def compress_tiles(tiled_subpme):
compressed = []
for tiles in tiled_subpme:
compressed.append([])
i = 0
while i < len(tiles):
#for i, tile in enumerate( tiles ):
tile = tiles[i]
lhs, rhs = tile.get_children()
if isinstance(rhs, Predicate):
compressed[-1].append(copy.deepcopy(tile))
i += 1
continue
replaced = False
for j, other_tile in enumerate(tiles[i + 1:], start=i + 1):
olhs, orhs = other_tile.get_children()
lhs_ch = lhs.get_children()[0]
if contains(orhs, lhs_ch):
new_other = copy.deepcopy(other_tile)
#new_other = replace( new_other, [RewriteRule(lhs_ch, Replacement(rhs))] )
new_other.children[1] = replace(
new_other.rhs(),
[RewriteRule(lhs_ch, Replacement(rhs))])
tiles[j] = new_other
replaced = True
# if tile lhs = f(rhs) and other_tile overwrites lhs (lhs = f(lhs))
# stop replacing with "old" lhs
if lhs_ch in olhs.children:
break
if not replaced:
compressed[-1].append(copy.deepcopy(tile))
i += 1
return compressed
def code_dispatcher(node, out):
global indent_level, indent_char
indent = indent_level * indent_char
if isinstance(node, lpla.function):
code_function(node, out)
elif isinstance(node, lpla.declare):
code_declare(node, out)
elif isinstance(node, Equal):
node = replace(node, trsm_patterns)
if isinstance(node, str):
print(indent + node + ";", file=out)
else:
print(indent + click2matlab(node) + ";", file=out)
elif isinstance(node, lpla.partition):
code_partition(node, out)
elif isinstance(node, lpla.repartition):
code_repartition(node, out)
elif isinstance(node, lpla.progress):
code_progress(node, out)
elif isinstance(node, lpla.combine):
code_combine(node, out)
elif isinstance(node, lpla._while):
code_while(node, out)
elif isinstance(node, lpla.spacing):
code_spacing(node, out)
def update_TOE(rule):
for prop in TOE_properties:
for _expr in TOE[prop]:
#for rule in rewrite_rules:
expr = copy.deepcopy(_expr)
expr = replace(expr, [rule])
new = copy.deepcopy(expr)
new = simplify(to_canonical(new))
TOE.set_property(prop, new)
def tile( self, tree, node, match_dict ):
_T = TOS.new_temp()
temp = Symbol("T" + str(_T))
temp.set_property( properties.TEMPORARY )
#
if isinstance( node, Predicate ):
if node == tree:
print( "[Warning] If predicate has multiple outputs, may break if not careful from caller" )
return Equal([ NList([ temp ]), copy.deepcopy( node ) ]), \
replace( tree, [RewriteRule( copy.deepcopy( node ), Replacement(temp) )] )
else:
tile_expr = self.create_tile( match_dict )
propagate_properties( tile_expr, temp )
propagate_st_info( tile_expr, temp )
## [FIXME] Quick and dirty test
#if isUpperTriangular( tile_expr ):
#print( temp, "is upper triangular" )
#temp.set_property( properties.UPPER_TRIANGULAR )
return Equal([ NList([ temp ]), self.create_tile( match_dict ) ]), \
replace( tree, [self.create_rewrite_rule( match_dict, temp )] )
def _PassStorage(st):
if isinstance(st, lpla._while):
for s in st.body:
_PassStorage(s)
elif isinstance(st, Equal):
symbols = []
for n in st.iterate_preorder():
