Trait Mul

1.0.0 · Source

pub trait Mul<Rhs = Self> {
    type Output;

    // Required method
    fn mul(self, rhs: Rhs) -> Self::Output;
}

Available on crate feature mtls only.

Expand description

The multiplication operator *.

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

§Examples

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 {
    numerator: usize,
    denominator: usize,
}

impl Rational {
    fn new(numerator: 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(numerator, denominator);
        Self {
            numerator: numerator / 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 numerator = self.numerator * rhs.numerator;
        let denominator = self.denominator * rhs.denominator;
        Self::new(numerator, 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));

use std::ops::Mul;

struct Scalar { value: usize }

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

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

    fn mul(self, rhs: Scalar) -> Self::Output {
        Self { 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] });

Required Associated Types§

The resulting type after applying the * operator.

Required Methods§

Performs the * operation.

assert_eq!(12 * 2, 24);

Implementors§

UTerm * B0 = UTerm

UTerm * B1 = UTerm

Z0 * I = Z0

N * Z0 = Z0

P * Z0 = Z0

UTerm * U = UTerm

UInt * B0 = UTerm

UInt * B1 = UInt

UInt<U, B> * UTerm = UTerm

UInt<Ul, B0> * UInt<Ur, B> = UInt<(Ul * UInt<Ur, B>), B0>

UInt<Ul, B1> * UInt<Ur, B> = UInt<(Ul * UInt<Ur, B>), B0> + UInt<Ur, B>

N(Ul) * N(Ur) = P(Ul * Ur)

P(Ul) * N(Ur) = N(Ul * Ur)

N(Ul) * P(Ur) = N(Ul * Ur)

P(Ul) * P(Ur) = P(Ul * Ur)

Trait MulCopy item path

§Examples

§Multipliable rational numbers

§Multiplying vectors by scalars as in linear algebra

Required Associated Types§

type Output

Required Methods§

fn mul(self, rhs: Rhs) -> Self::Output

§Example

Implementors§

impl Mul for Sign

type Output = Sign

impl Mul for f16

type Output = f16

impl Mul for f32

type Output = f32

impl Mul for f64

type Output = f64

impl Mul for f128

type Output = f128

impl Mul for i8

type Output = i8

impl Mul for i16

type Output = i16

impl Mul for i32

type Output = i32

impl Mul for i64

type Output = i64

impl Mul for i128

type Output = i128

impl Mul for isize

type Output = isize

impl Mul for u8

type Output = u8

impl Mul for u16

type Output = u16

impl Mul for u32

type Output = u32

impl Mul for u64

type Output = u64

impl Mul for u128

type Output = u128

impl Mul for usize

type Output = usize

impl Mul for BigInt

type Output = BigInt

impl Mul for BigUint

type Output = BigUint

impl Mul for Saturating<i8>

type Output = Saturating<i8>

impl Mul for Saturating<i16>

type Output = Saturating<i16>

impl Mul for Saturating<i32>

type Output = Saturating<i32>

impl Mul for Saturating<i64>

type Output = Saturating<i64>

impl Mul for Saturating<i128>

type Output = Saturating<i128>

impl Mul for Saturating<isize>

type Output = Saturating<isize>

impl Mul for Saturating<u8>

type Output = Saturating<u8>

impl Mul for Saturating<u16>

type Output = Saturating<u16>

impl Mul for Saturating<u32>

type Output = Saturating<u32>

impl Mul for Saturating<u64>

type Output = Saturating<u64>

impl Mul for Saturating<u128>

type Output = Saturating<u128>

impl Mul for Saturating<usize>

type Output = Saturating<usize>

impl Mul for Wrapping<i8>

type Output = Wrapping<i8>

impl Mul for Wrapping<i16>

type Output = Wrapping<i16>

impl Mul for Wrapping<i32>

type Output = Wrapping<i32>

impl Mul for Wrapping<i64>

type Output = Wrapping<i64>

Trait Mul

§`Mul`tipliable rational numbers