def _arithmetic_helper(
a: "BitVecFunc", b: Union[BitVec, int], operation: Callable
) -> "BitVecFunc":
"""
Helper function for arithmetic operations on BitVecFuncs.
:param a: The BitVecFunc to perform the operation on.
:param b: A BitVec or int to perform the operation on.
:param operation: The arithmetic operation to perform.
:return: The resulting BitVecFunc
"""
if isinstance(b, int):
b = BitVec(z3.BitVecVal(b, a.size()))
raw = operation(a.raw, b.raw)
union = a.annotations.union(b.annotations)
if isinstance(b, BitVecFunc):
return BitVecFunc(
raw=raw,
func_name="Hybrid",
input_=BitVec(z3.BitVec("", 256), annotations=union),
nested_functions=a.nested_functions + b.nested_functions + [a, b],
)
return BitVecFunc(
raw=raw,
func_name=a.func_name,
input_=a.input_,
annotations=union,
nested_functions=a.nested_functions + [a],
)
def _arithmetic_helper(a: "BitVecFunc", b: Union[BitVec, int],
operation: Callable) -> "BitVecFunc":
"""
Helper function for arithmetic operations on BitVecFuncs.
:param a: The BitVecFunc to perform the operation on.
:param b: A BitVec or int to perform the operation on.
:param operation: The arithmetic operation to perform.
:return: The resulting BitVecFunc
"""
if isinstance(b, int):
b = BitVec(z3.BitVecVal(b, a.size()))
raw = operation(a.raw, b.raw)
union = a.annotations.union(b.annotations)
if isinstance(b, BitVecFunc):
# TODO: Find better value to set input and name to in this case?
input_string = "MisleadingNotationop(invhash({}) {} invhash({})".format(
hash(a), operation, hash(b))
return BitVecFunc(
raw=raw,
func_name="Hybrid",
input_=BitVec(z3.BitVec(input_string, 256), annotations=union),
)
return BitVecFunc(raw=raw,
func_name=a.func_name,
input_=a.input_,
annotations=union)
def Concat(*args: Union[BitVec, List[BitVec]]) -> BitVec:
"""Create a concatenation expression.
:param args:
:return:
"""
# The following statement is used if a list is provided as an argument to concat
if len(args) == 1 and isinstance(args[0], list):
bvs = args[0] # type: List[BitVec]
else:
bvs = cast(List[BitVec], args)
nraw = z3.Concat([a.raw for a in bvs])
annotations = set() # type: Annotations
nested_functions = [] # type: List[BitVecFunc]
for bv in bvs:
annotations = annotations.union(bv.annotations)
if isinstance(bv, BitVecFunc):
nested_functions += bv.nested_functions
nested_functions += [bv]
if nested_functions:
return BitVecFunc(
raw=nraw,
func_name="Hybrid",
input_=BitVec(z3.BitVec("", 256), annotations=annotations),
nested_functions=nested_functions,
)
return BitVec(nraw, annotations)
def BVAddNoOverflow(a: Union[BitVec, int], b: Union[BitVec, int],
signed: bool) -> Bool:
"""Creates predicate that verifies that the addition doesn't overflow.
:param a:
:param b:
:param signed:
:return:
"""
if not isinstance(a, BitVec):
a = BitVec(z3.BitVecVal(a, 256))
if not isinstance(b, BitVec):
b = BitVec(z3.BitVecVal(b, 256))
return Bool(z3.BVAddNoOverflow(a.raw, b.raw, signed))
def __getitem__(self, item: BitVec) -> BitVec:
"""Gets item from the array, item can be symbolic."""
if isinstance(item, slice):
raise ValueError(
"Instance of BaseArray, does not support getitem with slices")
return BitVec(cast(z3.BitVecRef, z3.Select(self.raw,
item.raw))) # type: ignore
def _comparison_helper(
a: "BitVecFunc",
b: Union[BitVec, int],
operation: Callable,
default_value: bool,
inputs_equal: bool,
) -> Bool:
"""
Helper function for comparison operations with BitVecFuncs.
:param a: The BitVecFunc to compare.
:param b: A BitVec or int to compare to.
:param operation: The comparison operation to perform.
