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+// 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
+//!
+//! ## Compatibility
+//!
+//! The `num-rational` crate is tested for rustc 1.15 and greater.
+
+#![doc(html_root_url = "https://docs.rs/num-rational/0.2")]
+
+#![no_std]
+
+#[cfg(feature = "serde")]
+extern crate serde;
+#[cfg(feature = "bigint")]
+extern crate num_bigint as bigint;
+
+extern crate num_traits as traits;
+extern crate num_integer as integer;
+
+#[cfg(feature = "std")]
+#[cfg_attr(test, macro_use)]
+extern crate std;
+
+use core::cmp;
+#[cfg(feature = "std")]
+use std::error::Error;
+use core::fmt;
+use core::hash::{Hash, Hasher};
+use core::ops::{Add, Div, Mul, Neg, Rem, Sub};
+use core::str::FromStr;
+
+#[cfg(feature = "bigint")]
+use bigint::{BigInt, BigUint, Sign};
+
+use integer::Integer;
+use traits::float::FloatCore;
+use traits::{Bounded, CheckedAdd, CheckedDiv, CheckedMul, CheckedSub, FromPrimitive, Inv, Num,
+ NumCast, One, Pow, Signed, Zero};
+
+/// Represents the ratio between two numbers.
+#[derive(Copy, Clone, Debug)]
+#[allow(missing_docs)]
+pub struct Ratio<T> {
+ /// Numerator.
+ numer: T,
+ /// Denominator.
+ denom: T,
+}
+
+/// Alias for a `Ratio` of machine-sized integers.
+pub type Rational = Ratio<isize>;
+/// Alias for a `Ratio` of 32-bit-sized integers.
+pub type Rational32 = Ratio<i32>;
+/// Alias for a `Ratio` of 64-bit-sized integers.
+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 new `Ratio`. Fails if `denom` is zero.
+ #[inline]
+ pub fn new(numer: T, denom: T) -> Ratio<T> {
+ if denom.is_zero() {
+ panic!("denominator == 0");
+ }
+ let mut ret = Ratio::new_raw(numer, denom);
+ ret.reduce();
+ ret
+ }
+
+ /// 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,
+ }
+ }
+
+ /// Converts to an integer, rounding towards zero.
+ #[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.is_one()
+ }
+
+ /// Puts 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;
+ // T: Clone + Integer != T: Clone + NumAssign
+ self.numer = self.numer.clone() / g.clone();
+ // FIXME(#5992): assignment operator overloads
+ // self.denom /= g;
+ // T: Clone + Integer != T: Clone + NumAssign
+ 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 reduced copy of self.
+ ///
+ /// In general, it is not necessary to use this method, as the only
+ /// method of procuring a non-reduced fraction is through `new_raw`.
+ pub fn reduced(&self) -> Ratio<T> {
+ let mut ret = self.clone();
+ ret.reduce();
+ ret
+ }
+
+ /// Returns the reciprocal.
+ ///
+ /// Fails if the `Ratio` is zero.
+ #[inline]
+ pub fn recip(&self) -> Ratio<T> {
+ match self.numer.cmp(&T::zero()) {
+ cmp::Ordering::Equal => panic!("numerator == 0"),
+ cmp::Ordering::Greater => Ratio::new_raw(self.denom.clone(), self.numer.clone()),
+ cmp::Ordering::Less => Ratio::new_raw(T::zero() - self.denom.clone(),
+ T::zero() - 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, with division rounded towards zero.
+ ///
+ /// Satisfies `self == self.trunc() + self.fract()`.
+ #[inline]
+ pub fn fract(&self) -> Ratio<T> {
+ Ratio::new_raw(self.numer.clone() % self.denom.clone(), self.denom.clone())
+ }
+}
+
+impl<T: Clone + Integer + Pow<u32, Output = T>> Ratio<T> {
+ /// Raises the `Ratio` to the power of an exponent.
+ #[inline]
+ pub fn pow(&self, expon: i32) -> Ratio<T> {
+ Pow::pow(self, expon)
+ }
+}
+
+macro_rules! pow_impl {
+ ($exp: ty) => {
+ pow_impl!($exp, $exp);
+ };
+ ($exp: ty, $unsigned: ty) => {
+ impl<T: Clone + Integer + Pow<$unsigned, Output = T>> Pow<$exp> for Ratio<T> {
+ type Output = Ratio<T>;
+ #[inline]
+ fn pow(self, expon: $exp) -> Ratio<T> {
+ match expon.cmp(&0) {
+ cmp::Ordering::Equal => One::one(),
+ cmp::Ordering::Less => {
+ let expon = expon.wrapping_abs() as $unsigned;
+ Ratio::new_raw(
+ Pow::pow(self.denom, expon),
+ Pow::pow(self.numer, expon),
+ )
+ },
+ cmp::Ordering::Greater => {
+ Ratio::new_raw(
+ Pow::pow(self.numer, expon as $unsigned),
+ Pow::pow(self.denom, expon as $unsigned),
+ )
+ }
+ }
+ }
+ }
+ impl<'a, T: Clone + Integer + Pow<$unsigned, Output = T>> Pow<$exp> for &'a Ratio<T> {
+ type Output = Ratio<T>;
+ #[inline]
+ fn pow(self, expon: $exp) -> Ratio<T> {
+ Pow::pow(self.clone(), expon)
+ }
+ }
+ impl<'a, T: Clone + Integer + Pow<$unsigned, Output = T>> Pow<&'a $exp> for Ratio<T> {
+ type Output = Ratio<T>;
+ #[inline]
+ fn pow(self, expon: &'a $exp) -> Ratio<T> {
+ Pow::pow(self, *expon)
+ }
+ }
+ impl<'a, 'b, T: Clone + Integer + Pow<$unsigned, Output = T>> Pow<&'a $exp> for &'b Ratio<T> {
+ type Output = Ratio<T>;
+ #[inline]
+ fn pow(self, expon: &'a $exp) -> Ratio<T> {
+ Pow::pow(self.clone(), *expon)
+ }
+ }
+ };
+}
+
+// this is solely to make `pow_impl!` work
+trait WrappingAbs: Sized {
+ fn wrapping_abs(self) -> Self {
+ self
+ }
+}
+impl WrappingAbs for u8 {}
+impl WrappingAbs for u16 {}
+impl WrappingAbs for u32 {}
+impl WrappingAbs for u64 {}
+impl WrappingAbs for usize {}
+
+pow_impl!(i8, u8);
+pow_impl!(i16, u16);
+pow_impl!(i32, u32);
+pow_impl!(i64, u64);
+pow_impl!(isize, usize);
+pow_impl!(u8);
+pow_impl!(u16);
+pow_impl!(u32);
+pow_impl!(u64);
+pow_impl!(usize);
+
+// TODO: pow_impl!(BigUint) and pow_impl!(BigInt, BigUint)
+
+#[cfg(feature = "bigint")]
+impl Ratio<BigInt> {
+ /// Converts a float into a rational number.
