use core::mem::size_of;
use core::num::Wrapping;
use core::{f32, f64};
#[cfg(has_i128)]
use core::{i128, u128};
use core::{i16, i32, i64, i8, isize};
use core::{u16, u32, u64, u8, usize};

/// A generic trait for converting a value to a number.
///
/// A value can be represented by the target type when it lies within
/// the range of scalars supported by the target type.
/// For example, a negative integer cannot be represented by an unsigned
/// integer type, and an `i64` with a very high magnitude might not be
/// convertible to an `i32`.
/// On the other hand, conversions with possible precision loss or truncation
/// are admitted, like an `f32` with a decimal part to an integer type, or
/// even a large `f64` saturating to `f32` infinity.
pub trait ToPrimitive {
    /// Converts the value of `self` to an `isize`. If the value cannot be
    /// represented by an `isize`, then `None` is returned.
    #[inline]
    fn to_isize(&self) -> Option<isize> {
        self.to_i64().as_ref().and_then(ToPrimitive::to_isize)
    }

    /// Converts the value of `self` to an `i8`. If the value cannot be
    /// represented by an `i8`, then `None` is returned.
    #[inline]
    fn to_i8(&self) -> Option<i8> {
        self.to_i64().as_ref().and_then(ToPrimitive::to_i8)
    }

    /// Converts the value of `self` to an `i16`. If the value cannot be
    /// represented by an `i16`, then `None` is returned.
    #[inline]
    fn to_i16(&self) -> Option<i16> {
        self.to_i64().as_ref().and_then(ToPrimitive::to_i16)
    }

    /// Converts the value of `self` to an `i32`. If the value cannot be
    /// represented by an `i32`, then `None` is returned.
    #[inline]
    fn to_i32(&self) -> Option<i32> {
        self.to_i64().as_ref().and_then(ToPrimitive::to_i32)
    }

    /// Converts the value of `self` to an `i64`. If the value cannot be
    /// represented by an `i64`, then `None` is returned.
    fn to_i64(&self) -> Option<i64>;

    /// Converts the value of `self` to an `i128`. If the value cannot be
    /// represented by an `i128` (`i64` under the default implementation), then
    /// `None` is returned.
    ///
    /// This method is only available with feature `i128` enabled on Rust >= 1.26.
    ///
    /// The default implementation converts through `to_i64()`. Types implementing
    /// this trait should override this method if they can represent a greater range.
    #[inline]
    #[cfg(has_i128)]
    fn to_i128(&self) -> Option<i128> {
        self.to_i64().map(From::from)
    }

    /// Converts the value of `self` to a `usize`. If the value cannot be
    /// represented by a `usize`, then `None` is returned.
    #[inline]
    fn to_usize(&self) -> Option<usize> {
        self.to_u64().as_ref().and_then(ToPrimitive::to_usize)
    }

    /// Converts the value of `self` to a `u8`. If the value cannot be
    /// represented by a `u8`, then `None` is returned.
    #[inline]
    fn to_u8(&self) -> Option<u8> {
        self.to_u64().as_ref().and_then(ToPrimitive::to_u8)
    }

    /// Converts the value of `self` to a `u16`. If the value cannot be
    /// represented by a `u16`, then `None` is returned.
    #[inline]
    fn to_u16(&self) -> Option<u16> {
        self.to_u64().as_ref().and_then(ToPrimitive::to_u16)
    }

    /// Converts the value of `self` to a `u32`. If the value cannot be
    /// represented by a `u32`, then `None` is returned.
    #[inline]
    fn to_u32(&self) -> Option<u32> {
        self.to_u64().as_ref().and_then(ToPrimitive::to_u32)
    }

    /// Converts the value of `self` to a `u64`. If the value cannot be
    /// represented by a `u64`, then `None` is returned.
    fn to_u64(&self) -> Option<u64>;

    /// Converts the value of `self` to a `u128`. If the value cannot be
    /// represented by a `u128` (`u64` under the default implementation), then
    /// `None` is returned.
    ///
    /// This method is only available with feature `i128` enabled on Rust >= 1.26.
    ///
    /// The default implementation converts through `to_u64()`. Types implementing
    /// this trait should override this method if they can represent a greater range.
    #[inline]
    #[cfg(has_i128)]
    fn to_u128(&self) -> Option<u128> {
        self.to_u64().map(From::from)
    }

