def test_equations_mixed_densedata_timedata(self, shape, dimensions):
"""
Test that equations using a mixture of DenseData and TimeData objects
are embedded within the same time loop.
"""
a = TimeData(name='a', shape=shape, time_order=2, dimensions=dimensions,
space_order=2, time_dim=6, save=False)
p_aux = Dimension(name='p_aux', size=10)
b = DenseData(name='b', shape=shape + (10,), dimensions=dimensions + (p_aux,),
space_order=2)
b.data[:] = 1.0
b2 = DenseData(name='b2', shape=(10,) + shape, dimensions=(p_aux,) + dimensions,
space_order=2)
b2.data[:] = 1.0
eqns = [Eq(a.forward, a.laplace + 1.),
Eq(b, time*b*a + b)]
eqns2 = [Eq(a.forward, a.laplace + 1.),
Eq(b2, time*b2*a + b2)]
subs = {x.spacing: 2.5, y.spacing: 1.5, z.spacing: 2.0}
op = Operator(eqns, subs=subs, dle='noop')
trees = retrieve_iteration_tree(op)
assert len(trees) == 2
assert all(trees[0][i] is trees[1][i] for i in range(3))
op2 = Operator(eqns2, subs=subs, dle='noop')
trees = retrieve_iteration_tree(op2)
assert len(trees) == 2
assert all(trees[0][i] is trees[1][i] for i in range(3))
# Verify both operators produce the same result
op()
op2()
assert(np.allclose(b2.data[2, ...].reshape(-1) -
b.data[..., 2].reshape(-1), 0.))
def decorate(nodes):
processed = []
for node in nodes:
mapper = {}
for tree in retrieve_iteration_tree(node):
vector_iterations = [i for i in tree if i.is_Vectorizable]
for i in vector_iterations:
handle = FindSymbols('symbolics').visit(i)
try:
aligned = [
j for j in handle
if j.is_Tensor and j.shape[-1] %
get_simd_items(j.dtype) == 0
]
except KeyError:
aligned = []
if aligned:
simd = omplang['simd-for-aligned']
simd = as_tuple(
simd(','.join([j.name for j in aligned]),
simdinfo[get_simd_flag()]))
else:
simd = as_tuple(omplang['simd-for'])
mapper[i] = i._rebuild(pragmas=i.pragmas +
ignore_deps + simd)
processed.append(Transformer(mapper).visit(node))
return processed
def test_multiple_loop_nests(self):
"""
Compute a simple stencil S, preceded by an "initialization loop" I and
followed by a "random loop" R.
* S is the trivial equation ``u[t+1,x,y,z] = u[t,x,y,z] + 1``;
* I initializes ``u`` to 0;
* R adds 2 to another field ``v`` along the ``z`` dimension but only
over the planes ``[x=0, y=2]`` and ``[x=0, y=5]``.
Out of these three loop nests, only S should be "offloaded" to YASK; indeed,
I is outside the time loop, while R does not loop over space dimensions.
This test checks that S is the only loop nest "offloaded" to YASK, and
that the numerical output is correct.
"""
u = TimeData(name='yu4D', shape=(12, 12, 12), dimensions=(x, y, z),
space_order=0)
v = TimeData(name='yv4D', shape=(12, 12, 12), dimensions=(x, y, z),
space_order=0)
v.data[:] = 0.
eqs = [Eq(u.indexed[0, x, y, z], 0),
Eq(u.indexed[1, x, y, z], 0),
Eq(u.forward, u + 1.),
Eq(v.indexed[t + 1, 0, 2, z], v.indexed[t + 1, 0, 2, z] + 2.),
Eq(v.indexed[t + 1, 0, 5, z], v.indexed[t + 1, 0, 5, z] + 2.)]
op = Operator(eqs, subs={t.spacing: 1})
op(yu4D=u, yv4D=v, t=1)
assert 'run_solution' in str(op)
assert len(retrieve_iteration_tree(op)) == 3
assert np.all(u.data[0] == 0.)
assert np.all(u.data[1] == 1.)
assert np.all(v.data[0] == 0.)
assert np.all(v.data[1, 0, 2] == 2.)
assert np.all(v.data[1, 0, 5] == 2.)
def test_different_section_nests(self, tu, ti0, t0, t1):
eq1 = Eq(ti0, t0*3.)
eq2 = Eq(tu, ti0 + t1*3.)
op = Operator([eq1, eq2], dse='noop', dle='noop')
trees = retrieve_iteration_tree(op)
assert len(trees) == 2
assert trees[0][-1].nodes[0].expr.rhs == eq1.rhs
assert trees[1][-1].nodes[0].expr.rhs == eq2.rhs
def decorate(nodes):
processed = []
for node in nodes:
mapper = {}
for tree in retrieve_iteration_tree(node):
for i in tree:
if i.is_Parallel:
mapper[i] = List(body=i, footer=fence)
break
transformed = Transformer(mapper).visit(node)
mapper = {}
for tree in retrieve_iteration_tree(transformed):
for i in tree:
if i.is_Vectorizable:
mapper[i] = List(header=pragma, body=i)
transformed = Transformer(mapper).visit(transformed)
processed.append(transformed)
return processed
def test_directly_indexed_expression(self, fa, ti0, t0, exprs):
"""
Emulates a potential implementation of boundary condition loops
"""
eqs = EVAL(exprs, ti0.base, t0)
op = Operator(eqs, dse='noop', dle='noop')
trees = retrieve_iteration_tree(op)
assert len(trees) == 2
assert trees[0][-1].nodes[0].expr.rhs == eqs[0].rhs
assert trees[1][-1].nodes[0].expr.rhs == eqs[1].rhs
def test_expressions_imperfect_loops(self, ti0, ti1, ti2, t0):
eq1 = Eq(ti2, t0 * 3.)
