def test_pysmt_operations(self, width, x, y):
try:
from pysmt import shortcuts as sc
except ImportError:
return
modulus = 2 ** width
x = x % modulus
y = y % modulus
bvx = Constant(x, width)
bvy = Constant(y, width)
psx = sc.BV(x, width)
psy = sc.BV(y, width)
def eval_pysmt(pysmt_var):
return pysmt_var.simplify().constant_value()
self.assertEqual(~bvx, eval_pysmt(sc.BVNot(psx)))
self.assertEqual(bvx & bvy, eval_pysmt(sc.BVAnd(psx, psy)))
self.assertEqual(bvx | bvy, eval_pysmt(sc.BVOr(psx, psy)))
self.assertEqual(bvx ^ bvy, eval_pysmt(sc.BVXor(psx, psy)))
self.assertEqual(BvComp(bvx, bvy), eval_pysmt(sc.BVComp(psx, psy)))
self.assertEqual((bvx < bvy), eval_pysmt(sc.BVULT(psx, psy)))
self.assertEqual((bvx <= bvy), eval_pysmt(sc.BVULE(psx, psy)))
self.assertEqual((bvx > bvy), eval_pysmt(sc.BVUGT(psx, psy)))
self.assertEqual((bvx >= bvy), eval_pysmt(sc.BVUGE(psx, psy)))
r = y % bvx.width
self.assertEqual(bvx << bvy, eval_pysmt(sc.BVLShl(psx, psy)))
self.assertEqual(bvx >> bvy, eval_pysmt(sc.BVLShr(psx, psy)))
self.assertEqual(RotateLeft(bvx, r), eval_pysmt(sc.BVRol(psx, r)))
self.assertEqual(RotateRight(bvx, r), eval_pysmt(sc.BVRor(psx, r)))
bvb = Constant(y % 2, 1)
psb = sc.Bool(bool(bvb))
self.assertEqual(Ite(bvb, bvx, bvy), eval_pysmt(sc.Ite(psb, psx, psy)))
j = y % bvx.width
self.assertEqual(bvx[:j], eval_pysmt(sc.BVExtract(psx, start=j)))
self.assertEqual(bvx[j:], eval_pysmt(sc.BVExtract(psx, end=j)))
self.assertEqual(Concat(bvx, bvy), eval_pysmt(sc.BVConcat(psx, psy)))
self.assertEqual(ZeroExtend(bvx, j), eval_pysmt(sc.BVZExt(psx, j)))
self.assertEqual(Repeat(bvx, 1 + j), eval_pysmt(psx.BVRepeat(1 + j)))
self.assertEqual(-bvx, eval_pysmt(sc.BVNeg(psx)))
self.assertEqual(bvx + bvy, eval_pysmt(sc.BVAdd(psx, psy)))
self.assertEqual(bvx - bvy, eval_pysmt(sc.BVSub(psx, psy)))
self.assertEqual(bvx * bvy, eval_pysmt(sc.BVMul(psx, psy)))
if bvy > 0:
self.assertEqual(bvx / bvy, eval_pysmt(sc.BVUDiv(psx, psy)))
self.assertEqual(bvx % bvy, eval_pysmt(sc.BVURem(psx, psy)))
def test_bv2pysmt(self):
bvx, bvy = Variable("x", 8), Variable("y", 8)
psx, psy = bv2pysmt(bvx), bv2pysmt(bvy)
self.assertEqual(bv2pysmt(Constant(0, 8)), sc.BV(0, 8))
self.assertEqual(psx, sc.Symbol("x", typing.BVType(8)))
self.assertEqual(bv2pysmt(~bvx), sc.BVNot(psx))
self.assertEqual(bv2pysmt(bvx & bvy), sc.BVAnd(psx, psy))
self.assertEqual(bv2pysmt(bvx | bvy), sc.BVOr(psx, psy))
self.assertEqual(bv2pysmt(bvx ^ bvy), sc.BVXor(psx, psy))
self.assertEqual(bv2pysmt(BvComp(bvx, bvy)), sc.Equals(psx, psy))
self.assertEqual(bv2pysmt(BvNot(BvComp(bvx, bvy))),
sc.Not(sc.Equals(psx, psy)))
self.assertEqual(bv2pysmt(bvx < bvy), sc.BVULT(psx, psy))
self.assertEqual(bv2pysmt(bvx <= bvy), sc.BVULE(psx, psy))
self.assertEqual(bv2pysmt(bvx > bvy), sc.BVUGT(psx, psy))
self.assertEqual(bv2pysmt(bvx >= bvy), sc.BVUGE(psx, psy))
self.assertEqual(bv2pysmt(bvx << bvy), sc.BVLShl(psx, psy))
self.assertEqual(bv2pysmt(bvx >> bvy), sc.BVLShr(psx, psy))
self.assertEqual(bv2pysmt(RotateLeft(bvx, 1)), sc.BVRol(psx, 1))
self.assertEqual(bv2pysmt(RotateRight(bvx, 1)), sc.BVRor(psx, 1))
self.assertEqual(bv2pysmt(bvx[4:2]), sc.BVExtract(psx, 2, 4))
self.assertEqual(bv2pysmt(Concat(bvx, bvy)), sc.BVConcat(psx, psy))
# zeroextend reduces to Concat
# self.assertEqual(bv2pysmt(ZeroExtend(bvx, 2)), sc.BVZExt(psx, 2))
self.assertEqual(bv2pysmt(Repeat(bvx, 2)), psx.BVRepeat(2))
self.assertEqual(bv2pysmt(-bvx), sc.BVNeg(psx))
self.assertEqual(bv2pysmt(bvx + bvy), sc.BVAdd(psx, psy))
