832 lines
24 KiB
Rust
832 lines
24 KiB
Rust
// Copyright 2013-2014 The Rust Project Developers. See the COPYRIGHT
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// file at the top-level directory of this distribution and at
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// http://rust-lang.org/COPYRIGHT.
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//
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// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
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// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
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// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
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// option. This file may not be copied, modified, or distributed
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// except according to those terms.
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//! Rational numbers
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use Integer;
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use std::cmp;
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use std::fmt;
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use std::ops::{Add, Div, Mul, Neg, Rem, Sub};
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use std::str::FromStr;
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use std::num::{FromPrimitive, FromStrRadix, Float};
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use bigint::{BigInt, BigUint, Sign};
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use {Num, Signed, Zero, One};
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/// Represents the ratio between 2 numbers.
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#[derive(Copy, Clone, Hash, RustcEncodable, RustcDecodable)]
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#[allow(missing_docs)]
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pub struct Ratio<T> {
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numer: T,
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denom: T
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}
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/// Alias for a `Ratio` of machine-sized integers.
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pub type Rational = Ratio<isize>;
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pub type Rational32 = Ratio<i32>;
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pub type Rational64 = Ratio<i64>;
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/// Alias for arbitrary precision rationals.
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pub type BigRational = Ratio<BigInt>;
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impl<T: Clone + Integer + PartialOrd>
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Ratio<T> {
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/// Creates a ratio representing the integer `t`.
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#[inline]
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pub fn from_integer(t: T) -> Ratio<T> {
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Ratio::new_raw(t, One::one())
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}
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/// Creates a ratio without checking for `denom == 0` or reducing.
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#[inline]
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pub fn new_raw(numer: T, denom: T) -> Ratio<T> {
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Ratio { numer: numer, denom: denom }
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}
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/// Create a new Ratio. Fails if `denom == 0`.
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#[inline]
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pub fn new(numer: T, denom: T) -> Ratio<T> {
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if denom == Zero::zero() {
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panic!("denominator == 0");
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}
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let mut ret = Ratio::new_raw(numer, denom);
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ret.reduce();
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ret
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}
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/// Converts to an integer.
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#[inline]
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pub fn to_integer(&self) -> T {
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self.trunc().numer
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}
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/// Gets an immutable reference to the numerator.
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#[inline]
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pub fn numer<'a>(&'a self) -> &'a T {
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&self.numer
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}
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/// Gets an immutable reference to the denominator.
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#[inline]
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pub fn denom<'a>(&'a self) -> &'a T {
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&self.denom
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}
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/// Returns true if the rational number is an integer (denominator is 1).
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#[inline]
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pub fn is_integer(&self) -> bool {
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self.denom == One::one()
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}
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/// Put self into lowest terms, with denom > 0.
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fn reduce(&mut self) {
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let g : T = self.numer.gcd(&self.denom);
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// FIXME(#5992): assignment operator overloads
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// self.numer /= g;
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self.numer = self.numer.clone() / g.clone();
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// FIXME(#5992): assignment operator overloads
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// self.denom /= g;
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self.denom = self.denom.clone() / g;
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// keep denom positive!
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if self.denom < Zero::zero() {
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self.numer = -self.numer.clone();
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self.denom = -self.denom.clone();
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}
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}
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/// Returns a `reduce`d copy of self.
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pub fn reduced(&self) -> Ratio<T> {
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let mut ret = self.clone();
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ret.reduce();
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ret
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}
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/// Returns the reciprocal.
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#[inline]
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pub fn recip(&self) -> Ratio<T> {
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Ratio::new_raw(self.denom.clone(), self.numer.clone())
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}
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/// Rounds towards minus infinity.
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#[inline]
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pub fn floor(&self) -> Ratio<T> {
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if *self < Zero::zero() {
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let one: T = One::one();
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Ratio::from_integer((self.numer.clone() - self.denom.clone() + one) / self.denom.clone())
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} else {
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Ratio::from_integer(self.numer.clone() / self.denom.clone())
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}
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}
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/// Rounds towards plus infinity.
