def max_eof_p(sch, max_degree=None, debug=False, max_tests=None):
"""
:param sch: Input scheme.
:param max_degree: Max degree of result polinomial.
:param debug: If True debug information will be printed due to process.
:return: Upper bound of probability of failure with up to max_degree-1 errors in scheme.
"""
n = sch.inputs()
m = sch.elements()
nonerror = (0,) * m
if max_degree is None:
max_degree = m
sch_process = d.make_process_func(sch)
if debug:
start = time.time()
counter = 0
while time.time() - start < 1:
output_true = sch_process((0,) * n, (0,) * m)
vec2num(output_true)
vec2num(output_true)
counter += 1
process_time = (time.time() - start) / counter
inputs = 2 ** n
errors = sum(choose(m, degree) for degree in range(max_degree + 1))
estimated_time = process_time * inputs * errors
print("Estimated time eof_p: ", estimated_time)
polinomial = [Fraction(0, 1)] * (m + 1)
sch_process = d.make_process_func(sch)
for input_values in product(range(2), repeat=n):
if debug:
print(input_values)
for degree in range(max_degree):
for error_comb in combinations(range(m), degree):
error_vec = [0] * m
for i in error_comb:
error_vec[i] = 1
if sch_process(input_values, error_vec) != sch_process(input_values, nonerror):
for i in range(degree, m + 1):
polinomial[i] += choose(m - degree, i - degree) * (-1) ** (i - degree)
polinomial = [coeff / 2 ** n for coeff in polinomial]
for degree in range(max_degree, m + 1):
for i in range(degree, m + 1):
polinomial[i] += choose(m, degree) * choose(m - degree, i - degree) * (-1) ** (i - degree)
return polinomial
def correlation_multiout(sch1, sch2): # compares correlation between two circuits (0% - 100%)
if sch1.inputs() != sch2.inputs():
return False
if sch1.outputs() != sch2.outputs():
return False
correl = 0
capacity = min(32, 2 ** sch1.inputs())
mask = 2 ** capacity - 1
sch1_func = d.make_process_func(sch1, capacity=capacity)
sch2_func = d.make_process_func(sch2, capacity=capacity)
n = sch1.inputs()
for i in inputs_combinations(sch1.inputs(), capacity=capacity):
output = (mask ^ out1 ^ out2 for out1, out2 in zip(sch1_func(i), sch2_func(i)))
correl += sum(map(ones, output))
correl /= 2 ** n * sch1.outputs()
return correl
def max_transition_table_p(sch, indexes=None, max_degree=None, debug=False):
"""
:param sch: Input scheme.
:param indexes: Indexes of scheme outputs.
:return: Table of probabilities (k coefficient in k*p + O(p)) of transition form one output combination to another.
"""
n = sch.inputs()
l = sch.elements()
m = sch.outputs()
if indexes is None:
ttable_size = 2 ** sch.outputs()
indexes = range(m)
else:
ttable_size = 2 ** len(indexes)
if max_degree is None or max_degree > l:
max_degree = l
ttable = [[[0 for i in range(l + 1)] for x in range(ttable_size)] for x in range(ttable_size)]
nonerror = [0] * l
tests = 2 ** n
errors = 2 ** l
sch_process = d.make_process_func(sch)
start = time.time()
counter = 0
while time.time() - start < 5:
output_true = sch_process((0,) * n, (0,) * l)
vec2num(output_true)
vec2num(output_true)
counter += 1
process_time = (time.time() - start) / counter
inputs = 2 ** n
errors = sum(choose(l, degree) for degree in range(max_degree + 1))
estimated_time = process_time * inputs * errors
print("Estimated time: ", estimated_time)
for input_values in product(range(2), repeat=n):
if debug:
print(input_values)
output_true = sch_process(input_values, nonerror)
if len(indexes) < m:
output_true = [output_true[index] for index in indexes]
for degree in range(max_degree):
for error_comb in combinations(range(l), degree):
error_vec = [0] * l
for i in error_comb:
error_vec[i] = 1
if len(indexes) < m:
output_error = [sch_process(input_values, error_vec)[index] for index in indexes]
else:
output_error = sch_process(input_values, error_vec)
true_index = vec2num(output_true)
error_index = vec2num(output_error)
for i in range(degree, max_degree + 1):
ttable[true_index][error_index][i] += (
choose(l - degree, i - degree) * (-1) ** (i - degree) / (2 ** n)
)
for degree in range(max_degree, l + 1):
pass
return ttable
def eof_p_interval(sch, max_degree=None, debug=False, max_tests=None):
"""
:param sch: Input scheme.
:param max_degree: Max degree of result polinomial.
:param debug: If True debug information will be printed due to process.
