Struct modtype::ModType

pub struct ModType<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> { /* fields omitted */ }

A modular arithmetic integer type which modulus is a constant.

Examples

use modtype::{use_modtype, DefaultModType};
use num::bigint::{Sign, ToBigInt as _, ToBigUint as _};
use num::pow::Pow as _;
use num::traits::{CheckedNeg as _, CheckedRem as _, Inv as _};
use num::{
    BigInt, BigUint, Bounded as _, CheckedAdd as _, CheckedDiv as _, CheckedMul as _,
    CheckedSub as _, FromPrimitive as _, Num as _, One as _, ToPrimitive as _, Unsigned,
    Zero as _,
};

#[use_modtype]
type F = DefaultModType<7u32>;

fn static_assert_unsigned<T: Unsigned>() {}

// Constructor, `new`, `new_unchecked`, `get`
assert_eq!(F::new(8), F(1));
assert_ne!(F::new_unchecked(8), F(1));
assert_eq!(F(3).get(), 3u32);

// `From<{T, BigUint, BigInt}>`
assert_eq!(F::from(3), F(3));
assert_eq!(F::from(BigUint::new(vec![3])), F(3));
assert_eq!(F::from(BigInt::new(Sign::Minus, vec![4])), F(3));

// `Display`, `Debug`
assert_eq!(F(3).to_string(), "3");
assert_eq!(format!("{:?}", F(3)), "3");

// `FromStr`
assert_eq!("3".parse::<F>(), Ok(F(3)));

// `Deref`
assert_eq!(*F(3), 3);
assert_eq!(F(3).to_i64(), Some(3i64));
assert_eq!(F(3).to_biguint(), 3u64.to_biguint());
assert_eq!(F(3).to_bigint(), 3u64.to_bigint());

// `Neg`
assert_eq!(-F(1), F(6));

// `Add`, `Sub`, `Mul`, `Div`, `Rem`
assert_eq!(F(3) + F(4), F(0));
assert_eq!(F(3) - F(4), F(6));
assert_eq!(F(3) * F(4), F(5));
assert_eq!(F(3) / F(4), F(6));
(0..=6).for_each(|x| (1..=6).for_each(|y| assert_eq!(F(x) % F(y), F(0))));

// `Num`
assert_eq!(F::from_str_radix("111", 2), Ok(F(0)));

// `Unsigned`
static_assert_unsigned::<F>();

// `Bounded`
assert_eq!((F::min_value(), F::max_value()), (F(0), F(6)));

// `Zero`, `One`
assert_eq!(F::zero(), F(0));
assert_eq!(F::one(), F(1));

// `FromPrimitive`
assert_eq!(F::from_i128(-1), Some(-F(1)));
assert_eq!(F::from_f64(0.5), Some(F(1) / F(2)));

// `Inv`
assert_eq!(F(3).inv(), F(5));

// `CheckedNeg`
(0..=6).for_each(|x| assert!(F(x).checked_neg().is_some()));

// `CheckedAdd`, `CheckedSub`, `CheckedMul`, `CheckedDiv`, `CheckedRem`
(0..=6).for_each(|x| (0..=6).for_each(|y| assert!(F(x).checked_add(&F(y)).is_some())));
assert_eq!(
    num::range_step(F(0), F(6), F(2)).collect::<Vec<_>>(),
    &[F(0), F(2), F(4)],
);
(0..=6).for_each(|x| (0..=6).for_each(|y| assert!(F(x).checked_sub(&F(y)).is_some())));
(0..=6).for_each(|x| (0..=6).for_each(|y| assert!(F(x).checked_mul(&F(y)).is_some())));
(0..=6).for_each(|x| (1..=6).for_each(|y| assert!(F(x).checked_div(&F(y)).is_some())));
(0..=6).for_each(|x| assert!(F(x).checked_div(&F(0)).is_none()));
(0..=6).for_each(|x| (1..=6).for_each(|y| assert!(F(x).checked_rem(&F(y)).is_some())));
(0..=6).for_each(|x| assert!(F(x).checked_rem(&F(0)).is_none()));

