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_cyclic_convolution():
# fft
a = [1, S(5)/3, sqrt(3), S(7)/5]
b = [9, 5, 5, 4, 3, 2]
assert convolution([1, 2, 3], [4, 5, 6], cycle=0) == \
convolution([1, 2, 3], [4, 5, 6], cycle=5) == \
convolution([1, 2, 3], [4, 5, 6])
assert convolution([1, 2, 3], [4, 5, 6], cycle=3) == [31, 31, 28]
assert convolution(a, b, fft=True, cycle=4) == \
convolution(a, b, cycle=4)
assert convolution(a, b, fft=True, dps=3, cycle=4) == \
convolution(a, b, dps=3, cycle=4)
a = [S(1)/3, S(7)/3, S(5)/9, S(2)/7, S(5)/8]
b = [S(3)/5, S(4)/7, S(7)/8, S(8)/9]
assert convolution(a, b, cycle=0) == \
convolution(a, b, cycle=len(a) + len(b) - 1)
assert convolution(a, b, cycle=4) == [S(87277)/26460, S(30521)/11340,
S(11125)/4032, S(3653)/1080]
assert convolution(a, b, cycle=6) == [S(20177)/20160, S(676)/315, S(47)/24,
S(3053)/1080, S(16397)/5292, S(2497)/2268]
assert convolution(a, b, cycle=9) == \
convolution(a, b, cycle=0) + [S.Zero]
# ntt
a = [2313, 5323532, S(3232), 42142, 42242421]
b = [S(33456), 56757, 45754, 432423]
assert convolution(a, b, prime=19*2**10 + 1, cycle=0) == \
convolution(a, b, prime=19*2**10 + 1, cycle=8) == \
convolution(a, b, prime=19*2**10 + 1)
assert convolution(a, b, prime=19*2**10 + 1, cycle=5) == [96, 17146, 2664,
15534, 3517]
assert convolution(a, b, prime=19*2**10 + 1, cycle=7) == [4643, 3458, 1260,
15534, 3517, 16314, 13688]
assert convolution(a, b, prime=19*2**10 + 1, cycle=9) == \
convolution(a, b, prime=19*2**10 + 1) + [0]
# fwht
assert convolution(a, b, dyadic=True, cycle=3) == [2499522285783,
19861417974796, 4702176579021]
assert convolution(a, b, dyadic=True, cycle=5) == [2718149225143,
2114320852171, 20571217906407, 246166418903, 1413262436976]
def test_cyclic_convolution():
# fft
a = [1, S(5) / 3, sqrt(3), S(7) / 5]
b = [9, 5, 5, 4, 3, 2]
assert convolution([1, 2, 3], [4, 5, 6], cycle=0) == \
convolution([1, 2, 3], [4, 5, 6], cycle=5) == \
convolution([1, 2, 3], [4, 5, 6])
assert convolution([1, 2, 3], [4, 5, 6], cycle=3) == [31, 31, 28]
a = [S(1) / 3, S(7) / 3, S(5) / 9, S(2) / 7, S(5) / 8]
b = [S(3) / 5, S(4) / 7, S(7) / 8, S(8) / 9]
assert convolution(a, b, cycle=0) == \
convolution(a, b, cycle=len(a) + len(b) - 1)
assert convolution(a, b, cycle=4) == [
S(87277) / 26460,
S(30521) / 11340,
S(11125) / 4032,
S(3653) / 1080
]
assert convolution(a, b, cycle=6) == [
S(20177) / 20160,
S(676) / 315,
S(47) / 24,
S(3053) / 1080,
S(16397) / 5292,
S(2497) / 2268
]
assert convolution(a, b, cycle=9) == \
convolution(a, b, cycle=0) + [S.Zero]
# ntt
a = [2313, 5323532, S(3232), 42142, 42242421]
b = [S(33456), 56757, 45754, 432423]
assert convolution(a, b, prime=19*2**10 + 1, cycle=0) == \
convolution(a, b, prime=19*2**10 + 1, cycle=8) == \
convolution(a, b, prime=19*2**10 + 1)
assert convolution(a, b, prime=19 * 2**10 + 1,
cycle=5) == [96, 17146, 2664, 15534, 3517]
assert convolution(a, b, prime=19 * 2**10 + 1, cycle=7) == [
4643, 3458, 1260, 15534, 3517, 16314, 13688
]
assert convolution(a, b, prime=19*2**10 + 1, cycle=9) == \
convolution(a, b, prime=19*2**10 + 1) + [0]
# fwht
u, v, w, x, y = symbols('u v w x y')
p, q, r, s, t = symbols('p q r s t')
c = [u, v, w, x, y]
d = [p, q, r, s, t]
assert convolution(a, b, dyadic=True, cycle=3) == \
[2499522285783, 19861417974796, 4702176579021]
assert convolution(a, b, dyadic=True, cycle=5) == [
2718149225143, 2114320852171, 20571217906407, 246166418903,
1413262436976
]
assert convolution(c, d, dyadic=True, cycle=4) == \
[p*u + p*y + q*v + r*w + s*x + t*u + t*y,
p*v + q*u + q*y + r*x + s*w + t*v,
p*w + q*x + r*u + r*y + s*v + t*w,
p*x + q*w + r*v + s*u + s*y + t*x]
assert convolution(c, d, dyadic=True, cycle=6) == \
[p*u + q*v + r*w + r*y + s*x + t*w + t*y,
p*v + q*u + r*x + s*w + s*y + t*x,
p*w + q*x + r*u + s*v,
p*x + q*w + r*v + s*u,
p*y + t*u,
q*y + t*v]
# subset
assert convolution(a, b, subset=True, cycle=7) == [
