def pad(cnf: Formula, a: List[Variable],
b: List[Variable]) -> Tuple[List[Variable], List[Variable]]:
aa = a[:]
bb = b[:]
if len(aa) < len(bb):
for i in range(len(aa), len(bb)):
aa.append(cnf.const_false())
elif len(bb) < len(aa):
for i in range(len(bb), len(aa)):
bb.append(cnf.const_false())
assert (len(aa) == len(bb))
return aa, bb
def cnf_enforce_pyth_trip(cnf: Formula, a: List[Variable], b: List[Variable],
c: List[Variable], primitive: bool) -> None:
assert (len(a) == len(b))
assert (len(a) == len(c))
bitdepth = len(a)
m = new_integer(cnf, bitdepth)
n = new_integer(cnf, bitdepth)
m2 = cnf_square(cnf, m)
n2 = cnf_square(cnf, n)
m2n2 = cnf_add(cnf, m2, n2)
two = [cnf.const_false(), cnf.const_true()]
mn = cnf_mult(cnf, m, n)
mn2 = cnf_mult(cnf, mn, two)
# a disgusting way to do subtraction. fix me please
m2subn2 = new_integer(cnf, bitdepth)
m2_tmp = cnf_add(cnf, m2subn2, n2)
cnf_equal(cnf, m2_tmp, m2)
if not primitive:
k = new_integer(cnf, bitdepth)
m2subn2 = cnf_mult(cnf, m2subn2, k)
mn2 = cnf_mult(cnf, mn2, k)
m2n2 = cnf_mult(cnf, m2n2, k)
cnf_equal(cnf, a, m2subn2)
cnf_equal(cnf, b, mn2)
cnf_equal(cnf, c, m2n2)
def cnf_add(cnf: Formula, a: List[Variable],
b: List[Variable]) -> List[Variable]:
#if the lengths are incorrect, just pad up with zero variables
a, b = cnf_padout(a, b)
carry = cnf.const_false() # The first carry is always 0
out = []
for (ai, bi) in zip(a, b):
res, carry = cnf_1bitadder(cnf, ai, bi, carry)
out.append(res)
out.append(carry)
return out