Extract num-rational

src/rational.rs

@@ -1,1013 +0,0 @@
-// 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::error::Error;
-use std::fmt;
-use std::ops::{Add, Div, Mul, Neg, Rem, Sub};
-use std::str::FromStr;
-
-#[cfg(feature = "serde")]
-use serde;
-
-#[cfg(feature = "bigint")]
-use bigint::{BigInt, BigUint, Sign};
-use traits::{FromPrimitive, Float, PrimInt};
-use {Num, Signed, Zero, One};
-
-/// Represents the ratio between 2 numbers.
-#[derive(Copy, Clone, Hash, Debug)]
-#[cfg_attr(feature = "rustc-serialize", derive(RustcEncodable, RustcDecodable))]
-#[allow(missing_docs)]
-pub struct Ratio<T> {
-    numer: T,
-    denom: T
-}
-
-/// Alias for a `Ratio` of machine-sized integers.
-pub type Rational = Ratio<isize>;
-pub type Rational32 = Ratio<i32>;
-pub type Rational64 = Ratio<i64>;
-
-#[cfg(feature = "bigint")]
-/// Alias for arbitrary precision rationals.
-pub type BigRational = Ratio<BigInt>;
-
-impl<T: Clone + Integer> Ratio<T> {
-    /// Creates a ratio representing the integer `t`.
-    #[inline]
-    pub fn from_integer(t: T) -> Ratio<T> {
-        Ratio::new_raw(t, One::one())
-    }
-
-    /// Creates 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() {
-            panic!("denominator == 0");
-        }
-        let mut ret = Ratio::new_raw(numer, denom);
-        ret.reduce();
-        ret
-    }
-
-    /// Converts 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
-    }
-
-    /// Returns 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.clone() / g.clone();
-        // FIXME(#5992): assignment operator overloads
-        // self.denom /= g;
-        self.denom = self.denom.clone() / g;
-
-        // keep denom positive!
-        if self.denom < T::zero() {
-            self.numer = T::zero() - self.numer.clone();
-            self.denom = T::zero() - self.denom.clone();
-        }
-    }
-
-    /// Returns a `reduce`d copy of self.
-    pub fn reduced(&self) -> Ratio<T> {
-        let mut ret = self.clone();
-        ret.reduce();
-        ret
-    }
-
-    /// Returns the reciprocal.
-    #[inline]
-    pub fn recip(&self) -> Ratio<T> {
-        Ratio::new_raw(self.denom.clone(), self.numer.clone())
-    }
-
-    /// Rounds towards minus infinity.
-    #[inline]
-    pub fn floor(&self) -> Ratio<T> {
-        if *self < Zero::zero() {
-            let one: T = One::one();
-            Ratio::from_integer((self.numer.clone() - self.denom.clone() + one) / self.denom.clone())
-        } else {
-            Ratio::from_integer(self.numer.clone() / self.denom.clone())
-        }
-    }
-
-    /// Rounds towards plus infinity.
-    #[inline]
-    pub fn ceil(&self) -> Ratio<T> {
-        if *self < Zero::zero() {
-            Ratio::from_integer(self.numer.clone() / self.denom.clone())
-        } else {
-            let one: T = One::one();
-            Ratio::from_integer((self.numer.clone() + self.denom.clone() - one) / self.denom.clone())
-        }
-    }
-
-    /// Rounds to the nearest integer. Rounds half-way cases away from zero.
-    #[inline]
-    pub fn round(&self) -> Ratio<T> {
-        let zero: Ratio<T> = Zero::zero();
-        let one: T = One::one();
-        let two: T = one.clone() + one.clone();
-
-        // Find unsigned fractional part of rational number
-        let mut fractional = self.fract();
-        if fractional < zero { fractional = zero - fractional };
-
-        // The algorithm compares the unsigned fractional part with 1/2, that
-        // is, a/b >= 1/2, or a >= b/2. For odd denominators, we use
-        // a >= (b/2)+1. This avoids overflow issues.
