#[repr(C)]pub struct Interval { /* private fields */ }
Expand description
An interval with f64
bounds.
It is sometimes referred to as a bare interval in contrast to a decorated interval (DecInterval
).
Implementations
sourceimpl Interval
impl Interval
sourceimpl Interval
impl Interval
sourcepub fn cancel_minus(self, rhs: Self) -> Self
pub fn cancel_minus(self, rhs: Self) -> Self
Returns the tightest interval z
such that rhs
$+$ z
$β$ self
,
if both self
and rhs
are bounded and the width of self
is greater than or equal to
that of rhs
. Otherwise, returns Interval::ENTIRE
.
Even when x.cancel_minus(y)
is not Interval::ENTIRE
, its value is generally
different from x - y
, as the latter gives the tightest enclosure of x
$-$ y
,
while the former does not always enclose x
$-$ y
.
In such case, x.cancel_minus(y)
$β$ x - y
holds, but generally not the equality.
Examples
Getting an enclosure of a partial sum omitting a single term from their total:
use inari::*;
let x = interval!("[0.1, 0.2]").unwrap();
let y = interval!("[0.3, 0.4]").unwrap();
let z = interval!("[0.5, 0.6]").unwrap();
let sum = x + y + z;
assert!((y + z).subset(sum.cancel_minus(x)));
assert!((x + z).subset(sum.cancel_minus(y)));
assert!((x + y).subset(sum.cancel_minus(z)));
sum.cancel_minus(x)
is a subset of sum - x
:
assert!(sum.cancel_minus(x).subset(sum - x));
But the inverse does not hold in general:
assert!((sum - x).subset(sum.cancel_minus(x)));
sum.cancel_minus(x)
, etc. returns Interval::ENTIRE
when sum
is unbounded:
use inari::*;
let x = const_interval!(1.0, 2.0);
let y = const_interval!(3.0, f64::MAX);
let sum = x + y;
assert_eq!(sum.cancel_minus(x), Interval::ENTIRE);
assert_eq!(sum.cancel_minus(y), Interval::ENTIRE);
sum.cancel_minus(x)
returns Interval::ENTIRE
when the width of βsum
β is
less than that of x
:
use inari::*;
let x = const_interval!(1.0, 2.0);
let sum = const_interval!(4.0, 4.5);
assert_eq!(sum.cancel_minus(x), Interval::ENTIRE);
sourcepub fn cancel_plus(self, rhs: Self) -> Self
pub fn cancel_plus(self, rhs: Self) -> Self
x.cancel_plus(y)
is equivalent to x.cancel_minus(-y)
.
See Interval::cancel_minus
for more information.
sourcepub fn mul_add(self, rhs: Self, addend: Self) -> Self
pub fn mul_add(self, rhs: Self, addend: Self) -> Self
Returns $(\self Γ \rhs) + \addend$.
The domain and the range of the point function are:
Domain | Range |
---|---|
$\R^3$ | $\R$ |
sourcepub fn recip(self) -> Self
pub fn recip(self) -> Self
Returns the multiplicative inverse of self
.
The domain and the range of the point function are:
Domain | Range |
---|---|
$\R β \set 0$ | $\R β \set 0$ |
sourceimpl Interval
impl Interval
sourcepub fn contains(self, rhs: f64) -> bool
pub fn contains(self, rhs: f64) -> bool
Returns true
if rhs
is a member of self
: $\rhs β \self$.
The result is false
whenever rhs
is infinite or NaN.
