Struct num_prime::detail::Mint

pub struct Mint<T: Integer, R: Reducer<T>>(/* private fields */);

Integer with fast modular arithmetics support, based on [MontgomeryInt] under the hood

This struct only designed to be working with this crate. Most binary operators assume that the modulus of two operands (when in montgomery form) are the same, and most implicit conversions between conventional form and montgomery form will be forbidden

Implementations

impl<T: Integer + Clone, R: Reducer<T> + Clone> Mint<T, R>

pub fn value(&self) -> T

Trait Implementations

impl<'a, 'b, T: Integer + Clone + for<'r> Add<&'r T, Output = T>, R: Reducer<T> + Clone> Add<&'b Mint<T, R>> for &'a Mint<T, R>

type Output = Mint<T, R>

The resulting type after applying the + operator.

fn add(self, rhs: &Mint<T, R>) -> Self::Output

Performs the + operation.

impl<T: Integer + Clone + for<'r> Add<&'r T, Output = T>, R: Reducer<T> + Clone> Add<&Mint<T, R>> for Mint<T, R>

type Output = Mint<T, R>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<T: Integer + Clone, R: Reducer<T> + Clone> Add<Mint<T, R>> for &Mint<T, R>

type Output = Mint<T, R>

The resulting type after applying the + operator.

fn add(self, rhs: Mint<T, R>) -> Self::Output

Performs the + operation.

impl<T: Integer + Clone, R: Reducer<T> + Clone> Add for Mint<T, R>

type Output = Mint<T, R>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<T: Integer + Clone + BitTest, R: Reducer<T>> BitTest for Mint<T, R>

fn bit(&self, position: usize) -> bool

Get the i-th bit of the integer, with i specified by position

fn bits(&self) -> usize

Get the minimum required number of bits to represent this integer

fn trailing_zeros(&self) -> usize

Get the number of trailing zeros in the integer

impl<T: Clone + Integer, R: Clone + Reducer<T>> Clone for Mint<T, R>

fn clone(&self) -> Mint<T, R>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<T: Debug + Integer, R: Debug + Reducer<T>> Debug for Mint<T, R>

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

Formats the value using the given formatter.

impl<'a, 'b, T: Integer + Clone + for<'r> Div<&'r T, Output = T>, R: Reducer<T>> Div<&'b Mint<T, R>> for &'a Mint<T, R>

type Output = Mint<T, R>

The resulting type after applying the / operator.

fn div(self, rhs: &Mint<T, R>) -> Self::Output

Performs the / operation.

impl<T: Integer + Clone + for<'r> Div<&'r T, Output = T>, R: Reducer<T>> Div<&Mint<T, R>> for Mint<T, R>

type Output = Mint<T, R>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<T: Integer + Clone, R: Reducer<T>> Div<Mint<T, R>> for &Mint<T, R>

type Output = Mint<T, R>

The resulting type after applying the / operator.

fn div(self, rhs: Mint<T, R>) -> Self::Output

Performs the / operation.

impl<T: Integer + Clone, R: Reducer<T>> Div for Mint<T, R>

type Output = Mint<T, R>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<T: Integer + Clone + ExactRoots, R: Reducer<T> + Clone> ExactRoots for Mint<T, R>

fn nth_root_exact(&self, n: u32) -> Option<Self>

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

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

fn is_nth_power(&self, n: u32) -> bool

fn is_square(&self) -> bool

fn is_cubic(&self) -> bool

impl<T: Integer, R: Reducer<T>> From<ReducedInt<T, R>> for Mint<T, R>

fn from(v: ReducedInt<T, R>) -> Self

Converts to this type from the input type.

impl<T: Integer, R: Reducer<T>> From<T> for Mint<T, R>

fn from(v: T) -> Self

Converts to this type from the input type.

impl<T: Integer + Clone + FromPrimitive, R: Reducer<T>> FromPrimitive for Mint<T, R>

fn from_f64(n: f64) -> Option<Self>

Converts a f64 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i64(n: i64) -> Option<Self>

Converts an i64 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u64(n: u64) -> Option<Self>

Converts an u64 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_isize(n: isize) -> Option<Self>

Converts an isize to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i8(n: i8) -> Option<Self>

Converts an i8 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i16(n: i16) -> Option<Self>

Converts an i16 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i32(n: i32) -> Option<Self>

Converts an i32 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i128(n: i128) -> Option<Self>

Converts an i128 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_usize(n: usize) -> Option<Self>

Converts a usize to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u8(n: u8) -> Option<Self>

Converts an u8 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u16(n: u16) -> Option<Self>

