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</pre><pre class="rust">
<span class="comment">// Copyright 2013-2014 The Rust Project Developers. See the COPYRIGHT</span>
<span class="comment">// file at the top-level directory of this distribution and at</span>
<span class="comment">// http://rust-lang.org/COPYRIGHT.</span>
<span class="comment">//</span>
<span class="comment">// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or</span>
<span class="comment">// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license</span>
<span class="comment">// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your</span>
<span class="comment">// option. This file may not be copied, modified, or distributed</span>
<span class="comment">// except according to those terms.</span>
<span class="doccomment">//! Integer trait and functions.</span>
<span class="doccomment">//!</span>
<span class="doccomment">//! ## Compatibility</span>
<span class="doccomment">//!</span>
<span class="doccomment">//! The `num-integer` crate is tested for rustc 1.8 and greater.</span>
<span class="attribute">#![<span class="ident">doc</span>(<span class="ident">html_root_url</span> <span class="op">=</span> <span class="string">"https://docs.rs/num-integer/0.1"</span>)]</span>
<span class="attribute">#![<span class="ident">no_std</span>]</span>
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"std"</span>)]</span>
<span class="kw">extern</span> <span class="kw">crate</span> <span class="ident">std</span>;
<span class="kw">extern</span> <span class="kw">crate</span> <span class="ident">num_traits</span> <span class="kw">as</span> <span class="ident">traits</span>;
<span class="kw">use</span> <span class="ident">core::mem</span>;
<span class="kw">use</span> <span class="ident">core::ops::Add</span>;
<span class="kw">use</span> <span class="ident">traits</span>::{<span class="ident">Num</span>, <span class="ident">Signed</span>, <span class="ident">Zero</span>};
<span class="kw">mod</span> <span class="ident">roots</span>;
<span class="kw">pub</span> <span class="kw">use</span> <span class="ident">roots::Roots</span>;
<span class="kw">pub</span> <span class="kw">use</span> <span class="ident">roots</span>::{<span class="ident">cbrt</span>, <span class="ident">nth_root</span>, <span class="ident">sqrt</span>};
<span class="kw">mod</span> <span class="ident">average</span>;
<span class="kw">pub</span> <span class="kw">use</span> <span class="ident">average::Average</span>;
<span class="kw">pub</span> <span class="kw">use</span> <span class="ident">average</span>::{<span class="ident">average_ceil</span>, <span class="ident">average_floor</span>};
<span class="kw">pub</span> <span class="kw">trait</span> <span class="ident">Integer</span>: <span class="ident">Sized</span> <span class="op">+</span> <span class="ident">Num</span> <span class="op">+</span> <span class="ident">PartialOrd</span> <span class="op">+</span> <span class="ident">Ord</span> <span class="op">+</span> <span class="ident">Eq</span> {
<span class="doccomment">/// Floored integer division.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ~~~</span>
<span class="doccomment">/// # use num_integer::Integer;</span>
<span class="doccomment">/// assert!(( 8).div_floor(& 3) == 2);</span>
<span class="doccomment">/// assert!(( 8).div_floor(&-3) == -3);</span>
<span class="doccomment">/// assert!((-8).div_floor(& 3) == -3);</span>
<span class="doccomment">/// assert!((-8).div_floor(&-3) == 2);</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(( 1).div_floor(& 2) == 0);</span>
<span class="doccomment">/// assert!(( 1).div_floor(&-2) == -1);</span>
<span class="doccomment">/// assert!((-1).div_floor(& 2) == -1);</span>
<span class="doccomment">/// assert!((-1).div_floor(&-2) == 0);</span>
<span class="doccomment">/// ~~~</span>
<span class="kw">fn</span> <span class="ident">div_floor</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span>;
<span class="doccomment">/// Floored integer modulo, satisfying:</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ~~~</span>
<span class="doccomment">/// # use num_integer::Integer;</span>
<span class="doccomment">/// # let n = 1; let d = 1;</span>
<span class="doccomment">/// assert!(n.div_floor(&d) * d + n.mod_floor(&d) == n)</span>
<span class="doccomment">/// ~~~</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ~~~</span>
<span class="doccomment">/// # use num_integer::Integer;</span>
<span class="doccomment">/// assert!(( 8).mod_floor(& 3) == 2);</span>
<span class="doccomment">/// assert!(( 8).mod_floor(&-3) == -1);</span>
<span class="doccomment">/// assert!((-8).mod_floor(& 3) == 1);</span>
<span class="doccomment">/// assert!((-8).mod_floor(&-3) == -2);</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert!(( 1).mod_floor(& 2) == 1);</span>
<span class="doccomment">/// assert!(( 1).mod_floor(&-2) == -1);</span>
<span class="doccomment">/// assert!((-1).mod_floor(& 2) == 1);</span>
<span class="doccomment">/// assert!((-1).mod_floor(&-2) == -1);</span>
<span class="doccomment">/// ~~~</span>
<span class="kw">fn</span> <span class="ident">mod_floor</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span>;
<span class="doccomment">/// Ceiled integer division.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ~~~</span>
<span class="doccomment">/// # use num_integer::Integer;</span>
<span class="doccomment">/// assert_eq!(( 8).div_ceil( &3), 3);</span>
<span class="doccomment">/// assert_eq!(( 8).div_ceil(&-3), -2);</span>
<span class="doccomment">/// assert_eq!((-8).div_ceil( &3), -2);</span>
<span class="doccomment">/// assert_eq!((-8).div_ceil(&-3), 3);</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert_eq!(( 1).div_ceil( &2), 1);</span>
<span class="doccomment">/// assert_eq!(( 1).div_ceil(&-2), 0);</span>
<span class="doccomment">/// assert_eq!((-1).div_ceil( &2), 0);</span>
<span class="doccomment">/// assert_eq!((-1).div_ceil(&-2), 1);</span>
<span class="doccomment">/// ~~~</span>
<span class="kw">fn</span> <span class="ident">div_ceil</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span> {
<span class="kw">let</span> (<span class="ident">q</span>, <span class="ident">r</span>) <span class="op">=</span> <span class="self">self</span>.<span class="ident">div_mod_floor</span>(<span class="ident">other</span>);
<span class="kw">if</span> <span class="ident">r</span>.<span class="ident">is_zero</span>() {
<span class="ident">q</span>
} <span class="kw">else</span> {
<span class="ident">q</span> <span class="op">+</span> <span class="self">Self</span><span class="ident">::one</span>()
}
}
<span class="doccomment">/// Greatest Common Divisor (GCD).</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ~~~</span>
<span class="doccomment">/// # use num_integer::Integer;</span>
<span class="doccomment">/// assert_eq!(6.gcd(&8), 2);</span>
<span class="doccomment">/// assert_eq!(7.gcd(&3), 1);</span>
<span class="doccomment">/// ~~~</span>
<span class="kw">fn</span> <span class="ident">gcd</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span>;
<span class="doccomment">/// Lowest Common Multiple (LCM).</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ~~~</span>
<span class="doccomment">/// # use num_integer::Integer;</span>
<span class="doccomment">/// assert_eq!(7.lcm(&3), 21);</span>
<span class="doccomment">/// assert_eq!(2.lcm(&4), 4);</span>
<span class="doccomment">/// assert_eq!(0.lcm(&0), 0);</span>
<span class="doccomment">/// ~~~</span>
<span class="kw">fn</span> <span class="ident">lcm</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span>;
<span class="doccomment">/// Greatest Common Divisor (GCD) and</span>
<span class="doccomment">/// Lowest Common Multiple (LCM) together.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// Potentially more efficient than calling `gcd` and `lcm`</span>
<span class="doccomment">/// individually for identical inputs.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ~~~</span>
<span class="doccomment">/// # use num_integer::Integer;</span>
<span class="doccomment">/// assert_eq!(10.gcd_lcm(&4), (2, 20));</span>
<span class="doccomment">/// assert_eq!(8.gcd_lcm(&9), (1, 72));</span>
<span class="doccomment">/// ~~~</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">gcd_lcm</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> (<span class="self">Self</span>, <span class="self">Self</span>) {
(<span class="self">self</span>.<span class="ident">gcd</span>(<span class="ident">other</span>), <span class="self">self</span>.<span class="ident">lcm</span>(<span class="ident">other</span>))
}
<span class="doccomment">/// Greatest common divisor and Bézout coefficients.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ~~~</span>
<span class="doccomment">/// # extern crate num_integer;</span>
<span class="doccomment">/// # extern crate num_traits;</span>
<span class="doccomment">/// # fn main() {</span>
<span class="doccomment">/// # use num_integer::{ExtendedGcd, Integer};</span>
<span class="doccomment">/// # use num_traits::NumAssign;</span>
<span class="doccomment">/// fn check<A: Copy + Integer + NumAssign>(a: A, b: A) -> bool {</span>
<span class="doccomment">/// let ExtendedGcd { gcd, x, y, .. } = a.extended_gcd(&b);</span>
<span class="doccomment">/// gcd == x * a + y * b</span>
<span class="doccomment">/// }</span>
<span class="doccomment">/// assert!(check(10isize, 4isize));</span>
<span class="doccomment">/// assert!(check(8isize, 9isize));</span>
<span class="doccomment">/// # }</span>
<span class="doccomment">/// ~~~</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">extended_gcd</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">ExtendedGcd</span><span class="op"><</span><span class="self">Self</span><span class="op">></span>
<span class="kw">where</span>
<span class="self">Self</span>: <span class="ident">Clone</span>,
{
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">s</span> <span class="op">=</span> (<span class="self">Self</span><span class="ident">::zero</span>(), <span class="self">Self</span><span class="ident">::one</span>());
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">t</span> <span class="op">=</span> (<span class="self">Self</span><span class="ident">::one</span>(), <span class="self">Self</span><span class="ident">::zero</span>());
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">r</span> <span class="op">=</span> (<span class="ident">other</span>.<span class="ident">clone</span>(), <span class="self">self</span>.<span class="ident">clone</span>());
<span class="kw">while</span> <span class="op">!</span><span class="ident">r</span>.<span class="number">0</span>.<span class="ident">is_zero</span>() {
<span class="kw">let</span> <span class="ident">q</span> <span class="op">=</span> <span class="ident">r</span>.<span class="number">1</span>.<span class="ident">clone</span>() <span class="op">/</span> <span class="ident">r</span>.<span class="number">0</span>.<span class="ident">clone</span>();
<span class="kw">let</span> <span class="ident">f</span> <span class="op">=</span> <span class="op">|</span><span class="kw-2">mut</span> <span class="ident">r</span>: (<span class="self">Self</span>, <span class="self">Self</span>)<span class="op">|</span> {
<span class="ident">mem::swap</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">r</span>.<span class="number">0</span>, <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">r</span>.<span class="number">1</span>);
<span class="ident">r</span>.<span class="number">0</span> <span class="op">=</span> <span class="ident">r</span>.<span class="number">0</span> <span class="op">-</span> <span class="ident">q</span>.<span class="ident">clone</span>() <span class="op">*</span> <span class="ident">r</span>.<span class="number">1</span>.<span class="ident">clone</span>();
<span class="ident">r</span>
};
<span class="ident">r</span> <span class="op">=</span> <span class="ident">f</span>(<span class="ident">r</span>);
<span class="ident">s</span> <span class="op">=</span> <span class="ident">f</span>(<span class="ident">s</span>);
<span class="ident">t</span> <span class="op">=</span> <span class="ident">f</span>(<span class="ident">t</span>);
}
<span class="kw">if</span> <span class="ident">r</span>.<span class="number">1</span> <span class="op">></span><span class="op">=</span> <span class="self">Self</span><span class="ident">::zero</span>() {
<span class="ident">ExtendedGcd</span> {
<span class="ident">gcd</span>: <span class="ident">r</span>.<span class="number">1</span>,
<span class="ident">x</span>: <span class="ident">s</span>.<span class="number">1</span>,
<span class="ident">y</span>: <span class="ident">t</span>.<span class="number">1</span>,
<span class="ident">_hidden</span>: (),
}
} <span class="kw">else</span> {
<span class="ident">ExtendedGcd</span> {
<span class="ident">gcd</span>: <span class="self">Self</span><span class="ident">::zero</span>() <span class="op">-</span> <span class="ident">r</span>.<span class="number">1</span>,
<span class="ident">x</span>: <span class="self">Self</span><span class="ident">::zero</span>() <span class="op">-</span> <span class="ident">s</span>.<span class="number">1</span>,
<span class="ident">y</span>: <span class="self">Self</span><span class="ident">::zero</span>() <span class="op">-</span> <span class="ident">t</span>.<span class="number">1</span>,
<span class="ident">_hidden</span>: (),
}
}
}
<span class="doccomment">/// Greatest common divisor, least common multiple, and Bézout coefficients.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">extended_gcd_lcm</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> (<span class="ident">ExtendedGcd</span><span class="op"><</span><span class="self">Self</span><span class="op">></span>, <span class="self">Self</span>)
<span class="kw">where</span>
<span class="self">Self</span>: <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">Signed</span>,
{
(<span class="self">self</span>.<span class="ident">extended_gcd</span>(<span class="ident">other</span>), <span class="self">self</span>.<span class="ident">lcm</span>(<span class="ident">other</span>))
}
<span class="doccomment">/// Deprecated, use `is_multiple_of` instead.</span>
<span class="kw">fn</span> <span class="ident">divides</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span>;
<span class="doccomment">/// Returns `true` if `self` is a multiple of `other`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ~~~</span>
<span class="doccomment">/// # use num_integer::Integer;</span>
<span class="doccomment">/// assert_eq!(9.is_multiple_of(&3), true);</span>
<span class="doccomment">/// assert_eq!(3.is_multiple_of(&9), false);</span>
<span class="doccomment">/// ~~~</span>
<span class="kw">fn</span> <span class="ident">is_multiple_of</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span>;
<span class="doccomment">/// Returns `true` if the number is even.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ~~~</span>
<span class="doccomment">/// # use num_integer::Integer;</span>
<span class="doccomment">/// assert_eq!(3.is_even(), false);</span>
<span class="doccomment">/// assert_eq!(4.is_even(), true);</span>
<span class="doccomment">/// ~~~</span>
<span class="kw">fn</span> <span class="ident">is_even</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span>;
<span class="doccomment">/// Returns `true` if the number is odd.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ~~~</span>
<span class="doccomment">/// # use num_integer::Integer;</span>
<span class="doccomment">/// assert_eq!(3.is_odd(), true);</span>
<span class="doccomment">/// assert_eq!(4.is_odd(), false);</span>
<span class="doccomment">/// ~~~</span>
