Struct scuttlebutt::field::polynomial::Polynomial

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pub struct Polynomial<FE: FiniteField> {
    pub constant: FE,
    pub coefficients: SmallVec<[FE; 3]>,
}

Expand description

A polynomial over some given finite field, represented as the coefficient vector.

Fields

constant: FE

The coefficient for $x^0$

coefficients: SmallVec<[FE; 3]>

The coefficients for $x^1, ..., x^n$

coefficients[i] is the coefficient for $x^{i+1}$

Implementations

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impl<FE: FiniteField> Polynomial<FE>

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pub fn random(rng: &mut impl RngCore + ?Sized, degree: usize) -> Self

Construct a random polynomial of the given degree.

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pub fn zero() -> Self

Return the zero polynomial.

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pub fn one() -> Self

Return the polynomial P(x) = 1

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pub fn constant(c: FE) -> Self

Return the polynomial P(x) = c

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pub fn x() -> Self

Return the polynomial P(x) = x

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pub fn degree(&self) -> usize

Return the degree of the polynomial

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pub fn eval(&self, at: FE) -> FE

Evaluate the polynomial at a given x value.

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pub fn divmod(&self, divisor: &Self) -> (Self, Self)

Return (self / divisor, self % divisor)

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pub fn interpolate(points: &[(FE, FE)]) -> Self

Interpolate a polynomial from the given (x,y) points

Panics

This function will panic if points is empty, or if any x values collide.

Trait Implementations

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impl<'a, FE: FiniteField> AddAssign<&'a Polynomial<FE>> for Polynomial<FE>

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fn add_assign(&mut self, rhs: &'a Polynomial<FE>)

Performs the += operation. Read more

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impl<FE: Clone + FiniteField> Clone for Polynomial<FE>

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fn clone(&self) -> Polynomial<FE>

Returns a copy of the value. Read more

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

Performs copy-assignment from source. Read more

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impl<FE: FiniteField> ConstantTimeEq for Polynomial<FE>

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fn ct_eq(&self, other: &Self) -> Choice

Determine if two items are equal. Read more

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impl<FE: FiniteField> Debug for Polynomial<FE>

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

Formats the value using the given formatter. Read more

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impl<FE: FiniteField> From<&[FE]> for Polynomial<FE>

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fn from(v: &[FE]) -> Self

Converts to this type from the input type.

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impl<FE: FiniteField> Index<usize> for Polynomial<FE>

Index into the Polynomial where 0 is the constant term.

type Output = FE

The returned type after indexing.

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fn index(&self, index: usize) -> &Self::Output

Performs the indexing (container[index]) operation. Read more

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impl<FE: FiniteField> IndexMut<usize> for Polynomial<FE>

Index into the Polynomial where 0 is the constant term.

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fn index_mut(&mut self, index: usize) -> &mut Self::Output

Performs the mutable indexing (container[index]) operation. Read more

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impl<'a, FE: FiniteField> MulAssign<&'a Polynomial<FE>> for Polynomial<FE>

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fn mul_assign(&mut self, rhs: &'a Polynomial<FE>)

Performs the *= operation. Read more

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impl<FE: FiniteField> MulAssign<FE> for Polynomial<FE>

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fn mul_assign(&mut self, rhs: FE)

Performs the *= operation. Read more

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impl<FE: FiniteField> PartialEq<Polynomial<FE>> for Polynomial<FE>

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

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

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

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason. Read more

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impl<'a, FE: FiniteField> SubAssign<&'a Polynomial<FE>> for Polynomial<FE>

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fn sub_assign(&mut self, rhs: &'a Polynomial<FE>)

Performs the -= operation. Read more

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impl<FE: Eq + FiniteField> Eq for Polynomial<FE>

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impl<FE: FiniteField> StructuralEq for Polynomial<FE>

