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 __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 __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 dspace(self): """ Derive the DataSpace of the Cluster from its expressions, IterationSpace, and Guards. """ accesses = detect_accesses(self.exprs) # Construct the `parts` of the DataSpace, that is a projection of the data # space for each Function appearing in `self.exprs` parts = {} for f, v in accesses.items(): if f is None: continue intervals = [ Interval(d, min(offs), max(offs)) for d, offs in v.items() ] intervals = IntervalGroup(intervals) # Factor in the IterationSpace -- if the min/max points aren't zero, # then the data intervals need to shrink/expand accordingly intervals = intervals.promote(lambda d: d.is_Block) shift = self.ispace.intervals.promote(lambda d: d.is_Block) intervals = intervals.add(shift) # Map SubIterators to the corresponding data space Dimension # E.g., `xs -> x -> x0_blk0 -> x` or `t0 -> t -> time` intervals = intervals.promote(lambda d: d.is_SubIterator) # If the bound of a Dimension is explicitly guarded, then we should # shrink the `parts` accordingly for d, v in self.guards.items(): ret = v.find(BaseGuardBoundNext) assert len(ret) <= 1 if len(ret) != 1: continue if ret.pop().direction is Forward: intervals = intervals.translate(d, v1=-1) else: intervals = intervals.translate(d, 1) # Special case: if the factor of a ConditionalDimension has value 1, # then we can safely resort to the parent's Interval intervals = intervals.promote( lambda d: d.is_Conditional and d.factor == 1) parts[f] = intervals # Determine the Dimensions requiring shifted min/max points to avoid # OOB accesses oobs = set() for f, v in parts.items(): for i in v: if i.dim.is_Sub: d = i.dim.parent else: d = i.dim try: if i.lower < 0 or \ i.upper > f._size_nodomain[d].left + f._size_halo[d].right: # It'd mean trying to access a point before the # left halo (test0) or after the right halo (test1) oobs.update(d._defines) except (KeyError, TypeError): # Unable to detect presence of OOB accesses (e.g., `d` not in # `f._size_halo`, that is typical of indirect accesses `A[B[i]]`) pass # Construct the `intervals` of the DataSpace, that is a global, # Dimension-centric view of the data space intervals = IntervalGroup.generate('union', *parts.values()) # E.g., `db0 -> time`, but `xi NOT-> x` intervals = intervals.promote(lambda d: not d.is_Sub) intervals = intervals.zero(set(intervals.dimensions) - oobs) return DataSpace(intervals, parts)
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