Struct Polynomial 

pub struct Polynomial { /* private fields */ }

A polynomial over GF(256) with at most 255 coefficients.

Coefficients are stored from degree 0 upward in a fixed stack-allocated array, so the type is Copy and never allocates.

Implementations

impl Polynomial

pub const MAX_DEGREE: u8 = POLYNOMIAL_MAX_DEGREE_U8

Maximum degree of a polynomial over GF(256).

pub const MAX_COEFFICIENTS: u8 = POLYNOMIAL_MAX_COEFFICIENTS_U8

Maximum number of coefficients in a polynomial.

impl Polynomial

pub fn coefficients(&self) -> &[u8]

Returns the coefficients of this polynomial, from degree 0 to the leading term.

Panics

Panics if the stored degree is 255, which exceeds Polynomial::MAX_DEGREE and cannot occur for a valid polynomial.

impl Polynomial

pub const fn degree(&self) -> u8

Returns the degree of this polynomial.

The zero polynomial has degree 0 by this definition.

impl Polynomial

pub fn div_rem( &self, divisor: impl AsRef<[u8]>, ) -> Result<(Self, Self), PolynomialDivError>

Divides this polynomial by a divisor, returning (quotient, remainder).

The divisor is interpreted as coefficients in ascending degree order. Trailing zeros are ignored when determining the divisor’s degree.

Errors

Returns ZeroDivisor if the divisor is the zero polynomial.

impl Polynomial

pub fn div_rem_inplace( &mut self, divisor: &Self, quotient: &mut Self, ) -> Result<(), PolynomialDivError>

In-place polynomial division: self becomes the remainder, quotient is output.

After this method, self contains the remainder and quotient contains the quotient of dividing the original self by divisor.

Errors

Returns PolynomialDivError::ZeroDivisor if the divisor is the zero polynomial. Returns PolynomialDivError::GFError if field inversion fails.

impl Polynomial

pub fn eval_at(&self, x: u8) -> u8

Evaluates this polynomial at the given point.

impl Polynomial

pub fn eval_coefficient_iter_at<I>(coefficients: I, x: u8) -> u8

where I: DoubleEndedIterator<Item = u8>,

Evaluates a polynomial from an iterator of coefficients at the given point.

Coefficients are yielded from degree 0 (constant term) to the leading term. Requires DoubleEndedIterator for Horner’s method.

impl Polynomial

pub fn eval_coefficient_slices_at(slices: &[&[u8]], x: u8) -> u8

Evaluates a polynomial from multiple coefficient slices at the given point.

Slices are concatenated in order, with the first slice containing the lowest degree terms.

impl Polynomial

pub fn eval_coefficients_at(coefficients: &[u8], x: u8) -> u8

Evaluates a polynomial given its coefficients at the given point using Horner’s method.

Coefficients are ordered from degree 0 (constant term) to the leading term.

impl Polynomial

pub fn eval_coefficients_derivative_at(coefficients: &[u8], x: u8) -> u8

Evaluates the formal derivative of a polynomial at the given point.

In characteristic 2, only odd-degree terms contribute to the derivative: p’(x) = a₁ + a₃x² + a₅x⁴ + …

Coefficients are ordered from degree 0 (constant term) to the leading term.

impl Polynomial

pub fn eval_derivative_at(&self, x: u8) -> u8

Evaluates the formal derivative of this polynomial at the given point.

In characteristic 2, only odd-degree terms contribute to the derivative.

impl Polynomial

pub fn first_n_coefficients(&self, n: usize) -> &[u8]

Returns the first n coefficients.

The returned slice has length min(n, 255).

impl Polynomial

pub fn from_slice(coeffs: &[u8]) -> Result<Self, PolynomialFromSliceError>

Creates a polynomial from a slice of coefficients.

Coefficients are ordered from degree 0 (constant term) to the leading term.

Errors

Returns PolynomialFromSliceError::TooLong if the slice exceeds 255 elements.

impl Polynomial

pub const fn is_zero(&self) -> bool

Returns true if this is the zero polynomial.

A polynomial is zero if all its coefficients are zero. Due to internal normalization, this is equivalent to having degree 0 and a zero constant term.

impl Polynomial

pub fn iter(&self) -> Iter<'_, u8>

Returns an iterator over the coefficients, from degree 0 to the leading term.

impl Polynomial

pub fn mul_xor_assign( &mut self, a: &Self, b: &Self, ) -> Result<(), PolynomialMulError>

Fused multiply-XOR: self ^= a * b

Computes the product of polynomials a and b, XORing the result into self. This avoids allocating an intermediate polynomial for the product.

In GF(2^8), XOR is equivalent to both addition and subtraction, so this computes self = self + a * b or equivalently self = self - a * b.

