def asvp_kernel(arg0, params=None, seed=None):
logger = logging.getLogger('asvp')
# Pool.map only supports a single parameter
if params is None and seed is None:
n, params, seed = arg0
else:
n = arg0
params = copy.copy(params)
load_matrix = params.pop("load_matrix")
pump_params = pop_prefixed_params("pump", params)
workout_params = pop_prefixed_params("workout", params)
verbose = params.pop("verbose")
if verbose:
workout_params["verbose"] = True
challenge_seed = params.pop("challenge_seed")
if load_matrix is None:
A, _ = load_svpchallenge_and_randomize(n, s=challenge_seed, seed=seed)
if verbose:
print(("Loaded challenge dim %d" % n))
else:
A, _ = load_matrix_file(load_matrix)
if verbose:
print(("Loaded file '%s'" % load_matrix))
g6k = Siever(A, params, seed=seed)
tracer = SieveTreeTracer(g6k,
root_label=("svp-challenge", n),
start_clocks=True)
gh = gaussian_heuristic([g6k.M.get_r(i, i) for i in range(n)])
goal_r0 = (1.05**2) * gh
if verbose:
print(("gh = %f, goal_r0/gh = %f, r0/gh = %f" %
(gh, goal_r0 / gh, sum([x * x for x in A[0]]) / gh)))
flast = workout(g6k,
tracer,
0,
n,
goal_r0=goal_r0,
pump_params=pump_params,
**workout_params)
tracer.exit()
stat = tracer.trace
stat.data["flast"] = flast
if verbose:
logger.info("sol %d, %s" % (n, A[0]))
norm = sum([x * x for x in A[0]])
if verbose:
logger.info("norm %.1f ,hf %.5f" % (norm**.5, (norm / gh)**.5))
return tracer.trace
def svp_kernel(arg0, params=None, seed=None):
# Pool.map only supports a single parameter
if params is None and seed is None:
n, params, seed = arg0
else:
n = arg0
params = copy.copy(params)
challenge_seed = params.pop("challenge_seed")
alg = params.pop("svp/alg")
workout_params = pop_prefixed_params("workout/", params)
pump_params = pop_prefixed_params("pump/", params)
goal_r0 = 1.001 * load_svpchallenge_norm(n, s=challenge_seed)
A, bkz = load_svpchallenge_and_randomize(n, s=challenge_seed, seed=seed)
g6k = Siever(A, params, seed=seed)
tracer = SieveTreeTracer(g6k,
root_label=("svp-exact", n),
start_clocks=True)
if alg == "enum":
assert len(workout_params) + len(pump_params) == 0
bkz_params = fplll_bkz.Param(
block_size=n,
max_loops=1,
strategies=fplll_bkz.DEFAULT_STRATEGY,
flags=fplll_bkz.GH_BND,
)
svp_enum(bkz, bkz_params, goal_r0)
flast = 0
elif alg == "duc18":
assert len(workout_params) + len(pump_params) == 0
flast = ducas18(g6k, tracer, goal=goal_r0)
elif alg == "workout":
flast = workout(g6k,
tracer,
0,
n,
goal_r0=goal_r0,
pump_params=pump_params,
**workout_params)
else:
raise ValueError("Unrecognized algorithm for SVP")
r0 = bkz.M.get_r(0, 0) if alg == "enum" else g6k.M.get_r(0, 0)
if r0 > goal_r0:
raise ValueError("Did not reach the goal")
if 1.002 * r0 < goal_r0:
raise ValueError(
"Found a vector shorter than the goal for n=%d s=%d." %
(n, challenge_seed))
tracer.exit()
stat = tracer.trace
stat.data["flast"] = flast
return stat
def __call__(cls,
M,
predicate,
block_size,
invalidate_cache=lambda: None,
threads=1,
max_loops=8,
**kwds):
params = SieverParams(threads=threads)
g6k = Siever(M, params)
tracer = SieveTreeTracer(g6k,
root_label="bkz-sieve",
start_clocks=True)
for b in range(20, block_size + 1, 10):
pump_n_jump_bkz_tour(g6k,
tracer,
b,
pump_params={"down_sieve": True})
auto_abort = BKZ.AutoAbort(M, M.d)
found, ntests, solution = False, 0, None
