def callback(self, cgroups, prefix):
# Toposort to maximize fusion
if self.toposort:
clusters = self._toposort(cgroups, prefix)
else:
clusters = ClusterGroup(cgroups)
# Fusion
processed = []
for k, g in groupby(clusters, key=self._key):
maybe_fusible = list(g)
if len(maybe_fusible) == 1:
processed.extend(maybe_fusible)
else:
try:
# Perform fusion
fused = Cluster.from_clusters(*maybe_fusible)
processed.append(fused)
except ValueError:
# We end up here if, for example, some Clusters have same
# iteration Dimensions but different (partial) orderings
processed.extend(maybe_fusible)
return [ClusterGroup(processed, prefix)]
def _toposort(self, cgroups, prefix):
# Are there any ClusterGroups that could potentially be fused? If
# not, do not waste time computing a new topological ordering
counter = Counter(self._key(cg) for cg in cgroups)
if not any(v > 1 for it, v in counter.most_common()):
return ClusterGroup(cgroups)
# Similarly, if all ClusterGroups have the same exact prefix and
# use the same form of synchronization (if any at all), no need to
# attempt a topological sorting
if len(counter.most_common()) == 1:
return ClusterGroup(cgroups)
dag = self._build_dag(cgroups, prefix)
def choose_element(queue, scheduled):
# Heuristic: let `k0` be the key of the last scheduled node; then out of
# the possible schedulable nodes we pick the one with key `k1` such that
# `max_i : k0[:i] == k1[:i]` (i.e., the one with "the most similar key")
if not scheduled:
return queue.pop()
key = self._key(scheduled[-1])
for i in reversed(range(len(key) + 1)):
candidates = [e for e in queue if self._key(e)[:i] == key[:i]]
try:
# Ensure stability
e = min(candidates, key=lambda i: cgroups.index(i))
except ValueError:
continue
queue.remove(e)
return e
assert False
return ClusterGroup(dag.topological_sort(choose_element))
def _toposort(self, cgroups, prefix):
# Are there any ClusterGroups that could potentially be fused? If
# not, do not waste time computing a new topological ordering
counter = Counter(cg.itintervals for cg in cgroups)
if not any(v > 1 for it, v in counter.most_common()):
return ClusterGroup(cgroups)
# Similarly, if all ClusterGroups have the same exact prefix, no
# need to attempt a topological sorting
if len(counter.most_common()) == 1:
return ClusterGroup(cgroups)
dag = self._build_dag(cgroups, prefix)
def choose_element(queue, scheduled):
# Heuristic: prefer a node having same IterationSpace as that
# of the last scheduled node to maximize Cluster fusion
if not scheduled:
return queue.pop()
last = scheduled[-1]
for i in list(queue):
if i.itintervals == last.itintervals:
queue.remove(i)
return i
return queue.popleft()
return ClusterGroup(dag.topological_sort(choose_element))
def rewrite(clusters, mode='advanced'):
"""
Given a sequence of N Clusters, produce a sequence of M Clusters with reduced
operation count, with M >= N.
Parameters
----------
clusters : list of Cluster
The Clusters to be transformed.
mode : str, optional
The aggressiveness of the rewrite. Accepted:
- ``noop``: Do nothing.
- ``basic``: Apply common sub-expressions elimination.
- ``advanced``: Apply all transformations that will reduce the
operation count w/ minimum increase to the memory pressure,
namely 'basic', factorization, and cross-iteration redundancy
elimination ("CIRE") for time-invariants only.
- ``aggressive``: Like 'advanced', but apply CIRE to time-varying
sub-expressions too.
Further, seek and drop cross-cluster redundancies (this
is the only pass that attempts to optimize *across*
Clusters, rather than within a Cluster).
The 'aggressive' mode may substantially increase the
symbolic processing time; it may or may not reduce the
JIT-compilation time; it may or may not improve the
overall runtime performance.
"""
if not (mode is None or isinstance(mode, str)):
raise ValueError("Parameter 'mode' should be a string, not %s." %
type(mode))
if mode is None or mode == 'noop':
return clusters
# We use separate rewriters for dense and sparse clusters; sparse clusters have
# non-affine index functions, thus making it basically impossible, in general,
# to apply the more advanced DSE passes.
# Note: the sparse rewriter uses the same template for temporaries as
# the dense rewriter, thus temporaries are globally unique
try:
rewriter = modes[mode]()
except KeyError:
rewriter = CustomRewriter(mode)
fallback = BasicRewriter(False, rewriter.template)
states = [
rewriter.run(c) if c.is_dense else fallback.run(c) for c in clusters
]
# Print out profiling information
print_profiling(states)
# Schedule and optimize the Rewriters-produced clusters
clusters = ClusterGroup(optimize(flatten(i.clusters for i in states)))
# Turn unnecessary temporary Arrays into scalars
clusters = scalarize(clusters, rewriter.template)
return ClusterGroup(clusters)
def rewrite(clusters, mode='advanced'):
"""
Transform N :class:`Cluster` objects of SymPy expressions into M
:class:`Cluster` objects of SymPy expressions with reduced
operation count, with M >= N.