+ pub fn from_float<T: FloatCore>(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)))
+ }
+ }
+}
+
+// From integer
+impl<T> From<T> for Ratio<T> where T: Clone + Integer {
+ fn from(x: T) -> Ratio<T> {
+ Ratio::from_integer(x)
+ }
+}
+
+// From pair (through the `new` constructor)
+impl<T> From<(T, T)> for Ratio<T> where T: Clone + Integer {
+ fn from(pair: (T, T)) -> Ratio<T> {
+ Ratio::new(pair.0, pair.1)
+ }
+}
+
+// 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> {}
+
+// NB: We can't just `#[derive(Hash)]`, because it needs to agree
+// with `Eq` even for non-reduced ratios.
+impl<T: Clone + Integer + Hash> Hash for Ratio<T> {
+ fn hash<H: Hasher>(&self, state: &mut H) {
+ recurse(&self.numer, &self.denom, state);
+
+ fn recurse<T: Integer + Hash, H: Hasher>(numer: &T, denom: &T, state: &mut H) {
+ if !denom.is_zero() {
+ let (int, rem) = numer.div_mod_floor(denom);
+ int.hash(state);
+ recurse(denom, &rem, state);
+ } else {
+ denom.hash(state);
+ }
+ }
+ }
+}
+
+mod iter_sum_product {
+ use ::core::iter::{Sum, Product};
+ use Ratio;
+ use integer::Integer;
+ use traits::{Zero, One};
+
+ impl<T: Integer + Clone> Sum for Ratio<T> {
+ fn sum<I>(iter: I) -> Self
+ where
+ I: Iterator<Item = Ratio<T>>
+ {
+ iter.fold(Self::zero(), |sum, num| sum + num)
+ }
+ }
+
+ impl<'a, T: Integer + Clone> Sum<&'a Ratio<T>> for Ratio<T> {
+ fn sum<I>(iter: I) -> Self
+ where
+ I: Iterator<Item = &'a Ratio<T>>
+ {
+ iter.fold(Self::zero(), |sum, num| sum + num)
+ }
+ }
+
+ impl<T: Integer + Clone> Product for Ratio<T> {
+ fn product<I>(iter: I) -> Self
+ where
+ I: Iterator<Item = Ratio<T>>
+ {
+ iter.fold(Self::one(), |prod, num| prod * num)
+ }
+ }
+
+ impl<'a, T: Integer + Clone> Product<&'a Ratio<T>> for Ratio<T> {
+ fn product<I>(iter: I) -> Self
+ where
+ I: Iterator<Item = &'a Ratio<T>>
+ {
+ iter.fold(Self::one(), |prod, num| prod * num)
+ }
+ }
+}
+
+mod opassign {
+ use core::ops::{AddAssign, SubAssign, MulAssign, DivAssign, RemAssign};
+
+ use Ratio;
+ use integer::Integer;
+ use traits::NumAssign;
+
+ impl<T: Clone + Integer + NumAssign> AddAssign for Ratio<T> {
+ fn add_assign(&mut self, other: Ratio<T>) {
+ self.numer *= other.denom.clone();
+ self.numer += self.denom.clone() * other.numer;
+ self.denom *= other.denom;
+ self.reduce();
+ }
+ }
+
+ impl<T: Clone + Integer + NumAssign> DivAssign for Ratio<T> {
+ fn div_assign(&mut self, other: Ratio<T>) {
+ self.numer *= other.denom;
+ self.denom *= other.numer;
+ self.reduce();
+ }
+ }
+
+ impl<T: Clone + Integer + NumAssign> MulAssign for Ratio<T> {
+ fn mul_assign(&mut self, other: Ratio<T>) {
+ self.numer *= other.numer;
+ self.denom *= other.denom;
+ self.reduce();
+ }
+ }
+
+ impl<T: Clone + Integer + NumAssign> RemAssign for Ratio<T> {
+ fn rem_assign(&mut self, other: Ratio<T>) {
+ self.numer *= other.denom.clone();
+ self.numer %= self.denom.clone() * other.numer;
+ self.denom *= other.denom;
+ self.reduce();
+ }
+ }
+
+ impl<T: Clone + Integer + NumAssign> SubAssign for Ratio<T> {
+ fn sub_assign(&mut self, other: Ratio<T>) {
+ self.numer *= other.denom.clone();
+ self.numer -= self.denom.clone() * other.numer;
+ self.denom *= other.denom;
+ self.reduce();
+ }
+ }
+
+ // a/b + c/1 = (a*1 + b*c) / (b*1) = (a + b*c) / b
+ impl<T: Clone + Integer + NumAssign> AddAssign<T> for Ratio<T> {
+ fn add_assign(&mut self, other: T) {
+ self.numer += self.denom.clone() * other;
+ self.reduce();
+ }
+ }
+
+ impl<T: Clone + Integer + NumAssign> DivAssign<T> for Ratio<T> {
+ fn div_assign(&mut self, other: T) {
+ self.denom *= other;
+ self.reduce();
+ }
+ }
+
