halo2curves_axiom::bls12_381

Struct Fr

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pub struct Fr(/* private fields */);
Expand description

Represents an element of the scalar field $\mathbb{F}_q$ of the BLS12-381 elliptic curve construction.

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impl Scalar

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pub const fn zero() -> Scalar

Returns zero, the additive identity.

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pub const fn one() -> Scalar

Returns one, the multiplicative identity.

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pub const fn double(&self) -> Scalar

Doubles this field element.

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pub fn from_bytes(bytes: &[u8; 32]) -> CtOption<Scalar>

Attempts to convert a little-endian byte representation of a scalar into a Scalar, failing if the input is not canonical.

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pub fn to_bytes(&self) -> [u8; 32]

Converts an element of Scalar into a byte representation in little-endian byte order.

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pub fn from_bytes_wide(bytes: &[u8; 64]) -> Scalar

Converts a 512-bit little endian integer into a Scalar by reducing by the modulus.

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pub const fn from_raw(val: [u64; 4]) -> Self

Converts from an integer represented in little endian into its (congruent) Scalar representation.

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pub const fn square(&self) -> Scalar

Squares this element.

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pub fn pow(&self, by: &[u64; 4]) -> Self

Exponentiates self by by, where by is a little-endian order integer exponent.

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pub fn pow_vartime(&self, by: &[u64; 4]) -> Self

Exponentiates self by by, where by is a little-endian order integer exponent.

This operation is variable time with respect to the exponent. If the exponent is fixed, this operation is effectively constant time.

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pub fn invert(&self) -> CtOption<Self>

Computes the multiplicative inverse of this element, failing if the element is zero.

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

Multiplies rhs by self, returning the result.

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pub const fn sub(&self, rhs: &Self) -> Self

Subtracts rhs from self, returning the result.

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pub const fn add(&self, rhs: &Self) -> Self

Adds rhs to self, returning the result.

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pub const fn neg(&self) -> Self

Negates self.

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impl<'a, 'b> Add<&'b Scalar> for &'a Scalar

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type Output = Scalar

The resulting type after applying the + operator.
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fn add(self, rhs: &'b Scalar) -> Scalar

Performs the + operation. Read more
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impl<'b> Add<&'b Scalar> for Scalar

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type Output = Scalar

The resulting type after applying the + operator.
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fn add(self, rhs: &'b Scalar) -> Scalar

Performs the + operation. Read more
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impl<'a> Add<Scalar> for &'a Scalar

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type Output = Scalar

The resulting type after applying the + operator.
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fn add(self, rhs: Scalar) -> Scalar

Performs the + operation. Read more
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impl Add for Scalar

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type Output = Scalar

The resulting type after applying the + operator.
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fn add(self, rhs: Scalar) -> Scalar

Performs the + operation. Read more
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impl<'b> AddAssign<&'b Scalar> for Scalar

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fn add_assign(&mut self, rhs: &'b Scalar)

Performs the += operation. Read more
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impl AddAssign for Scalar

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fn add_assign(&mut self, rhs: Scalar)

Performs the += operation. Read more
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impl Clone for Scalar

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fn clone(&self) -> Scalar

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 ConditionallySelectable for Scalar

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fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self

Select a or b according to choice. Read more
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fn conditional_assign(&mut self, other: &Self, choice: Choice)

Conditionally assign other to self, according to choice. Read more
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fn conditional_swap(a: &mut Self, b: &mut Self, choice: Choice)

Conditionally swap self and other if choice == 1; otherwise, reassign both unto themselves. Read more
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impl ConstantTimeEq for Scalar

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

Determine if two items are equal. Read more
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fn ct_ne(&self, other: &Self) -> Choice

Determine if two items are NOT equal. Read more
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impl Debug for Scalar

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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 Default for Scalar

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fn default() -> Self

Returns the “default value” for a type. Read more
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impl Display for Scalar

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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 Field for Scalar

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const ZERO: Self = _

The zero element of the field, the additive identity.
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const ONE: Self = _

