497 lines
18 KiB
Rust
497 lines
18 KiB
Rust
// Copyright 2013-2014 The Rust Project Developers. See the COPYRIGHT
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// file at the top-level directory of this distribution and at
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// http://rust-lang.org/COPYRIGHT.
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//
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// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
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// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
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// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
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// option. This file may not be copied, modified, or distributed
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// except according to those terms.
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//! Integer trait and functions.
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pub trait Integer: Num + PartialOrd
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+ Div<Self, Self>
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+ Rem<Self, Self> {
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/// Floored integer division.
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///
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/// # Examples
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///
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/// ~~~
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/// # use num::Integer;
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/// assert!(( 8i).div_floor(& 3) == 2);
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/// assert!(( 8i).div_floor(&-3) == -3);
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/// assert!((-8i).div_floor(& 3) == -3);
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/// assert!((-8i).div_floor(&-3) == 2);
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///
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/// assert!(( 1i).div_floor(& 2) == 0);
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/// assert!(( 1i).div_floor(&-2) == -1);
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/// assert!((-1i).div_floor(& 2) == -1);
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/// assert!((-1i).div_floor(&-2) == 0);
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/// ~~~
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fn div_floor(&self, other: &Self) -> Self;
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/// Floored integer modulo, satisfying:
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///
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/// ~~~
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/// # use num::Integer;
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/// # let n = 1i; let d = 1i;
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/// assert!(n.div_floor(&d) * d + n.mod_floor(&d) == n)
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/// ~~~
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///
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/// # Examples
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///
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/// ~~~
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/// # use num::Integer;
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/// assert!(( 8i).mod_floor(& 3) == 2);
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/// assert!(( 8i).mod_floor(&-3) == -1);
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/// assert!((-8i).mod_floor(& 3) == 1);
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/// assert!((-8i).mod_floor(&-3) == -2);
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///
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/// assert!(( 1i).mod_floor(& 2) == 1);
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/// assert!(( 1i).mod_floor(&-2) == -1);
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/// assert!((-1i).mod_floor(& 2) == 1);
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/// assert!((-1i).mod_floor(&-2) == -1);
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/// ~~~
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fn mod_floor(&self, other: &Self) -> Self;
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/// Greatest Common Divisor (GCD).
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///
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/// # Examples
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///
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/// ~~~
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/// # use num::Integer;
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/// assert_eq!(6i.gcd(&8), 2);
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/// assert_eq!(7i.gcd(&3), 1);
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/// ~~~
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fn gcd(&self, other: &Self) -> Self;
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/// Lowest Common Multiple (LCM).
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///
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/// # Examples
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///
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/// ~~~
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/// # use num::Integer;
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/// assert_eq!(7i.lcm(&3), 21);
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/// assert_eq!(2i.lcm(&4), 4);
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/// ~~~
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fn lcm(&self, other: &Self) -> Self;
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/// Deprecated, use `is_multiple_of` instead.
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#[deprecated = "function renamed to `is_multiple_of`"]
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fn divides(&self, other: &Self) -> bool;
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/// Returns `true` if `other` is a multiple of `self`.
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///
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/// # Examples
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///
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/// ~~~
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/// # use num::Integer;
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/// assert_eq!(9i.is_multiple_of(&3), true);
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/// assert_eq!(3i.is_multiple_of(&9), false);
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/// ~~~
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fn is_multiple_of(&self, other: &Self) -> bool;
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/// Returns `true` if the number is even.
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///
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/// # Examples
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///
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/// ~~~
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/// # use num::Integer;
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/// assert_eq!(3i.is_even(), false);
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/// assert_eq!(4i.is_even(), true);
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/// ~~~
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fn is_even(&self) -> bool;
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/// Returns `true` if the number is odd.
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///
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/// # Examples
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///
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/// ~~~
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/// # use num::Integer;
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/// assert_eq!(3i.is_odd(), true);
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/// assert_eq!(4i.is_odd(), false);
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/// ~~~
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fn is_odd(&self) -> bool;
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/// Simultaneous truncated integer division and modulus.
