Struct ark_test_curves::fields::QuadExtField
source · pub struct QuadExtField<P>where
P: QuadExtConfig,{
pub c0: <P as QuadExtConfig>::BaseField,
pub c1: <P as QuadExtConfig>::BaseField,
}
Expand description
An element of a quadratic extension field F_p[X]/(X^2 - P::NONRESIDUE) is
represented as c0 + c1 * X, for c0, c1 in P::BaseField
.
Fields§
§c0: <P as QuadExtConfig>::BaseField
Coefficient c0
in the representation of the field element c = c0 + c1 * X
c1: <P as QuadExtConfig>::BaseField
Coefficient c1
in the representation of the field element c = c0 + c1 * X
Implementations§
source§impl<P> QuadExtField<Fp2ConfigWrapper<P>>where
P: Fp2Config,
impl<P> QuadExtField<Fp2ConfigWrapper<P>>where P: Fp2Config,
sourcepub fn mul_assign_by_fp(&mut self, other: &<P as Fp2Config>::Fp)
pub fn mul_assign_by_fp(&mut self, other: &<P as Fp2Config>::Fp)
In-place multiply both coefficients c0
and c1
of self
by an element from Fp
.
Examples
let c0: Fp = Fp::rand(&mut test_rng());
let c1: Fp = Fp::rand(&mut test_rng());
let mut ext_element: Fp2 = Fp2::new(c0, c1);
let base_field_element: Fp = Fp::rand(&mut test_rng());
ext_element.mul_assign_by_fp(&base_field_element);
assert_eq!(ext_element.c0, c0 * base_field_element);
assert_eq!(ext_element.c1, c1 * base_field_element);
source§impl<P> QuadExtField<Fp4ConfigWrapper<P>>where
P: Fp4Config,
impl<P> QuadExtField<Fp4ConfigWrapper<P>>where P: Fp4Config,
pub fn mul_by_fp( &mut self, element: &<<P as Fp4Config>::Fp2Config as Fp2Config>::Fp )
pub fn mul_by_fp2( &mut self, element: &QuadExtField<Fp2ConfigWrapper<<P as Fp4Config>::Fp2Config>> )
source§impl<P> QuadExtField<Fp6ConfigWrapper<P>>where
P: Fp6Config,
impl<P> QuadExtField<Fp6ConfigWrapper<P>>where P: Fp6Config,
pub fn mul_by_034( &mut self, c0: &<<P as Fp6Config>::Fp3Config as Fp3Config>::Fp, c3: &<<P as Fp6Config>::Fp3Config as Fp3Config>::Fp, c4: &<<P as Fp6Config>::Fp3Config as Fp3Config>::Fp )
pub fn mul_by_014( &mut self, c0: &<<P as Fp6Config>::Fp3Config as Fp3Config>::Fp, c1: &<<P as Fp6Config>::Fp3Config as Fp3Config>::Fp, c4: &<<P as Fp6Config>::Fp3Config as Fp3Config>::Fp )
source§impl<P> QuadExtField<Fp12ConfigWrapper<P>>where
P: Fp12Config,
impl<P> QuadExtField<Fp12ConfigWrapper<P>>where P: Fp12Config,
pub fn mul_by_fp( &mut self, element: &<QuadExtField<Fp12ConfigWrapper<P>> as Field>::BasePrimeField )
pub fn mul_by_034( &mut self, c0: &QuadExtField<Fp2ConfigWrapper<<<P as Fp12Config>::Fp6Config as Fp6Config>::Fp2Config>>, c3: &QuadExtField<Fp2ConfigWrapper<<<P as Fp12Config>::Fp6Config as Fp6Config>::Fp2Config>>, c4: &QuadExtField<Fp2ConfigWrapper<<<P as Fp12Config>::Fp6Config as Fp6Config>::Fp2Config>> )
pub fn mul_by_014( &mut self, c0: &QuadExtField<Fp2ConfigWrapper<<<P as Fp12Config>::Fp6Config as Fp6Config>::Fp2Config>>, c1: &QuadExtField<Fp2ConfigWrapper<<<P as Fp12Config>::Fp6Config as Fp6Config>::Fp2Config>>, c4: &QuadExtField<Fp2ConfigWrapper<<<P as Fp12Config>::Fp6Config as Fp6Config>::Fp2Config>> )
source§impl<P> QuadExtField<P>where
P: QuadExtConfig,
impl<P> QuadExtField<P>where P: QuadExtConfig,
sourcepub const fn new(
c0: <P as QuadExtConfig>::BaseField,
c1: <P as QuadExtConfig>::BaseField
) -> QuadExtField<P>
pub const fn new( c0: <P as QuadExtConfig>::BaseField, c1: <P as QuadExtConfig>::BaseField ) -> QuadExtField<P>
Create a new field element from coefficients c0
and c1
,
so that the result is of the form c0 + c1 * X
.
Examples
let c0: Fp = Fp::rand(&mut test_rng());
let c1: Fp = Fp::rand(&mut test_rng());
// `Fp2` a degree-2 extension over `Fp`.
let c: Fp2 = Fp2::new(c0, c1);
sourcepub fn conjugate_in_place(&mut self) -> &mut QuadExtField<P>
pub fn conjugate_in_place(&mut self) -> &mut QuadExtField<P>
This is only to be used when the element is known to be in the cyclotomic subgroup.
sourcepub fn norm(&self) -> <P as QuadExtConfig>::BaseField
pub fn norm(&self) -> <P as QuadExtConfig>::BaseField
Norm of QuadExtField over P::BaseField
:Norm(a) = a * a.conjugate()
.
This simplifies to: Norm(a) = a.x^2 - P::NON_RESIDUE * a.y^2
.
This is alternatively expressed as Norm(a) = a^(1 + p)
.
Examples
let c: Fp2 = Fp2::rand(&mut test_rng());
let norm = c.norm();
// We now compute the norm using the `a * a.conjugate()` approach.
