rust/src/libcore/num/mod.rs

// Copyright 2012-2014 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.
//
// ignore-lexer-test FIXME #15679

//! Numeric traits and functions for the built-in numeric types.

#![stable(feature = "rust1", since = "1.0.0")]
#![allow(missing_docs)]

use self::wrapping::{OverflowingOps, WrappingOps};

use char::CharExt;
use clone::Clone;
use cmp::{PartialEq, Eq, PartialOrd, Ord};
use error::Error;
use fmt;
use intrinsics;
use iter::IteratorExt;
use marker::Copy;
use mem::size_of;
use ops::{Add, Sub, Mul, Div, Rem, Neg};
use ops::{Not, BitAnd, BitOr, BitXor, Shl, Shr};
use option::Option::{self, Some, None};
use result::Result::{self, Ok, Err};
use str::{FromStr, StrExt};

#[unstable(feature = "core", reason = "may be removed or relocated")]
pub mod wrapping;

/// A built-in signed or unsigned integer.
#[stable(feature = "rust1", since = "1.0.0")]
pub trait Int
    : Copy + Clone
    + NumCast
    + PartialOrd + Ord
    + PartialEq + Eq
    + Add<Output=Self>
    + Sub<Output=Self>
    + Mul<Output=Self>
    + Div<Output=Self>
    + Rem<Output=Self>
    + Not<Output=Self>
    + BitAnd<Output=Self>
    + BitOr<Output=Self>
    + BitXor<Output=Self>
    + Shl<usize, Output=Self>
    + Shr<usize, Output=Self>
    + WrappingOps
    + OverflowingOps
{
    /// Returns the `0` value of this integer type.
    // FIXME (#5527): Should be an associated constant
    #[unstable(feature = "core",
               reason = "unsure about its place in the world")]
    fn zero() -> Self;

    /// Returns the `1` value of this integer type.
    // FIXME (#5527): Should be an associated constant
    #[unstable(feature = "core",
               reason = "unsure about its place in the world")]
    fn one() -> Self;

    /// Returns the smallest value that can be represented by this integer type.
    // FIXME (#5527): Should be and associated constant
    #[unstable(feature = "core",
               reason = "unsure about its place in the world")]
    fn min_value() -> Self;

    /// Returns the largest value that can be represented by this integer type.
    // FIXME (#5527): Should be and associated constant
    #[unstable(feature = "core",
               reason = "unsure about its place in the world")]
    fn max_value() -> Self;

    /// Returns the number of ones in the binary representation of `self`.
    ///
    /// # Examples
    ///
    /// ```
    /// # #![feature(core)]
    /// use std::num::Int;
    ///
    /// let n = 0b01001100u8;
    ///
    /// assert_eq!(n.count_ones(), 3);
    /// ```
    #[unstable(feature = "core",
               reason = "pending integer conventions")]
    fn count_ones(self) -> u32;

    /// Returns the number of zeros in the binary representation of `self`.
    ///
    /// # Examples
    ///
    /// ```
    /// # #![feature(core)]
    /// use std::num::Int;
    ///
    /// let n = 0b01001100u8;
    ///
    /// assert_eq!(n.count_zeros(), 5);
    /// ```
    #[unstable(feature = "core",
               reason = "pending integer conventions")]
    #[inline]
    fn count_zeros(self) -> u32 {
        (!self).count_ones()
    }

    /// Returns the number of leading zeros in the binary representation
    /// of `self`.
    ///
    /// # Examples
    ///
    /// ```
    /// # #![feature(core)]
    /// use std::num::Int;
    ///
    /// let n = 0b0101000u16;
    ///
    /// assert_eq!(n.leading_zeros(), 10);
    /// ```
    #[unstable(feature = "core",
               reason = "pending integer conventions")]
    fn leading_zeros(self) -> u32;

    /// Returns the number of trailing zeros in the binary representation
    /// of `self`.
    ///
    /// # Examples
    ///
    /// ```
    /// # #![feature(core)]
    /// use std::num::Int;
    ///
    /// let n = 0b0101000u16;
    ///
    /// assert_eq!(n.trailing_zeros(), 3);
    /// ```
    #[unstable(feature = "core",
               reason = "pending integer conventions")]
    fn trailing_zeros(self) -> u32;

    /// Shifts the bits to the left by a specified amount amount, `n`, wrapping
    /// the truncated bits to the end of the resulting integer.
    ///
    /// # Examples
    ///
    /// ```
    /// # #![feature(core)]
    /// use std::num::Int;
    ///
    /// let n = 0x0123456789ABCDEFu64;
    /// let m = 0x3456789ABCDEF012u64;
    ///
    /// assert_eq!(n.rotate_left(12), m);
    /// ```
    #[unstable(feature = "core",
               reason = "pending integer conventions")]
    fn rotate_left(self, n: u32) -> Self;

    /// Shifts the bits to the right by a specified amount amount, `n`, wrapping
    /// the truncated bits to the beginning of the resulting integer.
    ///
    /// # Examples
    ///
    /// ```
    /// # #![feature(core)]
    /// use std::num::Int;
    ///
    /// let n = 0x0123456789ABCDEFu64;
    /// let m = 0xDEF0123456789ABCu64;
    ///
    /// assert_eq!(n.rotate_right(12), m);
    /// ```
    #[unstable(feature = "core",
               reason = "pending integer conventions")]
    fn rotate_right(self, n: u32) -> Self;

    /// Reverses the byte order of the integer.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::num::Int;
    ///
    /// let n = 0x0123456789ABCDEFu64;
    /// let m = 0xEFCDAB8967452301u64;
    ///
    /// assert_eq!(n.swap_bytes(), m);
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    fn swap_bytes(self) -> Self;

    /// Convert an integer from big endian to the target's endianness.
    ///
    /// On big endian this is a no-op. On little endian the bytes are swapped.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::num::Int;
    ///
    /// let n = 0x0123456789ABCDEFu64;
    ///
    /// if cfg!(target_endian = "big") {
    ///     assert_eq!(Int::from_be(n), n)
    /// } else {
    ///     assert_eq!(Int::from_be(n), n.swap_bytes())
    /// }
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    fn from_be(x: Self) -> Self {
        if cfg!(target_endian = "big") { x } else { x.swap_bytes() }
    }

    /// Convert an integer from little endian to the target's endianness.
    ///
    /// On little endian this is a no-op. On big endian the bytes are swapped.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::num::Int;
    ///
    /// let n = 0x0123456789ABCDEFu64;
    ///
    /// if cfg!(target_endian = "little") {
    ///     assert_eq!(Int::from_le(n), n)
    /// } else {
    ///     assert_eq!(Int::from_le(n), n.swap_bytes())
    /// }
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    fn from_le(x: Self) -> Self {
        if cfg!(target_endian = "little") { x } else { x.swap_bytes() }
    }

    /// Convert `self` to big endian from the target's endianness.
    ///
    /// On big endian this is a no-op. On little endian the bytes are swapped.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::num::Int;
    ///
    /// let n = 0x0123456789ABCDEFu64;
    ///
    /// if cfg!(target_endian = "big") {
    ///     assert_eq!(n.to_be(), n)
    /// } else {
    ///     assert_eq!(n.to_be(), n.swap_bytes())
    /// }
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    fn to_be(self) -> Self { // or not to be?
        if cfg!(target_endian = "big") { self } else { self.swap_bytes() }
    }

    /// Convert `self` to little endian from the target's endianness.
    ///
    /// On little endian this is a no-op. On big endian the bytes are swapped.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::num::Int;
    ///
    /// let n = 0x0123456789ABCDEFu64;
    ///
    /// if cfg!(target_endian = "little") {
    ///     assert_eq!(n.to_le(), n)
    /// } else {
    ///     assert_eq!(n.to_le(), n.swap_bytes())
    /// }
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    fn to_le(self) -> Self {
        if cfg!(target_endian = "little") { self } else { self.swap_bytes() }
    }

    /// Checked integer addition. Computes `self + other`, returning `None` if
    /// overflow occurred.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::num::Int;
    ///
    /// assert_eq!(5u16.checked_add(65530), Some(65535));
    /// assert_eq!(6u16.checked_add(65530), None);
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    fn checked_add(self, other: Self) -> Option<Self>;

    /// Checked integer subtraction. Computes `self - other`, returning `None`
    /// if underflow occurred.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::num::Int;
    ///
    /// assert_eq!((-127i8).checked_sub(1), Some(-128));
    /// assert_eq!((-128i8).checked_sub(1), None);
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    fn checked_sub(self, other: Self) -> Option<Self>;

    /// Checked integer multiplication. Computes `self * other`, returning
    /// `None` if underflow or overflow occurred.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::num::Int;
    ///
    /// assert_eq!(5u8.checked_mul(51), Some(255));
    /// assert_eq!(5u8.checked_mul(52), None);
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    fn checked_mul(self, other: Self) -> Option<Self>;

    /// Checked integer division. Computes `self / other`, returning `None` if
    /// `other == 0` or the operation results in underflow or overflow.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::num::Int;
    ///
    /// assert_eq!((-127i8).checked_div(-1), Some(127));
    /// assert_eq!((-128i8).checked_div(-1), None);
    /// assert_eq!((1i8).checked_div(0), None);
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    fn checked_div(self, other: Self) -> Option<Self>;

    /// Saturating integer addition. Computes `self + other`, saturating at
    /// the numeric bounds instead of overflowing.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::num::Int;
    ///
    /// assert_eq!(5u16.saturating_add(65534), 65535);
    /// assert_eq!((-5i16).saturating_add(-32767), -32768);
    /// assert_eq!(100u32.saturating_add(4294967294), 4294967295);
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    fn saturating_add(self, other: Self) -> Self {
        match self.checked_add(other) {
            Some(x)                      => x,
            None if other >= Int::zero() => Int::max_value(),
            None                         => Int::min_value(),
        }
    }

    /// Saturating integer subtraction. Computes `self - other`, saturating at
    /// the numeric bounds instead of overflowing.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::num::Int;
    ///
    /// assert_eq!(5u16.saturating_sub(65534), 0);
    /// assert_eq!(5i16.saturating_sub(-32767), 32767);
    /// assert_eq!(100u32.saturating_sub(4294967294), 0);
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    fn saturating_sub(self, other: Self) -> Self {
        match self.checked_sub(other) {
            Some(x)                      => x,
            None if other >= Int::zero() => Int::min_value(),
            None                         => Int::max_value(),
        }
    }

