rational.rs

// Copyright 2013-2014 The Rust Project Developers. See the COPYRIGHT
// file at the top-level directory of this distribution and at
// http://rust-lang.org/COPYRIGHT.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.

//! Rational numbers

use Integer;

use std::cmp;
use std::fmt;
use std::from_str::FromStr;
use std::num::{Zero, One, ToStrRadix, FromStrRadix};
use bigint::{BigInt, BigUint, Sign, Plus, Minus};

/// Represents the ratio between 2 numbers.
#[deriving(Clone)]
#[allow(missing_doc)]
pub struct Ratio<T> {
    numer: T,
    denom: T
}

/// Alias for a `Ratio` of machine-sized integers.
pub type Rational = Ratio<int>;
pub type Rational32 = Ratio<i32>;
pub type Rational64 = Ratio<i64>;

/// Alias for arbitrary precision rationals.
pub type BigRational = Ratio<BigInt>;

impl<T: Clone + Integer + PartialOrd>
    Ratio<T> {
    /// Create a ratio representing the integer `t`.
    #[inline]
    pub fn from_integer(t: T) -> Ratio<T> {
        Ratio::new_raw(t, One::one())
    }

    /// Create a ratio without checking for `denom == 0` or reducing.
    #[inline]
    pub fn new_raw(numer: T, denom: T) -> Ratio<T> {
        Ratio { numer: numer, denom: denom }
    }

    /// Create a new Ratio. Fails if `denom == 0`.
    #[inline]
    pub fn new(numer: T, denom: T) -> Ratio<T> {
        if denom == Zero::zero() {
            fail!("denominator == 0");
        }
        let mut ret = Ratio::new_raw(numer, denom);
        ret.reduce();
        ret
    }

    /// Convert to an integer.
    #[inline]
    pub fn to_integer(&self) -> T {
        self.trunc().numer
    }

    /// Gets an immutable reference to the numerator.
    #[inline]
    pub fn numer<'a>(&'a self) -> &'a T {
        &self.numer
    }

    /// Gets an immutable reference to the denominator.
    #[inline]
    pub fn denom<'a>(&'a self) -> &'a T {
        &self.denom
    }

    /// Return true if the rational number is an integer (denominator is 1).
    #[inline]
    pub fn is_integer(&self) -> bool {
        self.denom == One::one()
    }

    /// Put self into lowest terms, with denom > 0.
    fn reduce(&mut self) {
        let g : T = self.numer.gcd(&self.denom);

        // FIXME(#5992): assignment operator overloads
        // self.numer /= g;
        self.numer = self.numer / g;
        // FIXME(#5992): assignment operator overloads
        // self.denom /= g;
        self.denom = self.denom / g;

        // keep denom positive!
        if self.denom < Zero::zero() {
            self.numer = -self.numer;
            self.denom = -self.denom;
        }
    }

    /// Return a `reduce`d copy of self.
    pub fn reduced(&self) -> Ratio<T> {
        let mut ret = self.clone();
        ret.reduce();
        ret
    }

    /// Return the reciprocal
    #[inline]
    pub fn recip(&self) -> Ratio<T> {
        Ratio::new_raw(self.denom.clone(), self.numer.clone())
    }

    pub fn floor(&self) -> Ratio<T> {
        if *self < Zero::zero() {
            Ratio::from_integer((self.numer - self.denom + One::one()) / self.denom)
        } else {
            Ratio::from_integer(self.numer / self.denom)
        }
    }

    pub fn ceil(&self) -> Ratio<T> {
        if *self < Zero::zero() {
            Ratio::from_integer(self.numer / self.denom)
        } else {
            Ratio::from_integer((self.numer + self.denom - One::one()) / self.denom)
        }
    }

    #[inline]
    pub fn round(&self) -> Ratio<T> {
        if *self < Zero::zero() {
            Ratio::from_integer((self.numer - self.denom + One::one()) / self.denom)
        } else {
            Ratio::from_integer((self.numer + self.denom - One::one()) / self.denom)
        }
    }

