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    // Copyright 2013-2014 The Rust Project Developers. See the COPYRIGHT
    // file at the top-level directory of this distribution and at
    // http://rust-lang.org/COPYRIGHT.
    //
    // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
    // http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
    // <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
    // option. This file may not be copied, modified, or distributed
    // except according to those terms.

    //! Numeric traits for generic mathematics
    //!
    //! ## Compatibility
    //!
    //! The `num-traits` crate is tested for rustc 1.8 and greater.

    #![doc(html_root_url = "https://docs.rs/num-traits/0.2")]
    #![deny(unconditional_recursion)]
    #![no_std]
    #[cfg(feature = "std")]
    extern crate std;

    use core::fmt;
    use core::num::Wrapping;
    use core::ops::{Add, Div, Mul, Rem, Sub};
    use core::ops::{AddAssign, DivAssign, MulAssign, RemAssign, SubAssign};

    pub use bounds::Bounded;
    #[cfg(feature = "std")]
    pub use float::Float;
    pub use float::FloatConst;
    // pub use real::{FloatCore, Real}; // NOTE: Don't do this, it breaks `use num_traits::*;`.
    pub use cast::{cast, AsPrimitive, FromPrimitive, NumCast, ToPrimitive};
    pub use identities::{one, zero, One, Zero};
    pub use int::PrimInt;
    pub use ops::checked::{
        CheckedAdd, CheckedDiv, CheckedMul, CheckedNeg, CheckedRem, CheckedShl, CheckedShr, CheckedSub,
    };
    pub use ops::inv::Inv;
    pub use ops::mul_add::{MulAdd, MulAddAssign};
    pub use ops::saturating::Saturating;
    pub use ops::wrapping::{WrappingAdd, WrappingMul, WrappingShl, WrappingShr, WrappingSub};
    pub use pow::{checked_pow, pow, Pow};
    pub use sign::{abs, abs_sub, signum, Signed, Unsigned};

    #[macro_use]
    mod macros;

    pub mod bounds;
    pub mod cast;
    pub mod float;
    pub mod identities;
    pub mod int;
    pub mod ops;
    pub mod pow;
    #[cfg(feature = "std")]
    pub mod real;
    pub mod sign;

    /// The base trait for numeric types, covering `0` and `1` values,
    /// comparisons, basic numeric operations, and string conversion.
    pub trait Num: PartialEq + Zero + One + NumOps {
        type FromStrRadixErr;

        /// Convert from a string and radix <= 36.
        ///
        /// # Examples
        ///
        /// ```rust
        /// use num_traits::Num;
        ///
        /// let result = <i32 as Num>::from_str_radix("27", 10);
        /// assert_eq!(result, Ok(27));
        ///
        /// let result = <i32 as Num>::from_str_radix("foo", 10);
        /// assert!(result.is_err());
        /// ```
        fn from_str_radix(str: &str, radix: u32) -> Result<Self, Self::FromStrRadixErr>;
    }

    /// The trait for types implementing basic numeric operations
    ///
    /// This is automatically implemented for types which implement the operators.
    pub trait NumOps<Rhs = Self, Output = Self>:
        Add<Rhs, Output = Output>
        + Sub<Rhs, Output = Output>
        + Mul<Rhs, Output = Output>
        + Div<Rhs, Output = Output>
        + Rem<Rhs, Output = Output>
    {
    }

    impl<T, Rhs, Output> NumOps<Rhs, Output> for T where
        T: Add<Rhs, Output = Output>
            + Sub<Rhs, Output = Output>
            + Mul<Rhs, Output = Output>
            + Div<Rhs, Output = Output>
            + Rem<Rhs, Output = Output>
    {
    }

    /// The trait for `Num` types which also implement numeric operations taking
    /// the second operand by reference.
    ///
    /// This is automatically implemented for types which implement the operators.
    pub trait NumRef: Num + for<'r> NumOps<&'r Self> {}
    impl<T> NumRef for T where T: Num + for<'r> NumOps<&'r T> {}

