use approx::AbsDiffEq;
use num::{Bounded, FromPrimitive, Signed};

use alga::general::{Lattice, Ring};
use na::allocator::Allocator;
use na::{DimMin, DimName, Scalar, U1};

/// A type-level number representing a vector, matrix row, or matrix column, dimension.
pub trait Dimension: DimName + DimMin<Self, Output = Self> {}
impl<D: DimName + DimMin<D, Output = Self>> Dimension for D {}

/// A number that can either be an integer or a float.
pub trait Number:
    Scalar + Copy + Ring + Lattice + AbsDiffEq<Epsilon = Self> + Signed + FromPrimitive + Bounded
{
}

impl<T: Scalar + Copy + Ring + Lattice + AbsDiffEq<Epsilon = Self> + Signed + FromPrimitive + Bounded>
    Number for T
{}

#[doc(hidden)]
pub trait Alloc<N: Scalar, R: Dimension, C: Dimension = U1>:
    Allocator<N, R>
    + Allocator<N, C>
    + Allocator<N, U1, R>
    + Allocator<N, U1, C>
    + Allocator<N, R, C>
    + Allocator<N, C, R>
    + Allocator<N, R, R>
    + Allocator<N, C, C>
    + Allocator<bool, R>
    + Allocator<bool, C>
    + Allocator<f32, R>
    + Allocator<f32, C>
    + Allocator<u32, R>
    + Allocator<u32, C>
    + Allocator<i32, R>
    + Allocator<i32, C>
    + Allocator<f64, R>
    + Allocator<f64, C>
    + Allocator<u64, R>
    + Allocator<u64, C>
    + Allocator<i64, R>
    + Allocator<i64, C>
    + Allocator<i16, R>
    + Allocator<i16, C>
    + Allocator<(usize, usize), R>
    + Allocator<(usize, usize), C>
{
}

impl<N: Scalar, R: Dimension, C: Dimension, T> Alloc<N, R, C> for T where T: Allocator<N, R>
        + Allocator<N, C>
        + Allocator<N, U1, R>
        + Allocator<N, U1, C>
        + Allocator<N, R, C>
        + Allocator<N, C, R>
        + Allocator<N, R, R>
        + Allocator<N, C, C>
        + Allocator<bool, R>
        + Allocator<bool, C>
        + Allocator<f32, R>
        + Allocator<f32, C>
        + Allocator<u32, R>
        + Allocator<u32, C>
        + Allocator<i32, R>
        + Allocator<i32, C>
        + Allocator<f64, R>
        + Allocator<f64, C>
        + Allocator<u64, R>
        + Allocator<u64, C>
        + Allocator<i64, R>
        + Allocator<i64, C>
        + Allocator<i16, R>
        + Allocator<i16, C>
        + Allocator<(usize, usize), R>
        + Allocator<(usize, usize), C>
{}