# Zero has no st_info...
if isinstance(n, Zero):
pass
elif isinstance(n, Symbol) and n.st_info[1] != n:
n_st = n.st_info[1]
n_st.st_info = n.st_info
# E.g., in Cholesky, n is L_11, and n_st is A_11
#if n.isLowerTriangular() and not n_st.isLowerTriangular():
#symbols.append( RewriteRule( n, Replacement(tril(n_st)) ) )
#elif n.isUpperTriangular() and not n_st.isUpperTriangular():
#symbols.append( RewriteRule( n, Replacement(triu(n_st)) ) )
#else:
symbols.append(RewriteRule(n, Replacement(n_st)))
replace(st, symbols)
def opt_copy_propagation(self):
for i, st in enumerate(self.statements):
if isinstance(st, Equal):
lhs, rhs = st.children
lhs = lhs.children
if len(lhs) == 1 and lhs[0].isTemporary() and isinstance(
st.rhs(), Symbol):
for oth_st in self.statements[i + 1:]:
if not isinstance(
oth_st, Equal
): #[CHECK] Careful. Not the case, but generally speaking could be some part/repart
continue
oth_lhs, oth_rhs = oth_st.lhs(), oth_st.rhs()
if contains(oth_rhs, lhs[0]):
#\ and not (isinstance( oth_rhs, Predicate ) and pm.DB[oth_rhs.name].overwrite): #[FIXME] Can be less restrictive
new_rhs = replace(
oth_rhs,
[RewriteRule(lhs[0], Replacement(rhs))])
oth_st.children[1] = new_rhs
if oth_lhs.children[0] == lhs[0] or oth_lhs == rhs:
break
def partition(self):
self.basic_partitionings = dict()
self.partitionings = dict()
rewrite_rules = []
for operand in self.operands:
op_name = operand.get_name()
# For code generation
#part = partition_shape( operand, self.part_shape[op_name] )
part = partition_shape_with_storage(operand,
self.part_shape[op_name])
self.basic_partitionings[op_name] = part
#
part = partition(operand, self.part_shape[op_name],
operand.get_properties())
self.partitionings[op_name] = part
#
rewrite_rules.append(RewriteRule(operand, Replacement(part)))
self.partitioned_postcondition = \
[replace( copy.deepcopy(eq), rewrite_rules ) for eq in self.equation]
print("* Partitioned postcondition")
for eq in self.partitioned_postcondition:
print("* ", eq)
def _checkPredicateOverwrite(statement):
lhs = statement.lhs()
rhs = statement.rhs()
if not isinstance(rhs, Predicate):
rhs_ops = [
node for node in rhs.iterate_preorder()
if isinstance(node, Symbol)
]
tmp_ops = [op for op in rhs_ops if op.isTemporary()]
if len(tmp_ops
) == 1: # [FIXME] Quick and dirty to play with temporaries
tmp = tmp_ops[0]
if lhs.children[0].size == tmp.size:
if not lhs.children[0].isTemporary():
overwrites = False
for op in rhs_ops:
try:
overwrites = lhs.children[0].st_info[
1] == op.st_info[1]
except AttributeError:
pass
if overwrites: break
if not overwrites:
statements = []
statements.append(Equal([NList(lhs.children), tmp]))
statement.children[1] = replace(
copy.deepcopy(rhs),
[RewriteRule(tmp, Replacement(lhs.children[0]))])
statements.append(statement)
return statements
else:
# TRSM 2x2 ...
pass
return [statement]
if not pm.DB[rhs.name].overwrite: # []
return [statement]
statements = []
# [FIXME] Assumes one single operands get overwritten. Will break in the future
already_copied = []
for inp, out in pm.DB[rhs.name].overwrite:
if inp in already_copied:
continue
already_copied.append(inp)
#
if rhs.children[inp] != lhs.children[
out]: # [FIXME] All should have st_into
try:
overwrites = lhs.children[out].st_info[1] == rhs.children[
inp].st_info[1]
except AttributeError:
overwrites = False
if overwrites:
statements.append(statement) #[FIXME] Gosh...
continue
inpop = rhs.children[inp]
outop = lhs.children[out]
if inpop.isTemporary() or inpop.isInput():
# if multiple outputs overwrite input (e.g., LU)
if len([o for i, o in pm.DB[rhs.name].overwrite if i == inp
]) > 1:
try:
outop = TOS._TOS[outop.st_info[1].name][
0] # LU (ABR = T3; [LBR,UBR] = LU(ABR))
except:
pass
outop.st_info = (None, outop)
#
statements.append(Equal([NList([outop]), inpop]))
rhs.children[inp] = outop
statements.append(statement)
else:
lhs.children[out] = rhs.children[inp]
statements.append(statement)
statements.append(Equal([NList([inpop]), outop]))
else:
statements.append(statement)
return statements
def generate_predicate_before(
self, pme, trav, linv,
linv_obj): # [TODO] Cleanup, no need for linv AND linv_obj
new = [copy.deepcopy(expr) for expr in itertools.chain(*linv)]
# Repartition
reparts = dict()
repart_rules = []
for op in linv_obj.linv_operands:
part = linv_obj.linv_operands_basic_part[op.get_name()]
# [CHECK] _shape or not? Regular one needed for inheritance
repart = repartition(op, part.shape, trav[op.get_name()])
#
#repart_shape = {(1,1):(1,1), (1,2):(1,3), (2,1):(3,1), (2,2):(3,3)}[part.shape]
#repart = repartition_shape( op, repart_shape )
#repart = repart_group( repart, repart_shape, trav[op.get_name()] )
#
for part_op, repart_op in zip(itertools.chain(*part),
itertools.chain(*repart)):
repart_rules.append(
RewriteRule(part_op, Replacement(repart_op)))
reparts[op.get_name()] = repart
# Apply repartitionings
new = [replace(expr, repart_rules) for expr in new]
# Explicit functions to BlockedExpression
# First flatten args, then replace
for expr in new:
lhs, rhs = expr.get_children()
if isinstance(rhs, Predicate):
for i, arg in enumerate(rhs.get_children()):
#rhs.set_children( i, flatten_blocked_operation(arg) )
rhs.set_children(i, flatten_blocked_operation_click(arg))
new = [replace(expr, known_pmes) for expr in new]
# Operators applied to BlockedExpression, into BlockedExpressions
for expr in new:
if isinstance(expr, BlockedExpression):
continue
_, rhs = expr.get_children()
#print( rhs ) # [TODO] Maybe "Sylv(...)"!!!