:param clusters: The clusters to be transformed.
:param mode: drive the expression transformation
The ``mode`` parameter recognises the following values: ::
* 'noop': Do nothing.
* 'basic': Apply common sub-expressions elimination.
* 'advanced': Apply all transformations that will reduce the
operation count w/ minimum increase to the memory pressure,
namely 'basic', factorization, CSRE for time-invariants only.
* 'speculative': Like 'advanced', but apply CSRE also to time-varying
sub-expressions, which might further increase the memory
pressure.
* 'aggressive': Like 'speculative', but apply CSRE to any non-trivial
sub-expression (i.e., anything that is at least in a
sum-of-products form). This may substantially increase
the memory pressure.
"""
if not (mode is None or isinstance(mode, str)):
raise ValueError("Parameter 'mode' should be a string, not %s." %
type(mode))
if mode is None or mode == 'noop':
return clusters
processed = ClusterGroup()
for cluster in clusters:
if cluster.is_dense:
if mode in modes:
processed.extend(modes[mode]().run(cluster))
else:
try:
processed.extend(CustomRewriter().run(cluster))
except DSEException:
dse_warning("Unknown rewrite mode(s) %s" % mode)
processed.append(cluster)
else:
# Downgrade sparse clusters to basic rewrite mode since it's
# pointless to expose loop-redundancies when the iteration space
# only consists of a few points
processed.extend(BasicRewriter(False).run(cluster))
return groupby(processed)
def _lower_clusters(cls, expressions, profiler, **kwargs):
"""
Clusters lowering:
* Group expressions into Clusters;
* Introduce guards for conditional Clusters.
"""
# Build a sequence of Clusters from a sequence of Eqs
clusters = clusterize(expressions)
clusters = cls._specialize_clusters(clusters, profiler=profiler, **kwargs)
return ClusterGroup(clusters)
def rewrite(clusters, mode='advanced'):
"""
Transform N :class:`Cluster` objects of SymPy expressions into M
:class:`Cluster` objects of SymPy expressions with reduced
operation count, with M >= N.
:param clusters: The clusters to be transformed.
:param mode: drive the expression transformation
The ``mode`` parameter recognises the following values: ::
* 'noop': Do nothing.
* 'basic': Apply common sub-expressions elimination.
* 'advanced': Apply all transformations that will reduce the
operation count w/ minimum increase to the memory pressure,
namely 'basic', factorization, CIRE for time-invariants only.
* 'speculative': Like 'advanced', but apply CIRE also to time-varying
sub-expressions, which might further increase the memory
pressure.
* 'aggressive': Like 'speculative', but apply CIRE to any non-trivial
sub-expression (i.e., anything that is at least in a
sum-of-products form). This may substantially increase
the memory pressure.
"""
if not (mode is None or isinstance(mode, str)):
raise ValueError("Parameter 'mode' should be a string, not %s." %
type(mode))
if mode is None or mode == 'noop':
return clusters
elif mode not in modes:
dse_warning("Unknown rewrite mode(s) %s" % mode)
return clusters
# Separate rewriters for dense and sparse clusters; sparse clusters have
# non-affine index functions, thus making it basically impossible, in general,
# to apply the more advanced DSE passes.
# Note: the sparse rewriter uses the same template for temporaries as
# the dense rewriter, thus temporaries are globally unique
rewriter = modes[mode]()
fallback = BasicRewriter(False, rewriter.template)
processed = ClusterGroup(
flatten(
rewriter.run(c) if c.is_dense else fallback.run(c)
for c in clusters))
return groupby(processed).finalize()
def _lower_clusters(cls, expressions, profiler, **kwargs):
"""
Clusters lowering:
* Group expressions into Clusters;
* Introduce guards for conditional Clusters;
* Analyze Clusters to detect computational properties such
as parallelism.
"""
# Build a sequence of Clusters from a sequence of Eqs
clusters = clusterize(expressions)
# Operation count before specialization
init_ops = sum(estimate_cost(c.exprs) for c in clusters if c.is_dense)
clusters = cls._specialize_clusters(clusters, **kwargs)
# Operation count after specialization
final_ops = sum(estimate_cost(c.exprs) for c in clusters if c.is_dense)
profiler.record_ops_variation(init_ops, final_ops)
return ClusterGroup(clusters)
def rewrite(clusters, mode='advanced'):
"""
Given a sequence of N Clusters, produce a sequence of M Clusters with reduced
operation count, with M >= N.
