cmp.rs

// Copyright 2012-2013 The Rust Project Developers. See the COPYRIGHT
// file at the top-level directory of this distribution and at
// http://rust-lang.org/COPYRIGHT.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.

//! Defines the `Ord` and `Eq` comparison traits.
//!
//! This module defines both `Ord` and `Eq` traits which are used by the
//! compiler to implement comparison operators. Rust programs may implement
//!`Ord` to overload the `<`, `<=`, `>`, and `>=` operators, and may implement
//! `Eq` to overload the `==` and `!=` operators.
//!
//! For example, to define a type with a customized definition for the Eq
//! operators, you could do the following:
//!
//! ```rust
//! // Our type.
//! struct SketchyNum {
//!     num : int
//! }
//!
//! // Our implementation of `Eq` to support `==` and `!=`.
//! impl Eq for SketchyNum {
//!     // Our custom eq allows numbers which are near each other to be equal! :D
//!     fn eq(&self, other: &SketchyNum) -> bool {
//!         (self.num - other.num).abs() < 5
//!     }
//! }
//!
//! // Now these binary operators will work when applied!
//! assert!(SketchyNum {num: 37} == SketchyNum {num: 34});
//! assert!(SketchyNum {num: 25} != SketchyNum {num: 57});
//! ```

/// Trait for values that can be compared for equality and inequality.
///
/// This trait allows partial equality, where types can be unordered instead of
/// strictly equal or unequal. For example, with the built-in floating-point
/// types `a == b` and `a != b` will both evaluate to false if either `a` or
/// `b` is NaN (cf. IEEE 754-2008 section 5.11).
///
/// Eq only requires the `eq` method to be implemented; `ne` is its negation by
/// default.
///
/// Eventually, this will be implemented by default for types that implement
/// `TotalEq`.
#[lang="eq"]
pub trait Eq {
    /// This method tests for `self` and `other` values to be equal, and is used by `==`.
    fn eq(&self, other: &Self) -> bool;

    /// This method tests for `!=`.
    #[inline]
    fn ne(&self, other: &Self) -> bool { !self.eq(other) }
}

/// Trait for equality comparisons which are [equivalence relations](
/// https://en.wikipedia.org/wiki/Equivalence_relation).
///
/// This means, that in addition to `a == b` and `a != b` being strict
/// inverses, the equality must be (for all `a`, `b` and `c`):
///
/// - reflexive: `a == a`;
/// - symmetric: `a == b` implies `b == a`; and
/// - transitive: `a == b` and `b == c` implies `a == c`.
pub trait TotalEq: Eq {
    // FIXME #13101: this method is used solely by #[deriving] to
    // assert that every component of a type implements #[deriving]
    // itself, the current deriving infrastructure means doing this
    // assertion without using a method on this trait is nearly
    // impossible.
    //
    // This should never be implemented by hand.
    #[doc(hidden)]
    #[inline(always)]
    fn assert_receiver_is_total_eq(&self) {}
}

/// An ordering is, e.g, a result of a comparison between two values.
#[deriving(Clone, Eq)]
pub enum Ordering {
   /// An ordering where a compared value is less [than another].
   Less = -1,
   /// An ordering where a compared value is equal [to another].
   Equal = 0,
   /// An ordering where a compared value is greater [than another].
   Greater = 1
}

/// Trait for types that form a [total order](
/// https://en.wikipedia.org/wiki/Total_order).
///
/// An order is a total order if it is (for all `a`, `b` and `c`):
///
/// - total and antisymmetric: exactly one of `a < b`, `a == b` or `a > b` is
///   true; and
/// - transitive, `a < b` and `b < c` implies `a < c`. The same must hold for
///   both `==` and `>`.
pub trait TotalOrd: TotalEq + Ord {
    /// This method returns an ordering between `self` and `other` values.
    ///
    /// By convention, `self.cmp(&other)` returns the ordering matching
    /// the expression `self <operator> other` if true.  For example:
    ///
    /// ```
    /// assert_eq!( 5u.cmp(&10), Less);     // because 5 < 10
    /// assert_eq!(10u.cmp(&5),  Greater);  // because 10 > 5
    /// assert_eq!( 5u.cmp(&5),  Equal);    // because 5 == 5
    /// ```
    fn cmp(&self, other: &Self) -> Ordering;
}

impl TotalEq for Ordering {}

impl TotalOrd for Ordering {
    #[inline]
    fn cmp(&self, other: &Ordering) -> Ordering {
        (*self as int).cmp(&(*other as int))
    }
}

impl Ord for Ordering {
    #[inline]
    fn lt(&self, other: &Ordering) -> bool { (*self as int) < (*other as int) }
}

/// Combine orderings, lexically.
///
/// For example for a type `(int, int)`, two comparisons could be done.
/// If the first ordering is different, the first ordering is all that must be returned.
/// If the first ordering is equal, then second ordering is returned.
#[inline]
pub fn lexical_ordering(o1: Ordering, o2: Ordering) -> Ordering {
    match o1 {
        Equal => o2,
        _ => o1
    }
}

/// Trait for values that can be compared for a sort-order.
///
/// Ord only requires implementation of the `lt` method,
/// with the others generated from default implementations.
///
/// However it remains possible to implement the others separately,
/// for compatibility with floating-point NaN semantics
/// (cf. IEEE 754-2008 section 5.11).
#[lang="ord"]
pub trait Ord: Eq {
    /// This method tests less than (for `self` and `other`) and is used by the `<` operator.
    fn lt(&self, other: &Self) -> bool;