Errors

Returns PolynomialMulError::DegreeOverflow if the product degree, a.degree() + b.degree(), exceeds Polynomial::MAX_DEGREE. self is unmodified on error.

impl Polynomial

pub fn set(&mut self, idx: u8, value: u8)

Sets the coefficient of degree idx to value.

If value is non-zero and idx exceeds the current degree, the degree increases to idx. If value is zero and idx equals the current degree, the degree decreases to the next non-zero coefficient.

Panics

Panics if idx exceeds 254, the maximum degree of a polynomial over GF(256).

impl Polynomial

pub fn set_coefficients( &mut self, offset: u8, values: &[u8], ) -> Result<(), PolynomialSetCoefficientsError>

Sets coefficients starting at degree offset from a slice.

Copies values into the coefficient array at offset..offset + values.len(), then adjusts the degree accordingly.

Empty slices are a no-op.

Errors

Returns OutOfBounds if offset + values.len() exceeds 255.

Trait Implementations

impl<B: Borrow<u8>, I: IntoIterator<Item = B>> Add<I> for Polynomial

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

Adds coefficients from an iterator to this polynomial.

In GF(256), addition is XOR. This delegates to BitXor.

Errors

Returns TooManyCoefficients if the iterator yields more than 255 elements.

type Output = Result<Polynomial, PolynomialXorError>

The resulting type after applying the + operator.

impl<B: Borrow<u8>, I: IntoIterator<Item = B>> Add<I> for &Polynomial

type Output = Result<Polynomial, PolynomialXorError>

The resulting type after applying the + operator.

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

Performs the + operation.

impl AddAssign for Polynomial

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl AddAssign<&Polynomial> for Polynomial

fn add_assign(&mut self, rhs: &Self)

Performs the += operation.

impl AsRef<[u8]> for Polynomial

fn as_ref(&self) -> &[u8]

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

impl<B: Borrow<u8>, I: IntoIterator<Item = B>> BitXor<I> for Polynomial

fn bitxor(self, rhs: I) -> Self::Output

XORs coefficients from an iterator into this polynomial.

Errors

Returns TooManyCoefficients if the iterator yields more than 255 elements.

type Output = Result<Polynomial, PolynomialXorError>

The resulting type after applying the ^ operator.

impl<B: Borrow<u8>, I: IntoIterator<Item = B>> BitXor<I> for &Polynomial

type Output = Result<Polynomial, PolynomialXorError>

The resulting type after applying the ^ operator.

fn bitxor(self, rhs: I) -> Self::Output

Performs the ^ operation.

impl BitXorAssign for Polynomial

fn bitxor_assign(&mut self, rhs: Self)

Performs the ^= operation.

impl BitXorAssign<&Polynomial> for Polynomial

fn bitxor_assign(&mut self, rhs: &Self)

Performs the ^= operation.

impl Clone for Polynomial

fn clone(&self) -> Polynomial

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Copy for Polynomial

impl Debug for Polynomial

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

Formats the value using the given formatter.

impl Default for Polynomial

fn default() -> Self

Returns the “default value” for a type.

impl<D: AsRef<[u8]>> Div<D> for &Polynomial

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

Divides two polynomials over GF(256), returning the quotient.

Errors

Returns ZeroDivisor if the divisor is the zero polynomial.

type Output = Result<Polynomial, PolynomialDivError>

The resulting type after applying the / operator.

impl<D: AsRef<[u8]>> Div<D> for Polynomial

type Output = Result<Polynomial, PolynomialDivError>

The resulting type after applying the / operator.

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

Performs the / operation.

impl Eq for Polynomial

impl FromIterator<u8> for Polynomial

fn from_iter<I: IntoIterator<Item = u8>>(iter: I) -> Self

Collects coefficients from degree 0 (constant term) to the leading term.

Consumes at most 255 elements; excess elements are ignored. Leading zeros are trimmed. Safe for infinite iterators.

impl Hash for Polynomial

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

Feeds this value into the given Hasher.

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

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl Index<u8> for Polynomial

type Output = u8

The returned type after indexing.

fn index(&self, index: u8) -> &Self::Output

Performs the indexing (container[index]) operation.

impl Index<usize> for Polynomial

type Output = u8

The returned type after indexing.

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

Performs the indexing (container[index]) operation.

impl IntoIterator for Polynomial

type Item = u8

The type of the elements being iterated over.

type IntoIter = Take<IntoIter<u8, POLYNOMIAL_MAX_COEFFICIENTS>>

Which kind of iterator are we turning this into?

fn into_iter(self) -> Self::IntoIter

Creates an iterator from a value.

impl<'a> IntoIterator for &'a Polynomial

type Item = &'a u8

The type of the elements being iterated over.

type IntoIter = Iter<'a, u8>

Which kind of iterator are we turning this into?

fn into_iter(self) -> Self::IntoIter

Creates an iterator from a value.

impl Mul for Polynomial

type Output = Result<Polynomial, PolynomialMulError>

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<&Polynomial> for &Polynomial

fn mul(self, rhs: &Polynomial) -> Self::Output

Multiplies two polynomials over GF(256).

