use std::fmt::{Debug, Display};
use std::ops::{Add, Sub, Mul, Div};

/// A linear coordinate.
pub trait Coordinate: Send + Sync + Copy
    + Add<Self, Output=Self>
    + Sub<Self, Output=Self>
    + Mul<Self, Output=Self>
    + Div<Self, Output=Self>
    + Ord + PartialEq + Eq
    + Debug + Display + Default
    + From<u16> + Into<u16>
    + Into<usize>
    + Into<f64>
{
    fn zero () -> Self { 0.into() }
    fn plus (self, other: Self) -> Self;
    fn minus (self, other: Self) -> Self {
        if self >= other {
            self - other
        } else {
            0.into()
        }
    }
}

impl Coordinate for u16 {
    fn plus (self, other: Self) -> Self {
        self.saturating_add(other)
    }
}