eq2 = Eq(ti0, ti1 + 4. + ti2 * 5.)
op = Operator([eq1, eq2], dse='noop', dle='noop')
trees = retrieve_iteration_tree(op)
assert len(trees) == 2
outer, inner = trees
assert len(outer) == 2 and len(inner) == 3
assert all(i == j for i, j in zip(outer, inner[:-1]))
assert outer[-1].nodes[0].expr.rhs == eq1.rhs
assert inner[-1].nodes[0].expr.rhs == eq2.rhs
def test_directly_indexed_expression(self, fa, ti0, t0, exprs):
"""
Test that equations using integer indices are inserted in the right
loop nest, at the right loop nest depth.
"""
eqs = EVAL(exprs, ti0.base, t0)
op = Operator(eqs, dse='noop', dle='noop')
trees = retrieve_iteration_tree(op)
assert len(trees) == 2
assert trees[0][-1].nodes[0].expr.rhs == eqs[0].rhs
assert trees[1][-1].nodes[0].expr.rhs == eqs[1].rhs
def _yaskize(self, state):
"""
Create a YASK representation of this Iteration/Expression tree.
"""
dle_warning("Be patient! The YASK backend is still a WIP")
dle_warning("This is the YASK AST that the Devito DLE can build")
for node in state.nodes:
for tree in retrieve_iteration_tree(node):
candidate = tree[-1]
# Set up the YASK solution
soln = cfac.new_stencil_solution("solution")
# Set up the YASK grids
grids = FindSymbols(mode='symbolics').visit(candidate)
grids = {
g.name: soln.new_grid(g.name, *[str(i) for i in g.indices])
for g in grids
}
# Vector folding API usage example
soln.set_fold_len('x', 1)
soln.set_fold_len('y', 1)
soln.set_fold_len('z', 8)
# Perform the translation on an expression basis
transformer = sympy2yask(grids)
expressions = [e for e in candidate.nodes if e.is_Expression]
# yaskASTs = [transformer(e.stencil) for e in expressions]
for i in expressions:
try:
ast = transformer(i.stencil)
# Scalar
print(ast.format_simple())
# AVX2 intrinsics
# print soln.format('avx2')
# AVX2 intrinsics to file
# import os
# path = os.path.join(os.environ.get('YASK_HOME', '.'), 'src')
# soln.write(os.path.join(path, 'stencil_code.hpp'), 'avx2')
except:
pass
dle_warning("Falling back to basic DLE optimizations...")
return {'nodes': state.nodes}
def __init__(self, expressions, **kwargs):
super(OperatorDebug, self).__init__(expressions, **kwargs)
self._includes.append('stdio.h')
# Minimize the trip count of the sequential loops
iterations = set(flatten(retrieve_iteration_tree(self.body)))
mapper = {
i: i._rebuild(limits=(max(i.offsets) + 2))
for i in iterations if i.is_Sequential
}
self.body = Transformer(mapper).visit(self.body)
# Mark entry/exit points of each non-sequential Iteration tree in the body
iterations = [
filter_iterations(i, lambda i: not i.is_Sequential, 'any')
for i in retrieve_iteration_tree(self.body)
]
iterations = [i[0] for i in iterations if i]
mapper = {
t: List(header=printmark('In nest %d' % i), body=t)
for i, t in enumerate(iterations)
}
self.body = Transformer(mapper).visit(self.body)
def test_cache_blocking_structure(blockinner, expected):
_, op = _new_operator1((10, 31, 45), dle=('blocking', {'blockalways': True,
'blockshape': (2, 9, 2),
'blockinner': blockinner}))
# Check presence of remainder loops
iterations = retrieve_iteration_tree(op)
assert len(iterations) == expected
assert not iterations[0][0].is_Remainder
assert all(i[0].is_Remainder for i in iterations[1:])
# Check presence of openmp pragmas at the right place
_, op = _new_operator1((10, 31, 45), dle=('blocking,openmp',
{'blockalways': True,
'blockshape': (2, 9, 2),
'blockinner': blockinner}))
iterations = retrieve_iteration_tree(op)
assert len(iterations) == expected
# All iterations except the last one an outermost parallel loop over blocks
assert not iterations[-1][0].is_Parallel
for i in iterations[:-1]:
outermost = i[0]
assert len(outermost.pragmas) == 1
assert 'omp for' in outermost.pragmas[0].value
def fold_blockable_tree(node, exclude_innermost=False):
"""
Create :class:`IterationFold`s from sequences of nested :class:`Iteration`.
