def compute_logical(vec, X, Y, ctx, use_esf):
nbits = X.nbits
e = imm(1)
for i in range(nbits):
e *= X.eval(vec, i, use_esf) + Y.eval(vec, i, use_esf) + imm(1)
simplify_inplace(e)
return e
def test_N(nbits, X, n):
ret = imm(1)
for i in range(nbits):
if ((n >> i) & 1) == 1:
ret *= X[i]
else:
ret *= X[i] + imm(1)
simplify_inplace(ret)
return ret
def matrix_v(i, j):
if i == j:
return imm(1)
if i < j:
return imm(0)
if i > j:
mask = (~((1 << (j)) - 1)) & self.max_uint
mask2 = ((1 << (i)) - 1) & self.max_uint
mask &= mask2
return imm((n & mask) == mask)
def sub_Y(self, X, Y):
carry = imm(0)
ret = Vector(self.nbits)
if self.use_esf:
for i in range(0, self.nbits):
ret[i] = simplify_inplace(X[i]+Y[i]+carry)
carry = esf(2, [X[i]+imm(1), Y[i], carry])
else:
for i in range(0, self.nbits):
sum_XY = simplify_inplace(X[i]+Y[i])
ret[i] = simplify_inplace(sum_XY+carry)
carry = simplify_inplace((X[i]+imm(1))*Y[i] + (carry * (sum_XY+imm(1))))
return ret
def evaluate_expr(E, nbits, map_):
# keys of map_ can be mba variables or symbols
# => an mba variable must map to an integer
# => a symbol must map to an expression
keys = []
values = []
for k,v in six.iteritems(map_):
# TOFIX: not a clean test
if hasattr(k, "vec"):
if not isinstance(v, six.integer_types):
raise ValueError("an MBAVariable must map to an integer value!")
keys.extend(k.vec)
values.extend(imm((v>>i)&1) for i in range(k.nbits))
elif isinstance(k, Expr):
if not k.is_sym():
raise ValueError("only symbols or MBAVariable can be a key")
if not isinstance(v, Expr):
raise ValueError("a symbol can only be mapped to an expression")
keys.append(k)
values.append(v)
E = expand_esf(E)
simplify_inplace(E)
subs_exprs_inplace(E, keys, values)
simplify_inplace(E)
try:
return E.get_int_be()
except RuntimeError:
return E
def __identify(app, in_name):
# TODO: identify number of independant inputs
NL = app.nl().vector()
M = app.matrix()
nbits_in = M.ncols()
nbits_out = M.nlines()
if nbits_in != nbits_out:
raise ValueError("do not yet support application with a different\
number of input and output bits!")
mba = MBA(nbits_in)
var_in = mba.var(in_name)
if NL != Vector(len(NL)):
return _identify_nonaffine(app, var_in)
C = EX.ExprCst(mba.from_vec(app.cst()).to_cst(), nbits_out)
if M == Matrix(nbits_out, nbits_in):
# This is just a constant
return C
ret = EX.ExprBV(var_in)
