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miden-crypto/src/dsa/rpo_falcon512/math/fft.rs
Bobbin Threadbare 913384600d chore: fix typos
2024-09-11 16:52:21 -07:00

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use alloc::vec::Vec;
use core::{
f64::consts::PI,
ops::{Add, AddAssign, Mul, MulAssign, Neg, Sub, SubAssign},
};
#[cfg(not(feature = "std"))]
use num::Float;
use num::{One, Zero};
use num_complex::Complex64;
use super::{field::FalconFelt, polynomial::Polynomial, Inverse};
/// Implements Cyclotomic FFT without bitreversing the outputs, and using precomputed powers of the
/// 2n-th primitive root of unity.
pub trait FastFft: Sized + Clone {
type Field: Add + Mul + AddAssign + MulAssign + Neg + Sub + SubAssign;
fn fft_inplace(&mut self);
fn fft(&self) -> Self {
let mut a = self.clone();
a.fft_inplace();
a
}
fn merge_fft(a: &Self, b: &Self) -> Self;
fn split_fft(&self) -> (Self, Self);
fn ifft_inplace(&mut self);
fn ifft(&self) -> Self {
let mut a = self.clone();
a.ifft_inplace();
a
}
}
pub trait CyclotomicFourier
where
Self: Sized
+ Copy
+ One
+ Zero
+ Add<Output = Self>
+ Sub<Output = Self>
+ Mul<Output = Self>
+ MulAssign
+ Inverse,
{
/// Gets the inverse of 2^n.
#[allow(dead_code)]
fn power_of_two_inverse(n: usize) -> Self {
let mut a = Self::one() + Self::one();
for _ in 0..n {
a *= a;
}
Self::inverse_or_zero(a)
}
/// Gets a primitive nth (with n a power of 2) root of unity.
#[allow(dead_code)]
fn primitive_root_of_unity(n: usize) -> Self;
/// Computes the integer whose n-bit binary expansion is the reverse of that of the argument.
fn bitreverse_index(arg: usize, n: usize) -> usize {
assert!(n > 0);
assert_eq!(n & (n - 1), 0);
let mut rev = 0;
let mut m = n >> 1;
let mut k = 1;
while m > 0 {
rev |= (((arg & m) != 0) as usize) * k;
k <<= 1;
m >>= 1;
}
rev
}
/// Computes the first n powers of the 2nd root of unity, and put them in bit-reversed order.
#[allow(dead_code)]
fn bitreversed_powers(n: usize) -> Vec<Self> {
let psi = Self::primitive_root_of_unity(2 * n);
let mut array = vec![Self::zero(); n];
let mut alpha = Self::one();
for a in array.iter_mut() {
*a = alpha;
alpha *= psi;
}
Self::bitreverse_array(&mut array);
array
}
/// Computes the first n powers of the 2nd root of unity, invert them, and put them in
/// bit-reversed order.
#[allow(dead_code)]
fn bitreversed_powers_inverse(n: usize) -> Vec<Self> {
let psi = Self::primitive_root_of_unity(2 * n).inverse_or_zero();
let mut array = vec![Self::zero(); n];
let mut alpha = Self::one();
for a in array.iter_mut() {
*a = alpha;
alpha *= psi;
}
Self::bitreverse_array(&mut array);
array
}
/// Reorders the given elements in the array by reversing the binary expansions of their
/// indices.
fn bitreverse_array<T>(array: &mut [T]) {
let n = array.len();
for i in 0..n {
let j = Self::bitreverse_index(i, n);
if i < j {
array.swap(i, j);
}
}
}
/// Computes the evaluations of the polynomial on the roots of the polynomial X^n + 1 using a
/// fast Fourier transform. Algorithm 1 from https://eprint.iacr.org/2016/504.pdf.
///
/// Arguments:
///
/// - a : &mut [Self] (a reference to) a mutable array of field elements which is to be
/// transformed under the FFT. The transformation happens in- place.
///
/// - psi_rev: &[Self] (a reference to) an array of powers of psi, from 0 to n-1, but ordered
/// by bit-reversed index. Here psi is a primitive root of order 2n. You can use
/// `Self::bitreversed_powers(psi, n)` for this purpose, but this trait implementation is not
/// const. For the performance benefit you want a precompiled array, which you can get if you
/// can get by implementing the same method and marking it "const".
fn fft(a: &mut [Self], psi_rev: &[Self]) {
let n = a.len();
let mut t = n;
let mut m = 1;
while m < n {
t >>= 1;
for i in 0..m {
let j1 = 2 * i * t;
let j2 = j1 + t - 1;
let s = psi_rev[m + i];
for j in j1..=j2 {
let u = a[j];
let v = a[j + t] * s;
a[j] = u + v;
a[j + t] = u - v;
}
}
m <<= 1;
}
}
/// Computes the coefficients of the polynomial with the given evaluations on the roots of
/// X^n + 1 using an inverse fast Fourier transform.
/// Algorithm 2 from https://eprint.iacr.org/2016/504.pdf.
///
/// Arguments:
///
/// - a : &mut [Self] (a reference to) a mutable array of field elements which is to be
/// transformed under the IFFT. The transformation happens in- place.
///
/// - psi_inv_rev: &[Self] (a reference to) an array of powers of psi^-1, from 0 to n-1, but
/// ordered by bit-reversed index. Here psi is a primitive root of order 2n. You can use
/// `Self::bitreversed_powers(Self::inverse_or_zero(psi), n)` for this purpose, but this
/// trait implementation is not const. For the performance benefit you want a precompiled
/// array, which you can get if you can get by implementing the same methods and marking them
/// "const".
fn ifft(a: &mut [Self], psi_inv_rev: &[Self], ninv: Self) {
let n = a.len();
let mut t = 1;
let mut m = n;
while m > 1 {
let h = m / 2;
let mut j1 = 0;
for i in 0..h {
let j2 = j1 + t - 1;
let s = psi_inv_rev[h + i];
for j in j1..=j2 {
let u = a[j];
let v = a[j + t];
a[j] = u + v;
a[j + t] = (u - v) * s;
}
j1 += 2 * t;
}
t <<= 1;
m >>= 1;
}
for ai in a.iter_mut() {
*ai *= ninv;
}
}
fn split_fft(f: &[Self], psi_inv_rev: &[Self]) -> (Vec<Self>, Vec<Self>) {
let n_over_2 = f.len() / 2;
let mut f0 = vec![Self::zero(); n_over_2];
let mut f1 = vec![Self::zero(); n_over_2];
let two_inv = (Self::one() + Self::one()).inverse_or_zero();
for i in 0..n_over_2 {
let two_i = i * 2;
let two_zeta_inv = two_inv * psi_inv_rev[n_over_2 + i];
f0[i] = two_inv * (f[two_i] + f[two_i + 1]);
f1[i] = two_zeta_inv * (f[two_i] - f[two_i + 1]);
}
(f0, f1)
}
fn merge_fft(f0: &[Self], f1: &[Self], psi_rev: &[Self]) -> Vec<Self> {
let n_over_2 = f0.len();
let n = 2 * n_over_2;
let mut f = vec![Self::zero(); n];
for i in 0..n_over_2 {
let two_i = i * 2;
f[two_i] = f0[i] + psi_rev[n_over_2 + i] * f1[i];
f[two_i + 1] = f0[i] - psi_rev[n_over_2 + i] * f1[i];
}
f
}
}
impl CyclotomicFourier for Complex64 {
fn primitive_root_of_unity(n: usize) -> Self {
let angle = 2. * PI / (n as f64);
Complex64::new(f64::cos(angle), f64::sin(angle))
}
/// Custom implementation of CyclotomicFourier::bitreversed_powers for
/// better precision.