"""
found = FindAdjacentIterations().visit(node)
found.pop('seen_iteration')
mapper = {}
for k, v in found.items():
for i in v:
# Pre-condition: they all must be perfect iterations
assert len(i) > 1
if any(not IsPerfectIteration().visit(j) for j in i):
continue
# Only retain consecutive trees having same depth
trees = [retrieve_iteration_tree(j)[0] for j in i]
handle = []
for j in trees:
if len(j) != len(trees[0]):
break
handle.append(j)
trees = handle
if not trees:
continue
# Check foldability
pairwise_folds = list(zip(*reversed(trees)))
if any(not is_foldable(j) for j in pairwise_folds):
continue
# Maybe heuristically exclude innermost Iteration
if exclude_innermost is True:
pairwise_folds = pairwise_folds[:-1]
# Perhaps there's nothing to fold
if len(pairwise_folds) == 1:
continue
# Perform folding
for j in pairwise_folds:
root, remainder = j[0], j[1:]
folds = [(tuple(y - x
for x, y in zip(i.offsets, root.offsets)),
i.nodes) for i in remainder]
mapper[root] = IterationFold(folds=folds, **root.args)
for k in remainder:
mapper[k] = None
# Insert the IterationFolds in the Iteration/Expression tree
processed = NestedTransformer(mapper).visit(node)
return processed
def test_consistency_perfect_loops(self, tu, tv, ti0, t0, t1):
eq1 = Eq(tu, tv * ti0 * t0 + ti0 * t1)
eq2 = Eq(ti0, tu + t0 * 3.)
eq3 = Eq(tv, ti0 * tu)
op1 = Operator([eq1, eq2, eq3], dse='noop', dle='noop')
op2 = Operator([eq2, eq1, eq3], dse='noop', dle='noop')
op3 = Operator([eq3, eq2, eq1], dse='noop', dle='noop')
trees = [retrieve_iteration_tree(i) for i in [op1, op2, op3]]
assert all(len(i) == 1 for i in trees)
trees = [i[0] for i in trees]
for tree in trees:
assert IsPerfectIteration().visit(tree[0])
assert len(tree[-1].nodes) == 3
pivot = set([j.expr for j in trees[0][-1].nodes])
assert all(set([j.expr for j in i[-1].nodes]) == pivot for i in trees)
def test_equations_emulate_bc(self, t0):
"""
Test that bc-like equations get inserted into the same loop nest
as the "main" equations.
"""
shape = (3, 3, 3)
a = DenseData(name='a', shape=shape).indexed
b = TimeData(name='b', shape=shape, save=True, time_dim=6).indexed
main = Eq(b[time + 1, x, y, z], b[time - 1, x, y, z] + a[x, y, z] + 3.*t0)
bcs = [Eq(b[time, 0, y, z], 0.),
Eq(b[time, x, 0, z], 0.),
Eq(b[time, x, y, 0], 0.)]
op = Operator([main] + bcs, dse='noop', dle='noop')
trees = retrieve_iteration_tree(op)
assert len(trees) == 4
assert all(id(trees[0][0]) == id(i[0]) for i in trees)
def test_expressions_imperfect_loops(self, ti0, ti1, ti2, t0):
"""
Test that equations depending only on a subset of all indices
appearing across all equations are placed within earlier loops
in the loop nest tree.
"""
eq1 = Eq(ti2, t0*3.)
eq2 = Eq(ti0, ti1 + 4. + ti2*5.)
op = Operator([eq1, eq2], dse='noop', dle='noop')
trees = retrieve_iteration_tree(op)
assert len(trees) == 2
outer, inner = trees
assert len(outer) == 2 and len(inner) == 3
assert all(i == j for i, j in zip(outer, inner[:-1]))
assert outer[-1].nodes[0].expr.rhs == eq1.rhs
assert inner[-1].nodes[0].expr.rhs == eq2.rhs
def unfold_blocked_tree(node):
"""
Unfold nested :class:`IterationFold`.
:Example:
Given a section of Iteration/Expression tree as below: ::
for i = 1 to N-1 // folded
for j = 1 to N-1 // folded
foo1()
Assuming a fold with offset 1 in both /i/ and /j/ and body ``foo2()``, create: ::
for i = 1 to N-1
for j = 1 to N-1
foo1()
for i = 2 to N-2
for j = 2 to N-2
foo2()
"""
# Search the unfolding candidates
candidates = []
for tree in retrieve_iteration_tree(node):
handle = tuple(i for i in tree if i.is_IterationFold)
if handle:
# Sanity check
assert IsPerfectIteration().visit(handle[0])
candidates.append(handle)
# Perform unfolding
tag = ntags()
mapper = {}
for tree in candidates:
trees = list(zip(*[i.unfold() for i in tree]))
# Update tag
for i, _tree in enumerate(list(trees)):
trees[i] = tuple(j.retag(tag + i) for j in _tree)
trees = optimize_unfolded_tree(trees[:-1], trees[-1])
mapper[tree[0]] = List(body=trees)
# Insert the unfolded Iterations in the Iteration/Expression tree
processed = Transformer(mapper).visit(node)
return processed
def _ompize(self, state, **kwargs):
"""
Add OpenMP pragmas to the Iteration/Expression tree to emit parallel code
"""
processed = []
for node in state.nodes:
# Reset denormals flag each time a parallel region is entered
denormals = FindNodes(Denormals).visit(state.nodes)
mapper = {
i: List(c.Comment('DLE: moved denormals flag'))
for i in denormals
}
# Handle parallelizable loops
for tree in retrieve_iteration_tree(node):
# Determine the number of consecutive parallelizable Iterations
key = lambda i: i.is_Parallel and not i.is_Vectorizable
candidates = filter_iterations(tree,
key=key,
stop='consecutive')
if not candidates:
continue
# Heuristic: if at least two parallel loops are available and the
# physical core count is greater than self.thresholds['collapse'],
# then omp-collapse the loops
nparallel = len(candidates)
if psutil.cpu_count(logical=False) < self.thresholds['collapse'] or\
nparallel < 2:
parallelism = omplang['for']
else:
parallelism = omplang['collapse'](nparallel)
root = candidates[0]
mapper[root] = Block(header=omplang['par-region'],
body=denormals +
[Element(parallelism), root])
processed.append(Transformer(mapper).visit(node))
return {'nodes': processed}