    /// The trait for references which implement numeric operations, taking the
    /// second operand either by value or by reference.
    ///
    /// This is automatically implemented for types which implement the operators.
    pub trait RefNum<Base>: NumOps<Base, Base> + for<'r> NumOps<&'r Base, Base> {}
    impl<T, Base> RefNum<Base> for T where T: NumOps<Base, Base> + for<'r> NumOps<&'r Base, Base> {}

    /// The trait for types implementing numeric assignment operators (like `+=`).
    ///
    /// This is automatically implemented for types which implement the operators.
    pub trait NumAssignOps<Rhs = Self>:
        AddAssign<Rhs> + SubAssign<Rhs> + MulAssign<Rhs> + DivAssign<Rhs> + RemAssign<Rhs>
    {
    }

    impl<T, Rhs> NumAssignOps<Rhs> for T where
        T: AddAssign<Rhs> + SubAssign<Rhs> + MulAssign<Rhs> + DivAssign<Rhs> + RemAssign<Rhs>
    {
    }

    /// The trait for `Num` types which also implement assignment operators.
    ///
    /// This is automatically implemented for types which implement the operators.
    pub trait NumAssign: Num + NumAssignOps {}
    impl<T> NumAssign for T where T: Num + NumAssignOps {}

    /// The trait for `NumAssign` types which also implement assignment operations
    /// taking the second operand by reference.
    ///
    /// This is automatically implemented for types which implement the operators.
    pub trait NumAssignRef: NumAssign + for<'r> NumAssignOps<&'r Self> {}
    impl<T> NumAssignRef for T where T: NumAssign + for<'r> NumAssignOps<&'r T> {}

    macro_rules! int_trait_impl {
        ($name:ident for $($t:ty)*) => ($(
            impl $name for $t {
                type FromStrRadixErr = ::core::num::ParseIntError;
                #[inline]
                fn from_str_radix(s: &str, radix: u32)
                                  -> Result<Self, ::core::num::ParseIntError>
                {
                    <$t>::from_str_radix(s, radix)
                }
            }
        )*)
    }
    int_trait_impl!(Num for usize u8 u16 u32 u64 isize i8 i16 i32 i64);
    #[cfg(has_i128)]
    int_trait_impl!(Num for u128 i128);

    impl<T: Num> Num for Wrapping<T>
    where
        Wrapping<T>: Add<Output = Wrapping<T>>
            + Sub<Output = Wrapping<T>>
            + Mul<Output = Wrapping<T>>
            + Div<Output = Wrapping<T>>
            + Rem<Output = Wrapping<T>>,
    {
        type FromStrRadixErr = T::FromStrRadixErr;
        fn from_str_radix(str: &str, radix: u32) -> Result<Self, Self::FromStrRadixErr> {
            T::from_str_radix(str, radix).map(Wrapping)
        }
    }

    #[derive(Debug)]
    pub enum FloatErrorKind {
        Empty,
        Invalid,
    }
    // FIXME: core::num::ParseFloatError is stable in 1.0, but opaque to us,
    // so there's not really any way for us to reuse it.
    #[derive(Debug)]
    pub struct ParseFloatError {
        pub kind: FloatErrorKind,
    }

    impl fmt::Display for ParseFloatError {
        fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
            let description = match self.kind {
                FloatErrorKind::Empty => "cannot parse float from empty string",
                FloatErrorKind::Invalid => "invalid float literal",
            };

            description.fmt(f)
        }
    }

    // FIXME: The standard library from_str_radix on floats was deprecated, so we're stuck
    // with this implementation ourselves until we want to make a breaking change.
    // (would have to drop it from `Num` though)
    macro_rules! float_trait_impl {
        ($name:ident for $($t:ident)*) => ($(
            impl $name for $t {
                type FromStrRadixErr = ParseFloatError;

                fn from_str_radix(src: &str, radix: u32)
                                  -> Result<Self, Self::FromStrRadixErr>
                {
                    use self::FloatErrorKind::*;
                    use self::ParseFloatError as PFE;