    /// Raises self to the power of `exp`, using exponentiation by squaring.
    ///
    /// # Examples
    ///
    /// ```
    /// # #![feature(core)]
    /// use std::num::Int;
    ///
    /// assert_eq!(2.pow(4), 16);
    /// ```
    #[unstable(feature = "core",
               reason = "pending integer conventions")]
    #[inline]
    fn pow(self, mut exp: u32) -> Self {
        let mut base = self;
        let mut acc: Self = Int::one();

        let mut prev_base = self;
        let mut base_oflo = false;
        while exp > 0 {
            if (exp & 1) == 1 {
                if base_oflo {
                    // ensure overflow occurs in the same manner it
                    // would have otherwise (i.e. signal any exception
                    // it would have otherwise).
                    acc = acc * (prev_base * prev_base);
                } else {
                    acc = acc * base;
                }
            }
            prev_base = base;
            let (new_base, new_base_oflo) = base.overflowing_mul(base);
            base = new_base;
            base_oflo = new_base_oflo;
            exp /= 2;
        }
        acc
    }
}

macro_rules! checked_op {
    ($T:ty, $U:ty, $op:path, $x:expr, $y:expr) => {{
        let (result, overflowed) = unsafe { $op($x as $U, $y as $U) };
        if overflowed { None } else { Some(result as $T) }
    }}
}

macro_rules! uint_impl {
    ($T:ty = $ActualT:ty, $BITS:expr,
     $ctpop:path,
     $ctlz:path,
     $cttz:path,
     $bswap:path,
     $add_with_overflow:path,
     $sub_with_overflow:path,
     $mul_with_overflow:path) => {
        #[stable(feature = "rust1", since = "1.0.0")]
        impl Int for $T {
            #[inline]
            fn zero() -> $T { 0 }

            #[inline]
            fn one() -> $T { 1 }

            #[inline]
            fn min_value() -> $T { 0 }

            #[inline]
            fn max_value() -> $T { -1 }

            #[inline]
            fn count_ones(self) -> u32 {
                unsafe { $ctpop(self as $ActualT) as u32 }
            }

            #[inline]
            fn leading_zeros(self) -> u32 {
                unsafe { $ctlz(self as $ActualT) as u32 }
            }

            #[inline]
            fn trailing_zeros(self) -> u32 {
                unsafe { $cttz(self as $ActualT) as u32 }
            }

            #[inline]
            fn rotate_left(self, n: u32) -> $T {
                // Protect against undefined behaviour for over-long bit shifts
                let n = n % $BITS;
                (self << n) | (self >> (($BITS - n) % $BITS))
            }

            #[inline]
            fn rotate_right(self, n: u32) -> $T {
                // Protect against undefined behaviour for over-long bit shifts
                let n = n % $BITS;
                (self >> n) | (self << (($BITS - n) % $BITS))
            }

            #[inline]
            fn swap_bytes(self) -> $T {
                unsafe { $bswap(self as $ActualT) as $T }
            }

            #[inline]
            fn checked_add(self, other: $T) -> Option<$T> {
                checked_op!($T, $ActualT, $add_with_overflow, self, other)
            }

            #[inline]
            fn checked_sub(self, other: $T) -> Option<$T> {
                checked_op!($T, $ActualT, $sub_with_overflow, self, other)
            }

            #[inline]
            fn checked_mul(self, other: $T) -> Option<$T> {
                checked_op!($T, $ActualT, $mul_with_overflow, self, other)
            }

            #[inline]
            fn checked_div(self, v: $T) -> Option<$T> {
                match v {
                    0 => None,
                    v => Some(self / v),
                }
            }
        }
    }
}

/// Swapping a single byte is a no-op. This is marked as `unsafe` for
/// consistency with the other `bswap` intrinsics.
unsafe fn bswap8(x: u8) -> u8 { x }

uint_impl! { u8 = u8, 8,
    intrinsics::ctpop8,
    intrinsics::ctlz8,
    intrinsics::cttz8,
    bswap8,
    intrinsics::u8_add_with_overflow,
    intrinsics::u8_sub_with_overflow,
    intrinsics::u8_mul_with_overflow }

uint_impl! { u16 = u16, 16,
    intrinsics::ctpop16,
    intrinsics::ctlz16,
    intrinsics::cttz16,
    intrinsics::bswap16,
    intrinsics::u16_add_with_overflow,
    intrinsics::u16_sub_with_overflow,
    intrinsics::u16_mul_with_overflow }

uint_impl! { u32 = u32, 32,
    intrinsics::ctpop32,
    intrinsics::ctlz32,
    intrinsics::cttz32,
    intrinsics::bswap32,
    intrinsics::u32_add_with_overflow,
    intrinsics::u32_sub_with_overflow,
    intrinsics::u32_mul_with_overflow }

uint_impl! { u64 = u64, 64,
    intrinsics::ctpop64,
    intrinsics::ctlz64,
    intrinsics::cttz64,
    intrinsics::bswap64,
    intrinsics::u64_add_with_overflow,
    intrinsics::u64_sub_with_overflow,
    intrinsics::u64_mul_with_overflow }

#[cfg(target_pointer_width = "32")]
uint_impl! { usize = u32, 32,
    intrinsics::ctpop32,
    intrinsics::ctlz32,
    intrinsics::cttz32,
    intrinsics::bswap32,
    intrinsics::u32_add_with_overflow,
    intrinsics::u32_sub_with_overflow,
    intrinsics::u32_mul_with_overflow }

#[cfg(target_pointer_width = "64")]
uint_impl! { usize = u64, 64,
    intrinsics::ctpop64,
    intrinsics::ctlz64,
    intrinsics::cttz64,
    intrinsics::bswap64,
    intrinsics::u64_add_with_overflow,
    intrinsics::u64_sub_with_overflow,
    intrinsics::u64_mul_with_overflow }

macro_rules! int_impl {
    ($T:ty = $ActualT:ty, $UnsignedT:ty, $BITS:expr,
     $add_with_overflow:path,
     $sub_with_overflow:path,
     $mul_with_overflow:path) => {
        #[stable(feature = "rust1", since = "1.0.0")]
        impl Int for $T {
            #[inline]
            fn zero() -> $T { 0 }

            #[inline]
            fn one() -> $T { 1 }

            #[inline]
            fn min_value() -> $T { (-1 as $T) << ($BITS - 1) }

            #[inline]
            fn max_value() -> $T { let min: $T = Int::min_value(); !min }

            #[inline]
            fn count_ones(self) -> u32 { (self as $UnsignedT).count_ones() }

            #[inline]
            fn leading_zeros(self) -> u32 {
                (self as $UnsignedT).leading_zeros()
            }

            #[inline]
            fn trailing_zeros(self) -> u32 {
                (self as $UnsignedT).trailing_zeros()
            }

            #[inline]
            fn rotate_left(self, n: u32) -> $T {
                (self as $UnsignedT).rotate_left(n) as $T
            }

            #[inline]
            fn rotate_right(self, n: u32) -> $T {
                (self as $UnsignedT).rotate_right(n) as $T
            }

            #[inline]
            fn swap_bytes(self) -> $T {
                (self as $UnsignedT).swap_bytes() as $T
            }

            #[inline]
            fn checked_add(self, other: $T) -> Option<$T> {
                checked_op!($T, $ActualT, $add_with_overflow, self, other)
            }

            #[inline]
            fn checked_sub(self, other: $T) -> Option<$T> {
                checked_op!($T, $ActualT, $sub_with_overflow, self, other)
            }

            #[inline]
            fn checked_mul(self, other: $T) -> Option<$T> {
                checked_op!($T, $ActualT, $mul_with_overflow, self, other)
            }

            #[inline]
            fn checked_div(self, v: $T) -> Option<$T> {
                match v {
                    0   => None,
                   -1 if self == Int::min_value()
                        => None,
                    v   => Some(self / v),
                }
            }
        }
    }
}

int_impl! { i8 = i8, u8, 8,
    intrinsics::i8_add_with_overflow,
    intrinsics::i8_sub_with_overflow,
    intrinsics::i8_mul_with_overflow }

int_impl! { i16 = i16, u16, 16,
    intrinsics::i16_add_with_overflow,
    intrinsics::i16_sub_with_overflow,
    intrinsics::i16_mul_with_overflow }

int_impl! { i32 = i32, u32, 32,
    intrinsics::i32_add_with_overflow,
    intrinsics::i32_sub_with_overflow,
    intrinsics::i32_mul_with_overflow }

int_impl! { i64 = i64, u64, 64,
    intrinsics::i64_add_with_overflow,
    intrinsics::i64_sub_with_overflow,
    intrinsics::i64_mul_with_overflow }

#[cfg(target_pointer_width = "32")]
int_impl! { isize = i32, u32, 32,
    intrinsics::i32_add_with_overflow,
    intrinsics::i32_sub_with_overflow,
    intrinsics::i32_mul_with_overflow }

#[cfg(target_pointer_width = "64")]
int_impl! { isize = i64, u64, 64,
    intrinsics::i64_add_with_overflow,
    intrinsics::i64_sub_with_overflow,
    intrinsics::i64_mul_with_overflow }

/// A built-in two's complement integer.
#[stable(feature = "rust1", since = "1.0.0")]
pub trait SignedInt
    : Int
    + Neg<Output=Self>
{
    /// Computes the absolute value of `self`. `Int::min_value()` will be
    /// returned if the number is `Int::min_value()`.
    #[unstable(feature = "core", reason = "overflow in debug builds?")]
    fn abs(self) -> Self;

    /// Returns a number representing sign of `self`.
    ///
    /// - `0` if the number is zero
    /// - `1` if the number is positive
    /// - `-1` if the number is negative
    #[stable(feature = "rust1", since = "1.0.0")]
    fn signum(self) -> Self;

    /// Returns `true` if `self` is positive and `false` if the number
    /// is zero or negative.
    #[stable(feature = "rust1", since = "1.0.0")]
    fn is_positive(self) -> bool;

    /// Returns `true` if `self` is negative and `false` if the number
    /// is zero or positive.
    #[stable(feature = "rust1", since = "1.0.0")]
    fn is_negative(self) -> bool;
}

macro_rules! signed_int_impl {
    ($T:ty) => {
        #[stable(feature = "rust1", since = "1.0.0")]
        impl SignedInt for $T {
            #[inline]
            fn abs(self) -> $T {
                if self.is_negative() { -self } else { self }
            }

            #[inline]
            fn signum(self) -> $T {
                match self {
                    n if n > 0 =>  1,
                    0          =>  0,
                    _          => -1,
                }
            }

            #[inline]
            fn is_positive(self) -> bool { self > 0 }

            #[inline]
            fn is_negative(self) -> bool { self < 0 }
        }
    }
}

signed_int_impl! { i8 }
signed_int_impl! { i16 }
signed_int_impl! { i32 }
signed_int_impl! { i64 }
signed_int_impl! { isize }

