def canMeasureWater(self, x, y, z):
"""
:type x: int
:type y: int
:type z: int
:rtype: bool
"""
if x + y < z:
return False
if z <= 0 or x == z or y == z or x + y == z:
return True
return z % gcd(x, y) == 0
# Can also be done using bfs but that's slower
# https://discuss.leetcode.com/topic/50425/breadth-first-search-with-explanation/2
python类gcd()的实例源码
cryptographically_secure_generators.py 文件源码
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def _verify_params(self):
phi = (self.p - 1) * (self.q - 1)
if self.p == self.q:
raise ValueError("p and q cannot be identical")
# verify that p and q are far enough apart - https://crypto.stackexchange.com/a/35096
if self.n >= 1024 and abs(self.p - self.q).bit_length() <= (self.n.bit_length() // 2 - 100):
raise ValueError("p and q are too close together")
if not is_prime(self.p):
raise ValueError("p must be a prime (probabilistic)")
if not is_prime(self.q):
raise ValueError("q must be a prime (probabilistic)")
if not (1 < self.e < phi):
raise ValueError("e must be between 1 and (p-1)(q-1)")
if gcd(self.e, phi) != 1:
raise ValueError("e must be co-prime to (p-1)(q-1)")
cryptographically_secure_generators.py 文件源码
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def __init__(self, pq=None, seed=None):
if pq is not None:
if len(pq) != 2:
raise ValueError("Parameter pq must be a triple of the values p and q")
self.p, self.q = pq
self.n = self.p * self.q
self._verify_params()
else:
self._gen_params(511)
self.x = None
if not seed:
seed = SystemRandom().randrange(1, self.n)
while gcd(seed, self.n) != 1:
seed = SystemRandom().randrange(1, self.n)
super().__init__(seed)
def lcm(a, b):
return (a * b) // math.gcd(a, b)
def compute_bin_size(dfs):
bin_sizes = []
for df in dfs.values():
bins = df.head(100000).index.get_level_values("Bin").astype(int)
bin_size = reduce(gcd, bins)
bin_sizes.append(bin_size)
assert len(set(bin_sizes)) == 1, "Matrixes have different bin sizes: " + str(bin_sizes)
bin_size = bin_sizes.pop()
logging.info("Bin size: " + str(bin_size))
return bin_size
def gcd_of_list(l):
return reduce(gcd, l, 0)
def test_alg_euclides(self, a, b):
x, y, d = alg_euclides(a, b)
assert x * a + y * b == d
assert d == gcd(a, b)
if (a // b) * b != a and (b // a) * a != b: # a no divide a b y viceversa
assert x < b // d
assert y < a // d
def test_alg_euclides_polinomios(self, l1, l2, primo):
assume(l1)
assume(l2)
g = PolinomioZp(l1, primo)
h = PolinomioZp(l2, primo)
cero = PolinomioZp([0], primo)
assume(g != cero)
s, t, d = alg_euclides_polinomios(g, h, p=primo)
assert s * g + t * h == d
assert g % d == 0 and h % d == 0 # vemos si el gcd divide a ambos
if h != cero:
assert s.grado() <= h.grado() and t.grado() <= g.grado()
def egypt_greedy(x, y):
if x == 1:
return [y]
else:
a = (-y) % (x)
b = y*(y//x + 1)
c = gcd(a, b)
if c > 1:
num, denom = a//c, b//c
else:
num, denom = a, b
return [y//x + 1] + egypt_greedy(num, denom)
def rsa_recover_prime_factors(n, e, d):
"""
Compute factors p and q from the private exponent d. We assume that n has
no more than two factors. This function is adapted from code in PyCrypto.
"""
# See 8.2.2(i) in Handbook of Applied Cryptography.
ktot = d * e - 1
# The quantity d*e-1 is a multiple of phi(n), even,
# and can be represented as t*2^s.
t = ktot
while t % 2 == 0:
t = t // 2
# Cycle through all multiplicative inverses in Zn.
# The algorithm is non-deterministic, but there is a 50% chance
# any candidate a leads to successful factoring.
# See "Digitalized Signatures and Public Key Functions as Intractable
# as Factorization", M. Rabin, 1979
spotted = False
a = 2
while not spotted and a < _MAX_RECOVERY_ATTEMPTS:
k = t
# Cycle through all values a^{t*2^i}=a^k
while k < ktot:
cand = pow(a, k, n)
# Check if a^k is a non-trivial root of unity (mod n)
if cand != 1 and cand != (n - 1) and pow(cand, 2, n) == 1:
# We have found a number such that (cand-1)(cand+1)=0 (mod n).
# Either of the terms divides n.
p = gcd(cand + 1, n)
spotted = True
break
k *= 2
# This value was not any good... let's try another!
a += 2
if not spotted:
raise ValueError("Unable to compute factors p and q from exponent d.")
