def runTest(self):
tree_list = dendropy.TreeList(stream=StringIO(
"""((t5:0.161175,t6:0.161175):0.392293,((t4:0.104381,(t2:0.075411,t1:0.075411):1):0.065840,t3:0.170221):0.383247);"""
),
schema="newick")
for i in tree_list:
_LOG.debug(i.get_indented_form())
treesplit.encode_splits(i)
_LOG.debug(i.get_indented_form(splits=True))
i.debug_check_tree(splits=True, logger_obj=_LOG)
root1 = tree_list[0].seed_node
root1e = root1.edge
self.assertEqual(treesplit.split_to_list(root1e.split_bitmask),
range(6))
self.assertEqual(
treesplit.split_to_list(root1e.split_bitmask, one_based=True),
range(1, 7))
self.assertEqual(
treesplit.split_to_list(root1e.split_bitmask,
mask=21,
one_based=True), [1, 3, 5])
self.assertEqual(
treesplit.split_to_list(root1e.split_bitmask, mask=21), [0, 2, 4])
self.assertEqual(treesplit.count_bits(root1e.split_bitmask), 6)
fc1 = root1.child_nodes()[0]
fc1e = fc1.edge
self.assertEqual(treesplit.split_to_list(fc1e.split_bitmask), [0, 1])
self.assertEqual(
treesplit.split_to_list(fc1e.split_bitmask, one_based=True),
[1, 2])
self.assertEqual(
treesplit.split_to_list(fc1e.split_bitmask,
mask=0x15,
one_based=True), [1])
self.assertEqual(
treesplit.split_to_list(fc1e.split_bitmask, mask=0x15), [0])
self.assertEqual(treesplit.count_bits(fc1e.split_bitmask), 2)
def runTest(self):
tree_list = dendropy.TreeList(
stream=StringIO("""((t5:0.161175,t6:0.161175):0.392293,((t4:0.104381,(t2:0.075411,t1:0.075411):1):0.065840,t3:0.170221):0.383247);"""),
schema="newick")
for i in tree_list:
_LOG.debug(i.get_indented_form())
treesplit.encode_splits(i)
_LOG.debug(i.get_indented_form(splits=True))
i.debug_check_tree(splits=True, logger_obj=_LOG)
root1 = tree_list[0].seed_node
root1e = root1.edge
self.assertEqual(treesplit.split_to_list(root1e.split_bitmask), range(6))
self.assertEqual(treesplit.split_to_list(root1e.split_bitmask, one_based=True), range(1,7))
self.assertEqual(treesplit.split_to_list(root1e.split_bitmask, mask=21, one_based=True), [1, 3, 5])
self.assertEqual(treesplit.split_to_list(root1e.split_bitmask, mask=21), [0, 2, 4])
self.assertEqual(treesplit.count_bits(root1e.split_bitmask), 6)
fc1 = root1.child_nodes()[0]
fc1e = fc1.edge
self.assertEqual(treesplit.split_to_list(fc1e.split_bitmask), [0, 1])
self.assertEqual(treesplit.split_to_list(fc1e.split_bitmask, one_based=True), [1, 2])
self.assertEqual(treesplit.split_to_list(fc1e.split_bitmask, mask=0x15, one_based=True), [1])
self.assertEqual(treesplit.split_to_list(fc1e.split_bitmask, mask=0x15), [0])
self.assertEqual(treesplit.count_bits(fc1e.split_bitmask), 2)
def reroot_on_lowest_common_index_path(t, common_mask):
"""This operation is only for unrooted trees that are being merged using
SCM. The path the separates the lowest index taxon in the leaf set
intersection is placed as the first descendant path of the "seed_node" for
the tree.
This assures that all split representations are oriented in the same way
for subsequent operations.
The mask most contain more that 2 bits (there must be an internal node in
the tree that is has degree > 2 wrt the common leafset).
