Struct BFieldElement

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

Base field element ∈ ℤ_{2^64 - 2^32 + 1}.

In Montgomery representation. This implementation follows https://eprint.iacr.org/2022/274.pdf and https://github.com/novifinancial/winterfell/pull/101/files.

Implementations

impl BFieldElement

pub const BYTES: usize = 8usize

pub const P: u64 = 18_446_744_069_414_584_321u64

The base field’s prime, i.e., 2^64 - 2^32 + 1.

pub const MAX: u64 = 18_446_744_069_414_584_320u64

pub const MINUS_TWO_INVERSE: BFieldElement = _

-2^-1

pub const fn new(value: u64) -> BFieldElement

pub const fn value(&self) -> u64

pub const fn power_accumulator<const N: usize, const M: usize>( base: [BFieldElement; N], tail: [BFieldElement; N], ) -> [BFieldElement; N]

Square the base M times and multiply the result by the tail value

pub const fn generator() -> BFieldElement

Get a generator for the entire field

pub const fn lift(&self) -> XFieldElement

pub fn increment(&mut self)

pub fn decrement(&mut self)

pub const fn mod_pow(&self, exp: u64) -> BFieldElement

pub fn from_ne_bytes(bytes: &[u8]) -> BFieldElement

👎Deprecated since 0.42.0: endianness must not be platform specific; use <&[u8]>::try_from() instead

Convert a BFieldElement from a byte slice in native endianness.

pub const fn montyred(x: u128) -> u64

Montgomery reduction

pub const fn raw_bytes(&self) -> [u8; 8]

Return the raw bytes or 8-bit chunks of the Montgomery representation, in little-endian byte order

pub const fn from_raw_bytes(bytes: &[u8; 8]) -> BFieldElement

Take a slice of 8 bytes and interpret it as an integer in little-endian byte order, and cast it to a BFieldElement in Montgomery representation

pub const fn raw_u16s(&self) -> [u16; 4]

Return the raw 16-bit chunks of the Montgomery representation, in little-endian chunk order

pub const fn from_raw_u16s(chunks: &[u16; 4]) -> BFieldElement

Take a slice of 4 16-bit chunks and interpret it as an integer in little-endian chunk order, and cast it to a BFieldElement in Montgomery representation

pub fn raw_u128(&self) -> u128

pub const fn from_raw_u64(e: u64) -> BFieldElement

pub const fn raw_u64(&self) -> u64

pub const fn is_canonical(x: u64) -> bool

Trait Implementations

impl Add<BFieldElement> for XFieldElement

type Output = XFieldElement

The resulting type after applying the + operator.

fn add(self, other: BFieldElement) -> XFieldElement

Performs the + operation.

impl Add<XFieldElement> for BFieldElement

The bfe + xfe -> xfe instance belongs to BFieldElement.

type Output = XFieldElement

The resulting type after applying the + operator.

fn add(self, other: XFieldElement) -> XFieldElement

Performs the + operation.

impl Add for BFieldElement

type Output = BFieldElement

The resulting type after applying the + operator.

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

Performs the + operation.

impl AddAssign<BFieldElement> for XFieldElement

fn add_assign(&mut self, rhs: BFieldElement)

Performs the += operation.

impl AddAssign for BFieldElement

fn add_assign(&mut self, rhs: BFieldElement)

Performs the += operation.

impl<'a> Arbitrary<'a> for BFieldElement

fn arbitrary(u: &mut Unstructured<'a>) -> Result<BFieldElement, Error>

Generate an arbitrary value of Self from the given unstructured data.

fn arbitrary_take_rest(u: Unstructured<'a>) -> Result<Self, Error>

Generate an arbitrary value of Self from the entirety of the given unstructured data.

fn size_hint(depth: usize) -> (usize, Option<usize>)

Get a size hint for how many bytes out of an Unstructured this type needs to construct itself.

impl BFieldCodec for BFieldElement

type Error = BFieldCodecError

fn decode( sequence: &[BFieldElement], ) -> Result<Box<BFieldElement>, <BFieldElement as BFieldCodec>::Error>

fn encode(&self) -> Vec<BFieldElement>

fn static_length() -> Option<usize>

Returns the length in number of BFieldElements if it is known at compile-time. Otherwise, None.

impl Clone for BFieldElement

fn clone(&self) -> BFieldElement

Returns a copy of the value.

