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Integer

deep_causality_num

Trait Integer

pub trait Integer:
    Ring
    + Ord
    + Copy
    + Sized
    + BitAnd<Output = Self>
    + BitOr<Output = Self>
    + BitXor<Output = Self>
    + Not<Output = Self>
    + Shl<u32, Output = Self>
    + Shr<u32, Output = Self> {
    const MIN: Self;
    const MAX: Self;
    const BITS: u32;
Show 23 methods
    // Required methods
    fn count_ones(self) -> u32;
    fn count_zeros(self) -> u32;
    fn leading_zeros(self) -> u32;
    fn trailing_zeros(self) -> u32;
    fn swap_bytes(self) -> Self;
    fn from_be(x: Self) -> Self;
    fn from_le(x: Self) -> Self;
    fn to_be(self) -> Self;
    fn to_le(self) -> Self;
    fn checked_add(self, rhs: Self) -> Option<Self>;
    fn checked_sub(self, rhs: Self) -> Option<Self>;
    fn checked_mul(self, rhs: Self) -> Option<Self>;
    fn checked_div(self, rhs: Self) -> Option<Self>;
    fn checked_rem(self, rhs: Self) -> Option<Self>;
    fn saturating_add(self, rhs: Self) -> Self;
    fn saturating_sub(self, rhs: Self) -> Self;
    fn saturating_mul(self, rhs: Self) -> Self;
    fn wrapping_add(self, rhs: Self) -> Self;
    fn wrapping_sub(self, rhs: Self) -> Self;
    fn wrapping_mul(self, rhs: Self) -> Self;
    fn pow(self, exp: u32) -> Self;
    fn div_euclid(self, rhs: Self) -> Self;
    fn rem_euclid(self, rhs: Self) -> Self;
}

Expand description

A trait for primitive integer types.

This trait abstracts over both signed and unsigned integers, providing common operations and constants. It extends Ring from the algebraic hierarchy, reflecting that integers form a ring under addition and multiplication.

§Mathematical Background

The integers $\mathbb{Z}$ form a Euclidean Domain:

A commutative ring with identity
Division with remainder is well-defined: $a = bq + r$ where $0 \le r < |b|$
This enables the Euclidean algorithm for GCD

Fixed-width integers in computers are technically $\mathbb{Z}/2^n\mathbb{Z}$ (integers modulo $2^n$), but overflow behavior varies by build configuration.

Required Associated Constants§

const MIN: Self

The minimum value representable by this type.

const MAX: Self

The maximum value representable by this type.

const BITS: u32

The size of this type in bits.

Required Methods§

fn count_ones(self) -> u32

Returns the number of ones in the binary representation.

fn count_zeros(self) -> u32

Returns the number of zeros in the binary representation.

fn leading_zeros(self) -> u32

Returns the number of leading zeros in the binary representation.

fn trailing_zeros(self) -> u32

Returns the number of trailing zeros in the binary representation.

fn swap_bytes(self) -> Self

Reverses the byte order of the integer.

fn from_be(x: Self) -> Self

Converts from big-endian to native byte order.

fn from_le(x: Self) -> Self

Converts from little-endian to native byte order.

fn to_be(self) -> Self

Converts to big-endian byte order.

fn to_le(self) -> Self

Converts to little-endian byte order.

fn checked_add(self, rhs: Self) -> Option<Self>

Checked addition. Returns None on overflow.

fn checked_sub(self, rhs: Self) -> Option<Self>

Checked subtraction. Returns None on underflow.

fn checked_mul(self, rhs: Self) -> Option<Self>

Checked multiplication. Returns None on overflow.

fn checked_div(self, rhs: Self) -> Option<Self>

Checked division. Returns None if rhs == 0.

fn checked_rem(self, rhs: Self) -> Option<Self>

Checked remainder. Returns None if rhs == 0.

fn saturating_add(self, rhs: Self) -> Self

Saturating addition. Clamps at MAX or MIN.

fn saturating_sub(self, rhs: Self) -> Self

Saturating subtraction. Clamps at MAX or MIN.

fn saturating_mul(self, rhs: Self) -> Self

Saturating multiplication. Clamps at MAX or MIN.