fn bitreversed_powers(n: usize) -> Vec<Self> {
let mut array = vec![Self::zero(); n];
let half_circle = PI;
for (i, a) in array.iter_mut().enumerate() {
let angle = (i as f64) * half_circle / (n as f64);
*a = Self::new(f64::cos(angle), f64::sin(angle));
}
Self::bitreverse_array(&mut array);
array
}
/// Custom implementation of CyclotomicFourier::bitreversed_powers_inverse
/// for better precision.
fn bitreversed_powers_inverse(n: usize) -> Vec<Self> {
let mut array = vec![Self::zero(); n];
let half_circle = PI;
for (i, a) in array.iter_mut().enumerate() {
let angle = (i as f64) * half_circle / (n as f64);
*a = Self::new(f64::cos(angle), -f64::sin(angle));
}
Self::bitreverse_array(&mut array);
array
}
}
impl FastFft for Polynomial<Complex64> {
type Field = Complex64;
fn fft_inplace(&mut self) {
let n = self.coefficients.len();
debug_assert!(
(1..=512).contains(&n),
"unsupported: n = {n} not a power of 2 or larger than 512"
);
Complex64::fft(&mut self.coefficients, &COMPLEX_BITREVERSED_POWERS);
}
fn ifft_inplace(&mut self) {
let n = self.coefficients.len();
debug_assert!(
(1..=512).contains(&n),
"unsupported: n = {n} not a power of 2 or larger than 512"
);
let psi_inv_rev: Vec<Complex64> =
COMPLEX_BITREVERSED_POWERS.iter().map(|c| Complex64::new(c.re, -c.im)).collect();
let ninv = Complex64::new(1.0 / (n as f64), 0.0);
Complex64::ifft(&mut self.coefficients, &psi_inv_rev, ninv);
}
fn merge_fft(a: &Self, b: &Self) -> Self {
let n = a.coefficients.len();
debug_assert!(
(1..=512).contains(&n),
"unsupported: n = {n} not a power of 2 or larger than 512"
);
Self {
coefficients: Self::Field::merge_fft(
&a.coefficients,
&b.coefficients,
&COMPLEX_BITREVERSED_POWERS,
),
}
}
fn split_fft(&self) -> (Self, Self) {
let n = self.coefficients.len();
debug_assert!(
(1..=512).contains(&n),
"unsupported: n = {n} not a power of 2 or larger than 512"
);
let psi_inv_rev: Vec<Complex64> =
COMPLEX_BITREVERSED_POWERS.iter().map(|c| Complex64::new(c.re, -c.im)).collect();
let (a, b) = Self::Field::split_fft(&self.coefficients, &psi_inv_rev);
(Self { coefficients: a }, Self { coefficients: b })
}
}
impl FastFft for Polynomial<FalconFelt> {
type Field = FalconFelt;
fn fft_inplace(&mut self) {
let n = self.coefficients.len();
debug_assert!(
(1..=512).contains(&n),
"unsupported: n = {n} not a power of 2 or larger than 512"
);
FalconFelt::fft(&mut self.coefficients, &FELT_BITREVERSED_POWERS);
}
fn ifft_inplace(&mut self) {
let n = self.coefficients.len();
debug_assert!(
(1..=512).contains(&n),
"unsupported: n = {n} not a power of 2 or larger than 512"
);
let ninv = match n {
1 => FELT_NINV_1,
2 => FELT_NINV_2,
4 => FELT_NINV_4,
8 => FELT_NINV_8,
16 => FELT_NINV_16,
32 => FELT_NINV_32,
64 => FELT_NINV_64,
128 => FELT_NINV_128,
256 => FELT_NINV_256,
512 => FELT_NINV_512,
_ => unreachable!("vector length is not power of 2 or larger than 512"),
};
FalconFelt::ifft(&mut self.coefficients, &FELT_BITREVERSED_POWERS_INVERSE, ninv);
}
fn merge_fft(a: &Self, b: &Self) -> Self {
let n = a.coefficients.len();
debug_assert!(
(1..=512).contains(&n),
"unsupported: n = {n} not a power of 2 or larger than 512"
);
Self {
coefficients: Self::Field::merge_fft(
&a.coefficients,
&b.coefficients,
&FELT_BITREVERSED_POWERS,
),
}
}
fn split_fft(&self) -> (Self, Self) {
let n = self.coefficients.len();
debug_assert!(
(1..=512).contains(&n),
"unsupported: n = {n} not a power of 2 or larger than 512"
);
let (a, b) = Self::Field::split_fft(&self.coefficients, &FELT_BITREVERSED_POWERS_INVERSE);
(Self { coefficients: a }, Self { coefficients: b })
}
}
#[allow(clippy::approx_constant)]
const COMPLEX_BITREVERSED_POWERS: [Complex64; 512] = [
Complex64::new(1.0, 0.0),
Complex64::new(0.00000000000000006123233995736766, 1.0),
Complex64::new(0.7071067811865476, 0.7071067811865475),
Complex64::new(-0.7071067811865475, 0.7071067811865476),
Complex64::new(0.9238795325112867, 0.3826834323650898),
Complex64::new(-0.3826834323650897, 0.9238795325112867),
Complex64::new(0.38268343236508984, 0.9238795325112867),
Complex64::new(-0.9238795325112867, 0.3826834323650899),
Complex64::new(0.9807852804032304, 0.19509032201612825),
Complex64::new(-0.1950903220161282, 0.9807852804032304),
Complex64::new(0.5555702330196023, 0.8314696123025452),
Complex64::new(-0.8314696123025453, 0.5555702330196022),
Complex64::new(0.8314696123025452, 0.5555702330196022),
Complex64::new(-0.555570233019602, 0.8314696123025455),
Complex64::new(0.19509032201612833, 0.9807852804032304),
Complex64::new(-0.9807852804032304, 0.1950903220161286),
Complex64::new(0.9951847266721969, 0.0980171403295606),
Complex64::new(-0.09801714032956065, 0.9951847266721969),
Complex64::new(0.6343932841636455, 0.773010453362737),
Complex64::new(-0.773010453362737, 0.6343932841636455),
Complex64::new(0.881921264348355, 0.47139673682599764),
Complex64::new(-0.4713967368259977, 0.881921264348355),
Complex64::new(0.29028467725446233, 0.9569403357322089),
Complex64::new(-0.9569403357322088, 0.2902846772544624),
Complex64::new(0.9569403357322088, 0.29028467725446233),
Complex64::new(-0.29028467725446216, 0.9569403357322089),
Complex64::new(0.4713967368259978, 0.8819212643483549),
Complex64::new(-0.8819212643483549, 0.47139673682599786),
Complex64::new(0.773010453362737, 0.6343932841636455),
Complex64::new(-0.6343932841636454, 0.7730104533627371),
Complex64::new(0.09801714032956077, 0.9951847266721968),
Complex64::new(-0.9951847266721968, 0.09801714032956083),
Complex64::new(0.9987954562051724, 0.049067674327418015),
Complex64::new(-0.04906767432741801, 0.9987954562051724),
Complex64::new(0.6715589548470183, 0.7409511253549591),
Complex64::new(-0.7409511253549589, 0.6715589548470186),
Complex64::new(0.9039892931234433, 0.4275550934302821),
