rusty-numbers/src/rational.rs

//! # Rational Numbers (fractions)

use crate::num::Sign::*;
use crate::num::*;
use std::cmp::{Ord, Ordering, PartialOrd};
use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};

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

#[macro_export]
/// Create a [Frac](rational/struct.Frac.html) type with signed or unsigned number literals
///
/// Accepts:
///
/// ```no-run
/// // Fractions
/// frac!(1/3);
///
/// // Whole numbers
/// frac!(5u8);
///
/// // Whole numbers and fractions
/// frac!(1 1/2);
/// ```
macro_rules! frac {
    ($w:literal $n:literal / $d:literal) => {
        frac!($w) + frac!($n / $d)
    };
    ($n:literal / $d:literal) => {
        $crate::rational::Frac::new($n, $d)
    };
    ($w:literal) => {
        $crate::rational::Frac::new($w, 1)
    };
}

#[derive(Debug, Copy, Clone, PartialEq)]
enum FracOp {
    Addition,
    Subtraction,
    Other,
}

impl<T: Unsigned> Frac<T> {
    /// Create a new rational number from signed or unsigned arguments
    ///
    /// Generally, you will probably prefer to use the [frac!](../macro.frac.html) macro
    /// instead, as that is easier for mixed fractions and whole numbers
    pub fn new<N: Int<Un = T>>(n: N, d: N) -> Frac<T> {
        Self::new_unreduced(n, d).reduce()
    }

    /// Create a new rational number from signed or unsigned arguments
    /// where the resulting fraction is not reduced
    pub fn new_unreduced<N: Int<Un = T>>(n: N, d: N) -> Frac<T> {
        if d.is_zero() {
            panic!("Fraction can not have a zero denominator");
        }

        let mut sign = Positive;

        if n.is_neg() {
            sign = !sign;
        }

        if d.is_neg() {
            sign = !sign;
        }

        // Convert the possibly signed arguments to unsigned values
        let numer = n.to_unsigned();
        let denom = d.to_unsigned();

        Frac { numer, denom, sign }
    }

    /// Create a new rational from all the raw parts
    fn raw(n: T, d: T, s: Sign) -> Frac<T> {
        if d.is_zero() {
            panic!("Fraction can not have a zero denominator");
        }

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

    /// Determine the output sign given the two input signs
    fn get_sign(a: Self, b: Self, op: FracOp) -> Sign {
        if op == FracOp::Addition {
            return if a.sign == Positive && b.sign == Positive {
                Positive
            } else {
                Negative
            };
        }

        if a.sign != b.sign {
            if op == FracOp::Subtraction && b.sign == Negative {
                Positive
            } else {
                Negative
            }
        } else {
            Positive
        }
    }

    /// Convert the fraction to its simplest form
    fn reduce(mut self) -> Self {
        let gcd = T::gcd(self.numer, self.denom);
        self.numer /= gcd;
        self.denom /= gcd;

        self
    }
}

impl<T> PartialOrd for Frac<T>
where
    T: Unsigned + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Div<Output = T>,
{
    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
        Some(self.cmp(other))
    }
}

impl<T> Ord for Frac<T>
where
    T: Unsigned + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Div<Output = T>,
{
    fn cmp(&self, other: &Self) -> Ordering {
        if self.sign != other.sign {
            return if self.sign == Positive {
                Ordering::Greater
            } else {
                Ordering::Less
            };
        }

        if self.denom == other.denom {
            return self.numer.cmp(&other.numer);
        }

        let mut a = self.reduce();
        let mut b = other.reduce();

        if a.denom == b.denom {
            return a.numer.cmp(&b.numer);
        }

        let lcm = T::lcm(self.denom, other.denom);
        let x = lcm / self.denom;
        let y = lcm / other.denom;

        a.numer *= x;
        a.denom *= x;

        b.numer *= y;
        b.denom *= y;

        debug_assert_eq!(
            a.denom, b.denom,
            "Denominators should be equal here. \n{:#?}\n{:#?}\n{:?}\n{:?}",
            a, b, x, y
        );

        a.numer.cmp(&b.numer)
    }
}

impl<T> Mul for Frac<T>
where
    T: Unsigned + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Div<Output = T>,
{
    type Output = Self;

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

        Self::raw(numer, denom, sign)
    }
}

impl<T> MulAssign for Frac<T>
where
    T: Unsigned + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Div<Output = T>,
{
    fn mul_assign(&mut self, rhs: Self) {
        *self = self.clone() * rhs
    }
}

impl<T> Div for Frac<T>
where
    T: Unsigned + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Div<Output = T>,
{
    type Output = Self;

    fn div(self, rhs: Self) -> Self {
        let numer = self.numer * rhs.denom;
        let denom = self.denom * rhs.numer;
        let sign = Self::get_sign(self, rhs, FracOp::Other);