// A Frobenius map sends an element of `Fp2` to one of its p_th powers:
// `a.frobenius_map_in_place(1) -> a^p` and `a^p` is also `a`'s Galois conjugate.
let mut c_conjugate = c;
c_conjugate.frobenius_map_in_place(1);
let norm2 = c * c_conjugate;
// Computing the norm of an `Fp2` element should result in an element
// in BaseField `Fp`, i.e. `c1 == 0`
assert!(norm2.c1.is_zero());
assert_eq!(norm, norm2.c0);
sourcepub fn mul_assign_by_basefield(
&mut self,
element: &<P as QuadExtConfig>::BaseField
)
pub fn mul_assign_by_basefield( &mut self, element: &<P as QuadExtConfig>::BaseField )
In-place multiply both coefficients c0
& c1
of the quadratic
extension field by an element from the base field.
Trait Implementations§
source§impl<'a, 'b, P> Add<&'a QuadExtField<P>> for &'b QuadExtField<P>where
P: QuadExtConfig,
impl<'a, 'b, P> Add<&'a QuadExtField<P>> for &'b QuadExtField<P>where P: QuadExtConfig,
§type Output = QuadExtField<P>
type Output = QuadExtField<P>
+
operator.source§fn add(self, other: &'a QuadExtField<P>) -> QuadExtField<P>
fn add(self, other: &'a QuadExtField<P>) -> QuadExtField<P>
+
operation. Read moresource§impl<'a, P> Add<&'a QuadExtField<P>> for QuadExtField<P>where
P: QuadExtConfig,
impl<'a, P> Add<&'a QuadExtField<P>> for QuadExtField<P>where P: QuadExtConfig,
§type Output = QuadExtField<P>
type Output = QuadExtField<P>
+
operator.source§fn add(self, other: &QuadExtField<P>) -> QuadExtField<P>
fn add(self, other: &QuadExtField<P>) -> QuadExtField<P>
+
operation. Read moresource§impl<'a, 'b, P> Add<&'a mut QuadExtField<P>> for &'b QuadExtField<P>where
P: QuadExtConfig,
impl<'a, 'b, P> Add<&'a mut QuadExtField<P>> for &'b QuadExtField<P>where P: QuadExtConfig,
§type Output = QuadExtField<P>
type Output = QuadExtField<P>
+
operator.source§fn add(self, other: &'a mut QuadExtField<P>) -> QuadExtField<P>
fn add(self, other: &'a mut QuadExtField<P>) -> QuadExtField<P>
+
operation. Read moresource§impl<'a, P> Add<&'a mut QuadExtField<P>> for QuadExtField<P>where
P: QuadExtConfig,
impl<'a, P> Add<&'a mut QuadExtField<P>> for QuadExtField<P>where P: QuadExtConfig,
§type Output = QuadExtField<P>
type Output = QuadExtField<P>
+
operator.source§fn add(self, other: &'a mut QuadExtField<P>) -> QuadExtField<P>
fn add(self, other: &'a mut QuadExtField<P>) -> QuadExtField<P>
+
operation. Read moresource§impl<'b, P> Add<QuadExtField<P>> for &'b QuadExtField<P>where
P: QuadExtConfig,
impl<'b, P> Add<QuadExtField<P>> for &'b QuadExtField<P>where P: QuadExtConfig,
§type Output = QuadExtField<P>
type Output = QuadExtField<P>
+
operator.source§fn add(self, other: QuadExtField<P>) -> QuadExtField<P>
fn add(self, other: QuadExtField<P>) -> QuadExtField<P>
+
operation. Read moresource§impl<P> Add<QuadExtField<P>> for QuadExtField<P>where
P: QuadExtConfig,
impl<P> Add<QuadExtField<P>> for QuadExtField<P>where P: QuadExtConfig,
§type Output = QuadExtField<P>
type Output = QuadExtField<P>
+
operator.source§fn add(self, other: QuadExtField<P>) -> QuadExtField<P>
fn add(self, other: QuadExtField<P>) -> QuadExtField<P>
+
operation. Read moresource§impl<'a, P> AddAssign<&'a QuadExtField<P>> for QuadExtField<P>where
P: QuadExtConfig,
impl<'a, P> AddAssign<&'a QuadExtField<P>> for QuadExtField<P>where P: QuadExtConfig,
source§fn add_assign(&mut self, other: &QuadExtField<P>)
fn add_assign(&mut self, other: &QuadExtField<P>)
+=
operation. Read moresource§impl<'a, P> AddAssign<&'a mut QuadExtField<P>> for QuadExtField<P>where
P: QuadExtConfig,
impl<'a, P> AddAssign<&'a mut QuadExtField<P>> for QuadExtField<P>where P: QuadExtConfig,
source§fn add_assign(&mut self, other: &'a mut QuadExtField<P>)
fn add_assign(&mut self, other: &'a mut QuadExtField<P>)
+=
operation. Read moresource§impl<P> AddAssign<QuadExtField<P>> for QuadExtField<P>where
P: QuadExtConfig,
impl<P> AddAssign<QuadExtField<P>> for QuadExtField<P>where P: QuadExtConfig,
source§fn add_assign(&mut self, other: QuadExtField<P>)
fn add_assign(&mut self, other: QuadExtField<P>)
+=
operation. Read moresource§impl<P> CanonicalDeserialize for QuadExtField<P>where
P: QuadExtConfig,
impl<P> CanonicalDeserialize for QuadExtField<P>where P: QuadExtConfig,
source§fn deserialize_with_mode<R>(
reader: R,
compress: Compress,
validate: Validate
) -> Result<QuadExtField<P>, SerializationError>where
R: Read,
fn deserialize_with_mode<R>( reader: R, compress: Compress, validate: Validate ) -> Result<QuadExtField<P>, SerializationError>where R: Read,
fn deserialize_compressed<R>(reader: R) -> Result<Self, SerializationError>where R: Read,
fn deserialize_compressed_unchecked<R>( reader: R ) -> Result<Self, SerializationError>where R: Read,
fn deserialize_uncompressed<R>(reader: R) -> Result<Self, SerializationError>where R: Read,
fn deserialize_uncompressed_unchecked<R>( reader: R ) -> Result<Self, SerializationError>where R: Read,
source§impl<P> CanonicalDeserializeWithFlags for QuadExtField<P>where
P: QuadExtConfig,
impl<P> CanonicalDeserializeWithFlags for QuadExtField<P>where P: QuadExtConfig,
source§fn deserialize_with_flags<R, F>(
reader: R
) -> Result<(QuadExtField<P>, F), SerializationError>where
R: Read,
F: Flags,
fn deserialize_with_flags<R, F>( reader: R ) -> Result<(QuadExtField<P>, F), SerializationError>where R: Read, F: Flags,
Self
and Flags
from reader
.
