def compute_intervals(expr):
"""Return an iterable of :class:`Interval`s representing the data items
accessed by the :class:`sympy.Eq` ``expr``."""
# Detect the indexeds' offsets along each dimension
stencil = Stencil()
for e in retrieve_indexed(expr, mode='all', deep=True):
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 += [int(i)]
if d is not None:
stencil[d].update(off)
# Determine intervals and their iterators
iterators = OrderedDict()
for i in stencil.dimensions:
if i.is_NonlinearDerived:
iterators.setdefault(i.parent, []).append(stencil.entry(i))
else:
iterators.setdefault(i, [])
intervals = []
for k, v in iterators.items():
offs = set.union(set(stencil.get(k)), *[i.ofs for i in v])
intervals.append(Interval(k, min(offs), max(offs)))
return intervals, iterators
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 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 build_intervals(mapper):
"""
Given M as produced by :func:`detect_accesses`, return: ::
* An iterable of :class:`Interval`s, representing the data items
accessed in each :class:`Dimension` in M;
* A dictionary of ``iterators``, suitable to build an
:class:`IterationSpace`.
"""
iterators = OrderedDict()
stencil = Stencil.union(*mapper.values())
for i in stencil.dimensions:
if i.is_NonlinearDerived:
iterators.setdefault(i.parent, []).append(stencil.entry(i))
else:
iterators.setdefault(i, [])
intervals = []
for k, v in iterators.items():
offs = set.union(set(stencil.get(k)), *[i.ofs for i in v])
intervals.append(Interval(k, min(offs), max(offs)))
return intervals, iterators