//! Numeric Helper Traits
#![allow(unused_comparisons)]
use core::convert::TryFrom;
use core::fmt::Debug;
use core::ops::{
    Add, AddAssign, BitAnd, BitAndAssign, BitOr, BitOrAssign, BitXor, BitXorAssign, Div, DivAssign,
    Mul, MulAssign, Not, Rem, RemAssign, Shl, ShlAssign, Shr, ShrAssign, Sub, SubAssign,
};

/// Native number type
pub trait Num:
    Add
    + AddAssign
    + Debug
    + Div
    + DivAssign
    + Mul
    + MulAssign
    + Rem
    + RemAssign
    + PartialOrd
    + PartialEq
    + Copy
    + Sub
    + SubAssign
{
    /// Is this number type signed?
    fn is_signed(&self) -> bool {
        true
    }
}

/// Float primitive
pub trait Float: Num {
    fn is_neg(self) -> bool;
}

/// Integer primitive
pub trait Int:
    Num
    + BitAnd
    + BitAndAssign
    + BitOr
    + BitOrAssign
    + BitXor
    + BitXorAssign
    + Eq
    + Ord
    + Not
    + Shl
    + Shr
    + ShlAssign
    + ShrAssign
{
    /// The maximum value of the type
    fn max_value() -> Self;

    /// Is this a zero value?
    fn is_zero(self) -> bool;

    /// Is this number less than zero?
    fn is_neg(self) -> bool;
}

/// A Trait representing unsigned integer primitives
pub trait Unsigned: Int {
    /// Find the greatest common denominator of two numbers
    fn gcd(a: Self, b: Self) -> Self;

    /// Find the least common multiple of two numbers
    fn lcm(a: Self, b: Self) -> Self;

    fn is_signed(self) -> bool {
        false
    }
}

/// A Trait representing signed integer primitives
pub trait Signed: Int {
    type Un;

    fn to_unsigned(self) -> Self::Un;
}

#[derive(Debug, Copy, Clone, PartialEq, Eq)]
pub enum Sign {
    Positive,
    Negative,
}

impl Default for Sign {
    fn default() -> Self {
        Sign::Positive
    }
}

impl Not for Sign {
    type Output = Sign;

    fn not(self) -> Self::Output {
        match self {
            Self::Positive => Self::Negative,
            Self::Negative => Self::Positive,
        }
    }
}

macro_rules! impl_num {
    ($( $Type: ty ),* ) => {
        $(
            impl Num for $Type {

            }
        )*
    }
}

macro_rules! impl_float {
    ($( $Type: ty ),* ) => {
        $(
            impl Float for $Type {
                fn is_neg(self) -> bool {
                    self < 0.0
                }
            }
        )*
    }
}

macro_rules! impl_int {
    ($( $Type: ty ),* ) => {
        $(
            impl Int for $Type {
                fn is_zero(self) -> bool {
                    self == 0
                }

                fn max_value() -> $Type {
                    <$Type>::max_value()
                }

                /// Is this number less than zero?

                fn is_neg(self) -> bool {
                    if self.is_signed() == false {
                        false
                    } else {
                        self < 0
                    }
                }
            }
        )*
    }
}

macro_rules! impl_unsigned {
    ($($Type: ty),* ) => {
        $(
            impl Unsigned for $Type {
                /// Implementation based on https://en.wikipedia.org/wiki/Binary_GCD_algorithm
                fn gcd(a: $Type, b: $Type) -> $Type {
                    if a == b {
                        return a;
                    } else if a == 0 {
                        return b;
                    } else if b == 0 {
                        return a;
                    }

                    let a_even = a % 2 == 0;
                    let b_even = b % 2 == 0;

                    if a_even {
                        if b_even {
                            // Both a & b are even
                            return Self::gcd(a >> 1, b >> 1) << 1;
                        } else if !b_even {
                            // b is odd
                            return Self::gcd(a >> 1, b);
                        }
                    }

                    // a is odd, b is even
                    if (!a_even) && b_even {
                        return Self::gcd(a, b >> 1);
                    }

                    if a > b {
                        return Self::gcd((a - b) >> 1, b);
                    }

                    Self::gcd((b - a) >> 1, a)
                }

                fn lcm(a: $Type, b: $Type) -> $Type {
                    if (a == 0 && b == 0) {
                        return 0;
                    }

                    a * b / Self::gcd(a, b)
                }
            }
        )*
    };
}

macro_rules! impl_signed {
    ($(($type: ty, $un_type: ty)),* ) => {
        $(
            impl Signed for $type {
                type Un = $un_type;

                fn to_unsigned(self) -> $un_type {
                    // Converting from signed to unsigned should always be safe
                    // when using the absolute value, especially since I'm converting
                    // between the same bit size
                    <$un_type>::try_from(self).unwrap()
                }
            }
        )*
    }
}

impl_num!(i8, u8, i16, u16, f32, i32, u32, f64, i64, u64, i128, u128, isize, usize);
impl_float!(f32, f64);
impl_int!(i8, u8, i16, u16, i32, u32, i64, u64, i128, u128, isize, usize);
impl_unsigned!(u8, u16, u32, u64, u128, usize);
impl_signed!(
    (i8, u8),
    (i16, u16),
    (i32, u32),
    (i64, u64),
    (i128, u128),
    (isize, usize)
);

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

    #[test]
    fn test_gcd() {
        assert_eq!(u8::gcd(2, 2), 2);
        assert_eq!(u16::gcd(36, 48), 12);
    }

    #[test]
    fn test_lcm() {
        assert_eq!(usize::lcm(15, 30), 30);
        assert_eq!(u128::lcm(1, 5), 5);
    }
}