    /// Converts the value of `self` to an `f32`. Overflows may map to positive
    /// or negative inifinity, otherwise `None` is returned if the value cannot
    /// be represented by an `f32`.
    #[inline]
    fn to_f32(&self) -> Option<f32> {
        self.to_f64().as_ref().and_then(ToPrimitive::to_f32)
    }

    /// Converts the value of `self` to an `f64`. Overflows may map to positive
    /// or negative inifinity, otherwise `None` is returned if the value cannot
    /// be represented by an `f64`.
    ///
    /// The default implementation tries to convert through `to_i64()`, and
    /// failing that through `to_u64()`. Types implementing this trait should
    /// override this method if they can represent a greater range.
    #[inline]
    fn to_f64(&self) -> Option<f64> {
        match self.to_i64() {
            Some(i) => i.to_f64(),
            None => self.to_u64().as_ref().and_then(ToPrimitive::to_f64),
        }
    }
}

macro_rules! impl_to_primitive_int_to_int {
    ($SrcT:ident : $( $(#[$cfg:meta])* fn $method:ident -> $DstT:ident ; )*) => {$(
        #[inline]
        $(#[$cfg])*
        fn $method(&self) -> Option<$DstT> {
            let min = $DstT::MIN as $SrcT;
            let max = $DstT::MAX as $SrcT;
            if size_of::<$SrcT>() <= size_of::<$DstT>() || (min <= *self && *self <= max) {
                Some(*self as $DstT)
            } else {
                None
            }
        }
    )*}
}

macro_rules! impl_to_primitive_int_to_uint {
    ($SrcT:ident : $( $(#[$cfg:meta])* fn $method:ident -> $DstT:ident ; )*) => {$(
        #[inline]
        $(#[$cfg])*
        fn $method(&self) -> Option<$DstT> {
            let max = $DstT::MAX as $SrcT;
            if 0 <= *self && (size_of::<$SrcT>() <= size_of::<$DstT>() || *self <= max) {
                Some(*self as $DstT)
            } else {
                None
            }
        }
    )*}
}

macro_rules! impl_to_primitive_int {
    ($T:ident) => {
        impl ToPrimitive for $T {
            impl_to_primitive_int_to_int! { $T:
                fn to_isize -> isize;
                fn to_i8 -> i8;
                fn to_i16 -> i16;
                fn to_i32 -> i32;
                fn to_i64 -> i64;
                #[cfg(has_i128)]
                fn to_i128 -> i128;
            }

            impl_to_primitive_int_to_uint! { $T:
                fn to_usize -> usize;
                fn to_u8 -> u8;
                fn to_u16 -> u16;
                fn to_u32 -> u32;
                fn to_u64 -> u64;
                #[cfg(has_i128)]
                fn to_u128 -> u128;
            }

            #[inline]
            fn to_f32(&self) -> Option<f32> {
                Some(*self as f32)
            }
            #[inline]
            fn to_f64(&self) -> Option<f64> {
                Some(*self as f64)
            }
        }
    };
}

impl_to_primitive_int!(isize);
impl_to_primitive_int!(i8);
impl_to_primitive_int!(i16);
impl_to_primitive_int!(i32);
impl_to_primitive_int!(i64);
#[cfg(has_i128)]
impl_to_primitive_int!(i128);

macro_rules! impl_to_primitive_uint_to_int {
    ($SrcT:ident : $( $(#[$cfg:meta])* fn $method:ident -> $DstT:ident ; )*) => {$(
        #[inline]
        $(#[$cfg])*
        fn $method(&self) -> Option<$DstT> {
            let max = $DstT::MAX as $SrcT;
            if size_of::<$SrcT>() < size_of::<$DstT>() || *self <= max {
                Some(*self as $DstT)
            } else {
                None
            }
        }
    )*}
}