def test_create_elemental_functions_simple(simple_function):
roots = [i[-1] for i in retrieve_iteration_tree(simple_function)]
retagged = [i._rebuild(properties=tagger(0)) for i in roots]
mapper = {i: j._rebuild(properties=(j.properties + (ELEMENTAL,)))
for i, j in zip(roots, retagged)}
function = Transformer(mapper).visit(simple_function)
handle = transform(function, mode='split')
block = List(body=handle.nodes + handle.elemental_functions)
output = str(block.ccode)
# Make output compiler independent
output = [i for i in output.split('\n')
if all([j not in i for j in ('#pragma', '/*')])]
assert '\n'.join(output) == \
("""void foo(float *restrict a_vec, float *restrict b_vec,"""
""" float *restrict c_vec, float *restrict d_vec)
{
float (*restrict a) __attribute__((aligned(64))) = (float (*)) a_vec;
float (*restrict b) __attribute__((aligned(64))) = (float (*)) b_vec;
float (*restrict c)[5] __attribute__((aligned(64))) = (float (*)[5]) c_vec;
float (*restrict d)[5][7] __attribute__((aligned(64))) = (float (*)[5][7]) d_vec;
for (int i = 0; i < 3; i += 1)
{
for (int j = 0; j < 5; j += 1)
{
f_0(0,7,(float*)a,(float*)b,(float*)c,(float*)d,i,j);
}
}
}
void f_0(const int k_start, const int k_finish,"""
""" float *restrict a_vec, float *restrict b_vec,"""
""" float *restrict c_vec, float *restrict d_vec, const int i, const int j)
{
float (*restrict a) __attribute__((aligned(64))) = (float (*)) a_vec;
float (*restrict b) __attribute__((aligned(64))) = (float (*)) b_vec;
float (*restrict c)[5] __attribute__((aligned(64))) = (float (*)[5]) c_vec;
float (*restrict d)[5][7] __attribute__((aligned(64))) = (float (*)[5][7]) d_vec;
for (int k = k_start; k < k_finish; k += 1)
{
a[i] = a[i] + b[i] + 5.0F;
a[i] = -a[i]*c[i][j] + b[i]*d[i][j][k];
}
}""")
def test_consistency_coupled_w_ofs(self, exprs, ti0, ti1, ti3):
"""
Test that no matter what is the order in which the equations are
provided to an Operator, the resulting loop nest is the same.
The array accesses in the equations may or may not use offsets;
these impact the loop bounds, but not the resulting tree
structure.
"""
eq1, eq2, eq3 = EVAL(exprs, ti0.base, ti1.base, ti3.base)
op1 = Operator([eq1, eq2, eq3], dse='noop', dle='noop')
op2 = Operator([eq2, eq1, eq3], dse='noop', dle='noop')
op3 = Operator([eq3, eq2, eq1], dse='noop', dle='noop')
trees = [retrieve_iteration_tree(i) for i in [op1, op2, op3]]
assert all(len(i) == 1 for i in trees)
trees = [i[0] for i in trees]
for tree in trees:
assert IsPerfectIteration().visit(tree[0])
assert len(tree[-1].nodes) == 3
pivot = set([j.expr for j in trees[0][-1].nodes])
assert all(set([j.expr for j in i[-1].nodes]) == pivot for i in trees)
def test_consistency_coupled_wo_ofs(self, tu, tv, ti0, t0, t1):
"""
Test that no matter what is the order in which the equations are
provided to an Operator, the resulting loop nest is the same.
None of the array accesses in the equations use offsets.
"""
eq1 = Eq(tu, tv*ti0*t0 + ti0*t1)
eq2 = Eq(ti0, tu + t0*3.)
eq3 = Eq(tv, ti0*tu)
op1 = Operator([eq1, eq2, eq3], dse='noop', dle='noop')
op2 = Operator([eq2, eq1, eq3], dse='noop', dle='noop')
op3 = Operator([eq3, eq2, eq1], dse='noop', dle='noop')
trees = [retrieve_iteration_tree(i) for i in [op1, op2, op3]]
assert all(len(i) == 1 for i in trees)
trees = [i[0] for i in trees]
for tree in trees:
assert IsPerfectIteration().visit(tree[0])
assert len(tree[-1].nodes) == 3
pivot = set([j.expr for j in trees[0][-1].nodes])
assert all(set([j.expr for j in i[-1].nodes]) == pivot for i in trees)
def _loop_fission(self, state, **kwargs):
"""
Apply loop fission to innermost :class:`Iteration` objects. This pass
is not applied if the number of statements in an Iteration's body is
lower than ``self.thresholds['fission'].``
"""
processed = []
for node in state.nodes:
mapper = {}
for tree in retrieve_iteration_tree(node):
if len(tree) <= 1:
# Heuristically avoided
continue
candidate = tree[-1]
expressions = [e for e in candidate.nodes if e.is_Expression]
if len(expressions) < self.thresholds['max_fission']:
# Heuristically avoided
continue
if len(expressions) != len(candidate.nodes):
# Dangerous for correctness
continue
functions = list(
set.union(*[set(e.functions) for e in expressions]))
wrapped = [e.expr for e in expressions]
if not functions or not wrapped:
# Heuristically avoided
continue
# Promote temporaries from scalar to tensors
handle = functions[0]
dim = handle.indices[-1]
size = handle.shape[-1]
if any(dim != i.indices[-1] for i in functions):
# Dangerous for correctness
continue
wrapped = promote_scalar_expressions(wrapped, (size, ),
(dim, ), True)
assert len(wrapped) == len(expressions)
rebuilt = [
Expression(s, e.dtype)
for s, e in zip(wrapped, expressions)
]
# Group statements
# TODO: Need a heuristic here to maximize reuse
args_frozen = candidate.args_frozen
properties = as_tuple(
args_frozen['properties']) + (ELEMENTAL, )
args_frozen['properties'] = properties
n = self.thresholds['min_fission']
fissioned = [
Iteration(g, **args_frozen) for g in grouper(rebuilt, n)
]
mapper[candidate] = List(body=fissioned)
processed.append(Transformer(mapper).visit(node))
return {'nodes': processed}
def _minimize_remainders(self, state, **kwargs):
"""
Reshape temporary tensors and adjust loop trip counts to prevent as many
compiler-generated remainder loops as possible.
