# Trait std::ops::Mul1.0.0 [−] [src]

```#[lang = "mul"]
pub trait Mul<RHS = Self> {
type Output;
fn mul(self, rhs: RHS) -> Self::Output;
}```

The multiplication operator `*`.

Note that `RHS` is `Self` by default, but this is not mandatory.

# Examples

## `Mul`tipliable rational numbers

```use std::ops::Mul;

// By the fundamental theorem of arithmetic, rational numbers in lowest
// terms are unique. So, by keeping `Rational`s in reduced form, we can
// derive `Eq` and `PartialEq`.
#[derive(Debug, Eq, PartialEq)]
struct Rational {
nominator: usize,
denominator: usize,
}

impl Rational {
fn new(nominator: usize, denominator: usize) -> Self {
if denominator == 0 {
panic!("Zero is an invalid denominator!");
}

// Reduce to lowest terms by dividing by the greatest common
// divisor.
let gcd = gcd(nominator, denominator);
Rational {
nominator: nominator / gcd,
denominator: denominator / gcd,
}
}
}

impl Mul for Rational {
// The multiplication of rational numbers is a closed operation.
type Output = Self;

fn mul(self, rhs: Self) -> Self {
let nominator = self.nominator * rhs.nominator;
let denominator = self.denominator * rhs.denominator;
Rational::new(nominator, denominator)
}
}

// Euclid's two-thousand-year-old algorithm for finding the greatest common
// divisor.
fn gcd(x: usize, y: usize) -> usize {
let mut x = x;
let mut y = y;
while y != 0 {
let t = y;
y = x % y;
x = t;
}
x
}

assert_eq!(Rational::new(1, 2), Rational::new(2, 4));
assert_eq!(Rational::new(2, 3) * Rational::new(3, 4),
Rational::new(1, 2));Run```