                    // Special values
                    match src {
                        "inf"   => return Ok(core::$t::INFINITY),
                        "-inf"  => return Ok(core::$t::NEG_INFINITY),
                        "NaN"   => return Ok(core::$t::NAN),
                        _       => {},
                    }

                    fn slice_shift_char(src: &str) -> Option<(char, &str)> {
                        src.chars().nth(0).map(|ch| (ch, &src[1..]))
                    }

                    let (is_positive, src) =  match slice_shift_char(src) {
                        None             => return Err(PFE { kind: Empty }),
                        Some(('-', ""))  => return Err(PFE { kind: Empty }),
                        Some(('-', src)) => (false, src),
                        Some((_, _))     => (true,  src),
                    };

                    // The significand to accumulate
                    let mut sig = if is_positive { 0.0 } else { -0.0 };
                    // Necessary to detect overflow
                    let mut prev_sig = sig;
                    let mut cs = src.chars().enumerate();
                    // Exponent prefix and exponent index offset
                    let mut exp_info = None::<(char, usize)>;

                    // Parse the integer part of the significand
                    for (i, c) in cs.by_ref() {
                        match c.to_digit(radix) {
                            Some(digit) => {
                                // shift significand one digit left
                                sig = sig * (radix as $t);

                                // add/subtract current digit depending on sign
                                if is_positive {
                                    sig = sig + ((digit as isize) as $t);
                                } else {
                                    sig = sig - ((digit as isize) as $t);
                                }

                                // Detect overflow by comparing to last value, except
                                // if we've not seen any non-zero digits.
                                if prev_sig != 0.0 {
                                    if is_positive && sig <= prev_sig
                                        { return Ok(core::$t::INFINITY); }
                                    if !is_positive && sig >= prev_sig
                                        { return Ok(core::$t::NEG_INFINITY); }

                                    // Detect overflow by reversing the shift-and-add process
                                    if is_positive && (prev_sig != (sig - digit as $t) / radix as $t)
                                        { return Ok(core::$t::INFINITY); }
                                    if !is_positive && (prev_sig != (sig + digit as $t) / radix as $t)
                                        { return Ok(core::$t::NEG_INFINITY); }
                                }
                                prev_sig = sig;
                            },
                            None => match c {
                                'e' | 'E' | 'p' | 'P' => {
                                    exp_info = Some((c, i + 1));
                                    break;  // start of exponent
                                },
                                '.' => {
                                    break;  // start of fractional part
                                },
                                _ => {
                                    return Err(PFE { kind: Invalid });
                                },
                            },
                        }
                    }

                    // If we are not yet at the exponent parse the fractional
                    // part of the significand
                    if exp_info.is_none() {
                        let mut power = 1.0;
                        for (i, c) in cs.by_ref() {
                            match c.to_digit(radix) {
                                Some(digit) => {
                                    // Decrease power one order of magnitude
                                    power = power / (radix as $t);
                                    // add/subtract current digit depending on sign
                                    sig = if is_positive {
                                        sig + (digit as $t) * power
                                    } else {
                                        sig - (digit as $t) * power
                                    };
                                    // Detect overflow by comparing to last value
                                    if is_positive && sig < prev_sig
                                        { return Ok(core::$t::INFINITY); }
                                    if !is_positive && sig > prev_sig
                                        { return Ok(core::$t::NEG_INFINITY); }
                                    prev_sig = sig;
                                },
                                None => match c {
                                    'e' | 'E' | 'p' | 'P' => {
                                        exp_info = Some((c, i + 1));
                                        break; // start of exponent
                                    },
                                    _ => {
                                        return Err(PFE { kind: Invalid });
                                    },
                                },
                            }
                        }
                    }

                    // Parse and calculate the exponent
                    let exp = match exp_info {
                        Some((c, offset)) => {
                            let base = match c {
                                'E' | 'e' if radix == 10 => 10.0,
                                'P' | 'p' if radix == 16 => 2.0,
                                _ => return Err(PFE { kind: Invalid }),
                            };

                            // Parse the exponent as decimal integer
                            let src = &src[offset..];
                            let (is_positive, exp) = match slice_shift_char(src) {
                                Some(('-', src)) => (false, src.parse::<usize>()),
                                Some(('+', src)) => (true,  src.parse::<usize>()),
                                Some((_, _))     => (true,  src.parse::<usize>()),
                                None             => return Err(PFE { kind: Invalid }),
                            };