    #[inline]
    pub fn trunc(&self) -> Ratio<T> {
        Ratio::from_integer(self.numer / self.denom)
    }

    pub fn fract(&self) -> Ratio<T> {
        Ratio::new_raw(self.numer % self.denom, self.denom.clone())
    }
}

impl Ratio<BigInt> {
    /// Converts a float into a rational number
    pub fn from_float<T: Float>(f: T) -> Option<BigRational> {
        if !f.is_finite() {
            return None;
        }
        let (mantissa, exponent, sign) = f.integer_decode();
        let bigint_sign: Sign = if sign == 1 { Plus } else { Minus };
        if exponent < 0 {
            let one: BigInt = One::one();
            let denom: BigInt = one << ((-exponent) as uint);
            let numer: BigUint = FromPrimitive::from_u64(mantissa).unwrap();
            Some(Ratio::new(BigInt::from_biguint(bigint_sign, numer), denom))
        } else {
            let mut numer: BigUint = FromPrimitive::from_u64(mantissa).unwrap();
            numer = numer << (exponent as uint);
            Some(Ratio::from_integer(BigInt::from_biguint(bigint_sign, numer)))
        }
    }
}

/* Comparisons */

// comparing a/b and c/d is the same as comparing a*d and b*c, so we
// abstract that pattern. The following macro takes a trait and either
// a comma-separated list of "method name -> return value" or just
// "method name" (return value is bool in that case)
macro_rules! cmp_impl {
    (impl $imp:ident, $($method:ident),+) => {
        cmp_impl!(impl $imp, $($method -> bool),+)
    };
    // return something other than a Ratio<T>
    (impl $imp:ident, $($method:ident -> $res:ty),*) => {
        impl<T: Mul<T,T> + $imp> $imp for Ratio<T> {
            $(
                #[inline]
                fn $method(&self, other: &Ratio<T>) -> $res {
                    (self.numer * other.denom). $method (&(self.denom*other.numer))
                }
            )*
        }
    };
}
cmp_impl!(impl PartialEq, eq, ne)
cmp_impl!(impl PartialOrd, lt -> bool, gt -> bool, le -> bool, ge -> bool,
          partial_cmp -> Option<cmp::Ordering>)
cmp_impl!(impl Eq, )
cmp_impl!(impl Ord, cmp -> cmp::Ordering)

/* Arithmetic */
// a/b * c/d = (a*c)/(b*d)
impl<T: Clone + Integer + PartialOrd>
    Mul<Ratio<T>,Ratio<T>> for Ratio<T> {
    #[inline]
    fn mul(&self, rhs: &Ratio<T>) -> Ratio<T> {
        Ratio::new(self.numer * rhs.numer, self.denom * rhs.denom)
    }
}

// (a/b) / (c/d) = (a*d)/(b*c)
impl<T: Clone + Integer + PartialOrd>
    Div<Ratio<T>,Ratio<T>> for Ratio<T> {
    #[inline]
    fn div(&self, rhs: &Ratio<T>) -> Ratio<T> {
        Ratio::new(self.numer * rhs.denom, self.denom * rhs.numer)
    }
}

// Abstracts the a/b `op` c/d = (a*d `op` b*d) / (b*d) pattern
macro_rules! arith_impl {
    (impl $imp:ident, $method:ident) => {
        impl<T: Clone + Integer + PartialOrd>
            $imp<Ratio<T>,Ratio<T>> for Ratio<T> {
            #[inline]
            fn $method(&self, rhs: &Ratio<T>) -> Ratio<T> {
                Ratio::new((self.numer * rhs.denom).$method(&(self.denom * rhs.numer)),
                           self.denom * rhs.denom)
            }
        }
    }
}

// a/b + c/d = (a*d + b*c)/(b*d
arith_impl!(impl Add, add)

// a/b - c/d = (a*d - b*c)/(b*d)
arith_impl!(impl Sub, sub)

// a/b % c/d = (a*d % b*c)/(b*d)
arith_impl!(impl Rem, rem)

impl<T: Clone + Integer + PartialOrd>
    Neg<Ratio<T>> for Ratio<T> {
    #[inline]
    fn neg(&self) -> Ratio<T> {
        Ratio::new_raw(-self.numer, self.denom.clone())
    }
}

/* Constants */
impl<T: Clone + Integer + PartialOrd>
    Zero for Ratio<T> {
    #[inline]
    fn zero() -> Ratio<T> {
        Ratio::new_raw(Zero::zero(), One::one())
    }

