def normalize_minus( expr ):
ld = PatternDot("ld")
md = PatternDot("md")
l = PatternStar("l")
r = PatternStar("r")
return replace_all( expr, [RewriteRule( Times([ ld, l, Minus([md]), r ]),
Replacement( lambda d: Times([ Minus([d["ld"]]), d["l"], d["md"], d["r"]]) )),
RewriteRule( Times([ Minus([Minus([ld])]), l ]),
Replacement( lambda d: Times([ d["ld"], d["l"]]) )),
RewriteRule( Minus([ Times([ ld, l ]) ]),
Replacement( lambda d: Times([ Minus([d["ld"]]), d["l"]]) )) ] )
def initial_rewrite(operand, part, trav_shape):
part_ch = part.get_children()
part_shape = (len(part_ch), len(part_ch[0]))
zero = Zero((sZERO, sZERO))
if part_shape == (1, 1):
#rewrite = [[operand]]
return []
elif part_shape == (1, 2): # [L|R]
if trav_shape == (
0, 1
): # Left to Right, initially Left is empty, Right is the full operand
rewrite = [[zero, operand]]
elif trav_shape == (0, -1): # Right to Left
rewrite = [[operand, zero]]
elif part_shape == (2, 1): # [T;B]
if trav_shape == (1, 0): # Top to Bottom
rewrite = [[zero], [operand]]
elif trav_shape == (-1, 0): # Bottom to Top
rewrite = [[operand], [zero]]
elif part_shape == (2, 2): # [TL TR; BL BR]
if trav_shape == (1, 1): # Top Left to Bottom Right
rewrite = [[zero, zero], [zero, operand]]
elif trav_shape == (1, -1): # Top Right to Bottom Left
rewrite = [[zero, zero], [operand, zero]]
elif trav_shape == (-1, 1): # Bottom Left to Top Right
rewrite = [[zero, operand], [zero, zero]]
elif trav_shape == (-1, -1): # Bottom Right to Top Left
rewrite = [[operand, zero], [zero, zero]]
return list(
itertools.chain(*[[
RewriteRule(p, Replacement(rew)) for p, rew in zip(p_row, rew_row)
] for p_row, rew_row in zip(part, rewrite)]))
def expr_to_rule_lhs_rhs(self, predicates):
rules = []
for p in predicates:
lhs, rhs = p.children
if len(lhs.children) == 1:
rules.append([RewriteRule(lhs.children[0], Replacement(rhs))])
return rules
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 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 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 _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 before_to_rule(self, before):
lhs, rhs = before.get_children()
if isinstance(rhs, Plus):
rules = [
RewriteRule(
Plus([PatternStar("rest")] + rhs.get_children()),
Replacement(lambda d: Plus(d["rest"].get_children() + lhs.
get_children()))),
#Replacement("Plus(rest+lhs.get_children())") )
RewriteRule(
Plus([
Times([PatternStar("l")] + [ch] + [PatternStar("r")])
for ch in rhs.get_children()
]),
Replacement(lambda d: Times(d["l"].get_children(
) + lhs.get_children() + d["r"].get_children()))),
RewriteRule(
to_canonical(
Plus([
Times([PatternStar("l")] + [ch] +
[PatternStar("r")])
for ch in rhs.get_children()
])),
Replacement(lambda d: Times(d["l"].get_children(
) + lhs.get_children() + d["r"].get_children())))
]
elif isinstance(rhs, Times):
rules = [
RewriteRule(
Times([PatternStar("l")] + rhs.get_children() +
[PatternStar("r")]),
Replacement(lambda d: Times(d["l"].get_children(
) + lhs.get_children() + d["r"].get_children()))),
# [TODO] For chol loop invariants 2 and 3, should fix elsewhere (maybe -1 instead of minus operator)
RewriteRule(
Times([PatternStar("l")] +
[to_canonical(Minus([Times(rhs.get_children())]))] +
[PatternStar("r")]),
Replacement(lambda d: Times(d["l"].get_children() + [
to_canonical(Minus([Times(lhs.get_children())]))
] + d["r"].get_children())))
]
else: # [FIX] what if multiple outputs?