+ impl<T: Clone + Integer + NumAssign> MulAssign<T> for Ratio<T> {
+ fn mul_assign(&mut self, other: T) {
+ self.numer *= other;
+ self.reduce();
+ }
+ }
+
+ // a/b % c/1 = (a*1 % b*c) / (b*1) = (a % b*c) / b
+ impl<T: Clone + Integer + NumAssign> RemAssign<T> for Ratio<T> {
+ fn rem_assign(&mut self, other: T) {
+ self.numer %= self.denom.clone() * other;
+ self.reduce();
+ }
+ }
+
+ // a/b - c/1 = (a*1 - b*c) / (b*1) = (a - b*c) / b
+ impl<T: Clone + Integer + NumAssign> SubAssign<T> for Ratio<T> {
+ fn sub_assign(&mut self, other: T) {
+ self.numer -= self.denom.clone() * other;
+ self.reduce();
+ }
+ }
+
+ macro_rules! forward_op_assign {
+ (impl $imp:ident, $method:ident) => {
+ impl<'a, T: Clone + Integer + NumAssign> $imp<&'a Ratio<T>> for Ratio<T> {
+ #[inline]
+ fn $method(&mut self, other: &Ratio<T>) {
+ self.$method(other.clone())
+ }
+ }
+ impl<'a, T: Clone + Integer + NumAssign> $imp<&'a T> for Ratio<T> {
+ #[inline]
+ fn $method(&mut self, other: &T) {
+ self.$method(other.clone())
+ }
+ }
+ }
+ }
+
+ forward_op_assign!(impl AddAssign, add_assign);
+ forward_op_assign!(impl DivAssign, div_assign);
+ forward_op_assign!(impl MulAssign, mul_assign);
+ forward_op_assign!(impl RemAssign, rem_assign);
+ forward_op_assign!(impl SubAssign, sub_assign);
+}
+
+macro_rules! forward_ref_ref_binop {
+ (impl $imp:ident, $method:ident) => {
+ impl<'a, 'b, T: Clone + Integer> $imp<&'b Ratio<T>> for &'a Ratio<T> {
+ type Output = Ratio<T>;
+
+ #[inline]
+ fn $method(self, other: &'b Ratio<T>) -> Ratio<T> {
+ self.clone().$method(other.clone())
+ }
+ }
+ impl<'a, 'b, T: Clone + Integer> $imp<&'b T> for &'a Ratio<T> {
+ type Output = Ratio<T>;
+
+ #[inline]
+ fn $method(self, other: &'b T) -> Ratio<T> {
+ self.clone().$method(other.clone())
+ }
+ }
+ }
+}
+
+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 $method(self, other: Ratio<T>) -> Ratio<T> {
+ self.clone().$method(other)
+ }
+ }
+ impl<'a, T> $imp<T> for &'a Ratio<T> where
+ T: Clone + Integer
+ {
+ type Output = Ratio<T>;
+
+ #[inline]
+ fn $method(self, other: T) -> Ratio<T> {
+ self.clone().$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.clone())
+ }
+ }
+ impl<'a, T> $imp<&'a T> for Ratio<T> where
+ T: Clone + Integer
+ {
+ type Output = Ratio<T>;
+
+ #[inline]
+ fn $method(self, other: &T) -> Ratio<T> {
+ self.$method(other.clone())
+ }
+ }
+ }
+}
+
+macro_rules! forward_all_binop {
+ (impl $imp:ident, $method:ident) => {
+ forward_ref_ref_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<T> Mul<Ratio<T>> for Ratio<T>
+ where T: Clone + Integer
+{
+ type Output = Ratio<T>;
+ #[inline]
+ fn mul(self, rhs: Ratio<T>) -> Ratio<T> {
+ Ratio::new(self.numer * rhs.numer,
+ self.denom * rhs.denom)
+ }
+}
+// a/b * c/1 = (a*c) / (b*1) = (a*c) / b
+impl<T> Mul<T> for Ratio<T>
+ where T: Clone + Integer
+{
+ type Output = Ratio<T>;
+ #[inline]
+ fn mul(self, rhs: T) -> Ratio<T> {
+ Ratio::new(self.numer * rhs,
+ self.denom)
+ }
+}
+
+forward_all_binop!(impl Div, div);
+// (a/b) / (c/d) = (a*d) / (b*c)
+impl<T> Div<Ratio<T>> for Ratio<T>
+ where T: Clone + Integer
+{
+ type Output = Ratio<T>;
+
+ #[inline]
+ fn div(self, rhs: Ratio<T>) -> Ratio<T> {
+ Ratio::new(self.numer * rhs.denom,
+ self.denom * rhs.numer)
+ }
+}
+// (a/b) / (c/1) = (a*1) / (b*c) = a / (b*c)
+impl<T> Div<T> for Ratio<T>
+ where T: Clone + Integer
+{
+ type Output = Ratio<T>;
+
+ #[inline]
+ fn div(self, rhs: T) -> Ratio<T> {
+ Ratio::new(self.numer,
+ self.denom * rhs)
+ }
+}
+
+macro_rules! arith_impl {
+ (impl $imp:ident, $method:ident) => {
+ forward_all_binop!(impl $imp, $method);
