# Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved. # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. import collections from enum import Enum from paddle.fluid.core import TracerEventType from .statistic_helper import * _AllTracerEventType = [ TracerEventType.Operator, TracerEventType.Dataloader, TracerEventType.ProfileStep, TracerEventType.CudaRuntime, TracerEventType.Kernel, TracerEventType.Memcpy, TracerEventType.Memset, TracerEventType.UserDefined, TracerEventType.OperatorInner, TracerEventType.Forward, TracerEventType.Backward, TracerEventType.Optimization, TracerEventType.Communication, TracerEventType.PythonOp, TracerEventType.PythonUserDefined ] _CommunicationOpName = ['reduce', 'broadcast', 'rpc'] class SortedKeys(Enum): r""" Sorted keys for printing summary table. """ CPUTotal = 0 CPUAvg = 1 CPUMax = 2 CPUMin = 3 GPUTotal = 4 GPUAvg = 5 GPUMax = 6 GPUMin = 7 class HostStatisticNode: r''' Wrap original node for calculating statistic metrics. ''' def __init__(self, hostnode): self.hostnode = hostnode self.children_node = [] self.runtime_node = [] self.cpu_time = 0 self.self_cpu_time = 0 self.gpu_time = 0 self.self_gpu_time = 0 def cal_statistic(self): for child in self.children_node: child.cal_statistic() for rt in self.runtime_node: rt.cal_statistic() self.cpu_time = self.hostnode.end_ns - self.hostnode.start_ns for child in self.children_node: self.gpu_time += child.gpu_time self.self_cpu_time -= (child.end_ns - child.start_ns) for rt in self.runtime_node: self.self_cpu_time -= (rt.end_ns - rt.start_ns) self.gpu_time += rt.gpu_time self.self_gpu_time += rt.gpu_time for device in self.hostnode.device_node: self.gpu_time += (device.end_ns - device.start_ns) self.self_gpu_time += (device.end_ns - device.start_ns) @property def end_ns(self): return self.hostnode.end_ns @property def start_ns(self): return self.hostnode.start_ns def __getattr__(self, name): return getattr(self.hostnode, name) def traverse_tree(nodetrees): results = collections.defaultdict(list) for thread_id, rootnode in nodetrees.items(): stack = [] stack.append(rootnode) threadlist = results[thread_id] while stack: current_node = stack.pop() threadlist.append(current_node) for childnode in current_node.children_node: stack.append(childnode) return results def wrap_tree(nodetrees): ''' Using HostStatisticNode to wrap original profiler result tree, and calculate node statistic metrics. ''' node_statistic_tree = {} results = collections.defaultdict(list) newresults = collections.defaultdict(list) for thread_id, rootnode in nodetrees.items(): stack = [] stack.append(rootnode) root_statistic_node = HostStatisticNode(rootnode) newstack = [] newstack.append(root_statistic_node) node_statistic_tree[thread_id] = root_statistic_node threadlist = results[thread_id] newthreadlist = newresults[thread_id] while stack: current_node = stack.pop() threadlist.append(current_node) current_statistic_node = newstack.pop() newthreadlist.append(current_statistic_node) for childnode in current_node.children_node: stack.append(childnode) child_statistic_node = HostStatisticNode(childnode) current_statistic_node.children_node.append( child_statistic_node) newstack.append(child_statistic_node) for runtimenode in current_node.runtime_node: runtime_statistic_node = HostStatisticNode(runtimenode) current_statistic_node.runtime_node.append( runtime_statistic_node) # recursive calculate node statistic values for thread_id, root_statistic_node in node_statistic_tree.items(): root_statistic_node.cal_statistic() return node_statistic_tree, newresults class TimeRangeSummary: r""" Analyse time ranges for each TracerEventType, and summarize the time. """ def __init__(self): self.CPUTimeRange = collections.defaultdict(list) self.GPUTimeRange = collections.defaultdict( lambda: collections.defaultdict(list) ) # GPU events should be divided into different devices self.CPUTimeRangeSum = collections.defaultdict(int) self.GPUTimeRangeSum = collections.defaultdict( lambda: collections.defaultdict(int)) self.call_times = collections.defaultdict(int) def parse(self, nodetrees): r""" Analysis node trees in profiler result, and get time range for different tracer event type. """ thread2hostnodes = traverse_tree(nodetrees) for threadid, hostnodes in thread2hostnodes.items(): CPUTimeRange = collections.defaultdict(list) GPUTimeRange = collections.defaultdict( lambda: collections.defaultdict(lambda: collections.defaultdict(list)) ) # device_id/type/stream_id for hostnode in hostnodes[1:]: #skip root node CPUTimeRange[hostnode.type].append( (hostnode.start_ns, hostnode.end_ns)) self.call_times[hostnode.type] += 1 if hostnode.type == TracerEventType.Operator and any( [name in hostnode.name for name in _CommunicationOpName]): # special case, communication op CPUTimeRange[TracerEventType.Communication].append( (hostnode.start_ns, hostnode.end_ns)) self.call_times[TracerEventType.Communication] += 1 is_communication_node = ( hostnode.type == TracerEventType.Communication ) or (hostnode.type == TracerEventType.Operator and any( [name in hostnode.name for name in _CommunicationOpName])) for runtimenode in hostnode.runtime_node: CPUTimeRange[runtimenode.type].append( (runtimenode.start_ns, runtimenode.end_ns)) self.call_times[runtimenode.type] += 1 for devicenode in runtimenode.device_node: GPUTimeRange[devicenode.device_id][devicenode.type][ devicenode.stream_id].append( (devicenode.start_ns, devicenode.end_ns)) self.call_times[devicenode.type] += 1 if is_communication_node: # gpu activity for communication node GPUTimeRange[devicenode.device_id][ TracerEventType.Communication][ devicenode.stream_id].append(( devicenode.start_ns, devicenode.end_ns)) self.call_times[TracerEventType.Communication] += 1 for event_type, time_ranges in CPUTimeRange.items(): time_ranges = merge_self_ranges(time_ranges, is_sorted=False) self.CPUTimeRange[event_type] = merge_ranges( self.CPUTimeRange[event_type], time_ranges, is_sorted=True) for device_id, device_time_ranges in GPUTimeRange.items(): for event_type, event_time_ranges in device_time_ranges.items(): for stream_id, time_ranges in event_time_ranges.items(): time_ranges = merge_self_ranges( time_ranges, is_sorted=False) self.GPUTimeRange[device_id][event_type] = merge_ranges( self.GPUTimeRange[device_id][event_type], time_ranges, is_sorted=True) for event_type, time_ranges in self.CPUTimeRange.items(): self.CPUTimeRangeSum[event_type] = sum_ranges(time_ranges) for device_id, device_time_ranges in self.GPUTimeRange.items(): for event_type, time_ranges in device_time_ranges.items(): self.GPUTimeRangeSum[device_id][event_type] = sum_ranges( time_ranges) def get_gpu_devices(self): return self.GPUTimeRange.keys() def get_gpu_range_sum(self, device_id, event_type): return self.GPUTimeRangeSum[device_id][event_type] def get_cpu_range_sum(self, event_type): return self.CPUTimeRangeSum[event_type] class EventSummary: r""" Analyse operator event in profiling data, correlate with its device event. """ class DeviceItem: def __init__(self, name): self.name = name self.call = 0 self.gpu_time = 0 self.max_gpu_time = 0 self.min_gpu_time = float('inf') @property def avg_gpu_time(self): return self.gpu_time / self.call def add_gpu_time(self, time): if time > self.max_gpu_time: self.max_gpu_time = time if time < self.min_gpu_time: self.min_gpu_time = time self.gpu_time += time def add_item(self, node): self.call += 1 self.add_gpu_time(node.end_ns - node.start_ns) class OperatorItem: def __init__(self, name): self.name = name self.call = 0 self.cpu_time = 0 self.gpu_time = 0 self.max_cpu_time = 0 self.min_cpu_time = float('inf') self.max_gpu_time = 0 self.min_gpu_time = float('inf') self.devices = {} self.operator_inners = {} @property def avg_cpu_time(self): return self.cpu_time / self.call @property def avg_gpu_time(self): return self.gpu_time / self.call def add_cpu_time(self, time): if time > self.max_cpu_time: self.max_cpu_time = time if time < self.min_cpu_time: self.min_cpu_time = time self.cpu_time += time def add_gpu_time(self, time): if time > self.max_gpu_time: self.max_gpu_time = time if time < self.min_gpu_time: self.min_gpu_time = time self.gpu_time += time def add_call(self): self.call += 1 def add_item(self, node): self.add_call() self.add_cpu_time(node.cpu_time) self.add_gpu_time(node.gpu_time) for child in node.children_node: if child.name not in self.operator_inners: self.operator_inners[ child.name] = EventSummary.OperatorItem(child.name) self.operator_inners[child.name].add_item(child) for runtimenode in node.runtime_node: for devicenode in runtimenode.device_node: if devicenode.name not in self.devices: self.devices[devicenode.name] = EventSummary.DeviceItem( devicenode.name) self.devices[devicenode.name].add_item(devicenode) class GeneralItem: def __init__(self, name): self.name = name self.call = 0 self.cpu_time = 0 self.max_cpu_time = 0 self.min_cpu_time = float('inf') self.gpu_time = 0 self.max_gpu_time = 0 self.min_gpu_time = float('inf') @property def avg_cpu_time(self): return self.cpu_time / self.call @property def avg_gpu_time(self): return self.gpu_time / self.call def add_cpu_time(self, time): if time > self.max_cpu_time: self.max_cpu_time = time if time < self.min_cpu_time: self.min_cpu_time = time self.cpu_time += time def add_gpu_time(self, time): if time > self.max_gpu_time: self.max_gpu_time = time if time < self.min_gpu_time: self.min_gpu_time = time self.gpu_time += time def add_call(self): self.call += 1 def add_item(self, node): self.add_call() self.add_cpu_time(node.cpu_time) self.add_gpu_time(node.gpu_time) def __init__(self): self.items = {} # for operator summary self.thread_items = collections.defaultdict( dict) # for operator summary self.userdefined_items = {} # for userdefined summary self.userdefined_thread_items = collections.defaultdict( dict) # for userdefined summary self.model_perspective_items = {} # for model summary self.memory_manipulation_items = {} # for memory manipulation summary def parse(self, nodetrees): r""" Analysis operator event in the nodetress. """ node_statistic_trees, thread2host_statistic_nodes = wrap_tree(nodetrees) for threadid, host_statistic_nodes in thread2host_statistic_nodes.items( ): for host_statistic_node in host_statistic_nodes[ 1:]: #skip root node if host_statistic_node.type == TracerEventType.Operator: self.add_operator_item(host_statistic_node) if host_statistic_node.type == TracerEventType.UserDefined\ or host_statistic_node.type == TracerEventType.PythonUserDefined: if 'memcpy' in host_statistic_node.name.lower() or 'memorycopy' in host_statistic_node.name.lower()\ or 'memset' in host_statistic_node.name.lower(): self.add_memory_manipulation_item(host_statistic_node) else: self.add_userdefined_item(host_statistic_node) for threadid, root_statistic_node in node_statistic_trees.items(): deque = collections.deque() deque.append(root_statistic_node) while deque: current_node = deque.popleft() for child in current_node.children_node: if child.type == TracerEventType.Forward or child.type == TracerEventType.Dataloader\ or child.type == TracerEventType.Backward or child.type == TracerEventType.Optimization: self.add_model_perspective_item( child) #find first model perspective node else: deque.append(child) def add_operator_item(self, operator_node): if operator_node.name not in self.items: self.items[operator_node.name] = EventSummary.OperatorItem( operator_node.name) self.items[operator_node.name].add_item(operator_node) if operator_node.name not in self.thread_items[operator_node.thread_id]: self.thread_items[operator_node.thread_id][ operator_node.name] = EventSummary.OperatorItem( operator_node.name) self.thread_items[operator_node.thread_id][operator_node.name].add_item( operator_node) def add_userdefined_item(self, userdefined_node): if userdefined_node.name not in self.userdefined_items: self.userdefined_items[ userdefined_node.name] = EventSummary.GeneralItem( userdefined_node.name) self.userdefined_items[userdefined_node.name].add_item(userdefined_node) if