Trait Additive

Source

pub trait Additive:
    Object
    + for<'a> AddAssign<&'a Self>
    + for<'a> Add<&'a Self, Output = Self>
    + for<'a> SubAssign<&'a Self>
    + for<'a> Sub<&'a Self, Output = Self>
    + Neg<Output = Self> {
    // Required method
    fn zero() -> Self;

    // Provided methods
    fn double(&mut self) { ... }
    fn scale(&self, bits_le: &[u64]) -> Self { ... }
}

Expand description

A type that supports addition, subtraction, and negation.

For some type T implementing this trait, the following operations must be supported:

&mut T += &T,
T + &T,
&mut T -= &T,
T - &T,
-T.

There are other combinations of borrowing that could be chosen, but these should be efficiently implementable, even for a “heavier” struct, e.g. a vector of values.

§Properties

Implementations are expected to form a commutative group under addition:

+= and -= agree with + and -,
addition satisfies a + b = b + a and (a + b) + c = a + (b + c),
Additive::zero satisfies 0 + a = a,
negation satisfies a + (-a) = 0 and a - b = a + (-b),
Additive::scale satisfies a.scale(&[]) = 0, a.scale(&[1]) = a, and a.scale(m + n) = a.scale(m) + a.scale(n).

§Usage


// We use .clone() whenever ownership is needed.
fn example<T: Additive>(mut x: T, y: T) {
    x += &y;
    x.clone() + &y;
    x -= &y;
    x.clone() - &y;
    -x.clone();
    T::zero();
}