class MMCRWPolicy(object):
def __init__(self,
cache_entries_limit,
ghost_entries_limit,
trace_size_limit,
csv_suffix="_mmc.csv"):
self.full_cache = FastRBTree()
self.was_hit = None
self.was_ghost_hit = None
self.num_hits = 0
self.num_requests = 0
self.cache_entries_limit = cache_entries_limit
self.ghost_entries_limit = ghost_entries_limit
self.trace_size_limit = trace_size_limit
self.trace = collections.deque()
self.stack = RBTree()
self.ranker = RBTree()
self.generation = 0
# During startup, this will act like an LRU.
self.startup = True
self.EM_period = 50 * int(np.ceil(np.log(trace_size_limit)))
self.countdown_to_EM = trace_size_limit // 2
self.tau = [0.25, 0.25, 0.25, 0.25]
self.theta = [0.5, 0.5, 0.5, 0.5]
self.acc_tau = [0.0, 0.0, 0.0, 0.0]
self.acc_theta = [0.0, 0.0, 0.0, 0.0]
self.num_in_cache = 0
self.num_in_full_cache = 0
self.num_reads = 0
self.csv_suffix = csv_suffix
self.ts_order = [
'row', 'hit', 'ghost_hit', 'tau_R_SDD', 'tau_R_IRM', 'tau_W_SDD',
'tau_W_IRM', 'theta_R_SDD', 'theta_R_IRM', 'theta_W_SDD',
'theta_W_IRM', 'depth', 'rank', 'Z_R_SDD', 'Z_R_IRM', 'Z_W_SDD',
'Z_W_IRM', 'Z_sum'
]
self.ts_datapoint = {key: None for key in self.ts_order}
self.ts_datapoint['row'] = 0
self.ts_file = open("csv/mmc_rw" + self.csv_suffix, "w")
self.ts_writer = csv.writer(self.ts_file)
self.ts_writer.writerow(self.ts_order)
self.evict_order = ['row', 'depth', 'rank', 'value', 'opcode']
self.evict_datapoint = {key: None for key in self.evict_order}
self.evict_datapoint['row'] = 0
self.evict_file = open("csv/mmc_rw_evict" + self.csv_suffix, "w")
self.evict_writer = csv.writer(self.evict_file)
self.evict_writer.writerow(self.evict_order)
self.purge_order = ['row', 'depth', 'rank', 'value', 'opcode']
self.purge_datapoint = {key: None for key in self.purge_order}
self.purge_datapoint['row'] = 0
self.purge_file = open("csv/mmc_rw_purge" + self.csv_suffix, "w")
self.purge_writer = csv.writer(self.purge_file)
self.purge_writer.writerow(self.purge_order)
def request(self, page, opcode):
self.num_requests += 1
self.was_hit = False
self.was_ghost_hit = False
node = self.get_node(page)
if node:
self.was_ghost_hit = True
if not node.is_evicted:
self.num_hits += 1
self.was_hit = True
Z = self.calculate_Z(node.depth, node.rank, node.opcode)
node.hit_count += Z[R_IRM] + Z[W_IRM]
else:
node = Node(self)
node.hit_count = self.tau[R_IRM] + self.tau[W_IRM]
node.page_key = page
self.full_cache[page] = node
if not self.was_hit:
self.num_in_cache += 1
if not self.was_ghost_hit:
self.num_in_full_cache += 1
else:
if node.opcode == 'r':
self.num_reads -= 1
if opcode == 'r':
self.num_reads += 1
node.is_evicted = node.is_purged = False
record = Record(self, node)
self.add_trace_record(record)
node.opcode = opcode
if len(self.trace) > self.trace_size_limit:
popped_record = self.trace.popleft()
self.update_tau_and_theta_accs(record, increment=True)
self.update_tau_and_theta_accs(popped_record, increment=False)
self.refresh_params()
popped_record.node.hit_count -= popped_record.Z[R_IRM]
popped_record.node.hit_count -= popped_record.Z[W_IRM]
node.restack()
node.rerank()
self.countdown_to_EM -= 1
if self.countdown_to_EM == 0:
self.EM_algorithm(delta=0.00001)
self.countdown_to_EM = self.EM_period
self.startup = False
if (self.num_in_cache > self.cache_entries_limit
or self.num_in_full_cache >
self.cache_entries_limit + self.ghost_entries_limit):
self.pageout()
#dump_cache(self, "exp")
def add_trace_record(self, record):
self.ts_datapoint['row'] = self.num_requests
if self.was_hit:
self.ts_datapoint['hit'] = 1
else:
self.ts_datapoint['hit'] = 0
if self.was_ghost_hit:
self.ts_datapoint['ghost_hit'] = 1
else:
self.ts_datapoint['ghost_hit'] = 0
self.ts_datapoint['tau_R_SDD'] = self.tau[R_SDD]
self.ts_datapoint['tau_R_IRM'] = self.tau[R_IRM]
self.ts_datapoint['tau_W_SDD'] = self.tau[W_SDD]
self.ts_datapoint['tau_W_IRM'] = self.tau[W_IRM]
self.ts_datapoint['theta_R_SDD'] = self.theta[R_SDD]
self.ts_datapoint['theta_R_IRM'] = self.theta[R_IRM]
self.ts_datapoint['theta_W_SDD'] = self.theta[W_SDD]
self.ts_datapoint['theta_W_IRM'] = self.theta[W_IRM]
self.ts_datapoint['Z_R_SDD'] = record.Z[R_SDD]
self.ts_datapoint['Z_R_IRM'] = record.Z[R_IRM]
self.ts_datapoint['Z_W_SDD'] = record.Z[W_SDD]
self.ts_datapoint['Z_W_IRM'] = record.Z[W_IRM]
self.ts_datapoint['Z_sum'] = sum(record.Z)
self.ts_datapoint['depth'] = record.depth
self.ts_datapoint['rank'] = record.node.rank
self.ts_writer.writerow(
[self.ts_datapoint[key] for key in self.ts_order])
self.ts_file.flush()
self.trace.append(record)
def pageout(self):
min_node = None
min_node_value = None
min_ghost = None
min_ghost_value = None
for depth, node in enumerate(self.stack.values()):
node.depth_memo = depth
for rank, node in enumerate(self.ranker.values()):
node.recompute_expected_value(depth=node.depth_memo, rank=rank)
value = node.expected_value
if not node.is_evicted:
if min_node is None or value < min_node_value:
min_node = node
min_node_value = value
if min_ghost is None or value < min_ghost_value:
min_ghost = node
min_ghost_value = value
if self.num_in_cache > self.cache_entries_limit:
self.evict(min_node)
if (self.num_in_full_cache >
self.cache_entries_limit + self.ghost_entries_limit):
self.purge(min_ghost)
def EM_algorithm(self, delta):
def abs_sum():
return sum(self.tau) + sum(self.theta)
before = delta + 4.0
i = 0
# We need to detect if we're in a "nonsense" local optimum. The
# algorithm will optimize to the global maximum if we aren't in one of
# these cases.
if (self.startup or min(self.tau) < 0.00001
or min(self.theta) < 0.00001):
use_hard_Z = True
else:
use_hard_Z = False
while abs(before - abs_sum()) > delta:
before = abs_sum()
hard_Z = [0.25, 0.25, 0.25, 0.25
] if use_hard_Z and i == 0 else None
self.E_step(hard_Z=hard_Z)
i += 1
self.M_step()
# Since we are rearranging the ranks, it's possible that we can
# get into a situation where the ranks shift in a cycle such
# that the tau delta is always exeeded. I've only seen this limit
# hit when the trace size is very small (e.g. 10).
if i > 50:
break
def E_step(self, hard_Z=None):
"""Treat self.tau and self.theta as constants."""
for node in self.full_cache.values():
node._hit_count = 0.0
for record in self.trace:
if hard_Z is None:
if record.node.is_purged:
rank = record.node.rank_purge_memo
else:
rank = record.node.rank
record._Z = self.calculate_Z(record.depth, rank, record.opcode)
else:
record._Z = hard_Z
record.node._hit_count += record._Z[R_IRM] + record._Z[W_IRM]
new_ranker = RBTree()
for node in self.full_cache.values():
node.ranker_key = node.new_ranker_key()
new_ranker[node.ranker_key] = node
self.ranker = new_ranker
def M_step(self):
"""Treat Record.Z as constant."""
