Struct FilterBound 

pub struct FilterBound {
    pub degree: u32,
    pub epsilon_in_u: String,
    pub kappa_exact: String,
    pub products: u32,
    /* private fields */
}

The exact error bound of the f64 evaluation of a difference form.

For a call, let delta be the largest magnitude of the computed leaves (the differences of the coordinates of the approximations of the points), E the sum of the two largest errors of the approximations, and D = delta + E. The f64 value of the form differs from the exact value at the exact points by at most (epsilon * D + kappa * E) * D^(k - 1), where k is the degree, as long as no product underflows; see FilterBound::constants for the range in which underflow and overflow are accounted for.

Fields

degree: u32

The degree k of the form in the differences.

epsilon_in_u: String

epsilon / u, with u = 2^-53, as an exact fraction.

kappa_exact: String

kappa as an exact fraction.

products: u32

The number of products N in the form; a product used several times is counted once.

Implementations

impl FilterBound

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

Whether n u <= epsilon < n u (1 + 2^-40), exactly.

The exact epsilon is slightly above an integer multiple of u, because of the terms in u^2 and beyond.

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

Whether n <= kappa < n (1 + 2^-40), exactly.

pub fn constants(&self) -> FilterConstants

The constants of the filter.

epsilon and kappa are the exact values times 1 + 2^-30, rounded up; the inflation covers the rounding of the evaluation of the bound itself and an allowance for products that underflow. d_min is the smallest power of two below 1 for which that allowance covers underflow and the bound stays a normal number, and d_max the largest above 1 for which no computed node exceeds 2^1022; both exist, or filter_bound would have returned an error.

Trait Implementations

impl Clone for FilterBound

fn clone(&self) -> Self

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for FilterBound

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

Formats the value using the given formatter.