767 lines
31 KiB
Python
767 lines
31 KiB
Python
import unittest
|
|
import unittest.mock
|
|
import random
|
|
import time
|
|
import pickle
|
|
import warnings
|
|
from functools import partial
|
|
from math import log, exp, pi, fsum, sin
|
|
from test import support
|
|
|
|
class TestBasicOps:
|
|
# Superclass with tests common to all generators.
|
|
# Subclasses must arrange for self.gen to retrieve the Random instance
|
|
# to be tested.
|
|
|
|
def randomlist(self, n):
|
|
"""Helper function to make a list of random numbers"""
|
|
return [self.gen.random() for i in range(n)]
|
|
|
|
def test_autoseed(self):
|
|
self.gen.seed()
|
|
state1 = self.gen.getstate()
|
|
time.sleep(0.1)
|
|
self.gen.seed() # diffent seeds at different times
|
|
state2 = self.gen.getstate()
|
|
self.assertNotEqual(state1, state2)
|
|
|
|
def test_saverestore(self):
|
|
N = 1000
|
|
self.gen.seed()
|
|
state = self.gen.getstate()
|
|
randseq = self.randomlist(N)
|
|
self.gen.setstate(state) # should regenerate the same sequence
|
|
self.assertEqual(randseq, self.randomlist(N))
|
|
|
|
def test_seedargs(self):
|
|
# Seed value with a negative hash.
|
|
class MySeed(object):
|
|
def __hash__(self):
|
|
return -1729
|
|
for arg in [None, 0, 0, 1, 1, -1, -1, 10**20, -(10**20),
|
|
3.14, 1+2j, 'a', tuple('abc'), MySeed()]:
|
|
self.gen.seed(arg)
|
|
for arg in [list(range(3)), dict(one=1)]:
|
|
self.assertRaises(TypeError, self.gen.seed, arg)
|
|
self.assertRaises(TypeError, self.gen.seed, 1, 2, 3, 4)
|
|
self.assertRaises(TypeError, type(self.gen), [])
|
|
|
|
@unittest.mock.patch('random._urandom') # os.urandom
|
|
def test_seed_when_randomness_source_not_found(self, urandom_mock):
|
|
# Random.seed() uses time.time() when an operating system specific
|
|
# randomness source is not found. To test this on machines were it
|
|
# exists, run the above test, test_seedargs(), again after mocking
|
|
# os.urandom() so that it raises the exception expected when the
|
|
# randomness source is not available.
|
|
urandom_mock.side_effect = NotImplementedError
|
|
self.test_seedargs()
|
|
|
|
def test_shuffle(self):
|
|
shuffle = self.gen.shuffle
|
|
lst = []
|
|
shuffle(lst)
|
|
self.assertEqual(lst, [])
|
|
lst = [37]
|
|
shuffle(lst)
|
|
self.assertEqual(lst, [37])
|
|
seqs = [list(range(n)) for n in range(10)]
|
|
shuffled_seqs = [list(range(n)) for n in range(10)]
|
|
for shuffled_seq in shuffled_seqs:
|
|
shuffle(shuffled_seq)
|
|
for (seq, shuffled_seq) in zip(seqs, shuffled_seqs):
|
|
self.assertEqual(len(seq), len(shuffled_seq))
|
|
self.assertEqual(set(seq), set(shuffled_seq))
