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<span id="1112">1112</span>
</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'>//! Rational numbers</span>
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>feature</span> <span class='op'>=</span> <span class='string'>"rustc-serialize"</span>)]</span>
<span class='kw'>extern</span> <span class='kw'>crate</span> <span class='ident'>rustc_serialize</span>;
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>feature</span> <span class='op'>=</span> <span class='string'>"serde"</span>)]</span>
<span class='kw'>extern</span> <span class='kw'>crate</span> <span class='ident'>serde</span>;
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>feature</span> <span class='op'>=</span> <span class='string'>"num-bigint"</span>)]</span>
<span class='kw'>extern</span> <span class='kw'>crate</span> <span class='ident'>num_bigint</span> <span class='kw'>as</span> <span class='ident'>bigint</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'>extern</span> <span class='kw'>crate</span> <span class='ident'>num_integer</span> <span class='kw'>as</span> <span class='ident'>integer</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>cmp</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>error</span>::<span class='ident'>Error</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>fmt</span>;
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>test</span>)]</span>
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>hash</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>ops</span>::{<span class='ident'>Add</span>, <span class='ident'>Div</span>, <span class='ident'>Mul</span>, <span class='ident'>Neg</span>, <span class='ident'>Rem</span>, <span class='ident'>Sub</span>};
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>str</span>::<span class='ident'>FromStr</span>;
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>feature</span> <span class='op'>=</span> <span class='string'>"serde"</span>)]</span>
<span class='kw'>use</span> <span class='ident'>serde</span>;
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>feature</span> <span class='op'>=</span> <span class='string'>"num-bigint"</span>)]</span>
<span class='kw'>use</span> <span class='ident'>bigint</span>::{<span class='ident'>BigInt</span>, <span class='ident'>BigUint</span>, <span class='ident'>Sign</span>};
<span class='kw'>use</span> <span class='ident'>integer</span>::<span class='ident'>Integer</span>;
<span class='kw'>use</span> <span class='ident'>traits</span>::{<span class='ident'>FromPrimitive</span>, <span class='ident'>Float</span>, <span class='ident'>PrimInt</span>, <span class='ident'>Num</span>, <span class='ident'>Signed</span>, <span class='ident'>Zero</span>, <span class='ident'>One</span>};
<span class='doccomment'>/// Represents the ratio between 2 numbers.</span>
<span class='attribute'>#[<span class='ident'>derive</span>(<span class='ident'>Copy</span>, <span class='ident'>Clone</span>, <span class='ident'>Hash</span>, <span class='ident'>Debug</span>)]</span>
<span class='attribute'>#[<span class='ident'>cfg_attr</span>(<span class='ident'>feature</span> <span class='op'>=</span> <span class='string'>"rustc-serialize"</span>, <span class='ident'>derive</span>(<span class='ident'>RustcEncodable</span>, <span class='ident'>RustcDecodable</span>))]</span>
<span class='attribute'>#[<span class='ident'>allow</span>(<span class='ident'>missing_docs</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>struct</span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='ident'>numer</span>: <span class='ident'>T</span>,
<span class='ident'>denom</span>: <span class='ident'>T</span>,
}
<span class='doccomment'>/// Alias for a `Ratio` of machine-sized integers.</span>
<span class='kw'>pub</span> <span class='kw'>type</span> <span class='ident'>Rational</span> <span class='op'>=</span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>isize</span><span class='op'>></span>;
<span class='kw'>pub</span> <span class='kw'>type</span> <span class='ident'>Rational32</span> <span class='op'>=</span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>i32</span><span class='op'>></span>;
<span class='kw'>pub</span> <span class='kw'>type</span> <span class='ident'>Rational64</span> <span class='op'>=</span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>i64</span><span class='op'>></span>;
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>feature</span> <span class='op'>=</span> <span class='string'>"num-bigint"</span>)]</span>
<span class='doccomment'>/// Alias for arbitrary precision rationals.</span>
<span class='kw'>pub</span> <span class='kw'>type</span> <span class='ident'>BigRational</span> <span class='op'>=</span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>BigInt</span><span class='op'>></span>;
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>Clone</span> <span class='op'>+</span> <span class='ident'>Integer</span><span class='op'>></span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='doccomment'>/// Creates a ratio representing the integer `t`.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>from_integer</span>(<span class='ident'>t</span>: <span class='ident'>T</span>) <span class='op'>-></span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='ident'>Ratio</span>::<span class='ident'>new_raw</span>(<span class='ident'>t</span>, <span class='ident'>One</span>::<span class='ident'>one</span>())
}
<span class='doccomment'>/// Creates a ratio without checking for `denom == 0` or reducing.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>new_raw</span>(<span class='ident'>numer</span>: <span class='ident'>T</span>, <span class='ident'>denom</span>: <span class='ident'>T</span>) <span class='op'>-></span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='ident'>Ratio</span> {
<span class='ident'>numer</span>: <span class='ident'>numer</span>,
<span class='ident'>denom</span>: <span class='ident'>denom</span>,
}
}
<span class='doccomment'>/// Create a new Ratio. Fails if `denom == 0`.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>new</span>(<span class='ident'>numer</span>: <span class='ident'>T</span>, <span class='ident'>denom</span>: <span class='ident'>T</span>) <span class='op'>-></span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='kw'>if</span> <span class='ident'>denom</span> <span class='op'>==</span> <span class='ident'>Zero</span>::<span class='ident'>zero</span>() {
<span class='macro'>panic</span><span class='macro'>!</span>(<span class='string'>"denominator == 0"</span>);
}
<span class='kw'>let</span> <span class='kw-2'>mut</span> <span class='ident'>ret</span> <span class='op'>=</span> <span class='ident'>Ratio</span>::<span class='ident'>new_raw</span>(<span class='ident'>numer</span>, <span class='ident'>denom</span>);
<span class='ident'>ret</span>.<span class='ident'>reduce</span>();
<span class='ident'>ret</span>
}
<span class='doccomment'>/// Converts to an integer.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>to_integer</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>T</span> {
<span class='self'>self</span>.<span class='ident'>trunc</span>().<span class='ident'>numer</span>
}
<span class='doccomment'>/// Gets an immutable reference to the numerator.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>numer</span><span class='op'><</span><span class='lifetime'>'a</span><span class='op'>></span>(<span class='kw-2'>&</span><span class='lifetime'>'a</span> <span class='self'>self</span>) <span class='op'>-></span> <span class='kw-2'>&</span><span class='lifetime'>'a</span> <span class='ident'>T</span> {
<span class='kw-2'>&</span><span class='self'>self</span>.<span class='ident'>numer</span>
}
<span class='doccomment'>/// Gets an immutable reference to the denominator.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>denom</span><span class='op'><</span><span class='lifetime'>'a</span><span class='op'>></span>(<span class='kw-2'>&</span><span class='lifetime'>'a</span> <span class='self'>self</span>) <span class='op'>-></span> <span class='kw-2'>&</span><span class='lifetime'>'a</span> <span class='ident'>T</span> {
<span class='kw-2'>&</span><span class='self'>self</span>.<span class='ident'>denom</span>
}
<span class='doccomment'>/// Returns true if the rational number is an integer (denominator is 1).</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>is_integer</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>bool</span> {
<span class='self'>self</span>.<span class='ident'>denom</span> <span class='op'>==</span> <span class='ident'>One</span>::<span class='ident'>one</span>()
}
<span class='doccomment'>/// Put self into lowest terms, with denom > 0.</span>
<span class='kw'>fn</span> <span class='ident'>reduce</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>) {
<span class='kw'>let</span> <span class='ident'>g</span>: <span class='ident'>T</span> <span class='op'>=</span> <span class='self'>self</span>.<span class='ident'>numer</span>.<span class='ident'>gcd</span>(<span class='kw-2'>&</span><span class='self'>self</span>.<span class='ident'>denom</span>);
<span class='comment'>// FIXME(#5992): assignment operator overloads</span>
<span class='comment'>// self.numer /= g;</span>
<span class='self'>self</span>.<span class='ident'>numer</span> <span class='op'>=</span> <span class='self'>self</span>.<span class='ident'>numer</span>.<span class='ident'>clone</span>() <span class='op'>/</span> <span class='ident'>g</span>.<span class='ident'>clone</span>();
<span class='comment'>// FIXME(#5992): assignment operator overloads</span>
<span class='comment'>// self.denom /= g;</span>
<span class='self'>self</span>.<span class='ident'>denom</span> <span class='op'>=</span> <span class='self'>self</span>.<span class='ident'>denom</span>.<span class='ident'>clone</span>() <span class='op'>/</span> <span class='ident'>g</span>;
<span class='comment'>// keep denom positive!</span>
<span class='kw'>if</span> <span class='self'>self</span>.<span class='ident'>denom</span> <span class='op'><</span> <span class='ident'>T</span>::<span class='ident'>zero</span>() {
<span class='self'>self</span>.<span class='ident'>numer</span> <span class='op'>=</span> <span class='ident'>T</span>::<span class='ident'>zero</span>() <span class='op'>-</span> <span class='self'>self</span>.<span class='ident'>numer</span>.<span class='ident'>clone</span>();
<span class='self'>self</span>.<span class='ident'>denom</span> <span class='op'>=</span> <span class='ident'>T</span>::<span class='ident'>zero</span>() <span class='op'>-</span> <span class='self'>self</span>.<span class='ident'>denom</span>.<span class='ident'>clone</span>();
}
}
<span class='doccomment'>/// Returns a `reduce`d copy of self.</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>reduced</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>Ratio</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'>ret</span> <span class='op'>=</span> <span class='self'>self</span>.<span class='ident'>clone</span>();
<span class='ident'>ret</span>.<span class='ident'>reduce</span>();
<span class='ident'>ret</span>
}
<span class='doccomment'>/// Returns the reciprocal.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>recip</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='ident'>Ratio</span>::<span class='ident'>new_raw</span>(<span class='self'>self</span>.<span class='ident'>denom</span>.<span class='ident'>clone</span>(), <span class='self'>self</span>.<span class='ident'>numer</span>.<span class='ident'>clone</span>())
}
<span class='doccomment'>/// Rounds towards minus infinity.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>floor</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='kw'>if</span> <span class='op'>*</span><span class='self'>self</span> <span class='op'><</span> <span class='ident'>Zero</span>::<span class='ident'>zero</span>() {
<span class='kw'>let</span> <span class='ident'>one</span>: <span class='ident'>T</span> <span class='op'>=</span> <span class='ident'>One</span>::<span class='ident'>one</span>();
<span class='ident'>Ratio</span>::<span class='ident'>from_integer</span>((<span class='self'>self</span>.<span class='ident'>numer</span>.<span class='ident'>clone</span>() <span class='op'>-</span> <span class='self'>self</span>.<span class='ident'>denom</span>.<span class='ident'>clone</span>() <span class='op'>+</span> <span class='ident'>one</span>) <span class='op'>/</span>
<span class='self'>self</span>.<span class='ident'>denom</span>.<span class='ident'>clone</span>())
} <span class='kw'>else</span> {
<span class='ident'>Ratio</span>::<span class='ident'>from_integer</span>(<span class='self'>self</span>.<span class='ident'>numer</span>.<span class='ident'>clone</span>() <span class='op'>/</span> <span class='self'>self</span>.<span class='ident'>denom</span>.<span class='ident'>clone</span>())
}
}
<span class='doccomment'>/// Rounds towards plus infinity.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>ceil</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='kw'>if</span> <span class='op'>*</span><span class='self'>self</span> <span class='op'><</span> <span class='ident'>Zero</span>::<span class='ident'>zero</span>() {
<span class='ident'>Ratio</span>::<span class='ident'>from_integer</span>(<span class='self'>self</span>.<span class='ident'>numer</span>.<span class='ident'>clone</span>() <span class='op'>/</span> <span class='self'>self</span>.<span class='ident'>denom</span>.<span class='ident'>clone</span>())
} <span class='kw'>else</span> {
<span class='kw'>let</span> <span class='ident'>one</span>: <span class='ident'>T</span> <span class='op'>=</span> <span class='ident'>One</span>::<span class='ident'>one</span>();
<span class='ident'>Ratio</span>::<span class='ident'>from_integer</span>((<span class='self'>self</span>.<span class='ident'>numer</span>.<span class='ident'>clone</span>() <span class='op'>+</span> <span class='self'>self</span>.<span class='ident'>denom</span>.<span class='ident'>clone</span>() <span class='op'>-</span> <span class='ident'>one</span>) <span class='op'>/</span>
<span class='self'>self</span>.<span class='ident'>denom</span>.<span class='ident'>clone</span>())
}
}