Complex64::new(-0.42755509343028186, 0.9039892931234434),
Complex64::new(0.33688985339222005, 0.9415440651830208),
Complex64::new(-0.9415440651830207, 0.33688985339222033),
Complex64::new(0.970031253194544, 0.24298017990326387),
Complex64::new(-0.24298017990326387, 0.970031253194544),
Complex64::new(0.5141027441932217, 0.8577286100002721),
Complex64::new(-0.857728610000272, 0.5141027441932218),
Complex64::new(0.8032075314806449, 0.5956993044924334),
Complex64::new(-0.5956993044924334, 0.8032075314806449),
Complex64::new(0.14673047445536175, 0.989176509964781),
Complex64::new(-0.989176509964781, 0.1467304744553618),
Complex64::new(0.989176509964781, 0.14673047445536175),
Complex64::new(-0.14673047445536164, 0.989176509964781),
Complex64::new(0.5956993044924335, 0.8032075314806448),
Complex64::new(-0.8032075314806448, 0.5956993044924335),
Complex64::new(0.8577286100002721, 0.5141027441932217),
Complex64::new(-0.5141027441932217, 0.8577286100002721),
Complex64::new(0.24298017990326398, 0.970031253194544),
Complex64::new(-0.970031253194544, 0.24298017990326407),
Complex64::new(0.9415440651830208, 0.33688985339222005),
Complex64::new(-0.33688985339221994, 0.9415440651830208),
Complex64::new(0.4275550934302822, 0.9039892931234433),
Complex64::new(-0.9039892931234433, 0.42755509343028203),
Complex64::new(0.7409511253549591, 0.6715589548470183),
Complex64::new(-0.6715589548470184, 0.740951125354959),
Complex64::new(0.049067674327418126, 0.9987954562051724),
Complex64::new(-0.9987954562051724, 0.049067674327417966),
Complex64::new(0.9996988186962042, 0.024541228522912288),
Complex64::new(-0.024541228522912142, 0.9996988186962042),
Complex64::new(0.6895405447370669, 0.7242470829514669),
Complex64::new(-0.7242470829514668, 0.689540544737067),
Complex64::new(0.9142097557035307, 0.40524131400498986),
Complex64::new(-0.40524131400498975, 0.9142097557035307),
Complex64::new(0.3598950365349883, 0.9329927988347388),
Complex64::new(-0.9329927988347388, 0.35989503653498833),
Complex64::new(0.9757021300385286, 0.2191012401568698),
Complex64::new(-0.21910124015686966, 0.9757021300385286),
Complex64::new(0.5349976198870973, 0.844853565249707),
Complex64::new(-0.8448535652497071, 0.5349976198870972),
Complex64::new(0.8175848131515837, 0.5758081914178453),
Complex64::new(-0.5758081914178453, 0.8175848131515837),
Complex64::new(0.17096188876030136, 0.9852776423889412),
Complex64::new(-0.9852776423889412, 0.17096188876030122),
Complex64::new(0.99247953459871, 0.1224106751992162),
Complex64::new(-0.12241067519921615, 0.99247953459871),
Complex64::new(0.6152315905806268, 0.7883464276266062),
Complex64::new(-0.7883464276266062, 0.6152315905806269),
Complex64::new(0.8700869911087115, 0.49289819222978404),
Complex64::new(-0.492898192229784, 0.8700869911087115),
Complex64::new(0.2667127574748984, 0.9637760657954398),
Complex64::new(-0.9637760657954398, 0.2667127574748985),
Complex64::new(0.9495281805930367, 0.3136817403988915),
Complex64::new(-0.3136817403988914, 0.9495281805930367),
Complex64::new(0.4496113296546066, 0.8932243011955153),
Complex64::new(-0.8932243011955152, 0.4496113296546069),
Complex64::new(0.7572088465064846, 0.6531728429537768),
Complex64::new(-0.6531728429537765, 0.7572088465064847),
Complex64::new(0.07356456359966745, 0.9972904566786902),
Complex64::new(-0.9972904566786902, 0.07356456359966773),
Complex64::new(0.9972904566786902, 0.07356456359966743),
Complex64::new(-0.07356456359966733, 0.9972904566786902),
Complex64::new(0.6531728429537768, 0.7572088465064845),
Complex64::new(-0.7572088465064846, 0.6531728429537766),
Complex64::new(0.8932243011955153, 0.44961132965460654),
Complex64::new(-0.4496113296546067, 0.8932243011955152),
Complex64::new(0.3136817403988916, 0.9495281805930367),
Complex64::new(-0.9495281805930367, 0.3136817403988914),
Complex64::new(0.9637760657954398, 0.26671275747489837),
Complex64::new(-0.2667127574748983, 0.9637760657954398),
Complex64::new(0.4928981922297841, 0.8700869911087113),
Complex64::new(-0.8700869911087113, 0.49289819222978415),
Complex64::new(0.7883464276266063, 0.6152315905806268),
Complex64::new(-0.6152315905806267, 0.7883464276266063),
Complex64::new(0.12241067519921628, 0.99247953459871),
Complex64::new(-0.99247953459871, 0.12241067519921635),
Complex64::new(0.9852776423889412, 0.17096188876030122),
Complex64::new(-0.17096188876030124, 0.9852776423889412),
Complex64::new(0.5758081914178453, 0.8175848131515837),
Complex64::new(-0.8175848131515836, 0.5758081914178454),
Complex64::new(0.8448535652497071, 0.5349976198870972),
Complex64::new(-0.534997619887097, 0.8448535652497072),
Complex64::new(0.21910124015686977, 0.9757021300385286),
Complex64::new(-0.9757021300385285, 0.21910124015687005),
Complex64::new(0.932992798834739, 0.3598950365349881),
Complex64::new(-0.35989503653498817, 0.9329927988347388),
Complex64::new(0.40524131400498986, 0.9142097557035307),
Complex64::new(-0.9142097557035307, 0.4052413140049899),
Complex64::new(0.724247082951467, 0.6895405447370668),
Complex64::new(-0.6895405447370669, 0.7242470829514669),
Complex64::new(0.024541228522912264, 0.9996988186962042),
Complex64::new(-0.9996988186962042, 0.024541228522912326),
Complex64::new(0.9999247018391445, 0.012271538285719925),
Complex64::new(-0.012271538285719823, 0.9999247018391445),
Complex64::new(0.6983762494089729, 0.7157308252838186),
Complex64::new(-0.7157308252838186, 0.6983762494089729),
Complex64::new(0.9191138516900578, 0.3939920400610481),
Complex64::new(-0.393992040061048, 0.9191138516900578),
Complex64::new(0.3713171939518376, 0.9285060804732155),
Complex64::new(-0.9285060804732155, 0.3713171939518377),
Complex64::new(0.9783173707196277, 0.20711137619221856),