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/// Returns `(quotient, remainder)`.
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///
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/// # Examples
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///
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/// ~~~
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/// # use num::Integer;
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/// assert_eq!(( 8i).div_rem( &3), ( 2, 2));
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/// assert_eq!(( 8i).div_rem(&-3), (-2, 2));
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/// assert_eq!((-8i).div_rem( &3), (-2, -2));
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/// assert_eq!((-8i).div_rem(&-3), ( 2, -2));
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///
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/// assert_eq!(( 1i).div_rem( &2), ( 0, 1));
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/// assert_eq!(( 1i).div_rem(&-2), ( 0, 1));
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/// assert_eq!((-1i).div_rem( &2), ( 0, -1));
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/// assert_eq!((-1i).div_rem(&-2), ( 0, -1));
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/// ~~~
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#[inline]
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fn div_rem(&self, other: &Self) -> (Self, Self) {
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(*self / *other, *self % *other)
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}
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/// Simultaneous floored integer division and modulus.
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/// Returns `(quotient, remainder)`.
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///
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/// # Examples
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///
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/// ~~~
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/// # use num::Integer;
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/// assert_eq!(( 8i).div_mod_floor( &3), ( 2, 2));
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/// assert_eq!(( 8i).div_mod_floor(&-3), (-3, -1));
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/// assert_eq!((-8i).div_mod_floor( &3), (-3, 1));
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/// assert_eq!((-8i).div_mod_floor(&-3), ( 2, -2));
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///
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/// assert_eq!(( 1i).div_mod_floor( &2), ( 0, 1));
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/// assert_eq!(( 1i).div_mod_floor(&-2), (-1, -1));
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/// assert_eq!((-1i).div_mod_floor( &2), (-1, 1));
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/// assert_eq!((-1i).div_mod_floor(&-2), ( 0, -1));
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/// ~~~
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fn div_mod_floor(&self, other: &Self) -> (Self, Self) {
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(self.div_floor(other), self.mod_floor(other))
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}
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}
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/// Simultaneous integer division and modulus
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#[inline] pub fn div_rem<T: Integer>(x: T, y: T) -> (T, T) { x.div_rem(&y) }
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/// Floored integer division
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#[inline] pub fn div_floor<T: Integer>(x: T, y: T) -> T { x.div_floor(&y) }
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/// Floored integer modulus
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#[inline] pub fn mod_floor<T: Integer>(x: T, y: T) -> T { x.mod_floor(&y) }
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/// Simultaneous floored integer division and modulus
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#[inline] pub fn div_mod_floor<T: Integer>(x: T, y: T) -> (T, T) { x.div_mod_floor(&y) }
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/// Calculates the Greatest Common Divisor (GCD) of the number and `other`. The
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/// result is always positive.
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#[inline(always)] pub fn gcd<T: Integer>(x: T, y: T) -> T { x.gcd(&y) }
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/// Calculates the Lowest Common Multiple (LCM) of the number and `other`.
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#[inline(always)] pub fn lcm<T: Integer>(x: T, y: T) -> T { x.lcm(&y) }
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macro_rules! impl_integer_for_int {
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($T:ty, $test_mod:ident) => (
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impl Integer for $T {
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/// Floored integer division
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#[inline]
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fn div_floor(&self, other: &$T) -> $T {
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// Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,
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// December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)
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match self.div_rem(other) {
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(d, r) if (r > 0 && *other < 0)
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|| (r < 0 && *other > 0) => d - 1,
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(d, _) => d,
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}
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}
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/// Floored integer modulo
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#[inline]
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fn mod_floor(&self, other: &$T) -> $T {
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// Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,
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// December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)
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match *self % *other {
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r if (r > 0 && *other < 0)
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|| (r < 0 && *other > 0) => r + *other,
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r => r,
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}
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}
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/// Calculates `div_floor` and `mod_floor` simultaneously
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#[inline]
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fn div_mod_floor(&self, other: &$T) -> ($T,$T) {
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// Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,
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// December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)
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match self.div_rem(other) {
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(d, r) if (r > 0 && *other < 0)
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|| (r < 0 && *other > 0) => (d - 1, r + *other),
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(d, r) => (d, r),
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}
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}
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/// Calculates the Greatest Common Divisor (GCD) of the number and
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/// `other`. The result is always positive.
