def __init__(self, exprs, **kwargs):
# Check input legality
mapper = OrderedDict([(i.lhs, i) for i in exprs])
if len(set(mapper)) != len(mapper):
raise DSEException(
"Found redundant node, cannot build TemporariesGraph.")
# Construct Temporaries, tracking reads and readby
tensor_map = DefaultOrderedDict(list)
for i in mapper:
tensor_map[as_symbol(i)].append(i)
reads = DefaultOrderedDict(set)
readby = DefaultOrderedDict(set)
for k, v in mapper.items():
handle = retrieve_terminals(v.rhs)
for i in list(handle):
if i.is_Indexed:
for idx in i.indices:
handle |= retrieve_terminals(idx)
reads[k].update(
set(flatten([tensor_map.get(as_symbol(i), [])
for i in handle])))
for i in reads[k]:
readby[i].add(k)
# Make sure read-after-writes are honored for scalar temporaries
processed = [i for i in mapper if i.is_Indexed]
queue = [i for i in mapper if i not in processed]
while queue:
k = queue.pop(0)
if not readby[k]:
processed.insert(0, k)
elif all(i in processed for i in readby[k]):
index = min(processed.index(i) for i in readby[k])
processed.insert(index, k)
else:
queue.append(k)
# Build up the TemporariesGraph
temporaries = [(i,
Temporary(*mapper[i].args,
inc=q_inc(mapper[i]),
reads=reads[i],
readby=readby[i])) for i in processed]
super(TemporariesGraph, self).__init__(temporaries, **kwargs)
# Determine indices along the space and time dimensions
terms = [
v for k, v in self.items() if v.is_tensor and not q_indirect(k)
]
indices = filter_ordered(flatten([i.function.indices for i in terms]))
self.space_indices = tuple(i for i in indices if i.is_Space)
self.time_indices = tuple(i for i in indices if i.is_Time)
def __init__(self, exprs, **kwargs):
# Always convert to SSA
exprs = convert_to_SSA(exprs)
mapper = OrderedDict([(i.lhs, i) for i in exprs])
assert len(set(mapper)) == len(exprs), "not SSA Cluster?"
# Construct the Nodes, tracking reads and readby
tensor_map = DefaultOrderedDict(list)
for i in mapper:
tensor_map[as_symbol(i)].append(i)
reads = DefaultOrderedDict(set)
readby = DefaultOrderedDict(set)
for k, v in mapper.items():
handle = retrieve_terminals(v.rhs)
for i in list(handle):
if i.is_Indexed:
for idx in i.indices:
handle |= retrieve_terminals(idx)
reads[k].update(
set(flatten([tensor_map.get(as_symbol(i), [])
for i in handle])))
for i in reads[k]:
readby[i].add(k)
# Make sure read-after-writes are honored for scalar temporaries
processed = [i for i in mapper if i.is_Indexed]
queue = [i for i in mapper if i not in processed]
while queue:
k = queue.pop(0)
if not readby[k]:
processed.insert(0, k)
elif all(i in processed for i in readby[k]):
index = min(processed.index(i) for i in readby[k])
processed.insert(index, k)
else:
queue.append(k)
# Build up the FlowGraph
temporaries = [(i,
Node(*mapper[i].args,
inc=q_inc(mapper[i]),
reads=reads[i],
readby=readby[i])) for i in processed]
super(FlowGraph, self).__init__(temporaries, **kwargs)
# Determine indices along the space and time dimensions
terms = [
v for k, v in self.items() if v.is_tensor and not q_indirect(k)
]
indices = filter_ordered(flatten([i.function.indices for i in terms]))
self.space_indices = tuple(i for i in indices if i.is_Space)
self.time_indices = tuple(i for i in indices if i.is_Time)
def __init__(self, exprs, rules=None):
"""
A Scope enables data dependence analysis on a totally ordered sequence
of expressions.
