Struct Constrained 

pub struct Constrained<T, C> { /* private fields */ }

IEEE 754 floating-point proxy that provides total ordering, equivalence, hashing, constraints, and error handling.

Constrained types wrap primitive floating-point type and extend their behavior. For example, all proxy types implement the standard Eq, Hash, and Ord traits, sometimes via the non-standard relations described in the cmp module when NaNs must be considered. Constraints and divergence can be composed to determine the subset of floating-point values that a proxy supports and how the proxy behaves when those constraints are violated.

Various type definitions are provided for various useful proxy constructions, such as the Total type, which extends floating-point types with a non-standard total ordering.

Implementations

impl<T, C> Constrained<T, C>

where T: Copy,

pub const fn into_inner(self) -> T

Converts a proxy into its underlying primitive floating-point type.

Examples

use decorum::R64;

fn f() -> R64 {
    // ...
}

let x: f64 = f().into_inner();
// The standard `From` and `Into` traits can also be used.
let y: f64 = f().into();

impl<T, C> Constrained<T, C>

where T: Debug, C: StaticDebug,

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

Writes a thorough debugging description of the proxy to the given Formatter.

This function is similar to debug, but writes a verbose description of the proxy into a Formatter rather than returning a Debug implementation.

pub const fn debug(&self) -> impl '_ + Copy + Debug

Gets a Debug implementation that thoroughly describes the proxy.

Constrained types implement Display and Debug, but these implementations omit more specific information about constraints and divergence. This function provides an instance of a verbose Debug type that more thoroughly describes the behavior of the proxy.

impl<T, C> Constrained<T, C>

where T: Primitive, C: Constraint,

pub fn new(inner: T) -> OutputFor<Self>

Constructs a proxy from a primitive IEEE 754 floating-point value.

This function returns the output type of the divergence of the proxy and invokes its error behavior if the floating-point value does not satisfy constraints. Note that this function never fails for Total, which has no constraints.

The distinctions in output and behavior are static and are determined by the type parameters of the Constrained type constructor.

Panics

This function panics if the primitive floating-point value does not satisfy the constraints of the proxy and the divergence of the proxy panics. For example, the OrPanic divergence asserts constraints and panics.

Errors

Returns an error if the primitive floating-point value does not satisfy the constraints of the proxy and the divergence of the proxy encodes errors in its output type. For example, the output type of the OrError<AsExpression> divergence is Expression and this function returns the Undefined variant if the constraint is violated.

Examples

Fallibly constructing proxies from primitive floating-point values:

use decorum::constraint::IsReal;
use decorum::divergence::{AsResult, OrError};
use decorum::proxy::Constrained;

// The output type of `Real` is `Result`.
type Real = Constrained<f64, IsReal<OrError<AsResult>>>;

let x = Real::new(2.0).unwrap(); // The output type of `new` is `Result` per `TryResult`.

Asserting proxy construction from primitive floating-point values:

use decorum::constraint::IsReal;
use decorum::divergence::OrPanic;
use decorum::proxy::Constrained;

// The output type of `OrPanic` is `Real`.
type Real = Constrained<f64, IsReal<OrPanic>>;

let x = Real::new(2.0); // The output type of `new` is `Real` per `OrPanic`.
let y = Real::new(0.0 / 0.0); // Panics.

pub fn try_new(inner: T) -> Result<Self, C::Error>

Fallibly constructs a proxy from a primitive IEEE 754 floating-point value.

This construction mirrors the TryFrom implementation and is independent of the divergence of the proxy; it always outputs a Result and never panics.

Errors

Returns an error if the primitive floating-point value does not satisfy the constraints of the proxy. Note that the error type of the IsFloat constraint is Infallible and the construction of Totals cannot fail here.

Examples

Constructing proxies from primitive floating-point values:

use decorum::constraint::IsReal;
use decorum::divergence::OrPanic;
use decorum::proxy::Constrained;

type Real = Constrained<f64, IsReal<OrPanic>>;

fn f(x: Real) -> Real {
    x * 2.0
}

let y = f(Real::try_new(2.0).unwrap());
// The `TryFrom` and `TryInto` traits can also be used.
let z = f(2.0.try_into().unwrap());

A proxy construction that fails:

use decorum::constraint::IsReal;
use decorum::divergence::OrPanic;
use decorum::proxy::Constrained;

type Real = Constrained<f64, IsReal<OrPanic>>;

// `IsReal` does not allow `NaN`s, but `0.0 / 0.0` produces a `NaN`.
let x = Real::try_new(0.0 / 0.0).unwrap(); // Panics when unwrapping.

pub fn assert(inner: T) -> Self

Constructs a proxy from a primitive IEEE 754 floating-point value and asserts that its constraints are satisfied.

This construction is independent of the divergence of the proxy and always asserts constraints (even when the divergence is fallible). Note that this function never fails (panics) for Total, which has no constraints.

Panics

This construction panics if the primitive floating-point value does not satisfy the constraints of the proxy.

Examples

Constructing proxies from primitive floating-point values:

use decorum::constraint::IsReal;
use decorum::divergence::OrPanic;
use decorum::proxy::Constrained;

type Real = Constrained<f64, IsReal<OrPanic>>;

fn f(x: Real) -> Real {
    x * 2.0
}

let y = f(Real::assert(2.0));

A proxy construction that fails:

use decorum::constraint::IsReal;
use decorum::divergence::OrPanic;
use decorum::proxy::Constrained;

type Real = Constrained<f64, IsReal<OrPanic>>;

// `IsReal` does not allow `NaN`s, but `0.0 / 0.0` produces a `NaN`.
let x = Real::assert(0.0 / 0.0); // Panics.

pub fn try_from_slice<'a>(slice: &'a [T]) -> Result<&'a [Self], C::Error>

Converts a slice of primitive IEEE 754 floating-point values into a slice of proxies.

This conversion must check the constraints of the proxy against each floating-point value and so has O(N) time complexity. When using the IsFloat constraint, prefer the infallible and O(1) from_slice function.