Complex64::new(-0.20711137619221845, 0.9783173707196277),
Complex64::new(0.5453249884220465, 0.838224705554838),
Complex64::new(-0.8382247055548381, 0.5453249884220464),
Complex64::new(0.8245893027850253, 0.5657318107836131),
Complex64::new(-0.5657318107836132, 0.8245893027850252),
Complex64::new(0.18303988795514106, 0.9831054874312163),
Complex64::new(-0.9831054874312163, 0.1830398879551409),
Complex64::new(0.9939069700023561, 0.11022220729388306),
Complex64::new(-0.11022220729388306, 0.9939069700023561),
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Complex64::new(-0.042938256934940834, 0.9990777277526454),
Complex64::new(0.676092703575316, 0.7368165688773698),
Complex64::new(-0.7368165688773699, 0.6760927035753159),
Complex64::new(0.9065957045149153, 0.4220002707997997),
Complex64::new(-0.4220002707997997, 0.9065957045149153),
Complex64::new(0.3426607173119944, 0.9394592236021899),
Complex64::new(-0.9394592236021899, 0.34266071731199443),
Complex64::new(0.9715038909862518, 0.2370236059943672),
Complex64::new(-0.23702360599436723, 0.9715038909862518),
Complex64::new(0.5193559901655895, 0.8545579883654005),
Complex64::new(-0.8545579883654004, 0.5193559901655898),
Complex64::new(0.8068475535437993, 0.5907597018588742),
Complex64::new(-0.590759701858874, 0.8068475535437994),
Complex64::new(0.1527971852584434, 0.9882575677307495),
Complex64::new(-0.9882575677307495, 0.15279718525844369),
Complex64::new(0.9900582102622971, 0.1406582393328492),
Complex64::new(-0.14065823933284913, 0.9900582102622971),
Complex64::new(0.600616479383869, 0.799537269107905),
Complex64::new(-0.7995372691079051, 0.6006164793838689),
Complex64::new(0.8608669386377673, 0.508830142543107),
Complex64::new(-0.5088301425431071, 0.8608669386377672),
Complex64::new(0.24892760574572026, 0.9685220942744173),
Complex64::new(-0.9685220942744174, 0.2489276057457201),
Complex64::new(0.9435934581619604, 0.33110630575987643),
Complex64::new(-0.3311063057598763, 0.9435934581619604),
Complex64::new(0.433093818853152, 0.901348847046022),
Complex64::new(-0.9013488470460219, 0.43309381885315207),
Complex64::new(0.7450577854414661, 0.6669999223036375),
Complex64::new(-0.6669999223036374, 0.7450577854414661),
Complex64::new(0.05519524434969003, 0.9984755805732948),
Complex64::new(-0.9984755805732948, 0.055195244349690094),
Complex64::new(0.9957674144676598, 0.09190895649713272),
Complex64::new(-0.09190895649713257, 0.9957674144676598),
Complex64::new(0.6391244448637757, 0.7691033376455796),
Complex64::new(-0.7691033376455795, 0.6391244448637758),
Complex64::new(0.8847970984309378, 0.4659764957679662),
Complex64::new(-0.465976495767966, 0.8847970984309379),
Complex64::new(0.29615088824362396, 0.9551411683057707),
Complex64::new(-0.9551411683057707, 0.296150888243624),
Complex64::new(0.9587034748958716, 0.2844075372112719),
Complex64::new(-0.2844075372112717, 0.9587034748958716),
Complex64::new(0.47679923006332225, 0.8790122264286334),
Complex64::new(-0.8790122264286335, 0.4767992300633221),
Complex64::new(0.7768884656732324, 0.629638238914927),
Complex64::new(-0.6296382389149271, 0.7768884656732324),
Complex64::new(0.10412163387205473, 0.9945645707342554),
Complex64::new(-0.9945645707342554, 0.10412163387205457),
Complex64::new(0.9819638691095552, 0.1890686641498062),
Complex64::new(-0.18906866414980616, 0.9819638691095552),
Complex64::new(0.560661576197336, 0.8280450452577558),
Complex64::new(-0.8280450452577557, 0.5606615761973361),
Complex64::new(0.83486287498638, 0.5504579729366048),
Complex64::new(-0.5504579729366047, 0.8348628749863801),
Complex64::new(0.20110463484209196, 0.9795697656854405),
Complex64::new(-0.9795697656854405, 0.201104634842092),
Complex64::new(0.9262102421383114, 0.37700741021641826),
Complex64::new(-0.3770074102164182, 0.9262102421383114),
Complex64::new(0.3883450466988263, 0.9215140393420419),
Complex64::new(-0.9215140393420418, 0.3883450466988266),
Complex64::new(0.7114321957452164, 0.7027547444572253),
Complex64::new(-0.7027547444572251, 0.7114321957452167),
Complex64::new(0.006135884649154515, 0.9999811752826011),
Complex64::new(-0.9999811752826011, 0.006135884649154799),
];
const FELT_BITREVERSED_POWERS: [FalconFelt; 512] = [
FalconFelt::new(1),
FalconFelt::new(1479),
FalconFelt::new(8246),
FalconFelt::new(5146),
FalconFelt::new(4134),
FalconFelt::new(6553),
FalconFelt::new(11567),
FalconFelt::new(1305),
FalconFelt::new(5860),
FalconFelt::new(3195),
FalconFelt::new(1212),
FalconFelt::new(10643),
FalconFelt::new(3621),
FalconFelt::new(9744),
FalconFelt::new(8785),
FalconFelt::new(3542),
FalconFelt::new(7311),
FalconFelt::new(10938),
FalconFelt::new(8961),
FalconFelt::new(5777),
FalconFelt::new(5023),
FalconFelt::new(6461),
FalconFelt::new(5728),
FalconFelt::new(4591),
FalconFelt::new(3006),
FalconFelt::new(9545),
FalconFelt::new(563),
FalconFelt::new(9314),
FalconFelt::new(2625),
FalconFelt::new(11340),
FalconFelt::new(4821),
FalconFelt::new(2639),
FalconFelt::new(12149),
FalconFelt::new(1853),
FalconFelt::new(726),
FalconFelt::new(4611),
FalconFelt::new(11112),
FalconFelt::new(4255),
FalconFelt::new(2768),
FalconFelt::new(1635),
FalconFelt::new(2963),
FalconFelt::new(7393),
FalconFelt::new(2366),
FalconFelt::new(9238),
FalconFelt::new(9198),
FalconFelt::new(12208),
FalconFelt::new(11289),
FalconFelt::new(7969),
FalconFelt::new(8736),
FalconFelt::new(4805),
FalconFelt::new(11227),
FalconFelt::new(2294),
FalconFelt::new(9542),
FalconFelt::new(4846),
FalconFelt::new(9154),
FalconFelt::new(8577),
FalconFelt::new(9275),
FalconFelt::new(3201),
FalconFelt::new(7203),
FalconFelt::new(10963),
FalconFelt::new(1170),
FalconFelt::new(9970),
FalconFelt::new(955),
FalconFelt::new(11499),
FalconFelt::new(8340),
FalconFelt::new(8993),