Auto Trait Implementations

impl<FE> RefUnwindSafe for Polynomial<FE>where
FE: RefUnwindSafe,

impl<FE> Send for Polynomial<FE>

impl<FE> Sync for Polynomial<FE>

impl<FE> Unpin for Polynomial<FE>where
FE: Unpin,

impl<FE> UnwindSafe for Polynomial<FE>where
FE: UnwindSafe + RefUnwindSafe,

Blanket Implementations

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impl<T> Any for Twhere
T: 'static + ?Sized,

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fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more

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impl<T> Borrow<T> for Twhere
T: ?Sized,

const: unstable · source

fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more

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impl<T> BorrowMut<T> for Twhere
T: ?Sized,

const: unstable · source

fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more

impl<T> Conv for T

fn conv<T>(self) -> Twhere
Self: Into<T>,

Converts self into T using Into<T>. Read more

impl<T> FmtForward for T

fn fmt_binary(self) -> FmtBinary<Self>where
Self: Binary,

Causes self to use its Binary implementation when Debug-formatted.

fn fmt_display(self) -> FmtDisplay<Self>where
Self: Display,

Causes self to use its Display implementation when Debug-formatted. Read more

fn fmt_lower_exp(self) -> FmtLowerExp<Self>where
Self: LowerExp,

Causes self to use its LowerExp implementation when Debug-formatted. Read more

fn fmt_lower_hex(self) -> FmtLowerHex<Self>where
Self: LowerHex,

Causes self to use its LowerHex implementation when Debug-formatted. Read more

fn fmt_octal(self) -> FmtOctal<Self>where
Self: Octal,

Causes self to use its Octal implementation when Debug-formatted.

fn fmt_pointer(self) -> FmtPointer<Self>where
Self: Pointer,

Causes self to use its Pointer implementation when Debug-formatted. Read more

fn fmt_upper_exp(self) -> FmtUpperExp<Self>where
Self: UpperExp,

Causes self to use its UpperExp implementation when Debug-formatted. Read more

fn fmt_upper_hex(self) -> FmtUpperHex<Self>where
Self: UpperHex,

Causes self to use its UpperHex implementation when Debug-formatted. Read more

fn fmt_list(self) -> FmtList<Self>where
&'a Self: for<'a> IntoIterator,

Formats each item in a sequence. Read more

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impl<T> From<T> for T

const: unstable · source

fn from(t: T) -> T

Returns the argument unchanged.

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impl<T, U> Into for Twhere
U: From<T>,

const: unstable · source

fn into(self) -> U

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

impl<T> Pipe for Twhere
T: ?Sized,

fn pipe<R>(self, func: impl FnOnce(Self) -> R) -> R

Pipes by value. This is generally the method you want to use. Read more

fn pipe_ref<'a, R>(&'a self, func: impl FnOnce(&'a Self) -> R) -> Rwhere
R: 'a,

Borrows self and passes that borrow into the pipe function. Read more

fn pipe_ref_mut<'a, R>(&'a mut self, func: impl FnOnce(&'a mut Self) -> R) -> Rwhere
R: 'a,

Mutably borrows self and passes that borrow into the pipe function. Read more

fn pipe_borrow<'a, B, R>(&'a self, func: impl FnOnce(&'a B) -> R) -> Rwhere
 Self: Borrow,
 B: 'a + ?Sized,
 R: 'a,

Borrows self, then passes self.borrow() into the pipe function. Read more

fn pipe_borrow_mut<'a, B, R>(
 &'a mut self,
 func: impl FnOnce(&'a mut B) -> R
) -> Rwhere
 Self: BorrowMut,
 B: 'a + ?Sized,
 R: 'a,

Mutably borrows self, then passes self.borrow_mut() into the pipe function. Read more

fn pipe_as_ref<'a, U, R>(&'a self, func: impl FnOnce(&'a U) -> R) -> Rwhere
 Self: AsRef,
 U: 'a + ?Sized,
 R: 'a,

Borrows self, then passes self.as_ref() into the pipe function.

fn pipe_as_mut<'a, U, R>(&'a mut self, func: impl FnOnce(&'a mut U) -> R) -> Rwhere
 Self: AsMut,
 U: 'a + ?Sized,
 R: 'a,

