def test_l1_layer(byte_value: int, num_bytes: int) -> None:
bits = bitarray()
bits.frombytes(bytes([byte_value]) * num_bytes)
# Manually compute the popcount sums here.
level_1_size = math.ceil(len(bits) / 2048)
level_1: List[int] = [0] * level_1_size
v = memoryview(bits)
for byte_offset in range(0, len(v), 8):
level_1_idx = 1 + byte_offset // 256
if level_1_idx < len(level_1):
level_1[level_1_idx] += popcount(v[byte_offset:byte_offset + 8])
for byte_offset in range(0, num_bytes, 1 << 29):
level_1_idx = byte_offset // 256
level_1[level_1_idx] = 0
for i in range(1, len(level_1)):
level_1[i] += level_1[i - 1]
poppy = Poppy(bits)
# Python will literally asplode if we try to use list equality to compare
# the two lists.
for i in range(0, len(level_1)):
assert poppy._level_1[2 * i] == level_1[i], f"Failed at {i}"
def __init__(
self,
values: Iterator[int],
*,
num_values: int,
max_value: int,
num_lower_bits: Optional[int] = None
) -> None:
"""
Compressed representation of a monotonically-increasing sequence of
nonnegative integers.
"""
self._size = num_values
# Number of bits needed to store the largest value.
w = math.ceil(math.log2(max(1, max_value)))
# Number of lower-order bits of each value to store in the lower
# bit vector.
if num_lower_bits is None:
num_lower_bits = math.floor(max_value / num_values)
self._num_lower_bits = num_lower_bits
if num_lower_bits != 0:
self._lower_bits = bitarray()
else:
self._lower_bits = None
# Number of higher-order bits of each value to store in the upper bit
# vector.
self._num_upper_bits = w - num_lower_bits
self._upper_bits = bitarray()
previous_value = 0
for value in values:
if value > max_value:
raise ValueError(
f"The value '{value}' is larger than the max_value '{max_value}'"
)
if value < previous_value:
raise ValueError(
"Values must be non-decreasing. "
f"(Found '{previous_value}' followed by '{value}')"
)
if self._lower_bits is not None:
binary_str = f"{value:b}"
lower_bits_str = binary_str[-num_lower_bits:].rjust(num_lower_bits, '0')
self._lower_bits.extend(lower_bits_str)
upper_bits = value >> num_lower_bits
previous_upper_bits = previous_value >> num_lower_bits
if previous_value != -1:
self._upper_bits.extend([False] * max(0, upper_bits - previous_upper_bits))
self._upper_bits.append(True)
previous_value = value
self._upper_bits.append(False)
self._upper_poppy = Poppy(self._upper_bits)
def test_getitem(bb: bytes) -> None:
assume(len(bb) % 8 == 0)
bits = bitarray()
bits.frombytes(bb)
poppy = Poppy(bits)
for i in range(len(bits)):
assert poppy[i] == bits[i]
def test_rank_zero(bb: bytes) -> None:
assume(len(bb) % 8 == 0)
bits = bitarray()
bits.frombytes(bb)
poppy = Poppy(bits)
for i in range(len(bits)):
assert poppy.rank_zero(i) == sum(1 - int(b) for b in bits[0:(i + 1)])
def test_select_structure(byte_value: int, num_bytes: int) -> None:
bits = bitarray()
bits.frombytes(bytes([byte_value]) * num_bytes)
poppy = Poppy(bits)
for level_0_idx, sampling_answers in enumerate(poppy._select_structure):
for i, sampling_answer in enumerate(sampling_answers):
sum_left = poppy._level_0[level_0_idx]
assert (poppy.rank(sampling_answer + ((1 << 32) * level_0_idx)) -
sum_left) == (i * 8192 + 1)
def test_select_binary_search_bug_is_not_present_2020_09_06() -> None:
i = 3586
bits = bitarray(i)
bits.setall(False)
bits[0] = True
bits[i - 1] = True
poppy = Poppy(bits)
assert poppy.select(0) == 0
assert poppy.select(1) == i - 1
def test_select_poppy_big(byte_value: int, num_bytes: int,
step_size: int) -> None:
bits = bitarray()
bits.frombytes(bytes([byte_value]) * num_bytes)
poppy = Poppy(bits)
a = 0
for i, b in enumerate(bits):
if b:
if i % step_size == 0:
assert poppy.select(a) == i
a += 1
def test_rank_big(byte_value: int, num_bytes: int, step_size: int) -> None:
bits = bitarray()
bits.frombytes(bytes([byte_value]) * num_bytes)
poppy = Poppy(bits)
i = 0
sum_bits = sum(bits[0:1])
while i < len(bits):
assert poppy.rank(i) == sum_bits
next_i = i + step_size
partial_sum = sum(bits[(i + 1):min(next_i + 1, len(bits))])
i = next_i
sum_bits += partial_sum
def test_select_zero_poppy(bb: bytes) -> None:
assume(len(bb) % 8 == 0)
bits = bitarray()
bits.frombytes(bb)
poppy = Poppy(bits)
select_zero_answers: List[int] = []
for i in range(len(bits)):
if not bits[i]:
select_zero_answers.append(i)
for i, pos in enumerate(select_zero_answers):
assert poppy.select_zero(i) == pos
def __init__(
self,
*,
root: A,
get_left_child: Callable[[A], Optional[A]],
get_right_child: Callable[[A], Optional[A]]
) -> None:
queue = deque([root])
self._bits = bitarray()
while queue:
tree_node = queue.popleft()
for child in [get_left_child(tree_node), get_right_child(tree_node)]:
if child is not None:
self._bits.append(True)
queue.append(child)
else:
self._bits.append(False)
self._poppy = Poppy(self._bits)
def test_l0_layer(byte_value: int, num_bytes: int) -> None:
bits = bitarray()
bits.frombytes(bytes([byte_value]) * num_bytes)
