def traffic(self):
"""
The Cluster compulsary traffic (number of reads/writes), as a mapper
from Functions to IntervalGroups.
Notes
-----
If a Function is both read and written, then it is counted twice.
"""
reads, writes = detect_io(self.exprs, relax=True)
accesses = [(i, 'r') for i in reads] + [(i, 'w') for i in writes]
ret = {}
for i, mode in accesses:
if not i.is_Tensor:
continue
elif i in self.dspace.parts:
# Stencils extend the data spaces beyond the iteration spaces
intervals = self.dspace.parts[i]
# Assume that invariant dimensions always cause new loads/stores
invariants = self.ispace.intervals.drop(intervals.dimensions)
intervals = intervals.generate('union', invariants, intervals)
ret[(i, mode)] = intervals
else:
ret[(i, mode)] = self.ispace.intervals
return ret
def __expr_finalize__(self, expr):
"""Finalize the Expression initialization."""
self._expr = expr
self._reads, _ = detect_io(expr, relax=True)
self._dimensions = flatten(i.indices for i in self.functions
if i.is_Indexed)
self._dimensions = tuple(filter_ordered(self._dimensions))
def traffic(self):
"""
The Cluster compulsary traffic (number of reads/writes), as a mapper
from Functions to IntervalGroups.
Notes
-----
If a Function is both read and written, then it is counted twice.
"""
reads, writes = detect_io(self.exprs, relax=True)
accesses = [(i, 'r') for i in reads] + [(i, 'w') for i in writes]
ret = {}
for i, mode in accesses:
if not i.is_Tensor:
continue
elif i in self.dspace.parts:
# Stencils extend the data spaces beyond the iteration spaces
intervals = self.dspace.parts[i]
# Assume that invariant dimensions always cause new loads/stores
invariants = self.ispace.intervals.drop(intervals.dimensions)
intervals = intervals.generate('union', invariants, intervals)
ret[(i, mode)] = intervals
else:
ret[(i, mode)] = self.ispace.intervals
return ret
def __new__(cls, *args, **kwargs):
# Parse input
if len(args) == 1:
input_expr = args[0]
assert type(input_expr) != LoweredEq
assert isinstance(input_expr, Eq)
elif len(args) == 2:
# Reconstructing from existing Eq. E.g., we end up here after xreplace
stamp = kwargs.pop('stamp')
expr = Eq.__new__(cls, *args, evaluate=False)
assert isinstance(stamp, Eq)
expr.is_Increment = stamp.is_Increment
expr.ispace = stamp.ispace
return expr
else:
raise ValueError("Cannot construct LoweredEq from args=%s "
"and kwargs=%s" % (str(args), str(kwargs)))
# Indexification
expr = indexify(input_expr)
# Apply caller-provided substitution
subs = kwargs.get('subs')
if subs is not None:
expr = expr.xreplace(subs)
# Well-defined dimension ordering
ordering = dimension_sort(expr, key=lambda i: not i.is_Time)
# Introduce space sub-dimensions if need to
region = getattr(input_expr, '_region', DOMAIN)
if region == INTERIOR:
mapper = {
i: SubDimension("%si" % i, i, 1, -1)
for i in ordering if i.is_Space
}
expr = expr.xreplace(mapper)
ordering = [mapper.get(i, i) for i in ordering]
# Compute iteration space
intervals, iterators = compute_intervals(expr)
intervals = sorted(intervals, key=lambda i: ordering.index(i.dim))
directions, _ = compute_directions(expr, lambda i: Any)
ispace = IterationSpace([i.negate() for i in intervals], iterators,
directions)
# Finally create the LoweredEq with all metadata attached
expr = super(LoweredEq, cls).__new__(cls,
expr.lhs,
expr.rhs,
evaluate=False)
expr.is_Increment = getattr(input_expr, 'is_Increment', False)
expr.ispace = ispace
expr.dimensions = ordering
expr.reads, expr.writes = detect_io(expr)
return expr
def __new__(cls, *args, **kwargs):
