num_traits/

int.rs

use core::ops::{BitAnd, BitOr, BitXor, Not, Shl, Shr};

use crate::bounds::Bounded;
use crate::ops::checked::*;
use crate::ops::saturating::Saturating;
use crate::{Num, NumCast};

/// Generic trait for primitive integers.
///
/// The `PrimInt` trait is an abstraction over the builtin primitive integer types (e.g., `u8`,
/// `u32`, `isize`, `i128`, ...). It inherits the basic numeric traits and extends them with
/// bitwise operators and non-wrapping arithmetic.
///
/// The trait explicitly inherits `Copy`, `Eq`, `Ord`, and `Sized`. The intention is that all
/// types implementing this trait behave like primitive types that are passed by value by default
/// and behave like builtin integers. Furthermore, the types are expected to expose the integer
/// value in binary representation and support bitwise operators. The standard bitwise operations
/// (e.g., bitwise-and, bitwise-or, right-shift, left-shift) are inherited and the trait extends
/// these with introspective queries (e.g., `PrimInt::count_ones()`, `PrimInt::leading_zeros()`),
/// bitwise combinators (e.g., `PrimInt::rotate_left()`), and endianness converters (e.g.,
/// `PrimInt::to_be()`).
///
/// All `PrimInt` types are expected to be fixed-width binary integers. The width can be queried
/// via `T::zero().count_zeros()`. The trait currently lacks a way to query the width at
/// compile-time.
///
/// While a default implementation for all builtin primitive integers is provided, the trait is in
/// no way restricted to these. Other integer types that fulfil the requirements are free to
/// implement the trait was well.
///
/// This trait and many of the method names originate in the unstable `core::num::Int` trait from
/// the rust standard library. The original trait was never stabilized and thus removed from the
/// standard library.
pub trait PrimInt:
    Sized
    + Copy
    + Num
    + NumCast
    + Bounded
    + PartialOrd
    + Ord
    + Eq
    + Not<Output = Self>
    + BitAnd<Output = Self>
    + BitOr<Output = Self>
    + BitXor<Output = Self>
    + Shl<usize, Output = Self>
    + Shr<usize, Output = Self>
    + CheckedAdd<Output = Self>
    + CheckedSub<Output = Self>
    + CheckedMul<Output = Self>
    + CheckedDiv<Output = Self>
    + Saturating
{
    /// Returns the number of ones in the binary representation of `self`.
    ///
    /// # Examples
    ///
    /// ```
    /// use num_traits::PrimInt;
    ///
    /// let n = 0b01001100u8;
    ///
    /// assert_eq!(n.count_ones(), 3);
    /// ```
    fn count_ones(self) -> u32;

    /// Returns the number of zeros in the binary representation of `self`.
    ///
    /// # Examples
    ///
    /// ```
    /// use num_traits::PrimInt;
    ///
    /// let n = 0b01001100u8;
    ///
    /// assert_eq!(n.count_zeros(), 5);
    /// ```
    fn count_zeros(self) -> u32;

    /// Returns the number of leading ones in the binary representation
    /// of `self`.
    ///
    /// # Examples
    ///
    /// ```
    /// use num_traits::PrimInt;
    ///
    /// let n = 0xF00Du16;
    ///
    /// assert_eq!(n.leading_ones(), 4);
    /// ```
    fn leading_ones(self) -> u32 {
        (!self).leading_zeros()
    }

    /// Returns the number of leading zeros in the binary representation
    /// of `self`.
    ///
    /// # Examples
    ///
    /// ```
    /// use num_traits::PrimInt;
    ///
    /// let n = 0b0101000u16;
    ///
    /// assert_eq!(n.leading_zeros(), 10);
    /// ```
    fn leading_zeros(self) -> u32;

    /// Returns the number of trailing ones in the binary representation
    /// of `self`.
    ///
    /// # Examples
    ///
    /// ```
    /// use num_traits::PrimInt;
    ///
    /// let n = 0xBEEFu16;
    ///
    /// assert_eq!(n.trailing_ones(), 4);
    /// ```
    fn trailing_ones(self) -> u32 {
        (!self).trailing_zeros()
    }

    /// Returns the number of trailing zeros in the binary representation
    /// of `self`.
    ///
    /// # Examples
    ///
    /// ```
    /// use num_traits::PrimInt;
    ///
    /// let n = 0b0101000u16;
    ///
    /// assert_eq!(n.trailing_zeros(), 3);
    /// ```
    fn trailing_zeros(self) -> u32;