// `Int` + `SignedInt` implemented for signed integers
macro_rules! int_impl {
    ($T:ty = $ActualT:ty, $UnsignedT:ty, $BITS:expr,
     $add_with_overflow:path,
     $sub_with_overflow:path,
     $mul_with_overflow:path) => {
        /// Returns the `0` value of this integer type.
        // FIXME (#5527): Should be an associated constant
        #[unstable(feature = "core",
                   reason = "unsure about its place in the world")]
        #[inline]
        pub fn zero() -> $T { 0 }

        /// Returns the `1` value of this integer type.
        // FIXME (#5527): Should be an associated constant
        #[unstable(feature = "core",
                   reason = "unsure about its place in the world")]
        #[inline]
        pub fn one() -> $T { 1 }

        /// Returns the smallest value that can be represented by this integer
        /// type.
        // FIXME (#5527): Should be and associated constant
        #[unstable(feature = "core",
                   reason = "unsure about its place in the world")]
        #[inline]
        pub fn min_value() -> $T { (-1 as $T) << ($BITS - 1) }

        /// Returns the largest value that can be represented by this integer
        /// type.
        // FIXME (#5527): Should be and associated constant
        #[unstable(feature = "core",
                   reason = "unsure about its place in the world")]
        #[inline]
        pub fn max_value() -> $T { let min: $T = <$T>::min_value(); !min }

        /// Returns the number of ones in the binary representation of `self`.
        ///
        /// # Examples
        ///
        /// ```rust
        /// # #![feature(core)]
        /// use std::num::Int;
        ///
        /// let n = 0b01001100u8;
        ///
        /// assert_eq!(n.count_ones(), 3);
        /// ```
        #[unstable(feature = "core",
                   reason = "pending integer conventions")]
        #[inline]
        pub fn count_ones(self) -> u32 { (self as $UnsignedT).count_ones() }

        /// Returns the number of zeros in the binary representation of `self`.
        ///
        /// # Examples
        ///
        /// ```rust
        /// # #![feature(core)]
        /// use std::num::Int;
        ///
        /// let n = 0b01001100u8;
        ///
        /// assert_eq!(n.count_zeros(), 5);
        /// ```
        #[unstable(feature = "core",
                   reason = "pending integer conventions")]
        #[inline]
        pub fn count_zeros(self) -> u32 {
            (!self).count_ones()
        }

        /// Returns the number of leading zeros in the binary representation
        /// of `self`.
        ///
        /// # Examples
        ///
        /// ```rust
        /// # #![feature(core)]
        /// use std::num::Int;
        ///
        /// let n = 0b0101000u16;
        ///
        /// assert_eq!(n.leading_zeros(), 10);
        /// ```
        #[unstable(feature = "core",
                   reason = "pending integer conventions")]
        #[inline]
        pub fn leading_zeros(self) -> u32 {
            (self as $UnsignedT).leading_zeros()
        }

        /// Returns the number of trailing zeros in the binary representation
        /// of `self`.
        ///
        /// # Examples
        ///
        /// ```rust
        /// # #![feature(core)]
        /// use std::num::Int;
        ///
        /// let n = 0b0101000u16;
        ///
        /// assert_eq!(n.trailing_zeros(), 3);
        /// ```
        #[unstable(feature = "core",
                   reason = "pending integer conventions")]
        #[inline]
        pub fn trailing_zeros(self) -> u32 {
            (self as $UnsignedT).trailing_zeros()
        }

        /// Shifts the bits to the left by a specified amount amount, `n`,
        /// wrapping the truncated bits to the end of the resulting integer.
        ///
        /// # Examples
        ///
        /// ```rust
        /// # #![feature(core)]
        /// use std::num::Int;
        ///
        /// let n = 0x0123456789ABCDEFu64;
        /// let m = 0x3456789ABCDEF012u64;
        ///
        /// assert_eq!(n.rotate_left(12), m);
        /// ```
        #[unstable(feature = "core",
                   reason = "pending integer conventions")]
        #[inline]
        pub fn rotate_left(self, n: u32) -> $T {
            (self as $UnsignedT).rotate_left(n) as $T
        }

        /// Shifts the bits to the right by a specified amount amount, `n`,
        /// wrapping the truncated bits to the beginning of the resulting
        /// integer.
        ///
        /// # Examples
        ///
        /// ```rust
        /// # #![feature(core)]
        /// use std::num::Int;
        ///
        /// let n = 0x0123456789ABCDEFu64;
        /// let m = 0xDEF0123456789ABCu64;
        ///
        /// assert_eq!(n.rotate_right(12), m);
        /// ```
        #[unstable(feature = "core",
                   reason = "pending integer conventions")]
        #[inline]
        pub fn rotate_right(self, n: u32) -> $T {
            (self as $UnsignedT).rotate_right(n) as $T
        }

        /// Reverses the byte order of the integer.
        ///
        /// # Examples
        ///
        /// ```rust
        /// use std::num::Int;
        ///
        /// let n = 0x0123456789ABCDEFu64;
        /// let m = 0xEFCDAB8967452301u64;
        ///
        /// assert_eq!(n.swap_bytes(), m);
        /// ```
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn swap_bytes(self) -> $T {
            (self as $UnsignedT).swap_bytes() as $T
        }

        /// Convert an integer from big endian to the target's endianness.
        ///
        /// On big endian this is a no-op. On little endian the bytes are
        /// swapped.
        ///
        /// # Examples
        ///
        /// ```rust
        /// use std::num::Int;
        ///
        /// let n = 0x0123456789ABCDEFu64;
        ///
        /// if cfg!(target_endian = "big") {
        ///     assert_eq!(Int::from_be(n), n)
        /// } else {
        ///     assert_eq!(Int::from_be(n), n.swap_bytes())
        /// }
        /// ```
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn from_be(x: $T) -> $T {
            if cfg!(target_endian = "big") { x } else { x.swap_bytes() }
        }

        /// Convert an integer from little endian to the target's endianness.
        ///
        /// On little endian this is a no-op. On big endian the bytes are
        /// swapped.
        ///
        /// # Examples
        ///
        /// ```rust
        /// use std::num::Int;
        ///
        /// let n = 0x0123456789ABCDEFu64;
        ///
        /// if cfg!(target_endian = "little") {
        ///     assert_eq!(Int::from_le(n), n)
        /// } else {
        ///     assert_eq!(Int::from_le(n), n.swap_bytes())
        /// }
        /// ```
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn from_le(x: $T) -> $T {
            if cfg!(target_endian = "little") { x } else { x.swap_bytes() }
        }

        /// Convert `self` to big endian from the target's endianness.
        ///
        /// On big endian this is a no-op. On little endian the bytes are
        /// swapped.
        ///
        /// # Examples
        ///
        /// ```rust
        /// use std::num::Int;
        ///
        /// let n = 0x0123456789ABCDEFu64;
        ///
        /// if cfg!(target_endian = "big") {
        ///     assert_eq!(n.to_be(), n)
        /// } else {
        ///     assert_eq!(n.to_be(), n.swap_bytes())
        /// }
        /// ```
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn to_be(self) -> $T { // or not to be?
            if cfg!(target_endian = "big") { self } else { self.swap_bytes() }
        }

        /// Convert `self` to little endian from the target's endianness.
        ///
        /// On little endian this is a no-op. On big endian the bytes are
        /// swapped.
        ///
        /// # Examples
        ///
        /// ```rust
        /// use std::num::Int;
        ///
        /// let n = 0x0123456789ABCDEFu64;
        ///
        /// if cfg!(target_endian = "little") {
        ///     assert_eq!(n.to_le(), n)
        /// } else {
        ///     assert_eq!(n.to_le(), n.swap_bytes())
        /// }
        /// ```
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn to_le(self) -> $T {
            if cfg!(target_endian = "little") { self } else { self.swap_bytes() }
        }

        /// Checked integer addition. Computes `self + other`, returning `None`
        /// if overflow occurred.
        ///
        /// # Examples
        ///
        /// ```rust
        /// use std::num::Int;
        ///
        /// assert_eq!(5u16.checked_add(65530), Some(65535));
        /// assert_eq!(6u16.checked_add(65530), None);
        /// ```
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn checked_add(self, other: $T) -> Option<$T> {
            checked_op!($T, $ActualT, $add_with_overflow, self, other)
        }

        /// Checked integer subtraction. Computes `self - other`, returning
        /// `None` if underflow occurred.
        ///
        /// # Examples
        ///
        /// ```rust
        /// use std::num::Int;
        ///
        /// assert_eq!((-127i8).checked_sub(1), Some(-128));
        /// assert_eq!((-128i8).checked_sub(1), None);
        /// ```
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn checked_sub(self, other: $T) -> Option<$T> {
            checked_op!($T, $ActualT, $sub_with_overflow, self, other)
        }

        /// Checked integer multiplication. Computes `self * other`, returning
        /// `None` if underflow or overflow occurred.
        ///
        /// # Examples
        ///
        /// ```rust
        /// use std::num::Int;
        ///
        /// assert_eq!(5u8.checked_mul(51), Some(255));
        /// assert_eq!(5u8.checked_mul(52), None);
        /// ```
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn checked_mul(self, other: $T) -> Option<$T> {
            checked_op!($T, $ActualT, $mul_with_overflow, self, other)
        }

        /// Checked integer division. Computes `self / other`, returning `None`
        /// if `other == 0` or the operation results in underflow or overflow.
        ///
        /// # Examples
        ///
        /// ```rust
        /// use std::num::Int;
        ///
        /// assert_eq!((-127i8).checked_div(-1), Some(127));
        /// assert_eq!((-128i8).checked_div(-1), None);
        /// assert_eq!((1i8).checked_div(0), None);
        /// ```
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn checked_div(self, v: $T) -> Option<$T> {
            match v {
                0   => None,
               -1 if self == <$T>::min_value()
                    => None,
                v   => Some(self / v),
            }
        }

        /// Saturating integer addition. Computes `self + other`, saturating at
        /// the numeric bounds instead of overflowing.
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn saturating_add(self, other: $T) -> $T {
            match self.checked_add(other) {
                Some(x)                       => x,
                None if other >= <$T>::zero() => <$T>::max_value(),
                None                          => <$T>::min_value(),
            }
        }

        /// Saturating integer subtraction. Computes `self - other`, saturating
        /// at the numeric bounds instead of overflowing.
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn saturating_sub(self, other: $T) -> $T {
            match self.checked_sub(other) {
                Some(x)                      => x,
                None if other >= <$T>::zero() => <$T>::min_value(),
                None                          => <$T>::max_value(),
            }
        }