"""
exprs = as_tuple(exprs)
self.reads = {}
self.writes = {}
self.initialized = set()
for i, e in enumerate(exprs):
# Reads
for j in retrieve_terminals(e.rhs):
v = self.reads.setdefault(j.function, [])
mode = 'RI' if e.is_Increment and j.function is e.lhs.function else 'R'
v.append(TimedAccess(j, mode, i, e.ispace))
# Write
if q_terminal(e.lhs):
v = self.writes.setdefault(e.lhs.function, [])
mode = 'WI' if e.is_Increment else 'W'
v.append(TimedAccess(e.lhs, mode, i, e.ispace))
# If an increment, we got one implicit read
if e.is_Increment:
v = self.reads.setdefault(e.lhs.function, [])
v.append(TimedAccess(e.lhs, 'RI', i, e.ispace))
# If writing to a scalar, we have an initialization
if not e.is_Increment and e.is_scalar:
self.initialized.add(e.lhs.function)
# Look up ConditionalDimensions
for v in e.conditionals.values():
for j in retrieve_terminals(v):
v = self.reads.setdefault(j.function, [])
v.append(TimedAccess(j, 'R', -1, e.ispace))
# The iteration symbols too
dimensions = set().union(*[e.dimensions for e in exprs])
for d in dimensions:
for i in d._defines_symbols:
for j in i.free_symbols:
v = self.reads.setdefault(j.function, [])
v.append(TimedAccess(j, 'R', -1))
# A set of rules to drive the collection of dependencies
self.rules = as_tuple(rules)
assert all(callable(i) for i in self.rules)
def _retrieve_symbols(self, expressions):
"""
Retrieve the symbolic functions read or written by the Operator,
as well as all traversed dimensions.
"""
terms = flatten(retrieve_terminals(i) for i in expressions)
input = []
for i in terms:
try:
input.append(i.base.function)
except AttributeError:
pass
input = filter_sorted(input, key=attrgetter('name'))
output = [i.lhs.base.function for i in expressions if i.lhs.is_Indexed]
indexeds = [i for i in terms if i.is_Indexed]
dimensions = []
for indexed in indexeds:
for i in indexed.indices:
dimensions.extend(
[k for k in i.free_symbols if isinstance(k, Dimension)])
dimensions.extend(list(indexed.base.function.indices))
dimensions.extend([d.parent for d in dimensions if d.is_Stepping])
dimensions = filter_sorted(dimensions, key=attrgetter('name'))
return input, output, dimensions
def detect_free_dimensions(expr):
"""
Return a degenerate :class:`Stencil` for the :class:`Dimension`s used
as plain symbols, rather than as array indices, in ``expr``.
"""
return Stencil([(i, 0) for i in retrieve_terminals(expr)
if isinstance(i, Dimension)])
def detect_accesses(expr):
"""
Return a mapper ``M : F -> S``, where F are Functions appearing
in ``expr`` and S are Stencils. ``M[f]`` represents all data accesses
to ``f`` within ``expr``. Also map ``M[None]`` to all Dimensions used in
``expr`` as plain symbols, rather than as array indices.
"""
# Compute M : F -> S
mapper = defaultdict(Stencil)
for e in retrieve_indexed(expr, mode='all', deep=True):
f = e.function
for a in e.indices:
if isinstance(a, Dimension):
mapper[f][a].update([0])
d = None
off = []
for i in a.args:
if isinstance(i, Dimension):
d = i
elif i.is_integer:
off += [int(i)]
if d is not None:
mapper[f][d].update(off or [0])
# Compute M[None]
other_dims = [i for i in retrieve_terminals(expr) if isinstance(i, Dimension)]
other_dims.extend(list(expr.implicit_dims))
mapper[None] = Stencil([(i, 0) for i in other_dims])
return mapper
def detect_accesses(expr):
"""
Return a mapper ``M : F -> S``, where F are Functions appearing
in ``expr`` and S are Stencils. ``M[f]`` represents all data accesses
to ``f`` within ``expr``. Also map ``M[None]`` to all Dimensions used in
``expr`` as plain symbols, rather than as array indices.
