Struct inari::Interval

#[repr(C)]pub struct Interval { /* fields omitted */ }

The bare inf-sup interval type with f64 bounds.

Implementations

impl Interval

pub fn abs(self) -> Self

Returns the absolute value of self.

Tightness: tightest

pub fn max(self, rhs: Self) -> Self

Returns $[\max(a, c), \max(b, d)]$ if both $\self = [a, b]$ and $\rhs = [c, d]$ are nonempty; otherwise, $∅$.

Tightness: tightest

pub fn min(self, rhs: Self) -> Self

Returns $[\min(a, c), \min(b, d)]$ if both $\self = [a, b]$ and $\rhs = [c, d]$ are nonempty; otherwise $∅$.

Tightness: tightest

impl Interval

pub fn mul_add(self, rhs: Self, addend: Self) -> Self

Returns $\self × \rhs + \addend$.

Tightness: tightest

pub fn recip(self) -> Self

Returns the multiplicative inverse of self.

Tightness: tightest

pub fn sqr(self) -> Self

Returns the square of self.

Tightness: tightest

pub fn sqrt(self) -> Self

Returns the principal square root of self.

Tightness: tightest

impl Interval

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

Returns true if rhs is a member of self ($\rhs ∈ \self$).

If rhs is not a real number, false is returned.

pub fn disjoint(self, rhs: Self) -> bool

Returns true if self and rhs are disjoint ($\self ∩ \rhs = ∅$).

Formal Definition

$∀x ∈ \self, ∀y ∈ \rhs : x ≠ y$.

pub fn interior(self, rhs: Self) -> bool

Returns true if self is interior to rhs.

Formal Definition

$(∀x ∈ \self, ∃y ∈ \rhs : x < y) ∧ (∀x ∈ \self, ∃y ∈ \rhs : y < x)$.

pub fn is_common_interval(self) -> bool

Returns true if self is nonempty and bounded.

pub fn is_empty(self) -> bool

Returns true if self is empty ($\self = ∅$).

pub fn is_entire(self) -> bool

Returns true if $\self = [-∞, ∞]$.

pub fn is_singleton(self) -> bool

Returns true if self consists of a single real number.

pub fn less(self, rhs: Self) -> bool

Returns true if self is weakly less than rhs.

Formal Definition

$(∀x ∈ \self, ∃y ∈ \rhs : x ≤ y) ∧ (∀y ∈ \rhs, ∃x ∈ \self : x ≤ y)$.

pub fn precedes(self, rhs: Self) -> bool

Returns true if self is to the left of but may touch rhs.

Formal Definition

$∀x ∈ \self, ∀y ∈ \rhs : x ≤ y$.

pub fn strict_less(self, rhs: Self) -> bool

Returns true if self is strictly less than rhs.

Formal Definition

$(∀x ∈ \self, ∃y ∈ \rhs : x < y) ∧ (∀y ∈ \self, ∃x ∈ \rhs : x < y)$.

pub fn strict_precedes(self, rhs: Self) -> bool

Returns true if self is strictly to the left of rhs.

Formal Definition

$∀x ∈ \self, ∀y ∈ \rhs : x < y$.

pub fn subset(self, rhs: Self) -> bool

Returns true if self is a subset of rhs ($\self ⊆ \rhs$).

Formal Definition

$∀x ∈ \self, ∃y ∈ \rhs : x = y$.

impl Interval

pub fn to_be_bytes(self) -> [u8; 16]

Returns the big-endian interchange representation of self.

pub fn to_le_bytes(self) -> [u8; 16]

Returns the little-endian interchange representation of self.

pub fn to_ne_bytes(self) -> [u8; 16]

Returns the native-byte-order interchange representation of self.

pub fn try_from_be_bytes(bytes: [u8; 16]) -> Result<Self>

Creates an interval from its big-endian interchange representation.

pub fn try_from_le_bytes(bytes: [u8; 16]) -> Result<Self>

Creates an interval from its little-endian interchange representation.

pub fn try_from_ne_bytes(bytes: [u8; 16]) -> Result<Self>

Creates an interval from its native-byte-order interchange representation.

impl Interval

pub const EMPTY: Self

$∅$, the empty interval.

pub const ENTIRE: Self

$[-∞, ∞]$.

pub const E: Self

The tightest interval enclosing $\e$, the base of natural logarithms.

pub const FRAC_1_PI: Self

The tightest interval enclosing $1 / \pi$.

pub const FRAC_1_SQRT_2: Self

The tightest interval enclosing $1 / \sqrt{2}$.

pub const FRAC_2_PI: Self

The tightest interval enclosing $2 / \pi$.

pub const FRAC_2_SQRT_PI: Self

The tightest interval enclosing $2 / \sqrt{\pi}$.

pub const FRAC_PI_2: Self

The tightest interval enclosing $\pi / 2$.

pub const FRAC_PI_3: Self

The tightest interval enclosing $\pi / 3$.

pub const FRAC_PI_4: Self

The tightest interval enclosing $\pi / 4$.