|
|
# The above tests all would pass if the shuffle was a
|
|
# no-op. The following non-deterministic test covers that. It
|
|
# asserts that the shuffled sequence of 1000 distinct elements
|
|
# must be different from the original one. Although there is
|
|
# mathematically a non-zero probability that this could
|
|
# actually happen in a genuinely random shuffle, it is
|
|
# completely negligible, given that the number of possible
|
|
# permutations of 1000 objects is 1000! (factorial of 1000),
|
|
# which is considerably larger than the number of atoms in the
|
|
# universe...
|
|
lst = list(range(1000))
|
|
shuffled_lst = list(range(1000))
|
|
shuffle(shuffled_lst)
|
|
self.assertTrue(lst != shuffled_lst)
|
|
shuffle(lst)
|
|
self.assertTrue(lst != shuffled_lst)
|
|
|
|
def test_choice(self):
|
|
choice = self.gen.choice
|
|
with self.assertRaises(IndexError):
|
|
choice([])
|
|
self.assertEqual(choice([50]), 50)
|
|
self.assertIn(choice([25, 75]), [25, 75])
|
|
|
|
def test_sample(self):
|
|
# For the entire allowable range of 0 <= k <= N, validate that
|
|
# the sample is of the correct length and contains only unique items
|
|
N = 100
|
|
population = range(N)
|
|
for k in range(N+1):
|
|
s = self.gen.sample(population, k)
|
|
self.assertEqual(len(s), k)
|
|
uniq = set(s)
|
|
self.assertEqual(len(uniq), k)
|
|
self.assertTrue(uniq <= set(population))
|
|
self.assertEqual(self.gen.sample([], 0), []) # test edge case N==k==0
|
|
# Exception raised if size of sample exceeds that of population
|
|
self.assertRaises(ValueError, self.gen.sample, population, N+1)
|
|
|
|
def test_sample_distribution(self):
|
|
# For the entire allowable range of 0 <= k <= N, validate that
|
|
# sample generates all possible permutations
|
|
n = 5
|
|
pop = range(n)
|
|
trials = 10000 # large num prevents false negatives without slowing normal case
|
|
def factorial(n):
|
|
if n == 0:
|
|
return 1
|
|
return n * factorial(n - 1)
|
|
for k in range(n):
|
|
expected = factorial(n) // factorial(n-k)
|
|
perms = {}
|
|
for i in range(trials):
|
|
perms[tuple(self.gen.sample(pop, k))] = None
|
|
if len(perms) == expected:
|
|
break
|
|
else:
|
|
self.fail()
|
|
|
|
def test_sample_inputs(self):
|
|
# SF bug #801342 -- population can be any iterable defining __len__()
|
|
self.gen.sample(set(range(20)), 2)
|
|
self.gen.sample(range(20), 2)
|
|
self.gen.sample(range(20), 2)
|
|
self.gen.sample(str('abcdefghijklmnopqrst'), 2)
|
|
self.gen.sample(tuple('abcdefghijklmnopqrst'), 2)
|
|
|
|
def test_sample_on_dicts(self):
|
|
self.assertRaises(TypeError, self.gen.sample, dict.fromkeys('abcdef'), 2)
|
|
|
|
def test_gauss(self):
|
|
# Ensure that the seed() method initializes all the hidden state. In
|
|
# particular, through 2.2.1 it failed to reset a piece of state used
|
|
# by (and only by) the .gauss() method.
|
|
|
|
for seed in 1, 12, 123, 1234, 12345, 123456, 654321:
|
|
self.gen.seed(seed)
|
|
x1 = self.gen.random()
|
|
y1 = self.gen.gauss(0, 1)
|
|
|
|
self.gen.seed(seed)
|
|
x2 = self.gen.random()
|
|
y2 = self.gen.gauss(0, 1)
|
|
|
|
self.assertEqual(x1, x2)
|
|
self.assertEqual(y1, y2)
|
|
|
|
def test_pickling(self):
|
|
for proto in range(pickle.HIGHEST_PROTOCOL + 1):
|
|
state = pickle.dumps(self.gen, proto)
|
|
origseq = [self.gen.random() for i in range(10)]
|
|
newgen = pickle.loads(state)
|
|
restoredseq = [newgen.random() for i in range(10)]
|
|
self.assertEqual(origseq, restoredseq)
|
|
|
|
def test_bug_1727780(self):
|
|
# verify that version-2-pickles can be loaded
|
|
# fine, whether they are created on 32-bit or 64-bit
|
|
# platforms, and that version-3-pickles load fine.
|
|
files = [("randv2_32.pck", 780),
|
|
("randv2_64.pck", 866),
|
|
("randv3.pck", 343)]
|
|
for file, value in files:
|
|
f = open(support.findfile(file),"rb")
|
|
r = pickle.load(f)
|
|
f.close()
|
|
self.assertEqual(int(r.random()*1000), value)
|
|
|
|
def test_bug_9025(self):
|
|
# Had problem with an uneven distribution in int(n*random())
|
|
# Verify the fix by checking that distributions fall within expectations.
|
|
n = 100000
|
|
randrange = self.gen.randrange
|
|
k = sum(randrange(6755399441055744) % 3 == 2 for i in range(n))
|
|
self.assertTrue(0.30 < k/n < .37, (k/n))
|
|
|
|
try:
|
|
random.SystemRandom().random()
|
|
except NotImplementedError:
|
|
SystemRandom_available = False
|
|
else:
|
|
SystemRandom_available = True
|
|
|
|
@unittest.skipUnless(SystemRandom_available, "random.SystemRandom not available")
|
|
class SystemRandom_TestBasicOps(TestBasicOps, unittest.TestCase):
|
|
gen = random.SystemRandom()
|
|
|
|
def test_autoseed(self):
|
|
# Doesn't need to do anything except not fail
|
|
self.gen.seed()
|
|
|
|
def test_saverestore(self):
|
|
self.assertRaises(NotImplementedError, self.gen.getstate)
|
|
self.assertRaises(NotImplementedError, self.gen.setstate, None)
|
|
|
|
def test_seedargs(self):
|
|
# Doesn't need to do anything except not fail
|
|
self.gen.seed(100)
|
|
|
|
def test_gauss(self):
|
|
self.gen.gauss_next = None
|
|
self.gen.seed(100)
|
|
self.assertEqual(self.gen.gauss_next, None)
|
|
|
|
def test_pickling(self):
|
|
for proto in range(pickle.HIGHEST_PROTOCOL + 1):
|
|
self.assertRaises(NotImplementedError, pickle.dumps, self.gen, proto)
|
|
|
|
def test_53_bits_per_float(self):