# Found !
q, r = divmod(n, p)
assert r == 0
p, q = sorted((p, q), reverse=True)
return (p, q)
def rsa_recover_prime_factors(n, e, d):
"""
Compute factors p and q from the private exponent d. We assume that n has
no more than two factors. This function is adapted from code in PyCrypto.
"""
# See 8.2.2(i) in Handbook of Applied Cryptography.
ktot = d * e - 1
# The quantity d*e-1 is a multiple of phi(n), even,
# and can be represented as t*2^s.
t = ktot
while t % 2 == 0:
t = t // 2
# Cycle through all multiplicative inverses in Zn.
# The algorithm is non-deterministic, but there is a 50% chance
# any candidate a leads to successful factoring.
# See "Digitalized Signatures and Public Key Functions as Intractable
# as Factorization", M. Rabin, 1979
spotted = False
a = 2
while not spotted and a < _MAX_RECOVERY_ATTEMPTS:
k = t
# Cycle through all values a^{t*2^i}=a^k
while k < ktot:
cand = pow(a, k, n)
# Check if a^k is a non-trivial root of unity (mod n)
if cand != 1 and cand != (n - 1) and pow(cand, 2, n) == 1:
# We have found a number such that (cand-1)(cand+1)=0 (mod n).
# Either of the terms divides n.
p = gcd(cand + 1, n)
spotted = True
break
k *= 2
# This value was not any good... let's try another!
a += 2
if not spotted:
raise ValueError("Unable to compute factors p and q from exponent d.")
# Found !
q, r = divmod(n, p)
assert r == 0
p, q = sorted((p, q), reverse=True)
return (p, q)
def mul_by_constant_modN(eng, c, N, quint_in):
"""
Multiplies a quantum integer by a classical number a modulo N, i.e.,
|x> -> |a*x mod N>
(only works if a and N are relative primes, otherwise the modular inverse
does not exist).
"""
assert(c < N and c >= 0)
assert(gcd(c, N) == 1)
n = len(quint_in)
quint_out = eng.allocate_qureg(n + 1)
for i in range(n):
with Control(eng, quint_in[i]):
AddConstantModN((c << i) % N, N) | quint_out
for i in range(n):
Swap | (quint_out[i], quint_in[i])
cinv = inv_mod_N(c, N)
for i in range(n):
with Control(eng, quint_in[i]):
SubConstantModN((cinv << i) % N, N) | quint_out
del quint_out
# calculates the inverse of a modulo N
cryptographically_secure_generators.py 文件源码
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def _gen_param_e(self):
# use builtin RNG
rand = SystemRandom()
phi = (self.p - 1) * (self.q - 1)
self.e = rand.randint(2, phi - 1)
while gcd(self.e, phi) != 1:
self.e = rand.randint(2, phi - 1)
cryptographically_secure_generators.py 文件源码
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def _gen_param_e(self):
# use builtin RNG
rand = SystemRandom()
n_bits = self.n.bit_length()
phi = (self.p - 1) * (self.q - 1)
mx = min(phi - 1, n_bits // 80) # top limits are phi (exclusive) and N/80 (inclusive)
self.e = rand.randint(2, mx)
while gcd(self.e, phi) != 1:
self.e = rand.randint(2, mx)
cryptographically_secure_generators.py 文件源码
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def seed(self, a=None, version=2):
"""Initialize the internal state of the generator."""