// `Pow`
assert_eq!(F(3).pow(2u8), F(2));
assert_eq!(F(3).pow(2u16), F(2));
assert_eq!(F(3).pow(2u32), F(2));
assert_eq!(F(3).pow(2u64), F(2));
assert_eq!(F(3).pow(2u128), F(2));
assert_eq!(F(3).pow(2usize), F(2));
assert_eq!(F(3).pow(-2i8), F(4));
assert_eq!(F(3).pow(-2i16), F(4));
assert_eq!(F(3).pow(-2i32), F(4));
assert_eq!(F(3).pow(-2i64), F(4));
assert_eq!(F(3).pow(-2i128), F(4));
assert_eq!(F(3).pow(-2isize), F(4));

Methods

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> ModType<T, C, M>

pub fn modulus() -> T

Gets the modulus.

pub fn new(value: T) -> Self

Creates a new ModType.

pub fn new_unchecked(value: T) -> Self

Creates a new ModType without checking value.

pub fn get(self) -> T

Gets the inner value.

pub fn get_mut_unchecked(&mut self) -> &mut T

Returns a mutable reference to the inner value.

Trait Implementations

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> PartialOrd<ModType<T, C, M>> for ModType<T, C, M>

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: &Self) -> bool

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

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

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

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

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

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

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

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> PartialEq<ModType<T, C, M>> for ModType<T, C, M>

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: &Self) -> bool

This method tests for !=.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Copy for ModType<T, C, M>

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Ord for ModType<T, C, M>

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

This method returns an Ordering between self and other.

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

Compares and returns the maximum of two values.

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

Compares and returns the minimum of two values.

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

🔬 This is a nightly-only experimental API. (clamp)

Restrict a value to a certain interval.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Eq for ModType<T, C, M>

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Default for ModType<T, C, M>

fn default() -> Self

Returns the "default value" for a type.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> From<T> for ModType<T, C, M>

fn from(from: T) -> Self

Performs the conversion.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> From<BigUint> for ModType<T, C, M>

fn from(from: BigUint) -> Self

Performs the conversion.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> From<BigInt> for ModType<T, C, M>

fn from(from: BigInt) -> Self

Performs the conversion.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Clone for ModType<T, C, M>

fn clone(&self) -> Self

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Deref for ModType<T, C, M>

type Target = T

The resulting type after dereferencing.

fn deref(&self) -> &T

Dereferences the value.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Add<ModType<T, C, M>> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Addition = True>, 

type Output = ModType<T, C, M>

The resulting type after applying the + operator.

fn add(self, rhs: ModType<T, C, M>) -> ModType<T, C, M>

Performs the + operation.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Add<&'_ ModType<T, C, M>> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Addition = True>, 

type Output = ModType<T, C, M>

The resulting type after applying the + operator.

fn add(self, rhs: &ModType<T, C, M>) -> ModType<T, C, M>

Performs the + operation.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Add<ModType<T, C, M>> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Addition = True>, 

type Output = ModType<T, C, M>

The resulting type after applying the + operator.

fn add(self, rhs: ModType<T, C, M>) -> ModType<T, C, M>

Performs the + operation.

impl<'_, '_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Add<&'_ ModType<T, C, M>> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Addition = True>, 

type Output = ModType<T, C, M>

The resulting type after applying the + operator.

fn add(self, rhs: &ModType<T, C, M>) -> ModType<T, C, M>

Performs the + operation.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Sub<ModType<T, C, M>> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Subtraction = True>, 

type Output = ModType<T, C, M>

The resulting type after applying the - operator.

fn sub(self, rhs: ModType<T, C, M>) -> ModType<T, C, M>

Performs the - operation.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Sub<&'_ ModType<T, C, M>> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Subtraction = True>, 

type Output = ModType<T, C, M>

The resulting type after applying the - operator.