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#[inline]
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pub fn ceil(&self) -> Ratio<T> {
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if *self < Zero::zero() {
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Ratio::from_integer(self.numer.clone() / self.denom.clone())
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} else {
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let one: T = One::one();
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Ratio::from_integer((self.numer.clone() + self.denom.clone() - one) / self.denom.clone())
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}
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}
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/// Rounds to the nearest integer. Rounds half-way cases away from zero.
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#[inline]
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pub fn round(&self) -> Ratio<T> {
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let one: T = One::one();
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let two: T = one.clone() + one.clone();
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// Find unsigned fractional part of rational number
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let fractional = self.fract().abs();
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// The algorithm compares the unsigned fractional part with 1/2, that
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// is, a/b >= 1/2, or a >= b/2. For odd denominators, we use
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// a >= (b/2)+1. This avoids overflow issues.
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let half_or_larger = if fractional.denom().is_even() {
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*fractional.numer() >= fractional.denom().clone() / two.clone()
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} else {
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*fractional.numer() >= (fractional.denom().clone() / two.clone()) + one.clone()
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};
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if half_or_larger {
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let one: Ratio<T> = One::one();
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if *self >= Zero::zero() {
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self.trunc() + one
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} else {
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self.trunc() - one
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}
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} else {
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self.trunc()
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}
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}
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/// Rounds towards zero.
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#[inline]
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pub fn trunc(&self) -> Ratio<T> {
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Ratio::from_integer(self.numer.clone() / self.denom.clone())
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}
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/// Returns the fractional part of a number.
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#[inline]
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pub fn fract(&self) -> Ratio<T> {
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Ratio::new_raw(self.numer.clone() % self.denom.clone(), self.denom.clone())
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}
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}
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impl Ratio<BigInt> {
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/// Converts a float into a rational number.
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pub fn from_float<T: Float>(f: T) -> Option<BigRational> {
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if !f.is_finite() {
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return None;
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}
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let (mantissa, exponent, sign) = f.integer_decode();
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let bigint_sign = if sign == 1 { Sign::Plus } else { Sign::Minus };
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if exponent < 0 {
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let one: BigInt = One::one();
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let denom: BigInt = one << ((-exponent) as usize);
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let numer: BigUint = FromPrimitive::from_u64(mantissa).unwrap();
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Some(Ratio::new(BigInt::from_biguint(bigint_sign, numer), denom))
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} else {
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let mut numer: BigUint = FromPrimitive::from_u64(mantissa).unwrap();
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numer = numer << (exponent as usize);
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Some(Ratio::from_integer(BigInt::from_biguint(bigint_sign, numer)))
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}
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}
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}
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/* Comparisons */
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// comparing a/b and c/d is the same as comparing a*d and b*c, so we
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// abstract that pattern. The following macro takes a trait and either
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// a comma-separated list of "method name -> return value" or just
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// "method name" (return value is bool in that case)
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macro_rules! cmp_impl {
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(impl $imp:ident, $($method:ident),+) => {
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cmp_impl!(impl $imp, $($method -> bool),+);
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};
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// return something other than a Ratio<T>
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(impl $imp:ident, $($method:ident -> $res:ty),*) => {
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impl<T: Clone + Mul<T, Output = T> + $imp> $imp for Ratio<T> {
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$(
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#[inline]
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fn $method(&self, other: &Ratio<T>) -> $res {
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(self.numer.clone() * other.denom.clone()). $method (&(self.denom.clone()*other.numer.clone()))
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}
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)*
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}
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};
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}
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cmp_impl!(impl PartialEq, eq, ne);
