expected struct `Vec3d`, found type parameter `u32` when implmenting the Mul trait for a custom struct - rust

Question

I am trying to implement the Mul trait for the Vec3d struct. I want the mul function to multiply each element of Vec3d by a number and return a Vec3d. However I am getting faced with this error:
error[E0053]: method `mul` has an incompatible type for trait
--> src\vec_3d.rs:26:21
|
23 | impl<u32> Mul for Vec3d<u32> {
| --- this type parameter
...
26 | fn mul(self, t: u32) -> Self::Output {
| ^^^
| |
| expected struct `Vec3d`, found type parameter `u32`
| help: change the parameter type to match the trait: `Vec3d<u32>`
|
= note: expected fn pointer `fn(Vec3d<_>, Vec3d<u32>) -> Vec3d<_>`
found fn pointer `fn(Vec3d<_>, u32) -> Vec3d<_>`
My code looks like this:
use std::ops::Add;
use std::ops::Mul;
#[derive(Debug, Copy, Clone, PartialEq, Eq)]
pub struct Vec3d<T> {
pub x: T,
pub y: T,
pub z: T,
}
impl<u32> Mul for Vec3d<u32> {
type Output = Self;
fn mul(self, t: u32) -> Self::Output {
Self {
x: self.x * t,
y: self.x * t,
z: self.x * t,
}
}
}
I had this originally with the generic type parameter T:
impl<T: Mul<Output = T>> Mul for Vec3d<T> {
type Output = Self;
fn mul(self, t: T) -> Self::Output {
Self {
x: self.x * t,
y: self.x * t,
z: self.x * t,
}
}
}
I have seen this be done the same way in some examples and other questions. What is wrong and how I can implement this the correct way?

Answer 1

This is nearly the same as the example on the Mul documentation: Multiplying vectors by scalars as in linear algebra
Mul has a default generic, which you can see in the trait definition:
pub trait Mul<Rhs = Self> {
This offers convenience since most implementers of Mul will be multiplying against Self. You aren't, so you need to specify the generic:
impl Mul<u32> for Vec3d<u32> {
type Output = Self;
fn mul(self, t: u32) -> Self::Output {
Self {
x: self.x * t,
y: self.y * t,
z: self.z * t,
}
}
}
To make this fully generic, you might try this:
impl<T: Mul<Output = T>> Mul<T> for Vec3d<T>
However, since you're using a single T 3 times, you would need to restrict it to Clone or Copy. The usual way to get around this is to implement Mul for references:
impl<'a, T> Mul<&'a T> for Vec3d<T>
where
T: Mul<&'a T, Output = T>,
{
type Output = Self;
fn mul(self, t: &'a T) -> Self::Output {
Self {
x: self.x * t,
y: self.y * t,
z: self.z * t,
}
}
}
Then you probably want a non-reference version for when the type implements Copy:
impl<T> Mul<T> for Vec3d<T>
where
T: Mul<Output = T> + Copy,
{
type Output = Self;
fn mul(self, t: T) -> Self::Output {
Self {
x: self.x * t,
y: self.y * t,
z: self.z * t,
}
}
}
But even better, you can do both of those in one impl:
impl<T, R> Mul<R> for Vec3d<T>
where
R: Copy,
T: Mul<R, Output = T>,
{
type Output = Self;
fn mul(self, t: R) -> Self::Output {
Self {
x: self.x * t,
y: self.y * t,
z: self.z * t,
}
}
}
When R is &T you cover the first impl, and when R is T and Copy you cover the second impl. & references are always Copy.
Another common thing to do is implement Mul for every integer type, which allows you more control over the implementation, for example if you wanted to optimize them for certain sized integers.