+ // Abstracts the a/b `op` c/d = (a*d `op` b*c) / (b*d) pattern
+ impl<T: Clone + Integer> $imp<Ratio<T>> for Ratio<T> {
+ type Output = Ratio<T>;
+ #[inline]
+ fn $method(self, rhs: Ratio<T>) -> Ratio<T> {
+ Ratio::new((self.numer * rhs.denom.clone()).$method(self.denom.clone() * rhs.numer),
+ self.denom * rhs.denom)
+ }
+ }
+ // Abstracts the a/b `op` c/1 = (a*1 `op` b*c) / (b*1) = (a `op` b*c) / b pattern
+ impl<T: Clone + Integer> $imp<T> for Ratio<T> {
+ type Output = Ratio<T>;
+ #[inline]
+ fn $method(self, rhs: T) -> Ratio<T> {
+ Ratio::new(self.numer.$method(self.denom.clone() * rhs),
+ self.denom)
+ }
+ }
+ }
+}
+
+arith_impl!(impl Add, add);
+arith_impl!(impl Sub, sub);
+arith_impl!(impl Rem, rem);
+
+// Like `std::try!` for Option<T>, unwrap the value or early-return None.
+// Since Rust 1.22 this can be replaced by the `?` operator.
+macro_rules! otry {
+ ($expr:expr) => (match $expr {
+ Some(val) => val,
+ None => return None,
+ })
+}
+
+// a/b * c/d = (a*c)/(b*d)
+impl<T> CheckedMul for Ratio<T>
+ where T: Clone + Integer + CheckedMul
+{
+ #[inline]
+ fn checked_mul(&self, rhs: &Ratio<T>) -> Option<Ratio<T>> {
+ Some(Ratio::new(otry!(self.numer.checked_mul(&rhs.numer)),
+ otry!(self.denom.checked_mul(&rhs.denom))))
+ }
+}
+
+// (a/b) / (c/d) = (a*d)/(b*c)
+impl<T> CheckedDiv for Ratio<T>
+ where T: Clone + Integer + CheckedMul
+{
+ #[inline]
+ fn checked_div(&self, rhs: &Ratio<T>) -> Option<Ratio<T>> {
+ let bc = otry!(self.denom.checked_mul(&rhs.numer));
+ if bc.is_zero() {
+ None
+ } else {
+ Some(Ratio::new(otry!(self.numer.checked_mul(&rhs.denom)), bc))
+ }
+ }
+}
+
+// As arith_impl! but for Checked{Add,Sub} traits
+macro_rules! checked_arith_impl {
+ (impl $imp:ident, $method:ident) => {
+ impl<T: Clone + Integer + CheckedMul + $imp> $imp for Ratio<T> {
+ #[inline]
+ fn $method(&self, rhs: &Ratio<T>) -> Option<Ratio<T>> {
+ let ad = otry!(self.numer.checked_mul(&rhs.denom));
+ let bc = otry!(self.denom.checked_mul(&rhs.numer));
+ let bd = otry!(self.denom.checked_mul(&rhs.denom));
+ Some(Ratio::new(otry!(ad.$method(&bc)), bd))
+ }
+ }
+ }
+}
+
+// a/b + c/d = (a*d + b*c)/(b*d)
+checked_arith_impl!(impl CheckedAdd, checked_add);
+
+// a/b - c/d = (a*d - b*c)/(b*d)
+checked_arith_impl!(impl CheckedSub, checked_sub);
+
+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()
+ }
+}
+
+impl<T> Inv for Ratio<T>
+ where T: Clone + Integer
+{
+ type Output = Ratio<T>;
+
+ #[inline]
+ fn inv(self) -> Ratio<T> {
+ self.recip()
+ }
+}
+
+impl<'a, T> Inv for &'a Ratio<T>
+ where T: Clone + Integer
+{
+ type Output = Ratio<T>;
+
+ #[inline]
+ fn inv(self) -> Ratio<T> {
+ self.recip()
+ }
+}
+
+// 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())
+ }
+
+ #[inline]
+ fn is_one(&self) -> bool {
+ self.numer == self.denom
+ }
+}
+
+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> {
+ if s.splitn(2, '/').count() == 2 {
+ let mut parts = s.splitn(2, '/').map(|ss| T::from_str_radix(ss, radix).map_err(|_| {
+ ParseRatioError { kind: RatioErrorKind::ParseError }
+ }));
+ let numer: T = parts.next().unwrap()?;
+ let denom: T = parts.next().unwrap()?;
+ if denom.is_zero() {
+ Err(ParseRatioError { kind: RatioErrorKind::ZeroDenominator })
+ } else {
+ Ok(Ratio::new(numer, denom))
+ }
+ } else {
+ Err(ParseRatioError { kind: RatioErrorKind::ParseError })
+ }
+ }
+}
+
+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.numer.is_positive() && self.denom.is_positive()) ||
+ (self.numer.is_negative() && self.denom.is_negative())
+ }
+
+ #[inline]
+ fn is_negative(&self) -> bool {
+ (self.numer.is_negative() && self.denom.is_positive()) ||
