Struct ark_ed_on_bw6_761::FrConfig
source · pub struct FrConfig;
Trait Implementations§
source§impl MontConfig<6> for FrConfig
impl MontConfig<6> for FrConfig
source§fn neg_in_place(a: &mut Fp<MontBackend<FrConfig, 6>, 6>)
fn neg_in_place(a: &mut Fp<MontBackend<FrConfig, 6>, 6>)
Sets a = -a
.
source§const MODULUS: BigInt<6> = BigInt([4684667634276979349u64, 3748803659444032385u64,
16273581227874629698u64, 7152942431629910641u64,
6397188139321141543u64, 15137289088311837u64])
const MODULUS: BigInt<6> = BigInt([4684667634276979349u64, 3748803659444032385u64, 16273581227874629698u64, 7152942431629910641u64, 6397188139321141543u64, 15137289088311837u64])
The modulus of the field.
source§const GENERATOR: Fp<MontBackend<FrConfig, 6>, 6> = {
let (is_positive, limbs) = (true, [13u64]);
::ark_ff::Fp::from_sign_and_limbs(is_positive, &limbs)
}
const GENERATOR: Fp<MontBackend<FrConfig, 6>, 6> = { let (is_positive, limbs) = (true, [13u64]); ::ark_ff::Fp::from_sign_and_limbs(is_positive, &limbs) }
A multiplicative generator of the field.
Self::GENERATOR
is an element having multiplicative order
Self::MODULUS - 1
.source§const TWO_ADIC_ROOT_OF_UNITY: Fp<MontBackend<FrConfig, 6>, 6> = {
let (is_positive, limbs) =
(true,
[17916322498767434621u64, 11161566994721143350u64,
11008150882468515010u64, 15239700324980761407u64,
453813437906364039u64, 12103696378766319u64]);
::ark_ff::Fp::from_sign_and_limbs(is_positive, &limbs)
}
const TWO_ADIC_ROOT_OF_UNITY: Fp<MontBackend<FrConfig, 6>, 6> = { let (is_positive, limbs) = (true, [17916322498767434621u64, 11161566994721143350u64, 11008150882468515010u64, 15239700324980761407u64, 453813437906364039u64, 12103696378766319u64]); ::ark_ff::Fp::from_sign_and_limbs(is_positive, &limbs) }
2^s root of unity computed by GENERATOR^t
source§fn add_assign(
a: &mut Fp<MontBackend<FrConfig, 6>, 6>,
b: &Fp<MontBackend<FrConfig, 6>, 6>
)
fn add_assign(
a: &mut Fp<MontBackend<FrConfig, 6>, 6>,
b: &Fp<MontBackend<FrConfig, 6>, 6>
)
Sets
a = a + b
.source§fn sub_assign(
a: &mut Fp<MontBackend<FrConfig, 6>, 6>,
b: &Fp<MontBackend<FrConfig, 6>, 6>
)
fn sub_assign(
a: &mut Fp<MontBackend<FrConfig, 6>, 6>,
b: &Fp<MontBackend<FrConfig, 6>, 6>
)
Sets
a = a - b
.source§fn double_in_place(a: &mut Fp<MontBackend<FrConfig, 6>, 6>)
fn double_in_place(a: &mut Fp<MontBackend<FrConfig, 6>, 6>)
Sets
a = 2 * a
.source§fn mul_assign(
a: &mut Fp<MontBackend<FrConfig, 6>, 6>,
b: &Fp<MontBackend<FrConfig, 6>, 6>
)
fn mul_assign(
a: &mut Fp<MontBackend<FrConfig, 6>, 6>,
b: &Fp<MontBackend<FrConfig, 6>, 6>
)
This modular multiplication algorithm uses Montgomery
reduction for efficient implementation. It also additionally
uses the “no-carry optimization” outlined
here if
Self::MODULUS
has (a) a non-zero MSB, and (b) at least one
zero bit in the rest of the modulus.fn square_in_place(a: &mut Fp<MontBackend<FrConfig, 6>, 6>)
fn sum_of_products<const M: usize>(
a: &[Fp<MontBackend<FrConfig, 6>, 6>; M],
b: &[Fp<MontBackend<FrConfig, 6>, 6>; M]
) -> Fp<MontBackend<FrConfig, 6>, 6>
§const R: BigInt<N> = Self::MODULUS.montgomery_r()
const R: BigInt<N> = Self::MODULUS.montgomery_r()
Let
M
be the power of 2^64 nearest to Self::MODULUS_BITS
. Then
R = M % Self::MODULUS
.§const SMALL_SUBGROUP_BASE: Option<u32> = None
const SMALL_SUBGROUP_BASE: Option<u32> = None
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> = None
const SMALL_SUBGROUP_BASE_ADICITY: Option<u32> = None
The integer
k
such that there exists a multiplicative subgroup
of size Self::SMALL_SUBGROUP_BASE^k
.§const LARGE_SUBGROUP_ROOT_OF_UNITY: Option<Fp<MontBackend<Self, N>, N>> = None
const LARGE_SUBGROUP_ROOT_OF_UNITY: Option<Fp<MontBackend<Self, N>, N>> = None
GENERATOR^((MODULUS-1) / (2^s *
SMALL_SUBGROUP_BASE^SMALL_SUBGROUP_BASE_ADICITY)).
Used for mixed-radix FFT.
§const SQRT_PRECOMP: Option<SqrtPrecomputation<Fp<MontBackend<Self, N>, N>>> = sqrt_precomputation::<N, Self>()
const SQRT_PRECOMP: Option<SqrtPrecomputation<Fp<MontBackend<Self, N>, N>>> = sqrt_precomputation::<N, Self>()
Precomputed material for use when computing square roots.
The default is to use the standard Tonelli-Shanks algorithm.