Mutably borrows self, then passes self.as_mut() into the pipe function. Read more

fn pipe_deref<'a, T, R>(&'a self, func: impl FnOnce(&'a T) -> R) -> Rwhere
 Self: Deref<Target = T>,
 T: 'a + ?Sized,
 R: 'a,

Borrows self, then passes self.deref() into the pipe function.

fn pipe_deref_mut<'a, T, R>(&'a mut self, func: impl FnOnce(&'a mut T) -> R) -> Rwhere
 Self: DerefMut<Target = T> + Deref,
 T: 'a + ?Sized,
 R: 'a,

Mutably borrows self, then passes self.deref_mut() into the pipe function. Read more

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impl<T> Same<T> for T

type Output = T

Should always be Self

impl<T> Tap for T

fn tap(self, func: impl FnOnce(&Self)) -> Self

Immutable access to a value. Read more

fn tap_mut(self, func: impl FnOnce(&mut Self)) -> Self

Mutable access to a value. Read more

fn tap_borrow(self, func: impl FnOnce(&B)) -> Selfwhere
Self: Borrow,
B: ?Sized,

Immutable access to the Borrow of a value. Read more

fn tap_borrow_mut(self, func: impl FnOnce(&mut B)) -> Selfwhere
Self: BorrowMut,
B: ?Sized,

Mutable access to the BorrowMut of a value. Read more

fn tap_ref<R>(self, func: impl FnOnce(&R)) -> Selfwhere
Self: AsRef<R>,
R: ?Sized,

Immutable access to the AsRef<R> view of a value. Read more

fn tap_ref_mut<R>(self, func: impl FnOnce(&mut R)) -> Selfwhere
Self: AsMut<R>,
R: ?Sized,

Mutable access to the AsMut<R> view of a value. Read more

fn tap_deref<T>(self, func: impl FnOnce(&T)) -> Selfwhere
Self: Deref<Target = T>,
T: ?Sized,

Immutable access to the Deref::Target of a value. Read more

fn tap_deref_mut<T>(self, func: impl FnOnce(&mut T)) -> Selfwhere
Self: DerefMut<Target = T> + Deref,
T: ?Sized,

Mutable access to the Deref::Target of a value. Read more

fn tap_dbg(self, func: impl FnOnce(&Self)) -> Self

Calls .tap() only in debug builds, and is erased in release builds.

fn tap_mut_dbg(self, func: impl FnOnce(&mut Self)) -> Self

Calls .tap_mut() only in debug builds, and is erased in release builds. Read more

fn tap_borrow_dbg(self, func: impl FnOnce(&B)) -> Selfwhere
Self: Borrow,
B: ?Sized,

Calls .tap_borrow() only in debug builds, and is erased in release builds. Read more

fn tap_borrow_mut_dbg(self, func: impl FnOnce(&mut B)) -> Selfwhere
Self: BorrowMut,
B: ?Sized,

Calls .tap_borrow_mut() only in debug builds, and is erased in release builds. Read more

fn tap_ref_dbg<R>(self, func: impl FnOnce(&R)) -> Selfwhere
Self: AsRef<R>,
R: ?Sized,

Calls .tap_ref() only in debug builds, and is erased in release builds. Read more

fn tap_ref_mut_dbg<R>(self, func: impl FnOnce(&mut R)) -> Selfwhere
Self: AsMut<R>,
R: ?Sized,

Calls .tap_ref_mut() only in debug builds, and is erased in release builds. Read more

fn tap_deref_dbg<T>(self, func: impl FnOnce(&T)) -> Selfwhere
Self: Deref<Target = T>,
T: ?Sized,

Calls .tap_deref() only in debug builds, and is erased in release builds. Read more

fn tap_deref_mut_dbg<T>(self, func: impl FnOnce(&mut T)) -> Selfwhere
Self: DerefMut<Target = T> + Deref,
T: ?Sized,

Calls .tap_deref_mut() only in debug builds, and is erased in release builds. Read more

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impl<T> ToOwned for Twhere
T: Clone,

type Owned = T

The resulting type after obtaining ownership.