The one element of the field, the multiplicative identity.
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fn random(rng: impl RngCore) -> Self

Returns an element chosen uniformly at random using a user-provided RNG.
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fn square(&self) -> Self

Squares this element.
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fn double(&self) -> Self

Doubles this element.
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fn invert(&self) -> CtOption<Self>

Computes the multiplicative inverse of this element, failing if the element is zero.
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fn sqrt_ratio(num: &Self, div: &Self) -> (Choice, Self)

Computes: Read more
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fn sqrt(&self) -> CtOption<Self>

Returns the square root of the field element, if it is quadratic residue. Read more
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fn is_zero_vartime(&self) -> bool

Returns true iff this element is zero. Read more
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fn is_zero(&self) -> Choice

Returns true iff this element is zero.
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fn cube(&self) -> Self

Cubes this element.
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fn sqrt_alt(&self) -> (Choice, Self)

Equivalent to Self::sqrt_ratio(self, one()). Read more
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fn pow<S>(&self, exp: S) -> Self
where S: AsRef<[u64]>,

Exponentiates self by exp, where exp is a little-endian order integer exponent. Read more
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fn pow_vartime<S>(&self, exp: S) -> Self
where S: AsRef<[u64]>,

Exponentiates self by exp, where exp is a little-endian order integer exponent. Read more
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impl<'a> From<&'a Scalar> for [u8; 32]

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fn from(value: &'a Scalar) -> [u8; 32]

Converts to this type from the input type.
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impl From<[u64; 4]> for Scalar

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fn from(digits: [u64; 4]) -> Self

Converts to this type from the input type.
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impl From<Scalar> for [u8; 32]

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fn from(value: Scalar) -> [u8; 32]

Converts to this type from the input type.
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impl From<bool> for Scalar

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fn from(bit: bool) -> Scalar

Converts to this type from the input type.
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impl From<u64> for Scalar

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fn from(val: u64) -> Scalar

Converts to this type from the input type.
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impl FromUniformBytes<64> for Scalar

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fn from_uniform_bytes(bytes: &[u8; 64]) -> Self

Converts a 512-bit little endian integer into an Fq by reducing by the modulus.

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impl Hash for Scalar

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

Feeds this value into the given Hasher. Read more
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fn hash_slice<H>(data: &[Self], state: &mut H)
where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher. Read more
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impl HashToField for Scalar

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type InputLength = UInt<UInt<UInt<UInt<UInt<UInt<UTerm, B1>, B1>, B0>, B0>, B0>, B0>

The length of the data used to produce an individual field element. Read more
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fn from_okm(okm: &GenericArray<u8, U48>) -> Scalar

Interprets the given output keying material as a big endian integer, and reduces it into a field element.
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fn hash_to_field<X: ExpandMessage>( message: &[u8], dst: &[u8], output: &mut [Self], )

Hashes a byte string of arbitrary length into one or more elements of Self, using ExpandMessage variant X. Read more
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impl<'a, 'b> Mul<&'b G1Affine> for &'a Scalar

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type Output = G1Projective

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b G1Affine) -> Self::Output

Performs the * operation. Read more
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impl<'b> Mul<&'b G1Affine> for Scalar

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type Output = G1Projective

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b G1Affine) -> G1Projective

Performs the * operation. Read more
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impl<'a, 'b> Mul<&'b G1Projective> for &'a Scalar

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type Output = G1Projective

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b G1Projective) -> Self::Output

Performs the * operation. Read more
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impl<'b> Mul<&'b G1Projective> for Scalar

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type Output = G1Projective

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b G1Projective) -> G1Projective

Performs the * operation. Read more
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impl<'a, 'b> Mul<&'b G2Affine> for &'a Scalar

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type Output = G2Projective

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b G2Affine) -> Self::Output

Performs the * operation. Read more
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impl<'b> Mul<&'b G2Affine> for Scalar

