def _convert(self, obj):
if isinstance(obj, FSort):
return z3.FPSort(obj.exp, obj.mantissa, ctx=self._context)
elif isinstance(obj, RM):
if obj == RM_RNE:
return z3.RNE(ctx=self._context)
elif obj == RM_RNA:
return z3.RNA(ctx=self._context)
elif obj == RM_RTP:
return z3.RTP(ctx=self._context)
elif obj == RM_RTN:
return z3.RTN(ctx=self._context)
elif obj == RM_RTZ:
return z3.RTZ(ctx=self._context)
else:
raise BackendError("unrecognized rounding mode")
elif obj is True:
return z3.BoolVal(True, ctx=self._context)
elif obj is False:
return z3.BoolVal(False, ctx=self._context)
elif isinstance(obj, (numbers.Number, str)):
return obj
elif hasattr(obj, '__module__') and obj.__module__ in ('z3', 'z3.z3'):
return obj
else:
l.debug("BackendZ3 encountered unexpected type %s", type(obj))
raise BackendError("unexpected type %s encountered in BackendZ3" %
type(obj))
def _convert(self, obj, result=None):
if type(obj) is NativeBVV:
return z3.BitVecVal(obj.value, obj.bits)
elif isinstance(obj, FSort):
return z3.FPSort(obj.exp, obj.mantissa)
elif isinstance(obj, RM):
if obj == RM_RNE:
return z3.RNE()
elif obj == RM_RNA:
return z3.RNA()
elif obj == RM_RTP:
return z3.RTP()
elif obj == RM_RTN:
return z3.RTN()
elif obj == RM_RTZ:
return z3.RTZ()
else:
raise BackendError("unrecognized rounding mode")
elif isinstance(obj, NativeFPV):
val = str(obj.value)
sort = self._convert(obj.sort)
if val == 'inf':
return z3.fpPlusInfinity(sort)
elif val == '-inf':
return z3.fpMinusInfinity(sort)
elif val == '0.0':
return z3.fpPlusZero(sort)
elif val == '-0.0':
return z3.fpMinusZero(sort)
elif val == 'nan':
return z3.fpNaN(sort)
else:
better_val = str(Decimal(obj.value))
return z3.FPVal(better_val, sort)
elif obj is True:
return z3.BoolVal(True)
elif obj is False:
return z3.BoolVal(False)
elif type(obj) in (int, long, float, str):
return obj
elif hasattr(obj, '__module__') and obj.__module__ == 'z3':
return obj
else:
l.debug("BackendZ3 encountered unexpected type %s", type(obj))
raise BackendError("unexpected type %s encountered in BackendZ3" %
type(obj))
# We do float16 because it lets the solver run much faster. These results
# should generalize to fp32 and fp64, and you can verify this by changing the
# value of FLOAT_TY (and then waiting a while).
FLOAT_TY = z3.Float16
a = z3.FP("a", FLOAT_TY())
b = z3.FP("b", FLOAT_TY())
c = z3.FP("c", FLOAT_TY())
s = z3.Solver()
# C must be a power of 2, i.e. significand bits must all be 0.
s.add(z3.Extract(FLOAT_TY().sbits() - 1, 0, z3.fpToIEEEBV(c)) == 0)
for rm in [z3.RTZ(), z3.RNE()]:
z3.set_default_rounding_mode(rm)