# Manually compute the popcount sums here.
num_popcount_sums = math.ceil(len(bits) / (2**32))
popcount_sums: List[int] = [0] * num_popcount_sums
v = memoryview(bits)
for byte_offset in range(0, len(v), 8):
popcount_idx = 1 + byte_offset // (2**29)
if popcount_idx < len(popcount_sums):
popcount_sums[popcount_idx] += popcount(v[byte_offset:byte_offset +
8])
for i in range(1, len(popcount_sums)):
popcount_sums[i] += popcount_sums[i - 1]
poppy = Poppy(bits)
assert list(poppy._level_0) == popcount_sums
def _extract_runs(self, values: IndexedIntSequence) -> List[HuffmanTreeNode]:
run_starts: List[int] = [0]
for i in range(1, len(values)):
if values[i] < values[i - 1]:
run_starts.append(i)
run_starts_bitarray = bitarray(len(values))
run_starts_bitarray.setall(False)
for start in run_starts:
run_starts_bitarray[start] = True
self._run_starts = Poppy(run_starts_bitarray)
runs: List[HuffmanTreeNode] = []
for i in range(len(run_starts)):
from_index = run_starts[i]
until_index = run_starts[i + 1] if i + 1 < len(run_starts) else len(values)
runs.append(Run(from_=from_index, until=until_index))
return runs
def test_l2_layer(bb: bytes) -> None:
assume(len(bb) % 8 == 0)
bits = bitarray()
bits.frombytes(bb)
poppy = Poppy(bits)
for byte_offset in range(0, len(bb), 64):
basic_block_idx = (byte_offset % 256) // 64
if basic_block_idx != 3:
# Calculate the sum of the bits in the 64-byte block.
bit_start = 8 * byte_offset
bit_end = min(len(bits), bit_start + 512)
expected_pop_count = sum(bits[bit_start:bit_end])
level_2_idx = (byte_offset // 256) * 2 + 1
packed_relative_counts = poppy._level_1[level_2_idx]
actual_pop_count = poppy._get_relative_count(
basic_block_index=basic_block_idx,
packed_relative_counts=packed_relative_counts)
assert expected_pop_count == actual_pop_count
def test_rank_boundary() -> None:
bits = bitarray()
bits.frombytes(bytes([255]) * ((1 << 29) + 32))
poppy = Poppy(bits)
i = 1 << 32
assert poppy.rank(i) == i + 1
def _build_huffman_tree(self, values: IndexedIntSequence, tree_nodes: List[HuffmanTreeNode]) -> None:
# Determine the tree topology.
heapq.heapify(tree_nodes)
merge_sort_bitarray = bitarray()
merge_sort_offset = 0
while len(tree_nodes) > 1:
x = heapq.heappop(tree_nodes)
y = heapq.heappop(tree_nodes)
merged = HuffmanInnerNode(
size=len(x) + len(y),
left_child=x,
right_child=y,
merge_sort_offset=merge_sort_offset
)
# Populate the merge sort bitarray's values
it_left = ((value, False) for value in x.iterator(values, merge_sort_bitarray))
it_right = ((value, True) for value in y.iterator(values, merge_sort_bitarray))
for _, b in heapq.merge(it_left, it_right):
merge_sort_bitarray.append(b)
merge_sort_offset += 1
heapq.heappush(tree_nodes, merged)
# Build a LOUDS representation of the tree topology
louds = LoudsBinaryTree(
root=tree_nodes[0],
get_left_child=lambda n: n.left_child if isinstance(n, HuffmanInnerNode) else None,
get_right_child=lambda n: n.right_child if isinstance(n, HuffmanInnerNode) else None
)
# The data stored at each node of the tree is:
# - The offset into a bitarray (if a node is an inner node)
# - The offset into the original permutation (if a node is a leaf node)
node_data: List[int] = []
sizes: List[int] = []
queue = deque(tree_nodes)
while queue:
tree_node = queue.popleft()
if isinstance(tree_node, HuffmanInnerNode):
node_data.append(tree_node.merge_sort_offset)
sizes.append(len(tree_node))
queue.append(tree_node.left_child)
queue.append(tree_node.right_child)
elif isinstance(tree_node, Run):
node_data.append(tree_node.from_)
sizes.append(len(tree_node))
else:
raise TypeError
self._louds = louds
self._node_data = node_data
self._merge_sort_poppy = Poppy(merge_sort_bitarray)
number_of_runs = self._run_starts.rank(len(self._run_starts) - 1)
self._run_rank_to_louds_id = [0] * number_of_runs
for louds_id in range(len(self._node_data)):
if self._louds.is_leaf(louds_id):
run_offset = self._node_data[louds_id]
run_rank = self._run_starts.rank(run_offset)
self._run_rank_to_louds_id[run_rank - 1] = louds_id