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type Output = G2Projective

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b G2Affine) -> G2Projective

Performs the * operation. Read more
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impl<'a, 'b> Mul<&'b G2Projective> for &'a Scalar

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type Output = G2Projective

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b G2Projective) -> Self::Output

Performs the * operation. Read more
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impl<'b> Mul<&'b G2Projective> for Scalar

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type Output = G2Projective

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b G2Projective) -> G2Projective

Performs the * operation. Read more
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impl<'a, 'b> Mul<&'b Scalar> for &'a G1Affine

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type Output = G1Projective

The resulting type after applying the * operator.
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fn mul(self, other: &'b Scalar) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b> Mul<&'b Scalar> for &'a G1Projective

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type Output = G1Projective

The resulting type after applying the * operator.
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fn mul(self, other: &'b Scalar) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b> Mul<&'b Scalar> for &'a G2Affine

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type Output = G2Projective

The resulting type after applying the * operator.
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fn mul(self, other: &'b Scalar) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b> Mul<&'b Scalar> for &'a G2Projective

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type Output = G2Projective

The resulting type after applying the * operator.
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fn mul(self, other: &'b Scalar) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b> Mul<&'b Scalar> for &'a Gt

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type Output = Gt

The resulting type after applying the * operator.
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fn mul(self, other: &'b Scalar) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b> Mul<&'b Scalar> for &'a Scalar

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type Output = Scalar

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Scalar) -> Scalar

Performs the * operation. Read more
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impl<'b> Mul<&'b Scalar> for G1Affine

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type Output = G1Projective

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Scalar) -> G1Projective

Performs the * operation. Read more
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impl<'b> Mul<&'b Scalar> for G1Projective

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type Output = G1Projective

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Scalar) -> G1Projective

Performs the * operation. Read more
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impl<'b> Mul<&'b Scalar> for G2Affine

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type Output = G2Projective

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Scalar) -> G2Projective

Performs the * operation. Read more
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impl<'b> Mul<&'b Scalar> for G2Projective

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type Output = G2Projective

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Scalar) -> G2Projective

Performs the * operation. Read more
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impl<'b> Mul<&'b Scalar> for Gt

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type Output = Gt

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Scalar) -> Gt

Performs the * operation. Read more
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impl<'b> Mul<&'b Scalar> for Scalar

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type Output = Scalar

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Scalar) -> Scalar

Performs the * operation. Read more
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impl<'a> Mul<G1Affine> for &'a Scalar

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type Output = G1Projective

The resulting type after applying the * operator.
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fn mul(self, rhs: G1Affine) -> G1Projective

Performs the * operation. Read more
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impl Mul<G1Affine> for Scalar

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type Output = G1Projective

The resulting type after applying the * operator.
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fn mul(self, rhs: G1Affine) -> G1Projective

Performs the * operation. Read more
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impl<'a> Mul<G1Projective> for &'a Scalar

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type Output = G1Projective

The resulting type after applying the * operator.
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fn mul(self, rhs: G1Projective) -> G1Projective

Performs the * operation. Read more
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impl Mul<G1Projective> for Scalar

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type Output = G1Projective

The resulting type after applying the * operator.
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fn mul(self, rhs: G1Projective) -> G1Projective

Performs the * operation. Read more
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impl<'a> Mul<G2Affine> for &'a Scalar

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type Output = G2Projective

The resulting type after applying the * operator.
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fn mul(self, rhs: G2Affine) -> G2Projective

Performs the * operation. Read more
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impl Mul<G2Affine> for Scalar

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type Output = G2Projective

The resulting type after applying the * operator.
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fn mul(self, rhs: G2Affine) -> G2Projective

Performs the * operation. Read more
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impl<'a> Mul<G2Projective> for &'a Scalar

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type Output = G2Projective

The resulting type after applying the * operator.
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fn mul(self, rhs: G2Projective) -> G2Projective

Performs the * operation. Read more
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impl Mul<G2Projective> for Scalar

