feanor_math/
ordered.rs

1use crate::ring::*;
2use std::cmp::*;
3
4///
5/// Trait for rings that have a total ordering on their elements.
6/// The ordering must be compatible with addition and multiplication
7/// in the usual sense.
8/// 
9/// In particular, this should only be implemented for rings that are
10/// subrings of the real numbers.
11/// 
12pub trait OrderedRing: RingBase {
13
14    ///
15    /// Returns whether `lhs` is [`Ordering::Less`], [`Ordering::Equal`] or [`Ordering::Greater`]
16    /// than `rhs`.
17    /// 
18    fn cmp(&self, lhs: &Self::Element, rhs: &Self::Element) -> Ordering;
19
20    ///
21    /// Returns whether `abs(lhs)` is [`Ordering::Less`], [`Ordering::Equal`] or [`Ordering::Greater`]
22    /// than `abs(rhs)`.
23    /// 
24    fn abs_cmp(&self, lhs: &Self::Element, rhs: &Self::Element) -> Ordering {
25        self.cmp(&self.abs(self.clone_el(lhs)), &self.abs(self.clone_el(rhs)))
26    }
27
28    ///
29    /// Returns whether `lhs <= rhs`.
30    /// 
31    fn is_leq(&self, lhs: &Self::Element, rhs: &Self::Element) -> bool {
32        self.cmp(lhs, rhs) != Ordering::Greater
33    }
34    
35    ///
36    /// Returns whether `lhs >= rhs`.
37    /// 
38    fn is_geq(&self, lhs: &Self::Element, rhs: &Self::Element) -> bool {
39        self.cmp(lhs, rhs) != Ordering::Less
40    }
41
42    ///
43    /// Returns whether `lhs < rhs`.
44    /// 
45    fn is_lt(&self, lhs: &Self::Element, rhs: &Self::Element) -> bool {
46        self.cmp(lhs, rhs) == Ordering::Less
47    }
48    
49    ///
50    /// Returns whether `lhs > rhs`.
51    /// 
52    fn is_gt(&self, lhs: &Self::Element, rhs: &Self::Element) -> bool {
53        self.cmp(lhs, rhs) == Ordering::Greater
54    }
55
56    ///
57    /// Returns whether `value < 0`.
58    /// 
59    fn is_neg(&self, value: &Self::Element) -> bool {
60        self.is_lt(value, &self.zero())
61    }
62
63    ///
64    /// Returns whether `value > 0`.
65    /// 
66    fn is_pos(&self, value: &Self::Element) -> bool {
67        self.is_gt(value, &self.zero())
68    }
69
70    ///
71    /// Returns the absolute value of `value`, i.e. `value` if `value >= 0` and `-value` otherwise.
72    /// 
73    fn abs(&self, value: Self::Element) -> Self::Element {
74        if self.is_neg(&value) {
75            self.negate(value)
76        } else {
77            value
78        }
79    }
80
81    ///
82    /// Returns the larger one of `fst` and `snd`.
83    /// 
84    fn max<'a>(&self, fst: &'a Self::Element, snd: &'a Self::Element) -> &'a Self::Element {
85        if self.is_geq(fst, snd) {
86            return fst;
87        } else {
88            return snd;
89        }
90    }
91}
92
93///
94/// Trait for [`RingStore`]s that store [`OrderedRing`]s. Mainly used
95/// to provide a convenient interface to the `OrderedRing`-functions.
96/// 
97pub trait OrderedRingStore: RingStore
98    where Self::Type: OrderedRing
99{
100    delegate!{ OrderedRing, fn cmp(&self, lhs: &El<Self>, rhs: &El<Self>) -> Ordering }
101    delegate!{ OrderedRing, fn abs_cmp(&self, lhs: &El<Self>, rhs: &El<Self>) -> Ordering }
102    delegate!{ OrderedRing, fn is_leq(&self, lhs: &El<Self>, rhs: &El<Self>) -> bool }
103    delegate!{ OrderedRing, fn is_geq(&self, lhs: &El<Self>, rhs: &El<Self>) -> bool }
104    delegate!{ OrderedRing, fn is_lt(&self, lhs: &El<Self>, rhs: &El<Self>) -> bool }
105    delegate!{ OrderedRing, fn is_gt(&self, lhs: &El<Self>, rhs: &El<Self>) -> bool }
106    delegate!{ OrderedRing, fn is_neg(&self, value: &El<Self>) -> bool }
107    delegate!{ OrderedRing, fn is_pos(&self, value: &El<Self>) -> bool }
108    delegate!{ OrderedRing, fn abs(&self, value: El<Self>) -> El<Self> }
109    
110    ///
111    /// See [`OrderedRing::max()`].
112    /// 
113    fn max<'a>(&self, fst: &'a El<Self>, snd: &'a El<Self>) -> &'a El<Self> {
114        self.get_ring().max(fst, snd)
115    }
116}
117
118impl<R: ?Sized> OrderedRingStore for R
119    where R: RingStore,
120        R::Type: OrderedRing
121{}
feanor_math/ordered.rs

feanor_math/
ordered.rs