:return: The resulting Bool
"""
# Is there some hack for gt/lt comparisons?
if isinstance(b, int):
b = BitVec(z3.BitVecVal(b, a.size()))
union = a.annotations.union(b.annotations)
if not a.symbolic and not b.symbolic:
return Bool(z3.BoolVal(operation(a.value, b.value)), annotations=union)
if (not isinstance(b, BitVecFunc) or not a.func_name or not a.input_
or not a.func_name == b.func_name):
return Bool(z3.BoolVal(default_value), annotations=union)
return And(
Bool(cast(z3.BoolRef, operation(a.raw, b.raw)), annotations=union),
a.input_ == b.input_ if inputs_equal else a.input_ != b.input_,
)
return a.input_ == b.input_
def _arithmetic_helper(a: "BitVecFunc", b: Union[BitVec, int],
operation: Callable) -> "BitVecFunc":
"""
Helper function for arithmetic operations on BitVecFuncs.
:param a: The BitVecFunc to perform the operation on.
:param b: A BitVec or int to perform the operation on.
:param operation: The arithmetic operation to perform.
:return: The resulting BitVecFunc
"""
if isinstance(b, int):
b = BitVec(z3.BitVecVal(b, a.size()))
raw = operation(a.raw, b.raw)
union = a.annotations.union(b.annotations)
if isinstance(b, BitVecFunc):
# TODO: Find better value to set input and name to in this case?
return BitVecFunc(raw=raw,
func_name=None,
input_=None,
annotations=union)
return BitVecFunc(raw=raw,
func_name=a.func_name,
input_=a.input_,
annotations=union)
def __xor__(self, other: Union[int, "BitVec"]) -> "BitVecFunc":
"""Create a xor expression.
:param other: The int or BitVec to xor with this BitVecFunc
:return: The resulting BitVecFunc
"""
if not isinstance(other, BitVec):
other = BitVec(z3.BitVecVal(other, self.size()))
return _arithmetic_helper(self, other, operator.xor)
def __ge__(self, other: Union[int, "BitVec"]) -> Bool:
"""Create a signed greater than or equal to expression.
:param other: The int or BitVec to compare to this BitVecFunc
:return: The resulting Bool
"""
if not isinstance(other, BitVec):
other = BitVec(z3.BitVecVal(other, self.size()))
return Or(self > other, self == other)
def _arithmetic_helper(a: BitVec, b: BitVec, operation: Callable) -> BitVec:
raw = operation(a.raw, b.raw)
union = a.annotations.union(b.annotations)
if isinstance(a, BitVecFunc):
return _func_arithmetic_helper(a, b, operation)
elif isinstance(b, BitVecFunc):
return _func_arithmetic_helper(b, a, operation)
return BitVec(raw, annotations=union)
def __ne__(self, other: Union[int, "BitVec"]) -> Bool: # type: ignore
"""Create an inequality expression.
:param other: The int or BitVec to compare to this BitVecFunc
:return: The resulting Bool
"""
if not isinstance(other, BitVec):
other = BitVec(z3.BitVecVal(other, self.size()))
return _comparison_helper(
self, other, operator.ne, default_value=True, inputs_equal=False
)
def __gt__(self, other: Union[int, "BitVec"]) -> Bool:
"""Create a signed greater than expression.
:param other: The int or BitVec to compare to this BitVecFunc
:return: The resulting Bool
"""
if not isinstance(other, BitVec):
other = BitVec(z3.BitVecVal(other, self.size()))
return _comparison_helper(
self, other, operator.gt, default_value=False, inputs_equal=False
)
def Extract(high: int, low: int, bv: BitVec) -> BitVec:
"""Create an extract expression.
:param high:
:param low:
:param bv:
:return:
"""
raw = z3.Extract(high, low, bv.raw)
if isinstance(bv, BitVecFunc):
input_string = ""
# Is there a better value to set func_name and input to in this case?
return BitVecFunc(
raw=raw,
func_name="Hybrid",
input_=BitVec(z3.BitVec(input_string, 256),
annotations=bv.annotations),
nested_functions=bv.nested_functions + [bv],
)
return BitVec(raw, annotations=bv.annotations)
def If(a: Union[Bool, bool], b: Union[BitVec, int], c: Union[BitVec,
int]) -> BitVec:
"""Create an if-then-else expression.