Errors

Returns an error if any of the primitive floating-point values in the slice do not satisfy the constraints of the proxy.

pub fn try_from_mut_slice<'a>( slice: &'a mut [T], ) -> Result<&'a mut [Self], C::Error>

Converts a mutable slice of primitive IEEE 754 floating-point values into a mutable slice of proxies.

This conversion must check the constraints of the proxy against each floating-point value and so has O(N) time complexity. When using the IsFloat constraint, prefer the infallible and O(1) from_mut_slice function.

Errors

Returns an error if any of the primitive floating-point values in the slice do not satisfy the constraints of the proxy.

pub fn from_subset<C2>(other: Constrained<T, C2>) -> Self

where C2: Constraint + SubsetOf<C>,

Converts a proxy into another proxy that is capable of representing a superset of its values per its constraint.

Examples

use decorum::divergence::OrPanic;
use decorum::real::UnaryRealFunction;
use decorum::{E64, R64};

let x = R64::<OrPanic>::ZERO;
let y = E64::from_subset(x); // `E64` allows a superset of the values of `R64`.

pub fn into_superset<C2>(self) -> Constrained<T, C2>

where C2: Constraint + SupersetOf<C>,

Converts a proxy into another proxy that is capable of representing a superset of its values per its constraint.

Examples

use decorum::real::UnaryRealFunction;
use decorum::{E64, R64};

let x = R64::ZERO;
let y: E64 = x.into_superset(); // `E64` allows a superset of the values of `R64`.

pub fn into_expression(self) -> ExpressionFor<Self>

Converts a proxy into its corresponding Expression.

The output of this function is always the Defined variant.

impl<T> Constrained<T, IsFloat>

where T: Primitive,

pub fn from_slice<'a>(slice: &'a [T]) -> &'a [Self]

Converts a slice of primitive IEEE 754 floating-point values into a slice of Totals.

Unlike try_from_slice, this conversion is infallible and trivial and so has O(1) time complexity.

pub fn from_mut_slice<'a>(slice: &'a mut [T]) -> &'a mut [Self]

Converts a mutable slice of primitive floating-point values into a mutable slice of Totals.

Unlike try_from_mut_slice, this conversion is infallible and trivial and so has O(1) time complexity.

Trait Implementations

impl<T, C> AbsDiffEq for Constrained<T, C>

where T: AbsDiffEq<Epsilon = T> + Primitive, C: Constraint,

type Epsilon = Constrained<T, C>

Used for specifying relative comparisons.

fn default_epsilon() -> Self::Epsilon

The default tolerance to use when testing values that are close together.

fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool

A test for equality that uses the absolute difference to compute the approximate equality of two numbers.

fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of AbsDiffEq::abs_diff_eq.

impl<T, C> Add<Constrained<T, C>> for ExpressionFor<Constrained<T, C>>

where T: Primitive, C: Constraint, C::Divergence: Divergence<Continue = AsExpression>,

type Output = Expression<Constrained<T, C>, <<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Error>

The resulting type after applying the + operator.

fn add(self, other: Constrained<T, C>) -> Self::Output

Performs the + operation.

impl<C> Add<Constrained<f32, C>> for f32

where C: Constraint,

type Output = <<<<Constrained<f32, C> as ConstrainedProxy>::Constraint as Constraint>::Divergence as Divergence>::Continue as Continue>::As<Constrained<f32, C>, <<Constrained<f32, C> as ConstrainedProxy>::Constraint as Constraint>::Error>

The resulting type after applying the + operator.

fn add(self, other: Constrained<f32, C>) -> Self::Output

Performs the + operation.

impl<C> Add<Constrained<f64, C>> for f64

where C: Constraint,

type Output = <<<<Constrained<f64, C> as ConstrainedProxy>::Constraint as Constraint>::Divergence as Divergence>::Continue as Continue>::As<Constrained<f64, C>, <<Constrained<f64, C> as ConstrainedProxy>::Constraint as Constraint>::Error>

The resulting type after applying the + operator.

fn add(self, other: Constrained<f64, C>) -> Self::Output

Performs the + operation.

impl<T, C> Add<Expression<Constrained<T, C>, <<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Error>> for Constrained<T, C>

where T: Primitive, C: Constraint, C::Divergence: Divergence<Continue = AsExpression>,

type Output = Expression<Constrained<T, C>, <<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Error>

The resulting type after applying the + operator.

fn add(self, other: ExpressionFor<Self>) -> Self::Output

Performs the + operation.

impl<T, C> Add<T> for Constrained<T, C>

where T: Primitive, C: Constraint,

type Output = <<<<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Divergence as Divergence>::Continue as Continue>::As<Constrained<T, C>, <<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Error>

The resulting type after applying the + operator.

fn add(self, other: T) -> Self::Output

Performs the + operation.

impl<T, C> Add for Constrained<T, C>

where T: Primitive, C: Constraint,

type Output = <<<<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Divergence as Divergence>::Continue as Continue>::As<Constrained<T, C>, <<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Error>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<T, C, E> AddAssign<T> for Constrained<T, C>

where T: Primitive, C: Constraint<Error = E>, ContinueFor<C::Divergence>: NonResidual<Self, E>,

fn add_assign(&mut self, other: T)

Performs the += operation.

impl<T, C, E> AddAssign for Constrained<T, C>

where T: Primitive, C: Constraint<Error = E>, ContinueFor<C::Divergence>: NonResidual<Self, E>,

fn add_assign(&mut self, other: Self)

Performs the += operation.

