def offs_expr_const (addr_expr, sp_expr, rep, hyps, extra_defs = {},
cache = None):
"""if the offset between a stack addr and the initial stack pointer
is a constant offset, try to compute it."""
addr_x = solver.parse_s_expression (addr_expr)
sp_x = solver.parse_s_expression (sp_expr)
vs = [(addr_x, 1), (sp_x, -1)]
const = 0
while True:
start_vs = list (vs)
new_vs = {}
for (x, mult) in vs:
(var, c) = split_sum_s_expr (x, rep.solv, extra_defs)
for v in var:
new_vs.setdefault (v, 0)
new_vs[v] += var[v] * mult
const += c * mult
vs = [(x, n) for (x, n) in new_vs.iteritems () if n != 0]
if not vs:
return const
vs = [(simplify_expr_whyps (x, rep, hyps,
cache = cache, extra_defs = extra_defs), n)
for (x, n) in vs]
if sorted (vs) == sorted (start_vs):
trace ('offs_expr_const: not const')
trace ('%s - %s' % (addr_expr, sp_expr))
trace (str (vs))
last_10_non_const.append ((addr_expr, sp_expr, vs))
del last_10_non_const[:-10]
return None
def investigate_funcall_pair(rep,
m,
l_n_vc,
r_n_vc,
verbose=False,
verbose_imp=False,
simplify=True):
l_nm = "%s @ %s" % (rep.p.nodes[l_n_vc[0]].fname,
rep.node_count_name(l_n_vc))
r_nm = "%s @ %s" % (rep.p.nodes[r_n_vc[0]].fname,
rep.node_count_name(r_n_vc))
print 'Attempt match %s -> %s' % (l_nm, r_nm)
imp = rep.get_func_assert(l_n_vc, r_n_vc)
imp = logic.weaken_assert(imp)
if verbose_imp:
imp2 = solver.smt_expr(imp, {}, rep.solv)
if simplify:
imp2 = simplify_sexp(imp2, rep, m)
print imp2
assert imp.is_op('Implies'), imp
[pred, concl] = imp.vals
pred = solver.smt_expr(pred, {}, rep.solv)
pred = solver.parse_s_expression(pred)
bits = solver.split_hyp_sexpr(pred, [])
xs = [eval_model_bool(m, v) for v in bits]
print ' %s' % xs
for (v, bit) in zip(xs, bits):
if v != True or verbose:
print ' %s: %s' % (v, bit)
if bit[0] == 'word32-eq':
vs = [model_sx_word(m, x) for x in bit[1:]]
print ' (%s = %s)' % tuple(vs)
def investigate_funcall_pair(rep, m, l_n_vc, r_n_vc, verbose=False, verbose_imp=False, simplify=True):
l_nm = "%s @ %s" % (rep.p.nodes[l_n_vc[0]].fname, rep.node_count_name(l_n_vc))
r_nm = "%s @ %s" % (rep.p.nodes[r_n_vc[0]].fname, rep.node_count_name(r_n_vc))
print "Attempt match %s -> %s" % (l_nm, r_nm)
imp = rep.get_func_assert(l_n_vc, r_n_vc)
if verbose_imp:
imp2 = logic.weaken_assert(imp)
imp2 = solver.smt_expr(imp2, {}, rep.solv)
if simplify:
imp2 = simplify_sexp(imp2, rep, m)
print imp2
assert imp.is_op("Implies"), imp
[pred, concl] = imp.vals
pred = solver.smt_expr(pred, {}, rep.solv)
pred = solver.parse_s_expression(pred)
bits = solver.split_hyp_sexpr(pred, [])
xs = [eval_model_bool(m, v) for v in bits]
print " %s" % xs
for (v, bit) in zip(xs, bits):
if v != True or verbose:
print " %s: %s" % (v, bit)
if bit[0] == "word32-eq":
vs = [model_sx_word(m, x) for x in bit[1:]]
print " (%s = %s)" % tuple(vs)
def eval(expr, env):
try:
s = solver.smt_expr(expr, env, rep.solv)
s_x = solver.parse_s_expression(s)
ev = search.eval_model(m, s_x)
return (s, solver.smt_expr(ev, {}, None))
except solver.EnvMiss, e:
return None
def get_extra_sp_defs (rep, tag):
"""all functions will keep the stack pointer equal, whether they have
pairing partners or not. add these extra defs/equalities for the
purposes of stack depth analysis."""
# FIXME how to parametrise this?
sp = mk_var ('r13', syntax.word32T)
defs = {}
items = [(n_vc, x) for (n_vc, x) in rep.funcs.iteritems ()
if logic.is_int (n_vc[0])]
for ((n, vc), (inputs, outputs, _)) in items:
if rep.p.node_tags[n][0] == tag:
inp_sp = solver.smt_expr (sp, inputs, rep.solv)
inp_sp = solver.parse_s_expression (inp_sp)
out_sp = solver.smt_expr (sp, outputs, rep.solv)
out_sp = solver.parse_s_expression (out_sp)
if inp_sp != out_sp:
defs[out_sp] = inp_sp
return defs
def eval_model_bool(m, x):
if hasattr(x, "typ"):
x = solver.smt_expr(x, {}, None)
x = solver.parse_s_expression(x)
try:
r = search.eval_model(m, x)
assert r in [syntax.true_term, syntax.false_term], r
return r == syntax.true_term
except:
return "EXCEPT"
def eval_model_bool(m, x):
if hasattr(x, 'typ'):
x = solver.smt_expr(x, {}, None)
x = solver.parse_s_expression(x)
try:
r = search.eval_model(m, x)
assert r in [syntax.true_term, syntax.false_term], r
return r == syntax.true_term
except:
return 'EXCEPT'
def offs_expr_const(addr_expr,
sp_expr,
rep,
hyps,
extra_defs={},
cache=None,
typ=syntax.word32T):
"""if the offset between a stack addr and the initial stack pointer
is a constant offset, try to compute it."""