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type Output = G2Projective

The resulting type after applying the * operator.
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fn mul(self, rhs: G2Projective) -> G2Projective

Performs the * operation. Read more
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impl<'a> Mul<Scalar> for &'a G1Affine

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type Output = G1Projective

The resulting type after applying the * operator.
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fn mul(self, rhs: Scalar) -> G1Projective

Performs the * operation. Read more
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impl<'a> Mul<Scalar> for &'a G1Projective

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type Output = G1Projective

The resulting type after applying the * operator.
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fn mul(self, rhs: Scalar) -> G1Projective

Performs the * operation. Read more
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impl<'a> Mul<Scalar> for &'a G2Affine

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type Output = G2Projective

The resulting type after applying the * operator.
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fn mul(self, rhs: Scalar) -> G2Projective

Performs the * operation. Read more
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impl<'a> Mul<Scalar> for &'a G2Projective

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type Output = G2Projective

The resulting type after applying the * operator.
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fn mul(self, rhs: Scalar) -> G2Projective

Performs the * operation. Read more
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impl<'a> Mul<Scalar> for &'a Gt

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type Output = Gt

The resulting type after applying the * operator.
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fn mul(self, rhs: Scalar) -> Gt

Performs the * operation. Read more
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impl<'a> Mul<Scalar> for &'a Scalar

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type Output = Scalar

The resulting type after applying the * operator.
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fn mul(self, rhs: Scalar) -> Scalar

Performs the * operation. Read more
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impl Mul<Scalar> for G1Affine

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type Output = G1Projective

The resulting type after applying the * operator.
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fn mul(self, rhs: Scalar) -> G1Projective

Performs the * operation. Read more
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impl Mul<Scalar> for G1Projective

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type Output = G1Projective

The resulting type after applying the * operator.
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fn mul(self, rhs: Scalar) -> G1Projective

Performs the * operation. Read more
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impl Mul<Scalar> for G2Affine

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type Output = G2Projective

The resulting type after applying the * operator.
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fn mul(self, rhs: Scalar) -> G2Projective

Performs the * operation. Read more
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impl Mul<Scalar> for G2Projective

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type Output = G2Projective

The resulting type after applying the * operator.
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fn mul(self, rhs: Scalar) -> G2Projective

Performs the * operation. Read more
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impl Mul<Scalar> for Gt

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type Output = Gt

The resulting type after applying the * operator.
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fn mul(self, rhs: Scalar) -> Gt

Performs the * operation. Read more
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impl Mul for Scalar

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type Output = Scalar

The resulting type after applying the * operator.
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fn mul(self, rhs: Scalar) -> Scalar

Performs the * operation. Read more
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impl<'b> MulAssign<&'b Scalar> for G1Projective

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fn mul_assign(&mut self, rhs: &'b Scalar)

Performs the *= operation. Read more
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impl<'b> MulAssign<&'b Scalar> for G2Projective

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fn mul_assign(&mut self, rhs: &'b Scalar)

Performs the *= operation. Read more
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impl<'b> MulAssign<&'b Scalar> for Gt

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fn mul_assign(&mut self, rhs: &'b Scalar)

Performs the *= operation. Read more
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impl<'b> MulAssign<&'b Scalar> for Scalar

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fn mul_assign(&mut self, rhs: &'b Scalar)

Performs the *= operation. Read more
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impl MulAssign<Scalar> for G1Projective

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fn mul_assign(&mut self, rhs: Scalar)

Performs the *= operation. Read more
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impl MulAssign<Scalar> for G2Projective

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fn mul_assign(&mut self, rhs: Scalar)

Performs the *= operation. Read more
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impl MulAssign<Scalar> for Gt

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fn mul_assign(&mut self, rhs: Scalar)

Performs the *= operation. Read more
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impl MulAssign for Scalar

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fn mul_assign(&mut self, rhs: Scalar)

Performs the *= operation. Read more
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impl<'a> Neg for &'a Scalar

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type Output = Scalar

The resulting type after applying the - operator.
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fn neg(self) -> Scalar

