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from collections import deque
from dataclasses import dataclass
@dataclass(eq=True, frozen=True)
class ScheduledNode:
type: str
chunk: int
stage: int
minibatch: int
start_time: int
completion_time: int
rollback: bool = False
class PipelineGraph(object):
def __init__(
self, n_stage, n_micro, f_cost, b_cost, w_cost, c_cost,
f_mem, b_mem, w_mem, max_mem=None,
):
self.n_node = 6 * n_stage * n_micro
self.n_stage = n_stage
self.n_micro = n_micro
self.f_cost = f_cost
self.b_cost = b_cost
self.w_cost = w_cost
self.c_cost = c_cost
self.f_mem = f_mem
self.b_mem = b_mem
self.w_mem = w_mem
self.fbw_cost = [f_cost, b_cost, w_cost]
self.fbw_mem = [f_mem, b_mem, w_mem]
self.max_mem = max_mem or f_mem * self.n_stage * 2
def get_id(self, cat, chunk, stage, micro):
return cat * 2 * self.n_stage * self.n_micro + \
chunk * self.n_stage * self.n_micro + \
stage * self.n_micro + \
micro
def try_v_schedule(self, fill_f=True, fill_b=True, approved_bubble=None):
count = []
for i in range(self.n_stage):
count.append([0] * 6)
end_time = [-1] * self.n_node
cur_time = [0] * self.n_stage
mem = [0] * self.n_stage
stage_bubble = [0] * self.n_stage
pending_w = [deque() for _ in range(self.n_stage)]
schedule = [[] for _ in range(self.n_stage)]
stage_str = [" " * i for i in range(self.n_stage)]
if approved_bubble is None:
approved_bubble = [-1] * self.n_stage
max_approved_bubble = max(approved_bubble)
def get_max_stage_bubble(stage=-1):
max_stage_bubble = 0
for bb in stage_bubble:
max_stage_bubble = max(max_stage_bubble, bb)
if stage >= 0:
max_stage_bubble = max(max_stage_bubble, max_approved_bubble - approved_bubble[stage])
return max_stage_bubble
def put_w(stage):
assert len(pending_w[stage]) > 0
_, chunk_, _ = pending_w[stage].popleft()
put(2, chunk_, stage)
def put(cat, chunk, stage, assert_cnt=True):
_tmp = _no_bubble = cur_time[stage] + self.fbw_cost[cat]
_cnt = count[stage][cat * 2 + chunk]
# assert _cnt < self.n_micro
if _cnt >= self.n_micro:
if not assert_cnt:
stage_str[stage] += " "
cur_time[stage] = _tmp # TODO
return
assert False
assert mem[stage] + self.fbw_mem[cat] <= self.max_mem
stage_str[stage] += "FfBbWw"[cat * 2 + chunk] + str(_cnt + 1) + " " * (3 - len(str(_cnt + 1)))
if cat > 0 or chunk > 0:
last_id = cat * 2 + chunk - 1
if cat < 2:
# if end_time[self.get_id(last_id // 2, last_id % 2, stage, _cnt)] < 0:
# print(cat, chunk, stage, _cnt)
# self.print_details(end_time)
assert end_time[self.get_id(last_id // 2, last_id % 2, stage, _cnt)] >= 0
else:
assert end_time[self.get_id(1, chunk, stage, _cnt)] >= 0
if chunk == 1 and cat < 2:
if stage < self.n_stage - 1:
_fa_id = self.get_id(cat, chunk, stage + 1, _cnt)
assert end_time[_fa_id] >= 0
_tmp = max(_tmp, end_time[_fa_id] + self.c_cost + self.fbw_cost[cat])
if chunk == 0 and cat < 2:
if stage > 0:
_fa_id = self.get_id(cat, chunk, stage - 1, _cnt)
