def _(iet):
# TODO: we need to pick the rank from `comm_shm`, not `comm`,
# so that we have nranks == ngpus (as long as the user has launched
# the right number of MPI processes per node given the available
# number of GPUs per node)
objcomm = None
for i in iet.parameters:
if isinstance(i, MPICommObject):
objcomm = i
break
devicetype = as_list(self.lang[self.platform])
try:
lang_init = [self.lang['init'](devicetype)]
except TypeError:
# Not all target languages need to be explicitly initialized
lang_init = []
deviceid = DeviceID()
if objcomm is not None:
rank = Symbol(name='rank')
rank_decl = LocalExpression(DummyEq(rank, 0))
rank_init = Call('MPI_Comm_rank', [objcomm, Byref(rank)])
ngpus = Symbol(name='ngpus')
call = self.lang['num-devices'](devicetype)
ngpus_init = LocalExpression(DummyEq(ngpus, call))
osdd_then = self.lang['set-device']([deviceid] + devicetype)
osdd_else = self.lang['set-device']([rank % ngpus] +
devicetype)
body = lang_init + [
Conditional(
CondNe(deviceid, -1),
osdd_then,
List(
body=[rank_decl, rank_init, ngpus_init, osdd_else
]),
)
]
header = c.Comment('Begin of %s+MPI setup' % self.lang['name'])
footer = c.Comment('End of %s+MPI setup' % self.lang['name'])
else:
body = lang_init + [
Conditional(
CondNe(deviceid, -1),
self.lang['set-device']([deviceid] + devicetype))
]
header = c.Comment('Begin of %s setup' % self.lang['name'])
footer = c.Comment('End of %s setup' % self.lang['name'])
init = List(header=header, body=body, footer=(footer, c.Line()))
iet = iet._rebuild(body=(init, ) + iet.body)
return iet, {'args': deviceid}
def test_cse(exprs, expected):
"""Test common subexpressions elimination."""
grid = Grid((3, 3, 3))
dims = grid.dimensions
tu = TimeFunction(name="tu", grid=grid, space_order=2) # noqa
tv = TimeFunction(name="tv", grid=grid, space_order=2) # noqa
tw = TimeFunction(name="tw", grid=grid, space_order=2) # noqa
tz = TimeFunction(name="tz", grid=grid, space_order=2) # noqa
ti0 = Array(name='ti0', shape=(3, 5, 7),
dimensions=dims).indexify() # noqa
ti1 = Array(name='ti1', shape=(3, 5, 7),
dimensions=dims).indexify() # noqa
t0 = Scalar(name='t0') # noqa
t1 = Scalar(name='t1') # noqa
t2 = Scalar(name='t2') # noqa
# List comprehension would need explicit locals/globals mappings to eval
for i, e in enumerate(list(exprs)):
exprs[i] = DummyEq(indexify(eval(e).evaluate))
counter = generator()
make = lambda: Scalar(name='r%d' % counter()).indexify()
processed = _cse(exprs, make)
assert len(processed) == len(expected)
assert all(str(i.rhs) == j for i, j in zip(processed, expected))
def common_subexprs_elimination(exprs, make, mode='default'):
"""
Perform common sub-expressions elimination, or CSE.
Note: the output is guaranteed to be topologically sorted.
Parameters
----------
exprs : expr-like or list of expr-like
One or more expressions to which CSE is applied.
make : callable
Build symbols to store temporary, redundant values.
mode : str, optional
The CSE algorithm applied. Accepted: ['default'].
"""
# Note: not defaulting to SymPy's CSE() function for three reasons:
# - it also captures array index access functions (eg, i+1 in A[i+1] and B[i+1]);
# - it sometimes "captures too much", losing factorization opportunities;
# - very slow
# TODO: a second "sympy" mode will be provided, relying on SymPy's CSE() but
# also ensuring some sort of post-processing
assert mode == 'default' # Only supported mode ATM
processed = list(exprs)
mapped = []
while True:
# Detect redundancies
counted = count(mapped + processed, q_xop).items()
targets = OrderedDict([(k, estimate_cost(k, True)) for k, v in counted if v > 1])
if not targets:
break
# Create temporaries
hit = max(targets.values())
picked = [k for k, v in targets.items() if v == hit]
mapper = OrderedDict([(e, make()) for i, e in enumerate(picked)])
# Apply replacements
processed = [e.xreplace(mapper) for e in processed]
mapped = [e.xreplace(mapper) for e in mapped]
mapped = [DummyEq(v, k) for k, v in reversed(list(mapper.items()))] + mapped
# Prepare for the next round
for k in picked:
targets.pop(k)
processed = mapped + processed
# At this point we may have useless temporaries (e.g., r0=r1). Let's drop them
processed = _compact_temporaries(processed)
# Perform topological sorting so that reads-after-writes are honored
processed = _topological_sort(processed)
return processed
def _make_partree(self, candidates, nthreads=None):
"""Parallelize the `candidates` Iterations attaching suitable OpenMP pragmas."""