Converts an u16 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u32(n: u32) -> Option<Self>

Converts an u32 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u128(n: u128) -> Option<Self>

Converts an u128 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_f32(n: f32) -> Option<Self>

Converts a f32 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

impl<T: Integer + Clone, R: Reducer<T> + Clone> Integer for Mint<T, R>

fn div_floor(&self, other: &Self) -> Self

Floored integer division.

fn mod_floor(&self, other: &Self) -> Self

Floored integer modulo, satisfying:

fn lcm(&self, other: &Self) -> Self

Lowest Common Multiple (LCM).

fn divides(&self, other: &Self) -> bool

👎Deprecated: Please use is_multiple_of instead

Deprecated, use is_multiple_of instead.

fn is_multiple_of(&self, other: &Self) -> bool

Returns true if self is a multiple of other.

fn is_even(&self) -> bool

Returns true if the number is even.

fn is_odd(&self) -> bool

Returns true if the number is odd.

fn div_rem(&self, other: &Self) -> (Self, Self)

Simultaneous truncated integer division and modulus. Returns (quotient, remainder).

fn gcd(&self, other: &Self) -> Self

Greatest Common Divisor (GCD).

fn div_ceil(&self, other: &Self) -> Self

Ceiled integer division.

fn gcd_lcm(&self, other: &Self) -> (Self, Self)

Greatest Common Divisor (GCD) and Lowest Common Multiple (LCM) together.

fn extended_gcd(&self, other: &Self) -> ExtendedGcd<Self>

where Self: Clone,

Greatest common divisor and Bézout coefficients.

fn div_mod_floor(&self, other: &Self) -> (Self, Self)

Simultaneous floored integer division and modulus. Returns (quotient, remainder).

fn next_multiple_of(&self, other: &Self) -> Self

where Self: Clone,

Rounds up to nearest multiple of argument.

fn prev_multiple_of(&self, other: &Self) -> Self

where Self: Clone,

Rounds down to nearest multiple of argument.

fn dec(&mut self)

where Self: Clone,

Decrements self by one.

fn inc(&mut self)

where Self: Clone,

Increments self by one.

impl<'a, 'b, T: Integer + Clone, R: Reducer<T> + Clone> ModularCoreOps<&'b Mint<T, R>, &'b Mint<T, R>> for &'a Mint<T, R>

type Output = Mint<T, R>

fn addm(self, rhs: &Mint<T, R>, m: &Mint<T, R>) -> Self::Output

Return (self + rhs) % m

fn subm(self, rhs: &Mint<T, R>, m: &Mint<T, R>) -> Self::Output

Return (self - rhs) % m

fn mulm(self, rhs: &Mint<T, R>, m: &Mint<T, R>) -> Self::Output

Return (self * rhs) % m

impl<T: Integer + Clone, R: Reducer<T> + Clone> ModularCoreOps<&Mint<T, R>, &Mint<T, R>> for Mint<T, R>

type Output = Mint<T, R>

fn addm(self, rhs: &Self, m: &Self) -> Self::Output

Return (self + rhs) % m

fn subm(self, rhs: &Self, m: &Self) -> Self::Output

Return (self - rhs) % m

fn mulm(self, rhs: &Self, m: &Self) -> Self::Output

Return (self * rhs) % m

impl<T: Integer + Clone, R: Reducer<T> + Clone> ModularPow<&Mint<T, R>, &Mint<T, R>> for Mint<T, R>

type Output = Mint<T, R>

fn powm(self, exp: &Self, m: &Self) -> Self::Output

Return (self ^ exp) % m

impl<T: Integer + Clone + for<'r> ModularSymbols<&'r T>, R: Reducer<T> + Clone> ModularSymbols<&Mint<T, R>> for Mint<T, R>

fn checked_jacobi(&self, n: &Self) -> Option<i8>

Checked version of jacobi(), return None if n is negative or even

fn checked_legendre(&self, n: &Self) -> Option<i8>

Checked version of legendre(), return None if n is not prime

fn kronecker(&self, n: &Self) -> i8

Calculate Kronecker Symbol (a|n), where a is self

fn legendre(&self, n: Modulus) -> i8

Calculate Legendre Symbol (a|n), where a is self.

fn jacobi(&self, n: Modulus) -> i8

Calculate Jacobi Symbol (a|n), where a is self

impl<'a, 'b, T: Integer + Clone, R: Reducer<T> + Clone> ModularUnaryOps<&'b Mint<T, R>> for &'a Mint<T, R>

type Output = Mint<T, R>

fn negm(self, m: &Mint<T, R>) -> Self::Output

Return (-self) % m and make sure the result is normalized in range [0,m)

fn invm(self, _: &Mint<T, R>) -> Option<Self::Output>

Calculate modular inverse (x such that self*x = 1 mod m).

