def enum(self, M, k, target_prob, preproc_time):
b = self.b
r = [M.get_r(i, i) for i in range(k, k + b)]
radius = r[0] * .99
gh_radius = gaussian_heuristic(r)
if b > 30:
radius = min(radius, 1.1 * gh_radius)
if b < YOLO_PRUNER_MIN_BLOCK_SIZE:
return radius, self.strategy.get_pruning(radius, gh_radius)
R = tuple([M.get_r(i, i) for i in range(k, k + b)])
overhead = (preproc_time + RESTART_PENALTY) * NODE_PER_SEC
start_from = self.last_prunings
pruning = prune(radius,
overhead,
target_prob, [R],
descent_method="gradient",
precision=53,
start_from=start_from)
self.last_prunings = pruning.coefficients
self.proba = (self.proba * YOLO_MEMORY_LENGTH) + pruning.expectation
self.proba /= YOLO_MEMORY_LENGTH + 1
return radius, pruning
def enum(self, M, k, target_prob, preproc_time):
b = self.b
radius = M.get_r(k, k) * .99
root_det = M.get_root_det(k, k + b - 1)
gh_radius, ge = gaussian_heuristic(radius, 0, b, root_det, 1.)
if b > 30:
radius = min(radius, 1.21 * gh_radius * 2**ge)
if b < YOLO_PRUNER_MIN_BLOCK_SIZE:
return radius, self.strategy.get_pruning(radius, gh_radius * 2**ge)
R = tuple([M.get_r(i, i) for i in range(k, k + b)])
overhead = (preproc_time + RESTART_PENALTY) * NODE_PER_SEC
start_from = self.last_prunings
pruning = prune(radius,
overhead,
target_prob, [R],
descent_method="gradient",
precision=53,
start_from=start_from)
self.last_prunings = pruning.coefficients
self.proba = (self.proba * YOLO_MEMORY_LENGTH) + pruning.probability
self.proba /= YOLO_MEMORY_LENGTH + 1
return radius, pruning
def decide_enumeration(self,
kappa,
block_size,
param,
stats=None,
preproc_time=0.1,
target_probability=.5):
radius = self.M.get_r(kappa, kappa)
root_det = self.M.get_root_det(kappa, kappa + block_size)
gh_radius, ge = gaussian_heuristic(radius, 0, block_size, root_det,
1.0)
if block_size < AUTO_MIN_BLOCK_SIZE:
strategy = param.strategies[block_size]
return radius, strategy.get_pruning(radius, gh_radius * 2**ge)
else:
with stats.context("pruner"):
R = [
self.M.get_r(i, i)
for i in range(kappa, kappa + block_size)
]
overhead = preproc_time * AUTO_NODE_PER_SEC
start_from = self.last_pruning[block_size]
pruning = prune(radius,
overhead,
target_probability, [R],
descent_method="gradient",
precision=53,
start_from=start_from)
self.last_pruning[block_size] = pruning.coefficients
return radius, pruning
def test_pruner_vec(n=20, m=20):
M = prepare(n, m)
if have_numpy:
vec = []
for m in M:
vec.append(tuple(dump_r(m, 0, n)))
radius = sum([mat.get_r(0, 0) for mat in M])/len(M)
pruning = prune(radius, 0, 0.9, vec)
assert pruning.probability >= 0.89
def get_pruning(self, M, kappa, target_prob, preproc_time):
block_size = self.block_size
r = tuple([M.get_r(i, i) for i in range(kappa, kappa+block_size)])
radius = r[0] * .99
gh_radius = gaussian_heuristic(r)
if block_size > YOLO_GHBOUND_MIN_BLOCK_SIZE:
radius = min(radius, 1.21 * gh_radius)
if block_size < YOLO_PRUNER_MIN_BLOCK_SIZE:
return radius, self.strategy.get_pruning(radius, gh_radius)
overhead = (preproc_time + RETRY_PENALTY) * NODE_PER_SEC
self.last_pruning = prune(radius, overhead, target_prob, [r],
descent_method="gradient", metric="probability",
float_type="double", pruning=self.last_pruning)
return radius, self.last_pruning
def yolo_hsvp(n, A, gh_factor, core=0):
timer = Timer()
ybkz = YoloBKZ(A, tuners=tuners)
start_from = None
start_from_rec = None
first_len = ybkz.M.get_r(0, 0)
root_det = ybkz.M.get_root_det(0, n)
gh_radius, ge = gaussian_heuristic(first_len, 0, n, root_det, 1.)
gh_radius = abs(gh_radius * 2**ge)
radius = gh_factor * gh_radius
target_prob = (1. / gh_factor)**(n / 2)
trial = 0
count = 0
restarted = 0
ybkz.randomize(0, n, density=1)
while True:
timer.reset()
max_efficiency = 0.