"""
l = lowest_bit_only(common_mask)
assert (l > 0)
assert (count_bits(common_mask) > 2)
# start at the lowest leaf in common.
curr_n = t.split_edges[l].head_node
# walk back toward the root until we find a node that has another bit
p = curr_n.parent_node
while p:
if (p.edge.split_bitmask & common_mask) != l:
break
curr_n = p
p = curr_n.parent_node
without_lowest = common_mask ^ l
taxa_mask = t.seed_node.edge.split_bitmask
if (curr_n.edge.split_bitmask & common_mask) == l:
# we did not make it to the root. Make curr_n, the first_child of the root
t.to_outgroup_position(curr_n,
update_splits=True,
delete_outdegree_one=True)
avoid = curr_n
nd_source = iter(t.seed_node.child_nodes())
try:
while True:
curr_n = nd_source.next()
if curr_n is not avoid:
cm = (curr_n.edge.split_bitmask & without_lowest)
if cm:
if cm == without_lowest:
r = t.seed_node
assert curr_n.parent_node is r
t.reseed_at(curr_n,
update_splits=True,
delete_outdegree_one=True)
t.to_outgroup_position(r,
update_splits=True,
delete_outdegree_one=True)
nd_source = iter(curr_n.child_nodes())
avoid = r
else:
return
except StopIteration:
assert False
return
# we hit the root, now we walk up the tree, to find the a relevant internal
lowest_on_path_to_l = curr_n
comp_mask = (~common_mask) & taxa_mask
children = curr_n.child_nodes()
assert (len(children) > 1)
nd_source = iter(children)
try:
while True:
c = nd_source.next()
cm = c.edge.split_bitmask
masked_cm = cm & common_mask
if masked_cm:
if masked_cm == without_lowest:
curr_n = c
children = curr_n.child_nodes()
assert (len(children) > 1)
nd_source = iter(children)
else:
break
except StopIteration:
raise AssertionError("Reaching supposedly unreachable code")
if curr_n is not t.seed_node:
# We have found the first relevant internal node, we want to make it
# the root. We can do this by putting one of its children into the
# "outgroup position" and then putting the path to lowest commond
# leaf in the outgroup position (this last operation is just a
# rearrangement of the order of children in the root.
children = curr_n.child_nodes()
assert (len(children) > 1)
p = curr_n.parent
t.to_outgroup_position(children[0],
update_splits=True,
delete_outdegree_one=True)
t.to_outgroup_position(p,
update_splits=True,
delete_outdegree_one=True)
else:
# if the root first relevant, node then we just make the path leading
# to the lowest index node the first child of the root
t.to_outgroup_position(lowest_on_path_to_l,
update_splits=True,
delete_outdegree_one=True)
def add_to_scm(to_modify, to_consume, rooted=False, gordons_supertree=False):
"""Adds the tree `to_consume` to the tree `to_modify` in a strict consensus
merge operation. Both trees must have had encode_splits called on them."""
assert (to_modify.taxon_set is to_consume.taxon_set)
taxon_set = to_consume.taxon_set
if rooted:
raise NotImplementedError("rooted form of add_to_scm not implemented")
to_mod_root = to_modify.seed_node
to_mod_split = to_mod_root.edge.split_bitmask
to_consume_root = to_consume.seed_node
to_consume_split = to_consume_root.edge.split_bitmask
leaf_intersection = to_mod_split & to_consume_split
if _IS_DEBUG_LOGGING:
_LOG.debug("add_to_scm:\n %s\n + %s\n%s" %
(str(to_modify), str(to_consume),
format_split(leaf_intersection, taxon_set=taxon_set)))
n_common_leaves = count_bits(leaf_intersection)
if n_common_leaves < 2:
_LOG.error('trees must have at least 2 common leaves')
raise ValueError('trees must have at least 2 common leaves')
if n_common_leaves == 2:
# SCM with 2 leaves in common results in a polytomy
collapse_clade(to_mod_root)
collapse_clade(to_consume_root)
leaves_to_steal = [
c for c in to_consume_root.child_nodes()
if not (leaf_intersection & c.edge.split_bitmask)
]
for leaf in leaves_to_steal:
to_mod_root.add_child(leaf)
to_mod_root.edge.split_bitmask |= leaf.edge.split_bitmask
