Struct Integer 

pub struct Integer(/* private fields */);

Big integer type used in this crate

Implementations

impl Integer

pub fn to_bytes_lsf(&self) -> Vec<u8>

Converts to bytes, with bytes representing least significant base256 digits appearing first. Discards the sign

Example

let x = Integer::from(0x11223344);
assert_eq!(x.to_bytes_lsf(), vec![0x44, 0x33, 0x22, 0x11]);

pub fn to_bytes_msf(&self) -> Vec<u8>

Converts to bytes, with bytes representing most significant base256 digits appearing first. Discards the sign

Example

let x = Integer::from(0x11223344);
assert_eq!(x.to_bytes_msf(), vec![0x11, 0x22, 0x33, 0x44]);

pub fn to_bytes_msf_signed(&self) -> (Vec<u8>, Sign)

Converts to bytes, with bytes representing most significant base256 digits appearing first

Example

let x = Integer::from(-0x11223344);
assert_eq!(x.to_bytes_msf_signed(), (vec![0x11, 0x22, 0x33, 0x44],
Sign::Negative));

pub fn from_bytes_msf(bytes: &[u8]) -> Integer

Converts bytes to Integer. Inverse of Integer::to_bytes_msf

pub fn from_bytes_msf_signed(bytes: &[u8], sign: Sign) -> Integer

Converts bytes to Integer. Inverse of Integer::to_bytes_msf_signed

pub fn to_str_radix(&self, radix: u16) -> String

Returns a string representation of the number for the specified radix

pub fn from_str_radix(s: &str, radix: u16) -> Option<Integer>

Parses the integer using the given radix

pub fn to_num_bigint(self) -> BigInt

Convert the number to the underlying backend representation

pub fn from_num_bigint(x: BigInt) -> Integer

Convert the number from the underlying backend representation

impl Integer

pub fn one() -> Integer

pub fn zero() -> Integer

pub fn is_one(&self) -> bool

pub fn is_even(&self) -> bool

pub fn abs(self) -> Integer

pub fn cmp_abs(&self, other: &Integer) -> Ordering

pub fn lcm_ref(&self, other: &Integer) -> Integer

pub fn gcd_ref(&self, other: &Integer) -> Integer

pub fn cmp0(&self) -> Ordering

pub fn sign(&self) -> Sign

pub fn pow_mod(self, exponent: &Integer, modulo: &Integer) -> Option<Integer>

pub fn pow_mod_ref( &self, exponent: &Integer, modulo: &Integer, ) -> Option<Integer>

pub fn u_pow_u(base: u32, exponent: u32) -> Integer

pub fn square(self) -> Integer

pub fn square_ref(&self) -> Integer

pub fn sqrt(self) -> Option<Integer>

pub fn sqrt_ref(&self) -> Option<Integer>

pub fn modulo(self, divisor: &Integer) -> Integer

pub fn modulo_ref(&self, divisor: &Integer) -> Integer

pub fn modulo_mut(&mut self, divisor: &Integer) -> &mut Integer

pub fn mod_u(&self, modulo: u32) -> u32

pub fn significant_bits(&self) -> u64

pub fn significant_dwords(&self) -> usize

pub fn invert(self, modulo: &Integer) -> Option<Integer>

pub fn invert_ref(&self, modulo: &Integer) -> Option<Integer>

pub fn set_bit(&mut self, index: u32, value: bool) -> &mut Integer

pub fn random_below(self, rng: &mut impl RngCore) -> Integer

pub fn random_below_ref(&self, rng: &mut impl RngCore) -> Integer

pub fn random_bits(bits: u32, rng: &mut impl RngCore) -> Integer

pub fn random_bits_signed(bits: u32, rng: &mut impl RngCore) -> Integer

pub fn assign_random_below( &mut self, modulo: &Integer, rng: &mut impl RngCore, ) -> &mut Integer

pub fn assign_random_bits( &mut self, bits: u32, rng: &mut impl RngCore, ) -> &mut Integer

pub fn is_probably_prime(&self, _reps: u32, rng: &mut impl RngCore) -> IsPrime

pub fn generate_prime(rng: &mut impl RngCore, bit_size: u32) -> Integer

pub fn jacobi(&self, n: &Integer) -> i32

Compute jacobi symbol of a over n

Requires odd n >= 3. If it doesn’t hold, function panics if debug asserts are enabled, or returns 0 otherwise.