# if end_time[_fa_id] < 0:
# print(cat, chunk, stage, _cnt)
# self.print_details(end_time)
assert end_time[_fa_id] >= 0, f"{cat}, {chunk}, {stage}, {_cnt}"
_tmp = max(_tmp, end_time[_fa_id] + self.c_cost + self.fbw_cost[cat])
_id = self.get_id(cat, chunk, stage, _cnt)
if count[stage][0] > 0:
stage_bubble[stage] += _tmp - _no_bubble
end_time[_id] = _tmp
cur_time[stage] = _tmp
mem[stage] += self.fbw_mem[cat]
# noinspection PyTypeChecker
schedule[stage].append((cat, chunk, _cnt))
if cat == 1:
pending_w[stage].append((2, chunk, _cnt))
count[stage][cat * 2 + chunk] += 1
# for _ in range(2 * self.n_stage):
# for i in range(self.n_stage):
# if count[i][1] >= count[i][0]:
# put(0, 0, i, assert_cnt=False)
# continue
# if i == self.n_stage - 1:
# put(0, 1, i, assert_cnt=False)
# continue
# fa_id = self.get_id(0, 1, i + 1, count[i][1])
# if 0 <= end_time[fa_id] < cur_time[i + 1]: # TODO
# put(0, 1, i, assert_cnt=False)
# else:
# put(0, 0, i, assert_cnt=False)
for i in range(self.n_stage):
put(0, 0, i)
for i in range(self.n_stage - 1, -1, -1):
if i == self.n_stage - 1:
put(0, 1, i)
continue
tmp = end_time[self.get_id(0, 1, i + 1, 0)] + self.c_cost
while mem[i] + self.fbw_mem[0] * (2 + i * 2) <= self.max_mem and cur_time[i] + self.fbw_cost[0] <= tmp and count[i][0] < self.n_micro:
for j in range(i + 1):
put(0, 0, j)
put(0, 1, i)
iter_chunk_ = 0
end_tmp = 0
for i in range(self.n_stage):
if i == 0:
end_tmp = cur_time[0] + self.fbw_cost[1]
continue
tmp = end_tmp + self.c_cost
while count[i][0] + count[i][1] < count[i - 1][0] + count[i - 1][1] or count[i][1] <= count[i - 1][1] < self.n_micro:
for j in range(self.n_stage - 1, i - 1, -1):
if count[j][iter_chunk_] < self.n_micro:
put(0, iter_chunk_, j)
iter_chunk_ = 1 - iter_chunk_
# while mem[i] + self.fbw_mem[0] <= self.max_mem and cur_time[i] + self.fbw_cost[0] <= tmp:
# if iter_chunk_ == 0 and count[i][0] >= count[i - 1][0]:
# break
# for j in range(self.n_stage - 1, i - 1, -1):
# if count[j][iter_chunk_] < self.n_micro:
# put(0, iter_chunk_, j)
# iter_chunk_ = 1 - iter_chunk_
# end_tmp = max(tmp, cur_time[i]) + self.fbw_cost[1]
# init_bubble = get_max_stage_bubble()
# print(stage_bubble)
for _ in range(2 * self.n_micro):
# check mem before putting b
for i in range(self.n_stage):
while mem[i] + self.fbw_mem[1] > self.max_mem:
assert len(pending_w[i]) > 0
put_w(i)
b0_ranks, b1_ranks = [], []
for i in range(self.n_stage):
if count[i][3] >= count[i][2]:
b0_ranks.append(i)
elif i == self.n_stage - 1:
b1_ranks.append(i)
else:
fa_id = self.get_id(1, 1, i + 1, count[i][3])
if end_time[fa_id] >= 0 or count[i][2] >= self.n_micro:
b1_ranks.append(i)
else:
b0_ranks.append(i)
b_ranks = []
# put b1
for i in reversed(b1_ranks):
b_ranks.append((i, 1))
# put b0
for i in b0_ranks:
b_ranks.append((i, 0))
for i, _chunk_ in b_ranks:
fa_id = -1
if _chunk_ == 1 and i < self.n_stage - 1:
fa_id = self.get_id(1, 1, i + 1, count[i][3])
if _chunk_ == 0 and i > 0:
fa_id = self.get_id(1, 0, i - 1, count[i][2])