                            #[cfg(feature = "std")]
                            fn pow(base: $t, exp: usize) -> $t {
                                Float::powi(base, exp as i32)
                            }
                            // otherwise uses the generic `pow` from the root

                            match (is_positive, exp) {
                                (true,  Ok(exp)) => pow(base, exp),
                                (false, Ok(exp)) => 1.0 / pow(base, exp),
                                (_, Err(_))      => return Err(PFE { kind: Invalid }),
                            }
                        },
                        None => 1.0, // no exponent
                    };

                    Ok(sig * exp)
                }
            }
        )*)
    }
    float_trait_impl!(Num for f32 f64);

    /// A value bounded by a minimum and a maximum
    ///
    ///  If input is less than min then this returns min.
    ///  If input is greater than max then this returns max.
    ///  Otherwise this returns input.
    #[inline]
    pub fn clamp<T: PartialOrd>(input: T, min: T, max: T) -> T {
        debug_assert!(min <= max, "min must be less than or equal to max");
        if input < min {
            min
        } else if input > max {
            max
        } else {
            input
        }
    }

    #[test]
    fn clamp_test() {
        // Int test
        assert_eq!(1, clamp(1, -1, 2));
        assert_eq!(-1, clamp(-2, -1, 2));
        assert_eq!(2, clamp(3, -1, 2));

        // Float test
        assert_eq!(1.0, clamp(1.0, -1.0, 2.0));
        assert_eq!(-1.0, clamp(-2.0, -1.0, 2.0));
        assert_eq!(2.0, clamp(3.0, -1.0, 2.0));
    }

    #[test]
    fn from_str_radix_unwrap() {
        // The Result error must impl Debug to allow unwrap()

        let i: i32 = Num::from_str_radix("0", 10).unwrap();
        assert_eq!(i, 0);

        let f: f32 = Num::from_str_radix("0.0", 10).unwrap();
        assert_eq!(f, 0.0);
    }

    #[test]
    fn wrapping_is_num() {
        fn require_num<T: Num>(_: &T) {}
        require_num(&Wrapping(42_u32));
        require_num(&Wrapping(-42));
    }

    #[test]
    fn wrapping_from_str_radix() {
        macro_rules! test_wrapping_from_str_radix {
            ($($t:ty)+) => {
                $(
                    for &(s, r) in &[("42", 10), ("42", 2), ("-13.0", 10), ("foo", 10)] {
                        let w = Wrapping::<$t>::from_str_radix(s, r).map(|w| w.0);
                        assert_eq!(w, <$t as Num>::from_str_radix(s, r));
                    }
                )+
            };
        }

        test_wrapping_from_str_radix!(usize u8 u16 u32 u64 isize i8 i16 i32 i64);
    }

    #[test]
    fn check_num_ops() {
        fn compute<T: Num + Copy>(x: T, y: T) -> T {
            x * y / y % y + y - y
        }
        assert_eq!(compute(1, 2), 1)
    }

    #[test]
    fn check_numref_ops() {
        fn compute<T: NumRef>(x: T, y: &T) -> T {
            x * y / y % y + y - y
        }
        assert_eq!(compute(1, &2), 1)
    }

    #[test]
    fn check_refnum_ops() {
        fn compute<T: Copy>(x: &T, y: T) -> T
        where
            for<'a> &'a T: RefNum<T>,
        {
            &(&(&(&(x * y) / y) % y) + y) - y
        }
        assert_eq!(compute(&1, 2), 1)
    }

    #[test]
    fn check_refref_ops() {
        fn compute<T>(x: &T, y: &T) -> T
        where
            for<'a> &'a T: RefNum<T>,
        {
            &(&(&(&(x * y) / y) % y) + y) - y
        }
        assert_eq!(compute(&1, &2), 1)
    }

    #[test]
    fn check_numassign_ops() {
        fn compute<T: NumAssign + Copy>(mut x: T, y: T) -> T {
            x *= y;
            x /= y;
            x %= y;
            x += y;
            x -= y;
            x
        }
        assert_eq!(compute(1, 2), 1)
    }

    // TODO test `NumAssignRef`, but even the standard numeric types don't
    // implement this yet. (see rust pr41336)

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