self.acc_tau = [0.0 for d in range(D)]
self.acc_theta = [0.0 for d in range(D)]
for record in self.trace:
self.update_tau_and_theta_accs(record, increment=True)
self.refresh_params()
def calculate_Z(self, depth, rank, opcode):
Z = [0.0 for d in range(D)]
H = [depth, rank, depth, rank]
def num_on_hit(i):
return (self.tau[i] * self.theta[i] * (1 - self.theta[i])**H[i])
def den_on_hit(i, j):
acc = 0.0
for x in [i, j]:
acc += num_on_hit(x)
return acc
if opcode is None:
num = [0.0 for d in range(D)]
for i in range(D):
num[i] = num_on_hit(i)
den = sum(num)
return [n / den for n in num]
elif opcode is 'r':
num = [num_on_hit(R_SDD), num_on_hit(R_IRM)]
den = den_on_hit(R_SDD, R_IRM)
try:
return [num[0] / den, num[1] / den, 0.0, 0.0]
except ZeroDivisionError:
return [0.5, 0.5, 0.0, 0.0]
elif opcode is 'w':
num = [num_on_hit(W_SDD), num_on_hit(W_IRM)]
den = den_on_hit(W_SDD, W_IRM)
try:
return [0.0, 0.0, num[0] / den, num[1] / den]
except ZeroDivisionError:
return [0.0, 0.0, 0.5, 0.5]
def refresh_params(self):
R = len(self.trace)
self.tau = [self.acc_tau[d] / R for d in range(D)]
self.theta = [0.0, 0.0, 0.0, 0.0]
for d in range(D):
try:
self.theta[d] = (R * self.tau[d] /
(R * self.tau[d] + self.acc_theta[d]))
except ZeroDivisionError as err:
pass
def _update_tau_and_theta_accs(self, Z, depth, rank, increment=True):
H = [depth, rank, depth, rank]
if increment:
self.acc_tau = [self.acc_tau[d] + Z[d] for d in range(D)]
self.acc_theta = [
self.acc_theta[d] + Z[d] * H[d] for d in range(D)
]
else:
self.acc_tau = [self.acc_tau[d] - Z[d] for d in range(D)]
self.acc_theta = [
max(0.0, self.acc_theta[d] - Z[d] * H[d]) for d in range(D)
]
def update_tau_and_theta_accs(self, record, increment=True):
if record.node.is_purged:
rank = record.node.rank_purge_memo
else:
rank = record.node.rank
self._update_tau_and_theta_accs(record.Z, record.depth, rank,
increment)
def evict(self, node):
self.evict_datapoint['row'] += 1
self.evict_datapoint['depth'] = node.depth
self.evict_datapoint['rank'] = node.rank
self.evict_datapoint['value'] = node.expected_value
self.evict_datapoint['opcode'] = node.opcode
self.evict_writer.writerow(
[self.evict_datapoint[key] for key in self.evict_order])
self.evict_file.flush()
self.num_in_cache -= 1
node.is_evicted = True
def purge(self, node):
self.purge_datapoint['row'] += 1
self.purge_datapoint['depth'] = node.depth
self.purge_datapoint['rank'] = node.rank
self.purge_datapoint['value'] = node.expected_value
self.purge_datapoint['opcode'] = node.opcode
self.purge_writer.writerow(
[self.purge_datapoint[key] for key in self.purge_order])
self.purge_file.flush()
self.num_in_full_cache -= 1
if node.opcode == 'r':
self.num_reads -= 1
node.purge()
@property
def cache_list(self):
return filter(lambda node: not node.is_evicted, self.full_cache_list)
@property
def full_cache_list(self):
return list(self.full_cache.values())
def hit_rate(self):
return float(self.num_hits) / self.num_requests
def get_node(self, page):
try:
node = self.full_cache[page]
return node
except KeyError:
return None
class Tdigest(object):
def __init__(self, delta=0.01, K=25, CX=1.1):
self.delta = delta
self.K = K
self.CX = CX
self.centroids = RBTree()
self.nreset = 0
self.reset()
def reset(self):
self.centroids.clear()
self.n = 0
self.nreset += 1
self.last_cumulate = 0
self.compressing = False
def push(self, x, n=1):
if not isinstance(x, list):
x = [x]
for item in x:
self._digest(item, n)
def percentile(self, p):
if self.size() == 0:
return None
self._cumulate(True)
cumn = self.n * p
lower = self.centroids.min_item()[1]
upper = self.centroids.max_item()[1]
for c in self.centroids.values():
if c.cumn <= cumn:
lower = c
else:
upper = c
break
if lower == upper:
return lower.mean
return lower.mean + (cumn - lower.cumn) * (upper.mean - lower.mean) / \
(upper.cumn - lower.cumn)
def serialize(self):
result = '%s~%s~%s~' % (self.delta, self.K, self.size())
if self.size() == 0:
return result
self._cumulate(True)
means = []
counts = []
for c in self.centroids.values():
means.append(str(c.mean))
counts.append(str(c.n))
return '%s%s~%s' % (result, '~'.join(means), '~'.join(counts))
@classmethod
def deserialize(cls, serialized_str):
if not isinstance(serialized_str, basestring):
raise Exception(u'serialized_str must be str')
data = serialized_str.split('~')
t = Tdigest(delta=float(data[0]), K=int(data[1]))
size = int(data[2])
for i in xrange(size):
t.push(float(data[i + 3]), int(data[size + i + 3]))
t._cumulate(True)
return t
def _digest(self, x, n):
if self.size() == 0:
self._new_centroid(x, n, 0)
else:
_min = self.centroids.min_item()[1]
_max = self.centroids.max_item()[1]
nearest = self.find_nearest(x)
if nearest and nearest.mean == x:
self._addweight(nearest, x, n)
elif nearest == _min:
self._new_centroid(x, n, 0)
elif nearest == _max:
self._new_centroid(x, n, self.n)
else:
p = (nearest.cumn + nearest.n / 2.0) / self.n
max_n = int(4 * self.n * self.delta * p * (1 - p))
if max_n >= nearest.n + n:
self._addweight(nearest, x, n)
else:
self._new_centroid(x, n, nearest.cumn)
self._cumulate(False)
if self.K and self.size() > self.K / self.delta:
self.compress()
def find_nearest(self, x):
if self.size() == 0:
return None
try:
lower = self.centroids.ceiling_item(x)[1]
except KeyError:
lower = None
if lower and lower.mean == x:
return lower
try:
prev = self.centroids.floor_item(x)[1]
except KeyError:
prev = None
if not lower:
return prev
if not prev:
return lower
if abs(prev.mean - x) < abs(lower.mean - x):
return prev
else:
return lower
def size(self):
return len(self.centroids)
def compress(self):
if self.compressing:
return
points = self.toList()
self.reset()
self.compressing = True
for point in sorted(points, key=lambda x: random()):
self.push(point['mean'], point['n'])
self._cumulate(True)
self.compressing = False
def _cumulate(self, exact):
if self.n == self.last_cumulate:
return
if not exact and self.CX and self.last_cumulate and \
self.CX > (self.n / self.last_cumulate):
return
cumn = 0
for c in self.centroids.values():
cumn = c.cumn = cumn + c.n
self.n = self.last_cumulate = cumn
def toList(self):
return [dict(mean=c.mean, n=c.n, cumn=c.cumn) for
c in self.centroids.values()]
def _addweight(self, nearest, x, n):
if x != nearest.mean:
nearest.mean += n * (x - nearest.mean) / (nearest.n + n)
nearest.cumn += n
nearest.n += n
self.n += n
def _new_centroid(self, x, n, cumn):
c = Centroid(x, n, cumn)
self.centroids.insert(x, c)
self.n += n
return c
class MMCPolicy(object):
def __init__(self, cache_entries_limit, ghost_entries_limit,
trace_size_limit, csv_suffix="_mmc.csv", draw_dump=False):
self.full_cache = FastRBTree()
self.was_hit = None
self.was_ghost_hit = None
self.num_hits = 0
self.num_requests = 0
self.cache_entries_limit = cache_entries_limit
self.ghost_entries_limit = ghost_entries_limit
self.trace_size_limit = trace_size_limit
self.trace = collections.deque()
self.stack = RBTree()
self.ranker = RBTree()