macro_rules! impl_to_primitive_uint_to_uint {
    ($SrcT:ident : $( $(#[$cfg:meta])* fn $method:ident -> $DstT:ident ; )*) => {$(
        #[inline]
        $(#[$cfg])*
        fn $method(&self) -> Option<$DstT> {
            let max = $DstT::MAX as $SrcT;
            if size_of::<$SrcT>() <= size_of::<$DstT>() || *self <= max {
                Some(*self as $DstT)
            } else {
                None
            }
        }
    )*}
}

macro_rules! impl_to_primitive_uint {
    ($T:ident) => {
        impl ToPrimitive for $T {
            impl_to_primitive_uint_to_int! { $T:
                fn to_isize -> isize;
                fn to_i8 -> i8;
                fn to_i16 -> i16;
                fn to_i32 -> i32;
                fn to_i64 -> i64;
                #[cfg(has_i128)]
                fn to_i128 -> i128;
            }

            impl_to_primitive_uint_to_uint! { $T:
                fn to_usize -> usize;
                fn to_u8 -> u8;
                fn to_u16 -> u16;
                fn to_u32 -> u32;
                fn to_u64 -> u64;
                #[cfg(has_i128)]
                fn to_u128 -> u128;
            }

            #[inline]
            fn to_f32(&self) -> Option<f32> {
                Some(*self as f32)
            }
            #[inline]
            fn to_f64(&self) -> Option<f64> {
                Some(*self as f64)
            }
        }
    };
}

impl_to_primitive_uint!(usize);
impl_to_primitive_uint!(u8);
impl_to_primitive_uint!(u16);
impl_to_primitive_uint!(u32);
impl_to_primitive_uint!(u64);
#[cfg(has_i128)]
impl_to_primitive_uint!(u128);

macro_rules! impl_to_primitive_float_to_float {
    ($SrcT:ident : $( fn $method:ident -> $DstT:ident ; )*) => {$(
        #[inline]
        fn $method(&self) -> Option<$DstT> {
            // We can safely cast all values, whether NaN, +-inf, or finite.
            // Finite values that are reducing size may saturate to +-inf.
            Some(*self as $DstT)
        }
    )*}
}

#[cfg(has_to_int_unchecked)]
macro_rules! float_to_int_unchecked {
    // SAFETY: Must not be NaN or infinite; must be representable as the integer after truncating.
    // We already checked that the float is in the exclusive range `(MIN-1, MAX+1)`.
    ($float:expr => $int:ty) => {
        unsafe { $float.to_int_unchecked::<$int>() }
    };
}

#[cfg(not(has_to_int_unchecked))]
macro_rules! float_to_int_unchecked {
    ($float:expr => $int:ty) => {
        $float as $int
    };
}

macro_rules! impl_to_primitive_float_to_signed_int {
    ($f:ident : $( $(#[$cfg:meta])* fn $method:ident -> $i:ident ; )*) => {$(
        #[inline]
        $(#[$cfg])*
        fn $method(&self) -> Option<$i> {
            // Float as int truncates toward zero, so we want to allow values
            // in the exclusive range `(MIN-1, MAX+1)`.
            if size_of::<$f>() > size_of::<$i>() {
                // With a larger size, we can represent the range exactly.
                const MIN_M1: $f = $i::MIN as $f - 1.0;
                const MAX_P1: $f = $i::MAX as $f + 1.0;
                if *self > MIN_M1 && *self < MAX_P1 {
                    return Some(float_to_int_unchecked!(*self => $i));
                }
            } else {
                // We can't represent `MIN-1` exactly, but there's no fractional part
                // at this magnitude, so we can just use a `MIN` inclusive boundary.
                const MIN: $f = $i::MIN as $f;
                // We can't represent `MAX` exactly, but it will round up to exactly
                // `MAX+1` (a power of two) when we cast it.
                const MAX_P1: $f = $i::MAX as $f;
                if *self >= MIN && *self < MAX_P1 {
                    return Some(float_to_int_unchecked!(*self => $i));
                }
            }
            None
        }
    )*}
}