fn sub(self, rhs: &ModType<T, C, M>) -> ModType<T, C, M>

Performs the - operation.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Sub<ModType<T, C, M>> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Subtraction = True>, 

type Output = ModType<T, C, M>

The resulting type after applying the - operator.

fn sub(self, rhs: ModType<T, C, M>) -> ModType<T, C, M>

Performs the - operation.

impl<'_, '_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Sub<&'_ ModType<T, C, M>> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Subtraction = True>, 

type Output = ModType<T, C, M>

The resulting type after applying the - operator.

fn sub(self, rhs: &ModType<T, C, M>) -> ModType<T, C, M>

Performs the - operation.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Mul<ModType<T, C, M>> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

type Output = ModType<T, C, M>

The resulting type after applying the * operator.

fn mul(self, rhs: ModType<T, C, M>) -> ModType<T, C, M>

Performs the * operation.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Mul<&'_ ModType<T, C, M>> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

type Output = ModType<T, C, M>

The resulting type after applying the * operator.

fn mul(self, rhs: &ModType<T, C, M>) -> ModType<T, C, M>

Performs the * operation.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Mul<ModType<T, C, M>> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

type Output = ModType<T, C, M>

The resulting type after applying the * operator.

fn mul(self, rhs: ModType<T, C, M>) -> ModType<T, C, M>

Performs the * operation.

impl<'_, '_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Mul<&'_ ModType<T, C, M>> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

type Output = ModType<T, C, M>

The resulting type after applying the * operator.

fn mul(self, rhs: &ModType<T, C, M>) -> ModType<T, C, M>

Performs the * operation.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Div<ModType<T, C, M>> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = ModType<T, C, M>

The resulting type after applying the / operator.

fn div(self, rhs: ModType<T, C, M>) -> ModType<T, C, M>

Performs the / operation.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Div<&'_ ModType<T, C, M>> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = ModType<T, C, M>

The resulting type after applying the / operator.

fn div(self, rhs: &ModType<T, C, M>) -> ModType<T, C, M>

Performs the / operation.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Div<ModType<T, C, M>> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = ModType<T, C, M>

The resulting type after applying the / operator.

fn div(self, rhs: ModType<T, C, M>) -> ModType<T, C, M>

Performs the / operation.

impl<'_, '_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Div<&'_ ModType<T, C, M>> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = ModType<T, C, M>

The resulting type after applying the / operator.

fn div(self, rhs: &ModType<T, C, M>) -> ModType<T, C, M>

Performs the / operation.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Rem<ModType<T, C, M>> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = ModType<T, C, M>

The resulting type after applying the % operator.

fn rem(self, rhs: ModType<T, C, M>) -> ModType<T, C, M>

Performs the % operation.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Rem<&'_ ModType<T, C, M>> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = ModType<T, C, M>

The resulting type after applying the % operator.

fn rem(self, rhs: &ModType<T, C, M>) -> ModType<T, C, M>

Performs the % operation.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Rem<ModType<T, C, M>> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = ModType<T, C, M>

The resulting type after applying the % operator.

fn rem(self, rhs: ModType<T, C, M>) -> ModType<T, C, M>

Performs the % operation.

impl<'_, '_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Rem<&'_ ModType<T, C, M>> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = ModType<T, C, M>

The resulting type after applying the % operator.

fn rem(self, rhs: &ModType<T, C, M>) -> ModType<T, C, M>

Performs the % operation.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Neg for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Subtraction = True>, 

type Output = Self

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Neg for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Subtraction = True>, 

type Output = ModType<T, C, M>

The resulting type after applying the - operator.

fn neg(self) -> ModType<T, C, M>

Performs the unary - operation.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> AddAssign<ModType<T, C, M>> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Addition = True>, 