matrix_empty = 0
# Find empty columns in the matrix.
for j in range(nbits_in):
is_zero = reduce(operator.and_, (M.at(i, j) == imm(0)
for i in range(nbits_out)), True)
if is_zero:
matrix_empty |= 1 << j
matrix_and_mask = (~matrix_empty) % (2**nbits_out)
if matrix_empty != 0:
ret = EX.ExprAnd(ret, EX.ExprCst(matrix_and_mask, nbits_out))
if mba.from_vec(M * var_in.vec) ^ (var_in & matrix_empty) == var_in:
# This is a XOR
return EX.ExprXor(ret, C)
raise ValueError("unable to identify an expression")
def or_n(self, X, n):
ret = Vector(self.nbits)
for i in range(self.nbits):
if n & (1 << i):
ret[i] = imm(1)
else:
ret[i] = X[i]
return ret
def iadd_lshifted_Y(self, X, Y, offset):
if self.use_esf:
self.iadd_Y(X, self.lshift_n(Y, offset))
simplify_inplace(X)
return
carry = imm(0)
for i in range(0, self.nbits):
if i < offset:
Yi = imm(0)
else:
Yi = Y[i - offset]
Xi = X[i]
mul_XY = simplify_inplace(Xi * Yi)
Xi += Yi
simplify_inplace(Xi)
carry_new = simplify_inplace(mul_XY + (carry * Xi))
Xi += carry
simplify_inplace(Xi)
carry = carry_new
def solve(self, X):
nbits = len(X.vec)
idx_base = X[0].sym_idx()
for I0 in self.I0s:
I0.difference_update(self.I1)
if (len(I0) == 0):
return []
self.I0s = [I0 for I0 in self.I0s if len(I0) > 0]
fix1 = Vector(X.vec)
for idx in self.I1:
idx = self.__idx(idx, idx_base, nbits)
fix1[idx] = imm(1)
if (len(self.I0s) == 0):
return [fix1]
ret = []
def iter_zeros(idxes, I0s):
if len(I0s) == 0:
yield idxes
return
for i,I0 in enumerate(I0s):
if I0.isdisjoint(idxes):
next_I0 = I0
next_idx = i
break
else:
yield idxes
return
for idx in next_I0:
new_idxes = idxes + [idx]
for z in iter_zeros(new_idxes, I0s[next_idx+1:]):
yield z
for idxes in iter_zeros([], self.I0s):
new = Vector(fix1)
for idx in idxes:
new[self.__idx(idx, idx_base, nbits)] = imm(0)
ret.append(new)
return ret
def compute(self, vec, i, args, ctx, use_esf):
if ((self.mask >> i) & 1) == 1:
return imm(1)
args = list(args)
ret = esf(1, args)
for i in range(2, len(args) + 1):
ret += esf(i, args)
if not use_esf:
expand_esf_inplace(ret)
simplify_inplace(ret)
return ret
def compute_binop_(vec, i, X, Y, CC, use_esf):
carry = CC.carry
sum_args = simplify_inplace(X + Y)
ret = simplify_inplace(sum_args + carry)
carry = esf(2, [X + imm(1), Y, carry])
if not use_esf:
expand_esf_inplace(carry)
carry = simplify_inplace(carry)
CC.carry = carry
return ret
def iadd_Y(self, X, Y):
carry = imm(0)
ret = Vector(self.nbits)
if self.use_esf:
for i in range(0, self.nbits):
new_carry = esf(2, [X[i], Y[i], carry])
X[i] += simplify_inplace(Y[i] + carry)
carry = new_carry
else:
for i in range(0, self.nbits):
sum_XY = simplify_inplace(X[i] + Y[i])
new_carry = simplify_inplace(X[i] * Y[i] + (carry * sum_XY))
X[i] = sum_XY + carry
carry = new_carry
return ret
def permut2expr(self, P, X):
ret = Vector(self.nbits)
v0 = P[0]
nbits_in = (len(P) - 1).bit_length()
for k, v in enumerate(P[1:]):
v ^= v0
if v == 0:
continue
k += 1
test = test_N(nbits_in, X, k)
for i in range(self.nbits):
if ((v >> i) & 1) == 1:
ret[i] += test
for i in range(self.nbits):
ret[i] += imm((v0 >> i) & 1)
simplify_inplace(ret)
return ret
def eval(self, vec, i, ctx, args, use_esf):
return imm((self.n >> i) & 1)
def compute_logical(vec, X, Y, ctx, use_esf):
return simplify_inplace(
ExprCmpEq.compute_logical(vec, X, Y, ctx, use_esf) + imm(1))
def __init__(self, nbits):
self.cache = [CtxUninitialized] * nbits
self.last_bit = -1
self.carry = imm(0)
def eval(self, vec, i, ctx, args, use_esf):
if (i >= self.arg_nbits):
return imm(0)
return args[0].eval(vec, i, use_esf)
def eval(self, vec, i, ctx, args, use_esf):
if i >= self.nbits - self.n:
return imm(False)
return args[0].eval(vec, i + self.n, use_esf)
def compute(self, vec, i, args, ctx, use_esf):
if ((self.mask >> i) & 1) == 0:
return imm(0)
return reduce(lambda x, y: x * y, args)
def compute(self, vec, i, args, ctx, use_esf):
return sum(args, imm(0))
def eval(self, vec, i, ctx, args, use_esf):
return args[0].eval(vec, i, use_esf) + imm(True)
def f(i, j):
if i != j:
return imm(0)
return X[i]
def from_bytes(self, s):
ret = Vector(self.nbits)
for i, c in enumerate(six.iterbytes(s)):
for j in range(8):
ret[i * 8 + j] = imm((c >> j) & 1)
return ret