fn wrapping_add(self, rhs: Self) -> Self

Wrapping addition. Wraps around on overflow.

fn wrapping_sub(self, rhs: Self) -> Self

Wrapping subtraction. Wraps around on underflow.

fn wrapping_mul(self, rhs: Self) -> Self

Wrapping multiplication. Wraps around on overflow.

fn pow(self, exp: u32) -> Self

Raises self to the power exp, using exponentiation by squaring.

fn div_euclid(self, rhs: Self) -> Self

Calculates the quotient of Euclidean division.

fn rem_euclid(self, rhs: Self) -> Self

Calculates the remainder of Euclidean division.

The result satisfies 0 <= r < |rhs| for all inputs.

Dyn Compatibility§

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementations on Foreign Types§

impl Integer for i8

const MIN: Self = i8::MIN

const MAX: Self = i8::MAX

const BITS: u32 = i8::BITS

fn count_ones(self) -> u32

fn count_zeros(self) -> u32

fn leading_zeros(self) -> u32

fn trailing_zeros(self) -> u32

fn swap_bytes(self) -> Self

fn from_be(x: Self) -> Self

fn from_le(x: Self) -> Self

fn to_be(self) -> Self

fn to_le(self) -> Self

fn checked_add(self, rhs: Self) -> Option<Self>

fn checked_sub(self, rhs: Self) -> Option<Self>

fn checked_mul(self, rhs: Self) -> Option<Self>

fn checked_div(self, rhs: Self) -> Option<Self>

fn checked_rem(self, rhs: Self) -> Option<Self>

fn saturating_add(self, rhs: Self) -> Self

fn saturating_sub(self, rhs: Self) -> Self

fn saturating_mul(self, rhs: Self) -> Self

fn wrapping_add(self, rhs: Self) -> Self

fn wrapping_sub(self, rhs: Self) -> Self

fn wrapping_mul(self, rhs: Self) -> Self

fn pow(self, exp: u32) -> Self

fn div_euclid(self, rhs: Self) -> Self

fn rem_euclid(self, rhs: Self) -> Self

impl Integer for i16

const MIN: Self = i16::MIN

const MAX: Self = i16::MAX

const BITS: u32 = i16::BITS

fn count_ones(self) -> u32

fn count_zeros(self) -> u32

fn leading_zeros(self) -> u32

fn trailing_zeros(self) -> u32

fn swap_bytes(self) -> Self

fn from_be(x: Self) -> Self

fn from_le(x: Self) -> Self

fn to_be(self) -> Self

fn to_le(self) -> Self

fn checked_add(self, rhs: Self) -> Option<Self>

fn checked_sub(self, rhs: Self) -> Option<Self>

fn checked_mul(self, rhs: Self) -> Option<Self>

fn checked_div(self, rhs: Self) -> Option<Self>

fn checked_rem(self, rhs: Self) -> Option<Self>

fn saturating_add(self, rhs: Self) -> Self

fn saturating_sub(self, rhs: Self) -> Self

fn saturating_mul(self, rhs: Self) -> Self

fn wrapping_add(self, rhs: Self) -> Self

fn wrapping_sub(self, rhs: Self) -> Self

fn wrapping_mul(self, rhs: Self) -> Self

fn pow(self, exp: u32) -> Self

fn div_euclid(self, rhs: Self) -> Self

fn rem_euclid(self, rhs: Self) -> Self

impl Integer for i32

const MIN: Self = i32::MIN

const MAX: Self = i32::MAX

const BITS: u32 = i32::BITS

fn count_ones(self) -> u32

fn count_zeros(self) -> u32

fn leading_zeros(self) -> u32

fn trailing_zeros(self) -> u32

fn swap_bytes(self) -> Self

fn from_be(x: Self) -> Self

fn from_le(x: Self) -> Self

fn to_be(self) -> Self

fn to_le(self) -> Self

fn checked_add(self, rhs: Self) -> Option<Self>

fn checked_sub(self, rhs: Self) -> Option<Self>