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#[inline]
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fn gcd(&self, other: &$T) -> $T {
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// Use Euclid's algorithm
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let mut m = *self;
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let mut n = *other;
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while m != 0 {
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let temp = m;
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m = n % temp;
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n = temp;
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}
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n.abs()
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}
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/// Calculates the Lowest Common Multiple (LCM) of the number and
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/// `other`.
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#[inline]
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fn lcm(&self, other: &$T) -> $T {
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// should not have to recalculate abs
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((*self * *other) / self.gcd(other)).abs()
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}
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/// Deprecated, use `is_multiple_of` instead.
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#[deprecated = "function renamed to `is_multiple_of`"]
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#[inline]
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fn divides(&self, other: &$T) -> bool { return self.is_multiple_of(other); }
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/// Returns `true` if the number is a multiple of `other`.
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#[inline]
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fn is_multiple_of(&self, other: &$T) -> bool { *self % *other == 0 }
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/// Returns `true` if the number is divisible by `2`
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#[inline]
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fn is_even(&self) -> bool { self & 1 == 0 }
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/// Returns `true` if the number is not divisible by `2`
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#[inline]
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fn is_odd(&self) -> bool { !self.is_even() }
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}
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#[cfg(test)]
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mod $test_mod {
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use Integer;
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/// Checks that the division rule holds for:
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///
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/// - `n`: numerator (dividend)
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/// - `d`: denominator (divisor)
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/// - `qr`: quotient and remainder
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#[cfg(test)]
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fn test_division_rule((n,d): ($T,$T), (q,r): ($T,$T)) {
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assert_eq!(d * q + r, n);
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}
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#[test]
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fn test_div_rem() {
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fn test_nd_dr(nd: ($T,$T), qr: ($T,$T)) {
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let (n,d) = nd;
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let separate_div_rem = (n / d, n % d);
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let combined_div_rem = n.div_rem(&d);
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assert_eq!(separate_div_rem, qr);
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assert_eq!(combined_div_rem, qr);
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test_division_rule(nd, separate_div_rem);
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test_division_rule(nd, combined_div_rem);
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}
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test_nd_dr(( 8, 3), ( 2, 2));
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test_nd_dr(( 8, -3), (-2, 2));
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test_nd_dr((-8, 3), (-2, -2));
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test_nd_dr((-8, -3), ( 2, -2));
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test_nd_dr(( 1, 2), ( 0, 1));
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test_nd_dr(( 1, -2), ( 0, 1));
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test_nd_dr((-1, 2), ( 0, -1));
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test_nd_dr((-1, -2), ( 0, -1));
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}
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#[test]
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fn test_div_mod_floor() {
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fn test_nd_dm(nd: ($T,$T), dm: ($T,$T)) {
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let (n,d) = nd;
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let separate_div_mod_floor = (n.div_floor(&d), n.mod_floor(&d));
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let combined_div_mod_floor = n.div_mod_floor(&d);
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assert_eq!(separate_div_mod_floor, dm);
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assert_eq!(combined_div_mod_floor, dm);
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test_division_rule(nd, separate_div_mod_floor);
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test_division_rule(nd, combined_div_mod_floor);
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}
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test_nd_dm(( 8, 3), ( 2, 2));
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test_nd_dm(( 8, -3), (-3, -1));
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test_nd_dm((-8, 3), (-3, 1));
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test_nd_dm((-8, -3), ( 2, -2));
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test_nd_dm(( 1, 2), ( 0, 1));
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test_nd_dm(( 1, -2), (-1, -1));
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test_nd_dm((-1, 2), (-1, 1));
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test_nd_dm((-1, -2), ( 0, -1));
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}
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#[test]
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fn test_gcd() {
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assert_eq!((10 as $T).gcd(&2), 2 as $T);