userdefined_node.name not in self.userdefined_thread_items[ userdefined_node.thread_id]: self.userdefined_thread_items[userdefined_node.thread_id][ userdefined_node.name] = EventSummary.GeneralItem( userdefined_node.name) self.userdefined_thread_items[userdefined_node.thread_id][ userdefined_node.name].add_item(userdefined_node) def add_memory_manipulation_item(self, memory_manipulation_node): if memory_manipulation_node.name not in self.memory_manipulation_items: self.memory_manipulation_items[ memory_manipulation_node.name] = EventSummary.GeneralItem( memory_manipulation_node.name) self.memory_manipulation_items[memory_manipulation_node.name].add_item( memory_manipulation_node) def add_model_perspective_item(self, model_perspective_node): if model_perspective_node.type == TracerEventType.Forward: name = 'Forward' elif model_perspective_node.type == TracerEventType.Backward: name = 'Backward' elif model_perspective_node.type == TracerEventType.Optimization: name = 'Optimization' elif model_perspective_node.type == TracerEventType.Dataloader: name = 'Dataloader' else: return if name not in self.model_perspective_items: self.model_perspective_items[name] = EventSummary.GeneralItem(name) self.model_perspective_items[name].add_item(model_perspective_node) class StatisticData: r""" Hold all analysed results. """ def __init__(self, node_trees, extra_info): self.node_trees = node_trees self.extra_info = extra_info self.time_range_summary = TimeRangeSummary() self.event_summary = EventSummary() self.time_range_summary.parse(node_trees) self.event_summary.parse(node_trees) def _build_table(statistic_data, sorted_by=SortedKeys.CPUTotal, op_detail=True, thread_sep=False, time_unit='ms', row_limit=100, max_src_column_width=75): """Prints a summary of events.""" # format table row SPACING_SIZE = 2 row_format_list = [""] header_sep_list = [""] line_length_list = [-SPACING_SIZE] def add_column(padding, text_dir='<'): row_format_list[0] += '{: ' + text_dir + str(padding) + '}' + ( ' ' * SPACING_SIZE) header_sep_list[0] += '-' * padding + (' ' * SPACING_SIZE) line_length_list[0] += padding + SPACING_SIZE def add_title(padding, text): left_length = padding - len(text) half = left_length // 2 return '-' * half + text + '-' * (left_length - half) result = [] def append(s): result.append(s) result.append('\n') def format_time(time, unit='ms', indent=0): r""" Transform time in ns to time in unit. """ if time == float('inf'): return '-' else: result = float(time) if unit == 's': result /= 1e9 elif unit == 'ms': result /= 1e6 elif unit == 'us': result /= 1e3 return '{}{:.2f}'.format(' ' * indent, result) def format_ratio(ratio, indent=0): r""" Transform ratio within [0, 1] to percentage presentation. """ return '{}{:.2f}'.format(' ' * indent, ratio * 100) total_time = statistic_data.time_range_summary.get_cpu_range_sum( TracerEventType.ProfileStep) ###### Print Device Summary ###### headers = ['Device', 'Utilization (%)'] name_column_width = 30 DEFAULT_COLUMN_WIDTH = 20 add_column(name_column_width) for _ in headers[1:]: add_column(DEFAULT_COLUMN_WIDTH) row_format = row_format_list[0] header_sep = header_sep_list[0] line_length = line_length_list[0] # construct table string append(add_title(line_length, "Device Summary")) append('Time unit: {}'.format(time_unit)) append(header_sep) append(row_format.format(*headers)) append(header_sep) row_values = [ 'CPU(Process)', format_ratio( float(statistic_data.extra_info['Process Cpu Utilization'])) ] append(row_format.format(*row_values)) row_values = [ 'CPU(System)', format_ratio( float(statistic_data.extra_info['System Cpu Utilization'])) ] append(row_format.format(*row_values)) for gpu_name in statistic_data.time_range_summary.get_gpu_devices(): gpu_time = float( statistic_data.time_range_summary.get_gpu_range_sum( gpu_name, TracerEventType.Kernel)) utilization = gpu_time / total_time row_values = ['GPU{}'.format(gpu_name), format_ratio(utilization)] append(row_format.format(*row_values)) append(header_sep) append( "Note:\nCPU(Process) Utilization = Current process CPU time over all cpu cores / elapsed time, so max utilization can be reached 100% * number of cpu cores.