impl<T, C> AsRef<T> for Constrained<T, C>

fn as_ref(&self) -> &T

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, C> BaseEncoding for Constrained<T, C>

where T: Primitive,

const MAX_FINITE: Self

const MIN_FINITE: Self

const MIN_POSITIVE_NORMAL: Self

const EPSILON: Self

fn classify(self) -> FpCategory

fn is_normal(self) -> bool

fn is_sign_positive(self) -> bool

fn is_sign_negative(self) -> bool

fn signum(self) -> Self

fn integer_decode(self) -> (u64, i16, i8)

impl<T, C> BinaryRealFunction<Constrained<T, C>> for ExpressionFor<Constrained<T, C>>

where ErrorFor<Constrained<T, C>>: Clone + EmptyInhabitant, T: Primitive, C: Constraint, C::Divergence: Divergence<Continue = AsExpression>,

fn div_euclid(self, n: Constrained<T, C>) -> Self::Codomain

fn rem_euclid(self, n: Constrained<T, C>) -> Self::Codomain

fn pow(self, n: Constrained<T, C>) -> Self::Codomain

fn log(self, base: Constrained<T, C>) -> Self::Codomain

fn hypot(self, other: Constrained<T, C>) -> Self::Codomain

fn atan2(self, other: Constrained<T, C>) -> Self::Codomain

impl<T, C> BinaryRealFunction<Expression<Constrained<T, C>, <<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Error>> for Constrained<T, C>

where ErrorFor<Constrained<T, C>>: Clone + EmptyInhabitant, T: Primitive, C: Constraint, C::Divergence: Divergence<Continue = AsExpression>,

fn div_euclid(self, n: ExpressionFor<Constrained<T, C>>) -> Self::Codomain

fn rem_euclid(self, n: ExpressionFor<Constrained<T, C>>) -> Self::Codomain

fn pow(self, n: ExpressionFor<Constrained<T, C>>) -> Self::Codomain

fn log(self, base: ExpressionFor<Constrained<T, C>>) -> Self::Codomain

fn hypot(self, other: ExpressionFor<Constrained<T, C>>) -> Self::Codomain

fn atan2(self, other: ExpressionFor<Constrained<T, C>>) -> Self::Codomain

impl<T, C> BinaryRealFunction<T> for Constrained<T, C>

where T: Primitive, C: Constraint,

fn div_euclid(self, n: T) -> Self::Codomain

fn rem_euclid(self, n: T) -> Self::Codomain

fn pow(self, n: T) -> Self::Codomain

fn log(self, base: T) -> Self::Codomain

fn hypot(self, other: T) -> Self::Codomain

fn atan2(self, other: T) -> Self::Codomain

impl<T, C> BinaryRealFunction for Constrained<T, C>

where T: Primitive, C: Constraint,

fn div_euclid(self, n: Self) -> Self::Codomain

fn rem_euclid(self, n: Self) -> Self::Codomain

fn pow(self, n: Self) -> Self::Codomain

fn log(self, base: Self) -> Self::Codomain

fn hypot(self, other: Self) -> Self::Codomain

fn atan2(self, other: Self) -> Self::Codomain

impl<T, C> Bounded for Constrained<T, C>

where T: Primitive,

fn min_value() -> Self

Returns the smallest finite number this type can represent

fn max_value() -> Self

Returns the largest finite number this type can represent

impl<T, C> Clone for Constrained<T, C>

where T: Clone,

fn clone(&self) -> Self

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<T, C> ConstrainedProxy for Constrained<T, C>

where T: Primitive, C: Constraint,

type Constraint = C

impl<T, D> Debug for Constrained<T, IsExtendedReal<D>>

where T: Debug, D: Divergence,

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

Formats the value using the given formatter.

impl<T> Debug for Constrained<T, IsFloat>

where T: Debug,

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

Formats the value using the given formatter.

impl<T, D> Debug for Constrained<T, IsReal<D>>

where T: Debug, D: Divergence,

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

Formats the value using the given formatter.

impl<T, C> Default for Constrained<T, C>

where T: Primitive, C: Constraint,

fn default() -> Self

Returns the “default value” for a type.

impl<'de, T, C> Deserialize<'de> for Constrained<T, C>

where T: Deserialize<'de> + Primitive, C: Constraint, C::Error: Display,

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<T, C> Display for Constrained<T, C>

where T: Display,

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

Formats the value using the given formatter.

impl<T, C> Div<Constrained<T, C>> for ExpressionFor<Constrained<T, C>>

where T: Primitive, C: Constraint, C::Divergence: Divergence<Continue = AsExpression>,

type Output = Expression<Constrained<T, C>, <<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Error>

The resulting type after applying the / operator.

fn div(self, other: Constrained<T, C>) -> Self::Output

Performs the / operation.

impl<C> Div<Constrained<f32, C>> for f32

where C: Constraint,

type Output = <<<<Constrained<f32, C> as ConstrainedProxy>::Constraint as Constraint>::Divergence as Divergence>::Continue as Continue>::As<Constrained<f32, C>, <<Constrained<f32, C> as ConstrainedProxy>::Constraint as Constraint>::Error>

The resulting type after applying the / operator.

fn div(self, other: Constrained<f32, C>) -> Self::Output

Performs the / operation.

impl<C> Div<Constrained<f64, C>> for f64

where C: Constraint,

type Output = <<<<Constrained<f64, C> as ConstrainedProxy>::Constraint as Constraint>::Divergence as Divergence>::Continue as Continue>::As<Constrained<f64, C>, <<Constrained<f64, C> as ConstrainedProxy>::Constraint as Constraint>::Error>

The resulting type after applying the / operator.

fn div(self, other: Constrained<f64, C>) -> Self::Output

Performs the / operation.

impl<T, C> Div<Expression<Constrained<T, C>, <<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Error>> for Constrained<T, C>

where T: Primitive, C: Constraint, C::Divergence: Divergence<Continue = AsExpression>,

type Output = Expression<Constrained<T, C>, <<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Error>

The resulting type after applying the / operator.

fn div(self, other: ExpressionFor<Self>) -> Self::Output

Performs the / operation.

impl<T, C> Div<T> for Constrained<T, C>

where T: Primitive, C: Constraint,

type Output = <<<<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Divergence as Divergence>::Continue as Continue>::As<Constrained<T, C>, <<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Error>

The resulting type after applying the / operator.

fn div(self, other: T) -> Self::Output

Performs the / operation.

impl<T, C> Div for Constrained<T, C>

where T: Primitive, C: Constraint,

type Output = <<<<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Divergence as Divergence>::Continue as Continue>::As<Constrained<T, C>, <<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Error>

The resulting type after applying the / operator.

fn div(self, other: Self) -> Self::Output

Performs the / operation.