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cmp_impl!(impl PartialOrd, lt -> bool, gt -> bool, le -> bool, ge -> bool,
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partial_cmp -> Option<cmp::Ordering>);
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cmp_impl!(impl Eq, );
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cmp_impl!(impl Ord, cmp -> cmp::Ordering);
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macro_rules! forward_val_val_binop {
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(impl $imp:ident, $method:ident) => {
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impl<T: Clone + Integer + PartialOrd> $imp<Ratio<T>> for Ratio<T> {
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type Output = Ratio<T>;
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#[inline]
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fn $method(self, other: Ratio<T>) -> Ratio<T> {
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(&self).$method(&other)
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}
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}
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}
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}
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macro_rules! forward_ref_val_binop {
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(impl $imp:ident, $method:ident) => {
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impl<'a, T: Clone + Integer + PartialOrd> $imp<Ratio<T>> for &'a Ratio<T> {
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type Output = Ratio<T>;
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#[inline]
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fn $method(self, other: Ratio<T>) -> Ratio<T> {
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self.$method(&other)
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}
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}
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}
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}
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macro_rules! forward_val_ref_binop {
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(impl $imp:ident, $method:ident) => {
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impl<'a, T: Clone + Integer + PartialOrd> $imp<&'a Ratio<T>> for Ratio<T> {
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type Output = Ratio<T>;
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#[inline]
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fn $method(self, other: &Ratio<T>) -> Ratio<T> {
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(&self).$method(other)
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}
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}
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}
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}
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macro_rules! forward_all_binop {
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(impl $imp:ident, $method:ident) => {
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forward_val_val_binop!(impl $imp, $method);
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forward_ref_val_binop!(impl $imp, $method);
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forward_val_ref_binop!(impl $imp, $method);
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};
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}
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/* Arithmetic */
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forward_all_binop!(impl Mul, mul);
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// a/b * c/d = (a*c)/(b*d)
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impl<'a, 'b, T> Mul<&'b Ratio<T>> for &'a Ratio<T>
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where T: Clone + Integer + PartialOrd
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{
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type Output = Ratio<T>;
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#[inline]
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fn mul(self, rhs: &Ratio<T>) -> Ratio<T> {
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Ratio::new(self.numer.clone() * rhs.numer.clone(), self.denom.clone() * rhs.denom.clone())
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}
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}
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forward_all_binop!(impl Div, div);
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// (a/b) / (c/d) = (a*d)/(b*c)
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impl<'a, 'b, T> Div<&'b Ratio<T>> for &'a Ratio<T>
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where T: Clone + Integer + PartialOrd
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{
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type Output = Ratio<T>;
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#[inline]
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fn div(self, rhs: &Ratio<T>) -> Ratio<T> {
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Ratio::new(self.numer.clone() * rhs.denom.clone(), self.denom.clone() * rhs.numer.clone())
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}
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}
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// Abstracts the a/b `op` c/d = (a*d `op` b*d) / (b*d) pattern
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macro_rules! arith_impl {
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(impl $imp:ident, $method:ident) => {
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forward_all_binop!(impl $imp, $method);
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impl<'a, 'b, T: Clone + Integer + PartialOrd>
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$imp<&'b Ratio<T>> for &'a Ratio<T> {
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type Output = Ratio<T>;
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#[inline]
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fn $method(self, rhs: &Ratio<T>) -> Ratio<T> {
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Ratio::new((self.numer.clone() * rhs.denom.clone()).$method(self.denom.clone() * rhs.numer.clone()),
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self.denom.clone() * rhs.denom.clone())
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}
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}
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}
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}
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// a/b + c/d = (a*d + b*c)/(b*d)
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arith_impl!(impl Add, add);
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// a/b - c/d = (a*d - b*c)/(b*d)
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arith_impl!(impl Sub, sub);
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// a/b % c/d = (a*d % b*c)/(b*d)
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arith_impl!(impl Rem, rem);
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impl<T> Neg for Ratio<T>
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where T: Clone + Integer + PartialOrd
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{
