【unitrix数间混合计算】2.20 比较计算（cmp.rs)

一、源码

这段代码是用Rust实现的一个类型级别的二进制数比较系统，它通过类型系统在编译期完成数值比较。

use crate::number::{
    Z0, O, I, Bin, BDecimal, BFrac, Negative, Greater, Less, Equal,
    Bit, Ord, BinPos, BinUnsigned, BinInt, BinNonZeroFrac, BinFrac,
};

// ========== 核心特征 ==========
/// 类型比较（类似 `core::cmp::Ord::cmp`）
pub trait Cmp<Lhs, Rhs> where Self: Ord { 
    type Output: Ord;
}

// ========== 默认实现 ==========
impl<Lhs, Rhs> Cmp<Lhs, Rhs> for Greater { type Output = Greater; }
impl<Lhs, Rhs> Cmp<Lhs, Rhs> for Less    { type Output = Less;    }

// ========== 位比较 ==========
impl Cmp<O, O> for Equal { type Output = Equal;  }
impl Cmp<O, I> for Equal { type Output = Less;   }
impl Cmp<I, O> for Equal { type Output = Greater; }
impl Cmp<I, I> for Equal { type Output = Equal;  }

// ========== 整数比较 ==========
// -- 零比较 --
impl Cmp<Z0, Z0> for Equal { type Output = Equal; }
impl<P: BinPos> Cmp<Z0, P> for Equal          { type Output = Less;    }
impl<P: BinPos> Cmp<Z0, Negative<P>> for Equal { type Output = Greater; }

// -- 正数比较 --
impl<P: BinPos> Cmp<P, Z0> for Equal { type Output = Greater; }
impl<H1, L1, H2, L2> Cmp<Bin<H1, L1>, Bin<H2, L2>> for Equal
where
    H1: BinUnsigned, L1: Bit, H2: BinUnsigned, L2: Bit,
    Bin<H1, L1>: BinPos, Bin<H2, L2>: BinPos,
    Self: Cmp<H1, H2>,
    <Self as Cmp<H1, H2>>::Output: Cmp<L1, L2>,
{
    type Output = <<Self as Cmp<H1, H2>>::Output as Cmp<L1, L2>>::Output;
}
impl<P1: BinPos, P2: BinPos> Cmp<P1, Negative<P2>> for Equal { type Output = Greater; }

// -- 负数比较 --
impl<P: BinPos> Cmp<Negative<P>, Z0> for Equal { type Output = Less; }
impl<P1: BinPos, P2: BinPos> Cmp<Negative<P1>, P2> for Equal { type Output = Less; }
impl<P1: BinPos, P2: BinPos> Cmp<Negative<P1>, Negative<P2>> for Equal
where Self: Cmp<P2, P1> {
    type Output = <Self as Cmp<P2, P1>>::Output;
}

// ========== 小数比较 ==========
impl<H1, L1, H2, L2> Cmp<BDecimal<H1, L1>, BDecimal<H2, L2>> for Equal
where
    H1: BinInt, L1: BinFrac, H2: BinInt, L2: BinFrac,
    Equal: Cmp<H1, H2>,
    <Equal as Cmp<H1, H2>>::Output: Cmp<L1, L2>,
{
    type Output = <<Equal as Cmp<H1, H2>>::Output as Cmp<L1, L2>>::Output;
}

// ========== 纯小数部分比较 ==========
impl<H, L> Cmp<Z0, BFrac<H, L>> for Equal 
where H: Bit, L: BinFrac, BFrac<H, L>: BinNonZeroFrac {
    type Output = Less;
}
impl<H, L> Cmp<BFrac<H, L>, Z0> for Equal 
where H: Bit, L: BinFrac, BFrac<H, L>: BinNonZeroFrac {
    type Output = Greater;
}
impl<H1, L1, H2, L2> Cmp<BFrac<H1, L1>, BFrac<H2, L2>> for Equal
where
    H1: Bit, L1: BinNonZeroFrac, H2: Bit, L2: BinNonZeroFrac,
    Equal: Cmp<H1, H2>,
    <Equal as Cmp<H1, H2>>::Output: Cmp<L1, L2>,
{
    type Output = <<Equal as Cmp<H1, H2>>::Output as Cmp<L1, L2>>::Output;
}

二、核心特征

pub trait Cmp<Lhs, Rhs> where Self: Ord { 
    type Output: Ord;
}

定义了一个核心特征Cmp，用于比较两个类型Lhs和Rhs。Output关联类型表示比较结果，可以是Greater、Less或Equal。

三、默认实现

impl<Lhs, Rhs> Cmp<Lhs, Rhs> for Greater { type Output = Greater; }
impl<Lhs, Rhs> Cmp<Lhs, Rhs> for Less    { type Output = Less;    }

为Greater和Less提供了默认实现，直接返回自身。

四、位比较

impl Cmp<O, O> for Equal { type Output = Equal; }
impl Cmp<O, I> for Equal { type Output = Less; }
impl Cmp<I, O> for Equal { type Output = Greater; }
impl Cmp<I, I> for Equal { type Output = Equal; }

比较二进制位O(0)和I(1)的大小关系。

五、整数比较

1. 零比较

impl Cmp<Z0, Z0> for Equal { type Output = Equal; }
impl<P: BinPos> Cmp<Z0, P> for Equal { type Output = Less; }
impl<P: BinPos> Cmp<Z0, Negative<P>> for Equal { type Output = Greater; }

比较零(Z0)与其他数的关系：零等于零，零小于任何正数，零大于任何负数。
2. 正数比较

impl<P: BinPos> Cmp<P, Z0> for Equal { type Output = Greater; }
impl<H1, L1, H2, L2> Cmp<Bin<H1, L1>, Bin<H2, L2>> for Equal
where ...
{
    type Output = ...;
}

正数比较：正数大于零，两个正数的比较通过递归比较高位和低位。
3. 负数比较

impl<P: BinPos> Cmp<Negative<P>, Z0> for Equal { type Output = Less; }
impl<P1: BinPos, P2: BinPos> Cmp<Negative<P1>, P2> for Equal { type Output = Less; }
impl<P1: BinPos, P2: BinPos> Cmp<Negative<P1>, Negative<P2>> for Equal
where ...
{
    type Output = ...;
}

负数比较：负数小于零和任何正数，两个负数的比较转换为比较它们的绝对值（正数部分）。

六、小数比较

impl<H1, L1, H2, L2> Cmp<BDecimal<H1, L1>, BDecimal<H2, L2>> for Equal
where ...
{
    type Output = ...;
}

小数比较：先比较整数部分，如果相等再比较小数部分。

七、纯小数比较

impl<H, L> Cmp<Z0, BFrac<H, L>> for Equal ... { type Output = Less; }
impl<H, L> Cmp<BFrac<H, L>, Z0> for Equal ... { type Output = Greater; }
impl<H1, L1, H2, L2> Cmp<BFrac<H1, L1>, BFrac<H2, L2>> for Equal
where ...
{
    type Output = ...;
}

纯小数比较：零小于任何纯小数，纯小数大于零，两个纯小数的比较先比较整数部分再比较小数部分。

八、总结

这个系统通过Rust的类型系统实现了编译期的数值比较，包括：

• 二进制位比较

• 整数比较（正数、零、负数）

• 小数比较

• 纯小数比较

所有比较操作都在编译期完成，不产生运行时开销。这种技术常用于需要高性能计算的领域或嵌入式系统编程。