impl<T, C, E> DivAssign<T> for Constrained<T, C>

where T: Primitive, C: Constraint<Error = E>, ContinueFor<C::Divergence>: NonResidual<Self, E>,

fn div_assign(&mut self, other: T)

Performs the /= operation.

impl<T, C, E> DivAssign for Constrained<T, C>

where T: Primitive, C: Constraint<Error = E>, ContinueFor<C::Divergence>: NonResidual<Self, E>,

fn div_assign(&mut self, other: Self)

Performs the /= operation.

impl<T, C> EmptyOrd for Constrained<T, C>

where T: Primitive, C: Constraint,

type Empty = <C as FromEmpty>::Empty<T>

fn from_empty(empty: Self::Empty) -> Self

fn is_empty(&self) -> bool

fn cmp_empty(&self, other: &Self) -> Result<Ordering, Self::Empty>

impl<T, C, E> Float for Constrained<T, C>

where T: Float + Primitive, C: Constraint<Error = E> + Member<InfinitySet> + Member<NanSet>, ContinueFor<C::Divergence>: NonResidual<Self, E>,

fn infinity() -> Self

Returns the infinite value.

fn neg_infinity() -> Self

Returns the negative infinite value.

fn is_infinite(self) -> bool

Returns true if this value is positive infinity or negative infinity and false otherwise.

fn is_finite(self) -> bool

Returns true if this number is neither infinite nor NaN.

fn nan() -> Self

Returns the NaN value.

fn is_nan(self) -> bool

Returns true if this value is NaN and false otherwise.

fn max_value() -> Self

Returns the largest finite value that this type can represent.

fn min_value() -> Self

Returns the smallest finite value that this type can represent.

fn min_positive_value() -> Self

Returns the smallest positive, normalized value that this type can represent.

fn epsilon() -> Self

Returns epsilon, a small positive value.

fn min(self, other: Self) -> Self

Returns the minimum of the two numbers.

fn max(self, other: Self) -> Self

Returns the maximum of the two numbers.

fn neg_zero() -> Self

Returns -0.0.

fn is_sign_positive(self) -> bool

Returns true if self is positive, including +0.0, Float::infinity(), and Float::nan().

fn is_sign_negative(self) -> bool

Returns true if self is negative, including -0.0, Float::neg_infinity(), and -Float::nan().

fn signum(self) -> Self

Returns a number that represents the sign of self.

fn abs(self) -> Self

Computes the absolute value of self. Returns Float::nan() if the number is Float::nan().

fn classify(self) -> FpCategory

Returns the floating point category of the number. If only one property is going to be tested, it is generally faster to use the specific predicate instead.

fn is_normal(self) -> bool

Returns true if the number is neither zero, infinite, subnormal, or NaN.

fn integer_decode(self) -> (u64, i16, i8)

Returns the mantissa, base 2 exponent, and sign as integers, respectively. The original number can be recovered by sign * mantissa * 2 ^ exponent.

fn floor(self) -> Self

Returns the largest integer less than or equal to a number.

fn ceil(self) -> Self

Returns the smallest integer greater than or equal to a number.

fn round(self) -> Self

Returns the nearest integer to a number. Round half-way cases away from 0.0.

fn trunc(self) -> Self

Return the integer part of a number.

fn fract(self) -> Self

Returns the fractional part of a number.

fn recip(self) -> Self

Take the reciprocal (inverse) of a number, 1/x.

fn mul_add(self, a: Self, b: Self) -> Self

Fused multiply-add. Computes (self * a) + b with only one rounding error, yielding a more accurate result than an unfused multiply-add.

fn abs_sub(self, other: Self) -> Self

The positive difference of two numbers.

fn powi(self, n: i32) -> Self

Raise a number to an integer power.

fn powf(self, n: Self) -> Self

Raise a number to a floating point power.

fn sqrt(self) -> Self

Take the square root of a number.

fn cbrt(self) -> Self

Take the cubic root of a number.

fn exp(self) -> Self

Returns e^(self), (the exponential function).

fn exp2(self) -> Self

Returns 2^(self).

fn exp_m1(self) -> Self

Returns e^(self) - 1 in a way that is accurate even if the number is close to zero.

fn log(self, base: Self) -> Self

Returns the logarithm of the number with respect to an arbitrary base.

fn ln(self) -> Self

Returns the natural logarithm of the number.

fn log2(self) -> Self

Returns the base 2 logarithm of the number.

fn log10(self) -> Self

Returns the base 10 logarithm of the number.

fn ln_1p(self) -> Self

Returns ln(1+n) (natural logarithm) more accurately than if the operations were performed separately.

fn hypot(self, other: Self) -> Self

Calculate the length of the hypotenuse of a right-angle triangle given legs of length x and y.

fn sin(self) -> Self

Computes the sine of a number (in radians).

fn cos(self) -> Self

Computes the cosine of a number (in radians).

fn tan(self) -> Self

Computes the tangent of a number (in radians).

fn asin(self) -> Self

Computes the arcsine of a number. Return value is in radians in the range [-pi/2, pi/2] or NaN if the number is outside the range [-1, 1].

fn acos(self) -> Self

Computes the arccosine of a number. Return value is in radians in the range [0, pi] or NaN if the number is outside the range [-1, 1].

fn atan(self) -> Self

Computes the arctangent of a number. Return value is in radians in the range [-pi/2, pi/2];

fn atan2(self, other: Self) -> Self

Computes the four quadrant arctangent of self (y) and other (x).

fn sin_cos(self) -> (Self, Self)

Simultaneously computes the sine and cosine of the number, x. Returns (sin(x), cos(x)).

fn sinh(self) -> Self

Hyperbolic sine function.

fn cosh(self) -> Self

Hyperbolic cosine function.

fn tanh(self) -> Self

Hyperbolic tangent function.

fn asinh(self) -> Self

Inverse hyperbolic sine function.

fn acosh(self) -> Self

Inverse hyperbolic cosine function.

fn atanh(self) -> Self

Inverse hyperbolic tangent function.

fn is_subnormal(self) -> bool

Returns true if the number is subnormal.

fn to_degrees(self) -> Self

Converts radians to degrees.

fn to_radians(self) -> Self

Converts degrees to radians.