FalconFelt::new(2396),
FalconFelt::new(4452),
FalconFelt::new(6915),
FalconFelt::new(2837),
FalconFelt::new(130),
FalconFelt::new(7935),
FalconFelt::new(11336),
FalconFelt::new(3748),
FalconFelt::new(6522),
FalconFelt::new(11462),
FalconFelt::new(5067),
FalconFelt::new(10092),
FalconFelt::new(12171),
FalconFelt::new(9813),
FalconFelt::new(8011),
FalconFelt::new(1673),
FalconFelt::new(5331),
FalconFelt::new(7300),
FalconFelt::new(10908),
FalconFelt::new(9764),
FalconFelt::new(4177),
FalconFelt::new(8705),
FalconFelt::new(480),
FalconFelt::new(9447),
FalconFelt::new(1022),
FalconFelt::new(12280),
FalconFelt::new(5791),
FalconFelt::new(11745),
FalconFelt::new(9821),
FalconFelt::new(11950),
FalconFelt::new(12144),
FalconFelt::new(6747),
FalconFelt::new(8652),
FalconFelt::new(3459),
FalconFelt::new(2731),
FalconFelt::new(8357),
FalconFelt::new(6378),
FalconFelt::new(7399),
FalconFelt::new(10530),
FalconFelt::new(3707),
FalconFelt::new(8595),
FalconFelt::new(5179),
FalconFelt::new(3382),
FalconFelt::new(355),
FalconFelt::new(4231),
FalconFelt::new(2548),
FalconFelt::new(9048),
FalconFelt::new(11560),
FalconFelt::new(3289),
FalconFelt::new(10276),
FalconFelt::new(9005),
FalconFelt::new(9408),
FalconFelt::new(5092),
FalconFelt::new(10200),
FalconFelt::new(6534),
FalconFelt::new(4632),
FalconFelt::new(4388),
FalconFelt::new(1260),
FalconFelt::new(334),
FalconFelt::new(2426),
FalconFelt::new(1428),
FalconFelt::new(10593),
FalconFelt::new(3400),
FalconFelt::new(2399),
FalconFelt::new(5191),
FalconFelt::new(9153),
FalconFelt::new(9273),
FalconFelt::new(243),
FalconFelt::new(3000),
FalconFelt::new(671),
FalconFelt::new(3531),
FalconFelt::new(11813),
FalconFelt::new(3985),
FalconFelt::new(7384),
FalconFelt::new(10111),
FalconFelt::new(10745),
FalconFelt::new(6730),
FalconFelt::new(11869),
FalconFelt::new(9042),
FalconFelt::new(2686),
FalconFelt::new(2969),
FalconFelt::new(3978),
FalconFelt::new(8779),
FalconFelt::new(6957),
FalconFelt::new(9424),
FalconFelt::new(2370),
FalconFelt::new(8241),
FalconFelt::new(10040),
FalconFelt::new(9405),
FalconFelt::new(11136),
FalconFelt::new(3186),
FalconFelt::new(5407),
FalconFelt::new(10163),
FalconFelt::new(1630),
FalconFelt::new(3271),
FalconFelt::new(8232),
FalconFelt::new(10600),
FalconFelt::new(8925),
FalconFelt::new(4414),
FalconFelt::new(2847),
FalconFelt::new(10115),
FalconFelt::new(4372),
FalconFelt::new(9509),
FalconFelt::new(5195),
FalconFelt::new(7394),
FalconFelt::new(10805),
FalconFelt::new(9984),
FalconFelt::new(7247),
FalconFelt::new(4053),
FalconFelt::new(9644),
FalconFelt::new(12176),
FalconFelt::new(4919),
FalconFelt::new(2166),
FalconFelt::new(8374),
FalconFelt::new(12129),
FalconFelt::new(9140),
FalconFelt::new(7852),
FalconFelt::new(3),
FalconFelt::new(1426),
FalconFelt::new(7635),
FalconFelt::new(10512),
FalconFelt::new(1663),
FalconFelt::new(8653),
FalconFelt::new(4938),
FalconFelt::new(2704),
FalconFelt::new(5291),
FalconFelt::new(5277),
FalconFelt::new(1168),
FalconFelt::new(11082),
FalconFelt::new(9041),
FalconFelt::new(2143),
FalconFelt::new(11224),
FalconFelt::new(11885),
FalconFelt::new(4645),
FalconFelt::new(4096),
FalconFelt::new(11796),
FalconFelt::new(5444),
FalconFelt::new(2381),
FalconFelt::new(10911),
FalconFelt::new(1912),
FalconFelt::new(4337),
FalconFelt::new(11854),
FalconFelt::new(4976),
FalconFelt::new(10682),
FalconFelt::new(11414),
FalconFelt::new(8509),
FalconFelt::new(11287),
FalconFelt::new(5011),
FalconFelt::new(8005),
FalconFelt::new(5088),
FalconFelt::new(9852),
FalconFelt::new(8643),
FalconFelt::new(9302),
FalconFelt::new(6267),
FalconFelt::new(2422),
FalconFelt::new(6039),
FalconFelt::new(2187),
FalconFelt::new(2566),
FalconFelt::new(10849),
FalconFelt::new(8526),
FalconFelt::new(9223),
FalconFelt::new(27),
FalconFelt::new(7205),
FalconFelt::new(1632),
FalconFelt::new(7404),
FalconFelt::new(1017),
FalconFelt::new(4143),
FalconFelt::new(7575),
FalconFelt::new(12047),
FalconFelt::new(10752),
FalconFelt::new(8585),
FalconFelt::new(2678),
FalconFelt::new(7270),
FalconFelt::new(11744),
FalconFelt::new(3833),
FalconFelt::new(3778),
FalconFelt::new(11899),
FalconFelt::new(773),
FalconFelt::new(5101),
FalconFelt::new(11222),
FalconFelt::new(9888),
FalconFelt::new(442),
FalconFelt::new(9377),
FalconFelt::new(6591),
FalconFelt::new(354),
FalconFelt::new(7428),
FalconFelt::new(5012),
FalconFelt::new(2481),
FalconFelt::new(1045),
FalconFelt::new(9430),
FalconFelt::new(10302),
FalconFelt::new(10587),
FalconFelt::new(8724),
FalconFelt::new(11635),
FalconFelt::new(7083),
FalconFelt::new(5529),
FalconFelt::new(9090),
FalconFelt::new(12233),
FalconFelt::new(6152),
FalconFelt::new(4948),
FalconFelt::new(400),
FalconFelt::new(1728),
FalconFelt::new(6427),
FalconFelt::new(6136),
FalconFelt::new(6874),
FalconFelt::new(3643),
FalconFelt::new(10930),
FalconFelt::new(5435),
FalconFelt::new(1254),
FalconFelt::new(11316),
FalconFelt::new(10256),
FalconFelt::new(3998),
FalconFelt::new(10367),
FalconFelt::new(8410),
FalconFelt::new(11821),
FalconFelt::new(8301),
FalconFelt::new(11907),
FalconFelt::new(316),
FalconFelt::new(6950),
FalconFelt::new(5446),
FalconFelt::new(6093),
FalconFelt::new(3710),
FalconFelt::new(7822),
FalconFelt::new(4789),
FalconFelt::new(7540),
FalconFelt::new(5537),
FalconFelt::new(3789),
FalconFelt::new(147),
FalconFelt::new(5456),
FalconFelt::new(7840),
FalconFelt::new(11239),
FalconFelt::new(7753),
FalconFelt::new(5445),
FalconFelt::new(3860),
FalconFelt::new(9606),
FalconFelt::new(1190),
FalconFelt::new(8471),
FalconFelt::new(6118),
FalconFelt::new(5925),
FalconFelt::new(1018),
FalconFelt::new(8775),
FalconFelt::new(1041),
FalconFelt::new(1973),
FalconFelt::new(5574),
FalconFelt::new(11011),
FalconFelt::new(2344),