Performs the unary - operation. Read more
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impl Neg for Scalar

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type Output = Scalar

The resulting type after applying the - operator.
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fn neg(self) -> Scalar

Performs the unary - operation. Read more
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impl Ord for Scalar

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

This method returns an Ordering between self and other. Read more
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fn max(self, other: Self) -> Self
where Self: Sized,

Compares and returns the maximum of two values. Read more
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fn min(self, other: Self) -> Self
where Self: Sized,

Compares and returns the minimum of two values. Read more
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fn clamp(self, min: Self, max: Self) -> Self
where Self: Sized,

Restrict a value to a certain interval. Read more
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impl PartialEq for Scalar

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

Tests for self and other values to be equal, and is used by ==.
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fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.
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impl PartialOrd for Scalar

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

This method returns an ordering between self and other values if one exists. Read more
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fn lt(&self, other: &Rhs) -> bool

Tests less than (for self and other) and is used by the < operator. Read more
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fn le(&self, other: &Rhs) -> bool

Tests less than or equal to (for self and other) and is used by the <= operator. Read more
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fn gt(&self, other: &Rhs) -> bool

Tests greater than (for self and other) and is used by the > operator. Read more
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fn ge(&self, other: &Rhs) -> bool

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

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const MODULUS: &'static str = "0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001"

Modulus of the field written as a string for debugging purposes. Read more
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const NUM_BITS: u32 = 255u32

How many bits are needed to represent an element of this field.
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const CAPACITY: u32 = 254u32

How many bits of information can be reliably stored in the field element. Read more
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const TWO_INV: Self = TWO_INV

Inverse of $2$ in the field.
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const MULTIPLICATIVE_GENERATOR: Self = GENERATOR

A fixed multiplicative generator of modulus - 1 order. This element must also be a quadratic nonresidue. Read more
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const S: u32 = 32u32

An integer s satisfying the equation 2^s * t = modulus - 1 with t odd. Read more
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const ROOT_OF_UNITY: Self = ROOT_OF_UNITY

The 2^s root of unity. Read more
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const ROOT_OF_UNITY_INV: Self = ROOT_OF_UNITY_INV

Inverse of Self::ROOT_OF_UNITY.
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const DELTA: Self = DELTA

Generator of the t-order multiplicative subgroup. Read more
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type Repr = [u8; 32]

The prime field can be converted back and forth into this binary representation.
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fn from_repr(r: Self::Repr) -> CtOption<Self>

Attempts to convert a byte representation of a field element into an element of this prime field, failing if the input is not canonical (is not smaller than the field’s modulus). Read more
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fn to_repr(&self) -> Self::Repr

Converts an element of the prime field into the standard byte representation for this field. Read more
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fn is_odd(&self) -> Choice

Returns true iff this element is odd.
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fn from_str_vartime(s: &str) -> Option<Self>

Interpret a string of numbers as a (congruent) prime field element. Does not accept unnecessary leading zeroes or a blank string. Read more
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fn from_u128(v: u128) -> Self

Obtains a field element congruent to the integer v. Read more
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fn from_repr_vartime(repr: Self::Repr) -> Option<Self>

Attempts to convert a byte representation of a field element into an element of this prime field, failing if the input is not canonical (is not smaller than the field’s modulus). Read more
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fn is_even(&self) -> Choice

Returns true iff this element is even.
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impl PrimeFieldBits for Scalar

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type ReprBits = [u64; 4]

The backing store for a bit representation of a prime field element.
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fn to_le_bits(&self) -> FieldBits<Self::ReprBits>

Converts an element of the prime field into a little-endian sequence of bits.
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fn char_le_bits() -> FieldBits<Self::ReprBits>

Returns the bits of the field characteristic (the modulus) in little-endian order.
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impl<T> Product<T> for Scalar
where T: Borrow<Scalar>,

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fn product<I>(iter: I) -> Self
where I: Iterator<Item = T>,

