libstd: add basic rational numbers

src/libstd/num/rational.rs

@@ -0,0 +1,511 @@
+// Copyright 2013 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 core::num::{Zero,One,ToStrRadix,FromStrRadix,Round};
+use core::from_str::FromStr;
+use core::to_str::ToStr;
+use core::prelude::*;
+use core::cmp::TotalEq;
+use super::bigint::BigInt;
+
+/// Represents the ratio between 2 numbers.
+#[deriving(Clone)]
+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: Copy + Div<T,T> + Modulo<T,T> + Neg<T> + Zero + One + Ord + Eq>
+    Ratio<T> {
+    /// Create a ratio representing the integer `t`.
+    #[inline(always)]
+    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(always)]
+    pub fn new_raw(numer: T, denom: T) -> Ratio<T> {
+        Ratio { numer: numer, denom: denom }
+    }
+
+    // Create a new Ratio. Fails if `denom == 0`.
+    #[inline(always)]
+    pub fn new(numer: T, denom: T) -> Ratio<T> {
+        if denom == Zero::zero() {
+            fail!(~"divide by 0");
+        }
+        let mut ret = Ratio::new_raw(numer, denom);
+        ret.reduce();
+        ret
+    }
+
+    /// Put self into lowest terms, with denom > 0.
+    fn reduce(&mut self) {
+        let mut g : T = gcd(self.numer, self.denom);
+
+        self.numer /= g;
+        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.
+    fn reduced(&self) -> Ratio<T> {
+        let mut ret = copy *self;
+        ret.reduce();
+        ret
+    }
+}
+
+/**
+Compute the greatest common divisor of two numbers, via Euclid's algorithm.
+
+The result can be negative.
+*/
+#[inline]
+pub fn gcd_raw<T: Modulo<T,T> + Zero + Eq>(n: T, m: T) -> T {
+    let mut m = m, n = n;
+    while m != Zero::zero() {
+        let temp = m;
+        m = n % temp;
+        n = temp;
+    }
+    n
+}
+
+/**
+Compute the greatest common divisor of two numbers, via Euclid's algorithm.
+
+The result is always positive.
+*/
+#[inline]
+pub fn gcd<T: Modulo<T,T> + Neg<T> + Zero + Ord + Eq>(n: T, m: T) -> T {
+    let g = gcd_raw(n, m);
+    if g < Zero::zero() { -g }
+    else { g }
+}
+
+/* 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 Eq, eq, ne)
+cmp_impl!(impl TotalEq, equals)
+cmp_impl!(impl Ord, lt, gt, le, ge)
+cmp_impl!(impl TotalOrd, cmp -> cmp::Ordering)
+
+/* Arithmetic */
+// a/b * c/d = (a*c)/(b*d)
+impl<T: Copy + Mul<T,T> + Div<T,T> + Modulo<T,T> + Neg<T> + Zero + One + Ord + Eq>
+    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: Copy + Mul<T,T> + Div<T,T> + Modulo<T,T> + Neg<T> + Zero + One + Ord + Eq>
+    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: Copy +
+                Add<T,T> + Sub<T,T> + Mul<T,T> + Div<T,T> + Modulo<T,T> + Neg<T> +
+                Zero + One + Ord + Eq>
+            $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 Modulo, modulo)
+
+impl<T: Copy + Div<T,T> + Modulo<T,T> + Neg<T> + Zero + One + Ord + Eq>
+    Neg<Ratio<T>> for Ratio<T> {
+    #[inline]
+    fn neg(&self) -> Ratio<T> {
+        Ratio::new_raw(-self.numer, self.denom)
+    }
+}
+
+/* Constants */
+impl<T: Copy + Div<T,T> + Modulo<T,T> + Neg<T> + Zero + One + Ord + Eq>
+    Zero for Ratio<T> {
+    #[inline]
+    fn zero() -> Ratio<T> {
+        Ratio::new_raw(Zero::zero(), One::one())
+    }
+}
+
+impl<T: Copy + Div<T,T> + Modulo<T,T> + Neg<T> + Zero + One + Ord + Eq>
+    One for Ratio<T> {
+    #[inline]
+    fn one() -> Ratio<T> {
+        Ratio::new_raw(One::one(), One::one())
+    }
+}
+
+/* Utils */
+impl<T: Copy + Add<T,T> + Sub<T,T> + Mul<T,T> + Div<T,T> + Modulo<T,T> + Neg<T> +
+    Zero + One + Ord + Eq>
+    Round for Ratio<T> {
+    fn round(&self, mode: num::RoundMode) -> Ratio<T> {
+        match mode {
+            num::RoundUp => { self.ceil() }
+            num::RoundDown => { self.floor()}
+            num::RoundToZero => { Ratio::from_integer(self.numer / self.denom) }
+            num::RoundFromZero => {
+                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)
+                }
+            }
+        }
+    }
+
+    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)
+        }
+    }
+    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)
+        }
+    }
+    fn fract(&self) -> Ratio<T> {
+        Ratio::new_raw(self.numer % self.denom, self.denom)
+    }
+}
+
+
+/* String conversions */
+impl<T: ToStr> ToStr for Ratio<T> {
+    /// Renders as `numer/denom`.