Examples
use inari::*;
assert!(const_interval!(1.0, 2.0).contains(1.0));
assert!(!Interval::EMPTY.contains(1.0));
assert!(Interval::ENTIRE.contains(1.0));
$Β±β$ and NaN are not real numbers, thus do not belong to any interval:
use inari::*;
assert!(!Interval::ENTIRE.contains(f64::INFINITY));
assert!(!Interval::ENTIRE.contains(f64::NEG_INFINITY));
assert!(!Interval::ENTIRE.contains(f64::NAN));
sourcepub fn disjoint(self, rhs: Self) -> bool
pub fn disjoint(self, rhs: Self) -> bool
Returns true
if self
and rhs
are disjoint:
$$ \self β© \rhs = β , $$
or equivalently,
$$ βx β \self, βy β \rhs : x β y, $$
or equivalently,
$\rhs = β $ | $\rhs = [c, d]$ | |
---|---|---|
$\self = β $ | true | true |
$\self = [a, b]$ | true | $b < c β¨ d < a$ |
Examples
use inari::*;
assert!(const_interval!(1.0, 2.0).disjoint(const_interval!(3.0, 4.0)));
assert!(!const_interval!(1.0, 3.0).disjoint(const_interval!(3.0, 4.0)));
assert!(!const_interval!(1.0, 5.0).disjoint(const_interval!(3.0, 4.0)));
assert!(Interval::EMPTY.disjoint(Interval::EMPTY));
assert!(Interval::EMPTY.disjoint(Interval::ENTIRE));
sourcepub fn interior(self, rhs: Self) -> bool
pub fn interior(self, rhs: Self) -> bool
Returns true
if self
is interior to rhs
:
$$ (βx β \self, βy β \rhs : x < y) β§ (βx β \self, βy β \rhs : y < x), $$
or equivalently,
$\rhs = β $ | $\rhs = [c, d]$ | |
---|---|---|
$\self = β $ | true | true |
$\self = [a, b]$ | false | $c <β² a β§ b <β² d$ |
where $<β²$ is defined as:
$$ x <β² y :βΊ x < y β¨ x = y = -β β¨ x = y = +β. $$
Examples
use inari::*;
assert!(const_interval!(1.1, 1.9).interior(const_interval!(1.0, 2.0)));
assert!(!const_interval!(1.1, 2.0).interior(const_interval!(1.0, 2.0)));
assert!(Interval::EMPTY.interior(Interval::EMPTY));
assert!(Interval::ENTIRE.interior(Interval::ENTIRE));
sourcepub fn is_common_interval(self) -> bool
pub fn is_common_interval(self) -> bool
Returns true
if self
is nonempty and bounded.
Examples
use inari::*;
assert!(const_interval!(1.0, 2.0).is_common_interval());
assert!(!const_interval!(1.0, f64::INFINITY).is_common_interval());
assert!(!Interval::EMPTY.is_common_interval());
assert!(!Interval::ENTIRE.is_common_interval());
sourcepub fn is_empty(self) -> bool
pub fn is_empty(self) -> bool
Returns true
if self
is empty: $\self = β
$.
Examples
use inari::*;
assert!(!const_interval!(1.0, 1.0).is_empty());
assert!(Interval::EMPTY.is_empty());
assert!(!Interval::ENTIRE.is_empty());
sourcepub fn is_entire(self) -> bool
pub fn is_entire(self) -> bool
Returns true
if $\self = [-β, +β]$.
Examples
use inari::*;
assert!(!const_interval!(1.0, f64::INFINITY).is_entire());
assert!(!Interval::EMPTY.is_entire());
assert!(Interval::ENTIRE.is_entire());
sourcepub fn is_singleton(self) -> bool
pub fn is_singleton(self) -> bool
Returns true
if self
consists of a single real number:
$$ βx β β : \self = [x, x]. $$
The result is false
whenever self
is empty or unbounded.
Examples
use inari::*;
assert!(const_interval!(1.0, 1.0).is_singleton());
assert!(!const_interval!(1.0, 2.0).is_singleton());
assert!(!Interval::EMPTY.is_singleton());
assert!(!Interval::ENTIRE.is_singleton());
0.1 is not representable as a f64
number:
use inari::*;
// The singleton interval that consists of the closest [`f64`] number to 0.1.
assert!(const_interval!(0.1, 0.1).is_singleton());
// The tightest interval that encloses 0.1.
