def test_ifft():
p = 337
domain = [FQ(i) for i in [1, 85, 148, 111, 336, 252, 189, 226]]
poly = [3, 1, 4, 1, 5, 9, 2, 6]
result = []
p_x = fft(p, domain, poly)
result = ifft(p, domain, p_x)
assert result == poly
def test_degree_reduction():
a = [1, 0, 0, 0, 0, 0, 0, 1]
b = [0, 1, 0, 0, 0, 0, 0, 0]
domain = [FQ(i) for i in [1, 85, 148, 111, 336, 252, 189, 226]]
p = 337
a_fft = fft(p, domain, a)
b_fft = fft(p, domain, b)
c = [a * b for a, b in zip(a_fft, b_fft)]
res = ifft(p, domain, c)
assert res == [1, 1, 0, 0, 0, 0, 0, 0]
def test_mul_poly():
# (x + 1) **2
a = [1, 1, 0, 0, 0, 0, 0, 0]
b = [1, 1, 0, 0, 0, 0, 0, 0]
domain = [FQ(i) for i in [1, 85, 148, 111, 336, 252, 189, 226]]
p = 337
a_fft = fft(p, domain, a)
b_fft = fft(p, domain, b)
c = [a * b for a, b in zip(a_fft, b_fft)]
res = ifft(p, domain, c)
assert res == [1, 2, 1, 0, 0, 0, 0, 0]
def test_poly_add():
a = [1, 1, 0, 0, 0, 0, 0, 0]
b = [1, 1, 0, 0, 0, 0, 0, 0]
domain = [FQ(i) for i in [1, 85, 148, 111, 336, 252, 189, 226]]
p = 337
a_fft = fft(p, domain, a)
b_fft = fft(p, domain, b)
c = [a * b for a, b in zip(a_fft, b_fft)]
c = [a + b for a, b in zip(c, a_fft)]
res = ifft(p, domain, c)
assert res == [2, 3, 1, 0, 0, 0, 0, 0]
def test_constant_add():
a = [1, 1, 0, 0, 0, 0, 0, 0]
b = [1, 1, 0, 0, 0, 0, 0, 0]
domain = [FQ(i) for i in [1, 85, 148, 111, 336, 252, 189, 226]]
p = 337
constant = 330
a_fft = fft(p, domain, a)
b_fft = fft(p, domain, b)
c = [a * b for a, b in zip(a_fft, b_fft)]
c = [a + constant for a in c]
res = ifft(p, domain, c)
assert res == [331, 2, 1, 0, 0, 0, 0, 0]
def test_mul():
a = [3, 5, 2, 1, 0, 0, 0, 0]
b = [5, 9, 8, 1, 0, 0, 0, 0]
domain = [FQ(i) for i in [1, 85, 148, 111, 336, 252, 189, 226]]
p = 337
a_fft = fft(p, domain, a)
b_fft = fft(p, domain, b)
a_b_fft = [a * b for a, b in zip(a_fft, b_fft)]
res = ifft(p, domain, a_b_fft)
for i, x in enumerate(res):
res[i] = x % 10
if int(x / 10) != 0:
res[i + 1] += int(x / 10)
assert res == [5, 3, 4, 4, 7, 3, 2, 0]