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【PhysUnits】13 改进减法(sub.rs)

ops 2025/7/21 13:55:16

源码

这段代码实现了一个类型级别的二进制数减法系统，通过 Rust 的特质(trait)系统在编译期完成计算。

use core::ops::{Neg, Not, Sub};
use super::basic::{B0, B1, Z0, N1, Integer, NonZero, NonNegOne};
use super::add1::Add1;
use super::sub1::Sub1;
use super::standardization::{IfB0, IfB1};// ==================== 带借位减法 Trait ====================
/// 带借位减法运算
/// Subtraction with borrow operation
///
/// 表示 a - b - 1 的运算 (相当于 a - (b + 1))
/// Represents the operation of a - b - 1 (equivalent to a - (b + 1))
pub trait SubWithBorrow<Rhs> {type Output;
}// ==================== 带借位减法实现 ====================// Z0 - I (带借位) = !I (!I+1-1)
impl<I:Integer + Not> SubWithBorrow<I> for Z0 {type Output = I::Output;
}// I - Z0 (带借位) = I-1
impl<I: NonZero + Sub1> SubWithBorrow<Z0> for I{type Output = I::Output;
}// N1 - I (带借位,非0) = !I-1 (即N1+（!I+1）-1)
impl<I: NonZero + Not> SubWithBorrow<I> for N1
where<I as Not>::Output:Sub1,
{type Output = <I::Output as Sub1>::Output;
}// I - N1 (带借位) = I
impl<I: NonZero + NonNegOne> SubWithBorrow<N1> for I {type Output = I;
}// B0 - B0 (带借位)
impl<H1: Integer + SubWithBorrow<H2>, H2: Integer> SubWithBorrow<B0<H2>> for B0<H1>
whereH1::Output: IfB1,
{type Output = <H1::Output as IfB1>::Output;
}// B0 - B1 (带借位)
impl<H1: Integer + SubWithBorrow<H2>, H2: Integer> SubWithBorrow<B1<H2>> for B0<H1>
where<H1 as SubWithBorrow<H2>>::Output: IfB0,
{type Output = <H1::Output as IfB0>::Output;
}// B1 - B0 (带借位)
impl<H1: Integer + Sub<H2>, H2: Integer> SubWithBorrow<B0<H2>> for B1<H1>
where<H1 as Sub<H2>>::Output: IfB0,
{type Output = <H1::Output as IfB0>::Output;
}// B1 - B1 (带借位)
impl<H1: Integer + SubWithBorrow<H2>, H2: Integer> SubWithBorrow<B1<H2>> for B1<H1>
where<H1 as SubWithBorrow<H2>>::Output: IfB1,
{type Output = <H1::Output as IfB1>::Output;
}// ==================== 标准减法实现 (Sub trait) ====================// Z0 - I = -I
impl<I: Integer + Neg> Sub<I> for Z0 {type Output = I::Output;fn sub(self, _: I) -> Self::Output {Self::Output::new()}
}// I - Z0 = I,I=N1、B0、B1
impl Sub<Z0> for N1 {type Output = N1;fn sub(self, _: Z0) -> Self::Output {N1::new()}
}
impl<H: Integer> Sub<Z0> for B0<H> {type Output = B0<H>;fn sub(self, _: Z0) -> Self::Output {B0::new()}
}
impl<H: Integer> Sub<Z0> for B1<H> {type Output = B1<H>;fn sub(self, _: Z0) -> Self::Output {B1::new()}
}// N1 - 非0 = ！I
impl<I: NonZero + Not> Sub<I> for N1 {type Output = I::Output;fn sub(self, _: I) -> Self::Output {Self::Output::new()}
}// B0、B1 - N1
impl<H: NonNegOne> Sub<N1> for B0<H> {type Output = B1<H>;fn sub(self, _: N1) -> Self::Output {Self::Output::new()}
}impl Sub<N1> for B0<N1> {type Output = N1;fn sub(self, _: N1) -> Self::Output {N1::new()}
}// B1<H> - N1 = B0<H>
impl<H: Integer + Add1> Sub<N1> for B1<H> {type Output = B0<H::Output>;fn sub(self, _: N1) -> Self::Output {Self::Output::new()}
}// B0 - B0
impl<H1: Integer + Sub<H2>, H2: Integer> Sub<B0<H2>> for B0<H1>
where<H1 as Sub<H2>>::Output: IfB0,
{type Output = <H1::Output as IfB0>::Output;fn sub(self, _: B0<H2>) -> Self::Output {Self::Output::new()}
}// B0 - B1 (需要借位)
impl<H1: Integer + SubWithBorrow<H2>, H2: Integer> Sub<B1<H2>> for B0<H1>
where<H1 as SubWithBorrow<H2>>::Output: IfB1,
{type Output = <H1::Output as IfB1>::Output;fn sub(self, _: B1<H2>) -> Self::Output {Self::Output::new()}
}// B1 - B0
impl<H1: Integer + Sub<H2>, H2: Integer> Sub<B0<H2>> for B1<H1>
where<H1 as Sub<H2>>::Output: IfB1,
{type Output = <H1::Output as IfB1>::Output;fn sub(self, _: B0<H2>) -> Self::Output {Self::Output::new()}
}// B1 - B1
impl<H1: Integer + Sub<H2>, H2: Integer> Sub<B1<H2>> for B1<H1>
where<H1 as Sub<H2>>::Output: IfB0,
{type Output = <H1::Output as IfB0>::Output;fn sub(self, _: B1<H2>) -> Self::Output {Self::Output::new()}
}