macro_rules! impl_to_primitive_float_to_unsigned_int {
    ($f:ident : $( $(#[$cfg:meta])* fn $method:ident -> $u:ident ; )*) => {$(
        #[inline]
        $(#[$cfg])*
        fn $method(&self) -> Option<$u> {
            // Float as int truncates toward zero, so we want to allow values
            // in the exclusive range `(-1, MAX+1)`.
            if size_of::<$f>() > size_of::<$u>() {
                // With a larger size, we can represent the range exactly.
                const MAX_P1: $f = $u::MAX as $f + 1.0;
                if *self > -1.0 && *self < MAX_P1 {
                    return Some(float_to_int_unchecked!(*self => $u));
                }
            } else {
                // We can't represent `MAX` exactly, but it will round up to exactly
                // `MAX+1` (a power of two) when we cast it.
                // (`u128::MAX as f32` is infinity, but this is still ok.)
                const MAX_P1: $f = $u::MAX as $f;
                if *self > -1.0 && *self < MAX_P1 {
                    return Some(float_to_int_unchecked!(*self => $u));
                }
            }
            None
        }
    )*}
}

macro_rules! impl_to_primitive_float {
    ($T:ident) => {
        impl ToPrimitive for $T {
            impl_to_primitive_float_to_signed_int! { $T:
                fn to_isize -> isize;
                fn to_i8 -> i8;
                fn to_i16 -> i16;
                fn to_i32 -> i32;
                fn to_i64 -> i64;
                #[cfg(has_i128)]
                fn to_i128 -> i128;
            }

            impl_to_primitive_float_to_unsigned_int! { $T:
                fn to_usize -> usize;
                fn to_u8 -> u8;
                fn to_u16 -> u16;
                fn to_u32 -> u32;
                fn to_u64 -> u64;
                #[cfg(has_i128)]
                fn to_u128 -> u128;
            }

            impl_to_primitive_float_to_float! { $T:
                fn to_f32 -> f32;
                fn to_f64 -> f64;
            }
        }
    };
}

impl_to_primitive_float!(f32);
impl_to_primitive_float!(f64);

/// A generic trait for converting a number to a value.
///
/// A value can be represented by the target type when it lies within
/// the range of scalars supported by the target type.
/// For example, a negative integer cannot be represented by an unsigned
/// integer type, and an `i64` with a very high magnitude might not be
/// convertible to an `i32`.
/// On the other hand, conversions with possible precision loss or truncation
/// are admitted, like an `f32` with a decimal part to an integer type, or
/// even a large `f64` saturating to `f32` infinity.
pub trait FromPrimitive: Sized {
    /// Converts an `isize` to return an optional value of this type. If the
    /// value cannot be represented by this type, then `None` is returned.
    #[inline]
    fn from_isize(n: isize) -> Option<Self> {
        n.to_i64().and_then(FromPrimitive::from_i64)
    }

    /// Converts an `i8` to return an optional value of this type. If the
    /// value cannot be represented by this type, then `None` is returned.
    #[inline]
    fn from_i8(n: i8) -> Option<Self> {
        FromPrimitive::from_i64(From::from(n))
    }

    /// Converts an `i16` to return an optional value of this type. If the
    /// value cannot be represented by this type, then `None` is returned.
    #[inline]
    fn from_i16(n: i16) -> Option<Self> {
        FromPrimitive::from_i64(From::from(n))
    }

    /// Converts an `i32` to return an optional value of this type. If the
    /// value cannot be represented by this type, then `None` is returned.
    #[inline]
    fn from_i32(n: i32) -> Option<Self> {
        FromPrimitive::from_i64(From::from(n))
    }

    /// Converts an `i64` to return an optional value of this type. If the
    /// value cannot be represented by this type, then `None` is returned.
    fn from_i64(n: i64) -> Option<Self>;

    /// Converts an `i128` to return an optional value of this type. If the
    /// value cannot be represented by this type, then `None` is returned.
    ///
    /// This method is only available with feature `i128` enabled on Rust >= 1.26.
    ///
    /// The default implementation converts through `from_i64()`. Types implementing
    /// this trait should override this method if they can represent a greater range.
    #[inline]
    #[cfg(has_i128)]
    fn from_i128(n: i128) -> Option<Self> {
        n.to_i64().and_then(FromPrimitive::from_i64)
    }