        /// Raises self to the power of `exp`, using exponentiation by squaring.
        ///
        /// # Examples
        ///
        /// ```rust
        /// # #![feature(core)]
        /// use std::num::Int;
        ///
        /// assert_eq!(2.pow(4), 16);
        /// ```
        #[unstable(feature = "core",
                   reason = "pending integer conventions")]
        #[inline]
        pub fn pow(self, mut exp: u32) -> $T {
            let mut base = self;
            let mut acc = <$T>::one();

            let mut prev_base = self;
            let mut base_oflo = false;
            while exp > 0 {
                if (exp & 1) == 1 {
                    if base_oflo {
                        // ensure overflow occurs in the same manner it
                        // would have otherwise (i.e. signal any exception
                        // it would have otherwise).
                        acc = acc * (prev_base * prev_base);
                    } else {
                        acc = acc * base;
                    }
                }
                prev_base = base;
                let (new_base, new_base_oflo) = base.overflowing_mul(base);
                base = new_base;
                base_oflo = new_base_oflo;
                exp /= 2;
            }
            acc
        }

        /// Computes the absolute value of `self`. `Int::min_value()` will be
        /// returned if the number is `Int::min_value()`.
        #[unstable(feature = "core", reason = "overflow in debug builds?")]
        #[inline]
        pub fn abs(self) -> $T {
            if self.is_negative() { -self } else { self }
        }

        /// Returns a number representing sign of `self`.
        ///
        /// - `0` if the number is zero
        /// - `1` if the number is positive
        /// - `-1` if the number is negative
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn signum(self) -> $T {
            match self {
                n if n > 0 =>  1,
                0          =>  0,
                _          => -1,
            }
        }

        /// Returns `true` if `self` is positive and `false` if the number
        /// is zero or negative.
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn is_positive(self) -> bool { self > 0 }

        /// Returns `true` if `self` is negative and `false` if the number
        /// is zero or positive.
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn is_negative(self) -> bool { self < 0 }
    }
}

#[lang = "i8"]
impl i8 {
    int_impl! { i8 = i8, u8, 8,
        intrinsics::i8_add_with_overflow,
        intrinsics::i8_sub_with_overflow,
        intrinsics::i8_mul_with_overflow }
}

#[lang = "i16"]
impl i16 {
    int_impl! { i16 = i16, u16, 16,
        intrinsics::i16_add_with_overflow,
        intrinsics::i16_sub_with_overflow,
        intrinsics::i16_mul_with_overflow }
}

#[lang = "i32"]
impl i32 {
    int_impl! { i32 = i32, u32, 32,
        intrinsics::i32_add_with_overflow,
        intrinsics::i32_sub_with_overflow,
        intrinsics::i32_mul_with_overflow }
}

#[lang = "i64"]
impl i64 {
    int_impl! { i64 = i64, u64, 64,
        intrinsics::i64_add_with_overflow,
        intrinsics::i64_sub_with_overflow,
        intrinsics::i64_mul_with_overflow }
}

#[cfg(target_pointer_width = "32")]
#[lang = "isize"]
impl isize {
    int_impl! { isize = i32, u32, 32,
        intrinsics::i32_add_with_overflow,
        intrinsics::i32_sub_with_overflow,
        intrinsics::i32_mul_with_overflow }
}

#[cfg(target_pointer_width = "64")]
#[lang = "isize"]
impl isize {
    int_impl! { isize = i64, u64, 64,
        intrinsics::i64_add_with_overflow,
        intrinsics::i64_sub_with_overflow,
        intrinsics::i64_mul_with_overflow }
}

// `Int` + `UnsignedInt` implemented for signed integers
macro_rules! uint_impl {
    ($T:ty = $ActualT:ty, $BITS:expr,
     $ctpop:path,
     $ctlz:path,
     $cttz:path,
     $bswap:path,
     $add_with_overflow:path,
     $sub_with_overflow:path,
     $mul_with_overflow:path) => {
        /// Returns the `0` value of this integer type.
        // FIXME (#5527): Should be an associated constant
        #[unstable(feature = "core",
                   reason = "unsure about its place in the world")]
        #[inline]
        pub fn zero() -> $T { 0 }

        /// Returns the `1` value of this integer type.
        // FIXME (#5527): Should be an associated constant
        #[unstable(feature = "core",
                   reason = "unsure about its place in the world")]
        #[inline]
        pub fn one() -> $T { 1 }

        /// Returns the smallest value that can be represented by this integer
        /// type.
        // FIXME (#5527): Should be and associated constant
        #[unstable(feature = "core",
                   reason = "unsure about its place in the world")]
        #[inline]
        pub fn min_value() -> $T { 0 }

        /// Returns the largest value that can be represented by this integer
        /// type.
        // FIXME (#5527): Should be and associated constant
        #[unstable(feature = "core",
                   reason = "unsure about its place in the world")]
        #[inline]
        pub fn max_value() -> $T { -1 }

        /// Returns the number of ones in the binary representation of `self`.
        ///
        /// # Examples
        ///
        /// ```rust
        /// # #![feature(core)]
        /// use std::num::Int;
        ///
        /// let n = 0b01001100u8;
        ///
        /// assert_eq!(n.count_ones(), 3);
        /// ```
        #[unstable(feature = "core",
                   reason = "pending integer conventions")]
        #[inline]
        pub fn count_ones(self) -> u32 {
            unsafe { $ctpop(self as $ActualT) as u32 }
        }

        /// Returns the number of zeros in the binary representation of `self`.
        ///
        /// # Examples
        ///
        /// ```rust
        /// # #![feature(core)]
        /// use std::num::Int;
        ///
        /// let n = 0b01001100u8;
        ///
        /// assert_eq!(n.count_zeros(), 5);
        /// ```
        #[unstable(feature = "core",
                   reason = "pending integer conventions")]
        #[inline]
        pub fn count_zeros(self) -> u32 {
            (!self).count_ones()
        }

        /// Returns the number of leading zeros in the binary representation
        /// of `self`.
        ///
        /// # Examples
        ///
        /// ```rust
        /// # #![feature(core)]
        /// use std::num::Int;
        ///
        /// let n = 0b0101000u16;
        ///
        /// assert_eq!(n.leading_zeros(), 10);
        /// ```
        #[unstable(feature = "core",
                   reason = "pending integer conventions")]
        #[inline]
        pub fn leading_zeros(self) -> u32 {
            unsafe { $ctlz(self as $ActualT) as u32 }
        }

        /// Returns the number of trailing zeros in the binary representation
        /// of `self`.
        ///
        /// # Examples
        ///
        /// ```rust
        /// # #![feature(core)]
        /// use std::num::Int;
        ///
        /// let n = 0b0101000u16;
        ///
        /// assert_eq!(n.trailing_zeros(), 3);
        /// ```
        #[unstable(feature = "core",
                   reason = "pending integer conventions")]
        #[inline]
        pub fn trailing_zeros(self) -> u32 {
            unsafe { $cttz(self as $ActualT) as u32 }
        }

        /// Shifts the bits to the left by a specified amount amount, `n`,
        /// wrapping the truncated bits to the end of the resulting integer.
        ///
        /// # Examples
        ///
        /// ```rust
        /// # #![feature(core)]
        /// use std::num::Int;
        ///
        /// let n = 0x0123456789ABCDEFu64;
        /// let m = 0x3456789ABCDEF012u64;
        ///
        /// assert_eq!(n.rotate_left(12), m);
        /// ```
        #[unstable(feature = "core",
                   reason = "pending integer conventions")]
        #[inline]
        pub fn rotate_left(self, n: u32) -> $T {
            // Protect against undefined behaviour for over-long bit shifts
            let n = n % $BITS;
            (self << n) | (self >> (($BITS - n) % $BITS))
        }

        /// Shifts the bits to the right by a specified amount amount, `n`,
        /// wrapping the truncated bits to the beginning of the resulting
        /// integer.
        ///
        /// # Examples
        ///
        /// ```rust
        /// # #![feature(core)]
        /// use std::num::Int;
        ///
        /// let n = 0x0123456789ABCDEFu64;
        /// let m = 0xDEF0123456789ABCu64;
        ///
        /// assert_eq!(n.rotate_right(12), m);
        /// ```
        #[unstable(feature = "core",
                   reason = "pending integer conventions")]
        #[inline]
        pub fn rotate_right(self, n: u32) -> $T {
            // Protect against undefined behaviour for over-long bit shifts
            let n = n % $BITS;
            (self >> n) | (self << (($BITS - n) % $BITS))
        }

        /// Reverses the byte order of the integer.
        ///
        /// # Examples
        ///
        /// ```rust
        /// use std::num::Int;
        ///
        /// let n = 0x0123456789ABCDEFu64;
        /// let m = 0xEFCDAB8967452301u64;
        ///
        /// assert_eq!(n.swap_bytes(), m);
        /// ```
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn swap_bytes(self) -> $T {
            unsafe { $bswap(self as $ActualT) as $T }
        }

        /// Convert an integer from big endian to the target's endianness.
        ///
        /// On big endian this is a no-op. On little endian the bytes are
        /// swapped.
        ///
        /// # Examples
        ///
        /// ```rust
        /// use std::num::Int;
        ///
        /// let n = 0x0123456789ABCDEFu64;
        ///
        /// if cfg!(target_endian = "big") {
        ///     assert_eq!(Int::from_be(n), n)
        /// } else {
        ///     assert_eq!(Int::from_be(n), n.swap_bytes())
        /// }
        /// ```
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn from_be(x: $T) -> $T {
            if cfg!(target_endian = "big") { x } else { x.swap_bytes() }
        }

        /// Convert an integer from little endian to the target's endianness.
        ///
        /// On little endian this is a no-op. On big endian the bytes are
        /// swapped.
        ///
        /// # Examples
        ///
        /// ```rust
        /// use std::num::Int;
        ///
        /// let n = 0x0123456789ABCDEFu64;
        ///
        /// if cfg!(target_endian = "little") {
        ///     assert_eq!(Int::from_le(n), n)
        /// } else {
        ///     assert_eq!(Int::from_le(n), n.swap_bytes())
        /// }
        /// ```
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn from_le(x: $T) -> $T {
            if cfg!(target_endian = "little") { x } else { x.swap_bytes() }
        }

        /// Convert `self` to big endian from the target's endianness.
        ///
        /// On big endian this is a no-op. On little endian the bytes are
        /// swapped.
        ///
        /// # Examples
        ///
        /// ```rust
        /// use std::num::Int;
        ///
        /// let n = 0x0123456789ABCDEFu64;
        ///
        /// if cfg!(target_endian = "big") {
        ///     assert_eq!(n.to_be(), n)
        /// } else {
        ///     assert_eq!(n.to_be(), n.swap_bytes())
        /// }
        /// ```
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn to_be(self) -> $T { // or not to be?
            if cfg!(target_endian = "big") { self } else { self.swap_bytes() }
        }

