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</pre><pre class='rust '>
<span class='comment'>// Copyright 2014-2016 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'>//! A collection of numeric types and traits for Rust.</span>
<span class='doccomment'>//!</span>
<span class='doccomment'>//! This includes new types for big integers, rationals, and complex numbers,</span>
<span class='doccomment'>//! new traits for generic programming on numeric properties like `Integer`,</span>
<span class='doccomment'>//! and generic range iterators.</span>
<span class='doccomment'>//!</span>
<span class='doccomment'>//! ## Example</span>
<span class='doccomment'>//!</span>
<span class='doccomment'>//! This example uses the BigRational type and [Newton's method][newt] to</span>
<span class='doccomment'>//! approximate a square root to arbitrary precision:</span>
<span class='doccomment'>//!</span>
<span class='doccomment'>//! ```</span>
<span class='doccomment'>//! extern crate num;</span>
<span class='doccomment'>//! # #[cfg(all(feature = "bigint", feature="rational"))]</span>
<span class='doccomment'>//! # mod test {</span>
<span class='doccomment'>//!</span>
<span class='doccomment'>//! use num::FromPrimitive;</span>
<span class='doccomment'>//! use num::bigint::BigInt;</span>
<span class='doccomment'>//! use num::rational::{Ratio, BigRational};</span>
<span class='doccomment'>//!</span>
<span class='doccomment'>//! # pub</span>
<span class='doccomment'>//! fn approx_sqrt(number: u64, iterations: usize) -> BigRational {</span>
<span class='doccomment'>//! let start: Ratio<BigInt> = Ratio::from_integer(FromPrimitive::from_u64(number).unwrap());</span>
<span class='doccomment'>//! let mut approx = start.clone();</span>
<span class='doccomment'>//!</span>
<span class='doccomment'>//! for _ in 0..iterations {</span>
<span class='doccomment'>//! approx = (&approx + (&start / &approx)) /</span>
<span class='doccomment'>//! Ratio::from_integer(FromPrimitive::from_u64(2).unwrap());</span>
<span class='doccomment'>//! }</span>
<span class='doccomment'>//!</span>
<span class='doccomment'>//! approx</span>
<span class='doccomment'>//! }</span>
<span class='doccomment'>//! # }</span>
<span class='doccomment'>//! # #[cfg(not(all(feature = "bigint", feature="rational")))]</span>
<span class='doccomment'>//! # mod test { pub fn approx_sqrt(n: u64, _: usize) -> u64 { n } }</span>
<span class='doccomment'>//! # use test::approx_sqrt;</span>
<span class='doccomment'>//!</span>
<span class='doccomment'>//! fn main() {</span>
<span class='doccomment'>//! println!("{}", approx_sqrt(10, 4)); // prints 4057691201/1283082416</span>
<span class='doccomment'>//! }</span>
<span class='doccomment'>//!</span>
<span class='doccomment'>//! ```</span>
<span class='doccomment'>//!</span>
<span class='doccomment'>//! [newt]: https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method</span>
<span class='attribute'>#<span class='op'>!</span>[<span class='ident'>doc</span>(<span class='ident'>html_logo_url</span> <span class='op'>=</span> <span class='string'>"http://rust-num.github.io/num/rust-logo-128x128-blk-v2.png"</span>,
<span class='ident'>html_favicon_url</span> <span class='op'>=</span> <span class='string'>"http://rust-num.github.io/num/favicon.ico"</span>,
<span class='ident'>html_root_url</span> <span class='op'>=</span> <span class='string'>"http://rust-num.github.io/num/"</span>,
<span class='ident'>html_playground_url</span> <span class='op'>=</span> <span class='string'>"http://play.rust-lang.org/"</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>extern</span> <span class='kw'>crate</span> <span class='ident'>num_traits</span>;
<span class='kw'>pub</span> <span class='kw'>extern</span> <span class='kw'>crate</span> <span class='ident'>num_integer</span>;
<span class='kw'>pub</span> <span class='kw'>extern</span> <span class='kw'>crate</span> <span class='ident'>num_iter</span>;
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>feature</span> <span class='op'>=</span> <span class='string'>"num-complex"</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>extern</span> <span class='kw'>crate</span> <span class='ident'>num_complex</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'>extern</span> <span class='kw'>crate</span> <span class='ident'>num_bigint</span>;
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>feature</span> <span class='op'>=</span> <span class='string'>"num-rational"</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>extern</span> <span class='kw'>crate</span> <span class='ident'>num_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'>pub</span> <span class='kw'>use</span> <span class='ident'>num_bigint</span>::{<span class='ident'>BigInt</span>, <span class='ident'>BigUint</span>};