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

Performs copy-assignment from source.

impl ConstOne for BFieldElement

const ONE: BFieldElement = _

The multiplicative identity element of Self, 1.

impl ConstZero for BFieldElement

const ZERO: BFieldElement = _

The additive identity element of Self, 0.

impl CyclicGroupGenerator for BFieldElement

fn get_cyclic_group_elements(&self, max: Option<usize>) -> Vec<BFieldElement>

impl Debug for BFieldElement

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

Formats the value using the given formatter.

impl Default for BFieldElement

fn default() -> BFieldElement

Returns the “default value” for a type.

impl<'de> Deserialize<'de> for BFieldElement

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

where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Display for BFieldElement

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

Formats the value using the given formatter.

impl Div for BFieldElement

type Output = BFieldElement

The resulting type after applying the / operator.

fn div(self, other: BFieldElement) -> BFieldElement

Performs the / operation.

impl Evaluable<BFieldElement> for MasterAuxTable

fn evaluate_initial_constraints( main_row: ArrayView1<'_, BFieldElement>, aux_row: ArrayView1<'_, XFieldElement>, challenges: &Challenges, ) -> Vec<XFieldElement>

fn evaluate_consistency_constraints( main_row: ArrayView1<'_, BFieldElement>, aux_row: ArrayView1<'_, XFieldElement>, challenges: &Challenges, ) -> Vec<XFieldElement>

fn evaluate_transition_constraints( current_main_row: ArrayView1<'_, BFieldElement>, current_aux_row: ArrayView1<'_, XFieldElement>, next_main_row: ArrayView1<'_, BFieldElement>, next_aux_row: ArrayView1<'_, XFieldElement>, challenges: &Challenges, ) -> Vec<XFieldElement>

fn evaluate_terminal_constraints( main_row: ArrayView1<'_, BFieldElement>, aux_row: ArrayView1<'_, XFieldElement>, challenges: &Challenges, ) -> Vec<XFieldElement>

impl FiniteField for BFieldElement

fn batch_inversion(input: Vec<Self>) -> Vec<Self>

Montgomery Batch Inversion

fn square(self) -> Self

impl From<&NumberOfWords> for BFieldElement

fn from(_: &NumberOfWords) -> BFieldElement

Converts to this type from the input type.

impl From<&OpStackElement> for BFieldElement

fn from(_: &OpStackElement) -> BFieldElement

Converts to this type from the input type.

impl From<BFieldElement> for [u8; 8]

Convert a B-field element to a byte array. The client uses this for its database.

fn from(bfe: BFieldElement) -> [u8; 8]

Converts to this type from the input type.

impl From<HashTableMode> for BFieldElement

fn from(mode: HashTableMode) -> BFieldElement

Converts to this type from the input type.

impl From<NumberOfWords> for BFieldElement

fn from(num_words: NumberOfWords) -> BFieldElement

Converts to this type from the input type.

impl From<OpStackElement> for BFieldElement

fn from(stack_element: OpStackElement) -> BFieldElement

Converts to this type from the input type.

impl From<i16> for BFieldElement

fn from(value: i16) -> BFieldElement

Converts to this type from the input type.

impl From<i32> for BFieldElement

fn from(value: i32) -> BFieldElement

Converts to this type from the input type.

impl From<i64> for BFieldElement

fn from(value: i64) -> BFieldElement

Converts to this type from the input type.

impl From<i8> for BFieldElement

fn from(value: i8) -> BFieldElement

Converts to this type from the input type.

impl From<isize> for BFieldElement

fn from(value: isize) -> BFieldElement

Converts to this type from the input type.

impl From<u128> for BFieldElement

fn from(value: u128) -> BFieldElement

Converts to this type from the input type.

impl From<u16> for BFieldElement

fn from(value: u16) -> BFieldElement

Converts to this type from the input type.

impl From<u32> for BFieldElement

fn from(value: u32) -> BFieldElement

Converts to this type from the input type.

impl From<u64> for BFieldElement

fn from(value: u64) -> BFieldElement

Converts to this type from the input type.

impl From<u8> for BFieldElement

fn from(value: u8) -> BFieldElement

Converts to this type from the input type.

impl From<usize> for BFieldElement

fn from(value: usize) -> BFieldElement

Converts to this type from the input type.

impl FromStr for BFieldElement

type Err = ParseBFieldElementError

The associated error which can be returned from parsing.