FalconFelt::new(4075),
FalconFelt::new(5315),
FalconFelt::new(4324),
FalconFelt::new(4916),
FalconFelt::new(10120),
FalconFelt::new(11767),
FalconFelt::new(7210),
FalconFelt::new(9027),
FalconFelt::new(6281),
FalconFelt::new(11404),
FalconFelt::new(7280),
FalconFelt::new(1956),
FalconFelt::new(11286),
FalconFelt::new(3532),
FalconFelt::new(12048),
FalconFelt::new(12231),
FalconFelt::new(1105),
FalconFelt::new(12147),
FalconFelt::new(5681),
FalconFelt::new(8812),
FalconFelt::new(8851),
FalconFelt::new(2844),
FalconFelt::new(975),
FalconFelt::new(4212),
FalconFelt::new(8687),
FalconFelt::new(6068),
FalconFelt::new(421),
FalconFelt::new(8209),
FalconFelt::new(3600),
FalconFelt::new(3263),
FalconFelt::new(7665),
FalconFelt::new(6077),
FalconFelt::new(4782),
FalconFelt::new(6403),
FalconFelt::new(9260),
FalconFelt::new(5594),
FalconFelt::new(8076),
FalconFelt::new(11785),
FalconFelt::new(605),
FalconFelt::new(9987),
FalconFelt::new(5468),
FalconFelt::new(1010),
FalconFelt::new(787),
FalconFelt::new(8807),
FalconFelt::new(5241),
FalconFelt::new(9369),
FalconFelt::new(9162),
FalconFelt::new(8120),
FalconFelt::new(5057),
FalconFelt::new(7591),
FalconFelt::new(3445),
FalconFelt::new(7509),
FalconFelt::new(2049),
FalconFelt::new(7377),
FalconFelt::new(10968),
FalconFelt::new(192),
FalconFelt::new(431),
FalconFelt::new(10710),
FalconFelt::new(2505),
FalconFelt::new(5906),
FalconFelt::new(12138),
FalconFelt::new(10162),
FalconFelt::new(8332),
FalconFelt::new(9450),
FalconFelt::new(6415),
FalconFelt::new(677),
FalconFelt::new(6234),
FalconFelt::new(3336),
FalconFelt::new(12237),
FalconFelt::new(9115),
FalconFelt::new(1323),
FalconFelt::new(2766),
FalconFelt::new(3150),
FalconFelt::new(1319),
FalconFelt::new(8243),
FalconFelt::new(709),
FalconFelt::new(8049),
FalconFelt::new(8719),
FalconFelt::new(11454),
FalconFelt::new(6224),
FalconFelt::new(922),
FalconFelt::new(11848),
FalconFelt::new(8210),
FalconFelt::new(1058),
FalconFelt::new(1958),
FalconFelt::new(7967),
FalconFelt::new(10211),
FalconFelt::new(11177),
FalconFelt::new(64),
FalconFelt::new(8633),
FalconFelt::new(11606),
FalconFelt::new(9830),
FalconFelt::new(6507),
FalconFelt::new(1566),
FalconFelt::new(2948),
FalconFelt::new(9786),
FalconFelt::new(6370),
FalconFelt::new(7856),
FalconFelt::new(3834),
FalconFelt::new(5257),
FalconFelt::new(10542),
FalconFelt::new(9166),
FalconFelt::new(9235),
FalconFelt::new(5486),
FalconFelt::new(1404),
FalconFelt::new(11964),
FalconFelt::new(1146),
FalconFelt::new(11341),
FalconFelt::new(3728),
FalconFelt::new(8240),
FalconFelt::new(6299),
FalconFelt::new(1159),
FalconFelt::new(6099),
FalconFelt::new(295),
FalconFelt::new(5766),
FalconFelt::new(11637),
FalconFelt::new(8527),
FalconFelt::new(2919),
FalconFelt::new(8273),
FalconFelt::new(8212),
FalconFelt::new(3329),
FalconFelt::new(7991),
FalconFelt::new(9597),
FalconFelt::new(168),
FalconFelt::new(10695),
FalconFelt::new(1962),
FalconFelt::new(5106),
FalconFelt::new(6328),
FalconFelt::new(5297),
FalconFelt::new(6170),
FalconFelt::new(3956),
FalconFelt::new(1360),
FalconFelt::new(11089),
FalconFelt::new(7105),
FalconFelt::new(9734),
FalconFelt::new(6167),
FalconFelt::new(9407),
FalconFelt::new(1805),
FalconFelt::new(1954),
FalconFelt::new(2051),
FalconFelt::new(6142),
FalconFelt::new(2447),
FalconFelt::new(3963),
FalconFelt::new(11713),
FalconFelt::new(8855),
FalconFelt::new(8760),
FalconFelt::new(9381),
FalconFelt::new(218),
FalconFelt::new(9928),
FalconFelt::new(10446),
FalconFelt::new(9259),
FalconFelt::new(4115),
FalconFelt::new(5333),
FalconFelt::new(10258),
FalconFelt::new(5876),
FalconFelt::new(2281),
FalconFelt::new(156),
FalconFelt::new(9522),
FalconFelt::new(8320),
FalconFelt::new(3991),
FalconFelt::new(453),
FalconFelt::new(6381),
FalconFelt::new(11871),
FalconFelt::new(8517),
FalconFelt::new(4774),
FalconFelt::new(6860),
FalconFelt::new(4737),
FalconFelt::new(1293),
FalconFelt::new(10232),
FalconFelt::new(5369),
FalconFelt::new(9087),
FalconFelt::new(7796),
FalconFelt::new(350),
FalconFelt::new(1512),
FalconFelt::new(10474),
FalconFelt::new(6906),
FalconFelt::new(1489),
FalconFelt::new(2500),
FalconFelt::new(1583),
FalconFelt::new(6347),
FalconFelt::new(11026),
FalconFelt::new(12240),
FalconFelt::new(6374),
FalconFelt::new(1483),
FalconFelt::new(3009),
FalconFelt::new(1693),
FalconFelt::new(723),
FalconFelt::new(174),
FalconFelt::new(2738),
FalconFelt::new(6421),
FalconFelt::new(2655),
FalconFelt::new(6554),
FalconFelt::new(10314),
FalconFelt::new(3757),
FalconFelt::new(9364),
FalconFelt::new(11942),
FalconFelt::new(7535),
FalconFelt::new(10431),
FalconFelt::new(426),
FalconFelt::new(3315),
];
const FELT_BITREVERSED_POWERS_INVERSE: [FalconFelt; 512] = [
FalconFelt::new(1),
FalconFelt::new(10810),
FalconFelt::new(7143),
FalconFelt::new(4043),
FalconFelt::new(10984),
FalconFelt::new(722),
FalconFelt::new(5736),
FalconFelt::new(8155),
FalconFelt::new(8747),
FalconFelt::new(3504),
FalconFelt::new(2545),
FalconFelt::new(8668),
FalconFelt::new(1646),
FalconFelt::new(11077),
FalconFelt::new(9094),
FalconFelt::new(6429),
FalconFelt::new(9650),
FalconFelt::new(7468),
FalconFelt::new(949),
FalconFelt::new(9664),
FalconFelt::new(2975),
FalconFelt::new(11726),
FalconFelt::new(2744),
FalconFelt::new(9283),
FalconFelt::new(7698),
FalconFelt::new(6561),
FalconFelt::new(5828),
FalconFelt::new(7266),
FalconFelt::new(6512),
FalconFelt::new(3328),
FalconFelt::new(1351),
FalconFelt::new(4978),
FalconFelt::new(790),
FalconFelt::new(11334),
FalconFelt::new(2319),
FalconFelt::new(11119),
FalconFelt::new(1326),
FalconFelt::new(5086),
FalconFelt::new(9088),
FalconFelt::new(3014),
FalconFelt::new(3712),
FalconFelt::new(3135),
FalconFelt::new(7443),
FalconFelt::new(2747),
FalconFelt::new(9995),