fn checked_mul(self, rhs: Self) -> Option<Self>

fn checked_div(self, rhs: Self) -> Option<Self>

fn checked_rem(self, rhs: Self) -> Option<Self>

fn saturating_add(self, rhs: Self) -> Self

fn saturating_sub(self, rhs: Self) -> Self

fn saturating_mul(self, rhs: Self) -> Self

fn wrapping_add(self, rhs: Self) -> Self

fn wrapping_sub(self, rhs: Self) -> Self

fn wrapping_mul(self, rhs: Self) -> Self

fn pow(self, exp: u32) -> Self

fn div_euclid(self, rhs: Self) -> Self

fn rem_euclid(self, rhs: Self) -> Self

impl Integer for i64

const MIN: Self = i64::MIN

const MAX: Self = i64::MAX

const BITS: u32 = i64::BITS

fn count_ones(self) -> u32

fn count_zeros(self) -> u32

fn leading_zeros(self) -> u32

fn trailing_zeros(self) -> u32

fn swap_bytes(self) -> Self

fn from_be(x: Self) -> Self

fn from_le(x: Self) -> Self

fn to_be(self) -> Self

fn to_le(self) -> Self

fn checked_add(self, rhs: Self) -> Option<Self>

fn checked_sub(self, rhs: Self) -> Option<Self>

fn checked_mul(self, rhs: Self) -> Option<Self>

fn checked_div(self, rhs: Self) -> Option<Self>

fn checked_rem(self, rhs: Self) -> Option<Self>

fn saturating_add(self, rhs: Self) -> Self

fn saturating_sub(self, rhs: Self) -> Self

fn saturating_mul(self, rhs: Self) -> Self

fn wrapping_add(self, rhs: Self) -> Self

fn wrapping_sub(self, rhs: Self) -> Self

fn wrapping_mul(self, rhs: Self) -> Self

fn pow(self, exp: u32) -> Self

fn div_euclid(self, rhs: Self) -> Self

fn rem_euclid(self, rhs: Self) -> Self

impl Integer for i128

const MIN: Self = i128::MIN

const MAX: Self = i128::MAX

const BITS: u32 = i128::BITS

fn count_ones(self) -> u32

fn count_zeros(self) -> u32

fn leading_zeros(self) -> u32

fn trailing_zeros(self) -> u32

fn swap_bytes(self) -> Self

fn from_be(x: Self) -> Self

fn from_le(x: Self) -> Self

fn to_be(self) -> Self

fn to_le(self) -> Self

fn checked_add(self, rhs: Self) -> Option<Self>

fn checked_sub(self, rhs: Self) -> Option<Self>

fn checked_mul(self, rhs: Self) -> Option<Self>

fn checked_div(self, rhs: Self) -> Option<Self>

fn checked_rem(self, rhs: Self) -> Option<Self>

fn saturating_add(self, rhs: Self) -> Self

fn saturating_sub(self, rhs: Self) -> Self

fn saturating_mul(self, rhs: Self) -> Self

fn wrapping_add(self, rhs: Self) -> Self

fn wrapping_sub(self, rhs: Self) -> Self

fn wrapping_mul(self, rhs: Self) -> Self

fn pow(self, exp: u32) -> Self

fn div_euclid(self, rhs: Self) -> Self

fn rem_euclid(self, rhs: Self) -> Self

impl Integer for isize

const MIN: Self = isize::MIN

const MAX: Self = isize::MAX

const BITS: u32 = isize::BITS

fn count_ones(self) -> u32

fn count_zeros(self) -> u32

fn leading_zeros(self) -> u32

fn trailing_zeros(self) -> u32

fn swap_bytes(self) -> Self

fn from_be(x: Self) -> Self

fn from_le(x: Self) -> Self

fn to_be(self) -> Self

fn to_le(self) -> Self

fn checked_add(self, rhs: Self) -> Option<Self>

fn checked_sub(self, rhs: Self) -> Option<Self>

fn checked_mul(self, rhs: Self) -> Option<Self>

fn checked_div(self, rhs: Self) -> Option<Self>

fn checked_rem(self, rhs: Self) -> Option<Self>

fn saturating_add(self, rhs: Self) -> Self