    /// Converts a `usize` to return an optional value of this type. If the
    /// value cannot be represented by this type, then `None` is returned.
    #[inline]
    fn from_usize(n: usize) -> Option<Self> {
        n.to_u64().and_then(FromPrimitive::from_u64)
    }

    /// Converts an `u8` to return an optional value of this type. If the
    /// value cannot be represented by this type, then `None` is returned.
    #[inline]
    fn from_u8(n: u8) -> Option<Self> {
        FromPrimitive::from_u64(From::from(n))
    }

    /// Converts an `u16` to return an optional value of this type. If the
    /// value cannot be represented by this type, then `None` is returned.
    #[inline]
    fn from_u16(n: u16) -> Option<Self> {
        FromPrimitive::from_u64(From::from(n))
    }

    /// Converts an `u32` to return an optional value of this type. If the
    /// value cannot be represented by this type, then `None` is returned.
    #[inline]
    fn from_u32(n: u32) -> Option<Self> {
        FromPrimitive::from_u64(From::from(n))
    }

    /// Converts an `u64` to return an optional value of this type. If the
    /// value cannot be represented by this type, then `None` is returned.
    fn from_u64(n: u64) -> Option<Self>;

    /// Converts an `u128` to return an optional value of this type. If the
    /// value cannot be represented by this type, then `None` is returned.
    ///
    /// This method is only available with feature `i128` enabled on Rust >= 1.26.
    ///
    /// The default implementation converts through `from_u64()`. Types implementing
    /// this trait should override this method if they can represent a greater range.
    #[inline]
    #[cfg(has_i128)]
    fn from_u128(n: u128) -> Option<Self> {
        n.to_u64().and_then(FromPrimitive::from_u64)
    }

    /// Converts a `f32` to return an optional value of this type. If the
    /// value cannot be represented by this type, then `None` is returned.
    #[inline]
    fn from_f32(n: f32) -> Option<Self> {
        FromPrimitive::from_f64(From::from(n))
    }

    /// Converts a `f64` to return an optional value of this type. If the
    /// value cannot be represented by this type, then `None` is returned.
    ///
    /// The default implementation tries to convert through `from_i64()`, and
    /// failing that through `from_u64()`. Types implementing this trait should
    /// override this method if they can represent a greater range.
    #[inline]
    fn from_f64(n: f64) -> Option<Self> {
        match n.to_i64() {
            Some(i) => FromPrimitive::from_i64(i),
            None => n.to_u64().and_then(FromPrimitive::from_u64),
        }
    }
}

macro_rules! impl_from_primitive {
    ($T:ty, $to_ty:ident) => {
        #[allow(deprecated)]
        impl FromPrimitive for $T {
            #[inline]
            fn from_isize(n: isize) -> Option<$T> {
                n.$to_ty()
            }
            #[inline]
            fn from_i8(n: i8) -> Option<$T> {
                n.$to_ty()
            }
            #[inline]
            fn from_i16(n: i16) -> Option<$T> {
                n.$to_ty()
            }
            #[inline]
            fn from_i32(n: i32) -> Option<$T> {
                n.$to_ty()
            }
            #[inline]
            fn from_i64(n: i64) -> Option<$T> {
                n.$to_ty()
            }
            #[cfg(has_i128)]
            #[inline]
            fn from_i128(n: i128) -> Option<$T> {
                n.$to_ty()
            }

            #[inline]
            fn from_usize(n: usize) -> Option<$T> {
                n.$to_ty()
            }
            #[inline]
            fn from_u8(n: u8) -> Option<$T> {
                n.$to_ty()
            }
            #[inline]
            fn from_u16(n: u16) -> Option<$T> {
                n.$to_ty()
            }
            #[inline]
            fn from_u32(n: u32) -> Option<$T> {
                n.$to_ty()
            }
            #[inline]
            fn from_u64(n: u64) -> Option<$T> {
                n.$to_ty()
            }
            #[cfg(has_i128)]
            #[inline]
            fn from_u128(n: u128) -> Option<$T> {
                n.$to_ty()
            }