Implementation is taken from Handbook of Applied cryptography, p. 73, Algorithm 2.149

pub fn combine( &self, l: &Integer, le: &Integer, r: &Integer, re: &Integer, ) -> Option<Integer>

Compute l^le * r^re modulo self

impl Integer

pub fn in_mult_group_of(&self, n: &Integer) -> bool

Checks that self is in Z*_n

pub fn abs_in_mult_group_of(&self, n: &Integer) -> bool

Checks that abs(self) is in Z*_n

pub fn sample_in_mult_group_of(rng: &mut impl RngCore, n: &Integer) -> Integer

Samples x in Z*_n

pub fn sample_pm_in_mult_group_of( rng: &mut impl RngCore, n: &Integer, ) -> Integer

Samples x such that abs(x) is in Z*_n

pub fn generate_safe_prime(rng: &mut impl RngCore, bits: u32) -> Integer

Generates a random safe prime

Trait Implementations

impl Add<&Integer> for &Integer

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: &Integer) -> Integer

Performs the + operation.

impl Add<&Integer> for Integer

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: &Integer) -> Integer

Performs the + operation.

impl Add<&Integer> for u32

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: &Integer) -> Integer

Performs the + operation.

impl Add<Integer> for &Integer

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: Integer) -> Integer

Performs the + operation.

impl Add<Integer> for u32

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: Integer) -> Integer

Performs the + operation.

impl Add<i16> for &Integer

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: i16) -> Integer

Performs the + operation.

impl Add<i16> for Integer

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: i16) -> Integer

Performs the + operation.

impl Add<i32> for &Integer

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: i32) -> Integer

Performs the + operation.

impl Add<i32> for Integer

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: i32) -> Integer

Performs the + operation.

impl Add<i64> for &Integer

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: i64) -> Integer

Performs the + operation.

impl Add<i64> for Integer

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: i64) -> Integer

Performs the + operation.

impl Add<i8> for &Integer

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: i8) -> Integer

Performs the + operation.

impl Add<i8> for Integer

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: i8) -> Integer

Performs the + operation.

impl Add<isize> for &Integer

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: isize) -> Integer

Performs the + operation.

impl Add<isize> for Integer

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: isize) -> Integer

Performs the + operation.

impl Add<u16> for &Integer

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: u16) -> Integer

Performs the + operation.

impl Add<u16> for Integer

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: u16) -> Integer

Performs the + operation.

impl Add<u32> for &Integer

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: u32) -> Integer

Performs the + operation.

impl Add<u32> for Integer

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: u32) -> Integer

Performs the + operation.

impl Add<u64> for &Integer

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: u64) -> Integer

Performs the + operation.

impl Add<u64> for Integer

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: u64) -> Integer

Performs the + operation.

impl Add<u8> for &Integer

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: u8) -> Integer

Performs the + operation.

impl Add<u8> for Integer

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: u8) -> Integer

Performs the + operation.

impl Add<usize> for &Integer

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: usize) -> Integer

Performs the + operation.

impl Add<usize> for Integer

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: usize) -> Integer

Performs the + operation.

impl Add for Integer

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: Integer) -> Integer

Performs the + operation.

impl AddAssign<&Integer> for Integer

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

Performs the += operation.

impl AddAssign<i16> for Integer

fn add_assign(&mut self, rhs: i16)

Performs the += operation.

impl AddAssign<i32> for Integer

fn add_assign(&mut self, rhs: i32)

Performs the += operation.

impl AddAssign<i64> for Integer

fn add_assign(&mut self, rhs: i64)

Performs the += operation.

impl AddAssign<i8> for Integer

fn add_assign(&mut self, rhs: i8)