#[cfg(feature = "gmp")]
assert!(!interval!("[0.1, 0.1]").unwrap().is_singleton());
sourcepub fn less(self, rhs: Self) -> bool
pub fn less(self, rhs: Self) -> bool
Returns true
if self
is weakly less than rhs
:
$$ (βx β \self, βy β \rhs : x β€ y) β§ (βy β \rhs, βx β \self : x β€ y), $$
or equivalently,
$\rhs = β $ | $\rhs = [c, d]$ | |
---|---|---|
$\self = β $ | true | false |
$\self = [a, b]$ | false | $a β€ c β§ b β€ d$ |
Examples
use inari::*;
assert!(const_interval!(1.0, 2.0).less(const_interval!(3.0, 4.0)));
assert!(const_interval!(1.0, 3.0).less(const_interval!(2.0, 4.0)));
assert!(const_interval!(1.0, 4.0).less(const_interval!(1.0, 4.0)));
assert!(Interval::EMPTY.less(Interval::EMPTY));
assert!(!Interval::EMPTY.less(Interval::ENTIRE));
assert!(!Interval::ENTIRE.less(Interval::EMPTY));
assert!(Interval::ENTIRE.less(Interval::ENTIRE));
sourcepub fn precedes(self, rhs: Self) -> bool
pub fn precedes(self, rhs: Self) -> bool
Returns true
if self
is to the left of rhs
but may touch it:
$$ βx β \self, βy β \rhs : x β€ y, $$
or equivalently,
$\rhs = β $ | $\rhs = [c, d]$ | |
---|---|---|
$\self = β $ | true | true |
$\self = [a, b]$ | true | $b β€ c$ |
Examples
use inari::*;
assert!(const_interval!(1.0, 2.0).precedes(const_interval!(3.0, 4.0)));
assert!(const_interval!(1.0, 3.0).precedes(const_interval!(3.0, 4.0)));
assert!(!const_interval!(1.0, 3.0).precedes(const_interval!(2.0, 4.0)));
assert!(Interval::EMPTY.precedes(Interval::EMPTY));
assert!(Interval::EMPTY.precedes(Interval::ENTIRE));
assert!(Interval::ENTIRE.precedes(Interval::EMPTY));
assert!(!Interval::ENTIRE.precedes(Interval::ENTIRE));
sourcepub fn strict_less(self, rhs: Self) -> bool
pub fn strict_less(self, rhs: Self) -> bool
Returns true
if self
is strictly less than rhs
:
$$ (βx β \self, βy β \rhs : x < y) β§ (βy β \self, βx β \rhs : x < y), $$
or equivalently,
$\rhs = β $ | $\rhs = [c, d]$ | |
---|---|---|
$\self = β $ | true | false |
$\self = [a, b]$ | false | $a <β² c β§ b <β² d$ |
where $<β²$ is defined as:
$$ x <β² y :βΊ x < y β¨ x = y = -β β¨ x = y = +β. $$
Examples
use inari::*;
assert!(const_interval!(1.0, 2.0).strict_less(const_interval!(3.0, 4.0)));
assert!(const_interval!(1.0, 3.0).strict_less(const_interval!(2.0, 4.0)));
assert!(!const_interval!(1.0, 4.0).strict_less(const_interval!(2.0, 4.0)));
assert!(const_interval!(1.0, f64::INFINITY).strict_less(const_interval!(2.0, f64::INFINITY)));
assert!(Interval::EMPTY.strict_less(Interval::EMPTY));
assert!(!Interval::EMPTY.strict_less(Interval::ENTIRE));
assert!(!Interval::ENTIRE.strict_less(Interval::EMPTY));
assert!(Interval::ENTIRE.strict_less(Interval::ENTIRE));
sourcepub fn strict_precedes(self, rhs: Self) -> bool
pub fn strict_precedes(self, rhs: Self) -> bool
Returns true
if self
is strictly to the left of rhs
:
$$ βx β \self, βy β \rhs : x < y, $$
or equivalently,
$\rhs = β $ | $\rhs = [c, d]$ | |
---|---|---|
$\self = β $ | true | true |
$\self = [a, b]$ | true | $b < c$ |
sourcepub fn subset(self, rhs: Self) -> bool
pub fn subset(self, rhs: Self) -> bool
Returns true
if self
is a subset of rhs
:
$$ \self β \rhs, $$
or equivalently,
$$ βx β \self, βy β \rhs : x = y, $$
or equivalently,
$\rhs = β $ | $\rhs = [c, d]$ | |
---|---|---|
$\self = β $ | true | true |
$\self = [a, b]$ | false | $c β€ a β§ b β€ d$ |
Examples
use inari::*;
assert!(const_interval!(1.0, 2.0).subset(const_interval!(1.0, 2.0)));
assert!(Interval::EMPTY.subset(Interval::EMPTY));
assert!(Interval::EMPTY.subset(Interval::ENTIRE));
assert!(Interval::ENTIRE.subset(Interval::ENTIRE));
sourceimpl Interval
impl Interval
sourcepub fn to_be_bytes(self) -> [u8; 16]
pub fn to_be_bytes(self) -> [u8; 16]
Returns the interchange representation of self
in the big-endian byte order.
sourcepub fn to_le_bytes(self) -> [u8; 16]
pub fn to_le_bytes(self) -> [u8; 16]
Returns the interchange representation of self
in the little-endian byte order.
sourcepub fn to_ne_bytes(self) -> [u8; 16]
pub fn to_ne_bytes(self) -> [u8; 16]
Returns the interchange representation of self
in the native byte order of the target platform.
