from __future__ import print_function

import collections
import functools
import math
import multiprocessing
import os
import random
import subprocess
import sys
import threading

import numpy as np

import numba.unittest_support as unittest
from numba import jit, _helperlib, types
from numba.compiler import compile_isolated
from .support import TestCase, compile_function, tag


# State size of the Mersenne Twister
N = 624


def get_py_state_ptr():
    return _helperlib.rnd_get_py_state_ptr()

def get_np_state_ptr():
    return _helperlib.rnd_get_np_state_ptr()


def numpy_randint1(a):
    return np.random.randint(a)

def numpy_randint2(a, b):
    return np.random.randint(a, b)

def random_randint(a, b):
    return random.randint(a, b)

def random_randrange1(a):
    return random.randrange(a)

def random_randrange2(a, b):
    return random.randrange(a, b)

def random_randrange3(a, b, c):
    return random.randrange(a, b, c)

def numpy_choice1(a):
    return np.random.choice(a)

def numpy_choice2(a, size):
    return np.random.choice(a, size=size)

def numpy_choice3(a, size, replace):
    return np.random.choice(a, size=size, replace=replace)

def numpy_multinomial2(n, pvals):
    return np.random.multinomial(n, pvals)

def numpy_multinomial3(n, pvals, size):
    return np.random.multinomial(n, pvals=pvals, size=size)

def numpy_check_rand(seed, a, b):
    np.random.seed(seed)
    expected = np.random.random((a, b))
    np.random.seed(seed)
    got = np.random.rand(a, b)
    return expected, got

def numpy_check_randn(seed, a, b):
    np.random.seed(seed)
    expected = np.random.standard_normal((a, b))
    np.random.seed(seed)
    got = np.random.randn(a, b)
    return expected, got

def jit_with_args(name, argstring):
    code = """def func(%(argstring)s):
        return %(name)s(%(argstring)s)
""" % locals()
    pyfunc = compile_function("func", code, globals())
    return jit(nopython=True)(pyfunc)

def jit_nullary(name):
    return jit_with_args(name, "")

def jit_unary(name):
    return jit_with_args(name, "a")

def jit_binary(name):
    return jit_with_args(name, "a, b")

def jit_ternary(name):
    return jit_with_args(name, "a, b, c")


random_gauss = jit_binary("random.gauss")
random_random = jit_nullary("random.random")
random_seed = jit_unary("random.seed")

numpy_normal = jit_binary("np.random.normal")
numpy_random = jit_nullary("np.random.random")
numpy_seed = jit_unary("np.random.seed")


def _copy_py_state(r, ptr):
    """
    Copy state of Python random *r* to Numba state *ptr*.
    """
    mt = r.getstate()[1]
    ints, index = mt[:-1], mt[-1]
    _helperlib.rnd_set_state(ptr, (index, list(ints)))
    return ints, index

def _copy_np_state(r, ptr):
    """
    Copy state of Numpy random *r* to Numba state *ptr*.
    """
    ints, index = r.get_state()[1:3]
    _helperlib.rnd_set_state(ptr, (index, [int(x) for x in ints]))
    return ints, index

def sync_to_numpy(r):
    _ver, mt_st, _gauss_next = r.getstate()
    mt_pos = mt_st[-1]
    mt_ints = mt_st[:-1]
    assert len(mt_ints) == 624

    np_st = ('MT19937', np.array(mt_ints, dtype='uint32'), mt_pos)
    if _gauss_next is None:
        np_st += (0, 0.0)
    else:
        np_st += (1, _gauss_next)

    np.random.set_state(np_st)

# Pure Python equivalents of some of the Numpy distributions, using
# Python's basic generators.

def py_chisquare(r, df):
    return 2.0 * r.gammavariate(df / 2.0, 1.0)

def py_f(r, num, denom):
    return ((py_chisquare(r, num) * denom) /
            (py_chisquare(r, denom) * num))


class BaseTest(TestCase):

    def _follow_cpython(self, ptr, seed=2):
        r = random.Random(seed)
        _copy_py_state(r, ptr)
        return r

    def _follow_numpy(self, ptr, seed=2):
        r = np.random.RandomState(seed)
        _copy_np_state(r, ptr)
        return r


class TestInternals(BaseTest):
    """
    Test low-level internals of the implementation.
    """