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assert_eq!((10 as $T).gcd(&3), 1 as $T);
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assert_eq!((0 as $T).gcd(&3), 3 as $T);
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assert_eq!((3 as $T).gcd(&3), 3 as $T);
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assert_eq!((56 as $T).gcd(&42), 14 as $T);
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assert_eq!((3 as $T).gcd(&-3), 3 as $T);
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assert_eq!((-6 as $T).gcd(&3), 3 as $T);
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assert_eq!((-4 as $T).gcd(&-2), 2 as $T);
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}
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#[test]
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fn test_lcm() {
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assert_eq!((1 as $T).lcm(&0), 0 as $T);
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assert_eq!((0 as $T).lcm(&1), 0 as $T);
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assert_eq!((1 as $T).lcm(&1), 1 as $T);
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assert_eq!((-1 as $T).lcm(&1), 1 as $T);
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assert_eq!((1 as $T).lcm(&-1), 1 as $T);
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assert_eq!((-1 as $T).lcm(&-1), 1 as $T);
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assert_eq!((8 as $T).lcm(&9), 72 as $T);
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assert_eq!((11 as $T).lcm(&5), 55 as $T);
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}
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#[test]
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fn test_even() {
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assert_eq!((-4 as $T).is_even(), true);
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assert_eq!((-3 as $T).is_even(), false);
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assert_eq!((-2 as $T).is_even(), true);
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assert_eq!((-1 as $T).is_even(), false);
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assert_eq!((0 as $T).is_even(), true);
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assert_eq!((1 as $T).is_even(), false);
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assert_eq!((2 as $T).is_even(), true);
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assert_eq!((3 as $T).is_even(), false);
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assert_eq!((4 as $T).is_even(), true);
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}
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#[test]
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fn test_odd() {
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assert_eq!((-4 as $T).is_odd(), false);
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assert_eq!((-3 as $T).is_odd(), true);
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assert_eq!((-2 as $T).is_odd(), false);
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assert_eq!((-1 as $T).is_odd(), true);
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assert_eq!((0 as $T).is_odd(), false);
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assert_eq!((1 as $T).is_odd(), true);
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assert_eq!((2 as $T).is_odd(), false);
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assert_eq!((3 as $T).is_odd(), true);
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assert_eq!((4 as $T).is_odd(), false);
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}
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}
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)
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}
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impl_integer_for_int!(i8, test_integer_i8)
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impl_integer_for_int!(i16, test_integer_i16)
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impl_integer_for_int!(i32, test_integer_i32)
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impl_integer_for_int!(i64, test_integer_i64)
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impl_integer_for_int!(int, test_integer_int)
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macro_rules! impl_integer_for_uint {
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($T:ty, $test_mod:ident) => (
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impl Integer for $T {
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/// Unsigned integer division. Returns the same result as `div` (`/`).
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#[inline]
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fn div_floor(&self, other: &$T) -> $T { *self / *other }
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/// Unsigned integer modulo operation. Returns the same result as `rem` (`%`).
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#[inline]
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fn mod_floor(&self, other: &$T) -> $T { *self % *other }
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/// Calculates the Greatest Common Divisor (GCD) of the number and `other`
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#[inline]
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fn gcd(&self, other: &$T) -> $T {
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// Use Euclid's algorithm
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let mut m = *self;
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let mut n = *other;
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while m != 0 {
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let temp = m;
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m = n % temp;
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n = temp;
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}
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n
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}
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/// Calculates the Lowest Common Multiple (LCM) of the number and `other`.
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#[inline]
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fn lcm(&self, other: &$T) -> $T {
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(*self * *other) / self.gcd(other)
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}
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/// Deprecated, use `is_multiple_of` instead.
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#[deprecated = "function renamed to `is_multiple_of`"]
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#[inline]
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fn divides(&self, other: &$T) -> bool { return self.is_multiple_of(other); }
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/// Returns `true` if the number is a multiple of `other`.