\n" "CPU(System) Utilization = All processes CPU time over all cpu cores(busy time) / (busy time + idle time).\n" "GPU Utilization = Current process GPU time / elapsed time") append('-' * line_length) append('') append('') if total_time == 0: return ''.join(result) ###### Print Overview Summary ###### headers = ['Event Type', 'CPU Time', 'Ratio (%)'] row_format_list = [""] header_sep_list = [""] line_length_list = [-SPACING_SIZE] DEFAULT_COLUMN_WIDTH = 25 for _ in headers: add_column(DEFAULT_COLUMN_WIDTH) row_format = row_format_list[0] header_sep = header_sep_list[0] line_length = line_length_list[0] # construct table string append(add_title(line_length, "Overview Summary")) append('Time unit: {}'.format(time_unit)) append(header_sep) append(row_format.format(*headers)) append(header_sep) row_values = [ 'Total Time', format_time( total_time, unit=time_unit), format_ratio(1) ] append(row_format.format(*row_values)) cpu_type_time = collections.defaultdict(int) gpu_type_time = collections.defaultdict(int) for event_type, value in statistic_data.time_range_summary.CPUTimeRangeSum.items( ): cpu_type_time[event_type] = value gpu_time_range = collections.defaultdict(list) for device_id, device_time_ranges in statistic_data.time_range_summary.GPUTimeRange.items( ): for event_type, time_range in device_time_ranges.items(): gpu_time_range[event_type] = merge_ranges( gpu_time_range[event_type], time_range, is_sorted=True) for event_type, time_range in gpu_time_range.items(): gpu_type_time[event_type] = sum_ranges(time_range) sorted_items = sorted( cpu_type_time.items(), key=lambda x: x[1], reverse=True) for event_type, time in sorted_items: row_values = [ ' {}'.format(str(event_type).split('.')[1]), format_time( time, unit=time_unit), format_ratio(float(time) / total_time) ] append(row_format.format(*row_values)) append(header_sep) headers = ['', 'GPU Time', 'Ratio (%)'] append(row_format.format(*headers)) append(header_sep) for event_type, time in gpu_type_time.items(): row_values = [ ' {}'.format(str(event_type).split('.')[1]), format_time( time, unit=time_unit), format_ratio(float(time) / total_time) ] append(row_format.format(*row_values)) append(header_sep) append( "Note:\nIn this table, We sum up all collected events in terms of event type.\n" "The time of events collected on host are presented as CPU Time, and as GPU Time if on device.\n" "ratio = CPU(GPU) Time / Total Time." "Events with different types may overlap or inclusion, e.g. Operator includes OperatorInner, so the sum of ratios is not 100%.\n" "The time of events in the same type with overlap will not calculate twice, and all time is summed after merged.\n" "Example:\n" "Thread 1:\n" " Operator: |___________| |__________|\n" "Thread 2:\n" " Operator: |____________| |___|\n" "After merged:\n" " Result: |______________| |__________|\n") append('-' * line_length) append('') append('') ###### Print Operator Summary Report ###### if statistic_data.event_summary.items: headers = [ 'Name', 'Calls', 'CPU Total / Avg / Max / Min / Ratio(%)', 'GPU Total / Avg / Max / Min / Ratio(%)' ] row_format_list = [""] header_sep_list = [""] line_length_list = [-SPACING_SIZE] name_column_width = 50 add_column(name_column_width) add_column(6) add_column(40) add_column(40) row_format = row_format_list[0] header_sep = header_sep_list[0] line_length = line_length_list[0] # construct table string append(add_title(line_length, "Operator Summary")) append('Time unit: {}'.format(time_unit)) append(header_sep) append(row_format.format(*headers)) append(header_sep) if thread_sep == True: thread_items = statistic_data.event_summary.thread_items else: thread_items = { 'All threads merged': statistic_data.event_summary.items } for thread_id, items