for tour in range(max_loops):
pump_n_jump_bkz_tour(g6k,
tracer,
block_size,
pump_params={"down_sieve": True})
invalidate_cache()
if auto_abort.test_abort():
break
with tracer.context("check"):
for i, v in enumerate(M.B):
ntests += 1
if predicate(v, standard_basis=True):
solution = tuple([int(v_) for v_ in v])
found = True
break
if found:
break
tracer.exit()
b0, b0e = M.get_r_exp(0, 0)
return USVPPredSolverResults(
success=found,
ntests=ntests,
solution=solution,
b0=b0**(0.5) * 2**(b0e / 2.0),
cputime=tracer.trace.data["cputime"],
walltime=tracer.trace.data["walltime"],
data=tracer.trace,
)
def find_norm_kernel_trial(arg0, params=None, seed=None, goal_r0=None):
# Pool.map only supports a single parameter
if params is None and seed is None:
n, params, seed = arg0
else:
n = arg0
params = copy.copy(params)
dim4free_dec = params.pop("workout/dim4free_dec")
pump_params = pop_prefixed_params("pump", params)
load_matrix = params.pop("load_matrix")
verbose = params.pop("verbose")
A, _ = load_matrix_file(load_matrix,
randomize=True,
seed=None,
float_type="double")
if A.nrows != n:
raise ValueError(
f"wrong dimension:: Expected dim(A) = {A.nrows}, got n = {n}")
g6k = Siever(A, params, seed=seed)
tracer = SieveTreeTracer(g6k,
root_label=("svp-challenge", n),
start_clocks=True)
gh = gaussian_heuristic([g6k.M.get_r(i, i) for i in range(n)])
ds = list(range(0, n - 40, dim4free_dec))[::-1] + 10 * [0]
if goal_r0 is None:
goal_r0 = 1.1 * gh
if verbose and n < 90:
verbose = False
for d in ds:
workout(g6k,
tracer,
0,
n,
dim4free_dec=dim4free_dec,
goal_r0=goal_r0 * 1.001,
pump_params=pump_params,
verbose=verbose)
tracer.exit()
return int(g6k.M.get_r(0, 0)), gh
def full_sieve_kernel(arg0, params=None, seed=None):
# Pool.map only supports a single parameter
if params is None and seed is None:
n, params, seed = arg0
else:
n = arg0
pump_params = pop_prefixed_params("pump", params)
verbose = params.pop("verbose")
reserved_n = n
params = params.new(reserved_n=reserved_n, otf_lift=False)
challenge_seed = params.pop("challenge_seed")
A, _ = load_svpchallenge_and_randomize(n, s=challenge_seed, seed=seed)
g6k = Siever(A, params, seed=seed)
tracer = SieveTreeTracer(g6k,
root_label=("full-sieve", n),
start_clocks=True)
# Actually runs a workout with very large decrements, so that the basis is kind-of reduced
# for the final full-sieve
workout(
g6k,
tracer,
0,
n,
dim4free_min=0,
dim4free_dec=15,
pump_params=pump_params,
verbose=verbose,
)
return tracer.exit()
def hkz_kernel(arg0, params=None, seed=None):
# Pool.map only supports a single parameter
if params is None and seed is None:
n, params, seed = arg0
else:
n = arg0
reserved_n = n
params = params.new(reserved_n=reserved_n, otf_lift=False)
verbose = params.pop("verbose")
pump_params = pop_prefixed_params("pump", params)
workout_params = pop_prefixed_params("workout", params)
verbose = params.pop("verbose")
if verbose:
workout_params["verbose"] = True
challenge_seed = params.pop("challenge_seed")
A, _ = load_svpchallenge_and_randomize(n, s=challenge_seed, seed=seed)
g6k = Siever(A, params, seed=seed)
tracer = SieveTreeTracer(g6k, root_label=("hkz", n), start_clocks=True)
# runs a workout woth pump-down down until the end
workout(g6k, tracer, 0, n, pump_params=pump_params, verbose=verbose, **workout_params)
