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use std::fmt::Debug;
use std::ops::*;

pub trait Scalar: Copy + Debug + PartialEq + PartialOrd {
    fn min(self, other: Self) -> Self {
        if self < other { self } else { other }
    }

    fn max(self, other: Self) -> Self {
        if self > other { self } else { other }
    }
}

impl<S: Copy + Debug + PartialEq + PartialOrd> Scalar for S {}

pub trait Number: Scalar + 
    Add<Output=Self> + AddAssign +
    Sub<Output=Self> + SubAssign + 
    Mul<Output=Self> + MulAssign +
    Div<Output=Self> + DivAssign +
    Rem<Output=Self> + RemAssign
{    
    const ZERO: Self;
    const ONE: Self;
    const TWO: Self;
}

macro_rules! impl_number {
    ($ty: ty, $zero: tt, $one: tt) => {
        impl Number for $ty {
            const ZERO: Self = $zero;
            const ONE: Self = $one;
            const TWO: Self = $one + $one;
        }
    }
}

impl_number!(i8, 0, 1);
impl_number!(u8, 0, 1);
impl_number!(i16, 0, 1);
impl_number!(u16, 0, 1);
impl_number!(i32, 0, 1);
impl_number!(u32, 0, 1);
impl_number!(i64, 0, 1);
impl_number!(u64, 0, 1);
impl_number!(i128, 0, 1);
impl_number!(u128, 0, 1);
impl_number!(isize, 0, 1);
impl_number!(usize, 0, 1);
impl_number!(f32, 0.0, 1.0);
impl_number!(f64, 0.0, 1.0);

pub trait Signed: Number + Neg<Output=Self> {
    fn abs(self) -> Self;
    fn signum(self) -> Self;
}

macro_rules! impl_signed {
    ($ty: ty) => {
        impl Signed for $ty {
            #[inline(always)]
            fn abs(self) -> Self {
                Self::abs(self)
            } 

            #[inline(always)]
            fn signum(self) -> Self {
                Self::signum(self)
            }
        }
    };
}

impl_signed!(i8);
impl_signed!(i32);
impl_signed!(i64);
impl_signed!(i128);
impl_signed!(isize);
impl_signed!(f32);
impl_signed!(f64);

pub trait Float: Signed + From<f32> {
    type Bits;

    const HALF: Self;
    const RADIX: u32;
    const MANTISSA_DIGITS: u32;
    const DIGITS: u32;
    const EPSILON: Self;
    const MIN: Self;
    const MIN_POSITIVE: Self;
    const MAX: Self;
    const MIN_EXP: i32;
    const MAX_EXP: i32;
    const MIN_10_EXP: i32;
    const MAX_10_EXP: i32;
    const NAN: Self;
    const INFINITY: Self;
    const NEG_INFINITY: Self;

    fn floor(self) -> Self;
    fn ceil(self) -> Self;
    fn round(self) -> Self;
    fn trunc(self) -> Self;
    fn fract(self) -> Self;
    fn copysign(self, other: Self) -> Self;
    fn mul_add(self, a: Self, b: Self) -> Self;
    fn div_euclid(self, other: Self) -> Self;
    fn rem_euclid(self, other: Self) -> Self;
    fn powi(self, pow: i32) -> Self;
    fn powf(self, pow: Self) -> Self;
    fn sqrt(self) -> Self;
    fn exp(self) -> Self;
    fn exp2(self) -> Self;
    fn ln(self) -> Self;
    fn log(self, base: Self) -> Self;
    fn log10(self) -> Self;
    fn log2(self) -> Self;
    fn cbrt(self) -> Self;
    fn hypot(self, other: Self) -> Self;
    fn sin(self) -> Self;
    fn cos(self) -> Self;
    fn tan(self) -> Self;
    fn asin(self) -> Self;
    fn acos(self) -> Self;
    fn atan(self) -> Self;
    fn sin_cos(self) -> (Self, Self);
    fn exp_m1(self) -> Self;
    fn ln_1p(self) -> Self;
    fn sinh(self) -> Self;
    fn cosh(self) -> Self;
    fn tanh(self) -> Self;
    fn asinh(self) -> Self;
    fn acosh(self) -> Self;
    fn atanh(self) -> Self;
    fn recip(self) -> Self;
    fn to_radians(self) -> Self;
    fn to_degrees(self) -> Self;
    fn from_bits(bits: Self::Bits) -> Self;
    fn to_bits(self) -> Self::Bits;
}

macro_rules! impl_float {
    ($ty: tt, $bits: ty) => {
        impl Float for $ty {
            type Bits = $bits;

