Struct ModNum

pub struct ModNum<N> { /* private fields */ }

Represents an integer a (mod m)

Implementations

impl<N: NumType> ModNum<N>

pub fn new(a: N, m: N) -> Self

Creates a new integer a (mod m)

pub fn iter(&self) -> ModNumIterator<N, Self>

Returns an iterator starting at a (mod m) and ending at a - 1 (mod m)

impl<N: NumType + Signed> ModNum<N>

pub fn chinese_remainder(&self, other: ModNum<N>) -> ModNum<N>

Solves a pair of modular equations using the Chinese Remainder Theorem.

This is my translation into Rust of Brent Yorgey’s Haskell implementation.

• self represents the modular equation x = a (mod m)
• other represents the modular equation x = b (mod n)
• It returns a ModNum corresponding to the equation x = c (mod mn) where c is congruent both to a (mod m) and b (mod n)

pub fn chinese_remainder_system<I: Iterator<Item = ModNum<N>>>( modnums: I, ) -> Option<ModNum<N>>

Solves a system of modular equations using ModMum::chinese_remainder().

Each equation in the system is an element of the modnums iterator parameter.

• Returns None if the iterator is empty.
• Returns Some(element) if the iterator has only one element.
• Returns Some(solution) if the iterator has two or more elements, where the solution is found by repeatedly calling ModNum::chinese_remainder().

impl<N: NumType + Signed> ModNum<N>

Exponentiates safely with negative exponents - if the inverse is undefined, it returns None, otherwise it returns Some(self.pow(rhs)).

pub fn pow_signed(&self, rhs: N) -> Option<Self>

Trait Implementations

impl<N: NumType> Add<N> for ModNum<N>

type Output = ModNum<N>

The resulting type after applying the + operator.

fn add(self, rhs: N) -> Self::Output

Performs the + operation.

impl<N: NumType> Add for ModNum<N>

type Output = ModNum<N>

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self::Output

Performs the + operation.

impl<N: NumType> AddAssign<N> for ModNum<N>

fn add_assign(&mut self, rhs: N)

Performs the += operation.

impl<N: NumType> AddAssign for ModNum<N>

fn add_assign(&mut self, rhs: ModNum<N>)

Performs the += operation.

impl<N: Clone> Clone for ModNum<N>

fn clone(&self) -> ModNum<N>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<N: Debug> Debug for ModNum<N>

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

Formats the value using the given formatter.

impl<N: NumType> Display for ModNum<N>

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

Formats the value using the given formatter.

impl<N: NumType + Signed> Div<N> for ModNum<N>

type Output = Option<ModNum<N>>

The resulting type after applying the / operator.

fn div(self, rhs: N) -> Self::Output

Performs the / operation.

impl<N: NumType + Signed> Div for ModNum<N>

type Output = Option<ModNum<N>>

The resulting type after applying the / operator.

fn div(self, rhs: Self) -> Self::Output

Performs the / operation.

impl<N: NumType + Signed> DivAssign<N> for ModNum<N>

fn div_assign(&mut self, rhs: N)

Performs the /= operation.

impl<N: NumType + Signed> DivAssign for ModNum<N>

fn div_assign(&mut self, rhs: ModNum<N>)

Performs the /= operation.

impl<N: Hash> Hash for ModNum<N>

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<N: NumType> MNum for ModNum<N>

type Num = N

fn a(&self) -> N

fn m(&self) -> N

fn with(&self, new_a: Self::Num) -> Self

fn replace(&mut self, new_a: Self::Num)

fn egcd(a: Self::Num, b: Self::Num) -> (Self::Num, Self::Num, Self::Num)

where Self::Num: Signed,

Extended Euclidean Algorithm for Greatest Common Divisor for GCD.

fn inverse(&self) -> Option<Self>

where Self::Num: Signed,

Returns the modular inverse, if it exists. Returns None if it does not exist.

impl<N: NumType> Mul<N> for ModNum<N>

type Output = ModNum<N>

The resulting type after applying the * operator.

fn mul(self, rhs: N) -> Self::Output

Performs the * operation.

impl<N: NumType> Mul for ModNum<N>

type Output = ModNum<N>

The resulting type after applying the * operator.

fn mul(self, rhs: Self) -> Self::Output

Performs the * operation.

impl<N: NumType> MulAssign<N> for ModNum<N>

fn mul_assign(&mut self, rhs: N)

Performs the *= operation.

impl<N: NumType> MulAssign for ModNum<N>

fn mul_assign(&mut self, rhs: ModNum<N>)

Performs the *= operation.

impl<N: NumType> Neg for ModNum<N>

type Output = ModNum<N>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<N: Ord> Ord for ModNum<N>

fn cmp(&self, other: &ModNum<N>) -> 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<N: NumType> PartialEq<N> for ModNum<N>

Returns true if other is congruent to self.a() (mod self.m())

fn eq(&self, other: &N) -> 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<N: PartialEq> PartialEq for ModNum<N>

fn eq(&self, other: &ModNum<N>) -> 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<N: NumType> PartialOrd<N> for ModNum<N>

fn partial_cmp(&self, other: &N) -> 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<N: PartialOrd> PartialOrd for ModNum<N>

fn partial_cmp(&self, other: &ModNum<N>) -> 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<N: NumType> Pow<ModNum<N>> for ModNum<N>

type Output = ModNum<N>

The result after applying the operator.

fn pow(self, rhs: Self) -> Self::Output

Returns self to the power rhs.

impl<N: NumType> Pow<N> for ModNum<N>

fn pow(self, rhs: N) -> Self::Output

Returns a^rhs (mod m), for rhs >= 0. Implements efficient modular exponentiation by repeated squaring.

Panics if rhs < 0. If negative exponents are possible, use .pow_signed()

type Output = ModNum<N>

The result after applying the operator.

impl<N: NumType> SaturatingAdd for ModNum<N>

fn saturating_add(&self, v: &Self) -> Self

Saturating addition. Computes self + other, saturating at the relevant high or low boundary of the type.

impl<N: NumType> SaturatingSub for ModNum<N>

fn saturating_sub(&self, v: &Self) -> Self

Saturating subtraction. Computes self - other, saturating at the relevant high or low boundary of the type.

impl<N: NumType> Sub<N> for ModNum<N>

type Output = ModNum<N>

The resulting type after applying the - operator.

fn sub(self, rhs: N) -> Self::Output

Performs the - operation.

impl<N: NumType> Sub for ModNum<N>

type Output = ModNum<N>

The resulting type after applying the - operator.

fn sub(self, rhs: Self) -> Self::Output

Performs the - operation.

impl<N: NumType> SubAssign<N> for ModNum<N>

fn sub_assign(&mut self, rhs: N)

Performs the -= operation.

impl<N: NumType> SubAssign for ModNum<N>

fn sub_assign(&mut self, rhs: ModNum<N>)

Performs the -= operation.

impl<N: Copy> Copy for ModNum<N>

impl<N: Eq> Eq for ModNum<N>

impl<N> StructuralPartialEq for ModNum<N>