Parameters
----------
clusters : list of Cluster
The Clusters to be transformed.
mode : str, optional
The aggressiveness of the rewrite. Accepted:
- ``noop``: Do nothing.
- ``basic``: Apply common sub-expressions elimination.
- ``advanced``: Apply all transformations that will reduce the
operation count w/ minimum increase to the memory pressure,
namely 'basic', factorization, CIRE for time-invariants only.
- ``speculative``: Like 'advanced', but apply CIRE also to time-varying
sub-expressions, which might further increase the memory
pressure.
* ``aggressive``: Like 'speculative', but apply CIRE to any non-trivial
sub-expression (i.e., anything that is at least in a
sum-of-product form).
Further, seek and drop cross-cluster redundancies (this
is the only pass that attempts to optimize *across*
clusters, rather than within a cluster).
The 'aggressive' mode may substantially increase the
symbolic processing time; it may or may not reduce the
JIT-compilation time; it may or may not improve the
overall runtime performance.
"""
if not (mode is None or isinstance(mode, str)):
raise ValueError("Parameter 'mode' should be a string, not %s." % type(mode))
if mode is None or mode == 'noop':
return clusters
elif mode not in dse_registry:
dse_warning("Unknown rewrite mode(s) %s" % mode)
return clusters
# 1) Local optimization
# ---------------------
# We use separate rewriters for dense and sparse clusters; sparse clusters have
# non-affine index functions, thus making it basically impossible, in general,
# to apply the more advanced DSE passes.
# Note: the sparse rewriter uses the same template for temporaries as
# the dense rewriter, thus temporaries are globally unique
rewriter = modes[mode]()
fallback = BasicRewriter(False, rewriter.template)
processed = ClusterGroup(flatten(rewriter.run(c) if c.is_dense else fallback.run(c)
for c in clusters))
# 2) Cluster grouping
# -------------------
# Different clusters may have created new (smaller) clusters which are
# potentially groupable within a single cluster
processed = groupby(processed)
# 3)Global optimization
# ---------------------
# After grouping, there may be redundancies in one or more clusters. This final
# pass searches and drops such redundancies
if mode == 'aggressive':
processed = cross_cluster_cse(processed)
return processed.finalize()
def rewrite(clusters, mode='advanced'):
"""
Given a sequence of N Clusters, produce a sequence of M Clusters with reduced
operation count, with M >= N.
Parameters
----------
clusters : list of Cluster
The Clusters to be transformed.
mode : str, optional
The aggressiveness of the rewrite. Accepted:
- ``noop``: Do nothing.
- ``basic``: Apply common sub-expressions elimination.
- ``advanced``: Apply all transformations that will reduce the
operation count w/ minimum increase to the memory pressure,
namely 'basic', factorization, CIRE for time-invariants only.
- ``speculative``: Like 'advanced', but apply CIRE also to time-varying
sub-expressions, which might further increase the memory
pressure.
* ``aggressive``: Like 'speculative', but apply CIRE to any non-trivial
sub-expression (i.e., anything that is at least in a
sum-of-product form).
Further, seek and drop cross-cluster redundancies (this
is the only pass that attempts to optimize *across*
clusters, rather than within a cluster).
The 'aggressive' mode may substantially increase the
symbolic processing time; it may or may not reduce the
JIT-compilation time; it may or may not improve the
overall runtime performance.
"""
if not (mode is None or isinstance(mode, str)):
raise ValueError("Parameter 'mode' should be a string, not %s." %
type(mode))
if mode is None or mode == 'noop':
return clusters
elif mode not in modes:
dse_warning("Unknown rewrite mode(s) %s" % mode)
return clusters
# 1) Local optimization
# ---------------------
# We use separate rewriters for dense and sparse clusters; sparse clusters have
# non-affine index functions, thus making it basically impossible, in general,
# to apply the more advanced DSE passes.
# Note: the sparse rewriter uses the same template for temporaries as
# the dense rewriter, thus temporaries are globally unique
rewriter = modes[mode]()
fallback = BasicRewriter(False, rewriter.template)
processed = ClusterGroup(
flatten(
rewriter.run(c) if c.is_dense else fallback.run(c)
for c in clusters))
# 2) Cluster grouping
# -------------------
# Different clusters may have created new (smaller) clusters which are
# potentially groupable within a single cluster
processed = groupby(processed)
# 3)Global optimization
# ---------------------
# After grouping, there may be redundancies in one or more clusters. This final
# pass searches and drops such redundancies
if mode == 'aggressive':
processed = cross_cluster_cse(processed)
return processed.finalize()
def process(self, clusters):
cgroups = [ClusterGroup(c, c.itintervals) for c in clusters]
cgroups = self._process_fdta(cgroups, 1)
clusters = ClusterGroup.concatenate(*cgroups)
return clusters