#rhs = flatten_blocked_operation( rhs )
rhs = flatten_blocked_operation_click(rhs)
expr.set_children(1, rhs)
# Flatten left-hand sides of the previous type of expressions
for expr in new:
if isinstance(expr, BlockedExpression):
continue
lhs, rhs = expr.get_children()
new_lhs = []
for out in lhs:
if isinstance(out, Symbol): # this is a temporary one
out.size = rhs.get_size()
#part = partition_shape( out, rhs.shape )
part = partition_shape(out, tuple(rhs.shape))
new_lhs.append(part)
else:
new_lhs.append(out)
lhs = BlockedExpression(map_thread(NList, new_lhs, 2), (0, 0),
rhs.shape)
expr.set_children(0, lhs)
# Flatten the last type of expressions
final = []
for expr in new:
if isinstance(expr, BlockedExpression):
final.extend([
simplify(to_canonical(eq)) for eq in itertools.chain(*expr)
])
else:
lhs, rhs = expr.get_children()
final.extend([
simplify(to_canonical(eq))
for eq in itertools.chain.from_iterable(
map_thread(Equal, [lhs, rhs], 2))
])
final = filter_zero_zero(final)
# remove expressions of the type " B_10^T = ..." (e.g., in symv)"
_final = final
final = []
for expr in _final:
lhs, rhs = expr.children
lhs = lhs.children
# [FIXME] == 1 only to make sure it does not affect other cases.
# Just want to let them break and study them in the future
if len(lhs) == 1 and (not isOperand(lhs[0]) or lhs[0].isZero()):
continue
final.append(expr)
#
# expand in terms of input parts
#
#expand_rules = list(itertools.chain(*self.expr_to_rule_lhs_rhs( final )))
#for expr in final:
#expr.children[1] = simplify(to_canonical(replace_all(copy.deepcopy(expr.children[1]), expand_rules)))
#
# Print and return
#
for expr in final:
print("* ", expr)
return (reparts, final)
def find_updates_v2(self, before, after):
# If a part is (partially) computed in the before and
# does not appear in the after or
# going from before to after requires undoing some computation
# it is potentially unstable, and more expensive: ignore
dict_bef = dict([(str(u.get_children()[0]), u) for u in before])
dict_aft = dict([(str(u.get_children()[0]), u) for u in after])
ignore = False
quadrant = None
for k, v in dict_bef.items():
if k not in dict_aft:
ignore = True
break
else:
rules = self.expr_to_rule_rhs_lhs([v])
rules = list(itertools.chain(*rules))
expr_copy = copy.deepcopy(dict_aft[k])
t = replace(expr_copy, rules)
#if v == replace( expr_copy, rules ):
if dict_aft[k] == t:
ignore = True
break
if ignore:
print("[INFO] Skipping invariant: %s" % reason)
return None
#
# Wrap outputs for before and after
WrapBefOut = WrapOutBef
for u in before:
u.children[0] = NList([WrapBefOut(l) for l in u.children[0]])
#
wrap_rules_after = []
for u in after:
u.children[0] = NList([WrapOutAft(l) for l in u.children[0]])
# replace before in after
wrap_rules_before = []
for u in before:
print(u)
lhs, rhs = u.get_children()
if len(lhs.children) > 1:
continue
rules = self.expr_to_rule_rhs_lhs([u])
wrap_rules_before.append(list(itertools.chain(*rules)))
#
for i, rule in enumerate(reversed(wrap_rules_before)):
idx = len(wrap_rules_before) - i - 1
for j in range(idx - 1, -1, -1):
for _rule in rule:
_rule.pattern = replace_all(_rule.pattern,
wrap_rules_before[j])
wrap_rules_before = list(itertools.chain(*wrap_rules_before))
#
for u in after:
_, rhs = u.get_children()
u.children[1] = simplify(
to_canonical(replace_all(copy.deepcopy(rhs),
wrap_rules_before)))
# replace after in after
done = False
while not done:
# replace after in after
wrap_rules_after = []
for u in after:
lhs, rhs = u.get_children()
if len(lhs.children) > 1:
wrap_rules_after.append([])
continue
rules = self.expr_to_rule_rhs_lhs([u])
wrap_rules_after.append(list(itertools.chain(*rules)))
#
after_top = [copy.deepcopy(u) for u in after]
for i, u in enumerate(after):
_, rhs = u.get_children()
rules = list(
itertools.chain.from_iterable(wrap_rules_after[:i] +
wrap_rules_after[i + 1:]))
u.children[1] = simplify(
to_canonical(replace_all(copy.deepcopy(rhs), rules)))
done = True
for top, bot in zip(after_top, after):
if top != bot:
done = False
break
# [TODO] Multiple lhss, won't work
updates = []
for u in after:
lhs, rhs = u.get_children()
lhs = lhs.children[0] # NList[op] -> op
if isinstance(rhs, WrapBefOut) and isinstance(lhs, WrapOutAft) and \
matchq(lhs.children[0], rhs.children[0]):
continue
updates.append(u)
#
tiled_updates = []
for u in updates:
print("* ", u)
tilings = list(tile_expr(u))
if len(tilings) > 1:
print("[WARNING] Multiple (%d) tilings for expression %s" %
(len(tilings), u))
print(" Discarding all but one")
tiled_updates.extend(tilings[0])
tiled_updates = sort(tiled_updates)
print("* Tiled update")
for t in tiled_updates:
print("* ", t)
# Drop WrapOutBef's
# Drop WrapOutAft's
s = PatternDot("s")
updates = []
for u in tiled_updates:
u = replace_all(
u, [RewriteRule(WrapOutAft(s), Replacement(lambda d: d["s"]))])
u = replace_all(
u, [RewriteRule(WrapOutBef(s), Replacement(lambda d: d["s"]))])
updates.append(u)
return updates
def find_updates(self, before, after):
# If a part is (partially) computed in the before and
# does not appear in the after or
# going from before to after requires undoing some computation
# it is potentially unstable, and more expensive: ignore
try:
before_finputs = self.express_in_terms_of_input(before)
after_finputs = self.express_in_terms_of_input(after)
except:
# [TODO] In LU's variant 5, parts of A appear as lhs's
return None
#
dict_bef = dict([(str(u.get_children()[0]), u)
for u in before_finputs])
dict_aft = dict([(str(u.get_children()[0]), u) for u in after_finputs])
same = []
ignore = False
for k, v in dict_bef.items():
if k in dict_aft and matchq(v, dict_aft[k]):
same.extend(v.children[0].children)
if k not in dict_aft:
ignore = True
reason = "%s not in %s" % (k, dict_aft.keys())
break
else:
rules = self.expr_to_rule_rhs_lhs([v])
rules = list(itertools.chain(*rules))
expr_copy = copy.deepcopy(dict_aft[k])
t = replace(expr_copy, rules)
#if v == replace( expr_copy, rules ):
if dict_aft[k] == t:
ignore = True
reason = "%s would require undoing job" % k
break
if ignore:
print("[INFO] Skipping invariant: %s" % reason)
return None
#
# Wrap outputs for before and after
WrapBefOut = WrapOutBef
lhss = []
for u in before:
lhss.extend(u.children[0])
u.children[0] = NList([WrapBefOut(l) for l in u.children[0]])
for u in before:
u.children[1] = replace(
u.children[1],
[RewriteRule(l, Replacement(WrapBefOut(l))) for l in lhss])
#
lhss = []
for u in after:
lhss.extend(u.children[0])
u.children[0] = NList([WrapOutAft(l) for l in u.children[0]])
wrap_rules_after = \
[
RewriteRule(l, Replacement(WrapBefOut(l))) if l in same else
RewriteRule(l, Replacement(WrapOutAft(l))) for l in lhss
]
for u in after:
u.children[1] = replace(u.children[1], wrap_rules_after)
# replace before in before
wrap_rules_before = []
for u in before:
lhs, rhs = u.get_children()
#if len(lhs.children) > 1:
#wrap_rules_before.append([])
#continue
rules = self.expr_to_rule_rhs_lhs([u])