    /// Shifts the bits to the left by a specified amount, `n`, wrapping
    /// the truncated bits to the end of the resulting integer.
    ///
    /// # Examples
    ///
    /// ```
    /// use num_traits::PrimInt;
    ///
    /// let n = 0x0123456789ABCDEFu64;
    /// let m = 0x3456789ABCDEF012u64;
    ///
    /// assert_eq!(n.rotate_left(12), m);
    /// ```
    fn rotate_left(self, n: u32) -> Self;

    /// Shifts the bits to the right by a specified amount, `n`, wrapping
    /// the truncated bits to the beginning of the resulting integer.
    ///
    /// # Examples
    ///
    /// ```
    /// use num_traits::PrimInt;
    ///
    /// let n = 0x0123456789ABCDEFu64;
    /// let m = 0xDEF0123456789ABCu64;
    ///
    /// assert_eq!(n.rotate_right(12), m);
    /// ```
    fn rotate_right(self, n: u32) -> Self;

    /// Shifts the bits to the left by a specified amount, `n`, filling
    /// zeros in the least significant bits.
    ///
    /// This is bitwise equivalent to signed `Shl`.
    ///
    /// # Examples
    ///
    /// ```
    /// use num_traits::PrimInt;
    ///
    /// let n = 0x0123456789ABCDEFu64;
    /// let m = 0x3456789ABCDEF000u64;
    ///
    /// assert_eq!(n.signed_shl(12), m);
    /// ```
    fn signed_shl(self, n: u32) -> Self;

    /// Shifts the bits to the right by a specified amount, `n`, copying
    /// the "sign bit" in the most significant bits even for unsigned types.
    ///
    /// This is bitwise equivalent to signed `Shr`.
    ///
    /// # Examples
    ///
    /// ```
    /// use num_traits::PrimInt;
    ///
    /// let n = 0xFEDCBA9876543210u64;
    /// let m = 0xFFFFEDCBA9876543u64;
    ///
    /// assert_eq!(n.signed_shr(12), m);
    /// ```
    fn signed_shr(self, n: u32) -> Self;

    /// Shifts the bits to the left by a specified amount, `n`, filling
    /// zeros in the least significant bits.
    ///
    /// This is bitwise equivalent to unsigned `Shl`.
    ///
    /// # Examples
    ///
    /// ```
    /// use num_traits::PrimInt;
    ///
    /// let n = 0x0123456789ABCDEFi64;
    /// let m = 0x3456789ABCDEF000i64;
    ///
    /// assert_eq!(n.unsigned_shl(12), m);
    /// ```
    fn unsigned_shl(self, n: u32) -> Self;

    /// Shifts the bits to the right by a specified amount, `n`, filling
    /// zeros in the most significant bits.
    ///
    /// This is bitwise equivalent to unsigned `Shr`.
    ///
    /// # Examples
    ///
    /// ```
    /// use num_traits::PrimInt;
    ///
    /// let n = -8i8; // 0b11111000
    /// let m = 62i8; // 0b00111110
    ///
    /// assert_eq!(n.unsigned_shr(2), m);
    /// ```
    fn unsigned_shr(self, n: u32) -> Self;

    /// Reverses the byte order of the integer.
    ///
    /// # Examples
    ///
    /// ```
    /// use num_traits::PrimInt;
    ///
    /// let n = 0x0123456789ABCDEFu64;
    /// let m = 0xEFCDAB8967452301u64;
    ///
    /// assert_eq!(n.swap_bytes(), m);
    /// ```
    fn swap_bytes(self) -> Self;

    /// Reverses the order of bits in the integer.
    ///
    /// The least significant bit becomes the most significant bit, second least-significant bit
    /// becomes second most-significant bit, etc.
    ///
    /// # Examples
    ///
    /// ```
    /// use num_traits::PrimInt;
    ///
    /// let n = 0x12345678u32;
    /// let m = 0x1e6a2c48u32;
    ///
    /// assert_eq!(n.reverse_bits(), m);
    /// assert_eq!(0u32.reverse_bits(), 0);
    /// ```
    fn reverse_bits(self) -> Self {
        reverse_bits_fallback(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 num_traits::PrimInt;
    ///
    /// let n = 0x0123456789ABCDEFu64;
    ///
    /// if cfg!(target_endian = "big") {
    ///     assert_eq!(u64::from_be(n), n)
    /// } else {
    ///     assert_eq!(u64::from_be(n), n.swap_bytes())
    /// }
    /// ```
    fn from_be(x: Self) -> Self;

