Struct HalfInteger 

pub struct HalfInteger { /* private fields */ }

Half-integer: numbers of the form n/2 where n ∈ ℤ

E₈ root coordinates are half-integers (elements of ℤ ∪ ½ℤ). This type represents them exactly as numerator / 2.

Invariant

The denominator is always 2 (enforced by construction).

Examples

use atlas_embeddings::arithmetic::HalfInteger;

let x = HalfInteger::new(1);  // 1/2
let y = HalfInteger::new(3);  // 3/2
let sum = x + y;               // 2 = 4/2

assert_eq!(sum.numerator(), 4);

Implementations

impl HalfInteger

pub const fn new(numerator: i64) -> Self

Create a half-integer from a numerator (denominator is always 2)

Examples

use atlas_embeddings::arithmetic::HalfInteger;

let half = HalfInteger::new(1);    // 1/2
let one = HalfInteger::new(2);     // 2/2 = 1
let neg_half = HalfInteger::new(-1); // -1/2

pub const fn from_integer(n: i64) -> Self

Create from an integer (multiply by 2 internally)

Examples

use atlas_embeddings::arithmetic::HalfInteger;

let two = HalfInteger::from_integer(1);  // 2/2 = 1
assert_eq!(two.numerator(), 2);

pub const fn numerator(self) -> i64

Get the numerator (denominator is always 2)

pub fn to_rational(self) -> Rational

Convert to rational number

pub fn from_rational(r: Rational) -> Self

Create from a rational number

Panics

Panics if the rational cannot be represented as n/2

pub fn square(self) -> Rational

Square of this half-integer (exact)

pub const fn is_integer(self) -> bool

Check if this is an integer (numerator is even)

pub const fn as_integer(self) -> Option<i64>

Get as integer if possible

Trait Implementations

impl Add for HalfInteger

type Output = HalfInteger

The resulting type after applying the + operator.

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

Performs the + operation.

impl Clone for HalfInteger

fn clone(&self) -> HalfInteger

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for HalfInteger

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

Formats the value using the given formatter.

impl Display for HalfInteger

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

Formats the value using the given formatter.

impl Hash for HalfInteger

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 Mul for HalfInteger

type Output = Ratio<i64>

The resulting type after applying the * operator.

fn mul(self, other: Self) -> Rational

Performs the * operation.

impl Neg for HalfInteger

type Output = HalfInteger

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl Ord for HalfInteger

fn cmp(&self, other: &HalfInteger) -> 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 PartialEq for HalfInteger

fn eq(&self, other: &HalfInteger) -> 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 PartialOrd for HalfInteger

fn partial_cmp(&self, other: &HalfInteger) -> 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 Sub for HalfInteger

type Output = HalfInteger

The resulting type after applying the - operator.

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

Performs the - operation.

impl Zero for HalfInteger

fn zero() -> Self

Returns the additive identity element of Self, 0.

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.

impl Copy for HalfInteger

impl Eq for HalfInteger

impl StructuralPartialEq for HalfInteger