fn clamp(self, min: Self, max: Self) -> Self

Clamps a value between a min and max.

fn copysign(self, sign: Self) -> Self

Returns a number composed of the magnitude of self and the sign of sign.

impl<T, C> FloatConst for Constrained<T, C>

where T: Primitive, C: Constraint,

fn E() -> Self

Return Euler’s number.

fn PI() -> Self

Return Archimedes’ constant π.

fn SQRT_2() -> Self

Return sqrt(2.0).

fn FRAC_1_PI() -> Self

Return 1.0 / π.

fn FRAC_2_PI() -> Self

Return 2.0 / π.

fn FRAC_1_SQRT_2() -> Self

Return 1.0 / sqrt(2.0).

fn FRAC_2_SQRT_PI() -> Self

Return 2.0 / sqrt(π).

fn FRAC_PI_2() -> Self

Return π / 2.0.

fn FRAC_PI_3() -> Self

Return π / 3.0.

fn FRAC_PI_4() -> Self

Return π / 4.0.

fn FRAC_PI_6() -> Self

Return π / 6.0.

fn FRAC_PI_8() -> Self

Return π / 8.0.

fn LN_10() -> Self

Return ln(10.0).

fn LN_2() -> Self

Return ln(2.0).

fn LOG10_E() -> Self

Return log10(e).

fn LOG2_E() -> Self

Return log2(e).

fn TAU() -> Self

where Self: Sized + Add<Output = Self>,

Return the full circle constant τ.

fn LOG10_2() -> Self

where Self: Sized + Div<Output = Self>,

Return log10(2.0).

fn LOG2_10() -> Self

where Self: Sized + Div<Output = Self>,

Return log2(10.0).

impl<T, C> From<Constrained<T, C>> for Expression<Constrained<T, C>, ErrorFor<Constrained<T, C>>>

where T: Primitive, C: Constraint,

fn from(proxy: Constrained<T, C>) -> Self

Converts to this type from the input type.

impl<T> From<Constrained<T, IsExtendedReal<OrPanic>>> for Total<T>

where T: Primitive,

fn from(other: ExtendedReal<T>) -> Self

Converts to this type from the input type.

impl<T> From<Constrained<T, IsReal<OrPanic>>> for ExtendedReal<T>

where T: Primitive,

fn from(other: Real<T>) -> Self

Converts to this type from the input type.

impl<T> From<Constrained<T, IsReal<OrPanic>>> for Total<T>

where T: Primitive,

fn from(other: Real<T>) -> Self

Converts to this type from the input type.

impl<C> From<Constrained<f32, C>> for f32

fn from(proxy: Constrained<f32, C>) -> Self

Converts to this type from the input type.

impl<C> From<Constrained<f64, C>> for f64

fn from(proxy: Constrained<f64, C>) -> Self

Converts to this type from the input type.

impl<T, C> FromPrimitive for Constrained<T, C>

where T: FromPrimitive + Primitive, C: Constraint,

fn from_i8(value: i8) -> Option<Self>

Converts an i8 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u8(value: u8) -> Option<Self>

Converts an u8 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i16(value: i16) -> Option<Self>

Converts an i16 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u16(value: u16) -> Option<Self>

Converts an u16 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i32(value: i32) -> Option<Self>

Converts an i32 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u32(value: u32) -> Option<Self>

Converts an u32 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i64(value: i64) -> Option<Self>

Converts an i64 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u64(value: u64) -> Option<Self>

Converts an u64 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_isize(value: isize) -> Option<Self>

Converts an isize to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_usize(value: usize) -> Option<Self>

Converts a usize to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_f32(value: f32) -> Option<Self>

Converts a f32 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_f64(value: f64) -> Option<Self>

Converts a f64 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i128(n: i128) -> Option<Self>

Converts an i128 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u128(n: u128) -> Option<Self>

Converts an u128 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

impl<T, C, E> FromStr for Constrained<T, C>

where T: FromStr + Primitive, C: Constraint<Error = E>, ContinueFor<C::Divergence>: NonResidual<Self, E>,

type Err = <T as FromStr>::Err

The associated error which can be returned from parsing.

fn from_str(string: &str) -> Result<Self, Self::Err>

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

impl<T, C> Function for Constrained<T, C>

where T: Primitive, C: Constraint,

type Codomain = <<<<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Divergence as Divergence>::Continue as Continue>::As<Constrained<T, C>, <<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Error>

impl<T, C> Hash for Constrained<T, C>

where T: Primitive + ToCanonical,

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

where H: Hasher,

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<T, C> InfinityEncoding for Constrained<T, C>

where T: Primitive, C: Constraint + Member<InfinitySet>,

const INFINITY: Self

const NEG_INFINITY: Self

fn is_infinite(self) -> bool

fn is_finite(self) -> bool

impl<T, C> LowerExp for Constrained<T, C>

where T: LowerExp + Primitive,

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

Formats the value using the given formatter.

impl<T, C> Mul<Constrained<T, C>> for ExpressionFor<Constrained<T, C>>

where T: Primitive, C: Constraint, C::Divergence: Divergence<Continue = AsExpression>,

type Output = Expression<Constrained<T, C>, <<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Error>

The resulting type after applying the * operator.

fn mul(self, other: Constrained<T, C>) -> Self::Output

Performs the * operation.

impl<C> Mul<Constrained<f32, C>> for f32

where C: Constraint,

type Output = <<<<Constrained<f32, C> as ConstrainedProxy>::Constraint as Constraint>::Divergence as Divergence>::Continue as Continue>::As<Constrained<f32, C>, <<Constrained<f32, C> as ConstrainedProxy>::Constraint as Constraint>::Error>

The resulting type after applying the * operator.

fn mul(self, other: Constrained<f32, C>) -> Self::Output

Performs the * operation.

impl<C> Mul<Constrained<f64, C>> for f64

where C: Constraint,

type Output = <<<<Constrained<f64, C> as ConstrainedProxy>::Constraint as Constraint>::Divergence as Divergence>::Continue as Continue>::As<Constrained<f64, C>, <<Constrained<f64, C> as ConstrainedProxy>::Constraint as Constraint>::Error>