    /// 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 num_traits::PrimInt;
    ///
    /// let n = 0x0123456789ABCDEFu64;
    ///
    /// if cfg!(target_endian = "little") {
    ///     assert_eq!(u64::from_le(n), n)
    /// } else {
    ///     assert_eq!(u64::from_le(n), n.swap_bytes())
    /// }
    /// ```
    fn from_le(x: Self) -> Self;

    /// 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 num_traits::PrimInt;
    ///
    /// let n = 0x0123456789ABCDEFu64;
    ///
    /// if cfg!(target_endian = "big") {
    ///     assert_eq!(n.to_be(), n)
    /// } else {
    ///     assert_eq!(n.to_be(), n.swap_bytes())
    /// }
    /// ```
    fn to_be(self) -> Self;

    /// 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 num_traits::PrimInt;
    ///
    /// let n = 0x0123456789ABCDEFu64;
    ///
    /// if cfg!(target_endian = "little") {
    ///     assert_eq!(n.to_le(), n)
    /// } else {
    ///     assert_eq!(n.to_le(), n.swap_bytes())
    /// }
    /// ```
    fn to_le(self) -> Self;

    /// Raises self to the power of `exp`, using exponentiation by squaring.
    ///
    /// # Examples
    ///
    /// ```
    /// use num_traits::PrimInt;
    ///
    /// assert_eq!(2i32.pow(4), 16);
    /// ```
    fn pow(self, exp: u32) -> Self;
}

fn one_per_byte<P: PrimInt>() -> P {
    // i8, u8: return 0x01
    // i16, u16: return 0x0101 = (0x01 << 8) | 0x01
    // i32, u32: return 0x01010101 = (0x0101 << 16) | 0x0101
    // ...
    let mut ret = P::one();
    let mut shift = 8;
    let mut b = ret.count_zeros() >> 3;
    while b != 0 {
        ret = (ret << shift) | ret;
        shift <<= 1;
        b >>= 1;
    }
    ret
}

fn reverse_bits_fallback<P: PrimInt>(i: P) -> P {
    let rep_01: P = one_per_byte();
    let rep_03 = (rep_01 << 1) | rep_01;
    let rep_05 = (rep_01 << 2) | rep_01;
    let rep_0f = (rep_03 << 2) | rep_03;
    let rep_33 = (rep_03 << 4) | rep_03;
    let rep_55 = (rep_05 << 4) | rep_05;

    // code above only used to determine rep_0f, rep_33, rep_55;
    // optimizer should be able to do it in compile time
    let mut ret = i.swap_bytes();
    ret = ((ret & rep_0f) << 4) | ((ret >> 4) & rep_0f);
    ret = ((ret & rep_33) << 2) | ((ret >> 2) & rep_33);
    ret = ((ret & rep_55) << 1) | ((ret >> 1) & rep_55);
    ret
}

macro_rules! prim_int_impl {
    ($T:ty, $S:ty, $U:ty) => {
        impl PrimInt for $T {
            #[inline]
            fn count_ones(self) -> u32 {
                <$T>::count_ones(self)
            }

            #[inline]
            fn count_zeros(self) -> u32 {
                <$T>::count_zeros(self)
            }

            #[cfg(has_leading_trailing_ones)]
            #[inline]
            fn leading_ones(self) -> u32 {
                <$T>::leading_ones(self)
            }

            #[inline]
            fn leading_zeros(self) -> u32 {
                <$T>::leading_zeros(self)
            }

            #[cfg(has_leading_trailing_ones)]
            #[inline]
            fn trailing_ones(self) -> u32 {
                <$T>::trailing_ones(self)
            }

            #[inline]
            fn trailing_zeros(self) -> u32 {
                <$T>::trailing_zeros(self)
            }

            #[inline]
            fn rotate_left(self, n: u32) -> Self {
                <$T>::rotate_left(self, n)
            }

            #[inline]
            fn rotate_right(self, n: u32) -> Self {
                <$T>::rotate_right(self, n)
            }

            #[inline]
            fn signed_shl(self, n: u32) -> Self {
                ((self as $S) << n) as $T
            }

            #[inline]
            fn signed_shr(self, n: u32) -> Self {
                ((self as $S) >> n) as $T
            }