+ (self.numer.is_positive() && 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.is_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))
+ }
+ }
+}
+
+impl<T> Into<(T, T)> for Ratio<T> {
+ fn into(self) -> (T, T) {
+ (self.numer, self.denom)
+ }
+}
+
+#[cfg(feature = "serde")]
+impl<T> serde::Serialize for Ratio<T>
+ where T: serde::Serialize + Clone + Integer + PartialOrd
+{
+ fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
+ where S: serde::Serializer
+ {
+ (self.numer(), self.denom()).serialize(serializer)
+ }
+}
+
+#[cfg(feature = "serde")]
+impl<'de, T> serde::Deserialize<'de> for Ratio<T>
+ where T: serde::Deserialize<'de> + Clone + Integer + PartialOrd
+{
+ fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>
+ where D: serde::Deserializer<'de>
+ {
+ use serde::de::Unexpected;
+ use serde::de::Error;
+ let (numer, denom): (T,T) = try!(serde::Deserialize::deserialize(deserializer));
+ if denom.is_zero() {
+ Err(Error::invalid_value(Unexpected::Signed(0), &"a ratio with non-zero denominator"))
+ } 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.kind.description().fmt(f)
+ }
+}
+
+#[cfg(feature = "std")]
+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(feature = "bigint")]
+impl FromPrimitive for Ratio<BigInt> {
+ fn from_i64(n: i64) -> Option<Self> {
+ Some(Ratio::from_integer(n.into()))
+ }
+
+ #[cfg(has_i128)]
+ fn from_i128(n: i128) -> Option<Self> {
+ Some(Ratio::from_integer(n.into()))
+ }
+
+ fn from_u64(n: u64) -> Option<Self> {
+ Some(Ratio::from_integer(n.into()))
+ }
+
+ #[cfg(has_i128)]
+ fn from_u128(n: u128) -> Option<Self> {
+ Some(Ratio::from_integer(n.into()))
+ }
+
+ fn from_f32(n: f32) -> Option<Self> {
+ Ratio::from_float(n)
+ }
+
+ fn from_f64(n: f64) -> Option<Self> {
+ Ratio::from_float(n)
+ }
+}
+
+macro_rules! from_primitive_integer {
+ ($typ:ty, $approx:ident) => {
+ impl FromPrimitive for Ratio<$typ> {
+ fn from_i64(n: i64) -> Option<Self> {
+ <$typ as FromPrimitive>::from_i64(n).map(Ratio::from_integer)
+ }
+
+ #[cfg(has_i128)]
+ fn from_i128(n: i128) -> Option<Self> {
+ <$typ as FromPrimitive>::from_i128(n).map(Ratio::from_integer)
+ }
+
+ fn from_u64(n: u64) -> Option<Self> {
+ <$typ as FromPrimitive>::from_u64(n).map(Ratio::from_integer)
+ }
+
+ #[cfg(has_i128)]
+ fn from_u128(n: u128) -> Option<Self> {
+ <$typ as FromPrimitive>::from_u128(n).map(Ratio::from_integer)
+ }
+
+ fn from_f32(n: f32) -> Option<Self> {
+ $approx(n, 10e-20, 30)
+ }
+
+ fn from_f64(n: f64) -> Option<Self> {
+ $approx(n, 10e-20, 30)
+ }
+ }
+ }
+}
+
+from_primitive_integer!(i8, approximate_float);
+from_primitive_integer!(i16, approximate_float);
+from_primitive_integer!(i32, approximate_float);
+from_primitive_integer!(i64, approximate_float);
+#[cfg(has_i128)]
+from_primitive_integer!(i128, approximate_float);
+from_primitive_integer!(isize, approximate_float);
+
+from_primitive_integer!(u8, approximate_float_unsigned);
+from_primitive_integer!(u16, approximate_float_unsigned);
+from_primitive_integer!(u32, approximate_float_unsigned);
+from_primitive_integer!(u64, approximate_float_unsigned);
+#[cfg(has_i128)]
+from_primitive_integer!(u128, approximate_float_unsigned);
+from_primitive_integer!(usize, approximate_float_unsigned);
+
+impl<T: Integer + Signed + Bounded + NumCast + Clone> Ratio<T> {
+ pub fn approximate_float<F: FloatCore + NumCast>(f: F) -> Option<Ratio<T>> {
+ // 1/10e-20 < 1/2**32 which seems like a good default, and 30 seems
+ // to work well. Might want to choose something based on the types in the future, e.g.
+ // T::max().recip() and T::bits() or something similar.
