def get_points(n, galois_field):
if n in cache:
return cache[n]
x = list(range(1, n + 1))
y = [randint(0, galois_field.modulus - 1) for i in range(1, n + 1)]
points = list(zip(x, y))
omega = get_omega(galois_field, n, 1)
cache[n] = x, y, points, omega
return x, y, points, omega
def test_interp_extrap_cpp(galois_field, polynomial):
d = randint(210, 300)
y = [galois_field.random().value for i in range(d)]
n = len(y)
n = n if n & n - 1 == 0 else 2**n.bit_length()
ys = y + [0] * (n - len(y))
omega = get_omega(galois_field, 2 * n)
values = polynomial.interp_extrap_cpp(ys, omega)
for a, b in zip(ys, values[0:201:2]): # verify only 100 points
assert a == b
def test_interpolate_fft(galois_field, polynomial):
d = randint(210, 300)
y = [galois_field.random().value for i in range(d)]
n = len(y)
n = n if n & n - 1 == 0 else 2**n.bit_length()
ys = y + [galois_field(0)] * (n - len(y))
omega = get_omega(galois_field, n)
poly = polynomial.interpolate_fft(ys, omega)
for i, a in zip(range(1, 201, 2), ys[1:201:2]): # verify only 100 points
assert poly(pow(omega, i)) == a
def test_evaluate_fft(galois_field, polynomial):
d = randint(210, 300)
coeffs = [galois_field.random().value for i in range(d)]
poly = polynomial(coeffs) # random polynomial of degree d
n = len(poly.coeffs)
n = n if n & n - 1 == 0 else 2**n.bit_length()
omega = get_omega(galois_field, n)
fft_result = poly.evaluate_fft(omega, n)
assert len(fft_result) == n
for i, a in zip(range(1, 201, 2),
fft_result[1:201:2]): # verify only 100 points
assert poly(pow(omega, i)) == a
def test_fft_decode(galois_field, polynomial):
d = randint(210, 300)
coeffs = [galois_field.random().value for i in range(d)]
poly = polynomial(coeffs)
n = d
n = n if n & n - 1 == 0 else 2**n.bit_length()
omega2 = get_omega(galois_field, 2 * n)
omega = omega2**2
# Create shares and erasures
zs = list(range(n))
shuffle(zs)
zs = zs[:d]
ys = list(poly.evaluate_fft(omega, n))
ys = [ys[i] for i in zs]
as_, ais_ = fnt_decode_step1(polynomial, zs, omega2, n)
prec_ = fnt_decode_step2(polynomial, zs, ys, as_, ais_, omega2, n)
print("Prec_(X):", prec_)
print("P(X):", poly)
assert prec_.coeffs == poly.coeffs