[inline]
             </span><span class="kw">fn </span>mod_floor(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; <span class="self">Self </span>{
                 <span class="comment">// Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,
                 // December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)
                 </span><span class="kw">let </span>r = <span class="kw-2">*</span><span class="self">self </span>% <span class="kw-2">*</span>other;
                 <span class="kw">if </span>(r &gt; <span class="number">0 </span>&amp;&amp; <span class="kw-2">*</span>other &lt; <span class="number">0</span>) || (r &lt; <span class="number">0 </span>&amp;&amp; <span class="kw-2">*</span>other &gt; <span class="number">0</span>) {
                     r + <span class="kw-2">*</span>other
                 } <span class="kw">else </span>{
                     r
                 }
             }

             <span class="doccomment">/// Calculates `div_floor` and `mod_floor` simultaneously
             </span><span class="attribute">#[inline]
             </span><span class="kw">fn </span>div_mod_floor(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; (<span class="self">Self</span>, <span class="self">Self</span>) {
                 <span class="comment">// Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,
                 // December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)
                 </span><span class="kw">let </span>(d, r) = <span class="self">self</span>.div_rem(other);
                 <span class="kw">if </span>(r &gt; <span class="number">0 </span>&amp;&amp; <span class="kw-2">*</span>other &lt; <span class="number">0</span>) || (r &lt; <span class="number">0 </span>&amp;&amp; <span class="kw-2">*</span>other &gt; <span class="number">0</span>) {
                     (d - <span class="number">1</span>, r + <span class="kw-2">*</span>other)
                 } <span class="kw">else </span>{
                     (d, r)
                 }
             }

             <span class="attribute">#[inline]
             </span><span class="kw">fn </span>div_ceil(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; <span class="self">Self </span>{
                 <span class="kw">let </span>(d, r) = <span class="self">self</span>.div_rem(other);
                 <span class="kw">if </span>(r &gt; <span class="number">0 </span>&amp;&amp; <span class="kw-2">*</span>other &gt; <span class="number">0</span>) || (r &lt; <span class="number">0 </span>&amp;&amp; <span class="kw-2">*</span>other &lt; <span class="number">0</span>) {
                     d + <span class="number">1
                 </span>} <span class="kw">else </span>{
                     d
                 }
             }

             <span class="doccomment">/// Calculates the Greatest Common Divisor (GCD) of the number and
             /// `other`. The result is always non-negative.
             </span><span class="attribute">#[inline]
             </span><span class="kw">fn </span>gcd(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; <span class="self">Self </span>{
                 <span class="comment">// Use Stein&#39;s algorithm
                 </span><span class="kw">let </span><span class="kw-2">mut </span>m = <span class="kw-2">*</span><span class="self">self</span>;
                 <span class="kw">let </span><span class="kw-2">mut </span>n = <span class="kw-2">*</span>other;
                 <span class="kw">if </span>m == <span class="number">0 </span>|| n == <span class="number">0 </span>{
                     <span class="kw">return </span>(m | n).abs();
                 }

                 <span class="comment">// find common factors of 2
                 </span><span class="kw">let </span>shift = (m | n).trailing_zeros();

                 <span class="comment">// The algorithm needs positive numbers, but the minimum value
                 // can&#39;t be represented as a positive one.
                 // It&#39;s also a power of two, so the gcd can be
                 // calculated by bitshifting in that case

                 // Assuming two&#39;s complement, the number created by the shift
                 // is positive for all numbers except gcd = abs(min value)
                 // The call to .abs() causes a panic in debug mode
                 </span><span class="kw">if </span>m == <span class="self">Self</span>::min_value() || n == <span class="self">Self</span>::min_value() {
                     <span class="kw">return </span>(<span class="number">1 </span>&lt;&lt; shift).abs();
                 }

                 <span class="comment">// guaranteed to be positive now, rest like unsigned algorithm
                 </span>m = m.abs();
                 n = n.abs();

                 <span class="comment">// divide n and m by 2 until odd
                 </span>m &gt;&gt;= m.trailing_zeros();
                 n &gt;&gt;= n.trailing_zeros();

                 <span class="kw">while </span>m != n {
                     <span class="kw">if </span>m &gt; n {
                         m -= n;
                         m &gt;&gt;= m.trailing_zeros();
                     } <span class="kw">else </span>{
                         n -= m;
                         n &gt;&gt;= n.trailing_zeros();
                     }
                 }
                 m &lt;&lt; shift
             }

             <span class="attribute">#[inline]
             </span><span class="kw">fn </span>extended_gcd_lcm(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; (ExtendedGcd&lt;<span class="self">Self</span>&gt;, <span class="self">Self</span>) {
                 <span class="kw">let </span>egcd = <span class="self">self</span>.extended_gcd(other);
                 <span class="comment">// should not have to recalculate abs
                 </span><span class="kw">let </span>lcm = <span class="kw">if </span>egcd.gcd.is_zero() {
                     <span class="self">Self</span>::zero()
                 } <span class="kw">else </span>{
                     (<span class="kw-2">*</span><span class="self">self </span>* (<span class="kw-2">*</span>other / egcd.gcd)).abs()
                 };
                 (egcd, lcm)
             }

             <span class="doccomment">/// Calculates the Lowest Common Multiple (LCM) of the number and
             /// `other`.
             </span><span class="attribute">#[inline]
             </span><span class="kw">fn </span>lcm(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; <span class="self">Self </span>{
                 <span class="self">self</span>.gcd_lcm(other).<span class="number">1
             </span>}

             <span class="doccomment">/// Calculates the Greatest Common Divisor (GCD) and
             /// Lowest Common Multiple (LCM) of the number and `other`.
             </span><span class="attribute">#[inline]
             </span><span class="kw">fn </span>gcd_lcm(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; (<span class="self">Self</span>, <span class="self">Self</span>) {
                 <span class="kw">if </span><span class="self">self</span>.is_zero() &amp;&amp; other.is_zero() {
                     <span class="kw">return </span>(<span class="self">Self</span>::zero(), <span class="self">Self</span>::zero());
                 }
                 <span class="kw">let </span>gcd = <span class="self">self</span>.gcd(other);
                 <span class="comment">// should not have to recalculate abs
                 </span><span class="kw">let </span>lcm = (<span class="kw-2">*</span><span class="self">self </span>* (<span class="kw-2">*</span>other / gcd)).abs();
                 (gcd, lcm)
             }

             <span class="doccomment">/// Deprecated, use `is_multiple_of` instead.
             </span><span class="attribute">#[inline]
             </span><span class="kw">fn </span>divides(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; bool {
                 <span class="self">self</span>.is_multiple_of(other)
             }

             <span class="doccomment">/// Returns `true` if the number is a multiple of `other`.
             </span><span class="attribute">#[inline]
             </span><span class="kw">fn </span>is_multiple_of(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; bool {
                 <span class="kw">if </span>other.is_zero() {
                     <span class="kw">return </span><span class="self">self</span>.is_zero();
                 }
                 <span class="kw-2">*</span><span class="self">self </span>% <span class="kw-2">*</span>other == <span class="number">0
             </span>}

             <span class="doccomment">/// Returns `true` if the number is divisible by `2`
             </span><span class="attribute">#[inline]
             </span><span class="kw">fn </span>is_even(<span class="kw-2">&amp;</span><span class="self">self</span>) -&gt; bool {
                 (<span class="kw-2">*</span><span class="self">self</span>) &amp; <span class="number">1 </span>== <span class="number">0
             </span>}

             <span class="doccomment">/// Returns `true` if the number is not divisible by `2`
             </span><span class="attribute">#[inline]
             </span><span class="kw">fn </span>is_odd(<span class="kw-2">&amp;</span><span class="self">self</span>) -&gt; bool {
                 !<span class="self">self</span>.is_even()
             }

             <span class="doccomment">/// Simultaneous truncated integer division and modulus.
             </span><span class="attribute">#[inline]
             </span><span class="kw">fn </span>div_rem(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; (<span class="self">Self</span>, <span class="self">Self</span>) {
                 (<span class="kw-2">*</span><span class="self">self </span>/ <span class="kw-2">*</span>other, <span class="kw-2">*</span><span class="self">self </span>% <span class="kw-2">*</span>other)
             }

