def test_convolution():
a = [1, S(5)/3, sqrt(3), S(7)/5]
b = [9, 5, 5, 4, 3, 2]
c = [3, 5, 3, 7, 8]
d = [1422, 6572, 3213, 5552]
assert convolution(a, b, fft=True) == convolution_fft(a, b)
assert convolution(a, b, dps=9, fft=True) == convolution_fft(a, b, dps=9)
assert convolution(a, d, fft=True, dps=7) == convolution_fft(d, a, dps=7)
assert convolution(a, d[1:], dps=3) == convolution_fft(d[1:], a, dps=3)
# prime moduli of the form (m*2**k + 1), sequence length
# should be a divisor of 2**k
p = 7*17*2**23 + 1
q = 19*2**10 + 1
assert convolution(d, b, ntt=True, prime=q) == convolution_ntt(b, d, prime=q)
assert convolution(c, b, prime=p) == convolution_ntt(b, c, prime=p)
assert convolution(d, c, prime=p, ntt=True) == convolution_ntt(c, d, prime=p)
raises(TypeError, lambda: convolution(b, d, ntt=True))
raises(TypeError, lambda: convolution(b, d, ntt=True, cycle=0))
raises(TypeError, lambda: convolution(b, d, dps=5, prime=q))
raises(TypeError, lambda: convolution(b, d, dps=6, ntt=True, prime=q))
raises(TypeError, lambda: convolution(b, d, fft=True, dps=7, ntt=True, prime=q))
# ntt is a specialized variant of fft, TypeError should not be raised
assert convolution(b, d, fft=True, ntt=True, prime=q) == \
convolution_ntt(b, d, prime=q)
def test_convolution():
# fft
a = [1, S(5) / 3, sqrt(3), S(7) / 5]
b = [9, 5, 5, 4, 3, 2]
c = [3, 5, 3, 7, 8]
d = [1422, 6572, 3213, 5552]
assert convolution(a, b) == convolution_fft(a, b)
assert convolution(a, b, dps=9) == convolution_fft(a, b, dps=9)
assert convolution(a, d, dps=7) == convolution_fft(d, a, dps=7)
assert convolution(a, d[1:], dps=3) == convolution_fft(d[1:], a, dps=3)
# prime moduli of the form (m*2**k + 1), sequence length
# should be a divisor of 2**k
p = 7 * 17 * 2**23 + 1
q = 19 * 2**10 + 1
# ntt
assert convolution(d, b, prime=q) == convolution_ntt(b, d, prime=q)
assert convolution(c, b, prime=p) == convolution_ntt(b, c, prime=p)
assert convolution(d, c, prime=p) == convolution_ntt(c, d, prime=p)
raises(TypeError, lambda: convolution(b, d, dps=5, prime=q))
raises(TypeError, lambda: convolution(b, d, dps=6, prime=q))
# fwht
assert convolution(a, b, dyadic=True) == convolution_fwht(a, b)
assert convolution(a, b, dyadic=False) == convolution(a, b)
raises(TypeError, lambda: convolution(b, d, dps=2, dyadic=True))
raises(TypeError, lambda: convolution(b, d, prime=p, dyadic=True))
raises(TypeError, lambda: convolution(a, b, dps=2, dyadic=True))
raises(TypeError, lambda: convolution(b, c, prime=p, dyadic=True))
# subset
assert convolution(a, b, subset=True) == convolution_subset(a, b) == \
convolution(a, b, subset=True, dyadic=False) == \
convolution(a, b, subset=True)
assert convolution(a, b, subset=False) == convolution(a, b)
raises(TypeError, lambda: convolution(a, b, subset=True, dyadic=True))
raises(TypeError, lambda: convolution(c, d, subset=True, dps=6))
raises(TypeError, lambda: convolution(a, c, subset=True, prime=q))
def test_convolution():
# fft
a = [1, S(5)/3, sqrt(3), S(7)/5]
b = [9, 5, 5, 4, 3, 2]
c = [3, 5, 3, 7, 8]
d = [1422, 6572, 3213, 5552]
assert convolution(a, b, fft=True) == convolution_fft(a, b)
assert convolution(a, b, dps=9, fft=True) == convolution_fft(a, b, dps=9)
assert convolution(a, d, fft=True, dps=7) == convolution_fft(d, a, dps=7)
assert convolution(a, d[1:], dps=3) == convolution_fft(d[1:], a, dps=3)
# prime moduli of the form (m*2**k + 1), sequence length
# should be a divisor of 2**k
p = 7*17*2**23 + 1
q = 19*2**10 + 1