Returns empty flags by default.source§impl<P> CanonicalSerialize for QuadExtField<P>where
P: QuadExtConfig,
impl<P> CanonicalSerialize for QuadExtField<P>where P: QuadExtConfig,
source§fn serialize_with_mode<W>(
&self,
writer: W,
_compress: Compress
) -> Result<(), SerializationError>where
W: Write,
fn serialize_with_mode<W>( &self, writer: W, _compress: Compress ) -> Result<(), SerializationError>where W: Write,
fn serialized_size(&self, _compress: Compress) -> usize
fn serialize_compressed<W>(&self, writer: W) -> Result<(), SerializationError>where W: Write,
fn compressed_size(&self) -> usize
fn serialize_uncompressed<W>(&self, writer: W) -> Result<(), SerializationError>where W: Write,
fn uncompressed_size(&self) -> usize
source§impl<P> CanonicalSerializeWithFlags for QuadExtField<P>where
P: QuadExtConfig,
impl<P> CanonicalSerializeWithFlags for QuadExtField<P>where P: QuadExtConfig,
source§fn serialize_with_flags<W, F>(
&self,
writer: W,
flags: F
) -> Result<(), SerializationError>where
W: Write,
F: Flags,
fn serialize_with_flags<W, F>( &self, writer: W, flags: F ) -> Result<(), SerializationError>where W: Write, F: Flags,
self
and flags
into writer
.source§fn serialized_size_with_flags<F>(&self) -> usizewhere
F: Flags,
fn serialized_size_with_flags<F>(&self) -> usizewhere F: Flags,
self
and flags
into writer
.source§impl<P> Clone for QuadExtField<P>where
P: QuadExtConfig,
impl<P> Clone for QuadExtField<P>where P: QuadExtConfig,
source§fn clone(&self) -> QuadExtField<P>
fn clone(&self) -> QuadExtField<P>
1.0.0 · source§fn clone_from(&mut self, source: &Self)
fn clone_from(&mut self, source: &Self)
source
. Read moresource§impl<P> CyclotomicMultSubgroup for QuadExtField<Fp12ConfigWrapper<P>>where
P: Fp12Config,
impl<P> CyclotomicMultSubgroup for QuadExtField<Fp12ConfigWrapper<P>>where P: Fp12Config,
source§const INVERSE_IS_FAST: bool = true
const INVERSE_IS_FAST: bool = true
false
, but should be set to true
for quadratic extensions.source§fn cyclotomic_inverse_in_place(
&mut self
) -> Option<&mut QuadExtField<Fp12ConfigWrapper<P>>>
fn cyclotomic_inverse_in_place( &mut self ) -> Option<&mut QuadExtField<Fp12ConfigWrapper<P>>>
self
. See Self::INVERSE_IS_FAST
for details.
Returns None
if self.is_zero()
, and Some
otherwise. Read moresource§fn cyclotomic_square_in_place(
&mut self
) -> &mut QuadExtField<Fp12ConfigWrapper<P>>
fn cyclotomic_square_in_place( &mut self ) -> &mut QuadExtField<Fp12ConfigWrapper<P>>
self
in place. By default this is computed using
Field::square_in_place
, but for degree 12 extensions,
this can be computed faster than normal squaring. Read moresource§fn cyclotomic_square(&self) -> Self
fn cyclotomic_square(&self) -> Self
Field::square
, but for
degree 12 extensions, this can be computed faster than normal squaring. Read moresource§fn cyclotomic_inverse(&self) -> Option<Self>
fn cyclotomic_inverse(&self) -> Option<Self>
self
. See Self::INVERSE_IS_FAST
for details.
Returns None
if self.is_zero()
, and Some
otherwise. Read moresource§fn cyclotomic_exp(&self, e: impl AsRef<[u64]>) -> Self
fn cyclotomic_exp(&self, e: impl AsRef<[u64]>) -> Self
source§impl<P> CyclotomicMultSubgroup for QuadExtField<Fp2ConfigWrapper<P>>where
P: Fp2Config,
impl<P> CyclotomicMultSubgroup for QuadExtField<Fp2ConfigWrapper<P>>where P: Fp2Config,
source§const INVERSE_IS_FAST: bool = true
const INVERSE_IS_FAST: bool = true
false
, but should be set to true
for quadratic extensions.source§fn cyclotomic_inverse_in_place(
&mut self
) -> Option<&mut QuadExtField<Fp2ConfigWrapper<P>>>
fn cyclotomic_inverse_in_place( &mut self ) -> Option<&mut QuadExtField<Fp2ConfigWrapper<P>>>
self
. See Self::INVERSE_IS_FAST
for details.
Returns None
if self.is_zero()
, and Some
otherwise. Read moresource§fn cyclotomic_square(&self) -> Self
fn cyclotomic_square(&self) -> Self
Field::square
, but for
degree 12 extensions, this can be computed faster than normal squaring. Read moresource§fn cyclotomic_square_in_place(&mut self) -> &mut Self
fn cyclotomic_square_in_place(&mut self) -> &mut Self
self
in place. By default this is computed using
Field::square_in_place
, but for degree 12 extensions,
this can be computed faster than normal squaring. Read moresource§fn cyclotomic_inverse(&self) -> Option<Self>
fn cyclotomic_inverse(&self) -> Option<Self>
self
. See Self::INVERSE_IS_FAST
for details.
