def test_conditional_dimension(self):
"""Test that different ConditionalDimensions have different hash value."""
d0 = Dimension(name='d')
s0 = Scalar(name='s')
d1 = Dimension(name='d', spacing=s0)
cd0 = ConditionalDimension(name='cd', parent=d0, factor=4)
cd1 = ConditionalDimension(name='cd', parent=d0, factor=5)
assert cd0 is not cd1
assert hash(cd0) != hash(cd1)
cd2 = ConditionalDimension(name='cd',
parent=d0,
factor=4,
indirect=True)
assert hash(cd0) != hash(cd2)
cd3 = ConditionalDimension(name='cd', parent=d1, factor=4)
assert hash(cd0) != hash(cd3)
s1 = Scalar(name='s', dtype=np.int32)
cd4 = ConditionalDimension(name='cd',
parent=d0,
factor=4,
condition=s0 > 3)
assert hash(cd0) != hash(cd4)
cd5 = ConditionalDimension(name='cd',
parent=d0,
factor=4,
condition=s1 > 3)
assert hash(cd0) != hash(cd5)
assert hash(cd4) != hash(cd5)
def _extract_time_invariants(self,
cluster,
template,
with_cse=True,
costmodel=None,
**kwargs):
"""
Extract time-invariant subexpressions, and assign them to temporaries.
"""
# Extract time invariants
make = lambda i: Scalar(name=template(i)).indexify()
rule = iq_timeinvariant(cluster.trace)
costmodel = costmodel or (lambda e: estimate_cost(e) > 0)
processed, found = xreplace_constrained(cluster.exprs, make, rule,
costmodel)
if with_cse:
leaves = [i for i in processed if i not in found]
# Search for common sub-expressions amongst them (and only them)
make = lambda i: Scalar(name=template(i + len(found))).indexify()
found = common_subexprs_elimination(found, make)
# Some temporaries may be droppable at this point
processed = compact_temporaries(found, leaves)
return cluster.rebuild(processed)
def test_shared_data():
s = Scalar(name='s')
a = Scalar(name='a')
sdata = SharedData(name='sdata',
npthreads=2,
fields=[s],
dynamic_fields=[a])
pkl_sdata = pickle.dumps(sdata)
new_sdata = pickle.loads(pkl_sdata)
assert sdata.name == new_sdata.name
assert sdata.size == new_sdata.size
assert sdata.fields == new_sdata.fields
assert sdata.pfields == new_sdata.pfields
assert sdata.dynamic_fields == new_sdata.dynamic_fields
ffp = FieldFromPointer(sdata._field_flag, sdata.symbolic_base)
pkl_ffp = pickle.dumps(ffp)
new_ffp = pickle.loads(pkl_ffp)
assert ffp == new_ffp
indexed = sdata[0]
pkl_indexed = pickle.dumps(indexed)
new_indexed = pickle.loads(pkl_indexed)
assert indexed.name == new_indexed.name
assert indexed.shape == new_indexed.shape
def test_collect_aliases(fc, fd, exprs, expected):
grid = Grid(shape=(4, 4))
x, y = grid.dimensions # noqa
xi, yi = grid.interior.dimensions # noqa
t0 = Scalar(name='t0') # noqa
t1 = Scalar(name='t1') # noqa
t2 = Scalar(name='t2') # noqa
t3 = Scalar(name='t3') # noqa
fa = Function(name='fa', grid=grid, shape=(4, ), dimensions=(x, )) # noqa
fb = Function(name='fb', grid=grid, shape=(4, ), dimensions=(x, )) # noqa
fc = Function(name='fc', grid=grid) # noqa
fd = Function(name='fd', grid=grid) # noqa
# List/dict comprehension would need explicit locals/globals mappings to eval
for i, e in enumerate(list(exprs)):
exprs[i] = eval(e)
for k, v in list(expected.items()):
expected[eval(k)] = eval(v)
aliases = collect(exprs)
assert len(aliases) > 0
for k, v in aliases.items():
assert ((len(v.aliased) == 1 and expected[k] is None)
or v.anti_stencil == expected[k])
def test_cse(exprs, expected):
"""Test common subexpressions elimination."""