fn saturating_sub(self, rhs: Self) -> Self

fn saturating_mul(self, rhs: Self) -> Self

fn wrapping_add(self, rhs: Self) -> Self

fn wrapping_sub(self, rhs: Self) -> Self

fn wrapping_mul(self, rhs: Self) -> Self

fn pow(self, exp: u32) -> Self

fn div_euclid(self, rhs: Self) -> Self

fn rem_euclid(self, rhs: Self) -> Self

impl Integer for u8

const MIN: Self = u8::MIN

const MAX: Self = u8::MAX

const BITS: u32 = u8::BITS

fn count_ones(self) -> u32

fn count_zeros(self) -> u32

fn leading_zeros(self) -> u32

fn trailing_zeros(self) -> u32

fn swap_bytes(self) -> Self

fn from_be(x: Self) -> Self

fn from_le(x: Self) -> Self

fn to_be(self) -> Self

fn to_le(self) -> Self

fn checked_add(self, rhs: Self) -> Option<Self>

fn checked_sub(self, rhs: Self) -> Option<Self>

fn checked_mul(self, rhs: Self) -> Option<Self>

fn checked_div(self, rhs: Self) -> Option<Self>

fn checked_rem(self, rhs: Self) -> Option<Self>

fn saturating_add(self, rhs: Self) -> Self

fn saturating_sub(self, rhs: Self) -> Self

fn saturating_mul(self, rhs: Self) -> Self

fn wrapping_add(self, rhs: Self) -> Self

fn wrapping_sub(self, rhs: Self) -> Self

fn wrapping_mul(self, rhs: Self) -> Self

fn pow(self, exp: u32) -> Self

fn div_euclid(self, rhs: Self) -> Self

fn rem_euclid(self, rhs: Self) -> Self

impl Integer for u16

const MIN: Self = u16::MIN

const MAX: Self = u16::MAX

const BITS: u32 = u16::BITS

fn count_ones(self) -> u32

fn count_zeros(self) -> u32

fn leading_zeros(self) -> u32

fn trailing_zeros(self) -> u32

fn swap_bytes(self) -> Self

fn from_be(x: Self) -> Self

fn from_le(x: Self) -> Self

fn to_be(self) -> Self

fn to_le(self) -> Self

fn checked_add(self, rhs: Self) -> Option<Self>

fn checked_sub(self, rhs: Self) -> Option<Self>

fn checked_mul(self, rhs: Self) -> Option<Self>

fn checked_div(self, rhs: Self) -> Option<Self>

fn checked_rem(self, rhs: Self) -> Option<Self>

fn saturating_add(self, rhs: Self) -> Self

fn saturating_sub(self, rhs: Self) -> Self

fn saturating_mul(self, rhs: Self) -> Self

fn wrapping_add(self, rhs: Self) -> Self

fn wrapping_sub(self, rhs: Self) -> Self

fn wrapping_mul(self, rhs: Self) -> Self

fn pow(self, exp: u32) -> Self

fn div_euclid(self, rhs: Self) -> Self

fn rem_euclid(self, rhs: Self) -> Self

impl Integer for u32

const MIN: Self = u32::MIN

const MAX: Self = u32::MAX

const BITS: u32 = u32::BITS

fn count_ones(self) -> u32

fn count_zeros(self) -> u32

fn leading_zeros(self) -> u32

fn trailing_zeros(self) -> u32

fn swap_bytes(self) -> Self

fn from_be(x: Self) -> Self

fn from_le(x: Self) -> Self

fn to_be(self) -> Self

fn to_le(self) -> Self

fn checked_add(self, rhs: Self) -> Option<Self>

fn checked_sub(self, rhs: Self) -> Option<Self>

fn checked_mul(self, rhs: Self) -> Option<Self>

fn checked_div(self, rhs: Self) -> Option<Self>

fn checked_rem(self, rhs: Self) -> Option<Self>

fn saturating_add(self, rhs: Self) -> Self

fn saturating_sub(self, rhs: Self) -> Self

fn saturating_mul(self, rhs: Self) -> Self

fn wrapping_add(self, rhs: Self) -> Self

fn wrapping_sub(self, rhs: Self) -> Self

