//! # Rational Numbers (fractions)
//!
//! Traits to implement:
//! * Add
//! * AddAssign
//! * Div
//! * DivAssign
//! * Mul
//! * MulAssign
//! * Neg
//! * Sub
//! * SubAssign

use crate::num::*;
use std::ops::{Mul, Neg};

#[derive(Debug, Default, Copy, Clone, Eq, PartialEq)]
pub struct Frac<T: Unsigned = usize> {
    numer: T,
    denom: T,
    sign: Sign,
}

impl<T: Unsigned> Frac<T> {
    /// Create a new rational number
    pub fn new(n: T, d: T) -> Self {
        if d.is_zero() {
            panic!("Fraction can not have a zero denominator");
        }

        Frac {
            numer: n,
            denom: d,
            sign: Sign::Positive,
        }
        .reduce()
    }

    pub fn new_neg(n: T, d: T) -> Self {
        let mut frac = Frac::new(n, d);
        frac.sign = Sign::Negative;

        frac
    }

    fn reduce(mut self) -> Self {
        let gcd = T::gcd(self.numer, self.denom);
        self.numer /= gcd;
        self.denom /= gcd;

        self
    }
}

macro_rules! impl_mul {
    ($( $Type: ty ),* ) => {
        $(
            impl Mul for Frac<$Type> {
                type Output = Self;

                fn mul(self, rhs: Self) -> Self {
                    let numer = self.numer * rhs.numer;
                    let denom = self.denom * rhs.denom;

                    // Figure out the sign
                    if self.sign != rhs.sign {
                        Self::new_neg(numer, denom)
                    } else {
                        Self::new(numer, denom)
                    }
                }
            }
        )*
    };
}
impl_mul!(u8, u16, u32, u64, usize, u128);

impl<T: Unsigned> Neg for Frac<T> {
    type Output = Self;

    fn neg(self) -> Self::Output {
        let mut out = self.clone();
        out.sign = !self.sign;

        out
    }
}

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

    #[test]
    fn mul_test() {
        let frac1 = Frac::new(1u8, 3u8);
        let frac2 = Frac::new(2u8, 3u8);

        let expected = Frac::new(2u8, 9u8);

        assert_eq!(frac1 * frac2, expected);
    }
}