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fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more

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fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more

impl<T> TryConv for T

fn try_conv<T>(self) -> Result<T, Self::Error>where
Self: TryInto<T>,

Attempts to convert self into T using TryInto<T>. Read more

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impl<T, U> TryFrom for Twhere
U: Into<T>,

type Error = Infallible

The type returned in the event of a conversion error.

const: unstable · source

fn try_from(value: U) -> Result<T, <T as TryFrom>::Error>

Performs the conversion.

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impl<T, U> TryInto for Twhere
U: TryFrom<T>,

type Error = >::Error

The type returned in the event of a conversion error.

const: unstable · source

fn try_into(self) -> Result<U, >::Error>

Performs the conversion.

Struct scuttlebutt::field::polynomial::Polynomial

Fields

Implementations

impl<FE: FiniteField> Polynomial<FE>

pub fn random(rng: &mut impl RngCore + ?Sized, degree: usize) -> Self

pub fn zero() -> Self

pub fn one() -> Self

pub fn constant(c: FE) -> Self

pub fn x() -> Self

pub fn degree(&self) -> usize

pub fn eval(&self, at: FE) -> FE

pub fn divmod(&self, divisor: &Self) -> (Self, Self)

pub fn interpolate(points: &[(FE, FE)]) -> Self

Trait Implementations

impl<'a, FE: FiniteField> AddAssign<&'a Polynomial<FE>> for Polynomial<FE>

fn add_assign(&mut self, rhs: &'a Polynomial<FE>)

impl<FE: Clone + FiniteField> Clone for Polynomial<FE>

fn clone(&self) -> Polynomial<FE>

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

impl<FE: FiniteField> ConstantTimeEq for Polynomial<FE>

fn ct_eq(&self, other: &Self) -> Choice

impl<FE: FiniteField> Debug for Polynomial<FE>

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

impl<FE: FiniteField> From<&[FE]> for Polynomial<FE>

fn from(v: &[FE]) -> Self

impl<FE: FiniteField> Index<usize> for Polynomial<FE>

type Output = FE

fn index(&self, index: usize) -> &Self::Output

impl<FE: FiniteField> IndexMut<usize> for Polynomial<FE>

fn index_mut(&mut self, index: usize) -> &mut Self::Output

impl<'a, FE: FiniteField> MulAssign<&'a Polynomial<FE>> for Polynomial<FE>

fn mul_assign(&mut self, rhs: &'a Polynomial<FE>)

impl<FE: FiniteField> MulAssign<FE> for Polynomial<FE>

fn mul_assign(&mut self, rhs: FE)

impl<FE: FiniteField> PartialEq<Polynomial<FE>> for Polynomial<FE>

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

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

impl<'a, FE: FiniteField> SubAssign<&'a Polynomial<FE>> for Polynomial<FE>

fn sub_assign(&mut self, rhs: &'a Polynomial<FE>)

