class ECMData(PerformanceModel):
"""Representation of Data portion of the Execution-Cache-Memory Model."""
name = "Execution-Cache-Memory (data transfers only)"
def __init__(self,
kernel,
machine,
args=None,
parser=None,
cores=1,
cache_predictor=CacheSimulationPredictor,
verbose=0):
"""
Create Execcution-Cache-Memory data model from kernel and machine objects.
*kernel* is a Kernel object
*machine* describes the machine (cpu, cache and memory) characteristics
*args* (optional) are the parsed arguments from the comand line
If *args* is None, *cores*, *cache_predictor* and *verbose* are taken into account,
otherwise *args* takes precedence.
"""
self.kernel = kernel
self.machine = machine
self._args = args
self._parser = parser
self.results = {}
if args:
self.verbose = self._args.verbose
self.cores = self._args.cores
if self._args.cache_predictor == 'SIM':
self.predictor = CacheSimulationPredictor(
self.kernel, self.machine, self.cores)
elif self._args.cache_predictor == 'LC':
self.predictor = LayerConditionPredictor(
self.kernel, self.machine, self.cores)
else:
raise NotImplementedError(
"Unknown cache predictor, only LC (layer condition) and "
"SIM (cache simulation with pycachesim) is supported.")
else:
self.cores = cores
self.predictor = cache_predictor(self.kernel, self.machine,
self.cores)
self.verbose = verbose
def calculate_cache_access(self):
"""Dispatch to cache predictor to get cache stats."""
self.results.update({
'cycles': [], # will be filled by caclculate_cycles()
'misses': self.predictor.get_misses(),
'hits': self.predictor.get_hits(),
'evicts': self.predictor.get_evicts(),
'verbose infos': self.predictor.get_infos()
}) # only for verbose outputs
def calculate_cycles(self):
"""
Calculate performance model cycles from cache stats.
calculate_cache_access() needs to have been execute before.
"""
element_size = self.kernel.datatypes_size[self.kernel.datatype]
elements_per_cacheline = float(
self.machine['cacheline size']) // element_size
cacheline_size = float(self.machine['cacheline size'])
loads, stores = (self.predictor.get_loads(),
self.predictor.get_stores())
for cache_level, cache_info in list(
enumerate(self.machine['memory hierarchy']))[1:]:
throughput, duplexness = cache_info[
'non-overlap upstream throughput']
if type(throughput
) is str and throughput == 'full socket memory bandwidth':
# Memory transfer
# we use bandwidth to calculate cycles and then add panalty cycles (if given)
# choose bw according to cache level and problem
# first, compile stream counts at current cache level
# write-allocate is allready resolved in cache predictor
read_streams = loads[cache_level]
write_streams = stores[cache_level]
# second, try to find best fitting kernel (closest to stream seen stream counts):
threads_per_core = 1
bw, measurement_kernel = self.machine.get_bandwidth(
cache_level, read_streams, write_streams, threads_per_core)
# calculate cycles
if duplexness == 'half-duplex':
cycles = float(loads[cache_level] + stores[cache_level]) * \
float(elements_per_cacheline) * float(element_size) * \
float(self.machine['clock']) / float(bw)
else: # full-duplex
raise NotImplementedError(
"full-duplex mode is not (yet) supported for memory transfers."
)
# add penalty cycles for each read stream
if 'penalty cycles per read stream' in cache_info:
cycles += stores[cache_level] * \
cache_info['penalty cycles per read stream']
self.results.update({
'memory bandwidth kernel': measurement_kernel,
'memory bandwidth': bw
})
else:
# since throughput is given in B/cy, and we need CL/cy:
throughput = float(throughput) / cacheline_size
# only cache cycles count
if duplexness == 'half-duplex':
cycles = (loads[cache_level] +
stores[cache_level]) / float(throughput)
elif duplexness == 'full-duplex':
cycles = max(loads[cache_level] / float(throughput),
stores[cache_level] / float(throughput))
else:
raise ValueError(
"Duplexness of cache throughput may only be 'half-duplex'"
"or 'full-duplex', found {} in {}.".format(
duplexness, cache_info['name']))
self.results['cycles'].append((cache_info['level'], cycles))
self.results[cache_info['level']] = cycles
return self.results
def analyze(self):
"""Run complete anaylysis and return results."""
self.calculate_cache_access()
self.calculate_cycles()
self.results['flops per iteration'] = sum(self.kernel._flops.values())
return self.results
def conv_cy(self, cy_cl):
"""Convert cycles (cy/CL) to other units, such as FLOP/s or It/s."""