|
|
# This should pass whenever a C double has 53 bit precision.
|
|
span = 2 ** 53
|
|
cum = 0
|
|
for i in range(100):
|
|
cum |= int(self.gen.random() * span)
|
|
self.assertEqual(cum, span-1)
|
|
|
|
def test_bigrand(self):
|
|
# The randrange routine should build-up the required number of bits
|
|
# in stages so that all bit positions are active.
|
|
span = 2 ** 500
|
|
cum = 0
|
|
for i in range(100):
|
|
r = self.gen.randrange(span)
|
|
self.assertTrue(0 <= r < span)
|
|
cum |= r
|
|
self.assertEqual(cum, span-1)
|
|
|
|
def test_bigrand_ranges(self):
|
|
for i in [40,80, 160, 200, 211, 250, 375, 512, 550]:
|
|
start = self.gen.randrange(2 ** (i-2))
|
|
stop = self.gen.randrange(2 ** i)
|
|
if stop <= start:
|
|
continue
|
|
self.assertTrue(start <= self.gen.randrange(start, stop) < stop)
|
|
|
|
def test_rangelimits(self):
|
|
for start, stop in [(-2,0), (-(2**60)-2,-(2**60)), (2**60,2**60+2)]:
|
|
self.assertEqual(set(range(start,stop)),
|
|
set([self.gen.randrange(start,stop) for i in range(100)]))
|
|
|
|
def test_randrange_nonunit_step(self):
|
|
rint = self.gen.randrange(0, 10, 2)
|
|
self.assertIn(rint, (0, 2, 4, 6, 8))
|
|
rint = self.gen.randrange(0, 2, 2)
|
|
self.assertEqual(rint, 0)
|
|
|
|
def test_randrange_errors(self):
|
|
raises = partial(self.assertRaises, ValueError, self.gen.randrange)
|
|
# Empty range
|
|
raises(3, 3)
|
|
raises(-721)
|
|
raises(0, 100, -12)
|
|
# Non-integer start/stop
|
|
raises(3.14159)
|
|
raises(0, 2.71828)
|
|
# Zero and non-integer step
|
|
raises(0, 42, 0)
|
|
raises(0, 42, 3.14159)
|
|
|
|
def test_genrandbits(self):
|
|
# Verify ranges
|
|
for k in range(1, 1000):
|
|
self.assertTrue(0 <= self.gen.getrandbits(k) < 2**k)
|
|
|
|
# Verify all bits active
|
|
getbits = self.gen.getrandbits
|
|
for span in [1, 2, 3, 4, 31, 32, 32, 52, 53, 54, 119, 127, 128, 129]:
|
|
cum = 0
|
|
for i in range(100):
|
|
cum |= getbits(span)
|
|
self.assertEqual(cum, 2**span-1)
|
|
|
|
# Verify argument checking
|
|
self.assertRaises(TypeError, self.gen.getrandbits)
|
|
self.assertRaises(TypeError, self.gen.getrandbits, 1, 2)
|
|
self.assertRaises(ValueError, self.gen.getrandbits, 0)
|
|
self.assertRaises(ValueError, self.gen.getrandbits, -1)
|
|
self.assertRaises(TypeError, self.gen.getrandbits, 10.1)
|
|
|
|
def test_randbelow_logic(self, _log=log, int=int):
|
|
# check bitcount transition points: 2**i and 2**(i+1)-1
|
|
# show that: k = int(1.001 + _log(n, 2))
|
|
# is equal to or one greater than the number of bits in n
|
|
for i in range(1, 1000):
|
|
n = 1 << i # check an exact power of two
|
|
numbits = i+1
|
|
k = int(1.00001 + _log(n, 2))
|
|
self.assertEqual(k, numbits)
|
|
self.assertEqual(n, 2**(k-1))
|
|
|
|
n += n - 1 # check 1 below the next power of two
|
|
k = int(1.00001 + _log(n, 2))
|
|
self.assertIn(k, [numbits, numbits+1])
|
|
self.assertTrue(2**k > n > 2**(k-2))
|
|
|
|
n -= n >> 15 # check a little farther below the next power of two
|
|
k = int(1.00001 + _log(n, 2))
|
|
self.assertEqual(k, numbits) # note the stronger assertion
|
|
self.assertTrue(2**k > n > 2**(k-1)) # note the stronger assertion
|
|
|
|
|
|