to_modify.split_edges = {
to_mod_root.edge.split_bitmask: to_mod_root.edge
}
for child in to_mod_root.child_nodes():
to_modify.split_edges[child.edge.split_bitmask] = child.edge
return
# at least 3 leaves in common
tmse = to_modify.split_edges
to_mod_relevant_splits = {}
to_consume_relevant_splits = {}
if not rooted:
if _IS_DEBUG_LOGGING:
to_modify.debug_check_tree(check_splits=True, logger_obj=_LOG)
to_consume.debug_check_tree(check_splits=True, logger_obj=_LOG)
reroot_on_lowest_common_index_path(to_modify, leaf_intersection)
reroot_on_lowest_common_index_path(to_consume, leaf_intersection)
if _IS_DEBUG_LOGGING:
to_modify.debug_check_tree(check_splits=True, logger_obj=_LOG)
to_consume.debug_check_tree(check_splits=True, logger_obj=_LOG)
to_mod_root = to_modify.seed_node
assert (to_mod_root.edge.split_bitmask == to_mod_split)
to_consume_root = to_consume.seed_node
assert (to_consume_root.edge.split_bitmask == to_consume_split)
for s, e in tmse.iteritems():
s = e.split_bitmask
masked = s & leaf_intersection
if masked and masked != leaf_intersection:
e_list = to_mod_relevant_splits.setdefault(masked, [])
e_list.append((s, e))
for s, e in to_consume.split_edges.iteritems():
s = e.split_bitmask
masked = s & leaf_intersection
if masked and masked != leaf_intersection:
e_list = to_consume_relevant_splits.setdefault(masked, [])
e_list.append((s, e))
# Because each of these paths radiates away from the root (none of the paths
# cross the root), the split_bitmasks for deeper edges will be supersets
# of the split_bitmasks for shallower nodes. Thus if we reverse sort we
# get the edges in the order root->tip
for split, path in to_mod_relevant_splits.iteritems():
path.sort(reverse=True)
t = [i[1] for i in path]
del path[:]
path.extend(t)
for split, path in to_consume_relevant_splits.iteritems():
path.sort(reverse=True)
t = [i[1] for i in path]
del path[:]
path.extend(t)
if _IS_DEBUG_LOGGING:
to_modify.debug_check_tree(check_splits=True, logger_obj=_LOG)
to_consume.debug_check_tree(check_splits=True, logger_obj=_LOG)
# first we'll collapse all paths in the common leafset in to_modify that
# are not in to_consume
_collapse_paths_not_found(to_mod_relevant_splits,
to_consume_relevant_splits, tmse)
# Now we'll collapse all paths in the common leafset in to_consume that
# are not in to_modify
_collapse_paths_not_found(to_consume_relevant_splits,
to_mod_relevant_splits)
# first we'll deal with subtrees that are:
# - not in the leaf intersection set, and
# - attached to "relevant" nodes
# We simply move these subtrees from the to_consume tree to the appropriate
# node in to_modify
to_steal = [
i for i in to_consume_root.child_nodes()
if (i.edge.split_bitmask & leaf_intersection) == 0
]
for child in to_steal:
to_mod_root.add_child(child)
to_mod_root.edge.split_bitmask |= child.edge.split_bitmask
for masked_split, to_consume_path in to_consume_relevant_splits.iteritems(
):
to_mod_path = to_mod_relevant_splits.get(masked_split)
if _IS_DEBUG_LOGGING and to_mod_path is None: #to_mod_path is None:
_LOG.debug("%s = mask" %
format_split(leaf_intersection, taxon_set=taxon_set))
_LOG.debug("%s = masked" %
format_split(masked_split, taxon_set=taxon_set))
_LOG.debug("%s = raw" % format_split(
to_consume_path[-1].split_bitmask, taxon_set=taxon_set))
for k, v in to_mod_relevant_splits.iteritems():
_LOG.debug("%s in to_mod_relevant_splits" %
format_split(k, taxon_set=taxon_set))
assert to_mod_path is not None
to_mod_head = to_mod_path[-1].head_node
to_mod_head_edge = to_mod_head.edge
to_consume_head = to_consume_path[-1].head_node
for child in to_consume_head.child_nodes():
if (child.edge.split_bitmask & leaf_intersection) == 0:
# child is the root of a subtree that has no children in the leaf_intersection
to_mod_head.add_child(child)
to_mod_head_edge.split_bitmask |= child.edge.split_bitmask
if len(to_consume_path) > 1:
if len(to_mod_path) > 1:
# collision
if gordons_supertree:
for edge in to_mod_path[2:]:
p = edge.tail_node
c = edge.head_node
sibs = p.child_nodes()
for sib in sibs:
_LOG.debug("sib is %s" % (sib.compose_newick()))
if sib is not c:
if not sib.is_leaf():
collapse_clade(sib)
collapse_edge(sib.edge)
collapse_edge(p.edge)
mid_node = to_mod_path[0].head_node
for edge in to_consume_path[1:]:
p = edge.tail_node
avoid = edge.head_node
for child in p.child_nodes():
_LOG.debug("child is %s" %
(child.compose_newick()))
if child is not avoid:
mid_node.add_child(child)
collapse_clade(child)
if not child.is_leaf():
collapse_edge(child.edge)
mid_node.edge.split_bitmask |= child.edge.split_bitmask
else:
for edge in to_mod_path[1:-1]:
collapse_edge(edge)
mid_node = to_mod_path[0].head_node
for edge in to_consume_path[1:]:
p = edge.tail_node
avoid = edge.head_node
for child in p.child_nodes():
if child is not avoid:
mid_node.add_child(child)
mid_node.edge.split_bitmask |= child.edge.split_bitmask
else:
# we have to move the subtrees from to_consume to to_modify
to_mod_edge = to_mod_path[0]
to_mod_tail, to_mod_head = to_mod_edge.tail_node, to_mod_edge.head_node
deepest_edge_to_move = to_consume_path[0]
deepest_node_to_move = deepest_edge_to_move.head_node
tipmost_edge_to_move = to_consume_path[-1]
tipmost_node_to_move = tipmost_edge_to_move.tail_node
prev_head = tipmost_edge_to_move.head_node
to_mod_tail.add_child(deepest_node_to_move)
to_mod_tail.remove_child(to_mod_head)
tipmost_node_to_move.add_child(to_mod_head)
tipmost_node_to_move.remove_child(prev_head)
encode_splits(to_modify)
def reroot_on_lowest_common_index_path(t, common_mask):
"""This operation is only for unrooted trees that are being merged using
SCM. The path the separates the lowest index taxon in the leaf set
intersection is placed as the first descendant path of the "seed_node" for
the tree.
This assures that all split representations are oriented in the same way
for subsequent operations.
The mask most contain more that 2 bits (there must be an internal node in
the tree that is has degree > 2 wrt the common leafset).
"""
l = lowest_bit_only(common_mask)
assert(l > 0)
assert(count_bits(common_mask) > 2)
# start at the lowest leaf in common.
curr_n = t.split_edges[l].head_node
# walk back toward the root until we find a node that has another bit
p = curr_n.parent_node
while p:
if (p.edge.split_bitmask & common_mask) != l:
break
curr_n = p
p = curr_n.parent_node
without_lowest = common_mask^l
taxa_mask = t.seed_node.edge.split_bitmask
if (curr_n.edge.split_bitmask & common_mask) == l:
# we did not make it to the root. Make curr_n, the first_child of the root
t.to_outgroup_position(curr_n, update_splits=True, delete_outdegree_one=True)
avoid = curr_n
nd_source = iter(t.seed_node.child_nodes())
try:
while True:
curr_n = nd_source.next()
if curr_n is not avoid:
cm = (curr_n.edge.split_bitmask & without_lowest)
if cm:
if cm == without_lowest:
r = t.seed_node
assert curr_n.parent_node is r
t.reseed_at(curr_n, update_splits=True, delete_outdegree_one=True)
t.to_outgroup_position(r, update_splits=True, delete_outdegree_one=True)
nd_source = iter(curr_n.child_nodes())
avoid = r
else:
return
except StopIteration:
assert False
return
# we hit the root, now we walk up the tree, to find the a relevant internal
lowest_on_path_to_l = curr_n
comp_mask = (~common_mask) & taxa_mask
children = curr_n.child_nodes()
assert(len(children) > 1)
nd_source = iter(children)
try:
while True:
c = nd_source.next()
cm = c.edge.split_bitmask
masked_cm = cm & common_mask
if masked_cm:
if masked_cm == without_lowest:
curr_n = c
children = curr_n.child_nodes()
assert(len(children) > 1)
nd_source = iter(children)
else:
break
except StopIteration:
raise AssertionError("Reaching supposedly unreachable code")
if curr_n is not t.seed_node:
# We have found the first relevant internal node, we want to make it
# the root. We can do this by putting one of its children into the
# "outgroup position" and then putting the path to lowest commond
# leaf in the outgroup position (this last operation is just a
# rearrangement of the order of children in the root.
children = curr_n.child_nodes()
assert(len(children) > 1)
p = curr_n.parent
t.to_outgroup_position(children[0], update_splits=True, delete_outdegree_one=True)
t.to_outgroup_position(p, update_splits=True, delete_outdegree_one=True)
else:
# if the root first relevant, node then we just make the path leading
# to the lowest index node the first child of the root
t.to_outgroup_position(lowest_on_path_to_l, update_splits=True, delete_outdegree_one=True)
def add_to_scm(to_modify, to_consume, rooted=False, gordons_supertree=False):
"""Adds the tree `to_consume` to the tree `to_modify` in a strict consensus
merge operation. Both trees must have had encode_splits called on them."""
assert(to_modify.taxon_set is to_consume.taxon_set)
taxon_set = to_consume.taxon_set
if rooted:
raise NotImplementedError("rooted form of add_to_scm not implemented")
to_mod_root = to_modify.seed_node
to_mod_split = to_mod_root.edge.split_bitmask
to_consume_root = to_consume.seed_node
to_consume_split = to_consume_root.edge.split_bitmask
leaf_intersection = to_mod_split & to_consume_split
if _IS_DEBUG_LOGGING:
_LOG.debug("add_to_scm:\n %s\n + %s\n%s" % (str(to_modify), str(to_consume), format_split(leaf_intersection, taxon_set=taxon_set)))
n_common_leaves = count_bits(leaf_intersection)
if n_common_leaves < 2:
_LOG.error('trees must have at least 2 common leaves')
raise ValueError('trees must have at least 2 common leaves')
if n_common_leaves == 2:
# SCM with 2 leaves in common results in a polytomy
collapse_clade(to_mod_root)
collapse_clade(to_consume_root)
leaves_to_steal = [c for c in to_consume_root.child_nodes() if not (leaf_intersection & c.edge.split_bitmask)]
for leaf in leaves_to_steal:
to_mod_root.add_child(leaf)
to_mod_root.edge.split_bitmask |= leaf.edge.split_bitmask
to_modify.split_edges = {to_mod_root.edge.split_bitmask : to_mod_root.edge}
for child in to_mod_root.child_nodes():
to_modify.split_edges[child.edge.split_bitmask] = child.edge
return
# at least 3 leaves in common
tmse = to_modify.split_edges
to_mod_relevant_splits = {}
to_consume_relevant_splits = {}
if not rooted:
if _IS_DEBUG_LOGGING:
to_modify.debug_check_tree(check_splits=True, logger_obj=_LOG)
to_consume.debug_check_tree(check_splits=True, logger_obj=_LOG)
reroot_on_lowest_common_index_path(to_modify, leaf_intersection)
reroot_on_lowest_common_index_path(to_consume, leaf_intersection)
if _IS_DEBUG_LOGGING:
to_modify.debug_check_tree(check_splits=True, logger_obj=_LOG)
to_consume.debug_check_tree(check_splits=True, logger_obj=_LOG)
to_mod_root = to_modify.seed_node
assert(to_mod_root.edge.split_bitmask == to_mod_split)
to_consume_root = to_consume.seed_node
assert(to_consume_root.edge.split_bitmask == to_consume_split)
for s, e in tmse.iteritems():
s = e.split_bitmask
masked = s & leaf_intersection
if masked and masked != leaf_intersection:
e_list = to_mod_relevant_splits.setdefault(masked, [])
e_list.append((s, e))
for s, e in to_consume.split_edges.iteritems():
s = e.split_bitmask
masked = s & leaf_intersection
if masked and masked != leaf_intersection:
e_list = to_consume_relevant_splits.setdefault(masked, [])
e_list.append((s, e))
# Because each of these paths radiates away from the root (none of the paths
# cross the root), the split_bitmasks for deeper edges will be supersets
# of the split_bitmasks for shallower nodes. Thus if we reverse sort we
# get the edges in the order root->tip
for split, path in to_mod_relevant_splits.iteritems():
path.sort(reverse=True)
t = [i[1] for i in path]
del path[:]
