def test_unate():
# ~c & (~a | ~b)
f = truthtable([aa, bb, cc], "11100000")
assert f.is_neg_unate([aa, bb, cc])
assert f.is_neg_unate([aa, bb])
assert f.is_neg_unate([aa, cc])
assert f.is_neg_unate([bb, cc])
assert f.is_neg_unate(aa)
assert f.is_neg_unate(bb)
assert f.is_neg_unate(cc)
assert f.is_neg_unate()
# c & (a | b)
f = truthtable([a, b, c], "00000111")
assert f.is_pos_unate([aa, bb, cc])
assert f.is_pos_unate([aa, bb])
assert f.is_pos_unate([aa, cc])
assert f.is_pos_unate([bb, cc])
assert f.is_pos_unate(aa)
assert f.is_pos_unate(bb)
assert f.is_pos_unate(cc)
assert f.is_pos_unate()
# Xor(a, b, c)
f = truthtable([a, b, c], "01101001")
assert f.is_binate([aa, bb, cc])
assert f.is_binate([aa, bb])
assert f.is_binate([aa, cc])
assert f.is_binate([bb, cc])
assert f.is_binate(aa)
assert f.is_binate(bb)
assert f.is_binate(cc)
def test_table():
assert truthtable([], [0]).is_zero()
assert truthtable([], [1]).is_one()
f = Xor(a, b, c, d)
tt = expr2truthtable(f)
assert truthtable2expr(tt).equivalent(f)
assert truthtable2expr(tt, conj=True).equivalent(f)
assert str(tt) == XOR_STR
assert repr(tt) == XOR_STR
assert tt.support == {aa, bb, cc, dd}
assert tt.inputs == (aa, bb, cc, dd)
assert truthtable2expr(tt.restrict({aa: 0})).equivalent(Xor(b, c, d))
assert tt.restrict({ee: 0}) == tt
assert tt.satisfy_one() == {aa: 1, bb: 0, cc: 0, dd: 0}
assert [p for p in tt.satisfy_all()] == [{aa: 1, bb: 0, cc: 0, dd: 0},
{aa: 0, bb: 1, cc: 0, dd: 0},
{aa: 0, bb: 0, cc: 1, dd: 0},
{aa: 1, bb: 1, cc: 1, dd: 0},
{aa: 0, bb: 0, cc: 0, dd: 1},
{aa: 1, bb: 1, cc: 0, dd: 1},
{aa: 1, bb: 0, cc: 1, dd: 1},
{aa: 0, bb: 1, cc: 1, dd: 1}]
assert tt.satisfy_count() == 8
assert truthtable((a, b), "0000").satisfy_one() == None
def test_unate():
# ~c & (~a | ~b)
f = truthtable([aa, bb, cc], "11100000")
assert f.is_neg_unate([aa, bb, cc])
assert f.is_neg_unate([aa, bb])
assert f.is_neg_unate([aa, cc])
assert f.is_neg_unate([bb, cc])
assert f.is_neg_unate(aa)
assert f.is_neg_unate(bb)
assert f.is_neg_unate(cc)
assert f.is_neg_unate()
# c & (a | b)
f = truthtable([a, b, c], "00000111")
assert f.is_pos_unate([aa, bb, cc])
assert f.is_pos_unate([aa, bb])
assert f.is_pos_unate([aa, cc])
assert f.is_pos_unate([bb, cc])
assert f.is_pos_unate(aa)
assert f.is_pos_unate(bb)
assert f.is_pos_unate(cc)
assert f.is_pos_unate()
