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""" Optimizations of the expression tree representation for better CSE
opportunities.
"""
from sympy.core import Add, Basic, Mul
from sympy.core.singleton import S
from sympy.core.sorting import default_sort_key
from sympy.core.traversal import preorder_traversal
def sub_pre(e):
""" Replace y - x with -(x - y) if -1 can be extracted from y - x.
"""
# replacing Add, A, from which -1 can be extracted with -1*-A
adds = [a for a in e.atoms(Add) if a.could_extract_minus_sign()]
reps = {}
ignore = set()
for a in adds:
na = -a
if na.is_Mul: # e.g. MatExpr
ignore.add(a)
continue
reps[a] = Mul._from_args([S.NegativeOne, na])
e = e.xreplace(reps)
# repeat again for persisting Adds but mark these with a leading 1, -1
# e.g. y - x -> 1*-1*(x - y)
if isinstance(e, Basic):
negs = {}
for a in sorted(e.atoms(Add), key=default_sort_key):
if a in ignore:
continue
if a in reps:
negs[a] = reps[a]
elif a.could_extract_minus_sign():
negs[a] = Mul._from_args([S.One, S.NegativeOne, -a])
e = e.xreplace(negs)
return e
def sub_post(e):
""" Replace 1*-1*x with -x.
"""
replacements = []
for node in preorder_traversal(e):
if isinstance(node, Mul) and \
node.args[0] is S.One and node.args[1] is S.NegativeOne:
replacements.append((node, -Mul._from_args(node.args[2:])))
for node, replacement in replacements:
e = e.xreplace({node: replacement})
return e
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