#rules = [ RewriteRule( rhs, Replacement( lhs ) ) ]
rules = [RewriteRule(rhs, Replacement(lhs.children[0]))]
return rules
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 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)
pm.DB["rdiv_utu_ow"].overwrite = [(1, 0)]
A = PatternDot("A")
B = PatternDot("B")
X = PatternDot("X")
trsm2lgen_rules = [
# X = i(t(A)) B -> ldiv_lni
RewriteRule((
Equal([NList([X]), Times([Inverse([A]), B])]),
Constraint(
"A.isLowerTriangular() and A.isImplicitUnitDiagonal() and X.st_info[1].name == X.name"
)),
Replacement(lambda d: Equal([
NList([d["X"]]),
Predicate("ldiv_lni", [d["A"], d["B"]],
[d["A"].get_size(), d["B"].get_size()])
]))),
# X = i(t(A)) B -> ldiv_lni_ow
RewriteRule(
(Equal([NList([X]), Times([Inverse([A]), B])]),
Constraint(
"A.isLowerTriangular() and A.isImplicitUnitDiagonal() and X.st_info[1].name != X.name"
)),
Replacement(lambda d: Equal([
NList([d["X"]]),
Predicate("ldiv_lni_ow", [d["A"], d["B"]],
[d["A"].get_size(), d["B"].get_size()])
]))),
# X = i(t(A)) B -> ldiv_lnu
RewriteRule(
def expr_to_rule_rhs_lhs(self, predicates):
rules = []
t = PatternStar("t")
l = PatternStar("l")
ld = PatternDot("ld")
r = PatternStar("r")
for p in predicates:
pr = []
lhs, rhs = p.children
if len(lhs.children) == 1:
#lhs_sym = WrapOutBef( lhs.children[0] )
lhs_sym = lhs.children[0]
if isinstance(rhs, Plus):
# t___ + rhs -> t + lhs
repl_f = (lambda lhs: lambda d: Plus(d["t"].children +
[lhs]))(lhs_sym)
pr.append(
RewriteRule(Plus([t] + rhs.children),
Replacement(repl_f)))
# t___ + l___ rhs_i r___ + ... -> t + l lhs r
repl_f = (lambda lhs: lambda d: Plus(d["t"].children + [
Times(d["l"].children + [lhs] + d["r"].children)
]))(lhs_sym)
pr.append(
RewriteRule(
Plus([t] + [
Times([l] + [ch] + [r]) for ch in rhs.children
]), Replacement(repl_f)))
repl_f = (lambda lhs: lambda d: Plus(d["t"].children + [
Times([simplify(to_canonical(Minus([lhs])))] + d["r"].
children)
]))(lhs_sym)
pr.append(
RewriteRule(
Plus([t] + [
Times([simplify(to_canonical(Minus([ch])))] +
[r]) for ch in rhs.children
]), Replacement(repl_f)))
# A - B C in L B C R + -L A R (minus pushed all the way to the left, and whole thing negated)
repl_f = (lambda lhs: lambda d: normalize_minus(
Plus(d["t"].children + [
Times([d["ld"]] + d["l"].children + [Minus([lhs])]
+ d["r"].children)
])))(lhs_sym)
pr.append(
RewriteRule(
Plus([t] + [
normalize_minus(Times([ld, l,
Minus([ch]), r]))
for ch in rhs.children
]), Replacement(repl_f)))
# A - B C in -L B C R + L A R (minus pushed all the way to the left)
repl_f = (lambda lhs: lambda d: Plus(d["t"].children + [
Times([d["ld"]] + d["l"].children + [lhs] + d["r"].