assert candidates
root = candidates[0]
# Get the collapsable Iterations
collapsable = self._find_collapsable(root, candidates)
ncollapse = 1 + len(collapsable)
# Prepare to build a ParallelTree
if all(i.is_Affine for i in candidates):
bundles = FindNodes(ExpressionBundle).visit(root)
sops = sum(i.ops for i in bundles)
if sops >= self.dynamic_work:
schedule = 'dynamic'
else:
schedule = 'static'
if nthreads is None:
# pragma omp for ... schedule(..., 1)
nthreads = self.nthreads
body = OpenMPIteration(schedule=schedule,
ncollapse=ncollapse,
**root.args)
else:
# pragma omp parallel for ... schedule(..., 1)
body = OpenMPIteration(schedule=schedule,
parallel=True,
ncollapse=ncollapse,
nthreads=nthreads,
**root.args)
prefix = []
else:
# pragma omp for ... schedule(..., expr)
assert nthreads is None
nthreads = self.nthreads_nonaffine
chunk_size = Symbol(name='chunk_size')
body = OpenMPIteration(ncollapse=ncollapse,
chunk_size=chunk_size,
**root.args)
niters = prod([root.symbolic_size] +
[j.symbolic_size for j in collapsable])
value = INT(Max(niters / (nthreads * self.chunk_nonaffine), 1))
prefix = [Expression(DummyEq(chunk_size, value, dtype=np.int32))]
# Create a ParallelTree
partree = ParallelTree(prefix, body, nthreads=nthreads)
collapsed = [partree] + collapsable
return root, partree, collapsed
def _make_partree(self, candidates, nthreads=None):
"""Parallelize the `candidates` Iterations attaching suitable OpenMP pragmas."""
assert candidates
root = candidates[0]
# Get the collapsable Iterations
collapsable = self._find_collapsable(root, candidates)
ncollapse = 1 + len(collapsable)
# Prepare to build a ParallelTree
prefix = []
if all(i.is_Affine for i in candidates):
if nthreads is None:
# pragma omp for ... schedule(..., 1)
nthreads = self.nthreads
omp_pragma = self.lang['for'](ncollapse, 1)
else:
# pragma omp parallel for ... schedule(..., 1)
omp_pragma = self.lang['par-for'](ncollapse, 1, nthreads)
else:
# pragma omp for ... schedule(..., expr)
assert nthreads is None
nthreads = self.nthreads_nonaffine
chunk_size = Symbol(name='chunk_size')
omp_pragma = self.lang['for'](ncollapse, chunk_size)
niters = prod([root.symbolic_size] +
[j.symbolic_size for j in collapsable])
value = INT(Max(niters / (nthreads * self.CHUNKSIZE_NONAFFINE), 1))
prefix.append(
Expression(DummyEq(chunk_size, value, dtype=np.int32)))
# Create a ParallelTree
body = root._rebuild(pragmas=root.pragmas + (omp_pragma, ),
properties=root.properties +
(COLLAPSED(ncollapse), ))
partree = ParallelTree(prefix, body, nthreads=nthreads)
collapsed = [partree] + collapsable
return root, partree, collapsed
def _cse(maybe_exprs, make, mode='default'):
"""
Main common sub-expressions elimination routine.
Note: the output is guaranteed to be topologically sorted.
Parameters
----------
maybe_exprs : expr-like or list of expr-like or Cluster
One or more expressions to which CSE is applied.
make : callable
Build symbols to store temporary, redundant values.
mode : str, optional
The CSE algorithm applied. Accepted: ['default'].
