const POSITIVE_MASK: u64 = 0x0000_0000_0000_0000;

const NEGATIVE_MASK: u64 = 0xFFFF_FFFF_FFFF_FFFF;

#[inline]

fn bool_mask(is_negative: bool) -> u64 {

    if is_negative {

        NEGATIVE_MASK

    } else {

        POSITIVE_MASK

    }

}

#[derive(Clone, Debug, Copy)]

pub struct FPNum {

    sign_mask: u64,

    value: u64,

}

impl FPNum {

    #[inline]

    pub fn new(numerator: i32, denominator: u32) -> Self {

        FPNum::from(numerator) / denominator

    }

    #[inline]

    pub fn signum(&self) -> i8 {

        (1u64 ^ self.sign_mask).wrapping_sub(self.sign_mask) as i8

    }

    #[inline]

    pub const fn is_negative(&self) -> bool {

        self.sign_mask != POSITIVE_MASK

    }

    #[inline]

    pub const fn is_positive(&self) -> bool {

        self.sign_mask == POSITIVE_MASK

    }

    #[inline]

    pub const fn is_zero(&self) -> bool {

        self.value == 0

    }

    #[inline]

    pub const fn abs(&self) -> Self {

        Self {

            sign_mask: POSITIVE_MASK,

            value: self.value,

        }

    }

    #[inline]

    pub fn round(&self) -> i32 {

        ((self.value >> 32) as i32 ^ self.sign_mask as i32).wrapping_sub(self.sign_mask as i32)

    }

    #[inline]

    pub const fn abs_round(&self) -> u32 {

        (self.value >> 32) as u32

    }

    #[inline]

    pub fn sqr(&self) -> Self {

        Self {

            sign_mask: 0,

        }

    }

    #[inline]

    pub fn sqrt(&self) -> Self {

        debug_assert!(self.is_positive());

        Self {

            sign_mask: POSITIVE_MASK,

            value: integral_sqrt(self.value) << 16,

        }

    }

    #[inline]

    pub fn with_sign(&self, is_negative: bool) -> FPNum {

        FPNum {

            sign_mask: bool_mask(is_negative),

            ..*self

        }

    }

    #[inline]

    pub const fn with_sign_as(self, other: FPNum) -> FPNum {

        FPNum {

            sign_mask: other.sign_mask,

            ..self

        }

    }

    #[inline]

    pub const fn point(self) -> FPPoint {

        FPPoint::new(self, self)

    }

    #[inline]

    const fn temp_i128(self) -> i128 {

        ((self.value ^ self.sign_mask) as i128).wrapping_sub(self.sign_mask as i128)

    }

}

impl From<i32> for FPNum {

    #[inline]

    fn from(n: i32) -> Self {

        FPNum {

            sign_mask: bool_mask(n < 0),

            value: (n.abs() as u64) << 32,

        }

    }

}

impl From<u32> for FPNum {

    #[inline]

    fn from(n: u32) -> Self {

        Self {

            sign_mask: POSITIVE_MASK,

            value: (n as u64) << 32,

        }

    }

}

impl From<FPNum> for f64 {

    #[inline]

    fn from(n: FPNum) -> Self {

        if n.is_negative() {

            n.value as f64 / -0x1_0000_0000i64 as f64

        } else {

            n.value as f64 / 0x1_0000_0000i64 as f64

        }

    }

}

impl PartialEq for FPNum {

    #[inline]

    fn eq(&self, other: &Self) -> bool {

        self.value == other.value && (self.sign_mask == other.sign_mask || self.value == 0)

    }

}

impl Eq for FPNum {}

impl PartialOrd for FPNum {

    #[inline]

        Some(self.cmp(rhs))

    }

}

impl Ord for FPNum {

    #[inline]

    fn cmp(&self, rhs: &Self) -> cmp::Ordering {

        self.temp_i128().cmp(&(rhs.temp_i128()))

    }

}

impl ops::Add for FPNum {

    type Output = Self;

    #[inline]

    fn add(self, rhs: Self) -> Self {

        let tmp = self.temp_i128() + rhs.temp_i128();

        let mask = bool_mask(tmp < 0);

        Self {

            sign_mask: mask,

            value: ((tmp as u64) ^ mask).wrapping_sub(mask),

        }

    }

}

impl ops::Sub for FPNum {

    type Output = Self;

    #[inline]

    fn sub(self, mut rhs: Self) -> Self {

        rhs.sign_mask = !rhs.sign_mask;

        self + rhs

    }

}

impl ops::Neg for FPNum {

    type Output = Self;

    #[inline]

    fn neg(self) -> Self {

        Self {

            sign_mask: !self.sign_mask,

            value: self.value,

        }

    }

}

impl ops::Mul for FPNum {

    type Output = Self;

    #[inline]

    fn mul(self, rhs: Self) -> Self {

        Self {

            sign_mask: self.sign_mask ^ rhs.sign_mask,

        }

    }

}

impl ops::Mul<i32> for FPNum {

    type Output = Self;

    #[inline]

    fn mul(self, rhs: i32) -> Self {

        Self {

            sign_mask: self.sign_mask ^ bool_mask(rhs < 0),

        }

    }

}

impl ops::Div for FPNum {

    type Output = Self;

    #[inline]

    fn div(self, rhs: Self) -> Self {

        Self {

            sign_mask: self.sign_mask ^ rhs.sign_mask,

        }

    }

}

impl ops::Div<i32> for FPNum {

    type Output = Self;

    #[inline]

    fn div(self, rhs: i32) -> Self {

        Self {

            sign_mask: self.sign_mask ^ bool_mask(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 {

            sign_mask: self.sign_mask,

            value: self.value / rhs as u64,

        }

    }

}

#[macro_export]

macro_rules! fp {

    ($n: literal / $d: tt) => {

        FPNum::new($n, $d)

    };

    ($n: literal) => {

        FPNum::from($n)

    };

}

const LINEARIZE_TRESHOLD: u64 = 0x1_0000;

#[derive(Clone, Copy, Debug)]

pub struct FPPoint {

    x_sign_mask: u32,

    y_sign_mask: u32,

    x_value: u64,

    y_value: u64,

}

impl FPPoint {

    #[inline]

    pub const fn new(x: FPNum, y: FPNum) -> Self {

        Self {

            x_sign_mask: x.sign_mask as u32,

            y_sign_mask: y.sign_mask as u32,

            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 const fn x(&self) -> FPNum {

        FPNum {

            sign_mask: self.x_sign_mask as i32 as u64,

            value: self.x_value,

        }

    }

    #[inline]

    pub const fn y(&self) -> FPNum {

        FPNum {

            sign_mask: self.y_sign_mask as i32 as u64,

            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 {

    }

    #[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 sqr: u128 = (self.x_value as u128).pow(2) + (self.y_value as u128).pow(2);

            FPNum {

                sign_mask: POSITIVE_MASK,

                value: integral_sqrt_ext(sqr),

            }

        }

    }

    #[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 {

    ($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, /);

pub fn integral_sqrt(value: u64) -> u64 {

    let mut digits = (64u32 - 1).saturating_sub(value.leading_zeros()) & 0xFE;

    let mut result = if value == 0 { 0u64 } else { 1u64 };

    while digits != 0 {

        result <<= 1;

        if (result + 1).pow(2) <= value >> (digits - 2) {

            result += 1;

        }

        digits -= 2;

    }

    result

}

pub fn integral_sqrt_ext(value: u128) -> u64 {

    let mut digits = (128u32 - 1).saturating_sub(value.leading_zeros()) & 0xFE;

    let mut result = if value == 0 { 0u64 } else { 1u64 };