sourcepub fn try_from_be_bytes(bytes: [u8; 16]) -> Option<Self>
pub fn try_from_be_bytes(bytes: [u8; 16]) -> Option<Self>
Creates an Interval
from its interchange representation in the big-endian byte order.
sourceimpl Interval
impl Interval
sourcepub const FRAC_1_SQRT_2: Self = _
pub const FRAC_1_SQRT_2: Self = _
The tightest interval enclosing $1 / \sqrt{2}$.
sourcepub const FRAC_2_SQRT_PI: Self = _
pub const FRAC_2_SQRT_PI: Self = _
The tightest interval enclosing $2 / \sqrt{Ο}$.
sourceimpl Interval
impl Interval
sourcepub fn acos(self) -> Self
pub fn acos(self) -> Self
Returns the inverse cosine of self
.
The domain and the range of the point function are:
Domain | Range |
---|---|
$[-1, 1]$ | $[0, Ο]$ |
sourcepub fn acosh(self) -> Self
pub fn acosh(self) -> Self
Returns the inverse hyperbolic cosine of self
.
The domain and the range of the point function are:
Domain | Range |
---|---|
$[1, β)$ | $[0, β)$ |
sourcepub fn asin(self) -> Self
pub fn asin(self) -> Self
Returns the inverse sine of self
.
The domain and the range of the point function are:
Domain | Range |
---|---|
$[-1, 1]$ | $[-Ο/2, Ο/2]$ |
sourcepub fn asinh(self) -> Self
pub fn asinh(self) -> Self
Returns the inverse hyperbolic sine of self
.
The domain and the range of the point function are:
Domain | Range |
---|---|
$\R$ | $\R$ |
sourcepub fn atan(self) -> Self
pub fn atan(self) -> Self
Returns the inverse tangent of self
.
The domain and the range of the point function are:
Domain | Range |
---|---|
$\R$ | $(-Ο/2, Ο/2)$ |
sourcepub fn atan2(self, rhs: Self) -> Self
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 plane.
The domain and the range of the point function are:
Domain | Range |
---|---|
$\R^2 β \set{(0, 0)}$ | $(-Ο, Ο]$ |
sourcepub fn atanh(self) -> Self
pub fn atanh(self) -> Self
Returns the inverse hyperbolic tangent of self
.
The domain and the range of the point function are:
Domain | Range |
---|---|
$(-1, 1)$ | $\R$ |
sourcepub fn cos(self) -> Self
pub fn cos(self) -> Self
Returns the cosine of self
.
The domain and the range of the point function are:
Domain | Range |
---|---|
$\R$ | $[-1, 1]$ |
sourcepub fn cosh(self) -> Self
pub fn cosh(self) -> Self
Returns the hyperbolic cosine of self
.
The domain and the range of the point function are:
Domain | Range |
---|---|
$\R$ | $[1, β)$ |
sourcepub fn exp(self) -> Self
pub fn exp(self) -> Self
Returns self
raised to the power of $\e$.
The domain and the range of the point function are:
Domain | Range |
---|---|
$\R$ | $(0, β)$ |
sourcepub fn exp10(self) -> Self
pub fn exp10(self) -> Self
Returns self
raised to the power of 10.
The domain and the range of the point function are:
Domain | Range |
---|---|
$\R$ | $(0, β)$ |
sourcepub fn exp2(self) -> Self
pub fn exp2(self) -> Self
Returns self
raised to the power of 2.
The domain and the range of the point function are:
Domain | Range |
---|---|
$\R$ | $(0, β)$ |
sourcepub fn ln(self) -> Self
pub fn ln(self) -> Self
Returns the natural logarithm of self
.
The domain and the range of the point function are:
Domain | Range |
---|---|
$(0, β)$ | $\R$ |
sourcepub fn log10(self) -> Self
pub fn log10(self) -> Self
Returns the base-10 logarithm of self
.
The domain and the range of the point function are:
Domain | Range |
---|---|
$(0, β)$ | $\R$ |
sourcepub fn log2(self) -> Self
pub fn log2(self) -> Self
Returns the base-2 logarithm of self
.
The domain and the range of the point function are:
Domain | Range |
---|---|
$(0, β)$ | $\R$ |
sourcepub fn pow(self, rhs: Self) -> Self
pub fn pow(self, rhs: Self) -> Self
Returns self
raised to the power of rhs
.
