halo2/rustdoc/latest/halo2_proofs/arithmetic/sidebar-items.js

window.SIDEBAR_ITEMS = {"fn":[["best_fft","Performs a radix-$2$ Fast-Fourier Transformation (FFT) on a vector of size $n = 2^k$, when provided `log_n` = $k$ and an element of multiplicative order $n$ called `omega` ($\\omega$). The result is that the vector `a`, when interpreted as the coefficients of a polynomial of degree $n - 1$, is transformed into the evaluations of this polynomial at each of the $n$ distinct powers of $\\omega$. This transformation is invertible by providing $\\omega^{-1}$ in place of $\\omega$ and dividing each resulting field element by $n$."],["best_multiexp","Performs a multi-exponentiation operation."],["compute_inner_product","This computes the inner product of two vectors `a` and `b`."],["eval_polynomial","This evaluates a provided polynomial (in coefficient form) at `point`."],["kate_division","Divides polynomial `a` in `X` by `X - b` with no remainder."],["lagrange_interpolate","Returns coefficients of an n - 1 degree polynomial given a set of n points and their evaluations. This function will panic if two values in `points` are the same."],["parallelize","This simple utility function will parallelize an operation that is to be performed over a mutable slice."],["recursive_butterfly_arithmetic","This perform recursive butterfly arithmetic"],["small_multiexp","Performs a small multi-exponentiation operation. Uses the double-and-add algorithm with doublings shared across points."]],"struct":[["Coordinates","The affine coordinates of a point on an elliptic curve."],["SqrtTables","Tables used for square root computation."]],"trait":[["CurveAffine","This trait is the affine counterpart to `Curve` and is used for serialization, storage in memory, and inspection of $x$ and $y$ coordinates."],["CurveExt","This trait is a common interface for dealing with elements of an elliptic curve group in a “projective” form, where that arithmetic is usually more efficient."],["Field","This trait represents an element of a field."],["FieldExt","This trait is a common interface for dealing with elements of a finite field."],["Group","This represents an element of a group with basic operations that can be performed. This allows an FFT implementation (for example) to operate generically over either a field or elliptic curve group."],["SqrtRatio","A trait that exposes additional operations related to calculating square roots of prime-order finite fields."]]};