grid = Grid((3, 3, 3))
dims = grid.dimensions
tu = TimeFunction(name="tu", grid=grid, space_order=2) # noqa
tv = TimeFunction(name="tv", grid=grid, space_order=2) # noqa
tw = TimeFunction(name="tw", grid=grid, space_order=2) # noqa
tz = TimeFunction(name="tz", grid=grid, space_order=2) # noqa
ti0 = Array(name='ti0', shape=(3, 5, 7),
dimensions=dims).indexify() # noqa
ti1 = Array(name='ti1', shape=(3, 5, 7),
dimensions=dims).indexify() # noqa
t0 = Scalar(name='t0') # noqa
t1 = Scalar(name='t1') # noqa
t2 = Scalar(name='t2') # noqa
# List comprehension would need explicit locals/globals mappings to eval
for i, e in enumerate(list(exprs)):
exprs[i] = DummyEq(indexify(eval(e).evaluate))
counter = generator()
make = lambda: Scalar(name='r%d' % counter()).indexify()
processed = _cse(exprs, make)
assert len(processed) == len(expected)
assert all(str(i.rhs) == j for i, j in zip(processed, expected))
def test_estimate_cost(expr, expected, estimate):
# Note: integer arithmetic isn't counted
grid = Grid(shape=(4, 4))
x, y = grid.dimensions # noqa
t0 = Scalar(name='t0') # noqa
t1 = Scalar(name='t1') # noqa
t2 = Scalar(name='t2') # noqa
fa = Function(name='fa', grid=grid, shape=(4, ), dimensions=(x, )) # noqa
fb = Function(name='fb', grid=grid, shape=(4, ), dimensions=(x, )) # noqa
fc = Function(name='fc', grid=grid) # noqa
assert estimate_cost(eval(expr), estimate) == expected
def test_dimension(self):
"""Test that different Dimensions have different hash value."""
d0 = Dimension(name='d')
s0 = Scalar(name='s')
d1 = Dimension(name='d', spacing=s0)
assert hash(d0) != hash(d1)
s1 = Scalar(name='s', dtype=np.int32)
d2 = Dimension(name='d', spacing=s1)
assert hash(d1) != hash(d2)
d3 = Dimension(name='d', spacing=Constant(name='s1'))
assert hash(d3) != hash(d0)
assert hash(d3) != hash(d1)
def test_scalar(self):
"""
Test that Scalars with same name but different attributes do not alias to
the same Scalar. Conversely, if the name and the attributes are the same,
they must alias to the same Scalar.
"""
s0 = Scalar(name='s0')
s1 = Scalar(name='s0')
assert s0 is s1
s2 = Scalar(name='s0', dtype=np.int32)
assert s2 is not s1
s3 = Scalar(name='s0', is_const=True)
assert s3 is not s1
def extract(cls, n, context, min_cost, cluster, sregistry):
make = lambda: Scalar(name=sregistry.make_name(), dtype=cluster.dtype
).indexify()
exclude = {
i.source.indexed
for i in cluster.scope.d_flow.independent()
}
rule0 = lambda e: not e.free_symbols & exclude
rule1 = make_is_time_invariant(context)
rule2 = lambda e: estimate_cost(e, True) >= min_cost
rule = lambda e: rule0(e) and rule1(e) and rule2(e)
extracted = []
mapper = OrderedDict()
for e in cluster.exprs:
for i in search(e, rule, 'all', 'dfs_first_hit'):
if i not in mapper:
symbol = make()
mapper[i] = symbol
extracted.append(e.func(symbol, i))
processed = [uxreplace(e, mapper) for e in cluster.exprs]
return extracted + processed, extracted
def test_common_subexprs_elimination(tu, tv, tw, ti0, ti1, t0, t1, exprs,
expected):
make = lambda i: Scalar(name='r%d' % i).indexify()
processed = common_subexprs_elimination(
EVAL(exprs, tu, tv, tw, ti0, ti1, t0, t1), make)
assert len(processed) == len(expected)
assert all(str(i.rhs) == j for i, j in zip(processed, expected))
def visit_Iteration(self, o, subs, offsets=defaultdict(set)):
nodes, subs = self.visit(o.children, subs, offsets=offsets)
if o.dim.is_Stepping:
# For SteppingDimension insert the explicit
# definition of buffered variables, eg. t+1 => t1
init = []