+    fn to_str(&self) -> ~str {
+        fmt!("%s/%s", self.numer.to_str(), self.denom.to_str())
+    }
+}
+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) -> ~str {
+        fmt!("%s/%s", self.numer.to_str_radix(radix), self.denom.to_str_radix(radix))
+    }
+}
+
+impl<T: FromStr + Copy + Div<T,T> + Modulo<T,T> + Neg<T> + Zero + One + Ord + Eq>
+    FromStr for Ratio<T> {
+    /// Parses `numer/denom`.
+    fn from_str(s: &str) -> Option<Ratio<T>> {
+        let split = vec::build(|push| {
+            for str::each_splitn_char(s, '/', 1) |s| {
+                push(s.to_owned());
+            }
+        });
+        if split.len() < 2 { return None; }
+        do FromStr::from_str(split[0]).chain |a| {
+            do FromStr::from_str(split[1]).chain |b| {
+                Some(Ratio::new(a,b))
+            }
+        }
+    }
+}
+impl<T: FromStrRadix + Copy + Div<T,T> + Modulo<T,T> + Neg<T> + Zero + One + Ord + Eq>
+    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::build(|push| {
+            for str::each_splitn_char(s, '/', 1) |s| {
+                push(s.to_owned());
+            }
+        });
+        if split.len() < 2 { None }
+        else {
+            do FromStrRadix::from_str_radix(split[0], radix).chain |a| {
+                do FromStrRadix::from_str_radix(split[1], radix).chain |b| {
+                    Some(Ratio::new(a,b))
+                }
+            }
+        }
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use core::prelude::*;
+    use super::*;
+    use core::num::{Zero,One,FromStrRadix};
+    use core::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};
+
+    #[test]
+    fn test_gcd() {
+        assert_eq!(gcd(10,2),2);
+        assert_eq!(gcd(10,3),1);
+        assert_eq!(gcd(0,3),3);
+        assert_eq!(gcd(3,3),3);
+
+        assert_eq!(gcd(3,-3), 3);
+        assert_eq!(gcd(-6,3), 3);
+        assert_eq!(gcd(-4,-2), 2);
+    }
+
+    #[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(2));
+        assert_eq!(_1_2, Ratio::new(1,2));
+        assert_eq!(_3_2, Ratio::new(3,2));
+        assert_eq!(_neg1_2, Ratio::new(-1,2));
+    }
+
+    #[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(1,0);
+    }
+
+
+    #[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));
+    }
+
+
+    mod arith {
+        use super::*;
+        use super::super::*;
+
+
+        #[test]
+        fn test_add() {
+            assert_eq!(_1 + _1_2, _3_2);
+            assert_eq!(_1 + _1, _2);
+            assert_eq!(_1_2 + _3_2, _2);
+            assert_eq!(_1_2 + _neg1_2, _0);
+        }
+
+        #[test]
+        fn test_sub() {
+            assert_eq!(_1 - _1_2, _1_2);
+            assert_eq!(_3_2 - _1_2, _1);
+            assert_eq!(_1 - _neg1_2, _3_2);
+        }
+
+        #[test]
+        fn test_mul() {
+            assert_eq!(_1 * _1_2, _1_2);
+            assert_eq!(_1_2 * _3_2, Ratio::new(3,4));
+            assert_eq!(_1_2 * _neg1_2, Ratio::new(-1, 4));
+        }
+
+        #[test]
+        fn test_div() {
+            assert_eq!(_1 / _1_2, _2);