# ntt
assert convolution(d, b, ntt=True, prime=q) == convolution_ntt(b, d, prime=q)
assert convolution(c, b, prime=p) == convolution_ntt(b, c, prime=p)
assert convolution(d, c, prime=p, ntt=True) == convolution_ntt(c, d, prime=p)
raises(TypeError, lambda: convolution(b, d, ntt=True))
raises(TypeError, lambda: convolution(b, d, ntt=True, cycle=0))
raises(TypeError, lambda: convolution(b, d, dps=5, prime=q))
raises(TypeError, lambda: convolution(b, d, dps=6, ntt=True, prime=q))
raises(TypeError, lambda: convolution(b, d, fft=True, dps=7, ntt=True, prime=q))
# ntt is a specialized variant of fft, TypeError should not be raised
assert convolution(b, d, fft=True, ntt=True, prime=q) == \
convolution_ntt(b, d, prime=q)
# fwht
assert convolution(a, b, dyadic=True) == convolution_fwht(a, b)
assert convolution(a, b, dyadic=False) == convolution(a, b)
raises(TypeError, lambda: convolution(b, d, fft=True, dps=2, dyadic=True))
raises(TypeError, lambda: convolution(b, d, ntt=True, prime=p, dyadic=True))
raises(TypeError, lambda: convolution(b, d, fft=True, dyadic=True))
raises(TypeError, lambda: convolution(a, b, dps=2, dyadic=True))
raises(TypeError, lambda: convolution(b, c, prime=p, dyadic=True))
def test_convolution_ntt():
# prime moduli of the form (m*2**k + 1), sequence length
# should be a divisor of 2**k
p = 7*17*2**23 + 1
q = 19*2**10 + 1
r = 2*500000003 + 1 # only for sequences of length 1 or 2
s = 2*3*5*7 # composite modulus
assert all(convolution_ntt([], x, prime=y) == [] for x in ([], [1]) for y in (p, q, r))
assert convolution_ntt([2], [3], r) == [6]
assert convolution_ntt([2, 3], [4], r) == [8, 12]
assert convolution_ntt([32121, 42144, 4214, 4241], [32132, 3232, 87242], p) == [33867619,
459741727, 79180879, 831885249, 381344700, 369993322]
assert convolution_ntt([121913, 3171831, 31888131, 12], [17882, 21292, 29921, 312], q) == \
[8158, 3065, 3682, 7090, 1239, 2232, 3744]
assert convolution_ntt([12, 19, 21, 98, 67], [2, 6, 7, 8, 9], p) == \
convolution_ntt([12, 19, 21, 98, 67], [2, 6, 7, 8, 9], q)
assert convolution_ntt([12, 19, 21, 98, 67], [21, 76, 17, 78, 69], p) == \
convolution_ntt([12, 19, 21, 98, 67], [21, 76, 17, 78, 69], q)
raises(ValueError, lambda: convolution_ntt([2, 3], [4, 5], r))
raises(ValueError, lambda: convolution_ntt([x, y], [y, x], q))
raises(TypeError, lambda: convolution_ntt(x, y, p))
def test_convolution_ntt():
# prime moduli of the form (m*2**k + 1), sequence length
# should be a divisor of 2**k
p = 7 * 17 * 2**23 + 1
q = 19 * 2**10 + 1
r = 2 * 500000003 + 1 # only for sequences of length 1 or 2
s = 2 * 3 * 5 * 7 # composite modulus
assert all(
convolution_ntt([], x, prime=y) == [] for x in ([], [1])
for y in (p, q, r))
assert convolution_ntt([2], [3], r) == [6]
assert convolution_ntt([2, 3], [4], r) == [8, 12]
assert convolution_ntt(
[32121, 42144, 4214, 4241], [32132, 3232, 87242],
p) == [33867619, 459741727, 79180879, 831885249, 381344700, 369993322]
assert convolution_ntt([121913, 3171831, 31888131, 12], [17882, 21292, 29921, 312], q) == \
[8158, 3065, 3682, 7090, 1239, 2232, 3744]
assert convolution_ntt([12, 19, 21, 98, 67], [2, 6, 7, 8, 9], p) == \
convolution_ntt([12, 19, 21, 98, 67], [2, 6, 7, 8, 9], q)
assert convolution_ntt([12, 19, 21, 98, 67], [21, 76, 17, 78, 69], p) == \
convolution_ntt([12, 19, 21, 98, 67], [21, 76, 17, 78, 69], q)
raises(ValueError, lambda: convolution_ntt([2, 3], [4, 5], r))
raises(ValueError, lambda: convolution_ntt([x, y], [y, x], q))
raises(TypeError, lambda: convolution_ntt(x, y, p))