Errors

Returns DegreeOverflow if the result degree exceeds 254.

type Output = Result<Polynomial, PolynomialMulError>

The resulting type after applying the * operator.

impl Mul<&Polynomial> for Polynomial

type Output = Result<Polynomial, PolynomialMulError>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<const N: usize> Mul<&[u8; N]> for &Polynomial

type Output = Result<Polynomial, PolynomialMulError>

The resulting type after applying the * operator.

fn mul(self, rhs: &[u8; N]) -> Self::Output

Performs the * operation.

impl<const N: usize> Mul<&[u8; N]> for Polynomial

type Output = Result<Polynomial, PolynomialMulError>

The resulting type after applying the * operator.

fn mul(self, rhs: &[u8; N]) -> Self::Output

Performs the * operation.

impl Mul<&[u8]> for &Polynomial

fn mul(self, rhs: &[u8]) -> Self::Output

Multiplies a polynomial by a coefficient slice over GF(256).

Errors

Returns DegreeOverflow if the result degree exceeds 254.

type Output = Result<Polynomial, PolynomialMulError>

The resulting type after applying the * operator.

impl Mul<&[u8]> for Polynomial

type Output = Result<Polynomial, PolynomialMulError>

The resulting type after applying the * operator.

fn mul(self, rhs: &[u8]) -> Self::Output

Performs the * operation.

impl Mul<Polynomial> for &Polynomial

type Output = Result<Polynomial, PolynomialMulError>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<const N: usize> Mul<[u8; N]> for &Polynomial

type Output = Result<Polynomial, PolynomialMulError>

The resulting type after applying the * operator.

fn mul(self, rhs: [u8; N]) -> Self::Output

Performs the * operation.

impl<const N: usize> Mul<[u8; N]> for Polynomial

type Output = Result<Polynomial, PolynomialMulError>

The resulting type after applying the * operator.

fn mul(self, rhs: [u8; N]) -> Self::Output

Performs the * operation.

impl MulAssign<u8> for Polynomial

fn mul_assign(&mut self, scalar: u8)

Multiplies all coefficients by a scalar in GF(2^8).

If scalar is zero, the result is the zero polynomial. Otherwise, the degree is preserved since GF(2^8) has no zero divisors.

impl Ord for Polynomial

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 PartialEq for Polynomial

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

Equality operator ==.

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

Inequality operator !=.

impl PartialOrd for Polynomial

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<D: AsRef<[u8]>> Rem<D> for &Polynomial

fn rem(self, rhs: D) -> Self::Output

Computes the remainder of polynomial division over GF(256).

Errors

Returns ZeroDivisor if the divisor is the zero polynomial.

type Output = Result<Polynomial, PolynomialDivError>

The resulting type after applying the % operator.

impl<D: AsRef<[u8]>> Rem<D> for Polynomial

type Output = Result<Polynomial, PolynomialDivError>

The resulting type after applying the % operator.

fn rem(self, rhs: D) -> Self::Output

Performs the % operation.

impl<B: Borrow<u8>, I: IntoIterator<Item = B>> Sub<I> for Polynomial

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

Subtracts coefficients from an iterator from this polynomial.

In GF(256), subtraction is equivalent to addition, which is XOR. This delegates to BitXor.

Errors

Returns TooManyCoefficients if the iterator yields more than 255 elements.

type Output = Result<Polynomial, PolynomialXorError>

The resulting type after applying the - operator.

impl<B: Borrow<u8>, I: IntoIterator<Item = B>> Sub<I> for &Polynomial

type Output = Result<Polynomial, PolynomialXorError>

The resulting type after applying the - operator.

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

Performs the - operation.

impl SubAssign for Polynomial

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.

impl SubAssign<&Polynomial> for Polynomial

fn sub_assign(&mut self, rhs: &Self)

Performs the -= operation.

impl<const N: usize> TryFrom<&[u8; N]> for Polynomial

type Error = PolynomialFromSliceError

The type returned in the event of a conversion error.

fn try_from(value: &[u8; N]) -> Result<Self, Self::Error>

Performs the conversion.

impl TryFrom<&[u8]> for Polynomial

type Error = PolynomialFromSliceError

The type returned in the event of a conversion error.

fn try_from(value: &[u8]) -> Result<Self, Self::Error>

Performs the conversion.

impl<const N: usize> TryFrom<[u8; N]> for Polynomial

type Error = PolynomialFromSliceError

The type returned in the event of a conversion error.

fn try_from(value: [u8; N]) -> Result<Self, Self::Error>

Performs the conversion.