How do I use integer number literals when using generic types?

Many things are going wrong here:

1. As Shepmaster says, 0 and 1 cannot be converted to everything implementing Integer. Use Zero::zero and One::one instead.
2. 10 can definitely not be converted to anything implementing Integer, you need to use NumCast for that
3. a /= b is not sugar for a = a / b but an separate trait that Integer does not require.
4. -x is an unary operation which is not part of Integer but requires the Neg trait (since it only makes sense for signed types).

Here's an implementation. Note that you need a bound on Neg, to make sure that it results in the same type as T

extern crate num;

use num::{Integer, NumCast};
use std::ops::Neg;

fn int_length<T>(mut x: T) -> u8
where
    T: Integer + Neg<Output = T> + NumCast,
{
    if x == T::zero() {
        return 1;
    }

    let mut length = 0;
    if x < T::zero() {
        length += 1;
        x = -x;
    }

    while x > T::zero() {
        x = x / NumCast::from(10).unwrap();
        length += 1;
    }

    length
}

fn main() {
    println!("{}", int_length(45));
    println!("{}", int_length(-45));
}

The problem is that the Integer trait can be implemented by anything. For example, you could choose to implement it on your own struct! There wouldn't be a way to convert the literal 0 or 1 to your struct. I'm too lazy to show an example of implementing it, because there's 10 or so methods. ^_^

num::Zero and num::One

This is why Zero::zero and One::one exist. You can (very annoyingly) create all the other constants from repeated calls to those.

use num::{One, Zero}; // 0.4.0

fn three<T>() -> T
where
    T: Zero + One,
{
    let mut three = Zero::zero();
    for _ in 0..3 {
        three = three + One::one();
    }
    three
}

From and Into

You can also use the From and Into traits to convert to your generic type:

use num::Integer; // 0.4.0
use std::ops::{DivAssign, Neg};

fn int_length<T>(mut x: T) -> u8
where
    T: Integer + Neg<Output = T> + DivAssign,
    u8: Into<T>,
{
    let zero = 0.into();
    if x == zero {
        return 1;
    }

    let mut length = 0u8;
    if x < zero {
        length += 1;
        x = -x;
    }

    while x > zero {
        x /= 10.into();
        length += 1;
    }

    length
}

fn main() {
    println!("{}", int_length(45));
    println!("{}", int_length(-45));
}

See also:

• How do I use floating point number literals when using generic types?