Returns None
if self.is_zero()
, and Some
otherwise. Read moresource§fn cyclotomic_exp(&self, e: impl AsRef<[u64]>) -> Self
fn cyclotomic_exp(&self, e: impl AsRef<[u64]>) -> Self
source§impl<P> CyclotomicMultSubgroup for QuadExtField<Fp4ConfigWrapper<P>>where
P: Fp4Config,
impl<P> CyclotomicMultSubgroup for QuadExtField<Fp4ConfigWrapper<P>>where P: Fp4Config,
source§const INVERSE_IS_FAST: bool = true
const INVERSE_IS_FAST: bool = true
false
, but should be set to true
for quadratic extensions.source§fn cyclotomic_inverse_in_place(
&mut self
) -> Option<&mut QuadExtField<Fp4ConfigWrapper<P>>>
fn cyclotomic_inverse_in_place( &mut self ) -> Option<&mut QuadExtField<Fp4ConfigWrapper<P>>>
self
. See Self::INVERSE_IS_FAST
for details.
Returns None
if self.is_zero()
, and Some
otherwise. Read moresource§fn cyclotomic_square(&self) -> Self
fn cyclotomic_square(&self) -> Self
Field::square
, but for
degree 12 extensions, this can be computed faster than normal squaring. Read moresource§fn cyclotomic_square_in_place(&mut self) -> &mut Self
fn cyclotomic_square_in_place(&mut self) -> &mut Self
self
in place. By default this is computed using
Field::square_in_place
, but for degree 12 extensions,
this can be computed faster than normal squaring. Read moresource§fn cyclotomic_inverse(&self) -> Option<Self>
fn cyclotomic_inverse(&self) -> Option<Self>
self
. See Self::INVERSE_IS_FAST
for details.
Returns None
if self.is_zero()
, and Some
otherwise. Read moresource§fn cyclotomic_exp(&self, e: impl AsRef<[u64]>) -> Self
fn cyclotomic_exp(&self, e: impl AsRef<[u64]>) -> Self
source§impl<P> CyclotomicMultSubgroup for QuadExtField<Fp6ConfigWrapper<P>>where
P: Fp6Config,
impl<P> CyclotomicMultSubgroup for QuadExtField<Fp6ConfigWrapper<P>>where P: Fp6Config,
source§const INVERSE_IS_FAST: bool = true
const INVERSE_IS_FAST: bool = true
false
, but should be set to true
for quadratic extensions.source§fn cyclotomic_inverse_in_place(
&mut self
) -> Option<&mut QuadExtField<Fp6ConfigWrapper<P>>>
fn cyclotomic_inverse_in_place( &mut self ) -> Option<&mut QuadExtField<Fp6ConfigWrapper<P>>>
self
. See Self::INVERSE_IS_FAST
for details.
Returns None
if self.is_zero()
, and Some
otherwise. Read moresource§fn cyclotomic_square(&self) -> Self
fn cyclotomic_square(&self) -> Self
Field::square
, but for
degree 12 extensions, this can be computed faster than normal squaring. Read moresource§fn cyclotomic_square_in_place(&mut self) -> &mut Self
fn cyclotomic_square_in_place(&mut self) -> &mut Self
self
in place. By default this is computed using
Field::square_in_place
, but for degree 12 extensions,
this can be computed faster than normal squaring. Read moresource§fn cyclotomic_inverse(&self) -> Option<Self>
fn cyclotomic_inverse(&self) -> Option<Self>
self
. See Self::INVERSE_IS_FAST
for details.
Returns None
if self.is_zero()
, and Some
otherwise. Read moresource§fn cyclotomic_exp(&self, e: impl AsRef<[u64]>) -> Self
fn cyclotomic_exp(&self, e: impl AsRef<[u64]>) -> Self
source§impl<P> Debug for QuadExtField<P>where
P: QuadExtConfig,
impl<P> Debug for QuadExtField<P>where P: QuadExtConfig,
source§impl<P> Default for QuadExtField<P>where
P: QuadExtConfig,
impl<P> Default for QuadExtField<P>where P: QuadExtConfig,
source§fn default() -> QuadExtField<P>
fn default() -> QuadExtField<P>
source§impl<P> Display for QuadExtField<P>where
P: QuadExtConfig,
impl<P> Display for QuadExtField<P>where P: QuadExtConfig,
source§impl<'a, 'b, P> Div<&'a QuadExtField<P>> for &'b QuadExtField<P>where
P: QuadExtConfig,
impl<'a, 'b, P> Div<&'a QuadExtField<P>> for &'b QuadExtField<P>where P: QuadExtConfig,
§type Output = QuadExtField<P>
type Output = QuadExtField<P>
/
operator.source§fn div(self, other: &'a QuadExtField<P>) -> QuadExtField<P>
fn div(self, other: &'a QuadExtField<P>) -> QuadExtField<P>
/
operation. Read moresource§impl<'a, P> Div<&'a QuadExtField<P>> for QuadExtField<P>where
P: QuadExtConfig,
impl<'a, P> Div<&'a QuadExtField<P>> for QuadExtField<P>where P: QuadExtConfig,
§type Output = QuadExtField<P>
type Output = QuadExtField<P>
/
operator.source§fn div(self, other: &QuadExtField<P>) -> QuadExtField<P>
fn div(self, other: &QuadExtField<P>) -> QuadExtField<P>
/
operation. Read moresource§impl<'a, 'b, P> Div<&'a mut QuadExtField<P>> for &'b QuadExtField<P>where
P: QuadExtConfig,
impl<'a, 'b, P> Div<&'a mut QuadExtField<P>> for &'b QuadExtField<P>where P: QuadExtConfig,
§type Output = QuadExtField<P>
type Output = QuadExtField<P>
/
operator.source§fn div(self, other: &'a mut QuadExtField<P>) -> QuadExtField<P>
fn div(self, other: &'a mut QuadExtField<P>) -> QuadExtField<P>
/
operation. Read moresource§impl<'a, P> Div<&'a mut QuadExtField<P>> for QuadExtField<P>where
P: QuadExtConfig,
impl<'a, P> Div<&'a mut QuadExtField<P>> for QuadExtField<P>where P: QuadExtConfig,
§type Output = QuadExtField<P>
