def fold_blockable_tree(iet, blockinner=True):
"""
Create IterationFolds from sequences of nested Iterations.
"""
mapper = {}
for k, sequence in FindAdjacent(Iteration).visit(iet).items():
# Group based on Dimension
groups = []
for subsequence in sequence:
for _, v in groupby(subsequence, lambda i: i.dim):
i = list(v)
if len(i) >= 2:
groups.append(i)
for i in groups:
# Pre-condition: they all must be perfect iterations
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 blockinner is False:
pairwise_folds = pairwise_folds[:-1]
# Perhaps there's nothing to fold
if len(pairwise_folds) == 0:
continue
# TODO: we do not currently support blocking if any of the foldable
# iterations writes to user data (need min/max loop bounds?)
exprs = flatten(FindNodes(Expression).visit(j.root) for j in trees[:-1])
if any(j.write.is_Input for j in exprs):
continue
# Perform folding
for j in pairwise_folds:
r, remainder = j[0], j[1:]
folds = [(tuple(y-x for x, y in zip(i.offsets, r.offsets)), i.nodes)
for i in remainder]
mapper[r] = IterationFold(folds=folds, **r.args)
for k in remainder:
mapper[k] = None
# Insert the IterationFolds in the Iteration/Expression tree
iet = Transformer(mapper, nested=True).visit(iet)
return iet
def fold_blockable_tree(node, exclude_innermost=False):
"""
Create IterationFolds from sequences of nested Iterations.
"""
found = FindAdjacent(Iteration).visit(node)
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
# TODO: we do not currently support blocking if any of the foldable
# iterations writes to user data (need min/max loop bounds?)
exprs = flatten(
FindNodes(Expression).visit(j.root) for j in trees[:-1])
if any(j.write.is_Input for j in exprs):
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 = Transformer(mapper, nested=True).visit(node)
return processed
def test_is_perfect_iteration(block1, block2, block3):
checker = IsPerfectIteration()
assert checker.visit(block1) is True
assert checker.visit(block1.nodes[0]) is True
assert checker.visit(block1.nodes[0].nodes[0]) is True
assert checker.visit(block2) is False
assert checker.visit(block2.nodes[1]) is True
assert checker.visit(block2.nodes[1].nodes[0]) is True
assert checker.visit(block3) is False
assert checker.visit(block3.nodes[0]) is True
assert checker.visit(block3.nodes[1]) is True
assert checker.visit(block3.nodes[2]) is True
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 unfold_blocked_tree(node):
"""
Unfold nested IterationFolds.
Examples
--------
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 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])
exprs = FindNodes(Expression).visit(tree[-1])
assert len(exprs) == 3
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])
exprs = FindNodes(Expression).visit(tree[-1])
assert len(exprs) == 3
def _ncollapse(self, root, candidates):
# The OpenMP specification forbids collapsed loops to use iteration variables
# in initializer expressions. For example, the following is forbidden:
#
# #pragma omp ... collapse(2)
# for (int i = ... )
# for (int j = i ...)
# ...
#
# Below, we make sure this won't happen
for n, i in enumerate(candidates):
if any(j.dim in i.symbolic_min.free_symbols
for j in candidates[:n]):
break
candidates = candidates[:n]
# Heuristic: if at least two parallel loops are available and the
# physical core count is greater than COLLAPSE, then omp-collapse them
nparallel = len(candidates)
isperfect = IsPerfectIteration().visit(root)
if ncores() < Ompizer.COLLAPSE or nparallel < 2 or not isperfect:
return 1
else:
return nparallel
def detect_innermost_unitstride(tree, deps_graph, mapper=None):
"""
Update ``mapper``, a dictionary from :class:`Iteration`s to
:class:`IterationProperty`s, by annotating the innermost Iteration as
vectorizable if all array accesses along its dimension turn out to
be unit-strided.
"""
if mapper is None:
mapper = OrderedDict()
innermost = tree[-1]
if not IsPerfectIteration().visit(innermost):
return mapper
if len(tree) == 1 or SEQUENTIAL in mapper.get(tree[-2], []):
# Heuristic: there should be at least an outer parallel Iteration
# to mark /innermost/ as vectorizable, otherwise it is preferable
# to save it for shared-memory parallelism
return mapper
is_US = True
for k, v in deps_graph.items():
is_US &= all(k.indices[-1] == i.indices[-1] for i in v)
if is_US or PARALLEL in mapper.get(innermost, []):
mapper.setdefault(innermost, []).append(VECTOR)
return mapper
def make_blocking(self, iet):
"""
Apply loop blocking to PARALLEL Iteration trees.