The point function is defined as follows:
$$ x^y = \begin{cases} 0 & \for x = 0 β§ y > 0, \\ e^{y \ln x} & \for x > 0. \end{cases} $$
The domain and the range of the point function are:
Domain | Range |
---|---|
$((0, β) Γ \R) βͺ (\set 0 Γ (0, β))$ | $[0, β)$ |
sourcepub fn powi(self, rhs: i32) -> Self
pub fn powi(self, rhs: i32) -> Self
Returns self
raised to the power of rhs
.
The point functions are indexed by $n$, and are defined as follows:
$$ x^n = \begin{cases} \overbrace{x Γ β― Γ x}^{n \text{ copies}} & \for n > 0, \\ 1 & \for n = 0, \\ 1 / x^{-n} & \for n < 0. \end{cases} $$
The domains and the ranges of the point functions are:
Domain | Range | |
---|---|---|
$n > 0$, odd | $\R$ | $\R$ |
$n > 0$, even | $\R$ | $[0, β)$ |
$n = 0$ | $\R$ | $\set 1$ |
$n < 0$, odd | $\R β \set 0$ | $\R β \set 0$ |
$n < 0$, even | $\R β \set 0$ | $(0, β)$ |
sourcepub fn sin(self) -> Self
pub fn sin(self) -> Self
Returns the sine of self
.
The domain and the range of the point function are:
Domain | Range |
---|---|
$\R$ | $[-1, 1]$ |
sourcepub fn sinh(self) -> Self
pub fn sinh(self) -> Self
Returns the hyperbolic sine of self
.
The domain and the range of the point function are:
Domain | Range |
---|---|
$\R$ | $\R$ |
sourceimpl Interval
impl Interval
sourcepub fn ceil(self) -> Self
pub fn ceil(self) -> Self
Rounds self
to the closest integer toward $+β$.
The domain and the range of the point function are:
Domain | Range |
---|---|
$\R$ | $\Z$ |
Examples
use inari::*;
assert_eq!(const_interval!(0.2, 1.2).ceil(), const_interval!(1.0, 2.0));
assert_eq!(const_interval!(0.8, 1.8).ceil(), const_interval!(1.0, 2.0));
assert_eq!(const_interval!(-1.2, -0.2).ceil(), const_interval!(-1.0, 0.0));
assert_eq!(const_interval!(-1.8, -0.8).ceil(), const_interval!(-1.0, 0.0));
assert_eq!(Interval::EMPTY.ceil(), Interval::EMPTY);
assert_eq!(Interval::ENTIRE.ceil(), Interval::ENTIRE);
See also: Interval::floor
, Interval::trunc
.
sourcepub fn floor(self) -> Self
pub fn floor(self) -> Self
Rounds self
to the closest integer toward $-β$.
The domain and the range of the point function are:
Domain | Range |
---|---|
$\R$ | $\Z$ |
Examples
use inari::*;
assert_eq!(const_interval!(0.2, 1.2).floor(), const_interval!(0.0, 1.0));
assert_eq!(const_interval!(0.8, 1.8).floor(), const_interval!(0.0, 1.0));
assert_eq!(const_interval!(-1.2, -0.2).floor(), const_interval!(-2.0, -1.0));
assert_eq!(const_interval!(-1.8, -0.8).floor(), const_interval!(-2.0, -1.0));
assert_eq!(Interval::EMPTY.floor(), Interval::EMPTY);
assert_eq!(Interval::ENTIRE.floor(), Interval::ENTIRE);
See also: Interval::ceil
, Interval::trunc
.
sourcepub fn round(self) -> Self
pub fn round(self) -> Self
Rounds self
to the closest integer, away from zero in case of ties.
The domain and the range of the point function are:
Domain | Range |
---|---|
$\R$ | $\Z$ |
Examples
use inari::*;
assert_eq!(const_interval!(0.2, 1.2).round(), const_interval!(0.0, 1.0));
assert_eq!(const_interval!(0.5, 1.5).round(), const_interval!(1.0, 2.0));
assert_eq!(const_interval!(0.8, 1.8).round(), const_interval!(1.0, 2.0));
assert_eq!(const_interval!(-1.2, -0.2).round(), const_interval!(-1.0, 0.0));
assert_eq!(const_interval!(-1.5, -0.5).round(), const_interval!(-2.0, -1.0));
assert_eq!(const_interval!(-1.8, -0.8).round(), const_interval!(-2.0, -1.0));
assert_eq!(Interval::EMPTY.round(), Interval::EMPTY);
assert_eq!(Interval::ENTIRE.round(), Interval::ENTIRE);
See also: Interval::round_ties_to_even
.
sourcepub fn round_ties_to_even(self) -> Self
pub fn round_ties_to_even(self) -> Self
Rounds self
to the closest integer, the even number in case of ties.