# Xor(a, b, c)
f = truthtable([a, b, c], "01101001")
assert f.is_binate([aa, bb, cc])
assert f.is_binate([aa, bb])
assert f.is_binate([aa, cc])
assert f.is_binate([bb, cc])
assert f.is_binate(aa)
assert f.is_binate(bb)
assert f.is_binate(cc)
def test_espresso():
A = bitvec('a', 16)
B = bitvec('b', 16)
S, C = ripple_carry_add(A, B)
s0, s1, s2, s3 = espresso_exprs(S[0].to_dnf(), S[1].to_dnf(),
S[2].to_dnf(), S[3].to_dnf())
assert s0.equivalent(S[0])
assert s1.equivalent(S[1])
assert s2.equivalent(S[2])
assert s3.equivalent(S[3])
X = bitvec('x', 4)
f1 = truthtable(X, "0000011111------")
f2 = truthtable(X, "0001111100------")
f1m, f2m = espresso_tts(f1, f2)
truthtable2expr(f1).equivalent(f1m)
truthtable2expr(f2).equivalent(f2m)
def test_espresso():
assert espresso.FTYPE == 1
assert espresso.DTYPE == 2
assert espresso.RTYPE == 4
A = exprvars('a', 16)
B = exprvars('b', 16)
S, C = ripple_carry_add(A, B)
s0, s1, s2, s3 = espresso_exprs(S[0].to_dnf(), S[1].to_dnf(),
S[2].to_dnf(), S[3].to_dnf())
assert s0.equivalent(S[0])
assert s1.equivalent(S[1])
assert s2.equivalent(S[2])
assert s3.equivalent(S[3])
X = exprvars('x', 4)
f1 = truthtable(X, "0000011111------")
f2 = truthtable(X, "0001111100------")
f1m, f2m = espresso_tts(f1, f2)
truthtable2expr(f1).equivalent(f1m)
truthtable2expr(f2).equivalent(f2m)
def test_ops():
f = truthtable([aa, bb], "0001")
assert str(f) == "b a\n0 0 : 0\n0 1 : 0\n1 0 : 0\n1 1 : 1\n"
assert str(~f) == "b a\n0 0 : 1\n0 1 : 1\n1 0 : 1\n1 1 : 0\n"
assert str(f | 0) == "b a\n0 0 : 0\n0 1 : 0\n1 0 : 0\n1 1 : 1\n"
assert str(f | 1) == "b a\n0 0 : 1\n0 1 : 1\n1 0 : 1\n1 1 : 1\n"
assert str(0 | f) == "b a\n0 0 : 0\n0 1 : 0\n1 0 : 0\n1 1 : 1\n"
assert str(1 | f) == "b a\n0 0 : 1\n0 1 : 1\n1 0 : 1\n1 1 : 1\n"
assert str(f & 0) == "b a\n0 0 : 0\n0 1 : 0\n1 0 : 0\n1 1 : 0\n"
assert str(f & 1) == "b a\n0 0 : 0\n0 1 : 0\n1 0 : 0\n1 1 : 1\n"
assert str(0 & f) == "b a\n0 0 : 0\n0 1 : 0\n1 0 : 0\n1 1 : 0\n"
assert str(1 & f) == "b a\n0 0 : 0\n0 1 : 0\n1 0 : 0\n1 1 : 1\n"
assert str(f ^ 0) == "b a\n0 0 : 0\n0 1 : 0\n1 0 : 0\n1 1 : 1\n"
assert str(f ^ 1) == "b a\n0 0 : 1\n0 1 : 1\n1 0 : 1\n1 1 : 0\n"
f = truthtable([aa, bb], "01-0")
assert str(~f) == "b a\n0 0 : 1\n0 1 : 0\n1 0 : -\n1 1 : 1\n"
f = truthtable([aa, bb], "0011")
g = truthtable([aa, bb], "0101")
