def common_subexprs_elimination(exprs, make, mode='default'):
"""
Perform common sub-expressions elimination, or CSE.
Note: the output is guaranteed to be topologically sorted.
Parameters
----------
exprs : expr-like or list of expr-like
One or more expressions to which CSE is applied.
make : callable
Build symbols to store temporary, redundant values.
mode : str, optional
The CSE algorithm applied. Accepted: ['default'].
"""
# Note: not defaulting to SymPy's CSE() function for three reasons:
# - it also captures array index access functions (eg, i+1 in A[i+1] and B[i+1]);
# - it sometimes "captures too much", losing factorization opportunities;
# - very slow
# TODO: a second "sympy" mode will be provided, relying on SymPy's CSE() but
# also ensuring some sort of post-processing
assert mode == 'default' # Only supported mode ATM
processed = list(exprs)
mapped = []
while True:
# Detect redundancies
counted = count(mapped + processed, q_xop).items()
targets = OrderedDict([(k, estimate_cost(k, True)) for k, v in counted if v > 1])
if not targets:
break
# Create temporaries
hit = max(targets.values())
picked = [k for k, v in targets.items() if v == hit]
mapper = OrderedDict([(e, make()) for i, e in enumerate(picked)])
# Apply replacements
processed = [e.xreplace(mapper) for e in processed]
mapped = [e.xreplace(mapper) for e in mapped]
mapped = [DummyEq(v, k) for k, v in reversed(list(mapper.items()))] + mapped
# Prepare for the next round
for k in picked:
targets.pop(k)
processed = mapped + processed
# At this point we may have useless temporaries (e.g., r0=r1). Let's drop them
processed = _compact_temporaries(processed)
# Perform topological sorting so that reads-after-writes are honored
processed = _topological_sort(processed)
return processed
def common_subexprs_elimination(exprs, make, mode='default'):
"""
Perform common sub-expressions elimination, or CSE.
Note: the output is not guranteed to be topologically sorted.
Parameters
----------
exprs : expr-like or list of expr-like
One or more expressions to which CSE is applied.
make : callable
Build symbols to store temporary, redundant values.
mode : str, optional
The CSE algorithm applied. Accepted: ['default'].
"""
# Note: not defaulting to SymPy's CSE() function for three reasons:
# - it also captures array index access functions (eg, i+1 in A[i+1] and B[i+1]);
# - it sometimes "captures too much", losing factorization opportunities;
# - very slow
# TODO: a second "sympy" mode will be provided, relying on SymPy's CSE() but
# also ensuring some sort of post-processing
assert mode == 'default' # Only supported mode ATM
processed = list(exprs)
mapped = []
while True:
# Detect redundancies
counted = count(mapped + processed, q_op).items()
targets = OrderedDict([(k, estimate_cost(k)) for k, v in counted if v > 1])
if not targets:
break
# Create temporaries
hit = max(targets.values())
picked = [k for k, v in targets.items() if v == hit]
mapper = OrderedDict([(e, make()) for i, e in enumerate(picked)])
# Apply replacements
processed = [e.xreplace(mapper) for e in processed]
mapped = [e.xreplace(mapper) for e in mapped]
mapped = [Eq(v, k) for k, v in reversed(list(mapper.items()))] + mapped
# Prepare for the next round
for k in picked:
targets.pop(k)
processed = mapped + processed
# Simply renumber the temporaries in ascending order
mapper = {i.lhs: j.lhs for i, j in zip(mapped, reversed(mapped))}
processed = [e.xreplace(mapper) for e in processed]
return processed
def common_subexprs_elimination(exprs, make, mode='default'):
"""
Perform common subexpressions elimination.
Note: the output is not guranteed to be topologically sorted.
:param exprs: The target SymPy expression, or a collection of SymPy expressions.
:param make: A function to construct symbols used for replacement.
The function takes as input an integer ID; ID is computed internally
and used as a unique identifier for the constructed symbols.