"""
# Make sure loop blocking will span as many Iterations as possible
iet = fold_blockable_tree(iet, self.blockinner)
mapper = {}
efuncs = []
block_dims = []
for tree in retrieve_iteration_tree(iet):
# Is the Iteration tree blockable ?
iterations = filter_iterations(tree, lambda i: i.is_Parallel and i.is_Affine)
if not self.blockinner:
iterations = iterations[:-1]
if len(iterations) <= 1:
continue
root = iterations[0]
if not self.blockalways:
# Heuristically bypass loop blocking if we think `tree`
# won't be computationally expensive. This will help with code
# size/readbility, JIT time, and auto-tuning time
if not (tree.root.is_Sequential or iet.is_Callable):
# E.g., not inside a time-stepping Iteration
continue
if any(i.dim.is_Sub and i.dim.local for i in tree):
# At least an outer Iteration is over a local SubDimension,
# which suggests the computational cost of this Iteration
# nest will be negligible w.r.t. the "core" Iteration nest
# (making use of non-local (Sub)Dimensions only)
continue
if not IsPerfectIteration().visit(root):
# Don't know how to block non-perfect nests
continue
# Apply hierarchical loop blocking to `tree`
level_0 = [] # Outermost level of blocking
level_i = [[] for i in range(1, self.nlevels)] # Inner levels of blocking
intra = [] # Within the smallest block
for i in iterations:
template = "%s%d_blk%s" % (i.dim.name, self.nblocked, '%d')
properties = (PARALLEL,) + ((AFFINE,) if i.is_Affine else ())
# Build Iteration across `level_0` blocks
d = BlockDimension(i.dim, name=template % 0)
level_0.append(Iteration([], d, d.symbolic_max, properties=properties))
# Build Iteration across all `level_i` blocks, `i` in (1, self.nlevels]
for n, li in enumerate(level_i, 1):
di = BlockDimension(d, name=template % n)
li.append(Iteration([], di, limits=(d, d+d.step-1, di.step),
properties=properties))
d = di
# Build Iteration within the smallest block
intra.append(i._rebuild([], limits=(d, d+d.step-1, 1), offsets=(0, 0)))
level_i = flatten(level_i)
# Track all constructed BlockDimensions
block_dims.extend(i.dim for i in level_0 + level_i)
# Construct the blocked tree
blocked = compose_nodes(level_0 + level_i + intra + [iterations[-1].nodes])
blocked = unfold_blocked_tree(blocked)
# Promote to a separate Callable
dynamic_parameters = flatten((l0.dim, l0.step) for l0 in level_0)
dynamic_parameters.extend([li.step for li in level_i])
efunc = make_efunc("bf%d" % self.nblocked, blocked, dynamic_parameters)
efuncs.append(efunc)
# Compute the iteration ranges
ranges = []
for i, l0 in zip(iterations, level_0):
maxb = i.symbolic_max - (i.symbolic_size % l0.step)
ranges.append(((i.symbolic_min, maxb, l0.step),
(maxb + 1, i.symbolic_max, i.symbolic_max - maxb)))
# Build Calls to the `efunc`
body = []
for p in product(*ranges):
dynamic_args_mapper = {}
for l0, (m, M, b) in zip(level_0, p):
dynamic_args_mapper[l0.dim] = (m, M)
dynamic_args_mapper[l0.step] = (b,)
for li in level_i:
if li.dim.root is l0.dim.root:
value = li.step if b is l0.step else b
dynamic_args_mapper[li.step] = (value,)
call = efunc.make_call(dynamic_args_mapper)
body.append(List(body=call))
mapper[root] = List(body=body)
# Next blockable nest, use different (unique) variable/function names
self.nblocked += 1
iet = Transformer(mapper).visit(iet)
# Force-unfold if some folded Iterations haven't been blocked in the end
iet = unfold_blocked_tree(iet)
return iet, {'dimensions': block_dims,
'efuncs': efuncs,
'args': [i.step for i in block_dims]}
def _loop_blocking(self, iet):
"""
Apply loop blocking to PARALLEL Iteration trees.