type Output = QuadExtField<P>
/
operator.source§fn div(self, other: &'a mut QuadExtField<P>) -> QuadExtField<P>
fn div(self, other: &'a mut QuadExtField<P>) -> QuadExtField<P>
/
operation. Read moresource§impl<'b, P> Div<QuadExtField<P>> for &'b QuadExtField<P>where
P: QuadExtConfig,
impl<'b, P> Div<QuadExtField<P>> for &'b QuadExtField<P>where P: QuadExtConfig,
§type Output = QuadExtField<P>
type Output = QuadExtField<P>
/
operator.source§fn div(self, other: QuadExtField<P>) -> QuadExtField<P>
fn div(self, other: QuadExtField<P>) -> QuadExtField<P>
/
operation. Read moresource§impl<P> Div<QuadExtField<P>> for QuadExtField<P>where
P: QuadExtConfig,
impl<P> Div<QuadExtField<P>> for QuadExtField<P>where P: QuadExtConfig,
§type Output = QuadExtField<P>
type Output = QuadExtField<P>
/
operator.source§fn div(self, other: QuadExtField<P>) -> QuadExtField<P>
fn div(self, other: QuadExtField<P>) -> QuadExtField<P>
/
operation. Read moresource§impl<'a, P> DivAssign<&'a QuadExtField<P>> for QuadExtField<P>where
P: QuadExtConfig,
impl<'a, P> DivAssign<&'a QuadExtField<P>> for QuadExtField<P>where P: QuadExtConfig,
source§fn div_assign(&mut self, other: &QuadExtField<P>)
fn div_assign(&mut self, other: &QuadExtField<P>)
/=
operation. Read moresource§impl<'a, P> DivAssign<&'a mut QuadExtField<P>> for QuadExtField<P>where
P: QuadExtConfig,
impl<'a, P> DivAssign<&'a mut QuadExtField<P>> for QuadExtField<P>where P: QuadExtConfig,
source§fn div_assign(&mut self, other: &'a mut QuadExtField<P>)
fn div_assign(&mut self, other: &'a mut QuadExtField<P>)
/=
operation. Read moresource§impl<P> DivAssign<QuadExtField<P>> for QuadExtField<P>where
P: QuadExtConfig,
impl<P> DivAssign<QuadExtField<P>> for QuadExtField<P>where P: QuadExtConfig,
source§fn div_assign(&mut self, other: QuadExtField<P>)
fn div_assign(&mut self, other: QuadExtField<P>)
/=
operation. Read moresource§impl<P> Field for QuadExtField<P>where
P: QuadExtConfig,
impl<P> Field for QuadExtField<P>where P: QuadExtConfig,
type BasePrimeField = <P as QuadExtConfig>::BasePrimeField
type BasePrimeFieldIter = Chain<<<P as QuadExtConfig>::BaseField as Field>::BasePrimeFieldIter, <<P as QuadExtConfig>::BaseField as Field>::BasePrimeFieldIter>
source§const SQRT_PRECOMP: Option<SqrtPrecomputation<QuadExtField<P>>> = None
const SQRT_PRECOMP: Option<SqrtPrecomputation<QuadExtField<P>>> = None
source§const ZERO: QuadExtField<P> = Self::new(<P::BaseField>::ZERO, <P::BaseField>::ZERO)
const ZERO: QuadExtField<P> = Self::new(<P::BaseField>::ZERO, <P::BaseField>::ZERO)
source§const ONE: QuadExtField<P> = Self::new(<P::BaseField>::ONE, <P::BaseField>::ZERO)
const ONE: QuadExtField<P> = Self::new(<P::BaseField>::ONE, <P::BaseField>::ZERO)
source§fn extension_degree() -> u64
fn extension_degree() -> u64
Self::BasePrimeField
.source§fn from_base_prime_field(
elem: <QuadExtField<P> as Field>::BasePrimeField
) -> QuadExtField<P>
fn from_base_prime_field( elem: <QuadExtField<P> as Field>::BasePrimeField ) -> QuadExtField<P>
fn to_base_prime_field_elements( &self ) -> <QuadExtField<P> as Field>::BasePrimeFieldIter
source§fn from_base_prime_field_elems(
elems: &[<QuadExtField<P> as Field>::BasePrimeField]
) -> Option<QuadExtField<P>>
fn from_base_prime_field_elems( elems: &[<QuadExtField<P> as Field>::BasePrimeField] ) -> Option<QuadExtField<P>>
source§fn double(&self) -> QuadExtField<P>
fn double(&self) -> QuadExtField<P>
self + self
.source§fn double_in_place(&mut self) -> &mut QuadExtField<P>
fn double_in_place(&mut self) -> &mut QuadExtField<P>
self
in place.source§fn neg_in_place(&mut self) -> &mut QuadExtField<P>
fn neg_in_place(&mut self) -> &mut QuadExtField<P>
self
in place.source§fn square(&self) -> QuadExtField<P>
fn square(&self) -> QuadExtField<P>
self * self
.source§fn from_random_bytes_with_flags<F>(bytes: &[u8]) -> Option<(QuadExtField<P>, F)>where
F: Flags,
fn from_random_bytes_with_flags<F>(bytes: &[u8]) -> Option<(QuadExtField<P>, F)>where F: Flags,
F
specification. Returns None
if the deserialization
fails. Read moresource§fn from_random_bytes(bytes: &[u8]) -> Option<QuadExtField<P>>
fn from_random_bytes(bytes: &[u8]) -> Option<QuadExtField<P>>
None
if the
deserialization fails. Read moresource§fn square_in_place(&mut self) -> &mut QuadExtField<P>
fn square_in_place(&mut self) -> &mut QuadExtField<P>
self
in place.source§fn inverse(&self) -> Option<QuadExtField<P>>
fn inverse(&self) -> Option<QuadExtField<P>>
self
if self
is nonzero.source§fn inverse_in_place(&mut self) -> Option<&mut QuadExtField<P>>
fn inverse_in_place(&mut self) -> Option<&mut QuadExtField<P>>
self.inverse().is_none()
, this just returns None
. Otherwise, it sets
self
to self.inverse().unwrap()
.source§fn frobenius_map_in_place(&mut self, power: usize)
fn frobenius_map_in_place(&mut self, power: usize)
self
to self^s
, where s = Self::BasePrimeField::MODULUS^power
.