The resulting type after applying the * operator.

fn mul(self, other: Constrained<f64, C>) -> Self::Output

Performs the * operation.

impl<T, C> Mul<Expression<Constrained<T, C>, <<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Error>> for Constrained<T, C>

where T: Primitive, C: Constraint, C::Divergence: Divergence<Continue = AsExpression>,

type Output = Expression<Constrained<T, C>, <<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Error>

The resulting type after applying the * operator.

fn mul(self, other: ExpressionFor<Self>) -> Self::Output

Performs the * operation.

impl<T, C> Mul<T> for Constrained<T, C>

where T: Primitive, C: Constraint,

type Output = <<<<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Divergence as Divergence>::Continue as Continue>::As<Constrained<T, C>, <<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Error>

The resulting type after applying the * operator.

fn mul(self, other: T) -> Self::Output

Performs the * operation.

impl<T, C> Mul for Constrained<T, C>

where T: Primitive, C: Constraint,

type Output = <<<<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Divergence as Divergence>::Continue as Continue>::As<Constrained<T, C>, <<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Error>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T, C, E> MulAssign<T> for Constrained<T, C>

where T: Primitive, C: Constraint<Error = E>, ContinueFor<C::Divergence>: NonResidual<Self, E>,

fn mul_assign(&mut self, other: T)

Performs the *= operation.

impl<T, C, E> MulAssign for Constrained<T, C>

where T: Primitive, C: Constraint<Error = E>, ContinueFor<C::Divergence>: NonResidual<Self, E>,

fn mul_assign(&mut self, other: Self)

Performs the *= operation.

impl<T, C> NanEncoding for Constrained<T, C>

where T: Primitive, C: Constraint + Member<NanSet>,

const NAN: Self::Nan

An arbitrary representation of NaN.

type Nan = Constrained<T, C>

The type of the arbitrary Nan representation NAN.

fn is_nan(self) -> bool

impl<T, C> Neg for Constrained<T, C>

where T: Primitive,

type Output = Constrained<T, C>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<T, C, E> Num for Constrained<T, C>

where T: Num + Primitive, C: Constraint<Error = E>, ContinueFor<C::Divergence>: NonResidual<Self, E>,

type FromStrRadixErr = ()

fn from_str_radix( source: &str, radix: u32, ) -> Result<Self, Self::FromStrRadixErr>

Convert from a string and radix (typically 2..=36).

impl<T, C> NumCast for Constrained<T, C>

where T: NumCast + Primitive + ToPrimitive, C: Constraint,

fn from<U>(value: U) -> Option<Self>

where U: ToPrimitive,

Creates a number from another value that can be converted into a primitive via the ToPrimitive trait. If the source value cannot be represented by the target type, then None is returned.

impl<T, C, E> One for Constrained<T, C>

where T: Primitive, C: Constraint<Error = E>, ContinueFor<C::Divergence>: NonResidual<Self, E>,

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool

where Self: PartialEq,

Returns true if self is equal to the multiplicative identity.

impl<T, C> Ord for Constrained<T, C>

where T: Primitive,

fn cmp(&self, other: &Self) -> Ordering

This method returns an Ordering between self and other.

fn max(self, other: Self) -> Self

where Self: Sized,

Compares and returns the maximum of two values.

fn min(self, other: Self) -> Self

where Self: Sized,

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

where Self: Sized,

Restrict a value to a certain interval.

impl<T, C> PartialEq<T> for Constrained<T, C>

where T: Primitive, C: Constraint,

fn eq(&self, other: &T) -> 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<T, C> PartialEq for Constrained<T, C>

where T: Primitive,

fn eq(&self, other: &Self) -> 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<T, C> PartialOrd<T> for Constrained<T, C>

where T: Primitive, C: Constraint,

fn partial_cmp(&self, other: &T) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

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

Tests less than (for self and other) and is used by the < operator.

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

Tests less than or equal to (for self and other) and is used by the <= operator.

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

Tests greater than (for self and other) and is used by the > operator.

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

Tests greater than or equal to (for self and other) and is used by the >= operator.

impl<T, C> PartialOrd for Constrained<T, C>

where T: Primitive,

fn partial_cmp(&self, other: &Self) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

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

Tests less than (for self and other) and is used by the < operator.

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

Tests less than or equal to (for self and other) and is used by the <= operator.

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

Tests greater than (for self and other) and is used by the > operator.

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

Tests greater than or equal to (for self and other) and is used by the >= operator.

impl<T, C, E> Product for Constrained<T, C>

where T: Primitive, C: Constraint<Error = E>, ContinueFor<C::Divergence>: NonResidual<Self, E>,

fn product<I>(input: I) -> Self

where I: Iterator<Item = Self>,

Takes an iterator and generates Self from the elements by multiplying the items.

impl<T, C> Proxy for Constrained<T, C>

where T: Primitive,

type Primitive = T

impl<T, C> RelativeEq for Constrained<T, C>

where T: Primitive + RelativeEq<Epsilon = T>, C: Constraint,

fn default_max_relative() -> Self::Epsilon

The default relative tolerance for testing values that are far-apart.

fn relative_eq( &self, other: &Self, epsilon: Self::Epsilon, max_relative: Self::Epsilon, ) -> bool

A test for equality that uses a relative comparison if the values are far apart.

fn relative_ne( &self, other: &Rhs, epsilon: Self::Epsilon, max_relative: Self::Epsilon, ) -> bool

The inverse of RelativeEq::relative_eq.

impl<T, C> Rem<Constrained<T, C>> for ExpressionFor<Constrained<T, C>>

where T: Primitive, C: Constraint, C::Divergence: Divergence<Continue = AsExpression>,

type Output = Expression<Constrained<T, C>, <<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Error>

The resulting type after applying the % operator.

fn rem(self, other: Constrained<T, C>) -> Self::Output

Performs the % operation.

impl<C> Rem<Constrained<f32, C>> for f32

where C: Constraint,

type Output = <<<<Constrained<f32, C> as ConstrainedProxy>::Constraint as Constraint>::Divergence as Divergence>::Continue as Continue>::As<Constrained<f32, C>, <<Constrained<f32, C> as ConstrainedProxy>::Constraint as Constraint>::Error>