wrap_rules_before.append(list(itertools.chain(*rules)))
#
new_rules = []
for i, rules in enumerate(wrap_rules_before):
new_rules.append([])
for rule in rules:
new_r = copy.deepcopy(rule)
new_r.pattern = replace_all(
new_r.pattern,
list(
itertools.chain.from_iterable(wrap_rules_before[:i] +
wrap_rules_before[i +
1:])))
if new_r.pattern != rule.pattern:
new_rules[-1].append(new_r)
for r1, r2 in zip(new_rules, wrap_rules_before):
r2.extend(r1)
#
wrap_rules_before = list(itertools.chain(*wrap_rules_before))
done = False
while not done:
after_top = [copy.deepcopy(u) for u in after]
for i, u in enumerate(after):
_, rhs = u.get_children()
u.children[1] = simplify(
to_canonical(
replace_all(copy.deepcopy(rhs), wrap_rules_before)))
done = True
for top, bot in zip(after_top, after):
if top != bot:
done = False
break
# replace after in after
done = False
while not done:
# replace after in after
wrap_rules_after = []
for u in after:
lhs, rhs = u.get_children()
#if len(lhs.children) > 1:
#wrap_rules_after.append([])
#continue
rules = self.expr_to_rule_rhs_lhs([u])
wrap_rules_after.append(list(itertools.chain(*rules)))
#
after_top = [copy.deepcopy(u) for u in after]
for i, u in enumerate(after):
_, rhs = u.get_children()
rules = list(
itertools.chain.from_iterable(wrap_rules_after[:i] +
wrap_rules_after[i + 1:]))
u.children[1] = simplify(
to_canonical(replace_all(copy.deepcopy(rhs), rules)))
done = True
for top, bot in zip(after_top, after):
if top != bot:
done = False
break
# [TODO] Multiple lhss, won't work
updates = []
for u in after:
lhs, rhs = u.get_children()
if len(lhs.children) == 1:
lhs = lhs.children[0] # NList[op] -> op
if isinstance(rhs, WrapBefOut) and isinstance(lhs, WrapOutAft) and \
matchq(lhs.children[0], rhs.children[0]):
continue
elif not isinstance(rhs,
NList): # multiple outputs/predicate in rhs,
# but not complete (otherwise it would be NList)
pass
else:
to_skip = True
for l, r in zip(lhs.children, rhs.children):
if not( isinstance(r, WrapBefOut) and isinstance(l, WrapOutAft) and \
matchq(l.children[0], r.children[0]) ):
to_skip = False
break
if to_skip:
continue
updates.append(u)
#
tiled_updates = []
for u in updates:
print("* ", u)
tilings = list(tile_expr(u))
if len(tilings) > 1:
print("[WARNING] Multiple (%d) tilings for expression %s" %
(len(tilings), u))
print(" Discarding all but one")
tiled_updates.extend(tilings[0])
tiled_updates = sort(tiled_updates)
print("* Tiled update")
for t in tiled_updates:
print("* ", t)
# Drop WrapOutBef's
# Drop WrapOutAft's
s = PatternDot("s")
updates = []
for u in tiled_updates:
u = replace_all(
u, [RewriteRule(WrapOutAft(s), Replacement(lambda d: d["s"]))])
u = replace_all(
u, [RewriteRule(WrapOutBef(s), Replacement(lambda d: d["s"]))])
updates.append(u)
return updates
def flatten_blocked_operation_click( expr ):
PD = PatternDot("PD")
rule = RewriteRule( WrapOutBef( PD ), \
Replacement(lambda d: BlockedExpression( map_thread( WrapOutBef, [d["PD"]], 2 ), d["PD"].size, d["PD"].shape)) )
expr = replace( copy.deepcopy(expr), [rule] )
return flatten_blocked_operation( expr )
def solve_equations(self):
dist = self.distributed_partitioned_postcondition
# Update TOE
for eq in dist.flatten_children():
for subeq in eq:
lhs, rhs = subeq.get_children()
update_TOE(RewriteRule(lhs, Replacement(rhs)))
update_TOE(RewriteRule(rhs, Replacement(lhs)))
# Collect all output parts to be computed
basic_part = self.basic_partitionings
basic_part = self.partitionings #[TODO] Ok?