Takes an iterator and generates Self from the elements by multiplying the items.
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impl<'a, 'b> Sub<&'b Scalar> for &'a Scalar

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type Output = Scalar

The resulting type after applying the - operator.
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fn sub(self, rhs: &'b Scalar) -> Scalar

Performs the - operation. Read more
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impl<'b> Sub<&'b Scalar> for Scalar

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type Output = Scalar

The resulting type after applying the - operator.
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fn sub(self, rhs: &'b Scalar) -> Scalar

Performs the - operation. Read more
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impl<'a> Sub<Scalar> for &'a Scalar

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type Output = Scalar

The resulting type after applying the - operator.
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fn sub(self, rhs: Scalar) -> Scalar

Performs the - operation. Read more
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impl Sub for Scalar

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type Output = Scalar

The resulting type after applying the - operator.
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fn sub(self, rhs: Scalar) -> Scalar

Performs the - operation. Read more
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impl<'b> SubAssign<&'b Scalar> for Scalar

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fn sub_assign(&mut self, rhs: &'b Scalar)

Performs the -= operation. Read more
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impl SubAssign for Scalar

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fn sub_assign(&mut self, rhs: Scalar)

Performs the -= operation. Read more
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impl<T> Sum<T> for Scalar
where T: Borrow<Scalar>,

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fn sum<I>(iter: I) -> Self
where I: Iterator<Item = T>,

Takes an iterator and generates Self from the elements by “summing up” the items.
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impl WithSmallOrderMulGroup<3> for Scalar

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const ZETA: Self = ZETA

A field element of small multiplicative order $N$. Read more
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impl Copy for Scalar

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impl Eq for Scalar

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impl StructuralPartialEq for Scalar

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impl Freeze for Scalar

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impl RefUnwindSafe for Scalar

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impl Send for Scalar

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impl Sync for Scalar

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impl Unpin for Scalar

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impl UnwindSafe for Scalar

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impl<T> Any for T
where 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 T
where T: ?Sized,

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fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
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impl<T> BorrowMut<T> for T
where T: ?Sized,

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

Mutably borrows from an owned value. Read more
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impl<T> CloneToUninit for T
where T: Clone,

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unsafe fn clone_to_uninit(&self, dst: *mut T)

🔬This is a nightly-only experimental API. (clone_to_uninit)
Performs copy-assignment from self to dst. Read more
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impl<T> ConditionallyNegatable for T
where T: ConditionallySelectable, &'a T: for<'a> Neg<Output = T>,

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fn conditional_negate(&mut self, choice: Choice)

Negate self if choice == Choice(1); otherwise, leave it unchanged. Read more
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impl<T> Conv for T

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

Converts self into T using Into<T>. Read more
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impl<T> FmtForward for T

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

Causes self to use its Binary implementation when Debug-formatted.
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fn fmt_display(self) -> FmtDisplay<Self>
where Self: Display,

Causes self to use its Display implementation when Debug-formatted.
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fn fmt_lower_exp(self) -> FmtLowerExp<Self>
where Self: LowerExp,

Causes self to use its LowerExp implementation when Debug-formatted.
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fn fmt_lower_hex(self) -> FmtLowerHex<Self>
where Self: LowerHex,

Causes self to use its LowerHex implementation when Debug-formatted.
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fn fmt_octal(self) -> FmtOctal<Self>
where Self: Octal,

Causes self to use its Octal implementation when Debug-formatted.
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fn fmt_pointer(self) -> FmtPointer<Self>
where Self: Pointer,

Causes self to use its Pointer implementation when Debug-formatted.
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fn fmt_upper_exp(self) -> FmtUpperExp<Self>
where Self: UpperExp,

Causes self to use its UpperExp implementation when Debug-formatted.
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fn fmt_upper_hex(self) -> FmtUpperHex<Self>
where Self: UpperHex,

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

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fn from(t: T) -> T

Returns the argument unchanged.

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

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fn into(self) -> U

Calls U::from(self).