The resulting type after applying the % operator.

fn rem(self, other: Constrained<f32, C>) -> Self::Output

Performs the % operation.

impl<C> Rem<Constrained<f64, C>> for f64

where C: Constraint,

type Output = <<<<Constrained<f64, C> as ConstrainedProxy>::Constraint as Constraint>::Divergence as Divergence>::Continue as Continue>::As<Constrained<f64, C>, <<Constrained<f64, C> as ConstrainedProxy>::Constraint as Constraint>::Error>

The resulting type after applying the % operator.

fn rem(self, other: Constrained<f64, C>) -> Self::Output

Performs the % operation.

impl<T, C> Rem<Expression<Constrained<T, C>, <<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Error>> for Constrained<T, C>

where T: Primitive, C: Constraint, C::Divergence: Divergence<Continue = AsExpression>,

type Output = Expression<Constrained<T, C>, <<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Error>

The resulting type after applying the % operator.

fn rem(self, other: ExpressionFor<Self>) -> Self::Output

Performs the % operation.

impl<T, C> Rem<T> for Constrained<T, C>

where T: Primitive, C: Constraint,

type Output = <<<<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Divergence as Divergence>::Continue as Continue>::As<Constrained<T, C>, <<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Error>

The resulting type after applying the % operator.

fn rem(self, other: T) -> Self::Output

Performs the % operation.

impl<T, C> Rem for Constrained<T, C>

where T: Primitive, C: Constraint,

type Output = <<<<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Divergence as Divergence>::Continue as Continue>::As<Constrained<T, C>, <<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Error>

The resulting type after applying the % operator.

fn rem(self, other: Self) -> Self::Output

Performs the % operation.

impl<T, C, E> RemAssign<T> for Constrained<T, C>

where T: Primitive, C: Constraint<Error = E>, ContinueFor<C::Divergence>: NonResidual<Self, E>,

fn rem_assign(&mut self, other: T)

Performs the %= operation.

impl<T, C, E> RemAssign for Constrained<T, C>

where T: Primitive, C: Constraint<Error = E>, ContinueFor<C::Divergence>: NonResidual<Self, E>,

fn rem_assign(&mut self, other: Self)

Performs the %= operation.

impl<T, C> Serialize for Constrained<T, C>

where T: Primitive + Serialize, C: Constraint,

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl<T, C, E> Signed for Constrained<T, C>

where T: Primitive + Signed, C: Constraint<Error = E>, ContinueFor<C::Divergence>: NonResidual<Self, E>,

fn abs(&self) -> Self

Computes the absolute value.

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

The positive difference of two numbers.

fn signum(&self) -> Self

Returns the sign of the number.

fn is_positive(&self) -> bool

Returns true if the number is positive and false if the number is zero or negative.

fn is_negative(&self) -> bool

Returns true if the number is negative and false if the number is zero or positive.

impl<T, C> Sub<Constrained<T, C>> for ExpressionFor<Constrained<T, C>>

where T: Primitive, C: Constraint, C::Divergence: Divergence<Continue = AsExpression>,

type Output = Expression<Constrained<T, C>, <<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Error>

The resulting type after applying the - operator.

fn sub(self, other: Constrained<T, C>) -> Self::Output

Performs the - operation.

impl<C> Sub<Constrained<f32, C>> for f32

where C: Constraint,

type Output = <<<<Constrained<f32, C> as ConstrainedProxy>::Constraint as Constraint>::Divergence as Divergence>::Continue as Continue>::As<Constrained<f32, C>, <<Constrained<f32, C> as ConstrainedProxy>::Constraint as Constraint>::Error>

The resulting type after applying the - operator.

fn sub(self, other: Constrained<f32, C>) -> Self::Output

Performs the - operation.

impl<C> Sub<Constrained<f64, C>> for f64

where C: Constraint,

type Output = <<<<Constrained<f64, C> as ConstrainedProxy>::Constraint as Constraint>::Divergence as Divergence>::Continue as Continue>::As<Constrained<f64, C>, <<Constrained<f64, C> as ConstrainedProxy>::Constraint as Constraint>::Error>

The resulting type after applying the - operator.

fn sub(self, other: Constrained<f64, C>) -> Self::Output

Performs the - operation.

impl<T, C> Sub<Expression<Constrained<T, C>, <<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Error>> for Constrained<T, C>

where T: Primitive, C: Constraint, C::Divergence: Divergence<Continue = AsExpression>,

type Output = Expression<Constrained<T, C>, <<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Error>

The resulting type after applying the - operator.

fn sub(self, other: ExpressionFor<Self>) -> Self::Output

Performs the - operation.

impl<T, C> Sub<T> for Constrained<T, C>

where T: Primitive, C: Constraint,

type Output = <<<<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Divergence as Divergence>::Continue as Continue>::As<Constrained<T, C>, <<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Error>

The resulting type after applying the - operator.

fn sub(self, other: T) -> Self::Output

Performs the - operation.

impl<T, C> Sub for Constrained<T, C>

where T: Primitive, C: Constraint,

type Output = <<<<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Divergence as Divergence>::Continue as Continue>::As<Constrained<T, C>, <<Constrained<T, C> as ConstrainedProxy>::Constraint as Constraint>::Error>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<T, C, E> SubAssign<T> for Constrained<T, C>

where T: Primitive, C: Constraint<Error = E>, ContinueFor<C::Divergence>: NonResidual<Self, E>,

fn sub_assign(&mut self, other: T)

Performs the -= operation.

impl<T, C, E> SubAssign for Constrained<T, C>

where T: Primitive, C: Constraint<Error = E>, ContinueFor<C::Divergence>: NonResidual<Self, E>,

fn sub_assign(&mut self, other: Self)

Performs the -= operation.

impl<T, C, E> Sum for Constrained<T, C>

where T: Primitive, C: Constraint<Error = E>, ContinueFor<C::Divergence>: NonResidual<Self, E>,

fn sum<I>(input: I) -> Self

where I: Iterator<Item = Self>,

Takes an iterator and generates Self from the elements by “summing up” the items.