#Just making sure
pump(g6k, tracer, 15, n-15, 0, **pump_params)
g6k.lll(0, n)
return tracer.exit()
def asvp_kernel(arg0, params=None, seed=None):
logger = logging.getLogger('asvp')
# Pool.map only supports a single parameter
if params is None and seed is None:
n, params, seed = arg0
else:
n = arg0
params = copy.copy(params)
load_matrix = params.pop("load_matrix")
pump_params = pop_prefixed_params("pump", params)
workout_params = pop_prefixed_params("workout", params)
verbose = params.pop("verbose")
if verbose:
workout_params["verbose"] = True
challenge_seed = params.pop("challenge_seed")
if load_matrix is None:
A, _ = load_svpchallenge_and_randomize(n, s=challenge_seed, seed=seed)
if verbose:
print("Loaded challenge dim %d" % n)
else:
A, _ = load_matrix_file(load_matrix)
if verbose:
print("Loaded file '%s'" % load_matrix)
g6k = Siever(A, params, seed=seed)
tracer = SieveTreeTracer(g6k, root_label=("svp-challenge", n), start_clocks=True)
gh = gaussian_heuristic([g6k.M.get_r(i, i) for i in range(n)])
flast = workout(g6k, tracer, 0, n, pump_params=pump_params, **workout_params)
tracer.exit()
stat = tracer.trace
f = workout_params["dim4free_min"]
gh2 = gaussian_heuristic([g6k.M.get_r(i, i) for i in range(f, n)])
quality = (gh * (n - f)) / (gh2 * n)
stat.data["quality"] = quality
print >> sys.stderr, g6k.M.B
return tracer.trace
def asvp_kernel(arg0, params=None, seed=None):
# Pool.map only supports a single parameter
if params is None and seed is None:
n, params, seed = arg0
else:
n = arg0
params = copy.copy(params)
load_matrix = params.pop("load_matrix")
goal_r0__gh = params.pop('goal_r0__gh')
pump_params = pop_prefixed_params("pump", params)
workout_params = pop_prefixed_params("workout", params)
verbose = params.pop("verbose")
if verbose:
workout_params["verbose"] = True
A, _ = load_matrix_file(load_matrix, randomize=False, seed=None, float_type="double")
if verbose:
print(("Loaded file '%s'" % load_matrix))
g6k = Siever(A, params, seed=seed)
tracer = SieveTreeTracer(g6k, root_label=("svp-challenge", n), start_clocks=True)
gh = gaussian_heuristic([g6k.M.get_r(i, i) for i in range(n)])
goal_r0 = (goal_r0__gh**2) * gh
if verbose:
print(("gh = %f, goal_r0/gh = %f, r0/gh = %f" % (gh, goal_r0/gh, sum([x*x for x in A[0]])/gh)))
flast = workout(g6k, tracer, 0, n, goal_r0=goal_r0, **workout_params)
tracer.exit()
stat = tracer.trace
sol = tuple(A[0])
stat.data["flast"] = flast
tracer.trace.data['res'] = A
if verbose:
print(f"svp: sol {sol}")
norm = sum([x*x for x in sol])
if verbose:
print("svp: norm %.1f ,hf %.5f" % (norm**.5, (norm/gh)**.5))
return tracer.trace
def plain_sieve_kernel(arg0, params=None, seed=None):
# Pool.map only supports a single parameter
if params is None and seed is None:
n, params, seed = arg0
else:
n = arg0
alg = params.pop("alg")
reserved_n = n
params = params.new(reserved_n=reserved_n, otf_lift=False)
A, _ = load_svpchallenge_and_randomize(n, s=0, seed=seed)
g6k = Siever(A, params, seed=seed)
tracer = SieveTreeTracer(g6k, root_label=("plain-sieve", n), start_clocks=True)
g6k.initialize_local(0, 0, n)
g6k(alg=alg, tracer=tracer)
tracer.exit()
return tracer.trace
def bkz_kernel(arg0, params=None, seed=None):
"""
Run the BKZ algorithm with different parameters.