<span class="kw">fn</span> <span class="ident">is_odd</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span>;
<span class="doccomment">/// Simultaneous truncated integer division and modulus.</span>
<span class="doccomment">/// Returns `(quotient, remainder)`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ~~~</span>
<span class="doccomment">/// # use num_integer::Integer;</span>
<span class="doccomment">/// assert_eq!(( 8).div_rem( &3), ( 2, 2));</span>
<span class="doccomment">/// assert_eq!(( 8).div_rem(&-3), (-2, 2));</span>
<span class="doccomment">/// assert_eq!((-8).div_rem( &3), (-2, -2));</span>
<span class="doccomment">/// assert_eq!((-8).div_rem(&-3), ( 2, -2));</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert_eq!(( 1).div_rem( &2), ( 0, 1));</span>
<span class="doccomment">/// assert_eq!(( 1).div_rem(&-2), ( 0, 1));</span>
<span class="doccomment">/// assert_eq!((-1).div_rem( &2), ( 0, -1));</span>
<span class="doccomment">/// assert_eq!((-1).div_rem(&-2), ( 0, -1));</span>
<span class="doccomment">/// ~~~</span>
<span class="kw">fn</span> <span class="ident">div_rem</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> (<span class="self">Self</span>, <span class="self">Self</span>);
<span class="doccomment">/// Simultaneous floored integer division and modulus.</span>
<span class="doccomment">/// Returns `(quotient, remainder)`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ~~~</span>
<span class="doccomment">/// # use num_integer::Integer;</span>
<span class="doccomment">/// assert_eq!(( 8).div_mod_floor( &3), ( 2, 2));</span>
<span class="doccomment">/// assert_eq!(( 8).div_mod_floor(&-3), (-3, -1));</span>
<span class="doccomment">/// assert_eq!((-8).div_mod_floor( &3), (-3, 1));</span>
<span class="doccomment">/// assert_eq!((-8).div_mod_floor(&-3), ( 2, -2));</span>
<span class="doccomment">///</span>
<span class="doccomment">/// assert_eq!(( 1).div_mod_floor( &2), ( 0, 1));</span>
<span class="doccomment">/// assert_eq!(( 1).div_mod_floor(&-2), (-1, -1));</span>
<span class="doccomment">/// assert_eq!((-1).div_mod_floor( &2), (-1, 1));</span>
<span class="doccomment">/// assert_eq!((-1).div_mod_floor(&-2), ( 0, -1));</span>
<span class="doccomment">/// ~~~</span>
<span class="kw">fn</span> <span class="ident">div_mod_floor</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> (<span class="self">Self</span>, <span class="self">Self</span>) {
(<span class="self">self</span>.<span class="ident">div_floor</span>(<span class="ident">other</span>), <span class="self">self</span>.<span class="ident">mod_floor</span>(<span class="ident">other</span>))
}
<span class="doccomment">/// Rounds up to nearest multiple of argument.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Notes</span>
<span class="doccomment">///</span>
<span class="doccomment">/// For signed types, `a.next_multiple_of(b) = a.prev_multiple_of(b.neg())`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ~~~</span>
<span class="doccomment">/// # use num_integer::Integer;</span>
<span class="doccomment">/// assert_eq!(( 16).next_multiple_of(& 8), 16);</span>
<span class="doccomment">/// assert_eq!(( 23).next_multiple_of(& 8), 24);</span>
<span class="doccomment">/// assert_eq!(( 16).next_multiple_of(&-8), 16);</span>
<span class="doccomment">/// assert_eq!(( 23).next_multiple_of(&-8), 16);</span>
<span class="doccomment">/// assert_eq!((-16).next_multiple_of(& 8), -16);</span>
<span class="doccomment">/// assert_eq!((-23).next_multiple_of(& 8), -16);</span>
<span class="doccomment">/// assert_eq!((-16).next_multiple_of(&-8), -16);</span>
<span class="doccomment">/// assert_eq!((-23).next_multiple_of(&-8), -24);</span>
<span class="doccomment">/// ~~~</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">next_multiple_of</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span>
<span class="kw">where</span>
<span class="self">Self</span>: <span class="ident">Clone</span>,
{
<span class="kw">let</span> <span class="ident">m</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">mod_floor</span>(<span class="ident">other</span>);
<span class="self">self</span>.<span class="ident">clone</span>()
<span class="op">+</span> <span class="kw">if</span> <span class="ident">m</span>.<span class="ident">is_zero</span>() {
<span class="self">Self</span><span class="ident">::zero</span>()
} <span class="kw">else</span> {
<span class="ident">other</span>.<span class="ident">clone</span>() <span class="op">-</span> <span class="ident">m</span>
}
}
<span class="doccomment">/// Rounds down to nearest multiple of argument.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Notes</span>
<span class="doccomment">///</span>
<span class="doccomment">/// For signed types, `a.prev_multiple_of(b) = a.next_multiple_of(b.neg())`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ~~~</span>
<span class="doccomment">/// # use num_integer::Integer;</span>
<span class="doccomment">/// assert_eq!(( 16).prev_multiple_of(& 8), 16);</span>
<span class="doccomment">/// assert_eq!(( 23).prev_multiple_of(& 8), 16);</span>
<span class="doccomment">/// assert_eq!(( 16).prev_multiple_of(&-8), 16);</span>
<span class="doccomment">/// assert_eq!(( 23).prev_multiple_of(&-8), 24);</span>
<span class="doccomment">/// assert_eq!((-16).prev_multiple_of(& 8), -16);</span>
<span class="doccomment">/// assert_eq!((-23).prev_multiple_of(& 8), -24);</span>
<span class="doccomment">/// assert_eq!((-16).prev_multiple_of(&-8), -16);</span>
<span class="doccomment">/// assert_eq!((-23).prev_multiple_of(&-8), -16);</span>
<span class="doccomment">/// ~~~</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">prev_multiple_of</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span>
<span class="kw">where</span>
<span class="self">Self</span>: <span class="ident">Clone</span>,
{
<span class="self">self</span>.<span class="ident">clone</span>() <span class="op">-</span> <span class="self">self</span>.<span class="ident">mod_floor</span>(<span class="ident">other</span>)
}
}
<span class="doccomment">/// Greatest common divisor and Bézout coefficients</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```no_build</span>
<span class="doccomment">/// let e = isize::extended_gcd(a, b);</span>
<span class="doccomment">/// assert_eq!(e.gcd, e.x*a + e.y*b);</span>
<span class="doccomment">/// ```</span>
<span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Debug</span>, <span class="ident">Clone</span>, <span class="ident">Copy</span>, <span class="ident">PartialEq</span>, <span class="ident">Eq</span>)]</span>
<span class="kw">pub</span> <span class="kw">struct</span> <span class="ident">ExtendedGcd</span><span class="op"><</span><span class="ident">A</span><span class="op">></span> {
<span class="kw">pub</span> <span class="ident">gcd</span>: <span class="ident">A</span>,
<span class="kw">pub</span> <span class="ident">x</span>: <span class="ident">A</span>,
<span class="kw">pub</span> <span class="ident">y</span>: <span class="ident">A</span>,
<span class="ident">_hidden</span>: (),
}
<span class="doccomment">/// Simultaneous integer division and modulus</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">div_rem</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Integer</span><span class="op">></span>(<span class="ident">x</span>: <span class="ident">T</span>, <span class="ident">y</span>: <span class="ident">T</span>) <span class="op">-</span><span class="op">></span> (<span class="ident">T</span>, <span class="ident">T</span>) {
<span class="ident">x</span>.<span class="ident">div_rem</span>(<span class="kw-2">&</span><span class="ident">y</span>)
}
<span class="doccomment">/// Floored integer division</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">div_floor</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Integer</span><span class="op">></span>(<span class="ident">x</span>: <span class="ident">T</span>, <span class="ident">y</span>: <span class="ident">T</span>) <span class="op">-</span><span class="op">></span> <span class="ident">T</span> {
<span class="ident">x</span>.<span class="ident">div_floor</span>(<span class="kw-2">&</span><span class="ident">y</span>)
}
<span class="doccomment">/// Floored integer modulus</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">mod_floor</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Integer</span><span class="op">></span>(<span class="ident">x</span>: <span class="ident">T</span>, <span class="ident">y</span>: <span class="ident">T</span>) <span class="op">-</span><span class="op">></span> <span class="ident">T</span> {
<span class="ident">x</span>.<span class="ident">mod_floor</span>(<span class="kw-2">&</span><span class="ident">y</span>)
}
<span class="doccomment">/// Simultaneous floored integer division and modulus</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">div_mod_floor</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Integer</span><span class="op">></span>(<span class="ident">x</span>: <span class="ident">T</span>, <span class="ident">y</span>: <span class="ident">T</span>) <span class="op">-</span><span class="op">></span> (<span class="ident">T</span>, <span class="ident">T</span>) {
<span class="ident">x</span>.<span class="ident">div_mod_floor</span>(<span class="kw-2">&</span><span class="ident">y</span>)
}
<span class="doccomment">/// Ceiled integer division</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">div_ceil</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Integer</span><span class="op">></span>(<span class="ident">x</span>: <span class="ident">T</span>, <span class="ident">y</span>: <span class="ident">T</span>) <span class="op">-</span><span class="op">></span> <span class="ident">T</span> {
<span class="ident">x</span>.<span class="ident">div_ceil</span>(<span class="kw-2">&</span><span class="ident">y</span>)
}
<span class="doccomment">/// Calculates the Greatest Common Divisor (GCD) of the number and `other`. The</span>
<span class="doccomment">/// result is always positive.</span>
<span class="attribute">#[<span class="ident">inline</span>(<span class="ident">always</span>)]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">gcd</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Integer</span><span class="op">></span>(<span class="ident">x</span>: <span class="ident">T</span>, <span class="ident">y</span>: <span class="ident">T</span>) <span class="op">-</span><span class="op">></span> <span class="ident">T</span> {
<span class="ident">x</span>.<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="ident">y</span>)
}
<span class="doccomment">/// Calculates the Lowest Common Multiple (LCM) of the number and `other`.</span>
<span class="attribute">#[<span class="ident">inline</span>(<span class="ident">always</span>)]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">lcm</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Integer</span><span class="op">></span>(<span class="ident">x</span>: <span class="ident">T</span>, <span class="ident">y</span>: <span class="ident">T</span>) <span class="op">-</span><span class="op">></span> <span class="ident">T</span> {
<span class="ident">x</span>.<span class="ident">lcm</span>(<span class="kw-2">&</span><span class="ident">y</span>)
}
<span class="doccomment">/// Calculates the Greatest Common Divisor (GCD) and</span>
<span class="doccomment">/// Lowest Common Multiple (LCM) of the number and `other`.</span>
<span class="attribute">#[<span class="ident">inline</span>(<span class="ident">always</span>)]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">gcd_lcm</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Integer</span><span class="op">></span>(<span class="ident">x</span>: <span class="ident">T</span>, <span class="ident">y</span>: <span class="ident">T</span>) <span class="op">-</span><span class="op">></span> (<span class="ident">T</span>, <span class="ident">T</span>) {
<span class="ident">x</span>.<span class="ident">gcd_lcm</span>(<span class="kw-2">&</span><span class="ident">y</span>)
}
<span class="macro">macro_rules!</span> <span class="ident">impl_integer_for_isize</span> {
(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>:<span class="ident">ty</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">test_mod</span>:<span class="ident">ident</span>) <span class="op">=</span><span class="op">></span> {
<span class="kw">impl</span> <span class="ident">Integer</span> <span class="kw">for</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span> {
<span class="doccomment">/// Floored integer division</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">div_floor</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span> {
<span class="comment">// Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,</span>
<span class="comment">// December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)</span>
<span class="kw">let</span> (<span class="ident">d</span>, <span class="ident">r</span>) <span class="op">=</span> <span class="self">self</span>.<span class="ident">div_rem</span>(<span class="ident">other</span>);
<span class="kw">if</span> (<span class="ident">r</span> <span class="op">></span> <span class="number">0</span> <span class="op">&&</span> <span class="kw-2">*</span><span class="ident">other</span> <span class="op"><</span> <span class="number">0</span>) <span class="op">|</span><span class="op">|</span> (<span class="ident">r</span> <span class="op"><</span> <span class="number">0</span> <span class="op">&&</span> <span class="kw-2">*</span><span class="ident">other</span> <span class="op">></span> <span class="number">0</span>) {
<span class="ident">d</span> <span class="op">-</span> <span class="number">1</span>
} <span class="kw">else</span> {
<span class="ident">d</span>
}
}
<span class="doccomment">/// Floored integer modulo</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">mod_floor</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span> {
<span class="comment">// Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,</span>
<span class="comment">// December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)</span>
<span class="kw">let</span> <span class="ident">r</span> <span class="op">=</span> <span class="kw-2">*</span><span class="self">self</span> <span class="op">%</span> <span class="kw-2">*</span><span class="ident">other</span>;
<span class="kw">if</span> (<span class="ident">r</span> <span class="op">></span> <span class="number">0</span> <span class="op">&&</span> <span class="kw-2">*</span><span class="ident">other</span> <span class="op"><</span> <span class="number">0</span>) <span class="op">|</span><span class="op">|</span> (<span class="ident">r</span> <span class="op"><</span> <span class="number">0</span> <span class="op">&&</span> <span class="kw-2">*</span><span class="ident">other</span> <span class="op">></span> <span class="number">0</span>) {
<span class="ident">r</span> <span class="op">+</span> <span class="kw-2">*</span><span class="ident">other</span>
} <span class="kw">else</span> {
<span class="ident">r</span>
}
}
<span class="doccomment">/// Calculates `div_floor` and `mod_floor` simultaneously</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">div_mod_floor</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> (<span class="self">Self</span>, <span class="self">Self</span>) {
<span class="comment">// Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,</span>
<span class="comment">// December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)</span>
<span class="kw">let</span> (<span class="ident">d</span>, <span class="ident">r</span>) <span class="op">=</span> <span class="self">self</span>.<span class="ident">div_rem</span>(<span class="ident">other</span>);