<span class='doccomment'>/// Rounds to the nearest integer. Rounds half-way cases away from zero.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>round</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='kw'>let</span> <span class='ident'>zero</span>: <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> <span class='op'>=</span> <span class='ident'>Zero</span>::<span class='ident'>zero</span>();
<span class='kw'>let</span> <span class='ident'>one</span>: <span class='ident'>T</span> <span class='op'>=</span> <span class='ident'>One</span>::<span class='ident'>one</span>();
<span class='kw'>let</span> <span class='ident'>two</span>: <span class='ident'>T</span> <span class='op'>=</span> <span class='ident'>one</span>.<span class='ident'>clone</span>() <span class='op'>+</span> <span class='ident'>one</span>.<span class='ident'>clone</span>();
<span class='comment'>// Find unsigned fractional part of rational number</span>
<span class='kw'>let</span> <span class='kw-2'>mut</span> <span class='ident'>fractional</span> <span class='op'>=</span> <span class='self'>self</span>.<span class='ident'>fract</span>();
<span class='kw'>if</span> <span class='ident'>fractional</span> <span class='op'><</span> <span class='ident'>zero</span> {
<span class='ident'>fractional</span> <span class='op'>=</span> <span class='ident'>zero</span> <span class='op'>-</span> <span class='ident'>fractional</span>
};
<span class='comment'>// The algorithm compares the unsigned fractional part with 1/2, that</span>
<span class='comment'>// is, a/b >= 1/2, or a >= b/2. For odd denominators, we use</span>
<span class='comment'>// a >= (b/2)+1. This avoids overflow issues.</span>
<span class='kw'>let</span> <span class='ident'>half_or_larger</span> <span class='op'>=</span> <span class='kw'>if</span> <span class='ident'>fractional</span>.<span class='ident'>denom</span>().<span class='ident'>is_even</span>() {
<span class='op'>*</span><span class='ident'>fractional</span>.<span class='ident'>numer</span>() <span class='op'>>=</span> <span class='ident'>fractional</span>.<span class='ident'>denom</span>().<span class='ident'>clone</span>() <span class='op'>/</span> <span class='ident'>two</span>.<span class='ident'>clone</span>()
} <span class='kw'>else</span> {
<span class='op'>*</span><span class='ident'>fractional</span>.<span class='ident'>numer</span>() <span class='op'>>=</span> (<span class='ident'>fractional</span>.<span class='ident'>denom</span>().<span class='ident'>clone</span>() <span class='op'>/</span> <span class='ident'>two</span>.<span class='ident'>clone</span>()) <span class='op'>+</span> <span class='ident'>one</span>.<span class='ident'>clone</span>()
};
<span class='kw'>if</span> <span class='ident'>half_or_larger</span> {
<span class='kw'>let</span> <span class='ident'>one</span>: <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> <span class='op'>=</span> <span class='ident'>One</span>::<span class='ident'>one</span>();
<span class='kw'>if</span> <span class='op'>*</span><span class='self'>self</span> <span class='op'>>=</span> <span class='ident'>Zero</span>::<span class='ident'>zero</span>() {
<span class='self'>self</span>.<span class='ident'>trunc</span>() <span class='op'>+</span> <span class='ident'>one</span>
} <span class='kw'>else</span> {
<span class='self'>self</span>.<span class='ident'>trunc</span>() <span class='op'>-</span> <span class='ident'>one</span>
}
} <span class='kw'>else</span> {
<span class='self'>self</span>.<span class='ident'>trunc</span>()
}
}
<span class='doccomment'>/// Rounds towards zero.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>trunc</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='ident'>Ratio</span>::<span class='ident'>from_integer</span>(<span class='self'>self</span>.<span class='ident'>numer</span>.<span class='ident'>clone</span>() <span class='op'>/</span> <span class='self'>self</span>.<span class='ident'>denom</span>.<span class='ident'>clone</span>())
}
<span class='doccomment'>/// Returns the fractional part of a number.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>fract</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='ident'>Ratio</span>::<span class='ident'>new_raw</span>(<span class='self'>self</span>.<span class='ident'>numer</span>.<span class='ident'>clone</span>() <span class='op'>%</span> <span class='self'>self</span>.<span class='ident'>denom</span>.<span class='ident'>clone</span>(), <span class='self'>self</span>.<span class='ident'>denom</span>.<span class='ident'>clone</span>())
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>Clone</span> <span class='op'>+</span> <span class='ident'>Integer</span> <span class='op'>+</span> <span class='ident'>PrimInt</span><span class='op'>></span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='doccomment'>/// Raises the ratio to the power of an exponent</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>pow</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>expon</span>: <span class='ident'>i32</span>) <span class='op'>-></span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='kw'>match</span> <span class='ident'>expon</span>.<span class='ident'>cmp</span>(<span class='kw-2'>&</span><span class='number'>0</span>) {
<span class='ident'>cmp</span>::<span class='ident'>Ordering</span>::<span class='ident'>Equal</span> <span class='op'>=></span> <span class='ident'>One</span>::<span class='ident'>one</span>(),
<span class='ident'>cmp</span>::<span class='ident'>Ordering</span>::<span class='ident'>Less</span> <span class='op'>=></span> <span class='self'>self</span>.<span class='ident'>recip</span>().<span class='ident'>pow</span>(<span class='op'>-</span><span class='ident'>expon</span>),
<span class='ident'>cmp</span>::<span class='ident'>Ordering</span>::<span class='ident'>Greater</span> <span class='op'>=></span> {
<span class='ident'>Ratio</span>::<span class='ident'>new_raw</span>(<span class='self'>self</span>.<span class='ident'>numer</span>.<span class='ident'>pow</span>(<span class='ident'>expon</span> <span class='kw'>as</span> <span class='ident'>u32</span>), <span class='self'>self</span>.<span class='ident'>denom</span>.<span class='ident'>pow</span>(<span class='ident'>expon</span> <span class='kw'>as</span> <span class='ident'>u32</span>))
}
}
}
}
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>feature</span> <span class='op'>=</span> <span class='string'>"num-bigint"</span>)]</span>
<span class='kw'>impl</span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>BigInt</span><span class='op'>></span> {
<span class='doccomment'>/// Converts a float into a rational number.</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>from_float</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>Float</span><span class='op'>></span>(<span class='ident'>f</span>: <span class='ident'>T</span>) <span class='op'>-></span> <span class='prelude-ty'>Option</span><span class='op'><</span><span class='ident'>BigRational</span><span class='op'>></span> {
<span class='kw'>if</span> <span class='op'>!</span><span class='ident'>f</span>.<span class='ident'>is_finite</span>() {
<span class='kw'>return</span> <span class='prelude-val'>None</span>;
}
<span class='kw'>let</span> (<span class='ident'>mantissa</span>, <span class='ident'>exponent</span>, <span class='ident'>sign</span>) <span class='op'>=</span> <span class='ident'>f</span>.<span class='ident'>integer_decode</span>();
<span class='kw'>let</span> <span class='ident'>bigint_sign</span> <span class='op'>=</span> <span class='kw'>if</span> <span class='ident'>sign</span> <span class='op'>==</span> <span class='number'>1</span> {
<span class='ident'>Sign</span>::<span class='ident'>Plus</span>
} <span class='kw'>else</span> {
<span class='ident'>Sign</span>::<span class='ident'>Minus</span>
};
<span class='kw'>if</span> <span class='ident'>exponent</span> <span class='op'><</span> <span class='number'>0</span> {
<span class='kw'>let</span> <span class='ident'>one</span>: <span class='ident'>BigInt</span> <span class='op'>=</span> <span class='ident'>One</span>::<span class='ident'>one</span>();
<span class='kw'>let</span> <span class='ident'>denom</span>: <span class='ident'>BigInt</span> <span class='op'>=</span> <span class='ident'>one</span> <span class='op'><<</span> ((<span class='op'>-</span><span class='ident'>exponent</span>) <span class='kw'>as</span> <span class='ident'>usize</span>);
<span class='kw'>let</span> <span class='ident'>numer</span>: <span class='ident'>BigUint</span> <span class='op'>=</span> <span class='ident'>FromPrimitive</span>::<span class='ident'>from_u64</span>(<span class='ident'>mantissa</span>).<span class='ident'>unwrap</span>();
<span class='prelude-val'>Some</span>(<span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='ident'>BigInt</span>::<span class='ident'>from_biguint</span>(<span class='ident'>bigint_sign</span>, <span class='ident'>numer</span>), <span class='ident'>denom</span>))
} <span class='kw'>else</span> {
<span class='kw'>let</span> <span class='kw-2'>mut</span> <span class='ident'>numer</span>: <span class='ident'>BigUint</span> <span class='op'>=</span> <span class='ident'>FromPrimitive</span>::<span class='ident'>from_u64</span>(<span class='ident'>mantissa</span>).<span class='ident'>unwrap</span>();
<span class='ident'>numer</span> <span class='op'>=</span> <span class='ident'>numer</span> <span class='op'><<</span> (<span class='ident'>exponent</span> <span class='kw'>as</span> <span class='ident'>usize</span>);
<span class='prelude-val'>Some</span>(<span class='ident'>Ratio</span>::<span class='ident'>from_integer</span>(<span class='ident'>BigInt</span>::<span class='ident'>from_biguint</span>(<span class='ident'>bigint_sign</span>, <span class='ident'>numer</span>)))
}
}
}
<span class='comment'>// Comparisons</span>
<span class='comment'>// Mathematically, comparing a/b and c/d is the same as comparing a*d and b*c, but it's very easy</span>
<span class='comment'>// for those multiplications to overflow fixed-size integers, so we need to take care.</span>
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>Clone</span> <span class='op'>+</span> <span class='ident'>Integer</span><span class='op'>></span> <span class='ident'>Ord</span> <span class='kw'>for</span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>cmp</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='ident'>cmp</span>::<span class='ident'>Ordering</span> {
<span class='comment'>// With equal denominators, the numerators can be directly compared</span>
<span class='kw'>if</span> <span class='self'>self</span>.<span class='ident'>denom</span> <span class='op'>==</span> <span class='ident'>other</span>.<span class='ident'>denom</span> {
<span class='kw'>let</span> <span class='ident'>ord</span> <span class='op'>=</span> <span class='self'>self</span>.<span class='ident'>numer</span>.<span class='ident'>cmp</span>(<span class='kw-2'>&</span><span class='ident'>other</span>.<span class='ident'>numer</span>);
<span class='kw'>return</span> <span class='kw'>if</span> <span class='self'>self</span>.<span class='ident'>denom</span> <span class='op'><</span> <span class='ident'>T</span>::<span class='ident'>zero</span>() {
<span class='ident'>ord</span>.<span class='ident'>reverse</span>()
} <span class='kw'>else</span> {
<span class='ident'>ord</span>
};
}
<span class='comment'>// With equal numerators, the denominators can be inversely compared</span>
<span class='kw'>if</span> <span class='self'>self</span>.<span class='ident'>numer</span> <span class='op'>==</span> <span class='ident'>other</span>.<span class='ident'>numer</span> {
<span class='kw'>let</span> <span class='ident'>ord</span> <span class='op'>=</span> <span class='self'>self</span>.<span class='ident'>denom</span>.<span class='ident'>cmp</span>(<span class='kw-2'>&</span><span class='ident'>other</span>.<span class='ident'>denom</span>);
<span class='kw'>return</span> <span class='kw'>if</span> <span class='self'>self</span>.<span class='ident'>numer</span> <span class='op'><</span> <span class='ident'>T</span>::<span class='ident'>zero</span>() {
<span class='ident'>ord</span>
} <span class='kw'>else</span> {
<span class='ident'>ord</span>.<span class='ident'>reverse</span>()
};
}
<span class='comment'>// Unfortunately, we don't have CheckedMul to try. That could sometimes avoid all the</span>
<span class='comment'>// division below, or even always avoid it for BigInt and BigUint.</span>
<span class='comment'>// FIXME- future breaking change to add Checked* to Integer?</span>
<span class='comment'>// Compare as floored integers and remainders</span>
<span class='kw'>let</span> (<span class='ident'>self_int</span>, <span class='ident'>self_rem</span>) <span class='op'>=</span> <span class='self'>self</span>.<span class='ident'>numer</span>.<span class='ident'>div_mod_floor</span>(<span class='kw-2'>&</span><span class='self'>self</span>.<span class='ident'>denom</span>);
<span class='kw'>let</span> (<span class='ident'>other_int</span>, <span class='ident'>other_rem</span>) <span class='op'>=</span> <span class='ident'>other</span>.<span class='ident'>numer</span>.<span class='ident'>div_mod_floor</span>(<span class='kw-2'>&</span><span class='ident'>other</span>.<span class='ident'>denom</span>);
<span class='kw'>match</span> <span class='ident'>self_int</span>.<span class='ident'>cmp</span>(<span class='kw-2'>&</span><span class='ident'>other_int</span>) {
<span class='ident'>cmp</span>::<span class='ident'>Ordering</span>::<span class='ident'>Greater</span> <span class='op'>=></span> <span class='ident'>cmp</span>::<span class='ident'>Ordering</span>::<span class='ident'>Greater</span>,
<span class='ident'>cmp</span>::<span class='ident'>Ordering</span>::<span class='ident'>Less</span> <span class='op'>=></span> <span class='ident'>cmp</span>::<span class='ident'>Ordering</span>::<span class='ident'>Less</span>,
<span class='ident'>cmp</span>::<span class='ident'>Ordering</span>::<span class='ident'>Equal</span> <span class='op'>=></span> {
<span class='kw'>match</span> (<span class='ident'>self_rem</span>.<span class='ident'>is_zero</span>(), <span class='ident'>other_rem</span>.<span class='ident'>is_zero</span>()) {
(<span class='bool-val'>true</span>, <span class='bool-val'>true</span>) <span class='op'>=></span> <span class='ident'>cmp</span>::<span class='ident'>Ordering</span>::<span class='ident'>Equal</span>,
(<span class='bool-val'>true</span>, <span class='bool-val'>false</span>) <span class='op'>=></span> <span class='ident'>cmp</span>::<span class='ident'>Ordering</span>::<span class='ident'>Less</span>,