impl<FE: Eq + FiniteField> Eq for Polynomial<FE>

impl<FE: FiniteField> StructuralEq for Polynomial<FE>

Auto Trait Implementations

impl<FE> RefUnwindSafe for Polynomial<FE>where FE: RefUnwindSafe,

impl<FE> Send for Polynomial<FE>

impl<FE> Sync for Polynomial<FE>

impl<FE> Unpin for Polynomial<FE>where FE: Unpin,

impl<FE> UnwindSafe for Polynomial<FE>where FE: UnwindSafe + RefUnwindSafe,

Blanket Implementations

impl<T> Any for Twhere T: 'static + ?Sized,

fn type_id(&self) -> TypeId

impl<T> Borrow<T> for Twhere T: ?Sized,

fn borrow(&self) -> &T

impl<T> BorrowMut<T> for Twhere T: ?Sized,

fn borrow_mut(&mut self) -> &mut T

impl<T> Conv for T

fn conv<T>(self) -> Twhere Self: Into<T>,

impl<T> FmtForward for T

fn fmt_binary(self) -> FmtBinary<Self>where Self: Binary,

fn fmt_display(self) -> FmtDisplay<Self>where Self: Display,

fn fmt_lower_exp(self) -> FmtLowerExp<Self>where Self: LowerExp,

fn fmt_lower_hex(self) -> FmtLowerHex<Self>where Self: LowerHex,

fn fmt_octal(self) -> FmtOctal<Self>where Self: Octal,

fn fmt_pointer(self) -> FmtPointer<Self>where Self: Pointer,

fn fmt_upper_exp(self) -> FmtUpperExp<Self>where Self: UpperExp,

fn fmt_upper_hex(self) -> FmtUpperHex<Self>where Self: UpperHex,

fn fmt_list(self) -> FmtList<Self>where &'a Self: for<'a> IntoIterator,

impl<T> From<T> for T

fn from(t: T) -> T

impl<T, U> Into<U> for Twhere U: From<T>,

fn into(self) -> U

impl<T> Pipe for Twhere T: ?Sized,

fn pipe<R>(self, func: impl FnOnce(Self) -> R) -> R

fn pipe_ref<'a, R>(&'a self, func: impl FnOnce(&'a Self) -> R) -> Rwhere R: 'a,

fn pipe_ref_mut<'a, R>(&'a mut self, func: impl FnOnce(&'a mut Self) -> R) -> Rwhere R: 'a,

fn pipe_borrow<'a, B, R>(&'a self, func: impl FnOnce(&'a B) -> R) -> Rwhere Self: Borrow<B>, B: 'a + ?Sized, R: 'a,

fn pipe_borrow_mut<'a, B, R>( &'a mut self, func: impl FnOnce(&'a mut B) -> R) -> Rwhere Self: BorrowMut<B>, B: 'a + ?Sized, R: 'a,

fn pipe_as_ref<'a, U, R>(&'a self, func: impl FnOnce(&'a U) -> R) -> Rwhere Self: AsRef<U>, U: 'a + ?Sized, R: 'a,

fn pipe_as_mut<'a, U, R>(&'a mut self, func: impl FnOnce(&'a mut U) -> R) -> Rwhere Self: AsMut<U>, U: 'a + ?Sized, R: 'a,

fn pipe_deref<'a, T, R>(&'a self, func: impl FnOnce(&'a T) -> R) -> Rwhere Self: Deref<Target = T>, T: 'a + ?Sized, R: 'a,

fn pipe_deref_mut<'a, T, R>(&'a mut self, func: impl FnOnce(&'a mut T) -> R) -> Rwhere Self: DerefMut<Target = T> + Deref, T: 'a + ?Sized, R: 'a,

impl<FE> RefUnwindSafe for Polynomial<FE>where
FE: RefUnwindSafe,

impl<FE> Unpin for Polynomial<FE>where
FE: Unpin,

impl<FE> UnwindSafe for Polynomial<FE>where
FE: UnwindSafe + RefUnwindSafe,

impl<T> Any for Twhere
T: 'static + ?Sized,

impl<T> Borrow<T> for Twhere
T: ?Sized,

impl<T> BorrowMut<T> for Twhere
T: ?Sized,

fn conv<T>(self) -> Twhere
Self: Into<T>,

fn fmt_binary(self) -> FmtBinary<Self>where
Self: Binary,

fn fmt_display(self) -> FmtDisplay<Self>where
Self: Display,

fn fmt_lower_exp(self) -> FmtLowerExp<Self>where
Self: LowerExp,

fn fmt_lower_hex(self) -> FmtLowerHex<Self>where
Self: LowerHex,

fn fmt_octal(self) -> FmtOctal<Self>where
Self: Octal,

fn fmt_pointer(self) -> FmtPointer<Self>where
Self: Pointer,

fn fmt_upper_exp(self) -> FmtUpperExp<Self>where
Self: UpperExp,

fn fmt_upper_hex(self) -> FmtUpperHex<Self>where
Self: UpperHex,

fn fmt_list(self) -> FmtList<Self>where
&'a Self: for<'a> IntoIterator,

impl<T, U> Into<U> for Twhere
U: From<T>,

impl<T> Pipe for Twhere
T: ?Sized,

fn pipe_ref<'a, R>(&'a self, func: impl FnOnce(&'a Self) -> R) -> Rwhere
R: 'a,

fn pipe_ref_mut<'a, R>(&'a mut self, func: impl FnOnce(&'a mut Self) -> R) -> Rwhere
R: 'a,

