【typenum】 5 类型操作符别名（operator_aliases.rs）

一、源码

typenum是一个在类型级别上进行数字计算的库。这段代码主要定义了一系列类型操作符的别名，目的是提高类型操作的易用性。

//! Aliases for the type operators used in this crate.

//! Their purpose is to increase the ergonomics of performing operations on the types defined
//! here. For even more ergonomics, consider using the `op!` macro instead.
//!
//! For example, type `X` and type `Y` are the same here:
//!
//! ```rust
//! # #[macro_use] extern crate typenum;
//! use std::ops::Mul;
//! use typenum::{Prod, P5, P7};
//!
//! type X = >::Output;
//! type Y = Prod;
//!
//! assert_type_eq!(X, Y);
//! ```

// Aliases!!!
use crate::type_operators::{
    Abs, Cmp, FoldAdd, FoldMul, Gcd, Len, Logarithm2, Max, Min, PartialDiv, Pow, SquareRoot,
};
use core::ops::{Add, BitAnd, BitOr, BitXor, Div, Mul, Neg, Rem, Shl, Shr, Sub};

/// Alias for the associated type of `BitAnd`: `And = >::Output`
pub type And<A, B> = <A as BitAnd<B>>::Output;
/// Alias for the associated type of `BitOr`: `Or = >::Output`
pub type Or<A, B> = <A as BitOr<B>>::Output;
/// Alias for the associated type of `BitXor`: `Xor = >::Output`
pub type Xor<A, B> = <A as BitXor<B>>::Output;

/// Alias for the associated type of `Shl`: `Shleft = >::Output`
pub type Shleft<A, B> = <A as Shl<B>>::Output;
/// Alias for the associated type of `Shr`: `Shright = >::Output`
pub type Shright<A, B> = <A as Shr<B>>::Output;

/// Alias for the associated type of `Add`: `Sum = >::Output`
pub type Sum<A, B> = <A as Add<B>>::Output;
/// Alias for the associated type of `Sub`: `Diff = >::Output`
pub type Diff<A, B> = <A as Sub<B>>::Output;
/// Alias for the associated type of `Mul`: `Prod = >::Output`
pub type Prod<A, B> = <A as Mul<B>>::Output;
/// Alias for the associated type of `Div`: `Quot = >::Output`
pub type Quot<A, B> = <A as Div<B>>::Output;
/// Alias for the associated type of `Rem`: `Mod = >::Output`
pub type Mod<A, B> = <A as Rem<B>>::Output;

/// Alias for the associated type of
/// `PartialDiv`: `PartialQuot = >::Output`
pub type PartialQuot<A, B> = <A as PartialDiv<B>>::Output;

/// Alias for the associated type of `Neg`: `Negate = ::Output`
pub type Negate<A> = <A as Neg>::Output;

/// Alias for the associated type of `Abs`: `AbsVal = ::Output`
pub type AbsVal<A> = <A as Abs>::Output;

/// Alias for the associated type of `Pow`: `Exp = >::Output`
pub type Exp<A, B> = <A as Pow<B>>::Output;

/// Alias for the associated type of `Gcd`: `Gcf = >::Output>`
pub type Gcf<A, B> = <A as Gcd<B>>::Output;

/// Alias to make it easy to add 1: `Add1 = >::Output`
pub type Add1<A> = <A as Add<crate::bit::B1>>::Output;
/// Alias to make it easy to subtract 1: `Sub1 = >::Output`
pub type Sub1<A> = <A as Sub<crate::bit::B1>>::Output;

/// Alias to make it easy to multiply by 2. `Double = Shleft`
pub type Double<A> = Shleft<A, crate::bit::B1>;

/// Alias to make it easy to square. `Square = >::Output`
pub type Square<A> = <A as Mul>::Output;
/// Alias to make it easy to cube. `Cube =  as Mul>::Output`
pub type Cube<A> = <Square<A> as Mul<A>>::Output;