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type Output = Ratio<T>;
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#[inline]
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fn neg(self) -> Ratio<T> { -&self }
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}
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impl<'a, T> Neg for &'a Ratio<T>
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where T: Clone + Integer + PartialOrd
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{
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type Output = Ratio<T>;
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#[inline]
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fn neg(self) -> Ratio<T> {
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Ratio::new_raw(-self.numer.clone(), self.denom.clone())
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}
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}
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/* Constants */
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impl<T: Clone + Integer + PartialOrd>
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Zero for Ratio<T> {
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#[inline]
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fn zero() -> Ratio<T> {
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Ratio::new_raw(Zero::zero(), One::one())
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}
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#[inline]
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fn is_zero(&self) -> bool {
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*self == Zero::zero()
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}
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}
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impl<T: Clone + Integer + PartialOrd>
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One for Ratio<T> {
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#[inline]
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fn one() -> Ratio<T> {
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Ratio::new_raw(One::one(), One::one())
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}
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}
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impl<T: Clone + Integer + PartialOrd>
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Num for Ratio<T> {}
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impl<T: Clone + Integer + PartialOrd>
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Signed for Ratio<T> {
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#[inline]
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fn abs(&self) -> Ratio<T> {
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if self.is_negative() { -self.clone() } else { self.clone() }
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}
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#[inline]
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fn abs_sub(&self, other: &Ratio<T>) -> Ratio<T> {
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if *self <= *other { Zero::zero() } else { self - other }
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}
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#[inline]
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fn signum(&self) -> Ratio<T> {
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if *self > Zero::zero() {
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One::one()
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} else if self.is_zero() {
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Zero::zero()
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} else {
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- ::one::<Ratio<T>>()
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}
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}
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#[inline]
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fn is_positive(&self) -> bool { *self > Zero::zero() }
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#[inline]
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fn is_negative(&self) -> bool { *self < Zero::zero() }
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}
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/* String conversions */
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impl<T: fmt::Show + Eq + One> fmt::Show for Ratio<T> {
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/// Renders as `numer/denom`. If denom=1, renders as numer.
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fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
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if self.denom == One::one() {
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write!(f, "{:?}", self.numer)
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} else {
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write!(f, "{:?}/{:?}", self.numer, self.denom)
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}
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}
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}
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impl<T: fmt::String + Eq + One> fmt::String for Ratio<T> {
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/// Renders as `numer/denom`. If denom=1, renders as numer.
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fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
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if self.denom == One::one() {
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write!(f, "{}", self.numer)
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} else {
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write!(f, "{}/{}", self.numer, self.denom)
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}
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}
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}
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impl<T: FromStr + Clone + Integer + PartialOrd>
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FromStr for Ratio<T> {
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/// Parses `numer/denom` or just `numer`.
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fn from_str(s: &str) -> Option<Ratio<T>> {
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let mut split = s.splitn(1, '/');
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let num = split.next().and_then(|n| FromStr::from_str(n));
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let den = split.next().or(Some("1")).and_then(|d| FromStr::from_str(d));
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match (num, den) {
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(Some(n), Some(d)) => Some(Ratio::new(n, d)),
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_ => None
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}
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}
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}
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impl<T: FromStrRadix + Clone + Integer + PartialOrd>
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FromStrRadix for Ratio<T> {
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/// Parses `numer/denom` where the numbers are in base `radix`.
