Struct Felt 

pub struct Felt { /* private fields */ }

Lightweight representation of a constant value.

The actual value is interned which allows this type to be Copy and avoids duplication of commonly used values.

Implementations

impl Felt

pub fn new<F: PrimeField>(f: F) -> Self

Creates a new felt from an implementation of PrimeField.

pub fn from_parts(value: BigUint, prime: Prime) -> Self

Creates a new felt from its raw parts.

pub fn prime(&self) -> Prime

Returns the value of the field prime.

pub fn is_minus_one(&self) -> bool

Returns true if the felt represents -1 mod P.

Methods from Deref<Target = BigUint>

pub const ZERO: BigUint

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

Returns the byte representation of the BigUint in big-endian byte order.

Examples

use num_bigint::BigUint;

let i = BigUint::parse_bytes(b"1125", 10).unwrap();
assert_eq!(i.to_bytes_be(), vec![4, 101]);

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

Returns the byte representation of the BigUint in little-endian byte order.

Examples

use num_bigint::BigUint;

let i = BigUint::parse_bytes(b"1125", 10).unwrap();
assert_eq!(i.to_bytes_le(), vec![101, 4]);

pub fn to_u32_digits(&self) -> Vec<u32>

Returns the u32 digits representation of the BigUint ordered least significant digit first.

Examples

use num_bigint::BigUint;

assert_eq!(BigUint::from(1125u32).to_u32_digits(), vec![1125]);
assert_eq!(BigUint::from(4294967295u32).to_u32_digits(), vec![4294967295]);
assert_eq!(BigUint::from(4294967296u64).to_u32_digits(), vec![0, 1]);
assert_eq!(BigUint::from(112500000000u64).to_u32_digits(), vec![830850304, 26]);

pub fn to_u64_digits(&self) -> Vec<u64>

Returns the u64 digits representation of the BigUint ordered least significant digit first.

Examples

use num_bigint::BigUint;

assert_eq!(BigUint::from(1125u32).to_u64_digits(), vec![1125]);
assert_eq!(BigUint::from(4294967295u32).to_u64_digits(), vec![4294967295]);
assert_eq!(BigUint::from(4294967296u64).to_u64_digits(), vec![4294967296]);
assert_eq!(BigUint::from(112500000000u64).to_u64_digits(), vec![112500000000]);
assert_eq!(BigUint::from(1u128 << 64).to_u64_digits(), vec![0, 1]);

pub fn iter_u32_digits(&self) -> U32Digits<'_>

Returns an iterator of u32 digits representation of the BigUint ordered least significant digit first.

Examples

use num_bigint::BigUint;

assert_eq!(BigUint::from(1125u32).iter_u32_digits().collect::<Vec<u32>>(), vec![1125]);
assert_eq!(BigUint::from(4294967295u32).iter_u32_digits().collect::<Vec<u32>>(), vec![4294967295]);
assert_eq!(BigUint::from(4294967296u64).iter_u32_digits().collect::<Vec<u32>>(), vec![0, 1]);
assert_eq!(BigUint::from(112500000000u64).iter_u32_digits().collect::<Vec<u32>>(), vec![830850304, 26]);

pub fn iter_u64_digits(&self) -> U64Digits<'_>

Returns an iterator of u64 digits representation of the BigUint ordered least significant digit first.

Examples

use num_bigint::BigUint;

assert_eq!(BigUint::from(1125u32).iter_u64_digits().collect::<Vec<u64>>(), vec![1125]);
assert_eq!(BigUint::from(4294967295u32).iter_u64_digits().collect::<Vec<u64>>(), vec![4294967295]);
assert_eq!(BigUint::from(4294967296u64).iter_u64_digits().collect::<Vec<u64>>(), vec![4294967296]);
assert_eq!(BigUint::from(112500000000u64).iter_u64_digits().collect::<Vec<u64>>(), vec![112500000000]);
assert_eq!(BigUint::from(1u128 << 64).iter_u64_digits().collect::<Vec<u64>>(), vec![0, 1]);

pub fn to_str_radix(&self, radix: u32) -> String

Returns the integer formatted as a string in the given radix. radix must be in the range 2...36.

Examples

use num_bigint::BigUint;

let i = BigUint::parse_bytes(b"ff", 16).unwrap();
assert_eq!(i.to_str_radix(16), "ff");

pub fn to_radix_be(&self, radix: u32) -> Vec<u8>

Returns the integer in the requested base in big-endian digit order. The output is not given in a human readable alphabet but as a zero based u8 number. radix must be in the range 2...256.

