Struct SmallFp 

pub struct SmallFp<P: SmallFpConfig> {
    pub value: P::T,
    /* private fields */
}

Represents an element of the prime field F_p, where p == P::MODULUS.

This type can represent elements in any field of size up to 128 bits. The arithmetic implementation is determined by the P: SmallFpConfig parameter, which can be configured to use different backends

Fields

value: P::T

Implementations

impl<P: SmallFpConfig> SmallFp<P>

pub const fn from_raw(value: P::T) -> Self

pub fn new(value: P::T) -> Self

pub const fn num_bits_to_shave() -> usize

Trait Implementations

impl<'b, P: SmallFpConfig> Add<&'b SmallFp<P>> for &SmallFp<P>

type Output = SmallFp<P>

The resulting type after applying the + operator.

fn add(self, other: &'b SmallFp<P>) -> SmallFp<P>

Performs the + operation.

impl<P: SmallFpConfig> Add<&SmallFp<P>> for SmallFp<P>

type Output = SmallFp<P>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, P: SmallFpConfig> Add<&'a mut SmallFp<P>> for SmallFp<P>

type Output = SmallFp<P>

The resulting type after applying the + operator.

fn add(self, other: &'a mut Self) -> Self

Performs the + operation.

impl<P: SmallFpConfig> Add for SmallFp<P>

type Output = SmallFp<P>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<P: SmallFpConfig> AddAssign<&SmallFp<P>> for SmallFp<P>

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

Performs the += operation.

impl<'a, P: SmallFpConfig> AddAssign<&'a mut SmallFp<P>> for SmallFp<P>

fn add_assign(&mut self, other: &'a mut Self)

Performs the += operation.

impl<P: SmallFpConfig> AddAssign for SmallFp<P>

fn add_assign(&mut self, other: Self)

Performs the += operation.

impl<P: SmallFpConfig> AdditiveGroup for SmallFp<P>

const ZERO: Self = P::ZERO

The additive identity of the field.

type Scalar = SmallFp<P>

fn double(&self) -> Self

Doubles self.

fn double_in_place(&mut self) -> &mut Self

Doubles self in place.

fn neg_in_place(&mut self) -> &mut Self

Negates self in place.

impl<P: SmallFpConfig> CanonicalDeserialize for SmallFp<P>

fn deserialize_with_mode<R: Read>( reader: R, _compress: Compress, _validate: Validate, ) -> Result<Self, SerializationError>

The general deserialize method that takes in customization flags.

fn deserialize_compressed<R>(reader: R) -> Result<Self, SerializationError>

where R: Read,

Reads Self from reader using the compressed form if applicable. Performs validation if applicable.

fn deserialize_compressed_unchecked<R>( reader: R, ) -> Result<Self, SerializationError>

where R: Read,

Reads Self from reader using the compressed form if applicable, without validating the deserialized value.

fn deserialize_uncompressed<R>(reader: R) -> Result<Self, SerializationError>

where R: Read,

Reads Self from reader using the uncompressed form. Performs validation if applicable.

fn deserialize_uncompressed_unchecked<R>( reader: R, ) -> Result<Self, SerializationError>

where R: Read,

Reads Self from reader using the uncompressed form, without validating the deserialized value.

impl<P: SmallFpConfig> CanonicalDeserializeWithFlags for SmallFp<P>

fn deserialize_with_flags<R: Read, F: Flags>( reader: R, ) -> Result<(Self, F), SerializationError>

Reads Self and Flags from reader. Returns empty flags by default.

impl<P: SmallFpConfig> CanonicalSerialize for SmallFp<P>

fn serialize_with_mode<W: Write>( &self, writer: W, _compress: Compress, ) -> Result<(), SerializationError>

The general serialize method that takes in customization flags.

fn serialized_size(&self, _compress: Compress) -> usize

Returns the size in bytes of the serialized version of self with the given compression mode.

fn serialize_compressed<W>(&self, writer: W) -> Result<(), SerializationError>

where W: Write,

Serializes self into writer using the compressed form if applicable.

fn compressed_size(&self) -> usize

Returns the size in bytes of the compressed serialized version of self.

fn serialize_uncompressed<W>(&self, writer: W) -> Result<(), SerializationError>

where W: Write,

Serializes self into writer using the uncompressed form.

fn uncompressed_size(&self) -> usize

Returns the size in bytes of the uncompressed serialized version of self.