for i, off in enumerate(filter_ordered(offsets[o.dim])):
vname = Scalar(name="%s%d" % (o.dim.name, i), dtype=np.int32)
value = (o.dim.parent + off) % o.dim.modulo
init.append(UnboundedIndex(vname, value, value))
subs[o.dim + off] = LoweredDimension(vname.name, o.dim, off)
# Always lower to symbol
subs[o.dim.parent] = Scalar(name=o.dim.parent.name, dtype=np.int32)
return o._rebuild(index=o.dim.parent.name, uindices=init), subs
else:
return o._rebuild(*nodes), subs
def test_iterations_ompized(self, exprs, expected):
grid = Grid(shape=(4, 4))
x, y = grid.dimensions # noqa
fa = Function(name='fa', grid=grid, dimensions=(x, ),
shape=(4, )) # noqa
fb = Function(name='fb', grid=grid, dimensions=(x, ),
shape=(4, )) # noqa
fc = Function(name='fc', grid=grid) # noqa
fd = Function(name='fd', grid=grid) # noqa
t0 = Scalar(name='t0') # noqa
eqns = []
for e in exprs:
eqns.append(eval(e))
op = Operator(eqns, dle='openmp')
iterations = FindNodes(Iteration).visit(op)
assert len(iterations) == len(expected)
# Check for presence of pragma omp
for i, j in zip(iterations, expected):
pragmas = i.pragmas
if j is True:
assert len(pragmas) == 1
pragma = pragmas[0]
assert 'omp for' in pragma.value
else:
for k in pragmas:
assert 'omp for' not in k.value
def test_conditional_dimension(self):
"""
Test that ConditionalDimensions with same name but different attributes do not
alias to the same ConditionalDimension. Conversely, if the name and the attributes
are the same, they must alias to the same ConditionalDimension.
"""
i = Dimension(name='i')
ci0 = ConditionalDimension(name='ci', parent=i, factor=4)
ci1 = ConditionalDimension(name='ci', parent=i, factor=4)
assert ci0 is ci1
ci2 = ConditionalDimension(name='ci', parent=i, factor=8)
assert ci2 is not ci1
ci3 = ConditionalDimension(name='ci',
parent=i,
factor=4,
indirect=True)
assert ci3 is not ci1
s = Scalar(name='s')
ci4 = ConditionalDimension(name='ci',
parent=i,
factor=4,
condition=s > 3)
assert ci4 is not ci1
ci5 = ConditionalDimension(name='ci',
parent=i,
factor=4,
condition=s > 3)
assert ci5 is ci4
def v_literal(self, x, y):
vx = Vector(x)
vxy = Vector(x, y)
vx1y = Vector(x + 1, y)
s = Scalar(name='s', nonnegative=True)
vs3 = Vector(s + 3, smart=True)
return vx, vxy, vx1y, vs3
def cse(cluster, template, *args):
"""
Common sub-expressions elimination (CSE).
"""
make = lambda: Scalar(name=template(), dtype=cluster.dtype).indexify()
processed = _cse(cluster.exprs, make)
return cluster.rebuild(processed)
def test_yreplace_time_invariants(exprs, expected):
grid = Grid((3, 3, 3))
dims = grid.dimensions
tu = TimeFunction(name="tu", grid=grid, space_order=4).indexify()
tv = TimeFunction(name="tv", grid=grid, space_order=4).indexify()
tw = TimeFunction(name="tw", grid=grid, space_order=4).indexify()
ti0 = Array(name='ti0', shape=(3, 5, 7), dimensions=dims).indexify()
ti1 = Array(name='ti1', shape=(3, 5, 7), dimensions=dims).indexify()
t0 = Scalar(name='t0').indexify()
t1 = Scalar(name='t1').indexify()
exprs = EVAL(exprs, tu, tv, tw, ti0, ti1, t0, t1)
counter = generator()
make = lambda: Scalar(name='r%d' % counter()).indexify()
processed, found = yreplace(exprs, make, make_is_time_invariant(exprs),
lambda i: estimate_cost(i) > 0)
assert len(found) == len(expected)
assert all(str(i.rhs) == j for i, j in zip(found, expected))
def extract(cls, n, context, min_cost, max_alias, cluster, sregistry):
make = lambda: Scalar(name=sregistry.make_name(), dtype=cluster.dtype
).indexify()