if not isinstance(cy_cl, PrefixedUnit):
cy_cl = PrefixedUnit(cy_cl, '', 'cy/CL')
clock = self.machine['clock']
element_size = self.kernel.datatypes_size[self.kernel.datatype]
elements_per_cacheline = int(
self.machine['cacheline size']) // element_size
if cy_cl != 0:
it_s = clock / cy_cl * elements_per_cacheline
it_s.unit = 'It/s'
else:
it_s = PrefixedUnit('inf It/S')
flops_per_it = sum(self.kernel._flops.values())
performance = it_s * flops_per_it
performance.unit = 'FLOP/s'
cy_it = cy_cl * elements_per_cacheline
cy_it.unit = 'cy/It'
return {
'It/s': it_s,
'cy/CL': cy_cl,
'cy/It': cy_it,
'FLOP/s': performance
}
def report_data_transfers(self):
cacheline_size = float(self.machine['cacheline size'])
r = "Data Transfers:\nLevel | Loads | Store |\n"
loads, stores = (self.predictor.get_loads(),
self.predictor.get_stores())
for cache_level, cache_info in list(
enumerate(self.machine['memory hierarchy']))[1:]:
r += ("{:>7} | {:>3.0f} B/CL | {:>3.0f} B/CL |\n".format(
self.machine['memory hierarchy'][cache_level - 1]['level'] +
'-' + cache_info['level'], loads[cache_level] * cacheline_size,
stores[cache_level] * cacheline_size))
return r
def report(self, output_file=sys.stdout):
"""Print generated model data in human readable format."""
if self.verbose > 1:
print('{}'.format(pprint.pformat(self.results['verbose infos'])),
file=output_file)
for level, cycles in self.results['cycles']:
print('{} = {}'.format(level,
self.conv_cy(cycles)[self._args.unit]),
file=output_file)
if self.verbose > 1:
if 'memory bandwidth kernel' in self.results:
print('memory cycles based on {} kernel with {}'.format(
self.results['memory bandwidth kernel'],
self.results['memory bandwidth']),
file=output_file)
if self.verbose > 1:
print(file=output_file)
print(self.report_data_transfers(), file=output_file)
class ECMData(PerformanceModel):
"""Representation of Data portion of the Execution-Cache-Memory Model."""
name = "Execution-Cache-Memory (data transfers only)"
def __init__(self, kernel, machine, args=None, parser=None, cores=1,
cache_predictor=CacheSimulationPredictor, verbose=0):
"""
Create Execcution-Cache-Memory data model from kernel and machine objects.
*kernel* is a Kernel object
*machine* describes the machine (cpu, cache and memory) characteristics
*args* (optional) are the parsed arguments from the comand line
If *args* is None, *cores*, *cache_predictor* and *verbose* are taken into account,
otherwise *args* takes precedence.
"""
self.kernel = kernel
self.machine = machine
self._args = args
self._parser = parser
self.results = {}
if args:
self.verbose = self._args.verbose
self.cores = self._args.cores
if self._args.cache_predictor == 'SIM':
self.predictor = CacheSimulationPredictor(self.kernel, self.machine, self.cores)
elif self._args.cache_predictor == 'LC':
self.predictor = LayerConditionPredictor(self.kernel, self.machine, self.cores)
else:
raise NotImplementedError("Unknown cache predictor, only LC (layer condition) and "
"SIM (cache simulation with pycachesim) is supported.")
else:
self.cores = cores
self.predictor = cache_predictor(self.kernel, self.machine, self.cores)
self.verbose = verbose
def calculate_cache_access(self):
"""Dispatch to cache predictor to get cache stats."""
self.results.update({
'cycles': [], # will be filled by caclculate_cycles()
'misses': self.predictor.get_misses(),
'hits': self.predictor.get_hits(),
'evicts': self.predictor.get_evicts(),
'verbose infos': self.predictor.get_infos()}) # only for verbose outputs
def calculate_cycles(self):
"""
Calculate performance model cycles from cache stats.
calculate_cache_access() needs to have been execute before.