             <span class="doccomment">/// Rounds up to nearest multiple of argument.
             </span><span class="attribute">#[inline]
             </span><span class="kw">fn </span>next_multiple_of(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; <span class="self">Self </span>{
                 <span class="comment">// Avoid the overflow of `MIN % -1`
                 </span><span class="kw">if </span><span class="kw-2">*</span>other == -<span class="number">1 </span>{
                     <span class="kw">return </span><span class="kw-2">*</span><span class="self">self</span>;
                 }

                 <span class="kw">let </span>m = Integer::mod_floor(<span class="self">self</span>, other);
                 <span class="kw-2">*</span><span class="self">self </span>+ <span class="kw">if </span>m == <span class="number">0 </span>{ <span class="number">0 </span>} <span class="kw">else </span>{ other - m }
             }

             <span class="doccomment">/// Rounds down to nearest multiple of argument.
             </span><span class="attribute">#[inline]
             </span><span class="kw">fn </span>prev_multiple_of(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; <span class="self">Self </span>{
                 <span class="comment">// Avoid the overflow of `MIN % -1`
                 </span><span class="kw">if </span><span class="kw-2">*</span>other == -<span class="number">1 </span>{
                     <span class="kw">return </span><span class="kw-2">*</span><span class="self">self</span>;
                 }

                 <span class="kw-2">*</span><span class="self">self </span>- Integer::mod_floor(<span class="self">self</span>, other)
             }
         }

         <span class="attribute">#[cfg(test)]
         </span><span class="kw">mod </span><span class="macro-nonterminal">$test_mod </span>{
             <span class="kw">use </span>core::mem;
             <span class="kw">use </span>Integer;

             <span class="doccomment">/// Checks that the division rule holds for:
             ///
             /// - `n`: numerator (dividend)
             /// - `d`: denominator (divisor)
             /// - `qr`: quotient and remainder
             </span><span class="attribute">#[cfg(test)]
             </span><span class="kw">fn </span>test_division_rule((n, d): (<span class="macro-nonterminal">$T</span>, <span class="macro-nonterminal">$T</span>), (q, r): (<span class="macro-nonterminal">$T</span>, <span class="macro-nonterminal">$T</span>)) {
                 <span class="macro">assert_eq!</span>(d * q + r, n);
             }

             <span class="attribute">#[test]
             </span><span class="kw">fn </span>test_div_rem() {
                 <span class="kw">fn </span>test_nd_dr(nd: (<span class="macro-nonterminal">$T</span>, <span class="macro-nonterminal">$T</span>), qr: (<span class="macro-nonterminal">$T</span>, <span class="macro-nonterminal">$T</span>)) {
                     <span class="kw">let </span>(n, d) = nd;
                     <span class="kw">let </span>separate_div_rem = (n / d, n % d);
                     <span class="kw">let </span>combined_div_rem = n.div_rem(<span class="kw-2">&amp;</span>d);

                     <span class="macro">assert_eq!</span>(separate_div_rem, qr);
                     <span class="macro">assert_eq!</span>(combined_div_rem, qr);

                     test_division_rule(nd, separate_div_rem);
                     test_division_rule(nd, combined_div_rem);
                 }

                 test_nd_dr((<span class="number">8</span>, <span class="number">3</span>), (<span class="number">2</span>, <span class="number">2</span>));
                 test_nd_dr((<span class="number">8</span>, -<span class="number">3</span>), (-<span class="number">2</span>, <span class="number">2</span>));
                 test_nd_dr((-<span class="number">8</span>, <span class="number">3</span>), (-<span class="number">2</span>, -<span class="number">2</span>));
                 test_nd_dr((-<span class="number">8</span>, -<span class="number">3</span>), (<span class="number">2</span>, -<span class="number">2</span>));

                 test_nd_dr((<span class="number">1</span>, <span class="number">2</span>), (<span class="number">0</span>, <span class="number">1</span>));
                 test_nd_dr((<span class="number">1</span>, -<span class="number">2</span>), (<span class="number">0</span>, <span class="number">1</span>));
                 test_nd_dr((-<span class="number">1</span>, <span class="number">2</span>), (<span class="number">0</span>, -<span class="number">1</span>));
                 test_nd_dr((-<span class="number">1</span>, -<span class="number">2</span>), (<span class="number">0</span>, -<span class="number">1</span>));
             }

             <span class="attribute">#[test]
             </span><span class="kw">fn </span>test_div_mod_floor() {
                 <span class="kw">fn </span>test_nd_dm(nd: (<span class="macro-nonterminal">$T</span>, <span class="macro-nonterminal">$T</span>), dm: (<span class="macro-nonterminal">$T</span>, <span class="macro-nonterminal">$T</span>)) {
                     <span class="kw">let </span>(n, d) = nd;
                     <span class="kw">let </span>separate_div_mod_floor =
                         (Integer::div_floor(<span class="kw-2">&amp;</span>n, <span class="kw-2">&amp;</span>d), Integer::mod_floor(<span class="kw-2">&amp;</span>n, <span class="kw-2">&amp;</span>d));
                     <span class="kw">let </span>combined_div_mod_floor = Integer::div_mod_floor(<span class="kw-2">&amp;</span>n, <span class="kw-2">&amp;</span>d);

                     <span class="macro">assert_eq!</span>(separate_div_mod_floor, dm);
                     <span class="macro">assert_eq!</span>(combined_div_mod_floor, dm);

                     test_division_rule(nd, separate_div_mod_floor);
                     test_division_rule(nd, combined_div_mod_floor);
                 }

                 test_nd_dm((<span class="number">8</span>, <span class="number">3</span>), (<span class="number">2</span>, <span class="number">2</span>));
                 test_nd_dm((<span class="number">8</span>, -<span class="number">3</span>), (-<span class="number">3</span>, -<span class="number">1</span>));
                 test_nd_dm((-<span class="number">8</span>, <span class="number">3</span>), (-<span class="number">3</span>, <span class="number">1</span>));
                 test_nd_dm((-<span class="number">8</span>, -<span class="number">3</span>), (<span class="number">2</span>, -<span class="number">2</span>));

                 test_nd_dm((<span class="number">1</span>, <span class="number">2</span>), (<span class="number">0</span>, <span class="number">1</span>));
                 test_nd_dm((<span class="number">1</span>, -<span class="number">2</span>), (-<span class="number">1</span>, -<span class="number">1</span>));
                 test_nd_dm((-<span class="number">1</span>, <span class="number">2</span>), (-<span class="number">1</span>, <span class="number">1</span>));
                 test_nd_dm((-<span class="number">1</span>, -<span class="number">2</span>), (<span class="number">0</span>, -<span class="number">1</span>));
             }

             <span class="attribute">#[test]
             </span><span class="kw">fn </span>test_gcd() {
                 <span class="macro">assert_eq!</span>((<span class="number">10 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).gcd(<span class="kw-2">&amp;</span><span class="number">2</span>), <span class="number">2 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">10 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).gcd(<span class="kw-2">&amp;</span><span class="number">3</span>), <span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).gcd(<span class="kw-2">&amp;</span><span class="number">3</span>), <span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).gcd(<span class="kw-2">&amp;</span><span class="number">3</span>), <span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">56 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).gcd(<span class="kw-2">&amp;</span><span class="number">42</span>), <span class="number">14 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).gcd(<span class="kw-2">&amp;</span>-<span class="number">3</span>), <span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>((-<span class="number">6 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).gcd(<span class="kw-2">&amp;</span><span class="number">3</span>), <span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>((-<span class="number">4 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).gcd(<span class="kw-2">&amp;</span>-<span class="number">2</span>), <span class="number">2 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
             }