            #[inline]
            fn from_f32(n: f32) -> Option<$T> {
                n.$to_ty()
            }
            #[inline]
            fn from_f64(n: f64) -> Option<$T> {
                n.$to_ty()
            }
        }
    };
}

impl_from_primitive!(isize, to_isize);
impl_from_primitive!(i8, to_i8);
impl_from_primitive!(i16, to_i16);
impl_from_primitive!(i32, to_i32);
impl_from_primitive!(i64, to_i64);
#[cfg(has_i128)]
impl_from_primitive!(i128, to_i128);
impl_from_primitive!(usize, to_usize);
impl_from_primitive!(u8, to_u8);
impl_from_primitive!(u16, to_u16);
impl_from_primitive!(u32, to_u32);
impl_from_primitive!(u64, to_u64);
#[cfg(has_i128)]
impl_from_primitive!(u128, to_u128);
impl_from_primitive!(f32, to_f32);
impl_from_primitive!(f64, to_f64);

macro_rules! impl_to_primitive_wrapping {
    ($( $(#[$cfg:meta])* fn $method:ident -> $i:ident ; )*) => {$(
        #[inline]
        $(#[$cfg])*
        fn $method(&self) -> Option<$i> {
            (self.0).$method()
        }
    )*}
}

impl<T: ToPrimitive> ToPrimitive for Wrapping<T> {
    impl_to_primitive_wrapping! {
        fn to_isize -> isize;
        fn to_i8 -> i8;
        fn to_i16 -> i16;
        fn to_i32 -> i32;
        fn to_i64 -> i64;
        #[cfg(has_i128)]
        fn to_i128 -> i128;

        fn to_usize -> usize;
        fn to_u8 -> u8;
        fn to_u16 -> u16;
        fn to_u32 -> u32;
        fn to_u64 -> u64;
        #[cfg(has_i128)]
        fn to_u128 -> u128;

        fn to_f32 -> f32;
        fn to_f64 -> f64;
    }
}

macro_rules! impl_from_primitive_wrapping {
    ($( $(#[$cfg:meta])* fn $method:ident ( $i:ident ); )*) => {$(
        #[inline]
        $(#[$cfg])*
        fn $method(n: $i) -> Option<Self> {
            T::$method(n).map(Wrapping)
        }
    )*}
}

impl<T: FromPrimitive> FromPrimitive for Wrapping<T> {
    impl_from_primitive_wrapping! {
        fn from_isize(isize);
        fn from_i8(i8);
        fn from_i16(i16);
        fn from_i32(i32);
        fn from_i64(i64);
        #[cfg(has_i128)]
        fn from_i128(i128);

        fn from_usize(usize);
        fn from_u8(u8);
        fn from_u16(u16);
        fn from_u32(u32);
        fn from_u64(u64);
        #[cfg(has_i128)]
        fn from_u128(u128);

        fn from_f32(f32);
        fn from_f64(f64);
    }
}

/// Cast from one machine scalar to another.
///
/// # Examples
///
/// ```
/// # use num_traits as num;
/// let twenty: f32 = num::cast(0x14).unwrap();
/// assert_eq!(twenty, 20f32);
/// ```
///
#[inline]
pub fn cast<T: NumCast, U: NumCast>(n: T) -> Option<U> {
    NumCast::from(n)
}

/// An interface for casting between machine scalars.
pub trait NumCast: Sized + ToPrimitive {
    /// Creates a number from another value that can be converted into
    /// a primitive via the `ToPrimitive` trait. If the source value cannot be
    /// represented by the target type, then `None` is returned.
    ///
    /// A value can be represented by the target type when it lies within
    /// the range of scalars supported by the target type.
    /// For example, a negative integer cannot be represented by an unsigned
    /// integer type, and an `i64` with a very high magnitude might not be
    /// convertible to an `i32`.
    /// On the other hand, conversions with possible precision loss or truncation
    /// are admitted, like an `f32` with a decimal part to an integer type, or
    /// even a large `f64` saturating to `f32` infinity.
    fn from<T: ToPrimitive>(n: T) -> Option<Self>;
}