        /// Convert `self` to little endian from the target's endianness.
        ///
        /// On little endian this is a no-op. On big endian the bytes are
        /// swapped.
        ///
        /// # Examples
        ///
        /// ```rust
        /// use std::num::Int;
        ///
        /// let n = 0x0123456789ABCDEFu64;
        ///
        /// if cfg!(target_endian = "little") {
        ///     assert_eq!(n.to_le(), n)
        /// } else {
        ///     assert_eq!(n.to_le(), n.swap_bytes())
        /// }
        /// ```
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn to_le(self) -> $T {
            if cfg!(target_endian = "little") { self } else { self.swap_bytes() }
        }

        /// Checked integer addition. Computes `self + other`, returning `None`
        /// if overflow occurred.
        ///
        /// # Examples
        ///
        /// ```rust
        /// use std::num::Int;
        ///
        /// assert_eq!(5u16.checked_add(65530), Some(65535));
        /// assert_eq!(6u16.checked_add(65530), None);
        /// ```
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn checked_add(self, other: $T) -> Option<$T> {
            checked_op!($T, $ActualT, $add_with_overflow, self, other)
        }

        /// Checked integer subtraction. Computes `self - other`, returning
        /// `None` if underflow occurred.
        ///
        /// # Examples
        ///
        /// ```rust
        /// use std::num::Int;
        ///
        /// assert_eq!((-127i8).checked_sub(1), Some(-128));
        /// assert_eq!((-128i8).checked_sub(1), None);
        /// ```
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn checked_sub(self, other: $T) -> Option<$T> {
            checked_op!($T, $ActualT, $sub_with_overflow, self, other)
        }

        /// Checked integer multiplication. Computes `self * other`, returning
        /// `None` if underflow or overflow occurred.
        ///
        /// # Examples
        ///
        /// ```rust
        /// use std::num::Int;
        ///
        /// assert_eq!(5u8.checked_mul(51), Some(255));
        /// assert_eq!(5u8.checked_mul(52), None);
        /// ```
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn checked_mul(self, other: $T) -> Option<$T> {
            checked_op!($T, $ActualT, $mul_with_overflow, self, other)
        }

        /// Checked integer division. Computes `self / other`, returning `None`
        /// if `other == 0` or the operation results in underflow or overflow.
        ///
        /// # Examples
        ///
        /// ```rust
        /// use std::num::Int;
        ///
        /// assert_eq!((-127i8).checked_div(-1), Some(127));
        /// assert_eq!((-128i8).checked_div(-1), None);
        /// assert_eq!((1i8).checked_div(0), None);
        /// ```
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn checked_div(self, v: $T) -> Option<$T> {
            match v {
                0 => None,
                v => Some(self / v),
            }
        }

        /// Saturating integer addition. Computes `self + other`, saturating at
        /// the numeric bounds instead of overflowing.
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn saturating_add(self, other: $T) -> $T {
            match self.checked_add(other) {
                Some(x)                       => x,
                None if other >= <$T>::zero() => <$T>::max_value(),
                None                          => <$T>::min_value(),
            }
        }

        /// Saturating integer subtraction. Computes `self - other`, saturating
        /// at the numeric bounds instead of overflowing.
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn saturating_sub(self, other: $T) -> $T {
            match self.checked_sub(other) {
                Some(x)                       => x,
                None if other >= <$T>::zero() => <$T>::min_value(),
                None                          => <$T>::max_value(),
            }
        }

        /// Raises self to the power of `exp`, using exponentiation by squaring.
        ///
        /// # Examples
        ///
        /// ```rust
        /// # #![feature(core)]
        /// use std::num::Int;
        ///
        /// assert_eq!(2.pow(4), 16);
        /// ```
        #[unstable(feature = "core",
                   reason = "pending integer conventions")]
        #[inline]
        pub fn pow(self, mut exp: u32) -> $T {
            let mut base = self;
            let mut acc = <$T>::one();

            let mut prev_base = self;
            let mut base_oflo = false;
            while exp > 0 {
                if (exp & 1) == 1 {
                    if base_oflo {
                        // ensure overflow occurs in the same manner it
                        // would have otherwise (i.e. signal any exception
                        // it would have otherwise).
                        acc = acc * (prev_base * prev_base);
                    } else {
                        acc = acc * base;
                    }
                }
                prev_base = base;
                let (new_base, new_base_oflo) = base.overflowing_mul(base);
                base = new_base;
                base_oflo = new_base_oflo;
                exp /= 2;
            }
            acc
        }

        /// Returns `true` iff `self == 2^k` for some `k`.
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn is_power_of_two(self) -> bool {
            (self.wrapping_sub(<$T>::one())) & self == <$T>::zero() &&
                !(self == <$T>::zero())
        }

        /// Returns the smallest power of two greater than or equal to `self`.
        /// Unspecified behavior on overflow.
        #[stable(feature = "rust1", since = "1.0.0")]
        #[inline]
        pub fn next_power_of_two(self) -> $T {
            let bits = size_of::<$T>() * 8;
            let one: $T = <$T>::one();
            one << ((bits - self.wrapping_sub(one).leading_zeros() as usize) % bits)
        }

        /// Returns the smallest power of two greater than or equal to `n`. If
        /// the next power of two is greater than the type's maximum value,
        /// `None` is returned, otherwise the power of two is wrapped in `Some`.
        #[stable(feature = "rust1", since = "1.0.0")]
        pub fn checked_next_power_of_two(self) -> Option<$T> {
            let npot = self.next_power_of_two();
            if npot >= self {
                Some(npot)
            } else {
                None
            }
        }
    }
}

#[lang = "u8"]
impl u8 {
    uint_impl! { u8 = u8, 8,
        intrinsics::ctpop8,
        intrinsics::ctlz8,
        intrinsics::cttz8,
        bswap8,
        intrinsics::u8_add_with_overflow,
        intrinsics::u8_sub_with_overflow,
        intrinsics::u8_mul_with_overflow }
}

#[lang = "u16"]
impl u16 {
    uint_impl! { u16 = u16, 16,
        intrinsics::ctpop16,
        intrinsics::ctlz16,
        intrinsics::cttz16,
        intrinsics::bswap16,
        intrinsics::u16_add_with_overflow,
        intrinsics::u16_sub_with_overflow,
        intrinsics::u16_mul_with_overflow }
}

#[lang = "u32"]
impl u32 {
    uint_impl! { u32 = u32, 32,
        intrinsics::ctpop32,
        intrinsics::ctlz32,
        intrinsics::cttz32,
        intrinsics::bswap32,
        intrinsics::u32_add_with_overflow,
        intrinsics::u32_sub_with_overflow,
        intrinsics::u32_mul_with_overflow }
}


#[lang = "u64"]
impl u64 {
    uint_impl! { u64 = u64, 64,
        intrinsics::ctpop64,
        intrinsics::ctlz64,
        intrinsics::cttz64,
        intrinsics::bswap64,
        intrinsics::u64_add_with_overflow,
        intrinsics::u64_sub_with_overflow,
        intrinsics::u64_mul_with_overflow }
}

#[cfg(target_pointer_width = "32")]
#[lang = "usize"]
impl usize {
    uint_impl! { usize = u32, 32,
        intrinsics::ctpop32,
        intrinsics::ctlz32,
        intrinsics::cttz32,
        intrinsics::bswap32,
        intrinsics::u32_add_with_overflow,
        intrinsics::u32_sub_with_overflow,
        intrinsics::u32_mul_with_overflow }
}

#[cfg(target_pointer_width = "64")]
#[lang = "usize"]
impl usize {
    uint_impl! { usize = u64, 64,
        intrinsics::ctpop64,
        intrinsics::ctlz64,
        intrinsics::cttz64,
        intrinsics::bswap64,
        intrinsics::u64_add_with_overflow,
        intrinsics::u64_sub_with_overflow,
        intrinsics::u64_mul_with_overflow }
}

/// A generic trait for converting a value to a number.
#[unstable(feature = "core", reason = "trait is likely to be removed")]
pub trait ToPrimitive {
    /// Converts the value of `self` to an `isize`.
    #[inline]
    #[unstable(feature = "core")]
    #[deprecated(since = "1.0.0", reason = "use to_isize")]
    fn to_int(&self) -> Option<isize> {
        self.to_i64().and_then(|x| x.to_isize())
    }

    /// Converts the value of `self` to an `isize`.
    #[inline]
    fn to_isize(&self) -> Option<isize> {
        self.to_i64().and_then(|x| x.to_isize())
    }

    /// Converts the value of `self` to an `i8`.
    #[inline]
    fn to_i8(&self) -> Option<i8> {
        self.to_i64().and_then(|x| x.to_i8())
    }

    /// Converts the value of `self` to an `i16`.
    #[inline]
    fn to_i16(&self) -> Option<i16> {
        self.to_i64().and_then(|x| x.to_i16())
    }

    /// Converts the value of `self` to an `i32`.
    #[inline]
    fn to_i32(&self) -> Option<i32> {
        self.to_i64().and_then(|x| x.to_i32())
    }

    /// Converts the value of `self` to an `i64`.
    fn to_i64(&self) -> Option<i64>;

    /// Converts the value of `self` to an `usize`.
    #[inline]
    #[unstable(feature = "core")]
    #[deprecated(since = "1.0.0", reason = "use to_usize")]
    fn to_uint(&self) -> Option<usize> {
        self.to_u64().and_then(|x| x.to_usize())
    }

    /// Converts the value of `self` to a `usize`.
    #[inline]
    fn to_usize(&self) -> Option<usize> {
        self.to_u64().and_then(|x| x.to_usize())
    }

    /// Converts the value of `self` to an `u8`.
    #[inline]
    fn to_u8(&self) -> Option<u8> {
        self.to_u64().and_then(|x| x.to_u8())
    }

    /// Converts the value of `self` to an `u16`.
    #[inline]
    fn to_u16(&self) -> Option<u16> {
        self.to_u64().and_then(|x| x.to_u16())
    }

    /// Converts the value of `self` to an `u32`.
    #[inline]
    fn to_u32(&self) -> Option<u32> {
        self.to_u64().and_then(|x| x.to_u32())
    }

    /// Converts the value of `self` to an `u64`.
    #[inline]
    fn to_u64(&self) -> Option<u64>;

    /// Converts the value of `self` to an `f32`.
    #[inline]
    fn to_f32(&self) -> Option<f32> {
        self.to_f64().and_then(|x| x.to_f32())
    }