The domain and the range of the point function are:
Domain | Range |
---|---|
$\R$ | $\Z$ |
Examples
use inari::*;
assert_eq!(const_interval!(0.2, 1.2).round_ties_to_even(), const_interval!(0.0, 1.0));
assert_eq!(const_interval!(0.5, 1.5).round_ties_to_even(), const_interval!(0.0, 2.0));
assert_eq!(const_interval!(0.8, 1.8).round_ties_to_even(), const_interval!(1.0, 2.0));
assert_eq!(const_interval!(-1.2, -0.2).round_ties_to_even(), const_interval!(-1.0, 0.0));
assert_eq!(const_interval!(-1.5, -0.5).round_ties_to_even(), const_interval!(-2.0, 0.0));
assert_eq!(const_interval!(-1.8, -0.8).round_ties_to_even(), const_interval!(-2.0, -1.0));
assert_eq!(Interval::EMPTY.round_ties_to_even(), Interval::EMPTY);
assert_eq!(Interval::ENTIRE.round_ties_to_even(), Interval::ENTIRE);
See also: Interval::round
.
sourcepub fn sign(self) -> Self
pub fn sign(self) -> Self
Returns the sign of self
.
The domain and the range of the point function are:
Domain | Range |
---|---|
$\R$ | $\set{-1, 0, 1}$ |
Note the difference in definition between f64::signum
and this function;
+0.0_f64.signum()
and -0.0_f64.signum()
return +1.0
and -1.0
, respectively,
while the sign of zero is just zero.
Examples
use inari::*;
assert_eq!(const_interval!(-10.0, -0.1).sign(), const_interval!(-1.0, -1.0));
assert_eq!(const_interval!(0.0, 0.0).sign(), const_interval!(0.0, 0.0));
assert_eq!(const_interval!(0.1, 10.0).sign(), const_interval!(1.0, 1.0));
assert_eq!(Interval::EMPTY.sign(), Interval::EMPTY);
assert_eq!(Interval::ENTIRE.sign(), const_interval!(-1.0, 1.0));
sourcepub fn trunc(self) -> Self
pub fn trunc(self) -> Self
Rounds self
to the closest integer toward zero.
The domain and the range of the point function are:
Domain | Range |
---|---|
$\R$ | $\Z$ |
Examples
use inari::*;
assert_eq!(const_interval!(0.2, 1.2).trunc(), const_interval!(0.0, 1.0));
assert_eq!(const_interval!(0.8, 1.8).trunc(), const_interval!(0.0, 1.0));
assert_eq!(const_interval!(-1.2, -0.2).trunc(), const_interval!(-1.0, 0.0));
assert_eq!(const_interval!(-1.8, -0.8).trunc(), const_interval!(-1.0, 0.0));
assert_eq!(Interval::EMPTY.trunc(), Interval::EMPTY);
assert_eq!(Interval::ENTIRE.trunc(), Interval::ENTIRE);
See also: Interval::ceil
, Interval::floor
.
sourceimpl Interval
impl Interval
sourcepub fn inf(self) -> f64
pub fn inf(self) -> f64
Returns the lower bound of self
.
The lower bound of an interval $π$ is:
$$ \inf(π) = \begin{cases} +β & \if π = β , \\ a & \if π = [a, b]. \end{cases} $$
The exact value is returned. When $a = 0$, -0.0
is returned.
Examples
use inari::*;
assert_eq!(const_interval!(-2.0, 3.0).inf(), -2.0);
assert_eq!(Interval::EMPTY.inf(), f64::INFINITY);
assert_eq!(Interval::ENTIRE.inf(), f64::NEG_INFINITY);
See also: Interval::sup
.
sourcepub fn mag(self) -> f64
pub fn mag(self) -> f64
Returns the magnitude of self
if it is nonempty; otherwise, a NaN.
The magnitude of a nonempty interval $π = [a, b]$ is:
$$ \begin{align*} \mag(π) &= \sup \set{|x| β£ x β π} \\ &= \max \set{|a|, |b|}. \end{align*} $$
The exact value is returned.
Examples
use inari::*;
assert_eq!(const_interval!(-2.0, 3.0).mag(), 3.0);
assert!(Interval::EMPTY.mag().is_nan());
assert_eq!(Interval::ENTIRE.mag(), f64::INFINITY);
See also: Interval::mig
.
sourcepub fn mid(self) -> f64
pub fn mid(self) -> f64
Returns the midpoint of self
if it is nonempty; otherwise, a NaN.