"""
# Compute M : F -> S
mapper = defaultdict(Stencil)
for e in retrieve_indexed(expr, deep=True):
f = e.function
for a in e.indices:
if isinstance(a, Dimension):
mapper[f][a].update([0])
d = None
off = []
for i in a.args:
if isinstance(i, Dimension):
d = i
elif i.is_integer:
off += [int(i)]
if d is not None:
mapper[f][d].update(off or [0])
# Compute M[None]
other_dims = [i for i in retrieve_terminals(expr) if isinstance(i, Dimension)]
other_dims.extend(list(expr.implicit_dims))
mapper[None] = Stencil([(i, 0) for i in other_dims])
return mapper
def __init__(self, exprs):
"""
A Scope enables data dependence analysis on a totally ordered sequence
of expressions.
"""
exprs = as_tuple(exprs)
self.reads = {}
self.writes = {}
for i, e in enumerate(exprs):
# Reads
for j in retrieve_terminals(e.rhs):
v = self.reads.setdefault(j.function, [])
mode = 'RI' if e.is_Increment and j.function is e.lhs.function else 'R'
v.append(TimedAccess(j, mode, i, e.ispace))
# Write
v = self.writes.setdefault(e.lhs.function, [])
mode = 'WI' if e.is_Increment else 'W'
v.append(TimedAccess(e.lhs, mode, i, e.ispace))
# If an increment, we got one implicit read
if e.is_Increment:
v = self.reads.setdefault(e.lhs.function, [])
v.append(TimedAccess(e.lhs, 'RI', i, e.ispace))
# The iterators read symbols too
dimensions = set().union(*[e.dimensions for e in exprs])
for d in dimensions:
for j in d.symbolic_size.free_symbols:
v = self.reads.setdefault(j.function, [])
v.append(TimedAccess(j, 'R', -1))
def __init__(self, exprs):
"""
A Scope represents a group of TimedAcces objects extracted
from some IREq ``exprs``. The expressions must be provided
in program order.
"""
exprs = as_tuple(exprs)
self.reads = {}
self.writes = {}
for i, e in enumerate(exprs):
# Reads
for j in retrieve_terminals(e.rhs):
v = self.reads.setdefault(j.function, [])
mode = 'RI' if e.is_Increment and j.function is e.lhs.function else 'R'
v.append(TimedAccess(j, mode, i, e.ispace.directions))
# Write
v = self.writes.setdefault(e.lhs.function, [])
mode = 'WI' if e.is_Increment else 'W'
v.append(TimedAccess(e.lhs, mode, i, e.ispace.directions))
# If an increment, we got one implicit read
if e.is_Increment:
v = self.reads.setdefault(e.lhs.function, [])
v.append(TimedAccess(e.lhs, 'RI', i, e.ispace.directions))
# The iterators read symbols too
dimensions = set().union(*[e.dimensions for e in exprs])
for d in dimensions:
for j in d.symbolic_size.free_symbols:
v = self.reads.setdefault(j.function, [])
v.append(TimedAccess(j, 'R', -1, {}))
def retrieve_symbols(expressions):
"""
Return the :class:`Function` and :class:`Dimension` objects appearing
in ``expressions``.