This is also called the Frobenius automorphism.source§fn legendre(&self) -> LegendreSymbol
fn legendre(&self) -> LegendreSymbol
LegendreSymbol
, which indicates whether this field element
is 1 : a quadratic residue
0 : equal to 0
-1 : a quadratic non-residuesource§fn sqrt(&self) -> Option<QuadExtField<P>>
fn sqrt(&self) -> Option<QuadExtField<P>>
source§fn sqrt_in_place(&mut self) -> Option<&mut QuadExtField<P>>
fn sqrt_in_place(&mut self) -> Option<&mut QuadExtField<P>>
self
to be the square root of self
, if it exists.source§fn characteristic() -> &'static [u64]
fn characteristic() -> &'static [u64]
source§fn sum_of_products<const T: usize>(a: &[Self; T], b: &[Self; T]) -> Self
fn sum_of_products<const T: usize>(a: &[Self; T], b: &[Self; T]) -> Self
sum([a_i * b_i])
.source§fn frobenius_map(&self, power: usize) -> Self
fn frobenius_map(&self, power: usize) -> Self
self^s
, where s = Self::BasePrimeField::MODULUS^power
.
This is also called the Frobenius automorphism.source§fn pow<S>(&self, exp: S) -> Selfwhere
S: AsRef<[u64]>,
fn pow<S>(&self, exp: S) -> Selfwhere S: AsRef<[u64]>,
self^exp
, where exp
is an integer represented with u64
limbs,
least significant limb first.source§fn pow_with_table<S>(powers_of_2: &[Self], exp: S) -> Option<Self>where
S: AsRef<[u64]>,
fn pow_with_table<S>(powers_of_2: &[Self], exp: S) -> Option<Self>where S: AsRef<[u64]>,
f
by a number represented with u64
limbs, using a precomputed table containing as many powers of 2 of
f
as the 1 + the floor of log2 of the exponent exp
, starting
from the 1st power. That is, powers_of_2
should equal &[p, p^2, p^4, ..., p^(2^n)]
when exp
has at most n
bits. Read moresource§impl<P> From<bool> for QuadExtField<P>where
P: QuadExtConfig,
impl<P> From<bool> for QuadExtField<P>where P: QuadExtConfig,
source§fn from(other: bool) -> QuadExtField<P>
fn from(other: bool) -> QuadExtField<P>
source§impl<P> From<i128> for QuadExtField<P>where
P: QuadExtConfig,
impl<P> From<i128> for QuadExtField<P>where P: QuadExtConfig,
source§fn from(val: i128) -> QuadExtField<P>
fn from(val: i128) -> QuadExtField<P>
source§impl<P> From<i16> for QuadExtField<P>where
P: QuadExtConfig,
impl<P> From<i16> for QuadExtField<P>where P: QuadExtConfig,
source§fn from(val: i16) -> QuadExtField<P>
fn from(val: i16) -> QuadExtField<P>
source§impl<P> From<i32> for QuadExtField<P>where
P: QuadExtConfig,
impl<P> From<i32> for QuadExtField<P>where P: QuadExtConfig,
source§fn from(val: i32) -> QuadExtField<P>
fn from(val: i32) -> QuadExtField<P>
source§impl<P> From<i64> for QuadExtField<P>where
P: QuadExtConfig,
impl<P> From<i64> for QuadExtField<P>where P: QuadExtConfig,
source§fn from(val: i64) -> QuadExtField<P>
fn from(val: i64) -> QuadExtField<P>
source§impl<P> From<i8> for QuadExtField<P>where
P: QuadExtConfig,
impl<P> From<i8> for QuadExtField<P>where P: QuadExtConfig,
source§fn from(val: i8) -> QuadExtField<P>
fn from(val: i8) -> QuadExtField<P>
source§impl<P> From<u128> for QuadExtField<P>where
P: QuadExtConfig,
impl<P> From<u128> for QuadExtField<P>where P: QuadExtConfig,
source§fn from(other: u128) -> QuadExtField<P>
fn from(other: u128) -> QuadExtField<P>
source§impl<P> From<u16> for QuadExtField<P>where
P: QuadExtConfig,
impl<P> From<u16> for QuadExtField<P>where P: QuadExtConfig,
source§fn from(other: u16) -> QuadExtField<P>
fn from(other: u16) -> QuadExtField<P>
source§impl<P> From<u32> for QuadExtField<P>where
P: QuadExtConfig,
impl<P> From<u32> for QuadExtField<P>where P: QuadExtConfig,
source§fn from(other: u32) -> QuadExtField<P>
fn from(other: u32) -> QuadExtField<P>
source§impl<P> From<u64> for QuadExtField<P>where
P: QuadExtConfig,
impl<P> From<u64> for QuadExtField<P>where P: QuadExtConfig,
source§fn from(other: u64) -> QuadExtField<P>
fn from(other: u64) -> QuadExtField<P>
source§impl<P> From<u8> for QuadExtField<P>where
P: QuadExtConfig,
impl<P> From<u8> for QuadExtField<P>where P: QuadExtConfig,
source§fn from(other: u8) -> QuadExtField<P>
fn from(other: u8) -> QuadExtField<P>