all_outputs = []
for op in self.operands:
if op.isOutput():
all_outputs.extend([
node
for node in basic_part[op.get_name()].iterate_preorder()
if isinstance(node, Symbol)
])
# Iterate until PME is solved
subeqs_to_solve = dist.flatten_children()
subeqs_to_solve = filter_zero_zero(subeqs_to_solve)
subeqs_solved = []
solved_outputs = set([
""
]) # any initialization that cannot render the equality below true
solved = False
#
while not solved:
for eq in subeqs_to_solve:
new = replace(copy.deepcopy(eq), self.known_ops)
if isinstance(new, Equal):
lhs, rhs = new.get_children()
# Set input property
if all([isinstance(elem, Symbol) for elem in lhs]):
if isinstance(rhs, Predicate):
rhs.set_property(INPUT) # SOLVED?
for op in lhs:
op.set_property(INPUT) # SOLVED?
subeqs_solved.append(new)
else:
#print( "Can it be?" )
# Yes, e.g., trans(X_BL) in lyapunov
#raise Exception
pass
cur_solved_outputs = set(
[op.get_name() for op in all_outputs if isInput(op)])
#print( "SOLVED:", cur_solved_outputs )
if solved_outputs == cur_solved_outputs:
print("")
print(
"[WARNING] PME Generation is stuck - Trying recursive instance"
)
print("")
minimum = (100000, 100000)
subeq = None
for eq in subeqs_to_solve:
unks = []
cnt = 0
for node in eq.iterate_preorder():
cnt += 1
if isinstance(node, Symbol) and node.isOutput(
) and node not in unks:
unks.append(node)
if (len(unks), cnt) < minimum:
subeq = eq
minimum = (len(unks), cnt)
from NestedInstance import rec_instance
((md_name, md_data), new_patts,
new_pmes) = rec_instance(subeq.children[0])
self.known_pmes.extend(new_pmes)
print("NPMES:", len(new_pmes))
for patt in new_patts:
self.known_ops.append(patt)
pm.DB[md_name] = md_data
#raise Exception
solved_outputs = cur_solved_outputs
if all([isInput(op) or op.isZero() for op in all_outputs]):
solved = True
else:
new_to_solve = []
for eq in subeqs_to_solve:
if not isinstance( eq, Equal ) and \
len([op for op in eq.iterate_preorder() if isinstance(op, Symbol) and isOutput(op)]) != 0:
new_to_solve.append(eq)
subeqs_to_solve = [
simplify(to_canonicalIO(eq))._cleanup()
for eq in new_to_solve
]
self.solved_subequations = subeqs_solved
# Replace rhs with lhs if they appear as subexpressions of other rhss
#
# Create replacements when suited
reuse_rules = []
for i, eq in enumerate(subeqs_solved):
eq_rules = []
lhs, rhs = eq.children
if not isinstance(rhs, Predicate) and rhs.get_head() not in (
Minus, Transpose, Inverse):
lhs_sym = lhs.children[0]
t = PatternStar("t")
l = PatternStar("l")
r = PatternStar("r")
repl_f = (lambda lhs_sym: lambda d: Plus(
[d["t"], Times([d["l"], lhs_sym, d["r"]])]))(lhs_sym)
eq_rules.append(
RewriteRule(Plus([t, Times([l, rhs, r])]),
Replacement(repl_f)))
# A - B C in -L B C R + L A R (minus pushed all the way to the left)
if len(rhs.children) > 1:
repl_f = (lambda lhs_sym: lambda d: Times(
[Minus([lhs_sym])] + d["r"].children))(lhs_sym)
eq_rules.append(
RewriteRule(
Times([
Minus([rhs.children[0]]), *rhs.children[1:], r
]), Replacement(repl_f)))
reuse_rules.append((i, eq_rules))
# Replace
self.solved_subequations = []
for i, eq in enumerate(subeqs_solved):
rules = [r for j, r in reuse_rules if i != j]
self.solved_subequations.append(
replace_all(eq, list(itertools.chain(*rules))))