             <span class="attribute">#[test]
             </span><span class="kw">fn </span>test_gcd_cmp_with_euclidean() {
                 <span class="kw">fn </span>euclidean_gcd(<span class="kw-2">mut </span>m: <span class="macro-nonterminal">$T</span>, <span class="kw-2">mut </span>n: <span class="macro-nonterminal">$T</span>) -&gt; <span class="macro-nonterminal">$T </span>{
                     <span class="kw">while </span>m != <span class="number">0 </span>{
                         mem::swap(<span class="kw-2">&amp;mut </span>m, <span class="kw-2">&amp;mut </span>n);
                         m %= n;
                     }

                     n.abs()
                 }

                 <span class="comment">// gcd(-128, b) = 128 is not representable as positive value
                 // for i8
                 </span><span class="kw">for </span>i <span class="kw">in </span>-<span class="number">127</span>..<span class="number">127 </span>{
                     <span class="kw">for </span>j <span class="kw">in </span>-<span class="number">127</span>..<span class="number">127 </span>{
                         <span class="macro">assert_eq!</span>(euclidean_gcd(i, j), i.gcd(<span class="kw-2">&amp;</span>j));
                     }
                 }

                 <span class="comment">// last value
                 // FIXME: Use inclusive ranges for above loop when implemented
                 </span><span class="kw">let </span>i = <span class="number">127</span>;
                 <span class="kw">for </span>j <span class="kw">in </span>-<span class="number">127</span>..<span class="number">127 </span>{
                     <span class="macro">assert_eq!</span>(euclidean_gcd(i, j), i.gcd(<span class="kw-2">&amp;</span>j));
                 }
                 <span class="macro">assert_eq!</span>(<span class="number">127</span>.gcd(<span class="kw-2">&amp;</span><span class="number">127</span>), <span class="number">127</span>);
             }

             <span class="attribute">#[test]
             </span><span class="kw">fn </span>test_gcd_min_val() {
                 <span class="kw">let </span>min = &lt;<span class="macro-nonterminal">$T</span>&gt;::min_value();
                 <span class="kw">let </span>max = &lt;<span class="macro-nonterminal">$T</span>&gt;::max_value();
                 <span class="kw">let </span>max_pow2 = max / <span class="number">2 </span>+ <span class="number">1</span>;
                 <span class="macro">assert_eq!</span>(min.gcd(<span class="kw-2">&amp;</span>max), <span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>(max.gcd(<span class="kw-2">&amp;</span>min), <span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>(min.gcd(<span class="kw-2">&amp;</span>max_pow2), max_pow2);
                 <span class="macro">assert_eq!</span>(max_pow2.gcd(<span class="kw-2">&amp;</span>min), max_pow2);
                 <span class="macro">assert_eq!</span>(min.gcd(<span class="kw-2">&amp;</span><span class="number">42</span>), <span class="number">2 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">42 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).gcd(<span class="kw-2">&amp;</span>min), <span class="number">2 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
             }

             <span class="attribute">#[test]
             #[should_panic]
             </span><span class="kw">fn </span>test_gcd_min_val_min_val() {
                 <span class="kw">let </span>min = &lt;<span class="macro-nonterminal">$T</span>&gt;::min_value();
                 <span class="macro">assert!</span>(min.gcd(<span class="kw-2">&amp;</span>min) &gt;= <span class="number">0</span>);
             }

             <span class="attribute">#[test]
             #[should_panic]
             </span><span class="kw">fn </span>test_gcd_min_val_0() {
                 <span class="kw">let </span>min = &lt;<span class="macro-nonterminal">$T</span>&gt;::min_value();
                 <span class="macro">assert!</span>(min.gcd(<span class="kw-2">&amp;</span><span class="number">0</span>) &gt;= <span class="number">0</span>);
             }

             <span class="attribute">#[test]
             #[should_panic]
             </span><span class="kw">fn </span>test_gcd_0_min_val() {
                 <span class="kw">let </span>min = &lt;<span class="macro-nonterminal">$T</span>&gt;::min_value();
                 <span class="macro">assert!</span>((<span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).gcd(<span class="kw-2">&amp;</span>min) &gt;= <span class="number">0</span>);
             }

             <span class="attribute">#[test]
             </span><span class="kw">fn </span>test_lcm() {
                 <span class="macro">assert_eq!</span>((<span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).lcm(<span class="kw-2">&amp;</span><span class="number">0</span>), <span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).lcm(<span class="kw-2">&amp;</span><span class="number">1</span>), <span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).lcm(<span class="kw-2">&amp;</span><span class="number">1</span>), <span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>((-<span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).lcm(<span class="kw-2">&amp;</span><span class="number">1</span>), <span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).lcm(<span class="kw-2">&amp;</span>-<span class="number">1</span>), <span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>((-<span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).lcm(<span class="kw-2">&amp;</span>-<span class="number">1</span>), <span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">8 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).lcm(<span class="kw-2">&amp;</span><span class="number">9</span>), <span class="number">72 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">11 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).lcm(<span class="kw-2">&amp;</span><span class="number">5</span>), <span class="number">55 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
             }

             <span class="attribute">#[test]
             </span><span class="kw">fn </span>test_gcd_lcm() {
                 <span class="kw">use </span>core::iter::once;
                 <span class="kw">for </span>i <span class="kw">in </span>once(<span class="number">0</span>)
                     .chain((<span class="number">1</span>..).take(<span class="number">127</span>).flat_map(|a| once(a).chain(once(-a))))
                     .chain(once(-<span class="number">128</span>))
                 {
                     <span class="kw">for </span>j <span class="kw">in </span>once(<span class="number">0</span>)
                         .chain((<span class="number">1</span>..).take(<span class="number">127</span>).flat_map(|a| once(a).chain(once(-a))))
                         .chain(once(-<span class="number">128</span>))
                     {
                         <span class="macro">assert_eq!</span>(i.gcd_lcm(<span class="kw-2">&amp;</span>j), (i.gcd(<span class="kw-2">&amp;</span>j), i.lcm(<span class="kw-2">&amp;</span>j)));
                     }
                 }
             }

             <span class="attribute">#[test]
             </span><span class="kw">fn </span>test_extended_gcd_lcm() {
                 <span class="kw">use </span>core::fmt::Debug;
                 <span class="kw">use </span>traits::NumAssign;
                 <span class="kw">use </span>ExtendedGcd;

                 <span class="kw">fn </span>check&lt;A: Copy + Debug + Integer + NumAssign&gt;(a: A, b: A) {
                     <span class="kw">let </span>ExtendedGcd { gcd, x, y, .. } = a.extended_gcd(<span class="kw-2">&amp;</span>b);
                     <span class="macro">assert_eq!</span>(gcd, x * a + y * b);
                 }

                 <span class="kw">use </span>core::iter::once;
                 <span class="kw">for </span>i <span class="kw">in </span>once(<span class="number">0</span>)
                     .chain((<span class="number">1</span>..).take(<span class="number">127</span>).flat_map(|a| once(a).chain(once(-a))))
                     .chain(once(-<span class="number">128</span>))
                 {
                     <span class="kw">for </span>j <span class="kw">in </span>once(<span class="number">0</span>)
                         .chain((<span class="number">1</span>..).take(<span class="number">127</span>).flat_map(|a| once(a).chain(once(-a))))
                         .chain(once(-<span class="number">128</span>))
                     {
                         check(i, j);
                         <span class="kw">let </span>(ExtendedGcd { gcd, .. }, lcm) = i.extended_gcd_lcm(<span class="kw-2">&amp;</span>j);
                         <span class="macro">assert_eq!</span>((gcd, lcm), (i.gcd(<span class="kw-2">&amp;</span>j), i.lcm(<span class="kw-2">&amp;</span>j)));
                     }
                 }
             }

             <span class="attribute">#[test]
             </span><span class="kw">fn </span>test_even() {
                 <span class="macro">assert_eq!</span>((-<span class="number">4 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_even(), <span class="bool-val">true</span>);
                 <span class="macro">assert_eq!</span>((-<span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_even(), <span class="bool-val">false</span>);
                 <span class="macro">assert_eq!</span>((-<span class="number">2 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_even(), <span class="bool-val">true</span>);
                 <span class="macro">assert_eq!</span>((-<span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_even(), <span class="bool-val">false</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_even(), <span class="bool-val">true</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_even(), <span class="bool-val">false</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">2 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_even(), <span class="bool-val">true</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_even(), <span class="bool-val">false</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">4 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_even(), <span class="bool-val">true</span>);
             }

