Struct ScalarWithErrorBound 

#[non_exhaustive]
pub struct ScalarWithErrorBound { /* private fields */ }

A scalar estimate paired with a certified absolute error bound.

Values of this type are produced by Vector::dot_with_errbound and Vector::dot_difference_with_errbound. The exact-real value of the corresponding expression over the stored binary64 inputs lies between lower_bound and upper_bound, and differs from estimate by at most absolute_error_bound.

The bound certifies floating-point roundoff in one specified arithmetic tree. It is not a caller-selected numerical tolerance and does not classify an interval containing zero as equality.

Callers cannot construct this type directly. Every value has a finite estimate, a finite non-negative absolute error bound, and finite ordered endpoints.

Examples

use core::assert_matches;
use la_stack::prelude::*;

let left = Vector::<2>::try_new([1.0, 2.0])?;
let right = Vector::<2>::try_new([3.0, 4.0])?;
let certificate = left.dot_with_errbound(&right)?;
assert_eq!(certificate.map(ScalarWithErrorBound::estimate), Some(11.0));
// Preserve None: without a certificate, an exact fallback is needed
// before making a claim about the exact-real result.
let enclosure = certificate.map(|bounded| (bounded.lower_bound(), bounded.upper_bound()));
assert_matches!(enclosure, Some((lower, upper)) if lower <= 11.0 && 11.0 <= upper);

Implementations

impl ScalarWithErrorBound

pub const fn estimate(self) -> f64

Return the rounded scalar estimate.

pub const fn absolute_error_bound(self) -> f64

Return the certified absolute error bound.

pub const fn lower_bound(self) -> f64

Return a finite outward-rounded lower bound on the exact-real value.

pub const fn upper_bound(self) -> f64

Return a finite outward-rounded upper bound on the exact-real value.

Trait Implementations

impl Clone for ScalarWithErrorBound

fn clone(&self) -> ScalarWithErrorBound

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Copy for ScalarWithErrorBound

impl Debug for ScalarWithErrorBound

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

Formats the value using the given formatter.

impl PartialEq for ScalarWithErrorBound

fn eq(&self, other: &ScalarWithErrorBound) -> bool

Equality operator ==.

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

Inequality operator !=.

impl StructuralPartialEq for ScalarWithErrorBound