macro_rules! impl_num_cast {
    ($T:ty, $conv:ident) => {
        impl NumCast for $T {
            #[inline]
            #[allow(deprecated)]
            fn from<N: ToPrimitive>(n: N) -> Option<$T> {
                // `$conv` could be generated using `concat_idents!`, but that
                // macro seems to be broken at the moment
                n.$conv()
            }
        }
    };
}

impl_num_cast!(u8, to_u8);
impl_num_cast!(u16, to_u16);
impl_num_cast!(u32, to_u32);
impl_num_cast!(u64, to_u64);
#[cfg(has_i128)]
impl_num_cast!(u128, to_u128);
impl_num_cast!(usize, to_usize);
impl_num_cast!(i8, to_i8);
impl_num_cast!(i16, to_i16);
impl_num_cast!(i32, to_i32);
impl_num_cast!(i64, to_i64);
#[cfg(has_i128)]
impl_num_cast!(i128, to_i128);
impl_num_cast!(isize, to_isize);
impl_num_cast!(f32, to_f32);
impl_num_cast!(f64, to_f64);

impl<T: NumCast> NumCast for Wrapping<T> {
    fn from<U: ToPrimitive>(n: U) -> Option<Self> {
        T::from(n).map(Wrapping)
    }
}

/// A generic interface for casting between machine scalars with the
/// `as` operator, which admits narrowing and precision loss.
/// Implementers of this trait `AsPrimitive` should behave like a primitive
/// numeric type (e.g. a newtype around another primitive), and the
/// intended conversion must never fail.
///
/// # Examples
///
/// ```
/// # use num_traits::AsPrimitive;
/// let three: i32 = (3.14159265f32).as_();
/// assert_eq!(three, 3);
/// ```
///
/// # Safety
///
/// **In Rust versions before 1.45.0**, some uses of the `as` operator were not entirely safe.
/// In particular, it was undefined behavior if
/// a truncated floating point value could not fit in the target integer
/// type ([#10184](https://github.com/rust-lang/rust/issues/10184)).
///
/// ```ignore
/// # use num_traits::AsPrimitive;
/// let x: u8 = (1.04E+17).as_(); // UB
/// ```
///
pub trait AsPrimitive<T>: 'static + Copy
where
    T: 'static + Copy,
{
    /// Convert a value to another, using the `as` operator.
    fn as_(self) -> T;
}

macro_rules! impl_as_primitive {
    (@ $T: ty => $(#[$cfg:meta])* impl $U: ty ) => {
        $(#[$cfg])*
        impl AsPrimitive<$U> for $T {
            #[inline] fn as_(self) -> $U { self as $U }
        }
    };
    (@ $T: ty => { $( $U: ty ),* } ) => {$(
        impl_as_primitive!(@ $T => impl $U);
    )*};
    ($T: ty => { $( $U: ty ),* } ) => {
        impl_as_primitive!(@ $T => { $( $U ),* });
        impl_as_primitive!(@ $T => { u8, u16, u32, u64, usize });
        impl_as_primitive!(@ $T => #[cfg(has_i128)] impl u128);
        impl_as_primitive!(@ $T => { i8, i16, i32, i64, isize });
        impl_as_primitive!(@ $T => #[cfg(has_i128)] impl i128);
    };
}

impl_as_primitive!(u8 => { char, f32, f64 });
impl_as_primitive!(i8 => { f32, f64 });
impl_as_primitive!(u16 => { f32, f64 });
impl_as_primitive!(i16 => { f32, f64 });
impl_as_primitive!(u32 => { f32, f64 });
impl_as_primitive!(i32 => { f32, f64 });
impl_as_primitive!(u64 => { f32, f64 });
impl_as_primitive!(i64 => { f32, f64 });
#[cfg(has_i128)]
impl_as_primitive!(u128 => { f32, f64 });
#[cfg(has_i128)]
impl_as_primitive!(i128 => { f32, f64 });
impl_as_primitive!(usize => { f32, f64 });
impl_as_primitive!(isize => { f32, f64 });
impl_as_primitive!(f32 => { f32, f64 });
impl_as_primitive!(f64 => { f32, f64 });
impl_as_primitive!(char => { char });
impl_as_primitive!(bool => {});