"""
# Note: not defaulting to SymPy's CSE() function for three reasons:
# - it also captures array index access functions (eg, i+1 in A[i+1] and B[i+1]);
# - it sometimes "captures too much", losing factorization opportunities;
# - very slow
# TODO: a second "sympy" mode will be provided, relying on SymPy's CSE() but
# also ensuring some form of post-processing
assert mode == 'default' # Only supported mode ATM
# Just for flexibility, accept either Clusters or exprs
if isinstance(maybe_exprs, Cluster):
cluster = maybe_exprs
processed = list(cluster.exprs)
scope = cluster.scope
else:
processed = list(maybe_exprs)
scope = Scope(maybe_exprs)
# Some sub-expressions aren't really "common" -- that's the case of Dimension-
# independent data dependences. For example:
#
# ... = ... a[i] + 1 ...
# a[i] = ...
# ... = ... a[i] + 1 ...
#
# `a[i] + 1` will be excluded, as there's a flow Dimension-independent data
# dependence involving `a`
exclude = {i.source.indexed for i in scope.d_flow.independent()}
mapped = []
while True:
# Detect redundancies
counted = count(mapped + processed, q_xop).items()
targets = OrderedDict([(k, estimate_cost(k, True)) for k, v in counted
if v > 1])
# Rule out Dimension-independent data dependencies
targets = OrderedDict([(k, v) for k, v in targets.items()
if not k.free_symbols & exclude])
if not targets:
break
# Create temporaries
hit = max(targets.values())
picked = [k for k, v in targets.items() if v == hit]
mapper = OrderedDict([(e, make()) for i, e in enumerate(picked)])
# Apply replacements
processed = [uxreplace(e, mapper) for e in processed]
mapped = [uxreplace(e, mapper) for e in mapped]
mapped = [DummyEq(v, k)
for k, v in reversed(list(mapper.items()))] + mapped
# Update `exclude` for the same reasons as above -- to rule out CSE across
# Dimension-independent data dependences
exclude.update({i for i in mapper.values()})
# Prepare for the next round
for k in picked:
targets.pop(k)
processed = mapped + processed
# At this point we may have useless temporaries (e.g., r0=r1). Let's drop them
processed = _compact_temporaries(processed)
return processed
def _make_partree(self, candidates, nthreads=None):
"""Parallelize `root` attaching a suitable OpenMP pragma."""
assert candidates
root = candidates[0]
# Get the collapsable Iterations
collapsable = []
if ncores() >= Ompizer.COLLAPSE_NCORES and IsPerfectIteration().visit(
root):
for n, i in enumerate(candidates[1:], 1):
# The OpenMP specification forbids collapsed loops to use iteration
# variables in initializer expressions. E.g., the following is forbidden:
#
# #pragma omp ... collapse(2)
# for (i = ... )
# for (j = i ...)
# ...
#
# Here, we make sure this won't happen
if any(j.dim in i.symbolic_min.free_symbols
for j in candidates[:n]):
break
# Also, we do not want to collapse vectorizable Iterations
if i.is_Vectorizable:
break
# Would there be enough work per parallel iteration?
try:
work = prod(
[int(j.dim.symbolic_size) for j in candidates[n + 1:]])
if work < Ompizer.COLLAPSE_WORK:
break
except TypeError:
pass
collapsable.append(i)
ncollapse = 1 + len(collapsable)
# Prepare to build a ParallelTree
prefix = []
if all(i.is_Affine for i in candidates):
if nthreads is None:
# pragma omp for ... schedule(..., 1)
nthreads = self.nthreads
omp_pragma = self.lang['for'](ncollapse, 1)
else:
# pragma omp parallel for ... schedule(..., 1)
omp_pragma = self.lang['par-for'](ncollapse, 1, nthreads)
else:
# pragma omp for ... schedule(..., expr)
assert nthreads is None
nthreads = self.nthreads_nonaffine
chunk_size = Symbol(name='chunk_size')
omp_pragma = self.lang['for'](ncollapse, chunk_size)
niters = prod([root.symbolic_size] +
[j.symbolic_size for j in collapsable])
value = INT(Max(niters / (nthreads * self.CHUNKSIZE_NONAFFINE), 1))
prefix.append(
Expression(DummyEq(chunk_size, value, dtype=np.int32)))
# Create a ParallelTree
body = root._rebuild(pragmas=root.pragmas + (omp_pragma, ),
properties=root.properties +
(COLLAPSED(ncollapse), ))
partree = ParallelTree(prefix, body, nthreads=nthreads)
collapsed = [partree] + collapsable
return root, partree, collapsed