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> AddAssign<&'_ ModType<T, C, M>> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Addition = True>, 

fn add_assign(&mut self, rhs: &Self)

Performs the += operation.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> SubAssign<ModType<T, C, M>> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Subtraction = True>, 

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> SubAssign<&'_ ModType<T, C, M>> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Subtraction = True>, 

fn sub_assign(&mut self, rhs: &Self)

Performs the -= operation.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> MulAssign<ModType<T, C, M>> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

fn mul_assign(&mut self, rhs: Self)

Performs the *= operation.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> MulAssign<&'_ ModType<T, C, M>> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

fn mul_assign(&mut self, rhs: &Self)

Performs the *= operation.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> DivAssign<ModType<T, C, M>> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Division = True>, 

fn div_assign(&mut self, rhs: Self)

Performs the /= operation.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> DivAssign<&'_ ModType<T, C, M>> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Division = True>, 

fn div_assign(&mut self, rhs: &Self)

Performs the /= operation.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> RemAssign<ModType<T, C, M>> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Division = True>, 

fn rem_assign(&mut self, rhs: Self)

Performs the %= operation.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> RemAssign<&'_ ModType<T, C, M>> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Division = True>, 

fn rem_assign(&mut self, rhs: &Self)

Performs the %= operation.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Debug for ModType<T, C, M>

fn fmt(&self, fmt: &mut Formatter) -> Result

Formats the value using the given formatter.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Display for ModType<T, C, M>

fn fmt(&self, fmt: &mut Formatter) -> Result

Formats the value using the given formatter.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> FromStr for ModType<T, C, M>

type Err = ParseIntError

The associated error which can be returned from parsing.

fn from_str(s: &str) -> Result<Self, ParseIntError>

Parses a string s to return a value of this type.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> CheckedMul for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

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

Multiplies two numbers, checking for underflow or overflow. If underflow or overflow happens, None is returned.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Zero for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Addition = True>, 

fn zero() -> Self

Returns the additive identity element of Self, 0. # Purity

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: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> One for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

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: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> FromPrimitive for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Subtraction = True, Multiplication = True, Division = True>, 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Inv for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = ModType<T, C, M>

The result after applying the operator.

fn inv(self) -> ModType<T, C, M>

Returns the multiplicative inverse of self.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Inv for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = ModType<T, C, M>

The result after applying the operator.

fn inv(self) -> ModType<T, C, M>

Returns the multiplicative inverse of self.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> CheckedNeg for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Subtraction = True>, 

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

Negates a number, returning None for results that can't be represented, like signed MIN values that can't be positive, or non-zero unsigned values that can't be negative.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> CheckedAdd for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Addition = True>, 

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

Adds two numbers, checking for overflow. If overflow happens, None is returned.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> CheckedSub for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Subtraction = True>, 

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

Subtracts two numbers, checking for underflow. If underflow happens, None is returned.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> CheckedDiv for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Division = True>, 

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

Divides two numbers, checking for underflow, overflow and division by zero. If any of that happens, None is returned.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> CheckedRem for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Division = True>, 

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

Finds the remainder of dividing two numbers, checking for underflow, overflow and division by zero. If any of that happens, None is returned.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<u8> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

type Output = Self

The result after applying the operator.

fn pow(self, exp: u8) -> Self

Returns self to the power rhs.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<&'_ u8> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

type Output = Self

The result after applying the operator.

fn pow(self, exp: &u8) -> Self

Returns self to the power rhs.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<u8> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

type Output = ModType<T, C, M>

The result after applying the operator.

fn pow(self, exp: u8) -> ModType<T, C, M>

Returns self to the power rhs.

impl<'_, '_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<&'_ u8> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

type Output = ModType<T, C, M>

The result after applying the operator.

fn pow(self, exp: &u8) -> ModType<T, C, M>

Returns self to the power rhs.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<u16> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

type Output = Self

The result after applying the operator.