             <span class="attribute">#[test]
             </span><span class="kw">fn </span>test_odd() {
                 <span class="macro">assert_eq!</span>((-<span class="number">4 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_odd(), <span class="bool-val">false</span>);
                 <span class="macro">assert_eq!</span>((-<span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_odd(), <span class="bool-val">true</span>);
                 <span class="macro">assert_eq!</span>((-<span class="number">2 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_odd(), <span class="bool-val">false</span>);
                 <span class="macro">assert_eq!</span>((-<span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_odd(), <span class="bool-val">true</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_odd(), <span class="bool-val">false</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_odd(), <span class="bool-val">true</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">2 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_odd(), <span class="bool-val">false</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_odd(), <span class="bool-val">true</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">4 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_odd(), <span class="bool-val">false</span>);
             }

             <span class="attribute">#[test]
             </span><span class="kw">fn </span>test_multiple_of_one_limits() {
                 <span class="kw">for </span>x <span class="kw">in </span><span class="kw-2">&amp;</span>[&lt;<span class="macro-nonterminal">$T</span>&gt;::min_value(), &lt;<span class="macro-nonterminal">$T</span>&gt;::max_value()] {
                     <span class="kw">for </span>one <span class="kw">in </span><span class="kw-2">&amp;</span>[<span class="number">1</span>, -<span class="number">1</span>] {
                         <span class="macro">assert_eq!</span>(Integer::next_multiple_of(x, one), <span class="kw-2">*</span>x);
                         <span class="macro">assert_eq!</span>(Integer::prev_multiple_of(x, one), <span class="kw-2">*</span>x);
                     }
                 }
             }
         }
     };
 }

 <span class="macro">impl_integer_for_isize!</span>(i8, test_integer_i8);
 <span class="macro">impl_integer_for_isize!</span>(i16, test_integer_i16);
 <span class="macro">impl_integer_for_isize!</span>(i32, test_integer_i32);
 <span class="macro">impl_integer_for_isize!</span>(i64, test_integer_i64);
 <span class="macro">impl_integer_for_isize!</span>(isize, test_integer_isize);
 <span class="attribute">#[cfg(has_i128)]
 </span><span class="macro">impl_integer_for_isize!</span>(i128, test_integer_i128);

 <span class="macro">macro_rules! </span>impl_integer_for_usize {
     (<span class="macro-nonterminal">$T</span>:ty, <span class="macro-nonterminal">$test_mod</span>:ident) =&gt; {
         <span class="kw">impl </span>Integer <span class="kw">for </span><span class="macro-nonterminal">$T </span>{
             <span class="doccomment">/// Unsigned integer division. Returns the same result as `div` (`/`).
             </span><span class="attribute">#[inline]
             </span><span class="kw">fn </span>div_floor(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; <span class="self">Self </span>{
                 <span class="kw-2">*</span><span class="self">self </span>/ <span class="kw-2">*</span>other
             }

             <span class="doccomment">/// Unsigned integer modulo operation. Returns the same result as `rem` (`%`).
             </span><span class="attribute">#[inline]
             </span><span class="kw">fn </span>mod_floor(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; <span class="self">Self </span>{
                 <span class="kw-2">*</span><span class="self">self </span>% <span class="kw-2">*</span>other
             }

             <span class="attribute">#[inline]
             </span><span class="kw">fn </span>div_ceil(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; <span class="self">Self </span>{
                 <span class="kw-2">*</span><span class="self">self </span>/ <span class="kw-2">*</span>other + (<span class="number">0 </span>!= <span class="kw-2">*</span><span class="self">self </span>% <span class="kw-2">*</span>other) <span class="kw">as </span><span class="self">Self
             </span>}

             <span class="doccomment">/// Calculates the Greatest Common Divisor (GCD) of the number and `other`
             </span><span class="attribute">#[inline]
             </span><span class="kw">fn </span>gcd(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; <span class="self">Self </span>{
                 <span class="comment">// Use Stein&#39;s algorithm
                 </span><span class="kw">let </span><span class="kw-2">mut </span>m = <span class="kw-2">*</span><span class="self">self</span>;
                 <span class="kw">let </span><span class="kw-2">mut </span>n = <span class="kw-2">*</span>other;
                 <span class="kw">if </span>m == <span class="number">0 </span>|| n == <span class="number">0 </span>{
                     <span class="kw">return </span>m | n;
                 }

                 <span class="comment">// find common factors of 2
                 </span><span class="kw">let </span>shift = (m | n).trailing_zeros();

                 <span class="comment">// divide n and m by 2 until odd
                 </span>m &gt;&gt;= m.trailing_zeros();
                 n &gt;&gt;= n.trailing_zeros();

                 <span class="kw">while </span>m != n {
                     <span class="kw">if </span>m &gt; n {
                         m -= n;
                         m &gt;&gt;= m.trailing_zeros();
                     } <span class="kw">else </span>{
                         n -= m;
                         n &gt;&gt;= n.trailing_zeros();
                     }
                 }
                 m &lt;&lt; shift
             }

             <span class="attribute">#[inline]
             </span><span class="kw">fn </span>extended_gcd_lcm(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; (ExtendedGcd&lt;<span class="self">Self</span>&gt;, <span class="self">Self</span>) {
                 <span class="kw">let </span>egcd = <span class="self">self</span>.extended_gcd(other);
                 <span class="comment">// should not have to recalculate abs
                 </span><span class="kw">let </span>lcm = <span class="kw">if </span>egcd.gcd.is_zero() {
                     <span class="self">Self</span>::zero()
                 } <span class="kw">else </span>{
                     <span class="kw-2">*</span><span class="self">self </span>* (<span class="kw-2">*</span>other / egcd.gcd)
                 };
                 (egcd, lcm)
             }

             <span class="doccomment">/// Calculates the Lowest Common Multiple (LCM) of the number and `other`.
             </span><span class="attribute">#[inline]
             </span><span class="kw">fn </span>lcm(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; <span class="self">Self </span>{
                 <span class="self">self</span>.gcd_lcm(other).<span class="number">1
             </span>}

             <span class="doccomment">/// Calculates the Greatest Common Divisor (GCD) and
             /// Lowest Common Multiple (LCM) of the number and `other`.
             </span><span class="attribute">#[inline]
             </span><span class="kw">fn </span>gcd_lcm(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; (<span class="self">Self</span>, <span class="self">Self</span>) {
                 <span class="kw">if </span><span class="self">self</span>.is_zero() &amp;&amp; other.is_zero() {
                     <span class="kw">return </span>(<span class="self">Self</span>::zero(), <span class="self">Self</span>::zero());
                 }
                 <span class="kw">let </span>gcd = <span class="self">self</span>.gcd(other);
                 <span class="kw">let </span>lcm = <span class="kw-2">*</span><span class="self">self </span>* (<span class="kw-2">*</span>other / gcd);
                 (gcd, lcm)
             }

             <span class="doccomment">/// Deprecated, use `is_multiple_of` instead.
             </span><span class="attribute">#[inline]
             </span><span class="kw">fn </span>divides(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; bool {
                 <span class="self">self</span>.is_multiple_of(other)
             }

             <span class="doccomment">/// Returns `true` if the number is a multiple of `other`.
             </span><span class="attribute">#[inline]
             </span><span class="kw">fn </span>is_multiple_of(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; bool {
                 <span class="kw">if </span>other.is_zero() {
                     <span class="kw">return </span><span class="self">self</span>.is_zero();
                 }
                 <span class="kw-2">*</span><span class="self">self </span>% <span class="kw-2">*</span>other == <span class="number">0
             </span>}

             <span class="doccomment">/// Returns `true` if the number is divisible by `2`.
             </span><span class="attribute">#[inline]
             </span><span class="kw">fn </span>is_even(<span class="kw-2">&amp;</span><span class="self">self</span>) -&gt; bool {
                 <span class="kw-2">*</span><span class="self">self </span>% <span class="number">2 </span>== <span class="number">0
             </span>}