"""
terms = flatten(retrieve_terminals(i) for i in expressions)
input = []
for i in terms:
try:
function = i.base.function
except AttributeError:
continue
if function.is_Constant or function.is_TensorFunction:
input.append(function)
input = filter_sorted(input, key=attrgetter('name'))
output = [i.lhs.base.function for i in expressions if i.lhs.is_Indexed]
output = filter_sorted(output, key=attrgetter('name'))
indexeds = [i for i in terms if i.is_Indexed]
dimensions = []
for indexed in indexeds:
for i in indexed.indices:
dimensions.extend(
[k for k in i.free_symbols if isinstance(k, Dimension)])
dimensions.extend(list(indexed.base.function.indices))
dimensions.extend([d.parent for d in dimensions if d.is_Stepping])
dimensions = filter_sorted(dimensions, key=attrgetter('name'))
return input, output, dimensions
def is_time_invariant(mapper, expr):
if any(
isinstance(i, Dimension) and i.is_Time
for i in expr.free_symbols):
return False
queue = [expr.rhs if expr.is_Equality else expr]
seen = set()
while queue:
item = queue.pop()
nodes = set()
for i in retrieve_terminals(item):
if i in seen:
# Already inspected, nothing more can be inferred
continue
elif any(
isinstance(j, Dimension) and j.is_Time
for j in i.free_symbols):
# Definitely not time-invariant
return False
elif i in mapper:
# Go on with the search
nodes.add(i)
elif isinstance(i, Dimension):
# Go on with the search, as `i` is not a time dimension
pass
elif not (i.function.is_DiscreteFunction
or i.function.is_Symbol and i.function.is_const):
# It didn't come from the outside and it's not in `mapper`, so
# cannot determine if time-invariant; assume time-varying then
return False
seen.add(i)
queue.extend([mapper[i].rhs for i in nodes])
return True
def topological_sort(exprs):
"""Topologically sort the temporaries in a list of equations."""
mapper = {e.lhs: e for e in exprs}
assert len(mapper) == len(exprs) # Expect SSA
# Build DAG and topologically-sort temporaries
temporaries, tensors = split(exprs, lambda e: not e.lhs.is_Indexed)
dag = DAG(nodes=temporaries)
for e in temporaries:
for r in retrieve_terminals(e.rhs):
if r not in mapper:
continue
elif mapper[r] is e:
# Avoid cyclic dependences, such as
# Eq(f, f + 1)
continue
elif r.is_Indexed:
# Only scalars enforce an ordering
continue
else:
dag.add_edge(mapper[r], e, force_add=True)
processed = dag.topological_sort()
# Append tensor equations at the end in user-provided order
processed.extend(tensors)
return processed
def unknown(self):
"""
Return all symbols appearing in self for which a node is not available.
"""
known = {v.function for v in self.values()}
reads = set([i.function for i in
flatten(retrieve_terminals(v.rhs) for v in self.values())])
return reads - known
def unknown(self):
"""
Return all symbols appearing in self for which a temporary is not available.
"""
known = {v.function for v in self.values()}
reads = set([i.base.function for i in
flatten(retrieve_terminals(v.rhs) for v in self.values())])
return reads - known
def __init__(self, exprs, **kwargs):
# Always convert to SSA
exprs = makeit_ssa(exprs)
mapper = OrderedDict([(i.lhs, i) for i in exprs])
assert len(set(mapper)) == len(exprs), "not SSA Cluster?"
# Construct the Nodes, tracking reads and readby
tensor_map = DefaultOrderedDict(list)
for i in mapper:
tensor_map[as_symbol(i)].append(i)
reads = DefaultOrderedDict(set)
readby = DefaultOrderedDict(set)
for k, v in mapper.items():
handle = retrieve_terminals(v.rhs)
for i in list(handle):
if i.is_Indexed:
for idx in i.indices:
handle |= retrieve_terminals(idx)
reads[k].update(set(flatten([tensor_map.get(as_symbol(i), [])
for i in handle])))
for i in reads[k]:
readby[i].add(k)
# Make sure read-after-writes are honored for scalar nodes
processed = [i for i in mapper if i.is_Indexed]
queue = [i for i in mapper if i not in processed]
while queue:
k = queue.pop(0)
if not readby[k] or k in readby[k]:
processed.insert(0, k)
elif all(i in processed for i in readby[k]):
index = min(processed.index(i) for i in readby[k])
processed.insert(index, k)
else:
queue.append(k)
# Build up the FlowGraph
nodes = [(i, Node(mapper[i], reads=reads[i], readby=readby[i]))
for i in processed]
super(FlowGraph, self).__init__(nodes, **kwargs)
# Determine indices along the space and time dimensions
terms = [v for k, v in self.items() if v.is_Tensor and not q_indirect(k)]
indices = filter_ordered(flatten([i.function.indices for i in terms]))
self.space_indices = tuple(i for i in indices if i.is_Space)
self.time_indices = tuple(i for i in indices if i.is_Time)
def detect_io(exprs, relax=False):
"""
``{exprs} -> ({reads}, {writes})``
Parameters
----------
exprs : expr-like or list of expr-like
The searched expressions.
