Trait winter_math::FieldElement [−][src]
pub trait FieldElement: Copy + Clone + Debug + Display + Default + Send + Sync + Eq + PartialEq + Sized + Add<Self, Output = Self> + Sub<Self, Output = Self> + Mul<Self, Output = Self> + Div<Self, Output = Self> + AddAssign<Self> + SubAssign<Self> + MulAssign<Self> + DivAssign<Self> + Neg<Output = Self> + From<Self::BaseField> + From<u128> + From<u64> + From<u32> + From<u16> + From<u8> + for<'a> TryFrom<&'a [u8]> + AsBytes + Randomizable + Serializable + Deserializable {
type PositiveInteger: Debug + Copy + PartialEq + PartialOrd + ShrAssign + Shl<u32, Output = Self::PositiveInteger> + Shr<u32, Output = Self::PositiveInteger> + BitAnd<Output = Self::PositiveInteger> + From<u32> + From<u64>;
type BaseField: StarkField;
const ELEMENT_BYTES: usize;
const IS_CANONICAL: bool;
const ZERO: Self;
const ONE: Self;
fn inv(self) -> Self;
fn conjugate(&self) -> Self;
fn elements_as_bytes(elements: &[Self]) -> &[u8];
unsafe fn bytes_as_elements(
bytes: &[u8]
) -> Result<&[Self], DeserializationError>;
fn as_base_elements(elements: &[Self]) -> &[Self::BaseField];
fn double(self) -> Self { ... }
fn square(self) -> Self { ... }
fn cube(self) -> Self { ... }
fn exp(self, power: Self::PositiveInteger) -> Self { ... }
fn zeroed_vector(n: usize) -> Vec<Self> { ... }
}
Expand description
Defines an element in a finite field.
This trait defines basic arithmetic operations for elements in finite fields (e.g. addition subtraction, multiplication, division) as well as several convenience functions (e.g. double, square cube). Moreover, it defines interfaces for serializing and deserializing field elements.
The elements could be in a prime field or an extension of a prime field. Currently, only quadratic field extensions are supported.
Associated Types
type PositiveInteger: Debug + Copy + PartialEq + PartialOrd + ShrAssign + Shl<u32, Output = Self::PositiveInteger> + Shr<u32, Output = Self::PositiveInteger> + BitAnd<Output = Self::PositiveInteger> + From<u32> + From<u64>
type PositiveInteger: Debug + Copy + PartialEq + PartialOrd + ShrAssign + Shl<u32, Output = Self::PositiveInteger> + Shr<u32, Output = Self::PositiveInteger> + BitAnd<Output = Self::PositiveInteger> + From<u32> + From<u64>
A type defining positive integers big enough to describe a field modulus for
Self::BaseField
with no loss of precision.
type BaseField: StarkField
type BaseField: StarkField
Base field type for this finite field. For prime fields, BaseField
should be set
to Self
.
Associated Constants
const ELEMENT_BYTES: usize
const ELEMENT_BYTES: usize
Number of bytes needed to encode an element
const IS_CANONICAL: bool
const IS_CANONICAL: bool
True if internal representation of the element is the same as its canonical representation.
Required methods
Returns a multiplicative inverse of this field element. If this element is ZERO, ZERO is returned.
Converts a list of elements into a list of bytes.
The elements may be in the internal representation rather than in the canonical representation. This conversion is intended to be zero-copy (i.e. by re-interpreting the underlying memory).
unsafe fn bytes_as_elements(
bytes: &[u8]
) -> Result<&[Self], DeserializationError>
unsafe fn bytes_as_elements(
bytes: &[u8]
) -> Result<&[Self], DeserializationError>
Converts a list of bytes into a list of field elements.
The elements are assumed to encoded in the internal representation rather than in the canonical representation. The conversion is intended to be zero-copy (i.e. by re-interpreting the underlying memory).
Errors
An error is returned if:
- Memory alignment of
bytes
does not match memory alignment of field element data. - Length of
bytes
does not divide into whole number of elements.
Safety
This function is unsafe because it does not check whether underlying bytes represent valid field elements according to their internal representation.
Converts a list of field elements into a list of elements in the underlying base field.
For base STARK fields, the input and output lists are the same. For extension field, the output list will contain decompositions of each extension element into underlying base elements.
Provided methods
fn exp(self, power: Self::PositiveInteger) -> Self
fn exp(self, power: Self::PositiveInteger) -> Self
Exponentiates this field element by power
parameter.
fn zeroed_vector(n: usize) -> Vec<Self>
fn zeroed_vector(n: usize) -> Vec<Self>
Returns a vector of length n
initialized with all ZERO elements.
Specialized implementations of this function may be faster than the generic implementation.