if not (1 <= a <= self.n - 1):
raise ValueError("Seed value must be between 1 and n-1=" + str(self.n - 1))
if gcd(a, self.n) != 1:
raise ValueError("Seed value must be co-prime to n=" + str(self.n))
super().seed(a, version)
self.x = pow(a, 2, self.n)
def print_results(best_result):
_, nominator, denominator = best_result
# print results
from math import gcd
gcd_of_both = gcd(nominator, denominator)
print("{}/{}".format(
nominator // gcd_of_both, denominator // gcd_of_both
))
exit()
def extract_n_elements(l, n):
while not gcd(n, len(l)) == n:
l.pop(0)
len_div = len(l)
step = len_div // n
ids = [i - 1 for i in np.arange(step, len_div + step, step)] # -1 for indexing
elements = np.asarray(l)[ids].tolist()
return elements
def populate_folds(yes_questions, no_questions, mb_size, verbose=False):
yes_to_pop, no_to_pop = yes_questions[:], no_questions[:]
num_questions = len(yes_questions) + len(no_questions)
min_fold_len = (num_questions - mb_size * GlobalConfigs.NUM_TEST_FOLDS) // GlobalConfigs.NUM_TEST_FOLDS # TODO loosing questions
task_folds = [[] for _ in range(GlobalConfigs.NUM_TEST_FOLDS)]
assert mb_size % 2 == 0 # must be even
# populate
for i in range(GlobalConfigs.NUM_TEST_FOLDS):
while gcd(mb_size, len(task_folds[i])) != mb_size or len(task_folds[i]) < min_fold_len:
task_folds[i].append(yes_to_pop.pop())
task_folds[i].append(no_to_pop.pop())
if verbose:
print('fold {} length: {}'.format(i, len(task_folds[i])))
return task_folds
def gen_task_mbs(self, style, test_fold_id):
num_task_iterations = int(''.join([c for c in self.regime if c.isdigit()]))
# make blocks
if style == 'train':
task_lines = list(chain(*[fold for n, fold in enumerate(self.task_folds)
if n != test_fold_id]))
windows_x, windows_y = self.make_windows(task_lines)
block_x = np.tile(windows_x, [num_task_iterations, 1])
block_y = np.tile(windows_y, [num_task_iterations, 1])
elif style == 'test':
task_lines = list(chain(*[fold for n, fold in enumerate(self.task_folds)
if n == test_fold_id]))
windows_x, windows_y = self.make_windows(task_lines)
block_x = windows_x
block_y = windows_y
elif style == 'train1':
task_lines = list(chain(*[fold for n, fold in enumerate(self.task_folds)
if n != test_fold_id]))
windows_x, windows_y = self.make_windows(task_lines)
block_x = windows_x
block_y = windows_y
else:
raise AttributeError('rnnlab: Invalid arg to "style"')
# split to mbs
if not gcd(self.mb_size, len(block_x)) == self.mb_size:
raise Exception(
'rnnlab: Number of task_lines must be divisible by mb_size')
num_splits = len(block_x) // self.mb_size
# generate
for x, y in zip(np.vsplit(block_x, num_splits),
np.vsplit(block_y, num_splits)):
yield x, y
def _safe_math_gcd(a, b):
safe_a = Number(a)
safe_b = Number(b)
if safe_a == 0 and safe_b == 0:
return 0
else:
return math.gcd(safe_a.__float__(), safe_b.__float__())
def __construct_byset(self, start, byxxx, base):
"""
If a `BYXXX` sequence is passed to the constructor at the same level as
`FREQ` (e.g. `FREQ=HOURLY,BYHOUR={2,4,7},INTERVAL=3`), there are some
specifications which cannot be reached given some starting conditions.
This occurs whenever the interval is not coprime with the base of a
given unit and the difference between the starting position and the
ending position is not coprime with the greatest common denominator
between the interval and the base. For example, with a FREQ of hourly
starting at 17:00 and an interval of 4, the only valid values for
BYHOUR would be {21, 1, 5, 9, 13, 17}, because 4 and 24 are not
coprime.
:param start:
Specifies the starting position.
:param byxxx:
An iterable containing the list of allowed values.
:param base:
The largest allowable value for the specified frequency (e.g.
24 hours, 60 minutes).
This does not preserve the type of the iterable, returning a set, since
the values should be unique and the order is irrelevant, this will
speed up later lookups.
In the event of an empty set, raises a :exception:`ValueError`, as this
results in an empty rrule.
"""
cset = set()
# Support a single byxxx value.
if isinstance(byxxx, integer_types):
byxxx = (byxxx, )
for num in byxxx:
i_gcd = gcd(self._interval, base)
# Use divmod rather than % because we need to wrap negative nums.
if i_gcd == 1 or divmod(num - start, i_gcd)[1] == 0:
cset.add(num)
if len(cset) == 0:
raise ValueError("Invalid rrule byxxx generates an empty set.")
return cset
def __construct_byset(self, start, byxxx, base):
"""
If a `BYXXX` sequence is passed to the constructor at the same level as
`FREQ` (e.g. `FREQ=HOURLY,BYHOUR={2,4,7},INTERVAL=3`), there are some
specifications which cannot be reached given some starting conditions.
