Trait IsFFTField 

pub trait IsFFTField: IsField {
    const TWO_ADICITY: u64;
    const TWO_ADIC_PRIMITVE_ROOT_OF_UNITY: Self::BaseType;

    // Provided methods
    fn field_name() -> &'static str { ... }
    fn get_primitive_root_of_unity(
        order: u64,
    ) -> Result<FieldElement<Self>, FieldError> { ... }
}

Trait to define necessary parameters for FFT-friendly Fields. Two-Adic fields are ones whose order is of the form $2^n k + 1$. Here $n$ is usually called the two-adicity of the field. The reason we care about it is that in an $n$-adic field there are $2^j$-roots of unity for every j between 1 and n, which is needed to do Fast Fourier. A two-adic primitive root of unity is a number w that satisfies w^(2^n) = 1 and w^(j) != 1 for every j below 2^n. With this primitive root we can generate any other root of unity we need to perform FFT.

Required Associated Constants

const TWO_ADICITY: u64

const TWO_ADIC_PRIMITVE_ROOT_OF_UNITY: Self::BaseType

Provided Methods

fn field_name() -> &'static str

Used for searching this field’s implementation in other languages, e.g in MSL for executing parallel operations with the Metal API.

fn get_primitive_root_of_unity( order: u64, ) -> Result<FieldElement<Self>, FieldError>

Returns a primitive root of unity of order $2^{order}$. This is an element w such that w^{2^order} = 1 modulo p and w^k <> 1 modulo p for k not congruent to 2^order

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementors

impl IsFFTField for Degree4BabyBearExtensionField

const TWO_ADICITY: u64 = 29u64

const TWO_ADIC_PRIMITVE_ROOT_OF_UNITY: Self::BaseType

impl IsFFTField for Degree4BabyBearU32ExtensionField

const TWO_ADICITY: u64 = 29u64

const TWO_ADIC_PRIMITVE_ROOT_OF_UNITY: Self::BaseType

impl IsFFTField for Degree2ExtensionField

const TWO_ADICITY: u64 = 31u64

const TWO_ADIC_PRIMITVE_ROOT_OF_UNITY: Self::BaseType

impl IsFFTField for FrField

const TWO_ADICITY: u64 = 32u64

const TWO_ADIC_PRIMITVE_ROOT_OF_UNITY: Self::BaseType

impl IsFFTField for lambdaworks_math::field::fields::fft_friendly::babybear::Babybear31PrimeField

Available on non-crate feature cuda only.

const TWO_ADICITY: u64 = 24u64

const TWO_ADIC_PRIMITVE_ROOT_OF_UNITY: Self::BaseType

impl IsFFTField for lambdaworks_math::field::fields::fft_friendly::babybear_u32::Babybear31PrimeField

Available on non-crate feature cuda only.

const TWO_ADICITY: u64 = 24u64

const TWO_ADIC_PRIMITVE_ROOT_OF_UNITY: Self::BaseType = {transmute(0x00000015): <field::fields::u32_montgomery_backend_prime_field::U32MontgomeryBackendPrimeField<2013265921> as field::traits::IsField>::BaseType}

impl IsFFTField for Stark101PrimeField

const TWO_ADICITY: u64 = 30u64

const TWO_ADIC_PRIMITVE_ROOT_OF_UNITY: U64

impl IsFFTField for Stark252PrimeField

const TWO_ADICITY: u64 = 192u64

const TWO_ADIC_PRIMITVE_ROOT_OF_UNITY: U256

impl IsFFTField for F17

const TWO_ADICITY: u64 = 4u64

const TWO_ADIC_PRIMITVE_ROOT_OF_UNITY: u64 = 3u64

impl IsFFTField for U32TestField

const TWO_ADICITY: u64 = 27u64

const TWO_ADIC_PRIMITVE_ROOT_OF_UNITY: u32 = 440_532_289u32

impl IsFFTField for U64TestField

const TWO_ADICITY: u64 = 32u64

const TWO_ADIC_PRIMITVE_ROOT_OF_UNITY: u64 = 1_753_635_133_440_165_772u64