            #[inline]
            fn unsigned_shl(self, n: u32) -> Self {
                ((self as $U) << n) as $T
            }

            #[inline]
            fn unsigned_shr(self, n: u32) -> Self {
                ((self as $U) >> n) as $T
            }

            #[inline]
            fn swap_bytes(self) -> Self {
                <$T>::swap_bytes(self)
            }

            #[cfg(has_reverse_bits)]
            #[inline]
            fn reverse_bits(self) -> Self {
                <$T>::reverse_bits(self)
            }

            #[inline]
            fn from_be(x: Self) -> Self {
                <$T>::from_be(x)
            }

            #[inline]
            fn from_le(x: Self) -> Self {
                <$T>::from_le(x)
            }

            #[inline]
            fn to_be(self) -> Self {
                <$T>::to_be(self)
            }

            #[inline]
            fn to_le(self) -> Self {
                <$T>::to_le(self)
            }

            #[inline]
            fn pow(self, exp: u32) -> Self {
                <$T>::pow(self, exp)
            }
        }
    };
}

// prim_int_impl!(type, signed, unsigned);
prim_int_impl!(u8, i8, u8);
prim_int_impl!(u16, i16, u16);
prim_int_impl!(u32, i32, u32);
prim_int_impl!(u64, i64, u64);
prim_int_impl!(u128, i128, u128);
prim_int_impl!(usize, isize, usize);
prim_int_impl!(i8, i8, u8);
prim_int_impl!(i16, i16, u16);
prim_int_impl!(i32, i32, u32);
prim_int_impl!(i64, i64, u64);
prim_int_impl!(i128, i128, u128);
prim_int_impl!(isize, isize, usize);

#[cfg(test)]
mod tests {
    use crate::int::PrimInt;

    #[test]
    pub fn reverse_bits() {
        use core::{i16, i32, i64, i8};

        assert_eq!(
            PrimInt::reverse_bits(0x0123_4567_89ab_cdefu64),
            0xf7b3_d591_e6a2_c480
        );

        assert_eq!(PrimInt::reverse_bits(0i8), 0);
        assert_eq!(PrimInt::reverse_bits(-1i8), -1);
        assert_eq!(PrimInt::reverse_bits(1i8), i8::MIN);
        assert_eq!(PrimInt::reverse_bits(i8::MIN), 1);
        assert_eq!(PrimInt::reverse_bits(-2i8), i8::MAX);
        assert_eq!(PrimInt::reverse_bits(i8::MAX), -2);

        assert_eq!(PrimInt::reverse_bits(0i16), 0);
        assert_eq!(PrimInt::reverse_bits(-1i16), -1);
        assert_eq!(PrimInt::reverse_bits(1i16), i16::MIN);
        assert_eq!(PrimInt::reverse_bits(i16::MIN), 1);
        assert_eq!(PrimInt::reverse_bits(-2i16), i16::MAX);
        assert_eq!(PrimInt::reverse_bits(i16::MAX), -2);

        assert_eq!(PrimInt::reverse_bits(0i32), 0);
        assert_eq!(PrimInt::reverse_bits(-1i32), -1);
        assert_eq!(PrimInt::reverse_bits(1i32), i32::MIN);
        assert_eq!(PrimInt::reverse_bits(i32::MIN), 1);
        assert_eq!(PrimInt::reverse_bits(-2i32), i32::MAX);
        assert_eq!(PrimInt::reverse_bits(i32::MAX), -2);

        assert_eq!(PrimInt::reverse_bits(0i64), 0);
        assert_eq!(PrimInt::reverse_bits(-1i64), -1);
        assert_eq!(PrimInt::reverse_bits(1i64), i64::MIN);
        assert_eq!(PrimInt::reverse_bits(i64::MIN), 1);
        assert_eq!(PrimInt::reverse_bits(-2i64), i64::MAX);
        assert_eq!(PrimInt::reverse_bits(i64::MAX), -2);
    }

    #[test]
    pub fn reverse_bits_i128() {
        use core::i128;

        assert_eq!(PrimInt::reverse_bits(0i128), 0);
        assert_eq!(PrimInt::reverse_bits(-1i128), -1);
        assert_eq!(PrimInt::reverse_bits(1i128), i128::MIN);
        assert_eq!(PrimInt::reverse_bits(i128::MIN), 1);
        assert_eq!(PrimInt::reverse_bits(-2i128), i128::MAX);
        assert_eq!(PrimInt::reverse_bits(i128::MAX), -2);
    }
}