children)
]))(lhs_sym)
pr.append(
RewriteRule(
Plus([t] + [
normalize_minus(Times([ld, l, ch, r]))
for ch in rhs.children
]), Replacement(repl_f)))
#repl_f = (lambda lhs: lambda d: Plus(d["t"].children + [Times([simplify(to_canonical(Minus(lhs.children)))] + d["r"].children)]))(lhs_sym)
#pr.append( RewriteRule( Plus([t] + [
#Times([ Minus([ld]), l, ch, r]) if not isinstance(ch, Minus) \
#else Times([ l, ch.children[0], r]) \
#for ch in rhs.children ]),
#Replacement(repl_f) ) )
repl_f = (lambda lhs: lambda d: Plus(d["t"].children + [
Times([
simplify(to_canonical(Minus([Transpose([lhs])])))
] + d["r"].children)
]))(lhs_sym)
pr.append( RewriteRule( Plus([t] + [
Times([ Minus([ld]), l, simplify(to_canonical(Transpose([ch]))), r]) if not isinstance(ch, Minus) \
else Times([ l, simplify(to_canonical(Transpose([ch]))), r]) \
for ch in rhs.children ]),
Replacement(repl_f) ) )
elif isinstance(rhs, Times):
repl_f = (lambda lhs: lambda d: Times(d[
"l"].children + [lhs] + d["r"].children))(lhs_sym)
pr.append(
RewriteRule(Times([l] + rhs.children + [r]),
Replacement(repl_f)))
repl_f = (lambda lhs: lambda d: Times(d[
"l"].children + [Transpose([lhs])] + d["r"].children)
)(lhs_sym)
pr.append(
RewriteRule(
Times([
l,
simplify(to_canonical(Transpose([rhs]))), r
]), Replacement(repl_f)))
# [TODO] Minus is a b*tch. Should go for -1 and remove the operator internally?
repl_f = (lambda lhs: lambda d: Times([
simplify(to_canonical(Minus([Times([lhs])])))
] + d["r"].children))(lhs_sym)
pr.append(
RewriteRule(
Times([
simplify(
to_canonical(
Minus([Times(rhs.get_children())])))
] + [r]), Replacement(repl_f)))
repl_f = (lambda lhs: lambda d: Times([
simplify(
to_canonical(Minus([Transpose([Times([lhs])])])))
] + d["r"].children))(lhs_sym)
pr.append(
RewriteRule(
Times([
simplify(
to_canonical(
Minus([
Transpose(
[Times(rhs.get_children())])
])))
] + [r]), Replacement(repl_f)))
else:
pr.append(RewriteRule(rhs, Replacement(lhs_sym)))
new_rhs = simplify(to_canonical(Transpose([rhs])))
if not isOperand(new_rhs):
pr.append(
RewriteRule(
simplify(to_canonical(Transpose([rhs]))),
Replacement(Transpose([lhs_sym]))))
else:
pr.append(RewriteRule(rhs, Replacement(lhs)))
rules.append(pr)
return rules
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 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 learn_pattern(self):
inops = [op for op in self.operands if op.isInput()]
outops = [op for op in self.operands if op.isOutput()]
#
single_assignment = len( self.equation.children ) == 1 and \
isinstance(self.equation.children[0].children[0], Symbol) # eq.lhs.single_entry_in_NL
#
op_to_pattern = [
RewriteRule(op, Replacement("PatternDot(%s.name)" % op.name))
for op in self.operands
]
pattern = NList([
replace_all(copy.deepcopy(eq), op_to_pattern)
for eq in self.equation
])
if single_assignment:
props_str = [
symbol_props_to_constraints_no_io(op) for op in self.operands