self.generation = 0
# During startup, this will act like an LRU.
self.startup = True
self.EM_period = 50 * int(np.ceil(np.log(trace_size_limit)))
self.countdown_to_EM = trace_size_limit // 2
self.tau = [0.5, 0.5]
self.theta = [0.5, 0.5]
self.acc_tau = [0.0]
self.acc_theta = [0.0, 0.0]
self.num_in_cache = 0
self.num_in_full_cache = 0
self.csv_suffix = csv_suffix
self.draw_dump = draw_dump
self.ts_order = [
'row', 'hit', 'ghost_hit', 'tau',
'theta0', 'theta1', 'Z', 'depth', 'rank']
self.ts_datapoint = {key: None for key in self.ts_order}
self.ts_datapoint['row'] = 0
self.ts_file = open("csv/mmc" + self.csv_suffix, "w")
self.ts_writer = csv.writer(self.ts_file)
self.ts_writer.writerow(self.ts_order)
self.evict_order = [
'row', 'depth', 'rank', 'value', 'Z', 'tau']
self.evict_datapoint = {key: None for key in self.evict_order}
self.evict_datapoint['row'] = 0
self.evict_file = open("csv/mmc_evict" + self.csv_suffix, "w")
self.evict_writer = csv.writer(self.evict_file)
self.evict_writer.writerow(self.evict_order)
self.purge_order = ['row', 'depth', 'rank', 'value', 'Z']
self.purge_datapoint = {key: None for key in self.purge_order}
self.purge_datapoint['row'] = 0
self.purge_file = open("csv/mmc_purge" + self.csv_suffix, "w")
self.purge_writer = csv.writer(self.purge_file)
self.purge_writer.writerow(self.purge_order)
def request(self, page):
self.num_requests += 1
self.was_hit = False
self.was_ghost_hit = False
node = self.get_node(page)
if node:
self.was_ghost_hit = True
if not node.is_evicted:
self.num_hits += 1
self.was_hit = True
node.hit_count += 1.0 - self.calculate_Z(node.depth, node.rank)
else:
node = Node(self)
node.hit_count = self.tau[1]
node.page_key = page
self.full_cache[page] = node
if not self.was_hit:
self.num_in_cache += 1
if not self.was_ghost_hit:
self.num_in_full_cache += 1
node.is_evicted = node.is_purged = False
record = Record(self, node)
self.add_trace_record(record)
if len(self.trace) > self.trace_size_limit:
popped_record = self.trace.popleft()
self.update_tau_and_theta_accs(record, increment=True)
self.update_tau_and_theta_accs(popped_record, increment=False)
self.refresh_params()
popped_record.node.hit_count -= 1.0 - popped_record.Z
node.restack()
node.rerank()
self.countdown_to_EM -= 1
if self.countdown_to_EM == 0:
self.EM_algorithm(delta=0.00001)
self.countdown_to_EM = self.EM_period
self.startup = False
if (
self.num_in_cache > self.cache_entries_limit or
self.num_in_full_cache >
self.cache_entries_limit + self.ghost_entries_limit
):
self.pageout()
if self.draw_dump:
dump_cache(self, self.csv_suffix)
def add_trace_record(self, record):
self.ts_datapoint['row'] = self.num_requests
if self.was_hit:
self.ts_datapoint['hit'] = 1
else:
self.ts_datapoint['hit'] = 0
if self.was_ghost_hit:
self.ts_datapoint['ghost_hit'] = 1
else:
self.ts_datapoint['ghost_hit'] = 0
self.ts_datapoint['tau'] = self.tau[0]
self.ts_datapoint['theta0'] = self.theta[0]
self.ts_datapoint['theta1'] = self.theta[1]
depth = record.depth
self.ts_datapoint['depth'] = depth
self.ts_datapoint['rank'] = record.node.rank
self.ts_datapoint['Z'] = record.Z
self.ts_writer.writerow(
[self.ts_datapoint[key] for key in self.ts_order])
self.ts_file.flush()
self.trace.append(record)
def pageout(self):
min_node = None
min_node_value = None
min_ghost = None
min_ghost_value = None
for depth, node in enumerate(self.stack.values()):
node.depth_memo = depth
for rank, node in enumerate(self.ranker.values()):
node.recompute_expected_value(depth=node.depth_memo, rank=rank)
value = node.expected_value
if not node.is_evicted:
if min_node is None or value < min_node_value:
min_node = node
min_node_value = value
if min_ghost is None or value < min_ghost_value:
min_ghost = node
min_ghost_value = value
if self.num_in_cache > self.cache_entries_limit:
self.evict(min_node)
if (
self.num_in_full_cache >
self.cache_entries_limit + self.ghost_entries_limit
):
self.purge(min_ghost)
def EM_algorithm(self, delta):
def abs_sum():
return abs(self.tau[0]) + abs(self.theta[0]) + abs(self.theta[1])
before = delta + 4.0
i = 0
# We need to detect if we're in a "nonsense" local optimum. The
# algorithm will optimize to the global maximum if we aren't in one of
# these cases.
if (self.startup or
self.tau[0] == 0.0 or
self.tau[0] == 1.0 or
self.theta[0] == 0.0 or
self.theta[0] == 0.0
):
use_hard_Z = True
else:
use_hard_Z = False
while abs(before - abs_sum()) > delta:
before = abs_sum()
hard_Z = 0.5 if use_hard_Z and i == 0 else None
self.E_step(hard_Z=hard_Z)
i += 1
self.M_step()
# Since we are rearranging the ranks, it's possible that we can
# get into a situation where the ranks shift in a cycle such
# that the tau delta is always exeeded. I've only seen this limit
# hit when the trace size is very small (e.g. 10).
if i > 50:
break
def E_step(self, hard_Z=None):
"""Treat self.tau and self.theta as constants."""
for node in self.full_cache.values():
node._hit_count = 0.0
for record in self.trace:
if hard_Z is None:
if record.node.is_purged:
rank = record.node.rank_purge_memo
else:
rank = record.node.rank
record._Z = self.calculate_Z(record.depth, rank)
else:
record._Z = hard_Z
record.node._hit_count += (1.0 - record._Z)
new_ranker = RBTree()
for node in self.full_cache.values():
node.ranker_key = node.new_ranker_key()
new_ranker[node.ranker_key] = node
self.ranker = new_ranker
def M_step(self):
"""Treat Record.Z as constant."""
self.acc_tau = [0.0]
self.acc_theta = [0.0, 0.0]
for record in self.trace:
self.update_tau_and_theta_accs(record, increment=True)
self.refresh_params()
def calculate_Z(self, depth, rank):
numerator = (
self.tau[0] *
self.theta[0] *
(1 - self.theta[0])**depth)
denominator = (
numerator +
self.tau[1] *
self.theta[1] *
(1 - self.theta[1])**rank)
try:
return float(numerator) / denominator
except ZeroDivisionError as err:
# This can happen when a node falls off the trace and rank and
# depth become greater than the limits.
return self.tau[0]
def refresh_params(self):
R = len(self.trace)
self.tau[0] = self.acc_tau[0] / R
self.tau[1] = 1.0 - self.tau[0]
try:
self.theta[0] = ((R * self.tau[0]) /
(R * self.tau[0] + self.acc_theta[0]))
except ZeroDivisionError:
self.theta[0] = 1.0 / len(self.full_cache)
try:
self.theta[1] = ((R * self.tau[1]) /
(R * self.tau[1] + self.acc_theta[1]))
except ZeroDivisionError:
self.theta[1] = 1.0 / len(self.full_cache)
def _update_tau_and_theta_accs(self, Z, depth, rank, increment=True):
if increment:
self.acc_tau[0] += Z
self.acc_theta[0] += Z * depth
self.acc_theta[1] += (1.0 - Z) * rank
else:
self.acc_tau[0] -= Z
self.acc_theta[0] -= Z * depth
self.acc_theta[1] -= (1.0 - Z) * rank
self.acc_theta = [max(0.0, acc) for acc in self.acc_theta]
def update_tau_and_theta_accs(self, record, increment=True):
depth = record.depth
if record.node.is_purged:
rank = record.node.rank_purge_memo
else:
rank = record.node.rank
self._update_tau_and_theta_accs(record.Z, depth, rank, increment)
def evict(self, node):
self.evict_datapoint['row'] += 1
self.evict_datapoint['depth'] = node.depth
self.evict_datapoint['rank'] = node.rank
self.evict_datapoint['value'] = node.expected_value
self.evict_datapoint['Z'] = self.calculate_Z(
node.depth, node.rank)
self.evict_datapoint['tau'] = self.tau[0]
self.evict_writer.writerow(
[self.evict_datapoint[key] for key in self.evict_order])
self.evict_file.flush()
self.num_in_cache -= 1
node.is_evicted = True
def purge(self, node):
self.purge_datapoint['row'] += 1
self.purge_datapoint['depth'] = node.depth
self.purge_datapoint['rank'] = node.rank
self.purge_datapoint['value'] = node.expected_value
self.purge_datapoint['Z'] = self.calculate_Z(
node.depth, node.rank)
self.purge_writer.writerow(
[self.purge_datapoint[key] for key in self.purge_order])
self.purge_file.flush()
self.num_in_full_cache -= 1
node.purge()
@property
def cache_list(self):
return filter(lambda node: not node.is_evicted, self.full_cache_list)
@property
def full_cache_list(self):
return list(self.full_cache.values())
def hit_rate(self):
return float(self.num_hits) / self.num_requests
def get_node(self, page):
try:
node = self.full_cache[page]
return node
except KeyError:
return None
class TDigest(object):
def __init__(self, delta=0.01, K=25):
self.C = RBTree()
self.n = 0
self.delta = delta
self.K = K
def __add__(self, other_digest):
C1 = list(self.C.values())
C2 = list(other_digest.C.values())
shuffle(C1)
shuffle(C2)
data = C1 + C2
new_digest = TDigest(self.delta, self.K)
for c in data:
new_digest.update(c.mean, c.count)
return new_digest
def __len__(self):
return len(self.C)
def __repr__(self):
return """<T-Digest: n=%d, centroids=%d>""" % (self.n, len(self))
def _add_centroid(self, centroid):
if centroid.mean not in self.C:
self.C.insert(centroid.mean, centroid)
else:
self.C[centroid.mean].update(centroid.mean, centroid.count)
def _compute_centroid_quantile(self, centroid):
denom = self.n
cumulative_sum = sum(
c_i.count for c_i in self.C.value_slice(-float('Inf'), centroid.mean))
return (centroid.count / 2. + cumulative_sum) / denom
def _update_centroid(self, centroid, x, w):
self.C.pop(centroid.mean)
centroid.update(x, w)
self._add_centroid(centroid)
def _find_closest_centroids(self, x):
try:
ceil_key = self.C.ceiling_key(x)
except KeyError:
floor_key = self.C.floor_key(x)
return [self.C[floor_key]]
try:
floor_key = self.C.floor_key(x)
except KeyError:
ceil_key = self.C.ceiling_key(x)
return [self.C[ceil_key]]
if abs(floor_key - x) < abs(ceil_key - x):
return [self.C[floor_key]]
elif abs(floor_key - x) == abs(ceil_key - x) and (ceil_key != floor_key):
return [self.C[ceil_key], self.C[floor_key]]
else:
return [self.C[ceil_key]]
def _theshold(self, q):
return 4 * self.n * self.delta * q * (1 - q)
def update(self, x, w=1):
"""
Update the t-digest with value x and weight w.
"""
self.n += w
if len(self) == 0:
self._add_centroid(Centroid(x, w))
return
S = self._find_closest_centroids(x)
while len(S) != 0 and w > 0:
j = choice(list(range(len(S))))
c_j = S[j]
q = self._compute_centroid_quantile(c_j)
# This filters the out centroids that do not satisfy the second part
# of the definition of S. See original paper by Dunning.
if c_j.count + w > self._theshold(q):
S.pop(j)
continue
delta_w = min(self._theshold(q) - c_j.count, w)
self._update_centroid(c_j, x, delta_w)
w -= delta_w
S.pop(j)
if w > 0:
self._add_centroid(Centroid(x, w))
if len(self) > self.K / self.delta:
self.compress()
return
def batch_update(self, values, w=1):
"""
Update the t-digest with an iterable of values. This assumes all points have the
same weight.
"""
for x in values:
self.update(x, w)
self.compress()
return
def compress(self):
T = TDigest(self.delta, self.K)
C = list(self.C.values())
shuffle(C)
for c_i in C:
T.update(c_i.mean, c_i.count)
self.C = T.C
def percentile(self, q):
"""
Computes the percentile of a specific value in [0,1], ie. computes F^{-1}(q) where F^{-1} denotes
the inverse CDF of the distribution.
"""
if not (0 <= q <= 1):
raise ValueError("q must be between 0 and 1, inclusive.")
t = 0
q *= self.n
for i, key in enumerate(self.C.keys()):
c_i = self.C[key]
k = c_i.count
if q < t + k:
if i == 0:
return c_i.mean
elif i == len(self) - 1:
return c_i.mean
else:
delta = (self.C.succ_item(key)[1].mean - self.C.prev_item(key)[1].mean) / 2.
return c_i.mean + ((q - t) / k - 0.5) * delta
t += k
return self.C.max_item()[1].mean
def quantile(self, q):
"""
Computes the quantile of a specific value, ie. computes F(q) where F denotes
the CDF of the distribution.
"""
t = 0
N = float(self.n)
for i, key in enumerate(self.C.keys()):
c_i = self.C[key]
if i == len(self) - 1:
delta = (c_i.mean - self.C.prev_item(key)[1].mean) / 2.
else:
delta = (self.C.succ_item(key)[1].mean - c_i.mean) / 2.
z = max(-1, (q - c_i.mean) / delta)
if z < 1:
return t / N + c_i.count / N * (z + 1) / 2
t += c_i.count
return 1
def trimmed_mean(self, q1, q2):
"""
Computes the mean of the distribution between the two percentiles q1 and q2.
This is a modified algorithm than the one presented in the original t-Digest paper.
"""
if not (q1 < q2):
raise ValueError("q must be between 0 and 1, inclusive.")
s = k = t = 0
q1 *= self.n
q2 *= self.n
for i, key in enumerate(self.C.keys()):
c_i = self.C[key]
k_i = c_i.count
if q1 < t + k_i:
if i == 0:
delta = self.C.succ_item(key)[1].mean - c_i.mean
elif i == len(self) - 1:
delta = c_i.mean - self.C.prev_item(key)[1].mean
else:
delta = (self.C.succ_item(key)[1].mean - self.C.prev_item(key)[1].mean) / 2.
nu = ((q1 - t) / k_i - 0.5) * delta
s += nu * k_i * c_i.mean
k += nu * k_i
if q2 < t + k_i:
return s/k
t += k_i
return s/k
class MMCRWPolicy(object):
def __init__(self, cache_entries_limit, ghost_entries_limit,
trace_size_limit, csv_suffix="_mmc.csv"):
self.full_cache = FastRBTree()
self.was_hit = None
self.was_ghost_hit = None
self.num_hits = 0
self.num_requests = 0
self.cache_entries_limit = cache_entries_limit
self.ghost_entries_limit = ghost_entries_limit
self.trace_size_limit = trace_size_limit
self.trace = collections.deque()
self.stack = RBTree()
self.ranker = RBTree()