## Multiplying vectors by scalars as in linear algebra

```use std::ops::Mul;

struct Scalar { value: usize }

#[derive(Debug, PartialEq)]
struct Vector { value: Vec<usize> }

impl Mul<Scalar> for Vector {
type Output = Vector;

fn mul(self, rhs: Scalar) -> Vector {
Vector { value: self.value.iter().map(|v| v * rhs.value).collect() }
}
}

let vector = Vector { value: vec![2, 4, 6] };
let scalar = Scalar { value: 3 };
assert_eq!(vector * scalar, Vector { value: vec![6, 12, 18] });Run```

## Associated Types

### `type Output`

The resulting type after applying the `*` operator.

## Required Methods

### `fn mul(self, rhs: RHS) -> Self::Output`

Performs the `*` operation.

## Implementors

• `impl<'a, 'b> Mul<&'a Wrapping<i8>> for &'b Wrapping<i8> type Output = <Wrapping<i8> as Mul<Wrapping<i8>>>::Output;`
• `impl<'a, 'b> Mul<&'a Wrapping<i128>> for &'b Wrapping<i128> type Output = <Wrapping<i128> as Mul<Wrapping<i128>>>::Output;`
• `impl<'a> Mul<Wrapping<i32>> for &'a Wrapping<i32> type Output = <Wrapping<i32> as Mul<Wrapping<i32>>>::Output;`
• `impl Mul<Wrapping<u32>> for Wrapping<u32> type Output = Wrapping<u32>;`
• `impl<'a> Mul<&'a Wrapping<u32>> for Wrapping<u32> type Output = <Wrapping<u32> as Mul<Wrapping<u32>>>::Output;`
• `impl<'a, 'b> Mul<&'a Wrapping<u128>> for &'b Wrapping<u128> type Output = <Wrapping<u128> as Mul<Wrapping<u128>>>::Output;`
• `impl<'a> Mul<i64> for &'a i64 type Output = <i64 as Mul<i64>>::Output;`
• `impl<'a> Mul<&'a Wrapping<i32>> for Wrapping<i32> type Output = <Wrapping<i32> as Mul<Wrapping<i32>>>::Output;`
• `impl<'a, 'b> Mul<&'a isize> for &'b isize type Output = <isize as Mul<isize>>::Output;`
• `impl<'a> Mul<&'a f32> for f32 type Output = <f32 as Mul<f32>>::Output;`
• `impl<'a, 'b> Mul<&'a u16> for &'b u16 type Output = <u16 as Mul<u16>>::Output;`
• `impl<'a> Mul<Wrapping<u32>> for &'a Wrapping<u32> type Output = <Wrapping<u32> as Mul<Wrapping<u32>>>::Output;`
• `impl<'a> Mul<&'a i128> for i128 type Output = <i128 as Mul<i128>>::Output;`
• `impl<'a, 'b> Mul<&'a Wrapping<isize>> for &'b Wrapping<isize> type Output = <Wrapping<isize> as Mul<Wrapping<isize>>>::Output;`
• `impl Mul<Wrapping<i8>> for Wrapping<i8> type Output = Wrapping<i8>;`
• `impl<'a> Mul<u16> for &'a u16 type Output = <u16 as Mul<u16>>::Output;`
• `impl<'a> Mul<&'a i32> for i32 type Output = <i32 as Mul<i32>>::Output;`
• `impl<'a> Mul<&'a u32> for u32 type Output = <u32 as Mul<u32>>::Output;`
• `impl<'a> Mul<&'a Wrapping<usize>> for Wrapping<usize> type Output = <Wrapping<usize> as Mul<Wrapping<usize>>>::Output;`
• `impl<'a> Mul<&'a Wrapping<u8>> for Wrapping<u8> type Output = <Wrapping<u8> as Mul<Wrapping<u8>>>::Output;`
• `impl<'a> Mul<i16> for &'a i16 type Output = <i16 as Mul<i16>>::Output;`
• `impl<'a, 'b> Mul<&'a i16> for &'b i16 type Output = <i16 as Mul<i16>>::Output;`
• `impl<'a> Mul<Wrapping<u128>> for &'a Wrapping<u128> type Output = <Wrapping<u128> as Mul<Wrapping<u128>>>::Output;`
• `impl<'a> Mul<f32> for &'a f32 type Output = <f32 as Mul<f32>>::Output;`
• `impl<'a, 'b> Mul<&'a Wrapping<usize>> for &'b Wrapping<usize> type Output = <Wrapping<usize> as Mul<Wrapping<usize>>>::Output;`
• `impl Mul<f64> for f64 type Output = f64;`
• `impl<'a> Mul<&'a Wrapping<u128>> for Wrapping<u128> type Output = <Wrapping<u128> as Mul<Wrapping<u128>>>::Output;`