assert str(f | g) == "b a\n0 0 : 0\n0 1 : 1\n1 0 : 1\n1 1 : 1\n"
assert str(f & g) == "b a\n0 0 : 0\n0 1 : 0\n1 0 : 0\n1 1 : 1\n"
assert str(f ^ g) == "b a\n0 0 : 0\n0 1 : 1\n1 0 : 1\n1 1 : 0\n"
f = truthtable([a, b, c], "00011-00")
g = truthtable([a, b, c], "01-1--00")
assert str(f | g) == "c b a\n0 0 0 : 0\n0 0 1 : 1\n0 1 0 : -\n0 1 1 : 1\n1 0 0 : 1\n1 0 1 : -\n1 1 0 : 0\n1 1 1 : 0\n"
assert str(f & g) == "c b a\n0 0 0 : 0\n0 0 1 : 0\n0 1 0 : 0\n0 1 1 : 1\n1 0 0 : -\n1 0 1 : -\n1 1 0 : 0\n1 1 1 : 0\n"
assert str(f ^ g) == "c b a\n0 0 0 : 0\n0 0 1 : 1\n0 1 0 : -\n0 1 1 : 0\n1 0 0 : -\n1 0 1 : -\n1 1 0 : 0\n1 1 1 : 0\n"
def test_ops():
f = truthtable([aa, bb], "0001")
assert str(f) == "inputs: b a\n00 0\n01 0\n10 0\n11 1\n"
assert str(~f) == "inputs: b a\n00 1\n01 1\n10 1\n11 0\n"
assert str(f | 0) == "inputs: b a\n00 0\n01 0\n10 0\n11 1\n"
assert str(f | 1) == "inputs: b a\n00 1\n01 1\n10 1\n11 1\n"
assert str(0 | f) == "inputs: b a\n00 0\n01 0\n10 0\n11 1\n"
assert str(1 | f) == "inputs: b a\n00 1\n01 1\n10 1\n11 1\n"
assert str(f & 0) == "inputs: b a\n00 0\n01 0\n10 0\n11 0\n"
assert str(f & 1) == "inputs: b a\n00 0\n01 0\n10 0\n11 1\n"
assert str(0 & f) == "inputs: b a\n00 0\n01 0\n10 0\n11 0\n"
assert str(1 & f) == "inputs: b a\n00 0\n01 0\n10 0\n11 1\n"
assert str(f ^ 0) == "inputs: b a\n00 0\n01 0\n10 0\n11 1\n"
assert str(f ^ 1) == "inputs: b a\n00 1\n01 1\n10 1\n11 0\n"
f = truthtable([aa, bb], "01-0")
assert str(~f) == "inputs: b a\n00 1\n01 0\n10 -\n11 1\n"
f = truthtable([aa, bb], "0011")
g = truthtable([aa, bb], "0101")
assert str(f | g) == "inputs: b a\n00 0\n01 1\n10 1\n11 1\n"
assert str(f & g) == "inputs: b a\n00 0\n01 0\n10 0\n11 1\n"
assert str(f ^ g) == "inputs: b a\n00 0\n01 1\n10 1\n11 0\n"
f = truthtable([a, b, c], "00011-00")
g = truthtable([a, b, c], "01-1--00")
assert str(f | g) == "inputs: c b a\n000 0\n001 1\n010 -\n011 1\n100 1\n101 -\n110 0\n111 0\n"
assert str(f & g) == "inputs: c b a\n000 0\n001 0\n010 0\n011 1\n100 -\n101 -\n110 0\n111 0\n"
assert str(f ^ g) == "inputs: c b a\n000 0\n001 1\n010 -\n011 0\n100 -\n101 -\n110 0\n111 0\n"
def test_ops():
f = truthtable([aa, bb], "0001")
assert str(f) == "b a\n0 0 : 0\n0 1 : 0\n1 0 : 0\n1 1 : 1\n"
assert str(~f) == "b a\n0 0 : 1\n0 1 : 1\n1 0 : 1\n1 1 : 0\n"
assert str(f | 0) == "b a\n0 0 : 0\n0 1 : 0\n1 0 : 0\n1 1 : 1\n"