<span class="kw">if</span> (<span class="ident">r</span> <span class="op">></span> <span class="number">0</span> <span class="op">&&</span> <span class="kw-2">*</span><span class="ident">other</span> <span class="op"><</span> <span class="number">0</span>) <span class="op">|</span><span class="op">|</span> (<span class="ident">r</span> <span class="op"><</span> <span class="number">0</span> <span class="op">&&</span> <span class="kw-2">*</span><span class="ident">other</span> <span class="op">></span> <span class="number">0</span>) {
(<span class="ident">d</span> <span class="op">-</span> <span class="number">1</span>, <span class="ident">r</span> <span class="op">+</span> <span class="kw-2">*</span><span class="ident">other</span>)
} <span class="kw">else</span> {
(<span class="ident">d</span>, <span class="ident">r</span>)
}
}
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">div_ceil</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span> {
<span class="kw">let</span> (<span class="ident">d</span>, <span class="ident">r</span>) <span class="op">=</span> <span class="self">self</span>.<span class="ident">div_rem</span>(<span class="ident">other</span>);
<span class="kw">if</span> (<span class="ident">r</span> <span class="op">></span> <span class="number">0</span> <span class="op">&&</span> <span class="kw-2">*</span><span class="ident">other</span> <span class="op">></span> <span class="number">0</span>) <span class="op">|</span><span class="op">|</span> (<span class="ident">r</span> <span class="op"><</span> <span class="number">0</span> <span class="op">&&</span> <span class="kw-2">*</span><span class="ident">other</span> <span class="op"><</span> <span class="number">0</span>) {
<span class="ident">d</span> <span class="op">+</span> <span class="number">1</span>
} <span class="kw">else</span> {
<span class="ident">d</span>
}
}
<span class="doccomment">/// Calculates the Greatest Common Divisor (GCD) of the number and</span>
<span class="doccomment">/// `other`. The result is always positive.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">gcd</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span> {
<span class="comment">// Use Stein's algorithm</span>
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">m</span> <span class="op">=</span> <span class="kw-2">*</span><span class="self">self</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">n</span> <span class="op">=</span> <span class="kw-2">*</span><span class="ident">other</span>;
<span class="kw">if</span> <span class="ident">m</span> <span class="op">=</span><span class="op">=</span> <span class="number">0</span> <span class="op">|</span><span class="op">|</span> <span class="ident">n</span> <span class="op">=</span><span class="op">=</span> <span class="number">0</span> {
<span class="kw">return</span> (<span class="ident">m</span> <span class="op">|</span> <span class="ident">n</span>).<span class="ident">abs</span>();
}
<span class="comment">// find common factors of 2</span>
<span class="kw">let</span> <span class="ident">shift</span> <span class="op">=</span> (<span class="ident">m</span> <span class="op">|</span> <span class="ident">n</span>).<span class="ident">trailing_zeros</span>();
<span class="comment">// The algorithm needs positive numbers, but the minimum value</span>
<span class="comment">// can't be represented as a positive one.</span>
<span class="comment">// It's also a power of two, so the gcd can be</span>
<span class="comment">// calculated by bitshifting in that case</span>
<span class="comment">// Assuming two's complement, the number created by the shift</span>
<span class="comment">// is positive for all numbers except gcd = abs(min value)</span>
<span class="comment">// The call to .abs() causes a panic in debug mode</span>
<span class="kw">if</span> <span class="ident">m</span> <span class="op">=</span><span class="op">=</span> <span class="self">Self</span><span class="ident">::min_value</span>() <span class="op">|</span><span class="op">|</span> <span class="ident">n</span> <span class="op">=</span><span class="op">=</span> <span class="self">Self</span><span class="ident">::min_value</span>() {
<span class="kw">return</span> (<span class="number">1</span> <span class="op"><</span><span class="op"><</span> <span class="ident">shift</span>).<span class="ident">abs</span>();
}
<span class="comment">// guaranteed to be positive now, rest like unsigned algorithm</span>
<span class="ident">m</span> <span class="op">=</span> <span class="ident">m</span>.<span class="ident">abs</span>();
<span class="ident">n</span> <span class="op">=</span> <span class="ident">n</span>.<span class="ident">abs</span>();
<span class="comment">// divide n and m by 2 until odd</span>
<span class="ident">m</span> <span class="op">></span><span class="op">></span><span class="op">=</span> <span class="ident">m</span>.<span class="ident">trailing_zeros</span>();
<span class="ident">n</span> <span class="op">></span><span class="op">></span><span class="op">=</span> <span class="ident">n</span>.<span class="ident">trailing_zeros</span>();
<span class="kw">while</span> <span class="ident">m</span> <span class="op">!</span><span class="op">=</span> <span class="ident">n</span> {
<span class="kw">if</span> <span class="ident">m</span> <span class="op">></span> <span class="ident">n</span> {
<span class="ident">m</span> <span class="op">-</span><span class="op">=</span> <span class="ident">n</span>;
<span class="ident">m</span> <span class="op">></span><span class="op">></span><span class="op">=</span> <span class="ident">m</span>.<span class="ident">trailing_zeros</span>();
} <span class="kw">else</span> {
<span class="ident">n</span> <span class="op">-</span><span class="op">=</span> <span class="ident">m</span>;
<span class="ident">n</span> <span class="op">></span><span class="op">></span><span class="op">=</span> <span class="ident">n</span>.<span class="ident">trailing_zeros</span>();
}
}
<span class="ident">m</span> <span class="op"><</span><span class="op"><</span> <span class="ident">shift</span>
}
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">extended_gcd_lcm</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> (<span class="ident">ExtendedGcd</span><span class="op"><</span><span class="self">Self</span><span class="op">></span>, <span class="self">Self</span>) {
<span class="kw">let</span> <span class="ident">egcd</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">extended_gcd</span>(<span class="ident">other</span>);
<span class="comment">// should not have to recalculate abs</span>
<span class="kw">let</span> <span class="ident">lcm</span> <span class="op">=</span> <span class="kw">if</span> <span class="ident">egcd</span>.<span class="ident">gcd</span>.<span class="ident">is_zero</span>() {
<span class="self">Self</span><span class="ident">::zero</span>()
} <span class="kw">else</span> {
(<span class="kw-2">*</span><span class="self">self</span> <span class="op">*</span> (<span class="kw-2">*</span><span class="ident">other</span> <span class="op">/</span> <span class="ident">egcd</span>.<span class="ident">gcd</span>)).<span class="ident">abs</span>()
};
(<span class="ident">egcd</span>, <span class="ident">lcm</span>)
}
<span class="doccomment">/// Calculates the Lowest Common Multiple (LCM) of the number and</span>
<span class="doccomment">/// `other`.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">lcm</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span> {
<span class="self">self</span>.<span class="ident">gcd_lcm</span>(<span class="ident">other</span>).<span class="number">1</span>
}
<span class="doccomment">/// Calculates the Greatest Common Divisor (GCD) and</span>
<span class="doccomment">/// Lowest Common Multiple (LCM) of the number and `other`.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">gcd_lcm</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> (<span class="self">Self</span>, <span class="self">Self</span>) {
<span class="kw">if</span> <span class="self">self</span>.<span class="ident">is_zero</span>() <span class="op">&&</span> <span class="ident">other</span>.<span class="ident">is_zero</span>() {
<span class="kw">return</span> (<span class="self">Self</span><span class="ident">::zero</span>(), <span class="self">Self</span><span class="ident">::zero</span>());
}
<span class="kw">let</span> <span class="ident">gcd</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">gcd</span>(<span class="ident">other</span>);
<span class="comment">// should not have to recalculate abs</span>
<span class="kw">let</span> <span class="ident">lcm</span> <span class="op">=</span> (<span class="kw-2">*</span><span class="self">self</span> <span class="op">*</span> (<span class="kw-2">*</span><span class="ident">other</span> <span class="op">/</span> <span class="ident">gcd</span>)).<span class="ident">abs</span>();
(<span class="ident">gcd</span>, <span class="ident">lcm</span>)
}
<span class="doccomment">/// Deprecated, use `is_multiple_of` instead.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">divides</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span> {
<span class="self">self</span>.<span class="ident">is_multiple_of</span>(<span class="ident">other</span>)
}
<span class="doccomment">/// Returns `true` if the number is a multiple of `other`.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">is_multiple_of</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span> {
<span class="kw-2">*</span><span class="self">self</span> <span class="op">%</span> <span class="kw-2">*</span><span class="ident">other</span> <span class="op">=</span><span class="op">=</span> <span class="number">0</span>
}
<span class="doccomment">/// Returns `true` if the number is divisible by `2`</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">is_even</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span> {
(<span class="kw-2">*</span><span class="self">self</span>) <span class="op">&</span> <span class="number">1</span> <span class="op">=</span><span class="op">=</span> <span class="number">0</span>
}
<span class="doccomment">/// Returns `true` if the number is not divisible by `2`</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">is_odd</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span> {
<span class="op">!</span><span class="self">self</span>.<span class="ident">is_even</span>()
}
<span class="doccomment">/// Simultaneous truncated integer division and modulus.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">div_rem</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> (<span class="self">Self</span>, <span class="self">Self</span>) {
(<span class="kw-2">*</span><span class="self">self</span> <span class="op">/</span> <span class="kw-2">*</span><span class="ident">other</span>, <span class="kw-2">*</span><span class="self">self</span> <span class="op">%</span> <span class="kw-2">*</span><span class="ident">other</span>)
}
}
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">test</span>)]</span>
<span class="kw">mod</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">test_mod</span> {
<span class="kw">use</span> <span class="ident">core::mem</span>;
<span class="kw">use</span> <span class="ident">Integer</span>;
<span class="doccomment">/// Checks that the division rule holds for:</span>
<span class="doccomment">///</span>
<span class="doccomment">/// - `n`: numerator (dividend)</span>
<span class="doccomment">/// - `d`: denominator (divisor)</span>
<span class="doccomment">/// - `qr`: quotient and remainder</span>
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">test</span>)]</span>
<span class="kw">fn</span> <span class="ident">test_division_rule</span>((<span class="ident">n</span>, <span class="ident">d</span>): (<span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>), (<span class="ident">q</span>, <span class="ident">r</span>): (<span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>)) {
<span class="macro">assert_eq!</span>(<span class="ident">d</span> <span class="op">*</span> <span class="ident">q</span> <span class="op">+</span> <span class="ident">r</span>, <span class="ident">n</span>);
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_div_rem</span>() {
<span class="kw">fn</span> <span class="ident">test_nd_dr</span>(<span class="ident">nd</span>: (<span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>), <span class="ident">qr</span>: (<span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>)) {
<span class="kw">let</span> (<span class="ident">n</span>, <span class="ident">d</span>) <span class="op">=</span> <span class="ident">nd</span>;
<span class="kw">let</span> <span class="ident">separate_div_rem</span> <span class="op">=</span> (<span class="ident">n</span> <span class="op">/</span> <span class="ident">d</span>, <span class="ident">n</span> <span class="op">%</span> <span class="ident">d</span>);
<span class="kw">let</span> <span class="ident">combined_div_rem</span> <span class="op">=</span> <span class="ident">n</span>.<span class="ident">div_rem</span>(<span class="kw-2">&</span><span class="ident">d</span>);
<span class="macro">assert_eq!</span>(<span class="ident">separate_div_rem</span>, <span class="ident">qr</span>);
<span class="macro">assert_eq!</span>(<span class="ident">combined_div_rem</span>, <span class="ident">qr</span>);
<span class="ident">test_division_rule</span>(<span class="ident">nd</span>, <span class="ident">separate_div_rem</span>);
<span class="ident">test_division_rule</span>(<span class="ident">nd</span>, <span class="ident">combined_div_rem</span>);
}
<span class="ident">test_nd_dr</span>((<span class="number">8</span>, <span class="number">3</span>), (<span class="number">2</span>, <span class="number">2</span>));
<span class="ident">test_nd_dr</span>((<span class="number">8</span>, <span class="op">-</span><span class="number">3</span>), (<span class="op">-</span><span class="number">2</span>, <span class="number">2</span>));
<span class="ident">test_nd_dr</span>((<span class="op">-</span><span class="number">8</span>, <span class="number">3</span>), (<span class="op">-</span><span class="number">2</span>, <span class="op">-</span><span class="number">2</span>));
<span class="ident">test_nd_dr</span>((<span class="op">-</span><span class="number">8</span>, <span class="op">-</span><span class="number">3</span>), (<span class="number">2</span>, <span class="op">-</span><span class="number">2</span>));
<span class="ident">test_nd_dr</span>((<span class="number">1</span>, <span class="number">2</span>), (<span class="number">0</span>, <span class="number">1</span>));
<span class="ident">test_nd_dr</span>((<span class="number">1</span>, <span class="op">-</span><span class="number">2</span>), (<span class="number">0</span>, <span class="number">1</span>));
<span class="ident">test_nd_dr</span>((<span class="op">-</span><span class="number">1</span>, <span class="number">2</span>), (<span class="number">0</span>, <span class="op">-</span><span class="number">1</span>));
<span class="ident">test_nd_dr</span>((<span class="op">-</span><span class="number">1</span>, <span class="op">-</span><span class="number">2</span>), (<span class="number">0</span>, <span class="op">-</span><span class="number">1</span>));
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_div_mod_floor</span>() {
<span class="kw">fn</span> <span class="ident">test_nd_dm</span>(<span class="ident">nd</span>: (<span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>), <span class="ident">dm</span>: (<span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>)) {