addr_x = solver.parse_s_expression(addr_expr)
sp_x = solver.parse_s_expression(sp_expr)
vs = [(addr_x, 1), (sp_x, -1)]
const = 0
while True:
start_vs = list(vs)
new_vs = {}
for (x, mult) in vs:
(var, c) = split_sum_s_expr(x, rep.solv, extra_defs, typ=typ)
for v in var:
new_vs.setdefault(v, 0)
new_vs[v] += var[v] * mult
const += c * mult
vs = [(x, n) for (x, n) in new_vs.iteritems() if n % (2**typ.num) != 0]
if not vs:
return const
vs = [(simplify_expr_whyps(x,
rep,
hyps,
cache=cache,
extra_defs=extra_defs), n) for (x, n) in vs]
if sorted(vs) == sorted(start_vs):
pass # vs = split_merge_ite_sum_sexpr (vs)
if sorted(vs) == sorted(start_vs):
trace('offs_expr_const: not const')
trace('%s - %s' % (addr_expr, sp_expr))
trace(str(vs))
trace(str(hyps))
last_10_non_const.append((addr_expr, sp_expr, vs, hyps))
del last_10_non_const[:-10]
return None
def fetch((n, vc)):
if n in vds and [(nm, typ)
for (nm, typ) in vs if (nm, typ) not in vds[n]]:
return None
try:
(_, env) = rep.get_node_pc_env((n, vc), tag)
s = solver.smt_expr(v, env, rep.solv)
s_x = solver.parse_s_expression(s)
ev = search.eval_model(m, s_x)
return (s, solver.smt_expr(ev, {}, None))
except solver.EnvMiss, e:
return None
def get_extra_sp_defs(rep, tag):
"""add extra defs/equalities about stack pointer for the
purposes of stack depth analysis."""
# FIXME how to parametrise this?
sp = mk_var('r13', syntax.word32T)
defs = {}
fcalls = [
n_vc for n_vc in rep.funcs if logic.is_int(n_vc[0])
if rep.p.node_tags[n_vc[0]][0] == tag
if preserves_sp(rep.p.nodes[n_vc[0]].fname)
]
for (n, vc) in fcalls:
(inputs, outputs, _) = rep.funcs[(n, vc)]
if (sp.name, sp.typ) not in outputs:
continue
inp_sp = solver.smt_expr(sp, inputs, rep.solv)
inp_sp = solver.parse_s_expression(inp_sp)
out_sp = solver.smt_expr(sp, outputs, rep.solv)
out_sp = solver.parse_s_expression(out_sp)
if inp_sp != out_sp:
defs[out_sp] = inp_sp
return defs
def simplify_sexp(smt_xp, rep, m, flatten=True):
if type(smt_xp) == str:
smt_xp = solver.parse_s_expression(smt_xp)
if smt_xp[0] == "ite":
(_, c, x, y) = smt_xp
if eval_model_bool(m, c):
return simplify_sexp(x, rep, m, flatten)
else:
return simplify_sexp(y, rep, m, flatten)
if type(smt_xp) == tuple:
smt_xp = tuple([simplify_sexp(x, rep, m, False) for x in smt_xp])
if flatten:
return solver.flat_s_expression(smt_xp)
else:
return smt_xp
def simplify_sexp(smt_xp, rep, m, flatten=True):
if type(smt_xp) == str:
smt_xp = solver.parse_s_expression(smt_xp)
if smt_xp[0] == 'ite':
(_, c, x, y) = smt_xp
if eval_model_bool(m, c):
return simplify_sexp(x, rep, m, flatten)
else:
return simplify_sexp(y, rep, m, flatten)
if type(smt_xp) == tuple:
smt_xp = tuple([simplify_sexp(x, rep, m, False) for x in smt_xp])
if flatten:
return solver.flat_s_expression(smt_xp)
else:
return smt_xp
def func_assert_premise_strength(rep, m, l_n_vc, r_n_vc):
imp = rep.get_func_assert(l_n_vc, r_n_vc)
assert imp.is_op('Implies'), imp
[pred, concl] = imp.vals
pred = solver.smt_expr(pred, {}, rep.solv)
pred = solver.parse_s_expression(pred)
bits = solver.split_hyp_sexpr(pred, [])
assert bits, bits
scores = []
for bit in bits:
try:
res = eval_model_bool(m, bit)
if res:
scores.append(1.0)
else:
scores.append(0.0)
except solver.EnvMiss, e:
scores.append(0.5)
except AssertionError, e:
scores.append(0.5)
def unfold_defs(defs, hyp, depthlimit=-1):
return solver.flat_s_expression(unfold_defs_sexpr(defs, solver.parse_s_expression(hyp), depthlimit))
def eval_model_expr (m, solv, v):
s = solver.smt_expr (v, {}, solv)
s_x = solver.parse_s_expression (s)
return eval_model (m, s_x)
def unfold_defs(defs, hyp, depthlimit=-1):
return solver.flat_s_expression(
unfold_defs_sexpr(defs, solver.parse_s_expression(hyp), depthlimit))