while len(pending_w[i]) > 0 and fa_id >= 0 and end_time[fa_id] + self.c_cost >= cur_time[i] + self.fbw_cost[2]:
# fill the bubble
put_w(i)
if len(pending_w[i]) > 0 and end_time[fa_id] + self.c_cost - cur_time[i] > get_max_stage_bubble(i) - stage_bubble[i]:
if _chunk_ == 1:
put_w(i)
elif fill_b:
put_w(i)
put(1, _chunk_, i)
# put f
for i in range(self.n_stage):
if count[i][1] >= self.n_micro:
continue
put_item = None
if count[i][1] >= count[i][0]:
put_item = 0
elif i == self.n_stage - 1:
put_item = 1
else:
if end_time[self.get_id(0, 1, i + 1, count[i][1])] >= 0:
put_item = 1
elif count[i][0] < self.n_micro:
if i == 0:
put_item = 0
elif end_time[self.get_id(0, 0, i - 1, count[i][0])] >= 0:
put_item = 0
if put_item is None:
continue
# check mem before putting f
while mem[i] + self.fbw_mem[0] > self.max_mem:
assert len(pending_w[i]) > 0
put_w(i)
fa_id = -1
if put_item == 0 and i > 0:
fa_id = self.get_id(0, 0, i - 1, count[i][0])
if put_item == 1 and i < self.n_stage - 1:
fa_id = self.get_id(0, 1, i + 1, count[i][1])
while len(pending_w[i]) > 0 and fa_id >= 0 and end_time[fa_id] + self.c_cost >= cur_time[i] + self.fbw_cost[2]:
# fill the bubble
put_w(i)
if len(pending_w[i]) > 0 and end_time[fa_id] + self.c_cost - cur_time[i] > get_max_stage_bubble(i) - stage_bubble[i]:
if fill_f:
put_w(i)
put(0, put_item, i)
for i in range(self.n_stage):
while len(pending_w[i]) > 0:
put_w(i)
# for i in range(self.n_stage):
# print(stage_str[i])
max_bubble = get_max_stage_bubble()
expected_time = sum(self.fbw_cost) * self.n_micro * 2
bubble_rate = max_bubble / expected_time
# print("%6.4f" % bubble_rate, "->", stage_bubble)
if max_approved_bubble < 0 or max_bubble < max_approved_bubble:
_schedule, _end_time, _max_bubble = self.try_v_schedule(
fill_f=fill_f, fill_b=fill_b,
approved_bubble=stage_bubble,
)
if _max_bubble < max_bubble:
return _schedule, _end_time, _max_bubble
# print("%2d %3d, [%5d %5d %5d], %6d -> %6.4f %6.4f" % \
# (self.n_stage, self.n_micro, *self.fbw_cost, self.max_mem // self.f_mem, init_bubble / expected_time, bubble_rate), max_bubble)
return schedule, end_time, max_bubble
def print_details(self, end_time, print_scaling=1):
for stage in range(self.n_stage):
stage_str = ['.'] * int(max(end_time) / print_scaling)
for _cat in range(3):
for _chunk in range(2):
for _micro in range(self.n_micro):
_id = self.get_id(_cat, _chunk, stage, _micro)
if end_time[_id] < 0:
continue
end = int(end_time[_id] / print_scaling)
start = int((end_time[_id] - self.fbw_cost[_cat]) / print_scaling)
for j in range(start, end):
if j == start or j == end - 1:
stage_str[j] = "FfBbWw"[_cat * 2 + _chunk]
elif j == start + 1:
if _micro >= 10:
stage_str[j] = str(_micro // 10)
else:
stage_str[j] = str(_micro)
elif j == start + 2 and _micro >= 10:
stage_str[j] = str(_micro % 10)
else:
stage_str[j] = "-"
_str = ""
for _c in stage_str:
_str += _c
print(_str)
def get_v_schedule(self, only_run_time=False):