/// Alias for the associated type of `SquareRoot`: `Sqrt = ::Output`
pub type Sqrt<A> = <A as SquareRoot>::Output;

/// Alias for the associated type of `Cmp`: `Compare = >::Output`
pub type Compare<A, B> = <A as Cmp<B>>::Output;

/// Alias for the associated type of `Len`: `Length = ::Output`
pub type Length<T> = <T as Len>::Output;

/// Alias for the associated type of `FoldAdd`: `FoldSum = ::Output`
pub type FoldSum<A> = <A as FoldAdd>::Output;

/// Alias for the associated type of `FoldMul`: `FoldProd = ::Output`
pub type FoldProd<A> = <A as FoldMul>::Output;

/// Alias for the associated type of `Min`: `Minimum = >::Output`
pub type Minimum<A, B> = <A as Min<B>>::Output;

/// Alias for the associated type of `Max`: `Maximum = >::Output`
pub type Maximum<A, B> = <A as Max<B>>::Output;

use crate::type_operators::{
    IsEqual, IsGreater, IsGreaterOrEqual, IsLess, IsLessOrEqual, IsNotEqual,
};
/// Alias for the associated type of `IsLess`: `Le = >::Output`
pub type Le<A, B> = <A as IsLess<B>>::Output;
/// Alias for the associated type of `IsEqual`: `Eq = >::Output`
pub type Eq<A, B> = <A as IsEqual<B>>::Output;
/// Alias for the associated type of `IsGreater`: `Gr = >::Output`
pub type Gr<A, B> = <A as IsGreater<B>>::Output;
/// Alias for the associated type of `IsGreaterOrEqual`:
/// `GrEq = >::Output`
pub type GrEq<A, B> = <A as IsGreaterOrEqual<B>>::Output;
/// Alias for the associated type of `IsLessOrEqual`: `LeEq = >::Output`
pub type LeEq<A, B> = <A as IsLessOrEqual<B>>::Output;
/// Alias for the associated type of `IsNotEqual`: `NotEq = >::Output`
pub type NotEq<A, B> = <A as IsNotEqual<B>>::Output;
/// Alias for the associated type of `Logarithm2`: `Log2 = ::Output`
pub type Log2<A> = <A as Logarithm2>::Output;

二、主要功能

1. 操作符别名：为各种trait的关联类型Output创建了更简洁的别名，使得类型操作更直观。

2. 类型级别计算：支持在编译时进行各种数学和逻辑运算。

三、别名分类

1. 位运算

• And: 位与运算

• Or: 位或运算

• Xor: 位异或运算

2. 位移运算

• Shleft: 左移

• Shright: 右移

3. 算术运算

• Sum: 加法

• Diff: 减法

• Prod: 乘法

• Quot: 除法

• Mod: 取模

• PartialQuot: 部分除法

• Negate: 取负

• AbsVal: 绝对值

• Exp: 幂运算

四、特殊运算

• Gcf: 最大公约数

• Add1, Sub1: 加1/减1

• Double: 乘以2（通过左移1位实现）

• Square, Cube: 平方和立方

• Sqrt: 平方根

五、比较运算

• Compare: 比较

• Le, Eq, Gr, GrEq, LeEq, NotEq: 各种比较操作的结果

六、其他

• Length: 长度

• FoldSum, FoldProd: 折叠求和/求积

• Minimum, Maximum: 最小/最大值

• Log2: 以2为底的对数

七、使用示例

如文档注释中所示，使用这些别名可以简化类型操作：

type X = <P7 as Mul<P5>>::Output;  // 原始写法
type Y = Prod<P7, P5>;             // 使用别名后的写法

这些别名使得在类型级别进行数学运算更加直观和简洁，同时库还提供了op!宏可以进一步简化操作。

typenum库的这种设计使得Rust能够在编译时进行复杂的类型计算，常用于需要编译时确定大小的场景，如数组长度、泛型常量等。