<span class="kw">let</span> (<span class="ident">n</span>, <span class="ident">d</span>) <span class="op">=</span> <span class="ident">nd</span>;
<span class="kw">let</span> <span class="ident">separate_div_mod_floor</span> <span class="op">=</span> (<span class="ident">n</span>.<span class="ident">div_floor</span>(<span class="kw-2">&</span><span class="ident">d</span>), <span class="ident">n</span>.<span class="ident">mod_floor</span>(<span class="kw-2">&</span><span class="ident">d</span>));
<span class="kw">let</span> <span class="ident">combined_div_mod_floor</span> <span class="op">=</span> <span class="ident">n</span>.<span class="ident">div_mod_floor</span>(<span class="kw-2">&</span><span class="ident">d</span>);
<span class="macro">assert_eq!</span>(<span class="ident">separate_div_mod_floor</span>, <span class="ident">dm</span>);
<span class="macro">assert_eq!</span>(<span class="ident">combined_div_mod_floor</span>, <span class="ident">dm</span>);
<span class="ident">test_division_rule</span>(<span class="ident">nd</span>, <span class="ident">separate_div_mod_floor</span>);
<span class="ident">test_division_rule</span>(<span class="ident">nd</span>, <span class="ident">combined_div_mod_floor</span>);
}
<span class="ident">test_nd_dm</span>((<span class="number">8</span>, <span class="number">3</span>), (<span class="number">2</span>, <span class="number">2</span>));
<span class="ident">test_nd_dm</span>((<span class="number">8</span>, <span class="op">-</span><span class="number">3</span>), (<span class="op">-</span><span class="number">3</span>, <span class="op">-</span><span class="number">1</span>));
<span class="ident">test_nd_dm</span>((<span class="op">-</span><span class="number">8</span>, <span class="number">3</span>), (<span class="op">-</span><span class="number">3</span>, <span class="number">1</span>));
<span class="ident">test_nd_dm</span>((<span class="op">-</span><span class="number">8</span>, <span class="op">-</span><span class="number">3</span>), (<span class="number">2</span>, <span class="op">-</span><span class="number">2</span>));
<span class="ident">test_nd_dm</span>((<span class="number">1</span>, <span class="number">2</span>), (<span class="number">0</span>, <span class="number">1</span>));
<span class="ident">test_nd_dm</span>((<span class="number">1</span>, <span class="op">-</span><span class="number">2</span>), (<span class="op">-</span><span class="number">1</span>, <span class="op">-</span><span class="number">1</span>));
<span class="ident">test_nd_dm</span>((<span class="op">-</span><span class="number">1</span>, <span class="number">2</span>), (<span class="op">-</span><span class="number">1</span>, <span class="number">1</span>));
<span class="ident">test_nd_dm</span>((<span class="op">-</span><span class="number">1</span>, <span class="op">-</span><span class="number">2</span>), (<span class="number">0</span>, <span class="op">-</span><span class="number">1</span>));
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_gcd</span>() {
<span class="macro">assert_eq!</span>((<span class="number">10</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="number">2</span>), <span class="number">2</span> <span class="kw">as</span> <span class="macro-nonterminal">$</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">$</span><span class="macro-nonterminal">T</span>).<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="number">3</span>), <span class="number">1</span> <span class="kw">as</span> <span class="macro-nonterminal">$</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">$</span><span class="macro-nonterminal">T</span>).<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="number">3</span>), <span class="number">3</span> <span class="kw">as</span> <span class="macro-nonterminal">$</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">$</span><span class="macro-nonterminal">T</span>).<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="number">3</span>), <span class="number">3</span> <span class="kw">as</span> <span class="macro-nonterminal">$</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">$</span><span class="macro-nonterminal">T</span>).<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="number">42</span>), <span class="number">14</span> <span class="kw">as</span> <span class="macro-nonterminal">$</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">$</span><span class="macro-nonterminal">T</span>).<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="op">-</span><span class="number">3</span>), <span class="number">3</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>);
<span class="macro">assert_eq!</span>((<span class="op">-</span><span class="number">6</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="number">3</span>), <span class="number">3</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>);
<span class="macro">assert_eq!</span>((<span class="op">-</span><span class="number">4</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="op">-</span><span class="number">2</span>), <span class="number">2</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>);
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_gcd_cmp_with_euclidean</span>() {
<span class="kw">fn</span> <span class="ident">euclidean_gcd</span>(<span class="kw-2">mut</span> <span class="ident">m</span>: <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>, <span class="kw-2">mut</span> <span class="ident">n</span>: <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>) <span class="op">-</span><span class="op">></span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span> {
<span class="kw">while</span> <span class="ident">m</span> <span class="op">!</span><span class="op">=</span> <span class="number">0</span> {
<span class="ident">mem::swap</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">m</span>, <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">n</span>);
<span class="ident">m</span> <span class="op">%</span><span class="op">=</span> <span class="ident">n</span>;
}
<span class="ident">n</span>.<span class="ident">abs</span>()
}
<span class="comment">// gcd(-128, b) = 128 is not representable as positive value</span>
<span class="comment">// for i8</span>
<span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> <span class="op">-</span><span class="number">127</span>..<span class="number">127</span> {
<span class="kw">for</span> <span class="ident">j</span> <span class="kw">in</span> <span class="op">-</span><span class="number">127</span>..<span class="number">127</span> {
<span class="macro">assert_eq!</span>(<span class="ident">euclidean_gcd</span>(<span class="ident">i</span>, <span class="ident">j</span>), <span class="ident">i</span>.<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="ident">j</span>));
}
}
<span class="comment">// last value</span>
<span class="comment">// FIXME: Use inclusive ranges for above loop when implemented</span>
<span class="kw">let</span> <span class="ident">i</span> <span class="op">=</span> <span class="number">127</span>;
<span class="kw">for</span> <span class="ident">j</span> <span class="kw">in</span> <span class="op">-</span><span class="number">127</span>..<span class="number">127</span> {
<span class="macro">assert_eq!</span>(<span class="ident">euclidean_gcd</span>(<span class="ident">i</span>, <span class="ident">j</span>), <span class="ident">i</span>.<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="ident">j</span>));
}
<span class="macro">assert_eq!</span>(<span class="number">127</span>.<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="number">127</span>), <span class="number">127</span>);
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_gcd_min_val</span>() {
<span class="kw">let</span> <span class="ident">min</span> <span class="op">=</span> <span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span><span class="op">></span><span class="ident">::min_value</span>();
<span class="kw">let</span> <span class="ident">max</span> <span class="op">=</span> <span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span><span class="op">></span><span class="ident">::max_value</span>();
<span class="kw">let</span> <span class="ident">max_pow2</span> <span class="op">=</span> <span class="ident">max</span> <span class="op">/</span> <span class="number">2</span> <span class="op">+</span> <span class="number">1</span>;
<span class="macro">assert_eq!</span>(<span class="ident">min</span>.<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="ident">max</span>), <span class="number">1</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>);
<span class="macro">assert_eq!</span>(<span class="ident">max</span>.<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="ident">min</span>), <span class="number">1</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>);
<span class="macro">assert_eq!</span>(<span class="ident">min</span>.<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="ident">max_pow2</span>), <span class="ident">max_pow2</span>);
<span class="macro">assert_eq!</span>(<span class="ident">max_pow2</span>.<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="ident">min</span>), <span class="ident">max_pow2</span>);
<span class="macro">assert_eq!</span>(<span class="ident">min</span>.<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="number">42</span>), <span class="number">2</span> <span class="kw">as</span> <span class="macro-nonterminal">$</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">$</span><span class="macro-nonterminal">T</span>).<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="ident">min</span>), <span class="number">2</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>);
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="attribute">#[<span class="ident">should_panic</span>]</span>
<span class="kw">fn</span> <span class="ident">test_gcd_min_val_min_val</span>() {
<span class="kw">let</span> <span class="ident">min</span> <span class="op">=</span> <span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span><span class="op">></span><span class="ident">::min_value</span>();
<span class="macro">assert!</span>(<span class="ident">min</span>.<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="ident">min</span>) <span class="op">></span><span class="op">=</span> <span class="number">0</span>);
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="attribute">#[<span class="ident">should_panic</span>]</span>
<span class="kw">fn</span> <span class="ident">test_gcd_min_val_0</span>() {
<span class="kw">let</span> <span class="ident">min</span> <span class="op">=</span> <span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span><span class="op">></span><span class="ident">::min_value</span>();
<span class="macro">assert!</span>(<span class="ident">min</span>.<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="number">0</span>) <span class="op">></span><span class="op">=</span> <span class="number">0</span>);
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="attribute">#[<span class="ident">should_panic</span>]</span>
<span class="kw">fn</span> <span class="ident">test_gcd_0_min_val</span>() {
<span class="kw">let</span> <span class="ident">min</span> <span class="op">=</span> <span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span><span class="op">></span><span class="ident">::min_value</span>();
<span class="macro">assert!</span>((<span class="number">0</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="ident">min</span>) <span class="op">></span><span class="op">=</span> <span class="number">0</span>);
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_lcm</span>() {
<span class="macro">assert_eq!</span>((<span class="number">1</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">lcm</span>(<span class="kw-2">&</span><span class="number">0</span>), <span class="number">0</span> <span class="kw">as</span> <span class="macro-nonterminal">$</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">$</span><span class="macro-nonterminal">T</span>).<span class="ident">lcm</span>(<span class="kw-2">&</span><span class="number">1</span>), <span class="number">0</span> <span class="kw">as</span> <span class="macro-nonterminal">$</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">$</span><span class="macro-nonterminal">T</span>).<span class="ident">lcm</span>(<span class="kw-2">&</span><span class="number">1</span>), <span class="number">1</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>);
<span class="macro">assert_eq!</span>((<span class="op">-</span><span class="number">1</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">lcm</span>(<span class="kw-2">&</span><span class="number">1</span>), <span class="number">1</span> <span class="kw">as</span> <span class="macro-nonterminal">$</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">$</span><span class="macro-nonterminal">T</span>).<span class="ident">lcm</span>(<span class="kw-2">&</span><span class="op">-</span><span class="number">1</span>), <span class="number">1</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>);
<span class="macro">assert_eq!</span>((<span class="op">-</span><span class="number">1</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">lcm</span>(<span class="kw-2">&</span><span class="op">-</span><span class="number">1</span>), <span class="number">1</span> <span class="kw">as</span> <span class="macro-nonterminal">$</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">$</span><span class="macro-nonterminal">T</span>).<span class="ident">lcm</span>(<span class="kw-2">&</span><span class="number">9</span>), <span class="number">72</span> <span class="kw">as</span> <span class="macro-nonterminal">$</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">$</span><span class="macro-nonterminal">T</span>).<span class="ident">lcm</span>(<span class="kw-2">&</span><span class="number">5</span>), <span class="number">55</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>);
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_gcd_lcm</span>() {
<span class="kw">use</span> <span class="ident">core::iter::once</span>;
<span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> <span class="ident">once</span>(<span class="number">0</span>)
.<span class="ident">chain</span>((<span class="number">1</span>..).<span class="ident">take</span>(<span class="number">127</span>).<span class="ident">flat_map</span>(<span class="op">|</span><span class="ident">a</span><span class="op">|</span> <span class="ident">once</span>(<span class="ident">a</span>).<span class="ident">chain</span>(<span class="ident">once</span>(<span class="op">-</span><span class="ident">a</span>))))
.<span class="ident">chain</span>(<span class="ident">once</span>(<span class="op">-</span><span class="number">128</span>))
{
<span class="kw">for</span> <span class="ident">j</span> <span class="kw">in</span> <span class="ident">once</span>(<span class="number">0</span>)
.<span class="ident">chain</span>((<span class="number">1</span>..).<span class="ident">take</span>(<span class="number">127</span>).<span class="ident">flat_map</span>(<span class="op">|</span><span class="ident">a</span><span class="op">|</span> <span class="ident">once</span>(<span class="ident">a</span>).<span class="ident">chain</span>(<span class="ident">once</span>(<span class="op">-</span><span class="ident">a</span>))))
.<span class="ident">chain</span>(<span class="ident">once</span>(<span class="op">-</span><span class="number">128</span>))
{
