use std::cmp;
use std::ops;

#[derive(Clone, Debug, Copy)]
pub struct FPNum {
    is_negative: bool,
    value: u64,
}

impl FPNum {
    #[inline]
    pub fn new(numerator: i32, denominator: u32) -> Self {
        FPNum::from(numerator) / denominator
    }

    #[inline]
    pub fn signum(&self) -> i8 {
        if self.is_negative {
            -1
        } else {
            1
        }
    }

    #[inline]
    pub fn is_negative(&self) -> bool {
        self.is_negative
    }

    #[inline]
    pub fn is_positive(&self) -> bool {
        !self.is_negative
    }

    #[inline]
    pub fn is_zero(&self) -> bool {
        self.value == 0
    }

    #[inline]
    pub fn abs(&self) -> Self {
        Self {
            is_negative: false,
            value: self.value,
        }
    }

    #[inline]
    pub fn round(&self) -> i64 {
        if self.is_negative {
            -((self.value >> 32) as i64)
        } else {
            (self.value >> 32) as i64
        }
    }

    #[inline]
    pub fn sqr(&self) -> Self {
        Self {
            is_negative: false,
            value: ((self.value as u128).pow(2) >> 32) as u64,
        }
    }

    pub fn sqrt(&self) -> Self {
        debug_assert!(!self.is_negative);

        let mut t: u64 = 0x4000000000000000;
        let mut r: u64 = 0;
        let mut q = self.value;

        for _ in 0..32 {
            let s = r + t;
            r >>= 1;

            if s <= q {
                q -= s;
                r += t;
            }
            t >>= 2;
        }

        Self {
            is_negative: false,
            value: r << 16,
        }
    }

    #[inline]
    pub fn with_sign(&self, is_negative: bool) -> FPNum {
        FPNum{ is_negative, ..*self}
    }

    #[inline]
    pub fn with_sign_as(self, other: FPNum) -> FPNum {
        self.with_sign(other.is_negative)
    }

    #[inline]
    pub fn point(self) -> FPPoint {
        FPPoint::new(self, self)
    }
}

impl From<i32> for FPNum {
    #[inline]
    fn from(n: i32) -> Self {
        FPNum {
            is_negative: n < 0,
            value: (n.abs() as u64) << 32,
        }
    }
}

impl From<u32> for FPNum {
    #[inline]
    fn from(n: u32) -> Self {
        Self {
            is_negative: false,
            value: (n as u64) << 32,
        }
    }
}

impl From<FPNum> for f64 {
    #[inline]
    fn from(n: FPNum) -> Self {
        if n.is_negative {
            n.value as f64 / (-0x10000000 as f64)
        } else {
            n.value as f64 / 0x10000000 as f64
        }
    }
}

impl PartialEq for FPNum {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.value == other.value && (self.is_negative == other.is_negative || self.value == 0)
    }
}

impl Eq for FPNum {}

impl PartialOrd for FPNum {
    #[inline]
    fn partial_cmp(&self, rhs: &Self) -> std::option::Option<std::cmp::Ordering> {
        Some(self.cmp(rhs))
    }
}

impl Ord for FPNum {
    #[inline]
    fn cmp(&self, rhs: &Self) -> cmp::Ordering {
        #[inline]
        fn extend(n: &FPNum) -> i128 {
            if n.is_negative {
                -(n.value as i128)
            } else {
                n.value as i128
            }
        }
        extend(self).cmp(&(extend(rhs)))
    }
}

impl ops::Add for FPNum {
    type Output = Self;

    #[inline]
    fn add(self, rhs: Self) -> Self {
        if self.is_negative == rhs.is_negative {
            Self {
                is_negative: self.is_negative,
                value: self.value + rhs.value,
            }
        } else if self.value > rhs.value {
            Self {
                is_negative: self.is_negative,
                value: self.value - rhs.value,
            }
        } else {
            Self {
                is_negative: rhs.is_negative,
                value: rhs.value - self.value,
            }
        }
    }
}

impl ops::Sub for FPNum {
    type Output = Self;

    #[inline]
    fn sub(self, rhs: Self) -> Self {
        if self.is_negative == rhs.is_negative {
            if self.value > rhs.value {
                Self {
                    is_negative: self.is_negative,
                    value: self.value - rhs.value,
                }
            } else {
                Self {
                    is_negative: !rhs.is_negative,
                    value: rhs.value - self.value,
                }
            }
        } else {
            Self {
                is_negative: self.is_negative,
                value: self.value + rhs.value,
            }
        }
    }
}

impl ops::Neg for FPNum {
    type Output = Self;

    #[inline]
    fn neg(self) -> Self {
        Self {
            is_negative: !self.is_negative,
            value: self.value,
        }
    }
}

impl ops::Mul for FPNum {
    type Output = Self;

    #[inline]
    fn mul(self, rhs: Self) -> Self {
        Self {
            is_negative: self.is_negative ^ rhs.is_negative,
            value: ((self.value as u128 * rhs.value as u128) >> 32) as u64,
        }
    }
}

impl ops::Mul<i32> for FPNum {
    type Output = Self;