# The `depth` determines "how big" the extracted sum-of-products will be.
# We observe that in typical FD codes:
# add(mul, mul, ...) -> stems from first order derivative
# add(mul(add(mul, mul, ...), ...), ...) -> stems from second order derivative
# To search the muls in the former case, we need `depth=0`; to search the outer
# muls in the latter case, we need `depth=2`
depth = n
exclude = {
i.source.indexed
for i in cluster.scope.d_flow.independent()
}
rule0 = lambda e: not e.free_symbols & exclude
rule1 = lambda e: e.is_Mul and q_terminalop(e, depth)
rule = lambda e: rule0(e) and rule1(e)
extracted = OrderedDict()
mapper = {}
for e in cluster.exprs:
for i in search(e, rule, 'all', 'bfs_first_hit'):
if i in mapper:
continue
key = lambda a: a.is_Add
terms, others = split(list(i.args), key)
if max_alias:
# Treat `e` as an FD expression and pull out the derivative
# coefficient from `i`
# Note: typically derivative coefficients are numbers, but
# sometimes they could be provided in symbolic form through an
# arbitrary Function. In the latter case, we rely on the
# heuristic that such Function's basically never span the whole
# grid, but rather a single Grid dimension (e.g., `c[z, n]` for a
# stencil of diameter `n` along `z`)
if e.grid is not None and terms:
key = partial(maybe_coeff_key, e.grid)
others, more_terms = split(others, key)
terms.extend(more_terms)
if terms:
k = i.func(*terms)
try:
symbol, _ = extracted[k]
except KeyError:
symbol, _ = extracted.setdefault(k, (make(), e))
mapper[i] = i.func(symbol, *others)
if mapper:
extracted = [e.func(v, k) for k, (v, e) in extracted.items()]
processed = [uxreplace(e, mapper) for e in cluster.exprs]
return extracted + processed, extracted
else:
return cluster.exprs, []
def test_clear_cache_with_alive_symbols(self,
operate_on_empty_cache,
nx=1000,
ny=1000):
"""
Test that `clear_cache` doesn't affect caching if an object is still alive.
"""
grid = Grid(shape=(nx, ny), dtype=np.float64)
f0 = Function(name='f', grid=grid, space_order=2)
f1 = Function(name='f', grid=grid, space_order=2)
# Obviously:
assert f0 is not f1
# And clearly, both still alive after a `clear_cache`
clear_cache()
assert f0 is not f1
assert f0.grid.dimensions[0] is grid.dimensions[0]
# Now we try with symbols
s0 = Scalar(name='s')
s1 = Scalar(name='s')
# Clearly:
assert s1 is s0
clear_cache()
s2 = Scalar(name='s')
# s2 must still be s1/so, even after a clear_cache, as so/s1 are both alive!
assert s2 is s1
del s0
del s1
s3 = Scalar(name='s')
# And obviously, still:
assert s3 is s2
cache_size = len(_SymbolCache)
del s2
del s3
clear_cache()
assert len(_SymbolCache) == cache_size - 1
def _eliminate_intra_stencil_redundancies(self, cluster, template, **kwargs):
"""
Perform common subexpression elimination, bypassing the tensor expressions
extracted in previous passes.
"""
make = lambda: Scalar(name=template(), dtype=cluster.dtype).indexify()
processed = common_subexprs_elimination(cluster.exprs, make)
return cluster.rebuild(processed)
def test_xreplace_constrained_time_varying(tu, tv, tw, ti0, ti1, t0, t1, exprs,
expected):
exprs = EVAL(exprs, tu, tv, tw, ti0, ti1, t0, t1)
make = lambda i: Scalar(name='r%d' % i).indexify()
processed, found = xreplace_constrained(
exprs, make, iq_timevarying(TemporariesGraph(exprs)),
lambda i: estimate_cost(i) > 0)
assert len(found) == len(expected)
assert all(str(i.rhs) == j for i, j in zip(found, expected))
def test_yreplace_time_invariants(tu, tv, tw, ti0, ti1, t0, t1, exprs, expected):
exprs = EVAL(exprs, tu, tv, tw, ti0, ti1, t0, t1)
counter = generator()
make = lambda: Scalar(name='r%d' % counter()).indexify()
processed, found = yreplace(exprs, make,
make_is_time_invariant(exprs),
lambda i: estimate_cost(i) > 0)
assert len(found) == len(expected)
assert all(str(i.rhs) == j for i, j in zip(found, expected))
def test_index_mode_detection(self, indexed, expected):
"""
Test detection of IterationInstance access modes (AFFINE vs IRREGULAR).
Proper detection of access mode is a prerequisite to any sort of
data dependence analysis.
