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linearization.py
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linearization.py
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from collections import defaultdict
from functools import singledispatch
import numpy as np
from devito.data import FULL
from devito.ir import (BlankLine, Call, DummyExpr, Dereference, Expression, List,
PointerCast, PragmaTransfer, FindNodes, FindSymbols,
Transformer)
from devito.passes.iet.engine import iet_pass
from devito.passes.iet.parpragma import PragmaLangBB
from devito.symbolics import (DefFunction, MacroArgument, ccode, retrieve_indexed,
uxreplace)
from devito.tools import Bunch, DefaultOrderedDict, filter_ordered, flatten, prod
from devito.types import Array, Symbol, FIndexed, Indexed, Wildcard
from devito.types.basic import IndexedData
from devito.types.dense import DiscreteFunction
__all__ = ['linearize']
def linearize(graph, **kwargs):
"""
Turn n-dimensional Indexeds into 1-dimensional Indexed with suitable index
access function, such as `a[i, j]` -> `a[i*n + j]`. The row-major format
of the underlying Function objects is honored.
"""
# Simple data structure to avoid generation of duplicated code
cache = defaultdict(lambda: Bunch(stmts0=[], stmts1=[], cbk=None))
linearization(graph, cache=cache, **kwargs)
@iet_pass
def linearization(iet, **kwargs):
"""
Carry out the actual work of `linearize`.
"""
mode = kwargs['mode']
sregistry = kwargs['sregistry']
cache = kwargs['cache']
# Pre-process the `mode` opt option
# `mode` may be a callback describing what Function types, and under what
# conditions, should linearization be applied
if not mode:
return iet, {}
elif callable(mode):
key = mode
else:
# Default
key = lambda f: f.is_DiscreteFunction or f.is_Array
iet, headers, args = linearize_accesses(iet, key, cache, sregistry)
iet = linearize_pointers(iet)
iet = linearize_transfers(iet, sregistry)
return iet, {'headers': headers, 'args': args}
def linearize_accesses(iet, key, cache, sregistry):
"""
Turn Indexeds into FIndexeds and create the necessary access Macros.
"""
# `functions` are all unseen Functions that `iet` may need linearizing
functions = [f for f in FindSymbols().visit(iet)
if f not in cache and key(f) and f.ndim > 1]
functions = sorted(functions, key=lambda f: len(f.dimensions), reverse=True)
# Find unique sizes (unique -> minimize necessary registers)
mapper = DefaultOrderedDict(list)
for f in functions:
# NOTE: the outermost dimension is unnecessary
for d in f.dimensions[1:]:
# TODO: same grid + same halo => same padding, however this is
# never asserted throughout the compiler yet... maybe should do
# it when in debug mode at `prepare_arguments` time, ie right
# before jumping to C?
mapper[(d, f._size_halo[d], getattr(f, 'grid', None))].append(f)
# Build all exprs such as `x_fsz0 = u_vec->size[1]`
imapper = DefaultOrderedDict(list)
for (d, halo, _), v in mapper.items():
expr = _generate_fsz(v[0], d, sregistry)
if expr:
for f in v:
imapper[f].append((d, expr.write))
cache[f].stmts0.append(expr)
# Build all exprs such as `y_slc0 = y_fsz0*z_fsz0`
built = {}
mapper = DefaultOrderedDict(list)
for f, v in imapper.items():
for n, (d, _) in enumerate(v):
expr = prod(list(zip(*v[n:]))[1])
try:
stmt = built[expr]
except KeyError:
name = sregistry.make_name(prefix='%s_slc' % d.name)
s = Symbol(name=name, dtype=np.uint32, is_const=True)
stmt = built[expr] = DummyExpr(s, expr, init=True)
mapper[f].append(stmt.write)
cache[f].stmts1.append(stmt)
mapper.update([(f, []) for f in functions if f not in mapper])
# Build defines. For example:
# `define uL(t, x, y, z) u[(t)*t_slc0 + (x)*x_slc0 + (y)*y_slc0 + (z)]`
headers = []
findexeds = {}
for f, szs in mapper.items():
if cache[f].cbk is not None:
# Perhaps we've already built an access macro for `f` through another efunc
findexeds[f] = cache[f].cbk
else:
header, cbk = _generate_macro(f, szs, sregistry)
headers.append(header)
cache[f].cbk = findexeds[f] = cbk
# Build "functional" Indexeds. For example:
# `u[t2, x+8, y+9, z+7] => uL(t2, x+8, y+9, z+7)`
mapper = {}
for n in FindNodes(Expression).visit(iet):
subs = {}
for i in retrieve_indexed(n.expr):
try:
subs[i] = findexeds[i.function](i)
except KeyError:
pass
mapper[n] = n._rebuild(expr=uxreplace(n.expr, subs))
# Introduce the linearized expressions
iet = Transformer(mapper).visit(iet)