"""
element_size = self.kernel.datatypes_size[self.kernel.datatype]
elements_per_cacheline = float(self.machine['cacheline size']) // element_size
iterations_per_cacheline = (sympy.Integer(self.machine['cacheline size']) /
sympy.Integer(self.kernel.bytes_per_iteration))
self.results['iterations per cacheline'] = iterations_per_cacheline
cacheline_size = float(self.machine['cacheline size'])
loads, stores = (self.predictor.get_loads(), self.predictor.get_stores())
for cache_level, cache_info in list(enumerate(self.machine['memory hierarchy']))[1:]:
throughput, duplexness = cache_info['non-overlap upstream throughput']
if type(throughput) is str and throughput == 'full socket memory bandwidth':
# Memory transfer
# we use bandwidth to calculate cycles and then add panalty cycles (if given)
# choose bw according to cache level and problem
# first, compile stream counts at current cache level
# write-allocate is allready resolved in cache predictor
read_streams = loads[cache_level]
write_streams = stores[cache_level]
# second, try to find best fitting kernel (closest to stream seen stream counts):
threads_per_core = 1
bw, measurement_kernel = self.machine.get_bandwidth(
cache_level, read_streams, write_streams, threads_per_core)
# calculate cycles
if duplexness == 'half-duplex':
cycles = float(loads[cache_level] + stores[cache_level]) * \
float(elements_per_cacheline) * float(element_size) * \
float(self.machine['clock']) / float(bw)
else: # full-duplex
raise NotImplementedError(
"full-duplex mode is not (yet) supported for memory transfers.")
# add penalty cycles for each read stream
if 'penalty cycles per read stream' in cache_info:
cycles += stores[cache_level] * \
cache_info['penalty cycles per read stream']
self.results.update({
'memory bandwidth kernel': measurement_kernel,
'memory bandwidth': bw})
else:
# since throughput is given in B/cy, and we need CL/cy:
throughput = float(throughput) / cacheline_size
# only cache cycles count
if duplexness == 'half-duplex':
cycles = (loads[cache_level] + stores[cache_level]) / float(throughput)
elif duplexness == 'full-duplex':
cycles = max(loads[cache_level] / float(throughput),
stores[cache_level] / float(throughput))
else:
raise ValueError("Duplexness of cache throughput may only be 'half-duplex'"
"or 'full-duplex', found {} in {}.".format(
duplexness, cache_info['name']))
self.results['cycles'].append((cache_info['level'], cycles))
self.results[cache_info['level']] = cycles
return self.results
def analyze(self):
"""Run complete anaylysis and return results."""
self.calculate_cache_access()
self.calculate_cycles()
self.results['flops per iteration'] = sum(self.kernel._flops.values())
return self.results
def conv_cy(self, cy_cl):
"""Convert cycles (cy/CL) to other units, such as FLOP/s or It/s."""
if not isinstance(cy_cl, PrefixedUnit):
cy_cl = PrefixedUnit(cy_cl, '', 'cy/CL')
clock = self.machine['clock']
element_size = self.kernel.datatypes_size[self.kernel.datatype]
elements_per_cacheline = int(self.machine['cacheline size']) // element_size
if cy_cl != 0:
it_s = clock/cy_cl*elements_per_cacheline
it_s.unit = 'It/s'
else:
it_s = PrefixedUnit('inf It/S')
flops_per_it = sum(self.kernel._flops.values())
performance = it_s*flops_per_it
performance.unit = 'FLOP/s'
cy_it = cy_cl*elements_per_cacheline
cy_it.unit = 'cy/It'
return {'It/s': it_s,
'cy/CL': cy_cl,
'cy/It': cy_it,
'FLOP/s': performance}
def report_data_transfers(self):
cacheline_size = float(self.machine['cacheline size'])
r = "Data Transfers:\nLevel | Loads | Store |\n"
loads, stores = (self.predictor.get_loads(), self.predictor.get_stores())
for cache_level, cache_info in list(enumerate(self.machine['memory hierarchy']))[1:]:
r += ("{:>7} | {:>3.0f} B/CL | {:>3.0f} B/CL |\n".format(
self.machine['memory hierarchy'][cache_level-1]['level']+'-'+cache_info['level'],
loads[cache_level] * cacheline_size,
stores[cache_level] * cacheline_size))
return r
def report(self, output_file=sys.stdout):
"""Print generated model data in human readable format."""
if self.verbose > 1:
print('{}'.format(pprint.pformat(self.results['verbose infos'])), file=output_file)
for level, cycles in self.results['cycles']:
print('{} = {}'.format(
level, self.conv_cy(cycles)[self._args.unit]), file=output_file)
if self.verbose > 1:
if 'memory bandwidth kernel' in self.results:
print('memory cycles based on {} kernel with {}'.format(
self.results['memory bandwidth kernel'],
self.results['memory bandwidth']),
file=output_file)
if self.verbose > 1:
print(file=output_file)
print(self.report_data_transfers(), file=output_file)
class Roofline(PerformanceModel):
"""
Representation of the Roofline model based on simplistic FLOP analysis.
more info to follow...