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>feature</span> <span class='op'>=</span> <span class='string'>"num-rational"</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>use</span> <span class='ident'>num_rational</span>::<span class='ident'>Rational</span>;
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>all</span>(<span class='ident'>feature</span> <span class='op'>=</span> <span class='string'>"num-rational"</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'>use</span> <span class='ident'>num_rational</span>::<span class='ident'>BigRational</span>;
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>feature</span> <span class='op'>=</span> <span class='string'>"num-complex"</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>use</span> <span class='ident'>num_complex</span>::<span class='ident'>Complex</span>;
<span class='kw'>pub</span> <span class='kw'>use</span> <span class='ident'>num_integer</span>::<span class='ident'>Integer</span>;
<span class='kw'>pub</span> <span class='kw'>use</span> <span class='ident'>num_iter</span>::{<span class='ident'>range</span>, <span class='ident'>range_inclusive</span>, <span class='ident'>range_step</span>, <span class='ident'>range_step_inclusive</span>};
<span class='kw'>pub</span> <span class='kw'>use</span> <span class='ident'>num_traits</span>::{<span class='ident'>Num</span>, <span class='ident'>Zero</span>, <span class='ident'>One</span>, <span class='ident'>Signed</span>, <span class='ident'>Unsigned</span>, <span class='ident'>Bounded</span>,
<span class='ident'>Saturating</span>, <span class='ident'>CheckedAdd</span>, <span class='ident'>CheckedSub</span>, <span class='ident'>CheckedMul</span>, <span class='ident'>CheckedDiv</span>,
<span class='ident'>PrimInt</span>, <span class='ident'>Float</span>, <span class='ident'>ToPrimitive</span>, <span class='ident'>FromPrimitive</span>, <span class='ident'>NumCast</span>, <span class='ident'>cast</span>};
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>ops</span>::{<span class='ident'>Mul</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'>use</span> <span class='ident'>num_bigint</span> <span class='kw'>as</span> <span class='ident'>bigint</span>;
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>feature</span> <span class='op'>=</span> <span class='string'>"num-complex"</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>use</span> <span class='ident'>num_complex</span> <span class='kw'>as</span> <span class='ident'>complex</span>;
<span class='kw'>pub</span> <span class='kw'>use</span> <span class='ident'>num_integer</span> <span class='kw'>as</span> <span class='ident'>integer</span>;
<span class='kw'>pub</span> <span class='kw'>use</span> <span class='ident'>num_iter</span> <span class='kw'>as</span> <span class='ident'>iter</span>;
<span class='kw'>pub</span> <span class='kw'>use</span> <span class='ident'>num_traits</span> <span class='kw'>as</span> <span class='ident'>traits</span>;
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>feature</span> <span class='op'>=</span> <span class='string'>"num-rational"</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>use</span> <span class='ident'>num_rational</span> <span class='kw'>as</span> <span class='ident'>rational</span>;
<span class='doccomment'>/// Returns the additive identity, `0`.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span> <span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>zero</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>Zero</span><span class='op'>></span>() <span class='op'>-></span> <span class='ident'>T</span> { <span class='ident'>Zero</span>::<span class='ident'>zero</span>() }
<span class='doccomment'>/// Returns the multiplicative identity, `1`.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span> <span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>one</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>One</span><span class='op'>></span>() <span class='op'>-></span> <span class='ident'>T</span> { <span class='ident'>One</span>::<span class='ident'>one</span>() }