    /// Converts the value of `self` to an `f64`.
    #[inline]
    fn to_f64(&self) -> Option<f64> {
        self.to_i64().and_then(|x| x.to_f64())
    }
}

macro_rules! impl_to_primitive_int_to_int {
    ($SrcT:ty, $DstT:ty, $slf:expr) => (
        {
            if size_of::<$SrcT>() <= size_of::<$DstT>() {
                Some($slf as $DstT)
            } else {
                let n = $slf as i64;
                let min_value: $DstT = Int::min_value();
                let max_value: $DstT = Int::max_value();
                if min_value as i64 <= n && n <= max_value as i64 {
                    Some($slf as $DstT)
                } else {
                    None
                }
            }
        }
    )
}

macro_rules! impl_to_primitive_int_to_uint {
    ($SrcT:ty, $DstT:ty, $slf:expr) => (
        {
            let zero: $SrcT = Int::zero();
            let max_value: $DstT = Int::max_value();
            if zero <= $slf && $slf as u64 <= max_value as u64 {
                Some($slf as $DstT)
            } else {
                None
            }
        }
    )
}

macro_rules! impl_to_primitive_int {
    ($T:ty) => (
        impl ToPrimitive for $T {
            #[inline]
            fn to_int(&self) -> Option<isize> { impl_to_primitive_int_to_int!($T, isize, *self) }
            #[inline]
            fn to_isize(&self) -> Option<isize> { impl_to_primitive_int_to_int!($T, isize, *self) }
            #[inline]
            fn to_i8(&self) -> Option<i8> { impl_to_primitive_int_to_int!($T, i8, *self) }
            #[inline]
            fn to_i16(&self) -> Option<i16> { impl_to_primitive_int_to_int!($T, i16, *self) }
            #[inline]
            fn to_i32(&self) -> Option<i32> { impl_to_primitive_int_to_int!($T, i32, *self) }
            #[inline]
            fn to_i64(&self) -> Option<i64> { impl_to_primitive_int_to_int!($T, i64, *self) }

            #[inline]
            fn to_uint(&self) -> Option<usize> { impl_to_primitive_int_to_uint!($T, usize, *self) }
            #[inline]
            fn to_usize(&self) -> Option<usize> { impl_to_primitive_int_to_uint!($T, usize, *self) }
            #[inline]
            fn to_u8(&self) -> Option<u8> { impl_to_primitive_int_to_uint!($T, u8, *self) }
            #[inline]
            fn to_u16(&self) -> Option<u16> { impl_to_primitive_int_to_uint!($T, u16, *self) }
            #[inline]
            fn to_u32(&self) -> Option<u32> { impl_to_primitive_int_to_uint!($T, u32, *self) }
            #[inline]
            fn to_u64(&self) -> Option<u64> { impl_to_primitive_int_to_uint!($T, u64, *self) }

            #[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 }

macro_rules! impl_to_primitive_uint_to_int {
    ($DstT:ty, $slf:expr) => (
        {
            let max_value: $DstT = Int::max_value();
            if $slf as u64 <= max_value as u64 {
                Some($slf as $DstT)
            } else {
                None
            }
        }
    )
}

macro_rules! impl_to_primitive_uint_to_uint {
    ($SrcT:ty, $DstT:ty, $slf:expr) => (
        {
            if size_of::<$SrcT>() <= size_of::<$DstT>() {
                Some($slf as $DstT)
            } else {
                let zero: $SrcT = Int::zero();
                let max_value: $DstT = Int::max_value();
                if zero <= $slf && $slf as u64 <= max_value as u64 {
                    Some($slf as $DstT)
                } else {
                    None
                }
            }
        }
    )
}

macro_rules! impl_to_primitive_uint {
    ($T:ty) => (
        impl ToPrimitive for $T {
            #[inline]
            fn to_int(&self) -> Option<isize> { impl_to_primitive_uint_to_int!(isize, *self) }
            #[inline]
            fn to_isize(&self) -> Option<isize> { impl_to_primitive_uint_to_int!(isize, *self) }
            #[inline]
            fn to_i8(&self) -> Option<i8> { impl_to_primitive_uint_to_int!(i8, *self) }
            #[inline]
            fn to_i16(&self) -> Option<i16> { impl_to_primitive_uint_to_int!(i16, *self) }
            #[inline]
            fn to_i32(&self) -> Option<i32> { impl_to_primitive_uint_to_int!(i32, *self) }
            #[inline]
            fn to_i64(&self) -> Option<i64> { impl_to_primitive_uint_to_int!(i64, *self) }

            #[inline]
            fn to_uint(&self) -> Option<usize> { impl_to_primitive_uint_to_uint!($T, usize, *self) }
            #[inline]
            fn to_usize(&self) -> Option<usize> {
                impl_to_primitive_uint_to_uint!($T, usize, *self)
            }
            #[inline]
            fn to_u8(&self) -> Option<u8> { impl_to_primitive_uint_to_uint!($T, u8, *self) }
            #[inline]
            fn to_u16(&self) -> Option<u16> { impl_to_primitive_uint_to_uint!($T, u16, *self) }
            #[inline]
            fn to_u32(&self) -> Option<u32> { impl_to_primitive_uint_to_uint!($T, u32, *self) }
            #[inline]
            fn to_u64(&self) -> Option<u64> { impl_to_primitive_uint_to_uint!($T, u64, *self) }

            #[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 }

macro_rules! impl_to_primitive_float_to_float {
    ($SrcT:ident, $DstT:ident, $slf:expr) => (
        if size_of::<$SrcT>() <= size_of::<$DstT>() {
            Some($slf as $DstT)
        } else {
            let n = $slf as f64;
            let max_value: $SrcT = ::$SrcT::MAX;
            if -max_value as f64 <= n && n <= max_value as f64 {
                Some($slf as $DstT)
            } else {
                None
            }
        }
    )
}

macro_rules! impl_to_primitive_float {
    ($T:ident) => (
        impl ToPrimitive for $T {
            #[inline]
            fn to_int(&self) -> Option<isize> { Some(*self as isize) }
            #[inline]
            fn to_isize(&self) -> Option<isize> { Some(*self as isize) }
            #[inline]
            fn to_i8(&self) -> Option<i8> { Some(*self as i8) }
            #[inline]
            fn to_i16(&self) -> Option<i16> { Some(*self as i16) }
            #[inline]
            fn to_i32(&self) -> Option<i32> { Some(*self as i32) }
            #[inline]
            fn to_i64(&self) -> Option<i64> { Some(*self as i64) }

            #[inline]
            fn to_uint(&self) -> Option<usize> { Some(*self as usize) }
            #[inline]
            fn to_usize(&self) -> Option<usize> { Some(*self as usize) }
            #[inline]
            fn to_u8(&self) -> Option<u8> { Some(*self as u8) }
            #[inline]
            fn to_u16(&self) -> Option<u16> { Some(*self as u16) }
            #[inline]
            fn to_u32(&self) -> Option<u32> { Some(*self as u32) }
            #[inline]
            fn to_u64(&self) -> Option<u64> { Some(*self as u64) }

            #[inline]
            fn to_f32(&self) -> Option<f32> { impl_to_primitive_float_to_float!($T, f32, *self) }
            #[inline]
            fn to_f64(&self) -> Option<f64> { impl_to_primitive_float_to_float!($T, f64, *self) }
        }
    )
}

impl_to_primitive_float! { f32 }
impl_to_primitive_float! { f64 }

/// A generic trait for converting a number to a value.
#[unstable(feature = "core", reason = "trait is likely to be removed")]
pub trait FromPrimitive : ::marker::Sized {
    /// Convert an `isize` to return an optional value of this type. If the
    /// value cannot be represented by this value, the `None` is returned.
    #[inline]
    #[unstable(feature = "core")]
    #[deprecated(since = "1.0.0", reason = "use from_isize")]
    fn from_int(n: isize) -> Option<Self> {
        FromPrimitive::from_i64(n as i64)
    }

    /// Convert an `isize` to return an optional value of this type. If the
    /// value cannot be represented by this value, the `None` is returned.
    #[inline]
    fn from_isize(n: isize) -> Option<Self> {
        FromPrimitive::from_i64(n as i64)
    }

    /// Convert an `i8` to return an optional value of this type. If the
    /// type cannot be represented by this value, the `None` is returned.
    #[inline]
    fn from_i8(n: i8) -> Option<Self> {
        FromPrimitive::from_i64(n as i64)
    }

    /// Convert an `i16` to return an optional value of this type. If the
    /// type cannot be represented by this value, the `None` is returned.
    #[inline]
    fn from_i16(n: i16) -> Option<Self> {
        FromPrimitive::from_i64(n as i64)
    }

    /// Convert an `i32` to return an optional value of this type. If the
    /// type cannot be represented by this value, the `None` is returned.
    #[inline]
    fn from_i32(n: i32) -> Option<Self> {
        FromPrimitive::from_i64(n as i64)
    }

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

    /// Convert an `usize` to return an optional value of this type. If the
    /// type cannot be represented by this value, the `None` is returned.
    #[inline]
    #[unstable(feature = "core")]
    #[deprecated(since = "1.0.0", reason = "use from_usize")]
    fn from_uint(n: usize) -> Option<Self> {
        FromPrimitive::from_u64(n as u64)
    }

    /// Convert a `usize` to return an optional value of this type. If the
    /// type cannot be represented by this value, the `None` is returned.
    #[inline]
    fn from_usize(n: usize) -> Option<Self> {
        FromPrimitive::from_u64(n as u64)
    }

    /// Convert an `u8` to return an optional value of this type. If the
    /// type cannot be represented by this value, the `None` is returned.
    #[inline]
    fn from_u8(n: u8) -> Option<Self> {
        FromPrimitive::from_u64(n as u64)
    }

    /// Convert an `u16` to return an optional value of this type. If the
    /// type cannot be represented by this value, the `None` is returned.
    #[inline]
    fn from_u16(n: u16) -> Option<Self> {
        FromPrimitive::from_u64(n as u64)
    }

    /// Convert an `u32` to return an optional value of this type. If the
    /// type cannot be represented by this value, the `None` is returned.
    #[inline]
    fn from_u32(n: u32) -> Option<Self> {
        FromPrimitive::from_u64(n as u64)
    }

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

    /// Convert a `f32` to return an optional value of this type. If the
    /// type cannot be represented by this value, the `None` is returned.
    #[inline]
    fn from_f32(n: f32) -> Option<Self> {
        FromPrimitive::from_f64(n as f64)
    }

    /// Convert a `f64` to return an optional value of this type. If the
    /// type cannot be represented by this value, the `None` is returned.
    #[inline]
    fn from_f64(n: f64) -> Option<Self> {
        FromPrimitive::from_i64(n as i64)
    }
}

/// A utility function that just calls `FromPrimitive::from_int`.
#[unstable(feature = "core", reason = "likely to be removed")]
#[deprecated(since = "1.0.0", reason = "use from_isize")]
pub fn from_int<A: FromPrimitive>(n: isize) -> Option<A> {
    FromPrimitive::from_isize(n)
}

