Struct Dyadic

pub struct Dyadic { /* private fields */ }

An exact value mantissa * 2^exponent.

Implementations

impl Dyadic

pub fn zero() -> Self

Zero.

pub fn from_parts(mantissa: BigInt, exponent: i64) -> Self

mantissa * 2^exponent, normalised.

pub fn try_from_f64(value: f64) -> Option<Self>

The exact value of a finite f64, or None for NaN and infinities.

pub fn mantissa(&self) -> &BigInt

The mantissa of the normalised form.

pub fn exponent(&self) -> i64

The power-of-two exponent of the normalised form.

pub fn enclosure(&self) -> Interval

A sound f64 interval containing the value.

The top 64 mantissa bits are taken with a floor shift (the value lies within one unit of them), converted with one rounding, then scaled by an exact power of two and widened two steps each way, which covers both errors even at a binade boundary. Values whose scaled result would leave the normal f64 range get the whole line: sound, and never decisive.

pub fn approx_parts(&self) -> (f64, i64)

(m, e) with the value within a relative 2^-52 of m * 2^e, where m is a double of magnitude in [2^52, 2^53), or (0, 0).

Unlike Dyadic::to_f64 this never overflows or underflows, so ratios and roots of huge or tiny values stay accurate: combine the parts first, apply the exponent last. For output only.

pub fn bits(&self) -> u64

Bits in the mantissa: the cost driver of every operation.

pub fn to_f64(&self) -> f64

A nearby double, for output only; never for decisions.

Takes the top 64 mantissa bits, so the result is within a few ulps of the value. Overflows to an infinity and underflows to zero like any f64 conversion.

Trait Implementations

impl Arith for Dyadic

fn from_f64(value: f64) -> Self

Panics

On NaN or an infinity, which have no exact value. The public entry points reject them first (crate::require_finite).

fn from_dyadic(value: &Dyadic) -> Self

The value of an exact dyadic number: itself in the exact tier, a sound enclosure in the interval tier (Dyadic::enclosure).

fn add(&self, other: &Self) -> Self

self + other.

fn sub(&self, other: &Self) -> Self

self - other.

fn mul(&self, other: &Self) -> Self

self * other.

fn neg(&self) -> Self

-self.

fn sign(&self) -> Option<Sign>

The sign, or None when this arithmetic cannot decide it.

fn sqrt_enclosure(&self) -> Option<Self>

An enclosure of sqrt(self), for approximate arithmetics only.

fn square(&self) -> Self

self * self.

impl Clone for Dyadic

fn clone(&self) -> Dyadic

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for Dyadic

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

Formats the value using the given formatter.

impl Hash for Dyadic

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl PartialEq for Dyadic

fn eq(&self, other: &Dyadic) -> 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 Eq for Dyadic

impl StructuralPartialEq for Dyadic