+            assert_eq!(_3_2 / _1_2, _1 + _2);
+            assert_eq!(_1 / _neg1_2, _neg1_2 + _neg1_2 + _neg1_2 + _neg1_2);
+        }
+
+        #[test]
+        fn test_modulo() {
+            assert_eq!(_3_2 % _1, _1_2);
+            assert_eq!(_2 % _neg1_2, _0);
+            assert_eq!(_1_2 % _2,  _1_2);
+        }
+
+        #[test]
+        fn test_neg() {
+            assert_eq!(-_0, _0);
+            assert_eq!(-_1_2, _neg1_2);
+            assert_eq!(-(-_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(num::RoundToZero), _0);
+        assert_eq!(_1_2.round(num::RoundFromZero), _1);
+
+        assert_eq!(_neg1_2.ceil(), _0);
+        assert_eq!(_neg1_2.floor(), -_1);
+        assert_eq!(_neg1_2.round(num::RoundToZero), _0);
+        assert_eq!(_neg1_2.round(num::RoundFromZero), -_1);
+
+        assert_eq!(_1.ceil(), _1);
+        assert_eq!(_1.floor(), _1);
+        assert_eq!(_1.round(num::RoundToZero), _1);
+        assert_eq!(_1.round(num::RoundFromZero), _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_to_from_str() {
+        fn test(r: Rational, s: ~str) {
+            assert_eq!(FromStr::from_str(s), Some(r));
+            assert_eq!(r.to_str(), s);
+        }
+        test(_1, ~"1/1");
+        test(_0, ~"0/1");
+        test(_1_2, ~"1/2");
+        test(_3_2, ~"3/2");
+        test(_2, ~"2/1");
+        test(_neg1_2, ~"-1/2");
+    }
+    #[test]
+    fn test_from_str_fail() {
+        fn test(s: &str) {
+            assert_eq!(FromStr::from_str::<Rational>(s), None);
+        }
+
+        for ["0 /1", "abc", "", "1/", "--1/2","3/2/1"].each |&s| {
+            test(s);
+        }
+    }
+
+    #[test]
+    fn test_to_from_str_radix() {
+        fn test(r: Rational, s: ~str, n: uint) {
+            assert_eq!(FromStrRadix::from_str_radix(s, n), Some(r));
+            assert_eq!(r.to_str_radix(n), s);
+        }
+        fn test3(r: Rational, s: ~str) { test(r, s, 3) }
+        fn test16(r: Rational, s: ~str) { test(r, s, 16) }
+
+        test3(_1, ~"1/1");
+        test3(_0, ~"0/1");
+        test3(_1_2, ~"1/2");
+        test3(_3_2, ~"10/2");
+        test3(_2, ~"2/1");
+        test3(_neg1_2, ~"-1/2");
+        test3(_neg1_2 / _2, ~"-1/11");
+
+        test16(_1, ~"1/1");
+        test16(_0, ~"0/1");
+        test16(_1_2, ~"1/2");
+        test16(_3_2, ~"3/2");
+        test16(_2, ~"2/1");
+        test16(_neg1_2, ~"-1/2");
+        test16(_neg1_2 / _2, ~"-1/4");
+        test16(Ratio::new(13,15), ~"d/f");
+        test16(_1_2*_1_2*_1_2*_1_2, ~"1/10");
+    }
+
+    #[test]
+    fn test_from_str_radix_fail() {
+        fn test(s: &str) {
+            assert_eq!(FromStrRadix::from_str_radix::<Rational>(s, 3), None);
+        }
+
+        for ["0 /1", "abc", "", "1/", "--1/2","3/2/1", "3/2"].each |&s| {
+            test(s);
+        }
+    }
+}

src/libstd/std.rc

@@ -97,6 +97,8 @@ pub mod rl;
 pub mod workcache;
 #[path="num/bigint.rs"]
 pub mod bigint;
+#[path="num/rational.rs"]
+pub mod rational;
 pub mod stats;
 pub mod semver;
 pub mod fileinput;