/// A utility function that just calls `FromPrimitive::from_isize`.
#[unstable(feature = "core", reason = "likely to be removed")]
pub fn from_isize<A: FromPrimitive>(n: isize) -> Option<A> {
    FromPrimitive::from_isize(n)
}

/// A utility function that just calls `FromPrimitive::from_i8`.
#[unstable(feature = "core", reason = "likely to be removed")]
pub fn from_i8<A: FromPrimitive>(n: i8) -> Option<A> {
    FromPrimitive::from_i8(n)
}

/// A utility function that just calls `FromPrimitive::from_i16`.
#[unstable(feature = "core", reason = "likely to be removed")]
pub fn from_i16<A: FromPrimitive>(n: i16) -> Option<A> {
    FromPrimitive::from_i16(n)
}

/// A utility function that just calls `FromPrimitive::from_i32`.
#[unstable(feature = "core", reason = "likely to be removed")]
pub fn from_i32<A: FromPrimitive>(n: i32) -> Option<A> {
    FromPrimitive::from_i32(n)
}

/// A utility function that just calls `FromPrimitive::from_i64`.
#[unstable(feature = "core", reason = "likely to be removed")]
pub fn from_i64<A: FromPrimitive>(n: i64) -> Option<A> {
    FromPrimitive::from_i64(n)
}

/// A utility function that just calls `FromPrimitive::from_uint`.
#[unstable(feature = "core", reason = "likely to be removed")]
#[deprecated(since = "1.0.0", reason = "use from_uint")]
pub fn from_uint<A: FromPrimitive>(n: usize) -> Option<A> {
    FromPrimitive::from_usize(n)
}

/// A utility function that just calls `FromPrimitive::from_usize`.
#[unstable(feature = "core", reason = "likely to be removed")]
pub fn from_usize<A: FromPrimitive>(n: usize) -> Option<A> {
    FromPrimitive::from_usize(n)
}

/// A utility function that just calls `FromPrimitive::from_u8`.
#[unstable(feature = "core", reason = "likely to be removed")]
pub fn from_u8<A: FromPrimitive>(n: u8) -> Option<A> {
    FromPrimitive::from_u8(n)
}

/// A utility function that just calls `FromPrimitive::from_u16`.
#[unstable(feature = "core", reason = "likely to be removed")]
pub fn from_u16<A: FromPrimitive>(n: u16) -> Option<A> {
    FromPrimitive::from_u16(n)
}

/// A utility function that just calls `FromPrimitive::from_u32`.
#[unstable(feature = "core", reason = "likely to be removed")]
pub fn from_u32<A: FromPrimitive>(n: u32) -> Option<A> {
    FromPrimitive::from_u32(n)
}

/// A utility function that just calls `FromPrimitive::from_u64`.
#[unstable(feature = "core", reason = "likely to be removed")]
pub fn from_u64<A: FromPrimitive>(n: u64) -> Option<A> {
    FromPrimitive::from_u64(n)
}

/// A utility function that just calls `FromPrimitive::from_f32`.
#[unstable(feature = "core", reason = "likely to be removed")]
pub fn from_f32<A: FromPrimitive>(n: f32) -> Option<A> {
    FromPrimitive::from_f32(n)
}

/// A utility function that just calls `FromPrimitive::from_f64`.
#[unstable(feature = "core", reason = "likely to be removed")]
pub fn from_f64<A: FromPrimitive>(n: f64) -> Option<A> {
    FromPrimitive::from_f64(n)
}

macro_rules! impl_from_primitive {
    ($T:ty, $to_ty:ident) => (
        #[allow(deprecated)]
        impl FromPrimitive for $T {
            #[inline] fn from_int(n: isize) -> Option<$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() }

            #[inline] fn from_uint(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() }

            #[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_int }
impl_from_primitive! { i8, to_i8 }
impl_from_primitive! { i16, to_i16 }
impl_from_primitive! { i32, to_i32 }
impl_from_primitive! { i64, to_i64 }
impl_from_primitive! { usize, to_uint }
impl_from_primitive! { u8, to_u8 }
impl_from_primitive! { u16, to_u16 }
impl_from_primitive! { u32, to_u32 }
impl_from_primitive! { u64, to_u64 }
impl_from_primitive! { f32, to_f32 }
impl_from_primitive! { f64, to_f64 }

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

/// An interface for casting between machine scalars.
#[unstable(feature = "core", reason = "trait is likely to be removed")]
pub trait NumCast: ToPrimitive {
    /// Creates a number from another value that can be converted into a primitive via the
    /// `ToPrimitive` trait.
    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 }
impl_num_cast! { usize,  to_uint }
impl_num_cast! { i8,    to_i8 }
impl_num_cast! { i16,   to_i16 }
impl_num_cast! { i32,   to_i32 }
impl_num_cast! { i64,   to_i64 }
impl_num_cast! { isize,   to_int }
impl_num_cast! { f32,   to_f32 }
impl_num_cast! { f64,   to_f64 }

/// Used for representing the classification of floating point numbers
#[derive(Copy, PartialEq, Debug)]
#[unstable(feature = "core", reason = "may be renamed")]
pub enum FpCategory {
    /// "Not a Number", often obtained by dividing by zero
    Nan,
    /// Positive or negative infinity
    Infinite ,
    /// Positive or negative zero
    Zero,
    /// De-normalized floating point representation (less precise than `Normal`)
    Subnormal,
    /// A regular floating point number
    Normal,
}

/// A built-in floating point number.
// FIXME(#5527): In a future version of Rust, many of these functions will
//               become constants.
//
// FIXME(#8888): Several of these functions have a parameter named
//               `unused_self`. Removing it requires #8888 to be fixed.
#[unstable(feature = "core",
           reason = "distribution of methods between core/std is unclear")]
pub trait Float
    : Copy + Clone
    + NumCast
    + PartialOrd
    + PartialEq
    + Neg<Output=Self>
    + Add<Output=Self>
    + Sub<Output=Self>
    + Mul<Output=Self>
    + Div<Output=Self>
    + Rem<Output=Self>
{
    /// Returns the NaN value.
    fn nan() -> Self;
    /// Returns the infinite value.
    fn infinity() -> Self;
    /// Returns the negative infinite value.
    fn neg_infinity() -> Self;
    /// Returns the `0` value.
    fn zero() -> Self;
    /// Returns -0.0.
    fn neg_zero() -> Self;
    /// Returns the `1` value.
    fn one() -> Self;

    // FIXME (#5527): These should be associated constants

    /// Returns the number of binary digits of mantissa that this type supports.
    #[unstable(feature = "core")]
    #[deprecated(since = "1.0.0",
                 reason = "use `std::f32::MANTISSA_DIGITS` or \
                           `std::f64::MANTISSA_DIGITS` as appropriate")]
    fn mantissa_digits(unused_self: Option<Self>) -> usize;
    /// Returns the number of base-10 digits of precision that this type supports.
    #[unstable(feature = "core")]
    #[deprecated(since = "1.0.0",
                 reason = "use `std::f32::DIGITS` or `std::f64::DIGITS` as appropriate")]
    fn digits(unused_self: Option<Self>) -> usize;
    /// Returns the difference between 1.0 and the smallest representable number larger than 1.0.
    #[unstable(feature = "core")]
    #[deprecated(since = "1.0.0",
                 reason = "use `std::f32::EPSILON` or `std::f64::EPSILON` as appropriate")]
    fn epsilon() -> Self;
    /// Returns the minimum binary exponent that this type can represent.
    #[unstable(feature = "core")]
    #[deprecated(since = "1.0.0",
                 reason = "use `std::f32::MIN_EXP` or `std::f64::MIN_EXP` as appropriate")]
    fn min_exp(unused_self: Option<Self>) -> isize;
    /// Returns the maximum binary exponent that this type can represent.
    #[unstable(feature = "core")]
    #[deprecated(since = "1.0.0",
                 reason = "use `std::f32::MAX_EXP` or `std::f64::MAX_EXP` as appropriate")]
    fn max_exp(unused_self: Option<Self>) -> isize;
    /// Returns the minimum base-10 exponent that this type can represent.
    #[unstable(feature = "core")]
    #[deprecated(since = "1.0.0",
                 reason = "use `std::f32::MIN_10_EXP` or `std::f64::MIN_10_EXP` as appropriate")]
    fn min_10_exp(unused_self: Option<Self>) -> isize;
    /// Returns the maximum base-10 exponent that this type can represent.
    #[unstable(feature = "core")]
    #[deprecated(since = "1.0.0",
                 reason = "use `std::f32::MAX_10_EXP` or `std::f64::MAX_10_EXP` as appropriate")]
    fn max_10_exp(unused_self: Option<Self>) -> isize;
    /// Returns the smallest finite value that this type can represent.
    #[unstable(feature = "core")]
    #[deprecated(since = "1.0.0",
                 reason = "use `std::f32::MIN` or `std::f64::MIN` as appropriate")]
    fn min_value() -> Self;
    /// Returns the smallest normalized positive number that this type can represent.
    #[unstable(feature = "core")]
    #[deprecated(since = "1.0.0",
                 reason = "use `std::f32::MIN_POSITIVE` or \
                           `std::f64::MIN_POSITIVE` as appropriate")]
    fn min_pos_value(unused_self: Option<Self>) -> Self;
    /// Returns the largest finite value that this type can represent.
    #[unstable(feature = "core")]
    #[deprecated(since = "1.0.0",
                 reason = "use `std::f32::MAX` or `std::f64::MAX` as appropriate")]
    fn max_value() -> Self;

    /// Returns true if this value is NaN and false otherwise.
    fn is_nan(self) -> bool;
    /// Returns true if this value is positive infinity or negative infinity and
    /// false otherwise.
    fn is_infinite(self) -> bool;
    /// Returns true if this number is neither infinite nor NaN.
    fn is_finite(self) -> bool;
    /// Returns true if this number is neither zero, infinite, denormal, or NaN.
    fn is_normal(self) -> bool;
    /// Returns the category that this number falls into.
    fn classify(self) -> FpCategory;

    /// Returns the mantissa, exponent and sign as integers, respectively.
    fn integer_decode(self) -> (u64, i16, i8);

    /// Return the largest integer less than or equal to a number.
    fn floor(self) -> Self;
    /// Return the smallest integer greater than or equal to a number.
    fn ceil(self) -> Self;
    /// Return the nearest integer to a number. Round half-way cases away from
    /// `0.0`.
    fn round(self) -> Self;
    /// Return the integer part of a number.
    fn trunc(self) -> Self;
    /// Return the fractional part of a number.
    fn fract(self) -> Self;