"""
# Note: not defaulting to SymPy's CSE() function for three reasons:
# - it also captures array index access functions (eg, i+1 in A[i+1] and B[i+1]);
# - it sometimes "captures too much", losing factorization opportunities;
# - very slow
# TODO: a second "sympy" mode will be provided, relying on SymPy's CSE() but
# also ensuring some sort of post-processing
assert mode == 'default' # Only supported mode ATM
processed = list(exprs)
mapped = []
while True:
# Detect redundancies
counted = count(mapped + processed, q_op).items()
targets = OrderedDict([(k, estimate_cost(k)) for k, v in counted if v > 1])
if not targets:
break
# Create temporaries
hit = max(targets.values())
picked = [k for k, v in targets.items() if v == hit]
mapper = OrderedDict([(e, make(len(mapped) + i)) for i, e in enumerate(picked)])
# Apply repleacements
processed = [e.xreplace(mapper) for e in processed]
mapped = [e.xreplace(mapper) for e in mapped]
mapped = [Eq(v, k) for k, v in reversed(list(mapper.items()))] + mapped
# Prepare for the next round
for k in picked:
targets.pop(k)
processed = mapped + processed
# Simply renumber the temporaries in ascending order
mapper = {i.lhs: j.lhs for i, j in zip(mapped, reversed(mapped))}
processed = [e.xreplace(mapper) for e in processed]
return processed
def _cse(maybe_exprs, make, mode='default'):
"""
Main common sub-expressions elimination routine.
Note: the output is guaranteed to be topologically sorted.
Parameters
----------
maybe_exprs : expr-like or list of expr-like or Cluster
One or more expressions to which CSE is applied.
make : callable
Build symbols to store temporary, redundant values.
mode : str, optional
The CSE algorithm applied. Accepted: ['default'].
"""
# Note: not defaulting to SymPy's CSE() function for three reasons:
# - it also captures array index access functions (eg, i+1 in A[i+1] and B[i+1]);
# - it sometimes "captures too much", losing factorization opportunities;
# - very slow
# TODO: a second "sympy" mode will be provided, relying on SymPy's CSE() but
# also ensuring some form of post-processing
assert mode == 'default' # Only supported mode ATM
# Just for flexibility, accept either Clusters or exprs
if isinstance(maybe_exprs, Cluster):
cluster = maybe_exprs
processed = list(cluster.exprs)
scope = cluster.scope
else:
processed = list(maybe_exprs)
scope = Scope(maybe_exprs)
# Some sub-expressions aren't really "common" -- that's the case of Dimension-
# independent data dependences. For example:
#
# ... = ... a[i] + 1 ...
# a[i] = ...
# ... = ... a[i] + 1 ...
#
# `a[i] + 1` will be excluded, as there's a flow Dimension-independent data
# dependence involving `a`
exclude = {i.source.access for i in scope.d_flow.independent()}
mapped = []
while True:
# Detect redundancies
counted = count(mapped + processed, q_xop).items()
targets = OrderedDict([(k, estimate_cost(k, True)) for k, v in counted
if v > 1])
# Rule out Dimension-independent data dependencies
targets = OrderedDict([(k, v) for k, v in targets.items()
if not k.free_symbols & exclude])
if not targets:
break
# Create temporaries
hit = max(targets.values())
picked = [k for k, v in targets.items() if v == hit]
mapper = OrderedDict([(e, make()) for i, e in enumerate(picked)])
# Apply replacements
processed = [uxreplace(e, mapper) for e in processed]
mapped = [uxreplace(e, mapper) for e in mapped]
mapped = [Eq(v, k) for k, v in reversed(list(mapper.items()))] + mapped
# Update `exclude` for the same reasons as above -- to rule out CSE across
# Dimension-independent data dependences
exclude.update({i for i in mapper.values()})
# Prepare for the next round
for k in picked:
targets.pop(k)
processed = mapped + processed
# At this point we may have useless temporaries (e.g., r0=r1). Let's drop them
processed = _compact_temporaries(processed)
return processed