fn pow(self, exp: u16) -> Self

Returns self to the power rhs.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<&'_ u16> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

type Output = Self

The result after applying the operator.

fn pow(self, exp: &u16) -> Self

Returns self to the power rhs.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<u16> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

type Output = ModType<T, C, M>

The result after applying the operator.

fn pow(self, exp: u16) -> ModType<T, C, M>

Returns self to the power rhs.

impl<'_, '_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<&'_ u16> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

type Output = ModType<T, C, M>

The result after applying the operator.

fn pow(self, exp: &u16) -> ModType<T, C, M>

Returns self to the power rhs.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<u32> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

type Output = Self

The result after applying the operator.

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

Returns self to the power rhs.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<&'_ u32> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

type Output = Self

The result after applying the operator.

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

Returns self to the power rhs.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<u32> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

type Output = ModType<T, C, M>

The result after applying the operator.

fn pow(self, exp: u32) -> ModType<T, C, M>

Returns self to the power rhs.

impl<'_, '_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<&'_ u32> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

type Output = ModType<T, C, M>

The result after applying the operator.

fn pow(self, exp: &u32) -> ModType<T, C, M>

Returns self to the power rhs.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<u64> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

type Output = Self

The result after applying the operator.

fn pow(self, exp: u64) -> Self

Returns self to the power rhs.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<&'_ u64> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

type Output = Self

The result after applying the operator.

fn pow(self, exp: &u64) -> Self

Returns self to the power rhs.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<u64> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

type Output = ModType<T, C, M>

The result after applying the operator.

fn pow(self, exp: u64) -> ModType<T, C, M>

Returns self to the power rhs.

impl<'_, '_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<&'_ u64> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

type Output = ModType<T, C, M>

The result after applying the operator.

fn pow(self, exp: &u64) -> ModType<T, C, M>

Returns self to the power rhs.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<u128> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

type Output = Self

The result after applying the operator.

fn pow(self, exp: u128) -> Self

Returns self to the power rhs.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<&'_ u128> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

type Output = Self

The result after applying the operator.

fn pow(self, exp: &u128) -> Self

Returns self to the power rhs.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<u128> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

type Output = ModType<T, C, M>

The result after applying the operator.

fn pow(self, exp: u128) -> ModType<T, C, M>

Returns self to the power rhs.

impl<'_, '_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<&'_ u128> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

type Output = ModType<T, C, M>

The result after applying the operator.

fn pow(self, exp: &u128) -> ModType<T, C, M>

Returns self to the power rhs.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<usize> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

type Output = Self

The result after applying the operator.

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

Returns self to the power rhs.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<&'_ usize> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

type Output = Self

The result after applying the operator.

fn pow(self, exp: &usize) -> Self

Returns self to the power rhs.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<usize> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

type Output = ModType<T, C, M>

The result after applying the operator.

fn pow(self, exp: usize) -> ModType<T, C, M>

Returns self to the power rhs.

impl<'_, '_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<&'_ usize> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>, 

type Output = ModType<T, C, M>

The result after applying the operator.

fn pow(self, exp: &usize) -> ModType<T, C, M>

Returns self to the power rhs.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<i8> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>,
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = Self

The result after applying the operator.

fn pow(self, exp: i8) -> Self

Returns self to the power rhs.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<&'_ i8> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>,
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = Self

The result after applying the operator.

fn pow(self, exp: &i8) -> Self

Returns self to the power rhs.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<i8> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>,
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = ModType<T, C, M>

The result after applying the operator.

fn pow(self, exp: i8) -> ModType<T, C, M>

Returns self to the power rhs.

impl<'_, '_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<&'_ i8> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>,
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = ModType<T, C, M>

The result after applying the operator.

fn pow(self, exp: &i8) -> ModType<T, C, M>

Returns self to the power rhs.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<i16> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>,
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = Self

The result after applying the operator.

fn pow(self, exp: i16) -> Self

Returns self to the power rhs.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<&'_ i16> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>,
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = Self