Examples

use num_bigint::BigUint;

assert_eq!(BigUint::from(0xFFFFu64).to_radix_be(159),
           vec![2, 94, 27]);
// 0xFFFF = 65535 = 2*(159^2) + 94*159 + 27

pub fn to_radix_le(&self, radix: u32) -> Vec<u8>

Returns the integer in the requested base in little-endian digit order. The output is not given in a human readable alphabet but as a zero based u8 number. radix must be in the range 2...256.

Examples

use num_bigint::BigUint;

assert_eq!(BigUint::from(0xFFFFu64).to_radix_le(159),
           vec![27, 94, 2]);
// 0xFFFF = 65535 = 27 + 94*159 + 2*(159^2)

pub fn bits(&self) -> u64

Determines the fewest bits necessary to express the BigUint.

pub fn pow(&self, exponent: u32) -> BigUint

Returns self ^ exponent.

pub fn modpow(&self, exponent: &BigUint, modulus: &BigUint) -> BigUint

Returns (self ^ exponent) % modulus.

Panics if the modulus is zero.

pub fn modinv(&self, modulus: &BigUint) -> Option<BigUint>

Returns the modular multiplicative inverse if it exists, otherwise None.

This solves for x in the interval [0, modulus) such that self * x ≡ 1 (mod modulus). The solution exists if and only if gcd(self, modulus) == 1.

use num_bigint::BigUint;
use num_traits::{One, Zero};

let m = BigUint::from(383_u32);

// Trivial cases
assert_eq!(BigUint::zero().modinv(&m), None);
assert_eq!(BigUint::one().modinv(&m), Some(BigUint::one()));
let neg1 = &m - 1u32;
assert_eq!(neg1.modinv(&m), Some(neg1));

let a = BigUint::from(271_u32);
let x = a.modinv(&m).unwrap();
assert_eq!(x, BigUint::from(106_u32));
assert_eq!(x.modinv(&m).unwrap(), a);
assert!((a * x % m).is_one());

pub fn sqrt(&self) -> BigUint

Returns the truncated principal square root of self – see Roots::sqrt

pub fn cbrt(&self) -> BigUint

Returns the truncated principal cube root of self – see Roots::cbrt.

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

Returns the truncated principal nth root of self – see Roots::nth_root.

pub fn trailing_zeros(&self) -> Option<u64>

Returns the number of least-significant bits that are zero, or None if the entire number is zero.

pub fn trailing_ones(&self) -> u64

Returns the number of least-significant bits that are ones.

pub fn count_ones(&self) -> u64

Returns the number of one bits.

pub fn bit(&self, bit: u64) -> bool

Returns whether the bit in the given position is set

Trait Implementations

impl Add for Felt

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

Panics

If the primes are different.

type Output = Felt

The resulting type after applying the + operator.

impl AddAssign for Felt

fn add_assign(&mut self, rhs: Self)

Panics

If the primes are different.

impl AsRef<BigUint> for Felt

fn as_ref(&self) -> &BigUint

Converts this type into a shared reference of the (usually inferred) input type.

impl Clone for Felt

fn clone(&self) -> Felt

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Felt

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

Formats the value using the given formatter.

impl Deref for Felt

type Target = BigUint

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl Display for Felt

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

Formats the value using the given formatter.

impl<F: PrimeField> From<F> for Felt

fn from(value: F) -> Self

Converts to this type from the input type.

impl Hash for Felt

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl Mul for Felt

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

Panics

If the primes are different.

type Output = Felt

The resulting type after applying the * operator.

impl MulAssign for Felt

fn mul_assign(&mut self, rhs: Self)

Panics

If the primes are different.

impl Neg for Felt

type Output = Felt

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl Ord for Felt

fn cmp(&self, other: &Felt) -> 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<T> PartialEq<T> for Felt

where T: Into<BigUint> + Copy,

fn eq(&self, other: &T) -> 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 PartialEq for Felt

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

fn partial_cmp(&self, other: &Felt) -> 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<Prime> for Felt

type Output = Felt

The resulting type after applying the % operator.

fn rem(self, prime: Prime) -> Self::Output

Performs the % operation.

impl Rem for Felt

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

Panics

If the primes are different.

type Output = Felt

The resulting type after applying the % operator.

impl RemAssign<Prime> for Felt

fn rem_assign(&mut self, rhs: Prime)

Performs the %= operation.

impl RemAssign for Felt

fn rem_assign(&mut self, rhs: Self)

Panics

If the primes are different.

impl Sub for Felt

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

Panics

If the primes are different.

type Output = Felt

The resulting type after applying the - operator.

impl SubAssign for Felt

fn sub_assign(&mut self, rhs: Self)

Panics

If the primes are different.

impl Copy for Felt

impl Eq for Felt

impl StructuralPartialEq for Felt