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

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impl<T> IntoEither for T

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fn into_either(self, into_left: bool) -> Either<Self, Self>

Converts self into a Left variant of Either<Self, Self> if into_left is true. Converts self into a Right variant of Either<Self, Self> otherwise. Read more
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fn into_either_with<F>(self, into_left: F) -> Either<Self, Self>
where F: FnOnce(&Self) -> bool,

Converts self into a Left variant of Either<Self, Self> if into_left(&self) returns true. Converts self into a Right variant of Either<Self, Self> otherwise. Read more
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impl<T> Pipe for T
where T: ?Sized,

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

Pipes by value. This is generally the method you want to use. Read more
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fn pipe_ref<'a, R>(&'a self, func: impl FnOnce(&'a Self) -> R) -> R
where R: 'a,

Borrows self and passes that borrow into the pipe function. Read more
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fn pipe_ref_mut<'a, R>(&'a mut self, func: impl FnOnce(&'a mut Self) -> R) -> R
where R: 'a,

Mutably borrows self and passes that borrow into the pipe function. Read more
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fn pipe_borrow<'a, B, R>(&'a self, func: impl FnOnce(&'a B) -> R) -> R
where Self: Borrow<B>, B: 'a + ?Sized, R: 'a,

Borrows self, then passes self.borrow() into the pipe function. Read more
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fn pipe_borrow_mut<'a, B, R>( &'a mut self, func: impl FnOnce(&'a mut B) -> R, ) -> R
where Self: BorrowMut<B>, B: 'a + ?Sized, R: 'a,

Mutably borrows self, then passes self.borrow_mut() into the pipe function. Read more
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fn pipe_as_ref<'a, U, R>(&'a self, func: impl FnOnce(&'a U) -> R) -> R
where Self: AsRef<U>, U: 'a + ?Sized, R: 'a,

Borrows self, then passes self.as_ref() into the pipe function.
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fn pipe_as_mut<'a, U, R>(&'a mut self, func: impl FnOnce(&'a mut U) -> R) -> R
where Self: AsMut<U>, U: 'a + ?Sized, R: 'a,

Mutably borrows self, then passes self.as_mut() into the pipe function.
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fn pipe_deref<'a, T, R>(&'a self, func: impl FnOnce(&'a T) -> R) -> R
where Self: Deref<Target = T>, T: 'a + ?Sized, R: 'a,

Borrows self, then passes self.deref() into the pipe function.
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fn pipe_deref_mut<'a, T, R>( &'a mut self, func: impl FnOnce(&'a mut T) -> R, ) -> R
where Self: DerefMut<Target = T> + Deref, T: 'a + ?Sized, R: 'a,

Mutably borrows self, then passes self.deref_mut() into the pipe function.
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impl<T> Pointable for T

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const ALIGN: usize = _

The alignment of pointer.
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type Init = T

The type for initializers.
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unsafe fn init(init: <T as Pointable>::Init) -> usize

Initializes a with the given initializer. Read more
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unsafe fn deref<'a>(ptr: usize) -> &'a T

Dereferences the given pointer. Read more
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unsafe fn deref_mut<'a>(ptr: usize) -> &'a mut T

Mutably dereferences the given pointer. Read more
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unsafe fn drop(ptr: usize)

Drops the object pointed to by the given pointer. Read more
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impl<T> Same for T

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type Output = T

Should always be Self
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impl<T> Tap for T

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

Immutable access to a value. Read more
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fn tap_mut(self, func: impl FnOnce(&mut Self)) -> Self

Mutable access to a value. Read more
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fn tap_borrow<B>(self, func: impl FnOnce(&B)) -> Self
where Self: Borrow<B>, B: ?Sized,

Immutable access to the Borrow<B> of a value. Read more
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fn tap_borrow_mut<B>(self, func: impl FnOnce(&mut B)) -> Self
where Self: BorrowMut<B>, B: ?Sized,

