Add a method for computing the absolute difference between unsigned integers

[Centril]

See discussion in #62103 (comment).

[ExpHP]

I suggest not calling it abs_sub due to the confusion created by the (terribly misnamed) function on floats, whose tortured legacy continues to this day in num_traits::Signed.

[Centril]

@ExpHP abs_diff perhaps?

[leonardo-m]

abs_difference ?

[Centril]

What do you think about adding:

fn abs_difference<T: Sub<Output = T> + Ord>(x: T, y: T) -> T {
    if x < y {
        y - x
    } else {
        x - y
    }
}

instead of doing it on just the unsigned integer types?

[scalexm]

distance is a good name, I think, as it is the mathematical term for abs(x-y).

I dislike @Centril’s above generalization, as what it does is unrelated with the name of the function in most cases (the first thing that comes to mind is that something called an « absolute difference » should be a non-negative real number).

[HeroicKatora]

The term distance seems too generic from the standpoint of a mathematical motivation, it is also used in the context of very different metric spaces than the normed space induced by the L1-norm. I think 'absolute difference' hits the nail on the head and with the given prior art of abbreviations that would make abs_diff my clear favorite. Similar to abs, checked_sub and other functions it doesn't seem necessary to add it in another way than as a method.

[Toniman575]

Until that happens, I've found the easiest way to do this is:
let x = max(y, z) - min(y, z);

[orlp]

If no one has any objections I can make a pull request implementing the following functions:

fn abs_diff(slf: u8,  other: u8)  -> u8;
fn abs_diff(slf: u16, other: u16) -> u16;
fn abs_diff(slf: u32, other: u32) -> u32;
fn abs_diff(slf: u64, other: u64) -> u64;
fn abs_diff(slf: u128, other: u128) -> u128;
fn abs_diff(slf: usize, other: usize) -> usize;
fn abs_diff(slf: i8,  other: i8)  -> u8;
fn abs_diff(slf: i16, other: i16) -> u16;
fn abs_diff(slf: i32, other: i32) -> u32;
fn abs_diff(slf: i64, other: i64) -> u64;
fn abs_diff(slf: i128, other: i128) -> u128;
fn abs_diff(slf: isize, other: isize) -> usize;

where for unsigned types the implementation would be

fn abs_diff(slf: U, other: U)  -> U {
    if slf < other {
        other - slf
    } else {
        slf - other
    }
}

and for signed types

fn abs_diff(slf: I, other: I)  -> U {
    if slf < other {
        (other as U).wrapping_sub(slf as U)
    } else {
        (slf as U).wrapping_sub(other as U)
    }
}

Especially the latter is a useful contribution as it is somewhat non-trivial and tricky to write correctly as a user, if you are not intimately familiar with two's complement.