    #[inline]
    fn mul(self, rhs: i32) -> Self {
        Self {
            is_negative: self.is_negative ^ (rhs < 0),
            value: self.value * rhs.abs() as u64,
        }
    }
}

impl ops::Div for FPNum {
    type Output = Self;

    #[inline]
    fn div(self, rhs: Self) -> Self {
        Self {
            is_negative: self.is_negative ^ rhs.is_negative,
            value: (((self.value as u128) << 32) / rhs.value as u128) as u64,
        }
    }
}

impl ops::Div<i32> for FPNum {
    type Output = Self;

    #[inline]
    fn div(self, rhs: i32) -> Self {
        Self {
            is_negative: self.is_negative ^ (rhs < 0),
            value: self.value / rhs.abs() as u64,
        }
    }
}

impl ops::Div<u32> for FPNum {
    type Output = Self;

    #[inline]
    fn div(self, rhs: u32) -> Self {
        Self {
            is_negative: self.is_negative,
            value: self.value / rhs as u64,
        }
    }
}

#[macro_export]
macro_rules! fp {
    (-$n: tt / $d: tt) => { FPNum::new(-$n, $d) };
    ($n: tt / $d: tt) => { FPNum::new($n, $d) };
    (-$n: tt) => { FPNum::from(-$n) };
    ($n: tt) => { FPNum::from($n) };
}

const LINEARIZE_TRESHOLD: u64 = 0x1_0000;

#[derive(Clone, Copy, Debug)]
pub struct FPPoint {
    x_is_negative: bool,
    y_is_negative: bool,
    x_value: u64,
    y_value: u64,
}

impl FPPoint {
    #[inline]
    pub fn new(x: FPNum, y: FPNum) -> Self {
        Self {
            x_is_negative: x.is_negative,
            y_is_negative: y.is_negative,
            x_value: x.value,
            y_value: y.value
        }
    }

    #[inline]
    pub fn zero() -> FPPoint { FPPoint::new(fp!(0), fp!(0)) }

    #[inline]
    pub fn unit_x() -> FPPoint { FPPoint::new(fp!(1), fp!(0)) }

    #[inline]
    pub fn unit_y() -> FPPoint { FPPoint::new(fp!(0), fp!(1)) }

    #[inline]
    pub fn x(&self) -> FPNum {
        FPNum {
            is_negative: self.x_is_negative,
            value: self.x_value
        }
    }

    #[inline]
    pub fn y(&self) -> FPNum {
        FPNum {
            is_negative: self.y_is_negative,
            value: self.y_value
        }
    }

    #[inline]
    pub fn max_norm(&self) -> FPNum {
        std::cmp::max(self.x(), self.y())
    }

    #[inline]
    pub fn sqr_distance(&self) -> FPNum {
        self.x().sqr() + self.y().sqr()
    }

    #[inline]
    pub fn distance(&self) -> FPNum {
        let r = self.x_value | self.y_value;
        if r < LINEARIZE_TRESHOLD {
            FPNum::from(r as u32)
        } else {
            self.sqr_distance().sqrt()
        }
    }

    #[inline]
    pub fn is_in_range(&self, radius: FPNum) -> bool {
        self.max_norm() < radius && self.sqr_distance() < radius.sqr()
    }

    #[inline]
    pub fn dot(&self, other: &FPPoint) -> FPNum {
        self.x() * other.x() + self.y() * other.y()
    }
}

impl PartialEq for FPPoint {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.x() == other.x() && self.y() == other.y()
    }
}

impl Eq for FPPoint {}

impl ops::Neg for FPPoint {
    type Output = Self;

    #[inline]
    fn neg(self) -> Self {
        Self::new(-self.x(), -self.y())
    }
}

macro_rules! bin_op_impl {
    ($op: ty, $name: tt) => {
        impl $op for FPPoint {
            type Output = Self;

            #[inline]
            fn $name(self, rhs: Self) -> Self {
                Self::new(self.x().$name(rhs.x()),
                          self.y().$name(rhs.y()))
            }
        }
    }
}

macro_rules! scalar_bin_op_impl {
    ($op: ty, $name: tt) => {
        impl $op for FPPoint {
            type Output = Self;

            #[inline]
            fn $name(self, rhs: FPNum) -> Self {
                Self::new(self.x().$name(rhs),
                          self.y().$name(rhs))
            }
        }
    }
}

bin_op_impl!(ops::Add, add);
bin_op_impl!(ops::Sub, sub);
bin_op_impl!(ops::Mul, mul);
bin_op_impl!(ops::Div, div);
scalar_bin_op_impl!(ops::Add<FPNum>, add);
scalar_bin_op_impl!(ops::Mul<FPNum>, mul);
scalar_bin_op_impl!(ops::Sub<FPNum>, sub);
scalar_bin_op_impl!(ops::Div<FPNum>, div);