This occurs whenever the interval is not coprime with the base of a
given unit and the difference between the starting position and the
ending position is not coprime with the greatest common denominator
between the interval and the base. For example, with a FREQ of hourly
starting at 17:00 and an interval of 4, the only valid values for
BYHOUR would be {21, 1, 5, 9, 13, 17}, because 4 and 24 are not
coprime.
:param start:
Specifies the starting position.
:param byxxx:
An iterable containing the list of allowed values.
:param base:
The largest allowable value for the specified frequency (e.g.
24 hours, 60 minutes).
This does not preserve the type of the iterable, returning a set, since
the values should be unique and the order is irrelevant, this will
speed up later lookups.
In the event of an empty set, raises a :exception:`ValueError`, as this
results in an empty rrule.
"""
cset = set()
# Support a single byxxx value.
if isinstance(byxxx, integer_types):
byxxx = (byxxx, )
for num in byxxx:
i_gcd = gcd(self._interval, base)
# Use divmod rather than % because we need to wrap negative nums.
if i_gcd == 1 or divmod(num - start, i_gcd)[1] == 0:
cset.add(num)
if len(cset) == 0:
raise ValueError("Invalid rrule byxxx generates an empty set.")
return cset
def __construct_byset(self, start, byxxx, base):
"""
If a `BYXXX` sequence is passed to the constructor at the same level as
`FREQ` (e.g. `FREQ=HOURLY,BYHOUR={2,4,7},INTERVAL=3`), there are some
specifications which cannot be reached given some starting conditions.
This occurs whenever the interval is not coprime with the base of a
given unit and the difference between the starting position and the
ending position is not coprime with the greatest common denominator
between the interval and the base. For example, with a FREQ of hourly
starting at 17:00 and an interval of 4, the only valid values for
BYHOUR would be {21, 1, 5, 9, 13, 17}, because 4 and 24 are not
coprime.
:param start:
Specifies the starting position.
:param byxxx:
An iterable containing the list of allowed values.
:param base:
The largest allowable value for the specified frequency (e.g.
24 hours, 60 minutes).
This does not preserve the type of the iterable, returning a set, since
the values should be unique and the order is irrelevant, this will
speed up later lookups.
In the event of an empty set, raises a :exception:`ValueError`, as this
results in an empty rrule.
"""
cset = set()
# Support a single byxxx value.
if isinstance(byxxx, integer_types):
byxxx = (byxxx, )
for num in byxxx:
i_gcd = gcd(self._interval, base)
# Use divmod rather than % because we need to wrap negative nums.
if i_gcd == 1 or divmod(num - start, i_gcd)[1] == 0:
cset.add(num)
if len(cset) == 0:
raise ValueError("Invalid rrule byxxx generates an empty set.")
return cset
def __construct_byset(self, start, byxxx, base):
"""
If a `BYXXX` sequence is passed to the constructor at the same level as
`FREQ` (e.g. `FREQ=HOURLY,BYHOUR={2,4,7},INTERVAL=3`), there are some
specifications which cannot be reached given some starting conditions.
This occurs whenever the interval is not coprime with the base of a
given unit and the difference between the starting position and the
ending position is not coprime with the greatest common denominator
between the interval and the base. For example, with a FREQ of hourly
starting at 17:00 and an interval of 4, the only valid values for
BYHOUR would be {21, 1, 5, 9, 13, 17}, because 4 and 24 are not
coprime.
:param start:
Specifies the starting position.
:param byxxx:
An iterable containing the list of allowed values.
:param base:
The largest allowable value for the specified frequency (e.g.
24 hours, 60 minutes).
This does not preserve the type of the iterable, returning a set, since
the values should be unique and the order is irrelevant, this will
speed up later lookups.
In the event of an empty set, raises a :exception:`ValueError`, as this
results in an empty rrule.
"""
cset = set()
# Support a single byxxx value.
if isinstance(byxxx, integer_types):
byxxx = (byxxx, )
for num in byxxx:
i_gcd = gcd(self._interval, base)
# Use divmod rather than % because we need to wrap negative nums.
if i_gcd == 1 or divmod(num - start, i_gcd)[1] == 0:
cset.add(num)
if len(cset) == 0:
raise ValueError("Invalid rrule byxxx generates an empty set.")
return cset
def __construct_byset(self, start, byxxx, base):
"""
If a `BYXXX` sequence is passed to the constructor at the same level as
`FREQ` (e.g. `FREQ=HOURLY,BYHOUR={2,4,7},INTERVAL=3`), there are some
specifications which cannot be reached given some starting conditions.