]
constraint = Constraint(" and ".join(
[prop for prop in props_str if prop]))
else:
constraint = Constraint(" and ".join(
[symbol_props_to_constraints(op) for op in self.operands]))
# [TODO] Tuple for get_size
replacement = Replacement(
"Equal([ NList([%s]), Predicate( \"%s\", [%s], [%s] ) ])" %
(", ".join([op.name for op in outops]), self.name, ", ".join([
op.name for op in inops
]), ", ".join(["%s.get_size()" % op.get_name() for op in outops])))
# [TODO] This should be part of the verbose option
print("* Learnt pattern")
print("* ", pattern, end="")
if constraint.to_eval:
print("with ", constraint.to_eval)
print(" --> ")
print("* ", replacement.to_eval)
print("**********************************")
# [TODO] Maybe sort known ops by specificity (a la mathematica)
#known_ops.insert( 0, RewriteRule( (pattern, constraint), replacement ) )
if single_assignment:
expr = pattern.children[0]
expr.children[0] = NList([expr.children[0]])
known_ops_single.insert(
0, RewriteRule((expr, constraint), replacement))
# With minus
replacement = Replacement(
"Equal([ NList([%s]), Minus([ Predicate( \"%s\", [%s], [%s] ) ]) ])"
% (", ".join([op.name for op in outops]), self.name, ", ".join(
[op.name for op in inops]), ", ".join(
["%s.get_size()" % op.get_name() for op in outops])))
expr = copy.deepcopy(expr)
expr.children[1] = Minus([expr.children[1]])
expr.children[1] = normalize_minus(copy.deepcopy(expr.children[1]))
known_ops_single.insert(
0, RewriteRule((expr, constraint), replacement))
#with open(os.path.join("OUTPUT", self.name+"_patterns"), "wb") as patt_f:
#pickle.dump( known_ops_single[1], patt_f )
#pickle.dump( known_ops_single[0], patt_f )
else:
known_ops.insert(0, RewriteRule((pattern, constraint),
replacement))
with open(os.path.join("OUTPUT", self.name + "_patterns"),
"wb") as patt_f:
pickle.dump(known_ops[0], patt_f)
pattern = Equal([
NList([PatternDot(op.get_name()) for op in outops]),
Predicate(self.name, [PatternDot(op.get_name()) for op in inops],
[op.get_size() for op in outops])
])
replacement = Replacement(equation2replacement(self.equation))
op_to_implicit.append(RewriteRule(pattern, replacement))
def generate_loop_based_algorithms(self):
print("* Generating Loop-based algorithms...")
self.algs = []
variant = 1
for pme, linvs in zip(self.pmes, self.linvs):
algs = []
for linv in linvs:
print("* ")
print("* Loop invariant", variant)
for expr in linv.expressions:
print("* ", expr)
print("* ")
trav, init_state, _ = linv.traversals[
0] # this would be another for loop
init = self.algorithm_initialization(init_state)
print("* Init")
#print( init_state )
print("* ", init)
s = PatternDot("s")
init = [
replace_all(i, [
RewriteRule(WrapOutBef(s),
Replacement(lambda d: d["s"]))
]) for i in init
]
print("* Before")
repart, before = self.generate_predicate_before(
pme, trav, linv.expressions, linv)