impl<T, C> ToCanonical for Constrained<T, C>

where T: Primitive,

type Canonical = <T as ToCanonical>::Canonical

fn to_canonical(self) -> Self::Canonical

Conversion to a canonical representation.

impl<T, C> ToPrimitive for Constrained<T, C>

where T: Primitive + ToPrimitive,

fn to_i8(&self) -> Option<i8>

Converts the value of self to an i8. If the value cannot be represented by an i8, then None is returned.

fn to_u8(&self) -> Option<u8>

Converts the value of self to a u8. If the value cannot be represented by a u8, then None is returned.

fn to_i16(&self) -> Option<i16>

Converts the value of self to an i16. If the value cannot be represented by an i16, then None is returned.

fn to_u16(&self) -> Option<u16>

Converts the value of self to a u16. If the value cannot be represented by a u16, then None is returned.

fn to_i32(&self) -> Option<i32>

Converts the value of self to an i32. If the value cannot be represented by an i32, then None is returned.

fn to_u32(&self) -> Option<u32>

Converts the value of self to a u32. If the value cannot be represented by a u32, then None is returned.

fn to_i64(&self) -> Option<i64>

Converts the value of self to an i64. If the value cannot be represented by an i64, then None is returned.

fn to_u64(&self) -> Option<u64>

Converts the value of self to a u64. If the value cannot be represented by a u64, then None is returned.

fn to_isize(&self) -> Option<isize>

Converts the value of self to an isize. If the value cannot be represented by an isize, then None is returned.

fn to_usize(&self) -> Option<usize>

Converts the value of self to a usize. If the value cannot be represented by a usize, then None is returned.

fn to_f32(&self) -> Option<f32>

Converts the value of self to an f32. Overflows may map to positive or negative inifinity, otherwise None is returned if the value cannot be represented by an f32.

fn to_f64(&self) -> Option<f64>

Converts the value of self to an f64. Overflows may map to positive or negative inifinity, otherwise None is returned if the value cannot be represented by an f64.

fn to_i128(&self) -> Option<i128>

Converts the value of self to an i128. If the value cannot be represented by an i128 (i64 under the default implementation), then None is returned.

fn to_u128(&self) -> Option<u128>

Converts the value of self to a u128. If the value cannot be represented by a u128 (u64 under the default implementation), then None is returned.

impl<C> TryFrom<Expression<Constrained<f32, C>, <C as Constraint>::Error>> for Constrained<f32, C>

where C: Constraint,

type Error = <C as Constraint>::Error

The type returned in the event of a conversion error.

fn try_from( expression: Expression<Constrained<f32, C>, C::Error>, ) -> Result<Self, Self::Error>

Performs the conversion.

impl<C> TryFrom<Expression<Constrained<f64, C>, <C as Constraint>::Error>> for Constrained<f64, C>

where C: Constraint,

type Error = <C as Constraint>::Error

The type returned in the event of a conversion error.

fn try_from( expression: Expression<Constrained<f64, C>, C::Error>, ) -> Result<Self, Self::Error>

Performs the conversion.

impl<T, C> UlpsEq for Constrained<T, C>

where T: Primitive + UlpsEq<Epsilon = T>, C: Constraint,

fn default_max_ulps() -> u32

The default ULPs to tolerate when testing values that are far-apart.

fn ulps_eq(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool

A test for equality that uses units in the last place (ULP) if the values are far apart.

fn ulps_ne(&self, other: &Rhs, epsilon: Self::Epsilon, max_ulps: u32) -> bool

The inverse of UlpsEq::ulps_eq.

impl<T, C> UnaryRealFunction for Constrained<T, C>

where T: Primitive, C: Constraint,

const ZERO: Self

const ONE: Self

const E: Self

const PI: Self

const FRAC_1_PI: Self

const FRAC_2_PI: Self

const FRAC_2_SQRT_PI: Self

const FRAC_PI_2: Self

const FRAC_PI_3: Self

const FRAC_PI_4: Self

const FRAC_PI_6: Self

const FRAC_PI_8: Self

const SQRT_2: Self

const FRAC_1_SQRT_2: Self

const LN_2: Self

const LN_10: Self

const LOG2_E: Self

const LOG10_E: Self

fn is_zero(self) -> bool

fn is_one(self) -> bool

fn sign(self) -> Sign

fn abs(self) -> Self

fn floor(self) -> Self

fn ceil(self) -> Self

fn round(self) -> Self

fn trunc(self) -> Self

fn fract(self) -> Self

fn recip(self) -> Self::Codomain

fn powi(self, n: i32) -> Self::Codomain

fn sqrt(self) -> Self::Codomain

fn cbrt(self) -> Self

fn exp(self) -> Self::Codomain

fn exp2(self) -> Self::Codomain

fn exp_m1(self) -> Self::Codomain

fn ln(self) -> Self::Codomain

fn log2(self) -> Self::Codomain

fn log10(self) -> Self::Codomain

fn ln_1p(self) -> Self::Codomain

fn to_degrees(self) -> Self::Codomain

fn to_radians(self) -> Self

fn sin(self) -> Self

fn cos(self) -> Self

fn tan(self) -> Self::Codomain

fn asin(self) -> Self::Codomain

fn acos(self) -> Self::Codomain

fn atan(self) -> Self

fn sin_cos(self) -> (Self, Self)

fn sinh(self) -> Self

fn cosh(self) -> Self

fn tanh(self) -> Self

fn asinh(self) -> Self::Codomain

fn acosh(self) -> Self::Codomain

fn atanh(self) -> Self::Codomain

impl<T, C> UpperExp for Constrained<T, C>

where T: UpperExp,

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

Formats the value using the given formatter.

impl<T, C, E> Zero for Constrained<T, C>

where T: Primitive, C: Constraint<Error = E>, ContinueFor<C::Divergence>: NonResidual<Self, E>,

fn zero() -> Self

Returns the additive identity element of Self, 0.

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.

impl<T, C> Copy for Constrained<T, C>

where T: Copy,

impl<T, C> Eq for Constrained<T, C>

where T: Primitive,