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import operator
from six import print_
from functools import reduce
import operator
try:
import unittest2 as unittest
except ImportError:
import unittest
import hypothesis.strategies as st
import pytest
from hypothesis import given, settings, example
try:
from hypothesis import HealthCheck
HC_PRESENT=True
except ImportError: # pragma: no cover
HC_PRESENT=False
from .numbertheory import (SquareRootError, factorization, gcd, lcm,
jacobi, inverse_mod,
is_prime, next_prime, smallprimes,
square_root_mod_prime)
BIGPRIMES = (999671,
999683,
999721,
999727,
999749,
999763,
999769,
999773,
999809,
999853,
999863,
999883,
999907,
999917,
999931,
999953,
999959,
999961,
999979,
999983)
@pytest.mark.parametrize(
"prime, next_p",
[(p, q) for p, q in zip(BIGPRIMES[:-1], BIGPRIMES[1:])])
def test_next_prime(prime, next_p):
assert next_prime(prime) == next_p
@pytest.mark.parametrize(
"val",
[-1, 0, 1])
def test_next_prime_with_nums_less_2(val):
assert next_prime(val) == 2
@pytest.mark.parametrize("prime", smallprimes)
def test_square_root_mod_prime_for_small_primes(prime):
squares = set()
for num in range(0, 1 + prime // 2):
sq = num * num % prime
squares.add(sq)
root = square_root_mod_prime(sq, prime)
# tested for real with TestNumbertheory.test_square_root_mod_prime
assert root * root % prime == sq
for nonsquare in range(0, prime):
if nonsquare in squares:
continue
with pytest.raises(SquareRootError):
square_root_mod_prime(nonsquare, prime)
@st.composite
def st_two_nums_rel_prime(draw):
# 521-bit is the biggest curve we operate on, use 1024 for a bit
# of breathing space
mod = draw(st.integers(min_value=2, max_value=2**1024))
num = draw(st.integers(min_value=1, max_value=mod-1)
.filter(lambda x: gcd(x, mod) == 1))
return num, mod
@st.composite
def st_primes(draw, *args, **kwargs):
if "min_value" not in kwargs: # pragma: no branch
kwargs["min_value"] = 1
prime = draw(st.sampled_from(smallprimes) |
st.integers(*args, **kwargs)
.filter(is_prime))
return prime
@st.composite
def st_num_square_prime(draw):
prime = draw(st_primes(max_value=2**1024))
num = draw(st.integers(min_value=0, max_value=1 + prime // 2))
sq = num * num % prime
return sq, prime
@st.composite
def st_comp_with_com_fac(draw):
"""
Strategy that returns lists of numbers, all having a common factor.
"""
primes = draw(st.lists(st_primes(max_value=2**512), min_size=1,
max_size=10))
# select random prime(s) that will make the common factor of composites
com_fac_primes = draw(st.lists(st.sampled_from(primes),
min_size=1, max_size=20))
com_fac = reduce(operator.mul, com_fac_primes, 1)
# select at most 20 lists (returned numbers),
# each having at most 30 primes (factors) including none (then the number
# will be 1)
comp_primes = draw(
st.integers(min_value=1, max_value=20).
flatmap(lambda n: st.lists(st.lists(st.sampled_from(primes),
max_size=30),
min_size=1, max_size=n)))
return [reduce(operator.mul, nums, 1) * com_fac for nums in comp_primes]
@st.composite
def st_comp_no_com_fac(draw):
"""
Strategy that returns lists of numbers that don't have a common factor.
"""
primes = draw(st.lists(st_primes(max_value=2**512),
min_size=2, max_size=10, unique=True))
# first select the primes that will create the uncommon factor
# between returned numbers
uncom_fac_primes = draw(st.lists(
st.sampled_from(primes),
min_size=1, max_size=len(primes)-1, unique=True))
uncom_fac = reduce(operator.mul, uncom_fac_primes, 1)
# then build composites from leftover primes
leftover_primes = [i for i in primes if i not in uncom_fac_primes]
assert leftover_primes
assert uncom_fac_primes
# select at most 20 lists, each having at most 30 primes
# selected from the leftover_primes list
number_primes = draw(
st.integers(min_value=1, max_value=20).
