def test_function_properties():
bdd = _bdd.BDD()
bdd.declare('x', 'y')
order = dict(x=0, y=1)
bdd.reorder(order)
u = bdd.add_expr('x \/ y')
y = bdd.add_expr('y')
# Assigned first because in presence of a bug
# different property calls could yield
# different values.
level = u.level
assert level == 0, level
var = u.var
assert var == 'x', var
low = u.low
assert low == y, low
high = u.high
assert high == bdd.true, high
ref = u.ref
assert ref == 1, ref
assert not u.negated
support = u.support
assert support == {'x', 'y'}, support
# terminal
u = bdd.false
assert u.var is None, u.var
assert u.low is None, u.low
assert u.high is None, u.high
def test_sifting():
# Figs. 6.24, 6.25 Baier 2008
g = BDD({'z1': 0, 'z2': 1, 'z3': 2, 'y1': 3, 'y2': 4, 'y3': 5})
u = g.add_expr('(z1 & y1) | (z2 & y2) | (z3 & y3)')
g.incref(u)
g.collect_garbage()
n = len(g)
assert n == 15, n
_bdd.reorder(g)
u_ = g.add_expr('(z1 & y1) | (z2 & y2) | (z3 & y3)')
g.incref(u)
g.collect_garbage()
g.assert_consistent()
assert u == u_, (u, u_)
def test_sifting():
# Figs. 6.24, 6.25 Baier 2008
g = BDD({'z1': 0, 'z2': 1, 'z3': 2,
'y1': 3, 'y2': 4, 'y3': 5})
u = g.add_expr('(z1 & y1) | (z2 & y2) | (z3 & y3)')
g.incref(u)
g.collect_garbage()
n = len(g)
assert n == 15, n
_bdd.reorder(g)
u_ = g.add_expr('(z1 & y1) | (z2 & y2) | (z3 & y3)')
g.incref(u)
g.collect_garbage()
g.assert_consistent()
assert u == u_, (u, u_)
def test_reorder_2():
bdd = _bdd.BDD()
vrs = [
'x', 'y', 'z', 'a', 'b', 'c', 'e', 'z1', 'z2', 'z3', 'y1', 'y2', 'y3'
]
bdd = _bdd.BDD()
bdd.declare(*vrs)
expr_1 = '(~ z \/ (c /\ b)) /\ e /\ (a /\ (~ x \/ y))'
# Figs. 6.24, 6.25 Baier 2008
expr_2 = '(z1 /\ y1) \/ (z2 /\ y2) \/ (z3 /\ y3)'
u = bdd.add_expr(expr_1)
v = bdd.add_expr(expr_2)
bdd.collect_garbage()
n = len(bdd)
assert n == 23, n
bdd.reorder()
n_ = len(bdd)
assert n > n_, (n, n_)
bdd.assert_consistent()
def test_reorder():
bdd = _bdd.BDD()
bdd.declare('x', 'y', 'z')
u = bdd.add_expr('(x /\ y) \/ z')
bdd.reorder()
assert u in bdd
def reorder(bdd, order=None):
"""Apply Rudell's sifting algorithm to `bdd`."""
_bdd.reorder(bdd._bdd, order=order)
def reorder(bdd, order=None):
"""Apply Rudell's sifting algorithm to `bdd`."""
_bdd.reorder(bdd._bdd, order=order)
def bdd_to_mdd(bdd, dvars):
"""Return MDD for given BDD.
Caution: collects garbage.
`dvars` must map each MDD variable to the
corresponding bits in BDD.
Also, it should give the order as "level" keys.
"""
# i = level in BDD
# j = level in MDD
# bit = BDD variable
# var = MDD variable
#
# map from bits to integers
bit_to_var = dict()
for var, d in dvars.iteritems():
bits = d['bitnames']
b = {bit: var for bit in bits}
bit_to_var.update(b)
# find target bit ordering
ordering = list() # target
levels = {d['level']: var for var, d in dvars.iteritems()}
m = len(levels)
for j in xrange(m):
var = levels[j]
bits = dvars[var]['bitnames']
ordering.extend(bits)
bit_to_sort = {bit: k for k, bit in enumerate(ordering)}
# reorder
bdd.collect_garbage()
_bdd.reorder(bdd, order=bit_to_sort)
# BDD -> MDD
mdd = MDD(dvars)
# zones of bits per integer var
zones = dict()
for var, d in dvars.iteritems():
bits = d['bitnames']
lsb = bits[0]
msb = bits[-1]
min_level = bit_to_sort[lsb]
max_level = bit_to_sort[msb]
zones[var] = (min_level, max_level)
# reverse edges
pred = {u: set() for u in bdd}
for u, (_, v, w) in bdd._succ.iteritems():
assert u > 0, u
# terminal ?
if u == 1:
continue
# non-terminal
pred[abs(v)].add(u)
pred[abs(w)].add(u)
# find BDD nodes mentioned from above
rm = set()
for u, p in pred.iteritems():
rc = bdd.ref(u)
k = len(p) # number of predecessors
# has external refs ?
if rc > k:
continue
# has refs from outside zone ?
i, _, _ = bdd._succ[u]
bit = bdd.var_at_level(i)
var = bit_to_var[bit]
min_level, _ = zones[var]
pred_levels = {bdd._succ[v][0] for v in p}
min_pred_level = min(pred_levels)
if min_pred_level < min_level:
continue
# referenced only from inside zone
rm.add(u)
pred = {u: p for u, p in pred.iteritems() if u not in rm}
# build layer by layer
# TODO: use bins, instad of iterating through all nodes
bdd.assert_consistent()
g = to_nx(bdd, roots=[u])
for u in pred:
g.add_node(u, color='red')
for u in g:
if u == 1:
continue
i, _, _ = bdd._succ[u]
var = bdd.var_at_level(i)
label = '{var}-{u}'.format(var=var, u=u)
g.add_node(u, label=label)
pd = nx.to_pydot(g)
pd.write_pdf('bdd_colored.pdf')
bdd.dump('bdd.pdf')
umap = dict()
umap[1] = 1
for u, i, v, w in bdd.levels(skip_terminals=True):
# ignore function ?
if u not in pred:
continue
# keep `u`
bit = bdd.var_at_level(i)
var = bit_to_var[bit]
bits = dvars[var]['bitnames']
bit_succ = list()
for d in _enumerate_integer(bits):
x = bdd.cofactor(u, d)
bit_succ.append(x)
# map edges
int_succ = [umap[abs(z)] if z > 0 else -umap[abs(z)]
for z in bit_succ]
# add new MDD node at level j
j = dvars[var]['level']
r = mdd.find_or_add(j, *int_succ)
# cache
# signed r, because low never inverted,
# opposite to canonicity chosen for BDDs
umap[u] = r
return mdd, umap