schedule, end_time, max_bubble = None, None, None
expected_time = sum(self.fbw_cost) * self.n_micro * 2
for fill_b in [True, False]:
for fill_f in [True, False]:
_schedule, _end_time, _max_bubble = self.try_v_schedule(
fill_b=fill_b, fill_f=fill_f
)
# print("")
if max_bubble is None or _max_bubble < max_bubble:
max_bubble = _max_bubble
schedule = _schedule
end_time = _end_time
if only_run_time:
return max_bubble + expected_time
# self.print_details(end_time, print_scaling=1)
bubble_rate = max_bubble / (expected_time + max_bubble)
print("%2d %3d, [%5d %5d %5d %5d], %6d -> %6.4f" % \
(self.n_stage, self.n_micro, *self.fbw_cost, self.c_cost, self.max_mem // self.f_mem, bubble_rate))
local_order = [[] for _ in range(self.n_stage)]
comm_id = {}
comm_id_counter = 0
post_validation_time = 0
for i in range(self.n_stage - 1, -1, -1):
pv_id = min(2 * (self.n_stage - 1 - i), self.n_micro - 1)
post_validation_time = max(post_validation_time, end_time[self.get_id(0, 0, i, pv_id)] - self.fbw_cost[0] - self.c_cost)
# post_validation_time = 0
# print(i, pv_id, post_validation_time)
for it in ["RECV_", "SEND_", ""]:
if i == 0 and it == "SEND_":
continue
if i == self.n_stage - 1 and it == "RECV_":
continue
# stage_ = i - 1 if it == "RECV_" else i
stage_ = i
local_order[stage_].append(ScheduledNode(
type=it + "POST_VALIDATION",
chunk=0,
stage=stage_,
minibatch=0,
start_time=post_validation_time,
completion_time=post_validation_time,
))
comm_id[local_order[stage_][-1]] = comm_id_counter
comm_id_counter += 1
for i in range(self.n_stage):
for _cat_, _chunk_, _micro_ in schedule[i]:
complete_time = end_time[self.get_id(_cat_, _chunk_, i, _micro_)]
local_order[i].append(ScheduledNode(
type="FBW"[_cat_],
chunk=_chunk_ if _cat_ == 0 else 1 - _chunk_,
stage=i,
minibatch=_micro_,
start_time=complete_time - self.fbw_cost[_cat_],
completion_time=complete_time,
))
if _cat_ == 2: # no communication for W
continue
cat_str = "FORWARD" if _cat_ == 0 else "BACKWARD"
def communicate(send_recv, stage_):
# noinspection PyTypeChecker
local_order[stage_].append(ScheduledNode(
type=send_recv + cat_str,
chunk=_chunk_ if _cat_ == 0 else 1 - _chunk_,
stage=stage_,
minibatch=_micro_,
start_time=complete_time,
completion_time=complete_time,
))
comm_id[local_order[stage_][-1]] = comm_id_counter
if _chunk_ == 1 and i > 0:
communicate("SEND_", i)
communicate("RECV_", i - 1)
if _chunk_ == 0 and i < self.n_stage - 1:
communicate("SEND_", i)
communicate("RECV_", i + 1)
comm_id_counter += 1
for rank in range(self.n_stage):
# For nodes with the same timestamp on the same stage, communication will be prioritized.
def even_breaker(x: ScheduledNode):
# Compute nodes are always delayed.
if x.type in ['F', 'B', 'W']:
return comm_id_counter
# For comm nodes, order by their unique comm id
return comm_id[x]
local_order[rank] = list(sorted(
local_order[rank],
key=lambda x: (x.start_time, even_breaker(x))
))