FalconFelt::new(1062),
FalconFelt::new(7484),
FalconFelt::new(3553),
FalconFelt::new(4320),
FalconFelt::new(1000),
FalconFelt::new(81),
FalconFelt::new(3091),
FalconFelt::new(3051),
FalconFelt::new(9923),
FalconFelt::new(4896),
FalconFelt::new(9326),
FalconFelt::new(10654),
FalconFelt::new(9521),
FalconFelt::new(8034),
FalconFelt::new(1177),
FalconFelt::new(7678),
FalconFelt::new(11563),
FalconFelt::new(10436),
FalconFelt::new(140),
FalconFelt::new(1696),
FalconFelt::new(10861),
FalconFelt::new(9863),
FalconFelt::new(11955),
FalconFelt::new(11029),
FalconFelt::new(7901),
FalconFelt::new(7657),
FalconFelt::new(5755),
FalconFelt::new(2089),
FalconFelt::new(7197),
FalconFelt::new(2881),
FalconFelt::new(3284),
FalconFelt::new(2013),
FalconFelt::new(9000),
FalconFelt::new(729),
FalconFelt::new(3241),
FalconFelt::new(9741),
FalconFelt::new(8058),
FalconFelt::new(11934),
FalconFelt::new(8907),
FalconFelt::new(7110),
FalconFelt::new(3694),
FalconFelt::new(8582),
FalconFelt::new(1759),
FalconFelt::new(4890),
FalconFelt::new(5911),
FalconFelt::new(3932),
FalconFelt::new(9558),
FalconFelt::new(8830),
FalconFelt::new(3637),
FalconFelt::new(5542),
FalconFelt::new(145),
FalconFelt::new(339),
FalconFelt::new(2468),
FalconFelt::new(544),
FalconFelt::new(6498),
FalconFelt::new(9),
FalconFelt::new(11267),
FalconFelt::new(2842),
FalconFelt::new(11809),
FalconFelt::new(3584),
FalconFelt::new(8112),
FalconFelt::new(2525),
FalconFelt::new(1381),
FalconFelt::new(4989),
FalconFelt::new(6958),
FalconFelt::new(10616),
FalconFelt::new(4278),
FalconFelt::new(2476),
FalconFelt::new(118),
FalconFelt::new(2197),
FalconFelt::new(7222),
FalconFelt::new(827),
FalconFelt::new(5767),
FalconFelt::new(8541),
FalconFelt::new(953),
FalconFelt::new(4354),
FalconFelt::new(12159),
FalconFelt::new(9452),
FalconFelt::new(5374),
FalconFelt::new(7837),
FalconFelt::new(9893),
FalconFelt::new(3296),
FalconFelt::new(3949),
FalconFelt::new(2859),
FalconFelt::new(11244),
FalconFelt::new(9808),
FalconFelt::new(7277),
FalconFelt::new(4861),
FalconFelt::new(11935),
FalconFelt::new(5698),
FalconFelt::new(2912),
FalconFelt::new(11847),
FalconFelt::new(2401),
FalconFelt::new(1067),
FalconFelt::new(7188),
FalconFelt::new(11516),
FalconFelt::new(390),
FalconFelt::new(8511),
FalconFelt::new(8456),
FalconFelt::new(545),
FalconFelt::new(5019),
FalconFelt::new(9611),
FalconFelt::new(3704),
FalconFelt::new(1537),
FalconFelt::new(242),
FalconFelt::new(4714),
FalconFelt::new(8146),
FalconFelt::new(11272),
FalconFelt::new(4885),
FalconFelt::new(10657),
FalconFelt::new(5084),
FalconFelt::new(12262),
FalconFelt::new(3066),
FalconFelt::new(3763),
FalconFelt::new(1440),
FalconFelt::new(9723),
FalconFelt::new(10102),
FalconFelt::new(6250),
FalconFelt::new(9867),
FalconFelt::new(6022),
FalconFelt::new(2987),
FalconFelt::new(3646),
FalconFelt::new(2437),
FalconFelt::new(7201),
FalconFelt::new(4284),
FalconFelt::new(7278),
FalconFelt::new(1002),
FalconFelt::new(3780),
FalconFelt::new(875),
FalconFelt::new(1607),
FalconFelt::new(7313),
FalconFelt::new(435),
FalconFelt::new(7952),
FalconFelt::new(10377),
FalconFelt::new(1378),
FalconFelt::new(9908),
FalconFelt::new(6845),
FalconFelt::new(493),
FalconFelt::new(8193),
FalconFelt::new(7644),
FalconFelt::new(404),
FalconFelt::new(1065),
FalconFelt::new(10146),
FalconFelt::new(3248),
FalconFelt::new(1207),
FalconFelt::new(11121),
FalconFelt::new(7012),
FalconFelt::new(6998),
FalconFelt::new(9585),
FalconFelt::new(7351),
FalconFelt::new(3636),
FalconFelt::new(10626),
FalconFelt::new(1777),
FalconFelt::new(4654),
FalconFelt::new(10863),
FalconFelt::new(12286),
FalconFelt::new(4437),
FalconFelt::new(3149),
FalconFelt::new(160),
FalconFelt::new(3915),
FalconFelt::new(10123),
FalconFelt::new(7370),
FalconFelt::new(113),
FalconFelt::new(2645),
FalconFelt::new(8236),
FalconFelt::new(5042),
FalconFelt::new(2305),
FalconFelt::new(1484),
FalconFelt::new(4895),
FalconFelt::new(7094),
FalconFelt::new(2780),
FalconFelt::new(7917),
FalconFelt::new(2174),
FalconFelt::new(9442),
FalconFelt::new(7875),
FalconFelt::new(3364),
FalconFelt::new(1689),
FalconFelt::new(4057),
FalconFelt::new(9018),
FalconFelt::new(10659),
FalconFelt::new(2126),
FalconFelt::new(6882),
FalconFelt::new(9103),
FalconFelt::new(1153),
FalconFelt::new(2884),
FalconFelt::new(2249),
FalconFelt::new(4048),
FalconFelt::new(9919),
FalconFelt::new(2865),
FalconFelt::new(5332),
FalconFelt::new(3510),
FalconFelt::new(8311),
FalconFelt::new(9320),
FalconFelt::new(9603),
FalconFelt::new(3247),
FalconFelt::new(420),
FalconFelt::new(5559),
FalconFelt::new(1544),
FalconFelt::new(2178),
FalconFelt::new(4905),
FalconFelt::new(8304),
FalconFelt::new(476),
FalconFelt::new(8758),
FalconFelt::new(11618),
FalconFelt::new(9289),
FalconFelt::new(12046),
FalconFelt::new(3016),
FalconFelt::new(3136),
FalconFelt::new(7098),
FalconFelt::new(9890),
FalconFelt::new(8889),
FalconFelt::new(8974),
FalconFelt::new(11863),
FalconFelt::new(1858),
FalconFelt::new(4754),
FalconFelt::new(347),
FalconFelt::new(2925),
FalconFelt::new(8532),
FalconFelt::new(1975),
FalconFelt::new(5735),
FalconFelt::new(9634),
FalconFelt::new(5868),
FalconFelt::new(9551),
FalconFelt::new(12115),
FalconFelt::new(11566),
FalconFelt::new(10596),
FalconFelt::new(9280),
FalconFelt::new(10806),
FalconFelt::new(5915),
FalconFelt::new(49),
FalconFelt::new(1263),
FalconFelt::new(5942),
FalconFelt::new(10706),
FalconFelt::new(9789),
FalconFelt::new(10800),
FalconFelt::new(5383),
FalconFelt::new(1815),
FalconFelt::new(10777),
FalconFelt::new(11939),
FalconFelt::new(4493),
FalconFelt::new(3202),
FalconFelt::new(6920),
FalconFelt::new(2057),
FalconFelt::new(10996),
FalconFelt::new(7552),
FalconFelt::new(5429),
FalconFelt::new(7515),