The midpoint of a nonempty interval $π = [a, b]$ is:
$$ \mid(π) = \frac{a + b}{2}. $$
As an approximation in f64
, it returns:
0.0
, if $\self = [-β, +β]$;f64::MIN
, if $\self = [-β, b]$, where $b β \R$;f64::MAX
, if $\self = [a, +β]$, where $a β \R$;- otherwise, the closest
f64
number to $\mid(\self)$, away from zero in case of ties.
Examples
use inari::*;
assert_eq!(const_interval!(-2.0, 3.0).mid(), 0.5);
assert_eq!(const_interval!(f64::NEG_INFINITY, 3.0).mid(), f64::MIN);
assert_eq!(const_interval!(-2.0, f64::INFINITY).mid(), f64::MAX);
assert!(Interval::EMPTY.mid().is_nan());
assert_eq!(Interval::ENTIRE.mid(), 0.0);
See also: Interval::rad
.
sourcepub fn mig(self) -> f64
pub fn mig(self) -> f64
Returns the mignitude of self
if it is nonempty; otherwise, a NaN.
The mignitude of a nonempty interval $π = [a, b]$ is:
$$ \begin{align*} \mig(π) &= \inf \set{|x| β£ x β π} \\ &= \begin{cases} \min \set{|a|, |b|} & \if \sgn(a) = \sgn(b), \\ 0 & \otherwise. \end{cases} \end{align*} $$
The exact value is returned.
Examples
use inari::*;
assert_eq!(const_interval!(-2.0, 3.0).mig(), 0.0);
assert_eq!(const_interval!(2.0, 3.0).mig(), 2.0);
assert!(Interval::EMPTY.mig().is_nan());
assert_eq!(Interval::ENTIRE.mig(), 0.0);
See also: Interval::mag
.
sourcepub fn rad(self) -> f64
pub fn rad(self) -> f64
Returns the radius of self
if it is nonempty; otherwise, a NaN.
The radius of a nonempty interval $π = [a, b]$ is:
$$ \rad(π) = \frac{b - a}{2}. $$
As an approximation in f64
, it returns the least f64
number r
that satisfies
$\self β [π - π, π + π]$, where m
is the midpoint returned by Self::mid
.
Examples
use inari::*;
assert_eq!(const_interval!(-2.0, 3.0).rad(), 2.5);
assert!(Interval::EMPTY.rad().is_nan());
assert_eq!(Interval::ENTIRE.rad(), f64::INFINITY);
See also: Interval::mid
.
sourcepub fn sup(self) -> f64
pub fn sup(self) -> f64
Returns the upper bound of self
.
The upper bound of an interval $π$ is:
$$ \sup(π) = \begin{cases} -β & \if π = β , \\ b & \if π = [a, b]. \end{cases} $$
The exact value is returned. When $b = 0$, 0.0
(the
positive zero) is returned.
Examples
use inari::*;
assert_eq!(const_interval!(-2.0, 3.0).sup(), 3.0);
assert_eq!(Interval::EMPTY.sup(), f64::NEG_INFINITY);
assert_eq!(Interval::ENTIRE.sup(), f64::INFINITY);
See also: Interval::inf
.
sourcepub fn wid(self) -> f64
pub fn wid(self) -> f64
Returns the width of self
if it is nonempty; otherwise, a NaN.
The width of a nonempty interval $π = [a, b]$ is:
$$ \wid(π) = b - a. $$
As an approximation in f64
, it returns the closest f64
number toward $+β$.
Examples
use inari::*;
assert_eq!(const_interval!(-2.0, 3.0).wid(), 5.0);
assert_eq!(const_interval!(-1.0, f64::MAX).wid(), f64::INFINITY);
assert!(Interval::EMPTY.wid().is_nan());
assert_eq!(Interval::ENTIRE.wid(), f64::INFINITY);
sourceimpl Interval
impl Interval
sourcepub fn convex_hull(self, rhs: Self) -> Self
pub fn convex_hull(self, rhs: Self) -> Self
Returns $\hull(\self βͺ \rhs)$, the tightest interval that contains both self
and rhs
as its subsets.
$\rhs = β $ | $\rhs = [c, d]$ | |
---|---|---|
$\self = β $ | $β $ | $[c, d]$ |
$\self = [a, b]$ | $[a, b]$ | $[\min \set{a, c}, \max \set{b, d}]$ |
sourcepub fn intersection(self, rhs: Self) -> Self
pub fn intersection(self, rhs: Self) -> Self
Returns $\self β© \rhs$, the intersection of self
and rhs
.