for b in range(8, n / 2, 4):
ybkz.tour(b, target_prob=.50)
restarted += 1
for b in range(n / 2, n - 10, 2):
count += 1
ybkz.tour(b, target_prob=.10)
overhead = NODE_PER_SEC * timer.elapsed()
R = tuple([ybkz.M.get_r(i, i) for i in range(0, n)])
title = "c=%d r=%d b=%d t=%.1fs" % (core, restarted, b,
timer.elapsed())
print title
pruning = prune(radius,
overhead,
target_prob, [R],
descent_method="hybrid",
precision=53,
start_from=start_from)
start_from = pruning.coefficients
print "c=%d pruning approximated t=%.1fs" % (core,
timer.elapsed())
pruning = prune(radius,
overhead,
target_prob, [R],
descent_method="gradient",
precision=YOLO_PRUNER_PREC,
start_from=start_from)
title = "c=%d r=%d b=%d t=%.1fs p=%1.2e e=%.1fs" % (
core, restarted, b, timer.elapsed(),
pruning.probability / target_prob,
(target_prob * timer.elapsed()) / pruning.probability)
print title
plot_and_save([log(x / gh_radius) / log(2.) for x in R], title,
'%d/c%ds%d.png' % (n, core, count))
start_from = pruning.coefficients
try:
enum_obj = Enumeration(ybkz.M)
solution, _ = enum_obj.enumerate(0,
n,
radius,
0,
pruning=pruning.coefficients)
ybkz.insert(0, n, solution)
print
print list(A[0])
return
except EnumerationError:
print "c=%d Enum failed t=%.1fs" % (core, timer.elapsed())
pass
efficiency = (pruning.probability / timer.elapsed())
# RECYCLING
r_start = count % 10
recycling_radius = ybkz.M.get_r(r_start, r_start) * .99
pruning = prune(recycling_radius,
overhead,
target_prob, [R[r_start:]],
descent_method="hybrid",
precision=53)
title = "REC c=%d r=%d b=%d t=%.1fs p=%1.2e e=%.1fs" % (
core, restarted, b, timer.elapsed(),
pruning.probability / target_prob,
(target_prob * timer.elapsed()) / pruning.probability)
print title
try:
hints = []
enum_obj = Enumeration(ybkz.M, n / 2)
solution, _ = enum_obj.enumerate(r_start,
n,
recycling_radius,
r_start,
pruning=pruning.coefficients,
aux_sols=hints)
hints = [sol for (sol, _) in hints[1:]]
ybkz.insert(r_start, n, solution, hints=hints)
print "c=%d Recycled %d t=%.1fs" % (core, len(hints) + 1,
timer.elapsed())
break
except EnumerationError:
pass
start_from_rec = pruning.coefficients
# END OF RECYCLING
if 2 * efficiency < max_efficiency:
ybkz.randomize(0, n, density=1)
ybkz.lll_obj(0, 0, n)
break
max_efficiency = max(efficiency, max_efficiency)
timer.reset()
def test_pruner_gso(n=20, m=20):
M = prepare(n, m)
radius = sum([mat.get_r(0, 0) for mat in M])/len(M)
pruning = prune(radius, 0, 0.9, M)
assert pruning.probability >= 0.89
def test_pruner():
# A dummy prune to load tabulated values
prune(5, 50, .5, 10*[1.])