impl<P: SmallFpConfig> CanonicalSerializeWithFlags for SmallFp<P>

fn serialize_with_flags<W: Write, F: Flags>( &self, writer: W, flags: F, ) -> Result<(), SerializationError>

Serializes self and flags into writer.

fn serialized_size_with_flags<F: Flags>(&self) -> usize

Serializes self and flags into writer.

impl<P: SmallFpConfig> Clone for SmallFp<P>

where P::T: Copy, PhantomData<P>: Copy,

fn clone(&self) -> Self

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<P: SmallFpConfig> Debug for SmallFp<P>

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

Formats the value using the given formatter.

impl<P: SmallFpConfig> Default for SmallFp<P>

where P::T: Default, PhantomData<P>: Default,

fn default() -> Self

Returns the “default value” for a type.

impl<P: SmallFpConfig> Display for SmallFp<P>

Outputs a string containing the value of self, represented as a decimal without leading zeroes.

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

Formats the value using the given formatter.

impl<P: SmallFpConfig> Distribution<SmallFp<P>> for Standard

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> SmallFp<P>

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T>

where R: Rng, Self: Sized,

Create an iterator that generates random values of T, using rng as the source of randomness.

fn map<F, S>(self, func: F) -> DistMap<Self, F, T, S>

where F: Fn(T) -> S, Self: Sized,

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F

impl<P: SmallFpConfig> Div<&SmallFp<P>> for &SmallFp<P>

type Output = SmallFp<P>

The resulting type after applying the / operator.

fn div(self, other: &SmallFp<P>) -> SmallFp<P>

Performs the / operation.

impl<P: SmallFpConfig> Div<&SmallFp<P>> for SmallFp<P>

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

Returns self * other.inverse() if other.inverse() is Some, and panics otherwise.

type Output = SmallFp<P>

The resulting type after applying the / operator.

impl<'a, P: SmallFpConfig> Div<&'a mut SmallFp<P>> for SmallFp<P>

type Output = SmallFp<P>

The resulting type after applying the / operator.

fn div(self, other: &'a mut Self) -> Self

Performs the / operation.

impl<P: SmallFpConfig> Div for SmallFp<P>

type Output = SmallFp<P>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<P: SmallFpConfig> DivAssign<&SmallFp<P>> for SmallFp<P>

Computes self *= other.inverse() if other.inverse() is Some, and panics otherwise.

fn div_assign(&mut self, other: &Self)

Performs the /= operation.

impl<'a, P: SmallFpConfig> DivAssign<&'a mut SmallFp<P>> for SmallFp<P>

fn div_assign(&mut self, other: &'a mut Self)

Performs the /= operation.

impl<P: SmallFpConfig> DivAssign for SmallFp<P>

fn div_assign(&mut self, other: Self)

Performs the /= operation.

impl<P: SmallFpConfig> FftField for SmallFp<P>

const GENERATOR: Self = P::GENERATOR

The generator of the multiplicative group of the field

const TWO_ADICITY: u32 = P::TWO_ADICITY

Let N be the size of the multiplicative group defined by the field. Then TWO_ADICITY is the two-adicity of N, i.e. the integer s such that N = 2^s * t for some odd integer t.

const TWO_ADIC_ROOT_OF_UNITY: Self = P::TWO_ADIC_ROOT_OF_UNITY

2^s root of unity computed by GENERATOR^t

const SMALL_SUBGROUP_BASE: Option<u32> = P::SMALL_SUBGROUP_BASE

An integer b such that there exists a multiplicative subgroup of size b^k for some integer k.

const SMALL_SUBGROUP_BASE_ADICITY: Option<u32> = P::SMALL_SUBGROUP_BASE_ADICITY

The integer k such that there exists a multiplicative subgroup of size Self::SMALL_SUBGROUP_BASE^k.

const LARGE_SUBGROUP_ROOT_OF_UNITY: Option<Self> = P::LARGE_SUBGROUP_ROOT_OF_UNITY

GENERATOR^((MODULUS-1) / (2^s * SMALL_SUBGROUP_BASE^SMALL_SUBGROUP_BASE_ADICITY)) Used for mixed-radix FFT.

fn get_root_of_unity(n: u64) -> Option<Self>

Returns the root of unity of order n, if one exists. If no small multiplicative subgroup is defined, this is the 2-adic root of unity of order n (for n a power of 2). If a small multiplicative subgroup is defined, this is the root of unity of order n for the larger subgroup generated by FftConfig::LARGE_SUBGROUP_ROOT_OF_UNITY (for n = 2^i * FftConfig::SMALL_SUBGROUP_BASE^j for some i, j).