fn wrapping_mul(self, rhs: Self) -> Self

fn pow(self, exp: u32) -> Self

fn div_euclid(self, rhs: Self) -> Self

fn rem_euclid(self, rhs: Self) -> Self

impl Integer for u64

const MIN: Self = u64::MIN

const MAX: Self = u64::MAX

const BITS: u32 = u64::BITS

fn count_ones(self) -> u32

fn count_zeros(self) -> u32

fn leading_zeros(self) -> u32

fn trailing_zeros(self) -> u32

fn swap_bytes(self) -> Self

fn from_be(x: Self) -> Self

fn from_le(x: Self) -> Self

fn to_be(self) -> Self

fn to_le(self) -> Self

fn checked_add(self, rhs: Self) -> Option<Self>

fn checked_sub(self, rhs: Self) -> Option<Self>

fn checked_mul(self, rhs: Self) -> Option<Self>

fn checked_div(self, rhs: Self) -> Option<Self>

fn checked_rem(self, rhs: Self) -> Option<Self>

fn saturating_add(self, rhs: Self) -> Self

fn saturating_sub(self, rhs: Self) -> Self

fn saturating_mul(self, rhs: Self) -> Self

fn wrapping_add(self, rhs: Self) -> Self

fn wrapping_sub(self, rhs: Self) -> Self

fn wrapping_mul(self, rhs: Self) -> Self

fn pow(self, exp: u32) -> Self

fn div_euclid(self, rhs: Self) -> Self

fn rem_euclid(self, rhs: Self) -> Self

impl Integer for u128

const MIN: Self = u128::MIN

const MAX: Self = u128::MAX

const BITS: u32 = u128::BITS

fn count_ones(self) -> u32

fn count_zeros(self) -> u32

fn leading_zeros(self) -> u32

fn trailing_zeros(self) -> u32

fn swap_bytes(self) -> Self

fn from_be(x: Self) -> Self

fn from_le(x: Self) -> Self

fn to_be(self) -> Self

fn to_le(self) -> Self

fn checked_add(self, rhs: Self) -> Option<Self>

fn checked_sub(self, rhs: Self) -> Option<Self>

fn checked_mul(self, rhs: Self) -> Option<Self>

fn checked_div(self, rhs: Self) -> Option<Self>

fn checked_rem(self, rhs: Self) -> Option<Self>

fn saturating_add(self, rhs: Self) -> Self

fn saturating_sub(self, rhs: Self) -> Self

fn saturating_mul(self, rhs: Self) -> Self

fn wrapping_add(self, rhs: Self) -> Self

fn wrapping_sub(self, rhs: Self) -> Self

fn wrapping_mul(self, rhs: Self) -> Self

fn pow(self, exp: u32) -> Self

fn div_euclid(self, rhs: Self) -> Self

fn rem_euclid(self, rhs: Self) -> Self

impl Integer for usize

const MIN: Self = usize::MIN

const MAX: Self = usize::MAX

const BITS: u32 = usize::BITS

fn count_ones(self) -> u32

fn count_zeros(self) -> u32

fn leading_zeros(self) -> u32

fn trailing_zeros(self) -> u32

fn swap_bytes(self) -> Self

fn from_be(x: Self) -> Self

fn from_le(x: Self) -> Self

fn to_be(self) -> Self

fn to_le(self) -> Self

fn checked_add(self, rhs: Self) -> Option<Self>

fn checked_sub(self, rhs: Self) -> Option<Self>

fn checked_mul(self, rhs: Self) -> Option<Self>

fn checked_div(self, rhs: Self) -> Option<Self>

fn checked_rem(self, rhs: Self) -> Option<Self>

fn saturating_add(self, rhs: Self) -> Self

fn saturating_sub(self, rhs: Self) -> Self

fn saturating_mul(self, rhs: Self) -> Self

fn wrapping_add(self, rhs: Self) -> Self

fn wrapping_sub(self, rhs: Self) -> Self

fn wrapping_mul(self, rhs: Self) -> Self

fn pow(self, exp: u32) -> Self

fn div_euclid(self, rhs: Self) -> Self

fn rem_euclid(self, rhs: Self) -> Self

Implementors§