class MersenneTwister_TestBasicOps(TestBasicOps, unittest.TestCase):
|
|
gen = random.Random()
|
|
|
|
def test_guaranteed_stable(self):
|
|
# These sequences are guaranteed to stay the same across versions of python
|
|
self.gen.seed(3456147, version=1)
|
|
self.assertEqual([self.gen.random().hex() for i in range(4)],
|
|
['0x1.ac362300d90d2p-1', '0x1.9d16f74365005p-1',
|
|
'0x1.1ebb4352e4c4dp-1', '0x1.1a7422abf9c11p-1'])
|
|
self.gen.seed("the quick brown fox", version=2)
|
|
self.assertEqual([self.gen.random().hex() for i in range(4)],
|
|
['0x1.1239ddfb11b7cp-3', '0x1.b3cbb5c51b120p-4',
|
|
'0x1.8c4f55116b60fp-1', '0x1.63eb525174a27p-1'])
|
|
|
|
def test_setstate_first_arg(self):
|
|
self.assertRaises(ValueError, self.gen.setstate, (1, None, None))
|
|
|
|
def test_setstate_middle_arg(self):
|
|
# Wrong type, s/b tuple
|
|
self.assertRaises(TypeError, self.gen.setstate, (2, None, None))
|
|
# Wrong length, s/b 625
|
|
self.assertRaises(ValueError, self.gen.setstate, (2, (1,2,3), None))
|
|
# Wrong type, s/b tuple of 625 ints
|
|
self.assertRaises(TypeError, self.gen.setstate, (2, ('a',)*625, None))
|
|
# Last element s/b an int also
|
|
self.assertRaises(TypeError, self.gen.setstate, (2, (0,)*624+('a',), None))
|
|
# Last element s/b between 0 and 624
|
|
with self.assertRaises((ValueError, OverflowError)):
|
|
self.gen.setstate((2, (1,)*624+(625,), None))
|
|
with self.assertRaises((ValueError, OverflowError)):
|
|
self.gen.setstate((2, (1,)*624+(-1,), None))
|
|
|
|
# Little trick to make "tuple(x % (2**32) for x in internalstate)"
|
|
# raise ValueError. I cannot think of a simple way to achieve this, so
|
|
# I am opting for using a generator as the middle argument of setstate
|
|
# which attempts to cast a NaN to integer.
|
|
state_values = self.gen.getstate()[1]
|
|
state_values = list(state_values)
|
|
state_values[-1] = float('nan')
|
|
state = (int(x) for x in state_values)
|
|
self.assertRaises(TypeError, self.gen.setstate, (2, state, None))
|
|
|
|
def test_referenceImplementation(self):
|
|
# Compare the python implementation with results from the original
|
|
# code. Create 2000 53-bit precision random floats. Compare only
|
|
# the last ten entries to show that the independent implementations
|
|
# are tracking. Here is the main() function needed to create the
|
|
# list of expected random numbers:
|
|
# void main(void){
|
|
# int i;
|
|
# unsigned long init[4]={61731, 24903, 614, 42143}, length=4;
|
|
# init_by_array(init, length);
|
|
# for (i=0; i<2000; i++) {
|
|
# printf("%.15f ", genrand_res53());
|
|
# if (i%5==4) printf("\n");
|
|
# }
|
|
# }
|
|
expected = [0.45839803073713259,
|
|
0.86057815201978782,
|
|
0.92848331726782152,
|
|
0.35932681119782461,
|
|
0.081823493762449573,
|
|
0.14332226470169329,
|
|
0.084297823823520024,
|
|
0.53814864671831453,
|
|
0.089215024911993401,
|
|
0.78486196105372907]
|
|
|
|
self.gen.seed(61731 + (24903<<32) + (614<<64) + (42143<<96))
|
|
actual = self.randomlist(2000)[-10:]
|
|
for a, e in zip(actual, expected):
|
|
self.assertAlmostEqual(a,e,places=14)
|
|
|
|
def test_strong_reference_implementation(self):