<span class='doccomment'>/// Computes the absolute value.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// For `f32` and `f64`, `NaN` will be returned if the number is `NaN`</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// For signed integers, `::MIN` will be returned if the number is `::MIN`.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>abs</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>Signed</span><span class='op'>></span>(<span class='ident'>value</span>: <span class='ident'>T</span>) <span class='op'>-></span> <span class='ident'>T</span> {
<span class='ident'>value</span>.<span class='ident'>abs</span>()
}
<span class='doccomment'>/// The positive difference of two numbers.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// Returns zero if `x` is less than or equal to `y`, otherwise the difference</span>
<span class='doccomment'>/// between `x` and `y` is returned.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>abs_sub</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>Signed</span><span class='op'>></span>(<span class='ident'>x</span>: <span class='ident'>T</span>, <span class='ident'>y</span>: <span class='ident'>T</span>) <span class='op'>-></span> <span class='ident'>T</span> {
<span class='ident'>x</span>.<span class='ident'>abs_sub</span>(<span class='kw-2'>&</span><span class='ident'>y</span>)
}
<span class='doccomment'>/// Returns the sign of the number.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// For `f32` and `f64`:</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// * `1.0` if the number is positive, `+0.0` or `INFINITY`</span>
<span class='doccomment'>/// * `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`</span>
<span class='doccomment'>/// * `NaN` if the number is `NaN`</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// For signed integers:</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// * `0` if the number is zero</span>
<span class='doccomment'>/// * `1` if the number is positive</span>
<span class='doccomment'>/// * `-1` if the number is negative</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span> <span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>signum</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>Signed</span><span class='op'>></span>(<span class='ident'>value</span>: <span class='ident'>T</span>) <span class='op'>-></span> <span class='ident'>T</span> { <span class='ident'>value</span>.<span class='ident'>signum</span>() }
<span class='doccomment'>/// Raises a value to the power of exp, using exponentiation by squaring.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// # Example</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// ```rust</span>
<span class='doccomment'>/// use num;</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// assert_eq!(num::pow(2i8, 4), 16);</span>
<span class='doccomment'>/// assert_eq!(num::pow(6u8, 3), 216);</span>
<span class='doccomment'>/// ```</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='op'><</span><span class='ident'>T</span>: <span class='ident'>Clone</span> <span class='op'>+</span> <span class='ident'>One</span> <span class='op'>+</span> <span class='ident'>Mul</span><span class='op'><</span><span class='ident'>T</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>T</span><span class='op'>>></span>(<span class='kw-2'>mut</span> <span class='ident'>base</span>: <span class='ident'>T</span>, <span class='kw-2'>mut</span> <span class='ident'>exp</span>: <span class='ident'>usize</span>) <span class='op'>-></span> <span class='ident'>T</span> {
<span class='kw'>if</span> <span class='ident'>exp</span> <span class='op'>==</span> <span class='number'>0</span> { <span class='kw'>return</span> <span class='ident'>T</span>::<span class='ident'>one</span>() }
<span class='kw'>while</span> <span class='ident'>exp</span> <span class='kw-2'>&</span> <span class='number'>1</span> <span class='op'>==</span> <span class='number'>0</span> {
<span class='ident'>base</span> <span class='op'>=</span> <span class='ident'>base</span>.<span class='ident'>clone</span>() <span class='op'>*</span> <span class='ident'>base</span>;
<span class='ident'>exp</span> <span class='op'>>>=</span> <span class='number'>1</span>;
}
<span class='kw'>if</span> <span class='ident'>exp</span> <span class='op'>==</span> <span class='number'>1</span> { <span class='kw'>return</span> <span class='ident'>base</span> }
<span class='kw'>let</span> <span class='kw-2'>mut</span> <span class='ident'>acc</span> <span class='op'>=</span> <span class='ident'>base</span>.<span class='ident'>clone</span>();
<span class='kw'>while</span> <span class='ident'>exp</span> <span class='op'>></span> <span class='number'>1</span> {
<span class='ident'>exp</span> <span class='op'>>>=</span> <span class='number'>1</span>;
