35 lines
1.2 KiB
Python
35 lines
1.2 KiB
Python
def _fft(vals, modulus, roots_of_unity):
|
|
if len(vals) == 1:
|
|
return vals
|
|
L = _fft(vals[::2], modulus, roots_of_unity[::2])
|
|
R = _fft(vals[1::2], modulus, roots_of_unity[::2])
|
|
o = [0 for i in vals]
|
|
for i, (x, y) in enumerate(zip(L, R)):
|
|
y_times_root = y*roots_of_unity[i]
|
|
o[i] = (x+y_times_root) % modulus
|
|
o[i+len(L)] = (x-y_times_root) % modulus
|
|
# print(vals, root_of_unity, o)
|
|
return o
|
|
|
|
def fft(vals, modulus, root_of_unity, inv=False):
|
|
# Build up roots of unity
|
|
rootz = [1, root_of_unity]
|
|
while rootz[-1] != 1:
|
|
rootz.append((rootz[-1] * root_of_unity) % modulus)
|
|
# Fill in vals with zeroes if needed
|
|
if len(rootz) > len(vals) + 1:
|
|
vals = vals + [0] * (len(rootz) - len(vals) - 1)
|
|
if inv:
|
|
# Inverse FFT
|
|
invlen = pow(len(vals), modulus-2, modulus)
|
|
return [(x*invlen) % modulus for x in _fft(vals, modulus, rootz[::-1])]
|
|
else:
|
|
# Regular FFT
|
|
return _fft(vals, modulus, rootz)
|
|
|
|
def mul_polys(a, b, modulus, root_of_unity):
|
|
x1 = fft(a, modulus, root_of_unity)
|
|
x2 = fft(b, modulus, root_of_unity)
|
|
return fft([(v1*v2)%modulus for v1,v2 in zip(x1,x2)],
|
|
modulus, root_of_unity, inv=True)
|