Struct XorAnd

pub struct XorAnd<T>(/* private fields */);

XorとAndの半環

Implementations

impl<T> XorAnd<T>

pub fn new() -> Self

XorAndを返す。

Trait Implementations

impl<T: Clone> Clone for XorAnd<T>

fn clone(&self) -> XorAnd<T>

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<T: Debug> Debug for XorAnd<T>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T: Default> Default for XorAnd<T>

fn default() -> XorAnd<T>

Returns the “default value” for a type.

impl<T: Hash> Hash for XorAnd<T>

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl<T: Ord> Ord for XorAnd<T>

fn cmp(&self, other: &XorAnd<T>) -> Ordering

This method returns an Ordering between self and other.

fn max(self, other: Self) -> Self

where Self: Sized,

Compares and returns the maximum of two values.

fn min(self, other: Self) -> Self

where Self: Sized,

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

where Self: Sized,

Restrict a value to a certain interval.

impl<T: PartialEq> PartialEq for XorAnd<T>

fn eq(&self, other: &XorAnd<T>) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<T: PartialOrd> PartialOrd for XorAnd<T>

fn partial_cmp(&self, other: &XorAnd<T>) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

fn lt(&self, other: &Rhs) -> bool

Tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &Rhs) -> bool

Tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, other: &Rhs) -> bool

Tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &Rhs) -> bool

Tests greater than or equal to (for self and other) and is used by the >= operator.

impl Ring for XorAnd<u128>

fn neg(&self, a: Self::Element) -> Self::Element

加法の逆元 $-a$

fn sub(&self, a: Self::Element, b: Self::Element) -> Self::Element

$a \oplus (-b)$

impl Ring for XorAnd<u16>

fn neg(&self, a: Self::Element) -> Self::Element

加法の逆元 $-a$

fn sub(&self, a: Self::Element, b: Self::Element) -> Self::Element

$a \oplus (-b)$

impl Ring for XorAnd<u32>

fn neg(&self, a: Self::Element) -> Self::Element

加法の逆元 $-a$

fn sub(&self, a: Self::Element, b: Self::Element) -> Self::Element

$a \oplus (-b)$

impl Ring for XorAnd<u64>

fn neg(&self, a: Self::Element) -> Self::Element

加法の逆元 $-a$

fn sub(&self, a: Self::Element, b: Self::Element) -> Self::Element

$a \oplus (-b)$

impl Ring for XorAnd<u8>

fn neg(&self, a: Self::Element) -> Self::Element

加法の逆元 $-a$

fn sub(&self, a: Self::Element, b: Self::Element) -> Self::Element

$a \oplus (-b)$

impl Ring for XorAnd<usize>

fn neg(&self, a: Self::Element) -> Self::Element

加法の逆元 $-a$

fn sub(&self, a: Self::Element, b: Self::Element) -> Self::Element

$a \oplus (-b)$

impl Semiring for XorAnd<u128>

type Element = u128

集合の元

fn zero(&self) -> Self::Element

加法の単位元

fn one(&self) -> Self::Element

乗法の単位元

fn add(&self, a: Self::Element, b: Self::Element) -> Self::Element

加法$\oplus$

fn mul(&self, a: Self::Element, b: Self::Element) -> Self::Element

乗法$\otimes$

fn times(&self, a: Self::Element, n: u64) -> Self::Element

$\underbrace{a \oplus a \oplus \dots \oplus a \oplus a}_{n}$を計算する。

impl Semiring for XorAnd<u16>

type Element = u16

集合の元

fn zero(&self) -> Self::Element

加法の単位元

fn one(&self) -> Self::Element

乗法の単位元

fn add(&self, a: Self::Element, b: Self::Element) -> Self::Element

加法$\oplus$

fn mul(&self, a: Self::Element, b: Self::Element) -> Self::Element

乗法$\otimes$

fn times(&self, a: Self::Element, n: u64) -> Self::Element

$\underbrace{a \oplus a \oplus \dots \oplus a \oplus a}_{n}$を計算する。

impl Semiring for XorAnd<u32>

type Element = u32

集合の元

fn zero(&self) -> Self::Element

加法の単位元

fn one(&self) -> Self::Element

乗法の単位元

fn add(&self, a: Self::Element, b: Self::Element) -> Self::Element

加法$\oplus$

fn mul(&self, a: Self::Element, b: Self::Element) -> Self::Element

乗法$\otimes$

fn times(&self, a: Self::Element, n: u64) -> Self::Element

$\underbrace{a \oplus a \oplus \dots \oplus a \oplus a}_{n}$を計算する。

impl Semiring for XorAnd<u64>

type Element = u64

集合の元

fn zero(&self) -> Self::Element

加法の単位元

fn one(&self) -> Self::Element

乗法の単位元

fn add(&self, a: Self::Element, b: Self::Element) -> Self::Element

加法$\oplus$

fn mul(&self, a: Self::Element, b: Self::Element) -> Self::Element

乗法$\otimes$

fn times(&self, a: Self::Element, n: u64) -> Self::Element

$\underbrace{a \oplus a \oplus \dots \oplus a \oplus a}_{n}$を計算する。

impl Semiring for XorAnd<u8>

type Element = u8

集合の元

fn zero(&self) -> Self::Element

加法の単位元

fn one(&self) -> Self::Element

乗法の単位元

fn add(&self, a: Self::Element, b: Self::Element) -> Self::Element

加法$\oplus$

fn mul(&self, a: Self::Element, b: Self::Element) -> Self::Element

乗法$\otimes$

fn times(&self, a: Self::Element, n: u64) -> Self::Element

$\underbrace{a \oplus a \oplus \dots \oplus a \oplus a}_{n}$を計算する。

impl Semiring for XorAnd<usize>

type Element = usize

集合の元

fn zero(&self) -> Self::Element

加法の単位元

fn one(&self) -> Self::Element

乗法の単位元

fn add(&self, a: Self::Element, b: Self::Element) -> Self::Element

加法$\oplus$

fn mul(&self, a: Self::Element, b: Self::Element) -> Self::Element

乗法$\otimes$

fn times(&self, a: Self::Element, n: u64) -> Self::Element

$\underbrace{a \oplus a \oplus \dots \oplus a \oplus a}_{n}$を計算する。

impl<T: Copy> Copy for XorAnd<T>

impl<T: Eq> Eq for XorAnd<T>

impl<T> StructuralPartialEq for XorAnd<T>