Performs the += operation.

impl AddAssign<isize> for Integer

fn add_assign(&mut self, rhs: isize)

Performs the += operation.

impl AddAssign<u16> for Integer

fn add_assign(&mut self, rhs: u16)

Performs the += operation.

impl AddAssign<u32> for Integer

fn add_assign(&mut self, rhs: u32)

Performs the += operation.

impl AddAssign<u64> for Integer

fn add_assign(&mut self, rhs: u64)

Performs the += operation.

impl AddAssign<u8> for Integer

fn add_assign(&mut self, rhs: u8)

Performs the += operation.

impl AddAssign<usize> for Integer

fn add_assign(&mut self, rhs: usize)

Performs the += operation.

impl AddAssign for Integer

fn add_assign(&mut self, rhs: Integer)

Performs the += operation.

impl BitAndAssign<u32> for Integer

fn bitand_assign(&mut self, rhs: u32)

Performs the &= operation.

impl BitOrAssign<u32> for Integer

fn bitor_assign(&mut self, rhs: u32)

Performs the |= operation.

impl Clone for Integer

fn clone(&self) -> Integer

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Integer

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

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for Integer

fn deserialize<D>( deserializer: D, ) -> Result<Integer, <D as Deserializer<'de>>::Error>

where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Display for Integer

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

Formats the value using the given formatter.

impl Div<&Integer> for &Integer

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: &Integer) -> Integer

Performs the / operation.

impl Div<&Integer> for Integer

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: &Integer) -> Integer

Performs the / operation.

impl Div<&Integer> for u32

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: &Integer) -> Integer

Performs the / operation.

impl Div<Integer> for &Integer

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: Integer) -> Integer

Performs the / operation.

impl Div<Integer> for u32

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: Integer) -> Integer

Performs the / operation.

impl Div<i16> for &Integer

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: i16) -> Integer

Performs the / operation.

impl Div<i16> for Integer

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: i16) -> Integer

Performs the / operation.

impl Div<i32> for &Integer

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: i32) -> Integer

Performs the / operation.

impl Div<i32> for Integer

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: i32) -> Integer

Performs the / operation.

impl Div<i64> for &Integer

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: i64) -> Integer

Performs the / operation.

impl Div<i64> for Integer

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: i64) -> Integer

Performs the / operation.

impl Div<i8> for &Integer

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: i8) -> Integer

Performs the / operation.

impl Div<i8> for Integer

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: i8) -> Integer

Performs the / operation.

impl Div<isize> for &Integer

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: isize) -> Integer

Performs the / operation.

impl Div<isize> for Integer

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: isize) -> Integer

Performs the / operation.

impl Div<u16> for &Integer

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: u16) -> Integer

Performs the / operation.

impl Div<u16> for Integer

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: u16) -> Integer

Performs the / operation.

impl Div<u32> for &Integer

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: u32) -> Integer

Performs the / operation.

impl Div<u32> for Integer

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: u32) -> Integer

Performs the / operation.

impl Div<u64> for &Integer

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: u64) -> Integer

Performs the / operation.

impl Div<u64> for Integer

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: u64) -> Integer

Performs the / operation.

impl Div<u8> for &Integer

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: u8) -> Integer

Performs the / operation.

impl Div<u8> for Integer

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: u8) -> Integer

Performs the / operation.

impl Div<usize> for &Integer

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: usize) -> Integer

Performs the / operation.

impl Div<usize> for Integer

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: usize) -> Integer

Performs the / operation.

impl Div for Integer

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: Integer) -> Integer

Performs the / operation.

impl DivAssign<&Integer> for Integer

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

Performs the /= operation.

impl DivAssign<i16> for Integer

fn div_assign(&mut self, rhs: i16)

Performs the /= operation.

impl DivAssign<i32> for Integer

fn div_assign(&mut self, rhs: i32)

Performs the /= operation.

impl DivAssign<i64> for Integer

fn div_assign(&mut self, rhs: i64)

Performs the /= operation.