fn get_root_of_unity_big_int(n: BigUint) -> Option<Self>

Returns the root of unity of order n, if one exists. If no small multiplicative subgroup is defined, this is the 2-adic root of unity of order n (for n a power of 2). If a small multiplicative subgroup is defined, this is the root of unity of order n for the larger subgroup generated by FftConfig::LARGE_SUBGROUP_ROOT_OF_UNITY (for n = 2^i * FftConfig::SMALL_SUBGROUP_BASE^j for some i, j).

impl<P: SmallFpConfig> Field for SmallFp<P>

fn frobenius_map_in_place(&mut self, _: usize)

The Frobenius map has no effect in a prime field.

const SQRT_PRECOMP: Option<SqrtPrecomputation<Self>> = P::SQRT_PRECOMP

Determines the algorithm for computing square roots.

const ONE: Self = P::ONE

The multiplicative identity of the field.

const NEG_ONE: Self = P::NEG_ONE

Negation of the multiplicative identity of the field.

type BasePrimeField = SmallFp<P>

fn extension_degree() -> u64

Returns the extension degree of this field with respect to Self::BasePrimeField.

fn from_base_prime_field(elem: Self::BasePrimeField) -> Self

Constructs a field element from a single base prime field elements.

fn to_base_prime_field_elements(&self) -> impl Iterator<Item = Self>

fn from_base_prime_field_elems( elems: impl IntoIterator<Item = Self::BasePrimeField>, ) -> Option<Self>

Convert a slice of base prime field elements into a field element. If the slice length != Self::extension_degree(), must return None.

fn characteristic() -> &'static [u64]

Returns the characteristic of the field, in little-endian representation.

fn sum_of_products<const T: usize>(a: &[Self; T], b: &[Self; T]) -> Self

Returns sum([a_i * b_i]).

fn from_random_bytes_with_flags<F: Flags>(bytes: &[u8]) -> Option<(Self, F)>

Attempt to deserialize a field element, splitting the bitflags metadata according to F specification. Returns None if the deserialization fails.

fn square(&self) -> Self

Returns self * self.

fn square_in_place(&mut self) -> &mut Self

Squares self in place.

fn inverse(&self) -> Option<Self>

Computes the multiplicative inverse of self if self is nonzero.

fn inverse_in_place(&mut self) -> Option<&mut Self>

If self.inverse().is_none(), this just returns None. Otherwise, it sets self to self.inverse().unwrap().

fn legendre(&self) -> LegendreSymbol

Returns a LegendreSymbol, which indicates whether this field element is 1 : a quadratic residue 0 : equal to 0 -1 : a quadratic non-residue

fn mul_by_base_prime_field(&self, elem: &Self::BasePrimeField) -> Self

fn from_random_bytes(bytes: &[u8]) -> Option<Self>

Attempt to deserialize a field element. Returns None if the deserialization fails.

fn sqrt(&self) -> Option<Self>

Returns the square root of self, if it exists.

fn sqrt_in_place(&mut self) -> Option<&mut Self>

Sets self to be the square root of self, if it exists.

fn frobenius_map(&self, power: usize) -> Self

Returns self^s, where s = Self::BasePrimeField::MODULUS^power. This is also called the Frobenius automorphism.

fn pow<S: AsRef<[u64]>>(&self, exp: S) -> Self

Returns self^exp, where exp is an integer represented with u64 limbs, least significant limb first.

fn pow_with_table<S: AsRef<[u64]>>(powers_of_2: &[Self], exp: S) -> Option<Self>

Exponentiates a field element 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.

impl<P: SmallFpConfig> From<BigInt<1>> for SmallFp<P>

fn from(int: BigInt<1>) -> Self

Converts to this type from the input type.

impl<P: SmallFpConfig> From<BigUint> for SmallFp<P>

fn from(val: BigUint) -> SmallFp<P>

Converts to this type from the input type.

impl<P: SmallFpConfig> From<SmallFp<P>> for BigInt<1>

fn from(fp: SmallFp<P>) -> Self

Converts to this type from the input type.

impl<P: SmallFpConfig> From<SmallFp<P>> for BigUint

fn from(other: SmallFp<P>) -> Self

Converts to this type from the input type.

impl<P: SmallFpConfig> From<bool> for SmallFp<P>

fn from(other: bool) -> Self

Converts to this type from the input type.