    #[inline]
    fn is_zero(&self) -> bool {
        *self == Zero::zero()
    }
}

impl<T: Clone + Integer + PartialOrd>
    One for Ratio<T> {
    #[inline]
    fn one() -> Ratio<T> {
        Ratio::new_raw(One::one(), One::one())
    }
}

impl<T: Clone + Integer + PartialOrd>
    Num for Ratio<T> {}

/* String conversions */
impl<T: fmt::Show> fmt::Show for Ratio<T> {
    /// Renders as `numer/denom`.
    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
        write!(f, "{}/{}", self.numer, self.denom)
    }
}
impl<T: ToStrRadix> ToStrRadix for Ratio<T> {
    /// Renders as `numer/denom` where the numbers are in base `radix`.
    fn to_str_radix(&self, radix: uint) -> String {
        format!("{}/{}",
                self.numer.to_str_radix(radix),
                self.denom.to_str_radix(radix))
    }
}

impl<T: FromStr + Clone + Integer + PartialOrd>
    FromStr for Ratio<T> {
    /// Parses `numer/denom`.
    fn from_str(s: &str) -> Option<Ratio<T>> {
        let split: Vec<&str> = s.splitn('/', 1).collect();
        if split.len() < 2 {
            return None
        }
        let a_option: Option<T> = FromStr::from_str(*split.get(0));
        a_option.and_then(|a| {
            let b_option: Option<T> = FromStr::from_str(*split.get(1));
            b_option.and_then(|b| {
                Some(Ratio::new(a.clone(), b.clone()))
            })
        })
    }
}
impl<T: FromStrRadix + Clone + Integer + PartialOrd>
    FromStrRadix for Ratio<T> {
    /// Parses `numer/denom` where the numbers are in base `radix`.
    fn from_str_radix(s: &str, radix: uint) -> Option<Ratio<T>> {
        let split: Vec<&str> = s.splitn('/', 1).collect();
        if split.len() < 2 {
            None
        } else {
            let a_option: Option<T> = FromStrRadix::from_str_radix(
                *split.get(0),
                radix);
            a_option.and_then(|a| {
                let b_option: Option<T> =
                    FromStrRadix::from_str_radix(*split.get(1), radix);
                b_option.and_then(|b| {
                    Some(Ratio::new(a.clone(), b.clone()))
                })
            })
        }
    }
}

#[cfg(test)]
mod test {

    use super::{Ratio, Rational, BigRational};
    use std::num::{Zero, One, FromStrRadix, FromPrimitive, ToStrRadix};
    use std::from_str::FromStr;

    pub static _0 : Rational = Ratio { numer: 0, denom: 1};
    pub static _1 : Rational = Ratio { numer: 1, denom: 1};
    pub static _2: Rational = Ratio { numer: 2, denom: 1};
    pub static _1_2: Rational = Ratio { numer: 1, denom: 2};
    pub static _3_2: Rational = Ratio { numer: 3, denom: 2};
    pub static _neg1_2: Rational =  Ratio { numer: -1, denom: 2};

    pub fn to_big(n: Rational) -> BigRational {
        Ratio::new(
            FromPrimitive::from_int(n.numer).unwrap(),
            FromPrimitive::from_int(n.denom).unwrap()
        )
    }

    #[test]
    fn test_test_constants() {
        // check our constants are what Ratio::new etc. would make.
        assert_eq!(_0, Zero::zero());
        assert_eq!(_1, One::one());
        assert_eq!(_2, Ratio::from_integer(2i));
        assert_eq!(_1_2, Ratio::new(1i,2i));
        assert_eq!(_3_2, Ratio::new(3i,2i));
        assert_eq!(_neg1_2, Ratio::new(-1i,2i));
    }

    #[test]
    fn test_new_reduce() {
        let one22 = Ratio::new(2i,2);

        assert_eq!(one22, One::one());
    }
    #[test]
    #[should_fail]
    fn test_new_zero() {
        let _a = Ratio::new(1i,0);
    }


    #[test]
    fn test_cmp() {
        assert!(_0 == _0 && _1 == _1);
        assert!(_0 != _1 && _1 != _0);
        assert!(_0 < _1 && !(_1 < _0));
        assert!(_1 > _0 && !(_0 > _1));

        assert!(_0 <= _0 && _1 <= _1);
        assert!(_0 <= _1 && !(_1 <= _0));

        assert!(_0 >= _0 && _1 >= _1);
        assert!(_1 >= _0 && !(_0 >= _1));
    }


    #[test]
    fn test_to_integer() {
        assert_eq!(_0.to_integer(), 0);
        assert_eq!(_1.to_integer(), 1);
        assert_eq!(_2.to_integer(), 2);
        assert_eq!(_1_2.to_integer(), 0);
        assert_eq!(_3_2.to_integer(), 1);
        assert_eq!(_neg1_2.to_integer(), 0);
    }