print("* After")
reversed_trav = dict([(k, (r * -1, c * -1))
for k, (r, c) in trav.items()])
cont_with, after = self.generate_predicate_before(
pme, reversed_trav, linv.expressions, linv)
# find updates
print("* Updates")
updates = self.find_updates(before, after)
if updates is None:
#variant += 1
continue
# Tile updates
for u in updates:
infer_properties(u)
final_updates = []
# [DIEGO] Fixing some output pieces being labeled as input
outputs = []
for u in updates:
lhs, rhs = u.children
for l in lhs:
if not l.isTemporary():
outputs.append(l)
l.set_property(OUTPUT)
#
for u in updates:
#[DIEGO] u.children[0].children[0].set_property( OUTPUT )
for node in u.children[1].iterate_preorder():
#if isinstance(node, Symbol):
if isinstance(node, Symbol) and node not in outputs:
node.set_property(INPUT)
#
#copy_u = replace( copy.deepcopy(u), known_ops_single )
copy_u = copy.deepcopy(u)
copy_u = tile_expr(copy.deepcopy(copy_u))[0] # One tiling
final_updates.extend(copy_u)
if len(updates) == 0:
print("No updates!! Should only happen in copy")
continue
algs.append(
Algorithm(linv, variant, init, repart, cont_with, before,
after, final_updates))
algs[-1].prepare_for_code_generation()
variant += 1
self.algs.append(algs)
LHS = PatternDot("LHS")
RHS = PatternDot("RHS")
subexpr = PatternDot("subexpr")
PD1 = PatternDot("PD1")
PD2 = PatternDot("PD2")
PS1 = PatternStar("PS1")
PS2 = PatternStar("PS2")
PS3 = PatternStar("PS3")
PSLeft = PatternStar("PSLeft")
PSRight = PatternStar("PSRight")
simplify_rules = [
# Minus
# --expr -> expr
RewriteRule(Minus([Minus([subexpr])]),
Replacement(lambda d: d["subexpr"])),
# -0 -> 0
RewriteRule((Minus([subexpr]), Constraint(lambda d: isZero(d["subexpr"]))),
Replacement(lambda d: d["subexpr"])),
# Plus
# Plus(a) -> a
RewriteRule(Plus([subexpr]), Replacement(lambda d: d["subexpr"])),
# Plus( a___, 0, b___ ) -> Plus( a, b )
RewriteRule((Plus([PS1, subexpr, PS2
]), Constraint(lambda d: isZero(d["subexpr"]))),
Replacement(lambda d: Plus([d["PS1"], d["PS2"]]))),
# a - a -> 0
RewriteRule(
Plus([PS1, subexpr, PS2, Minus([subexpr]), PS3]),
Replacement(lambda d: Plus(
[d["PS1"],
from Tiling import tile_expr
from utils import sort
from RewritingExtension import *
from BackEnd.MatlabCode import generate_matlab_code, click2matlab
#from BackEnd.LatexCode import generate_latex_code
from BackEnd.LGenCode import generate_lgen_files
#from BackEnd.CCode import generate_c_code
known_ops = [
# Straight assignment
RewriteRule(
(NList([Equal([PatternDot("LHS"), PatternDot("RHS")])]),
Constraint(
"isinstance(LHS, Symbol) and isOutput(LHS) and isInput(RHS)")),
Replacement("Equal([ NList([LHS]), RHS ])"))
]
known_ops_single = []
known_pmes = []
op_to_implicit = []
# Add a verbose option
# For now it would help to illustrate the process
class Operation(object):
def __init__(self, name, operands, equation, overwrite):