"""
grid = Grid(shape=(4, 4, 4))
x, y, z = grid.dimensions # noqa
sx = SubDimension.middle('sx', x, 1, 1) # noqa
u = Function(name='u', grid=grid) # noqa
c = Constant(name='c') # noqa
sc = Scalar(name='sc', is_const=True) # noqa
s = Scalar(name='s') # noqa
ii = IterationInstance(eval(indexed))
assert ii.index_mode == expected
def _extract_time_invariants(self, cluster, template, **kwargs):
"""
Extract time-invariant subexpressions, and assign them to temporaries.
"""
make = lambda: Scalar(name=template(), dtype=cluster.dtype).indexify()
rule = make_is_time_invariant(cluster.exprs)
costmodel = lambda e: estimate_cost(e, True) >= self.MIN_COST_ALIAS_INV
processed, found = yreplace(cluster.exprs, make, rule, costmodel, eager=True)
return cluster.rebuild(processed)
def test_internal_symbols():
s = dSymbol(name='s', dtype=np.float32)
pkl_s = pickle.dumps(s)
new_s = pickle.loads(pkl_s)
assert new_s.name == s.name
assert new_s.dtype is np.float32
s = Scalar(name='s', dtype=np.int32, is_const=True)
pkl_s = pickle.dumps(s)
new_s = pickle.loads(pkl_s)
assert new_s.name == s.name
assert new_s.dtype is np.int32
assert new_s.is_const is True
s = Scalar(name='s', nonnegative=True)
pkl_s = pickle.dumps(s)
new_s = pickle.loads(pkl_s)
assert new_s.name == s.name
assert new_s.assumptions0['nonnegative'] is True
def _extract_sum_of_products(self, cluster, template, **kwargs):
"""
Extract sub-expressions in sum-of-product form, and assign them to temporaries.
"""
make = lambda: Scalar(name=template(), dtype=cluster.dtype).indexify()
rule = q_sum_of_product
costmodel = lambda e: not (q_leaf(e) or q_terminalop(e))
processed, _ = yreplace(cluster.exprs, make, rule, costmodel)
return cluster.rebuild(processed)
def extract(cluster, rule1, model, template):
make = lambda: Scalar(name=template(), dtype=cluster.dtype).indexify()
# Rule out symbols inducing Dimension-independent data dependences
exclude = {i.source.indexed for i in cluster.scope.d_flow.independent()}
rule0 = lambda e: not e.free_symbols & exclude
# Composite extraction rule -- correctness(0) + logic(1)
rule = lambda e: rule0(e) and rule1(e)
return yreplace(cluster.exprs, make, rule, model, eager=True)
def test_sub_dimension(self):
"""Test that different SubDimensions have different hash value."""
d0 = Dimension(name='d')
d1 = Dimension(name='d', spacing=Scalar(name='s'))
di0 = SubDimension.middle('di', d0, 1, 1)
di1 = SubDimension.middle('di', d1, 1, 1)
assert hash(di0) != hash(d0)
assert hash(di0) != hash(di1)
dl0 = SubDimension.left('dl', d0, 2)
assert hash(dl0) != hash(di0)
def test_conditional_dimension():
d = Dimension(name='d')
s = Scalar(name='s')
cd = ConditionalDimension(name='ci', parent=d, factor=4, condition=s > 3)
pkl_cd = pickle.dumps(cd)
new_cd = pickle.loads(pkl_cd)
assert cd.name == new_cd.name
assert cd.parent == new_cd.parent
assert cd.factor == new_cd.factor
assert cd.condition == new_cd.condition
def test_dimension_cache():
"""
Test that :class:`Dimension`s with same name but different attributes do not
alias to the same Dimension.
"""
d0 = Dimension(name='d')
d1 = Dimension(name='d')
assert d0 is d1
s0 = Scalar(name='s0')
s1 = Scalar(name='s1')
d2 = Dimension(name='d', spacing=s0)
d3 = Dimension(name='d', spacing=s1)
assert d2 is not d3
d4 = Dimension(name='d', spacing=s1)
assert d3 is d4
d5 = Dimension(name='d', spacing=Constant(name='s1'))
assert d2 is not d5
def test_incr_dimension():
s = Scalar(name='s')
d = Dimension(name='d')
dd = IncrDimension(d, s, 5, 2, name='dd')
pkl_dd = pickle.dumps(dd)
new_dd = pickle.loads(pkl_dd)
assert dd.name == new_dd.name
assert dd.parent == new_dd.parent
assert dd.symbolic_min == new_dd.symbolic_min
assert dd.symbolic_max == new_dd.symbolic_max
assert dd.step == new_dd.step