if len(args) == 1 and isinstance(args[0], LoweredEq):
# origin: LoweredEq(devito.LoweredEq, **kwargs)
input_expr = args[0]
expr = sympy.Eq.__new__(cls, *input_expr.args, evaluate=False)
for i in cls._state:
setattr(expr, '_%s' % i, kwargs.get(i) or getattr(input_expr, i))
return expr
elif len(args) == 1 and isinstance(args[0], Eq):
# origin: LoweredEq(devito.Eq)
input_expr = expr = args[0]
elif len(args) == 2:
expr = sympy.Eq.__new__(cls, *args, evaluate=False)
for i in cls._state:
setattr(expr, '_%s' % i, kwargs.pop(i))
return expr
else:
raise ValueError("Cannot construct LoweredEq from args=%s "
"and kwargs=%s" % (str(args), str(kwargs)))
# Well-defined dimension ordering
ordering = dimension_sort(expr)
# Analyze the expression
mapper = detect_accesses(expr)
oobs = detect_oobs(mapper)
conditionals = [i for i in ordering if i.is_Conditional]
# The iteration space is constructed so that information always flows
# from an iteration to another (i.e., no anti-dependences are created)
directions, _ = force_directions(detect_flow_directions(expr), lambda i: Any)
iterators = build_iterators(mapper)
intervals = build_intervals(Stencil.union(*mapper.values()))
intervals = IntervalGroup(intervals, relations=ordering.relations)
ispace = IterationSpace(intervals.zero(), iterators, directions)
# The data space is relative to the computational domain. Note that we
# are deliberately dropping the intervals ordering (by turning `intervals`
# into a list), as this is irrelevant (even more: dangerous) for data spaces
intervals = [i if i.dim in oobs else i.zero() for i in intervals]
intervals += [Interval(i, 0, 0) for i in ordering
if i not in ispace.dimensions + conditionals]
parts = {k: IntervalGroup(build_intervals(v)) for k, v in mapper.items() if k}
dspace = DataSpace(intervals, parts)
# Finally create the LoweredEq with all metadata attached
expr = super(LoweredEq, cls).__new__(cls, expr.lhs, expr.rhs, evaluate=False)
expr._dspace = dspace
expr._ispace = ispace
expr._conditionals = tuple(conditionals)
expr._reads, expr._writes = detect_io(expr)
expr._is_Increment = input_expr.is_Increment
expr._implicit_dims = input_expr.implicit_dims
return expr
def __init__(self, expr):
assert isinstance(expr, ClusterizedEq)
assert isinstance(expr.lhs, (Symbol, Indexed))
self.expr = expr
self._functions = tuple(
filter_ordered(flatten(detect_io(expr, relax=True))))
self.dimensions = flatten(i.indices for i in self.functions
if i.is_Indexed)
self.dimensions = filter_ordered(self.dimensions)
def __new__(cls, *args, **kwargs):
if len(args) == 1 and isinstance(args[0], LoweredEq):
# origin: LoweredEq(devito.LoweredEq, **kwargs)
input_expr = args[0]
expr = Eq.__new__(cls, *input_expr.args, evaluate=False)
for i in cls._state:
setattr(expr, '_%s' % i, kwargs.get(i) or getattr(input_expr, i))
return expr
elif len(args) == 1 and isinstance(args[0], Eq):
# origin: LoweredEq(sympy.Eq)
input_expr = expr = args[0]
elif len(args) == 2:
expr = Eq.__new__(cls, *args, evaluate=False)
for i in cls._state:
setattr(expr, '_%s' % i, kwargs.pop(i))
return expr
else:
raise ValueError("Cannot construct LoweredEq from args=%s "
"and kwargs=%s" % (str(args), str(kwargs)))
# Well-defined dimension ordering
ordering = dimension_sort(expr)
# Analyze the expression
mapper = detect_accesses(expr)
oobs = detect_oobs(mapper)
conditionals = [i for i in ordering if i.is_Conditional]
# The iteration space is constructed so that information always flows
# from an iteration to another (i.e., no anti-dependences are created)
directions, _ = force_directions(detect_flow_directions(expr), lambda i: Any)