:param d: the dimension of the lattices to BKZ reduce
:param params: parameters for BKZ:
- bkz/alg: choose the underlying BKZ from
{fpylll, naive, pump_n_jump, slide}
- bkz/blocksizes: given as low:high:inc perform BKZ reduction
with blocksizes in range(low, high, inc) (after some light)
prereduction
- bkz/pre_blocksize: prereduce lattice with fpylll BKZ up
to this blocksize
- bkz/tours: the number of tours to do for each blocksize
- bkz/extra_dim4free: lift to indices extra_dim4free earlier in
the lattice than the currently sieved block
- bkz/jump: the number of blocks to jump in a BKZ tour after
each pump
- bkz/dim4free_fun: in blocksize x, try f(x) dimensions for free,
give as 'lambda x: f(x)', e.g. 'lambda x: 11.5 + 0.075*x'
- pump/down_sieve: sieve after each insert in the pump-down
phase of the pump
- slide/overlap: shift of the dual blocks when running slide reduction
- challenge_seed: a seed to randomise the generated lattice
- dummy_tracer: use a dummy tracer which capture less information
- verbose: print tracer information throughout BKZ run
"""
# Pool.map only supports a single parameter
if params is None and seed is None:
d, params, seed = arg0
else:
d = arg0
# params for underlying BKZ/workout/pump
dim4free_fun = params.pop("bkz/dim4free_fun")
extra_dim4free = params.pop("bkz/extra_dim4free")
jump = params.pop("bkz/jump")
overlap = params.pop("slide/overlap")
pump_params = pop_prefixed_params("pump", params)
workout_params = pop_prefixed_params("workout", params)
# flow of the bkz experiment
algbkz = params.pop("bkz/alg")
blocksizes = params.pop("bkz/blocksizes")
blocksizes = eval("range(%s)" % re.sub(":", ",", blocksizes))
pre_blocksize = params.pop("bkz/pre_blocksize")
tours = params.pop("bkz/tours")
# misc
verbose = params.pop("verbose")
dont_trace = params.pop("dummy_tracer", False)
if blocksizes[-1] > d:
print('set a smaller maximum blocksize with --blocksizes')
return
challenge_seed = params.pop("challenge_seed")
A, bkz = load_prebkz(d, s=challenge_seed, blocksize=pre_blocksize)
MM = GSO.Mat(A,
float_type="double",
U=IntegerMatrix.identity(A.nrows, int_type=A.int_type),
UinvT=IntegerMatrix.identity(A.nrows, int_type=A.int_type))
g6k = Siever(MM, params, seed=seed)
if dont_trace:
tracer = dummy_tracer
else:
tracer = SieveTreeTracer(g6k, root_label=("bkz", d), start_clocks=True)
if algbkz == "fpylll":
M = bkz.M
else:
M = g6k.M
T0 = time.time()
for blocksize in blocksizes:
for t in range(tours):
with tracer.context("tour", t, dump_gso=True):
if algbkz == "fpylll":
par = BKZ_FPYLLL.Param(
blocksize,
strategies=BKZ_FPYLLL.DEFAULT_STRATEGY,
max_loops=1)
bkz(par)
elif algbkz == "naive":
naive_bkz_tour(g6k,
tracer,
blocksize,
extra_dim4free=extra_dim4free,
dim4free_fun=dim4free_fun,
workout_params=workout_params,
pump_params=pump_params)
elif algbkz == "pump_and_jump":
pump_n_jump_bkz_tour(g6k,
tracer,
blocksize,
jump=jump,
dim4free_fun=dim4free_fun,
extra_dim4free=extra_dim4free,
pump_params=pump_params)
elif algbkz == "slide":
slide_tour(g6k,
dummy_tracer,
blocksize,
overlap=overlap,
dim4free_fun=dim4free_fun,
extra_dim4free=extra_dim4free,
workout_params=workout_params,
pump_params=pump_params)
else:
raise ValueError("bkz/alg=%s not recognized." % algbkz)
if verbose:
slope = basis_quality(M)["/"]
fmt = "{'alg': '%25s', 'jump':%2d, 'pds':%d, 'extra_d4f': %2d, 'beta': %2d, 'slope': %.5f, 'total walltime': %.3f}" # noqa
print(fmt % (algbkz + "+" + ("enum" if algbkz == "fpylll" else
g6k.params.default_sieve), jump,
pump_params["down_sieve"], extra_dim4free,
blocksize, slope, time.time() - T0))
tracer.exit()
slope = basis_quality(M)["/"]
stat = tracer.trace
try:
stat.data["slope"] = np.array(slope)
return stat
except AttributeError:
return None
def asvp_kernel(arg0, params=None, seed=None):
logger = logging.getLogger('asvp')
# Pool.map only supports a single parameter
if params is None and seed is None:
n, params, seed = arg0
else:
n = arg0
params = copy.copy(params)
load_matrix = params.pop("load_matrix")
pre_bkz = params.pop("pre_bkz")
pump_params = pop_prefixed_params("pump", params)
workout_params = pop_prefixed_params("workout", params)
verbose = params.pop("verbose")
if verbose:
workout_params["verbose"] = True
challenge_seed = params.pop("challenge_seed")
high_prec = params.pop("high_prec")
trace = params.pop("trace")
if load_matrix is None:
A, bkz = load_svpchallenge_and_randomize(n,
s=challenge_seed,
seed=seed)
if verbose:
print("Loaded challenge dim %d" % n)
if pre_bkz is not None:
par = BKZ_FPYLLL.Param(pre_bkz,
strategies=BKZ_FPYLLL.DEFAULT_STRATEGY,
max_loops=1)
bkz(par)
else:
A, _ = load_matrix_file(load_matrix, doLLL=False, high_prec=high_prec)
if verbose:
print("Loaded file '%s'" % load_matrix)
g6k = Siever(A, params, seed=seed)
if trace:
tracer = SieveTreeTracer(g6k,
root_label=("svp-challenge", n),
start_clocks=True)
else:
tracer = dummy_tracer
gh = gaussian_heuristic([g6k.M.get_r(i, i) for i in range(n)])
gamma = params.pop("gamma")
if gamma is None:
goal_r0 = (1.05**2) * gh
else:
goal_r0 = gamma**2 * gh
if verbose:
print("gh = %f, goal_r0/gh = %f, r0/gh = %f" %
(gh, goal_r0 / gh, sum([x * x for x in A[0]]) / gh))
flast = workout(g6k,
tracer,
0,
n,
goal_r0=goal_r0,
pump_params=pump_params,
**workout_params)
if verbose:
logger.info("sol %d, %s" % (n, A[0]))
norm = sum([x * x for x in A[0]])
if verbose:
logger.info("norm %.1f ,hf %.5f" % (norm**.5, (norm / gh)**.5))
tracer.exit()
if hasattr(tracer, "trace"):
stat = tracer.trace
stat.data["flast"] = flast
return stat
else:
return None
def __call__(cls,
M,
predicate,
invalidate_cache=lambda: None,
preproc_offset=20,
threads=1,
ph=0,
**kwds):
# TODO bkz_sieve would be neater here
if preproc_offset and M.d >= 40:
bkz_res = usvp_pred_bkz_enum_solve(
M,
predicate,
block_size=max(M.d - preproc_offset, 2),
max_loops=8,
threads=threads,
invalidate_cache=invalidate_cache,
)
ntests = bkz_res.ntests
if bkz_res.success: # this might be enough
return bkz_res
else:
bkz_res = None
ntests = 0
from fpylll import IntegerMatrix
# reduce size of entries
B = IntegerMatrix(M.B.nrows, M.B.ncols)
for i in range(M.B.nrows):
for j in range(M.B.ncols):
B[i, j] = M.B[i, j] // 2**ph
params = SieverParams(reserved_n=M.d, otf_lift=False, threads=threads)
g6k = Siever(B, params)
tracer = SieveTreeTracer(g6k, root_label="sieve", start_clocks=True)
g6k.initialize_local(0, M.d // 2, M.d)
while g6k.l:
g6k.extend_left()
with tracer.context("sieve"):
try:
g6k()
except SaturationError:
pass
# fill the database
with g6k.temp_params(**kwds):
g6k()
invalidate_cache()
found, solution = False, None
with tracer.context("check"):
for v in g6k.itervalues(): # heuristic: v has very small entries
ntests += 1
if predicate(v, standard_basis=False):
found = True
solution = tuple(
[int(v_) for v_ in g6k.M.B.multiply_left(v)])
break
tracer.exit()
cputime = tracer.trace.data[
"cputime"] + bkz_res.cputime if bkz_res else 0
walltime = tracer.trace.data[
"walltime"] + bkz_res.walltime if bkz_res else 0
b0, b0e = M.get_r_exp(0, 0)
return USVPPredSolverResults(
success=found,
ntests=ntests,
solution=solution,
b0=b0**(0.5) * 2**(b0e / 2.0),
cputime=cputime,
walltime=walltime,
data=tracer.trace,
)
def __call__(cls,
M,
predicate,
invalidate_cache=lambda: None,
preproc_offset=20,
threads=1,
**kwds):
if preproc_offset and M.d >= 40:
bkz_res = usvp_pred_bkz_sieve_solve(
M,
predicate,
block_size=max(M.d - preproc_offset, 2),
max_loops=8,
threads=threads,
invalidate_cache=invalidate_cache,
)
ntests = bkz_res.ntests
if bkz_res.success: # this might be enough
return bkz_res
else:
bkz_res = None
ntests = 0
params = SieverParams(reserved_n=M.d, otf_lift=False, threads=threads)
g6k = Siever(M, params)
tracer = SieveTreeTracer(g6k, root_label="sieve", start_clocks=True)
workout(g6k, tracer, 0, M.d, dim4free_min=0, dim4free_dec=15)
invalidate_cache()
found, solution = False, None
with tracer.context("check"): # check if the workout solved it for us
for i in range(g6k.M.d):
ntests += 1
if predicate(g6k.M.B[i], standard_basis=True):
found = True
solution = tuple([int(v_) for v_ in g6k.M.B[i]])
break
if found:
tracer.exit()
b0, b0e = M.get_r_exp(0, 0)
return USVPPredSolverResults(
success=found,
ntests=ntests,
solution=solution,
b0=b0**(0.5) * 2**(b0e / 2.0),
cputime=tracer.trace.data["cputime"],
walltime=tracer.trace.data["walltime"],
data=tracer.trace,
)
with tracer.context("sieve"):
try:
g6k()
except SaturationError:
pass
while g6k.l:
g6k.extend_left()
with tracer.context("sieve"):
try:
g6k()
except SaturationError:
pass
# fill the database
with g6k.temp_params(**kwds):
g6k()
invalidate_cache()
with tracer.context("check"):
for i in range(g6k.M.d):
ntests += 1
if predicate(g6k.M.B[i], standard_basis=True):
found = True
solution = tuple([int(v_) for v_ in g6k.M.B[i]])
break
if not found:
for v in g6k.itervalues():
ntests += 1
if predicate(v, standard_basis=False):
found = True
solution = tuple(
[int(v_) for v_ in g6k.M.B.multiply_left(v)])
break
tracer.exit()
cputime = tracer.trace.data[
"cputime"] + bkz_res.cputime if bkz_res else 0
walltime = tracer.trace.data[
"walltime"] + bkz_res.walltime if bkz_res else 0
b0, b0e = M.get_r_exp(0, 0)
return USVPPredSolverResults(
success=found,
ntests=ntests,
solution=solution,
b0=b0**(0.5) * 2**(b0e / 2.0),
cputime=cputime,
walltime=walltime,
data=tracer.trace,
)
def svp_kernel(arg0, params=None, seed=None):
# Pool.map only supports a single parameter
if params is None and seed is None:
n, params, seed = arg0
else:
n = arg0
params = copy.copy(params)
load_matrix = params.pop("load_matrix")
alg = params.pop("svp/alg")
goal_r0 = 1.001 * params.pop('goal_r0')
workout_params = pop_prefixed_params("workout/", params)
pump_params = pop_prefixed_params("pump/", params)
verbose = params.pop("verbose")
if verbose and alg == "workout":
workout_params["verbose"] = True
A, bkz = load_matrix_file(load_matrix,
randomize=True,
seed=seed,
float_type="double")
if verbose:
print(("Loaded file '%s'" % load_matrix))
g6k = Siever(A, params, seed=seed)
tracer = SieveTreeTracer(g6k,
root_label=("svp-exact", n),
start_clocks=True)
if alg == "enum":
assert len(workout_params) + len(pump_params) == 0
bkz_params = fplll_bkz.Param(block_size=n,
max_loops=1,
strategies=fplll_bkz.DEFAULT_STRATEGY,
flags=fplll_bkz.GH_BND)
svp_enum(bkz, bkz_params, goal_r0)
flast = -1
elif alg == "duc18":
assert len(workout_params) + len(pump_params) == 0
flast = ducas18(g6k, tracer, goal=goal_r0)
elif alg == "workout":
flast = workout(g6k,
tracer,
0,
n,
goal_r0=goal_r0,
pump_params=pump_params,
**workout_params)
else:
raise ValueError("Unrecognized algorithm for SVP")
r0 = bkz.M.get_r(0, 0) if alg == "enum" else g6k.M.get_r(0, 0)
if r0 > goal_r0:
raise ValueError('Did not reach the goal')
if 1.002 * r0 < goal_r0:
raise ValueError(
'Found a vector(%d) shorter than the goal(%d) for n=%d.' %
(r0, goal_r0, n))
if verbose:
print("sol %d, %s" % (n, A[0]))
tracer.exit()
stat = tracer.trace
stat.data["flast"] = flast
tracer.trace.data['res'] = A
return stat