<span class="macro">assert_eq!</span>(<span class="ident">i</span>.<span class="ident">gcd_lcm</span>(<span class="kw-2">&</span><span class="ident">j</span>), (<span class="ident">i</span>.<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="ident">j</span>), <span class="ident">i</span>.<span class="ident">lcm</span>(<span class="kw-2">&</span><span class="ident">j</span>)));
}
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_extended_gcd_lcm</span>() {
<span class="kw">use</span> <span class="ident">core::fmt::Debug</span>;
<span class="kw">use</span> <span class="ident">traits::NumAssign</span>;
<span class="kw">use</span> <span class="ident">ExtendedGcd</span>;
<span class="kw">fn</span> <span class="ident">check</span><span class="op"><</span><span class="ident">A</span>: <span class="ident">Copy</span> <span class="op">+</span> <span class="ident">Debug</span> <span class="op">+</span> <span class="ident">Integer</span> <span class="op">+</span> <span class="ident">NumAssign</span><span class="op">></span>(<span class="ident">a</span>: <span class="ident">A</span>, <span class="ident">b</span>: <span class="ident">A</span>) {
<span class="kw">let</span> <span class="ident">ExtendedGcd</span> { <span class="ident">gcd</span>, <span class="ident">x</span>, <span class="ident">y</span>, .. } <span class="op">=</span> <span class="ident">a</span>.<span class="ident">extended_gcd</span>(<span class="kw-2">&</span><span class="ident">b</span>);
<span class="macro">assert_eq!</span>(<span class="ident">gcd</span>, <span class="ident">x</span> <span class="op">*</span> <span class="ident">a</span> <span class="op">+</span> <span class="ident">y</span> <span class="op">*</span> <span class="ident">b</span>);
}
<span class="kw">use</span> <span class="ident">core::iter::once</span>;
<span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> <span class="ident">once</span>(<span class="number">0</span>)
.<span class="ident">chain</span>((<span class="number">1</span>..).<span class="ident">take</span>(<span class="number">127</span>).<span class="ident">flat_map</span>(<span class="op">|</span><span class="ident">a</span><span class="op">|</span> <span class="ident">once</span>(<span class="ident">a</span>).<span class="ident">chain</span>(<span class="ident">once</span>(<span class="op">-</span><span class="ident">a</span>))))
.<span class="ident">chain</span>(<span class="ident">once</span>(<span class="op">-</span><span class="number">128</span>))
{
<span class="kw">for</span> <span class="ident">j</span> <span class="kw">in</span> <span class="ident">once</span>(<span class="number">0</span>)
.<span class="ident">chain</span>((<span class="number">1</span>..).<span class="ident">take</span>(<span class="number">127</span>).<span class="ident">flat_map</span>(<span class="op">|</span><span class="ident">a</span><span class="op">|</span> <span class="ident">once</span>(<span class="ident">a</span>).<span class="ident">chain</span>(<span class="ident">once</span>(<span class="op">-</span><span class="ident">a</span>))))
.<span class="ident">chain</span>(<span class="ident">once</span>(<span class="op">-</span><span class="number">128</span>))
{
<span class="ident">check</span>(<span class="ident">i</span>, <span class="ident">j</span>);
<span class="kw">let</span> (<span class="ident">ExtendedGcd</span> { <span class="ident">gcd</span>, .. }, <span class="ident">lcm</span>) <span class="op">=</span> <span class="ident">i</span>.<span class="ident">extended_gcd_lcm</span>(<span class="kw-2">&</span><span class="ident">j</span>);
<span class="macro">assert_eq!</span>((<span class="ident">gcd</span>, <span class="ident">lcm</span>), (<span class="ident">i</span>.<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="ident">j</span>), <span class="ident">i</span>.<span class="ident">lcm</span>(<span class="kw-2">&</span><span class="ident">j</span>)));
}
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_even</span>() {
<span class="macro">assert_eq!</span>((<span class="op">-</span><span class="number">4</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">is_even</span>(), <span class="bool-val">true</span>);
<span class="macro">assert_eq!</span>((<span class="op">-</span><span class="number">3</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">is_even</span>(), <span class="bool-val">false</span>);
<span class="macro">assert_eq!</span>((<span class="op">-</span><span class="number">2</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">is_even</span>(), <span class="bool-val">true</span>);
<span class="macro">assert_eq!</span>((<span class="op">-</span><span class="number">1</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">is_even</span>(), <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">$</span><span class="macro-nonterminal">T</span>).<span class="ident">is_even</span>(), <span class="bool-val">true</span>);
<span class="macro">assert_eq!</span>((<span class="number">1</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">is_even</span>(), <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">$</span><span class="macro-nonterminal">T</span>).<span class="ident">is_even</span>(), <span class="bool-val">true</span>);
<span class="macro">assert_eq!</span>((<span class="number">3</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">is_even</span>(), <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">$</span><span class="macro-nonterminal">T</span>).<span class="ident">is_even</span>(), <span class="bool-val">true</span>);
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_odd</span>() {
<span class="macro">assert_eq!</span>((<span class="op">-</span><span class="number">4</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">is_odd</span>(), <span class="bool-val">false</span>);
<span class="macro">assert_eq!</span>((<span class="op">-</span><span class="number">3</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">is_odd</span>(), <span class="bool-val">true</span>);
<span class="macro">assert_eq!</span>((<span class="op">-</span><span class="number">2</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">is_odd</span>(), <span class="bool-val">false</span>);
<span class="macro">assert_eq!</span>((<span class="op">-</span><span class="number">1</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">is_odd</span>(), <span class="bool-val">true</span>);
<span class="macro">assert_eq!</span>((<span class="number">0</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">is_odd</span>(), <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">$</span><span class="macro-nonterminal">T</span>).<span class="ident">is_odd</span>(), <span class="bool-val">true</span>);
<span class="macro">assert_eq!</span>((<span class="number">2</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">is_odd</span>(), <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">$</span><span class="macro-nonterminal">T</span>).<span class="ident">is_odd</span>(), <span class="bool-val">true</span>);
<span class="macro">assert_eq!</span>((<span class="number">4</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">is_odd</span>(), <span class="bool-val">false</span>);
}
}
};
}
<span class="macro">impl_integer_for_isize!</span>(<span class="ident">i8</span>, <span class="ident">test_integer_i8</span>);
<span class="macro">impl_integer_for_isize!</span>(<span class="ident">i16</span>, <span class="ident">test_integer_i16</span>);
<span class="macro">impl_integer_for_isize!</span>(<span class="ident">i32</span>, <span class="ident">test_integer_i32</span>);
<span class="macro">impl_integer_for_isize!</span>(<span class="ident">i64</span>, <span class="ident">test_integer_i64</span>);
<span class="macro">impl_integer_for_isize!</span>(<span class="ident">isize</span>, <span class="ident">test_integer_isize</span>);
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">has_i128</span>)]</span>
<span class="macro">impl_integer_for_isize!</span>(<span class="ident">i128</span>, <span class="ident">test_integer_i128</span>);
<span class="macro">macro_rules!</span> <span class="ident">impl_integer_for_usize</span> {
(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>:<span class="ident">ty</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">test_mod</span>:<span class="ident">ident</span>) <span class="op">=</span><span class="op">></span> {
<span class="kw">impl</span> <span class="ident">Integer</span> <span class="kw">for</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span> {
<span class="doccomment">/// Unsigned integer division. Returns the same result as `div` (`/`).</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">div_floor</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span> {
<span class="kw-2">*</span><span class="self">self</span> <span class="op">/</span> <span class="kw-2">*</span><span class="ident">other</span>
}
<span class="doccomment">/// Unsigned integer modulo operation. Returns the same result as `rem` (`%`).</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">mod_floor</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span> {
<span class="kw-2">*</span><span class="self">self</span> <span class="op">%</span> <span class="kw-2">*</span><span class="ident">other</span>
}
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">div_ceil</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span> {
<span class="kw-2">*</span><span class="self">self</span> <span class="op">/</span> <span class="kw-2">*</span><span class="ident">other</span> <span class="op">+</span> (<span class="number">0</span> <span class="op">!</span><span class="op">=</span> <span class="kw-2">*</span><span class="self">self</span> <span class="op">%</span> <span class="kw-2">*</span><span class="ident">other</span>) <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">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">gcd</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span> {
<span class="comment">// Use Stein's algorithm</span>
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">m</span> <span class="op">=</span> <span class="kw-2">*</span><span class="self">self</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">n</span> <span class="op">=</span> <span class="kw-2">*</span><span class="ident">other</span>;
<span class="kw">if</span> <span class="ident">m</span> <span class="op">=</span><span class="op">=</span> <span class="number">0</span> <span class="op">|</span><span class="op">|</span> <span class="ident">n</span> <span class="op">=</span><span class="op">=</span> <span class="number">0</span> {
<span class="kw">return</span> <span class="ident">m</span> <span class="op">|</span> <span class="ident">n</span>;
}
<span class="comment">// find common factors of 2</span>
<span class="kw">let</span> <span class="ident">shift</span> <span class="op">=</span> (<span class="ident">m</span> <span class="op">|</span> <span class="ident">n</span>).<span class="ident">trailing_zeros</span>();
<span class="comment">// divide n and m by 2 until odd</span>
<span class="ident">m</span> <span class="op">></span><span class="op">></span><span class="op">=</span> <span class="ident">m</span>.<span class="ident">trailing_zeros</span>();
<span class="ident">n</span> <span class="op">></span><span class="op">></span><span class="op">=</span> <span class="ident">n</span>.<span class="ident">trailing_zeros</span>();
<span class="kw">while</span> <span class="ident">m</span> <span class="op">!</span><span class="op">=</span> <span class="ident">n</span> {
<span class="kw">if</span> <span class="ident">m</span> <span class="op">></span> <span class="ident">n</span> {
<span class="ident">m</span> <span class="op">-</span><span class="op">=</span> <span class="ident">n</span>;
<span class="ident">m</span> <span class="op">></span><span class="op">></span><span class="op">=</span> <span class="ident">m</span>.<span class="ident">trailing_zeros</span>();
} <span class="kw">else</span> {
<span class="ident">n</span> <span class="op">-</span><span class="op">=</span> <span class="ident">m</span>;
<span class="ident">n</span> <span class="op">></span><span class="op">></span><span class="op">=</span> <span class="ident">n</span>.<span class="ident">trailing_zeros</span>();
}
}
<span class="ident">m</span> <span class="op"><</span><span class="op"><</span> <span class="ident">shift</span>
}
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">extended_gcd_lcm</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> (<span class="ident">ExtendedGcd</span><span class="op"><</span><span class="self">Self</span><span class="op">></span>, <span class="self">Self</span>) {
<span class="kw">let</span> <span class="ident">egcd</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">extended_gcd</span>(<span class="ident">other</span>);
<span class="comment">// should not have to recalculate abs</span>
<span class="kw">let</span> <span class="ident">lcm</span> <span class="op">=</span> <span class="kw">if</span> <span class="ident">egcd</span>.<span class="ident">gcd</span>.<span class="ident">is_zero</span>() {
<span class="self">Self</span><span class="ident">::zero</span>()
} <span class="kw">else</span> {
<span class="kw-2">*</span><span class="self">self</span> <span class="op">*</span> (<span class="kw-2">*</span><span class="ident">other</span> <span class="op">/</span> <span class="ident">egcd</span>.<span class="ident">gcd</span>)
};
(<span class="ident">egcd</span>, <span class="ident">lcm</span>)
}
<span class="doccomment">/// Calculates the Lowest Common Multiple (LCM) of the number and `other`.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">lcm</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="self">Self</span> {
<span class="self">self</span>.<span class="ident">gcd_lcm</span>(<span class="ident">other</span>).<span class="number">1</span>
}
<span class="doccomment">/// Calculates the Greatest Common Divisor (GCD) and</span>
<span class="doccomment">/// Lowest Common Multiple (LCM) of the number and `other`.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">gcd_lcm</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> (<span class="self">Self</span>, <span class="self">Self</span>) {
<span class="kw">if</span> <span class="self">self</span>.<span class="ident">is_zero</span>() <span class="op">&&</span> <span class="ident">other</span>.<span class="ident">is_zero</span>() {
<span class="kw">return</span> (<span class="self">Self</span><span class="ident">::zero</span>(), <span class="self">Self</span><span class="ident">::zero</span>());
}
<span class="kw">let</span> <span class="ident">gcd</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">gcd</span>(<span class="ident">other</span>);
<span class="kw">let</span> <span class="ident">lcm</span> <span class="op">=</span> <span class="kw-2">*</span><span class="self">self</span> <span class="op">*</span> (<span class="kw-2">*</span><span class="ident">other</span> <span class="op">/</span> <span class="ident">gcd</span>);
(<span class="ident">gcd</span>, <span class="ident">lcm</span>)
}
<span class="doccomment">/// Deprecated, use `is_multiple_of` instead.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">divides</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span> {
<span class="self">self</span>.<span class="ident">is_multiple_of</span>(<span class="ident">other</span>)
}
<span class="doccomment">/// Returns `true` if the number is a multiple of `other`.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">is_multiple_of</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span> {
<span class="kw-2">*</span><span class="self">self</span> <span class="op">%</span> <span class="kw-2">*</span><span class="ident">other</span> <span class="op">=</span><span class="op">=</span> <span class="number">0</span>