fn dblm(self, m: &Mint<T, R>) -> Self::Output

Calculate modular double ( x+x mod m)

fn sqm(self, m: &Mint<T, R>) -> Self::Output

Calculate modular square ( x*x mod m )

impl<T: Integer + Clone, R: Reducer<T> + Clone> ModularUnaryOps<&Mint<T, R>> for Mint<T, R>

type Output = Mint<T, R>

fn negm(self, m: &Self) -> Self::Output

Return (-self) % m and make sure the result is normalized in range [0,m)

fn invm(self, _: &Self) -> Option<Self::Output>

Calculate modular inverse (x such that self*x = 1 mod m).

fn dblm(self, m: &Self) -> Self::Output

Calculate modular double ( x+x mod m)

fn sqm(self, m: &Self) -> Self::Output

Calculate modular square ( x*x mod m )

impl<'a, 'b, T: Integer + Clone + for<'r> Mul<&'r T, Output = T>, R: Reducer<T> + Clone> Mul<&'b Mint<T, R>> for &'a Mint<T, R>

type Output = Mint<T, R>

The resulting type after applying the * operator.

fn mul(self, rhs: &Mint<T, R>) -> Self::Output

Performs the * operation.

impl<T: Integer + Clone + for<'r> Mul<&'r T, Output = T>, R: Reducer<T> + Clone> Mul<&Mint<T, R>> for Mint<T, R>

type Output = Mint<T, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T: Integer + Clone, R: Reducer<T> + Clone> Mul<Mint<T, R>> for &Mint<T, R>

type Output = Mint<T, R>

The resulting type after applying the * operator.

fn mul(self, rhs: Mint<T, R>) -> Self::Output

Performs the * operation.

impl<T: Integer + Clone, R: Reducer<T> + Clone> Mul for Mint<T, R>

type Output = Mint<T, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T: Integer + Clone, R: Reducer<T> + Clone> Num for Mint<T, R>

type FromStrRadixErr = <T as Num>::FromStrRadixErr

fn from_str_radix(str: &str, radix: u32) -> Result<Self, Self::FromStrRadixErr>

Convert from a string and radix (typically 2..=36).

impl<T: Integer + Clone, R: Reducer<T> + Clone> One for Mint<T, R>

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool

Returns true if self is equal to the multiplicative identity.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

impl<T: Integer + Clone, R: Reducer<T> + Clone> Ord for Mint<T, R>

fn cmp(&self, other: &Self) -> 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 + PartialOrd,

Restrict a value to a certain interval.

impl<T: Integer + Clone, R: Reducer<T>> PartialEq for Mint<T, R>

fn eq(&self, other: &Self) -> bool

This method tests for self and other values to be equal, and is used by ==.

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

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

impl<T: Integer + Clone, R: Reducer<T> + Clone> PartialOrd for Mint<T, R>

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

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

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

This method tests less than (for self and other) and is used by the < operator.

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

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

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

This method tests greater than (for self and other) and is used by the > operator.

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

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

impl<T: Integer + Clone + Pow<u32, Output = T>, R: Reducer<T>> Pow<u32> for Mint<T, R>

type Output = Mint<T, R>

The result after applying the operator.

fn pow(self, rhs: u32) -> Self::Output

Returns self to the power rhs.

impl<'a, 'b, T: Integer + Clone, R: Reducer<T> + Clone> Rem<&'b Mint<T, R>> for &'a Mint<T, R>

type Output = Mint<T, R>

The resulting type after applying the % operator.

fn rem(self, rhs: &Mint<T, R>) -> Self::Output

Performs the % operation.

impl<T: Integer + Clone, R: Reducer<T> + Clone> Rem<&Mint<T, R>> for Mint<T, R>

type Output = Mint<T, R>

The resulting type after applying the % operator.

fn rem(self, rhs: &Self) -> Self::Output

Performs the % operation.

impl<T: Integer + Clone, R: Reducer<T> + Clone> Rem<Mint<T, R>> for &Mint<T, R>

type Output = Mint<T, R>

The resulting type after applying the % operator.

fn rem(self, rhs: Mint<T, R>) -> Self::Output

Performs the % operation.

impl<T: Integer + Clone, R: Reducer<T> + Clone> Rem for Mint<T, R>

type Output = Mint<T, R>

The resulting type after applying the % operator.