(<span class='bool-val'>false</span>, <span class='bool-val'>true</span>) <span class='op'>=></span> <span class='ident'>cmp</span>::<span class='ident'>Ordering</span>::<span class='ident'>Greater</span>,
(<span class='bool-val'>false</span>, <span class='bool-val'>false</span>) <span class='op'>=></span> {
<span class='comment'>// Compare the reciprocals of the remaining fractions in reverse</span>
<span class='kw'>let</span> <span class='ident'>self_recip</span> <span class='op'>=</span> <span class='ident'>Ratio</span>::<span class='ident'>new_raw</span>(<span class='self'>self</span>.<span class='ident'>denom</span>.<span class='ident'>clone</span>(), <span class='ident'>self_rem</span>);
<span class='kw'>let</span> <span class='ident'>other_recip</span> <span class='op'>=</span> <span class='ident'>Ratio</span>::<span class='ident'>new_raw</span>(<span class='ident'>other</span>.<span class='ident'>denom</span>.<span class='ident'>clone</span>(), <span class='ident'>other_rem</span>);
<span class='ident'>self_recip</span>.<span class='ident'>cmp</span>(<span class='kw-2'>&</span><span class='ident'>other_recip</span>).<span class='ident'>reverse</span>()
}
}
}
}
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>Clone</span> <span class='op'>+</span> <span class='ident'>Integer</span><span class='op'>></span> <span class='ident'>PartialOrd</span> <span class='kw'>for</span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>partial_cmp</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='prelude-ty'>Option</span><span class='op'><</span><span class='ident'>cmp</span>::<span class='ident'>Ordering</span><span class='op'>></span> {
<span class='prelude-val'>Some</span>(<span class='self'>self</span>.<span class='ident'>cmp</span>(<span class='ident'>other</span>))
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>Clone</span> <span class='op'>+</span> <span class='ident'>Integer</span><span class='op'>></span> <span class='ident'>PartialEq</span> <span class='kw'>for</span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>eq</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='ident'>bool</span> {
<span class='self'>self</span>.<span class='ident'>cmp</span>(<span class='ident'>other</span>) <span class='op'>==</span> <span class='ident'>cmp</span>::<span class='ident'>Ordering</span>::<span class='ident'>Equal</span>
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>Clone</span> <span class='op'>+</span> <span class='ident'>Integer</span><span class='op'>></span> <span class='ident'>Eq</span> <span class='kw'>for</span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {}
<span class='macro'>macro_rules</span><span class='macro'>!</span> <span class='ident'>forward_val_val_binop</span> {
(<span class='kw'>impl</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>imp</span>:<span class='ident'>ident</span>, <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>method</span>:<span class='ident'>ident</span>) <span class='op'>=></span> {
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>Clone</span> <span class='op'>+</span> <span class='ident'>Integer</span><span class='op'>></span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>imp</span><span class='op'><</span><span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>>></span> <span class='kw'>for</span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='kw'>type</span> <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span>;
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>method</span>(<span class='self'>self</span>, <span class='ident'>other</span>: <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
(<span class='kw-2'>&</span><span class='self'>self</span>).<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>method</span>(<span class='kw-2'>&</span><span class='ident'>other</span>)
}
}
}
}
<span class='macro'>macro_rules</span><span class='macro'>!</span> <span class='ident'>forward_ref_val_binop</span> {
(<span class='kw'>impl</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>imp</span>:<span class='ident'>ident</span>, <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>method</span>:<span class='ident'>ident</span>) <span class='op'>=></span> {
<span class='kw'>impl</span><span class='op'><</span><span class='lifetime'>'a</span>, <span class='ident'>T</span><span class='op'>></span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>imp</span><span class='op'><</span><span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>>></span> <span class='kw'>for</span> <span class='kw-2'>&</span><span class='lifetime'>'a</span> <span class='ident'>Ratio</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'>Clone</span> <span class='op'>+</span> <span class='ident'>Integer</span>
{
<span class='kw'>type</span> <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span>;
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>method</span>(<span class='self'>self</span>, <span class='ident'>other</span>: <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='self'>self</span>.<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>method</span>(<span class='kw-2'>&</span><span class='ident'>other</span>)
}
}
}
}
<span class='macro'>macro_rules</span><span class='macro'>!</span> <span class='ident'>forward_val_ref_binop</span> {
(<span class='kw'>impl</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>imp</span>:<span class='ident'>ident</span>, <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>method</span>:<span class='ident'>ident</span>) <span class='op'>=></span> {
<span class='kw'>impl</span><span class='op'><</span><span class='lifetime'>'a</span>, <span class='ident'>T</span><span class='op'>></span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>imp</span><span class='op'><</span><span class='kw-2'>&</span><span class='lifetime'>'a</span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>>></span> <span class='kw'>for</span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> <span class='kw'>where</span>
<span class='ident'>T</span>: <span class='ident'>Clone</span> <span class='op'>+</span> <span class='ident'>Integer</span>
{
<span class='kw'>type</span> <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span>;
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>method</span>(<span class='self'>self</span>, <span class='ident'>other</span>: <span class='kw-2'>&</span><span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
(<span class='kw-2'>&</span><span class='self'>self</span>).<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>method</span>(<span class='ident'>other</span>)
}
}
}
}
<span class='macro'>macro_rules</span><span class='macro'>!</span> <span class='ident'>forward_all_binop</span> {
(<span class='kw'>impl</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>imp</span>:<span class='ident'>ident</span>, <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>method</span>:<span class='ident'>ident</span>) <span class='op'>=></span> {
<span class='macro'>forward_val_val_binop</span><span class='macro'>!</span>(<span class='kw'>impl</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>imp</span>, <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>method</span>);
<span class='macro'>forward_ref_val_binop</span><span class='macro'>!</span>(<span class='kw'>impl</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>imp</span>, <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>method</span>);
<span class='macro'>forward_val_ref_binop</span><span class='macro'>!</span>(<span class='kw'>impl</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>imp</span>, <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>method</span>);
};
}
<span class='comment'>// Arithmetic</span>
<span class='macro'>forward_all_binop</span><span class='macro'>!</span>(<span class='kw'>impl</span> <span class='ident'>Mul</span>, <span class='ident'>mul</span>);
<span class='comment'>// a/b * c/d = (a*c)/(b*d)</span>
<span class='kw'>impl</span><span class='op'><</span><span class='lifetime'>'a</span>, <span class='lifetime'>'b</span>, <span class='ident'>T</span><span class='op'>></span> <span class='ident'>Mul</span><span class='op'><</span><span class='kw-2'>&</span><span class='lifetime'>'b</span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>>></span> <span class='kw'>for</span> <span class='kw-2'>&</span><span class='lifetime'>'a</span> <span class='ident'>Ratio</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'>Clone</span> <span class='op'>+</span> <span class='ident'>Integer</span>
{
<span class='kw'>type</span> <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span>;
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>mul</span>(<span class='self'>self</span>, <span class='ident'>rhs</span>: <span class='kw-2'>&</span><span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='self'>self</span>.<span class='ident'>numer</span>.<span class='ident'>clone</span>() <span class='op'>*</span> <span class='ident'>rhs</span>.<span class='ident'>numer</span>.<span class='ident'>clone</span>(),
<span class='self'>self</span>.<span class='ident'>denom</span>.<span class='ident'>clone</span>() <span class='op'>*</span> <span class='ident'>rhs</span>.<span class='ident'>denom</span>.<span class='ident'>clone</span>())
}
}
<span class='macro'>forward_all_binop</span><span class='macro'>!</span>(<span class='kw'>impl</span> <span class='ident'>Div</span>, <span class='ident'>div</span>);
<span class='comment'>// (a/b) / (c/d) = (a*d)/(b*c)</span>
<span class='kw'>impl</span><span class='op'><</span><span class='lifetime'>'a</span>, <span class='lifetime'>'b</span>, <span class='ident'>T</span><span class='op'>></span> <span class='ident'>Div</span><span class='op'><</span><span class='kw-2'>&</span><span class='lifetime'>'b</span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>>></span> <span class='kw'>for</span> <span class='kw-2'>&</span><span class='lifetime'>'a</span> <span class='ident'>Ratio</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'>Clone</span> <span class='op'>+</span> <span class='ident'>Integer</span>
{
<span class='kw'>type</span> <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span>;
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>div</span>(<span class='self'>self</span>, <span class='ident'>rhs</span>: <span class='kw-2'>&</span><span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='self'>self</span>.<span class='ident'>numer</span>.<span class='ident'>clone</span>() <span class='op'>*</span> <span class='ident'>rhs</span>.<span class='ident'>denom</span>.<span class='ident'>clone</span>(),
<span class='self'>self</span>.<span class='ident'>denom</span>.<span class='ident'>clone</span>() <span class='op'>*</span> <span class='ident'>rhs</span>.<span class='ident'>numer</span>.<span class='ident'>clone</span>())
}
}
<span class='comment'>// Abstracts the a/b `op` c/d = (a*d `op` b*d) / (b*d) pattern</span>
<span class='macro'>macro_rules</span><span class='macro'>!</span> <span class='ident'>arith_impl</span> {
(<span class='kw'>impl</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>imp</span>:<span class='ident'>ident</span>, <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>method</span>:<span class='ident'>ident</span>) <span class='op'>=></span> {
<span class='macro'>forward_all_binop</span><span class='macro'>!</span>(<span class='kw'>impl</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>imp</span>, <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>method</span>);
<span class='kw'>impl</span><span class='op'><</span><span class='lifetime'>'a</span>, <span class='lifetime'>'b</span>, <span class='ident'>T</span>: <span class='ident'>Clone</span> <span class='op'>+</span> <span class='ident'>Integer</span><span class='op'>></span>
<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>imp</span><span class='op'><</span><span class='kw-2'>&</span><span class='lifetime'>'b</span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>>></span> <span class='kw'>for</span> <span class='kw-2'>&</span><span class='lifetime'>'a</span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='kw'>type</span> <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span>;
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>method</span>(<span class='self'>self</span>, <span class='ident'>rhs</span>: <span class='kw-2'>&</span><span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='ident'>Ratio</span>::<span class='ident'>new</span>((<span class='self'>self</span>.<span class='ident'>numer</span>.<span class='ident'>clone</span>() <span class='op'>*</span> <span class='ident'>rhs</span>.<span class='ident'>denom</span>.<span class='ident'>clone</span>()).<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>method</span>(<span class='self'>self</span>.<span class='ident'>denom</span>.<span class='ident'>clone</span>() <span class='op'>*</span> <span class='ident'>rhs</span>.<span class='ident'>numer</span>.<span class='ident'>clone</span>()),
<span class='self'>self</span>.<span class='ident'>denom</span>.<span class='ident'>clone</span>() <span class='op'>*</span> <span class='ident'>rhs</span>.<span class='ident'>denom</span>.<span class='ident'>clone</span>())
}
}
}
}
<span class='comment'>// a/b + c/d = (a*d + b*c)/(b*d)</span>
<span class='macro'>arith_impl</span><span class='macro'>!</span>(<span class='kw'>impl</span> <span class='ident'>Add</span>, <span class='ident'>add</span>);
<span class='comment'>// a/b - c/d = (a*d - b*c)/(b*d)</span>
<span class='macro'>arith_impl</span><span class='macro'>!</span>(<span class='kw'>impl</span> <span class='ident'>Sub</span>, <span class='ident'>sub</span>);
<span class='comment'>// a/b % c/d = (a*d % b*c)/(b*d)</span>
<span class='macro'>arith_impl</span><span class='macro'>!</span>(<span class='kw'>impl</span> <span class='ident'>Rem</span>, <span class='ident'>rem</span>);
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> <span class='ident'>Neg</span> <span class='kw'>for</span> <span class='ident'>Ratio</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'>Clone</span> <span class='op'>+</span> <span class='ident'>Integer</span> <span class='op'>+</span> <span class='ident'>Neg</span><span class='op'><</span><span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>T</span><span class='op'>></span>