-        let half_or_larger = if fractional.denom().is_even() {
-            *fractional.numer() >= fractional.denom().clone() / two.clone()
-        } else {
-            *fractional.numer() >= (fractional.denom().clone() / two.clone()) + one.clone()
-        };
-
-        if half_or_larger {
-            let one: Ratio<T> = One::one();
-            if *self >= Zero::zero() {
-                self.trunc() + one
-            } else {
-                self.trunc() - one
-            }
-        } else {
-            self.trunc()
-        }
-    }
-
-    /// Rounds towards zero.
-    #[inline]
-    pub fn trunc(&self) -> Ratio<T> {
-        Ratio::from_integer(self.numer.clone() / self.denom.clone())
-    }
-
-    /// Returns the fractional part of a number.
-    #[inline]
-    pub fn fract(&self) -> Ratio<T> {
-        Ratio::new_raw(self.numer.clone() % self.denom.clone(), self.denom.clone())
-    }
-}
-
-impl<T: Clone + Integer + PrimInt> Ratio<T> {
-    /// Raises the ratio to the power of an exponent
-    #[inline]
-    pub fn pow(&self, expon: i32) -> Ratio<T> {
-        match expon.cmp(&0) {
-            cmp::Ordering::Equal => One::one(),
-            cmp::Ordering::Less => self.recip().pow(-expon),
-            cmp::Ordering::Greater => Ratio::new_raw(self.numer.pow(expon as u32),
-                                                     self.denom.pow(expon as u32)),
-        }
-    }
-}
-
-#[cfg(feature = "bigint")]
-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 = if sign == 1 { Sign::Plus } else { Sign::Minus };
-        if exponent < 0 {
-            let one: BigInt = One::one();
-            let denom: BigInt = one << ((-exponent) as usize);
-            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 usize);
-            Some(Ratio::from_integer(BigInt::from_biguint(bigint_sign, numer)))
-        }
-    }
-}
-
-/* Comparisons */
-
-// Mathematically, comparing a/b and c/d is the same as comparing a*d and b*c, but it's very easy
-// for those multiplications to overflow fixed-size integers, so we need to take care.
-
-impl<T: Clone + Integer> Ord for Ratio<T> {
-    #[inline]
-    fn cmp(&self, other: &Self) -> cmp::Ordering {
-        // With equal denominators, the numerators can be directly compared
-        if self.denom == other.denom {
-            let ord = self.numer.cmp(&other.numer);
-            return if self.denom < T::zero() { ord.reverse() } else { ord };
-        }
-
-        // With equal numerators, the denominators can be inversely compared
-        if self.numer == other.numer {
-            let ord = self.denom.cmp(&other.denom);
-            return if self.numer < T::zero() { ord } else { ord.reverse() };
-        }
-
-        // Unfortunately, we don't have CheckedMul to try.  That could sometimes avoid all the
-        // division below, or even always avoid it for BigInt and BigUint.
-        // FIXME- future breaking change to add Checked* to Integer?
