Struct Ball 

pub struct Ball {
    pub mid: f64,
    pub rad: f64,
}

A ball: midpoint ± radius, guaranteed to contain the true value.

Invariant: rad >= 0.

Fields

mid: f64

Midpoint of the enclosure interval.

rad: f64

Radius (non-negative) of the enclosure interval.

Implementations

impl Ball

pub fn new(mid: f64, rad: f64) -> Ball

Construct a ball with the given midpoint and radius.

Panics

In debug builds, panics when rad < 0.

pub fn from_exact(x: f64) -> Ball

Construct a point ball (exact representation, radius 0).

pub fn from_interval(lo: f64, hi: f64) -> Option<Ball>

Construct a ball from a closed interval [lo, hi].

Returns None when lo > hi.

pub fn lo(&self) -> f64

Lower bound of the enclosure interval.

pub fn hi(&self) -> f64

Upper bound of the enclosure interval.

pub fn contains(&self, x: f64) -> bool

Returns true when the ball strictly contains x.

pub fn overlaps(&self, other: &Ball) -> bool

Returns true when this ball overlaps with other.

pub fn is_valid(&self) -> bool

Returns true when the ball represents a valid enclosure (rad >= 0).

pub fn add(&self, other: &Ball) -> Ball

Add two balls, propagating the enclosure guarantee.

[a±r_a] + [b±r_b] = [a+b ± (r_a + r_b + fp_rounding)]

pub fn sub(&self, other: &Ball) -> Ball

Subtract two balls.

pub fn mul(&self, other: &Ball) -> Ball

Multiply two balls using the interval arithmetic rule.

Multiplication error bound: |a*b - mid_a*mid_b| <= |mid_a|*r_b + |mid_b|*r_a + r_a*r_b plus floating-point rounding of the midpoint product.

pub fn div(&self, other: &Ball) -> Option<Ball>

Divide two balls. Returns None when the divisor ball contains 0.

pub fn neg(&self) -> Ball

Negate a ball.

pub fn abs(&self) -> Ball

Absolute value of a ball.

pub fn sqrt(&self) -> Option<Ball>

Square root of a ball. Returns None if the interval contains a negative number.

pub fn powi(&self, n: i32) -> Ball

Raise a ball to an integer power.

Trait Implementations

impl Add for Ball

type Output = Ball

The resulting type after applying the + operator.

fn add(self, rhs: Ball) -> Ball

Performs the + operation.

impl Clone for Ball

fn clone(&self) -> Ball

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Copy for Ball

impl Debug for Ball

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

Formats the value using the given formatter.

impl Mul for Ball

type Output = Ball

The resulting type after applying the * operator.

fn mul(self, rhs: Ball) -> Ball

Performs the * operation.

impl Neg for Ball

type Output = Ball

The resulting type after applying the - operator.

fn neg(self) -> Ball

Performs the unary - operation.

impl PartialEq for Ball

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

Tests for self and other values to be equal, and is used by ==.

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

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

impl StructuralPartialEq for Ball

impl Sub for Ball

type Output = Ball

The resulting type after applying the - operator.

fn sub(self, rhs: Ball) -> Ball

Performs the - operation.