{
<span class='kw'>type</span> <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span>;
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>neg</span>(<span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='ident'>Ratio</span>::<span class='ident'>new_raw</span>(<span class='op'>-</span><span class='self'>self</span>.<span class='ident'>numer</span>, <span class='self'>self</span>.<span class='ident'>denom</span>)
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='lifetime'>'a</span>, <span class='ident'>T</span><span class='op'>></span> <span class='ident'>Neg</span> <span class='kw'>for</span> <span class='kw-2'>&</span><span class='lifetime'>'a</span> <span class='ident'>Ratio</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'>Clone</span> <span class='op'>+</span> <span class='ident'>Integer</span> <span class='op'>+</span> <span class='ident'>Neg</span><span class='op'><</span><span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>T</span><span class='op'>></span>
{
<span class='kw'>type</span> <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span>;
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>neg</span>(<span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='op'>-</span><span class='self'>self</span>.<span class='ident'>clone</span>()
}
}
<span class='comment'>// Constants</span>
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>Clone</span> <span class='op'>+</span> <span class='ident'>Integer</span><span class='op'>></span> <span class='ident'>Zero</span> <span class='kw'>for</span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>zero</span>() <span class='op'>-></span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='ident'>Ratio</span>::<span class='ident'>new_raw</span>(<span class='ident'>Zero</span>::<span class='ident'>zero</span>(), <span class='ident'>One</span>::<span class='ident'>one</span>())
}
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>is_zero</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>bool</span> {
<span class='self'>self</span>.<span class='ident'>numer</span>.<span class='ident'>is_zero</span>()
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>Clone</span> <span class='op'>+</span> <span class='ident'>Integer</span><span class='op'>></span> <span class='ident'>One</span> <span class='kw'>for</span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>one</span>() <span class='op'>-></span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='ident'>Ratio</span>::<span class='ident'>new_raw</span>(<span class='ident'>One</span>::<span class='ident'>one</span>(), <span class='ident'>One</span>::<span class='ident'>one</span>())
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>Clone</span> <span class='op'>+</span> <span class='ident'>Integer</span><span class='op'>></span> <span class='ident'>Num</span> <span class='kw'>for</span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='kw'>type</span> <span class='ident'>FromStrRadixErr</span> <span class='op'>=</span> <span class='ident'>ParseRatioError</span>;
<span class='doccomment'>/// Parses `numer/denom` where the numbers are in base `radix`.</span>
<span class='kw'>fn</span> <span class='ident'>from_str_radix</span>(<span class='ident'>s</span>: <span class='kw-2'>&</span><span class='ident'>str</span>, <span class='ident'>radix</span>: <span class='ident'>u32</span>) <span class='op'>-></span> <span class='prelude-ty'>Result</span><span class='op'><</span><span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span>, <span class='ident'>ParseRatioError</span><span class='op'>></span> {
<span class='kw'>let</span> <span class='ident'>split</span>: <span class='ident'>Vec</span><span class='op'><</span><span class='kw-2'>&</span><span class='ident'>str</span><span class='op'>></span> <span class='op'>=</span> <span class='ident'>s</span>.<span class='ident'>splitn</span>(<span class='number'>2</span>, <span class='string'>'/'</span>).<span class='ident'>collect</span>();
<span class='kw'>if</span> <span class='ident'>split</span>.<span class='ident'>len</span>() <span class='op'><</span> <span class='number'>2</span> {
<span class='prelude-val'>Err</span>(<span class='ident'>ParseRatioError</span> { <span class='ident'>kind</span>: <span class='ident'>RatioErrorKind</span>::<span class='ident'>ParseError</span> })
} <span class='kw'>else</span> {
<span class='kw'>let</span> <span class='ident'>a_result</span>: <span class='prelude-ty'>Result</span><span class='op'><</span><span class='ident'>T</span>, _<span class='op'>></span> <span class='op'>=</span> <span class='ident'>T</span>::<span class='ident'>from_str_radix</span>(<span class='ident'>split</span>[<span class='number'>0</span>], <span class='ident'>radix</span>).<span class='ident'>map_err</span>(<span class='op'>|</span>_<span class='op'>|</span> {
<span class='ident'>ParseRatioError</span> { <span class='ident'>kind</span>: <span class='ident'>RatioErrorKind</span>::<span class='ident'>ParseError</span> }
});
<span class='ident'>a_result</span>.<span class='ident'>and_then</span>(<span class='op'>|</span><span class='ident'>a</span><span class='op'>|</span> {
<span class='kw'>let</span> <span class='ident'>b_result</span>: <span class='prelude-ty'>Result</span><span class='op'><</span><span class='ident'>T</span>, _<span class='op'>></span> <span class='op'>=</span> <span class='ident'>T</span>::<span class='ident'>from_str_radix</span>(<span class='ident'>split</span>[<span class='number'>1</span>], <span class='ident'>radix</span>).<span class='ident'>map_err</span>(<span class='op'>|</span>_<span class='op'>|</span> {
<span class='ident'>ParseRatioError</span> { <span class='ident'>kind</span>: <span class='ident'>RatioErrorKind</span>::<span class='ident'>ParseError</span> }
});
<span class='ident'>b_result</span>.<span class='ident'>and_then</span>(<span class='op'>|</span><span class='ident'>b</span><span class='op'>|</span> {
<span class='kw'>if</span> <span class='ident'>b</span>.<span class='ident'>is_zero</span>() {
<span class='prelude-val'>Err</span>(<span class='ident'>ParseRatioError</span> { <span class='ident'>kind</span>: <span class='ident'>RatioErrorKind</span>::<span class='ident'>ZeroDenominator</span> })
} <span class='kw'>else</span> {
<span class='prelude-val'>Ok</span>(<span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='ident'>a</span>.<span class='ident'>clone</span>(), <span class='ident'>b</span>.<span class='ident'>clone</span>()))
}
})
})
}
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>Clone</span> <span class='op'>+</span> <span class='ident'>Integer</span> <span class='op'>+</span> <span class='ident'>Signed</span><span class='op'>></span> <span class='ident'>Signed</span> <span class='kw'>for</span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>abs</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>Ratio</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'>is_negative</span>() {
<span class='op'>-</span><span class='self'>self</span>.<span class='ident'>clone</span>()
} <span class='kw'>else</span> {
<span class='self'>self</span>.<span class='ident'>clone</span>()
}
}
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>abs_sub</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>other</span>: <span class='kw-2'>&</span><span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='kw'>if</span> <span class='op'>*</span><span class='self'>self</span> <span class='op'><=</span> <span class='op'>*</span><span class='ident'>other</span> {
<span class='ident'>Zero</span>::<span class='ident'>zero</span>()
} <span class='kw'>else</span> {
<span class='self'>self</span> <span class='op'>-</span> <span class='ident'>other</span>
}
}
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>signum</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>Ratio</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'>is_positive</span>() {
<span class='self'>Self</span>::<span class='ident'>one</span>()
} <span class='kw'>else</span> <span class='kw'>if</span> <span class='self'>self</span>.<span class='ident'>is_zero</span>() {
<span class='self'>Self</span>::<span class='ident'>zero</span>()
} <span class='kw'>else</span> {
<span class='op'>-</span><span class='self'>Self</span>::<span class='ident'>one</span>()
}
}
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>is_positive</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>bool</span> {
(<span class='self'>self</span>.<span class='ident'>numer</span>.<span class='ident'>is_positive</span>() <span class='op'>&&</span> <span class='self'>self</span>.<span class='ident'>denom</span>.<span class='ident'>is_positive</span>()) <span class='op'>||</span>
(<span class='self'>self</span>.<span class='ident'>numer</span>.<span class='ident'>is_negative</span>() <span class='op'>&&</span> <span class='self'>self</span>.<span class='ident'>denom</span>.<span class='ident'>is_negative</span>())
}
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>is_negative</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>bool</span> {
(<span class='self'>self</span>.<span class='ident'>numer</span>.<span class='ident'>is_negative</span>() <span class='op'>&&</span> <span class='self'>self</span>.<span class='ident'>denom</span>.<span class='ident'>is_positive</span>()) <span class='op'>||</span>
(<span class='self'>self</span>.<span class='ident'>numer</span>.<span class='ident'>is_positive</span>() <span class='op'>&&</span> <span class='self'>self</span>.<span class='ident'>denom</span>.<span class='ident'>is_negative</span>())
}
}
<span class='comment'>// String conversions</span>
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> <span class='ident'>fmt</span>::<span class='ident'>Display</span> <span class='kw'>for</span> <span class='ident'>Ratio</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'>fmt</span>::<span class='ident'>Display</span> <span class='op'>+</span> <span class='ident'>Eq</span> <span class='op'>+</span> <span class='ident'>One</span>
{
<span class='doccomment'>/// Renders as `numer/denom`. If denom=1, renders as numer.</span>
<span class='kw'>fn</span> <span class='ident'>fmt</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>f</span>: <span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='ident'>fmt</span>::<span class='ident'>Formatter</span>) <span class='op'>-></span> <span class='ident'>fmt</span>::<span class='prelude-ty'>Result</span> {
<span class='kw'>if</span> <span class='self'>self</span>.<span class='ident'>denom</span> <span class='op'>==</span> <span class='ident'>One</span>::<span class='ident'>one</span>() {
<span class='macro'>write</span><span class='macro'>!</span>(<span class='ident'>f</span>, <span class='string'>"{}"</span>, <span class='self'>self</span>.<span class='ident'>numer</span>)
} <span class='kw'>else</span> {
<span class='macro'>write</span><span class='macro'>!</span>(<span class='ident'>f</span>, <span class='string'>"{}/{}"</span>, <span class='self'>self</span>.<span class='ident'>numer</span>, <span class='self'>self</span>.<span class='ident'>denom</span>)
}
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>FromStr</span> <span class='op'>+</span> <span class='ident'>Clone</span> <span class='op'>+</span> <span class='ident'>Integer</span><span class='op'>></span> <span class='ident'>FromStr</span> <span class='kw'>for</span> <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='kw'>type</span> <span class='prelude-val'>Err</span> <span class='op'>=</span> <span class='ident'>ParseRatioError</span>;
<span class='doccomment'>/// Parses `numer/denom` or just `numer`.</span>
<span class='kw'>fn</span> <span class='ident'>from_str</span>(<span class='ident'>s</span>: <span class='kw-2'>&</span><span class='ident'>str</span>) <span class='op'>-></span> <span class='prelude-ty'>Result</span><span class='op'><</span><span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span>, <span class='ident'>ParseRatioError</span><span class='op'>></span> {
<span class='kw'>let</span> <span class='kw-2'>mut</span> <span class='ident'>split</span> <span class='op'>=</span> <span class='ident'>s</span>.<span class='ident'>splitn</span>(<span class='number'>2</span>, <span class='string'>'/'</span>);
<span class='kw'>let</span> <span class='ident'>n</span> <span class='op'>=</span> <span class='macro'>try</span><span class='macro'>!</span>(<span class='ident'>split</span>.<span class='ident'>next</span>().<span class='ident'>ok_or</span>(<span class='ident'>ParseRatioError</span> { <span class='ident'>kind</span>: <span class='ident'>RatioErrorKind</span>::<span class='ident'>ParseError</span> }));
<span class='kw'>let</span> <span class='ident'>num</span> <span class='op'>=</span> <span class='macro'>try</span><span class='macro'>!</span>(<span class='ident'>FromStr</span>::<span class='ident'>from_str</span>(<span class='ident'>n</span>)
.<span class='ident'>map_err</span>(<span class='op'>|</span>_<span class='op'>|</span> <span class='ident'>ParseRatioError</span> { <span class='ident'>kind</span>: <span class='ident'>RatioErrorKind</span>::<span class='ident'>ParseError</span> }));
<span class='kw'>let</span> <span class='ident'>d</span> <span class='op'>=</span> <span class='ident'>split</span>.<span class='ident'>next</span>().<span class='ident'>unwrap_or</span>(<span class='string'>"1"</span>);
<span class='kw'>let</span> <span class='ident'>den</span> <span class='op'>=</span> <span class='macro'>try</span><span class='macro'>!</span>(<span class='ident'>FromStr</span>::<span class='ident'>from_str</span>(<span class='ident'>d</span>)
.<span class='ident'>map_err</span>(<span class='op'>|</span>_<span class='op'>|</span> <span class='ident'>ParseRatioError</span> { <span class='ident'>kind</span>: <span class='ident'>RatioErrorKind</span>::<span class='ident'>ParseError</span> }));
<span class='kw'>if</span> <span class='ident'>Zero</span>::<span class='ident'>is_zero</span>(<span class='kw-2'>&</span><span class='ident'>den</span>) {
<span class='prelude-val'>Err</span>(<span class='ident'>ParseRatioError</span> { <span class='ident'>kind</span>: <span class='ident'>RatioErrorKind</span>::<span class='ident'>ZeroDenominator</span> })
} <span class='kw'>else</span> {
<span class='prelude-val'>Ok</span>(<span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='ident'>num</span>, <span class='ident'>den</span>))
}