             <span class="doccomment">/// Returns `true` if the number is not divisible by `2`.
             </span><span class="attribute">#[inline]
             </span><span class="kw">fn </span>is_odd(<span class="kw-2">&amp;</span><span class="self">self</span>) -&gt; bool {
                 !<span class="self">self</span>.is_even()
             }

             <span class="doccomment">/// Simultaneous truncated integer division and modulus.
             </span><span class="attribute">#[inline]
             </span><span class="kw">fn </span>div_rem(<span class="kw-2">&amp;</span><span class="self">self</span>, other: <span class="kw-2">&amp;</span><span class="self">Self</span>) -&gt; (<span class="self">Self</span>, <span class="self">Self</span>) {
                 (<span class="kw-2">*</span><span class="self">self </span>/ <span class="kw-2">*</span>other, <span class="kw-2">*</span><span class="self">self </span>% <span class="kw-2">*</span>other)
             }
         }

         <span class="attribute">#[cfg(test)]
         </span><span class="kw">mod </span><span class="macro-nonterminal">$test_mod </span>{
             <span class="kw">use </span>core::mem;
             <span class="kw">use </span>Integer;

             <span class="attribute">#[test]
             </span><span class="kw">fn </span>test_div_mod_floor() {
                 <span class="macro">assert_eq!</span>(&lt;<span class="macro-nonterminal">$T </span><span class="kw">as </span>Integer&gt;::div_floor(<span class="kw-2">&amp;</span><span class="number">10</span>, <span class="kw-2">&amp;</span><span class="number">3</span>), <span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>(&lt;<span class="macro-nonterminal">$T </span><span class="kw">as </span>Integer&gt;::mod_floor(<span class="kw-2">&amp;</span><span class="number">10</span>, <span class="kw-2">&amp;</span><span class="number">3</span>), <span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>(&lt;<span class="macro-nonterminal">$T </span><span class="kw">as </span>Integer&gt;::div_mod_floor(<span class="kw-2">&amp;</span><span class="number">10</span>, <span class="kw-2">&amp;</span><span class="number">3</span>), (<span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>, <span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>));
                 <span class="macro">assert_eq!</span>(&lt;<span class="macro-nonterminal">$T </span><span class="kw">as </span>Integer&gt;::div_floor(<span class="kw-2">&amp;</span><span class="number">5</span>, <span class="kw-2">&amp;</span><span class="number">5</span>), <span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>(&lt;<span class="macro-nonterminal">$T </span><span class="kw">as </span>Integer&gt;::mod_floor(<span class="kw-2">&amp;</span><span class="number">5</span>, <span class="kw-2">&amp;</span><span class="number">5</span>), <span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>(&lt;<span class="macro-nonterminal">$T </span><span class="kw">as </span>Integer&gt;::div_mod_floor(<span class="kw-2">&amp;</span><span class="number">5</span>, <span class="kw-2">&amp;</span><span class="number">5</span>), (<span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>, <span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>));
                 <span class="macro">assert_eq!</span>(&lt;<span class="macro-nonterminal">$T </span><span class="kw">as </span>Integer&gt;::div_floor(<span class="kw-2">&amp;</span><span class="number">3</span>, <span class="kw-2">&amp;</span><span class="number">7</span>), <span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>(&lt;<span class="macro-nonterminal">$T </span><span class="kw">as </span>Integer&gt;::div_floor(<span class="kw-2">&amp;</span><span class="number">3</span>, <span class="kw-2">&amp;</span><span class="number">7</span>), <span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>(&lt;<span class="macro-nonterminal">$T </span><span class="kw">as </span>Integer&gt;::mod_floor(<span class="kw-2">&amp;</span><span class="number">3</span>, <span class="kw-2">&amp;</span><span class="number">7</span>), <span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>(&lt;<span class="macro-nonterminal">$T </span><span class="kw">as </span>Integer&gt;::div_mod_floor(<span class="kw-2">&amp;</span><span class="number">3</span>, <span class="kw-2">&amp;</span><span class="number">7</span>), (<span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>, <span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>));
             }

             <span class="attribute">#[test]
             </span><span class="kw">fn </span>test_gcd() {
                 <span class="macro">assert_eq!</span>((<span class="number">10 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).gcd(<span class="kw-2">&amp;</span><span class="number">2</span>), <span class="number">2 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">10 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).gcd(<span class="kw-2">&amp;</span><span class="number">3</span>), <span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).gcd(<span class="kw-2">&amp;</span><span class="number">3</span>), <span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).gcd(<span class="kw-2">&amp;</span><span class="number">3</span>), <span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">56 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).gcd(<span class="kw-2">&amp;</span><span class="number">42</span>), <span class="number">14 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
             }

             <span class="attribute">#[test]
             </span><span class="kw">fn </span>test_gcd_cmp_with_euclidean() {
                 <span class="kw">fn </span>euclidean_gcd(<span class="kw-2">mut </span>m: <span class="macro-nonterminal">$T</span>, <span class="kw-2">mut </span>n: <span class="macro-nonterminal">$T</span>) -&gt; <span class="macro-nonterminal">$T </span>{
                     <span class="kw">while </span>m != <span class="number">0 </span>{
                         mem::swap(<span class="kw-2">&amp;mut </span>m, <span class="kw-2">&amp;mut </span>n);
                         m %= n;
                     }
                     n
                 }

                 <span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..<span class="number">255 </span>{
                     <span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..<span class="number">255 </span>{
                         <span class="macro">assert_eq!</span>(euclidean_gcd(i, j), i.gcd(<span class="kw-2">&amp;</span>j));
                     }
                 }

                 <span class="comment">// last value
                 // FIXME: Use inclusive ranges for above loop when implemented
                 </span><span class="kw">let </span>i = <span class="number">255</span>;
                 <span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..<span class="number">255 </span>{
                     <span class="macro">assert_eq!</span>(euclidean_gcd(i, j), i.gcd(<span class="kw-2">&amp;</span>j));
                 }
                 <span class="macro">assert_eq!</span>(<span class="number">255</span>.gcd(<span class="kw-2">&amp;</span><span class="number">255</span>), <span class="number">255</span>);
             }

             <span class="attribute">#[test]
             </span><span class="kw">fn </span>test_lcm() {
                 <span class="macro">assert_eq!</span>((<span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).lcm(<span class="kw-2">&amp;</span><span class="number">0</span>), <span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).lcm(<span class="kw-2">&amp;</span><span class="number">1</span>), <span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).lcm(<span class="kw-2">&amp;</span><span class="number">1</span>), <span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">8 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).lcm(<span class="kw-2">&amp;</span><span class="number">9</span>), <span class="number">72 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">11 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).lcm(<span class="kw-2">&amp;</span><span class="number">5</span>), <span class="number">55 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">15 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).lcm(<span class="kw-2">&amp;</span><span class="number">17</span>), <span class="number">255 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
             }

             <span class="attribute">#[test]
             </span><span class="kw">fn </span>test_gcd_lcm() {
                 <span class="kw">for </span>i <span class="kw">in </span>(<span class="number">0</span>..).take(<span class="number">256</span>) {
                     <span class="kw">for </span>j <span class="kw">in </span>(<span class="number">0</span>..).take(<span class="number">256</span>) {
                         <span class="macro">assert_eq!</span>(i.gcd_lcm(<span class="kw-2">&amp;</span>j), (i.gcd(<span class="kw-2">&amp;</span>j), i.lcm(<span class="kw-2">&amp;</span>j)));
                     }
                 }
             }

             <span class="attribute">#[test]
             </span><span class="kw">fn </span>test_is_multiple_of() {
                 <span class="macro">assert!</span>((<span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_multiple_of(<span class="kw-2">&amp;</span>(<span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>)));
                 <span class="macro">assert!</span>((<span class="number">6 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_multiple_of(<span class="kw-2">&amp;</span>(<span class="number">6 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>)));
                 <span class="macro">assert!</span>((<span class="number">6 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_multiple_of(<span class="kw-2">&amp;</span>(<span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>)));
                 <span class="macro">assert!</span>((<span class="number">6 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_multiple_of(<span class="kw-2">&amp;</span>(<span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>)));