"""
blockinner = bool(self.params.get('blockinner'))
blockalways = bool(self.params.get('blockalways'))
# Make sure loop blocking will span as many Iterations as possible
iet = fold_blockable_tree(iet, blockinner)
mapper = {}
efuncs = []
block_dims = []
for tree in retrieve_iteration_tree(iet):
# Is the Iteration tree blockable ?
iterations = filter_iterations(tree, lambda i: i.is_Parallel)
if not blockinner:
iterations = iterations[:-1]
if len(iterations) <= 1:
continue
root = iterations[0]
if not blockalways:
# Heuristically bypass loop blocking if we think `tree`
# won't be computationally expensive. This will help with code
# size/redability, JIT time, and auto-tuning time
if not (tree.root.is_Sequential or iet.is_Callable):
# E.g., not inside a time-stepping Iteration
continue
if any(i.dim.is_Sub and i.dim.local for i in tree):
# At least an outer Iteration is over a local SubDimension,
# which suggests the computational cost of this Iteration
# nest will be negligible w.r.t. the "core" Iteration nest
# (making use of non-local (Sub)Dimensions only)
continue
if not IsPerfectIteration().visit(root):
# Don't know how to block non-perfect nests
continue
# Apply loop blocking to `tree`
interb = []
intrab = []
for i in iterations:
d = BlockDimension(i.dim, name="%s%d_blk" % (i.dim.name, len(mapper)))
block_dims.append(d)
# Build Iteration over blocks
properties = (PARALLEL,) + ((AFFINE,) if i.is_Affine else ())
interb.append(Iteration([], d, d.symbolic_max, properties=properties))
# Build Iteration within a block
intrab.append(i._rebuild([], limits=(d, d+d.step-1, 1), offsets=(0, 0)))
# Construct the blocked tree
blocked = compose_nodes(interb + intrab + [iterations[-1].nodes])
blocked = unfold_blocked_tree(blocked)
# Promote to a separate Callable
dynamic_parameters = flatten((bi.dim, bi.dim.symbolic_size) for bi in interb)
efunc = make_efunc("bf%d" % len(mapper), blocked, dynamic_parameters)
efuncs.append(efunc)
# Compute the iteration ranges
ranges = []
for i, bi in zip(iterations, interb):
maxb = i.symbolic_max - (i.symbolic_size % bi.dim.step)
ranges.append(((i.symbolic_min, maxb, bi.dim.step),
(maxb + 1, i.symbolic_max, i.symbolic_max - maxb)))
# Build Calls to the `efunc`
body = []
for p in product(*ranges):
dynamic_args_mapper = {}
for bi, (m, M, b) in zip(interb, p):
dynamic_args_mapper[bi.dim] = (m, M)
dynamic_args_mapper[bi.dim.step] = (b,)
call = efunc.make_call(dynamic_args_mapper)
body.append(List(body=call))
mapper[root] = List(body=body)
iet = Transformer(mapper).visit(iet)
return iet, {'dimensions': block_dims, 'efuncs': efuncs,
'args': [i.step for i in block_dims]}
def _loop_blocking(self, nodes, state):
"""
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)
# Make sure loop blocking will span as many Iterations as possible
fold = fold_blockable_tree(nodes, exclude_innermost)
mapper = {}
blocked = OrderedDict()
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:
name = "%s%d_block" % (i.dim.name, len(mapper))
# Build Iteration over blocks
dim = blocked.setdefault(i, Dimension(name=name))
bsize = dim.symbolic_size
bstart = i.limits[0]
binnersize = i.dim.symbolic_extent + (i.offsets[1] -
i.offsets[0])
bfinish = i.dim.symbolic_end - (binnersize % bsize) - 1
inter_block = Iteration([],
dim, [bstart, bfinish, bsize],
offsets=i.offsets,
properties=PARALLEL)
inter_blocks.append(inter_block)
# Build Iteration within a block
limits = (dim, dim + bsize - 1, 1)
intra_block = i._rebuild([],
limits=limits,
offsets=(0, 0),
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.
remainder = i._rebuild(
[],
limits=[bfinish + 1, i.dim.symbolic_end, 1],
offsets=(i.offsets[1], i.offsets[1]))
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 = unfold_blocked_tree(rebuilt)
# All blocked dimensions
if not blocked:
return 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 processed, {'arguments': arguments, 'flags': 'blocking'}
def _loop_blocking(self, nodes, state):
"""Apply loop blocking to PARALLEL Iteration trees."""