relax : bool, optional
If False, as by default, collect only Constants and Functions.
Otherwise, collect any Basic object.
"""
exprs = as_tuple(exprs)
if relax is False:
rule = lambda i: i.is_Input
else:
rule = lambda i: i.is_Scalar or i.is_Tensor
# Don't forget the nasty case with indirections on the LHS:
# >>> u[t, a[x]] = f[x] -> (reads={a, f}, writes={u})
roots = []
for i in exprs:
try:
roots.append(i.rhs)
roots.extend(list(i.lhs.indices))
roots.extend(list(i.conditionals.values()))
except AttributeError:
# E.g., FunctionFromPointer
roots.append(i)
reads = []
terminals = flatten(retrieve_terminals(i, deep=True) for i in roots)
for i in terminals:
candidates = i.free_symbols
try:
candidates.update({i.function})
except AttributeError:
pass
for j in candidates:
try:
if rule(j):
reads.append(j)
except AttributeError:
pass
writes = []
for i in exprs:
try:
f = i.lhs.function
except AttributeError:
continue
if rule(f):
writes.append(f)
return filter_sorted(reads), filter_sorted(writes)
def detect_io(exprs, relax=False):
"""
``{exprs} -> ({reads}, {writes})``
Parameters
----------
exprs : expr-like or list of expr-like
The searched expressions.
relax : bool, optional
If False, as by default, collect only Constants and Functions.
Otherwise, collect any Basic object.
"""
exprs = as_tuple(exprs)
if relax is False:
rule = lambda i: i.is_Input
else:
rule = lambda i: i.is_Scalar or i.is_Tensor
# Don't forget this nasty case, with indirections on the LHS:
# >>> u[t, a[x]] = f[x] -> (reads={a, f}, writes={u})
roots = []
for i in exprs:
try:
roots.append(i.rhs)
roots.extend(list(i.lhs.indices))
except AttributeError:
# E.g., FunctionFromPointer
roots.append(i)
reads = []
terminals = flatten(retrieve_terminals(i, deep=True) for i in roots)
for i in terminals:
candidates = i.free_symbols
try:
candidates.update({i.function})
except AttributeError:
pass
for j in candidates:
try:
if rule(j):
reads.append(j)
except AttributeError:
pass
writes = []
for i in exprs:
try:
f = i.lhs.function
except AttributeError:
continue
if rule(f):
writes.append(f)
return filter_sorted(reads), filter_sorted(writes)
def __init__(self, expr, dtype=None):
assert isinstance(expr, Eq)
assert isinstance(expr.lhs, (Symbol, Indexed))
self.expr = expr
self.dtype = dtype
# Traverse /expression/ to determine meta information
# Note: at this point, expressions have already been indexified
self.reads = [i for i in retrieve_terminals(self.expr.rhs)
if isinstance(i, (types.Indexed, types.Symbol))]
self.reads = filter_ordered(self.reads)
# Filter collected dimensions and functions
self.dimensions = flatten(i.indices for i in self.functions)
self.dimensions = filter_ordered(self.dimensions)
def extract(cls, expr):
"""
Compute the stencil of ``expr``.