# `candidates` are all Functions actually requiring linearization in `iet`
candidates = []
indexeds = FindSymbols('indexeds').visit(iet)
candidates.extend(filter_ordered(i.function for i in indexeds))
calls = FindNodes(Call).visit(iet)
symbols = filter_ordered(flatten(i.expr_symbols for i in calls))
candidates.extend(i.function for i in symbols if isinstance(i, IndexedData))
# `defines` are all Functions that can be linearized in `iet`
defines = FindSymbols('defines').visit(iet)
# Place the linearization expressions or delegate to ancestor efunc
stmts0 = []
stmts1 = []
args = []
for f in candidates:
if f in defines:
stmts0.extend(cache[f].stmts0)
stmts1.extend(cache[f].stmts1)
else:
args.extend([e.write for e in cache[f].stmts1])
if stmts0:
assert len(stmts1) > 0
stmts0 = filter_ordered(stmts0) + [BlankLine]
stmts1 = filter_ordered(stmts1) + [BlankLine]
body = iet.body._rebuild(body=tuple(stmts0) + tuple(stmts1) + iet.body.body)
iet = iet._rebuild(body=body)
else:
assert len(stmts0) == 0
return iet, headers, args
@singledispatch
def _generate_fsz(f, d, sregistry):
return
@_generate_fsz.register(DiscreteFunction)
def _(f, d, sregistry):
name = sregistry.make_name(prefix='%s_fsz' % d.name)
s = Symbol(name=name, dtype=np.uint32, is_const=True)
return DummyExpr(s, f._C_get_field(FULL, d).size, init=True)
@_generate_fsz.register(Array)
def _(f, d, sregistry):
name = sregistry.make_name(prefix='%s_fsz' % d.name)
s = Symbol(name=name, dtype=np.uint32, is_const=True)
return DummyExpr(s, f.symbolic_shape[d], init=True)
@singledispatch
def _generate_macro(f, szs, sregistry):
return
@_generate_macro.register(DiscreteFunction)
@_generate_macro.register(Array)
def _(f, szs, sregistry):
assert len(szs) == len(f.dimensions) - 1
pname = sregistry.make_name(prefix='%sL' % f.name)
cbk = lambda i, pname=pname: FIndexed(i, pname)
expr = sum([MacroArgument(d.name)*s for d, s in zip(f.dimensions, szs)])
expr += MacroArgument(f.dimensions[-1].name)
expr = Indexed(IndexedData(f.name, None, f), expr)
define = DefFunction(pname, f.dimensions)
header = (ccode(define), ccode(expr))
return header, cbk
def linearize_pointers(iet):
"""
Flatten n-dimensional PointerCasts/Dereferences.
"""
indexeds = [i for i in FindSymbols('indexeds').visit(iet)]
candidates = {i.function for i in indexeds if isinstance(i, FIndexed)}
mapper = {}
# Linearize casts, e.g. `float *u = (float*) u_vec->data`
mapper.update({n: n._rebuild(flat=n.function.name)
for n in FindNodes(PointerCast).visit(iet)
if n.function in candidates})
# Linearize array dereferences, e.g. `float *r1 = (float*) pr1[tid]`
mapper.update({n: n._rebuild(flat=n.pointee.name)
for n in FindNodes(Dereference).visit(iet)
if n.pointer.is_PointerArray and n.pointee in candidates})
iet = Transformer(mapper).visit(iet)
return iet
def linearize_transfers(iet, sregistry):
casts = FindNodes(PointerCast).visit(iet)
candidates = {i.function for i in casts if i.flat is not None}
mapper = {}
for n in FindNodes(PragmaTransfer).visit(iet):
if n.function not in candidates:
continue
try:
imask0 = n.kwargs['imask']
except KeyError:
imask0 = []
try:
index = imask0.index(FULL)
except ValueError:
index = len(imask0)
# Drop entries being flatten
imask = imask0[:index]
# The NVC 21.2 compiler (as well as all previous and potentially some
# future versions as well) suffers from a bug in the parsing of pragmas
# using subarrays in data clauses. For example, the following pragma
# excerpt `... copyin(a[0]:b[0])` leads to a compiler error, despite
# being perfectly legal OpenACC code. The workaround consists of
# generating `const int ofs = a[0]; ... copyin(n:b[0])`
exprs = []
if len(imask) < len(imask0) and len(imask) > 0:
assert len(imask) == 1
try:
start, size = imask[0]
except TypeError:
start, size = imask[0], 1
if start != 0: # Spare the ugly generated code if unneccesary (occurs often)
name = sregistry.make_name(prefix='%s_ofs' % n.function.name)
wildcard = Wildcard(name=name, dtype=np.int32, is_const=True)
symsect = PragmaLangBB._make_symbolic_sections_from_imask(n.function,
imask)
assert len(symsect) == 1
start, _ = symsect[0]
exprs.append(DummyExpr(wildcard, start, init=True))
imask = [(wildcard, size)]
rebuilt = n._rebuild(imask=imask)
if exprs:
mapper[n] = List(body=exprs + [rebuilt])
else:
mapper[n] = rebuilt
iet = Transformer(mapper).visit(iet)
return iet