def _schedule_expressions(self, clusters):
"""Wrap :class:`Expression` objects, already grouped in :class:`Cluster`
objects, within nested :class:`Iteration` objects (representing loops),
according to dimensions and stencils."""
# Topologically sort Iterations
ordering = partial_order([i.stencil.dimensions for i in clusters])
for i, d in enumerate(list(ordering)):
if d.is_Buffered:
ordering.insert(i, d.parent)
# Build the Iteration/Expression tree
processed = []
schedule = OrderedDict()
atomics = ()
for i in clusters:
# Build the Expression objects to be inserted within an Iteration tree
expressions = [Expression(v, np.int32 if i.trace.is_index(k) else self.dtype)
for k, v in i.trace.items()]
if not i.stencil.empty:
root = None
entries = i.stencil.entries
# Reorder based on the globally-established loop ordering
entries = sorted(entries, key=lambda i: ordering.index(i.dim))
# Can I reuse any of the previously scheduled Iterations ?
index = 0
for j0, j1 in zip(entries, list(schedule)):
if j0 != j1 or j0.dim in atomics:
break
root = schedule[j1]
index += 1
needed = entries[index:]
# Build and insert the required Iterations
iters = [Iteration([], j.dim, j.dim.size, offsets=j.ofs) for j in needed]
body, tree = compose_nodes(iters + [expressions], retrieve=True)
scheduling = OrderedDict(zip(needed, tree))
if root is None:
processed.append(body)
schedule = scheduling
else:
nodes = list(root.nodes) + [body]
mapper = {root: root._rebuild(nodes, **root.args_frozen)}
transformer = Transformer(mapper)
processed = list(transformer.visit(processed))
schedule = OrderedDict(list(schedule.items())[:index] +
list(scheduling.items()))
for k, v in list(schedule.items()):
schedule[k] = transformer.rebuilt.get(v, v)
else:
# No Iterations are needed
processed.extend(expressions)
# Track dimensions that cannot be fused at next stage
atomics = i.atomics
return List(body=processed)
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 _insert_declarations(self, nodes):
"""Populate the Operator's body with the required array and variable
declarations, to generate a legal C file."""
# Resolve function calls first
scopes = []
for k, v in FindScopes().visit(nodes).items():
if k.is_FunCall:
func = self.func_table[k.name]
if func.local:
scopes.extend(FindScopes().visit(func.root,
queue=list(v)).items())
else:
scopes.append((k, v))
# Determine all required declarations
allocator = Allocator()
mapper = OrderedDict()
for k, v in scopes:
if k.is_scalar:
# Inline declaration
mapper[k] = LocalExpression(**k.args)
elif k.output_function._mem_external:
# Nothing to do, variable passed as kernel argument
continue
elif k.output_function._mem_stack:
# On the stack, as established by the DLE
key = lambda i: not i.is_Parallel
site = filter_iterations(v, key=key, stop='asap') or [nodes]
allocator.push_stack(site[-1], k.output_function)
else:
# On the heap, as a tensor that must be globally accessible
allocator.push_heap(k.output_function)
# Introduce declarations on the stack
for k, v in allocator.onstack:
mapper[k] = tuple(Element(i) for i in v)
nodes = NestedTransformer(mapper).visit(nodes)
for k, v in list(self.func_table.items()):
if v.local:
self.func_table[k] = FunMeta(
Transformer(mapper).visit(v.root), v.local)
# Introduce declarations on the heap (if any)
if allocator.onheap:
decls, allocs, frees = zip(*allocator.onheap)
nodes = List(header=decls + allocs, body=nodes, footer=frees)
return nodes
def _insert_declarations(self, dle_state, parameters):
"""Populate the Operator's body with the required array and
variable declarations, to generate a legal C file."""