:param capacity: Number of bits in used numbers.
:param max_tests: Maximum number of tests to process.
:return: First max_degree+1 members of polinomial EOF(p) for input scheme.
"""
tests_performed = 0
n = sch.inputs()
m = sch.elements()
sch_process = d.make_process_func(sch)
nonerror = (0,) * m
min_polynomial = [Fraction(0, 1)] * (m + 1)
max_polynomial = [Fraction(1, 1)] + [Fraction(0, 1)] * m
if max_degree is None:
max_degree = m
if max_tests is None or max_tests >= 2 ** (n + m):
max_tests = 2 ** (n + m)
def inputs_generator(rand=False):
if rand:
return product(*[random.choice(((0, 1), (1, 0))) for _ in range(n)])
else:
return product((0, 1), repeat=n)
def make_errors_vector(indexes):
errors_vector = [0] * m
for index in indexes:
errors_vector[index] = 1
return tuple(errors_vector)
def errors_generator(degree, rand=False):
if rand:
return (
make_errors_vector(indexes=combination)
for combination in combinations(random.sample(list(range(m)), m), r=degree)
)
else:
return (make_errors_vector(indexes=combination) for combination in combinations(list(range(m)), r=degree))
def update_polynomials(successes, fails, degree):
for i in range(m + 1 - degree):
min_polynomial[i + degree] += Fraction((-1) ** i * choose(m - degree, i) * fails, 2 ** n)
max_polynomial[i + degree] -= Fraction((-1) ** i * choose(m - degree, i) * successes, 2 ** n)
for degree in range(max_degree + 1):
tests_remained = max_tests - tests_performed
if debug:
print(max_tests, tests_remained)
rand = tests_remained < choose(m, degree) * 2 ** n
errors_number = choose(m, degree)
if rand:
inputs_number = max(1, min(int(tests_remained / errors_number), 2 ** n))
else:
inputs_number = 2 ** n
total_fails = 0
total_successes = 0
for errors in errors_generator(degree, rand):
if not tests_remained:
return min_polynomial, max_polynomial
inputs_number = min(inputs_number, tests_remained)
fails = sum(
sch_process(inputs, errors) != sch_process(inputs)
for inputs in islice(inputs_generator(rand), inputs_number)
)
successes = inputs_number - fails
total_fails += fails
total_successes += successes
tests_remained -= inputs_number
tests_performed += inputs_number
update_polynomials(total_successes, total_fails, degree)
return min_polynomial, max_polynomial
def eof_p_opt(sch, max_degree=None, debug=False, capacity=None):
"""
:param sch: Input scheme.
:param max_degree: Max degree of result polinomial.
:param debug: If True debug information will be printed due to process.
:return: First max_degree+1 members of polinomial EOF(p) for input scheme.
"""
n = sch.inputs()
m = sch.elements()
if capacity is None:
capacity = min([2 ** sch.inputs(), 32])
nonerror = (0,) * m
if max_degree is None:
max_degree = m
sch_process = d.make_process_func(sch, capacity=capacity)
if debug:
start = time.time()
counter = 0
while time.time() - start < 1:
output_true = sch_process((0,) * n, (0,) * m)
vec2num(output_true)
vec2num(output_true)
counter += 1
process_time = (time.time() - start) / counter
inputs = 2 ** n / capacity
errors = sum(choose(m, degree) for degree in range(max_degree + 1))
estimated_time = process_time * inputs * errors
print("Estimated time eof_p: ", estimated_time)
poly = Polynomial([Fraction(0, 1)])
input_prob = Fraction(1, 2 ** n)
p = Polynomial([Fraction(0, 1), Fraction(1, 1)])
sum_poly = Polynomial([Fraction(0, 1)])
for input_values in inputs_combinations(n, capacity=capacity):
output_true = sch_process(input_values, nonerror)
if debug:
print(input_values)
for degree in range(max_degree + 1):
error_prob = Polynomial(polypow(p.coef, degree, maxpower=100)) * Polynomial(
polypow((1 - p).coef, m - degree, maxpower=100)
)
# print(error_prob.coef)
errors_number = 0
if debug:
print(len(list(combinations(range(m), r=degree))))
for error_comb in combinations(range(m), r=degree):
error_vec = [0] * m
for i in error_comb:
error_vec[i] = 2 ** capacity - 1
output_error = sch_process(input_values, error_vec)
errors = [i ^ j for i, j in zip(output_true, output_error)]
errors_number += ones(reduce(or_, errors))
if debug:
print(errors_number)
if errors_number:
poly += errors_number * input_prob * error_prob
result = list(poly.coef)
# removing trailing zeros
while not result[-1]:
result.pop()
return result