source§impl<P> Hash for QuadExtField<P>where
P: QuadExtConfig,
impl<P> Hash for QuadExtField<P>where P: QuadExtConfig,
source§impl<'a, 'b, P> Mul<&'a QuadExtField<P>> for &'b QuadExtField<P>where
P: QuadExtConfig,
impl<'a, 'b, P> Mul<&'a QuadExtField<P>> for &'b QuadExtField<P>where P: QuadExtConfig,
§type Output = QuadExtField<P>
type Output = QuadExtField<P>
*
operator.source§fn mul(self, other: &'a QuadExtField<P>) -> QuadExtField<P>
fn mul(self, other: &'a QuadExtField<P>) -> QuadExtField<P>
*
operation. Read moresource§impl<'a, P> Mul<&'a QuadExtField<P>> for QuadExtField<P>where
P: QuadExtConfig,
impl<'a, P> Mul<&'a QuadExtField<P>> for QuadExtField<P>where P: QuadExtConfig,
§type Output = QuadExtField<P>
type Output = QuadExtField<P>
*
operator.source§fn mul(self, other: &QuadExtField<P>) -> QuadExtField<P>
fn mul(self, other: &QuadExtField<P>) -> QuadExtField<P>
*
operation. Read moresource§impl<'a, 'b, P> Mul<&'a mut QuadExtField<P>> for &'b QuadExtField<P>where
P: QuadExtConfig,
impl<'a, 'b, P> Mul<&'a mut QuadExtField<P>> for &'b QuadExtField<P>where P: QuadExtConfig,
§type Output = QuadExtField<P>
type Output = QuadExtField<P>
*
operator.source§fn mul(self, other: &'a mut QuadExtField<P>) -> QuadExtField<P>
fn mul(self, other: &'a mut QuadExtField<P>) -> QuadExtField<P>
*
operation. Read moresource§impl<'a, P> Mul<&'a mut QuadExtField<P>> for QuadExtField<P>where
P: QuadExtConfig,
impl<'a, P> Mul<&'a mut QuadExtField<P>> for QuadExtField<P>where P: QuadExtConfig,
§type Output = QuadExtField<P>
type Output = QuadExtField<P>
*
operator.source§fn mul(self, other: &'a mut QuadExtField<P>) -> QuadExtField<P>
fn mul(self, other: &'a mut QuadExtField<P>) -> QuadExtField<P>
*
operation. Read moresource§impl<'b, P> Mul<QuadExtField<P>> for &'b QuadExtField<P>where
P: QuadExtConfig,
impl<'b, P> Mul<QuadExtField<P>> for &'b QuadExtField<P>where P: QuadExtConfig,
§type Output = QuadExtField<P>
type Output = QuadExtField<P>
*
operator.source§fn mul(self, other: QuadExtField<P>) -> QuadExtField<P>
fn mul(self, other: QuadExtField<P>) -> QuadExtField<P>
*
operation. Read moresource§impl<P> Mul<QuadExtField<P>> for QuadExtField<P>where
P: QuadExtConfig,
impl<P> Mul<QuadExtField<P>> for QuadExtField<P>where P: QuadExtConfig,
§type Output = QuadExtField<P>
type Output = QuadExtField<P>
*
operator.source§fn mul(self, other: QuadExtField<P>) -> QuadExtField<P>
fn mul(self, other: QuadExtField<P>) -> QuadExtField<P>
*
operation. Read moresource§impl<'a, P> MulAssign<&'a QuadExtField<P>> for QuadExtField<P>where
P: QuadExtConfig,
impl<'a, P> MulAssign<&'a QuadExtField<P>> for QuadExtField<P>where P: QuadExtConfig,
source§fn mul_assign(&mut self, other: &QuadExtField<P>)
fn mul_assign(&mut self, other: &QuadExtField<P>)
*=
operation. Read moresource§impl<'a, P> MulAssign<&'a mut QuadExtField<P>> for QuadExtField<P>where
P: QuadExtConfig,
impl<'a, P> MulAssign<&'a mut QuadExtField<P>> for QuadExtField<P>where P: QuadExtConfig,
source§fn mul_assign(&mut self, other: &'a mut QuadExtField<P>)
fn mul_assign(&mut self, other: &'a mut QuadExtField<P>)
*=
operation. Read moresource§impl<P> MulAssign<QuadExtField<P>> for QuadExtField<P>where
P: QuadExtConfig,
impl<P> MulAssign<QuadExtField<P>> for QuadExtField<P>where P: QuadExtConfig,
source§fn mul_assign(&mut self, other: QuadExtField<P>)
fn mul_assign(&mut self, other: QuadExtField<P>)
*=
operation. Read moresource§impl<P> Neg for QuadExtField<P>where
P: QuadExtConfig,
impl<P> Neg for QuadExtField<P>where P: QuadExtConfig,
§type Output = QuadExtField<P>
type Output = QuadExtField<P>
-
operator.source§fn neg(self) -> QuadExtField<P>
fn neg(self) -> QuadExtField<P>
-
operation. Read moresource§impl<P> One for QuadExtField<P>where
P: QuadExtConfig,
impl<P> One for QuadExtField<P>where P: QuadExtConfig,
source§impl<P> Ord for QuadExtField<P>where
P: QuadExtConfig,
impl<P> Ord for QuadExtField<P>where P: QuadExtConfig,
QuadExtField
elements are ordered lexicographically.