for (n, overhead) in dim_oh:
print(" \n ~~~~ Dim %d \n" % n)
M = prepare(n)
r = [M.get_r(i, i) for i in range(n)]
print(" \n GREEDY")
radius = gaussian_heuristic(r) * 1.6
print("pre-greedy radius %.4e" % radius)
tt = clock()
(radius, pruning) = prune(radius, overhead, 200, r,
descent_method="greedy", metric="solutions")
print("Time %.4e"%(clock() - tt))
print("post-greedy radius %.4e" % radius)
print(pruning)
print("cost %.4e" % sum(pruning.detailed_cost))
solutions = Enumeration(M, nr_solutions=10000).enumerate(0, n, radius, 0, pruning=pruning.coefficients)
print(len(solutions))
assert len(solutions)/pruning.expectation < 2
assert len(solutions)/pruning.expectation > .2
print(" \n GREEDY \n")
print("pre-greedy radius %.4e" % radius)
tt = clock()
(radius, pruning) = prune(radius, overhead, 200, r, descent_method="greedy", metric="solutions")
print("Time %.4e"%(clock() - tt))
print("post-greedy radius %.4e" % radius)
print(pruning)
print("cost %.4e" % sum(pruning.detailed_cost))
solutions = Enumeration(M, nr_solutions=10000).enumerate(0, n, radius, 0, pruning=pruning.coefficients)
print(len(solutions))
assert len(solutions)/pruning.expectation < 2
assert len(solutions)/pruning.expectation > .2
print(" \n GRADIENT \n")
print("radius %.4e" % radius)
tt = clock()
pruning = prune(radius, overhead, 200, r, descent_method="gradient", metric="solutions")
print("Time %.4e"%(clock() - tt))
print(pruning)
print("cost %.4e" % sum(pruning.detailed_cost))
solutions = Enumeration(M, nr_solutions=10000).enumerate(0, n, radius, 0, pruning=pruning.coefficients)
print(len(solutions))
assert len(solutions)/pruning.expectation < 2
assert len(solutions)/pruning.expectation > .2
print(" \n HYBRID \n")
print("radius %.4e" % radius)
tt = clock()
pruning = prune(radius, overhead, 200, r, descent_method="hybrid", metric="solutions")
print("Time %.4e"%(clock() - tt))
print(pruning)
print("cost %.4e" % sum(pruning.detailed_cost))
solutions = Enumeration(M, nr_solutions=10000).enumerate(0, n, radius, 0, pruning=pruning.coefficients)
print(len(solutions))
assert len(solutions)/pruning.expectation < 2
assert len(solutions)/pruning.expectation > .2
def recycled_svp_reduction(self, kappa, block_size, param, stats):
"""
:param kappa:
:param block_size:
:param params:
:param stats:
"""
if stats is None:
stats = DummyStats(self)
self.M.update_gso()
self.lll_obj.size_reduction(0, kappa + 1)
self.lll_obj(kappa, kappa, kappa + block_size)
old_first, old_first_expo = self.M.get_r_exp(kappa, kappa)
remaining_probability, rerandomize = 1.0, False
print " - ",
preproc_block_size = PREPROC_BLOCK_SIZE_INIT
while remaining_probability > 1. - param.min_success_probability:
preproc_block_size += PREPROC_BLOCK_SIZE_INCR
start_preproc = time()
with stats.context("preproc"):
rec_clean = self.recycled_svp_preprocessing(
kappa, block_size, param, stats, preproc_block_size)
time_preproc = time() - start_preproc
radius, expo = self.M.get_r_exp(kappa, kappa)
if param.flags & BKZ.GH_BND:
root_det = self.M.get_root_det(kappa, kappa + block_size)
radius, expo = gaussian_heuristic(radius, expo, block_size,
root_det, param.gh_factor)
overhead = NODE_PER_SEC * time_preproc
with stats.context("postproc"):
self.M.update_gso()
R = dump_r(self.M, kappa, block_size)
# print R
goal_proba = 1.01 * ((param.min_success_probability - 1) /
remaining_probability + 1)
pruning = prune(radius * 2**expo,
overhead,
goal_proba, [R],
descent_method="gradient",
precision=53)
print goal_proba, pruning.probability
try:
enum_obj = Enumeration(self.M, self.recycling_pool_max_size)
aux_sols = []
with stats.context("svp", E=enum_obj):
K = [x for x in pruning.coefficients]
radius *= 1.05
for i in range(5, preproc_block_size):
K[i] /= 1.05
solution, max_dist = enum_obj.enumerate(kappa,
kappa + block_size,
radius,
expo,
pruning=K,
aux_sols=aux_sols)
V = [v for (v, _) in aux_sols[:10]]
self.multi_insert(V, kappa, block_size, stats)
except EnumerationError:
print 0,
pass
remaining_probability *= (1 - pruning.probability)
self.lll_obj.size_reduction(0, kappa + 1)
new_first, new_first_expo = self.M.get_r_exp(kappa, kappa)
clean = old_first <= new_first * 2**(new_first_expo - old_first_expo)
return clean
# def to_cannonical(A, v, kappa, block_size):
# v = kappa*[0] + [x for x in v] + (A.nrows - (kappa + block_size)) * [0]
# v = IntegerMatrix.from_iterable(1, A.nrows, map(lambda x: int(round(x)), v))
# v = tuple((v*A)[0])
# return v
# def multi_insert_from_cannonical(M, V, kappa, block_size):
# d = M.d
# s = d
# l = len(V)
# for v in V:
# w = M.babai(v)
# for i in range(kappa+block_size, d):
# assert w[i] == 0
# M.create_row()
# with self.M.row_ops(s, s+1):
# for i in range(kappa + block_size):
# self.M.row_addmul(s, i, w[i])
# s += 1
# for i in range(l).reversed():
# self.M.move_row(kappa, d+i)
# with stats.context("lll"):
# self.lll_obj(kappa, kappa, kappa + block_size + 1)
# for i in range(l):
# self.M.move_row(kappa + block_size + i, s)
# for i in range(l):
# self.M.remove_last_row()