def test_pow(prime):
simplifier = ExpressionSimplifier(prime)
assert simplifier.visit(parse_expr('4 ** 3 ** 2')).format() == '262144'
if prime is not None:
# Make sure the exponent is not computed modulo prime (if it were,
# the result would have been 1).
assert simplifier.visit(
parse_expr('(3 * 2**30 + 4) ** (3 * 2**30 + 1)')).format() == '3'
with pytest.raises(
SimplifierError,
match='Power is not supported with a negative exponent'):
simplifier.visit(parse_expr('2 ** (-1)'))
def converge(
self, reference_manager: ReferenceManager, other: 'FlowTrackingData',
group_alloc: Callable):
if not isinstance(other, FlowTrackingDataActual):
return other.converge(reference_manager, self, group_alloc)
new_ap_tracking = self.ap_tracking.converge(other.ap_tracking, group_alloc)
simplifier = ExpressionSimplifier()
# Allow different references from different branches to unite if they have the same name
# and the same expression at the converged ap_tracking.
reference_ids = {}
for name, ref_id in self.reference_ids.items():
other_ref_id = other.reference_ids.get(name)
if other_ref_id is None:
continue
reference = reference_manager.get_ref(ref_id)
other_ref = reference_manager.get_ref(other_ref_id)
try:
ref_expr = reference.eval(self.ap_tracking)
if simplifier.visit(ref_expr) == \
simplifier.visit(other_ref.eval(other.ap_tracking)):
# Same expression.
if self.ap_tracking != new_ap_tracking:
# Create a new reference on the new ap tracking.
new_reference = Reference(
pc=reference.pc,
value=ref_expr,
ap_tracking_data=new_ap_tracking,
)
ref_id = reference_manager.get_id(new_reference)
reference_ids[name] = ref_id
except FlowTrackingError:
pass
return FlowTrackingDataActual(
ap_tracking=new_ap_tracking,
reference_ids=reference_ids,
)
def test_division_by_zero(prime):
simplifier = ExpressionSimplifier(prime)
with pytest.raises(SimplifierError, match='Division by zero'):
simplifier.visit(parse_expr('fp / 0'))
with pytest.raises(SimplifierError, match='Division by zero'):
simplifier.visit(parse_expr('5 / 0'))
if prime is not None:
with pytest.raises(SimplifierError, match='Division by zero'):
simplifier.visit(parse_expr(f'fp / {prime}'))
def test_modulo():
PRIME = 19
simplifier = ExpressionSimplifier(PRIME)
# Check that the range is (-PRIME/2, PRIME/2).
assert simplifier.visit(parse_expr('-9')).format() == '-9'
assert simplifier.visit(parse_expr('-10')).format() == '9'
assert simplifier.visit(parse_expr('9')).format() == '9'
assert simplifier.visit(parse_expr('10')).format() == '-9'
# Check value which is bigger than PRIME.
assert simplifier.visit(parse_expr('20')).format() == '1'
# Check operators.
assert simplifier.visit(parse_expr('10 + 10')).format() == '1'
assert simplifier.visit(parse_expr('10 - 30')).format() == '-1'
assert simplifier.visit(parse_expr('10 * 10')).format() == '5'
assert simplifier.visit(parse_expr('2 / 3')).format() == '7'
def test_rotation(prime):
simplifier = ExpressionSimplifier(prime)
assert simplifier.visit(parse_expr('(fp + 10) + 1')).format() == 'fp + 11'
assert simplifier.visit(parse_expr('(fp + 10) - 1')).format() == 'fp + 9'
assert simplifier.visit(
parse_expr('(fp - 10) + 1')).format() == 'fp + (-9)'
assert simplifier.visit(
parse_expr('(fp - 10) - 1')).format() == 'fp + (-11)'
assert simplifier.visit(parse_expr('(10 + fp) - 1')).format() == 'fp + 9'
assert simplifier.visit(parse_expr('10 + (fp - 1)')).format() == 'fp + 9'
assert simplifier.visit(parse_expr('10 + (1 + fp)')).format() == 'fp + 11'
assert simplifier.visit(
parse_expr('10 + (1 + fp) + 100')).format() == 'fp + 111'
assert simplifier.visit(
parse_expr('10 + (1 + (fp + 100))')).format() == 'fp + 111'
def test_simplifier(prime):
assignments = {'x': 10, 'y': 3, 'z': -2, 'w': -60}
simplifier = ExpressionSimplifier(prime)
simplify = lambda expr: simplifier.visit(
substitute_identifiers(expr, lambda var: assignments[var.name]))
assert simplify(parse_expr('fp + x * (y + -1)')).format() == 'fp + 20'
assert simplify(parse_expr('[fp + x] + [ap - (-z)]')).format() == \
'[fp + 10] + [ap + (-2)]'
assert simplify(parse_expr('fp + x - y')).format() == 'fp + 7'
assert simplify(parse_expr('[1 + fp + 5]')).format() == '[fp + 6]'
assert simplify(parse_expr('[fp] - 3')).format() == '[fp] + (-3)'
if prime is not None:
assert simplify(parse_expr('fp * (x - 1) / y')).format() == 'fp * 3'
assert simplify(parse_expr('fp * w / x / y / z')).format() == 'fp'
else:
assert simplify(
parse_expr('fp * (x - 1) / y')).format() == 'fp * 9 / 3'
assert simplify(parse_expr('fp * w / x / y / z')).format() == \
'fp * (-60) / 10 / 3 / (-2)'
assert simplify(parse_expr('fp * 1')).format() == 'fp'
assert simplify(parse_expr('1 * fp')).format() == 'fp'