<span class='ident'>base</span> <span class='op'>=</span> <span class='ident'>base</span>.<span class='ident'>clone</span>() <span class='op'>*</span> <span class='ident'>base</span>;
<span class='kw'>if</span> <span class='ident'>exp</span> <span class='kw-2'>&</span> <span class='number'>1</span> <span class='op'>==</span> <span class='number'>1</span> {
<span class='ident'>acc</span> <span class='op'>=</span> <span class='ident'>acc</span> <span class='op'>*</span> <span class='ident'>base</span>.<span class='ident'>clone</span>();
}
}
<span class='ident'>acc</span>
}
<span class='doccomment'>/// Raises a value to the power of exp, returning `None` if an overflow occurred.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// Otherwise same as the `pow` function.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// # Example</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// ```rust</span>
<span class='doccomment'>/// use num;</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// assert_eq!(num::checked_pow(2i8, 4), Some(16));</span>
<span class='doccomment'>/// assert_eq!(num::checked_pow(7i8, 8), None);</span>
<span class='doccomment'>/// assert_eq!(num::checked_pow(7u32, 8), Some(5_764_801));</span>
<span class='doccomment'>/// ```</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>checked_pow</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>Clone</span> <span class='op'>+</span> <span class='ident'>One</span> <span class='op'>+</span> <span class='ident'>CheckedMul</span><span class='op'>></span>(<span class='kw-2'>mut</span> <span class='ident'>base</span>: <span class='ident'>T</span>, <span class='kw-2'>mut</span> <span class='ident'>exp</span>: <span class='ident'>usize</span>) <span class='op'>-></span> <span class='prelude-ty'>Option</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='kw'>if</span> <span class='ident'>exp</span> <span class='op'>==</span> <span class='number'>0</span> { <span class='kw'>return</span> <span class='prelude-val'>Some</span>(<span class='ident'>T</span>::<span class='ident'>one</span>()) }
<span class='macro'>macro_rules</span><span class='macro'>!</span> <span class='ident'>optry</span> {
( $ <span class='ident'>expr</span> : <span class='ident'>expr</span> ) <span class='op'>=></span> {
<span class='kw'>if</span> <span class='kw'>let</span> <span class='prelude-val'>Some</span>(<span class='ident'>val</span>) <span class='op'>=</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>expr</span> { <span class='ident'>val</span> } <span class='kw'>else</span> { <span class='kw'>return</span> <span class='prelude-val'>None</span> }
}
}
<span class='kw'>while</span> <span class='ident'>exp</span> <span class='kw-2'>&</span> <span class='number'>1</span> <span class='op'>==</span> <span class='number'>0</span> {
<span class='ident'>base</span> <span class='op'>=</span> <span class='macro'>optry</span><span class='macro'>!</span>(<span class='ident'>base</span>.<span class='ident'>checked_mul</span>(<span class='kw-2'>&</span><span class='ident'>base</span>));
<span class='ident'>exp</span> <span class='op'>>>=</span> <span class='number'>1</span>;
}
<span class='kw'>if</span> <span class='ident'>exp</span> <span class='op'>==</span> <span class='number'>1</span> { <span class='kw'>return</span> <span class='prelude-val'>Some</span>(<span class='ident'>base</span>) }
<span class='kw'>let</span> <span class='kw-2'>mut</span> <span class='ident'>acc</span> <span class='op'>=</span> <span class='ident'>base</span>.<span class='ident'>clone</span>();
<span class='kw'>while</span> <span class='ident'>exp</span> <span class='op'>></span> <span class='number'>1</span> {
<span class='ident'>exp</span> <span class='op'>>>=</span> <span class='number'>1</span>;
<span class='ident'>base</span> <span class='op'>=</span> <span class='macro'>optry</span><span class='macro'>!</span>(<span class='ident'>base</span>.<span class='ident'>checked_mul</span>(<span class='kw-2'>&</span><span class='ident'>base</span>));
<span class='kw'>if</span> <span class='ident'>exp</span> <span class='kw-2'>&</span> <span class='number'>1</span> <span class='op'>==</span> <span class='number'>1</span> {
<span class='ident'>acc</span> <span class='op'>=</span> <span class='macro'>optry</span><span class='macro'>!</span>(<span class='ident'>acc</span>.<span class='ident'>checked_mul</span>(<span class='kw-2'>&</span><span class='ident'>base</span>));
}
}
<span class='prelude-val'>Some</span>(<span class='ident'>acc</span>)
}
</pre>
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