"""
assert expr.is_Equality
# Collect all indexed objects appearing in /expr/
terminals = retrieve_terminals(expr, mode='all')
indexeds = [i for i in terminals if i.is_Indexed]
indexeds += flatten([retrieve_indexed(i) for i in e.indices]
for e in indexeds)
# Enforce deterministic dimension ordering...
dims = OrderedDict()
for e in terminals:
if isinstance(e, Dimension):
dims[(e, )] = e
elif e.is_Indexed:
d = []
for a in e.indices:
found = [
i for i in a.free_symbols if isinstance(i, Dimension)
]
d.extend([i for i in found if i not in d])
dims[tuple(d)] = e
# ... giving higher priority to TimeFunction objects; time always go first
dims = sorted(
list(dims),
key=lambda i: not (isinstance(dims[i], Dimension) or dims[i].base.
function.is_TimeFunction))
stencil = Stencil([(i, set()) for i in partial_order(dims)])
# Determine the points accessed along each dimension
for e in indexeds:
for a in e.indices:
if isinstance(a, Dimension):
stencil[a].update([0])
d = None
off = [0]
for i in a.args:
if isinstance(i, Dimension):
d = i
elif i.is_integer:
off += [i]
if d is not None:
stencil[d].update(off)
return stencil
def __init__(self, exprs):
"""
A Scope enables data dependence analysis on a totally ordered sequence
of expressions.
A Scope may be used only if IterationSpaces and Function's Dimensions
follow the same ordering. For example, given ``f(x, y, z)`` and ``g(x,
y)``, the IterationSpace must be ``[x, y, z]`` (and not ``[x, z, y]``).
In Devito, this is guaranteed by construction -- IterationSpaces are
built from a deterministic partial ordering of Dimensions. This
condition ensures that the lexicographic ordering of the iterations for
the iteration vector ``(x, y, z)`` is ``(0, 0, 0), (0, 0, 1), ..., (0,
1, 0), (0, 1, 1), ...``, which greatly simplifies the collection and
classification of data dependences.
"""
exprs = as_tuple(exprs)
self.reads = {}
self.writes = {}
for i, e in enumerate(exprs):
# Reads
for j in retrieve_terminals(e.rhs):
v = self.reads.setdefault(j.function, [])
mode = 'RI' if e.is_Increment and j.function is e.lhs.function else 'R'
v.append(TimedAccess(j, mode, i, e.ispace))
# Write
v = self.writes.setdefault(e.lhs.function, [])
mode = 'WI' if e.is_Increment else 'W'
v.append(TimedAccess(e.lhs, mode, i, e.ispace))
# If an increment, we got one implicit read
if e.is_Increment:
v = self.reads.setdefault(e.lhs.function, [])
v.append(TimedAccess(e.lhs, 'RI', i, e.ispace))
# The iterators read symbols too
dimensions = set().union(*[e.dimensions for e in exprs])
for d in dimensions:
for j in d.symbolic_size.free_symbols:
v = self.reads.setdefault(j.function, [])
v.append(TimedAccess(j, 'R', -1))
def detect_io(exprs, relax=False):
"""
``{exprs} -> ({reads}, {writes})
Parameters
----------
exprs : expr-like or list of expr-like
The searched expressions.
relax : bool, optional
If False, as by default, collect only :class:`Constant`s and
:class:`Function`s. Otherwise, collect any :class:`types.Basic`s.
"""
exprs = as_tuple(exprs)
if relax is False:
rule = lambda i: i.is_Input
else:
rule = lambda i: i.is_Scalar or i.is_Tensor
reads = []
for i in flatten(retrieve_terminals(i, deep=True) for i in exprs):
candidates = i.free_symbols
try:
candidates.update({i.base.function})
except AttributeError:
pass
for j in candidates:
try:
if rule(j):
reads.append(j)
except AttributeError:
pass
writes = []
for i in exprs:
try:
f = i.lhs.base.function
except AttributeError:
continue
if rule(f):
writes.append(f)
return filter_sorted(reads), filter_sorted(writes)
def __init__(self, exprs):
"""
A Scope represents a group of :class:`TimedAccess` objects extracted
from some :class:`IREq` ``exprs``. The expressions must be provided
in program order.