source§fn cmp(&self, other: &QuadExtField<P>) -> Ordering
fn cmp(&self, other: &QuadExtField<P>) -> Ordering
1.21.0 · source§fn max(self, other: Self) -> Selfwhere
Self: Sized,
fn max(self, other: Self) -> Selfwhere Self: Sized,
source§impl<P> PartialEq<QuadExtField<P>> for QuadExtField<P>where
P: QuadExtConfig,
impl<P> PartialEq<QuadExtField<P>> for QuadExtField<P>where P: QuadExtConfig,
source§fn eq(&self, other: &QuadExtField<P>) -> bool
fn eq(&self, other: &QuadExtField<P>) -> bool
self
and other
values to be equal, and is used
by ==
.source§impl<P> PartialOrd<QuadExtField<P>> for QuadExtField<P>where
P: QuadExtConfig,
impl<P> PartialOrd<QuadExtField<P>> for QuadExtField<P>where P: QuadExtConfig,
source§fn partial_cmp(&self, other: &QuadExtField<P>) -> Option<Ordering>
fn partial_cmp(&self, other: &QuadExtField<P>) -> Option<Ordering>
1.0.0 · source§fn le(&self, other: &Rhs) -> bool
fn le(&self, other: &Rhs) -> bool
self
and other
) and is used by the <=
operator. Read moresource§impl<'a, P> Product<&'a QuadExtField<P>> for QuadExtField<P>where
P: QuadExtConfig,
impl<'a, P> Product<&'a QuadExtField<P>> for QuadExtField<P>where P: QuadExtConfig,
source§fn product<I>(iter: I) -> QuadExtField<P>where
I: Iterator<Item = &'a QuadExtField<P>>,
fn product<I>(iter: I) -> QuadExtField<P>where I: Iterator<Item = &'a QuadExtField<P>>,
Self
from the elements by
multiplying the items.source§impl<P> Product<QuadExtField<P>> for QuadExtField<P>where
P: QuadExtConfig,
impl<P> Product<QuadExtField<P>> for QuadExtField<P>where P: QuadExtConfig,
source§fn product<I>(iter: I) -> QuadExtField<P>where
I: Iterator<Item = QuadExtField<P>>,
fn product<I>(iter: I) -> QuadExtField<P>where I: Iterator<Item = QuadExtField<P>>,
Self
from the elements by
multiplying the items.source§impl<'a, 'b, P> Sub<&'a QuadExtField<P>> for &'b QuadExtField<P>where
P: QuadExtConfig,
impl<'a, 'b, P> Sub<&'a QuadExtField<P>> for &'b QuadExtField<P>where P: QuadExtConfig,
§type Output = QuadExtField<P>
type Output = QuadExtField<P>
-
operator.source§fn sub(self, other: &'a QuadExtField<P>) -> QuadExtField<P>
fn sub(self, other: &'a QuadExtField<P>) -> QuadExtField<P>
-
operation. Read moresource§impl<'a, P> Sub<&'a QuadExtField<P>> for QuadExtField<P>where
P: QuadExtConfig,
impl<'a, P> Sub<&'a QuadExtField<P>> for QuadExtField<P>where P: QuadExtConfig,
§type Output = QuadExtField<P>
type Output = QuadExtField<P>
-
operator.source§fn sub(self, other: &QuadExtField<P>) -> QuadExtField<P>
fn sub(self, other: &QuadExtField<P>) -> QuadExtField<P>
-
operation. Read moresource§impl<'a, 'b, P> Sub<&'a mut QuadExtField<P>> for &'b QuadExtField<P>where
P: QuadExtConfig,
impl<'a, 'b, P> Sub<&'a mut QuadExtField<P>> for &'b QuadExtField<P>where P: QuadExtConfig,
§type Output = QuadExtField<P>
type Output = QuadExtField<P>
-
operator.source§fn sub(self, other: &'a mut QuadExtField<P>) -> QuadExtField<P>
fn sub(self, other: &'a mut QuadExtField<P>) -> QuadExtField<P>
-
operation. Read moresource§impl<'a, P> Sub<&'a mut QuadExtField<P>> for QuadExtField<P>where
P: QuadExtConfig,
impl<'a, P> Sub<&'a mut QuadExtField<P>> for QuadExtField<P>where P: QuadExtConfig,
§type Output = QuadExtField<P>
type Output = QuadExtField<P>
-
operator.source§fn sub(self, other: &'a mut QuadExtField<P>) -> QuadExtField<P>
fn sub(self, other: &'a mut QuadExtField<P>) -> QuadExtField<P>
-
operation. Read moresource§impl<'b, P> Sub<QuadExtField<P>> for &'b QuadExtField<P>where
P: QuadExtConfig,
impl<'b, P> Sub<QuadExtField<P>> for &'b QuadExtField<P>where P: QuadExtConfig,
§type Output = QuadExtField<P>
type Output = QuadExtField<P>
-
operator.source§fn sub(self, other: QuadExtField<P>) -> QuadExtField<P>
fn sub(self, other: QuadExtField<P>) -> QuadExtField<P>
-
operation. Read moresource§impl<P> Sub<QuadExtField<P>> for QuadExtField<P>where
P: QuadExtConfig,
impl<P> Sub<QuadExtField<P>> for QuadExtField<P>where P: QuadExtConfig,
§type Output = QuadExtField<P>
type Output = QuadExtField<P>
-
operator.source§fn sub(self, other: QuadExtField<P>) -> QuadExtField<P>
fn sub(self, other: QuadExtField<P>) -> QuadExtField<P>
-
operation. Read moresource§impl<'a, P> SubAssign<&'a QuadExtField<P>> for QuadExtField<P>where
P: QuadExtConfig,
impl<'a, P> SubAssign<&'a QuadExtField<P>> for QuadExtField<P>where P: QuadExtConfig,
source§fn sub_assign(&mut self, other: &QuadExtField<P>)
fn sub_assign(&mut self, other: &QuadExtField<P>)
-=
operation. Read moresource§impl<'a, P> SubAssign<&'a mut QuadExtField<P>> for QuadExtField<P>where
P: QuadExtConfig,
impl<'a, P> SubAssign<&'a mut QuadExtField<P>> for QuadExtField<P>where P: QuadExtConfig,
source§fn sub_assign(&mut self, other: &'a mut QuadExtField<P>)
fn sub_assign(&mut self, other: &'a mut QuadExtField<P>)
-=
operation. Read moresource§impl<P> SubAssign<QuadExtField<P>> for QuadExtField<P>where
P: QuadExtConfig,
impl<P> SubAssign<QuadExtField<P>> for QuadExtField<P>where P: QuadExtConfig,
source§fn sub_assign(&mut self, other: QuadExtField<P>)
fn sub_assign(&mut self, other: QuadExtField<P>)
-=
operation. Read moresource§impl<'a, P> Sum<&'a QuadExtField<P>> for QuadExtField<P>where
P: QuadExtConfig,
impl<'a, P> Sum<&'a QuadExtField<P>> for QuadExtField<P>where P: QuadExtConfig,
source§fn sum<I>(iter: I) -> QuadExtField<P>where
I: Iterator<Item = &'a QuadExtField<P>>,
fn sum<I>(iter: I) -> QuadExtField<P>where I: Iterator<Item = &'a QuadExtField<P>>,
Self
from the elements by
“summing up” the items.source§impl<P> Sum<QuadExtField<P>> for QuadExtField<P>where
P: QuadExtConfig,
impl<P> Sum<QuadExtField<P>> for QuadExtField<P>where P: QuadExtConfig,
source§fn sum<I>(iter: I) -> QuadExtField<P>where
I: Iterator<Item = QuadExtField<P>>,
fn sum<I>(iter: I) -> QuadExtField<P>where I: Iterator<Item = QuadExtField<P>>,
Self
from the elements by
“summing up” the items.