impl<P: SmallFpConfig> From<i128> for SmallFp<P>

fn from(other: i128) -> Self

Converts to this type from the input type.

impl<P: SmallFpConfig> From<i16> for SmallFp<P>

fn from(other: i16) -> Self

Converts to this type from the input type.

impl<P: SmallFpConfig> From<i32> for SmallFp<P>

fn from(other: i32) -> Self

Converts to this type from the input type.

impl<P: SmallFpConfig> From<i64> for SmallFp<P>

fn from(other: i64) -> Self

Converts to this type from the input type.

impl<P: SmallFpConfig> From<i8> for SmallFp<P>

fn from(other: i8) -> Self

Converts to this type from the input type.

impl<P: SmallFpConfig> From<u128> for SmallFp<P>

fn from(other: u128) -> Self

Converts to this type from the input type.

impl<P: SmallFpConfig> From<u16> for SmallFp<P>

fn from(other: u16) -> Self

Converts to this type from the input type.

impl<P: SmallFpConfig> From<u32> for SmallFp<P>

fn from(other: u32) -> Self

Converts to this type from the input type.

impl<P: SmallFpConfig> From<u64> for SmallFp<P>

fn from(other: u64) -> Self

Converts to this type from the input type.

impl<P: SmallFpConfig> From<u8> for SmallFp<P>

fn from(other: u8) -> Self

Converts to this type from the input type.

impl<P: SmallFpConfig> FromStr for SmallFp<P>

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

Interpret a string of numbers as a (congruent) prime field element. Does not accept unnecessary leading zeroes or a blank string.

type Err = ParseSmallFpError

The associated error which can be returned from parsing.

impl<P: SmallFpConfig> Hash for SmallFp<P>

where P::T: Hash, PhantomData<P>: Hash,

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<P: SmallFpConfig> Mul<&SmallFp<P>> for &SmallFp<P>

type Output = SmallFp<P>

The resulting type after applying the * operator.

fn mul(self, other: &SmallFp<P>) -> SmallFp<P>

Performs the * operation.

impl<P: SmallFpConfig> Mul<&SmallFp<P>> for SmallFp<P>

type Output = SmallFp<P>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, P: SmallFpConfig> Mul<&'a mut SmallFp<P>> for SmallFp<P>

type Output = SmallFp<P>

The resulting type after applying the * operator.

fn mul(self, other: &'a mut Self) -> Self

Performs the * operation.

impl<P: SmallFpConfig> Mul for SmallFp<P>

type Output = SmallFp<P>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<P: SmallFpConfig> MulAssign<&SmallFp<P>> for SmallFp<P>

fn mul_assign(&mut self, other: &Self)

Performs the *= operation.

impl<'a, P: SmallFpConfig> MulAssign<&'a mut SmallFp<P>> for SmallFp<P>

fn mul_assign(&mut self, other: &'a mut Self)

Performs the *= operation.

impl<P: SmallFpConfig> MulAssign for SmallFp<P>

fn mul_assign(&mut self, other: Self)

Performs the *= operation.

impl<P: SmallFpConfig> Neg for SmallFp<P>

type Output = SmallFp<P>

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl<P: SmallFpConfig> One for SmallFp<P>

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool

Returns true if self is equal to the multiplicative identity.

fn set_one(&mut self)

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

impl<P: SmallFpConfig> Ord for SmallFp<P>

Note that this implementation of Ord compares field elements viewing them as integers in the range 0, 1, …, P::MODULUS - 1. However, other implementations of PrimeField might choose a different ordering, and as such, users should use this Ord for applications where any ordering suffices (like in a BTreeMap), and not in applications where a particular ordering is required.

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<P: SmallFpConfig> PartialEq for SmallFp<P>

where P::T: PartialEq, PhantomData<P>: PartialEq,

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

Tests for self and other values to be equal, and is used by ==.

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

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

impl<P: SmallFpConfig> PartialOrd for SmallFp<P>

Note that this implementation of PartialOrd compares field elements viewing them as integers in the range 0, 1, …, P::MODULUS - 1. However, other implementations of PrimeField might choose a different ordering, and as such, users should use this PartialOrd for applications where any ordering suffices (like in a BTreeMap), and not in applications where a particular ordering is required.