nodes = dle_state.nodes
# Resolve function calls first
scopes = []
for k, v in FindScopes().visit(nodes).items():
if k.is_FunCall:
function = dle_state.func_table[k.name]
scopes.extend(FindScopes().visit(function,
queue=list(v)).items())
else:
scopes.append((k, v))
# Determine all required declarations
allocator = Allocator()
mapper = OrderedDict()
for k, v in scopes:
if k.is_scalar:
# Inline declaration
mapper[k] = LocalExpression(**k.args)
elif k.output_function._mem_external:
# Nothing to do, variable passed as kernel argument
continue
elif k.output_function._mem_stack:
# On the stack, as established by the DLE
key = lambda i: i.dim not in k.output_function.indices
site = filter_iterations(v, key=key, stop='consecutive')
allocator.push_stack(site[-1], k.output_function)
else:
# On the heap, as a tensor that must be globally accessible
allocator.push_heap(k.output_function)
# Introduce declarations on the stack
for k, v in allocator.onstack:
allocs = as_tuple([Element(i) for i in v])
mapper[k] = Iteration(allocs + k.nodes, **k.args_frozen)
nodes = Transformer(mapper).visit(nodes)
elemental_functions = Transformer(mapper).visit(
dle_state.elemental_functions)
# Introduce declarations on the heap (if any)
if allocator.onheap:
decls, allocs, frees = zip(*allocator.onheap)
nodes = List(header=decls + allocs, body=nodes, footer=frees)
return nodes, elemental_functions
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_create_elemental_functions_simple(simple_function):
old = Rewriter.thresholds['elemental']
Rewriter.thresholds['elemental'] = 0
handle = transform(simple_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((float*) a,(float*) b,(float*) c,(float*) d,i,j);
}
}
}
void f_0_0(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 = 0; k < 7; k += 1)
{
a[i] = a[i] + b[i] + 5.0F;
a[i] = -a[i]*c[i][j] + b[i]*d[i][j][k];
}
}""")
Rewriter.thresholds['elemental'] = old
def visit_Iteration(self, o, subs={}, offsets=defaultdict(set)):
nodes = self.visit(o.children, subs=subs, offsets=offsets)
if o.dim.is_Buffered:
# For buffered dimensions insert the explicit
# definition of buffered variables, eg. t+1 => t1
init = []
for i, off in enumerate(filter_ordered(offsets[o.dim])):
vname = "%s%d" % (o.dim.name, i)
value = o.dim.parent + off
modulo = o.dim.modulo
init += [
c.Initializer(c.Value('int', vname),
"(%s) %% %d" % (value, modulo))
]
subs[o.dim + off] = LoweredDimension(vname, o.dim, off)
# Always lower to symbol
subs[o.dim.parent] = Symbol(o.dim.parent.name)
# Insert block with modulo initialisations
newnodes = (List(header=init, body=nodes[0]), )
return o._rebuild(newnodes, index=o.dim.parent.name)
else:
return o._rebuild(*nodes)
def compose_nodes(nodes, retrieve=False):
"""
Build an Iteration/Expression tree by nesting the nodes in ``nodes``.
"""
l = list(nodes)
tree = []
if not isinstance(l[0], Iteration):
# Nothing to compose
body = List(body=flatten(l))
else:
body = l.pop(-1)
while l:
handle = l.pop(-1)
body = handle._rebuild(body, **handle.args_frozen)
tree.append(body)
if retrieve is True:
tree = list(reversed(tree))
return body, tree
else:
return body
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 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.shape[-1] % get_simd_items(j.dtype) == 0
]
except KeyError:
aligned = []
if aligned:
simd = omplang['simd-for-aligned']
simd = simd(','.join([j.name for j in aligned]),
simdinfo[get_simd_flag()])
else:
simd = omplang['simd-for']
mapper[i] = List(ignore_deps + as_tuple(simd), i)
processed.append(Transformer(mapper).visit(node))
return processed
def _profile_sections(self, nodes):
"""Introduce C-level profiling nodes within the Iteration/Expression tree."""
mapper = {}
for node in nodes:
for itspace in FindSections().visit(node).keys():
for i in itspace:
if IsPerfectIteration().visit(i):
# Insert `TimedList` block. This should come from
# the profiler, but we do this manually for now.
lname = 'loop_%s_%d' % (i.index, len(mapper))
mapper[i] = TimedList(gname=self.profiler.varname,
lname=lname,
body=i)
self.profiler.add(lname)
# Estimate computational properties of the timed section
# (operational intensity, memory accesses)
expressions = FindNodes(Expression).visit(i)
ops = estimate_cost([e.expr for e in expressions])
memory = estimate_memory([e.expr for e in expressions])
self.sections[itspace] = Profile(lname, ops, memory)
break
processed = Transformer(mapper).visit(List(body=nodes))
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'
}
def _profile_sections(self, nodes):
"""Introduce C-level profiling nodes within the Iteration/Expression tree."""
return List(body=nodes)
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 _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 _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}