    /// This method tests less than or equal to (`<=`).
    #[inline]
    fn le(&self, other: &Self) -> bool { !other.lt(self) }

    /// This method tests greater than (`>`).
    #[inline]
    fn gt(&self, other: &Self) -> bool {  other.lt(self) }

    /// This method tests greater than or equal to (`>=`).
    #[inline]
    fn ge(&self, other: &Self) -> bool { !self.lt(other) }
}

/// The equivalence relation. Two values may be equivalent even if they are
/// of different types. The most common use case for this relation is
/// container types; e.g. it is often desirable to be able to use `&str`
/// values to look up entries in a container with `~str` keys.
pub trait Equiv<T> {
    /// Implement this function to decide equivalent values.
    fn equiv(&self, other: &T) -> bool;
}

/// Compare and return the minimum of two values.
#[inline]
pub fn min<T: TotalOrd>(v1: T, v2: T) -> T {
    if v1 < v2 { v1 } else { v2 }
}

/// Compare and return the maximum of two values.
#[inline]
pub fn max<T: TotalOrd>(v1: T, v2: T) -> T {
    if v1 > v2 { v1 } else { v2 }
}

// Implementation of Eq/TotalEq for some primitive types
#[cfg(not(test))]
mod impls {
    use cmp::{Ord, TotalOrd, Eq, TotalEq, Ordering, Equal};

    impl Eq for () {
        #[inline]
        fn eq(&self, _other: &()) -> bool { true }
        #[inline]
        fn ne(&self, _other: &()) -> bool { false }
    }
    impl TotalEq for () {}
    impl Ord for () {
        #[inline]
        fn lt(&self, _other: &()) -> bool { false }
    }
    impl TotalOrd for () {
        #[inline]
        fn cmp(&self, _other: &()) -> Ordering { Equal }
    }

    // & pointers
    impl<'a, T: Eq> Eq for &'a T {
        #[inline]
        fn eq(&self, other: & &'a T) -> bool { *(*self) == *(*other) }
        #[inline]
        fn ne(&self, other: & &'a T) -> bool { *(*self) != *(*other) }
    }
    impl<'a, T: Ord> Ord for &'a T {
        #[inline]
        fn lt(&self, other: & &'a T) -> bool { *(*self) < *(*other) }
        #[inline]
        fn le(&self, other: & &'a T) -> bool { *(*self) <= *(*other) }
        #[inline]
        fn ge(&self, other: & &'a T) -> bool { *(*self) >= *(*other) }
        #[inline]
        fn gt(&self, other: & &'a T) -> bool { *(*self) > *(*other) }
    }
    impl<'a, T: TotalOrd> TotalOrd for &'a T {
        #[inline]
        fn cmp(&self, other: & &'a T) -> Ordering { (**self).cmp(*other) }
    }
    impl<'a, T: TotalEq> TotalEq for &'a T {}

    // @ pointers
    impl<T:Eq> Eq for @T {
        #[inline]
        fn eq(&self, other: &@T) -> bool { *(*self) == *(*other) }
        #[inline]
        fn ne(&self, other: &@T) -> bool { *(*self) != *(*other) }
    }
    impl<T:Ord> Ord for @T {
        #[inline]
        fn lt(&self, other: &@T) -> bool { *(*self) < *(*other) }
        #[inline]
        fn le(&self, other: &@T) -> bool { *(*self) <= *(*other) }
        #[inline]
        fn ge(&self, other: &@T) -> bool { *(*self) >= *(*other) }
        #[inline]
        fn gt(&self, other: &@T) -> bool { *(*self) > *(*other) }
    }
    impl<T: TotalOrd> TotalOrd for @T {
        #[inline]
        fn cmp(&self, other: &@T) -> Ordering { (**self).cmp(*other) }
    }
    impl<T: TotalEq> TotalEq for @T {}
}

#[cfg(test)]
mod test {
    use super::lexical_ordering;

    #[test]
    fn test_int_totalord() {
        assert_eq!(5u.cmp(&10), Less);
        assert_eq!(10u.cmp(&5), Greater);
        assert_eq!(5u.cmp(&5), Equal);
        assert_eq!((-5u).cmp(&12), Less);
        assert_eq!(12u.cmp(-5), Greater);
    }

    #[test]
    fn test_ordering_order() {
        assert!(Less < Equal);
        assert_eq!(Greater.cmp(&Less), Greater);
    }

    #[test]
    fn test_lexical_ordering() {
        fn t(o1: Ordering, o2: Ordering, e: Ordering) {
            assert_eq!(lexical_ordering(o1, o2), e);
        }

        let xs = [Less, Equal, Greater];
        for &o in xs.iter() {
            t(Less, o, Less);
            t(Equal, o, o);
            t(Greater, o, Greater);
         }
    }

    #[test]
    fn test_user_defined_eq() {
        // Our type.
        struct SketchyNum {
            num : int
        }

        // Our implementation of `Eq` to support `==` and `!=`.
        impl Eq for SketchyNum {
            // Our custom eq allows numbers which are near each other to be equal! :D
            fn eq(&self, other: &SketchyNum) -> bool {
                (self.num - other.num).abs() < 5
            }
        }

        // Now these binary operators will work when applied!
        assert!(SketchyNum {num: 37} == SketchyNum {num: 34});
        assert!(SketchyNum {num: 25} != SketchyNum {num: 57});
    }
}