# [−][src]Struct num::rational::Ratio

`pub struct Ratio<T> { /* fields omitted */ }`

Represents the ratio between two numbers.

## Methods

### `impl<T> Ratio<T>`[src]

These method are `const` for Rust 1.31 and later.

#### `pub const fn new_raw(numer: T, denom: T) -> Ratio<T>`[src]

Creates a `Ratio` without checking for `denom == 0` or reducing.

#### `pub const fn numer(&self) -> &T`[src]

Gets an immutable reference to the numerator.

#### `pub const fn denom(&self) -> &T`[src]

Gets an immutable reference to the denominator.

### `impl<T> Ratio<T> where    T: Clone + Integer, `[src]

#### `pub fn new(numer: T, denom: T) -> Ratio<T>`[src]

Creates a new `Ratio`. Fails if `denom` is zero.

#### `pub fn from_integer(t: T) -> Ratio<T>`[src]

Creates a `Ratio` representing the integer `t`.

#### `pub fn to_integer(&self) -> T`[src]

Converts to an integer, rounding towards zero.

#### `pub fn is_integer(&self) -> bool`[src]

Returns true if the rational number is an integer (denominator is 1).

#### `pub fn reduced(&self) -> Ratio<T>`[src]

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 recip(&self) -> Ratio<T>`[src]

Returns the reciprocal.

Fails if the `Ratio` is zero.

#### `pub fn floor(&self) -> Ratio<T>`[src]

Rounds towards minus infinity.

#### `pub fn ceil(&self) -> Ratio<T>`[src]

Rounds towards plus infinity.

#### `pub fn round(&self) -> Ratio<T>`[src]

Rounds to the nearest integer. Rounds half-way cases away from zero.

#### `pub fn trunc(&self) -> Ratio<T>`[src]

Rounds towards zero.

#### `pub fn fract(&self) -> Ratio<T>`[src]

Returns the fractional part of a number, with division rounded towards zero.

Satisfies `self == self.trunc() + self.fract()`.

### `impl<T> Ratio<T> where    T: Clone + Integer + Pow<u32, Output = T>, `[src]

#### `pub fn pow(&self, expon: i32) -> Ratio<T>`[src]

Raises the `Ratio` to the power of an exponent.

### `impl Ratio<BigInt>`[src]

#### `pub fn from_float<T>(f: T) -> Option<Ratio<BigInt>> where    T: FloatCore, `[src]

Converts a float into a rational number.

## Trait Implementations

### `impl<'a, T> Add<&'a Ratio<T>> for Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `+` operator.

### `impl<'a, T> Add<&'a T> for Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `+` operator.

### `impl<'a, 'b, T> Add<&'b Ratio<T>> for &'a Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `+` operator.

### `impl<'a, 'b, T> Add<&'b T> for &'a Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `+` operator.

### `impl<'a, T> Add<Ratio<T>> for &'a Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `+` operator.

### `impl<T> Add<Ratio<T>> for Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `+` operator.

### `impl<T> Add<T> for Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `+` operator.

### `impl<'a, T> Add<T> for &'a Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `+` operator.

### `impl<T> Display for Ratio<T> where    T: Display + Eq + One, `[src]

#### `fn fmt(&self, f: &mut Formatter) -> Result<(), Error>`[src]

Renders as `numer/denom`. If denom=1, renders as numer.

### `impl<'a, T> Div<&'a Ratio<T>> for Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `/` operator.

### `impl<'a, T> Div<&'a T> for Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `/` operator.

### `impl<'a, 'b, T> Div<&'b Ratio<T>> for &'a Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `/` operator.

### `impl<'a, 'b, T> Div<&'b T> for &'a Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `/` operator.

### `impl<T> Div<Ratio<T>> for Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `/` operator.

### `impl<'a, T> Div<Ratio<T>> for &'a Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `/` operator.

### `impl<T> Div<T> for Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `/` operator.

### `impl<'a, T> Div<T> for &'a Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `/` operator.

### `impl<T> FromStr for Ratio<T> where    T: Clone + FromStr + Integer, `[src]

#### `type Err = ParseRatioError`

The associated error which can be returned from parsing.