}
<span class="doccomment">/// Returns `true` if the number is divisible by `2`.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">is_even</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span> {
<span class="kw-2">*</span><span class="self">self</span> <span class="op">%</span> <span class="number">2</span> <span class="op">=</span><span class="op">=</span> <span class="number">0</span>
}
<span class="doccomment">/// Returns `true` if the number is not divisible by `2`.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">is_odd</span>(<span class="kw-2">&</span><span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span> {
<span class="op">!</span><span class="self">self</span>.<span class="ident">is_even</span>()
}
<span class="doccomment">/// Simultaneous truncated integer division and modulus.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">div_rem</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="self">Self</span>) <span class="op">-</span><span class="op">></span> (<span class="self">Self</span>, <span class="self">Self</span>) {
(<span class="kw-2">*</span><span class="self">self</span> <span class="op">/</span> <span class="kw-2">*</span><span class="ident">other</span>, <span class="kw-2">*</span><span class="self">self</span> <span class="op">%</span> <span class="kw-2">*</span><span class="ident">other</span>)
}
}
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">test</span>)]</span>
<span class="kw">mod</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">test_mod</span> {
<span class="kw">use</span> <span class="ident">core::mem</span>;
<span class="kw">use</span> <span class="ident">Integer</span>;
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_div_mod_floor</span>() {
<span class="macro">assert_eq!</span>((<span class="number">10</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">div_floor</span>(<span class="kw-2">&</span>(<span class="number">3</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>)), <span class="number">3</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>);
<span class="macro">assert_eq!</span>((<span class="number">10</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">mod_floor</span>(<span class="kw-2">&</span>(<span class="number">3</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>)), <span class="number">1</span> <span class="kw">as</span> <span class="macro-nonterminal">$</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">$</span><span class="macro-nonterminal">T</span>).<span class="ident">div_mod_floor</span>(<span class="kw-2">&</span>(<span class="number">3</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>)), (<span class="number">3</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>, <span class="number">1</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>));
<span class="macro">assert_eq!</span>((<span class="number">5</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">div_floor</span>(<span class="kw-2">&</span>(<span class="number">5</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>)), <span class="number">1</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>);
<span class="macro">assert_eq!</span>((<span class="number">5</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">mod_floor</span>(<span class="kw-2">&</span>(<span class="number">5</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>)), <span class="number">0</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>);
<span class="macro">assert_eq!</span>((<span class="number">5</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">div_mod_floor</span>(<span class="kw-2">&</span>(<span class="number">5</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>)), (<span class="number">1</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>, <span class="number">0</span> <span class="kw">as</span> <span class="macro-nonterminal">$</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">$</span><span class="macro-nonterminal">T</span>).<span class="ident">div_floor</span>(<span class="kw-2">&</span>(<span class="number">7</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>)), <span class="number">0</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>);
<span class="macro">assert_eq!</span>((<span class="number">3</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">mod_floor</span>(<span class="kw-2">&</span>(<span class="number">7</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>)), <span class="number">3</span> <span class="kw">as</span> <span class="macro-nonterminal">$</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">$</span><span class="macro-nonterminal">T</span>).<span class="ident">div_mod_floor</span>(<span class="kw-2">&</span>(<span class="number">7</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>)), (<span class="number">0</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>, <span class="number">3</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>));
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_gcd</span>() {
<span class="macro">assert_eq!</span>((<span class="number">10</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="number">2</span>), <span class="number">2</span> <span class="kw">as</span> <span class="macro-nonterminal">$</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">$</span><span class="macro-nonterminal">T</span>).<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="number">3</span>), <span class="number">1</span> <span class="kw">as</span> <span class="macro-nonterminal">$</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">$</span><span class="macro-nonterminal">T</span>).<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="number">3</span>), <span class="number">3</span> <span class="kw">as</span> <span class="macro-nonterminal">$</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">$</span><span class="macro-nonterminal">T</span>).<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="number">3</span>), <span class="number">3</span> <span class="kw">as</span> <span class="macro-nonterminal">$</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">$</span><span class="macro-nonterminal">T</span>).<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="number">42</span>), <span class="number">14</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>);
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_gcd_cmp_with_euclidean</span>() {
<span class="kw">fn</span> <span class="ident">euclidean_gcd</span>(<span class="kw-2">mut</span> <span class="ident">m</span>: <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>, <span class="kw-2">mut</span> <span class="ident">n</span>: <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>) <span class="op">-</span><span class="op">></span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span> {
<span class="kw">while</span> <span class="ident">m</span> <span class="op">!</span><span class="op">=</span> <span class="number">0</span> {
<span class="ident">mem::swap</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">m</span>, <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">n</span>);
<span class="ident">m</span> <span class="op">%</span><span class="op">=</span> <span class="ident">n</span>;
}
<span class="ident">n</span>
}
<span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> <span class="number">0</span>..<span class="number">255</span> {
<span class="kw">for</span> <span class="ident">j</span> <span class="kw">in</span> <span class="number">0</span>..<span class="number">255</span> {
<span class="macro">assert_eq!</span>(<span class="ident">euclidean_gcd</span>(<span class="ident">i</span>, <span class="ident">j</span>), <span class="ident">i</span>.<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="ident">j</span>));
}
}
<span class="comment">// last value</span>
<span class="comment">// FIXME: Use inclusive ranges for above loop when implemented</span>
<span class="kw">let</span> <span class="ident">i</span> <span class="op">=</span> <span class="number">255</span>;
<span class="kw">for</span> <span class="ident">j</span> <span class="kw">in</span> <span class="number">0</span>..<span class="number">255</span> {
<span class="macro">assert_eq!</span>(<span class="ident">euclidean_gcd</span>(<span class="ident">i</span>, <span class="ident">j</span>), <span class="ident">i</span>.<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="ident">j</span>));
}
<span class="macro">assert_eq!</span>(<span class="number">255</span>.<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="number">255</span>), <span class="number">255</span>);
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_lcm</span>() {
<span class="macro">assert_eq!</span>((<span class="number">1</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">lcm</span>(<span class="kw-2">&</span><span class="number">0</span>), <span class="number">0</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>);
<span class="macro">assert_eq!</span>((<span class="number">0</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">lcm</span>(<span class="kw-2">&</span><span class="number">1</span>), <span class="number">0</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>);
<span class="macro">assert_eq!</span>((<span class="number">1</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">lcm</span>(<span class="kw-2">&</span><span class="number">1</span>), <span class="number">1</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>);
<span class="macro">assert_eq!</span>((<span class="number">8</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">lcm</span>(<span class="kw-2">&</span><span class="number">9</span>), <span class="number">72</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>);
<span class="macro">assert_eq!</span>((<span class="number">11</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">lcm</span>(<span class="kw-2">&</span><span class="number">5</span>), <span class="number">55</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>);
<span class="macro">assert_eq!</span>((<span class="number">15</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">lcm</span>(<span class="kw-2">&</span><span class="number">17</span>), <span class="number">255</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>);
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_gcd_lcm</span>() {
<span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> (<span class="number">0</span>..).<span class="ident">take</span>(<span class="number">256</span>) {
<span class="kw">for</span> <span class="ident">j</span> <span class="kw">in</span> (<span class="number">0</span>..).<span class="ident">take</span>(<span class="number">256</span>) {
<span class="macro">assert_eq!</span>(<span class="ident">i</span>.<span class="ident">gcd_lcm</span>(<span class="kw-2">&</span><span class="ident">j</span>), (<span class="ident">i</span>.<span class="ident">gcd</span>(<span class="kw-2">&</span><span class="ident">j</span>), <span class="ident">i</span>.<span class="ident">lcm</span>(<span class="kw-2">&</span><span class="ident">j</span>)));
}
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_is_multiple_of</span>() {
<span class="macro">assert!</span>((<span class="number">6</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">is_multiple_of</span>(<span class="kw-2">&</span>(<span class="number">6</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>)));
<span class="macro">assert!</span>((<span class="number">6</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">is_multiple_of</span>(<span class="kw-2">&</span>(<span class="number">3</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>)));
<span class="macro">assert!</span>((<span class="number">6</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">is_multiple_of</span>(<span class="kw-2">&</span>(<span class="number">1</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>)));
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_even</span>() {
<span class="macro">assert_eq!</span>((<span class="number">0</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">is_even</span>(), <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">$</span><span class="macro-nonterminal">T</span>).<span class="ident">is_even</span>(), <span class="bool-val">false</span>);
<span class="macro">assert_eq!</span>((<span class="number">2</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">is_even</span>(), <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">$</span><span class="macro-nonterminal">T</span>).<span class="ident">is_even</span>(), <span class="bool-val">false</span>);
<span class="macro">assert_eq!</span>((<span class="number">4</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">is_even</span>(), <span class="bool-val">true</span>);
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_odd</span>() {
<span class="macro">assert_eq!</span>((<span class="number">0</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">is_odd</span>(), <span class="bool-val">false</span>);
<span class="macro">assert_eq!</span>((<span class="number">1</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">is_odd</span>(), <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">$</span><span class="macro-nonterminal">T</span>).<span class="ident">is_odd</span>(), <span class="bool-val">false</span>);
<span class="macro">assert_eq!</span>((<span class="number">3</span> <span class="kw">as</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>).<span class="ident">is_odd</span>(), <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">$</span><span class="macro-nonterminal">T</span>).<span class="ident">is_odd</span>(), <span class="bool-val">false</span>);
}
}
};
}
<span class="macro">impl_integer_for_usize!</span>(<span class="ident">u8</span>, <span class="ident">test_integer_u8</span>);
<span class="macro">impl_integer_for_usize!</span>(<span class="ident">u16</span>, <span class="ident">test_integer_u16</span>);
<span class="macro">impl_integer_for_usize!</span>(<span class="ident">u32</span>, <span class="ident">test_integer_u32</span>);
<span class="macro">impl_integer_for_usize!</span>(<span class="ident">u64</span>, <span class="ident">test_integer_u64</span>);
<span class="macro">impl_integer_for_usize!</span>(<span class="ident">usize</span>, <span class="ident">test_integer_usize</span>);
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">has_i128</span>)]</span>
<span class="macro">impl_integer_for_usize!</span>(<span class="ident">u128</span>, <span class="ident">test_integer_u128</span>);
<span class="doccomment">/// An iterator over binomial coefficients.</span>
<span class="kw">pub</span> <span class="kw">struct</span> <span class="ident">IterBinomial</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="ident">a</span>: <span class="ident">T</span>,
<span class="ident">n</span>: <span class="ident">T</span>,
<span class="ident">k</span>: <span class="ident">T</span>,
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="ident">IterBinomial</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>
<span class="kw">where</span>
<span class="ident">T</span>: <span class="ident">Integer</span>,
{
<span class="doccomment">/// For a given n, iterate over all binomial coefficients binomial(n, k), for k=0...n.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// Note that this might overflow, depending on `T`. For the primitive</span>
<span class="doccomment">/// integer types, the following n are the largest ones for which there will</span>
<span class="doccomment">/// be no overflow:</span>
<span class="doccomment">///</span>