-
-        // Compare as floored integers and remainders
-        let (self_int, self_rem) = self.numer.div_mod_floor(&self.denom);
-        let (other_int, other_rem) = other.numer.div_mod_floor(&other.denom);
-        match self_int.cmp(&other_int) {
-            cmp::Ordering::Greater => cmp::Ordering::Greater,
-            cmp::Ordering::Less => cmp::Ordering::Less,
-            cmp::Ordering::Equal => {
-                match (self_rem.is_zero(), other_rem.is_zero()) {
-                    (true, true) => cmp::Ordering::Equal,
-                    (true, false) => cmp::Ordering::Less,
-                    (false, true) => cmp::Ordering::Greater,
-                    (false, false) => {
-                        // Compare the reciprocals of the remaining fractions in reverse
-                        let self_recip = Ratio::new_raw(self.denom.clone(), self_rem);
-                        let other_recip = Ratio::new_raw(other.denom.clone(), other_rem);
-                        self_recip.cmp(&other_recip).reverse()
-                    }
-                }
-            },
-        }
-    }
-}
-
-impl<T: Clone + Integer> PartialOrd for Ratio<T> {
-    #[inline]
-    fn partial_cmp(&self, other: &Self) -> Option<cmp::Ordering> {
-        Some(self.cmp(other))
-    }
-}
-
-impl<T: Clone + Integer> PartialEq for Ratio<T> {
-    #[inline]
-    fn eq(&self, other: &Self) -> bool {
-        self.cmp(other) == cmp::Ordering::Equal
-    }
-}
-
-impl<T: Clone + Integer> Eq for Ratio<T> {}
-
-
-macro_rules! forward_val_val_binop {
-    (impl $imp:ident, $method:ident) => {
-        impl<T: Clone + Integer> $imp<Ratio<T>> for Ratio<T> {
-            type Output = Ratio<T>;
-
-            #[inline]
-            fn $method(self, other: Ratio<T>) -> Ratio<T> {
-                (&self).$method(&other)
-            }
-        }
-    }
-}
-
-macro_rules! forward_ref_val_binop {
-    (impl $imp:ident, $method:ident) => {
-        impl<'a, T> $imp<Ratio<T>> for &'a Ratio<T> where
-            T: Clone + Integer
-        {
-            type Output = Ratio<T>;
-
-            #[inline]
-            fn $method(self, other: Ratio<T>) -> Ratio<T> {
-                self.$method(&other)
-            }
-        }
-    }
-}
-
-macro_rules! forward_val_ref_binop {
-    (impl $imp:ident, $method:ident) => {
-        impl<'a, T> $imp<&'a Ratio<T>> for Ratio<T> where
-            T: Clone + Integer
-        {
-            type Output = Ratio<T>;
-
-            #[inline]
-            fn $method(self, other: &Ratio<T>) -> Ratio<T> {
-                (&self).$method(other)
-            }
-        }
-    }
-}
-
-macro_rules! forward_all_binop {
-    (impl $imp:ident, $method:ident) => {
-        forward_val_val_binop!(impl $imp, $method);
-        forward_ref_val_binop!(impl $imp, $method);
-        forward_val_ref_binop!(impl $imp, $method);
-    };
-}
-
-/* Arithmetic */
-forward_all_binop!(impl Mul, mul);
-// a/b * c/d = (a*c)/(b*d)
-impl<'a, 'b, T> Mul<&'b Ratio<T>> for &'a Ratio<T>
-    where T: Clone + Integer
-{
-
-        type Output = Ratio<T>;
-    #[inline]
-    fn mul(self, rhs: &Ratio<T>) -> Ratio<T> {
-        Ratio::new(self.numer.clone() * rhs.numer.clone(), self.denom.clone() * rhs.denom.clone())
-    }
-}
-
-forward_all_binop!(impl Div, div);
-// (a/b) / (c/d) = (a*d)/(b*c)
-impl<'a, 'b, T> Div<&'b Ratio<T>> for &'a Ratio<T>
-    where T: Clone + Integer
-{
-    type Output = Ratio<T>;
-
-    #[inline]
-    fn div(self, rhs: &Ratio<T>) -> Ratio<T> {
-        Ratio::new(self.numer.clone() * rhs.denom.clone(), self.denom.clone() * rhs.numer.clone())