}
}
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>feature</span> <span class='op'>=</span> <span class='string'>"serde"</span>)]</span>
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> <span class='ident'>serde</span>::<span class='ident'>Serialize</span> <span class='kw'>for</span> <span class='ident'>Ratio</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'>serde</span>::<span class='ident'>Serialize</span> <span class='op'>+</span> <span class='ident'>Clone</span> <span class='op'>+</span> <span class='ident'>Integer</span> <span class='op'>+</span> <span class='ident'>PartialOrd</span>
{
<span class='kw'>fn</span> <span class='ident'>serialize</span><span class='op'><</span><span class='ident'>S</span><span class='op'>></span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>serializer</span>: <span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='ident'>S</span>) <span class='op'>-></span> <span class='prelude-ty'>Result</span><span class='op'><</span>(), <span class='ident'>S</span>::<span class='ident'>Error</span><span class='op'>></span>
<span class='kw'>where</span> <span class='ident'>S</span>: <span class='ident'>serde</span>::<span class='ident'>Serializer</span>
{
(<span class='self'>self</span>.<span class='ident'>numer</span>(), <span class='self'>self</span>.<span class='ident'>denom</span>()).<span class='ident'>serialize</span>(<span class='ident'>serializer</span>)
}
}
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>feature</span> <span class='op'>=</span> <span class='string'>"serde"</span>)]</span>
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> <span class='ident'>serde</span>::<span class='ident'>Deserialize</span> <span class='kw'>for</span> <span class='ident'>Ratio</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'>serde</span>::<span class='ident'>Deserialize</span> <span class='op'>+</span> <span class='ident'>Clone</span> <span class='op'>+</span> <span class='ident'>Integer</span> <span class='op'>+</span> <span class='ident'>PartialOrd</span>
{
<span class='kw'>fn</span> <span class='ident'>deserialize</span><span class='op'><</span><span class='ident'>D</span><span class='op'>></span>(<span class='ident'>deserializer</span>: <span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='ident'>D</span>) <span class='op'>-></span> <span class='prelude-ty'>Result</span><span class='op'><</span><span class='self'>Self</span>, <span class='ident'>D</span>::<span class='ident'>Error</span><span class='op'>></span>
<span class='kw'>where</span> <span class='ident'>D</span>: <span class='ident'>serde</span>::<span class='ident'>Deserializer</span>
{
<span class='kw'>let</span> (<span class='ident'>numer</span>, <span class='ident'>denom</span>) <span class='op'>=</span> <span class='macro'>try</span><span class='macro'>!</span>(<span class='ident'>serde</span>::<span class='ident'>Deserialize</span>::<span class='ident'>deserialize</span>(<span class='ident'>deserializer</span>));
<span class='kw'>if</span> <span class='ident'>denom</span> <span class='op'>==</span> <span class='ident'>Zero</span>::<span class='ident'>zero</span>() {
<span class='prelude-val'>Err</span>(<span class='ident'>serde</span>::<span class='ident'>de</span>::<span class='ident'>Error</span>::<span class='ident'>invalid_value</span>(<span class='string'>"denominator is zero"</span>))
} <span class='kw'>else</span> {
<span class='prelude-val'>Ok</span>(<span class='ident'>Ratio</span>::<span class='ident'>new_raw</span>(<span class='ident'>numer</span>, <span class='ident'>denom</span>))
}
}
}
<span class='comment'>// FIXME: Bubble up specific errors</span>
<span class='attribute'>#[<span class='ident'>derive</span>(<span class='ident'>Copy</span>, <span class='ident'>Clone</span>, <span class='ident'>Debug</span>, <span class='ident'>PartialEq</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>struct</span> <span class='ident'>ParseRatioError</span> {
<span class='ident'>kind</span>: <span class='ident'>RatioErrorKind</span>,
}
<span class='attribute'>#[<span class='ident'>derive</span>(<span class='ident'>Copy</span>, <span class='ident'>Clone</span>, <span class='ident'>Debug</span>, <span class='ident'>PartialEq</span>)]</span>
<span class='kw'>enum</span> <span class='ident'>RatioErrorKind</span> {
<span class='ident'>ParseError</span>,
<span class='ident'>ZeroDenominator</span>,
}
<span class='kw'>impl</span> <span class='ident'>fmt</span>::<span class='ident'>Display</span> <span class='kw'>for</span> <span class='ident'>ParseRatioError</span> {
<span class='kw'>fn</span> <span class='ident'>fmt</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>f</span>: <span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='ident'>fmt</span>::<span class='ident'>Formatter</span>) <span class='op'>-></span> <span class='ident'>fmt</span>::<span class='prelude-ty'>Result</span> {
<span class='self'>self</span>.<span class='ident'>description</span>().<span class='ident'>fmt</span>(<span class='ident'>f</span>)
}
}
<span class='kw'>impl</span> <span class='ident'>Error</span> <span class='kw'>for</span> <span class='ident'>ParseRatioError</span> {
<span class='kw'>fn</span> <span class='ident'>description</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='kw-2'>&</span><span class='ident'>str</span> {
<span class='self'>self</span>.<span class='ident'>kind</span>.<span class='ident'>description</span>()
}
}
<span class='kw'>impl</span> <span class='ident'>RatioErrorKind</span> {
<span class='kw'>fn</span> <span class='ident'>description</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='kw-2'>&</span><span class='lifetime'>'static</span> <span class='ident'>str</span> {
<span class='kw'>match</span> <span class='op'>*</span><span class='self'>self</span> {
<span class='ident'>RatioErrorKind</span>::<span class='ident'>ParseError</span> <span class='op'>=></span> <span class='string'>"failed to parse integer"</span>,
<span class='ident'>RatioErrorKind</span>::<span class='ident'>ZeroDenominator</span> <span class='op'>=></span> <span class='string'>"zero value denominator"</span>,
}
}
}
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>test</span>)]</span>
<span class='kw'>fn</span> <span class='ident'>hash</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>hash</span>::<span class='ident'>Hash</span><span class='op'>></span>(<span class='ident'>x</span>: <span class='kw-2'>&</span><span class='ident'>T</span>) <span class='op'>-></span> <span class='ident'>u64</span> {
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>hash</span>::<span class='ident'>Hasher</span>;
<span class='kw'>let</span> <span class='kw-2'>mut</span> <span class='ident'>hasher</span> <span class='op'>=</span> <span class='ident'>hash</span>::<span class='ident'>SipHasher</span>::<span class='ident'>new</span>();
<span class='ident'>x</span>.<span class='ident'>hash</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='ident'>hasher</span>);
<span class='ident'>hasher</span>.<span class='ident'>finish</span>()
}
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>test</span>)]</span>
<span class='kw'>mod</span> <span class='ident'>test</span> {
<span class='kw'>use</span> <span class='kw'>super</span>::{<span class='ident'>Ratio</span>, <span class='ident'>Rational</span>};
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>feature</span> <span class='op'>=</span> <span class='string'>"num-bigint"</span>)]</span>
<span class='kw'>use</span> <span class='kw'>super</span>::<span class='ident'>BigRational</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>str</span>::<span class='ident'>FromStr</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>i32</span>;
<span class='kw'>use</span> <span class='ident'>traits</span>::{<span class='ident'>Zero</span>, <span class='ident'>One</span>, <span class='ident'>Signed</span>, <span class='ident'>FromPrimitive</span>, <span class='ident'>Float</span>};
<span class='kw'>pub</span> <span class='kw'>const</span> <span class='ident'>_0</span>: <span class='ident'>Rational</span> <span class='op'>=</span> <span class='ident'>Ratio</span> {
<span class='ident'>numer</span>: <span class='number'>0</span>,
<span class='ident'>denom</span>: <span class='number'>1</span>,
};
<span class='kw'>pub</span> <span class='kw'>const</span> <span class='ident'>_1</span>: <span class='ident'>Rational</span> <span class='op'>=</span> <span class='ident'>Ratio</span> {
<span class='ident'>numer</span>: <span class='number'>1</span>,
<span class='ident'>denom</span>: <span class='number'>1</span>,
};
<span class='kw'>pub</span> <span class='kw'>const</span> <span class='ident'>_2</span>: <span class='ident'>Rational</span> <span class='op'>=</span> <span class='ident'>Ratio</span> {
<span class='ident'>numer</span>: <span class='number'>2</span>,
<span class='ident'>denom</span>: <span class='number'>1</span>,
};
<span class='kw'>pub</span> <span class='kw'>const</span> <span class='ident'>_1_2</span>: <span class='ident'>Rational</span> <span class='op'>=</span> <span class='ident'>Ratio</span> {
<span class='ident'>numer</span>: <span class='number'>1</span>,
<span class='ident'>denom</span>: <span class='number'>2</span>,
};
<span class='kw'>pub</span> <span class='kw'>const</span> <span class='ident'>_3_2</span>: <span class='ident'>Rational</span> <span class='op'>=</span> <span class='ident'>Ratio</span> {
<span class='ident'>numer</span>: <span class='number'>3</span>,
<span class='ident'>denom</span>: <span class='number'>2</span>,
};
<span class='kw'>pub</span> <span class='kw'>const</span> <span class='ident'>_NEG1_2</span>: <span class='ident'>Rational</span> <span class='op'>=</span> <span class='ident'>Ratio</span> {
<span class='ident'>numer</span>: <span class='op'>-</span><span class='number'>1</span>,
<span class='ident'>denom</span>: <span class='number'>2</span>,
};
<span class='kw'>pub</span> <span class='kw'>const</span> <span class='ident'>_1_NEG2</span>: <span class='ident'>Rational</span> <span class='op'>=</span> <span class='ident'>Ratio</span> {
<span class='ident'>numer</span>: <span class='number'>1</span>,
<span class='ident'>denom</span>: <span class='op'>-</span><span class='number'>2</span>,
};
<span class='kw'>pub</span> <span class='kw'>const</span> <span class='ident'>_NEG1_NEG2</span>: <span class='ident'>Rational</span> <span class='op'>=</span> <span class='ident'>Ratio</span> {
<span class='ident'>numer</span>: <span class='op'>-</span><span class='number'>1</span>,
<span class='ident'>denom</span>: <span class='op'>-</span><span class='number'>2</span>,
};
<span class='kw'>pub</span> <span class='kw'>const</span> <span class='ident'>_1_3</span>: <span class='ident'>Rational</span> <span class='op'>=</span> <span class='ident'>Ratio</span> {
<span class='ident'>numer</span>: <span class='number'>1</span>,
<span class='ident'>denom</span>: <span class='number'>3</span>,
};
<span class='kw'>pub</span> <span class='kw'>const</span> <span class='ident'>_NEG1_3</span>: <span class='ident'>Rational</span> <span class='op'>=</span> <span class='ident'>Ratio</span> {
<span class='ident'>numer</span>: <span class='op'>-</span><span class='number'>1</span>,
<span class='ident'>denom</span>: <span class='number'>3</span>,
};
<span class='kw'>pub</span> <span class='kw'>const</span> <span class='ident'>_2_3</span>: <span class='ident'>Rational</span> <span class='op'>=</span> <span class='ident'>Ratio</span> {
<span class='ident'>numer</span>: <span class='number'>2</span>,
<span class='ident'>denom</span>: <span class='number'>3</span>,
};
<span class='kw'>pub</span> <span class='kw'>const</span> <span class='ident'>_NEG2_3</span>: <span class='ident'>Rational</span> <span class='op'>=</span> <span class='ident'>Ratio</span> {
<span class='ident'>numer</span>: <span class='op'>-</span><span class='number'>2</span>,
<span class='ident'>denom</span>: <span class='number'>3</span>,
};
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>feature</span> <span class='op'>=</span> <span class='string'>"num-bigint"</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>to_big</span>(<span class='ident'>n</span>: <span class='ident'>Rational</span>) <span class='op'>-></span> <span class='ident'>BigRational</span> {
<span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='ident'>FromPrimitive</span>::<span class='ident'>from_isize</span>(<span class='ident'>n</span>.<span class='ident'>numer</span>).<span class='ident'>unwrap</span>(),
<span class='ident'>FromPrimitive</span>::<span class='ident'>from_isize</span>(<span class='ident'>n</span>.<span class='ident'>denom</span>).<span class='ident'>unwrap</span>())
}
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>not</span>(<span class='ident'>feature</span> <span class='op'>=</span> <span class='string'>"num-bigint"</span>))]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>to_big</span>(<span class='ident'>n</span>: <span class='ident'>Rational</span>) <span class='op'>-></span> <span class='ident'>Rational</span> {
<span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='ident'>FromPrimitive</span>::<span class='ident'>from_isize</span>(<span class='ident'>n</span>.<span class='ident'>numer</span>).<span class='ident'>unwrap</span>(),
<span class='ident'>FromPrimitive</span>::<span class='ident'>from_isize</span>(<span class='ident'>n</span>.<span class='ident'>denom</span>).<span class='ident'>unwrap</span>())
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_test_constants</span>() {
<span class='comment'>// check our constants are what Ratio::new etc. would make.</span>
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_0</span>, <span class='ident'>Zero</span>::<span class='ident'>zero</span>());
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_1</span>, <span class='ident'>One</span>::<span class='ident'>one</span>());
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_2</span>, <span class='ident'>Ratio</span>::<span class='ident'>from_integer</span>(<span class='number'>2</span>));
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_1_2</span>, <span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='number'>1</span>, <span class='number'>2</span>));
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_3_2</span>, <span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='number'>3</span>, <span class='number'>2</span>));
