rusty-numbers/src/rational.rs
2020-02-14 17:24:51 -05:00

230 lines
5.6 KiB
Rust

//! # Rational Numbers (fractions)
//!
//! Traits to implement:
//! * Add
//! * AddAssign
//! * Div
//! * DivAssign
//! * Mul
//! * MulAssign
//! * Neg
//! * Sub
//! * SubAssign
use crate::num::*;
use std::ops::{Add, Div, Mul, Neg, Sub};
#[derive(Debug, Copy, Clone, Eq, PartialEq)]
pub struct Frac<T: Unsigned = usize> {
numer: T,
denom: T,
sign: Sign,
}
#[macro_export]
macro_rules! frac {
($n:literal / $d:literal) => {
Frac::new_conv($n, $d)
};
}
/* macro_rules! impl_from_signed {
($(($in_type: ty, $out_type: ty)),* ) => {
$(
impl Frac<$in_type> {
pub fn new(n: $in_type, d: $in_type) -> Frac<$out_type> {
// Converting from signed to unsigned should always be safe
// when using the absolute value, especially since I'm converting
// between the same bit size
let mut sign = $crate::num::Sign::Positive;
let numer = <$out_type>::try_from(n.abs()).unwrap();
let denom = <$out_type>::try_from(d.abs()).unwrap();
if n < 0 {
sign = !sign;
}
if d < 0 {
sign = !sign;
}
Frac::new_signed(numer, denom, sign)
}
fn new_signed(n: $in_type, d: $in_type, _: $crate::num::Sign) -> Frac<$out_type> {
Self::new(n, d)
}
}
)*
};
}
impl_from_signed!((i8, u8), (i16, u16), (i32, u32), (i64, u64), (i128, u128), (isize, usize)); */
impl<T: Signed, U: Unsigned> Frac<U> {
pub fn new_conv(n: T, d: T) -> Self {
// Converting from signed to unsigned should always be safe
// when using the absolute value, especially since I'm converting
// between the same bit size
let mut sign = Sign::Positive;
let numer:T::Un = n.to_unsigned();
let denom:T::Un = d.to_unsigned();
if n.is_neg() {
sign = !sign;
}
if d.is_neg() {
sign = !sign;
}
Self::new(numer, denom, sign)
}
}
impl<T: Unsigned> Frac<T> {
/// Create a new rational number
pub fn new(n: T, d: T, s: Sign) -> Self {
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) -> Sign {
if a.sign != b.sign {
Sign::Negative
} else {
Sign::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: Unsigned + Mul<Output = T>> Mul for Frac<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);
Self::new_signed(numer, denom, sign)
}
}
impl<T: Unsigned + Mul<Output = T>> Div for Frac<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);
Self::new_signed(numer, denom, sign)
}
}
impl<T: Unsigned + Add<Output = T> + Sub<Output = T> + Mul<Output = T>> 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 self.sign != rhs.sign {
if a.numer > b.numer {
return a - b
} else if a.numer < b.numer {
return b - a
}
}
// 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);
return Self::new_signed(numer, denom, sign);
}
let numer = a.numer + b.numer;
let denom = self.denom;
let sign = Self::get_sign(a, b);
Self::new_signed(numer, denom, sign)
}
}
impl<T: Unsigned + Sub<Output = T>> Sub for Frac<T> {
type Output = Self;
fn sub(self, rhs: Self) -> Self::Output {
let a = self;
let b = rhs;
unimplemented!()
}
}
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, Sign::Positive);
let frac2 = Frac::new(2u8, 3u8, Sign::Positive);
let expected = Frac::new(2u8, 9u8, Sign::Positive);
assert_eq!(frac1 * frac2, expected);
}
#[test]
fn add_test() {
assert_eq!(frac!(5u8 / 6), frac!(1 / 3) + frac!(1 / 2));
}
#[test]
fn macro_test() {
let frac1 = frac!(1u8 / 3);
let frac2 = Frac::new(1u8, 3, Sign::Positive);
assert_eq!(frac1, frac2);
let frac1 = -frac!(1u8 / 2);
let frac2 = Frac::new(1u8, 2, Sign::Negative);
assert_eq!(frac1, frac2);
}
}