"""
mapper = {}
for tree in retrieve_iteration_tree(state.nodes +
state.elemental_functions):
vector_iterations = [i for i in tree if i.is_Vectorizable]
if not vector_iterations:
continue
assert len(vector_iterations) == 1
root = vector_iterations[0]
if root.tag is None:
continue
# Padding
writes = [
i for i in FindSymbols('symbolics-writes').visit(root)
if i.is_TensorFunction
]
padding = []
for i in writes:
try:
simd_items = get_simd_items(i.dtype)
except KeyError:
# Fallback to 16 (maximum expectable padding, for AVX512 registers)
simd_items = simdinfo['avx512f'] / np.dtype(
i.dtype).itemsize
padding.append(simd_items - i.shape[-1] % simd_items)
if len(set(padding)) == 1:
padding = padding[0]
for i in writes:
i.update(shape=i.shape[:-1] + (i.shape[-1] + padding, ))
else:
# Padding must be uniform -- not the case, so giving up
continue
# Dynamic trip count adjustment
endpoint = root.end_symbolic
if not endpoint.is_Symbol:
continue
condition = []
externals = set(i.symbolic_shape[-1]
for i in FindSymbols().visit(root))
for i in root.uindices:
for j in externals:
condition.append(root.end_symbolic + padding < j)
condition = ' || '.join(ccode(i) for i in condition)
endpoint_padded = endpoint.func(name='_%s' % endpoint.name)
init = cgen.Initializer(
cgen.Value("const int", endpoint_padded),
cgen.Line('(%s) ? %s : %s' %
(condition, ccode(endpoint + padding), endpoint)))
# Update the Iteration bound
limits = list(root.limits)
limits[1] = endpoint_padded.func(endpoint_padded.name)
rebuilt = list(tree)
rebuilt[rebuilt.index(root)] = root._rebuild(limits=limits)
mapper[tree[0]] = List(header=init, body=compose_nodes(rebuilt))
nodes = Transformer(mapper).visit(state.nodes)
elemental_functions = Transformer(mapper).visit(
state.elemental_functions)
return {'nodes': nodes, 'elemental_functions': elemental_functions}
def _ompize(self, state, **kwargs):
"""
Add OpenMP pragmas to the Iteration/Expression tree to emit parallel code
"""
processed = []
for node in state.nodes:
# Reset denormals flag each time a parallel region is entered
denormals = FindNodes(Denormals).visit(state.nodes)
mapper = OrderedDict([(i, None) for i in denormals])
# Group by outer loop so that we can embed within the same parallel region
was_tagged = False
groups = OrderedDict()
for tree in retrieve_iteration_tree(node):
# Determine the number of consecutive parallelizable Iterations
key = lambda i: i.is_Parallel and\
not (i.is_Elementizable or i.is_Vectorizable)
candidates = filter_iterations(tree, key=key, stop='asap')
if not candidates:
was_tagged = False
continue
# Consecutive tagged Iteration go in the same group
is_tagged = any(i.tag is not None for i in tree)
key = len(groups) - (is_tagged & was_tagged)
handle = groups.setdefault(key, OrderedDict())
handle[candidates[0]] = candidates
was_tagged = is_tagged
# Handle parallelizable loops
for group in groups.values():
private = []
for root, tree in group.items():
# Heuristic: if at least two parallel loops are available and the
# physical core count is greater than self.thresholds['collapse'],
# then omp-collapse the loops
nparallel = len(tree)
if psutil.cpu_count(logical=False) < self.thresholds['collapse'] or\
nparallel < 2:
parallel = omplang['for']
else:
parallel = omplang['collapse'](nparallel)
mapper[root] = root._rebuild(pragmas=root.pragmas +
(parallel, ))
# Track the thread-private and thread-shared variables
private.extend([
i for i in FindSymbols('symbolics').visit(root)
if i.is_TensorFunction and i._mem_stack
])
# Build the parallel region
private = sorted(set([i.name for i in private]))
private = ('private(%s)' %
','.join(private)) if private else ''
rebuilt = [v for k, v in mapper.items() if k in group]
par_region = Block(header=omplang['par-region'](private),
body=denormals + rebuilt)
for k, v in list(mapper.items()):
if isinstance(v, Iteration):
mapper[k] = None if v.is_Remainder else par_region
handle = Transformer(mapper).visit(node)
if handle is not None:
processed.append(handle)
return {'nodes': processed}
def _loop_blocking(self, state, **kwargs):
"""
Apply loop blocking to :class:`Iteration` trees.
Blocking is applied to parallel iteration trees. Heuristically, innermost
dimensions are not blocked to maximize the trip count of the SIMD loops.