            const HALF: Self = 0.5;
            const RADIX: u32 = std::$ty::RADIX;
            const MANTISSA_DIGITS: u32 = std::$ty::MANTISSA_DIGITS;
            const DIGITS: u32 = std::$ty::DIGITS;
            const EPSILON: Self = std::$ty::EPSILON;
            const MIN: Self = std::$ty::MIN;
            const MIN_POSITIVE: Self = std::$ty::MIN_POSITIVE;
            const MAX: Self = std::$ty::MAX;
            const MIN_EXP: i32 = std::$ty::MIN_EXP;
            const MAX_EXP: i32 = std::$ty::MAX_EXP;
            const MIN_10_EXP: i32 = std::$ty::MIN_10_EXP;
            const MAX_10_EXP: i32 = std::$ty::MAX_10_EXP;
            const NAN: Self = std::$ty::NAN;
            const INFINITY: Self = std::$ty::INFINITY;
            const NEG_INFINITY: Self = std::$ty::NEG_INFINITY;

            #[inline(always)] fn floor(self) -> Self { Self::floor(self) }
            #[inline(always)] fn ceil(self) -> Self { Self::ceil(self) }
            #[inline(always)] fn round(self) -> Self { Self::round(self) }
            #[inline(always)] fn trunc(self) -> Self { Self::trunc(self) }
            #[inline(always)] fn fract(self) -> Self { Self::fract(self) }
            #[inline(always)] fn copysign(self, other: Self) -> Self { Self::copysign(self, other) }
            #[inline(always)] fn mul_add(self, a: Self, b: Self) -> Self { Self::mul_add(self, a, b) }
            #[inline(always)] fn div_euclid(self, other: Self) -> Self { Self::div_euclid(self, other) }
            #[inline(always)] fn rem_euclid(self, other: Self) -> Self { Self::rem_euclid(self, other) }
            #[inline(always)] fn powi(self, pow: i32) -> Self { Self::powi(self, pow) }
            #[inline(always)] fn powf(self, pow: Self) -> Self { Self::powf(self, pow) }
            #[inline(always)] fn sqrt(self) -> Self { Self::sqrt(self) }
            #[inline(always)] fn exp(self) -> Self { Self::exp(self) }
            #[inline(always)] fn exp2(self) -> Self { Self::exp2(self) }
            #[inline(always)] fn ln(self) -> Self { Self::ln(self) }
            #[inline(always)] fn log(self, base: Self) -> Self { Self::log(self, base) }
            #[inline(always)] fn log10(self) -> Self { Self::log10(self) }
            #[inline(always)] fn log2(self) -> Self { Self::log2(self) }
            #[inline(always)] fn cbrt(self) -> Self { Self::cbrt(self) }
            #[inline(always)] fn hypot(self, other: Self) -> Self { Self::hypot(self, other) }
            #[inline(always)] fn sin(self) -> Self { Self::sin(self) }
            #[inline(always)] fn cos(self) -> Self { Self::cos(self) }
            #[inline(always)] fn tan(self) -> Self { Self::tan(self) }
            #[inline(always)] fn asin(self) -> Self { Self::asin(self) }
            #[inline(always)] fn acos(self) -> Self { Self::acos(self) }
            #[inline(always)] fn atan(self) -> Self { Self::atan(self) }
            #[inline(always)] fn sin_cos(self) -> (Self, Self) { Self::sin_cos(self) }
            #[inline(always)] fn exp_m1(self) -> Self { Self::exp_m1(self) }
            #[inline(always)] fn ln_1p(self) -> Self { Self::ln_1p(self) }
            #[inline(always)] fn sinh(self) -> Self { Self::sinh(self) }
            #[inline(always)] fn cosh(self) -> Self { Self::cosh(self) }
            #[inline(always)] fn tanh(self) -> Self { Self::tanh(self) }
            #[inline(always)] fn asinh(self) -> Self { Self::asinh(self) }
            #[inline(always)] fn acosh(self) -> Self { Self::acosh(self) }
            #[inline(always)] fn atanh(self) -> Self { Self::atanh(self) }
            #[inline(always)] fn recip(self) -> Self { Self::recip(self) }
            #[inline(always)] fn to_radians(self) -> Self { Self::to_radians(self) }
            #[inline(always)] fn to_degrees(self) -> Self { Self::to_degrees(self) }
            #[inline(always)] fn from_bits(bits: Self::Bits) -> Self { Self::from_bits(bits) }
            #[inline(always)] fn to_bits(self) -> Self::Bits { Self::to_bits(self) }
        }
    };
}

impl_float!(f32, u32);
impl_float!(f64, u64);