self.generation = 0
# During startup, this will act like an LRU.
self.startup = True
self.EM_period = 50 * int(np.ceil(np.log(trace_size_limit)))
self.countdown_to_EM = trace_size_limit // 2
self.tau = [0.25, 0.25, 0.25, 0.25]
self.theta = [0.5, 0.5, 0.5, 0.5]
self.acc_tau = [0.0, 0.0, 0.0, 0.0]
self.acc_theta = [0.0, 0.0, 0.0, 0.0]
self.num_in_cache = 0
self.num_in_full_cache = 0
self.num_reads = 0
self.csv_suffix = csv_suffix
self.ts_order = [
'row', 'hit', 'ghost_hit',
'tau_R_SDD', 'tau_R_IRM', 'tau_W_SDD', 'tau_W_IRM',
'theta_R_SDD', 'theta_R_IRM', 'theta_W_SDD', 'theta_W_IRM',
'depth', 'rank',
'Z_R_SDD', 'Z_R_IRM', 'Z_W_SDD', 'Z_W_IRM', 'Z_sum'
]
self.ts_datapoint = {key: None for key in self.ts_order}
self.ts_datapoint['row'] = 0
self.ts_file = open("csv/mmc_rw" + self.csv_suffix, "w")
self.ts_writer = csv.writer(self.ts_file)
self.ts_writer.writerow(self.ts_order)
self.evict_order = [
'row', 'depth', 'rank', 'value', 'opcode']
self.evict_datapoint = {key: None for key in self.evict_order}
self.evict_datapoint['row'] = 0
self.evict_file = open("csv/mmc_rw_evict" + self.csv_suffix, "w")
self.evict_writer = csv.writer(self.evict_file)
self.evict_writer.writerow(self.evict_order)
self.purge_order = ['row', 'depth', 'rank', 'value', 'opcode']
self.purge_datapoint = {key: None for key in self.purge_order}
self.purge_datapoint['row'] = 0
self.purge_file = open("csv/mmc_rw_purge" + self.csv_suffix, "w")
self.purge_writer = csv.writer(self.purge_file)
self.purge_writer.writerow(self.purge_order)
def request(self, page, opcode):
self.num_requests += 1
self.was_hit = False
self.was_ghost_hit = False
node = self.get_node(page)
if node:
self.was_ghost_hit = True
if not node.is_evicted:
self.num_hits += 1
self.was_hit = True
Z = self.calculate_Z(node.depth, node.rank, node.opcode)
node.hit_count += Z[R_IRM] + Z[W_IRM]
else:
node = Node(self)
node.hit_count = self.tau[R_IRM] + self.tau[W_IRM]
node.page_key = page
self.full_cache[page] = node
if not self.was_hit:
self.num_in_cache += 1
if not self.was_ghost_hit:
self.num_in_full_cache += 1
else:
if node.opcode == 'r':
self.num_reads -= 1
if opcode == 'r':
self.num_reads += 1
node.is_evicted = node.is_purged = False
record = Record(self, node)
self.add_trace_record(record)
node.opcode = opcode
if len(self.trace) > self.trace_size_limit:
popped_record = self.trace.popleft()
self.update_tau_and_theta_accs(record, increment=True)
self.update_tau_and_theta_accs(popped_record, increment=False)
self.refresh_params()
popped_record.node.hit_count -= popped_record.Z[R_IRM]
popped_record.node.hit_count -= popped_record.Z[W_IRM]
node.restack()
node.rerank()
self.countdown_to_EM -= 1
if self.countdown_to_EM == 0:
self.EM_algorithm(delta=0.00001)
self.countdown_to_EM = self.EM_period
self.startup = False
if (
self.num_in_cache > self.cache_entries_limit or
self.num_in_full_cache >
self.cache_entries_limit + self.ghost_entries_limit
):
self.pageout()
#dump_cache(self, "exp")
def add_trace_record(self, record):
self.ts_datapoint['row'] = self.num_requests
if self.was_hit:
self.ts_datapoint['hit'] = 1
else:
self.ts_datapoint['hit'] = 0
if self.was_ghost_hit:
self.ts_datapoint['ghost_hit'] = 1
else:
self.ts_datapoint['ghost_hit'] = 0
self.ts_datapoint['tau_R_SDD'] = self.tau[R_SDD]
self.ts_datapoint['tau_R_IRM'] = self.tau[R_IRM]
self.ts_datapoint['tau_W_SDD'] = self.tau[W_SDD]
self.ts_datapoint['tau_W_IRM'] = self.tau[W_IRM]
self.ts_datapoint['theta_R_SDD'] = self.theta[R_SDD]
self.ts_datapoint['theta_R_IRM'] = self.theta[R_IRM]
self.ts_datapoint['theta_W_SDD'] = self.theta[W_SDD]
self.ts_datapoint['theta_W_IRM'] = self.theta[W_IRM]
self.ts_datapoint['Z_R_SDD'] = record.Z[R_SDD]
self.ts_datapoint['Z_R_IRM'] = record.Z[R_IRM]
self.ts_datapoint['Z_W_SDD'] = record.Z[W_SDD]
self.ts_datapoint['Z_W_IRM'] = record.Z[W_IRM]
self.ts_datapoint['Z_sum'] = sum(record.Z)
self.ts_datapoint['depth'] = record.depth
self.ts_datapoint['rank'] = record.node.rank
self.ts_writer.writerow(
[self.ts_datapoint[key] for key in self.ts_order])
self.ts_file.flush()
self.trace.append(record)
def pageout(self):
min_node = None
min_node_value = None
min_ghost = None
min_ghost_value = None
for depth, node in enumerate(self.stack.values()):
node.depth_memo = depth
for rank, node in enumerate(self.ranker.values()):
node.recompute_expected_value(depth=node.depth_memo, rank=rank)
value = node.expected_value
if not node.is_evicted:
if min_node is None or value < min_node_value:
min_node = node
min_node_value = value
if min_ghost is None or value < min_ghost_value:
min_ghost = node
min_ghost_value = value
if self.num_in_cache > self.cache_entries_limit:
self.evict(min_node)
if (
self.num_in_full_cache >
self.cache_entries_limit + self.ghost_entries_limit
):
self.purge(min_ghost)
def EM_algorithm(self, delta):
def abs_sum():
return sum(self.tau) + sum(self.theta)
before = delta + 4.0
i = 0
# We need to detect if we're in a "nonsense" local optimum. The
# algorithm will optimize to the global maximum if we aren't in one of
# these cases.
if (self.startup or
min(self.tau) < 0.00001 or
min(self.theta) < 0.00001
):
use_hard_Z = True
else:
use_hard_Z = False
while abs(before - abs_sum()) > delta:
before = abs_sum()
hard_Z = [0.25, 0.25, 0.25, 0.25] if use_hard_Z and i == 0 else None
self.E_step(hard_Z=hard_Z)
i += 1
self.M_step()
# Since we are rearranging the ranks, it's possible that we can
# get into a situation where the ranks shift in a cycle such
# that the tau delta is always exeeded. I've only seen this limit
# hit when the trace size is very small (e.g. 10).
if i > 50:
break
def E_step(self, hard_Z=None):
"""Treat self.tau and self.theta as constants."""
for node in self.full_cache.values():
node._hit_count = 0.0
for record in self.trace:
if hard_Z is None:
if record.node.is_purged:
rank = record.node.rank_purge_memo
else:
rank = record.node.rank
record._Z = self.calculate_Z(record.depth, rank, record.opcode)
else:
record._Z = hard_Z
record.node._hit_count += record._Z[R_IRM] + record._Z[W_IRM]
new_ranker = RBTree()
for node in self.full_cache.values():
node.ranker_key = node.new_ranker_key()
new_ranker[node.ranker_key] = node
self.ranker = new_ranker
def M_step(self):
"""Treat Record.Z as constant."""