fn from_str(s: &str) -> Result<BFieldElement, <BFieldElement as FromStr>::Err>

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

impl GetSize for BFieldElement

fn get_stack_size() -> usize

Determines how may bytes this object occupies inside the stack.

fn get_heap_size(&self) -> usize

Determines how many bytes this object occupies inside the heap.

fn get_size(&self) -> usize

Determines the total size of the object.

impl Hash for BFieldElement

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

where __H: Hasher,

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 Inverse for BFieldElement

fn inverse(&self) -> BFieldElement

fn inverse_or_zero(&self) -> Self

impl ModPowU32 for BFieldElement

fn mod_pow_u32(&self, exp: u32) -> BFieldElement

impl ModPowU64 for BFieldElement

fn mod_pow_u64(&self, pow: u64) -> BFieldElement

impl Mul<BFieldElement> for XFieldElement

XField * BField means scalar multiplication of the BFieldElement onto each coefficient of the XField.

type Output = XFieldElement

The resulting type after applying the * operator.

fn mul(self, other: BFieldElement) -> XFieldElement

Performs the * operation.

impl<FF, FF2> Mul<Polynomial<'_, FF>> for BFieldElement

where FF: FiniteField<Output = FF2> + Mul<BFieldElement>, FF2: 'static + FiniteField,

type Output = Polynomial<'static, FF2>

The resulting type after applying the * operator.

fn mul( self, other: Polynomial<'_, FF>, ) -> <BFieldElement as Mul<Polynomial<'_, FF>>>::Output

Performs the * operation.

impl Mul<XFieldElement> for BFieldElement

type Output = XFieldElement

The resulting type after applying the * operator.

fn mul(self, other: XFieldElement) -> XFieldElement

Performs the * operation.

impl Mul for BFieldElement

type Output = BFieldElement

The resulting type after applying the * operator.

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

Performs the * operation.

impl MulAssign<BFieldElement> for XFieldElement

fn mul_assign(&mut self, rhs: BFieldElement)

Performs the *= operation.

impl MulAssign for BFieldElement

fn mul_assign(&mut self, rhs: BFieldElement)

Performs the *= operation.

impl Neg for BFieldElement

type Output = BFieldElement

The resulting type after applying the - operator.

fn neg(self) -> BFieldElement

Performs the unary - operation.

impl One for BFieldElement

fn one() -> BFieldElement

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 PartialEq for BFieldElement

fn eq(&self, other: &BFieldElement) -> 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 PrimitiveRootOfUnity for BFieldElement

fn primitive_root_of_unity(n: u64) -> Option<BFieldElement>

impl Serialize for BFieldElement

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 Sub<BFieldElement> for XFieldElement

type Output = XFieldElement

The resulting type after applying the - operator.

fn sub(self, other: BFieldElement) -> XFieldElement

Performs the - operation.

impl Sub<XFieldElement> for BFieldElement

type Output = XFieldElement

The resulting type after applying the - operator.

fn sub(self, other: XFieldElement) -> XFieldElement

Performs the - operation.

impl Sub for BFieldElement

type Output = BFieldElement

The resulting type after applying the - operator.

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

Performs the - operation.

impl SubAssign<BFieldElement> for XFieldElement

fn sub_assign(&mut self, rhs: BFieldElement)

Performs the -= operation.

impl SubAssign for BFieldElement

fn sub_assign(&mut self, rhs: BFieldElement)

Performs the -= operation.

impl Sum for BFieldElement

fn sum<I>(iter: I) -> BFieldElement

where I: Iterator<Item = BFieldElement>,

Takes an iterator and generates Self from the elements by “summing up” the items.

impl TryFrom<&[u8]> for BFieldElement

type Error = ParseBFieldElementError

The type returned in the event of a conversion error.

fn try_from( bytes: &[u8], ) -> Result<BFieldElement, <BFieldElement as TryFrom<&[u8]>>::Error>

Performs the conversion.

impl TryFrom<[u8; 8]> for BFieldElement

type Error = ParseBFieldElementError

The type returned in the event of a conversion error.

fn try_from( array: [u8; 8], ) -> Result<BFieldElement, <BFieldElement as TryFrom<[u8; 8]>>::Error>

Performs the conversion.

impl Zero for BFieldElement

fn zero() -> BFieldElement

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 Copy for BFieldElement

impl Eq for BFieldElement

impl StructuralPartialEq for BFieldElement