#### `fn from_str(s: &str) -> Result<Ratio<T>, ParseRatioError>`[src]

Parses `numer/denom` or just `numer`.

### `impl<'a, T> Inv for &'a Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<T> Inv for Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<'a, T> Mul<&'a Ratio<T>> for Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `*` operator.

### `impl<'a, T> Mul<&'a T> for Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `*` operator.

### `impl<'a, 'b, T> Mul<&'b Ratio<T>> for &'a Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `*` operator.

### `impl<'a, 'b, T> Mul<&'b T> for &'a Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `*` operator.

### `impl<T> Mul<Ratio<T>> for Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `*` operator.

### `impl<'a, T> Mul<Ratio<T>> for &'a Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `*` operator.

### `impl<T> Mul<T> for Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `*` operator.

### `impl<'a, T> Mul<T> for &'a Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `*` operator.

### `impl<T> Neg for Ratio<T> where    T: Clone + Integer + Neg<Output = T>, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `-` operator.

### `impl<'a, T> Neg for &'a Ratio<T> where    T: Clone + Integer + Neg<Output = T>, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `-` operator.

### `impl<T> Num for Ratio<T> where    T: Clone + Integer, `[src]

#### `fn from_str_radix(s: &str, radix: u32) -> Result<Ratio<T>, ParseRatioError>`[src]

Parses `numer/denom` where the numbers are in base `radix`.

### `impl<'a, 'b, T> Pow<&'a i16> for &'b Ratio<T> where    T: Clone + Integer + Pow<u16, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<'a, T> Pow<&'a i16> for Ratio<T> where    T: Clone + Integer + Pow<u16, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<'a, T> Pow<&'a i32> for Ratio<T> where    T: Clone + Integer + Pow<u32, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<'a, 'b, T> Pow<&'a i32> for &'b Ratio<T> where    T: Clone + Integer + Pow<u32, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<'a, T> Pow<&'a i64> for Ratio<T> where    T: Clone + Integer + Pow<u64, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<'a, 'b, T> Pow<&'a i64> for &'b Ratio<T> where    T: Clone + Integer + Pow<u64, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<'a, T> Pow<&'a i8> for Ratio<T> where    T: Clone + Integer + Pow<u8, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<'a, 'b, T> Pow<&'a i8> for &'b Ratio<T> where    T: Clone + Integer + Pow<u8, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<'a, 'b, T> Pow<&'a isize> for &'b Ratio<T> where    T: Clone + Integer + Pow<usize, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<'a, T> Pow<&'a isize> for Ratio<T> where    T: Clone + Integer + Pow<usize, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<'a, 'b, T> Pow<&'a u16> for &'b Ratio<T> where    T: Clone + Integer + Pow<u16, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<'a, T> Pow<&'a u16> for Ratio<T> where    T: Clone + Integer + Pow<u16, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<'a, 'b, T> Pow<&'a u32> for &'b Ratio<T> where    T: Clone + Integer + Pow<u32, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<'a, T> Pow<&'a u32> for Ratio<T> where    T: Clone + Integer + Pow<u32, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<'a, 'b, T> Pow<&'a u64> for &'b Ratio<T> where    T: Clone + Integer + Pow<u64, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<'a, T> Pow<&'a u64> for Ratio<T> where    T: Clone + Integer + Pow<u64, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<'a, 'b, T> Pow<&'a u8> for &'b Ratio<T> where    T: Clone + Integer + Pow<u8, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<'a, T> Pow<&'a u8> for Ratio<T> where    T: Clone + Integer + Pow<u8, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<'a, T> Pow<&'a usize> for Ratio<T> where    T: Clone + Integer + Pow<usize, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<'a, 'b, T> Pow<&'a usize> for &'b Ratio<T> where    T: Clone + Integer + Pow<usize, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<T> Pow<i16> for Ratio<T> where    T: Clone + Integer + Pow<u16, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<'a, T> Pow<i16> for &'a Ratio<T> where    T: Clone + Integer + Pow<u16, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<'a, T> Pow<i32> for &'a Ratio<T> where    T: Clone + Integer + Pow<u32, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<T> Pow<i32> for Ratio<T> where    T: Clone + Integer + Pow<u32, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<'a, T> Pow<i64> for &'a Ratio<T> where    T: Clone + Integer + Pow<u64, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<T> Pow<i64> for Ratio<T> where    T: Clone + Integer + Pow<u64, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<T> Pow<i8> for Ratio<T> where    T: Clone + Integer + Pow<u8, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<'a, T> Pow<i8> for &'a Ratio<T> where    T: Clone + Integer + Pow<u8, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<T> Pow<isize> for Ratio<T> where    T: Clone + Integer + Pow<usize, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<'a, T> Pow<isize> for &'a Ratio<T> where    T: Clone + Integer + Pow<usize, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<T> Pow<u16> for Ratio<T> where    T: Clone + Integer + Pow<u16, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<'a, T> Pow<u16> for &'a Ratio<T> where    T: Clone + Integer + Pow<u16, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<T> Pow<u32> for Ratio<T> where    T: Clone + Integer + Pow<u32, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<'a, T> Pow<u32> for &'a Ratio<T> where    T: Clone + Integer + Pow<u32, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<T> Pow<u64> for Ratio<T> where    T: Clone + Integer + Pow<u64, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<'a, T> Pow<u64> for &'a Ratio<T> where    T: Clone + Integer + Pow<u64, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<'a, T> Pow<u8> for &'a Ratio<T> where    T: Clone + Integer + Pow<u8, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<T> Pow<u8> for Ratio<T> where    T: Clone + Integer + Pow<u8, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<T> Pow<usize> for Ratio<T> where    T: Clone + Integer + Pow<usize, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<'a, T> Pow<usize> for &'a Ratio<T> where    T: Clone + Integer + Pow<usize, Output = T>, `[src]