Different heuristics may be specified by passing the keywords ``blockshape``
and ``blockinner`` to the DLE. The former, a dictionary, is used to indicate
a specific block size for each blocked dimension. For example, for the
:class:`Iteration` tree: ::
for i
for j
for k
...
one may provide ``blockshape = {i: 4, j: 7}``, in which case the
two outer loops will blocked, and the resulting 2-dimensional block will
have size 4x7. The latter may be set to True to also block innermost parallel
:class:`Iteration` objects.
"""
exclude_innermost = not self.params.get('blockinner', False)
ignore_heuristic = self.params.get('blockalways', False)
blocked = OrderedDict()
processed = []
for node in state.nodes:
# Make sure loop blocking will span as many Iterations as possible
fold = fold_blockable_tree(node, exclude_innermost)
mapper = {}
for tree in retrieve_iteration_tree(fold):
# Is the Iteration tree blockable ?
iterations = [i for i in tree if i.is_Parallel]
if exclude_innermost:
iterations = [
i for i in iterations if not i.is_Vectorizable
]
if len(iterations) <= 1:
continue
root = iterations[0]
if not IsPerfectIteration().visit(root):
# Illegal/unsupported
continue
if not tree[0].is_Sequential and not ignore_heuristic:
# Heuristic: avoid polluting the generated code with blocked
# nests (thus increasing JIT compilation time and affecting
# readability) if the blockable tree isn't embedded in a
# sequential loop (e.g., a timestepping loop)
continue
# Decorate intra-block iterations with an IterationProperty
TAG = tagger(len(mapper))
# Build all necessary Iteration objects, individually. These will
# subsequently be composed to implement loop blocking.
inter_blocks = []
intra_blocks = []
remainders = []
for i in iterations:
# Build Iteration over blocks
dim = blocked.setdefault(
i, Dimension("%s_block" % i.dim.name))
block_size = dim.symbolic_size
iter_size = i.dim.size or i.dim.symbolic_size
start = i.limits[0] - i.offsets[0]
finish = iter_size - i.offsets[1]
innersize = iter_size - (-i.offsets[0] + i.offsets[1])
finish = finish - (innersize % block_size)
inter_block = Iteration([],
dim, [start, finish, block_size],
properties=PARALLEL)
inter_blocks.append(inter_block)
# Build Iteration within a block
start = inter_block.dim
finish = start + block_size
intra_block = i._rebuild([],
limits=[start, finish, 1],
offsets=None,
properties=i.properties +
(TAG, ELEMENTAL))
intra_blocks.append(intra_block)
# Build unitary-increment Iteration over the 'leftover' region.
# This will be used for remainder loops, executed when any
# dimension size is not a multiple of the block size.
start = inter_block.limits[1]
finish = iter_size - i.offsets[1]
remainder = i._rebuild([],
limits=[start, finish, 1],
offsets=None)
remainders.append(remainder)
# Build blocked Iteration nest
blocked_tree = compose_nodes(inter_blocks + intra_blocks +
[iterations[-1].nodes])
# Build remainder Iterations
remainder_trees = []
for n in range(len(iterations)):
for c in combinations([i.dim for i in iterations], n + 1):
# First all inter-block Interations
nodes = [
b._rebuild(properties=b.properties + (REMAINDER, ))
for b, r in zip(inter_blocks, remainders)
if r.dim not in c
]
# Then intra-block or remainder, for each dim (in order)
properties = (REMAINDER, TAG, ELEMENTAL)
for b, r in zip(intra_blocks, remainders):
handle = r if b.dim in c else b
nodes.append(
handle._rebuild(properties=properties))
nodes.extend([iterations[-1].nodes])
remainder_trees.append(compose_nodes(nodes))
# Will replace with blocked loop tree
mapper[root] = List(body=[blocked_tree] + remainder_trees)
rebuilt = Transformer(mapper).visit(fold)
# Finish unrolling any previously folded Iterations
processed.append(unfold_blocked_tree(rebuilt))
# All blocked dimensions
if not blocked:
return {'nodes': processed}
# Determine the block shape
blockshape = self.params.get('blockshape')
if not blockshape:
# Use trivial heuristic for a suitable blockshape
def heuristic(dim_size):
ths = 8 # FIXME: This really needs to be improved
return ths if dim_size > ths else 1
blockshape = {k: heuristic for k in blocked.keys()}
else:
try:
nitems, nrequired = len(blockshape), len(blocked)
blockshape = {k: v for k, v in zip(blocked, blockshape)}
if nitems > nrequired:
dle_warning("Provided 'blockshape' has more entries than "
"blocked loops; dropping entries ...")
if nitems < nrequired:
dle_warning("Provided 'blockshape' has fewer entries than "
"blocked loops; dropping dimensions ...")
except TypeError:
blockshape = {list(blocked)[0]: blockshape}
blockshape.update(
{k: None
for k in blocked.keys() if k not in blockshape})
# Track any additional arguments required to execute /state.nodes/
arguments = [
BlockingArg(v, k, blockshape[k]) for k, v in blocked.items()
]
return {
'nodes': processed,
'arguments': arguments,
'flags': 'blocking'
}
def _specialize(self, nodes, parameters):
"""
Create a YASK representation of this Iteration/Expression tree.
``parameters`` is modified in-place adding YASK-related arguments.
"""
log("Specializing a Devito Operator for YASK...")