"""
name = "Roofline"
@classmethod
def configure_arggroup(cls, parser):
"""Configure argument parser."""
pass
def __init__(self,
kernel,
machine,
args=None,
parser=None,
cores=1,
cache_predictor=LayerConditionPredictor,
verbose=0):
"""
Create roofline model from kernel and machine objects.
*kernel* is a Kernel object
*machine* describes the machine (cpu, cache and memory) characteristics
*args* (optional) are the parsed arguments from the comand line
If *args* is None, *asm_block*, *pointer_increment* and *verbose* will be used, otherwise
*args* takes precedence.
"""
self.kernel = kernel
self.machine = machine
self._args = args
self._parser = parser
self.results = None
if args:
self.verbose = self._args.verbose
self.cores = self._args.cores
if self._args.cache_predictor == 'SIM':
self.predictor = CacheSimulationPredictor(
self.kernel, self.machine, self.cores)
elif self._args.cache_predictor == 'LC':
self.predictor = LayerConditionPredictor(
self.kernel, self.machine, self.cores)
else:
raise NotImplementedError(
"Unknown cache predictor, only LC (layer condition) and "
"SIM (cache simulation with pycachesim) is supported.")
else:
self.cores = cores
self.predictor = cache_predictor(self.kernel, self.machine,
self.cores)
self.verbose = verbose
def calculate_cache_access(self):
"""Apply cache prediction to generate cache access behaviour."""
self.results = {
'loads': self.predictor.get_loads(),
'stores': self.predictor.get_stores(),
'verbose infos':
self.predictor.get_infos(), # only for verbose outputs
'bottleneck level': 0,
'mem bottlenecks': []
}
element_size = self.kernel.datatypes_size[self.kernel.datatype]
cacheline_size = float(self.machine['cacheline size'])
elements_per_cacheline = int(cacheline_size // element_size)
total_flops = sum(self.kernel._flops.values()) * elements_per_cacheline
# TODO let user choose threads_per_core:
threads_per_core = 1
# Compile relevant information
# CPU-L1 stats (in bytes!)
# We compile CPU-L1 stats on our own, because cacheprediction only works on cache lines
read_offsets, write_offsets = zip(*list(
self.kernel.compile_global_offsets(
iteration=range(0, elements_per_cacheline))))
read_offsets = set([
item for sublist in read_offsets if sublist is not None
for item in sublist
])
write_offsets = set([
item for sublist in write_offsets if sublist is not None
for item in sublist
])
write_streams = len(write_offsets)
read_streams = len(read_offsets) + write_streams # write-allocate
total_loads = read_streams * element_size
total_evicts = write_streams * element_size
bw, measurement_kernel = self.machine.get_bandwidth(
0,
read_streams,
0, # we do not consider stores to L1
threads_per_core,
cores=self.cores)
# Calculate performance (arithmetic intensity * bandwidth with
# arithmetic intensity = Iterations / bytes loaded
if total_loads == 0:
# This happens in case of full-caching
arith_intens = None
it_s = None
else:
arith_intens = 1.0 / (total_loads / elements_per_cacheline)
it_s = PrefixedUnit(float(bw) * arith_intens, 'It/s')
self.results['mem bottlenecks'].append({
'performance':
self.conv_perf(it_s),
'level':
self.machine['memory hierarchy'][0]['level'],
'arithmetic intensity':
arith_intens,
'bw kernel':
measurement_kernel,
'bandwidth':
bw,
'bytes transfered':
total_loads
})
self.results['bottleneck level'] = len(
self.results['mem bottlenecks']) - 1
self.results['min performance'] = self.conv_perf(it_s)
# for other cache and memory levels:
for cache_level, cache_info in list(
enumerate(self.machine['memory hierarchy']))[:-1]:
# Compiling stats (in bytes!)
total_loads = self.results['loads'][cache_level +
1] * cacheline_size
total_stores = self.results['stores'][cache_level +
1] * cacheline_size
# choose bw according to cache level and problem
# first, compile stream counts at current cache level
# write-allocate is allready resolved above
read_streams = self.results['loads'][cache_level + 1]
write_streams = self.results['stores'][cache_level + 1]
# second, try to find best fitting kernel (closest to stream seen stream counts):
bw, measurement_kernel = self.machine.get_bandwidth(
cache_level + 1,
read_streams,
write_streams,
threads_per_core,
cores=self.cores)
# Calculate performance (arithmetic intensity * bandwidth with
# arithmetic intensity = flops / bytes transfered)
bytes_transfered = total_loads + total_stores
if bytes_transfered == 0:
# This happens in case of full-caching
arith_intens = float('inf')
it_s = PrefixedUnit(float('inf'), 'It/s')
else:
arith_intens = 1 / (bytes_transfered / elements_per_cacheline)
it_s = PrefixedUnit(float(bw) * arith_intens, 'It/s')
self.results['mem bottlenecks'].append({
'performance':
self.conv_perf(it_s),
'level':
(self.machine['memory hierarchy'][cache_level + 1]['level']),
'arithmetic intensity':
arith_intens,
'bw kernel':
measurement_kernel,
'bandwidth':
bw,
'bytes transfered':
bytes_transfered
})
if it_s < self.results.get('min performance',
{'It/s': it_s})['It/s']:
self.results['bottleneck level'] = len(
self.results['mem bottlenecks']) - 1
self.results['min performance'] = self.conv_perf(it_s)
return self.results
def analyze(self):
"""Run analysis."""
precision = 'DP' if self.kernel.datatype == 'double' else 'SP'
self.calculate_cache_access()
self.results['max_perf'] = self.conv_perf(self.machine['clock'] * self.cores * \
self.machine['FLOPs per cycle'][precision]['total'])
def conv_perf(self, it_s):
"""Convert performance (It/s) to other units, such as FLOP/s or cy/CL."""
clock = self.machine['clock']
flops_per_it = sum(self.kernel._flops.values())
performance = it_s * flops_per_it
performance.unit = 'FLOP/s'
element_size = self.kernel.datatypes_size[self.kernel.datatype]
elements_per_cacheline = int(float(
self.machine['cacheline size'])) / element_size
cy_cl = clock / it_s * elements_per_cacheline
cy_cl.unit = 'cy/CL'
cy_it = clock / it_s
cy_it.unit = 'cy/It'
return {
'It/s': it_s,
'cy/CL': cy_cl,
'cy/It': cy_it,
'FLOP/s': performance
}
def report(self, output_file=sys.stdout):
"""Report analysis outcome in human readable form."""
max_perf = self.results['max_perf']
if self._args and self._args.verbose >= 3:
print('{}'.format(pformat(self.results)), file=output_file)
if self._args and self._args.verbose >= 1:
print('{}'.format(pformat(self.results['verbose infos'])),
file=output_file)
print('Bottlenecks:', file=output_file)
print(
' level | a. intensity | performance | peak bandwidth | peak bandwidth kernel',
file=output_file)
print(
'--------+--------------+-----------------+-------------------+----------------------',
file=output_file)
print(' CPU | | {!s:>15} | |'.
format(max_perf[self._args.unit]),
file=output_file)
for b in self.results['mem bottlenecks']:
print(
'{level:>7} | {arithmetic intensity:>7.2} It/B | {0!s:>15} |'
' {bandwidth!s:>17} | {bw kernel:<8}'.format(
b['performance'][self._args.unit], **b),
file=output_file)
print('', file=output_file)
if self.results['min performance']['FLOP/s'] > max_perf['FLOP/s']:
# CPU bound
print('CPU bound. {!s} due to CPU max. FLOP/s'.format(max_perf),
file=output_file)
else:
# Cache or mem bound
print('Cache or mem bound.', file=output_file)
bottleneck = self.results['mem bottlenecks'][
self.results['bottleneck level']]
print(
'{!s} due to {} transfer bottleneck (with bw from {} benchmark)'
.format(bottleneck['performance'][self._args.unit],
bottleneck['level'], bottleneck['bw kernel']),
file=output_file)
print('Arithmetic Intensity: {:.2f} It/B'.format(
bottleneck['arithmetic intensity']),
file=output_file)
if any([
'_Complex' in var_info[0]
for var_info in self.kernel.variables.values()
]):
print(
"WARNING: FLOP counts are probably wrong, because complex flops are counted\n"
" as single flops. All other units should not be affected.\n",
file=sys.stderr)
