def test_negative(self):
self.assertEqual(eratosthenes(50, 50), [])
self.assertEqual(eratosthenes(
50, -5), [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47])
self.assertEqual(eratosthenes(-5, 10), [])
self.assertEqual(eratosthenes(-5, 10, True), (False, []))
def test_negative(self):
self.assertEqual(eratosthenes(50, 50), [])
self.assertEqual(eratosthenes(50, -5),
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47])
self.assertEqual(eratosthenes(-5, 10), [])
self.assertEqual(eratosthenes(-5, 10, True), (False, []))
def test_positive(self):
self.assertEqual(
eratosthenes(50),
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47])
self.assertEqual(eratosthenes(51, 10),
[11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47])
self.assertEqual(eratosthenes(10, 1, True), (True, [2, 3, 5, 7]))
def test_positive(self):
self.assertEqual(eratosthenes(50),
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47])
self.assertEqual(eratosthenes(51, 10),
[11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47])
self.assertEqual(eratosthenes(10, 1, True),
(True, [2, 3, 5, 7]))
def test_eratosthenes_additional(self):
rv1 = eratosthenes(-10)
rv2 = eratosthenes(10)
rv3 = eratosthenes(100, 5)
rv4 = eratosthenes(100, -10)
self.assertEqual(rv1, [])
self.assertEqual(rv2, [2, 3, 5, 7])
self.assertEqual(rv3, [
5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67,
71, 73, 79, 83, 89, 97
])
self.assertEqual(rv4, [
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61,
67, 71, 73, 79, 83, 89, 97
])
def is_prime(number, cache=True):
if number < 2:
return False
global primes_cache_list, primes_cache_bool
if cache and len(primes_cache_list) == 0:
primes_cache_list, primes_cache_bool = eratosthenes(
CACHE_LIMIT, return_boolean=True
)
for prime in primes_cache_list:
primes_cache_bool[prime] = True
if number < len(primes_cache_bool):
return primes_cache_bool[number]
sqrt_number = sqrt(number)
for prime in primes_cache_list:
if prime > sqrt_number:
return True
if number % prime == 0:
return False
to_check = 2
if len(primes_cache_list) > 0:
to_check = primes_cache_list[-1] + 1
while to_check <= sqrt_number:
if number % to_check == 0:
return False
to_check += 1
return True
def is_prime(number, cache=True):
if number < 2:
return False
global primes_cache_list, primes_cache_bool
if cache and len(primes_cache_list) == 0:
primes_cache_list, primes_cache_bool = eratosthenes(
CACHE_LIMIT, return_boolean=True)
for prime in primes_cache_list:
primes_cache_bool[prime] = True
if number < len(primes_cache_bool):
return primes_cache_bool[number]
sqrt_number = sqrt(number)
for prime in primes_cache_list:
if prime > sqrt_number:
return True
if number % prime == 0:
return False
to_check = 2
if len(primes_cache_list) > 0:
to_check = primes_cache_list[-1] + 1
while to_check <= sqrt_number:
if number % to_check == 0:
return False
to_check += 1
return True
def is_prime(number, cache=True):
"""
Takes `number` and determines if it is prime.
:param number: The integer to be tested for primality.
:param cache: A boolean to determine if a cache should be used to
improve performance.
:rtype: A boolean that signifies if `number` is prime.
"""
if number < 2:
return False
global primes_cache_list, primes_cache_bool
if cache and len(primes_cache_list) == 0:
primes_cache_list, primes_cache_bool = eratosthenes(
CACHE_LIMIT, return_boolean=True)
for prime in primes_cache_list:
primes_cache_bool[prime] = True
if number < len(primes_cache_bool):
return primes_cache_bool[number]
sqrt_number = sqrt(number)
for prime in primes_cache_list:
if prime > sqrt_number:
return True
if number % prime == 0:
return False
to_check = 2
if len(primes_cache_list) > 0:
to_check = primes_cache_list[-1] + 1
while to_check <= sqrt_number:
if number % to_check == 0:
return False
to_check += 1
return True
def test_eratosthenes(self):
rv1 = eratosthenes(-10)
rv2 = eratosthenes(10)
rv3 = eratosthenes(100, 5)
rv4 = eratosthenes(100, -10)
self.assertEqual(rv1, [])
self.assertEqual(rv2, [2, 3, 5, 7])
self.assertEqual(
rv3,
[5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61,
67, 71, 73, 79, 83, 89, 97]
)
self.assertEqual(
rv4,
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59,
61, 67, 71, 73, 79, 83, 89, 97]
)
def trial_division(n):
prime_factors = []
if n < 2:
return prime_factors
for p in eratosthenes(int(n**0.5) + 1):
if p * p > n:
break
while n % p == 0:
prime_factors.append(p)
n //= p
if n > 1:
prime_factors.append(n)
return prime_factors
def mth_operations_1_input(f_code, v):
if f_code == 1:
res = approx_cdf.cdf(v)
return res
elif f_code == 4:
res = primality_test.is_prime(v)
return res
elif f_code == 5:
res = sieve_atkin.atkin(v)
return res
elif f_code == 6:
res = sieve_eratosthenes.eratosthenes(v)
return res
elif f_code == 7:
res = std_normal_pdf.pdf(v)
return res
def trial_division(n):
"""
Uses trial division to find prime factors of `n`.
:param n: An integer to factor.
:rtype: The prime factors of `n`
"""
prime_factors = []
if n < 2:
return prime_factors
for p in eratosthenes(int(n**0.5) + 1):
if p*p > n:
break
while n % p == 0:
prime_factors.append(p)
n //= p
if n > 1:
prime_factors.append(n)
return prime_factors
def trial_division(n):
"""
Uses trial division to find prime factors of `n`.
:param n: An integer to factor.
:rtype: The prime factors of `n`
"""
prime_factors = []
if n < 2:
return prime_factors
for p in eratosthenes(int(n**0.5) + 1):
if p * p > n:
break
while n % p == 0:
prime_factors.append(p)
n //= p
if n > 1:
prime_factors.append(n)
return prime_factors
def is_prime(number, cache=True):
"""
Takes `number` and determines if it is prime.
:param number: The integer to be tested for primality.
:param cache: A boolean to determine if a cache should be used to
improve performance.
:rtype: A boolean that signifies if `number` is prime.
"""
if number < 2:
return False
global primes_cache_list, primes_cache_bool
if cache and len(primes_cache_list) == 0:
primes_cache_list, primes_cache_bool = eratosthenes(
CACHE_LIMIT, return_boolean=True
)
for prime in primes_cache_list:
primes_cache_bool[prime] = True
if number < len(primes_cache_bool):
return primes_cache_bool[number]
sqrt_number = sqrt(number)
for prime in primes_cache_list:
if prime > sqrt_number:
return True
if number % prime == 0:
return False
to_check = 2
if len(primes_cache_list) > 0:
to_check = primes_cache_list[-1] + 1
while to_check <= sqrt_number:
if number % to_check == 0:
return False
to_check += 1
return True