|
|
# Like test_referenceImplementation, but checks for exact bit-level
|
|
# equality. This should pass on any box where C double contains
|
|
# at least 53 bits of precision (the underlying algorithm suffers
|
|
# no rounding errors -- all results are exact).
|
|
from math import ldexp
|
|
|
|
expected = [0x0eab3258d2231f,
|
|
0x1b89db315277a5,
|
|
0x1db622a5518016,
|
|
0x0b7f9af0d575bf,
|
|
0x029e4c4db82240,
|
|
0x04961892f5d673,
|
|
0x02b291598e4589,
|
|
0x11388382c15694,
|
|
0x02dad977c9e1fe,
|
|
0x191d96d4d334c6]
|
|
self.gen.seed(61731 + (24903<<32) + (614<<64) + (42143<<96))
|
|
actual = self.randomlist(2000)[-10:]
|
|
for a, e in zip(actual, expected):
|
|
self.assertEqual(int(ldexp(a, 53)), e)
|
|
|
|
def test_long_seed(self):
|
|
# This is most interesting to run in debug mode, just to make sure
|
|
# nothing blows up. Under the covers, a dynamically resized array
|
|
# is allocated, consuming space proportional to the number of bits
|
|
# in the seed. Unfortunately, that's a quadratic-time algorithm,
|
|
# so don't make this horribly big.
|
|
seed = (1 << (10000 * 8)) - 1 # about 10K bytes
|
|
self.gen.seed(seed)
|
|
|
|
def test_53_bits_per_float(self):
|
|
# This should pass whenever a C double has 53 bit precision.
|
|
span = 2 ** 53
|
|
cum = 0
|
|
for i in range(100):
|
|
cum |= int(self.gen.random() * span)
|
|
self.assertEqual(cum, span-1)
|
|
|
|
def test_bigrand(self):
|
|
# The randrange routine should build-up the required number of bits
|
|
# in stages so that all bit positions are active.
|
|
span = 2 ** 500
|
|
cum = 0
|
|
for i in range(100):
|
|
r = self.gen.randrange(span)
|
|
self.assertTrue(0 <= r < span)
|
|
cum |= r
|
|
self.assertEqual(cum, span-1)
|
|
|
|
def test_bigrand_ranges(self):
|
|
for i in [40,80, 160, 200, 211, 250, 375, 512, 550]:
|
|
start = self.gen.randrange(2 ** (i-2))
|
|
stop = self.gen.randrange(2 ** i)
|
|
if stop <= start:
|
|
continue
|
|
self.assertTrue(start <= self.gen.randrange(start, stop) < stop)
|
|
|
|
def test_rangelimits(self):
|
|
for start, stop in [(-2,0), (-(2**60)-2,-(2**60)), (2**60,2**60+2)]:
|
|
self.assertEqual(set(range(start,stop)),
|
|
set([self.gen.randrange(start,stop) for i in range(100)]))
|
|
|
|
def test_genrandbits(self):
|
|
# Verify cross-platform repeatability
|
|
self.gen.seed(1234567)
|
|
self.assertEqual(self.gen.getrandbits(100),
|
|
97904845777343510404718956115)
|
|
# Verify ranges
|
|
for k in range(1, 1000):
|
|
self.assertTrue(0 <= self.gen.getrandbits(k) < 2**k)
|
|
|
|
# Verify all bits active
|
|
getbits = self.gen.getrandbits
|
|
for span in [1, 2, 3, 4, 31, 32, 32, 52, 53, 54, 119, 127, 128, 129]:
|
|
cum = 0
|
|
for i in range(100):
|
|
cum |= getbits(span)
|
|
self.assertEqual(cum, 2**span-1)
|
|
|
|
# Verify argument checking
|
|
self.assertRaises(TypeError, self.gen.getrandbits)
|
|
self.assertRaises(TypeError, self.gen.getrandbits, 'a')
|
|
self.assertRaises(TypeError, self.gen.getrandbits, 1, 2)
|
|
self.assertRaises(ValueError, self.gen.getrandbits, 0)
|
|
self.assertRaises(ValueError, self.gen.getrandbits, -1)
|
|
|
|
def test_randbelow_logic(self, _log=log, int=int):
|
|
# check bitcount transition points: 2**i and 2**(i+1)-1
|
|
# show that: k = int(1.001 + _log(n, 2))
|
|
# is equal to or one greater than the number of bits in n
|
|
for i in range(1, 1000):
|
|
n = 1 << i # check an exact power of two
|
|
numbits = i+1
|
|
k = int(1.00001 + _log(n, 2))
|
|
self.assertEqual(k, numbits)
|
|
self.assertEqual(n, 2**(k-1))
|
|
|
|
n += n - 1 # check 1 below the next power of two
|
|
k = int(1.00001 + _log(n, 2))
|
|
self.assertIn(k, [numbits, numbits+1])
|
|
self.assertTrue(2**k > n > 2**(k-2))
|
|
|
|
n -= n >> 15 # check a little farther below the next power of two
|
|
k = int(1.00001 + _log(n, 2))
|
|
self.assertEqual(k, numbits) # note the stronger assertion
|
|
self.assertTrue(2**k > n > 2**(k-1)) # note the stronger assertion
|
|
|
|
@unittest.mock.patch('random.Random.random')
|
|
def test_randbelow_overridden_random(self, random_mock):