+ let epsilon = <F as NumCast>::from(10e-20).expect("Can't convert 10e-20");
+ approximate_float(f, epsilon, 30)
+ }
+}
+
+fn approximate_float<T, F>(val: F, max_error: F, max_iterations: usize) -> Option<Ratio<T>>
+ where T: Integer + Signed + Bounded + NumCast + Clone,
+ F: FloatCore + NumCast
+{
+ let negative = val.is_sign_negative();
+ let abs_val = val.abs();
+
+ let r = approximate_float_unsigned(abs_val, max_error, max_iterations);
+
+ // Make negative again if needed
+ if negative {
+ r.map(|r| r.neg())
+ } else {
+ r
+ }
+}
+
+// No Unsigned constraint because this also works on positive integers and is called
+// like that, see above
+fn approximate_float_unsigned<T, F>(val: F, max_error: F, max_iterations: usize) -> Option<Ratio<T>>
+ where T: Integer + Bounded + NumCast + Clone,
+ F: FloatCore + NumCast
+{
+ // Continued fractions algorithm
+ // http://mathforum.org/dr.math/faq/faq.fractions.html#decfrac
+
+ if val < F::zero() || val.is_nan() {
+ return None;
+ }
+
+ let mut q = val;
+ let mut n0 = T::zero();
+ let mut d0 = T::one();
+ let mut n1 = T::one();
+ let mut d1 = T::zero();
+
+ let t_max = T::max_value();
+ let t_max_f = match <F as NumCast>::from(t_max.clone()) {
+ None => return None,
+ Some(t_max_f) => t_max_f,
+ };
+
+ // 1/epsilon > T::MAX
+ let epsilon = t_max_f.recip();
+
+ // Overflow
+ if q > t_max_f {
+ return None;
+ }
+
+ for _ in 0..max_iterations {
+ let a = match <T as NumCast>::from(q) {
+ None => break,
+ Some(a) => a,
+ };
+
+ let a_f = match <F as NumCast>::from(a.clone()) {
+ None => break,
+ Some(a_f) => a_f,
+ };
+ let f = q - a_f;
+
+ // Prevent overflow
+ if !a.is_zero() &&
+ (n1 > t_max.clone() / a.clone() ||
+ d1 > t_max.clone() / a.clone() ||
+ a.clone() * n1.clone() > t_max.clone() - n0.clone() ||
+ a.clone() * d1.clone() > t_max.clone() - d0.clone()) {
+ break;
+ }
+
+ let n = a.clone() * n1.clone() + n0.clone();
+ let d = a.clone() * d1.clone() + d0.clone();
+
+ n0 = n1;
+ d0 = d1;
+ n1 = n.clone();
+ d1 = d.clone();
+
+ // Simplify fraction. Doing so here instead of at the end
+ // allows us to get closer to the target value without overflows
+ let g = Integer::gcd(&n1, &d1);
+ if !g.is_zero() {
+ n1 = n1 / g.clone();
+ d1 = d1 / g.clone();
+ }
+
+ // Close enough?
+ let (n_f, d_f) = match (<F as NumCast>::from(n), <F as NumCast>::from(d)) {
+ (Some(n_f), Some(d_f)) => (n_f, d_f),
+ _ => break,
+ };
+ if (n_f / d_f - val).abs() < max_error {
+ break;
+ }
+
+ // Prevent division by ~0
+ if f < epsilon {
+ break;
+ }
+ q = f.recip();
+ }
+
+ // Overflow
+ if d1.is_zero() {
+ return None;
+ }
+
+ Some(Ratio::new(n1, d1))
+}
+
+#[cfg(test)]
+#[cfg(feature = "std")]
+fn hash<T: Hash>(x: &T) -> u64 {
+ use std::hash::BuildHasher;
+ use std::collections::hash_map::RandomState;
+ let mut hasher = <RandomState as BuildHasher>::Hasher::new();
+ x.hash(&mut hasher);
+ hasher.finish()
+}
+
+#[cfg(test)]
+mod test {
+ use super::{Ratio, Rational};
+ #[cfg(feature = "bigint")]
+ use super::BigRational;
+
+ use core::str::FromStr;
+ use core::i32;
+ use core::f64;
+ use traits::{Zero, One, Signed, FromPrimitive, Pow};
+ use integer::Integer;
+
+ 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 _NEG2: 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_NEG2: Rational = Ratio {
+ numer: 1,
+ denom: -2,
+ };
+ pub const _NEG1_NEG2: 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));
+ assert_eq!(_2, From::from(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_approximate_float() {
+ assert_eq!(Ratio::from_f32(0.5f32), Some(Ratio::new(1i64, 2)));
+ assert_eq!(Ratio::from_f64(0.5f64), Some(Ratio::new(1i32, 2)));
+ assert_eq!(Ratio::from_f32(5f32), Some(Ratio::new(5i64, 1)));
+ assert_eq!(Ratio::from_f64(5f64), Some(Ratio::new(5i32, 1)));
+ assert_eq!(Ratio::from_f32(29.97f32), Some(Ratio::new(2997i64, 100)));
+ assert_eq!(Ratio::from_f32(-29.97f32), Some(Ratio::new(-2997i64, 100)));
+
+ assert_eq!(Ratio::<i8>::from_f32(63.5f32), Some(Ratio::new(127i8, 2)));
+ assert_eq!(Ratio::<i8>::from_f32(126.5f32), Some(Ratio::new(126i8, 1)));
+ assert_eq!(Ratio::<i8>::from_f32(127.0f32), Some(Ratio::new(127i8, 1)));
+ assert_eq!(Ratio::<i8>::from_f32(127.5f32), None);