-    }
-}
-
-// Abstracts the a/b `op` c/d = (a*d `op` b*d) / (b*d) pattern
-macro_rules! arith_impl {
-    (impl $imp:ident, $method:ident) => {
-        forward_all_binop!(impl $imp, $method);
-        impl<'a, 'b, T: Clone + Integer>
-            $imp<&'b Ratio<T>> for &'a Ratio<T> {
-            type Output = Ratio<T>;
-            #[inline]
-            fn $method(self, rhs: &Ratio<T>) -> Ratio<T> {
-                Ratio::new((self.numer.clone() * rhs.denom.clone()).$method(self.denom.clone() * rhs.numer.clone()),
-                           self.denom.clone() * rhs.denom.clone())
-            }
-        }
-    }
-}
-
-// 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> Neg for Ratio<T>
-    where T: Clone + Integer + Neg<Output = T>
-{
-    type Output = Ratio<T>;
-
-    #[inline]
-    fn neg(self) -> Ratio<T> {
-        Ratio::new_raw(-self.numer, self.denom)
-    }
-}
-
-impl<'a, T> Neg for &'a Ratio<T>
-    where T: Clone + Integer + Neg<Output = T>
-{
-    type Output = Ratio<T>;
-
-    #[inline]
-    fn neg(self) -> Ratio<T> {
-        -self.clone()
-    }
-}
-
-/* Constants */
-impl<T: Clone + Integer>
-    Zero for Ratio<T> {
-    #[inline]
-    fn zero() -> Ratio<T> {
-        Ratio::new_raw(Zero::zero(), One::one())
-    }
-
-    #[inline]
-    fn is_zero(&self) -> bool {
-        self.numer.is_zero()
-    }
-}
-
-impl<T: Clone + Integer>
-    One for Ratio<T> {
-    #[inline]
-    fn one() -> Ratio<T> {
-        Ratio::new_raw(One::one(), One::one())
-    }
-}
-
-impl<T: Clone + Integer> Num for Ratio<T> {
-    type FromStrRadixErr = ParseRatioError;
-
-    /// Parses `numer/denom` where the numbers are in base `radix`.
-    fn from_str_radix(s: &str, radix: u32) -> Result<Ratio<T>, ParseRatioError> {
-        let split: Vec<&str> = s.splitn(2, '/').collect();
-        if split.len() < 2 {
-            Err(ParseRatioError{kind: RatioErrorKind::ParseError})
-        } else {
-            let a_result: Result<T, _> = T::from_str_radix(
-                split[0],
-                radix).map_err(|_| ParseRatioError{kind: RatioErrorKind::ParseError});
-            a_result.and_then(|a| {
-                let b_result: Result<T, _>  =
-                    T::from_str_radix(split[1], radix).map_err(
-                        |_| ParseRatioError{kind: RatioErrorKind::ParseError});
-                b_result.and_then(|b| if b.is_zero() {
-                    Err(ParseRatioError{kind: RatioErrorKind::ZeroDenominator})
-                } else {
-                    Ok(Ratio::new(a.clone(), b.clone()))
-                })
-            })
-        }
-    }
-}
-
-impl<T: Clone + Integer + Signed> Signed for Ratio<T> {
-    #[inline]
-    fn abs(&self) -> Ratio<T> {
-        if self.is_negative() { -self.clone() } else { self.clone() }
-    }
-
-    #[inline]
-    fn abs_sub(&self, other: &Ratio<T>) -> Ratio<T> {
-        if *self <= *other { Zero::zero() } else { self - other }
-    }
-
-    #[inline]
-    fn signum(&self) -> Ratio<T> {
-        if self.is_positive() {
-            Self::one()
-        } else if self.is_zero() {
-            Self::zero()
-        } else {
-            - Self::one()
-        }
-    }
-
-    #[inline]
-    fn is_positive(&self) -> bool { !self.is_negative() }
-
-    #[inline]
-    fn is_negative(&self) -> bool {
-        self.numer.is_negative() ^ self.denom.is_negative()
-    }
-}
-
-/* String conversions */
-impl<T> fmt::Display for Ratio<T> where
-    T: fmt::Display + Eq + One
-{
-    /// Renders as `numer/denom`. If denom=1, renders as numer.