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#[inline]
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fn is_multiple_of(&self, other: &$T) -> bool { *self % *other == 0 }
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/// Returns `true` if the number is divisible by `2`.
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#[inline]
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fn is_even(&self) -> bool { self & 1 == 0 }
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/// Returns `true` if the number is not divisible by `2`.
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#[inline]
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fn is_odd(&self) -> bool { !self.is_even() }
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}
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#[cfg(test)]
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mod $test_mod {
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use Integer;
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#[test]
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fn test_div_mod_floor() {
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assert_eq!((10 as $T).div_floor(&(3 as $T)), 3 as $T);
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assert_eq!((10 as $T).mod_floor(&(3 as $T)), 1 as $T);
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assert_eq!((10 as $T).div_mod_floor(&(3 as $T)), (3 as $T, 1 as $T));
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assert_eq!((5 as $T).div_floor(&(5 as $T)), 1 as $T);
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assert_eq!((5 as $T).mod_floor(&(5 as $T)), 0 as $T);
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assert_eq!((5 as $T).div_mod_floor(&(5 as $T)), (1 as $T, 0 as $T));
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assert_eq!((3 as $T).div_floor(&(7 as $T)), 0 as $T);
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assert_eq!((3 as $T).mod_floor(&(7 as $T)), 3 as $T);
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assert_eq!((3 as $T).div_mod_floor(&(7 as $T)), (0 as $T, 3 as $T));
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}
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#[test]
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fn test_gcd() {
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assert_eq!((10 as $T).gcd(&2), 2 as $T);
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assert_eq!((10 as $T).gcd(&3), 1 as $T);
|
|
assert_eq!((0 as $T).gcd(&3), 3 as $T);
|
|
assert_eq!((3 as $T).gcd(&3), 3 as $T);
|
|
assert_eq!((56 as $T).gcd(&42), 14 as $T);
|
|
}
|
|
|
|
#[test]
|
|
fn test_lcm() {
|
|
assert_eq!((1 as $T).lcm(&0), 0 as $T);
|
|
assert_eq!((0 as $T).lcm(&1), 0 as $T);
|
|
assert_eq!((1 as $T).lcm(&1), 1 as $T);
|
|
assert_eq!((8 as $T).lcm(&9), 72 as $T);
|
|
assert_eq!((11 as $T).lcm(&5), 55 as $T);
|
|
assert_eq!((99 as $T).lcm(&17), 1683 as $T);
|
|
}
|
|
|
|
#[test]
|
|
fn test_is_multiple_of() {
|
|
assert!((6 as $T).is_multiple_of(&(6 as $T)));
|
|
assert!((6 as $T).is_multiple_of(&(3 as $T)));
|
|
assert!((6 as $T).is_multiple_of(&(1 as $T)));
|
|
}
|
|
|
|
#[test]
|
|
fn test_even() {
|
|
assert_eq!((0 as $T).is_even(), true);
|
|
assert_eq!((1 as $T).is_even(), false);
|
|
assert_eq!((2 as $T).is_even(), true);
|
|
assert_eq!((3 as $T).is_even(), false);
|
|
assert_eq!((4 as $T).is_even(), true);
|
|
}
|
|
|
|
#[test]
|
|
fn test_odd() {
|
|
assert_eq!((0 as $T).is_odd(), false);
|
|
assert_eq!((1 as $T).is_odd(), true);
|
|
assert_eq!((2 as $T).is_odd(), false);
|
|
assert_eq!((3 as $T).is_odd(), true);
|
|
assert_eq!((4 as $T).is_odd(), false);
|
|
}
|
|
}
|
|
)
|
|
}
|
|
|
|
impl_integer_for_uint!(u8, test_integer_u8)
|
|
impl_integer_for_uint!(u16, test_integer_u16)
|
|
impl_integer_for_uint!(u32, test_integer_u32)
|
|
impl_integer_for_uint!(u64, test_integer_u64)
|
|
impl_integer_for_uint!(uint, test_integer_uint)
|