|
|
# Random._randbelow() can only use random() when the built-in one
|
|
# has been overridden but no new getrandbits() method was supplied.
|
|
random_mock.side_effect = random.SystemRandom().random
|
|
maxsize = 1<<random.BPF
|
|
with warnings.catch_warnings():
|
|
warnings.simplefilter("ignore", UserWarning)
|
|
# Population range too large (n >= maxsize)
|
|
self.gen._randbelow(maxsize+1, maxsize = maxsize)
|
|
self.gen._randbelow(5640, maxsize = maxsize)
|
|
|
|
# This might be going too far to test a single line, but because of our
|
|
# noble aim of achieving 100% test coverage we need to write a case in
|
|
# which the following line in Random._randbelow() gets executed:
|
|
#
|
|
# rem = maxsize % n
|
|
# limit = (maxsize - rem) / maxsize
|
|
# r = random()
|
|
# while r >= limit:
|
|
# r = random() # <== *This line* <==<
|
|
#
|
|
# Therefore, to guarantee that the while loop is executed at least
|
|
# once, we need to mock random() so that it returns a number greater
|
|
# than 'limit' the first time it gets called.
|
|
|
|
n = 42
|
|
epsilon = 0.01
|
|
limit = (maxsize - (maxsize % n)) / maxsize
|
|
random_mock.side_effect = [limit + epsilon, limit - epsilon]
|
|
self.gen._randbelow(n, maxsize = maxsize)
|
|
|
|
def test_randrange_bug_1590891(self):
|
|
start = 1000000000000
|
|
stop = -100000000000000000000
|
|
step = -200
|
|
x = self.gen.randrange(start, stop, step)
|
|
self.assertTrue(stop < x <= start)
|
|
self.assertEqual((x+stop)%step, 0)
|
|
|
|
def gamma(z, sqrt2pi=(2.0*pi)**0.5):
|
|
# Reflection to right half of complex plane
|
|
if z < 0.5:
|
|
return pi / sin(pi*z) / gamma(1.0-z)
|
|
# Lanczos approximation with g=7
|
|
az = z + (7.0 - 0.5)
|
|
return az ** (z-0.5) / exp(az) * sqrt2pi * fsum([
|
|
0.9999999999995183,
|
|
676.5203681218835 / z,
|
|
-1259.139216722289 / (z+1.0),
|
|
771.3234287757674 / (z+2.0),
|
|
-176.6150291498386 / (z+3.0),
|
|
12.50734324009056 / (z+4.0),
|
|
-0.1385710331296526 / (z+5.0),
|
|
0.9934937113930748e-05 / (z+6.0),
|
|
0.1659470187408462e-06 / (z+7.0),
|
|
])
|
|
|
|
class TestDistributions(unittest.TestCase):
|
|
def test_zeroinputs(self):
|
|
# Verify that distributions can handle a series of zero inputs'
|
|
g = random.Random()
|
|
x = [g.random() for i in range(50)] + [0.0]*5
|
|
g.random = x[:].pop; g.uniform(1,10)
|
|
g.random = x[:].pop; g.paretovariate(1.0)
|
|
g.random = x[:].pop; g.expovariate(1.0)
|
|
g.random = x[:].pop; g.weibullvariate(1.0, 1.0)
|
|
g.random = x[:].pop; g.vonmisesvariate(1.0, 1.0)
|
|
g.random = x[:].pop; g.normalvariate(0.0, 1.0)
|
|
g.random = x[:].pop; g.gauss(0.0, 1.0)
|
|
g.random = x[:].pop; g.lognormvariate(0.0, 1.0)
|
|
g.random = x[:].pop; g.vonmisesvariate(0.0, 1.0)
|
|
g.random = x[:].pop; g.gammavariate(0.01, 1.0)
|
|
g.random = x[:].pop; g.gammavariate(1.0, 1.0)
|
|
g.random = x[:].pop; g.gammavariate(200.0, 1.0)
|
|
g.random = x[:].pop; g.betavariate(3.0, 3.0)
|
|
g.random = x[:].pop; g.triangular(0.0, 1.0, 1.0/3.0)
|
|
|
|
def test_avg_std(self):