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_NEG1_2</span>, <span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='op'>-</span><span class='number'>1</span>, <span class='number'>2</span>));
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_new_reduce</span>() {
<span class='kw'>let</span> <span class='ident'>one22</span> <span class='op'>=</span> <span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='number'>2</span>, <span class='number'>2</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>one22</span>, <span class='ident'>One</span>::<span class='ident'>one</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_new_zero</span>() {
<span class='kw'>let</span> <span class='ident'>_a</span> <span class='op'>=</span> <span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='number'>1</span>, <span class='number'>0</span>);
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_cmp</span>() {
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>_0</span> <span class='op'>==</span> <span class='ident'>_0</span> <span class='op'>&&</span> <span class='ident'>_1</span> <span class='op'>==</span> <span class='ident'>_1</span>);
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>_0</span> <span class='op'>!=</span> <span class='ident'>_1</span> <span class='op'>&&</span> <span class='ident'>_1</span> <span class='op'>!=</span> <span class='ident'>_0</span>);
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>_0</span> <span class='op'><</span> <span class='ident'>_1</span> <span class='op'>&&</span> <span class='op'>!</span>(<span class='ident'>_1</span> <span class='op'><</span> <span class='ident'>_0</span>));
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>_1</span> <span class='op'>></span> <span class='ident'>_0</span> <span class='op'>&&</span> <span class='op'>!</span>(<span class='ident'>_0</span> <span class='op'>></span> <span class='ident'>_1</span>));
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>_0</span> <span class='op'><=</span> <span class='ident'>_0</span> <span class='op'>&&</span> <span class='ident'>_1</span> <span class='op'><=</span> <span class='ident'>_1</span>);
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>_0</span> <span class='op'><=</span> <span class='ident'>_1</span> <span class='op'>&&</span> <span class='op'>!</span>(<span class='ident'>_1</span> <span class='op'><=</span> <span class='ident'>_0</span>));
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>_0</span> <span class='op'>>=</span> <span class='ident'>_0</span> <span class='op'>&&</span> <span class='ident'>_1</span> <span class='op'>>=</span> <span class='ident'>_1</span>);
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>_1</span> <span class='op'>>=</span> <span class='ident'>_0</span> <span class='op'>&&</span> <span class='op'>!</span>(<span class='ident'>_0</span> <span class='op'>>=</span> <span class='ident'>_1</span>));
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_cmp_overflow</span>() {
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>cmp</span>::<span class='ident'>Ordering</span>;
<span class='comment'>// issue #7 example:</span>
<span class='kw'>let</span> <span class='ident'>big</span> <span class='op'>=</span> <span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='number'>128u8</span>, <span class='number'>1</span>);
<span class='kw'>let</span> <span class='ident'>small</span> <span class='op'>=</span> <span class='ident'>big</span>.<span class='ident'>recip</span>();
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>big</span> <span class='op'>></span> <span class='ident'>small</span>);
<span class='comment'>// try a few that are closer together</span>
<span class='comment'>// (some matching numer, some matching denom, some neither)</span>
<span class='kw'>let</span> <span class='ident'>ratios</span> <span class='op'>=</span> <span class='macro'>vec</span><span class='macro'>!</span>[
<span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='number'>125_i8</span>, <span class='number'>127_i8</span>),
<span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='number'>63_i8</span>, <span class='number'>64_i8</span>),
<span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='number'>124_i8</span>, <span class='number'>125_i8</span>),
<span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='number'>125_i8</span>, <span class='number'>126_i8</span>),
<span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='number'>126_i8</span>, <span class='number'>127_i8</span>),
<span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='number'>127_i8</span>, <span class='number'>126_i8</span>),
];
<span class='kw'>fn</span> <span class='ident'>check_cmp</span>(<span class='ident'>a</span>: <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>i8</span><span class='op'>></span>, <span class='ident'>b</span>: <span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>i8</span><span class='op'>></span>, <span class='ident'>ord</span>: <span class='ident'>Ordering</span>) {
<span class='macro'>println</span><span class='macro'>!</span>(<span class='string'>"comparing {} and {}"</span>, <span class='ident'>a</span>, <span class='ident'>b</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>a</span>.<span class='ident'>cmp</span>(<span class='kw-2'>&</span><span class='ident'>b</span>), <span class='ident'>ord</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>b</span>.<span class='ident'>cmp</span>(<span class='kw-2'>&</span><span class='ident'>a</span>), <span class='ident'>ord</span>.<span class='ident'>reverse</span>());
}
<span class='kw'>for</span> (<span class='ident'>i</span>, <span class='kw-2'>&</span><span class='ident'>a</span>) <span class='kw'>in</span> <span class='ident'>ratios</span>.<span class='ident'>iter</span>().<span class='ident'>enumerate</span>() {
<span class='ident'>check_cmp</span>(<span class='ident'>a</span>, <span class='ident'>a</span>, <span class='ident'>Ordering</span>::<span class='ident'>Equal</span>);
<span class='ident'>check_cmp</span>(<span class='op'>-</span><span class='ident'>a</span>, <span class='ident'>a</span>, <span class='ident'>Ordering</span>::<span class='ident'>Less</span>);
<span class='kw'>for</span> <span class='kw-2'>&</span><span class='ident'>b</span> <span class='kw'>in</span> <span class='kw-2'>&</span><span class='ident'>ratios</span>[<span class='ident'>i</span> <span class='op'>+</span> <span class='number'>1</span>..] {
<span class='ident'>check_cmp</span>(<span class='ident'>a</span>, <span class='ident'>b</span>, <span class='ident'>Ordering</span>::<span class='ident'>Less</span>);
<span class='ident'>check_cmp</span>(<span class='op'>-</span><span class='ident'>a</span>, <span class='op'>-</span><span class='ident'>b</span>, <span class='ident'>Ordering</span>::<span class='ident'>Greater</span>);
<span class='ident'>check_cmp</span>(<span class='ident'>a</span>.<span class='ident'>recip</span>(), <span class='ident'>b</span>.<span class='ident'>recip</span>(), <span class='ident'>Ordering</span>::<span class='ident'>Greater</span>);
<span class='ident'>check_cmp</span>(<span class='op'>-</span><span class='ident'>a</span>.<span class='ident'>recip</span>(), <span class='op'>-</span><span class='ident'>b</span>.<span class='ident'>recip</span>(), <span class='ident'>Ordering</span>::<span class='ident'>Less</span>);
}
}
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_to_integer</span>() {
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_0</span>.<span class='ident'>to_integer</span>(), <span class='number'>0</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_1</span>.<span class='ident'>to_integer</span>(), <span class='number'>1</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_2</span>.<span class='ident'>to_integer</span>(), <span class='number'>2</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_1_2</span>.<span class='ident'>to_integer</span>(), <span class='number'>0</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_3_2</span>.<span class='ident'>to_integer</span>(), <span class='number'>1</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_NEG1_2</span>.<span class='ident'>to_integer</span>(), <span class='number'>0</span>);
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_numer</span>() {
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_0</span>.<span class='ident'>numer</span>(), <span class='kw-2'>&</span><span class='number'>0</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_1</span>.<span class='ident'>numer</span>(), <span class='kw-2'>&</span><span class='number'>1</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_2</span>.<span class='ident'>numer</span>(), <span class='kw-2'>&</span><span class='number'>2</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_1_2</span>.<span class='ident'>numer</span>(), <span class='kw-2'>&</span><span class='number'>1</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_3_2</span>.<span class='ident'>numer</span>(), <span class='kw-2'>&</span><span class='number'>3</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_NEG1_2</span>.<span class='ident'>numer</span>(), <span class='kw-2'>&</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_denom</span>() {
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_0</span>.<span class='ident'>denom</span>(), <span class='kw-2'>&</span><span class='number'>1</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_1</span>.<span class='ident'>denom</span>(), <span class='kw-2'>&</span><span class='number'>1</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_2</span>.<span class='ident'>denom</span>(), <span class='kw-2'>&</span><span class='number'>1</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_1_2</span>.<span class='ident'>denom</span>(), <span class='kw-2'>&</span><span class='number'>2</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_3_2</span>.<span class='ident'>denom</span>(), <span class='kw-2'>&</span><span class='number'>2</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_NEG1_2</span>.<span class='ident'>denom</span>(), <span class='kw-2'>&</span><span class='number'>2</span>);
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_is_integer</span>() {
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>_0</span>.<span class='ident'>is_integer</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>_1</span>.<span class='ident'>is_integer</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>_2</span>.<span class='ident'>is_integer</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='op'>!</span><span class='ident'>_1_2</span>.<span class='ident'>is_integer</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='op'>!</span><span class='ident'>_3_2</span>.<span class='ident'>is_integer</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='op'>!</span><span class='ident'>_NEG1_2</span>.<span class='ident'>is_integer</span>());
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_show</span>() {
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='macro'>format</span><span class='macro'>!</span>(<span class='string'>"{}"</span>, <span class='ident'>_2</span>), <span class='string'>"2"</span>.<span class='ident'>to_string</span>());
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='macro'>format</span><span class='macro'>!</span>(<span class='string'>"{}"</span>, <span class='ident'>_1_2</span>), <span class='string'>"1/2"</span>.<span class='ident'>to_string</span>());
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='macro'>format</span><span class='macro'>!</span>(<span class='string'>"{}"</span>, <span class='ident'>_0</span>), <span class='string'>"0"</span>.<span class='ident'>to_string</span>());
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='macro'>format</span><span class='macro'>!</span>(<span class='string'>"{}"</span>, <span class='ident'>Ratio</span>::<span class='ident'>from_integer</span>(<span class='op'>-</span><span class='number'>2</span>)), <span class='string'>"-2"</span>.<span class='ident'>to_string</span>());
}
<span class='kw'>mod</span> <span class='ident'>arith</span> {
<span class='kw'>use</span> <span class='kw'>super</span>::{<span class='ident'>_0</span>, <span class='ident'>_1</span>, <span class='ident'>_2</span>, <span class='ident'>_1_2</span>, <span class='ident'>_3_2</span>, <span class='ident'>_NEG1_2</span>, <span class='ident'>to_big</span>};
<span class='kw'>use</span> <span class='kw'>super</span>::<span class='kw'>super</span>::{<span class='ident'>Ratio</span>, <span class='ident'>Rational</span>};
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_add</span>() {
<span class='kw'>fn</span> <span class='ident'>test</span>(<span class='ident'>a</span>: <span class='ident'>Rational</span>, <span class='ident'>b</span>: <span class='ident'>Rational</span>, <span class='ident'>c</span>: <span class='ident'>Rational</span>) {
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>a</span> <span class='op'>+</span> <span class='ident'>b</span>, <span class='ident'>c</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>to_big</span>(<span class='ident'>a</span>) <span class='op'>+</span> <span class='ident'>to_big</span>(<span class='ident'>b</span>), <span class='ident'>to_big</span>(<span class='ident'>c</span>));
}
<span class='ident'>test</span>(<span class='ident'>_1</span>, <span class='ident'>_1_2</span>, <span class='ident'>_3_2</span>);
<span class='ident'>test</span>(<span class='ident'>_1</span>, <span class='ident'>_1</span>, <span class='ident'>_2</span>);
<span class='ident'>test</span>(<span class='ident'>_1_2</span>, <span class='ident'>_3_2</span>, <span class='ident'>_2</span>);
<span class='ident'>test</span>(<span class='ident'>_1_2</span>, <span class='ident'>_NEG1_2</span>, <span class='ident'>_0</span>);
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_sub</span>() {
<span class='kw'>fn</span> <span class='ident'>test</span>(<span class='ident'>a</span>: <span class='ident'>Rational</span>, <span class='ident'>b</span>: <span class='ident'>Rational</span>, <span class='ident'>c</span>: <span class='ident'>Rational</span>) {
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>a</span> <span class='op'>-</span> <span class='ident'>b</span>, <span class='ident'>c</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>to_big</span>(<span class='ident'>a</span>) <span class='op'>-</span> <span class='ident'>to_big</span>(<span class='ident'>b</span>), <span class='ident'>to_big</span>(<span class='ident'>c</span>))