exclude_innermost = not self.params.get('blockinner', False)
ignore_heuristic = self.params.get('blockalways', False)
# Make sure loop blocking will span as many Iterations as possible
fold = fold_blockable_tree(nodes, exclude_innermost)
mapper = {}
blocked = OrderedDict()
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.root.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
name = "%s%d_block" % (i.dim.name, len(mapper))
dim = blocked.setdefault(i, BlockDimension(i.dim, name=name))
binnersize = i.symbolic_size + (i.offsets[1] - i.offsets[0])
bmax = i.dim.symbolic_max - (binnersize % dim.step)
inter_block = Iteration([], dim, bmax, offsets=i.offsets,
properties=PARALLEL)
inter_blocks.append(inter_block)
# Build Iteration within a block
limits = (dim, dim + dim.step - 1, 1)
intra_block = i._rebuild([], limits=limits, offsets=(0, 0),
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.
remainder = i._rebuild([], limits=[bmax + 1, i.dim.symbolic_max, 1],
offsets=(i.offsets[1], i.offsets[1]))
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 = unfold_blocked_tree(rebuilt)
return processed, {'dimensions': list(blocked.values())}
def _loop_blocking(self, iet):
"""
Apply loop blocking to PARALLEL Iteration trees.
"""
blockinner = bool(self.params.get('blockinner'))
blockalways = bool(self.params.get('blockalways'))
noinline = self._compiler_decoration('noinline', cgen.Comment('noinline?'))
# Make sure loop blocking will span as many Iterations as possible
iet = fold_blockable_tree(iet, blockinner)
mapper = {}
efuncs = OrderedDict()
block_dims = []
for tree in retrieve_iteration_tree(iet):
# Is the Iteration tree blockable ?
candidates = [i for i in tree if i.is_Parallel]
if blockinner:
iterations = candidates
else:
iterations = [i for i in candidates if not i.is_Vectorizable]
if len(iterations) <= 1:
continue
root = iterations[0]
if not IsPerfectIteration().visit(root):
# Illegal/unsupported
continue
if not tree.root.is_Sequential and not blockalways:
# 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
# Apply loop blocking to `tree`
interb = []
intrab = []
for i in iterations:
d = BlockDimension(i.dim, name="%s%d_block" % (i.dim.name, len(mapper)))
# Build Iteration over blocks
interb.append(Iteration([], d, d.symbolic_max, offsets=i.offsets,
properties=PARALLEL))
# Build Iteration within a block
intrab.append(i._rebuild([], limits=(d, d+d.step-1, 1), offsets=(0, 0)))
# Record that a new BlockDimension has been introduced
block_dims.append(d)
# Construct the blocked tree
blocked = compose_nodes(interb + intrab + [iterations[-1].nodes])
blocked = unfold_blocked_tree(blocked)
# Promote to a separate Callable
dynamic_parameters = flatten((bi.dim, bi.dim.symbolic_size) for bi in interb)
efunc0 = make_efunc("bf%d" % len(mapper), blocked, dynamic_parameters)
# Compute the iteration ranges
ranges = []
for i, bi in zip(iterations, interb):
maxb = i.symbolic_max - (i.symbolic_size % bi.dim.step)
ranges.append(((i.symbolic_min, maxb, bi.dim.step),
(maxb + 1, i.symbolic_max, i.symbolic_max - maxb)))
# Build Calls to the `efunc`
body = []
for p in product(*ranges):
dynamic_args_mapper = {}
for bi, (m, M, b) in zip(interb, p):
dynamic_args_mapper[bi.dim] = (m, M)
dynamic_args_mapper[bi.dim.step] = (b,)
call = efunc0.make_call(dynamic_args_mapper)
body.append(List(header=noinline, body=call))
# Build indirect Call to the `efunc0` Calls
dynamic_parameters = [i.dim.root for i in candidates]
dynamic_parameters.extend([bi.dim.step for bi in interb])
efunc1 = make_efunc("f%d" % len(mapper), body, dynamic_parameters)
# Track everything to ultimately transform the input `iet`
mapper[root] = efunc1.make_call()
efuncs[efunc1] = None
efuncs[efunc0] = [efunc1.name]
iet = Transformer(mapper).visit(iet)
return iet, {'dimensions': block_dims, 'efuncs': efuncs}