macro_rules! bin_assign_op_impl {
    ($typ: tt, $($op: tt)::+, $name: tt, $delegate: tt) => {
        bin_assign_op_impl!($typ, $($op)::+<$typ>, $name, $delegate);
    };
    ($typ: tt, $($op: tt)::+<$arg: tt>, $name: tt, $delegate: tt) => {
        impl $($op)::+<$arg> for $typ {
            #[inline]
            fn $name(&mut self, rhs: $arg) {
                *self = *self $delegate rhs;
            }
        }
    }
}

bin_assign_op_impl!(FPNum, ops::AddAssign, add_assign, +);
bin_assign_op_impl!(FPNum, ops::SubAssign, sub_assign, -);
bin_assign_op_impl!(FPNum, ops::MulAssign, mul_assign, *);
bin_assign_op_impl!(FPNum, ops::DivAssign, div_assign, /);
bin_assign_op_impl!(FPNum, ops::MulAssign<i32>, mul_assign, *);
bin_assign_op_impl!(FPNum, ops::DivAssign<i32>, div_assign, /);
bin_assign_op_impl!(FPNum, ops::DivAssign<u32>, div_assign, /);

bin_assign_op_impl!(FPPoint, ops::AddAssign, add_assign, +);
bin_assign_op_impl!(FPPoint, ops::SubAssign, sub_assign, -);
bin_assign_op_impl!(FPPoint, ops::MulAssign, mul_assign, *);
bin_assign_op_impl!(FPPoint, ops::DivAssign, div_assign, /);
bin_assign_op_impl!(FPPoint, ops::AddAssign<FPNum>, add_assign, +);
bin_assign_op_impl!(FPPoint, ops::SubAssign<FPNum>, sub_assign, -);
bin_assign_op_impl!(FPPoint, ops::MulAssign<FPNum>, mul_assign, *);
bin_assign_op_impl!(FPPoint, ops::DivAssign<FPNum>, div_assign, /);

#[inline]
pub fn distance<T>(x: T, y: T) -> FPNum
    where T: ops::Add + ops::Mul + Copy +
             From<<T as ops::Add>::Output> +
             From<<T as ops::Mul>::Output> +
             Into<FPNum>
{
    let sqr: FPNum = T::from(T::from(x * x) + T::from(y * y)).into();
    sqr.sqrt()
}

/* TODO:
 AngleSin
 AngleCos
*/

#[cfg(test)]
#[test]
fn basics() {
    let n = fp!(15/2);
    assert!(n.is_positive());
    assert!(!n.is_negative());

    assert!(!(-n).is_positive());
    assert!((-n).is_negative());

    assert_eq!(-(-n), n);
    assert_eq!((-n).abs(), n);
    assert_eq!(-n, fp!(-15/2));

    assert_eq!(n.round(), 7);
    assert_eq!((-n).round(), -7);
}

#[test]
fn zero() {
    let z = fp!(0);
    let n = fp!(15/2);

    assert!(z.is_zero());
    assert!(z.is_positive());
    assert!((-z).is_negative);
    assert_eq!(n - n, z);
    assert_eq!(-n + n, z);
    assert_eq!(n.with_sign_as(-n), -n);
}

#[test]
fn ord() {
    let z = fp!(0);
    let n1_5 = fp!(3/2);
    let n2_25 = fp!(9/4);

    assert!(!(z > z));
    assert!(!(z < z));
    assert!(n2_25 > n1_5);
    assert!(-n2_25 < n1_5);
    assert!(-n2_25 < -n1_5);
}

#[test]
fn arith() {
    let n1_5 = fp!(3/2);
    let n2_25 = fp!(9/4);
    let n_0_15 = fp!(-15/100);

    assert_eq!(n1_5 + n1_5, fp!(3));
    assert_eq!(-n1_5 - n1_5, fp!(-3));

    assert_eq!(n1_5 * n1_5, n2_25);
    assert_eq!(-n1_5 * -n1_5, n2_25);
    assert_eq!(n1_5 * -n1_5, -n2_25);
    assert_eq!(-n1_5 * n1_5, -n2_25);

    assert_eq!(-n2_25 / -n1_5, n1_5);
    assert_eq!(n1_5 / -10, n_0_15);

    assert_eq!(n1_5.sqr(), n2_25);
    assert_eq!((-n1_5).sqr(), n2_25);

    assert_eq!(n2_25.sqrt(), n1_5);

    assert_eq!((n1_5 * n1_5 * n1_5.sqr()).sqrt(), n2_25);

    let mut m = fp!(1);
    m += n1_5;
    assert_eq!(m, fp!(5/2));
}

#[test]
fn point() {
    let z = FPPoint::zero();
    let p = FPPoint::new(fp!(1), fp!(-2));

    assert_eq!(p.sqr_distance(), fp!(5));
    assert_eq!(p + -p, FPPoint::zero());
    assert_eq!(p * z, z);
    assert_eq!(p.dot(&z), fp!(0));
    assert_eq!(distance(4, 3), fp!(5));
    assert_eq!(p * fp!(-3), FPPoint::new(fp!(-3), fp!(6)));
}