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use crate::VectorSpace;
use num_traits::One;

/// This trait makes it possible to deal with the bases of a vector in a generic way.
pub trait Basis<const I: usize>: VectorSpace {
    /// Creates an unit basis of the vector space.
    fn unit_basis() -> Self {
        Self::basis_of(<Self as VectorSpace>::Scalar::one())
    }
    /// Creates a scaled basis of the vector space of the specified magnitude.
    fn basis_of(magnitude: Self::Scalar) -> Self {
        Self::unit_basis() * magnitude
    }

    /// Queries a basis of a vector space.
    fn basis(&self) -> Self::Scalar;
    /// Queries a basis of a vector space as a mutable reference.
    fn basis_mut(&mut self) -> &mut Self::Scalar;

    /// Creates a new vector with a single basis set to a different value.
    fn with_basis(mut self, magnitude: Self::Scalar) -> Self {
        *self.basis_mut() = magnitude;
        self
    }
}

/// This trait makes it easy to deal with specified bases of a vector in a generic way.
pub trait Bases: VectorSpace {
    #[inline]
    /// Creates the specified unit basis of the vector space.
    fn unit_bases<const I: usize>() -> Self
    where
        Self: Basis<I>,
    {
        Basis::unit_basis()
    }
    #[inline]
    /// Creates the specified basis of the vector of the specified magnitude.
    fn bases_of<const I: usize>(magnitude: Self::Scalar) -> Self
    where
        Self: Basis<I>,
    {
        Basis::basis_of(magnitude)
    }

    #[inline]
    /// Queries the specified basis of a vector space.
    fn bases<const I: usize>(&self) -> Self::Scalar
    where
        Self: Basis<I>,
    {
        Basis::basis(self)
    }
    #[inline]
    /// Queries the specified basis of a vector space as a mutable reference.
    fn bases_mut<const I: usize>(&mut self) -> &mut Self::Scalar
    where
        Self: Basis<I>,
    {
        Basis::basis_mut(self)
    }

    #[inline]
    /// Creates a new vector with the specified basis set to a different value.
    fn with_bases<const I: usize>(self, magnitude: Self::Scalar) -> Self
    where
        Self: Basis<I>,
    {
        Basis::with_basis(self, magnitude)
    }
}

impl<T: VectorSpace> Bases for T {}