# Find offloadable Iteration/Expression trees
offloadable = []
for tree in retrieve_iteration_tree(nodes):
parallel = filter_iterations(tree, lambda i: i.is_Parallel)
if not parallel:
# Cannot offload non-parallel loops
continue
if not (IsPerfectIteration().visit(tree)
and all(i.is_Expression for i in tree[-1].nodes)):
# Don't know how to offload this Iteration/Expression to YASK
continue
functions = flatten(i.functions for i in tree[-1].nodes)
keys = set((i.indices, i.shape, i.dtype) for i in functions
if i.is_TimeData)
if len(keys) == 0:
continue
elif len(keys) > 1:
exit("Cannot handle Operators w/ heterogeneous grids")
dimensions, shape, dtype = keys.pop()
if len(dimensions) == len(tree) and\
all(i.dim == j for i, j in zip(tree, dimensions)):
# Detected a "full" Iteration/Expression tree (over both
# time and space dimensions)
offloadable.append((tree, dimensions, shape, dtype))
# Construct YASK ASTs given Devito expressions. New grids may be allocated.
if len(offloadable) == 0:
# No offloadable trees found
self.context = YaskNullContext()
self.yk_soln = YaskNullSolution()
processed = nodes
log("No offloadable trees found")
elif len(offloadable) == 1:
# Found *the* offloadable tree for this Operator
tree, dimensions, shape, dtype = offloadable[0]
self.context = contexts.fetch(dimensions, shape, dtype)
# Create a YASK compiler solution for this Operator
# Note: this can be dropped as soon as the kernel has been built
yc_soln = self.context.make_yc_solution(namespace['jit-yc-soln'])
transform = sympy2yask(self.context, yc_soln)
try:
for i in tree[-1].nodes:
transform(i.expr)
funcall = make_sharedptr_funcall(namespace['code-soln-run'],
['time'],
namespace['code-soln-name'])
funcall = Element(c.Statement(ccode(funcall)))
processed = Transformer({tree[1]: funcall}).visit(nodes)
# Track this is an external function call
self.func_table[namespace['code-soln-run']] = FunMeta(
None, False)
# JIT-compile the newly-created YASK kernel
self.yk_soln = self.context.make_yk_solution(
namespace['jit-yk-soln'], yc_soln)
# Now we must drop a pointer to the YASK solution down to C-land
parameters.append(
Object(namespace['code-soln-name'],
namespace['type-solution'],
self.yk_soln.rawpointer))
# Print some useful information about the newly constructed solution
log("Solution '%s' contains %d grid(s) and %d equation(s)." %
(yc_soln.get_name(), yc_soln.get_num_grids(),
yc_soln.get_num_equations()))
except:
self.yk_soln = YaskNullSolution()
processed = nodes
log("Unable to offload a candidate tree.")
else:
exit("Found more than one offloadable trees in a single Operator")
# Some Iteration/Expression trees are not offloaded to YASK and may
# require further processing to be executed in YASK, due to the differences
# in storage layout employed by Devito and YASK
processed = make_grid_accesses(processed)
# Update the parameters list adding all necessary YASK grids
for i in list(parameters):
try:
if i.from_YASK:
parameters.append(
Object(namespace['code-grid-name'](i.name),
namespace['type-grid'], i.data.rawpointer))
except AttributeError:
# Ignore e.g. Dimensions
pass
log("Specialization successfully performed!")
return processed
def _create_elemental_functions(self, state, **kwargs):
"""
Extract :class:`Iteration` sub-trees and move them into :class:`Function`s.
Currently, only tagged, elementizable Iteration objects are targeted.
"""
noinline = self._compiler_decoration('noinline',
c.Comment('noinline?'))
functions = OrderedDict()
processed = []
for node in state.nodes:
mapper = {}
for tree in retrieve_iteration_tree(node, mode='superset'):
# Search an elementizable sub-tree (if any)
tagged = filter_iterations(tree, lambda i: i.tag is not None,
'asap')
if not tagged:
continue
root = tagged[0]
if not root.is_Elementizable:
continue
target = tree[tree.index(root):]
# Elemental function arguments
args = [] # Found so far (scalars, tensors)
maybe_required = set(
) # Scalars that *may* have to be passed in
not_required = set(
) # Elemental function locally declared scalars
# Build a new Iteration/Expression tree with free bounds
free = []
for i in target:
name, bounds = i.dim.name, i.bounds_symbolic
# Iteration bounds
start = ScalarFunction(name='%s_start' % name,
dtype=np.int32)
finish = ScalarFunction(name='%s_finish' % name,
dtype=np.int32)
args.extend(
zip([ccode(j) for j in bounds], (start, finish)))
# Iteration unbounded indices
ufunc = [
ScalarFunction(name='%s_ub%d' % (name, j),
dtype=np.int32)
for j in range(len(i.uindices))
]
args.extend(
zip([ccode(j.start) for j in i.uindices], ufunc))
limits = [Symbol(start.name), Symbol(finish.name), 1]
uindices = [
UnboundedIndex(j.index, i.dim + as_symbol(k))
for j, k in zip(i.uindices, ufunc)
]
free.append(
i._rebuild(limits=limits,
offsets=None,
uindices=uindices))
not_required.update({i.dim},
set(j.index for j in i.uindices))
# Construct elemental function body, and inspect it
free = NestedTransformer(dict((zip(target, free)))).visit(root)
expressions = FindNodes(Expression).visit(free)
fsymbols = FindSymbols('symbolics').visit(free)
# Retrieve symbolic arguments
for i in fsymbols:
if i.is_TensorFunction:
args.append(
("(%s*)%s" % (c.dtype_to_ctype(i.dtype), i.name),
i))
elif i.is_TensorData:
args.append(("%s_vec" % i.name, i))
elif i.is_ConstantData:
args.append((i.name, i))
# Retrieve scalar arguments
not_required.update(
{i.output
for i in expressions if i.is_scalar})
maybe_required.update(
set(FindSymbols(mode='free-symbols').visit(free)))
for i in fsymbols:
not_required.update({as_symbol(i), i.indexify()})
for j in i.symbolic_shape:
maybe_required.update(j.free_symbols)
required = filter_sorted(maybe_required - not_required,
key=attrgetter('name'))
args.extend([(i.name,
ScalarFunction(name=i.name, dtype=np.int32))
for i in required])
call, params = zip(*args)
handle = flatten([p.rtargs for p in params])
name = "f_%d" % root.tag
# Produce the new FunCall
mapper[root] = List(header=noinline, body=FunCall(name, call))
# Produce the new Function
functions.setdefault(
name, Function(name, free, 'void', handle, ('static', )))
# Transform the main tree
processed.append(Transformer(mapper).visit(node))
return {'nodes': processed, 'elemental_functions': functions.values()}
def _loop_blocking(self, state, **kwargs):
"""
Apply loop blocking to :class:`Iteration` trees.