}
<span class='ident'>test</span>(<span class='ident'>_1</span>, <span class='ident'>_1_2</span>, <span class='ident'>_1_2</span>);
<span class='ident'>test</span>(<span class='ident'>_3_2</span>, <span class='ident'>_1_2</span>, <span class='ident'>_1</span>);
<span class='ident'>test</span>(<span class='ident'>_1</span>, <span class='ident'>_NEG1_2</span>, <span class='ident'>_3_2</span>);
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_mul</span>() {
<span class='kw'>fn</span> <span class='ident'>test</span>(<span class='ident'>a</span>: <span class='ident'>Rational</span>, <span class='ident'>b</span>: <span class='ident'>Rational</span>, <span class='ident'>c</span>: <span class='ident'>Rational</span>) {
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>a</span> <span class='op'>*</span> <span class='ident'>b</span>, <span class='ident'>c</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>to_big</span>(<span class='ident'>a</span>) <span class='op'>*</span> <span class='ident'>to_big</span>(<span class='ident'>b</span>), <span class='ident'>to_big</span>(<span class='ident'>c</span>))
}
<span class='ident'>test</span>(<span class='ident'>_1</span>, <span class='ident'>_1_2</span>, <span class='ident'>_1_2</span>);
<span class='ident'>test</span>(<span class='ident'>_1_2</span>, <span class='ident'>_3_2</span>, <span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='number'>3</span>, <span class='number'>4</span>));
<span class='ident'>test</span>(<span class='ident'>_1_2</span>, <span class='ident'>_NEG1_2</span>, <span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='op'>-</span><span class='number'>1</span>, <span class='number'>4</span>));
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_div</span>() {
<span class='kw'>fn</span> <span class='ident'>test</span>(<span class='ident'>a</span>: <span class='ident'>Rational</span>, <span class='ident'>b</span>: <span class='ident'>Rational</span>, <span class='ident'>c</span>: <span class='ident'>Rational</span>) {
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>a</span> <span class='op'>/</span> <span class='ident'>b</span>, <span class='ident'>c</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>to_big</span>(<span class='ident'>a</span>) <span class='op'>/</span> <span class='ident'>to_big</span>(<span class='ident'>b</span>), <span class='ident'>to_big</span>(<span class='ident'>c</span>))
}
<span class='ident'>test</span>(<span class='ident'>_1</span>, <span class='ident'>_1_2</span>, <span class='ident'>_2</span>);
<span class='ident'>test</span>(<span class='ident'>_3_2</span>, <span class='ident'>_1_2</span>, <span class='ident'>_1</span> <span class='op'>+</span> <span class='ident'>_2</span>);
<span class='ident'>test</span>(<span class='ident'>_1</span>, <span class='ident'>_NEG1_2</span>, <span class='ident'>_NEG1_2</span> <span class='op'>+</span> <span class='ident'>_NEG1_2</span> <span class='op'>+</span> <span class='ident'>_NEG1_2</span> <span class='op'>+</span> <span class='ident'>_NEG1_2</span>);
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_rem</span>() {
<span class='kw'>fn</span> <span class='ident'>test</span>(<span class='ident'>a</span>: <span class='ident'>Rational</span>, <span class='ident'>b</span>: <span class='ident'>Rational</span>, <span class='ident'>c</span>: <span class='ident'>Rational</span>) {
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>a</span> <span class='op'>%</span> <span class='ident'>b</span>, <span class='ident'>c</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>to_big</span>(<span class='ident'>a</span>) <span class='op'>%</span> <span class='ident'>to_big</span>(<span class='ident'>b</span>), <span class='ident'>to_big</span>(<span class='ident'>c</span>))
}
<span class='ident'>test</span>(<span class='ident'>_3_2</span>, <span class='ident'>_1</span>, <span class='ident'>_1_2</span>);
<span class='ident'>test</span>(<span class='ident'>_2</span>, <span class='ident'>_NEG1_2</span>, <span class='ident'>_0</span>);
<span class='ident'>test</span>(<span class='ident'>_1_2</span>, <span class='ident'>_2</span>, <span class='ident'>_1_2</span>);
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_neg</span>() {
<span class='kw'>fn</span> <span class='ident'>test</span>(<span class='ident'>a</span>: <span class='ident'>Rational</span>, <span class='ident'>b</span>: <span class='ident'>Rational</span>) {
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='op'>-</span><span class='ident'>a</span>, <span class='ident'>b</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='op'>-</span><span class='ident'>to_big</span>(<span class='ident'>a</span>), <span class='ident'>to_big</span>(<span class='ident'>b</span>))
}
<span class='ident'>test</span>(<span class='ident'>_0</span>, <span class='ident'>_0</span>);
<span class='ident'>test</span>(<span class='ident'>_1_2</span>, <span class='ident'>_NEG1_2</span>);
<span class='ident'>test</span>(<span class='op'>-</span><span class='ident'>_1</span>, <span class='ident'>_1</span>);
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_zero</span>() {
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_0</span> <span class='op'>+</span> <span class='ident'>_0</span>, <span class='ident'>_0</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_0</span> <span class='op'>*</span> <span class='ident'>_0</span>, <span class='ident'>_0</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_0</span> <span class='op'>*</span> <span class='ident'>_1</span>, <span class='ident'>_0</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_0</span> <span class='op'>/</span> <span class='ident'>_NEG1_2</span>, <span class='ident'>_0</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_0</span> <span class='op'>-</span> <span class='ident'>_0</span>, <span class='ident'>_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_div_0</span>() {
<span class='kw'>let</span> <span class='ident'>_a</span> <span class='op'>=</span> <span class='ident'>_1</span> <span class='op'>/</span> <span class='ident'>_0</span>;
}
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_round</span>() {
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_1_3</span>.<span class='ident'>ceil</span>(), <span class='ident'>_1</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_1_3</span>.<span class='ident'>floor</span>(), <span class='ident'>_0</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_1_3</span>.<span class='ident'>round</span>(), <span class='ident'>_0</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_1_3</span>.<span class='ident'>trunc</span>(), <span class='ident'>_0</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_NEG1_3</span>.<span class='ident'>ceil</span>(), <span class='ident'>_0</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_NEG1_3</span>.<span class='ident'>floor</span>(), <span class='op'>-</span><span class='ident'>_1</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_NEG1_3</span>.<span class='ident'>round</span>(), <span class='ident'>_0</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_NEG1_3</span>.<span class='ident'>trunc</span>(), <span class='ident'>_0</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_2_3</span>.<span class='ident'>ceil</span>(), <span class='ident'>_1</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_2_3</span>.<span class='ident'>floor</span>(), <span class='ident'>_0</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_2_3</span>.<span class='ident'>round</span>(), <span class='ident'>_1</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_2_3</span>.<span class='ident'>trunc</span>(), <span class='ident'>_0</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_NEG2_3</span>.<span class='ident'>ceil</span>(), <span class='ident'>_0</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_NEG2_3</span>.<span class='ident'>floor</span>(), <span class='op'>-</span><span class='ident'>_1</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_NEG2_3</span>.<span class='ident'>round</span>(), <span class='op'>-</span><span class='ident'>_1</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_NEG2_3</span>.<span class='ident'>trunc</span>(), <span class='ident'>_0</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_1_2</span>.<span class='ident'>ceil</span>(), <span class='ident'>_1</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_1_2</span>.<span class='ident'>floor</span>(), <span class='ident'>_0</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_1_2</span>.<span class='ident'>round</span>(), <span class='ident'>_1</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_1_2</span>.<span class='ident'>trunc</span>(), <span class='ident'>_0</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_NEG1_2</span>.<span class='ident'>ceil</span>(), <span class='ident'>_0</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_NEG1_2</span>.<span class='ident'>floor</span>(), <span class='op'>-</span><span class='ident'>_1</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_NEG1_2</span>.<span class='ident'>round</span>(), <span class='op'>-</span><span class='ident'>_1</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_NEG1_2</span>.<span class='ident'>trunc</span>(), <span class='ident'>_0</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_1</span>.<span class='ident'>ceil</span>(), <span class='ident'>_1</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_1</span>.<span class='ident'>floor</span>(), <span class='ident'>_1</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_1</span>.<span class='ident'>round</span>(), <span class='ident'>_1</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_1</span>.<span class='ident'>trunc</span>(), <span class='ident'>_1</span>);
<span class='comment'>// Overflow checks</span>
<span class='kw'>let</span> <span class='ident'>_neg1</span> <span class='op'>=</span> <span class='ident'>Ratio</span>::<span class='ident'>from_integer</span>(<span class='op'>-</span><span class='number'>1</span>);
<span class='kw'>let</span> <span class='ident'>_large_rat1</span> <span class='op'>=</span> <span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='ident'>i32</span>::<span class='ident'>MAX</span>, <span class='ident'>i32</span>::<span class='ident'>MAX</span> <span class='op'>-</span> <span class='number'>1</span>);
<span class='kw'>let</span> <span class='ident'>_large_rat2</span> <span class='op'>=</span> <span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='ident'>i32</span>::<span class='ident'>MAX</span> <span class='op'>-</span> <span class='number'>1</span>, <span class='ident'>i32</span>::<span class='ident'>MAX</span>);
<span class='kw'>let</span> <span class='ident'>_large_rat3</span> <span class='op'>=</span> <span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='ident'>i32</span>::<span class='ident'>MIN</span> <span class='op'>+</span> <span class='number'>2</span>, <span class='ident'>i32</span>::<span class='ident'>MIN</span> <span class='op'>+</span> <span class='number'>1</span>);
<span class='kw'>let</span> <span class='ident'>_large_rat4</span> <span class='op'>=</span> <span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='ident'>i32</span>::<span class='ident'>MIN</span> <span class='op'>+</span> <span class='number'>1</span>, <span class='ident'>i32</span>::<span class='ident'>MIN</span> <span class='op'>+</span> <span class='number'>2</span>);
<span class='kw'>let</span> <span class='ident'>_large_rat5</span> <span class='op'>=</span> <span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='ident'>i32</span>::<span class='ident'>MIN</span> <span class='op'>+</span> <span class='number'>2</span>, <span class='ident'>i32</span>::<span class='ident'>MAX</span>);
<span class='kw'>let</span> <span class='ident'>_large_rat6</span> <span class='op'>=</span> <span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='ident'>i32</span>::<span class='ident'>MAX</span>, <span class='ident'>i32</span>::<span class='ident'>MIN</span> <span class='op'>+</span> <span class='number'>2</span>);
<span class='kw'>let</span> <span class='ident'>_large_rat7</span> <span class='op'>=</span> <span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='number'>1</span>, <span class='ident'>i32</span>::<span class='ident'>MIN</span> <span class='op'>+</span> <span class='number'>1</span>);
<span class='kw'>let</span> <span class='ident'>_large_rat8</span> <span class='op'>=</span> <span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='number'>1</span>, <span class='ident'>i32</span>::<span class='ident'>MAX</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_large_rat1</span>.<span class='ident'>round</span>(), <span class='ident'>One</span>::<span class='ident'>one</span>());
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_large_rat2</span>.<span class='ident'>round</span>(), <span class='ident'>One</span>::<span class='ident'>one</span>());
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_large_rat3</span>.<span class='ident'>round</span>(), <span class='ident'>One</span>::<span class='ident'>one</span>());
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_large_rat4</span>.<span class='ident'>round</span>(), <span class='ident'>One</span>::<span class='ident'>one</span>());
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_large_rat5</span>.<span class='ident'>round</span>(), <span class='ident'>_neg1</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_large_rat6</span>.<span class='ident'>round</span>(), <span class='ident'>_neg1</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_large_rat7</span>.<span class='ident'>round</span>(), <span class='ident'>Zero</span>::<span class='ident'>zero</span>());
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_large_rat8</span>.<span class='ident'>round</span>(), <span class='ident'>Zero</span>::<span class='ident'>zero</span>());
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_fract</span>() {
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_1</span>.<span class='ident'>fract</span>(), <span class='ident'>_0</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_NEG1_2</span>.<span class='ident'>fract</span>(), <span class='ident'>_NEG1_2</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_1_2</span>.<span class='ident'>fract</span>(), <span class='ident'>_1_2</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_3_2</span>.<span class='ident'>fract</span>(), <span class='ident'>_1_2</span>);