<span class="doccomment">/// type | n</span>
<span class="doccomment">/// -----|---</span>
<span class="doccomment">/// u8 | 10</span>
<span class="doccomment">/// i8 | 9</span>
<span class="doccomment">/// u16 | 18</span>
<span class="doccomment">/// i16 | 17</span>
<span class="doccomment">/// u32 | 34</span>
<span class="doccomment">/// i32 | 33</span>
<span class="doccomment">/// u64 | 67</span>
<span class="doccomment">/// i64 | 66</span>
<span class="doccomment">///</span>
<span class="doccomment">/// For larger n, `T` should be a bigint type.</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">new</span>(<span class="ident">n</span>: <span class="ident">T</span>) <span class="op">-</span><span class="op">></span> <span class="ident">IterBinomial</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="ident">IterBinomial</span> {
<span class="ident">k</span>: <span class="ident">T::zero</span>(),
<span class="ident">a</span>: <span class="ident">T::one</span>(),
<span class="ident">n</span>: <span class="ident">n</span>,
}
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> <span class="ident">Iterator</span> <span class="kw">for</span> <span class="ident">IterBinomial</span><span class="op"><</span><span class="ident">T</span><span class="op">></span>
<span class="kw">where</span>
<span class="ident">T</span>: <span class="ident">Integer</span> <span class="op">+</span> <span class="ident">Clone</span>,
{
<span class="kw">type</span> <span class="ident">Item</span> <span class="op">=</span> <span class="ident">T</span>;
<span class="kw">fn</span> <span class="ident">next</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="self">self</span>) <span class="op">-</span><span class="op">></span> <span class="prelude-ty">Option</span><span class="op"><</span><span class="ident">T</span><span class="op">></span> {
<span class="kw">if</span> <span class="self">self</span>.<span class="ident">k</span> <span class="op">></span> <span class="self">self</span>.<span class="ident">n</span> {
<span class="kw">return</span> <span class="prelude-val">None</span>;
}
<span class="self">self</span>.<span class="ident">a</span> <span class="op">=</span> <span class="kw">if</span> <span class="op">!</span><span class="self">self</span>.<span class="ident">k</span>.<span class="ident">is_zero</span>() {
<span class="ident">multiply_and_divide</span>(
<span class="self">self</span>.<span class="ident">a</span>.<span class="ident">clone</span>(),
<span class="self">self</span>.<span class="ident">n</span>.<span class="ident">clone</span>() <span class="op">-</span> <span class="self">self</span>.<span class="ident">k</span>.<span class="ident">clone</span>() <span class="op">+</span> <span class="ident">T::one</span>(),
<span class="self">self</span>.<span class="ident">k</span>.<span class="ident">clone</span>(),
)
} <span class="kw">else</span> {
<span class="ident">T::one</span>()
};
<span class="self">self</span>.<span class="ident">k</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">k</span>.<span class="ident">clone</span>() <span class="op">+</span> <span class="ident">T::one</span>();
<span class="prelude-val">Some</span>(<span class="self">self</span>.<span class="ident">a</span>.<span class="ident">clone</span>())
}
}
<span class="doccomment">/// Calculate r * a / b, avoiding overflows and fractions.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// Assumes that b divides r * a evenly.</span>
<span class="kw">fn</span> <span class="ident">multiply_and_divide</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Integer</span> <span class="op">+</span> <span class="ident">Clone</span><span class="op">></span>(<span class="ident">r</span>: <span class="ident">T</span>, <span class="ident">a</span>: <span class="ident">T</span>, <span class="ident">b</span>: <span class="ident">T</span>) <span class="op">-</span><span class="op">></span> <span class="ident">T</span> {
<span class="comment">// See http://blog.plover.com/math/choose-2.html for the idea.</span>
<span class="kw">let</span> <span class="ident">g</span> <span class="op">=</span> <span class="ident">gcd</span>(<span class="ident">r</span>.<span class="ident">clone</span>(), <span class="ident">b</span>.<span class="ident">clone</span>());
<span class="ident">r</span> <span class="op">/</span> <span class="ident">g</span>.<span class="ident">clone</span>() <span class="op">*</span> (<span class="ident">a</span> <span class="op">/</span> (<span class="ident">b</span> <span class="op">/</span> <span class="ident">g</span>))
}
<span class="doccomment">/// Calculate the binomial coefficient.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// Note that this might overflow, depending on `T`. For the primitive integer</span>
<span class="doccomment">/// types, the following n are the largest ones possible such that there will</span>
<span class="doccomment">/// be no overflow for any k:</span>
<span class="doccomment">///</span>
<span class="doccomment">/// type | n</span>
<span class="doccomment">/// -----|---</span>
<span class="doccomment">/// u8 | 10</span>
<span class="doccomment">/// i8 | 9</span>
<span class="doccomment">/// u16 | 18</span>
<span class="doccomment">/// i16 | 17</span>
<span class="doccomment">/// u32 | 34</span>
<span class="doccomment">/// i32 | 33</span>
<span class="doccomment">/// u64 | 67</span>
<span class="doccomment">/// i64 | 66</span>
<span class="doccomment">///</span>
<span class="doccomment">/// For larger n, consider using a bigint type for `T`.</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">binomial</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Integer</span> <span class="op">+</span> <span class="ident">Clone</span><span class="op">></span>(<span class="kw-2">mut</span> <span class="ident">n</span>: <span class="ident">T</span>, <span class="ident">k</span>: <span class="ident">T</span>) <span class="op">-</span><span class="op">></span> <span class="ident">T</span> {
<span class="comment">// See http://blog.plover.com/math/choose.html for the idea.</span>
<span class="kw">if</span> <span class="ident">k</span> <span class="op">></span> <span class="ident">n</span> {
<span class="kw">return</span> <span class="ident">T::zero</span>();
}
<span class="kw">if</span> <span class="ident">k</span> <span class="op">></span> <span class="ident">n</span>.<span class="ident">clone</span>() <span class="op">-</span> <span class="ident">k</span>.<span class="ident">clone</span>() {
<span class="kw">return</span> <span class="ident">binomial</span>(<span class="ident">n</span>.<span class="ident">clone</span>(), <span class="ident">n</span> <span class="op">-</span> <span class="ident">k</span>);
}
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">r</span> <span class="op">=</span> <span class="ident">T::one</span>();
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">d</span> <span class="op">=</span> <span class="ident">T::one</span>();
<span class="kw">loop</span> {
<span class="kw">if</span> <span class="ident">d</span> <span class="op">></span> <span class="ident">k</span> {
<span class="kw">break</span>;
}
<span class="ident">r</span> <span class="op">=</span> <span class="ident">multiply_and_divide</span>(<span class="ident">r</span>, <span class="ident">n</span>.<span class="ident">clone</span>(), <span class="ident">d</span>.<span class="ident">clone</span>());
<span class="ident">n</span> <span class="op">=</span> <span class="ident">n</span> <span class="op">-</span> <span class="ident">T::one</span>();
<span class="ident">d</span> <span class="op">=</span> <span class="ident">d</span> <span class="op">+</span> <span class="ident">T::one</span>();
}
<span class="ident">r</span>
}
<span class="doccomment">/// Calculate the multinomial coefficient.</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">multinomial</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">Integer</span> <span class="op">+</span> <span class="ident">Clone</span><span class="op">></span>(<span class="ident">k</span>: <span class="kw-2">&</span>[<span class="ident">T</span>]) <span class="op">-</span><span class="op">></span> <span class="ident">T</span>
<span class="kw">where</span>
<span class="kw">for</span><span class="op"><</span><span class="lifetime">'a</span><span class="op">></span> <span class="ident">T</span>: <span class="ident">Add</span><span class="op"><</span><span class="kw-2">&</span><span class="lifetime">'a</span> <span class="ident">T</span>, <span class="ident">Output</span> <span class="op">=</span> <span class="ident">T</span><span class="op">></span>,
{
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">r</span> <span class="op">=</span> <span class="ident">T::one</span>();
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">p</span> <span class="op">=</span> <span class="ident">T::zero</span>();
<span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> <span class="ident">k</span> {
<span class="ident">p</span> <span class="op">=</span> <span class="ident">p</span> <span class="op">+</span> <span class="ident">i</span>;
<span class="ident">r</span> <span class="op">=</span> <span class="ident">r</span> <span class="op">*</span> <span class="ident">binomial</span>(<span class="ident">p</span>.<span class="ident">clone</span>(), <span class="ident">i</span>.<span class="ident">clone</span>());
}
<span class="ident">r</span>
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_lcm_overflow</span>() {
<span class="macro">macro_rules!</span> <span class="ident">check</span> {
(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">t</span>:<span class="ident">ty</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">x</span>:<span class="ident">expr</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">y</span>:<span class="ident">expr</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">r</span>:<span class="ident">expr</span>) <span class="op">=</span><span class="op">></span> {{
<span class="kw">let</span> <span class="ident">x</span>: <span class="macro-nonterminal">$</span><span class="macro-nonterminal">t</span> <span class="op">=</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">x</span>;
<span class="kw">let</span> <span class="ident">y</span>: <span class="macro-nonterminal">$</span><span class="macro-nonterminal">t</span> <span class="op">=</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">y</span>;
<span class="kw">let</span> <span class="ident">o</span> <span class="op">=</span> <span class="ident">x</span>.<span class="ident">checked_mul</span>(<span class="ident">y</span>);
<span class="macro">assert!</span>(
<span class="ident">o</span>.<span class="ident">is_none</span>(),
<span class="string">"sanity checking that {} input {} * {} overflows"</span>,
<span class="macro">stringify!</span>(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">t</span>),
<span class="ident">x</span>,
<span class="ident">y</span>
);
<span class="macro">assert_eq!</span>(<span class="ident">x</span>.<span class="ident">lcm</span>(<span class="kw-2">&</span><span class="ident">y</span>), <span class="macro-nonterminal">$</span><span class="macro-nonterminal">r</span>);
<span class="macro">assert_eq!</span>(<span class="ident">y</span>.<span class="ident">lcm</span>(<span class="kw-2">&</span><span class="ident">x</span>), <span class="macro-nonterminal">$</span><span class="macro-nonterminal">r</span>);
}};
}
<span class="comment">// Original bug (Issue #166)</span>
<span class="macro">check!</span>(<span class="ident">i64</span>, <span class="number">46656000000000000</span>, <span class="number">600</span>, <span class="number">46656000000000000</span>);
<span class="macro">check!</span>(<span class="ident">i8</span>, <span class="number">0x40</span>, <span class="number">0x04</span>, <span class="number">0x40</span>);
<span class="macro">check!</span>(<span class="ident">u8</span>, <span class="number">0x80</span>, <span class="number">0x02</span>, <span class="number">0x80</span>);
<span class="macro">check!</span>(<span class="ident">i16</span>, <span class="number">0x40_00</span>, <span class="number">0x04</span>, <span class="number">0x40_00</span>);
<span class="macro">check!</span>(<span class="ident">u16</span>, <span class="number">0x80_00</span>, <span class="number">0x02</span>, <span class="number">0x80_00</span>);
<span class="macro">check!</span>(<span class="ident">i32</span>, <span class="number">0x4000_0000</span>, <span class="number">0x04</span>, <span class="number">0x4000_0000</span>);
<span class="macro">check!</span>(<span class="ident">u32</span>, <span class="number">0x8000_0000</span>, <span class="number">0x02</span>, <span class="number">0x8000_0000</span>);
<span class="macro">check!</span>(<span class="ident">i64</span>, <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>(<span class="ident">u64</span>, <span class="number">0x8000_0000_0000_0000</span>, <span class="number">0x02</span>, <span class="number">0x8000_0000_0000_0000</span>);
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_iter_binomial</span>() {
<span class="macro">macro_rules!</span> <span class="ident">check_simple</span> {
(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">t</span>:<span class="ident">ty</span>) <span class="op">=</span><span class="op">></span> {{
<span class="kw">let</span> <span class="ident">n</span>: <span class="macro-nonterminal">$</span><span class="macro-nonterminal">t</span> <span class="op">=</span> <span class="number">3</span>;
<span class="kw">let</span> <span class="ident">expected</span> <span class="op">=</span> [<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> (<span class="ident">b</span>, <span class="kw-2">&</span><span class="ident">e</span>) <span class="kw">in</span> <span class="ident">IterBinomial::new</span>(<span class="ident">n</span>).<span class="ident">zip</span>(<span class="kw-2">&</span><span class="ident">expected</span>) {
<span class="macro">assert_eq!</span>(<span class="ident">b</span>, <span class="ident">e</span>);
}
}};
}
<span class="macro">check_simple!</span>(<span class="ident">u8</span>);
<span class="macro">check_simple!</span>(<span class="ident">i8</span>);
<span class="macro">check_simple!</span>(<span class="ident">u16</span>);
<span class="macro">check_simple!</span>(<span class="ident">i16</span>);
<span class="macro">check_simple!</span>(<span class="ident">u32</span>);
<span class="macro">check_simple!</span>(<span class="ident">i32</span>);
<span class="macro">check_simple!</span>(<span class="ident">u64</span>);
<span class="macro">check_simple!</span>(<span class="ident">i64</span>);
<span class="macro">macro_rules!</span> <span class="ident">check_binomial</span> {
(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">t</span>:<span class="ident">ty</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">n</span>:<span class="ident">expr</span>) <span class="op">=</span><span class="op">></span> {{
<span class="kw">let</span> <span class="ident">n</span>: <span class="macro-nonterminal">$</span><span class="macro-nonterminal">t</span> <span class="op">=</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">n</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">k</span>: <span class="macro-nonterminal">$</span><span class="macro-nonterminal">t</span> <span class="op">=</span> <span class="number">0</span>;
<span class="kw">for</span> <span class="ident">b</span> <span class="kw">in</span> <span class="ident">IterBinomial::new</span>(<span class="ident">n</span>) {
<span class="macro">assert_eq!</span>(<span class="ident">b</span>, <span class="ident">binomial</span>(<span class="ident">n</span>, <span class="ident">k</span>));