self.acc_tau = [0.0 for d in range(D)]
self.acc_theta = [0.0 for d in range(D)]
for record in self.trace:
self.update_tau_and_theta_accs(record, increment=True)
self.refresh_params()
def calculate_Z(self, depth, rank, opcode):
Z = [0.0 for d in range(D)]
H = [depth, rank, depth, rank]
def num_on_hit(i):
return (self.tau[i] *
self.theta[i] *
(1 - self.theta[i])**H[i])
def den_on_hit(i, j):
acc = 0.0
for x in [i, j]:
acc += num_on_hit(x)
return acc
if opcode is None:
num = [0.0 for d in range(D)]
for i in range(D):
num[i] = num_on_hit(i)
den = sum(num)
return [n / den for n in num]
elif opcode is 'r':
num = [num_on_hit(R_SDD), num_on_hit(R_IRM)]
den = den_on_hit(R_SDD, R_IRM)
try:
return [num[0] / den, num[1] / den, 0.0, 0.0]
except ZeroDivisionError:
return [0.5, 0.5, 0.0, 0.0]
elif opcode is 'w':
num = [num_on_hit(W_SDD), num_on_hit(W_IRM)]
den = den_on_hit(W_SDD, W_IRM)
try:
return [0.0, 0.0, num[0] / den, num[1] / den]
except ZeroDivisionError:
return [0.0, 0.0, 0.5, 0.5]
def refresh_params(self):
R = len(self.trace)
self.tau = [self.acc_tau[d] / R for d in range(D)]
self.theta = [0.0, 0.0, 0.0, 0.0]
for d in range(D):
try:
self.theta[d] = (R * self.tau[d] /
(R * self.tau[d] + self.acc_theta[d]))
except ZeroDivisionError as err:
pass
def _update_tau_and_theta_accs(self, Z, depth, rank, increment=True):
H = [depth, rank, depth, rank]
if increment:
self.acc_tau = [self.acc_tau[d] + Z[d] for d in range(D)]
self.acc_theta = [self.acc_theta[d] + Z[d] * H[d] for d in range(D)]
else:
self.acc_tau = [self.acc_tau[d] - Z[d] for d in range(D)]
self.acc_theta = [max(0.0, self.acc_theta[d] - Z[d] * H[d])
for d in range(D)]
def update_tau_and_theta_accs(self, record, increment=True):
if record.node.is_purged:
rank = record.node.rank_purge_memo
else:
rank = record.node.rank
self._update_tau_and_theta_accs(record.Z, record.depth, rank, increment)
def evict(self, node):
self.evict_datapoint['row'] += 1
self.evict_datapoint['depth'] = node.depth
self.evict_datapoint['rank'] = node.rank
self.evict_datapoint['value'] = node.expected_value
self.evict_datapoint['opcode'] = node.opcode
self.evict_writer.writerow(
[self.evict_datapoint[key] for key in self.evict_order])
self.evict_file.flush()
self.num_in_cache -= 1
node.is_evicted = True
def purge(self, node):
self.purge_datapoint['row'] += 1
self.purge_datapoint['depth'] = node.depth
self.purge_datapoint['rank'] = node.rank
self.purge_datapoint['value'] = node.expected_value
self.purge_datapoint['opcode'] = node.opcode
self.purge_writer.writerow(
[self.purge_datapoint[key] for key in self.purge_order])
self.purge_file.flush()
self.num_in_full_cache -= 1
if node.opcode == 'r':
self.num_reads -= 1
node.purge()
@property
def cache_list(self):
return filter(lambda node: not node.is_evicted, self.full_cache_list)
@property
def full_cache_list(self):
return list(self.full_cache.values())
def hit_rate(self):
return float(self.num_hits) / self.num_requests
def get_node(self, page):
try:
node = self.full_cache[page]
return node
except KeyError:
return None
class MINPolicy(object):
def __init__(self, cache_size_limit, trace, csv_suffix=".csv"):
self.cache_size_limit = cache_size_limit
self.cache = {}
self.hits = 0.0
self.requests = 0.0
self.ts_order = ['row', 'hit']
self.ts_datapoint = {key: None for key in self.ts_order}
self.ts_datapoint['row'] = 0
self.ts_file = open("csv/min" + csv_suffix, "w")
self.ts_writer = csv.writer(self.ts_file)
self.ts_writer.writerow(self.ts_order)
self.clairvoyance = FastRBTree()
self.precog = FastRBTree()
last_time = time.time()
for i, page_opcode in enumerate(trace):
if time.time() > last_time + 0.1:
last_time = time.time()
print '1', i, '\r',
sys.stdout.flush()
page, _ = page_opcode
try:
self.precog[page].append(i)
except KeyError:
self.precog[page] = collections.deque()
self.precog[page].append(i)
known_max = i
known_max += 2
for times in self.precog.values():
times.append(known_max)
known_max += 1
print
print 'Done loading.'
def hit_rate(self):
return self.hits / self.requests
def request(self, page):
self.requests += 1
if page in self.cache:
was_hit = True
self.hits += 1
else:
was_hit = False
self.cache[page] = self.precog[page].popleft()
# This happens on startup.
if self.cache[page] < self.requests:
self.cache[page] = self.precog[page].popleft()
self.clairvoyance[self.cache[page]] = page
self.ts_datapoint['row'] += 1
if was_hit:
self.ts_datapoint['hit'] = 1
else:
self.ts_datapoint['hit'] = 0
self.ts_writer.writerow(
[self.ts_datapoint[key] for key in self.ts_order])
self.ts_file.flush()
if len(self.cache) > self.cache_size_limit:
next_use, page = self.clairvoyance.pop_max()
del self.cache[page]
class Master(object):
__metaclass__ = ProcessMeta
def __init__(self, node_timeout):
self._logger = logging.getLogger(self.__class__.__name__)
self._nodes = {}
self._sessions = {}
self._sessions_by_owner = {}
self._keepalive_queue = FastRBTree()
self._priority_queue = FastRBTree()
self._node_timeout = node_timeout
self._culling_timer = runtime.greenpool.spawn(self._cull_dead_nodes)
def get_session(self, name, owner=None, dep_server=None, work_dir=None, worker_count=None, init=None):
try:
session = self._sessions[name]
session.dep_cache.set_dependency_server(dep_server)
return session
except KeyError:
if owner is None:
raise ValueError("An owner must be provided for new sessions")
if work_dir is None:
raise ValueError("Valid working directory required to create a new session")
if dep_server is None:
raise ValueError("Dependency server must be provided to create a new session")
session = Session(name, owner, dep_server, worker_count, self._spawn_workers, work_dir, init)
self._sessions[name] = session
self._sessions_by_owner.setdefault(owner, {})[name] = session
return RemoteCloud(name, owner, session.hub, session.created_on, len(session.workers), self)
def _spawn_workers(self, name, owner, worker_count, init):
all_nodes = itertools.imap(lambda nd: nd.itervalues(), self._priority_queue.values())
all_nodes = itertools.chain.from_iterable(all_nodes)
node_pool = NodePool(all_nodes, name, self._logger)
node_pool_size = len(node_pool)
if worker_count is None:
worker_count = node_pool_size
self._logger.info("Creating session %s:%s with %d workers", owner, name, worker_count)
# We can only ever have as many workers as there are processors in the cluster
if worker_count > node_pool_size:
self._logger.warning("Session %s: requested worker count %d will be capped to %d",
name, worker_count, node_pool_size)
worker_count = node_pool_size
workers = []
while len(workers) < worker_count and (len(node_pool) > 0):
results = node_pool.spawn_workers(worker_count - len(workers), init=init)
for nproc, result in results:
try:
worker_batch = result.get()
workers.extend(worker_batch)
except Exception as ex:
self._logger.error("Session %s: failed to spawn workers on node %s due to error:\n%s",
name, nproc, full_traceback(ex))
return workers
def shutdown_session(self, name):
session = self._sessions.pop(name)
owner_sessions = self._sessions_by_owner[session.owner]
del owner_sessions[name]
# Carry out the shutdown operation in the background
Tasklet.spawn(session.shutdown)
def node_update(self, node_proc, cpu_count, cpu_usage, ram_total, ram_usage):
# Remove the node from the queues if it is already registered
if node_proc in self._nodes:
node = self._nodes[node_proc]
self._dequeue(node)
else:
# Create a new node info if it doesn't exist yet
node = NodeInfo(node_proc, cpu_count)
self._nodes[node_proc] = node
# Update load based on a simple formula of tenancy and resource usage
node.update(cpu_usage + ram_usage, cpu_usage, ram_total, ram_usage)
self._logger.debug("Received ping %s", node)
# Enqueue the node again
self._enqueue(node)
def node_info(self):
return self._nodes.values()
def shutdown(self):
"""
Initiate cluster wide shutdown
"""
self._logger.warn("Shutting down cluster")
self._culling_timer.kill()
for node in self._nodes.values():
self._logger.info("Shutting down node %s", node.proc)
retry(lambda: node.proc.shutdown(), logger=self._logger)
def _cull_dead_nodes(self):
"""
Remove the node so that it cannot be included in new sessions.