path.extend(t)
for split, path in to_consume_relevant_splits.iteritems():
path.sort(reverse=True)
t = [i[1] for i in path]
del path[:]
path.extend(t)
if _IS_DEBUG_LOGGING:
to_modify.debug_check_tree(check_splits=True, logger_obj=_LOG)
to_consume.debug_check_tree(check_splits=True, logger_obj=_LOG)
# first we'll collapse all paths in the common leafset in to_modify that
# are not in to_consume
_collapse_paths_not_found(to_mod_relevant_splits, to_consume_relevant_splits, tmse)
# Now we'll collapse all paths in the common leafset in to_consume that
# are not in to_modify
_collapse_paths_not_found(to_consume_relevant_splits, to_mod_relevant_splits)
# first we'll deal with subtrees that are:
# - not in the leaf intersection set, and
# - attached to "relevant" nodes
# We simply move these subtrees from the to_consume tree to the appropriate
# node in to_modify
to_steal = [i for i in to_consume_root.child_nodes() if (i.edge.split_bitmask & leaf_intersection) == 0]
for child in to_steal:
to_mod_root.add_child(child)
to_mod_root.edge.split_bitmask |= child.edge.split_bitmask
for masked_split, to_consume_path in to_consume_relevant_splits.iteritems():
to_mod_path = to_mod_relevant_splits.get(masked_split)
if _IS_DEBUG_LOGGING and to_mod_path is None: #to_mod_path is None:
_LOG.debug("%s = mask" % format_split(leaf_intersection, taxon_set=taxon_set))
_LOG.debug("%s = masked" % format_split(masked_split, taxon_set=taxon_set))
_LOG.debug("%s = raw" % format_split(to_consume_path[-1].split_bitmask, taxon_set=taxon_set))
for k, v in to_mod_relevant_splits.iteritems():
_LOG.debug("%s in to_mod_relevant_splits" % format_split(k, taxon_set=taxon_set))
assert to_mod_path is not None
to_mod_head = to_mod_path[-1].head_node
to_mod_head_edge = to_mod_head.edge
to_consume_head = to_consume_path[-1].head_node
for child in to_consume_head.child_nodes():
if (child.edge.split_bitmask & leaf_intersection) == 0:
# child is the root of a subtree that has no children in the leaf_intersection
to_mod_head.add_child(child)
to_mod_head_edge.split_bitmask |= child.edge.split_bitmask
if len(to_consume_path) > 1:
if len(to_mod_path) > 1:
# collision
if gordons_supertree:
for edge in to_mod_path[2:]:
p = edge.tail_node
c = edge.head_node
sibs = p.child_nodes()
for sib in sibs:
_LOG.debug("sib is %s" % (sib.compose_newick()))
if sib is not c:
if not sib.is_leaf():
collapse_clade(sib)
collapse_edge(sib.edge)
collapse_edge(p.edge)
mid_node = to_mod_path[0].head_node
for edge in to_consume_path[1:]:
p = edge.tail_node
avoid = edge.head_node
for child in p.child_nodes():
_LOG.debug("child is %s" % (child.compose_newick()))
if child is not avoid:
mid_node.add_child(child)
collapse_clade(child)
if not child.is_leaf():
collapse_edge(child.edge)
mid_node.edge.split_bitmask |= child.edge.split_bitmask
else:
for edge in to_mod_path[1:-1]:
collapse_edge(edge)
mid_node = to_mod_path[0].head_node
for edge in to_consume_path[1:]:
p = edge.tail_node
avoid = edge.head_node
for child in p.child_nodes():
if child is not avoid:
mid_node.add_child(child)
mid_node.edge.split_bitmask |= child.edge.split_bitmask
else:
# we have to move the subtrees from to_consume to to_modify
to_mod_edge = to_mod_path[0]
to_mod_tail, to_mod_head = to_mod_edge.tail_node, to_mod_edge.head_node
deepest_edge_to_move = to_consume_path[0]
deepest_node_to_move = deepest_edge_to_move.head_node
tipmost_edge_to_move = to_consume_path[-1]
tipmost_node_to_move = tipmost_edge_to_move.tail_node
prev_head = tipmost_edge_to_move.head_node
to_mod_tail.add_child(deepest_node_to_move)
to_mod_tail.remove_child(to_mod_head)
tipmost_node_to_move.add_child(to_mod_head)
tipmost_node_to_move.remove_child(prev_head)
encode_splits(to_modify)
def runTest(self):
self.assertEqual(treesplit.count_bits(21), 3)
def runTest(self):
self.assertEqual(treesplit.count_bits(21), 3)