    #[test]
    fn test_numer() {
        assert_eq!(_0.numer(), &0);
        assert_eq!(_1.numer(), &1);
        assert_eq!(_2.numer(), &2);
        assert_eq!(_1_2.numer(), &1);
        assert_eq!(_3_2.numer(), &3);
        assert_eq!(_neg1_2.numer(), &(-1));
    }
    #[test]
    fn test_denom() {
        assert_eq!(_0.denom(), &1);
        assert_eq!(_1.denom(), &1);
        assert_eq!(_2.denom(), &1);
        assert_eq!(_1_2.denom(), &2);
        assert_eq!(_3_2.denom(), &2);
        assert_eq!(_neg1_2.denom(), &2);
    }


    #[test]
    fn test_is_integer() {
        assert!(_0.is_integer());
        assert!(_1.is_integer());
        assert!(_2.is_integer());
        assert!(!_1_2.is_integer());
        assert!(!_3_2.is_integer());
        assert!(!_neg1_2.is_integer());
    }


    mod arith {
        use super::{_0, _1, _2, _1_2, _3_2, _neg1_2, to_big};
        use super::super::{Ratio, Rational};

        #[test]
        fn test_add() {
            fn test(a: Rational, b: Rational, c: Rational) {
                assert_eq!(a + b, c);
                assert_eq!(to_big(a) + to_big(b), to_big(c));
            }

            test(_1, _1_2, _3_2);
            test(_1, _1, _2);
            test(_1_2, _3_2, _2);
            test(_1_2, _neg1_2, _0);
        }

        #[test]
        fn test_sub() {
            fn test(a: Rational, b: Rational, c: Rational) {
                assert_eq!(a - b, c);
                assert_eq!(to_big(a) - to_big(b), to_big(c))
            }

            test(_1, _1_2, _1_2);
            test(_3_2, _1_2, _1);
            test(_1, _neg1_2, _3_2);
        }

        #[test]
        fn test_mul() {
            fn test(a: Rational, b: Rational, c: Rational) {
                assert_eq!(a * b, c);
                assert_eq!(to_big(a) * to_big(b), to_big(c))
            }

            test(_1, _1_2, _1_2);
            test(_1_2, _3_2, Ratio::new(3i,4i));
            test(_1_2, _neg1_2, Ratio::new(-1i, 4i));
        }

        #[test]
        fn test_div() {
            fn test(a: Rational, b: Rational, c: Rational) {
                assert_eq!(a / b, c);
                assert_eq!(to_big(a) / to_big(b), to_big(c))
            }

            test(_1, _1_2, _2);
            test(_3_2, _1_2, _1 + _2);
            test(_1, _neg1_2, _neg1_2 + _neg1_2 + _neg1_2 + _neg1_2);
        }

        #[test]
        fn test_rem() {
            fn test(a: Rational, b: Rational, c: Rational) {
                assert_eq!(a % b, c);
                assert_eq!(to_big(a) % to_big(b), to_big(c))
            }

            test(_3_2, _1, _1_2);
            test(_2, _neg1_2, _0);
            test(_1_2, _2,  _1_2);
        }

        #[test]
        fn test_neg() {
            fn test(a: Rational, b: Rational) {
                assert_eq!(-a, b);
                assert_eq!(-to_big(a), to_big(b))
            }

            test(_0, _0);
            test(_1_2, _neg1_2);
            test(-_1, _1);
        }
        #[test]
        fn test_zero() {
            assert_eq!(_0 + _0, _0);
            assert_eq!(_0 * _0, _0);
            assert_eq!(_0 * _1, _0);
            assert_eq!(_0 / _neg1_2, _0);
            assert_eq!(_0 - _0, _0);
        }
        #[test]
        #[should_fail]
        fn test_div_0() {
            let _a =  _1 / _0;
        }
    }

    #[test]
    fn test_round() {
        assert_eq!(_1_2.ceil(), _1);
        assert_eq!(_1_2.floor(), _0);
        assert_eq!(_1_2.round(), _1);
        assert_eq!(_1_2.trunc(), _0);

        assert_eq!(_neg1_2.ceil(), _0);
        assert_eq!(_neg1_2.floor(), -_1);
        assert_eq!(_neg1_2.round(), -_1);
        assert_eq!(_neg1_2.trunc(), _0);

        assert_eq!(_1.ceil(), _1);
        assert_eq!(_1.floor(), _1);
        assert_eq!(_1.round(), _1);
        assert_eq!(_1.trunc(), _1);
    }

    #[test]
    fn test_fract() {
        assert_eq!(_1.fract(), _0);
        assert_eq!(_neg1_2.fract(), _neg1_2);
        assert_eq!(_1_2.fract(), _1_2);
        assert_eq!(_3_2.fract(), _1_2);
    }