"""
while True:
dead_nodes = list(self._keepalive_queue[:datetime.now() - timedelta(seconds=self._node_timeout)].values())
dead_node_count = len(dead_nodes)
if dead_node_count > 0:
self._logger.info("Culling %d nodes that are no longer responding.", dead_node_count)
for node_dicts in dead_nodes:
for node in node_dicts.values():
self._logger.info("Deleting dead node %s", node.proc)
self._delete_node(node)
else:
self._logger.info("No dead nodes.")
runtime.sleep(self._node_timeout)
def _delete_node(self, node):
del self._nodes[node.proc]
self._dequeue(node)
def _enqueue(self, node):
self._add_to_queue(self._keepalive_queue, node, node.last_ping)
self._add_to_queue(self._priority_queue, node, node.load)
def _dequeue(self, node):
self._delete_from_queue(self._keepalive_queue, node.proc, node.last_ping)
self._delete_from_queue(self._priority_queue, node.proc, node.load)
@staticmethod
def _add_to_queue(queue, node, key):
queue.setdefault(key, {})[node.proc] = node
@staticmethod
def _delete_from_queue(queue, node_id, key):
kq_nodes = queue.get(key)
del kq_nodes[node_id]
if not len(kq_nodes):
queue.discard(key)
class MMCPolicy(object):
def __init__(self,
cache_entries_limit,
ghost_entries_limit,
trace_size_limit,
csv_suffix="_mmc.csv",
draw_dump=False):
self.full_cache = FastRBTree()
self.was_hit = None
self.was_ghost_hit = None
self.num_hits = 0
self.num_requests = 0
self.cache_entries_limit = cache_entries_limit
self.ghost_entries_limit = ghost_entries_limit
self.trace_size_limit = trace_size_limit
self.trace = collections.deque()
self.stack = RBTree()
self.ranker = RBTree()
self.generation = 0
# During startup, this will act like an LRU.
self.startup = True
self.EM_period = 50 * int(np.ceil(np.log(trace_size_limit)))
self.countdown_to_EM = trace_size_limit // 2
self.tau = [0.5, 0.5]
self.theta = [0.5, 0.5]
self.acc_tau = [0.0]
self.acc_theta = [0.0, 0.0]
self.num_in_cache = 0
self.num_in_full_cache = 0
self.csv_suffix = csv_suffix
self.draw_dump = draw_dump
self.ts_order = [
'row', 'hit', 'ghost_hit', 'tau', 'theta0', 'theta1', 'Z', 'depth',
'rank'
]
self.ts_datapoint = {key: None for key in self.ts_order}
self.ts_datapoint['row'] = 0
self.ts_file = open("csv/mmc" + self.csv_suffix, "w")
self.ts_writer = csv.writer(self.ts_file)
self.ts_writer.writerow(self.ts_order)
self.evict_order = ['row', 'depth', 'rank', 'value', 'Z', 'tau']
self.evict_datapoint = {key: None for key in self.evict_order}
self.evict_datapoint['row'] = 0
self.evict_file = open("csv/mmc_evict" + self.csv_suffix, "w")
self.evict_writer = csv.writer(self.evict_file)
self.evict_writer.writerow(self.evict_order)
self.purge_order = ['row', 'depth', 'rank', 'value', 'Z']
self.purge_datapoint = {key: None for key in self.purge_order}
self.purge_datapoint['row'] = 0
self.purge_file = open("csv/mmc_purge" + self.csv_suffix, "w")
self.purge_writer = csv.writer(self.purge_file)
self.purge_writer.writerow(self.purge_order)
def request(self, page):
self.num_requests += 1
self.was_hit = False
self.was_ghost_hit = False
node = self.get_node(page)
if node:
self.was_ghost_hit = True
if not node.is_evicted:
self.num_hits += 1
self.was_hit = True
node.hit_count += 1.0 - self.calculate_Z(node.depth, node.rank)
else:
node = Node(self)
node.hit_count = self.tau[1]
node.page_key = page
self.full_cache[page] = node
if not self.was_hit:
self.num_in_cache += 1
if not self.was_ghost_hit:
self.num_in_full_cache += 1
node.is_evicted = node.is_purged = False
record = Record(self, node)
self.add_trace_record(record)
if len(self.trace) > self.trace_size_limit:
popped_record = self.trace.popleft()
self.update_tau_and_theta_accs(record, increment=True)
self.update_tau_and_theta_accs(popped_record, increment=False)
self.refresh_params()
popped_record.node.hit_count -= 1.0 - popped_record.Z
node.restack()
node.rerank()
self.countdown_to_EM -= 1
if self.countdown_to_EM == 0:
self.EM_algorithm(delta=0.00001)
self.countdown_to_EM = self.EM_period
self.startup = False
if (self.num_in_cache > self.cache_entries_limit
or self.num_in_full_cache >
self.cache_entries_limit + self.ghost_entries_limit):
self.pageout()
if self.draw_dump:
dump_cache(self, self.csv_suffix)
def add_trace_record(self, record):
self.ts_datapoint['row'] = self.num_requests
if self.was_hit:
self.ts_datapoint['hit'] = 1
else:
self.ts_datapoint['hit'] = 0
if self.was_ghost_hit:
self.ts_datapoint['ghost_hit'] = 1
else:
self.ts_datapoint['ghost_hit'] = 0
self.ts_datapoint['tau'] = self.tau[0]
self.ts_datapoint['theta0'] = self.theta[0]
self.ts_datapoint['theta1'] = self.theta[1]
depth = record.depth
self.ts_datapoint['depth'] = depth
self.ts_datapoint['rank'] = record.node.rank
self.ts_datapoint['Z'] = record.Z
self.ts_writer.writerow(
[self.ts_datapoint[key] for key in self.ts_order])
self.ts_file.flush()
self.trace.append(record)
def pageout(self):
min_node = None
min_node_value = None
min_ghost = None
min_ghost_value = None
for depth, node in enumerate(self.stack.values()):
node.depth_memo = depth
for rank, node in enumerate(self.ranker.values()):
node.recompute_expected_value(depth=node.depth_memo, rank=rank)
value = node.expected_value
if not node.is_evicted:
if min_node is None or value < min_node_value:
min_node = node
min_node_value = value
if min_ghost is None or value < min_ghost_value:
min_ghost = node
min_ghost_value = value
if self.num_in_cache > self.cache_entries_limit:
self.evict(min_node)
if (self.num_in_full_cache >
self.cache_entries_limit + self.ghost_entries_limit):
self.purge(min_ghost)
def EM_algorithm(self, delta):
def abs_sum():
return abs(self.tau[0]) + abs(self.theta[0]) + abs(self.theta[1])
before = delta + 4.0
i = 0
# We need to detect if we're in a "nonsense" local optimum. The
# algorithm will optimize to the global maximum if we aren't in one of
# these cases.
if (self.startup or self.tau[0] == 0.0 or self.tau[0] == 1.0
or self.theta[0] == 0.0 or self.theta[0] == 0.0):
use_hard_Z = True
else:
use_hard_Z = False
while abs(before - abs_sum()) > delta:
before = abs_sum()
hard_Z = 0.5 if use_hard_Z and i == 0 else None
self.E_step(hard_Z=hard_Z)
i += 1
self.M_step()
# Since we are rearranging the ranks, it's possible that we can
# get into a situation where the ranks shift in a cycle such
# that the tau delta is always exeeded. I've only seen this limit
# hit when the trace size is very small (e.g. 10).
if i > 50:
break
def E_step(self, hard_Z=None):
"""Treat self.tau and self.theta as constants."""
for node in self.full_cache.values():
node._hit_count = 0.0
for record in self.trace:
if hard_Z is None:
if record.node.is_purged:
rank = record.node.rank_purge_memo
else:
rank = record.node.rank
record._Z = self.calculate_Z(record.depth, rank)
else:
record._Z = hard_Z
record.node._hit_count += (1.0 - record._Z)
new_ranker = RBTree()
for node in self.full_cache.values():
node.ranker_key = node.new_ranker_key()
new_ranker[node.ranker_key] = node
self.ranker = new_ranker
def M_step(self):
"""Treat Record.Z as constant."""