impl DivAssign<i8> for Integer

fn div_assign(&mut self, rhs: i8)

Performs the /= operation.

impl DivAssign<isize> for Integer

fn div_assign(&mut self, rhs: isize)

Performs the /= operation.

impl DivAssign<u16> for Integer

fn div_assign(&mut self, rhs: u16)

Performs the /= operation.

impl DivAssign<u32> for Integer

fn div_assign(&mut self, rhs: u32)

Performs the /= operation.

impl DivAssign<u64> for Integer

fn div_assign(&mut self, rhs: u64)

Performs the /= operation.

impl DivAssign<u8> for Integer

fn div_assign(&mut self, rhs: u8)

Performs the /= operation.

impl DivAssign<usize> for Integer

fn div_assign(&mut self, rhs: usize)

Performs the /= operation.

impl DivAssign for Integer

fn div_assign(&mut self, rhs: Integer)

Performs the /= operation.

impl From<i32> for Integer

fn from(value: i32) -> Integer

Converts to this type from the input type.

impl From<u16> for Integer

fn from(value: u16) -> Integer

Converts to this type from the input type.

impl From<u32> for Integer

fn from(value: u32) -> Integer

Converts to this type from the input type.

impl From<u8> for Integer

fn from(value: u8) -> Integer

Converts to this type from the input type.

impl IntegerExt for Integer

fn to_scalar<C>(&self) -> Scalar<C>

where C: Curve,

Embed BigInt into chosen scalar type

fn curve_order<C>() -> Integer

where C: Curve,

Returns prime order of curve C

fn from_rng_half_pm<R>(rng: &mut R, range: &Integer) -> Integer

where R: RngCore,

Generates a random integer in interval [-range/2; range/2] if range is even [-(range-1)/2; (range-1)/2] if range is odd

fn is_in_half_pm(&self, range: &Integer) -> bool

Checks whether self is in interval [-range/2; range/2] when range is even [-(range-1)/2; (range-1)/2] when range is odd

impl Mul<&Integer> for &Integer

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: &Integer) -> Integer

Performs the * operation.

impl Mul<&Integer> for Integer

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: &Integer) -> Integer

Performs the * operation.

impl Mul<&Integer> for u32

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: &Integer) -> Integer

Performs the * operation.

impl Mul<Integer> for &Integer

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: Integer) -> Integer

Performs the * operation.

impl Mul<Integer> for u32

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: Integer) -> Integer

Performs the * operation.

impl Mul<i16> for &Integer

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: i16) -> Integer

Performs the * operation.

impl Mul<i16> for Integer

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: i16) -> Integer

Performs the * operation.

impl Mul<i32> for &Integer

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: i32) -> Integer

Performs the * operation.

impl Mul<i32> for Integer

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: i32) -> Integer

Performs the * operation.

impl Mul<i64> for &Integer

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: i64) -> Integer

Performs the * operation.

impl Mul<i64> for Integer

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: i64) -> Integer

Performs the * operation.

impl Mul<i8> for &Integer

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: i8) -> Integer

Performs the * operation.

impl Mul<i8> for Integer

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: i8) -> Integer

Performs the * operation.

impl Mul<isize> for &Integer

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: isize) -> Integer

Performs the * operation.

impl Mul<isize> for Integer

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: isize) -> Integer

Performs the * operation.

impl Mul<u16> for &Integer

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: u16) -> Integer

Performs the * operation.

impl Mul<u16> for Integer

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: u16) -> Integer

Performs the * operation.

impl Mul<u32> for &Integer

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: u32) -> Integer

Performs the * operation.

impl Mul<u32> for Integer

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: u32) -> Integer

Performs the * operation.

impl Mul<u64> for &Integer

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: u64) -> Integer

Performs the * operation.

impl Mul<u64> for Integer

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: u64) -> Integer

Performs the * operation.

impl Mul<u8> for &Integer

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: u8) -> Integer

Performs the * operation.

impl Mul<u8> for Integer

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: u8) -> Integer

Performs the * operation.