|
|
# Use integration to test distribution average and standard deviation.
|
|
# Only works for distributions which do not consume variates in pairs
|
|
g = random.Random()
|
|
N = 5000
|
|
x = [i/float(N) for i in range(1,N)]
|
|
for variate, args, mu, sigmasqrd in [
|
|
(g.uniform, (1.0,10.0), (10.0+1.0)/2, (10.0-1.0)**2/12),
|
|
(g.triangular, (0.0, 1.0, 1.0/3.0), 4.0/9.0, 7.0/9.0/18.0),
|
|
(g.expovariate, (1.5,), 1/1.5, 1/1.5**2),
|
|
(g.vonmisesvariate, (1.23, 0), pi, pi**2/3),
|
|
(g.paretovariate, (5.0,), 5.0/(5.0-1),
|
|
5.0/((5.0-1)**2*(5.0-2))),
|
|
(g.weibullvariate, (1.0, 3.0), gamma(1+1/3.0),
|
|
gamma(1+2/3.0)-gamma(1+1/3.0)**2) ]:
|
|
g.random = x[:].pop
|
|
y = []
|
|
for i in range(len(x)):
|
|
try:
|
|
y.append(variate(*args))
|
|
except IndexError:
|
|
pass
|
|
s1 = s2 = 0
|
|
for e in y:
|
|
s1 += e
|
|
s2 += (e - mu) ** 2
|
|
N = len(y)
|
|
self.assertAlmostEqual(s1/N, mu, places=2,
|
|
msg='%s%r' % (variate.__name__, args))
|
|
self.assertAlmostEqual(s2/(N-1), sigmasqrd, places=2,
|
|
msg='%s%r' % (variate.__name__, args))
|
|
|
|
def test_constant(self):
|
|
g = random.Random()
|
|
N = 100
|
|
for variate, args, expected in [
|
|
(g.uniform, (10.0, 10.0), 10.0),
|
|
(g.triangular, (10.0, 10.0), 10.0),
|
|
(g.triangular, (10.0, 10.0, 10.0), 10.0),
|
|
(g.expovariate, (float('inf'),), 0.0),
|
|
(g.vonmisesvariate, (3.0, float('inf')), 3.0),
|
|
(g.gauss, (10.0, 0.0), 10.0),
|
|
(g.lognormvariate, (0.0, 0.0), 1.0),
|
|
(g.lognormvariate, (-float('inf'), 0.0), 0.0),
|
|
(g.normalvariate, (10.0, 0.0), 10.0),
|
|
(g.paretovariate, (float('inf'),), 1.0),
|
|
(g.weibullvariate, (10.0, float('inf')), 10.0),
|
|
(g.weibullvariate, (0.0, 10.0), 0.0),
|
|
]:
|
|
for i in range(N):
|
|
self.assertEqual(variate(*args), expected)
|
|
|
|
def test_von_mises_range(self):
|
|
# Issue 17149: von mises variates were not consistently in the
|
|
# range [0, 2*PI].
|
|
g = random.Random()
|
|
N = 100
|
|
for mu in 0.0, 0.1, 3.1, 6.2:
|
|
for kappa in 0.0, 2.3, 500.0:
|
|
for _ in range(N):
|
|
sample = g.vonmisesvariate(mu, kappa)
|
|
self.assertTrue(
|
|
0 <= sample <= random.TWOPI,
|
|
msg=("vonmisesvariate({}, {}) produced a result {} out"
|
|
" of range [0, 2*pi]").format(mu, kappa, sample))
|
|
|
|
def test_von_mises_large_kappa(self):
|
|
# Issue #17141: vonmisesvariate() was hang for large kappas
|
|
random.vonmisesvariate(0, 1e15)
|
|
random.vonmisesvariate(0, 1e100)
|
|
|
|
def test_gammavariate_errors(self):
|
|
# Both alpha and beta must be > 0.0
|
|
self.assertRaises(ValueError, random.gammavariate, -1, 3)
|
|
self.assertRaises(ValueError, random.gammavariate, 0, 2)
|
|
self.assertRaises(ValueError, random.gammavariate, 2, 0)
|
|
self.assertRaises(ValueError, random.gammavariate, 1, -3)
|
|
|
|
@unittest.mock.patch('random.Random.random')
|
|
def test_gammavariate_full_code_coverage(self, random_mock):
|
|
# There are three different possibilities in the current implementation
|
|
# of random.gammavariate(), depending on the value of 'alpha'. What we
|
|
# are going to do here is to fix the values returned by random() to
|
|
# generate test cases that provide 100% line coverage of the method.
|
|
|
|
# #1: alpha > 1.0: we want the first random number to be outside the
|
|
# [1e-7, .9999999] range, so that the continue statement executes
|
|
# once. The values of u1 and u2 will be 0.5 and 0.3, respectively.
|
|
random_mock.side_effect = [1e-8, 0.5, 0.3]
|
|
returned_value = random.gammavariate(1.1, 2.3)
|
|
self.assertAlmostEqual(returned_value, 2.53)