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_recip</span>() {
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_1</span> <span class='op'>*</span> <span class='ident'>_1</span>.<span class='ident'>recip</span>(), <span class='ident'>_1</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_2</span> <span class='op'>*</span> <span class='ident'>_2</span>.<span class='ident'>recip</span>(), <span class='ident'>_1</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_1_2</span> <span class='op'>*</span> <span class='ident'>_1_2</span>.<span class='ident'>recip</span>(), <span class='ident'>_1</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_3_2</span> <span class='op'>*</span> <span class='ident'>_3_2</span>.<span class='ident'>recip</span>(), <span class='ident'>_1</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_NEG1_2</span> <span class='op'>*</span> <span class='ident'>_NEG1_2</span>.<span class='ident'>recip</span>(), <span class='ident'>_1</span>);
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_pow</span>() {
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_1_2</span>.<span class='ident'>pow</span>(<span class='number'>2</span>), <span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='number'>1</span>, <span class='number'>4</span>));
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_1_2</span>.<span class='ident'>pow</span>(<span class='op'>-</span><span class='number'>2</span>), <span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='number'>4</span>, <span class='number'>1</span>));
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_1</span>.<span class='ident'>pow</span>(<span class='number'>1</span>), <span class='ident'>_1</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_NEG1_2</span>.<span class='ident'>pow</span>(<span class='number'>2</span>), <span class='ident'>_1_2</span>.<span class='ident'>pow</span>(<span class='number'>2</span>));
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_NEG1_2</span>.<span class='ident'>pow</span>(<span class='number'>3</span>), <span class='op'>-</span><span class='ident'>_1_2</span>.<span class='ident'>pow</span>(<span class='number'>3</span>));
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_3_2</span>.<span class='ident'>pow</span>(<span class='number'>0</span>), <span class='ident'>_1</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_3_2</span>.<span class='ident'>pow</span>(<span class='op'>-</span><span class='number'>1</span>), <span class='ident'>_3_2</span>.<span class='ident'>recip</span>());
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_3_2</span>.<span class='ident'>pow</span>(<span class='number'>3</span>), <span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='number'>27</span>, <span class='number'>8</span>));
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_to_from_str</span>() {
<span class='kw'>fn</span> <span class='ident'>test</span>(<span class='ident'>r</span>: <span class='ident'>Rational</span>, <span class='ident'>s</span>: <span class='ident'>String</span>) {
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>FromStr</span>::<span class='ident'>from_str</span>(<span class='kw-2'>&</span><span class='ident'>s</span>), <span class='prelude-val'>Ok</span>(<span class='ident'>r</span>));
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>r</span>.<span class='ident'>to_string</span>(), <span class='ident'>s</span>);
}
<span class='ident'>test</span>(<span class='ident'>_1</span>, <span class='string'>"1"</span>.<span class='ident'>to_string</span>());
<span class='ident'>test</span>(<span class='ident'>_0</span>, <span class='string'>"0"</span>.<span class='ident'>to_string</span>());
<span class='ident'>test</span>(<span class='ident'>_1_2</span>, <span class='string'>"1/2"</span>.<span class='ident'>to_string</span>());
<span class='ident'>test</span>(<span class='ident'>_3_2</span>, <span class='string'>"3/2"</span>.<span class='ident'>to_string</span>());
<span class='ident'>test</span>(<span class='ident'>_2</span>, <span class='string'>"2"</span>.<span class='ident'>to_string</span>());
<span class='ident'>test</span>(<span class='ident'>_NEG1_2</span>, <span class='string'>"-1/2"</span>.<span class='ident'>to_string</span>());
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_from_str_fail</span>() {
<span class='kw'>fn</span> <span class='ident'>test</span>(<span class='ident'>s</span>: <span class='kw-2'>&</span><span class='ident'>str</span>) {
<span class='kw'>let</span> <span class='ident'>rational</span>: <span class='prelude-ty'>Result</span><span class='op'><</span><span class='ident'>Rational</span>, _<span class='op'>></span> <span class='op'>=</span> <span class='ident'>FromStr</span>::<span class='ident'>from_str</span>(<span class='ident'>s</span>);
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>rational</span>.<span class='ident'>is_err</span>());
}
<span class='kw'>let</span> <span class='ident'>xs</span> <span class='op'>=</span> [<span class='string'>"0 /1"</span>, <span class='string'>"abc"</span>, <span class='string'>""</span>, <span class='string'>"1/"</span>, <span class='string'>"--1/2"</span>, <span class='string'>"3/2/1"</span>, <span class='string'>"1/0"</span>];
<span class='kw'>for</span> <span class='kw-2'>&</span><span class='ident'>s</span> <span class='kw'>in</span> <span class='ident'>xs</span>.<span class='ident'>iter</span>() {
<span class='ident'>test</span>(<span class='ident'>s</span>);
}
}
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>feature</span> <span class='op'>=</span> <span class='string'>"num-bigint"</span>)]</span>
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_from_float</span>() {
<span class='kw'>fn</span> <span class='ident'>test</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>Float</span><span class='op'>></span>(<span class='ident'>given</span>: <span class='ident'>T</span>, (<span class='ident'>numer</span>, <span class='ident'>denom</span>): (<span class='kw-2'>&</span><span class='ident'>str</span>, <span class='kw-2'>&</span><span class='ident'>str</span>)) {
<span class='kw'>let</span> <span class='ident'>ratio</span>: <span class='ident'>BigRational</span> <span class='op'>=</span> <span class='ident'>Ratio</span>::<span class='ident'>from_float</span>(<span class='ident'>given</span>).<span class='ident'>unwrap</span>();
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>ratio</span>,
<span class='ident'>Ratio</span>::<span class='ident'>new</span>(<span class='ident'>FromStr</span>::<span class='ident'>from_str</span>(<span class='ident'>numer</span>).<span class='ident'>unwrap</span>(),
<span class='ident'>FromStr</span>::<span class='ident'>from_str</span>(<span class='ident'>denom</span>).<span class='ident'>unwrap</span>()));
}
<span class='comment'>// f32</span>
<span class='ident'>test</span>(<span class='number'>3.14159265359f32</span>, (<span class='string'>"13176795"</span>, <span class='string'>"4194304"</span>));
<span class='ident'>test</span>(<span class='number'>2f32</span>.<span class='ident'>powf</span>(<span class='number'>100.</span>), (<span class='string'>"1267650600228229401496703205376"</span>, <span class='string'>"1"</span>));
<span class='ident'>test</span>(<span class='op'>-</span><span class='number'>2f32</span>.<span class='ident'>powf</span>(<span class='number'>100.</span>), (<span class='string'>"-1267650600228229401496703205376"</span>, <span class='string'>"1"</span>));
<span class='ident'>test</span>(<span class='number'>1.0</span> <span class='op'>/</span> <span class='number'>2f32</span>.<span class='ident'>powf</span>(<span class='number'>100.</span>),
(<span class='string'>"1"</span>, <span class='string'>"1267650600228229401496703205376"</span>));
<span class='ident'>test</span>(<span class='number'>684729.48391f32</span>, (<span class='string'>"1369459"</span>, <span class='string'>"2"</span>));
<span class='ident'>test</span>(<span class='op'>-</span><span class='number'>8573.5918555f32</span>, (<span class='string'>"-4389679"</span>, <span class='string'>"512"</span>));
<span class='comment'>// f64</span>
<span class='ident'>test</span>(<span class='number'>3.14159265359f64</span>, (<span class='string'>"3537118876014453"</span>, <span class='string'>"1125899906842624"</span>));
<span class='ident'>test</span>(<span class='number'>2f64</span>.<span class='ident'>powf</span>(<span class='number'>100.</span>), (<span class='string'>"1267650600228229401496703205376"</span>, <span class='string'>"1"</span>));
<span class='ident'>test</span>(<span class='op'>-</span><span class='number'>2f64</span>.<span class='ident'>powf</span>(<span class='number'>100.</span>), (<span class='string'>"-1267650600228229401496703205376"</span>, <span class='string'>"1"</span>));
<span class='ident'>test</span>(<span class='number'>684729.48391f64</span>, (<span class='string'>"367611342500051"</span>, <span class='string'>"536870912"</span>));
<span class='ident'>test</span>(<span class='op'>-</span><span class='number'>8573.5918555f64</span>, (<span class='string'>"-4713381968463931"</span>, <span class='string'>"549755813888"</span>));
<span class='ident'>test</span>(<span class='number'>1.0</span> <span class='op'>/</span> <span class='number'>2f64</span>.<span class='ident'>powf</span>(<span class='number'>100.</span>),
(<span class='string'>"1"</span>, <span class='string'>"1267650600228229401496703205376"</span>));
}
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>feature</span> <span class='op'>=</span> <span class='string'>"num-bigint"</span>)]</span>
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_from_float_fail</span>() {
<span class='kw'>use</span> <span class='ident'>std</span>::{<span class='ident'>f32</span>, <span class='ident'>f64</span>};
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>Ratio</span>::<span class='ident'>from_float</span>(<span class='ident'>f32</span>::<span class='ident'>NAN</span>), <span class='prelude-val'>None</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>Ratio</span>::<span class='ident'>from_float</span>(<span class='ident'>f32</span>::<span class='ident'>INFINITY</span>), <span class='prelude-val'>None</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>Ratio</span>::<span class='ident'>from_float</span>(<span class='ident'>f32</span>::<span class='ident'>NEG_INFINITY</span>), <span class='prelude-val'>None</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>Ratio</span>::<span class='ident'>from_float</span>(<span class='ident'>f64</span>::<span class='ident'>NAN</span>), <span class='prelude-val'>None</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>Ratio</span>::<span class='ident'>from_float</span>(<span class='ident'>f64</span>::<span class='ident'>INFINITY</span>), <span class='prelude-val'>None</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>Ratio</span>::<span class='ident'>from_float</span>(<span class='ident'>f64</span>::<span class='ident'>NEG_INFINITY</span>), <span class='prelude-val'>None</span>);
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_signed</span>() {
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_NEG1_2</span>.<span class='ident'>abs</span>(), <span class='ident'>_1_2</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_3_2</span>.<span class='ident'>abs_sub</span>(<span class='kw-2'>&</span><span class='ident'>_1_2</span>), <span class='ident'>_1</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_1_2</span>.<span class='ident'>abs_sub</span>(<span class='kw-2'>&</span><span class='ident'>_3_2</span>), <span class='ident'>Zero</span>::<span class='ident'>zero</span>());
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_1_2</span>.<span class='ident'>signum</span>(), <span class='ident'>One</span>::<span class='ident'>one</span>());
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_NEG1_2</span>.<span class='ident'>signum</span>(), <span class='op'>-</span><span class='op'><</span><span class='ident'>Ratio</span><span class='op'><</span><span class='ident'>isize</span><span class='op'>>></span>::<span class='ident'>one</span>());
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>_0</span>.<span class='ident'>signum</span>(), <span class='ident'>Zero</span>::<span class='ident'>zero</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>_NEG1_2</span>.<span class='ident'>is_negative</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>_1_NEG2</span>.<span class='ident'>is_negative</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='op'>!</span><span class='ident'>_NEG1_2</span>.<span class='ident'>is_positive</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='op'>!</span><span class='ident'>_1_NEG2</span>.<span class='ident'>is_positive</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>_1_2</span>.<span class='ident'>is_positive</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>_NEG1_NEG2</span>.<span class='ident'>is_positive</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='op'>!</span><span class='ident'>_1_2</span>.<span class='ident'>is_negative</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='op'>!</span><span class='ident'>_NEG1_NEG2</span>.<span class='ident'>is_negative</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='op'>!</span><span class='ident'>_0</span>.<span class='ident'>is_positive</span>());
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='op'>!</span><span class='ident'>_0</span>.<span class='ident'>is_negative</span>());
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_hash</span>() {
<span class='macro'>assert</span><span class='macro'>!</span>(::<span class='ident'>hash</span>(<span class='kw-2'>&</span><span class='ident'>_0</span>) <span class='op'>!=</span> ::<span class='ident'>hash</span>(<span class='kw-2'>&</span><span class='ident'>_1</span>));
<span class='macro'>assert</span><span class='macro'>!</span>(::<span class='ident'>hash</span>(<span class='kw-2'>&</span><span class='ident'>_0</span>) <span class='op'>!=</span> ::<span class='ident'>hash</span>(<span class='kw-2'>&</span><span class='ident'>_3_2</span>));
}
}
</pre>
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