assert str(f | 1) == "b a\n0 0 : 1\n0 1 : 1\n1 0 : 1\n1 1 : 1\n"
assert str(0 | f) == "b a\n0 0 : 0\n0 1 : 0\n1 0 : 0\n1 1 : 1\n"
assert str(1 | f) == "b a\n0 0 : 1\n0 1 : 1\n1 0 : 1\n1 1 : 1\n"
assert str(f & 0) == "b a\n0 0 : 0\n0 1 : 0\n1 0 : 0\n1 1 : 0\n"
assert str(f & 1) == "b a\n0 0 : 0\n0 1 : 0\n1 0 : 0\n1 1 : 1\n"
assert str(0 & f) == "b a\n0 0 : 0\n0 1 : 0\n1 0 : 0\n1 1 : 0\n"
assert str(1 & f) == "b a\n0 0 : 0\n0 1 : 0\n1 0 : 0\n1 1 : 1\n"
assert str(f ^ 0) == "b a\n0 0 : 0\n0 1 : 0\n1 0 : 0\n1 1 : 1\n"
assert str(f ^ 1) == "b a\n0 0 : 1\n0 1 : 1\n1 0 : 1\n1 1 : 0\n"
f = truthtable([aa, bb], "01-0")
assert str(~f) == "b a\n0 0 : 1\n0 1 : 0\n1 0 : -\n1 1 : 1\n"
f = truthtable([aa, bb], "0011")
g = truthtable([aa, bb], "0101")
assert str(f | g) == "b a\n0 0 : 0\n0 1 : 1\n1 0 : 1\n1 1 : 1\n"
assert str(f & g) == "b a\n0 0 : 0\n0 1 : 0\n1 0 : 0\n1 1 : 1\n"
assert str(f ^ g) == "b a\n0 0 : 0\n0 1 : 1\n1 0 : 1\n1 1 : 0\n"
f = truthtable([a, b, c], "00011-00")
g = truthtable([a, b, c], "01-1--00")
assert str(
f | g
) == "c b a\n0 0 0 : 0\n0 0 1 : 1\n0 1 0 : -\n0 1 1 : 1\n1 0 0 : 1\n1 0 1 : -\n1 1 0 : 0\n1 1 1 : 0\n"
assert str(
f & g
) == "c b a\n0 0 0 : 0\n0 0 1 : 0\n0 1 0 : 0\n0 1 1 : 1\n1 0 0 : -\n1 0 1 : -\n1 1 0 : 0\n1 1 1 : 0\n"
assert str(
f ^ g
) == "c b a\n0 0 0 : 0\n0 0 1 : 1\n0 1 0 : -\n0 1 1 : 0\n1 0 0 : -\n1 0 1 : -\n1 1 0 : 0\n1 1 1 : 0\n"
def test_table():
assert truthtable([], [0]).is_zero()
assert truthtable([], [1]).is_one()
f = Xor(a, b, c, d)
tt = expr2truthtable(f)
assert truthtable2expr(tt).equivalent(f)
assert truthtable2expr(tt, conj=True).equivalent(f)
assert str(tt) == XOR_STR
assert repr(tt) == XOR_STR
assert tt.support == {aa, bb, cc, dd}
assert tt.inputs == (aa, bb, cc, dd)
assert truthtable2expr(tt.restrict({aa: 0})).equivalent(Xor(b, c, d))
assert tt.restrict({ee: 0}) == tt
assert tt.satisfy_one() == {aa: 1, bb: 0, cc: 0, dd: 0}
assert [p for p in tt.satisfy_all()] == [{
aa: 1,
bb: 0,
cc: 0,
dd: 0
}, {
aa: 0,
bb: 1,
cc: 0,
dd: 0
}, {
aa: 0,
bb: 0,
cc: 1,
dd: 0
}, {
aa: 1,
bb: 1,
cc: 1,
dd: 0
}, {
aa: 0,
bb: 0,
cc: 0,
dd: 1
}, {
aa: 1,
bb: 1,
cc: 0,
dd: 1
}, {
aa: 1,
bb: 0,
cc: 1,
dd: 1
}, {
aa: 0,
bb: 1,
cc: 1,
dd: 1
}]
assert tt.satisfy_count() == 8
assert truthtable((a, b), "0000").satisfy_one() == None