                 <span class="macro">assert!</span>(!(<span class="number">42 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_multiple_of(<span class="kw-2">&amp;</span>(<span class="number">5 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>)));
                 <span class="macro">assert!</span>(!(<span class="number">5 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_multiple_of(<span class="kw-2">&amp;</span>(<span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>)));
                 <span class="macro">assert!</span>(!(<span class="number">42 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_multiple_of(<span class="kw-2">&amp;</span>(<span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>)));
             }

             <span class="attribute">#[test]
             </span><span class="kw">fn </span>test_even() {
                 <span class="macro">assert_eq!</span>((<span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_even(), <span class="bool-val">true</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_even(), <span class="bool-val">false</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">2 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_even(), <span class="bool-val">true</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_even(), <span class="bool-val">false</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">4 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_even(), <span class="bool-val">true</span>);
             }

             <span class="attribute">#[test]
             </span><span class="kw">fn </span>test_odd() {
                 <span class="macro">assert_eq!</span>((<span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_odd(), <span class="bool-val">false</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_odd(), <span class="bool-val">true</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">2 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_odd(), <span class="bool-val">false</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_odd(), <span class="bool-val">true</span>);
                 <span class="macro">assert_eq!</span>((<span class="number">4 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_odd(), <span class="bool-val">false</span>);
             }
         }
     };
 }

 <span class="macro">impl_integer_for_usize!</span>(u8, test_integer_u8);
 <span class="macro">impl_integer_for_usize!</span>(u16, test_integer_u16);
 <span class="macro">impl_integer_for_usize!</span>(u32, test_integer_u32);
 <span class="macro">impl_integer_for_usize!</span>(u64, test_integer_u64);
 <span class="macro">impl_integer_for_usize!</span>(usize, test_integer_usize);
 <span class="attribute">#[cfg(has_i128)]
 </span><span class="macro">impl_integer_for_usize!</span>(u128, test_integer_u128);

 <span class="doccomment">/// An iterator over binomial coefficients.
 </span><span class="kw">pub struct </span>IterBinomial&lt;T&gt; {
     a: T,
     n: T,
     k: T,
 }

 <span class="kw">impl</span>&lt;T&gt; IterBinomial&lt;T&gt;
 <span class="kw">where
     </span>T: Integer,
 {
     <span class="doccomment">/// For a given n, iterate over all binomial coefficients binomial(n, k), for k=0...n.
     ///
     /// Note that this might overflow, depending on `T`. For the primitive
     /// integer types, the following n are the largest ones for which there will
     /// be no overflow:
     ///
     /// type | n
     /// -----|---
     /// u8   | 10
     /// i8   |  9
     /// u16  | 18
     /// i16  | 17
     /// u32  | 34
     /// i32  | 33
     /// u64  | 67
     /// i64  | 66
     ///
     /// For larger n, `T` should be a bigint type.
     </span><span class="kw">pub fn </span>new(n: T) -&gt; IterBinomial&lt;T&gt; {
         IterBinomial {
             k: T::zero(),
             a: T::one(),
             n: n,
         }
     }
 }

 <span class="kw">impl</span>&lt;T&gt; Iterator <span class="kw">for </span>IterBinomial&lt;T&gt;
 <span class="kw">where
     </span>T: Integer + Clone,
 {
     <span class="kw">type </span>Item = T;

     <span class="kw">fn </span>next(<span class="kw-2">&amp;mut </span><span class="self">self</span>) -&gt; <span class="prelude-ty">Option</span>&lt;T&gt; {
         <span class="kw">if </span><span class="self">self</span>.k &gt; <span class="self">self</span>.n {
             <span class="kw">return </span><span class="prelude-val">None</span>;
         }
         <span class="self">self</span>.a = <span class="kw">if </span>!<span class="self">self</span>.k.is_zero() {
             multiply_and_divide(
                 <span class="self">self</span>.a.clone(),
                 <span class="self">self</span>.n.clone() - <span class="self">self</span>.k.clone() + T::one(),
                 <span class="self">self</span>.k.clone(),
             )
         } <span class="kw">else </span>{
             T::one()
         };
         <span class="self">self</span>.k = <span class="self">self</span>.k.clone() + T::one();
         <span class="prelude-val">Some</span>(<span class="self">self</span>.a.clone())
     }
 }

 <span class="doccomment">/// Calculate r * a / b, avoiding overflows and fractions.
 ///
 /// Assumes that b divides r * a evenly.
 </span><span class="kw">fn </span>multiply_and_divide&lt;T: Integer + Clone&gt;(r: T, a: T, b: T) -&gt; T {
     <span class="comment">// See http://blog.plover.com/math/choose-2.html for the idea.
     </span><span class="kw">let </span>g = gcd(r.clone(), b.clone());
     r / g.clone() * (a / (b / g))
 }

 <span class="doccomment">/// Calculate the binomial coefficient.
 ///
 /// Note that this might overflow, depending on `T`. For the primitive integer
 /// types, the following n are the largest ones possible such that there will
 /// be no overflow for any k:
 ///
 /// type | n
 /// -----|---
 /// u8   | 10
 /// i8   |  9
 /// u16  | 18
 /// i16  | 17
 /// u32  | 34
 /// i32  | 33
 /// u64  | 67
 /// i64  | 66
 ///
 /// For larger n, consider using a bigint type for `T`.
 </span><span class="kw">pub fn </span>binomial&lt;T: Integer + Clone&gt;(<span class="kw-2">mut </span>n: T, k: T) -&gt; T {
     <span class="comment">// See http://blog.plover.com/math/choose.html for the idea.
     </span><span class="kw">if </span>k &gt; n {
         <span class="kw">return </span>T::zero();
     }
     <span class="kw">if </span>k &gt; n.clone() - k.clone() {
         <span class="kw">return </span>binomial(n.clone(), n - k);
     }
     <span class="kw">let </span><span class="kw-2">mut </span>r = T::one();
     <span class="kw">let </span><span class="kw-2">mut </span>d = T::one();
     <span class="kw">loop </span>{
         <span class="kw">if </span>d &gt; k {
             <span class="kw">break</span>;
         }
         r = multiply_and_divide(r, n.clone(), d.clone());
         n = n - T::one();
         d = d + T::one();
     }
     r
 }

 <span class="doccomment">/// Calculate the multinomial coefficient.
 </span><span class="kw">pub fn </span>multinomial&lt;T: Integer + Clone&gt;(k: <span class="kw-2">&amp;</span>[T]) -&gt; T
 <span class="kw">where
     for</span>&lt;<span class="lifetime">&#39;a</span>&gt; T: Add&lt;<span class="kw-2">&amp;</span><span class="lifetime">&#39;a </span>T, Output = T&gt;,
 {
     <span class="kw">let </span><span class="kw-2">mut </span>r = T::one();
     <span class="kw">let </span><span class="kw-2">mut </span>p = T::zero();
     <span class="kw">for </span>i <span class="kw">in </span>k {
         p = p + i;
         r = r * binomial(p.clone(), i.clone());
     }
     r
 }

 <span class="attribute">#[test]
 </span><span class="kw">fn </span>test_lcm_overflow() {
     <span class="macro">macro_rules! </span>check {
         (<span class="macro-nonterminal">$t</span>:ty, <span class="macro-nonterminal">$x</span>:expr, <span class="macro-nonterminal">$y</span>:expr, <span class="macro-nonterminal">$r</span>:expr) =&gt; {{
             <span class="kw">let </span>x: <span class="macro-nonterminal">$t </span>= <span class="macro-nonterminal">$x</span>;
             <span class="kw">let </span>y: <span class="macro-nonterminal">$t </span>= <span class="macro-nonterminal">$y</span>;
             <span class="kw">let </span>o = x.checked_mul(y);
             <span class="macro">assert!</span>(
                 o.is_none(),
                 <span class="string">&quot;sanity checking that {} input {} * {} overflows&quot;</span>,
                 <span class="macro">stringify!</span>(<span class="macro-nonterminal">$t</span>),
                 x,
                 y
             );
             <span class="macro">assert_eq!</span>(x.lcm(<span class="kw-2">&amp;</span>y), <span class="macro-nonterminal">$r</span>);
             <span class="macro">assert_eq!</span>(y.lcm(<span class="kw-2">&amp;</span>x), <span class="macro-nonterminal">$r</span>);
         }};
     }

