typerat 0.0.4

Type-level rational numbers based on `typenum`.
Documentation 
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use crate::{Denominator, Numerator, Q};
use core::ops::{Add, Mul};
use typenum::{Gcd, Gcf, PartialDiv, Prod, Sum};

pub trait PrivateAddHelper<Rhs> {
    type Output;
}

impl<Nl, Dl, Nr, Dr, No, Do> PrivateAddHelper<Q<Nr, Dr>> for Q<Nl, Dl>
where
    Nl: Numerator<Dl> + Mul<Dr>,
    Dl: Denominator + Mul<Dr>,
    Nr: Numerator<Dr> + Mul<Dl>,
    Dr: Denominator,
    No: Numerator<Do>,
    Do: Denominator,
    Prod<Nl, Dr>: Add<Prod<Nr, Dl>>,
    Sum<Prod<Nl, Dr>, Prod<Nr, Dl>>: Gcd<Prod<Dl, Dr>>
        + PartialDiv<Gcf<Sum<Prod<Nl, Dr>, Prod<Nr, Dl>>, Prod<Dl, Dr>>, Output = No>,
    Prod<Dl, Dr>: PartialDiv<Gcf<Sum<Prod<Nl, Dr>, Prod<Nr, Dl>>, Prod<Dl, Dr>>, Output = Do>,
{
    type Output = Q<No, Do>;
}

impl<Nl, Dl, Nr, Dr, No, Do> Add<Q<Nr, Dr>> for Q<Nl, Dl>
where
    Self: PrivateAddHelper<Q<Nr, Dr>, Output = Q<No, Do>>,
    Nl: Numerator<Dl>,
    Dl: Denominator,
    Nr: Numerator<Dr>,
    Dr: Denominator,
    No: Numerator<Do>,
    Do: Denominator,
{
    type Output = Q<No, Do>;

    fn add(self, rhs: Q<Nr, Dr>) -> Self::Output {
        let _ = rhs;
        Self::Output::new()
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    use typenum::consts::*;

    #[test]
    fn test_add() {
        // zero + zero
        assert!(Q::<Z0>::new() + Q::<Z0>::new() == Q::<Z0>::new());

        // zero + positive
        assert!(Q::<Z0>::new() + Q::<P1, P2>::new() == Q::<P1, P2>::new());

        // zero + negative
        assert!(Q::<Z0>::new() + Q::<N1, P2>::new() == Q::<N1, P2>::new());

        // positive + zero
        assert!(Q::<P1, P2>::new() + Q::<Z0>::new() == Q::<P1, P2>::new());

        // positive + positive
        assert!(Q::<P1, P2>::new() + Q::<P1, P3>::new() == Q::<P5, P6>::new());

        // positive + negative
        assert!(Q::<P1, P2>::new() + Q::<N1, P3>::new() == Q::<P1, P6>::new());

        // negative + zero
        assert!(Q::<N1, P2>::new() + Q::<Z0>::new() == Q::<N1, P2>::new());

        // negative + positive
        assert!(Q::<N1, P2>::new() + Q::<P1, P3>::new() == Q::<N1, P6>::new());

        // negative + negative
        assert!(Q::<N1, P2>::new() + Q::<N1, P3>::new() == Q::<N5, P6>::new());
    }
}