• `impl<'a, 'b> Mul<&'a u128> for &'b u128 type Output = <u128 as Mul<u128>>::Output;`
• `impl<'a, 'b> Mul<&'a f32> for &'b f32 type Output = <f32 as Mul<f32>>::Output;`
• `impl<'a> Mul<i32> for &'a i32 type Output = <i32 as Mul<i32>>::Output;`
• `impl<'a> Mul<u128> for &'a u128 type Output = <u128 as Mul<u128>>::Output;`
• `impl<'a> Mul<&'a Wrapping<i16>> for Wrapping<i16> type Output = <Wrapping<i16> as Mul<Wrapping<i16>>>::Output;`
• `impl<'a> Mul<u32> for &'a u32 type Output = <u32 as Mul<u32>>::Output;`
• `impl<'a, 'b> Mul<&'a i8> for &'b i8 type Output = <i8 as Mul<i8>>::Output;`
• `impl Mul<usize> for usize type Output = usize;`
• `impl Mul<Wrapping<isize>> for Wrapping<isize> type Output = Wrapping<isize>;`
• `impl<'a> Mul<f64> for &'a f64 type Output = <f64 as Mul<f64>>::Output;`
• `impl Mul<u128> for u128 type Output = u128;`
• `impl<'a> Mul<i128> for &'a i128 type Output = <i128 as Mul<i128>>::Output;`
• `impl<'a> Mul<Wrapping<usize>> for &'a Wrapping<usize> type Output = <Wrapping<usize> as Mul<Wrapping<usize>>>::Output;`
• `impl<'a, 'b> Mul<&'a Wrapping<u64>> for &'b Wrapping<u64> type Output = <Wrapping<u64> as Mul<Wrapping<u64>>>::Output;`
• `impl Mul<isize> for isize type Output = isize;`
• `impl<'a> Mul<Wrapping<u8>> for &'a Wrapping<u8> type Output = <Wrapping<u8> as Mul<Wrapping<u8>>>::Output;`
• `impl<'a> Mul<Wrapping<i64>> for &'a Wrapping<i64> type Output = <Wrapping<i64> as Mul<Wrapping<i64>>>::Output;`
• `impl Mul<u32> for Duration type Output = Duration;`
• `impl<'a> Mul<&'a u128> for u128 type Output = <u128 as Mul<u128>>::Output;`
• `impl Mul<u32> for u32 type Output = u32;`
• `impl<'a> Mul<u64> for &'a u64 type Output = <u64 as Mul<u64>>::Output;`
• `impl Mul<Wrapping<usize>> for Wrapping<usize> type Output = Wrapping<usize>;`
• `impl Mul<u64> for u64 type Output = u64;`
• `impl<'a> Mul<&'a Wrapping<isize>> for Wrapping<isize> type Output = <Wrapping<isize> as Mul<Wrapping<isize>>>::Output;`
• `impl<'a, 'b> Mul<&'a i128> for &'b i128 type Output = <i128 as Mul<i128>>::Output;`
• `impl Mul<i64> for i64 type Output = i64;`
• `impl<'a, 'b> Mul<&'a i32> for &'b i32 type Output = <i32 as Mul<i32>>::Output;`
• `impl<'a> Mul<&'a u64> for u64 type Output = <u64 as Mul<u64>>::Output;`
• `impl<'a, 'b> Mul<&'a usize> for &'b usize type Output = <usize as Mul<usize>>::Output;`
• `impl<'a> Mul<&'a Wrapping<i128>> for Wrapping<i128> type Output = <Wrapping<i128> as Mul<Wrapping<i128>>>::Output;`
• `impl<'a> Mul<&'a u8> for u8 type Output = <u8 as Mul<u8>>::Output;`
• `impl<'a> Mul<&'a i16> for i16 type Output = <i16 as Mul<i16>>::Output;`
• `impl<'a> Mul<Wrapping<i16>> for &'a Wrapping<i16> type Output = <Wrapping<i16> as Mul<Wrapping<i16>>>::Output;`
• `impl Mul<Wrapping<i32>> for Wrapping<i32> type Output = Wrapping<i32>;`
• `impl Mul<Wrapping<u16>> for Wrapping<u16> type Output = Wrapping<u16>;`
• `impl<'a> Mul<&'a Wrapping<u64>> for Wrapping<u64> type Output = <Wrapping<u64> as Mul<Wrapping<u64>>>::Output;`
• `impl<'a> Mul<&'a Wrapping<i64>> for Wrapping<i64> type Output = <Wrapping<i64> as Mul<Wrapping<i64>>>::Output;`
• `impl<'a> Mul<i8> for &'a i8 type Output = <i8 as Mul<i8>>::Output;`
• `impl<'a, 'b> Mul<&'a Wrapping<u8>> for &'b Wrapping<u8> type Output = <Wrapping<u8> as Mul<Wrapping<u8>>>::Output;`
