rusty-numbers/src/rational.rs

//! # Rational Numbers (fractions)

use core::cmp::{Ord, Ordering, PartialOrd};
use core::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};

use crate::num::Sign::{Negative, Positive};
use crate::num::{FracOp, Int, Sign, Unsigned};

/// Type representing a fraction
///
/// There are three basic constructors:
///
/// ```
/// use rusty_numbers::frac;
/// use rusty_numbers::rational::Frac;
///
/// // Macro
/// let reduced_macro = frac!(3 / 4);
///
/// // Frac::new (called by the macro)
/// let reduced = Frac::new(3, 4);
/// # assert_eq!(reduced_macro, reduced);
///
/// // Frac::new_unreduced
/// let unreduced = Frac::new_unreduced(4, 16);
/// ```
#[derive(Debug, Copy, Clone, Eq, PartialEq)]
pub struct Frac<T: Unsigned = usize> {
    numerator: T,
    denominator: T,
    sign: Sign,
}

/// Create a [Frac](rational/struct.Frac.html) type with signed or unsigned number literals
///
/// Example:
/// ```
/// use rusty_numbers::frac;
///
/// // Proper fractions
/// frac!(1 / 3);
///
/// // Improper fractions
/// frac!(4 / 3);
///
/// // Whole numbers
/// frac!(5u8);
///
/// // Whole numbers and fractions
/// frac!(1 1/2);
/// ```
#[macro_export]
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)
    };
}

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
    ///
    /// # Panics
    /// if `d` is 0, this constructor will panic
    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
    ///
    /// # Panics
    /// if `d` is 0, this constructor will panic
    pub fn new_unreduced<N: Int<Un = T>>(n: N, d: N) -> Frac<T> {
        assert!(!d.is_zero(), "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 numerator = n.to_unsigned();
        let denominator = d.to_unsigned();

        Frac {
            numerator,
            denominator,
            sign,
        }
    }

    /// Create a new, reduced rational from all the raw parts
    ///
    /// # Panics
    /// if `d` is 0, this constructor will panic
    fn raw(n: T, d: T, s: Sign) -> Frac<T> {
        assert!(!d.is_zero(), "Fraction can not have a zero denominator");

        Frac {
            numerator: n,
            denominator: d,
            sign: s,
        }
        .reduce()
    }

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

        // a - -b = c
        if op == FracOp::Subtraction && a.sign == Positive && b.sign == Negative {
            return Positive;
        }

        if a.sign == b.sign {
            Positive
        } else {
            Negative
        }
    }

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

        self
    }
}

impl<T: Unsigned> PartialOrd for Frac<T> {
    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
        Some(self.cmp(other))
    }
}

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

        if self.denominator == other.denominator {
            return self.numerator.cmp(&other.numerator);
        }

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

        if a.denominator == b.denominator {
            return a.numerator.cmp(&b.numerator);
        }

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

        a.numerator *= x;
        a.denominator *= x;

        b.numerator *= y;
        b.denominator *= y;

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

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

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

        Self::raw(numerator, denominator, sign)
    }
}

impl<T: Unsigned> MulAssign for Frac<T> {
    fn mul_assign(&mut self, rhs: Self) {
        *self = *self * rhs;
    }
}

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

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

        Self::raw(numerator, denominator, sign)
    }
}

impl<T: Unsigned> DivAssign for Frac<T> {
    fn div_assign(&mut self, rhs: Self) {
        *self = *self / rhs;
    }
}

impl<T: Unsigned> Add for Frac<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.denominator != b.denominator {
            // Let's just use the simplest method, rather than
            // worrying about reducing to the least common denominator
            let numerator = (a.numerator * b.denominator) + (b.numerator * a.denominator);
            let denominator = a.denominator * b.denominator;
            let sign = Self::get_sign(a, b, FracOp::Addition);

            return Self::raw(numerator, denominator, sign);
        }

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

        Self::raw(numerator, denominator, sign)
    }
}

impl<T: Unsigned> AddAssign for Frac<T> {
    fn add_assign(&mut self, rhs: Self) {
        *self = *self + rhs;
    }
}

impl<T: Unsigned> Sub for Frac<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.denominator != b.denominator {
            let (numerator, overflowed) =
                (a.numerator * b.denominator).left_overflowing_sub(b.numerator * a.denominator);

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

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

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

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

impl<T: Unsigned> SubAssign for Frac<T> {
    fn sub_assign(&mut self, rhs: Self) {
        *self = *self - 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)]
#[cfg(not(tarpaulin_include))]
mod tests {
    use super::*;

    #[test]
    #[should_panic(expected = "Fraction can not have a zero denominator")]
    fn zero_denominator() {
        Frac::raw(1u8, 0u8, Sign::default());
    }

    #[test]
    #[should_panic(expected = "Fraction can not have a zero denominator")]
    fn zero_denominator_new() {
        frac!(1 / 0);
    }

    #[test]
    fn test_get_sign() {
        assert_eq!(
            Sign::Positive,
            Frac::get_sign(frac!(1), frac!(-1), FracOp::Subtraction)
        );
        assert_eq!(
            Sign::Negative,
            Frac::get_sign(frac!(-1), frac!(-1), FracOp::Addition)
        );
        assert_eq!(
            Sign::Negative,
            Frac::get_sign(frac!(-1), frac!(1), FracOp::Addition)
        );
        assert_eq!(
            Sign::Negative,
            Frac::get_sign(frac!(-1), frac!(1), FracOp::Subtraction)
        );
        assert_eq!(
            Sign::Negative,
            Frac::get_sign(frac!(-1), frac!(1), FracOp::Other)
        );
    }

    #[test]
    fn test_cmp() {
        assert_eq!(Ordering::Greater, frac!(3 / 4).cmp(&frac!(1 / 4)));
        assert_eq!(Ordering::Less, frac!(1 / 4).cmp(&frac!(3 / 4)));
        assert_eq!(Ordering::Equal, frac!(1 / 2).cmp(&frac!(4 / 8)));
    }

    #[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));

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