This occurs whenever the interval is not coprime with the base of a
given unit and the difference between the starting position and the
ending position is not coprime with the greatest common denominator
between the interval and the base. For example, with a FREQ of hourly
starting at 17:00 and an interval of 4, the only valid values for
BYHOUR would be {21, 1, 5, 9, 13, 17}, because 4 and 24 are not
coprime.
:param start:
Specifies the starting position.
:param byxxx:
An iterable containing the list of allowed values.
:param base:
The largest allowable value for the specified frequency (e.g.
24 hours, 60 minutes).
This does not preserve the type of the iterable, returning a set, since
the values should be unique and the order is irrelevant, this will
speed up later lookups.
In the event of an empty set, raises a :exception:`ValueError`, as this
results in an empty rrule.
"""
cset = set()
# Support a single byxxx value.
if isinstance(byxxx, integer_types):
byxxx = (byxxx, )
for num in byxxx:
i_gcd = gcd(self._interval, base)
# Use divmod rather than % because we need to wrap negative nums.
if i_gcd == 1 or divmod(num - start, i_gcd)[1] == 0:
cset.add(num)
if len(cset) == 0:
raise ValueError("Invalid rrule byxxx generates an empty set.")
return cset
def __construct_byset(self, start, byxxx, base):
"""
If a `BYXXX` sequence is passed to the constructor at the same level as
`FREQ` (e.g. `FREQ=HOURLY,BYHOUR={2,4,7},INTERVAL=3`), there are some
specifications which cannot be reached given some starting conditions.
This occurs whenever the interval is not coprime with the base of a
given unit and the difference between the starting position and the
ending position is not coprime with the greatest common denominator
between the interval and the base. For example, with a FREQ of hourly
starting at 17:00 and an interval of 4, the only valid values for
BYHOUR would be {21, 1, 5, 9, 13, 17}, because 4 and 24 are not
coprime.
:param start:
Specifies the starting position.
:param byxxx:
An iterable containing the list of allowed values.
:param base:
The largest allowable value for the specified frequency (e.g.
24 hours, 60 minutes).
This does not preserve the type of the iterable, returning a set, since
the values should be unique and the order is irrelevant, this will
speed up later lookups.
In the event of an empty set, raises a :exception:`ValueError`, as this
results in an empty rrule.
"""
cset = set()
# Support a single byxxx value.
if isinstance(byxxx, integer_types):
byxxx = (byxxx, )
for num in byxxx:
i_gcd = gcd(self._interval, base)
# Use divmod rather than % because we need to wrap negative nums.
if i_gcd == 1 or divmod(num - start, i_gcd)[1] == 0:
cset.add(num)
if len(cset) == 0:
raise ValueError("Invalid rrule byxxx generates an empty set.")
return cset
def __construct_byset(self, start, byxxx, base):
"""
If a `BYXXX` sequence is passed to the constructor at the same level as
`FREQ` (e.g. `FREQ=HOURLY,BYHOUR={2,4,7},INTERVAL=3`), there are some
specifications which cannot be reached given some starting conditions.
This occurs whenever the interval is not coprime with the base of a
given unit and the difference between the starting position and the
ending position is not coprime with the greatest common denominator
between the interval and the base. For example, with a FREQ of hourly
starting at 17:00 and an interval of 4, the only valid values for
BYHOUR would be {21, 1, 5, 9, 13, 17}, because 4 and 24 are not
coprime.
:param start:
Specifies the starting position.
:param byxxx:
An iterable containing the list of allowed values.
:param base:
The largest allowable value for the specified frequency (e.g.
24 hours, 60 minutes).
This does not preserve the type of the iterable, returning a set, since
the values should be unique and the order is irrelevant, this will
speed up later lookups.
In the event of an empty set, raises a :exception:`ValueError`, as this
results in an empty rrule.
"""
cset = set()
# Support a single byxxx value.
if isinstance(byxxx, integer_types):
byxxx = (byxxx, )
for num in byxxx:
i_gcd = gcd(self._interval, base)
# Use divmod rather than % because we need to wrap negative nums.
if i_gcd == 1 or divmod(num - start, i_gcd)[1] == 0:
cset.add(num)
if len(cset) == 0:
raise ValueError("Invalid rrule byxxx generates an empty set.")
return cset
def __construct_byset(self, start, byxxx, base):
"""
If a `BYXXX` sequence is passed to the constructor at the same level as
`FREQ` (e.g. `FREQ=HOURLY,BYHOUR={2,4,7},INTERVAL=3`), there are some
specifications which cannot be reached given some starting conditions.