self.acc_tau = [0.0]
self.acc_theta = [0.0, 0.0]
for record in self.trace:
self.update_tau_and_theta_accs(record, increment=True)
self.refresh_params()
def calculate_Z(self, depth, rank):
numerator = (self.tau[0] * self.theta[0] * (1 - self.theta[0])**depth)
denominator = (numerator + self.tau[1] * self.theta[1] *
(1 - self.theta[1])**rank)
try:
return float(numerator) / denominator
except ZeroDivisionError as err:
# This can happen when a node falls off the trace and rank and
# depth become greater than the limits.
return self.tau[0]
def refresh_params(self):
R = len(self.trace)
self.tau[0] = self.acc_tau[0] / R
self.tau[1] = 1.0 - self.tau[0]
try:
self.theta[0] = ((R * self.tau[0]) /
(R * self.tau[0] + self.acc_theta[0]))
except ZeroDivisionError:
self.theta[0] = 1.0 / len(self.full_cache)
try:
self.theta[1] = ((R * self.tau[1]) /
(R * self.tau[1] + self.acc_theta[1]))
except ZeroDivisionError:
self.theta[1] = 1.0 / len(self.full_cache)
def _update_tau_and_theta_accs(self, Z, depth, rank, increment=True):
if increment:
self.acc_tau[0] += Z
self.acc_theta[0] += Z * depth
self.acc_theta[1] += (1.0 - Z) * rank
else:
self.acc_tau[0] -= Z
self.acc_theta[0] -= Z * depth
self.acc_theta[1] -= (1.0 - Z) * rank
self.acc_theta = [max(0.0, acc) for acc in self.acc_theta]
def update_tau_and_theta_accs(self, record, increment=True):
depth = record.depth
if record.node.is_purged:
rank = record.node.rank_purge_memo
else:
rank = record.node.rank
self._update_tau_and_theta_accs(record.Z, depth, rank, increment)
def evict(self, node):
self.evict_datapoint['row'] += 1
self.evict_datapoint['depth'] = node.depth
self.evict_datapoint['rank'] = node.rank
self.evict_datapoint['value'] = node.expected_value
self.evict_datapoint['Z'] = self.calculate_Z(node.depth, node.rank)
self.evict_datapoint['tau'] = self.tau[0]
self.evict_writer.writerow(
[self.evict_datapoint[key] for key in self.evict_order])
self.evict_file.flush()
self.num_in_cache -= 1
node.is_evicted = True
def purge(self, node):
self.purge_datapoint['row'] += 1
self.purge_datapoint['depth'] = node.depth
self.purge_datapoint['rank'] = node.rank
self.purge_datapoint['value'] = node.expected_value
self.purge_datapoint['Z'] = self.calculate_Z(node.depth, node.rank)
self.purge_writer.writerow(
[self.purge_datapoint[key] for key in self.purge_order])
self.purge_file.flush()
self.num_in_full_cache -= 1
node.purge()
@property
def cache_list(self):
return filter(lambda node: not node.is_evicted, self.full_cache_list)
@property
def full_cache_list(self):
return list(self.full_cache.values())
def hit_rate(self):
return float(self.num_hits) / self.num_requests
def get_node(self, page):
try:
node = self.full_cache[page]
return node
except KeyError:
return None
class TDigest(object):
def __init__(self, delta=0.01, K=25):
self.C = RBTree()
self.n = 0
self.delta = delta
self.K = K
def __add__(self, other_digest):
data = list(chain(self.C.values(), other_digest.C.values()))
new_digest = TDigest(self.delta, self.K)
if len(data) > 0:
for c in pyudorandom.items(data):
new_digest.update(c.mean, c.count)
return new_digest
def __len__(self):
return len(self.C)
def __repr__(self):
return """<T-Digest: n=%d, centroids=%d>""" % (self.n, len(self))
def _add_centroid(self, centroid):
if centroid.mean not in self.C:
self.C.insert(centroid.mean, centroid)
else:
self.C[centroid.mean].update(centroid.mean, centroid.count)
def _compute_centroid_quantile(self, centroid):
denom = self.n
cumulative_sum = sum(
c_i.count
for c_i in self.C.value_slice(-float('Inf'), centroid.mean))
return (centroid.count / 2. + cumulative_sum) / denom
def _update_centroid(self, centroid, x, w):
self.C.pop(centroid.mean)
centroid.update(x, w)
self._add_centroid(centroid)
def _find_closest_centroids(self, x):
try:
ceil_key = self.C.ceiling_key(x)
except KeyError:
floor_key = self.C.floor_key(x)
return [self.C[floor_key]]
try:
floor_key = self.C.floor_key(x)
except KeyError:
ceil_key = self.C.ceiling_key(x)
return [self.C[ceil_key]]
if abs(floor_key - x) < abs(ceil_key - x):
return [self.C[floor_key]]
elif abs(floor_key - x) == abs(ceil_key -
x) and (ceil_key != floor_key):
return [self.C[ceil_key], self.C[floor_key]]
else:
return [self.C[ceil_key]]
def _theshold(self, q):
return 4 * self.n * self.delta * q * (1 - q)
def update(self, x, w=1):
"""
Update the t-digest with value x and weight w.
"""
self.n += w
if len(self) == 0:
self._add_centroid(Centroid(x, w))
return
S = self._find_closest_centroids(x)
while len(S) != 0 and w > 0:
j = choice(list(range(len(S))))
c_j = S[j]
q = self._compute_centroid_quantile(c_j)
# This filters the out centroids that do not satisfy the second part
# of the definition of S. See original paper by Dunning.
if c_j.count + w > self._theshold(q):
S.pop(j)
continue
delta_w = min(self._theshold(q) - c_j.count, w)
self._update_centroid(c_j, x, delta_w)
w -= delta_w
S.pop(j)
if w > 0:
self._add_centroid(Centroid(x, w))
if len(self) > self.K / self.delta:
self.compress()
return
def batch_update(self, values, w=1):
"""
Update the t-digest with an iterable of values. This assumes all points have the
same weight.
"""
for x in values:
self.update(x, w)
self.compress()
return
def compress(self):
T = TDigest(self.delta, self.K)
C = list(self.C.values())
for c_i in pyudorandom.items(C):
T.update(c_i.mean, c_i.count)
self.C = T.C
def percentile(self, p):
"""
Computes the percentile of a specific value in [0,100].
"""
if not (0 <= p <= 100):
raise ValueError("p must be between 0 and 100, inclusive.")
t = 0
p = float(p) / 100.
p *= self.n
for i, key in enumerate(self.C.keys()):
c_i = self.C[key]
k = c_i.count
if p < t + k:
if i == 0:
return c_i.mean
elif i == len(self) - 1:
return c_i.mean
else:
delta = (self.C.succ_item(key)[1].mean -
self.C.prev_item(key)[1].mean) / 2.
return c_i.mean + ((p - t) / k - 0.5) * delta
t += k
return self.C.max_item()[1].mean
def quantile(self, q):
"""
Computes the quantile of a specific value, ie. computes F(q) where F denotes
the CDF of the distribution.
"""
t = 0
N = float(self.n)
for i, key in enumerate(self.C.keys()):
c_i = self.C[key]
if i == len(self) - 1:
delta = (c_i.mean - self.C.prev_item(key)[1].mean) / 2.
else:
delta = (self.C.succ_item(key)[1].mean - c_i.mean) / 2.
z = max(-1, (q - c_i.mean) / delta)
if z < 1:
return t / N + c_i.count / N * (z + 1) / 2
t += c_i.count
return 1
def trimmed_mean(self, p1, p2):
"""
Computes the mean of the distribution between the two percentiles p1 and p2.
This is a modified algorithm than the one presented in the original t-Digest paper.
"""
if not (p1 < p2):
raise ValueError("p1 must be between 0 and 100 and less than p2.")
s = k = t = 0
p1 /= 100.
p2 /= 100.
p1 *= self.n
p2 *= self.n
for i, key in enumerate(self.C.keys()):
c_i = self.C[key]
k_i = c_i.count
if p1 < t + k_i:
if i == 0:
delta = self.C.succ_item(key)[1].mean - c_i.mean
elif i == len(self) - 1:
delta = c_i.mean - self.C.prev_item(key)[1].mean
else:
delta = (self.C.succ_item(key)[1].mean -
self.C.prev_item(key)[1].mean) / 2.
nu = ((p1 - t) / k_i - 0.5) * delta
s += nu * k_i * c_i.mean
k += nu * k_i
if p2 < t + k_i:
return s / k
t += k_i
return s / k