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<P: SmallFpConfig> PrimeField for SmallFp<P>

const MODULUS: Self::BigInt

The modulus p.

const MODULUS_MINUS_ONE_DIV_TWO: Self::BigInt

The value (p - 1)/ 2.

const MODULUS_BIT_SIZE: u32

The size of the modulus in bits.

const TRACE: Self::BigInt

The trace of the field is defined as the smallest integer t such that by 2^s * t = p - 1, and t is coprime to 2.

const TRACE_MINUS_ONE_DIV_TWO: Self::BigInt

The value (t - 1)/ 2.

type BigInt = BigInt<1>

A BigInteger type that can represent elements of this field.

fn from_bigint(r: BigInt<1>) -> Option<Self>

Construct a prime field element from an integer in the range 0..(p - 1).

fn into_bigint(self) -> BigInt<1>

Converts an element of the prime field into an integer in the range 0..(p - 1).

fn from_be_bytes_mod_order(bytes: &[u8]) -> Self

Reads bytes in big-endian, and converts them to a field element. If the integer represented by bytes is larger than the modulus p, this method performs the appropriate reduction.

fn from_le_bytes_mod_order(bytes: &[u8]) -> Self

Reads bytes in little-endian, and converts them to a field element. If the integer represented by bytes is larger than the modulus p, this method performs the appropriate reduction.

impl<'a, P: SmallFpConfig> Product<&'a SmallFp<P>> for SmallFp<P>

fn product<I: Iterator<Item = &'a Self>>(iter: I) -> Self

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

impl<P: SmallFpConfig> Product for SmallFp<P>

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

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

impl<P: SmallFpConfig> Sub<&SmallFp<P>> for &SmallFp<P>

type Output = SmallFp<P>

The resulting type after applying the - operator.

fn sub(self, other: &SmallFp<P>) -> SmallFp<P>

Performs the - operation.

impl<P: SmallFpConfig> Sub<&SmallFp<P>> for SmallFp<P>

type Output = SmallFp<P>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, P: SmallFpConfig> Sub<&'a mut SmallFp<P>> for SmallFp<P>

type Output = SmallFp<P>

The resulting type after applying the - operator.

fn sub(self, other: &'a mut Self) -> Self

Performs the - operation.

impl<P: SmallFpConfig> Sub for SmallFp<P>

type Output = SmallFp<P>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<P: SmallFpConfig> SubAssign<&SmallFp<P>> for SmallFp<P>

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

Performs the -= operation.

impl<'a, P: SmallFpConfig> SubAssign<&'a mut SmallFp<P>> for SmallFp<P>

fn sub_assign(&mut self, other: &'a mut Self)

Performs the -= operation.

impl<P: SmallFpConfig> SubAssign for SmallFp<P>

fn sub_assign(&mut self, other: Self)

Performs the -= operation.

impl<'a, P: SmallFpConfig> Sum<&'a SmallFp<P>> for SmallFp<P>

fn sum<I: Iterator<Item = &'a Self>>(iter: I) -> Self

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

impl<P: SmallFpConfig> Sum for SmallFp<P>

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

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

impl<P: SmallFpConfig> Valid for SmallFp<P>

fn check(&self) -> Result<(), SerializationError>

Checks whether self is valid. If self is valid, returns Ok(()). Otherwise, returns an error describing the failure. This method is called by deserialize_with_mode if validate is Validate::Yes.

const TRIVIAL_CHECK: bool = false

Whether the check method is trivial (i.e. always returns Ok(())). If this is true, the batch_check method will skip all checks and return Ok(()). This should be set to true for types where check is trivial, e.g. integers, field elements, etc. This is false by default. This is primarily an optimization to skip unnecessary checks in batch_check.

fn batch_check<'a>( batch: impl Iterator<Item = &'a Self> + Send, ) -> Result<(), SerializationError>

where Self: 'a,

Checks whether all items in batch are valid. If all items are valid, returns Ok(()). Otherwise, returns an error describing the first failure.

impl<P: SmallFpConfig> Zero for SmallFp<P>

fn zero() -> Self

Returns the additive identity element of Self, 0.

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

fn set_zero(&mut self)

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

impl<P: SmallFpConfig> Zeroize for SmallFp<P>

fn zeroize(&mut self)

Zero out this object from memory using Rust intrinsics which ensure the zeroization operation is not “optimized away” by the compiler.

impl<P: SmallFpConfig> Copy for SmallFp<P>

where P::T: Copy, PhantomData<P>: Copy,

impl<P: SmallFpConfig> Eq for SmallFp<P>

where P::T: PartialEq, PhantomData<P>: PartialEq,