# [TODO] Add T to operands and bind dimensions
#self.bind_temporaries( )
# Reset outputs
for op in solved_outputs:
TOS[op][0].set_property(OUTPUT)
print("* PME ")
for eq in self.solved_subequations:
print("* ", eq)
def learn_pattern(self):
inops = [op for op in self.operands if op.isInput()]
outops = [op for op in self.operands if op.isOutput()]
# pattern
predicate_inops = []
predicate_outops = []
for op in self.operands:
rewrite_predicate_ops = []
basic_part = self.basic_partitionings[op.get_name()]
for part_op in itertools.chain(*basic_part):
rewrite_predicate_ops.append(
RewriteRule(part_op,
Replacement(PatternDot(part_op.get_name()))))
new = BlockedExpression(
copy.deepcopy(self.basic_partitionings[op.get_name()]),
op.get_size(), basic_part.shape)
if op.isInput():
predicate_inops.append(replace(new, rewrite_predicate_ops))
else:
predicate_outops.append(replace(new, rewrite_predicate_ops))
pattern = Equal([
NList(predicate_outops),
Predicate(self.name, predicate_inops,
[op.get_size() for op in outops])
])
# replacement
# [TODO] Tuple for get_size
#basic_parts = self.basic_partitionings
basic_parts = self.partitionings
lhss = map_thread(NList, [basic_parts[op.get_name()] for op in outops],
2)
# [TODO] This is a fix for lu (maybe coup sylv as well).
# Generalize and clean up
for i, row in enumerate(lhss):
for j, cell in enumerate(row):
cell = replace(cell, [
RewriteRule(
(NList([PatternPlus("PP"),
PatternDot("PD")
]), Constraint(lambda d: isZero(d["PD"]))),
Replacement(lambda d: NList(d["PP"].get_children()))),
RewriteRule(
(NList([PatternDot("PD"),
PatternPlus("PP")
]), Constraint(lambda d: isZero(d["PD"]))),
Replacement(lambda d: NList(d["PP"].get_children())))
])
lhss[i][j] = cell
#
# [CHECK] parts = self.partitionings
#parts = self.basic_partitionings
parts = self.partitionings
eqs = map_thread(Equal, [lhss, parts[outops[0].get_name()]], 2)
output_shape = self.basic_partitionings[outops[0].get_name()].shape
r, c = output_shape
for eq in self.solved_subequations:
lhs, rhs = eq.get_children()
for row in range(r):
for col in range(c):
this_lhs, this_rhs = eqs[row][col].get_children()
if lhs == this_lhs:
eqs[row][col].set_children(1, rhs)
#for row in range(r):
#for col in range(c):
#eqs[row][col] = equation2replacement( eqs[row][col].get_children()[1] )
replacement_str = equation2replacement(
BlockedExpression(eqs, (0, 0), output_shape))
#", ".join([
#"[ " + ", ".join( [ eq for eq in row ] ) + " ]"
#for row in eqs ]) + " ]" + \
#", (0,0), (%d, %d) )" % (r, c) + \
#"]), " + \
#"BlockedExpression([ " + \
#", ".join([
#"[ " + ", ".join( [ eq for eq in row ] ) + " ]"
#for row in eqs ]) + " ]" + \
#", (0,0), (%d, %d) )" % (r, c) + \
#"])" # size does not matter
print("* Learnt PME pattern")
print("* ", RewriteRule(pattern, Replacement(replacement_str)))
self.known_pmes.append(
RewriteRule(pattern, Replacement(replacement_str)))
with open(os.path.join("OUTPUT", self.name + "_pmes"),
"ab+") as pmes_f:
pickle.dump(self.known_pmes[-1], pmes_f)
def fix_temporaries(self):
temp_exprs = []
for expr in itertools.chain(*self.expressions):
lhs, rhs = expr.get_children()
for out in lhs:
if not out.isInput() and not out.isOutput(
): # [FIXME] Temporaries are not labeled. Now they are, fix.