By default, the blocked :class:`Iteration` objects and the block size are
determined heuristically. The heuristic consists of searching the deepest
Iteration/Expression tree and blocking all dimensions except:
* The innermost (eg, to retain SIMD vectorization);
* Those dimensions inducing loop-carried dependencies.
The caller may take over the heuristic through ``kwargs['blocking']``,
a dictionary indicating the block size of each blocked dimension. For
example, for the :class:`Iteration` tree below: ::
for i
for j
for k
...
one may pass in ``kwargs['blocking'] = {i: 4, j: 7}``, in which case the
two outer loops would be blocked, and the resulting 2-dimensional block
would be of size 4x7.
"""
Region = namedtuple('Region', 'main leftover')
blocked = OrderedDict()
processed = []
for node in state.nodes:
mapper = {}
for tree in retrieve_iteration_tree(node):
# Is the Iteration tree blockable ?
iterations = [i for i in tree if i.is_Parallel]
if 'blockinner' not in self.params:
iterations = [
i for i in iterations if not i.is_Vectorizable
]
if not iterations:
continue
root = iterations[0]
if not IsPerfectIteration().visit(root):
continue
# Construct the blocked loop nest, as well as all necessary
# remainder loops
regions = OrderedDict()
blocked_iterations = []
for i in iterations:
# Build Iteration over blocks
dim = blocked.setdefault(
i, Dimension("%s_block" % i.dim.name))
block_size = dim.symbolic_size
iter_size = i.dim.size or i.dim.symbolic_size
start = i.limits[0] - i.offsets[0]
finish = iter_size - i.offsets[1]
finish = finish - ((finish - i.offsets[1]) % block_size)
inter_block = Iteration([],
dim, [start, finish, block_size],
properties=as_tuple('parallel'))
# Build Iteration within a block
start = inter_block.dim
finish = start + block_size
properties = 'vector-dim' if i.is_Vectorizable else None
intra_block = Iteration([],
i.dim, [start, finish, 1],
i.index,
properties=as_tuple(properties))
blocked_iterations.append((inter_block, intra_block))
# Build unitary-increment Iteration over the 'main' region
# (the one blocked); necessary to generate code iterating over
# non-blocked ("remainder") iterations.
start = inter_block.limits[0]
finish = inter_block.limits[1]
main = Iteration([],
i.dim, [start, finish, 1],
i.index,
properties=i.properties)
# Build unitary-increment Iteration over the 'leftover' region:
# again as above, this may be necessary when the dimension size
# is not a multiple of the block size.
start = inter_block.limits[1]
finish = iter_size - i.offsets[1]
leftover = Iteration([],
i.dim, [start, finish, 1],
i.index,
properties=i.properties)
regions[i] = Region(main, leftover)
blocked_tree = list(flatten(zip(*blocked_iterations)))
blocked_tree = compose_nodes(blocked_tree +
[iterations[-1].nodes])
# Build remainder loops
remainder_tree = []
for n in range(len(iterations)):
for i in combinations(iterations, n + 1):
nodes = [
v.leftover if k in i else v.main
for k, v in regions.items()
]
nodes += [iterations[-1].nodes]
remainder_tree.append(compose_nodes(nodes))
# Will replace with blocked loop tree
mapper[root] = List(body=[blocked_tree] + remainder_tree)
rebuilt = Transformer(mapper).visit(node)
processed.append(rebuilt)
# All blocked dimensions
if not blocked:
return {'nodes': processed}
# Determine the block shape
blockshape = self.params.get('blockshape')
if not blockshape:
# Use trivial heuristic for a suitable blockshape
def heuristic(dim_size):
ths = 8 # FIXME: This really needs to be improved
return ths if dim_size > ths else 1
blockshape = {k: heuristic for k in blocked.keys()}
else:
try:
nitems, nrequired = len(blockshape), len(blocked)
blockshape = {k: v for k, v in zip(blocked, blockshape)}
if nitems > nrequired:
dle_warning("Provided 'blockshape' has more entries than "
"blocked loops; dropping entries ...")
if nitems < nrequired:
dle_warning("Provided 'blockshape' has fewer entries than "
"blocked loops; dropping dimensions ...")
except TypeError:
blockshape = {list(blocked)[0]: blockshape}
blockshape.update(
{k: None
for k in blocked.keys() if k not in blockshape})
# Track any additional arguments required to execute /state.nodes/
arguments = [
BlockingArg(v, k, blockshape[k]) for k, v in blocked.items()
]
return {
'nodes': processed,
'arguments': arguments,
'flags': 'blocking'
}