-    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
-        if self.denom == One::one() {
-            write!(f, "{}", self.numer)
-        } else {
-            write!(f, "{}/{}", self.numer, self.denom)
-        }
-    }
-}
-
-impl<T: FromStr + Clone + Integer> FromStr for Ratio<T> {
-    type Err = ParseRatioError;
-
-    /// Parses `numer/denom` or just `numer`.
-    fn from_str(s: &str) -> Result<Ratio<T>, ParseRatioError> {
-        let mut split = s.splitn(2, '/');
-
-        let n = try!(split.next().ok_or(
-            ParseRatioError{kind: RatioErrorKind::ParseError}));
-        let num = try!(FromStr::from_str(n).map_err(
-            |_| ParseRatioError{kind: RatioErrorKind::ParseError}));
-
-        let d = split.next().unwrap_or("1");
-        let den = try!(FromStr::from_str(d).map_err(
-            |_| ParseRatioError{kind: RatioErrorKind::ParseError}));
-
-        if Zero::is_zero(&den) {
-            Err(ParseRatioError{kind: RatioErrorKind::ZeroDenominator})
-        } else {
-            Ok(Ratio::new(num, den))
-        }
-    }
-}
-
-#[cfg(feature = "serde")]
-impl<T> serde::Serialize for Ratio<T>
-    where T: serde::Serialize + Clone + Integer + PartialOrd
-{
-    fn serialize<S>(&self, serializer: &mut S) -> Result<(), S::Error> where
-        S: serde::Serializer
-    {
-        (self.numer(), self.denom()).serialize(serializer)
-    }
-}
-
-#[cfg(feature = "serde")]
-impl<T> serde::Deserialize for Ratio<T>
-    where T: serde::Deserialize + Clone + Integer + PartialOrd
-{
-    fn deserialize<D>(deserializer: &mut D) -> Result<Self, D::Error> where
-        D: serde::Deserializer,
-    {
-        let (numer, denom) = try!(serde::Deserialize::deserialize(deserializer));
-        if denom == Zero::zero() {
-            Err(serde::de::Error::invalid_value("denominator is zero"))
-        } else {
-            Ok(Ratio::new_raw(numer, denom))
-        }
-    }
-}
-
-// FIXME: Bubble up specific errors
-#[derive(Copy, Clone, Debug, PartialEq)]
-pub struct ParseRatioError { kind: RatioErrorKind }
-
-#[derive(Copy, Clone, Debug, PartialEq)]
-enum RatioErrorKind {
-    ParseError,
-    ZeroDenominator,
-}
-
-impl fmt::Display for ParseRatioError {
-    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
-        self.description().fmt(f)
-    }
-}
-
-impl Error for ParseRatioError {
-    fn description(&self) -> &str { self.kind.description() }
-}
-
-impl RatioErrorKind {
-    fn description(&self) -> &'static str {
-        match *self {
-            RatioErrorKind::ParseError => "failed to parse integer",
-            RatioErrorKind::ZeroDenominator => "zero value denominator",
-        }
-    }
-}
-
-#[cfg(test)]
-mod test {
-
-    use super::{Ratio, Rational};
-    #[cfg(feature = "bigint")]
-    use super::BigRational;
-    use std::str::FromStr;
-    use std::i32;
-    use {Zero, One, Signed, FromPrimitive, Float};
-
-    pub const _0 : Rational = Ratio { numer: 0, denom: 1};
-    pub const _1 : Rational = Ratio { numer: 1, denom: 1};
-    pub const _2: Rational = Ratio { numer: 2, denom: 1};
-    pub const _1_2: Rational = Ratio { numer: 1, denom: 2};
-    pub const _3_2: Rational = Ratio { numer: 3, denom: 2};
-    pub const _NEG1_2: Rational = Ratio { numer: -1, denom: 2};
-    pub const _1_3: Rational = Ratio { numer: 1, denom: 3};