"""
exprs = as_tuple(exprs)
self.reads = {}
self.writes = {}
for i, e in enumerate(exprs):
# reads
for j in retrieve_terminals(e.rhs):
v = self.reads.setdefault(j.base.function, [])
mode = 'R' if not q_inc(e) else 'RI'
v.append(TimedAccess(j, mode, i, e.ispace.directions))
# write
v = self.writes.setdefault(e.lhs.base.function, [])
mode = 'W' if not q_inc(e) else 'WI'
v.append(TimedAccess(e.lhs, mode, i, e.ispace.directions))
def __init__(self, exprs):
"""
Initialize a Scope, which represents a group of :class:`Access` objects
extracted from some expressions ``exprs``. The expressions are to be
provided as they appear in program order.
"""
exprs = as_tuple(exprs)
assert all(isinstance(i, Eq) for i in exprs)
self.reads = {}
self.writes = {}
for i, e in enumerate(exprs):
# reads
for j in retrieve_terminals(e.rhs):
v = self.reads.setdefault(j.base.function, [])
mode = 'R' if not q_inc(e) else 'RI'
v.append(TimedAccess(j, mode, i))
# write
v = self.writes.setdefault(e.lhs.base.function, [])
mode = 'W' if not q_inc(e) else 'WI'
v.append(TimedAccess(e.lhs, mode, i))
def time_invariant(self, expr=None):
"""
Check if ``expr`` is time invariant. ``expr`` may be an expression ``e``
explicitly tracked by the FlowGraph or even a generic subexpression
of ``e``. If no ``expr`` is provided, then time invariance of the entire
FlowGraph is assessed.
"""
if expr is None:
return all(self.time_invariant(v) for v in self.values())
if any(q_timedimension(i) for i in expr.free_symbols):
return False
queue = [expr.rhs if expr.is_Equality else expr]
seen = set()
while queue:
item = queue.pop()
temporaries = set()
for i in retrieve_terminals(item):
if i in seen:
# Already inspected, nothing more can be inferred
continue
elif any(
isinstance(j, Dimension) and j.is_Time
for j in i.free_symbols):
# Definitely not time-invariant
return False
elif i in self:
# Go on with the search
temporaries.add(i)
elif isinstance(i, Dimension):
# Go on with the search, as /i/ is not a time dimension
pass
elif not i.base.function.is_TensorFunction:
# It didn't come from the outside and it's not in self, so
# cannot determine if time-invariant; assume time-varying
return False
seen.add(i)
queue.extend([self[i].rhs for i in temporaries])
return True
def time_invariant(self, expr=None):
"""
Check if ``expr`` is time invariant. ``expr`` may be an expression ``e``
explicitly tracked by the FlowGraph or even a generic subexpression
of ``e``. If no ``expr`` is provided, then time invariance of the entire
FlowGraph is assessed.
"""
if expr is None:
return all(self.time_invariant(v) for v in self.values())
if any(q_timedimension(i) for i in expr.free_symbols):
return False
queue = [expr.rhs if expr.is_Equality else expr]
seen = set()
while queue:
item = queue.pop()
nodes = set()
for i in retrieve_terminals(item):
if i in seen:
# Already inspected, nothing more can be inferred
continue
elif any(isinstance(j, Dimension) and j.is_Time for j in i.free_symbols):
# Definitely not time-invariant
return False
elif i in self:
# Go on with the search
nodes.add(i)
elif isinstance(i, Dimension):
# Go on with the search, as /i/ is not a time dimension
pass
elif not i.function.is_DiscreteFunction:
# It didn't come from the outside and it's not in self, so
# cannot determine if time-invariant; assume time-varying
return False
seen.add(i)
queue.extend([self[i].rhs for i in nodes])
return True
def topological_sort(exprs):
"""Topologically sort a list of equations."""