:param a:
:param b:
:param c:
:return:
"""
# TODO: Handle BitVecFunc
if not isinstance(a, Bool):
a = Bool(z3.BoolVal(a))
if not isinstance(b, BitVec):
b = BitVec(z3.BitVecVal(b, 256))
if not isinstance(c, BitVec):
c = BitVec(z3.BitVecVal(c, 256))
union = a.annotations.union(b.annotations).union(c.annotations)
bvf = [] # type: List[BitVecFunc]
if isinstance(a, BitVecFunc):
bvf += [a]
if isinstance(b, BitVecFunc):
bvf += [b]
if isinstance(c, BitVecFunc):
bvf += [c]
if bvf:
raw = z3.If(a.raw, b.raw, c.raw)
nested_functions = [
nf for func in bvf for nf in func.nested_functions
] + bvf
return BitVecFunc(raw,
func_name="Hybrid",
nested_functions=nested_functions)
return BitVec(z3.If(a.raw, b.raw, c.raw), union)
def Sum(*args: BitVec) -> BitVec:
"""Create sum expression.
:return:
"""
raw = z3.Sum([a.raw for a in args])
annotations = set() # type: Annotations
bitvecfuncs = []
for bv in args:
annotations = annotations.union(bv.annotations)
if isinstance(bv, BitVecFunc):
bitvecfuncs.append(bv)
nested_functions = [
nf for func in bitvecfuncs for nf in func.nested_functions
] + bitvecfuncs
if len(bitvecfuncs) >= 2:
return BitVecFunc(
raw=raw,
func_name="Hybrid",
input_=None,
annotations=annotations,
nested_functions=nested_functions,
)
elif len(bitvecfuncs) == 1:
return BitVecFunc(
raw=raw,
func_name=bitvecfuncs[0].func_name,
input_=bitvecfuncs[0].input_,
annotations=annotations,
nested_functions=nested_functions,
)
return BitVec(raw, annotations)
def BitVecSym(name: str,
size: int,
annotations: Annotations = None) -> BitVec:
"""Creates a new bit vector with a symbolic value."""
raw = z3.BitVec(name, size)
return BitVec(raw, annotations)
def BitVecVal(value: int,
size: int,
annotations: Annotations = None) -> BitVec:
"""Creates a new bit vector with a concrete value."""
raw = z3.BitVecVal(value, size)
return BitVec(raw, annotations)
def _comparison_helper(
a: "BitVecFunc",
b: Union[BitVec, int],
operation: Callable,
default_value: bool,
inputs_equal: bool,
) -> Bool:
"""
Helper function for comparison operations with BitVecFuncs.
:param a: The BitVecFunc to compare.
:param b: A BitVec or int to compare to.
:param operation: The comparison operation to perform.
:return: The resulting Bool
"""
# Is there some hack for gt/lt comparisons?
if isinstance(b, int):
b = BitVec(z3.BitVecVal(b, a.size()))
union = a.annotations.union(b.annotations)
if not a.symbolic and not b.symbolic:
if operation == z3.UGT:
operation = operator.gt
if operation == z3.ULT:
operation = operator.lt
return Bool(z3.BoolVal(operation(a.value, b.value)), annotations=union)
if (
not isinstance(b, BitVecFunc)
or not a.func_name
or not a.input_
or not a.func_name == b.func_name
or str(operation) not in ("<built-in function eq>", "<built-in function ne>")
):
return Bool(z3.BoolVal(default_value), annotations=union)
condition = True
for a_nest, b_nest in product(a.nested_functions, b.nested_functions):
if a_nest.func_name != b_nest.func_name:
continue
if a_nest.func_name == "Hybrid":
continue
# a.input (eq/neq) b.input ==> a == b
if inputs_equal:
condition = z3.And(
condition,
z3.Or(
z3.Not((a_nest.input_ == b_nest.input_).raw),
(a_nest.raw == b_nest.raw),
),
z3.Or(
z3.Not((a_nest.raw == b_nest.raw)),
(a_nest.input_ == b_nest.input_).raw,
),
)
else:
condition = z3.And(
condition,
z3.Or(
z3.Not((a_nest.input_ != b_nest.input_).raw),
(a_nest.raw == b_nest.raw),
),
z3.Or(
z3.Not((a_nest.raw == b_nest.raw)),
(a_nest.input_ != b_nest.input_).raw,
),
)
return And(
Bool(cast(z3.BoolRef, operation(a.raw, b.raw)), annotations=union),
Bool(condition) if b.nested_functions else Bool(True),
a.input_ == b.input_ if inputs_equal else a.input_ != b.input_,
)