iterators = build_iterators(mapper)
intervals = build_intervals(Stencil.union(*mapper.values()))
intervals = IntervalGroup(intervals, relations=ordering.relations)
ispace = IterationSpace(intervals.zero(), iterators, directions)
# The data space is relative to the computational domain. Note that we
# are deliberately dropping the intervals ordering (by turning `intervals`
# into a list), as this is irrelevant (even more: dangerous) for data spaces
intervals = [i if i.dim in oobs else i.zero() for i in intervals]
intervals += [Interval(i, 0, 0) for i in ordering
if i not in ispace.dimensions + conditionals]
parts = {k: IntervalGroup(build_intervals(v)) for k, v in mapper.items() if k}
dspace = DataSpace(intervals, parts)
# Finally create the LoweredEq with all metadata attached
expr = super(LoweredEq, cls).__new__(cls, expr.lhs, expr.rhs, evaluate=False)
expr._is_Increment = getattr(input_expr, 'is_Increment', False)
expr._dspace = dspace
expr._ispace = ispace
expr._conditionals = tuple(conditionals)
expr._reads, expr._writes = detect_io(expr)
return expr
def reads(self):
"""The Functions read by the Expression."""
return detect_io(self.expr, relax=True)[0]
def __new__(cls, *args, **kwargs):
if len(args) == 1 and isinstance(args[0], LoweredEq):
# origin: LoweredEq(devito.LoweredEq, **kwargs)
input_expr = args[0]
expr = sympy.Eq.__new__(cls, *input_expr.args, evaluate=False)
for i in cls._state:
setattr(expr, '_%s' % i,
kwargs.get(i) or getattr(input_expr, i))
return expr
elif len(args) == 1 and isinstance(args[0], Eq):
# origin: LoweredEq(devito.Eq)
input_expr = expr = args[0]
elif len(args) == 2:
expr = sympy.Eq.__new__(cls, *args, evaluate=False)
for i in cls._state:
setattr(expr, '_%s' % i, kwargs.pop(i))
return expr
else:
raise ValueError("Cannot construct LoweredEq from args=%s "
"and kwargs=%s" % (str(args), str(kwargs)))
# Well-defined dimension ordering
ordering = dimension_sort(expr)
# Analyze the expression
mapper = detect_accesses(expr)
oobs = detect_oobs(mapper)
conditionals = [i for i in ordering if i.is_Conditional]
# Construct Intervals for IterationSpace and DataSpace
intervals = build_intervals(Stencil.union(*mapper.values()))
iintervals = [] # iteration Intervals
dintervals = [] # data Intervals
for i in intervals:
d = i.dim
if d in oobs:
iintervals.append(i.zero())
dintervals.append(i)
else:
iintervals.append(i.zero())
dintervals.append(i.zero())
# Construct the IterationSpace
iintervals = IntervalGroup(iintervals, relations=ordering.relations)
iterators = build_iterators(mapper)
ispace = IterationSpace(iintervals, iterators)
# Construct the DataSpace
dintervals.extend([
Interval(i, 0, 0) for i in ordering
if i not in ispace.dimensions + conditionals
])
parts = {
k: IntervalGroup(build_intervals(v)).add(iintervals)
for k, v in mapper.items() if k
}
dspace = DataSpace(dintervals, parts)
# Lower all Differentiable operations into SymPy operations
rhs = diff2sympy(expr.rhs)
# Finally create the LoweredEq with all metadata attached
expr = super(LoweredEq, cls).__new__(cls,
expr.lhs,
rhs,
evaluate=False)
expr._dspace = dspace
expr._ispace = ispace
expr._conditionals = tuple(conditionals)
expr._reads, expr._writes = detect_io(expr)
expr._is_Increment = input_expr.is_Increment
expr._implicit_dims = input_expr.implicit_dims
return expr
def __new__(cls, *args, **kwargs):
if len(args) == 1:
# origin: LoweredEq(expr)
expr = input_expr = args[0]
assert not isinstance(expr, LoweredEq) and isinstance(expr, Eq)
elif len(args) == 2:
# origin: LoweredEq(lhs, rhs, stamp=...)
stamp = kwargs.pop('stamp')
expr = Eq.__new__(cls, *args, evaluate=False)
assert isinstance(stamp, Eq)
expr.is_Increment = stamp.is_Increment
expr._ispace, expr._dspace = stamp.ispace, stamp.dspace
expr.reads, expr.writes = stamp.reads, stamp.writes
return expr
elif len(args) == 5:
# origin: LoweredEq(expr, ispace, space)
input_expr, ispace, dspace, reads, writes = args
assert isinstance(ispace, IterationSpace) and isinstance(
dspace, DataSpace)
expr = Eq.__new__(cls, *input_expr.args, evaluate=False)
expr.is_Increment = input_expr.is_Increment
expr._ispace, expr._dspace = ispace, dspace
expr.reads, expr.writes = reads, writes
return expr
else:
raise ValueError("Cannot construct LoweredEq from args=%s "
"and kwargs=%s" % (str(args), str(kwargs)))
# Well-defined dimension ordering
ordering = dimension_sort(expr, key=lambda i: not i.is_Time)
# Introduce space sub-dimensions if need to
region = getattr(input_expr, '_region', DOMAIN)
if region == INTERIOR:
mapper = {
i: SubDimension("%si" % i, i, 1, -1)
for i in ordering if i.is_Space
}
expr = expr.xreplace(mapper)
ordering = [mapper.get(i, i) for i in ordering]
# Analyze data accesses
mapper = detect_accesses(expr)
oobs = detect_oobs(mapper)
# The iteration space is constructed so that information always flows
# from an iteration to another (i.e., no anti-dependences are created)
directions, _ = force_directions(detect_flow_directions(expr),
lambda i: Any)
intervals, iterators = build_intervals(mapper)
intervals = sorted(intervals, key=lambda i: ordering.index(i.dim))
ispace = IterationSpace([i.zero() for i in intervals], iterators,
directions)
# The data space is relative to the computational domain
intervals = [i if i.dim in oobs else i.zero() for i in intervals]
intervals += [
Interval(i, 0, 0) for i in ordering if i not in ispace.dimensions
]
parts = {
k:
IntervalGroup(Interval(i, min(j), max(j)) for i, j in v.items())
for k, v in mapper.items()
}
dspace = DataSpace(intervals, parts)
# Finally create the LoweredEq with all metadata attached
expr = super(LoweredEq, cls).__new__(cls,
expr.lhs,
expr.rhs,
evaluate=False)
expr.is_Increment = getattr(input_expr, 'is_Increment', False)
expr._dspace = dspace
expr._ispace = ispace
expr.reads, expr.writes = detect_io(expr)
return expr
def __new__(cls, *args, **kwargs):
if len(args) == 1 and isinstance(args[0], LoweredEq):
# origin: LoweredEq(devito.LoweredEq, **kwargs)
input_expr = args[0]
expr = sympy.Eq.__new__(cls, *input_expr.args, evaluate=False)
for i in cls._state:
setattr(expr, '_%s' % i,
kwargs.get(i) or getattr(input_expr, i))
return expr
elif len(args) == 1 and isinstance(args[0], Eq):
# origin: LoweredEq(devito.Eq)
input_expr = expr = args[0]
elif len(args) == 2:
expr = sympy.Eq.__new__(cls, *args, evaluate=False)
for i in cls._state:
setattr(expr, '_%s' % i, kwargs.pop(i))
return expr
else:
raise ValueError("Cannot construct LoweredEq from args=%s "
"and kwargs=%s" % (str(args), str(kwargs)))
# Well-defined dimension ordering
ordering = dimension_sort(expr)
# Analyze the expression
accesses = detect_accesses(expr)
dimensions = Stencil.union(*accesses.values())
# Separate out the SubIterators from the main iteration Dimensions, that
# is those which define an actual iteration space
iterators = {}
for d in dimensions:
if d.is_SubIterator:
iterators.setdefault(d.root, set()).add(d)
elif d.is_Conditional:
# Use `parent`, and `root`, because a ConditionalDimension may
# have a SubDimension as parent
iterators.setdefault(d.parent, set())
else:
iterators.setdefault(d, set())
# Construct the IterationSpace
intervals = IntervalGroup([Interval(d, 0, 0) for d in iterators],
relations=ordering.relations)
ispace = IterationSpace(intervals, iterators)
# Construct the conditionals and replace the ConditionalDimensions in `expr`
conditionals = {}
for d in ordering:
if not d.is_Conditional:
continue
if d.condition is None:
conditionals[d] = GuardFactor(d)
else:
conditionals[d] = diff2sympy(lower_exprs(d.condition))
if d.factor is not None:
expr = uxreplace(expr, {d: IntDiv(d.index, d.factor)})
conditionals = frozendict(conditionals)
# Lower all Differentiable operations into SymPy operations
rhs = diff2sympy(expr.rhs)
# Finally create the LoweredEq with all metadata attached
expr = super(LoweredEq, cls).__new__(cls,
expr.lhs,
rhs,
evaluate=False)
expr._ispace = ispace
expr._conditionals = conditionals
expr._reads, expr._writes = detect_io(expr)
expr._is_Increment = input_expr.is_Increment
expr._implicit_dims = input_expr.implicit_dims
return expr
def __new__(cls, *args, **kwargs):
if len(args) == 1 and isinstance(args[0], LoweredEq):
# origin: LoweredEq(devito.LoweredEq, **kwargs)
input_expr = args[0]
expr = Eq.__new__(cls, *input_expr.args, evaluate=False)
for i in cls._state:
setattr(expr, '_%s' % i,
kwargs.get(i) or getattr(input_expr, i))
return expr
elif len(args) == 1 and isinstance(args[0], Eq):
# origin: LoweredEq(sympy.Eq)
input_expr = expr = args[0]
elif len(args) == 2:
expr = Eq.__new__(cls, *args, evaluate=False)
for i in cls._state:
setattr(expr, '_%s' % i, kwargs.pop(i))
return expr
else:
raise ValueError("Cannot construct LoweredEq from args=%s "
"and kwargs=%s" % (str(args), str(kwargs)))
# Well-defined dimension ordering
ordering = dimension_sort(expr, key=lambda i: not i.is_Time)
# Introduce space sub-dimensions if need to
region = getattr(input_expr, '_region', DOMAIN)
if region == INTERIOR:
mapper = {
i: SubDimension.middle("%si" % i, i, 1, 1)
for i in ordering if i.is_Space
}
expr = expr.xreplace(mapper)
for k, v in mapper.items():
ordering.insert(ordering.index(k) + 1, v)
# Analyze the expression
mapper = detect_accesses(expr)
oobs = detect_oobs(mapper)
# The iteration space is constructed so that information always flows
# from an iteration to another (i.e., no anti-dependences are created)
directions, _ = force_directions(detect_flow_directions(expr),
lambda i: Any)
iterators = build_iterators(mapper)
intervals = build_intervals(Stencil.union(*mapper.values()))
intervals = sorted(intervals, key=lambda i: ordering.index(i.dim))
ispace = IterationSpace([i.zero() for i in intervals], iterators,
directions)
# The data space is relative to the computational domain
intervals = [i if i.dim in oobs else i.zero() for i in intervals]
intervals += [
Interval(i, 0, 0) for i in ordering if i not in ispace.dimensions
]
parts = {
k: IntervalGroup(build_intervals(v))
for k, v in mapper.items() if k
}
dspace = DataSpace(intervals, parts)
# Finally create the LoweredEq with all metadata attached
expr = super(LoweredEq, cls).__new__(cls,
expr.lhs,
expr.rhs,
evaluate=False)
expr._is_Increment = getattr(input_expr, 'is_Increment', False)
expr._dspace = dspace
expr._ispace = ispace
expr._reads, expr._writes = detect_io(expr)
return expr