flatmap(lambda n: st.lists(st.lists(st.sampled_from(leftover_primes),
max_size=30),
min_size=1, max_size=n)))
numbers = [reduce(operator.mul, nums, 1) for nums in number_primes]
insert_at = draw(st.integers(min_value=0, max_value=len(numbers)))
numbers.insert(insert_at, uncom_fac)
return numbers
HYP_SETTINGS = {}
if HC_PRESENT: # pragma: no branch
HYP_SETTINGS['suppress_health_check']=[HealthCheck.filter_too_much,
HealthCheck.too_slow]
# the factorization() sometimes takes a long time to finish
HYP_SETTINGS['deadline'] = 5000
HYP_SLOW_SETTINGS=dict(HYP_SETTINGS)
HYP_SLOW_SETTINGS["max_examples"] = 10
class TestNumbertheory(unittest.TestCase):
def test_gcd(self):
assert gcd(3 * 5 * 7, 3 * 5 * 11, 3 * 5 * 13) == 3 * 5
assert gcd([3 * 5 * 7, 3 * 5 * 11, 3 * 5 * 13]) == 3 * 5
assert gcd(3) == 3
@unittest.skipUnless(HC_PRESENT,
"Hypothesis 2.0.0 can't be made tolerant of hard to "
"meet requirements (like `is_prime()`), the test "
"case times-out on it")
@settings(**HYP_SLOW_SETTINGS)
@given(st_comp_with_com_fac())
def test_gcd_with_com_factor(self, numbers):
n = gcd(numbers)
assert 1 in numbers or n != 1
for i in numbers:
assert i % n == 0
@unittest.skipUnless(HC_PRESENT,
"Hypothesis 2.0.0 can't be made tolerant of hard to "
"meet requirements (like `is_prime()`), the test "
"case times-out on it")
@settings(**HYP_SLOW_SETTINGS)
@given(st_comp_no_com_fac())
def test_gcd_with_uncom_factor(self, numbers):
n = gcd(numbers)
assert n == 1
@given(st.lists(st.integers(min_value=1, max_value=2**8192),
min_size=1, max_size=20))
def test_gcd_with_random_numbers(self, numbers):
n = gcd(numbers)
for i in numbers:
# check that at least it's a divider
assert i % n == 0
def test_lcm(self):
assert lcm(3, 5 * 3, 7 * 3) == 3 * 5 * 7
assert lcm([3, 5 * 3, 7 * 3]) == 3 * 5 * 7
assert lcm(3) == 3
@given(st.lists(st.integers(min_value=1, max_value=2**8192),
min_size=1, max_size=20))
def test_lcm_with_random_numbers(self, numbers):
n = lcm(numbers)
for i in numbers:
assert n % i == 0
@unittest.skipUnless(HC_PRESENT,
"Hypothesis 2.0.0 can't be made tolerant of hard to "
"meet requirements (like `is_prime()`), the test "
"case times-out on it")
@settings(**HYP_SETTINGS)
@given(st_num_square_prime())
def test_square_root_mod_prime(self, vals):
square, prime = vals
calc = square_root_mod_prime(square, prime)
assert calc * calc % prime == square
@settings(**HYP_SETTINGS)
@given(st.integers(min_value=1, max_value=10**12))
@example(265399 * 1526929)
@example(373297 ** 2 * 553991)
def test_factorization(self, num):
factors = factorization(num)
mult = 1
for i in factors:
mult *= i[0] ** i[1]
assert mult == num
@settings(**HYP_SETTINGS)
@given(st.integers(min_value=3, max_value=1000).filter(lambda x: x % 2))
def test_jacobi(self, mod):
if is_prime(mod):
squares = set()
for root in range(1, mod):
assert jacobi(root * root, mod) == 1
squares.add(root * root % mod)
for i in range(1, mod):
if i not in squares:
assert jacobi(i, mod) == -1
else:
factors = factorization(mod)
for a in range(1, mod):
c = 1
for i in factors:
c *= jacobi(a, i[0]) ** i[1]
assert c == jacobi(a, mod)
@given(st_two_nums_rel_prime())
def test_inverse_mod(self, nums):
num, mod = nums
inv = inverse_mod(num, mod)
assert 0 < inv < mod
assert num * inv % mod == 1
def test_inverse_mod_with_zero(self):
assert 0 == inverse_mod(0, 11)
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