# bvsum reduces to add
# self.assertEqual(bv2pysmt(bvx - bvy), sc.BVSub(psx, psy))
self.assertEqual(bv2pysmt(bvx * bvy), sc.BVMul(psx, psy))
self.assertEqual(bv2pysmt(bvx / bvy), sc.BVUDiv(psx, psy))
self.assertEqual(bv2pysmt(bvx % bvy), sc.BVURem(psx, psy))
def bvnor(self, other):
return type(self)(smt.BVNot(smt.BVOr(self.value, other.value)))
def __getExpressionTree(symbolicExpression):
# TODO LATER: take into account bitwise shift operations
args = []
castType = None
if len(symbolicExpression.args) > 0:
for symbolicArg in symbolicExpression.args:
arg, type = Solver.__getExpressionTree(symbolicArg)
args.append(arg)
if castType is None:
castType = type
else:
if castType.literal == 'Integer':
if type.literal == 'Real':
castType = type
# TODO LATER: consider other possible castings
if castType.literal == 'Real':
for i in range(len(args)):
args[i] = pysmt.ToReal(args[i])
if isinstance(symbolicExpression, sympy.Not):
if castType.literal == 'Integer':
return pysmt.Equals(args[0], pysmt.Int(0)), Type('Bool')
elif castType.literal == 'Real':
return pysmt.Equals(args[0], pysmt.Real(0)), Type('Bool')
elif castType.literal == 'Bool':
return pysmt.Not(args[0]), Type('Bool')
else: # castType.literal == 'BitVector'
return pysmt.BVNot(args[0]), Type('BitVector')
elif isinstance(symbolicExpression, sympy.Lt):
return pysmt.LT(args[0], args[1]), Type('Bool')
elif isinstance(symbolicExpression, sympy.Gt):
return pysmt.GT(args[0], args[1]), Type('Bool')
elif isinstance(symbolicExpression, sympy.Ge):
return pysmt.GE(args[0], args[1]), Type('Bool')
elif isinstance(symbolicExpression, sympy.Le):
return pysmt.LE(args[0], args[1]), Type('Bool')
elif isinstance(symbolicExpression, sympy.Eq):
return pysmt.Equals(args[0], args[1]), Type('Bool')
elif isinstance(symbolicExpression, sympy.Ne):
return pysmt.NotEquals(args[0], args[1]), Type('Bool')
elif isinstance(symbolicExpression, sympy.And):
if castType.literal == 'Bool':
return pysmt.And(args[0], args[1]), Type('Bool')
else: # type.literal == 'BitVector'
return pysmt.BVAnd(args[0], args[1]), castType
elif isinstance(symbolicExpression, sympy.Or):
if castType.literal == 'Bool':
return pysmt.Or(args[0], args[1]), Type('Bool')
else: # type.literal == 'BitVector'
return pysmt.BVOr(args[0], args[1]), castType
elif isinstance(symbolicExpression, sympy.Xor):
return pysmt.BVXor(args[0], args[1]), castType
elif isinstance(symbolicExpression, sympy.Add):
return pysmt.Plus(args), castType
elif isinstance(symbolicExpression, sympy.Mul):
return pysmt.Times(args), castType
elif isinstance(symbolicExpression, sympy.Pow):
return pysmt.Pow(args[0], args[1]), castType
# TODO LATER: deal with missing modulo operator from pysmt
else:
if isinstance(symbolicExpression, sympy.Symbol):
symbolType = Variable.symbolTypes[symbolicExpression.name]
literal = symbolType.getTypeForSolver()
designator = symbolType.designatorExpr1
type = Type(literal, designator)
return Solver.__encodeTerminal(symbolicExpression, type), type
elif isinstance(symbolicExpression, sympy.Integer):
type = Type('Integer')
return Solver.__encodeTerminal(symbolicExpression, type), type
elif isinstance(symbolicExpression, sympy.Rational):
type = Type('Real')
return Solver.__encodeTerminal(symbolicExpression, type), type
elif isinstance(symbolicExpression, sympy.Float):
type = Type('Real')
return Solver.__encodeTerminal(symbolicExpression, type), type
else:
type = Type('Real')
return Solver.__encodeTerminal(symbolicExpression, type), type
def bv2pysmt(bv):
"""Convert a bit-vector type to a pySMT type.