        Self::raw(numer, denom, sign)
    }
}

impl<T> DivAssign for Frac<T>
where
    T: Unsigned + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Div<Output = T>,
{
    fn div_assign(&mut self, rhs: Self) {
        *self = self.clone() / rhs
    }
}

impl<T> Add for Frac<T>
where
    T: Unsigned + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Div<Output = T>,
{
    type Output = Self;

    fn add(self, rhs: Self) -> Self::Output {
        let a = self;
        let b = rhs;

        // If the sign of one input differs,
        // subtraction is equivalent
        if a.sign == Negative && b.sign == Positive {
            return b - -a;
        } else if a.sign == Positive && b.sign == Negative {
            return a - -b;
        }

        // Find a common denominator if needed
        if a.denom != b.denom {
            // Let's just use the simplest method, rather than
            // worrying about reducing to the least common denominator
            let numer = (a.numer * b.denom) + (b.numer * a.denom);
            let denom = a.denom * b.denom;
            let sign = Self::get_sign(a, b, FracOp::Addition);

            return Self::raw(numer, denom, sign);
        }

        let numer = a.numer + b.numer;
        let denom = self.denom;
        let sign = Self::get_sign(a, b, FracOp::Addition);

        Self::raw(numer, denom, sign)
    }
}

impl<T> AddAssign for Frac<T>
where
    T: Unsigned + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Div<Output = T>,
{
    fn add_assign(&mut self, rhs: Self) {
        *self = self.clone() + rhs
    }
}

impl<T> Sub for Frac<T>
where
    T: Unsigned + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Div<Output = T>,
{
    type Output = Self;

    fn sub(self, rhs: Self) -> Self::Output {
        let a = self;
        let b = rhs;

        if a.sign == Positive && b.sign == Negative {
            return a + -b;
        } else if a.sign == Negative && b.sign == Positive {
            return -(b + -a);
        }

        if a.denom != b.denom {
            let (numer, overflowed) = (a.numer * b.denom).left_overflowing_sub(b.numer * a.denom);

            let denom = a.denom * b.denom;
            let sign = Self::get_sign(a, b, FracOp::Subtraction);
            let res = Self::raw(numer, denom, sign);
            return if overflowed { -res } else { res };
        }

        let (numer, overflowed) = a.numer.left_overflowing_sub(b.numer);

        let denom = a.denom;
        let sign = Self::get_sign(a, b, FracOp::Subtraction);
        let res = Self::raw(numer, denom, sign);

        if overflowed { -res } else { res }
    }
}

impl<T> SubAssign for Frac<T>
where
    T: Unsigned + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Div<Output = T>,
{
    fn sub_assign(&mut self, rhs: Self) {
        *self = self.clone() - rhs
    }
}

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

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

        out
    }
}

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

    #[test]
    fn mul_test() {
        let frac1 = frac!(1 / 3u8);
        let frac2 = frac!(2u8 / 3);

        let expected = frac!(2u8 / 9);

        assert_eq!(frac1 * frac2, expected);
    }

    #[test]
    fn add_test() {
        assert_eq!(frac!(5 / 6), frac!(1 / 3) + frac!(1 / 2), "1/3 + 1/2");
        assert_eq!(frac!(1 / 3), frac!(2 / 3) + -frac!(1 / 3), "2/3 + -1/3");
    }

    #[test]
    fn sub_test() {
        assert_eq!(4u8.left_overflowing_sub(2).0, 2u8);
        assert_eq!(0u8.left_overflowing_sub(2).0, 2u8);
        assert_eq!(frac!(1 / 6), frac!(1 / 2) - frac!(1 / 3), "1/2 - 1/3");
    }

    #[test]
    fn cmp_test() {
        assert!(-frac!(5 / 3) < frac!(1 / 10_000));
        assert!(frac!(1 / 10_000) > -frac!(10));
        assert!(frac!(1 / 3) < frac!(1 / 2));
        assert_eq!(frac!(1 / 2), frac!(3 / 6));
    }

    #[test]
    fn negative_fractions() {
        assert_eq!(-frac!(1 / 3), -frac!(2 / 3) + frac!(1 / 3), "-2/3 + 1/3");
        assert_eq!(frac!(1), frac!(1 / 3) - -frac!(2 / 3), "1/3 - -2/3");
        assert_eq!(-frac!(1), -frac!(2 / 3) - frac!(1 / 3), "-2/3 - +1/3");
        assert_eq!(-frac!(1), -frac!(2 / 3) + -frac!(1 / 3), "-2/3 + -1/3");
    }

    #[test]
    fn macro_test() {
        let frac1 = frac!(1 / 3);
        let frac2 = frac!(1u32 / 3);
        assert_eq!(frac1, frac2);

        let frac1 = -frac!(1 / 2);
        let frac2 = -frac!(1u32 / 2);
        assert_eq!(frac1, frac2);

        assert_eq!(frac!(3 / 2), frac!(1 1/2));
        assert_eq!(frac!(3 / 1), frac!(3));
    }
}