# If a recv with intersects with previous computation, reorder them so that recv
# is executed before computation and hence can be overlapped.
for i in range(len(local_order[rank])):
if i > 0 and local_order[rank][i - 1].type in {'F', 'B', 'W'} and \
local_order[rank][i].type.startswith('RECV') and \
"POST_VALIDATION" not in local_order[rank][i].type and \
local_order[rank][i].start_time <= local_order[rank][i - 1].completion_time:
local_order[rank][i], local_order[rank][i - 1] = local_order[rank][i - 1], local_order[rank][i]
local_order_with_rollback = [[] for _ in range(self.n_stage)]
for rank in range(self.n_stage):
rollback_comm = set()
if rank > 0:
for node in local_order[rank - 1]:
if node.type == "POST_VALIDATION":
break
if node.type == "SEND_FORWARD":
assert node.chunk == 0
rollback_comm.add(node.minibatch)
for node in local_order[rank]:
if node.type == "RECV_FORWARD" and node.chunk == 0 and node.minibatch in rollback_comm:
rollback = True
rollback_comm.remove(node.minibatch)
else:
rollback = False
local_order_with_rollback[rank].append(ScheduledNode(
type=node.type,
chunk=node.chunk,
stage=node.stage,
minibatch=node.minibatch,
start_time=node.start_time,
completion_time=node.completion_time,
rollback=rollback,
))
assert len(rollback_comm) == 0
for node in local_order_with_rollback[rank]:
print(f"{node.type}-{node.minibatch}-{int(node.rollback)}", end=', ')
print()
return local_order_with_rollback
if __name__ == '__main__':
settings = [
# p, n, f, b, w, c, h, a, l
# (8, 24, 18522, 18086, 9337, 601, 2304, 24, 24),
# (8, 32, 18513, 18086, 9331, 626, 2304, 24, 24),
# (8, 64, 18546, 18097, 9321, 762, 2304, 24, 24),
# (8, 24, 29718, 29444, 19927, 527, 4096, 32, 32),
# (8, 32, 29802, 29428, 19530, 577, 4096, 32, 32),
# (8, 64, 29935, 29621, 19388, 535, 4096, 32, 32),
# (16, 48, 11347, 11248, 8132, 377, 5120, 40, 48),
# (16, 64, 11307, 11254, 8101, 379, 5120, 40, 48),
# (16, 128, 11325, 11308, 8109, 378, 5120, 40, 48),
# (32, 96, 10419, 10207, 7715, 408, 6144, 48, 64),
# (32, 128, 10408, 10204, 7703, 408, 6144, 48, 64),
# (32, 256, 10402, 10248, 7698, 460, 6144, 48, 64),
# (4, 8, 6, 4, 4, 1, 4096, 32, 32),
# (8, 24, 29444, 29718, 19927, 527, 4096, 32, 32),
# ( 8, 32, 16099, 16504, 7589, 540, 2304, 24, 16),
(16, 48, 14407, 14380, 9676, 1610, 4096, 32, 32),
(16, 64, 14412, 14393, 9688, 1621, 4096, 32, 32),
(16, 128,14316, 14306, 9639, 1619, 4096, 32, 32),
(24, 72, 6763, 6969, 5251, 755, 5120, 40, 48),
(24, 96, 6783, 6984, 5259, 758, 5120, 40, 48),
(24, 192, 6785, 6990, 5260, 770, 5120, 40, 48),
(32, 96, 9458, 9748, 7288, 879, 6144, 48, 64),
(32, 128, 9469, 9744, 7306, 892, 6144, 48, 64),
(32, 256, 9447, 9644, 7193, 887, 6144, 48, 64),
]
s = 1024
# h, a, s = 4096, 32, 1024
# cost_f, cost_b, cost_w, cost_c = 29718, 29444, 19927, 527
for p, n, f, b, w, c, h, a, _ in settings:
mem_f = 34 * h + 5 * a * s
mem_w = - 32 * h
mem_b = - mem_w - mem_f
for m_offset in range(p + 1):
graph = PipelineGraph(
n_stage=p,
n_micro=n,
f_cost=f,
b_cost=b,
w_cost=w,
c_cost=c,
f_mem=mem_f,
b_mem=mem_b,
w_mem=mem_w,
max_mem=mem_f * (p * 2 + m_offset),
)
graph.get_v_schedule()
break
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