pub const FRAC_PI_6: Self

The tightest interval enclosing $\pi / 6$.

pub const FRAC_PI_8: Self

The tightest interval enclosing $\pi / 8$.

pub const LN_10: Self

The tightest interval enclosing $\ln 10$.

pub const LN_2: Self

The tightest interval enclosing $\ln 2$.

pub const LOG10_2: Self

The tightest interval enclosing $\log_{10} 2$.

pub const LOG10_E: Self

The tightest interval enclosing $\log_{10} \e$.

pub const LOG2_10: Self

The tightest interval enclosing $\log_2 10$.

pub const LOG2_E: Self

The tightest interval enclosing $\log_2 \e$.

pub const PI: Self

The tightest interval enclosing $\pi$.

pub const SQRT_2: Self

The tightest interval enclosing $\sqrt{2}$.

pub const TAU: Self

The tightest interval enclosing $2 \pi$.

impl Interval

pub fn acos(self) -> Self

Returns the inverse cosine of self.

Tightness: tightest

pub fn acosh(self) -> Self

Returns the inverse hyperbolic cosine of self.

Tightness: tightest

pub fn asin(self) -> Self

Returns the inverse sine of self.

Tightness: tightest

pub fn asinh(self) -> Self

Returns the inverse hyperbolic sine of self.

Tightness: tightest

pub fn atan(self) -> Self

Returns the inverse tangent of self.

Tightness: tightest

pub fn atan2(self, rhs: Self) -> Self

Returns the angle of the point $(\rhs, \self)$ measured counterclockwise from the positive $x$-axis in the Euclidean $xy$-plane.

Tightness: tightest

pub fn atanh(self) -> Self

Returns the inverse hyperbolic tangent of self.

Tightness: tightest

pub fn cos(self) -> Self

Returns the cosine of self.

Tightness: tightest

pub fn cosh(self) -> Self

Returns the hyperbolic cosine of self.

Tightness: tightest

pub fn exp(self) -> Self

Returns the exponential of self.

Tightness: tightest

pub fn exp10(self) -> Self

Returns self raised to the power of 10.

Tightness: tightest

pub fn exp2(self) -> Self

Returns self raised to the power of 2.

Tightness: tightest

pub fn ln(self) -> Self

Returns the natural logarithm of self.

Tightness: tightest

pub fn log10(self) -> Self

Returns the base-10 logarithm of self.

Tightness: tightest

pub fn log2(self) -> Self

Returns the base-2 logarithm of self.

Tightness: tightest

pub fn pow(self, rhs: Self) -> Self

Returns self raised to the power of rhs.

Tightness: tightest

pub fn pown(self, rhs: i32) -> Self

Returns self raised to the power of rhs, where rhs is an integer.

Tightness: tightest

pub fn sin(self) -> Self

Returns the sine of self.

Tightness: tightest

pub fn sinh(self) -> Self

Returns the hyperbolic sine of self.

Tightness: tightest

pub fn tan(self) -> Self

Returns the tangent of self.

Tightness: tightest

pub fn tanh(self) -> Self

Returns the hyperbolic tangent of self.

Tightness: tightest

impl Interval

pub fn ceil(self) -> Self

Rounds the bounds of self to integers using directed rounding toward $+∞$.

Tightness: tightest

Examples

assert_eq!(const_interval!(1.2, 2.8).ceil(), const_interval!(2.0, 3.0));
assert_eq!(const_interval!(-2.8, -1.2).ceil(), const_interval!(-2.0, -1.0));

See also: Interval::floor, Interval::trunc.

pub fn floor(self) -> Self

Rounds the bounds of self to integers using directed rounding toward $-∞$.

Tightness: tightest

See also: Interval::ceil, Interval::trunc.

pub fn round_ties_to_away(self) -> Self

Rounds the bounds of self to the nearest integers, with halfway cases rounded away from zero.

Tightness: tightest

See also: Interval::round_ties_to_even.

pub fn round_ties_to_even(self) -> Self

Rounds the bounds of self to the nearest integers, with halfway cases rounded to even numbers.

Tightness: tightest

See also: Interval::round_ties_to_away.

pub fn sign(self) -> Self

Returns the sign of self.

Note the difference between the sign function and f64::signum; $\sgn(0)$ is always zero, while the values of +0.0_f64.signum() and -0.0_f64.signum() are +1.0 and -1.0, respectively.

Tightness: tightest

pub fn trunc(self) -> Self

Rounds the bounds of self to integers using directed rounding toward zero.

Tightness: tightest

See also: Interval::ceil, Interval::floor.

impl Interval

pub fn inf(self) -> f64

Returns the (greatest) lower bound of self.

Equivalently, it returns $a$ if $\self = [a, b]$ is nonempty; otherwise, $+∞$.

See also: Interval::sup.

pub fn mag(self) -> f64

Returns the magnitude of self if self is nonempty; otherwise, NaN.