The result after applying the operator.

fn pow(self, exp: &i16) -> Self

Returns self to the power rhs.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<i16> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>,
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = ModType<T, C, M>

The result after applying the operator.

fn pow(self, exp: i16) -> ModType<T, C, M>

Returns self to the power rhs.

impl<'_, '_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<&'_ i16> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>,
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = ModType<T, C, M>

The result after applying the operator.

fn pow(self, exp: &i16) -> ModType<T, C, M>

Returns self to the power rhs.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<i32> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>,
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = Self

The result after applying the operator.

fn pow(self, exp: i32) -> Self

Returns self to the power rhs.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<&'_ i32> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>,
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = Self

The result after applying the operator.

fn pow(self, exp: &i32) -> Self

Returns self to the power rhs.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<i32> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>,
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = ModType<T, C, M>

The result after applying the operator.

fn pow(self, exp: i32) -> ModType<T, C, M>

Returns self to the power rhs.

impl<'_, '_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<&'_ i32> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>,
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = ModType<T, C, M>

The result after applying the operator.

fn pow(self, exp: &i32) -> ModType<T, C, M>

Returns self to the power rhs.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<i64> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>,
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = Self

The result after applying the operator.

fn pow(self, exp: i64) -> Self

Returns self to the power rhs.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<&'_ i64> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>,
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = Self

The result after applying the operator.

fn pow(self, exp: &i64) -> Self

Returns self to the power rhs.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<i64> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>,
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = ModType<T, C, M>

The result after applying the operator.

fn pow(self, exp: i64) -> ModType<T, C, M>

Returns self to the power rhs.

impl<'_, '_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<&'_ i64> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>,
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = ModType<T, C, M>

The result after applying the operator.

fn pow(self, exp: &i64) -> ModType<T, C, M>

Returns self to the power rhs.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<i128> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>,
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = Self

The result after applying the operator.

fn pow(self, exp: i128) -> Self

Returns self to the power rhs.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<&'_ i128> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>,
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = Self

The result after applying the operator.

fn pow(self, exp: &i128) -> Self

Returns self to the power rhs.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<i128> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>,
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = ModType<T, C, M>

The result after applying the operator.

fn pow(self, exp: i128) -> ModType<T, C, M>

Returns self to the power rhs.

impl<'_, '_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<&'_ i128> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>,
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = ModType<T, C, M>

The result after applying the operator.

fn pow(self, exp: &i128) -> ModType<T, C, M>

Returns self to the power rhs.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<isize> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>,
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = Self

The result after applying the operator.

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

Returns self to the power rhs.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<&'_ isize> for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>,
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = Self

The result after applying the operator.

fn pow(self, exp: &isize) -> Self

Returns self to the power rhs.

impl<'_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<isize> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>,
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = ModType<T, C, M>

The result after applying the operator.

fn pow(self, exp: isize) -> ModType<T, C, M>

Returns self to the power rhs.

impl<'_, '_, T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Pow<&'_ isize> for &'_ ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Multiplication = True>,
    <C as Cartridge>::Features: Features<Division = True>, 

type Output = ModType<T, C, M>

The result after applying the operator.

fn pow(self, exp: &isize) -> ModType<T, C, M>

Returns self to the power rhs.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Bounded for ModType<T, C, M>

fn min_value() -> Self

returns the smallest finite number this type can represent

fn max_value() -> Self

returns the largest finite number this type can represent

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Num for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Addition = True, Subtraction = True, Multiplication = True, Division = True>, 

type FromStrRadixErr = ParseIntError

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

Convert from a string and radix <= 36.

impl<T: UnsignedPrimitive, C: Cartridge<Target = T>, M: ConstValue<Value = T>> Unsigned for ModType<T, C, M> where
    <C as Cartridge>::Features: Features<Addition = True, Subtraction = True, Multiplication = True, Division = True>,