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fn from_str_radix(s: &str, radix: usize) -> Option<Ratio<T>> {
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let split: Vec<&str> = s.splitn(1, '/').collect();
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if split.len() < 2 {
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None
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} else {
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let a_option: Option<T> = FromStrRadix::from_str_radix(
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split[0],
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radix);
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a_option.and_then(|a| {
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let b_option: Option<T> =
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FromStrRadix::from_str_radix(split[1], radix);
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b_option.and_then(|b| {
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Some(Ratio::new(a.clone(), b.clone()))
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})
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})
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}
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}
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}
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#[cfg(test)]
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mod test {
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use super::{Ratio, Rational, BigRational};
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use std::num::{FromPrimitive, Float};
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use std::str::FromStr;
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use std::i32;
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use {Zero, One, Signed};
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pub const _0 : Rational = Ratio { numer: 0, denom: 1};
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pub const _1 : Rational = Ratio { numer: 1, denom: 1};
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pub const _2: Rational = Ratio { numer: 2, denom: 1};
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pub const _1_2: Rational = Ratio { numer: 1, denom: 2};
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pub const _3_2: Rational = Ratio { numer: 3, denom: 2};
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pub const _NEG1_2: Rational = Ratio { numer: -1, denom: 2};
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pub const _1_3: Rational = Ratio { numer: 1, denom: 3};
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pub const _NEG1_3: Rational = Ratio { numer: -1, denom: 3};
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pub const _2_3: Rational = Ratio { numer: 2, denom: 3};
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pub const _NEG2_3: Rational = Ratio { numer: -2, denom: 3};
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pub fn to_big(n: Rational) -> BigRational {
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Ratio::new(
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FromPrimitive::from_int(n.numer).unwrap(),
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FromPrimitive::from_int(n.denom).unwrap()
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)
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}
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#[test]
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fn test_test_constants() {
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// check our constants are what Ratio::new etc. would make.
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assert_eq!(_0, Zero::zero());
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assert_eq!(_1, One::one());
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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_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));
|
|
}
|
|
|
|
|
|
#[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_fail]
|
|
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_to_from_str() {
|
|
fn test(r: Rational, s: String) {
|
|
assert_eq!(FromStr::from_str(&s[]), Some(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: Option<Rational> = FromStr::from_str(s);
|
|
assert_eq!(rational, None);
|
|
}
|
|
|
|
let xs = ["0 /1", "abc", "", "1/", "--1/2","3/2/1"];
|
|
for &s in xs.iter() {
|
|
test(s);
|
|
}
|
|
}
|
|
|
|
#[test]
|
|
fn test_from_float() {
|
|
fn test<T: Float>(given: T, (numer, denom): (&str, &str)) {
|
|
let ratio: BigRational = Ratio::from_float(given).unwrap();
|
|
assert_eq!(ratio, Ratio::new(
|
|
FromStr::from_str(numer).unwrap(),
|
|
FromStr::from_str(denom).unwrap()));
|
|
}
|
|
|
|
// f32
|
|
test(3.14159265359f32, ("13176795", "4194304"));
|
|
test(2f32.powf(100.), ("1267650600228229401496703205376", "1"));
|
|
test(-2f32.powf(100.), ("-1267650600228229401496703205376", "1"));
|
|
test(1.0 / 2f32.powf(100.), ("1", "1267650600228229401496703205376"));
|
|
test(684729.48391f32, ("1369459", "2"));
|
|
test(-8573.5918555f32, ("-4389679", "512"));
|
|
|
|
// f64
|
|
test(3.14159265359f64, ("3537118876014453", "1125899906842624"));
|
|
test(2f64.powf(100.), ("1267650600228229401496703205376", "1"));
|
|
test(-2f64.powf(100.), ("-1267650600228229401496703205376", "1"));
|
|
test(684729.48391f64, ("367611342500051", "536870912"));
|
|
test(-8573.5918555f64, ("-4713381968463931", "549755813888"));
|
|
test(1.0 / 2f64.powf(100.), ("1", "1267650600228229401496703205376"));
|
|
}
|
|
|
|
#[test]
|
|
fn test_from_float_fail() {
|
|
use std::{f32, f64};
|
|
|
|
assert_eq!(Ratio::from_float(f32::NAN), None);
|
|
assert_eq!(Ratio::from_float(f32::INFINITY), None);
|
|
assert_eq!(Ratio::from_float(f32::NEG_INFINITY), None);
|
|
assert_eq!(Ratio::from_float(f64::NAN), None);
|
|
assert_eq!(Ratio::from_float(f64::INFINITY), None);
|
|
assert_eq!(Ratio::from_float(f64::NEG_INFINITY), None);
|
|
}
|
|
|
|
#[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));
|
|
}
|
|
}
|