fn pipe_borrow<'a, B, R>(&'a self, func: impl FnOnce(&'a B) -> R) -> Rwhere
Self: Borrow<B>,
B: 'a + ?Sized,
R: 'a,

fn pipe_borrow_mut<'a, B, R>(
&'a mut self,
func: impl FnOnce(&'a mut B) -> R
) -> Rwhere
Self: BorrowMut<B>,
B: 'a + ?Sized,
R: 'a,

fn pipe_as_ref<'a, U, R>(&'a self, func: impl FnOnce(&'a U) -> R) -> Rwhere
Self: AsRef<U>,
U: 'a + ?Sized,
R: 'a,

fn pipe_as_mut<'a, U, R>(&'a mut self, func: impl FnOnce(&'a mut U) -> R) -> Rwhere
Self: AsMut<U>,
U: 'a + ?Sized,
R: 'a,

fn pipe_deref<'a, T, R>(&'a self, func: impl FnOnce(&'a T) -> R) -> Rwhere
Self: Deref<Target = T>,
T: 'a + ?Sized,
R: 'a,

fn pipe_deref_mut<'a, T, R>(&'a mut self, func: impl FnOnce(&'a mut T) -> R) -> Rwhere
Self: DerefMut<Target = T> + Deref,
T: 'a + ?Sized,
R: 'a,

fn tap_borrow<B>(self, func: impl FnOnce(&B)) -> Selfwhere
Self: Borrow<B>,
B: ?Sized,

fn tap_borrow_mut<B>(self, func: impl FnOnce(&mut B)) -> Selfwhere
Self: BorrowMut<B>,
B: ?Sized,

fn tap_ref<R>(self, func: impl FnOnce(&R)) -> Selfwhere
Self: AsRef<R>,
R: ?Sized,

fn tap_ref_mut<R>(self, func: impl FnOnce(&mut R)) -> Selfwhere
Self: AsMut<R>,
R: ?Sized,

fn tap_deref<T>(self, func: impl FnOnce(&T)) -> Selfwhere
Self: Deref<Target = T>,
T: ?Sized,

fn tap_deref_mut<T>(self, func: impl FnOnce(&mut T)) -> Selfwhere
Self: DerefMut<Target = T> + Deref,
T: ?Sized,

fn tap_borrow_dbg<B>(self, func: impl FnOnce(&B)) -> Selfwhere
Self: Borrow<B>,
B: ?Sized,

fn tap_borrow_mut_dbg<B>(self, func: impl FnOnce(&mut B)) -> Selfwhere
Self: BorrowMut<B>,
B: ?Sized,

fn tap_ref_dbg<R>(self, func: impl FnOnce(&R)) -> Selfwhere
Self: AsRef<R>,
R: ?Sized,

fn tap_ref_mut_dbg<R>(self, func: impl FnOnce(&mut R)) -> Selfwhere
Self: AsMut<R>,
R: ?Sized,

fn tap_deref_dbg<T>(self, func: impl FnOnce(&T)) -> Selfwhere
Self: Deref<Target = T>,
T: ?Sized,

fn tap_deref_mut_dbg<T>(self, func: impl FnOnce(&mut T)) -> Selfwhere
Self: DerefMut<Target = T> + Deref,
T: ?Sized,

impl<T> ToOwned for Twhere
T: Clone,

fn try_conv<T>(self) -> Result<T, Self::Error>where
Self: TryInto<T>,

impl<T, U> TryFrom<U> for Twhere
U: Into<T>,

impl<T, U> TryInto<U> for Twhere
U: TryFrom<T>,

impl<V, T> VZip<V> for Twhere
V: MultiLane<T>,