in thread_items.items(): append(add_title(line_length, "Thread: {}".format(thread_id))) if sorted_by == SortedKeys.CPUTotal: sorted_items = sorted( items.items(), key=lambda x: x[1].cpu_time, reverse=True) elif sorted_by == SortedKeys.CPUAvg: sorted_items = sorted( items.items(), key=lambda x: x[1].avg_cpu_time, reverse=True) elif sorted_by == SortedKeys.CPUMax: sorted_items = sorted( items.items(), key=lambda x: x[1].max_cpu_time, reverse=True) elif sorted_by == SortedKeys.CPUMin: sorted_items = sorted( items.items(), key=lambda x: x[1].min_cpu_time) elif sorted_by == SortedKeys.GPUTotal: sorted_items = sorted( items.items(), key=lambda x: x[1].gpu_time, reverse=True) elif sorted_by == SortedKeys.GPUAvg: sorted_items = sorted( items.items(), key=lambda x: x[1].avg_gpu_time, reverse=True) elif sorted_by == SortedKeys.GPUMax: sorted_items = sorted( items.items(), key=lambda x: x[1].max_gpu_time, reverse=True) elif sorted_by == SortedKeys.GPUMin: sorted_items = sorted( items.items(), key=lambda x: x[1].min_gpu_time) total_cpu_time = 0 total_gpu_time = 0 for name, item in sorted_items: total_cpu_time += item.cpu_time total_gpu_time += item.gpu_time for name, item in sorted_items: row_values = [ name, item.call, '{} / {} / {} / {} / {}'.format( format_time( item.cpu_time, unit=time_unit), format_time( item.avg_cpu_time, unit=time_unit), format_time( item.max_cpu_time, unit=time_unit), format_time( item.min_cpu_time, unit=time_unit), format_ratio(float(item.cpu_time) / total_cpu_time)), '{} / {} / {} / {} / {}'.format( format_time( item.gpu_time, unit=time_unit), format_time( item.avg_gpu_time, unit=time_unit), format_time( item.max_gpu_time, unit=time_unit), format_time( item.min_gpu_time, unit=time_unit), format_ratio(float(item.gpu_time) / total_gpu_time)) ] append(row_format.format(*row_values)) if op_detail: for innerop_name, innerop_node in item.operator_inners.items( ): row_values = [ ' {}'.format(innerop_name), innerop_node.call, '{} / {} / {} / {} / {}'.format( format_time( innerop_node.cpu_time, unit=time_unit), format_time( innerop_node.avg_cpu_time, unit=time_unit), format_time( innerop_node.max_cpu_time, unit=time_unit), format_time( innerop_node.min_cpu_time, unit=time_unit), format_ratio( float(innerop_node.cpu_time) / total_cpu_time)), '{} / {} / {} / {} / {}'.format( format_time( innerop_node.gpu_time, unit=time_unit), format_time( innerop_node.avg_gpu_time, unit=time_unit), format_time( innerop_node.max_gpu_time, unit=time_unit), format_time( innerop_node.min_gpu_time, unit=time_unit), format_ratio( float(innerop_node.gpu_time) / total_gpu_time)) ] append(row_format.format(*row_values)) for device_node_name, devicenode in innerop_node.devices.items( ): if len(device_node_name) + 4 > name_column_width: device_node_name = device_node_name[: name_column_width - 7] device_node_name += "..." row_values = [ ' {}'.format(device_node_name), devicenode.call, '- / - / - / - / -', '{} / {} / {} / {} / {}'.format( format_time( devicenode.gpu_time, unit=time_unit), format_time( devicenode.avg_gpu_time, unit=time_unit), format_time( devicenode.max_gpu_time, unit=time_unit), format_time( devicenode.min_gpu_time, unit=time_unit), format_ratio( float(devicenode.gpu_time) / total_gpu_time)) ] append(row_format.format(*row_values)) for device_node_name, device_node in item.devices.items(): if len(device_node_name) + 2 > name_column_width: device_node_name = device_node_name[: name_column_width - 5] device_node_name += "..." row_values = [ ' {}'.format(device_node_name), devicenode.call, '- / - / - / - / -', '{} / {} / {} / {} / {}'.format( format_time( devicenode.gpu_time, unit=time_unit), format_time( devicenode.avg_gpu_time, unit=time_unit), format_time( devicenode.max_gpu_time, unit=time_unit), format_time( devicenode.min_gpu_time, unit=time_unit), format_ratio( float(devicenode.gpu_time) / total_gpu_time)) ] append(row_format.format(*row_values)) append(header_sep) append('') append('') return ''.join(result)