impl Mul<usize> for &Integer

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: usize) -> Integer

Performs the * operation.

impl Mul<usize> for Integer

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: usize) -> Integer

Performs the * operation.

impl Mul for Integer

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: Integer) -> Integer

Performs the * operation.

impl MulAssign<&Integer> for Integer

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

Performs the *= operation.

impl MulAssign<i16> for Integer

fn mul_assign(&mut self, rhs: i16)

Performs the *= operation.

impl MulAssign<i32> for Integer

fn mul_assign(&mut self, rhs: i32)

Performs the *= operation.

impl MulAssign<i64> for Integer

fn mul_assign(&mut self, rhs: i64)

Performs the *= operation.

impl MulAssign<i8> for Integer

fn mul_assign(&mut self, rhs: i8)

Performs the *= operation.

impl MulAssign<isize> for Integer

fn mul_assign(&mut self, rhs: isize)

Performs the *= operation.

impl MulAssign<u16> for Integer

fn mul_assign(&mut self, rhs: u16)

Performs the *= operation.

impl MulAssign<u32> for Integer

fn mul_assign(&mut self, rhs: u32)

Performs the *= operation.

impl MulAssign<u64> for Integer

fn mul_assign(&mut self, rhs: u64)

Performs the *= operation.

impl MulAssign<u8> for Integer

fn mul_assign(&mut self, rhs: u8)

Performs the *= operation.

impl MulAssign<usize> for Integer

fn mul_assign(&mut self, rhs: usize)

Performs the *= operation.

impl MulAssign for Integer

fn mul_assign(&mut self, rhs: Integer)

Performs the *= operation.

impl Neg for &Integer

type Output = Integer

The resulting type after applying the - operator.

fn neg(self) -> <&Integer as Neg>::Output

Performs the unary - operation.

impl Neg for Integer

type Output = Integer

The resulting type after applying the - operator.

fn neg(self) -> <Integer as Neg>::Output

Performs the unary - operation.

impl Ord for Integer

fn cmp(&self, other: &Integer) -> 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 Integer

fn eq(&self, other: &Integer) -> 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 Integer

fn partial_cmp(&self, other: &Integer) -> 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 Rem<&Integer> for &Integer

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: &Integer) -> Integer

Performs the % operation.

impl Rem<&Integer> for Integer

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: &Integer) -> Integer

Performs the % operation.

impl Rem<&Integer> for u32

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: &Integer) -> Integer

Performs the % operation.

impl Rem<Integer> for &Integer

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: Integer) -> Integer

Performs the % operation.

impl Rem<Integer> for u32

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: Integer) -> Integer

Performs the % operation.

impl Rem<i16> for &Integer

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: i16) -> Integer

Performs the % operation.

impl Rem<i16> for Integer

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: i16) -> Integer

Performs the % operation.

impl Rem<i32> for &Integer

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: i32) -> Integer

Performs the % operation.

impl Rem<i32> for Integer

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: i32) -> Integer

Performs the % operation.

impl Rem<i64> for &Integer

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: i64) -> Integer

Performs the % operation.

impl Rem<i64> for Integer

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: i64) -> Integer

Performs the % operation.

impl Rem<i8> for &Integer

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: i8) -> Integer

Performs the % operation.

impl Rem<i8> for Integer

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: i8) -> Integer

Performs the % operation.

impl Rem<isize> for &Integer

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: isize) -> Integer

Performs the % operation.

impl Rem<isize> for Integer

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: isize) -> Integer

Performs the % operation.

impl Rem<u16> for &Integer

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: u16) -> Integer

Performs the % operation.

impl Rem<u16> for Integer

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: u16) -> Integer

Performs the % operation.

impl Rem<u32> for &Integer

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: u32) -> Integer

Performs the % operation.

impl Rem<u32> for Integer

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: u32) -> Integer

Performs the % operation.

impl Rem<u64> for &Integer

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: u64) -> Integer

Performs the % operation.

impl Rem<u64> for Integer

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: u64) -> Integer

Performs the % operation.