before = a * c + b * c
after = (a + b) * c
# Check that before == after, allowing that 0 == -0.
s.add(
z3.Not(
z3.Or(
before == after, #
z3.And(z3.fpIsZero(before), z3.fpIsZero(after)))))
for x in [
(a * c),
(b * c),
(a + b),
def cast(self, value, is_type, to_type):
if is_type is Types.STRING and isinstance(to_type,
z3.z3.DatatypeSortRef):
# the value is a string and it should be cast to a datatyperef
# (i.e. an enum-type), just return the value because we can deal with it
return value
value_is_int = isinstance(value, int)
value_is_float = isinstance(value, float)
if is_type is to_type: # already correct type, just return the value
return value
""" INT <---> INTEGER """
elif is_type is Types.INT and to_type is Types.INTEGER:
if value_is_int or value_is_float:
return value # this happens if it is an int numeral (e.g. 2)
else:
return z3.BV2Int(value)
elif is_type is Types.INTEGER and to_type is Types.INT:
if value_is_int or value_is_float:
return value
else:
return z3.Int2BV(value, 32)
""" INT <---> FLOAT """
elif is_type is Types.FLOAT and to_type is Types.INT:
if value_is_float:
return value # this happens if it is a float numeral (e.g. 3.14)
else:
return z3.fpToSBV(z3.RNE(), value, z3.BitVecSort(32))
elif is_type is Types.INT and to_type is Types.FLOAT:
if value_is_int:
return value
else:
return z3.fpSignedToFP(z3.RNE(), value, z3.Float32())
""" INTEGER <---> FLOAT """
elif is_type is Types.FLOAT and to_type is Types.INTEGER:
if value_is_float:
return value # this happens if it is a float numeral (e.g. 3.14)
else:
return self.cast(self.cast(value, Types.FLOAT, Types.INT),
Types.INT, Types.INTEGER)
elif is_type is Types.INTEGER and to_type is Types.FLOAT:
if value_is_int:
return value
else:
return self.cast(self.cast(value, Types.INTEGER, Types.INT),
Types.INT, Types.FLOAT)
""" from REAL """
elif is_type is Types.REAL and to_type is Types.INTEGER:
if value_is_float:
return value
else:
return z3.ToInt(value)
elif is_type is Types.REAL and to_type is Types.INT:
return self.cast(self.cast(value, Types.REAL, Types.INTEGER),
Types.INTEGER, Types.INT)
elif is_type is Types.REAL and to_type is Types.FLOAT:
"""
Rounding modes: probably should make these parameterizable!
roundNearestTiesToEven ... RNE() = default
roundNearestTiesToAway ... RNA()
roundTowardPositive ...... RTP()
roundTowardNegative ...... RTN()
roundTowardZero .......... RTZ()
"""
if value_is_int or value_is_float: # int numeral
return value
else:
return z3.fpRealToFP(z3.RNE(), value, z3.Float32())
""" to REAL """
elif is_type is Types.INT and to_type is Types.REAL:
if value_is_int or value_is_float: # int numeral
return value
else:
return z3.ToReal(self.cast(value, Types.INT, Types.INTEGER))
elif is_type is Types.INTEGER and to_type is Types.REAL:
if value_is_int or value_is_float: # int numeral
return value
else:
return z3.ToReal(value)
elif is_type is Types.FLOAT and to_type is Types.REAL:
if value_is_int or value_is_float:
return value # this happens if it is a float numeral (e.g. 3.14)
else:
return z3.fpToReal(value)
""" FROM BOOL conversions """
elif is_type is Types.BOOL and to_type is Types.INT:
return z3.If(value, z3.BitVecVal(1, 32), z3.BitVecVal(0, 32))
elif is_type is Types.BOOL and to_type is Types.INTEGER:
return z3.If(value, 1, 0)
elif is_type is Types.BOOL and to_type is Types.REAL:
return z3.If(value, 1.0, 0.0)
elif is_type is Types.BOOL and to_type is Types.FLOAT:
return z3.If(value, z3.FPVal(1.0, z3.Float32()),
z3.FPVal(0.0, z3.Float32()))
""" TO BOOL conversions """
elif is_type is Types.INT and to_type is Types.BOOL:
return value == 1
elif is_type is Types.INTEGER and to_type is Types.BOOL:
return value == 1
elif is_type is Types.REAL and to_type is Types.BOOL:
return value == 1
elif is_type is Types.FLOAT and to_type is Types.BOOL:
return value == 1
raise TypeError(f"Don't know how to cast from {is_type} to {to_type}!")
def _(term, smt):
v = smt.eval(term._args[0])
return z3.fpToFP(z3.RNE(), v, _ty_sort(smt.type(term)))