    /// Computes the absolute value of `self`. Returns `Float::nan()` if the
    /// number is `Float::nan()`.
    fn abs(self) -> Self;
    /// Returns a number that represents the sign of `self`.
    ///
    /// - `1.0` if the number is positive, `+0.0` or `Float::infinity()`
    /// - `-1.0` if the number is negative, `-0.0` or `Float::neg_infinity()`
    /// - `Float::nan()` if the number is `Float::nan()`
    fn signum(self) -> Self;
    /// Returns `true` if `self` is positive, including `+0.0` and
    /// `Float::infinity()`.
    fn is_positive(self) -> bool;
    /// Returns `true` if `self` is negative, including `-0.0` and
    /// `Float::neg_infinity()`.
    fn is_negative(self) -> bool;

    /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
    /// error. This produces a more accurate result with better performance than
    /// a separate multiplication operation followed by an add.
    fn mul_add(self, a: Self, b: Self) -> Self;
    /// Take the reciprocal (inverse) of a number, `1/x`.
    fn recip(self) -> Self;

    /// Raise a number to an integer power.
    ///
    /// Using this function is generally faster than using `powf`
    fn powi(self, n: i32) -> Self;
    /// Raise a number to a floating point power.
    fn powf(self, n: Self) -> Self;

    /// Take the square root of a number.
    ///
    /// Returns NaN if `self` is a negative number.
    fn sqrt(self) -> Self;
    /// Take the reciprocal (inverse) square root of a number, `1/sqrt(x)`.
    fn rsqrt(self) -> Self;

    /// Returns `e^(self)`, (the exponential function).
    fn exp(self) -> Self;
    /// Returns 2 raised to the power of the number, `2^(self)`.
    fn exp2(self) -> Self;
    /// Returns the natural logarithm of the number.
    fn ln(self) -> Self;
    /// Returns the logarithm of the number with respect to an arbitrary base.
    fn log(self, base: Self) -> Self;
    /// Returns the base 2 logarithm of the number.
    fn log2(self) -> Self;
    /// Returns the base 10 logarithm of the number.
    fn log10(self) -> Self;

    /// Convert radians to degrees.
    fn to_degrees(self) -> Self;
    /// Convert degrees to radians.
    fn to_radians(self) -> Self;
}

/// A generic trait for converting a string with a radix (base) to a value
#[unstable(feature = "core", reason = "needs reevaluation")]
pub trait FromStrRadix {
    type Err;
    fn from_str_radix(str: &str, radix: u32) -> Result<Self, Self::Err>;
}

/// A utility function that just calls `FromStrRadix::from_str_radix`.
#[unstable(feature = "core", reason = "needs reevaluation")]
pub fn from_str_radix<T: FromStrRadix>(str: &str, radix: u32)
                                       -> Result<T, T::Err> {
    FromStrRadix::from_str_radix(str, radix)
}

macro_rules! from_str_radix_float_impl {
    ($T:ty) => {
        #[stable(feature = "rust1", since = "1.0.0")]
        impl FromStr for $T {
            type Err = ParseFloatError;

            /// Convert a string in base 10 to a float.
            /// Accepts an optional decimal exponent.
            ///
            /// This function accepts strings such as
            ///
            /// * '3.14'
            /// * '+3.14', equivalent to '3.14'
            /// * '-3.14'
            /// * '2.5E10', or equivalently, '2.5e10'
            /// * '2.5E-10'
            /// * '.' (understood as 0)
            /// * '5.'
            /// * '.5', or, equivalently,  '0.5'
            /// * '+inf', 'inf', '-inf', 'NaN'
            ///
            /// Leading and trailing whitespace represent an error.
            ///
            /// # Arguments
            ///
            /// * src - A string
            ///
            /// # Return value
            ///
            /// `None` if the string did not represent a valid number.  Otherwise,
            /// `Some(n)` where `n` is the floating-point number represented by `src`.
            #[inline]
            fn from_str(src: &str) -> Result<$T, ParseFloatError> {
                from_str_radix(src, 10)
            }
        }

        #[stable(feature = "rust1", since = "1.0.0")]
        impl FromStrRadix for $T {
            type Err = ParseFloatError;

            /// Convert a string in a given base to a float.
            ///
            /// Due to possible conflicts, this function does **not** accept
            /// the special values `inf`, `-inf`, `+inf` and `NaN`, **nor**
            /// does it recognize exponents of any kind.
            ///
            /// Leading and trailing whitespace represent an error.
            ///
            /// # Arguments
            ///
            /// * src - A string
            /// * radix - The base to use. Must lie in the range [2 .. 36]
            ///
            /// # Return value
            ///
            /// `None` if the string did not represent a valid number.
            /// Otherwise, `Some(n)` where `n` is the floating-point number
            /// represented by `src`.
            fn from_str_radix(src: &str, radix: u32)
                              -> Result<$T, ParseFloatError> {
                use self::FloatErrorKind::*;
                use self::ParseFloatError as PFE;
                assert!(radix >= 2 && radix <= 36,
                       "from_str_radix_float: must lie in the range `[2, 36]` - found {}",
                       radix);

                // Special values
                match src {
                    "inf"   => return Ok(Float::infinity()),
                    "-inf"  => return Ok(Float::neg_infinity()),
                    "NaN"   => return Ok(Float::nan()),
                    _       => {},
                }

                let (is_positive, src) =  match src.slice_shift_char() {
                    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(Float::infinity()); }
                                if !is_positive && sig >= prev_sig
                                    { return Ok(Float::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(Float::infinity()); }
                                if !is_positive && (prev_sig != (sig + digit as $T) / radix as $T)
                                    { return Ok(Float::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(Float::infinity()); }
                                if !is_positive && sig > prev_sig
                                    { return Ok(Float::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 src.slice_shift_char() {
                            Some(('-', src)) => (false, src.parse::<usize>()),
                            Some(('+', src)) => (true,  src.parse::<usize>()),
                            Some((_, _))     => (true,  src.parse::<usize>()),
                            None             => return Err(PFE { kind: Invalid }),
                        };

                        match (is_positive, exp) {
                            (true,  Ok(exp)) => base.powi(exp as i32),
                            (false, Ok(exp)) => 1.0 / base.powi(exp as i32),
                            (_, Err(_))      => return Err(PFE { kind: Invalid }),
                        }
                    },
                    None => 1.0, // no exponent
                };

                Ok(sig * exp)
            }
        }
    }
}
from_str_radix_float_impl! { f32 }
from_str_radix_float_impl! { f64 }

macro_rules! from_str_radix_int_impl {
    ($T:ty) => {
        #[stable(feature = "rust1", since = "1.0.0")]
        impl FromStr for $T {
            type Err = ParseIntError;
            #[inline]
            fn from_str(src: &str) -> Result<$T, ParseIntError> {
                from_str_radix(src, 10)
            }
        }

        #[stable(feature = "rust1", since = "1.0.0")]
        impl FromStrRadix for $T {
            type Err = ParseIntError;
            fn from_str_radix(src: &str, radix: u32)
                              -> Result<$T, ParseIntError> {
                use self::IntErrorKind::*;
                use self::ParseIntError as PIE;
                assert!(radix >= 2 && radix <= 36,
                       "from_str_radix_int: must lie in the range `[2, 36]` - found {}",
                       radix);

                let is_signed_ty = (0 as $T) > Int::min_value();

                match src.slice_shift_char() {
                    Some(('-', "")) => Err(PIE { kind: Empty }),
                    Some(('-', src)) if is_signed_ty => {
                        // The number is negative
                        let mut result = 0;
                        for c in src.chars() {
                            let x = match c.to_digit(radix) {
                                Some(x) => x,
                                None => return Err(PIE { kind: InvalidDigit }),
                            };
                            result = match result.checked_mul(radix as $T) {
                                Some(result) => result,
                                None => return Err(PIE { kind: Underflow }),
                            };
                            result = match result.checked_sub(x as $T) {
                                Some(result) => result,
                                None => return Err(PIE { kind: Underflow }),
                            };
                        }
                        Ok(result)
                    },
                    Some((_, _)) => {
                        // The number is signed
                        let mut result = 0;
                        for c in src.chars() {
                            let x = match c.to_digit(radix) {
                                Some(x) => x,
                                None => return Err(PIE { kind: InvalidDigit }),
                            };
                            result = match result.checked_mul(radix as $T) {
                                Some(result) => result,
                                None => return Err(PIE { kind: Overflow }),
                            };
                            result = match result.checked_add(x as $T) {
                                Some(result) => result,
                                None => return Err(PIE { kind: Overflow }),
                            };
                        }
                        Ok(result)
                    },
                    None => Err(ParseIntError { kind: Empty }),
                }
            }
        }
    }
}
from_str_radix_int_impl! { isize }
from_str_radix_int_impl! { i8 }
from_str_radix_int_impl! { i16 }
from_str_radix_int_impl! { i32 }
from_str_radix_int_impl! { i64 }
from_str_radix_int_impl! { usize }
from_str_radix_int_impl! { u8 }
from_str_radix_int_impl! { u16 }
from_str_radix_int_impl! { u32 }
from_str_radix_int_impl! { u64 }

/// An error which can be returned when parsing an integer.
#[derive(Debug, Clone, PartialEq)]
#[stable(feature = "rust1", since = "1.0.0")]
pub struct ParseIntError { kind: IntErrorKind }

#[derive(Debug, Clone, PartialEq)]
enum IntErrorKind {
    Empty,
    InvalidDigit,
    Overflow,
    Underflow,
}

#[stable(feature = "rust1", since = "1.0.0")]
impl fmt::Display for ParseIntError {
    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
        self.description().fmt(f)
    }
}

#[stable(feature = "rust1", since = "1.0.0")]
impl Error for ParseIntError {
    fn description(&self) -> &str {
        match self.kind {
            IntErrorKind::Empty => "cannot parse integer from empty string",
            IntErrorKind::InvalidDigit => "invalid digit found in string",
            IntErrorKind::Overflow => "number too large to fit in target type",
            IntErrorKind::Underflow => "number too small to fit in target type",
        }
    }
}

/// An error which can be returned when parsing a float.
#[derive(Debug, Clone, PartialEq)]
#[stable(feature = "rust1", since = "1.0.0")]
pub struct ParseFloatError { kind: FloatErrorKind }

#[derive(Debug, Clone, PartialEq)]
enum FloatErrorKind {
    Empty,
    Invalid,
}

#[stable(feature = "rust1", since = "1.0.0")]
impl fmt::Display for ParseFloatError {
    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
        self.description().fmt(f)
    }
}

#[stable(feature = "rust1", since = "1.0.0")]
impl Error for ParseFloatError {
    fn description(&self) -> &str {
        match self.kind {
            FloatErrorKind::Empty => "cannot parse float from empty string",
            FloatErrorKind::Invalid => "invalid float literal",
        }
    }
}