Struct Ball 

pub struct Ball { /* private fields */ }

Enclosure mid ± rad used to certify that a rounded midpoint is unique.

Implementations

impl Ball

pub fn new(mid: ExactNum, rad: ExactNum) -> Self

mid ± rad. The radius is taken in absolute value.

pub fn mid(&self) -> &ExactNum

Midpoint of the enclosure.

pub fn rad(&self) -> &ExactNum

Non-negative radius.

pub fn add(&self, other: &Self, p: usize, rm: RoundingMode) -> Self

Sum of two balls: midpoint add at precision p, radius r1+r2 plus a rounding ulp.

pub fn mul(&self, other: &Self, p: usize, rm: RoundingMode) -> Self

Product of two balls with a first-order radius bound plus a rounding ulp.

pub fn exp(&self, p: usize, rm: RoundingMode, cc: &mut Consts) -> Self

Exponential of a ball. exp is increasing; the radius uses (\lvert\exp(m)\rvert(e^{r}-1)) plus a rounding ulp (same Up convention as add/mul).

pub fn sin(&self, p: usize, rm: RoundingMode, cc: &mut Consts) -> Self

Sine of a ball. (\lvert\sin’\rvert\le 1), so the image radius is at most rad plus a rounding ulp.

pub fn cos(&self, p: usize, rm: RoundingMode, cc: &mut Consts) -> Self

Cosine of a ball. (\lvert\cos’\rvert\le 1).

pub fn ln(&self, p: usize, rm: RoundingMode, cc: &mut Consts) -> Self

Natural log of a ball. Domain: the ball must lie in ((0,+\infty)). Lipschitz (\lvert\ln’\rvert=1/x\le 1/(m-r)).

pub fn sqrt(&self, p: usize, rm: RoundingMode) -> Self

Square root of a ball. Domain: the ball must lie in ((0,+\infty)). Lipschitz (1/(2\sqrt{x})\le 1/(2\sqrt{m-r})).

pub fn erf(&self, p: usize, rm: RoundingMode, cc: &mut Consts) -> Self

Error function of a ball. (\lvert\mathrm{erf}’\rvert\le 2/\sqrt{\pi}).

pub fn bessel_j0(&self, p: usize, rm: RoundingMode, cc: &mut Consts) -> Self

(J_0) of a ball. (\lvert J_0’\rvert=\lvert J_1\rvert\le 1).

pub fn bessel_j1(&self, p: usize, rm: RoundingMode, cc: &mut Consts) -> Self

(J_1) of a ball. (\lvert J_1’\rvert=\lvert J_0-J_1/x\rvert\le 1+1/(\lvert m\rvert-r)) when the ball excludes (0).

pub fn contains(&self, x: &ExactNum, p: usize) -> bool

True when x lies in [mid − rad, mid + rad] (NaN / Inf never contained).

Trait Implementations

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 Debug for Ball

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

Formats the value using the given formatter.