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【PhysUnits】15.6 引入P1后的左移运算(shl.rs)

news 来源：原创 2025/6/2 14:38:08

一、源码

代码实现了Rust的类型级二进制数的左移运算(<<)，使用类型系统在编译期进行计算。

use super::basic::{Z0, P1, N1, B0, B1, NonZero, NonOne, Unsigned};
use super::sub1::Sub1;
use core::ops::Shl;// ==================== 左移运算（<<） ====================
// Z0 << U
impl<R: Unsigned> Shl<R> for Z0 {type Output = Z0;fn shl(self, _: R) -> Self::Output {Z0  // 0 << n = 0}
}// P1 << U
impl Shl<Z0> for P1 {// P1 << Z0type Output = Self;fn shl(self, _: Z0) -> Self::Output {self}
}impl Shl<P1> for P1 {// P1 << P1type Output = B0<P1>;fn shl(self, _: P1) -> Self::Output {B0::new()}
}impl<R: Unsigned + NonZero + NonOne + Sub1> Shl<R> for P1
whereP1: Shl<<R as Sub1>::Output>
{// P1 << 超过1的数type Output = B0<<P1 as Shl<R::Output>>::Output>;fn shl(self, _: R) -> Self::Output {B0::new()}
}// N1 << U
impl Shl<Z0> for N1 {// N1 << Z0type Output = Self;fn shl(self, _: Z0) -> Self::Output {self}
}impl Shl<P1> for N1 {// N1 << P1type Output = B0<N1>;fn shl(self, _: P1) -> Self::Output {B0::new()}
}impl<R: Unsigned + NonZero + NonOne + Sub1> Shl<R> for N1
whereN1: Shl<<R as Sub1>::Output>
{// P1 << 超过1的数type Output = B0<<N1 as Shl<R::Output>>::Output>;fn shl(self, _: R) -> Self::Output {B0::new()}
}// B0 << U
impl<H: NonZero> Shl<Z0> for B0<H> {// B0 << Z0type Output = Self;fn shl(self, _: Z0) -> Self::Output {self}
}impl<H: NonZero> Shl<P1> for B0<H> {// B0 << P1type Output = B0<B0<H>>;fn shl(self, _: P1) -> Self::Output {B0::new()}
}impl<H: NonZero, R: Unsigned + NonZero + NonOne + Sub1> Shl<R> for B0<H>
whereB0<H>: Shl<<R as Sub1>::Output>
{// B0 << 超过1的数type Output = B0<<B0<H> as Shl<R::Output>>::Output>;fn shl(self, _: R) -> Self::Output {B0::new()}
}// B1 << U
impl<H: NonZero> Shl<Z0> for B1<H> {// B1 << Z0type Output = Self;fn shl(self, _: Z0) -> Self::Output {self}
}impl<H: NonZero> Shl<P1> for B1<H> {// B1 << P1type Output = B0<B1<H>>;fn shl(self, _: P1) -> Self::Output {B0::new()}
}impl<H: NonZero, R: Unsigned + NonZero + NonOne + Sub1> Shl<R> for B1<H>
whereB1<H>: Shl<<R as Sub1>::Output>
{// B1 << 超过1的数type Output = B0<<B1<H> as Shl<R::Output>>::Output>;fn shl(self, _: R) -> Self::Output {B0::new()}
}

二、类型和trait引入

use super::basic::{Z0, P1, N1, B0, B1, NonZero, NonOne, Unsigned};
use super::sub1::Sub1;
use core::ops::Shl;

从父模块引入基础类型：
- Z0: 表示0
- P1: 表示+1
- N1: 表示-1
- B0, B1: 二进制位(0和1)
- 标记trait: NonZero, NonOne, Unsigned
Sub1: 减1操作
Shl: Rust的左移运算符trait

三、零的左移实现

impl<R: Unsigned> Shl<R> for Z0 {type Output = Z0;fn shl(self, _: R) -> Self::Output {Z0  // 0 << n = 0}
}

任何数左移0还是0
适用于所有无符号类型R

四、正一(P1)的左移

impl Shl<Z0> for P1 { // P1 << 0 = P1type Output = Self;fn shl(self, _: Z0) -> Self::Output { self }
}impl Shl<P1> for P1 { // P1 << 1 = B0<P1> (即10，二进制表示)type Output = B0<P1>;fn shl(self, _: P1) -> Self::Output { B0::new() }
}impl<R: Unsigned + NonZero + NonOne + Sub1> Shl<R> for P1
where P1: Shl<<R as Sub1>::Output> {type Output = B0<<P1 as Shl<R::Output>>::Output>;fn shl(self, _: R) -> Self::Output { B0::new() }
}

分三种情况处理：
- 移0位：保持不变
- 移1位：变成B0(二进制10)
- 移多位：递归处理

五、负一(N1)的左移

impl Shl<Z0> for N1 { ... }  // 同P1
impl Shl<P1> for N1 { ... }  // 同P1
impl<R: Unsigned + NonZero + NonOne + Sub1> Shl<R> for N1 { ... }  // 同P1

处理逻辑与P1完全相同

六、B0(二进制0)的左移

impl<H: NonZero> Shl<Z0> for B0<H> { ... }  // 移0位
impl<H: NonZero> Shl<P1> for B0<H> { ... }  // 移1位
impl<H: NonZero, R: Unsigned + NonZero + NonOne + Sub1> Shl<R> for B0<H> { ... }  // 移多位

在二进制数前补0：
- B0 << 1 = B0<B0>
- 递归处理多位移动

七、B1(二进制1)的左移

impl<H: NonZero> Shl<Z0> for B1<H> { ... }  // 移0位
impl<H: NonZero> Shl<P1> for B1<H> { ... }  // 移1位
impl<H: NonZero, R: Unsigned + NonZero + NonOne + Sub1> Shl<R> for B1<H> { ... }  // 移多位