#### `type Output = Ratio<T>`

The result after applying the operator.

### `impl<'a, T> Rem<&'a Ratio<T>> for Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `%` operator.

### `impl<'a, T> Rem<&'a T> for Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `%` operator.

### `impl<'a, 'b, T> Rem<&'b Ratio<T>> for &'a Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `%` operator.

### `impl<'a, 'b, T> Rem<&'b T> for &'a Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `%` operator.

### `impl<T> Rem<Ratio<T>> for Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `%` operator.

### `impl<'a, T> Rem<Ratio<T>> for &'a Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `%` operator.

### `impl<'a, T> Rem<T> for &'a Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `%` operator.

### `impl<T> Rem<T> for Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `%` operator.

### `impl<'a, T> Sub<&'a Ratio<T>> for Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `-` operator.

### `impl<'a, T> Sub<&'a T> for Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `-` operator.

### `impl<'a, 'b, T> Sub<&'b Ratio<T>> for &'a Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `-` operator.

### `impl<'a, 'b, T> Sub<&'b T> for &'a Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `-` operator.

### `impl<T> Sub<Ratio<T>> for Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `-` operator.

### `impl<'a, T> Sub<Ratio<T>> for &'a Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `-` operator.

### `impl<T> Sub<T> for Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `-` operator.

### `impl<'a, T> Sub<T> for &'a Ratio<T> where    T: Clone + Integer, `[src]

#### `type Output = Ratio<T>`

The resulting type after applying the `-` operator.

## Blanket Implementations

### `impl<T> ToOwned for T where    T: Clone, `[src]

#### `type Owned = T`

The resulting type after obtaining ownership.

### `impl<T, U> TryFrom<U> for T where    U: Into<T>, `[src]

#### `type Error = Infallible`

The type returned in the event of a conversion error.

### `impl<T, U> TryInto<U> for T where    U: TryFrom<T>, `[src]

#### `type Error = <U as TryFrom<T>>::Error`

The type returned in the event of a conversion error.