     <span class="comment">// Original bug (Issue #166)
     </span><span class="macro">check!</span>(i64, <span class="number">46656000000000000</span>, <span class="number">600</span>, <span class="number">46656000000000000</span>);

     <span class="macro">check!</span>(i8, <span class="number">0x40</span>, <span class="number">0x04</span>, <span class="number">0x40</span>);
     <span class="macro">check!</span>(u8, <span class="number">0x80</span>, <span class="number">0x02</span>, <span class="number">0x80</span>);
     <span class="macro">check!</span>(i16, <span class="number">0x40_00</span>, <span class="number">0x04</span>, <span class="number">0x40_00</span>);
     <span class="macro">check!</span>(u16, <span class="number">0x80_00</span>, <span class="number">0x02</span>, <span class="number">0x80_00</span>);
     <span class="macro">check!</span>(i32, <span class="number">0x4000_0000</span>, <span class="number">0x04</span>, <span class="number">0x4000_0000</span>);
     <span class="macro">check!</span>(u32, <span class="number">0x8000_0000</span>, <span class="number">0x02</span>, <span class="number">0x8000_0000</span>);
     <span class="macro">check!</span>(i64, <span class="number">0x4000_0000_0000_0000</span>, <span class="number">0x04</span>, <span class="number">0x4000_0000_0000_0000</span>);
     <span class="macro">check!</span>(u64, <span class="number">0x8000_0000_0000_0000</span>, <span class="number">0x02</span>, <span class="number">0x8000_0000_0000_0000</span>);
 }

 <span class="attribute">#[test]
 </span><span class="kw">fn </span>test_iter_binomial() {
     <span class="macro">macro_rules! </span>check_simple {
         (<span class="macro-nonterminal">$t</span>:ty) =&gt; {{
             <span class="kw">let </span>n: <span class="macro-nonterminal">$t </span>= <span class="number">3</span>;
             <span class="kw">let </span>expected = [<span class="number">1</span>, <span class="number">3</span>, <span class="number">3</span>, <span class="number">1</span>];
             <span class="kw">for </span>(b, <span class="kw-2">&amp;</span>e) <span class="kw">in </span>IterBinomial::new(n).zip(<span class="kw-2">&amp;</span>expected) {
                 <span class="macro">assert_eq!</span>(b, e);
             }
         }};
     }

     <span class="macro">check_simple!</span>(u8);
     <span class="macro">check_simple!</span>(i8);
     <span class="macro">check_simple!</span>(u16);
     <span class="macro">check_simple!</span>(i16);
     <span class="macro">check_simple!</span>(u32);
     <span class="macro">check_simple!</span>(i32);
     <span class="macro">check_simple!</span>(u64);
     <span class="macro">check_simple!</span>(i64);

     <span class="macro">macro_rules! </span>check_binomial {
         (<span class="macro-nonterminal">$t</span>:ty, <span class="macro-nonterminal">$n</span>:expr) =&gt; {{
             <span class="kw">let </span>n: <span class="macro-nonterminal">$t </span>= <span class="macro-nonterminal">$n</span>;
             <span class="kw">let </span><span class="kw-2">mut </span>k: <span class="macro-nonterminal">$t </span>= <span class="number">0</span>;
             <span class="kw">for </span>b <span class="kw">in </span>IterBinomial::new(n) {
                 <span class="macro">assert_eq!</span>(b, binomial(n, k));
                 k += <span class="number">1</span>;
             }
         }};
     }

     <span class="comment">// Check the largest n for which there is no overflow.
     </span><span class="macro">check_binomial!</span>(u8, <span class="number">10</span>);
     <span class="macro">check_binomial!</span>(i8, <span class="number">9</span>);
     <span class="macro">check_binomial!</span>(u16, <span class="number">18</span>);
     <span class="macro">check_binomial!</span>(i16, <span class="number">17</span>);
     <span class="macro">check_binomial!</span>(u32, <span class="number">34</span>);
     <span class="macro">check_binomial!</span>(i32, <span class="number">33</span>);
     <span class="macro">check_binomial!</span>(u64, <span class="number">67</span>);
     <span class="macro">check_binomial!</span>(i64, <span class="number">66</span>);
 }

 <span class="attribute">#[test]
 </span><span class="kw">fn </span>test_binomial() {
     <span class="macro">macro_rules! </span>check {
         (<span class="macro-nonterminal">$t</span>:ty, <span class="macro-nonterminal">$x</span>:expr, <span class="macro-nonterminal">$y</span>:expr, <span class="macro-nonterminal">$r</span>:expr) =&gt; {{
             <span class="kw">let </span>x: <span class="macro-nonterminal">$t </span>= <span class="macro-nonterminal">$x</span>;
             <span class="kw">let </span>y: <span class="macro-nonterminal">$t </span>= <span class="macro-nonterminal">$y</span>;
             <span class="kw">let </span>expected: <span class="macro-nonterminal">$t </span>= <span class="macro-nonterminal">$r</span>;
             <span class="macro">assert_eq!</span>(binomial(x, y), expected);
             <span class="kw">if </span>y &lt;= x {
                 <span class="macro">assert_eq!</span>(binomial(x, x - y), expected);
             }
         }};
     }
     <span class="macro">check!</span>(u8, <span class="number">9</span>, <span class="number">4</span>, <span class="number">126</span>);
     <span class="macro">check!</span>(u8, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>);
     <span class="macro">check!</span>(u8, <span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>);

     <span class="macro">check!</span>(i8, <span class="number">9</span>, <span class="number">4</span>, <span class="number">126</span>);
     <span class="macro">check!</span>(i8, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>);
     <span class="macro">check!</span>(i8, <span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>);

     <span class="macro">check!</span>(u16, <span class="number">100</span>, <span class="number">2</span>, <span class="number">4950</span>);
     <span class="macro">check!</span>(u16, <span class="number">14</span>, <span class="number">4</span>, <span class="number">1001</span>);
     <span class="macro">check!</span>(u16, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>);
     <span class="macro">check!</span>(u16, <span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>);

     <span class="macro">check!</span>(i16, <span class="number">100</span>, <span class="number">2</span>, <span class="number">4950</span>);
     <span class="macro">check!</span>(i16, <span class="number">14</span>, <span class="number">4</span>, <span class="number">1001</span>);
     <span class="macro">check!</span>(i16, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>);
     <span class="macro">check!</span>(i16, <span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>);

     <span class="macro">check!</span>(u32, <span class="number">100</span>, <span class="number">2</span>, <span class="number">4950</span>);
     <span class="macro">check!</span>(u32, <span class="number">35</span>, <span class="number">11</span>, <span class="number">417225900</span>);
     <span class="macro">check!</span>(u32, <span class="number">14</span>, <span class="number">4</span>, <span class="number">1001</span>);
     <span class="macro">check!</span>(u32, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>);
     <span class="macro">check!</span>(u32, <span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>);

     <span class="macro">check!</span>(i32, <span class="number">100</span>, <span class="number">2</span>, <span class="number">4950</span>);
     <span class="macro">check!</span>(i32, <span class="number">35</span>, <span class="number">11</span>, <span class="number">417225900</span>);
     <span class="macro">check!</span>(i32, <span class="number">14</span>, <span class="number">4</span>, <span class="number">1001</span>);
     <span class="macro">check!</span>(i32, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>);
     <span class="macro">check!</span>(i32, <span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>);

     <span class="macro">check!</span>(u64, <span class="number">100</span>, <span class="number">2</span>, <span class="number">4950</span>);
     <span class="macro">check!</span>(u64, <span class="number">35</span>, <span class="number">11</span>, <span class="number">417225900</span>);
     <span class="macro">check!</span>(u64, <span class="number">14</span>, <span class="number">4</span>, <span class="number">1001</span>);
     <span class="macro">check!</span>(u64, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>);
     <span class="macro">check!</span>(u64, <span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>);

