Struct CircleDomain 

pub struct CircleDomain<F> { /* private fields */ }

A twin-coset of the circle group on F. It has a power-of-two size and an arbitrary shift.

X is generator, O is the first coset, goes counterclockwise

  O X .
 .     .
.       O <- start = shift
.   .   - (1,0)
O       .
 .     .
  . . O

For ordering reasons, the other half will start at gen / shift:

  . X O  <- start = gen/shift
 .     .
O       .
.   .   - (1,0)
.       O
 .     .
  O . .

The full domain is the interleaving of these two cosets

Implementations

impl<F: ComplexExtendable> CircleDomain<F>

pub const fn new(log_n: usize, shift: Point<F>) -> Self

pub fn standard(log_n: usize) -> Self

Trait Implementations

impl<F: Clone> Clone for CircleDomain<F>

fn clone(&self) -> CircleDomain<F>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<F: Copy> Copy for CircleDomain<F>

impl<F: Debug> Debug for CircleDomain<F>

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

Formats the value using the given formatter.

impl<F: Eq> Eq for CircleDomain<F>

impl<F: PartialEq> PartialEq for CircleDomain<F>

fn eq(&self, other: &CircleDomain<F>) -> bool

Equality operator ==.

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

Inequality operator !=.

impl<F: ComplexExtendable> PeriodicEvaluator<F, CircleDomain<F>> for CirclePeriodicEvaluator

fn eval_on_lde( periodic_table: &[Vec<F>], trace_domain: &CircleDomain<F>, lde_domain: &CircleDomain<F>, ) -> PeriodicLdeTable<F>

Evaluate all periodic columns on the LDE domain, returning a compact table.

fn eval_at_point<EF: ExtensionField<F>>( periodic_table: &[Vec<F>], trace_domain: &CircleDomain<F>, point: EF, ) -> Vec<EF>

Evaluate all periodic columns at a single point (for verification).

impl<F: ComplexExtendable> PolynomialSpace for CircleDomain<F>

fn split_domains(&self, num_chunks: usize) -> Vec<Self>

Decompose a domain into disjoint twin-cosets.

type Val = F

The base field F.

fn size(&self) -> usize

The number of elements of the space.

fn first_point(&self) -> Self::Val

The first point in the space.

fn next_point<Ext: ExtensionField<Self::Val>>(&self, x: Ext) -> Option<Ext>

An algebraic function which takes the i’th element of the space and returns the (i+1)’th evaluated on the given point.

fn try_create_disjoint_domain(&self, min_size: usize) -> Option<Self>

The non-panicking counterpart to Self::create_disjoint_domain.

fn split_evals( &self, num_chunks: usize, evals: RowMajorMatrix<Self::Val>, ) -> Vec<RowMajorMatrix<Self::Val>>

Split a set of polynomial evaluations over this PolynomialSpace into a vector of polynomial evaluations over each PolynomialSpace generated from split_domains.

fn vanishing_poly_at_point<Ext: ExtensionField<Self::Val>>( &self, point: Ext, ) -> Ext

Compute the vanishing polynomial of the space, evaluated at the given point.

fn selectors_at_point<Ext: ExtensionField<Self::Val>>( &self, point: Ext, ) -> LagrangeSelectors<Ext>

Compute several Lagrange selectors at a given point.

fn selectors_on_coset(&self, coset: Self) -> LagrangeSelectors<Vec<Self::Val>>

Compute several Lagrange selectors at all points of the given disjoint PolynomialSpace.

fn evaluate_polynomial_at<Ext: ExtensionField<F>>( &self, evals: &[F], point: Ext, ) -> Ext

Evaluate the polynomial defined by evals (evaluations over self) at point.

fn evaluate_periodic_column_at<Ext: ExtensionField<F>>( &self, col: &[F], point: Ext, ) -> Ext

Evaluate a periodic column polynomial at point.

fn create_disjoint_domain(&self, min_size: usize) -> Self

Return another PolynomialSpace with size at least min_size disjoint from this space.

fn evaluate_periodic_columns_at<Ext>( &self, periodic_columns: &[Vec<Self::Val>], point: Ext, ) -> Vec<Ext>

where Ext: ExtensionField<Self::Val>,

Evaluate several periodic column polynomials at point.

impl<F: PartialEq> StructuralPartialEq for CircleDomain<F>