This occurs whenever the interval is not coprime with the base of a
given unit and the difference between the starting position and the
ending position is not coprime with the greatest common denominator
between the interval and the base. For example, with a FREQ of hourly
starting at 17:00 and an interval of 4, the only valid values for
BYHOUR would be {21, 1, 5, 9, 13, 17}, because 4 and 24 are not
coprime.
:param start:
Specifies the starting position.
:param byxxx:
An iterable containing the list of allowed values.
:param base:
The largest allowable value for the specified frequency (e.g.
24 hours, 60 minutes).
This does not preserve the type of the iterable, returning a set, since
the values should be unique and the order is irrelevant, this will
speed up later lookups.
In the event of an empty set, raises a :exception:`ValueError`, as this
results in an empty rrule.
"""
cset = set()
# Support a single byxxx value.
if isinstance(byxxx, integer_types):
byxxx = (byxxx, )
for num in byxxx:
i_gcd = gcd(self._interval, base)
# Use divmod rather than % because we need to wrap negative nums.
if i_gcd == 1 or divmod(num - start, i_gcd)[1] == 0:
cset.add(num)
if len(cset) == 0:
raise ValueError("Invalid rrule byxxx generates an empty set.")
return cset
def __construct_byset(self, start, byxxx, base):
"""
If a `BYXXX` sequence is passed to the constructor at the same level as
`FREQ` (e.g. `FREQ=HOURLY,BYHOUR={2,4,7},INTERVAL=3`), there are some
specifications which cannot be reached given some starting conditions.
This occurs whenever the interval is not coprime with the base of a
given unit and the difference between the starting position and the
ending position is not coprime with the greatest common denominator
between the interval and the base. For example, with a FREQ of hourly
starting at 17:00 and an interval of 4, the only valid values for
BYHOUR would be {21, 1, 5, 9, 13, 17}, because 4 and 24 are not
coprime.
:param start:
Specifies the starting position.
:param byxxx:
An iterable containing the list of allowed values.
:param base:
The largest allowable value for the specified frequency (e.g.
24 hours, 60 minutes).
This does not preserve the type of the iterable, returning a set, since
the values should be unique and the order is irrelevant, this will
speed up later lookups.
In the event of an empty set, raises a :exception:`ValueError`, as this
results in an empty rrule.
"""
cset = set()
# Support a single byxxx value.
if isinstance(byxxx, integer_types):
byxxx = (byxxx, )
for num in byxxx:
i_gcd = gcd(self._interval, base)
# Use divmod rather than % because we need to wrap negative nums.
if i_gcd == 1 or divmod(num - start, i_gcd)[1] == 0:
cset.add(num)
if len(cset) == 0:
raise ValueError("Invalid rrule byxxx generates an empty set.")
return cset
def __construct_byset(self, start, byxxx, base):
"""
If a `BYXXX` sequence is passed to the constructor at the same level as
`FREQ` (e.g. `FREQ=HOURLY,BYHOUR={2,4,7},INTERVAL=3`), there are some
specifications which cannot be reached given some starting conditions.
This occurs whenever the interval is not coprime with the base of a
given unit and the difference between the starting position and the
ending position is not coprime with the greatest common denominator
between the interval and the base. For example, with a FREQ of hourly
starting at 17:00 and an interval of 4, the only valid values for
BYHOUR would be {21, 1, 5, 9, 13, 17}, because 4 and 24 are not
coprime.
:param start:
Specifies the starting position.
:param byxxx:
An iterable containing the list of allowed values.
:param base:
The largest allowable value for the specified frequency (e.g.
24 hours, 60 minutes).
This does not preserve the type of the iterable, returning a set, since
the values should be unique and the order is irrelevant, this will
speed up later lookups.
In the event of an empty set, raises a :exception:`ValueError`, as this
results in an empty rrule.
"""
cset = set()
# Support a single byxxx value.
if isinstance(byxxx, integer_types):
byxxx = (byxxx, )
for num in byxxx:
i_gcd = gcd(self._interval, base)
# Use divmod rather than % because we need to wrap negative nums.
if i_gcd == 1 or divmod(num - start, i_gcd)[1] == 0:
cset.add(num)
if len(cset) == 0:
raise ValueError("Invalid rrule byxxx generates an empty set.")
return cset