mapper = {e.lhs: e for e in exprs}
assert len(mapper) == len(exprs) # Expect SSA
dag = DAG(nodes=exprs)
for e in exprs:
for r in retrieve_terminals(e.rhs):
if r not in mapper:
continue
elif mapper[r] is e:
# Avoid cyclic dependences, such as
# Eq(f, f + 1)
continue
elif r.is_Indexed:
# Only scalars enforce an ordering
continue
else:
dag.add_edge(mapper[r], e, force_add=True)
processed = dag.topological_sort()
return processed
def __init__(self, exprs, **kwargs):
# Always convert to SSA
exprs = makeit_ssa(exprs)
mapper = OrderedDict([(i.lhs, i) for i in exprs])
assert len(set(mapper)) == len(exprs), "not SSA Cluster?"
# Construct the Nodes, tracking reads and readby
tensor_map = DefaultOrderedDict(list)
for i in mapper:
tensor_map[as_symbol(i)].append(i)
reads = DefaultOrderedDict(set)
readby = DefaultOrderedDict(set)
for k, v in mapper.items():
handle = retrieve_terminals(v.rhs, deep=True)
reads[k].update(
set(flatten([tensor_map.get(as_symbol(i), [])
for i in handle])))
for i in reads[k]:
readby[i].add(k)
# Make sure read-after-writes are honored for scalar nodes
processed = [i for i in mapper if i.is_Indexed]
queue = [i for i in mapper if i not in processed]
while queue:
k = queue.pop(0)
if not readby[k] or k in readby[k]:
processed.insert(0, k)
elif all(i in processed for i in readby[k]):
index = min(processed.index(i) for i in readby[k])
processed.insert(index, k)
else:
queue.append(k)
# Build up the FlowGraph
nodes = [(i, Node(mapper[i], reads=reads[i], readby=readby[i]))
for i in processed]
super(FlowGraph, self).__init__(nodes, **kwargs)
def __init__(self, exprs):
"""
A Scope represents a group of TimedAcces objects extracted
from some IREq ``exprs``. The expressions must be provided
in program order.
"""
exprs = as_tuple(exprs)
self.reads = {}
self.writes = {}
for i, e in enumerate(exprs):
# reads
for j in retrieve_terminals(e.rhs):
v = self.reads.setdefault(j.function, [])
mode = 'RI' if e.is_Increment and j.function is e.lhs.function else 'R'
v.append(TimedAccess(j, mode, i, e.ispace.directions))
# write
v = self.writes.setdefault(e.lhs.function, [])
mode = 'WI' if e.is_Increment else 'W'
v.append(TimedAccess(e.lhs, mode, i, e.ispace.directions))
# if an increment, we got one implicit read
if e.is_Increment:
v = self.reads.setdefault(e.lhs.function, [])
v.append(TimedAccess(e.lhs, 'RI', i, e.ispace.directions))
def __init__(self, exprs):
"""
A Scope represents a group of TimedAcces objects extracted
from some IREq ``exprs``. The expressions must be provided
in program order.
"""
exprs = as_tuple(exprs)
self.reads = {}
self.writes = {}
for i, e in enumerate(exprs):
# reads
for j in retrieve_terminals(e.rhs):
v = self.reads.setdefault(j.function, [])
mode = 'RI' if e.is_Increment and j.function is e.lhs.function else 'R'
v.append(TimedAccess(j, mode, i, e.ispace.directions))
# write
v = self.writes.setdefault(e.lhs.function, [])
mode = 'WI' if e.is_Increment else 'W'
v.append(TimedAccess(e.lhs, mode, i, e.ispace.directions))
# if an increment, we got one implicit read
if e.is_Increment:
v = self.reads.setdefault(e.lhs.function, [])
v.append(TimedAccess(e.lhs, 'RI', i, e.ispace.directions))