>>> from arxpy.bitvector.core import Constant, Variable
>>> from arxpy.diffcrypt.smt import bv2pysmt
>>> bv2pysmt(Constant(0b00000001, 8))
1_8
>>> x, y = Variable("x", 8), Variable("y", 8)
>>> bv2pysmt(x)
x
>>> bv2pysmt(x + y)
(x + y)
>>> bv2pysmt(x <= y)
(x u<= y)
>>> bv2pysmt(x[4: 2])
x[2:4]
"""
msg = "unknown conversion of {} to a pySMT type".format(type(bv).__name__)
if isinstance(bv, int):
return bv
if isinstance(bv, core.Variable):
return sc.Symbol(bv.name, typing.BVType(bv.width))
if isinstance(bv, core.Constant):
return sc.BV(bv.val, bv.width)
if isinstance(bv, operation.Operation):
args = [bv2pysmt(a) for a in bv.args]
if type(bv) == operation.BvNot:
if args[0].is_equals():
return sc.Not(*args)
else:
return sc.BVNot(*args)
if type(bv) == operation.BvAnd:
return sc.BVAnd(*args)
if type(bv) == operation.BvOr:
return sc.BVOr(*args)
if type(bv) == operation.BvXor:
return sc.BVXor(*args)
if type(bv) == operation.BvComp:
# return sc.BVComp(*args)
return sc.Equals(*args)
if type(bv) == operation.BvUlt:
return sc.BVULT(*args)
if type(bv) == operation.BvUle:
return sc.BVULE(*args)
if type(bv) == operation.BvUgt:
return sc.BVUGT(*args)
if type(bv) == operation.BvUge:
return sc.BVUGE(*args)
if type(bv) == operation.BvShl:
# Left hand side width must be a power of 2
if (args[0].bv_width() & (args[0].bv_width() - 1)) == 0:
return sc.BVLShl(*args)
else:
x, r = bv.args
offset = 0
while (x.width & (x.width - 1)) != 0:
x = operation.ZeroExtend(x, 1)
r = operation.ZeroExtend(r, 1)
offset += 1
shift = bv2pysmt(x << r)
return sc.BVExtract(shift, end=shift.bv_width() - offset - 1)
# width = args[0].bv_width()
# assert (width & (width - 1)) == 0 # power of 2
# return sc.BVLShl(*args)
if type(bv) == operation.BvLshr:
# Left hand side width must be a power of 2
if (args[0].bv_width() & (args[0].bv_width() - 1)) == 0:
return sc.BVLShr(*args)
else:
x, r = bv.args
offset = 0
while (x.width & (x.width - 1)) != 0:
x = operation.ZeroExtend(x, 1)
r = operation.ZeroExtend(r, 1)
offset += 1
shift = bv2pysmt(x >> r)
return sc.BVExtract(shift, end=shift.bv_width() - offset - 1)
# width = args[1].bv_width()
# assert (width & (width - 1)) == 0 # power of 2
# return sc.BVLShr(*args)
if type(bv) == operation.RotateLeft:
# Left hand side width must be a power of 2
if (args[0].bv_width() & (args[0].bv_width() - 1)) == 0:
return sc.BVRol(*args)
else:
x, r = bv.args
n = x.width
return bv2pysmt(operation.Concat(x[n - r - 1:],
x[n - 1:n - r]))
if type(bv) == operation.RotateRight:
# Left hand side width must be a power of 2
if (args[0].bv_width() & (args[0].bv_width() - 1)) == 0:
return sc.BVRor(*args)
else:
x, r = bv.args
n = x.width
return bv2pysmt(operation.Concat(x[r - 1:], x[n - 1:r]))
if type(bv) == operation.Ite:
if args[0].is_equals():
a0 = args[0]
else:
a0 = sc.Equals(args[0], bv2pysmt(core.Constant(1, 1)))
return sc.Ite(a0, *args[1:])
if type(bv) == operation.Extract:
return sc.BVExtract(args[0], args[2], args[1])
if type(bv) == operation.Concat:
return sc.BVConcat(*args)
if type(bv) == operation.ZeroExtend:
return sc.BVZExt(*args)
if type(bv) == operation.Repeat:
return args[0].BVRepeat(args[1])
if type(bv) == operation.BvNeg:
return sc.BVNeg(*args)
if type(bv) == operation.BvAdd:
return sc.BVAdd(*args)
if type(bv) == operation.BvSub:
return sc.BVSub(*args)
if type(bv) == operation.BvMul:
return sc.BVMul(*args)
if type(bv) == operation.BvMul:
return sc.BVMul(*args)
if type(bv) == operation.BvUdiv:
return sc.BVUDiv(*args)
if type(bv) == operation.BvUrem:
return sc.BVURem(*args)
raise NotImplementedError(msg)