18266671799811, 178235365533, 213958794, 246166418903, 1413262436976,
2397553088697, 1932759730434
]
assert convolution(a[1:], b, subset=True, cycle=4) == \
[178104086592, 302255835516, 244982785880, 3717819845434]
assert convolution(a, b[:-1], subset=True, cycle=6) == [
1932837114162, 178235365533, 213958794, 245166224504, 1413262436976,
2397553088697
]
assert convolution(c, d, subset=True, cycle=3) == \
[p*u + p*x + q*w + r*v + r*y + s*u + t*w,
p*v + p*y + q*u + s*y + t*u + t*x,
p*w + q*y + r*u + t*v]
assert convolution(c, d, subset=True, cycle=5) == \
[p*u + q*y + t*v,
p*v + q*u + r*y + t*w,
p*w + r*u + s*y + t*x,
p*x + q*w + r*v + s*u,
p*y + t*u]
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_cyclic_convolution():
# fft
a = [1, S(5) / 3, sqrt(3), S(7) / 5]
b = [9, 5, 5, 4, 3, 2]
assert convolution([1, 2, 3], [4, 5, 6], cycle=0) == \
convolution([1, 2, 3], [4, 5, 6], cycle=5) == \
convolution([1, 2, 3], [4, 5, 6])
assert convolution([1, 2, 3], [4, 5, 6], cycle=3) == [31, 31, 28]
assert convolution(a, b, fft=True, cycle=4) == \
convolution(a, b, cycle=4)
assert convolution(a, b, fft=True, dps=3, cycle=4) == \
convolution(a, b, dps=3, cycle=4)
a = [S(1) / 3, S(7) / 3, S(5) / 9, S(2) / 7, S(5) / 8]
b = [S(3) / 5, S(4) / 7, S(7) / 8, S(8) / 9]
assert convolution(a, b, cycle=0) == \
convolution(a, b, cycle=len(a) + len(b) - 1)
assert convolution(a, b, cycle=4) == [
S(87277) / 26460,
S(30521) / 11340,
S(11125) / 4032,
S(3653) / 1080
]
assert convolution(a, b, cycle=6) == [
S(20177) / 20160,
S(676) / 315,
S(47) / 24,
S(3053) / 1080,
S(16397) / 5292,
S(2497) / 2268
]
assert convolution(a, b, cycle=9) == \
convolution(a, b, cycle=0) + [S.Zero]
# ntt
a = [2313, 5323532, S(3232), 42142, 42242421]
b = [S(33456), 56757, 45754, 432423]
assert convolution(a, b, prime=19*2**10 + 1, cycle=0) == \
convolution(a, b, prime=19*2**10 + 1, cycle=8) == \
convolution(a, b, prime=19*2**10 + 1)
assert convolution(a, b, prime=19 * 2**10 + 1,
cycle=5) == [96, 17146, 2664, 15534, 3517]
assert convolution(a, b, prime=19 * 2**10 + 1, cycle=7) == [
4643, 3458, 1260, 15534, 3517, 16314, 13688
]
assert convolution(a, b, prime=19*2**10 + 1, cycle=9) == \
convolution(a, b, prime=19*2**10 + 1) + [0]
# fwht
assert convolution(a, b, dyadic=True, cycle=3) == [
2499522285783, 19861417974796, 4702176579021
]
assert convolution(a, b, dyadic=True, cycle=5) == [
2718149225143, 2114320852171, 20571217906407, 246166418903,
1413262436976
]
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_cyclic_convolution():
# fft
a = [1, S(5)/3, sqrt(3), S(7)/5]
b = [9, 5, 5, 4, 3, 2]
assert convolution([1, 2, 3], [4, 5, 6], cycle=0) == \
convolution([1, 2, 3], [4, 5, 6], cycle=5) == \
convolution([1, 2, 3], [4, 5, 6])
assert convolution([1, 2, 3], [4, 5, 6], cycle=3) == [31, 31, 28]
assert convolution(a, b, fft=True, cycle=4) == \
convolution(a, b, cycle=4)
assert convolution(a, b, fft=True, dps=3, cycle=4) == \
convolution(a, b, dps=3, cycle=4)
a = [S(1)/3, S(7)/3, S(5)/9, S(2)/7, S(5)/8]
b = [S(3)/5, S(4)/7, S(7)/8, S(8)/9]
assert convolution(a, b, cycle=0) == \
convolution(a, b, cycle=len(a) + len(b) - 1)
assert convolution(a, b, cycle=4) == [S(87277)/26460, S(30521)/11340,
S(11125)/4032, S(3653)/1080]
assert convolution(a, b, cycle=6) == [S(20177)/20160, S(676)/315, S(47)/24,
S(3053)/1080, S(16397)/5292, S(2497)/2268]
assert convolution(a, b, cycle=9) == \
convolution(a, b, cycle=0) + [S.Zero]
# ntt
a = [2313, 5323532, S(3232), 42142, 42242421]
b = [S(33456), 56757, 45754, 432423]
assert convolution(a, b, prime=19*2**10 + 1, cycle=0) == \
convolution(a, b, prime=19*2**10 + 1, cycle=8) == \
convolution(a, b, prime=19*2**10 + 1)
assert convolution(a, b, prime=19*2**10 + 1, cycle=5) == [96, 17146, 2664,
15534, 3517]
assert convolution(a, b, prime=19*2**10 + 1, cycle=7) == [4643, 3458, 1260,
15534, 3517, 16314, 13688]
assert convolution(a, b, prime=19*2**10 + 1, cycle=9) == \
convolution(a, b, prime=19*2**10 + 1) + [0]