<span class="ident">k</span> <span class="op">+</span><span class="op">=</span> <span class="number">1</span>;
}
}};
}
<span class="comment">// Check the largest n for which there is no overflow.</span>
<span class="macro">check_binomial!</span>(<span class="ident">u8</span>, <span class="number">10</span>);
<span class="macro">check_binomial!</span>(<span class="ident">i8</span>, <span class="number">9</span>);
<span class="macro">check_binomial!</span>(<span class="ident">u16</span>, <span class="number">18</span>);
<span class="macro">check_binomial!</span>(<span class="ident">i16</span>, <span class="number">17</span>);
<span class="macro">check_binomial!</span>(<span class="ident">u32</span>, <span class="number">34</span>);
<span class="macro">check_binomial!</span>(<span class="ident">i32</span>, <span class="number">33</span>);
<span class="macro">check_binomial!</span>(<span class="ident">u64</span>, <span class="number">67</span>);
<span class="macro">check_binomial!</span>(<span class="ident">i64</span>, <span class="number">66</span>);
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_binomial</span>() {
<span class="macro">macro_rules!</span> <span class="ident">check</span> {
(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">t</span>:<span class="ident">ty</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">x</span>:<span class="ident">expr</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">y</span>:<span class="ident">expr</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">r</span>:<span class="ident">expr</span>) <span class="op">=</span><span class="op">></span> {{
<span class="kw">let</span> <span class="ident">x</span>: <span class="macro-nonterminal">$</span><span class="macro-nonterminal">t</span> <span class="op">=</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">x</span>;
<span class="kw">let</span> <span class="ident">y</span>: <span class="macro-nonterminal">$</span><span class="macro-nonterminal">t</span> <span class="op">=</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">y</span>;
<span class="kw">let</span> <span class="ident">expected</span>: <span class="macro-nonterminal">$</span><span class="macro-nonterminal">t</span> <span class="op">=</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">r</span>;
<span class="macro">assert_eq!</span>(<span class="ident">binomial</span>(<span class="ident">x</span>, <span class="ident">y</span>), <span class="ident">expected</span>);
<span class="kw">if</span> <span class="ident">y</span> <span class="op"><</span><span class="op">=</span> <span class="ident">x</span> {
<span class="macro">assert_eq!</span>(<span class="ident">binomial</span>(<span class="ident">x</span>, <span class="ident">x</span> <span class="op">-</span> <span class="ident">y</span>), <span class="ident">expected</span>);
}
}};
}
<span class="macro">check!</span>(<span class="ident">u8</span>, <span class="number">9</span>, <span class="number">4</span>, <span class="number">126</span>);
<span class="macro">check!</span>(<span class="ident">u8</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>);
<span class="macro">check!</span>(<span class="ident">u8</span>, <span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>);
<span class="macro">check!</span>(<span class="ident">i8</span>, <span class="number">9</span>, <span class="number">4</span>, <span class="number">126</span>);
<span class="macro">check!</span>(<span class="ident">i8</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>);
<span class="macro">check!</span>(<span class="ident">i8</span>, <span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>);
<span class="macro">check!</span>(<span class="ident">u16</span>, <span class="number">100</span>, <span class="number">2</span>, <span class="number">4950</span>);
<span class="macro">check!</span>(<span class="ident">u16</span>, <span class="number">14</span>, <span class="number">4</span>, <span class="number">1001</span>);
<span class="macro">check!</span>(<span class="ident">u16</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>);
<span class="macro">check!</span>(<span class="ident">u16</span>, <span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>);
<span class="macro">check!</span>(<span class="ident">i16</span>, <span class="number">100</span>, <span class="number">2</span>, <span class="number">4950</span>);
<span class="macro">check!</span>(<span class="ident">i16</span>, <span class="number">14</span>, <span class="number">4</span>, <span class="number">1001</span>);
<span class="macro">check!</span>(<span class="ident">i16</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>);
<span class="macro">check!</span>(<span class="ident">i16</span>, <span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>);
<span class="macro">check!</span>(<span class="ident">u32</span>, <span class="number">100</span>, <span class="number">2</span>, <span class="number">4950</span>);
<span class="macro">check!</span>(<span class="ident">u32</span>, <span class="number">35</span>, <span class="number">11</span>, <span class="number">417225900</span>);
<span class="macro">check!</span>(<span class="ident">u32</span>, <span class="number">14</span>, <span class="number">4</span>, <span class="number">1001</span>);
<span class="macro">check!</span>(<span class="ident">u32</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>);
<span class="macro">check!</span>(<span class="ident">u32</span>, <span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>);
<span class="macro">check!</span>(<span class="ident">i32</span>, <span class="number">100</span>, <span class="number">2</span>, <span class="number">4950</span>);
<span class="macro">check!</span>(<span class="ident">i32</span>, <span class="number">35</span>, <span class="number">11</span>, <span class="number">417225900</span>);
<span class="macro">check!</span>(<span class="ident">i32</span>, <span class="number">14</span>, <span class="number">4</span>, <span class="number">1001</span>);
<span class="macro">check!</span>(<span class="ident">i32</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>);
<span class="macro">check!</span>(<span class="ident">i32</span>, <span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>);
<span class="macro">check!</span>(<span class="ident">u64</span>, <span class="number">100</span>, <span class="number">2</span>, <span class="number">4950</span>);
<span class="macro">check!</span>(<span class="ident">u64</span>, <span class="number">35</span>, <span class="number">11</span>, <span class="number">417225900</span>);
<span class="macro">check!</span>(<span class="ident">u64</span>, <span class="number">14</span>, <span class="number">4</span>, <span class="number">1001</span>);
<span class="macro">check!</span>(<span class="ident">u64</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>);
<span class="macro">check!</span>(<span class="ident">u64</span>, <span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>);
<span class="macro">check!</span>(<span class="ident">i64</span>, <span class="number">100</span>, <span class="number">2</span>, <span class="number">4950</span>);
<span class="macro">check!</span>(<span class="ident">i64</span>, <span class="number">35</span>, <span class="number">11</span>, <span class="number">417225900</span>);
<span class="macro">check!</span>(<span class="ident">i64</span>, <span class="number">14</span>, <span class="number">4</span>, <span class="number">1001</span>);
<span class="macro">check!</span>(<span class="ident">i64</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>);
<span class="macro">check!</span>(<span class="ident">i64</span>, <span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>);
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_multinomial</span>() {
<span class="macro">macro_rules!</span> <span class="ident">check_binomial</span> {
(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">t</span>:<span class="ident">ty</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">k</span>:<span class="ident">expr</span>) <span class="op">=</span><span class="op">></span> {{
<span class="kw">let</span> <span class="ident">n</span>: <span class="macro-nonterminal">$</span><span class="macro-nonterminal">t</span> <span class="op">=</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">k</span>.<span class="ident">iter</span>().<span class="ident">fold</span>(<span class="number">0</span>, <span class="op">|</span><span class="ident">acc</span>, <span class="kw-2">&</span><span class="ident">x</span><span class="op">|</span> <span class="ident">acc</span> <span class="op">+</span> <span class="ident">x</span>);
<span class="kw">let</span> <span class="ident">k</span>: <span class="kw-2">&</span>[<span class="macro-nonterminal">$</span><span class="macro-nonterminal">t</span>] <span class="op">=</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">k</span>;
<span class="macro">assert_eq!</span>(<span class="ident">k</span>.<span class="ident">len</span>(), <span class="number">2</span>);
<span class="macro">assert_eq!</span>(<span class="ident">multinomial</span>(<span class="ident">k</span>), <span class="ident">binomial</span>(<span class="ident">n</span>, <span class="ident">k</span>[<span class="number">0</span>]));
}};
}
<span class="macro">check_binomial!</span>(<span class="ident">u8</span>, <span class="kw-2">&</span>[<span class="number">4</span>, <span class="number">5</span>]);
<span class="macro">check_binomial!</span>(<span class="ident">i8</span>, <span class="kw-2">&</span>[<span class="number">4</span>, <span class="number">5</span>]);
<span class="macro">check_binomial!</span>(<span class="ident">u16</span>, <span class="kw-2">&</span>[<span class="number">2</span>, <span class="number">98</span>]);
<span class="macro">check_binomial!</span>(<span class="ident">u16</span>, <span class="kw-2">&</span>[<span class="number">4</span>, <span class="number">10</span>]);
<span class="macro">check_binomial!</span>(<span class="ident">i16</span>, <span class="kw-2">&</span>[<span class="number">2</span>, <span class="number">98</span>]);
<span class="macro">check_binomial!</span>(<span class="ident">i16</span>, <span class="kw-2">&</span>[<span class="number">4</span>, <span class="number">10</span>]);
<span class="macro">check_binomial!</span>(<span class="ident">u32</span>, <span class="kw-2">&</span>[<span class="number">2</span>, <span class="number">98</span>]);
<span class="macro">check_binomial!</span>(<span class="ident">u32</span>, <span class="kw-2">&</span>[<span class="number">11</span>, <span class="number">24</span>]);
<span class="macro">check_binomial!</span>(<span class="ident">u32</span>, <span class="kw-2">&</span>[<span class="number">4</span>, <span class="number">10</span>]);
<span class="macro">check_binomial!</span>(<span class="ident">i32</span>, <span class="kw-2">&</span>[<span class="number">2</span>, <span class="number">98</span>]);
<span class="macro">check_binomial!</span>(<span class="ident">i32</span>, <span class="kw-2">&</span>[<span class="number">11</span>, <span class="number">24</span>]);
<span class="macro">check_binomial!</span>(<span class="ident">i32</span>, <span class="kw-2">&</span>[<span class="number">4</span>, <span class="number">10</span>]);
<span class="macro">check_binomial!</span>(<span class="ident">u64</span>, <span class="kw-2">&</span>[<span class="number">2</span>, <span class="number">98</span>]);
<span class="macro">check_binomial!</span>(<span class="ident">u64</span>, <span class="kw-2">&</span>[<span class="number">11</span>, <span class="number">24</span>]);
<span class="macro">check_binomial!</span>(<span class="ident">u64</span>, <span class="kw-2">&</span>[<span class="number">4</span>, <span class="number">10</span>]);
<span class="macro">check_binomial!</span>(<span class="ident">i64</span>, <span class="kw-2">&</span>[<span class="number">2</span>, <span class="number">98</span>]);
<span class="macro">check_binomial!</span>(<span class="ident">i64</span>, <span class="kw-2">&</span>[<span class="number">11</span>, <span class="number">24</span>]);
<span class="macro">check_binomial!</span>(<span class="ident">i64</span>, <span class="kw-2">&</span>[<span class="number">4</span>, <span class="number">10</span>]);
<span class="macro">macro_rules!</span> <span class="ident">check_multinomial</span> {
(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">t</span>:<span class="ident">ty</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">k</span>:<span class="ident">expr</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">r</span>:<span class="ident">expr</span>) <span class="op">=</span><span class="op">></span> {{
<span class="kw">let</span> <span class="ident">k</span>: <span class="kw-2">&</span>[<span class="macro-nonterminal">$</span><span class="macro-nonterminal">t</span>] <span class="op">=</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">k</span>;
<span class="kw">let</span> <span class="ident">expected</span>: <span class="macro-nonterminal">$</span><span class="macro-nonterminal">t</span> <span class="op">=</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">r</span>;
<span class="macro">assert_eq!</span>(<span class="ident">multinomial</span>(<span class="ident">k</span>), <span class="ident">expected</span>);
}};
}
<span class="macro">check_multinomial!</span>(<span class="ident">u8</span>, <span class="kw-2">&</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>(<span class="ident">u8</span>, <span class="kw-2">&</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>(<span class="ident">i8</span>, <span class="kw-2">&</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>(<span class="ident">i8</span>, <span class="kw-2">&</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>(<span class="ident">u16</span>, <span class="kw-2">&</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>(<span class="ident">u16</span>, <span class="kw-2">&</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>(<span class="ident">i16</span>, <span class="kw-2">&</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>(<span class="ident">i16</span>, <span class="kw-2">&</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>(<span class="ident">u32</span>, <span class="kw-2">&</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>(<span class="ident">u32</span>, <span class="kw-2">&</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>(<span class="ident">i32</span>, <span class="kw-2">&</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>(<span class="ident">i32</span>, <span class="kw-2">&</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>(<span class="ident">u64</span>, <span class="kw-2">&</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>(<span class="ident">u64</span>, <span class="kw-2">&</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>(<span class="ident">i64</span>, <span class="kw-2">&</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>(<span class="ident">i64</span>, <span class="kw-2">&</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>(<span class="ident">u64</span>, <span class="kw-2">&</span>[], <span class="number">1</span>);
<span class="macro">check_multinomial!</span>(<span class="ident">u64</span>, <span class="kw-2">&</span>[<span class="number">0</span>], <span class="number">1</span>);
<span class="macro">check_multinomial!</span>(<span class="ident">u64</span>, <span class="kw-2">&</span>[<span class="number">12345</span>], <span class="number">1</span>);
}
</pre></div>
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