FalconFelt::new(3772),
FalconFelt::new(418),
FalconFelt::new(5908),
FalconFelt::new(11836),
FalconFelt::new(8298),
FalconFelt::new(3969),
FalconFelt::new(2767),
FalconFelt::new(12133),
FalconFelt::new(10008),
FalconFelt::new(6413),
FalconFelt::new(2031),
FalconFelt::new(6956),
FalconFelt::new(8174),
FalconFelt::new(3030),
FalconFelt::new(1843),
FalconFelt::new(2361),
FalconFelt::new(12071),
FalconFelt::new(2908),
FalconFelt::new(3529),
FalconFelt::new(3434),
FalconFelt::new(576),
FalconFelt::new(8326),
FalconFelt::new(9842),
FalconFelt::new(6147),
FalconFelt::new(10238),
FalconFelt::new(10335),
FalconFelt::new(10484),
FalconFelt::new(2882),
FalconFelt::new(6122),
FalconFelt::new(2555),
FalconFelt::new(5184),
FalconFelt::new(1200),
FalconFelt::new(10929),
FalconFelt::new(8333),
FalconFelt::new(6119),
FalconFelt::new(6992),
FalconFelt::new(5961),
FalconFelt::new(7183),
FalconFelt::new(10327),
FalconFelt::new(1594),
FalconFelt::new(12121),
FalconFelt::new(2692),
FalconFelt::new(4298),
FalconFelt::new(8960),
FalconFelt::new(4077),
FalconFelt::new(4016),
FalconFelt::new(9370),
FalconFelt::new(3762),
FalconFelt::new(652),
FalconFelt::new(6523),
FalconFelt::new(11994),
FalconFelt::new(6190),
FalconFelt::new(11130),
FalconFelt::new(5990),
FalconFelt::new(4049),
FalconFelt::new(8561),
FalconFelt::new(948),
FalconFelt::new(11143),
FalconFelt::new(325),
FalconFelt::new(10885),
FalconFelt::new(6803),
FalconFelt::new(3054),
FalconFelt::new(3123),
FalconFelt::new(1747),
FalconFelt::new(7032),
FalconFelt::new(8455),
FalconFelt::new(4433),
FalconFelt::new(5919),
FalconFelt::new(2503),
FalconFelt::new(9341),
FalconFelt::new(10723),
FalconFelt::new(5782),
FalconFelt::new(2459),
FalconFelt::new(683),
FalconFelt::new(3656),
FalconFelt::new(12225),
FalconFelt::new(1112),
FalconFelt::new(2078),
FalconFelt::new(4322),
FalconFelt::new(10331),
FalconFelt::new(11231),
FalconFelt::new(4079),
FalconFelt::new(441),
FalconFelt::new(11367),
FalconFelt::new(6065),
FalconFelt::new(835),
FalconFelt::new(3570),
FalconFelt::new(4240),
FalconFelt::new(11580),
FalconFelt::new(4046),
FalconFelt::new(10970),
FalconFelt::new(9139),
FalconFelt::new(9523),
FalconFelt::new(10966),
FalconFelt::new(3174),
FalconFelt::new(52),
FalconFelt::new(8953),
FalconFelt::new(6055),
FalconFelt::new(11612),
FalconFelt::new(5874),
FalconFelt::new(2839),
FalconFelt::new(3957),
FalconFelt::new(2127),
FalconFelt::new(151),
FalconFelt::new(6383),
FalconFelt::new(9784),
FalconFelt::new(1579),
FalconFelt::new(11858),
FalconFelt::new(12097),
FalconFelt::new(1321),
FalconFelt::new(4912),
FalconFelt::new(10240),
FalconFelt::new(4780),
FalconFelt::new(8844),
FalconFelt::new(4698),
FalconFelt::new(7232),
FalconFelt::new(4169),
FalconFelt::new(3127),
FalconFelt::new(2920),
FalconFelt::new(7048),
FalconFelt::new(3482),
FalconFelt::new(11502),
FalconFelt::new(11279),
FalconFelt::new(6821),
FalconFelt::new(2302),
FalconFelt::new(11684),
FalconFelt::new(504),
FalconFelt::new(4213),
FalconFelt::new(6695),
FalconFelt::new(3029),
FalconFelt::new(5886),
FalconFelt::new(7507),
FalconFelt::new(6212),
FalconFelt::new(4624),
FalconFelt::new(9026),
FalconFelt::new(8689),
FalconFelt::new(4080),
FalconFelt::new(11868),
FalconFelt::new(6221),
FalconFelt::new(3602),
FalconFelt::new(8077),
FalconFelt::new(11314),
FalconFelt::new(9445),
FalconFelt::new(3438),
FalconFelt::new(3477),
FalconFelt::new(6608),
FalconFelt::new(142),
FalconFelt::new(11184),
FalconFelt::new(58),
FalconFelt::new(241),
FalconFelt::new(8757),
FalconFelt::new(1003),
FalconFelt::new(10333),
FalconFelt::new(5009),
FalconFelt::new(885),
FalconFelt::new(6008),
FalconFelt::new(3262),
FalconFelt::new(5079),
FalconFelt::new(522),
FalconFelt::new(2169),
FalconFelt::new(7373),
FalconFelt::new(7965),
FalconFelt::new(6974),
FalconFelt::new(8214),
FalconFelt::new(9945),
FalconFelt::new(1278),
FalconFelt::new(6715),
FalconFelt::new(10316),
FalconFelt::new(11248),
FalconFelt::new(3514),
FalconFelt::new(11271),
FalconFelt::new(6364),
FalconFelt::new(6171),
FalconFelt::new(3818),
FalconFelt::new(11099),
FalconFelt::new(2683),
FalconFelt::new(8429),
FalconFelt::new(6844),
FalconFelt::new(4536),
FalconFelt::new(1050),
FalconFelt::new(4449),
FalconFelt::new(6833),
FalconFelt::new(12142),
FalconFelt::new(8500),
FalconFelt::new(6752),
FalconFelt::new(4749),
FalconFelt::new(7500),
FalconFelt::new(4467),
FalconFelt::new(8579),
FalconFelt::new(6196),
FalconFelt::new(6843),
FalconFelt::new(5339),
FalconFelt::new(11973),
FalconFelt::new(382),
FalconFelt::new(3988),
FalconFelt::new(468),
FalconFelt::new(3879),
FalconFelt::new(1922),
FalconFelt::new(8291),
FalconFelt::new(2033),
FalconFelt::new(973),
FalconFelt::new(11035),
FalconFelt::new(6854),
FalconFelt::new(1359),
FalconFelt::new(8646),
FalconFelt::new(5415),
FalconFelt::new(6153),
FalconFelt::new(5862),
FalconFelt::new(10561),
FalconFelt::new(11889),
FalconFelt::new(7341),
FalconFelt::new(6137),
FalconFelt::new(56),
FalconFelt::new(3199),
FalconFelt::new(6760),
FalconFelt::new(5206),
FalconFelt::new(654),
FalconFelt::new(3565),
FalconFelt::new(1702),
FalconFelt::new(1987),
];
const FELT_NINV_1: FalconFelt = FalconFelt::new(1);
const FELT_NINV_2: FalconFelt = FalconFelt::new(6145);
const FELT_NINV_4: FalconFelt = FalconFelt::new(9217);
const FELT_NINV_8: FalconFelt = FalconFelt::new(10753);
const FELT_NINV_16: FalconFelt = FalconFelt::new(11521);
const FELT_NINV_32: FalconFelt = FalconFelt::new(11905);
const FELT_NINV_64: FalconFelt = FalconFelt::new(12097);
const FELT_NINV_128: FalconFelt = FalconFelt::new(12193);
const FELT_NINV_256: FalconFelt = FalconFelt::new(12241);
const FELT_NINV_512: FalconFelt = FalconFelt::new(12265);
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