-    pub const _NEG1_3: Rational = Ratio { numer: -1, denom: 3};
-    pub const _2_3: Rational = Ratio { numer: 2, denom: 3};
-    pub const _NEG2_3: Rational = Ratio { numer: -2, denom: 3};
-
-    #[cfg(feature = "bigint")]
-    pub fn to_big(n: Rational) -> BigRational {
-        Ratio::new(
-            FromPrimitive::from_isize(n.numer).unwrap(),
-            FromPrimitive::from_isize(n.denom).unwrap()
-        )
-    }
-    #[cfg(not(feature = "bigint"))]
-    pub fn to_big(n: Rational) -> Rational {
-        Ratio::new(
-            FromPrimitive::from_isize(n.numer).unwrap(),
-            FromPrimitive::from_isize(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(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(2,2);
-
-        assert_eq!(one22, One::one());
-    }
-    #[test]
-    #[should_panic]
-    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));
-    }
-
-    #[test]
-    fn test_cmp_overflow() {
-        use std::cmp::Ordering;
-
-        // issue #7 example:
-        let big = Ratio::new(128u8, 1);
-        let small = big.recip();
-        assert!(big > small);
-
-        // try a few that are closer together
-        // (some matching numer, some matching denom, some neither)
-        let ratios = vec![
-            Ratio::new(125_i8, 127_i8),
-            Ratio::new(63_i8, 64_i8),
-            Ratio::new(124_i8, 125_i8),
-            Ratio::new(125_i8, 126_i8),
-            Ratio::new(126_i8, 127_i8),
-            Ratio::new(127_i8, 126_i8),
-        ];
-
-        fn check_cmp(a: Ratio<i8>, b: Ratio<i8>, ord: Ordering) {
-            println!("comparing {} and {}", a, b);
-            assert_eq!(a.cmp(&b), ord);
-            assert_eq!(b.cmp(&a), ord.reverse());
-        }
-
-        for (i, &a) in ratios.iter().enumerate() {
-            check_cmp(a, a, Ordering::Equal);
-            check_cmp(-a, a, Ordering::Less);
-            for &b in &ratios[i+1..] {
-                check_cmp(a, b, Ordering::Less);
-                check_cmp(-a, -b, Ordering::Greater);
-                check_cmp(a.recip(), b.recip(), Ordering::Greater);
-                check_cmp(-a.recip(), -b.recip(), Ordering::Less);
-            }
-        }
-    }
-
-    #[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());
-    }
-
-    #[test]
-    fn test_show() {
-        assert_eq!(format!("{}", _2), "2".to_string());
-        assert_eq!(format!("{}", _1_2), "1/2".to_string());
-        assert_eq!(format!("{}", _0), "0".to_string());
-        assert_eq!(format!("{}", Ratio::from_integer(-2)), "-2".to_string());
-    }
-
-    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(3,4));
-            test(_1_2, _NEG1_2, Ratio::new(-1, 4));
-        }
-
-        #[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_panic]
-        fn test_div_0() {
-            let _a =  _1 / _0;
-        }
-    }
-
-    #[test]
-    fn test_round() {
-        assert_eq!(_1_3.ceil(), _1);
-        assert_eq!(_1_3.floor(), _0);
-        assert_eq!(_1_3.round(), _0);
-        assert_eq!(_1_3.trunc(), _0);
-
-        assert_eq!(_NEG1_3.ceil(), _0);
-        assert_eq!(_NEG1_3.floor(), -_1);
-        assert_eq!(_NEG1_3.round(), _0);
-        assert_eq!(_NEG1_3.trunc(), _0);
-
-        assert_eq!(_2_3.ceil(), _1);
-        assert_eq!(_2_3.floor(), _0);