Mutable access to the BorrowMut<B> of a value. Read more
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fn tap_ref<R>(self, func: impl FnOnce(&R)) -> Self
where Self: AsRef<R>, R: ?Sized,

Immutable access to the AsRef<R> view of a value. Read more
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fn tap_ref_mut<R>(self, func: impl FnOnce(&mut R)) -> Self
where Self: AsMut<R>, R: ?Sized,

Mutable access to the AsMut<R> view of a value. Read more
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fn tap_deref<T>(self, func: impl FnOnce(&T)) -> Self
where Self: Deref<Target = T>, T: ?Sized,

Immutable access to the Deref::Target of a value. Read more
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fn tap_deref_mut<T>(self, func: impl FnOnce(&mut T)) -> Self
where Self: DerefMut<Target = T> + Deref, T: ?Sized,

Mutable access to the Deref::Target of a value. Read more
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fn tap_dbg(self, func: impl FnOnce(&Self)) -> Self

Calls .tap() only in debug builds, and is erased in release builds.
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fn tap_mut_dbg(self, func: impl FnOnce(&mut Self)) -> Self

Calls .tap_mut() only in debug builds, and is erased in release builds.
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fn tap_borrow_dbg<B>(self, func: impl FnOnce(&B)) -> Self
where Self: Borrow<B>, B: ?Sized,

Calls .tap_borrow() only in debug builds, and is erased in release builds.
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fn tap_borrow_mut_dbg<B>(self, func: impl FnOnce(&mut B)) -> Self
where Self: BorrowMut<B>, B: ?Sized,

Calls .tap_borrow_mut() only in debug builds, and is erased in release builds.
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fn tap_ref_dbg<R>(self, func: impl FnOnce(&R)) -> Self
where Self: AsRef<R>, R: ?Sized,

Calls .tap_ref() only in debug builds, and is erased in release builds.
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fn tap_ref_mut_dbg<R>(self, func: impl FnOnce(&mut R)) -> Self
where Self: AsMut<R>, R: ?Sized,

Calls .tap_ref_mut() only in debug builds, and is erased in release builds.
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fn tap_deref_dbg<T>(self, func: impl FnOnce(&T)) -> Self
where Self: Deref<Target = T>, T: ?Sized,

Calls .tap_deref() only in debug builds, and is erased in release builds.
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fn tap_deref_mut_dbg<T>(self, func: impl FnOnce(&mut T)) -> Self
where Self: DerefMut<Target = T> + Deref, T: ?Sized,

Calls .tap_deref_mut() only in debug builds, and is erased in release builds.
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impl<T> ToOwned for T
where T: Clone,

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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
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impl<T> ToString for T
where T: Display + ?Sized,

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default fn to_string(&self) -> String

Converts the given value to a String. Read more
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impl<T> TryConv for T

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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<U> for T
where U: Into<T>,

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type Error = Infallible

The type returned in the event of a conversion error.
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fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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impl<T, U> TryInto<U> for T
where U: TryFrom<T>,

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type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.
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fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.
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impl<V, T> VZip<V> for T
where V: MultiLane<T>,

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fn vzip(self) -> V

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impl<T, Scalar> FftGroup<Scalar> for T
where Scalar: Field, T: Copy + Send + Sync + 'static + GroupOpsOwned + ScalarMulOwned<Scalar>,

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impl<T, Rhs, Output> GroupOps<Rhs, Output> for T
where T: Add<Rhs, Output = Output> + Sub<Rhs, Output = Output> + AddAssign<Rhs> + SubAssign<Rhs>,

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impl<T, Rhs, Output> GroupOpsOwned<Rhs, Output> for T
where T: for<'r> GroupOps<&'r Rhs, Output>,

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impl<T, Rhs, Output> ScalarMul<Rhs, Output> for T
where T: Mul<Rhs, Output = Output> + MulAssign<Rhs>,

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impl<T, Rhs, Output> ScalarMulOwned<Rhs, Output> for T
where T: for<'r> ScalarMul<&'r Rhs, Output>,