"incomplete" generic impls of proper divisors, in Rust

divisors.rs

#![warn(clippy::pedantic, clippy::nursery)]

use core::iter::successors;
use num_integer::{Integer, Roots}; //0.1

pub fn divisors_fast<T: Integer + Roots + Clone>(x: &T) -> Vec<T> {
    let sq = x.sqrt();
    let mut divs = Vec::new();

    let n1 = T::one();
    let n2 = n1.clone() + n1;
    let mut i = n2;
    while i <= sq {
        if x.is_multiple_of(&i) {
            divs.push(i.clone());
        }
        // to-do: skip evens if x isn't even
        i.inc();
    }
    drop(i);

    for d in divs
        .clone()
        .into_iter()
        .rev()
        // if perfect square, then avoid dupe
        .skip(usize::from(sq.clone() * sq == *x))
    {
        divs.push(x.clone() / d.clone());
    }
    divs
}

pub fn divisors_iter<T>(x: &T) -> impl Iterator<Item = T> + '_
where
    T: Integer + Clone + 'static,
{
    let n1 = T::one();
    let n2 = n1.clone() + n1.clone();
    let n3 = n1.clone() + n2.clone();

    successors(if *x > n3 { Some(n2) } else { None }, move |i| {
        let i = i.clone() + n1.clone();
        if i < *x {
            Some(i)
        } else {
            None
        }
    })
    .filter(|i| x.is_multiple_of(i))
}

fn main() {
    for i in 0..=u8::MAX {
        let f = divisors_fast(&i);
        let t: Vec<_> = divisors_iter(&i).collect();
        assert_eq!(f, t);
        println!("{f:?}");
    }
}