1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76

//! 乗法に関する wrapper クラス。

use super::op_add;
use super::super::traits::binop;
use super::super::traits::multiplicative;

use std::fmt::Debug;

use binop::{Associative, Commutative, Identity, Magma, PartialRecip, Recip};
use multiplicative::{MulAssoc, MulComm, MulRecip, One};

/// 積を返す演算を持つ。
///
/// [`std::ops::Mul`](https://doc.rust-lang.org/std/ops/trait.Mul.html) により定義される。
/// 単位元は [`One`]、逆元は [`MulRecip`] で定義する。
/// 結合法則を満たすときは [`MulAssoc`]、交換法則を満たすときは [`MulComm`] を実装することで示す。
///
/// [`One`]: ../../traits/multiplicative/trait.One.html
/// [`MulRecip`]: ../../traits/multiplicative/trait.MulRecip.html
/// [`MulAssoc`]: ../../traits/multiplicative/trait.MulAssoc.html
/// [`MulComm`]: ../../traits/multiplicative/trait.MulComm.html
#[derive(Clone, Copy, Debug, Eq, PartialEq)]
pub enum OpMul<T> {
    OpMulV,
    _Marker(T),
}
pub use OpMul::OpMulV;

impl<T> Default for OpMul<T> {
    fn default() -> Self { OpMulV }
}

use std::ops::Mul;

impl<T> Magma for OpMul<T>
where
    T: Mul<Output = T> + Eq + Sized,
{
    type Set = T;
    fn op(&self, x: Self::Set, y: Self::Set) -> Self::Set { x * y }
}
impl<T> Identity for OpMul<T>
where
    T: Mul<Output = T> + Eq + Sized + One,
{
    fn id(&self) -> Self::Set { Self::Set::one() }
}
impl<T> PartialRecip for OpMul<T>
where
    T: Mul<Output = T> + Eq + Sized + MulRecip<Output = T>,
{
    fn partial_recip(&self, x: Self::Set) -> Option<Self::Set> {
        Some(x.mul_recip())
    }
}
impl<T> Recip for OpMul<T> where
    T: Mul<Output = T> + Eq + Sized + MulRecip<Output = T>
{
}
impl<T> Associative for OpMul<T> where T: Mul<Output = T> + Eq + Sized + MulAssoc
{}
impl<T> Commutative for OpMul<T> where T: Mul<Output = T> + Eq + Sized + MulComm {}

use op_add::OpAdd;

macro_rules! impl_distributive {
    ( $T:ty ) => {
        impl binop::Distributive<OpAdd<$T>> for OpMul<$T> {}
    };
    ( $( $T:ty, )* ) => { $( impl_distributive!($T); )* };
}

impl_distributive! {
    i8, i16, i32, i64, i128, isize,
    u8, u16, u32, u64, u128, usize,
}