     <span class="macro">check!</span>(i64, <span class="number">100</span>, <span class="number">2</span>, <span class="number">4950</span>);
     <span class="macro">check!</span>(i64, <span class="number">35</span>, <span class="number">11</span>, <span class="number">417225900</span>);
     <span class="macro">check!</span>(i64, <span class="number">14</span>, <span class="number">4</span>, <span class="number">1001</span>);
     <span class="macro">check!</span>(i64, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>);
     <span class="macro">check!</span>(i64, <span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>);
 }

 <span class="attribute">#[test]
 </span><span class="kw">fn </span>test_multinomial() {
     <span class="macro">macro_rules! </span>check_binomial {
         (<span class="macro-nonterminal">$t</span>:ty, <span class="macro-nonterminal">$k</span>:expr) =&gt; {{
             <span class="kw">let </span>n: <span class="macro-nonterminal">$t </span>= <span class="macro-nonterminal">$k</span>.iter().fold(<span class="number">0</span>, |acc, <span class="kw-2">&amp;</span>x| acc + x);
             <span class="kw">let </span>k: <span class="kw-2">&amp;</span>[<span class="macro-nonterminal">$t</span>] = <span class="macro-nonterminal">$k</span>;
             <span class="macro">assert_eq!</span>(k.len(), <span class="number">2</span>);
             <span class="macro">assert_eq!</span>(multinomial(k), binomial(n, k[<span class="number">0</span>]));
         }};
     }

     <span class="macro">check_binomial!</span>(u8, <span class="kw-2">&amp;</span>[<span class="number">4</span>, <span class="number">5</span>]);

     <span class="macro">check_binomial!</span>(i8, <span class="kw-2">&amp;</span>[<span class="number">4</span>, <span class="number">5</span>]);

     <span class="macro">check_binomial!</span>(u16, <span class="kw-2">&amp;</span>[<span class="number">2</span>, <span class="number">98</span>]);
     <span class="macro">check_binomial!</span>(u16, <span class="kw-2">&amp;</span>[<span class="number">4</span>, <span class="number">10</span>]);

     <span class="macro">check_binomial!</span>(i16, <span class="kw-2">&amp;</span>[<span class="number">2</span>, <span class="number">98</span>]);
     <span class="macro">check_binomial!</span>(i16, <span class="kw-2">&amp;</span>[<span class="number">4</span>, <span class="number">10</span>]);

     <span class="macro">check_binomial!</span>(u32, <span class="kw-2">&amp;</span>[<span class="number">2</span>, <span class="number">98</span>]);
     <span class="macro">check_binomial!</span>(u32, <span class="kw-2">&amp;</span>[<span class="number">11</span>, <span class="number">24</span>]);
     <span class="macro">check_binomial!</span>(u32, <span class="kw-2">&amp;</span>[<span class="number">4</span>, <span class="number">10</span>]);

     <span class="macro">check_binomial!</span>(i32, <span class="kw-2">&amp;</span>[<span class="number">2</span>, <span class="number">98</span>]);
     <span class="macro">check_binomial!</span>(i32, <span class="kw-2">&amp;</span>[<span class="number">11</span>, <span class="number">24</span>]);
     <span class="macro">check_binomial!</span>(i32, <span class="kw-2">&amp;</span>[<span class="number">4</span>, <span class="number">10</span>]);

     <span class="macro">check_binomial!</span>(u64, <span class="kw-2">&amp;</span>[<span class="number">2</span>, <span class="number">98</span>]);
     <span class="macro">check_binomial!</span>(u64, <span class="kw-2">&amp;</span>[<span class="number">11</span>, <span class="number">24</span>]);
     <span class="macro">check_binomial!</span>(u64, <span class="kw-2">&amp;</span>[<span class="number">4</span>, <span class="number">10</span>]);

     <span class="macro">check_binomial!</span>(i64, <span class="kw-2">&amp;</span>[<span class="number">2</span>, <span class="number">98</span>]);
     <span class="macro">check_binomial!</span>(i64, <span class="kw-2">&amp;</span>[<span class="number">11</span>, <span class="number">24</span>]);
     <span class="macro">check_binomial!</span>(i64, <span class="kw-2">&amp;</span>[<span class="number">4</span>, <span class="number">10</span>]);

     <span class="macro">macro_rules! </span>check_multinomial {
         (<span class="macro-nonterminal">$t</span>:ty, <span class="macro-nonterminal">$k</span>:expr, <span class="macro-nonterminal">$r</span>:expr) =&gt; {{
             <span class="kw">let </span>k: <span class="kw-2">&amp;</span>[<span class="macro-nonterminal">$t</span>] = <span class="macro-nonterminal">$k</span>;
             <span class="kw">let </span>expected: <span class="macro-nonterminal">$t </span>= <span class="macro-nonterminal">$r</span>;
             <span class="macro">assert_eq!</span>(multinomial(k), expected);
         }};
     }

     <span class="macro">check_multinomial!</span>(u8, <span class="kw-2">&amp;</span>[<span class="number">2</span>, <span class="number">1</span>, <span class="number">2</span>], <span class="number">30</span>);
     <span class="macro">check_multinomial!</span>(u8, <span class="kw-2">&amp;</span>[<span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>], <span class="number">10</span>);

     <span class="macro">check_multinomial!</span>(i8, <span class="kw-2">&amp;</span>[<span class="number">2</span>, <span class="number">1</span>, <span class="number">2</span>], <span class="number">30</span>);
     <span class="macro">check_multinomial!</span>(i8, <span class="kw-2">&amp;</span>[<span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>], <span class="number">10</span>);

     <span class="macro">check_multinomial!</span>(u16, <span class="kw-2">&amp;</span>[<span class="number">2</span>, <span class="number">1</span>, <span class="number">2</span>], <span class="number">30</span>);
     <span class="macro">check_multinomial!</span>(u16, <span class="kw-2">&amp;</span>[<span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>], <span class="number">10</span>);

     <span class="macro">check_multinomial!</span>(i16, <span class="kw-2">&amp;</span>[<span class="number">2</span>, <span class="number">1</span>, <span class="number">2</span>], <span class="number">30</span>);
     <span class="macro">check_multinomial!</span>(i16, <span class="kw-2">&amp;</span>[<span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>], <span class="number">10</span>);

     <span class="macro">check_multinomial!</span>(u32, <span class="kw-2">&amp;</span>[<span class="number">2</span>, <span class="number">1</span>, <span class="number">2</span>], <span class="number">30</span>);
     <span class="macro">check_multinomial!</span>(u32, <span class="kw-2">&amp;</span>[<span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>], <span class="number">10</span>);

     <span class="macro">check_multinomial!</span>(i32, <span class="kw-2">&amp;</span>[<span class="number">2</span>, <span class="number">1</span>, <span class="number">2</span>], <span class="number">30</span>);
     <span class="macro">check_multinomial!</span>(i32, <span class="kw-2">&amp;</span>[<span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>], <span class="number">10</span>);

     <span class="macro">check_multinomial!</span>(u64, <span class="kw-2">&amp;</span>[<span class="number">2</span>, <span class="number">1</span>, <span class="number">2</span>], <span class="number">30</span>);
     <span class="macro">check_multinomial!</span>(u64, <span class="kw-2">&amp;</span>[<span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>], <span class="number">10</span>);

     <span class="macro">check_multinomial!</span>(i64, <span class="kw-2">&amp;</span>[<span class="number">2</span>, <span class="number">1</span>, <span class="number">2</span>], <span class="number">30</span>);
     <span class="macro">check_multinomial!</span>(i64, <span class="kw-2">&amp;</span>[<span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>], <span class="number">10</span>);

     <span class="macro">check_multinomial!</span>(u64, <span class="kw-2">&amp;</span>[], <span class="number">1</span>);
     <span class="macro">check_multinomial!</span>(u64, <span class="kw-2">&amp;</span>[<span class="number">0</span>], <span class="number">1</span>);
     <span class="macro">check_multinomial!</span>(u64, <span class="kw-2">&amp;</span>[<span class="number">12345</span>], <span class="number">1</span>);
 }
 </code></pre></div>
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