impl Rem<u8> for &Integer

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: u8) -> Integer

Performs the % operation.

impl Rem<u8> for Integer

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: u8) -> Integer

Performs the % operation.

impl Rem<usize> for &Integer

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: usize) -> Integer

Performs the % operation.

impl Rem<usize> for Integer

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: usize) -> Integer

Performs the % operation.

impl Rem for Integer

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: Integer) -> Integer

Performs the % operation.

impl RemAssign<&Integer> for Integer

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

Performs the %= operation.

impl RemAssign<i16> for Integer

fn rem_assign(&mut self, rhs: i16)

Performs the %= operation.

impl RemAssign<i32> for Integer

fn rem_assign(&mut self, rhs: i32)

Performs the %= operation.

impl RemAssign<i64> for Integer

fn rem_assign(&mut self, rhs: i64)

Performs the %= operation.

impl RemAssign<i8> for Integer

fn rem_assign(&mut self, rhs: i8)

Performs the %= operation.

impl RemAssign<isize> for Integer

fn rem_assign(&mut self, rhs: isize)

Performs the %= operation.

impl RemAssign<u16> for Integer

fn rem_assign(&mut self, rhs: u16)

Performs the %= operation.

impl RemAssign<u32> for Integer

fn rem_assign(&mut self, rhs: u32)

Performs the %= operation.

impl RemAssign<u64> for Integer

fn rem_assign(&mut self, rhs: u64)

Performs the %= operation.

impl RemAssign<u8> for Integer

fn rem_assign(&mut self, rhs: u8)

Performs the %= operation.

impl RemAssign<usize> for Integer

fn rem_assign(&mut self, rhs: usize)

Performs the %= operation.

impl RemAssign for Integer

fn rem_assign(&mut self, rhs: Integer)

Performs the %= operation.

impl Serialize for Integer

fn serialize<S>( &self, serializer: S, ) -> Result<<S as Serializer>::Ok, <S as Serializer>::Error>

where S: Serializer,

Serialize this value into the given Serde serializer.

impl Shl<i32> for &Integer

type Output = Integer

The resulting type after applying the << operator.

fn shl(self, rhs: i32) -> Integer

Performs the << operation.

impl Shl<i32> for Integer

type Output = Integer

The resulting type after applying the << operator.

fn shl(self, rhs: i32) -> Integer

Performs the << operation.

impl Shl<u32> for &Integer

type Output = Integer

The resulting type after applying the << operator.

fn shl(self, rhs: u32) -> Integer

Performs the << operation.

impl Shl<u32> for Integer

type Output = Integer

The resulting type after applying the << operator.

fn shl(self, rhs: u32) -> Integer

Performs the << operation.

impl Shl<usize> for &Integer

type Output = Integer

The resulting type after applying the << operator.

fn shl(self, rhs: usize) -> Integer

Performs the << operation.

impl Shl<usize> for Integer

type Output = Integer

The resulting type after applying the << operator.

fn shl(self, rhs: usize) -> Integer

Performs the << operation.

impl ShlAssign<u32> for Integer

fn shl_assign(&mut self, rhs: u32)

Performs the <<= operation.

impl Shr<i32> for &Integer

type Output = Integer

The resulting type after applying the >> operator.

fn shr(self, rhs: i32) -> Integer

Performs the >> operation.

impl Shr<i32> for Integer

type Output = Integer

The resulting type after applying the >> operator.

fn shr(self, rhs: i32) -> Integer

Performs the >> operation.

impl Shr<u32> for &Integer

type Output = Integer

The resulting type after applying the >> operator.

fn shr(self, rhs: u32) -> Integer

Performs the >> operation.

impl Shr<u32> for Integer

type Output = Integer

The resulting type after applying the >> operator.

fn shr(self, rhs: u32) -> Integer

Performs the >> operation.

impl Shr<usize> for &Integer

type Output = Integer

The resulting type after applying the >> operator.

fn shr(self, rhs: usize) -> Integer

Performs the >> operation.