+ assert_eq!(Ratio::<i8>::from_f32(-63.5f32), Some(Ratio::new(-127i8, 2)));
+ assert_eq!(Ratio::<i8>::from_f32(-126.5f32), Some(Ratio::new(-126i8, 1)));
+ assert_eq!(Ratio::<i8>::from_f32(-127.0f32), Some(Ratio::new(-127i8, 1)));
+ assert_eq!(Ratio::<i8>::from_f32(-127.5f32), None);
+
+ assert_eq!(Ratio::<u8>::from_f32(-127f32), None);
+ assert_eq!(Ratio::<u8>::from_f32(127f32), Some(Ratio::new(127u8, 1)));
+ assert_eq!(Ratio::<u8>::from_f32(127.5f32), Some(Ratio::new(255u8, 2)));
+ assert_eq!(Ratio::<u8>::from_f32(256f32), None);
+
+ assert_eq!(Ratio::<i64>::from_f64(-10e200), None);
+ assert_eq!(Ratio::<i64>::from_f64(10e200), None);
+ assert_eq!(Ratio::<i64>::from_f64(f64::INFINITY), None);
+ assert_eq!(Ratio::<i64>::from_f64(f64::NEG_INFINITY), None);
+ assert_eq!(Ratio::<i64>::from_f64(f64::NAN), None);
+ assert_eq!(Ratio::<i64>::from_f64(f64::EPSILON), Some(Ratio::new(1, 4503599627370496)));
+ assert_eq!(Ratio::<i64>::from_f64(0.0), Some(Ratio::new(0, 1)));
+ assert_eq!(Ratio::<i64>::from_f64(-0.0), Some(Ratio::new(0, 1)));
+ }
+
+ #[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 core::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 = [
+ 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) {
+ #[cfg(feature = "std")]
+ 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]
+ #[cfg(feature = "std")]
+ fn test_show() {
+ use std::string::ToString;
+ 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};
+ use traits::{CheckedAdd, CheckedSub, CheckedMul, CheckedDiv};
+
+ #[test]
+ fn test_add() {
+ fn test(a: Rational, b: Rational, c: Rational) {
+ assert_eq!(a + b, c);
+ assert_eq!({ let mut x = a; x += b; x}, c);
+ assert_eq!(to_big(a) + to_big(b), to_big(c));
+ assert_eq!(a.checked_add(&b), Some(c));
+ assert_eq!(to_big(a).checked_add(&to_big(b)), Some(to_big(c)));
+ }
+ fn test_assign(a: Rational, b: isize, c: Rational) {
+ assert_eq!(a + b, c);
+ assert_eq!({ let mut x = a; x += b; x}, c);
+ }
+
+ test(_1, _1_2, _3_2);
+ test(_1, _1, _2);
+ test(_1_2, _3_2, _2);
+ test(_1_2, _NEG1_2, _0);
+ test_assign(_1_2, 1, _3_2);
+ }
+
+ #[test]
+ fn test_sub() {
+ fn test(a: Rational, b: Rational, c: Rational) {
+ assert_eq!(a - b, c);
+ assert_eq!({ let mut x = a; x -= b; x}, c);
+ assert_eq!(to_big(a) - to_big(b), to_big(c));
+ assert_eq!(a.checked_sub(&b), Some(c));
+ assert_eq!(to_big(a).checked_sub(&to_big(b)), Some(to_big(c)));
+ }
+ fn test_assign(a: Rational, b: isize, c: Rational) {
+ assert_eq!(a - b, c);
+ assert_eq!({ let mut x = a; x -= b; x}, c);
+ }
+
+ test(_1, _1_2, _1_2);
+ test(_3_2, _1_2, _1);
+ test(_1, _NEG1_2, _3_2);
+ test_assign(_1_2, 1, _NEG1_2);
+ }
+
+ #[test]
+ fn test_mul() {
+ fn test(a: Rational, b: Rational, c: Rational) {
+ assert_eq!(a * b, c);
+ assert_eq!({ let mut x = a; x *= b; x}, c);
+ assert_eq!(to_big(a) * to_big(b), to_big(c));
+ assert_eq!(a.checked_mul(&b), Some(c));
+ assert_eq!(to_big(a).checked_mul(&to_big(b)), Some(to_big(c)));
+ }
+ fn test_assign(a: Rational, b: isize, c: Rational) {
+ assert_eq!(a * b, c);
+ assert_eq!({ let mut x = a; x *= b; x}, 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_assign(_1_2, 2, _1);
+ }
+
+ #[test]
+ fn test_div() {
+ fn test(a: Rational, b: Rational, c: Rational) {
+ assert_eq!(a / b, c);
+ assert_eq!({ let mut x = a; x /= b; x}, c);
+ assert_eq!(to_big(a) / to_big(b), to_big(c));
+ assert_eq!(a.checked_div(&b), Some(c));
+ assert_eq!(to_big(a).checked_div(&to_big(b)), Some(to_big(c)));
+ }
+ fn test_assign(a: Rational, b: isize, c: Rational) {
+ assert_eq!(a / b, c);
+ assert_eq!({ let mut x = a; x /= b; x}, 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_assign(_1, 2, _1_2);
+ }
+
+ #[test]
+ fn test_rem() {
+ fn test(a: Rational, b: Rational, c: Rational) {
+ assert_eq!(a % b, c);
+ assert_eq!({ let mut x = a; x %= b; x}, c);
+ assert_eq!(to_big(a) % to_big(b), to_big(c))
+ }
+ fn test_assign(a: Rational, b: isize, c: Rational) {
+ assert_eq!(a % b, c);
+ assert_eq!({ let mut x = a; x %= b; x}, c);
+ }
+
+ test(_3_2, _1, _1_2);
+ test(_2, _NEG1_2, _0);
+ test(_1_2, _2, _1_2);
+ test_assign(_3_2, 1, _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_checked_failures() {
+ let big = Ratio::new(128u8, 1);
+ let small = Ratio::new(1, 128u8);
+ assert_eq!(big.checked_add(&big), None);