self.linv_operands.append(out)
temp_exprs.append(expr)
for expr in temp_exprs:
#print( expr )
lhs, rhs = expr.get_children()
lhs = lhs.get_children()[0]
# Determine to which operands in the temporary bound
# Also, which quadrant of the full temporary should be used
(rows_op, r_dim), (cols_op,
c_dim) = utils.size_as_func_of_operands(rhs)
# set in bound_dimensions
r = rows_op.parent_op.get_name() + "_" + r_dim.lower()
for s in self.linv_bound_dimensions:
if r in s:
s.append(lhs.get_name() + "_r")
c = cols_op.parent_op.get_name() + "_" + c_dim.lower()
for s in self.linv_bound_dimensions:
if c in s:
s.append(lhs.get_name() + "_c")
# partition temporary
rows_parent = rows_op.parent_op.get_name()
cols_parent = cols_op.parent_op.get_name()
shape_rows = self.pme.part_shape[rows_parent][{
"R": 0,
"C": 1
}[r_dim]]
shape_cols = self.pme.part_shape[cols_parent][{
"R": 0,
"C": 1
}[c_dim]]
size_rows = rows_op.parent_op.get_size()[{"R": 0, "C": 1}[r_dim]]
size_cols = cols_op.parent_op.get_size()[{"R": 0, "C": 1}[c_dim]]
lhs.size = (size_rows, size_cols)
part = partition_shape(lhs, (shape_rows, shape_cols))
self.linv_operands_basic_part[lhs.get_name()] = part
part_shape = (len(part.children), len(part.children[0]))
self.linv_operands_part_shape[lhs.get_name()] = part_shape
part_rows = rows_op.quadrant[{"R": 0, "C": 1}[r_dim]]
part_cols = cols_op.quadrant[{"R": 0, "C": 1}[c_dim]]
quadrant = part[part_rows][part_cols]
# replace the temporary with the proper quadrant in every expression of the linv
# [TODO] why is loop invariant a list of lists?
expressions = []
for expr_l in self.expressions:
expressions.append([
replace(copy.deepcopy(expr),
[RewriteRule(lhs, Replacement(quadrant))])
for expr in expr_l
])
self.expressions = expressions
def is_feasible(self):
pme = self.pme
linv = self.expressions
traversal_tuples = [[0] if shape == 1 else [1, -1]
for shape in pme.part_tuple]
feasible_traversals = []
# For peeling in slingen mode
#self.iteration_rules = []
for traversal_dirs in itertools.product(*traversal_tuples):
dims_to_part_shape = {}
#for dims, shape in zip( self.operation.bound_dimensions, traversal_dirs ):
for dims, shape in zip(self.linv_bound_dimensions, traversal_dirs):
for dim in dims:
dims_to_part_shape[dim] = shape
initial_rules = []
final_rules = []
trav_shape = dict()
#for operand in self.operation.operands:
for operand in self.linv_operands:
trav_shape[operand.get_name()] = (
dims_to_part_shape[operand.get_name() + "_r"],
dims_to_part_shape[operand.get_name() + "_c"])
initial_rules.extend(
#initial_rewrite(operand, pme.basic_partitionings[operand.get_name()], trav_shape[operand.get_name()])
initial_rewrite(
operand,
self.linv_operands_basic_part[operand.get_name()],
trav_shape[operand.get_name()]))
final_rules.extend(
#final_rewrite(operand, pme.basic_partitionings[operand.get_name()], trav_shape[operand.get_name()])
final_rewrite(
operand,
self.linv_operands_basic_part[operand.get_name()],
trav_shape[operand.get_name()]))
pre = []
post = []
for expr in itertools.chain(*linv):
new = copy.deepcopy(expr)
pre.append(simplify(to_canonical(replace(new, initial_rules))))
new = copy.deepcopy(expr)
post.append(simplify(to_canonical(replace(new, final_rules))))
# check if basic init
basic_init = True
for expr in pre:
lhs, rhs = expr.get_children()
if not all( op.isZero() for op in lhs ) and not \
isOperand( rhs ):
basic_init = False
break
if not basic_init:
continue
# check if linv and not guard -> post
#final_status = [ replace( copy.deepcopy(expr), self.op_to_implicit ) for expr in post ]
final_status = post
#rules1 = []
#rules2 = []
#neweq = replace( copy.deepcopy(self.operation.equation), [self.pme.known_ops[-1]] )
neweq = replace(copy.deepcopy(self.operation.equation),
self.pme.known_ops)
# [FIXME] Generalize
implies_post = True
if not neweq in final_status:
implies_post = False
continue
feasible_traversals.append((trav_shape, pre, post))
# Store these states for use in loop peeling (LGenCode)
#self.iteration_rules.append( (initial_rules, final_rules) )
if len(feasible_traversals) > 1:
print("* More than one traversal for this LoopInvariant: %d" %
len(feasible_traversals))
self.traversals = feasible_traversals
return bool(feasible_traversals)