• `impl<'a> Mul<&'a usize> for usize type Output = <usize as Mul<usize>>::Output;`
• `impl<'a> Mul<isize> for &'a isize type Output = <isize as Mul<isize>>::Output;`
• `impl<'a, 'b> Mul<&'a f64> for &'b f64 type Output = <f64 as Mul<f64>>::Output;`
• `impl<'a, 'b> Mul<&'a Wrapping<i16>> for &'b Wrapping<i16> type Output = <Wrapping<i16> as Mul<Wrapping<i16>>>::Output;`
• `impl Mul<Wrapping<u128>> for Wrapping<u128> type Output = Wrapping<u128>;`
• `impl<'a, 'b> Mul<&'a Wrapping<i64>> for &'b Wrapping<i64> type Output = <Wrapping<i64> as Mul<Wrapping<i64>>>::Output;`
• `impl<'a> Mul<Wrapping<i8>> for &'a Wrapping<i8> type Output = <Wrapping<i8> as Mul<Wrapping<i8>>>::Output;`
• `impl<'a> Mul<Wrapping<isize>> for &'a Wrapping<isize> type Output = <Wrapping<isize> as Mul<Wrapping<isize>>>::Output;`
• `impl Mul<i128> for i128 type Output = i128;`
• `impl<'a, 'b> Mul<&'a i64> for &'b i64 type Output = <i64 as Mul<i64>>::Output;`
• `impl<'a> Mul<&'a u16> for u16 type Output = <u16 as Mul<u16>>::Output;`
• `impl Mul<Wrapping<i16>> for Wrapping<i16> type Output = Wrapping<i16>;`
• `impl<'a> Mul<Wrapping<u64>> for &'a Wrapping<u64> type Output = <Wrapping<u64> as Mul<Wrapping<u64>>>::Output;`
• `impl Mul<u8> for u8 type Output = u8;`
• `impl<'a, 'b> Mul<&'a Wrapping<u32>> for &'b Wrapping<u32> type Output = <Wrapping<u32> as Mul<Wrapping<u32>>>::Output;`
• `impl<'a, 'b> Mul<&'a Wrapping<i32>> for &'b Wrapping<i32> type Output = <Wrapping<i32> as Mul<Wrapping<i32>>>::Output;`
• `impl Mul<Wrapping<u8>> for Wrapping<u8> type Output = Wrapping<u8>;`
• `impl Mul<i32> for i32 type Output = i32;`
• `impl<'a> Mul<&'a f64> for f64 type Output = <f64 as Mul<f64>>::Output;`
• `impl Mul<Wrapping<i64>> for Wrapping<i64> type Output = Wrapping<i64>;`
• `impl Mul<i8> for i8 type Output = i8;`
• `impl Mul<i16> for i16 type Output = i16;`
• `impl Mul<Wrapping<u64>> for Wrapping<u64> type Output = Wrapping<u64>;`
• `impl<'a> Mul<&'a i64> for i64 type Output = <i64 as Mul<i64>>::Output;`
• `impl<'a> Mul<Wrapping<i128>> for &'a Wrapping<i128> type Output = <Wrapping<i128> as Mul<Wrapping<i128>>>::Output;`
• `impl Mul<u16> for u16 type Output = u16;`
• `impl<'a, 'b> Mul<&'a Wrapping<u16>> for &'b Wrapping<u16> type Output = <Wrapping<u16> as Mul<Wrapping<u16>>>::Output;`
• `impl<'a> Mul<u8> for &'a u8 type Output = <u8 as Mul<u8>>::Output;`
• `impl<'a> Mul<Wrapping<u16>> for &'a Wrapping<u16> type Output = <Wrapping<u16> as Mul<Wrapping<u16>>>::Output;`
• `impl<'a, 'b> Mul<&'a u64> for &'b u64 type Output = <u64 as Mul<u64>>::Output;`
• `impl<'a, 'b> Mul<&'a u32> for &'b u32 type Output = <u32 as Mul<u32>>::Output;`
• `impl<'a, 'b> Mul<&'a u8> for &'b u8 type Output = <u8 as Mul<u8>>::Output;`
• `impl Mul<Wrapping<i128>> for Wrapping<i128> type Output = Wrapping<i128>;`
• `impl<'a> Mul<&'a Wrapping<u16>> for Wrapping<u16> type Output = <Wrapping<u16> as Mul<Wrapping<u16>>>::Output;`
• `impl<'a> Mul<usize> for &'a usize type Output = <usize as Mul<usize>>::Output;`
• `impl<'a> Mul<&'a isize> for isize type Output = <isize as Mul<isize>>::Output;`
• `impl<'a> Mul<&'a i8> for i8 type Output = <i8 as Mul<i8>>::Output;`
• `impl Mul<f32> for f32 type Output = f32;`
• `impl<'a> Mul<&'a Wrapping<i8>> for Wrapping<i8> type Output = <Wrapping<i8> as Mul<Wrapping<i8>>>::Output;`