+ assert_eq!(small.checked_sub(&big), None);
+ assert_eq!(big.checked_mul(&big), None);
+ assert_eq!(small.checked_div(&big), None);
+ assert_eq!(_1.checked_div(&_0), None);
+ }
+ }
+
+ #[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);
+
+ assert_eq!(_3_2.recip(), _2_3);
+ assert_eq!(_NEG1_2.recip(), _NEG2);
+ assert_eq!(_NEG1_2.recip().denom(), &1);
+ }
+
+ #[test]
+ #[should_panic(expected = "== 0")]
+ fn test_recip_fail() {
+ let _a = Ratio::new(0, 1).recip();
+ }
+
+ #[test]
+ fn test_pow() {
+ fn test(r: Rational, e: i32, expected: Rational) {
+ assert_eq!(r.pow(e), expected);
+ assert_eq!(Pow::pow(r, e), expected);
+ assert_eq!(Pow::pow(r, &e), expected);
+ assert_eq!(Pow::pow(&r, e), expected);
+ assert_eq!(Pow::pow(&r, &e), expected);
+ }
+
+ test(_1_2, 2, Ratio::new(1, 4));
+ test(_1_2, -2, Ratio::new(4, 1));
+ test(_1, 1, _1);
+ test(_1, i32::MAX, _1);
+ test(_1, i32::MIN, _1);
+ test(_NEG1_2, 2, _1_2.pow(2i32));
+ test(_NEG1_2, 3, -_1_2.pow(3i32));
+ test(_3_2, 0, _1);
+ test(_3_2, -1, _3_2.recip());
+ test(_3_2, 3, Ratio::new(27, 8));
+ }
+
+ #[test]
+ #[cfg(feature = "std")]
+ fn test_to_from_str() {
+ use std::string::{String, ToString};
+ 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() {
+ use traits::float::FloatCore;
+ fn test<T: FloatCore>(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 core::{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(), -<Ratio<isize>>::one());
+ assert_eq!(_0.signum(), Zero::zero());
+ assert!(_NEG1_2.is_negative());
+ assert!(_1_NEG2.is_negative());
+ assert!(!_NEG1_2.is_positive());
+ assert!(!_1_NEG2.is_positive());
+ assert!(_1_2.is_positive());
+ assert!(_NEG1_NEG2.is_positive());
+ assert!(!_1_2.is_negative());
+ assert!(!_NEG1_NEG2.is_negative());
+ assert!(!_0.is_positive());
+ assert!(!_0.is_negative());
+ }
+
+ #[test]
+ #[cfg(feature = "std")]
+ fn test_hash() {
+ assert!(::hash(&_0) != ::hash(&_1));
+ assert!(::hash(&_0) != ::hash(&_3_2));
+
+ // a == b -> hash(a) == hash(b)
+ let a = Rational::new_raw(4, 2);
+ let b = Rational::new_raw(6, 3);
+ assert_eq!(a, b);
+ assert_eq!(::hash(&a), ::hash(&b));
+
+ let a = Rational::new_raw(123456789, 1000);
+ let b = Rational::new_raw(123456789 * 5, 5000);
+ assert_eq!(a, b);
+ assert_eq!(::hash(&a), ::hash(&b));
+ }
+
+ #[test]
+ fn test_into_pair() {
+ assert_eq! ((0, 1), _0.into());
+ assert_eq! ((-2, 1), _NEG2.into());
+ assert_eq! ((1, -2), _1_NEG2.into());
+ }
+
+ #[test]
+ fn test_from_pair() {
+ assert_eq! (_0, Ratio::from ((0, 1)));
+ assert_eq! (_1, Ratio::from ((1, 1)));
+ assert_eq! (_NEG2, Ratio::from ((-2, 1)));
+ assert_eq! (_1_NEG2, Ratio::from ((1, -2)));
+ }
+
+ #[test]
+ fn ratio_iter_sum() {
+ // generic function to assure the iter method can be called
+ // for any Iterator with Item = Ratio<impl Integer> or Ratio<&impl Integer>
+ fn iter_sums<T: Integer + Clone>(slice: &[Ratio<T>]) -> [Ratio<T>; 3] {
+ let mut manual_sum = Ratio::new(T::zero(), T::one());
+ for ratio in slice {
+ manual_sum = manual_sum + ratio;
+ }
+ [
+ manual_sum,
+ slice.iter().sum(),
+ slice.iter().cloned().sum()
+ ]
+ }
+ // collect into array so test works on no_std
+ let mut nums = [Ratio::new(0,1); 1000];
+ for (i, r) in (0..1000).map(|n| Ratio::new(n, 500)).enumerate() {
+ nums[i] = r;
+ }
+ let sums = iter_sums(&nums[..]);
+ assert_eq!(sums[0], sums[1]);
+ assert_eq!(sums[0], sums[2]);
+ }
+
+ #[test]
+ fn ratio_iter_product() {
+ // generic function to assure the iter method can be called
+ // for any Iterator with Item = Ratio<impl Integer> or Ratio<&impl Integer>
+ fn iter_products<T: Integer + Clone>(slice: &[Ratio<T>]) -> [Ratio<T>; 3] {
+ let mut manual_prod = Ratio::new(T::one(), T::one());
+ for ratio in slice {
+ manual_prod = manual_prod * ratio;
+ }
+ [
+ manual_prod,
+ slice.iter().product(),
+ slice.iter().cloned().product()
+ ]
+ }
+
+ // collect into array so test works on no_std
+ let mut nums = [Ratio::new(0,1); 1000];
+ for (i, r) in (0..1000).map(|n| Ratio::new(n, 500)).enumerate() {
+ nums[i] = r;
+ }
+ let products = iter_products(&nums[..]);
+ assert_eq!(products[0], products[1]);
+ assert_eq!(products[0], products[2]);
+ }
+}
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