The magnitude of a nonempty interval $𝒙 = [a, b]$ is defined as follows:

$$ \operatorname{mag}(𝒙) = \sup\{|x| ∣ x ∈ 𝒙\} = \max(|a|, |b|). $$

See also: Interval::mig.

pub fn mid(self) -> f64

Returns the midpoint of self if self is nonempty; otherwise, NaN. For nonempty cases, the following values are returned.

• If $\self = [-∞, +∞]$, zero is returned.
• If $\self = [-∞, b]$ where $b < +∞$, f64::MIN is returned.
• If $\self = [a, +∞]$ where $a > -∞$, f64::MAX is returned.
• If self is bounded, $\operatorname{mid}(\self)$ rounded to the nearest f64 value is returned.

The midpoint of a nonempty interval $𝒙 = [a, b]$ is defined as follows:

$$ \operatorname{mid}(𝒙) = \frac{1}{2}(a + b). $$

See also: Interval::rad.

pub fn mig(self) -> f64

Returns the mignitude of self if self is nonempty; otherwise, NaN.

The mignitude of a nonempty interval $𝒙 = [a, b]$ is defined as follows:

$$ \operatorname{mig}(𝒙) = \inf\{|x| ∣ x ∈ 𝒙\} = \begin{cases} \min(|a|, |b|) & \text{if } \sgn(a) = \sgn(b), \\ 0 & \text{otherwise}. \end{cases} $$

See also: Interval::mag.

pub fn rad(self) -> f64

Returns the radius of self if self is nonempty; otherwise, NaN. The result $r$ is the smallest f64 number that satisfies $\self ⊆ [m - r, m + r]$ where $m$ is the f64 value returned by self.mid().

The radius of a nonempty interval $𝒙 = [a, b]$ is defined as follows:

$$ \operatorname{rad}(𝒙) = \frac{1}{2}(b - a). $$

See also: Interval::mid.

pub fn sup(self) -> f64

Returns the (least) upper bound of self.

Equivalently, it returns $b$ if $\self = [a, b]$ is nonempty; otherwise, $-∞$.

See also: Interval::inf.

pub fn wid(self) -> f64

Returns the width of self if self is nonempty; otherwise, NaN. The result is rounded toward $+∞$.

The width of a nonempty interval $𝒙 = [a, b]$ is defined as follows:

$$ \operatorname{wid}(𝒙) = b - a. $$

impl Interval

pub fn overlap(self, rhs: Self) -> OverlappingState

Returns the overlapping state of self and rhs. See OverlappingState for the possible values returned.

impl Interval

pub fn convex_hull(self, rhs: Self) -> Self

Returns $[\min(a, c), \max(b, d)]$ if both $\self = [a, b]$ and $\rhs = [c, d]$ are nonempty. If either interval is empty, the other is returned. If both are empty, $∅$ is returned.

This is equivalent to $\self ∪ \rhs$ if the intervals are not disjoint,

Tightness: tightest

pub fn intersection(self, rhs: Self) -> Self

Returns $\self ∩ \rhs$. If the result is nonempty, it is equivalent to $[\max(a, c), \min(b, d)]$, where both $\self = [a, b]$ and $\rhs = [c, d]$ are nonempty..

Tightness: tightest

Trait Implementations

impl Add<Interval> for Interval

type Output = Self

The resulting type after applying the + operator.

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

Tightness: tightest

impl AddAssign<Interval> for Interval

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl Clone for Interval

fn clone(&self) -> Interval

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Copy for Interval

impl Debug for Interval

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

Formats the value using the given formatter.

impl Display for Interval

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

Formats the value using the given formatter.

impl Div<Interval> for Interval

type Output = Self

The resulting type after applying the / operator.

fn div(self, rhs: Self) -> Self

Tightness: tightest

impl DivAssign<Interval> for Interval

fn div_assign(&mut self, rhs: Self)

Performs the /= operation.

impl Eq for Interval

impl FromStr for Interval

type Err = IntervalError<Self>

The associated error which can be returned from parsing.

fn from_str(s: &str) -> Result<Self>

Parses a string s to return a value of this type.

impl LowerExp for Interval

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

Formats the value using the given formatter.

impl LowerHex for Interval

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

Formats the value using the given formatter.

impl Mul<Interval> for Interval

type Output = Self

The resulting type after applying the * operator.

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

Tightness: tightest

impl MulAssign<Interval> for Interval

fn mul_assign(&mut self, rhs: Self)

Performs the *= operation.

impl Neg for Interval

type Output = Self

The resulting type after applying the - operator.

fn neg(self) -> Self

Tightness: tightest

impl PartialEq<Interval> for Interval

fn eq(&self, rhs: &Self) -> bool

This method tests for self and other values to be equal, and is used by ==.

#[must_use]fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl Sub<Interval> for Interval

type Output = Self

The resulting type after applying the - operator.

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

Tightness: tightest

impl SubAssign<Interval> for Interval

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.

impl TryFrom<(f64, f64)> for Interval

type Error = IntervalError<Self>

The type returned in the event of a conversion error.

fn try_from((a, b): (f64, f64)) -> Result<Self>

Performs the conversion.