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

Performs the % operation.

impl<T: Integer + Clone + Roots, R: Reducer<T> + Clone> Roots for Mint<T, R>

fn nth_root(&self, n: u32) -> Self

Returns the truncated principal nth root of an integer – if x >= 0 { ⌊ⁿ√x⌋ } else { ⌈ⁿ√x⌉ }

fn sqrt(&self) -> Self

Returns the truncated principal square root of an integer – ⌊√x⌋

fn cbrt(&self) -> Self

Returns the truncated principal cube root of an integer – if x >= 0 { ⌊∛x⌋ } else { ⌈∛x⌉ }

impl<T: Integer + Clone + Shr<usize, Output = T>, R: Reducer<T>> Shr<usize> for &Mint<T, R>

type Output = Mint<T, R>

The resulting type after applying the >> operator.

fn shr(self, rhs: usize) -> Self::Output

Performs the >> operation.

impl<T: Integer + Clone + Shr<usize, Output = T>, R: Reducer<T>> Shr<usize> for Mint<T, R>

type Output = Mint<T, R>

The resulting type after applying the >> operator.

fn shr(self, rhs: usize) -> Self::Output

Performs the >> operation.

impl<'a, 'b, T: Integer + Clone + for<'r> Sub<&'r T, Output = T>, R: Reducer<T> + Clone> Sub<&'b Mint<T, R>> for &'a Mint<T, R>

type Output = Mint<T, R>

The resulting type after applying the - operator.

fn sub(self, rhs: &Mint<T, R>) -> Self::Output

Performs the - operation.

impl<T: Integer + Clone + for<'r> Sub<&'r T, Output = T>, R: Reducer<T> + Clone> Sub<&Mint<T, R>> for Mint<T, R>

type Output = Mint<T, R>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<T: Integer + Clone, R: Reducer<T> + Clone> Sub<Mint<T, R>> for &Mint<T, R>

type Output = Mint<T, R>

The resulting type after applying the - operator.

fn sub(self, rhs: Mint<T, R>) -> Self::Output

Performs the - operation.

impl<T: Integer + Clone, R: Reducer<T> + Clone> Sub for Mint<T, R>

type Output = Mint<T, R>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<T: Integer + Clone + ToPrimitive, R: Reducer<T> + Clone> ToPrimitive for Mint<T, R>

fn to_f64(&self) -> Option<f64>

Converts the value of self to an f64. Overflows may map to positive or negative inifinity, otherwise None is returned if the value cannot be represented by an f64.

fn to_i64(&self) -> Option<i64>

Converts the value of self to an i64. If the value cannot be represented by an i64, then None is returned.

fn to_u64(&self) -> Option<u64>

Converts the value of self to a u64. If the value cannot be represented by a u64, then None is returned.

fn to_isize(&self) -> Option<isize>

Converts the value of self to an isize. If the value cannot be represented by an isize, then None is returned.

fn to_i8(&self) -> Option<i8>

Converts the value of self to an i8. If the value cannot be represented by an i8, then None is returned.

fn to_i16(&self) -> Option<i16>

Converts the value of self to an i16. If the value cannot be represented by an i16, then None is returned.

fn to_i32(&self) -> Option<i32>

Converts the value of self to an i32. If the value cannot be represented by an i32, then None is returned.

fn to_i128(&self) -> Option<i128>

Converts the value of self to an i128. If the value cannot be represented by an i128 (i64 under the default implementation), then None is returned.

fn to_usize(&self) -> Option<usize>

Converts the value of self to a usize. If the value cannot be represented by a usize, then None is returned.

fn to_u8(&self) -> Option<u8>

Converts the value of self to a u8. If the value cannot be represented by a u8, then None is returned.

fn to_u16(&self) -> Option<u16>

Converts the value of self to a u16. If the value cannot be represented by a u16, then None is returned.

fn to_u32(&self) -> Option<u32>

Converts the value of self to a u32. If the value cannot be represented by a u32, then None is returned.

fn to_u128(&self) -> Option<u128>

Converts the value of self to a u128. If the value cannot be represented by a u128 (u64 under the default implementation), then None is returned.

fn to_f32(&self) -> Option<f32>

Converts the value of self to an f32. Overflows may map to positive or negative inifinity, otherwise None is returned if the value cannot be represented by an f32.

impl<T: Integer + Clone, R: Reducer<T> + Clone> Zero for Mint<T, R>

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<T: Copy + Integer, R: Copy + Reducer<T>> Copy for Mint<T, R>

impl<T: Integer + Clone, R: Reducer<T>> Eq for Mint<T, R>