impl Shr<usize> for Integer

type Output = Integer

The resulting type after applying the >> operator.

fn shr(self, rhs: usize) -> Integer

Performs the >> operation.

impl ShrAssign<u32> for Integer

fn shr_assign(&mut self, rhs: u32)

Performs the >>= operation.

impl Sub<&Integer> for &Integer

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: &Integer) -> Integer

Performs the - operation.

impl Sub<&Integer> for Integer

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: &Integer) -> Integer

Performs the - operation.

impl Sub<&Integer> for u32

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: &Integer) -> Integer

Performs the - operation.

impl Sub<Integer> for &Integer

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: Integer) -> Integer

Performs the - operation.

impl Sub<Integer> for u32

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: Integer) -> Integer

Performs the - operation.

impl Sub<i16> for &Integer

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: i16) -> Integer

Performs the - operation.

impl Sub<i16> for Integer

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: i16) -> Integer

Performs the - operation.

impl Sub<i32> for &Integer

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: i32) -> Integer

Performs the - operation.

impl Sub<i32> for Integer

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: i32) -> Integer

Performs the - operation.

impl Sub<i64> for &Integer

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: i64) -> Integer

Performs the - operation.

impl Sub<i64> for Integer

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: i64) -> Integer

Performs the - operation.

impl Sub<i8> for &Integer

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: i8) -> Integer

Performs the - operation.

impl Sub<i8> for Integer

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: i8) -> Integer

Performs the - operation.

impl Sub<isize> for &Integer

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: isize) -> Integer

Performs the - operation.

impl Sub<isize> for Integer

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: isize) -> Integer

Performs the - operation.

impl Sub<u16> for &Integer

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: u16) -> Integer

Performs the - operation.

impl Sub<u16> for Integer

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: u16) -> Integer

Performs the - operation.

impl Sub<u32> for &Integer

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: u32) -> Integer

Performs the - operation.

impl Sub<u32> for Integer

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: u32) -> Integer

Performs the - operation.

impl Sub<u64> for &Integer

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: u64) -> Integer

Performs the - operation.

impl Sub<u64> for Integer

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: u64) -> Integer

Performs the - operation.

impl Sub<u8> for &Integer

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: u8) -> Integer

Performs the - operation.

impl Sub<u8> for Integer

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: u8) -> Integer

Performs the - operation.

impl Sub<usize> for &Integer

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: usize) -> Integer

Performs the - operation.

impl Sub<usize> for Integer

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: usize) -> Integer

Performs the - operation.

impl Sub for Integer

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: Integer) -> Integer

Performs the - operation.

impl SubAssign<&Integer> for Integer

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

Performs the -= operation.

impl SubAssign<i16> for Integer

fn sub_assign(&mut self, rhs: i16)

Performs the -= operation.

impl SubAssign<i32> for Integer

fn sub_assign(&mut self, rhs: i32)

Performs the -= operation.

impl SubAssign<i64> for Integer

fn sub_assign(&mut self, rhs: i64)

Performs the -= operation.

impl SubAssign<i8> for Integer

fn sub_assign(&mut self, rhs: i8)

Performs the -= operation.

impl SubAssign<isize> for Integer

fn sub_assign(&mut self, rhs: isize)

Performs the -= operation.

impl SubAssign<u16> for Integer

fn sub_assign(&mut self, rhs: u16)

Performs the -= operation.

impl SubAssign<u32> for Integer

fn sub_assign(&mut self, rhs: u32)

Performs the -= operation.

impl SubAssign<u64> for Integer

fn sub_assign(&mut self, rhs: u64)

Performs the -= operation.

impl SubAssign<u8> for Integer

fn sub_assign(&mut self, rhs: u8)

Performs the -= operation.

impl SubAssign<usize> for Integer

fn sub_assign(&mut self, rhs: usize)

Performs the -= operation.

impl SubAssign for Integer

fn sub_assign(&mut self, rhs: Integer)

Performs the -= operation.

impl Eq for Integer

impl StructuralPartialEq for Integer