Struct triton_vm::prelude::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 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

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 fn raw_u64(&self) -> u64

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 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 MasterExtTable

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

The code for this method must be generated by running cargo run --bin constraint-evaluation-generator

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

The code for this method must be generated by running cargo run --bin constraint-evaluation-generator

fn evaluate_transition_constraints( current_base_row: ArrayView1<'_, BFieldElement>, current_ext_row: ArrayView1<'_, XFieldElement>, next_base_row: ArrayView1<'_, BFieldElement>, next_ext_row: ArrayView1<'_, XFieldElement>, challenges: &Challenges ) -> Vec<XFieldElement>

The code for this method must be generated by running cargo run --bin constraint-evaluation-generator

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

The code for this method must be generated by running cargo run --bin constraint-evaluation-generator

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(num_words: &NumberOfWords) -> Self

Converts to this type from the input type.

impl From<&OpStackElement> for BFieldElement

fn from(stack_element: &OpStackElement) -> Self

Converts to this type from the input type.

impl From<[u8; 8]> for BFieldElement

fn from(array: [u8; 8]) -> 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) -> Self

Converts to this type from the input type.

impl From<NumberOfWords> for BFieldElement

fn from(num_words: NumberOfWords) -> Self

Converts to this type from the input type.

impl From<OpStackElement> for BFieldElement

fn from(stack_element: OpStackElement) -> Self

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<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 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 MasterTable<BFieldElement> for MasterBaseTable

fn trace_domain(&self) -> ArithmeticDomain

fn randomized_trace_domain(&self) -> ArithmeticDomain

fn quotient_domain(&self) -> ArithmeticDomain

fn fri_domain(&self) -> ArithmeticDomain

fn trace_table(&self) -> ArrayView2<'_, BFieldElement>

Presents underlying trace data, excluding trace randomizers and randomizer polynomials.

fn trace_table_mut(&mut self) -> ArrayViewMut2<'_, BFieldElement>

Mutably presents underlying trace data, excluding trace randomizers and randomizer polynomials.

fn randomized_trace_table(&self) -> ArrayView2<'_, BFieldElement>

fn randomized_trace_table_mut(&mut self) -> ArrayViewMut2<'_, BFieldElement>

fn quotient_domain_table(&self) -> ArrayView2<'_, BFieldElement>

The low-degree extended randomized trace data over the quotient domain. Includes randomizer polynomials. Requires having called low_degree_extend_all_columns first.

fn fri_domain_table(&self) -> ArrayView2<'_, BFieldElement>

The low-degree extended randomized trace data over the FRI domain. Includes randomizer polynomials. Requires having called low_degree_extend_all_columns first.

fn memoize_low_degree_extended_table( &mut self, low_degree_extended_columns: Array2<BFieldElement> )

Not intended for direct use, but through Self::low_degree_extend_all_columns.

fn low_degree_extended_table(&self) -> ArrayView2<'_, BFieldElement>

Requires having called low_degree_extend_all_columns first.

fn memoize_interpolation_polynomials( &mut self, interpolation_polynomials: Array1<Polynomial<BFieldElement>> )

Memoize the polynomials interpolating the columns. Not intended for direct use, but through Self::low_degree_extend_all_columns.

fn interpolation_polynomials(&self) -> ArrayView1<'_, Polynomial<XFieldElement>>

Requires having called low_degree_extend_all_columns first.

fn row(&self, row_index: XFieldElement) -> Array1<XFieldElement>

Get one row of the table at an arbitrary index. Notably, the index does not have to be in any of the domains. In other words, can be used to compute out-of-domain rows. Requires having called low_degree_extend_all_columns first. Does not include randomizer polynomials.

fn hash_one_row(row: ArrayView1<'_, BFieldElement>) -> Digest

fn randomize_trace(&mut self)

Set all rows not part of the actual (padded) trace to random values.

fn low_degree_extend_all_columns(&mut self)

Low-degree extend all columns of the randomized trace domain table. The resulting low-degree extended columns can be accessed using quotient_domain_table and fri_domain_table.

fn merkle_tree( &self, maybe_profiler: &mut Option<TritonProfiler> ) -> MerkleTree<Tip5>

Compute a Merkle tree of the FRI domain table. Every row gives one leaf in the tree. The function hash_row is used to hash each row.

fn hash_all_fri_domain_rows(&self) -> Vec<Digest>

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 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

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

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

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

impl 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>,

Method which takes an iterator and generates Self from the elements by “summing up” the items.

impl TryFrom<&BFieldElement> for NumberOfWords

type Error = NumberOfWordsError

The type returned in the event of a conversion error.

fn try_from(index: &BFieldElement) -> Result<Self, NumberOfWordsError>

Performs the conversion.

impl TryFrom<BFieldElement> for Instruction

type Error = InstructionError

The type returned in the event of a conversion error.

fn try_from(opcode: BFieldElement) -> Result<Self, InstructionError>

Performs the conversion.

impl TryFrom<BFieldElement> for NumberOfWords

type Error = NumberOfWordsError

The type returned in the event of a conversion error.

fn try_from(index: BFieldElement) -> Result<Self, NumberOfWordsError>

Performs the conversion.

impl TryFrom<BFieldElement> for OpStackElement

type Error = OpStackElementError

The type returned in the event of a conversion error.

fn try_from(stack_index: BFieldElement) -> Result<Self, OpStackElementError>

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