二、基本概念

类型表示：

Z0：表示数字 0
B0：表示二进制数末尾是 0 的数（相当于 H << 1）
B1：表示二进制数末尾是 1 的数（相当于 (H << 1) + 1）
N1：表示 -1

核心特质：

SubWithBorrow：带借位的减法（计算 a - b - 1）
Sub：标准减法（计算 a - b）

三、带借位减法实现 (SubWithBorrow)

零减去任何数：

impl<I: Integer + Not> SubWithBorrow<I> for Z0 {type Output = I::Output;  // !I
}

0 - I - 1 = -(I + 1) = !I（因为 !I 在二进制补码中表示 -I - 1）

任何数减去零：

impl<I: NonZero + Sub1> SubWithBorrow<Z0> for I {type Output = I::Output;  // I - 1
}

I - 0 - 1 = I - 1

-1 减去任何非零数：

impl<I: NonZero + Not> SubWithBorrow<I> for N1 {type Output = <I::Output as Sub1>::Output;  // !I - 1
}

-1 - I - 1 = -(I + 2) = !I - 1

任何数减去 -1：

impl<I: NonZero + NonNegOne> SubWithBorrow<N1> for I {type Output = I;  // I
}

I - (-1) - 1 = I

二进制数之间的带借位减法：
处理不同组合的二进制数相减（B0/B1 的各种组合），递归处理高位并考虑借位情况。

四、标准减法实现 (Sub)

零减去任何数：

impl<I: Integer + Neg> Sub<I> for Z0 {type Output = I::Output;  // -I
}

任何数减去零：

impl Sub<Z0> for N1 {type Output = N1;  // -1
}
impl<H: Integer> Sub<Z0> for B0<H> {type Output = B0<H>;  // 保持原值
}
impl<H: Integer> Sub<Z0> for B1<H> {type Output = B1<H>;  // 保持原值
}

-1 减去任何非零数：

impl<I: NonZero + Not> Sub<I> for N1 {type Output = I::Output;  // !I
}

-1 - I = -(I + 1) = !I

二进制数减去 -1：

impl<H: NonNegOne> Sub<N1> for B0<H> {type Output = B1<H>;  // 相当于加1
}
impl Sub<N1> for B0<N1> {type Output = N1;  // 特殊情况处理
}
impl<H: Integer + Add1> Sub<N1> for B1<H> {type Output = B0<H::Output>;  // 相当于加1后变为B0
}