$\rhs = β $ | $\rhs = [c, d]$ | |
---|---|---|
$\self = β $ | $β $ | $β $ |
$\self = [a, b]$ | $β $ | $[\max \set{a, c}, \min \set{b, d}]$ |
Trait Implementations
sourceimpl AddAssign<&Interval> for Interval
impl AddAssign<&Interval> for Interval
sourcefn add_assign(&mut self, other: &Interval)
fn add_assign(&mut self, other: &Interval)
Performs the +=
operation. Read more
sourceimpl AddAssign<Interval> for Interval
impl AddAssign<Interval> for Interval
sourcefn add_assign(&mut self, rhs: Self)
fn add_assign(&mut self, rhs: Self)
Performs the +=
operation. Read more
sourceimpl DivAssign<&Interval> for Interval
impl DivAssign<&Interval> for Interval
sourcefn div_assign(&mut self, other: &Interval)
fn div_assign(&mut self, other: &Interval)
Performs the /=
operation. Read more
sourceimpl DivAssign<Interval> for Interval
impl DivAssign<Interval> for Interval
sourcefn div_assign(&mut self, rhs: Self)
fn div_assign(&mut self, rhs: Self)
Performs the /=
operation. Read more
sourceimpl MulAssign<&Interval> for Interval
impl MulAssign<&Interval> for Interval
sourcefn mul_assign(&mut self, other: &Interval)
fn mul_assign(&mut self, other: &Interval)
Performs the *=
operation. Read more
sourceimpl MulAssign<Interval> for Interval
impl MulAssign<Interval> for Interval
sourcefn mul_assign(&mut self, rhs: Self)
fn mul_assign(&mut self, rhs: Self)
Performs the *=
operation. Read more
sourceimpl SubAssign<&Interval> for Interval
impl SubAssign<&Interval> for Interval
sourcefn sub_assign(&mut self, other: &Interval)
fn sub_assign(&mut self, other: &Interval)
Performs the -=
operation. Read more
sourceimpl SubAssign<Interval> for Interval
impl SubAssign<Interval> for Interval
sourcefn sub_assign(&mut self, rhs: Self)
fn sub_assign(&mut self, rhs: Self)
Performs the -=
operation. Read more
impl Copy for Interval
impl Eq for Interval
Auto Trait Implementations
impl RefUnwindSafe for Interval
impl Send for Interval
impl Sync for Interval
impl Unpin for Interval
impl UnwindSafe for Interval
Blanket Implementations
sourceimpl<T> BorrowMut<T> for T where
T: ?Sized,
impl<T> BorrowMut<T> for T where
T: ?Sized,
const: unstable Β· sourcefn borrow_mut(&mut self) -> &mut T
fn borrow_mut(&mut self) -> &mut T
Mutably borrows from an owned value. Read more
sourceimpl<T> CheckedAs for T
impl<T> CheckedAs for T
sourcefn checked_as<Dst>(self) -> Option<Dst> where
T: CheckedCast<Dst>,
fn checked_as<Dst>(self) -> Option<Dst> where
T: CheckedCast<Dst>,
Casts the value.
sourceimpl<T> OverflowingAs for T
impl<T> OverflowingAs for T
sourcefn overflowing_as<Dst>(self) -> (Dst, bool) where
T: OverflowingCast<Dst>,
fn overflowing_as<Dst>(self) -> (Dst, bool) where
T: OverflowingCast<Dst>,
Casts the value.
sourceimpl<T> SaturatingAs for T
impl<T> SaturatingAs for T
sourcefn saturating_as<Dst>(self) -> Dst where
T: SaturatingCast<Dst>,
fn saturating_as<Dst>(self) -> Dst where
T: SaturatingCast<Dst>,
Casts the value.
sourceimpl<T> UnwrappedAs for T
impl<T> UnwrappedAs for T
sourcefn unwrapped_as<Dst>(self) -> Dst where
T: UnwrappedCast<Dst>,
fn unwrapped_as<Dst>(self) -> Dst where
T: UnwrappedCast<Dst>,
Casts the value.
sourceimpl<T> WrappingAs for T
impl<T> WrappingAs for T
sourcefn wrapping_as<Dst>(self) -> Dst where
T: WrappingCast<Dst>,
fn wrapping_as<Dst>(self) -> Dst where
T: WrappingCast<Dst>,
Casts the value.