def _float_binary_operator(self, term, op):
logger.debug('_fbo: %s\n%s', term, self.attrs[term])
x = self.eval(term.x)
y = self.eval(term.y)
z = op(x, y)
conds = []
if 'nnan' in self.attrs[term]:
df = z3.And(z3.Not(z3.fpIsNaN(x)), z3.Not(z3.fpIsNaN(y)),
z3.Not(z3.fpIsNaN(z)))
conds.append(z3.Implies(self.attrs[term]['nnan'], df))
elif 'nnan' in term.flags:
conds += [
z3.Not(z3.fpIsNaN(x)),
z3.Not(z3.fpIsNaN(y)),
z3.Not(z3.fpIsNaN(z))
]
if 'ninf' in self.attrs[term]:
df = z3.And(z3.Not(z3.fpIsInf(x)), z3.Not(z3.fpIsInf(y)),
z3.Not(z3.fpIsInf(z)))
conds.append(z3.Implies(self.attrs[term]['ninf'], df))
elif 'ninf' in term.flags:
conds += [
z3.Not(z3.fpIsInf(x)),
z3.Not(z3.fpIsInf(y)),
z3.Not(z3.fpIsInf(z))
]
if 'nsz' in self.attrs[term] or 'nsz' in term.flags:
# NOTE: this will return a different qvar for each (in)direct reference
# to this term. Is this desirable?
b = self.fresh_bool()
self.add_qvar(b)
z = op(x, y)
c = z3.fpIsZero(z)
if 'nsz' in self.attrs[term]:
c = z3.And(self.attrs[term]['nsz'], c)
s = _ty_sort(self.type(term))
z = z3.If(c, z3.If(b, 0, z3.fpMinusZero(s)), z)
if isinstance(term, FDivInst):
c = [z3.Not(z3.fpIsZero(x)), z3.fpIsZero(y)]
if 'nsz' in self.attrs[term]:
c.append(self.attrs[term]['nsz'])
z = z3.If(
z3.And(c),
z3.If(b, z3.fpPlusInfinity(s), z3.fpMinusInfinity(s)), z)
return self._conditional_value(conds, z, term.name)
def _float_binary_operator(self, term, op):
logger.debug('_fbo: %s\n%s', term, self.attrs[term])
x = self.eval(term.x)
y = self.eval(term.y)
z = op(x,y)
conds = []
if 'nnan' in self.attrs[term]:
df = z3.And(z3.Not(z3.fpIsNaN(x)), z3.Not(z3.fpIsNaN(y)),
z3.Not(z3.fpIsNaN(z)))
conds.append(z3.Implies(self.attrs[term]['nnan'], df))
elif 'nnan' in term.flags:
conds += [z3.Not(z3.fpIsNaN(x)), z3.Not(z3.fpIsNaN(y)),
z3.Not(z3.fpIsNaN(z))]
if 'ninf' in self.attrs[term]:
df = z3.And(z3.Not(z3.fpIsInf(x)), z3.Not(z3.fpIsInf(y)),
z3.Not(z3.fpIsInf(z)))
conds.append(z3.Implies(self.attrs[term]['ninf'], df))
elif 'ninf' in term.flags:
conds += [z3.Not(z3.fpIsInf(x)), z3.Not(z3.fpIsInf(y)),
z3.Not(z3.fpIsInf(z))]
if 'nsz' in self.attrs[term] or 'nsz' in term.flags:
# NOTE: this will return a different qvar for each (in)direct reference
# to this term. Is this desirable?
b = self.fresh_bool()
self.add_qvar(b)
z = op(x,y)
c = z3.fpIsZero(z)
if 'nsz' in self.attrs[term]:
c = z3.And(self.attrs[term]['nsz'], c)
s = _ty_sort(self.type(term))
z = z3.If(c, z3.If(b, 0, z3.fpMinusZero(s)), z)
if isinstance(term, FDivInst):
c = [z3.Not(z3.fpIsZero(x)), z3.fpIsZero(y)]
if 'nsz' in self.attrs[term]:
c.append(self.attrs[term]['nsz'])
z = z3.If(z3.And(c),
z3.If(b, z3.fpPlusInfinity(s), z3.fpMinusInfinity(s)),
z)
return self._conditional_value(conds, z, term.name)
def _(src, tgt, v):
w = z3.fpToIEEEBV(v)
i = z3.If(z3.Or(z3.fpIsZero(v), z3.fpIsSubnormal(v)),
z3.BitVecVal(0,1),
z3.BitVecVal(1,1))
return z3.Concat(z3.Extract(78,63,w), i, z3.Extract(62,0,w))
def _(src, tgt, v):
w = z3.fpToIEEEBV(v)
i = z3.If(z3.Or(z3.fpIsZero(v), z3.fpIsSubnormal(v)),
z3.BitVecVal(0,1),
z3.BitVecVal(1,1))
return z3.Concat(z3.Extract(78,63,w), i, z3.Extract(62,0,w))
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),
]:
s.add(z3.Not(z3.fpIsSubnormal(x)))
s.add(z3.Not(z3.fpIsZero(x)))
s.add(z3.Not(z3.fpIsInf(x)))
if s.check() == z3.sat:
m = s.model()
print("Counterexample found!")
print(m)
print("a*c: ", z3.simplify(m[a] * m[c]))
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),
]:
s.add(z3.Not(z3.fpIsSubnormal(x)))
s.add(z3.Not(z3.fpIsZero(x)))
s.add(z3.Not(z3.fpIsInf(x)))
if s.check() == z3.sat:
m = s.model()
print("Counterexample found!")
print(m)
print("a*c: ", z3.simplify(m[a] * m[c]))