|
|
|
|
# #2: alpha == 1: first random number less than 1e-7 to that the body
|
|
# of the while loop executes once. Then random.random() returns 0.45,
|
|
# which causes while to stop looping and the algorithm to terminate.
|
|
random_mock.side_effect = [1e-8, 0.45]
|
|
returned_value = random.gammavariate(1.0, 3.14)
|
|
self.assertAlmostEqual(returned_value, 2.507314166123803)
|
|
|
|
# #3: 0 < alpha < 1. This is the most complex region of code to cover,
|
|
# as there are multiple if-else statements. Let's take a look at the
|
|
# source code, and determine the values that we need accordingly:
|
|
#
|
|
# while 1:
|
|
# u = random()
|
|
# b = (_e + alpha)/_e
|
|
# p = b*u
|
|
# if p <= 1.0: # <=== (A)
|
|
# x = p ** (1.0/alpha)
|
|
# else: # <=== (B)
|
|
# x = -_log((b-p)/alpha)
|
|
# u1 = random()
|
|
# if p > 1.0: # <=== (C)
|
|
# if u1 <= x ** (alpha - 1.0): # <=== (D)
|
|
# break
|
|
# elif u1 <= _exp(-x): # <=== (E)
|
|
# break
|
|
# return x * beta
|
|
#
|
|
# First, we want (A) to be True. For that we need that:
|
|
# b*random() <= 1.0
|
|
# r1 = random() <= 1.0 / b
|
|
#
|
|
# We now get to the second if-else branch, and here, since p <= 1.0,
|
|
# (C) is False and we take the elif branch, (E). For it to be True,
|
|
# so that the break is executed, we need that:
|
|
# r2 = random() <= _exp(-x)
|
|
# r2 <= _exp(-(p ** (1.0/alpha)))
|
|
# r2 <= _exp(-((b*r1) ** (1.0/alpha)))
|
|
|
|
_e = random._e
|
|
_exp = random._exp
|
|
_log = random._log
|
|
alpha = 0.35
|
|
beta = 1.45
|
|
b = (_e + alpha)/_e
|
|
epsilon = 0.01
|
|
|
|
r1 = 0.8859296441566 # 1.0 / b
|
|
r2 = 0.3678794411714 # _exp(-((b*r1) ** (1.0/alpha)))
|
|
|
|
# These four "random" values result in the following trace:
|
|
# (A) True, (E) False --> [next iteration of while]
|
|
# (A) True, (E) True --> [while loop breaks]
|
|
random_mock.side_effect = [r1, r2 + epsilon, r1, r2]
|
|
returned_value = random.gammavariate(alpha, beta)
|
|
self.assertAlmostEqual(returned_value, 1.4499999999997544)
|
|
|
|
# Let's now make (A) be False. If this is the case, when we get to the
|
|
# second if-else 'p' is greater than 1, so (C) evaluates to True. We
|
|
# now encounter a second if statement, (D), which in order to execute
|
|
# must satisfy the following condition:
|
|
# r2 <= x ** (alpha - 1.0)
|
|
# r2 <= (-_log((b-p)/alpha)) ** (alpha - 1.0)
|
|
# r2 <= (-_log((b-(b*r1))/alpha)) ** (alpha - 1.0)
|
|
r1 = 0.8959296441566 # (1.0 / b) + epsilon -- so that (A) is False
|
|
r2 = 0.9445400408898141
|
|
|
|
# And these four values result in the following trace:
|
|
# (B) and (C) True, (D) False --> [next iteration of while]
|
|
# (B) and (C) True, (D) True [while loop breaks]
|
|
random_mock.side_effect = [r1, r2 + epsilon, r1, r2]
|
|
returned_value = random.gammavariate(alpha, beta)
|
|
self.assertAlmostEqual(returned_value, 1.5830349561760781)
|
|
|
|
@unittest.mock.patch('random.Random.gammavariate')
|
|
def test_betavariate_return_zero(self, gammavariate_mock):
|
|
# betavariate() returns zero when the Gamma distribution
|
|
# that it uses internally returns this same value.
|
|
gammavariate_mock.return_value = 0.0
|
|
self.assertEqual(0.0, random.betavariate(2.71828, 3.14159))
|
|
|
|
class TestModule(unittest.TestCase):
|
|
def testMagicConstants(self):
|
|
self.assertAlmostEqual(random.NV_MAGICCONST, 1.71552776992141)
|
|
self.assertAlmostEqual(random.TWOPI, 6.28318530718)
|
|
self.assertAlmostEqual(random.LOG4, 1.38629436111989)
|
|
self.assertAlmostEqual(random.SG_MAGICCONST, 2.50407739677627)
|
|
|
|
def test__all__(self):
|
|
# tests validity but not completeness of the __all__ list
|
|
self.assertTrue(set(random.__all__) <= set(dir(random)))
|
|
|
|
def test_random_subclass_with_kwargs(self):
|
|
# SF bug #1486663 -- this used to erroneously raise a TypeError
|
|
class Subclass(random.Random):
|
|
def __init__(self, newarg=None):
|
|
random.Random.__init__(self)
|
|
Subclass(newarg=1)
|
|
|
|
|
|
if __name__ == "__main__":
|
|
unittest.main()
|