#[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) -> i32 {

        if self.is_negative {

            -((self.value >> 32) as i32)

        } else {

            (self.value >> 32) as i32

        }

    }

    #[inline]

    pub fn abs_round(&self) -> u32 {

        (self.value >> 32) as u32

    }

    #[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 is_zero(&self) -> bool {

        self.x().is_zero() && self.y().is_zero()

    }

    #[inline]

    pub fn max_norm(&self) -> FPNum {

        std::cmp::max(self.x().abs(), self.y().abs())

    }

    #[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 {

            let mut sqr: u128 = (self.x_value as u128).pow(2) + (self.y_value as u128).pow(2);

            let mut t: u128 = 0x40000000_00000000_00000000_00000000;

            let mut r: u128 = 0;

            for _ in 0..64 {

                let s = r + t;

                r >>= 1;

                if s <= sqr {

                    sqr -= s;

                    r += t;

                }

                t >>= 2;

            }

            FPNum {

                is_negative: false,

                value: r as u64,

            }

        }

    }

    #[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! right_scalar_bin_op_impl {

    ($($op: tt)::+, $name: tt) => {

        impl $($op)::+<FPNum> for FPPoint {

            type Output = Self;

            #[inline]

            fn $name(self, rhs: FPNum) -> Self {

                Self::new(self.x().$name(rhs),

                          self.y().$name(rhs))

            }

        }

    };

    ($($op: tt)::+<$arg: tt>, $name: tt) => {

        impl $($op)::+<$arg> for FPPoint {

            type Output = Self;

            #[inline]

            fn $name(self, rhs: $arg) -> Self {

                Self::new(self.x().$name(rhs),

                          self.y().$name(rhs))

            }

        }

    }

}

macro_rules! left_scalar_bin_op_impl {

    ($($op: tt)::+, $name: tt) => {

        impl $($op)::+<FPPoint> for FPNum {

            type Output = FPPoint;

            #[inline]

            fn $name(self, rhs: FPPoint) -> Self::Output {

                Self::Output::new(self.$name(rhs.x()),

                                  self.$name(rhs.y()))

            }

        }

    }

}

bin_op_impl!(ops::Add, add);

bin_op_impl!(ops::Sub, sub);

bin_op_impl!(ops::Mul, mul);

bin_op_impl!(ops::Div, div);

right_scalar_bin_op_impl!(ops::Add, add);

right_scalar_bin_op_impl!(ops::Mul, mul);

right_scalar_bin_op_impl!(ops::Sub, sub);

right_scalar_bin_op_impl!(ops::Div, div);

right_scalar_bin_op_impl!(ops::Div<u32>, div);

left_scalar_bin_op_impl!(ops::Mul, mul);

macro_rules! bin_assign_op_impl {