easel3d/fractional/src/fractional.rs

//
// Some code to support fractional numbers for full precision rational number
// calculations. (At least for the standard operations.)
// This also implements a sqrt on fractional numbers, which can not be precise
// because of the irrational nature of most sqare roots.
// Fractions can only represent rational numbers precise.
//
// Georg Hopp <georg@steffers.org>
//
// Copyright © 2019 Georg Hopp
//
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.
//
use std::cmp::Ordering;
use std::convert::{TryFrom, TryInto};
use std::fmt::{Formatter, Display};
use std::num::TryFromIntError;
use std::ops::{Add,Sub,Neg,Mul,Div};

use crate::continuous::Continuous;

#[derive(Debug, Eq, Clone, Copy)]
pub struct Fractional (pub i64, pub i64);

#[inline]
fn hcf(x :i64, y :i64) -> i64 {
    match y {
        0 => x,
        _ => hcf(y, x % y),
    }
}

pub fn from_vector(xs: &Vec<i64>) -> Vec<Fractional> {
    xs.iter().map(|x| Fractional(*x, 1)).collect()
}

impl Fractional {
    #[inline]
    pub fn gcd(self, other: Self) -> i64 {
        let Fractional(_, d1) = self;
        let Fractional(_, d2) = other;
        (d1 * d2) / hcf(d1, d2)
    }

    #[inline]
    pub fn reduce(self) -> Self {
        let Fractional(n, d) = self;
        let (_n, _d) = if n > d { (n, d) } else { (d, n) };

        // if the difference from _n % _d to _n is very big we are close to
        // a whole number and can ignore the fractional part... this reduces
        // the precision but ensures smaller numbers for numerator and
        // denominator.
        if _d > 1 && (_n % _d) * 10000000 < _n {
            if n == _n {
                Self(_n / _d, 1)
            } else {
                Self(1, _n / _d)
            }
        } else {
            // Self(n / hcf(n, d), d / hcf(n, d))
            // The above reduces prcisely but results in very large numerator
            // or denominator occasionally. The below is less precise but
            // keeps the numbers small… the bad point is, that it is not very
            // fast.
            let cont = Continuous::from_prec(&self, Some(5));
            (&cont).into()
        }
    }

    pub fn noreduce_add(self, other: Self) -> Self {
        let Fractional(n1, d1) = self;
        let Fractional(n2, d2) = other;
        let n = n1 * (self.gcd(other) / d1) + n2 * (self.gcd(other) / d2);
        Self(n, self.gcd(other))
    }

    pub fn noreduce_sub(self, other: Self) -> Self {
        self.noreduce_add(other.noreduce_neg())
    }

    pub fn noreduce_neg(self) -> Self {
        let Fractional(n, d) = self;
        Self(-n, d)
    }
}

impl From<i64> for Fractional {
    fn from(x: i64) -> Self {
        Self(x, 1)
    }
}

impl From<i32> for Fractional {
    fn from(x: i32) -> Self {
        Self(x as i64, 1)
    }
}

impl TryFrom<usize> for Fractional {
    type Error = &'static str;

    fn try_from(x: usize) -> Result<Self, Self::Error> {
        let v = i64::try_from(x);
        match v {
            Err(_) => Err("Conversion from usize to i32 failed"),
            Ok(_v) => Ok(Self(_v, 1)),
        }
    }
}

impl TryInto<f64> for Fractional {
    type Error = TryFromIntError;

    fn try_into(self) -> Result<f64, Self::Error> {
        let n :i32 = self.0.try_into()?;
        let d :i32 = self.1.try_into()?;
        Ok(f64::from(n) / f64::from(d))
    }
}

impl TryInto<(i32, i32)> for Fractional {
    type Error = TryFromIntError;

    fn try_into(self) -> Result<(i32, i32), Self::Error> {
        let a :i32 = (self.0 / self.1).try_into()?;
        let b :i32 = (self.0 % self.1).try_into()?;
        Ok((a, b))
    }
}

impl Display for Fractional {
    fn fmt(&self, f: &mut Formatter<'_>) -> std::fmt::Result {
        write!(f, "({}/{})", self.0, self.1)
    }
}

impl PartialEq for Fractional {
    fn eq(&self, other: &Self) -> bool {
        let Fractional(n1, d1) = self;
        let Fractional(n2, d2) = other;
        n1 * (self.gcd(*other) / d1) == n2 * (self.gcd(*other) / d2)
    }
}

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

impl Ord for Fractional {
    fn cmp(&self, other: &Self) -> Ordering {
        let Fractional(n1, d1) = self;
        let Fractional(n2, d2) = other;
        let x = n1 * (self.gcd(*other) / d1);
        let y = n2 * (self.gcd(*other) / d2);
        x.cmp(&y)
    }
}

impl Add for Fractional {
    type Output = Self;

    fn add(self, other: Self) -> Self {
        self.noreduce_add(other).reduce()
    }
}

impl Sub for Fractional {
    type Output = Self;

    fn sub(self, other: Self) -> Self {
        self + -other
    }
}

impl Neg for Fractional {
    type Output = Self;

    fn neg(self) -> Self {
        let Fractional(n, d) = self;
        Self(-n, d)
    }
}

impl Mul for Fractional {
    type Output = Self;

    fn mul(self, other :Self) -> Self {
        let Fractional(n1, d1) = self;
        let Fractional(n2, d2) = other;
        Self(n1 * n2, d1 * d2).reduce()
    }
}

impl Div for Fractional {
    type Output = Self;

    fn div(self, other: Self) -> Self {
        let Fractional(n, d) = other;
        self * Fractional(d, n)
    }
}

    /* some stuff that could be tested...
    let x = Fractional(1, 3);
    let y = Fractional(1, 6);

    println!(
        "Greatest common denominator of {} and {}: {}", x, y, x.gcd(y));
    println!("Numerator of {}: {}", x, x.numerator());
    println!("Denominator of {}: {}", x, x.denominator());
    assert_eq!(Fractional(1, 3), Fractional(2, 6));
    assert_eq!(Fractional(1, 3), Fractional(1, 3));
    assert_eq!(y < x, true);
    assert_eq!(y > x, false);
    assert_eq!(x == y, false);
    assert_eq!(x == x, true);
    assert_eq!(x + y, Fractional(1, 2));
    println!("{} + {} = {}", x, y, x + y);
    assert_eq!(x - y, Fractional(1, 6));
    println!("{} - {} = {}", x, y, x - y);
    assert_eq!(y - x, Fractional(-1, 6));
    println!("{} - {} = {}", y, x, y - x);
    assert_eq!(-x, Fractional(-1, 3));
    println!("-{} = {}", x, -x);
    assert_eq!(x * y, Fractional(1, 18));
    println!("{} * {} = {}", x, y, x * y);
    assert_eq!(x / y, Fractional(2, 1));
    println!("{} / {} = {}", x, y, x / y);
    assert_eq!(y / x, Fractional(1, 2));
    println!("{} / {} = {}", y, x, y / x);

    println!("Fractional from 3: {}", Fractional::from(3));
    let z :f64 = Fractional::into(x);
    println!("Floating point of {}: {}", x, z);
    let (d, r) = Fractional::into(x);
    println!("(div, rest) of {}: ({}, {})", x, d, r);
    */