self.name = name
self.operands = operands
self.equation = equation # list because it may be a coupled equation
self.overwrite = overwrite
pass
# [FIXME] Default?
# [TODO] Complete
instruction_set = [
# Basic Ops - Completeness of the instruction set
#
[
# Inverse
Instruction(
( Inverse([ A ]), Constraint("isOperand(A)") ),
lambda d, t: \
RewriteRule(
Inverse([ d["A"] ]),
Replacement( "%s" % t )
),
lambda d: Inverse([ d["A"] ])
),
# Transpose
Instruction(
( Transpose([ A ]), Constraint("isOperand(A)") ),
lambda d, t: \
RewriteRule(
Transpose([ d["A"] ]),
Replacement( "%s" % t )
),
lambda d: Transpose([ d["A"] ])
),
# Minus
#( Minus([ A ]), Constraint("isOperand(A, Symbol)") ),
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 )
class triu(Operator):
def __init__(self, arg):
Operator.__init__(self, [arg], [], UNARY)
self.size = arg.get_size()
# Patterns for inv to trsm
A = PatternDot("A")
B = PatternDot("B")
C = PatternDot("C")
# [TODO] Complete the set of patterns
trsm_patterns = [
#RewriteRule( (Equal([ C, Times([ B, Transpose([Inverse([A])]) ]) ]), Constraint("A.st_info[0] == ST_LOWER")), \
RewriteRule( Equal([ C, Times([ B, Transpose([Inverse([A])]) ]) ]), \
Replacement( lambda d: Equal([ d["C"], mrdiv([ Transpose([tril(d["A"])]), d["B"] ]) ]) ) ),
]
#
# Produces Matlab code for:
# - Loop-based code
#
def generate_matlab_code(operation, matlab_dir):
# Recursive code
out_path = os.path.join(matlab_dir, operation.name +
".m") # [FIX] At some this should be opname_rec.m
with open(out_path, "w") as out:
generate_matlab_recursive_code(operation, operation.pmes[-1],
out) # pmes[-1] should be the 2x2 one
# Loop based code
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 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
TOS.push_back_temp( )
TOS._TOS.unset_operand( tile.children[0].children[0] )
if matched_in_this_level: ###
break
PD1 = PatternDot("PD1")
PD2 = PatternDot("PD2")
PS1 = PatternStar("PS1")
PS2 = PatternStar("PS2")
grouping_rules = [
# A B + A C D -> A (B + C D)
RewriteRule(
Plus([ Times([ PD1, PS1 ]), Times([ PD1, PS2 ]) ]),
Replacement(lambda d: Times([ d["PD1"], Plus([Times([d["PS1"]]), Times([d["PS2"]])]) ]))
),
# A B - A C D -> A (B - C D)
RewriteRule(
Plus([ Times([ PD1, PS1 ]), Times([ Minus([PD1]), PD2, PS2 ]) ]),
Replacement(lambda d: Times([ d["PD1"], Plus([ Times([d["PS1"]]), Times([Minus([d["PD2"]]), Times([d["PS2"]])])]) ]))
),
# B A + C D A -> (B + C D) A
RewriteRule(
Plus([ Times([ PS1, PD1 ]), Times([ PS2, PD1 ]) ]),
Replacement(lambda d: Times([ Plus([ Times([d["PS1"]]), Times([d["PS2"]]) ]), d["PD1"] ]))
),
# B A - C D A -> (B - C D) A
RewriteRule(
Plus([ Times([ PS1, PD1 ]), Times([ Minus([PD2]), PS2, PD1 ]) ]),
Replacement(lambda d: Times([ Plus([ Times([d["PS1"]]), Times([Minus([d["PD2"]]), d["PS2"]])]), d["PD1"] ]))
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
subexpr = PatternDot("subexpr")
PD1 = PatternDot("PD1")
PD2 = PatternDot("PD2")
PS1 = PatternStar("PS1")
PS2 = PatternStar("PS2")
PS3 = PatternStar("PS3")
PSLeft = PatternStar("PSLeft")
PSRight = PatternStar("PSRight")
# TODO: where do we place A*inv(A) -> I?
canonical_rules = [
# a * ( b + c ) * e -> a*b*e + a*c*e
RewriteRule(
Times([PSLeft, Plus([PS1]), PSRight]),
Replacement(lambda d: Plus(
[Times([d["PSLeft"], term, d["PSRight"]]) for term in d["PS1"]]))),
# -( a + b) -> (-a)+(-b)
RewriteRule(
Minus([Plus([PS1])]),
Replacement(lambda d: Plus([Minus([term]) for term in d["PS1"]]))),
# -( a * b) -> (-a) * b
RewriteRule(Minus([Times([PD1, PS1])]),
Replacement(lambda d: Times([Minus([d["PD1"]]), d["PS1"]]))),
# a * b * (-c) -> (-a) * b * c
RewriteRule(
Times([PD1, PS1, Minus([PD2]), PS2]),
Replacement(lambda d: Times(
[Minus([d["PD1"]]), d["PS1"], d["PD2"], d["PS2"]]))),
# Transpose( A + B + C ) -> A^T + B^T + C^T
RewriteRule(
Transpose([Plus([PS1])]),