use std::ops::*;
use num_traits::{NumOps, NumAssignOps, Signed};
use num_traits::pow::Pow;
use num_traits::real::Real;

macro_rules! fold_array {
    ($method:ident, { $x:expr }) => { $x };
    ($method:ident, { $x:expr, $y:expr }) => { $x.$method($y) };
    ($method:ident, { $x:expr, $y:expr, $z:expr }) => { $x.$method($y).$method($z) };
}

macro_rules! impl_vector {
    ($VecN:ident { $($field:ident),+ }) => {
        #[derive(Debug, Default, Clone, Copy, Hash, PartialEq, Eq)]
        pub struct $VecN<T> {
            $(pub $field: T),+
        }
        
        impl<T> $VecN<T> {
            pub const fn new($($field: T),+) -> $VecN<T> {
                $VecN { $($field),+ }
            }
        }

        impl<T: NumOps + Ord + Signed + Copy> $VecN<T> {
            pub fn walking_distance(&self) -> T {
                fold_array!(max, { $(self.$field.abs()),+ })
            }
        }
        
        impl<T: NumOps + Pow<u8, Output=T> + Copy> $VecN<T> {
            pub fn magnitude_squared(&self) -> T {
                fold_array!(add, { $(self.$field.pow(2)),+ })
            }
        }

        impl<T: Real + Pow<u8, Output=T>> $VecN<T> {
            pub fn magnitude(&self) -> T {
                self.magnitude_squared().sqrt()
            }

            pub fn unit(&self) -> $VecN<T> {
                let mag = self.magnitude();
                $VecN {
                    $($field: self.$field / mag),+
                }
            }
        }

        impl<T: NumOps + Copy> $VecN<T> {
            pub fn dot(&self, other: $VecN<T>) -> T {
                fold_array!(add, { $(self.$field * other.$field),+ })
            }
        }

        impl<T: NumOps> Add for $VecN<T> {
            type Output = Self;

            fn add(self, other: Self) -> Self {
                $VecN {
                    $($field: self.$field + other.$field),+
                }
            }
        }

        impl<T: NumAssignOps> AddAssign for $VecN<T> {
            fn add_assign(&mut self, other: Self) {
                $(self.$field += other.$field);+
            }
        }

        impl<T: NumOps> Sub for $VecN<T> {
            type Output = Self;

            fn sub(self, other: Self) -> Self {
                $VecN {
                    $($field: self.$field - other.$field),+
                }
            }
        }

        impl<T: NumOps + Copy> Mul<T> for $VecN<T> {
            type Output = Self;

            fn mul(self, rhs: T) -> Self {
                $VecN {
                    $($field: self.$field * rhs),+
                }
            }
        }

        impl<T: Neg<Output=T>> Neg for $VecN<T> {
            type Output = Self;

            fn neg(self) -> Self {
                $VecN {
                    $($field: -self.$field),+
                }
            }
        }

    }
}

impl_vector!(Vec2d { x, y });
impl_vector!(Vec3d { x, y, z });

impl<T: Real + Pow<u8, Output=T>> Vec2d<T> {
    pub fn angle(&self) -> T {
        self.y.atan2(self.x)
    }
}


#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn right_angles_in_2d_vectors() {
        use std::f32::consts::{FRAC_PI_2, PI};

        assert_eq!(0., Vec2d::new(1., 0.).angle());
        assert_eq!(FRAC_PI_2, Vec2d::new(0., 1.).angle());
        assert_eq!(PI, Vec2d::new(-1., 0.).angle());
        assert_eq!(-FRAC_PI_2, Vec2d::new(0., -1.).angle());
    }

    #[test]
    fn unit_normalizes_2d_vector() {
        let before = Vec2d::new(2., 10.);
        let after = before.unit();

        assert_eq!(1., after.magnitude());
        assert_eq!(before.angle(), after.angle());
    }

    #[test]
    fn unit_normalizes_3d_vector() {
        let before = Vec3d::new(2., 10., -5.);
        let after = before.unit();

        assert_eq!(1., after.magnitude());
        // How to define 3d angle? 2 angles I suppose?
        // assert_eq!(before.angle(), after.angle());
    }
    
    #[test]
    fn dot_product_example_2d() {
        let a = Vec2d::new(-6., 8.);
        let b = Vec2d::new(5., 12.);
        assert_eq!(66., a.dot(b));
    }

    #[test]
    fn magnitude_squared_of_an_integer() {
        let a = Vec2d::new(3, 4);
        assert_eq!(25, a.magnitude_squared());
    }
}