    #[test]
    fn test_recip() {
        assert_eq!(_1 * _1.recip(), _1);
        assert_eq!(_2 * _2.recip(), _1);
        assert_eq!(_1_2 * _1_2.recip(), _1);
        assert_eq!(_3_2 * _3_2.recip(), _1);
        assert_eq!(_neg1_2 * _neg1_2.recip(), _1);
    }

    #[test]
    fn test_to_from_str() {
        fn test(r: Rational, s: String) {
            assert_eq!(FromStr::from_str(s.as_slice()), Some(r));
            assert_eq!(r.to_str(), s);
        }
        test(_1, "1/1".to_string());
        test(_0, "0/1".to_string());
        test(_1_2, "1/2".to_string());
        test(_3_2, "3/2".to_string());
        test(_2, "2/1".to_string());
        test(_neg1_2, "-1/2".to_string());
    }
    #[test]
    fn test_from_str_fail() {
        fn test(s: &str) {
            let rational: Option<Rational> = FromStr::from_str(s);
            assert_eq!(rational, None);
        }

        let xs = ["0 /1", "abc", "", "1/", "--1/2","3/2/1"];
        for &s in xs.iter() {
            test(s);
        }
    }

    #[test]
    fn test_to_from_str_radix() {
        fn test(r: Rational, s: String, n: uint) {
            assert_eq!(FromStrRadix::from_str_radix(s.as_slice(), n),
                       Some(r));
            assert_eq!(r.to_str_radix(n).to_string(), s);
        }
        fn test3(r: Rational, s: String) { test(r, s, 3) }
        fn test16(r: Rational, s: String) { test(r, s, 16) }

        test3(_1, "1/1".to_string());
        test3(_0, "0/1".to_string());
        test3(_1_2, "1/2".to_string());
        test3(_3_2, "10/2".to_string());
        test3(_2, "2/1".to_string());
        test3(_neg1_2, "-1/2".to_string());
        test3(_neg1_2 / _2, "-1/11".to_string());

        test16(_1, "1/1".to_string());
        test16(_0, "0/1".to_string());
        test16(_1_2, "1/2".to_string());
        test16(_3_2, "3/2".to_string());
        test16(_2, "2/1".to_string());
        test16(_neg1_2, "-1/2".to_string());
        test16(_neg1_2 / _2, "-1/4".to_string());
        test16(Ratio::new(13i,15i), "d/f".to_string());
        test16(_1_2*_1_2*_1_2*_1_2, "1/10".to_string());
    }

    #[test]
    fn test_from_str_radix_fail() {
        fn test(s: &str) {
            let radix: Option<Rational> = FromStrRadix::from_str_radix(s, 3);
            assert_eq!(radix, None);
        }

        let xs = ["0 /1", "abc", "", "1/", "--1/2","3/2/1", "3/2"];
        for &s in xs.iter() {
            test(s);
        }
    }

    #[test]
    fn test_from_float() {
        fn test<T: Float>(given: T, (numer, denom): (&str, &str)) {
            let ratio: BigRational = Ratio::from_float(given).unwrap();
            assert_eq!(ratio, Ratio::new(
                FromStr::from_str(numer).unwrap(),
                FromStr::from_str(denom).unwrap()));
        }

        // f32
        test(3.14159265359f32, ("13176795", "4194304"));
        test(2f32.powf(100.), ("1267650600228229401496703205376", "1"));
        test(-2f32.powf(100.), ("-1267650600228229401496703205376", "1"));
        test(1.0 / 2f32.powf(100.), ("1", "1267650600228229401496703205376"));
        test(684729.48391f32, ("1369459", "2"));
        test(-8573.5918555f32, ("-4389679", "512"));

        // f64
        test(3.14159265359f64, ("3537118876014453", "1125899906842624"));
        test(2f64.powf(100.), ("1267650600228229401496703205376", "1"));
        test(-2f64.powf(100.), ("-1267650600228229401496703205376", "1"));
        test(684729.48391f64, ("367611342500051", "536870912"));
        test(-8573.5918555f64, ("-4713381968463931", "549755813888"));
        test(1.0 / 2f64.powf(100.), ("1", "1267650600228229401496703205376"));
    }

    #[test]
    fn test_from_float_fail() {
        use std::{f32, f64};

        assert_eq!(Ratio::from_float(f32::NAN), None);
        assert_eq!(Ratio::from_float(f32::INFINITY), None);
        assert_eq!(Ratio::from_float(f32::NEG_INFINITY), None);
        assert_eq!(Ratio::from_float(f64::NAN), None);
        assert_eq!(Ratio::from_float(f64::INFINITY), None);
        assert_eq!(Ratio::from_float(f64::NEG_INFINITY), None);
    }
}