-        assert_eq!(_2_3.round(), _1);
-        assert_eq!(_2_3.trunc(), _0);
-
-        assert_eq!(_NEG2_3.ceil(), _0);
-        assert_eq!(_NEG2_3.floor(), -_1);
-        assert_eq!(_NEG2_3.round(), -_1);
-        assert_eq!(_NEG2_3.trunc(), _0);
-
-        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);
-
-        // Overflow checks
-
-        let _neg1 = Ratio::from_integer(-1);
-        let _large_rat1 = Ratio::new(i32::MAX, i32::MAX-1);
-        let _large_rat2 = Ratio::new(i32::MAX-1, i32::MAX);
-        let _large_rat3 = Ratio::new(i32::MIN+2, i32::MIN+1);
-        let _large_rat4 = Ratio::new(i32::MIN+1, i32::MIN+2);
-        let _large_rat5 = Ratio::new(i32::MIN+2, i32::MAX);
-        let _large_rat6 = Ratio::new(i32::MAX, i32::MIN+2);
-        let _large_rat7 = Ratio::new(1, i32::MIN+1);
-        let _large_rat8 = Ratio::new(1, i32::MAX);
-
-        assert_eq!(_large_rat1.round(), One::one());
-        assert_eq!(_large_rat2.round(), One::one());
-        assert_eq!(_large_rat3.round(), One::one());
-        assert_eq!(_large_rat4.round(), One::one());
-        assert_eq!(_large_rat5.round(), _neg1);
-        assert_eq!(_large_rat6.round(), _neg1);
-        assert_eq!(_large_rat7.round(), Zero::zero());
-        assert_eq!(_large_rat8.round(), Zero::zero());
-    }
-
-    #[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_pow() {
-        assert_eq!(_1_2.pow(2), Ratio::new(1, 4));
-        assert_eq!(_1_2.pow(-2), Ratio::new(4, 1));
-        assert_eq!(_1.pow(1), _1);
-        assert_eq!(_NEG1_2.pow(2), _1_2.pow(2));
-        assert_eq!(_NEG1_2.pow(3), -_1_2.pow(3));
-        assert_eq!(_3_2.pow(0), _1);
-        assert_eq!(_3_2.pow(-1), _3_2.recip());
-        assert_eq!(_3_2.pow(3), Ratio::new(27, 8));
-    }
-
-    #[test]
-    fn test_to_from_str() {
-        fn test(r: Rational, s: String) {
-            assert_eq!(FromStr::from_str(&s), Ok(r));
-            assert_eq!(r.to_string(), s);
-        }
-        test(_1, "1".to_string());
-        test(_0, "0".to_string());
-        test(_1_2, "1/2".to_string());
-        test(_3_2, "3/2".to_string());
-        test(_2, "2".to_string());
-        test(_NEG1_2, "-1/2".to_string());
-    }
-    #[test]
-    fn test_from_str_fail() {
-        fn test(s: &str) {
-            let rational: Result<Rational, _> = FromStr::from_str(s);
-            assert!(rational.is_err());
-        }
-
-        let xs = ["0 /1", "abc", "", "1/", "--1/2","3/2/1", "1/0"];
-        for &s in xs.iter() {
-            test(s);
-        }
-    }
-
-    #[cfg(feature = "bigint")]
-    #[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"));
-    }
-
-    #[cfg(feature = "bigint")]
-    #[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);
-    }
-
-    #[test]
-    fn test_signed() {
-        assert_eq!(_NEG1_2.abs(), _1_2);
-        assert_eq!(_3_2.abs_sub(&_1_2), _1);
-        assert_eq!(_1_2.abs_sub(&_3_2), Zero::zero());
-        assert_eq!(_1_2.signum(), One::one());
-        assert_eq!(_NEG1_2.signum(), - ::one::<Ratio<isize>>());
-        assert!(_NEG1_2.is_negative());
-        assert!(! _NEG1_2.is_positive());
-        assert!(! _1_2.is_negative());
-    }
-
-    #[test]
-    fn test_hash() {
-        assert!(::hash(&_0) != ::hash(&_1));
-        assert!(::hash(&_0) != ::hash(&_3_2));
-    }
-}