    def _check_get_set_state(self, ptr):
        state = _helperlib.rnd_get_state(ptr)
        i, ints = state
        self.assertIsInstance(i, int)
        self.assertIsInstance(ints, list)
        self.assertEqual(len(ints), N)
        j = (i * 100007) % N
        ints = [i * 3 for i in range(N)]
        # Roundtrip
        _helperlib.rnd_set_state(ptr, (j, ints))
        self.assertEqual(_helperlib.rnd_get_state(ptr), (j, ints))

    def _check_shuffle(self, ptr):
        # We test shuffling against CPython
        r = random.Random()
        ints, index = _copy_py_state(r, ptr)
        # Force shuffling in CPython generator
        for i in range(index, N + 1, 2):
            r.random()
        _helperlib.rnd_shuffle(ptr)
        # Check new integer keys
        mt = r.getstate()[1]
        ints, index = mt[:-1], mt[-1]
        self.assertEqual(_helperlib.rnd_get_state(ptr)[1], list(ints))

    def _check_init(self, ptr):
        # We use the same integer seeding as Numpy
        # (CPython is different: it treats the integer as a byte array)
        r = np.random.RandomState()
        for i in [0, 1, 125, 2**32 - 5]:
            # Need to cast to a C-sized int (for Numpy <= 1.7)
            r.seed(np.uint32(i))
            st = r.get_state()
            ints = list(st[1])
            index = st[2]
            assert index == N  # sanity check
            _helperlib.rnd_seed(ptr, i)
            self.assertEqual(_helperlib.rnd_get_state(ptr), (index, ints))

    def _check_perturb(self, ptr):
        states = []
        for i in range(10):
            # Initialize with known state
            _helperlib.rnd_seed(ptr, 0)
            # Perturb with entropy
            _helperlib.rnd_seed(ptr, os.urandom(512))
            states.append(tuple(_helperlib.rnd_get_state(ptr)[1]))
        # No two identical states
        self.assertEqual(len(set(states)), len(states))

    def test_get_set_state(self):
        self._check_get_set_state(get_py_state_ptr())

    def test_shuffle(self):
        self._check_shuffle(get_py_state_ptr())

    def test_init(self):
        self._check_init(get_py_state_ptr())

    def test_perturb(self):
        self._check_perturb(get_py_state_ptr())


class TestRandom(BaseTest):

    # NOTE: there may be cascading imprecision issues (e.g. between x87-using
    # C code and SSE-using LLVM code), which is especially brutal for some
    # iterative algorithms with sensitive exit conditions.
    # Therefore we stick to hardcoded integers for seed values.

    def _check_random_seed(self, seedfunc, randomfunc):
        """
        Check seed()- and random()-like functions.
        """
        # Our seed() mimicks Numpy's.
        r = np.random.RandomState()
        for i in [0, 1, 125, 2**32 - 1]:
            # Need to cast to a C-sized int (for Numpy <= 1.7)
            r.seed(np.uint32(i))
            seedfunc(i)
            # Be sure to trigger a reshuffle
            for j in range(N + 10):
                self.assertPreciseEqual(randomfunc(), r.uniform(0.0, 1.0))

    @tag('important')
    def test_random_random(self):
        self._check_random_seed(random_seed, random_random)

    @tag('important')
    def test_numpy_random(self):
        self._check_random_seed(numpy_seed, numpy_random)
        # Test aliases
        self._check_random_seed(numpy_seed, jit_nullary("np.random.random_sample"))
        self._check_random_seed(numpy_seed, jit_nullary("np.random.ranf"))
        self._check_random_seed(numpy_seed, jit_nullary("np.random.sample"))
        self._check_random_seed(numpy_seed, jit_nullary("np.random.rand"))

    def test_independent_generators(self):
        # PRNGs for Numpy and Python are independent.
        N = 10
        random_seed(1)
        py_numbers = [random_random() for i in range(N)]
        numpy_seed(2)
        np_numbers = [numpy_random() for i in range(N)]
        random_seed(1)
        numpy_seed(2)
        pairs = [(random_random(), numpy_random()) for i in range(N)]
        self.assertPreciseEqual([p[0] for p in pairs], py_numbers)
        self.assertPreciseEqual([p[1] for p in pairs], np_numbers)

    def _check_getrandbits(self, func, ptr):
        """
        Check a getrandbits()-like function.
        """
        # Our implementation follows CPython's for bits <= 64.
        r = self._follow_cpython(ptr)
        for nbits in range(1, 65):
            expected = r.getrandbits(nbits)
            got = func(nbits)
            self.assertPreciseEqual(expected, got)
        self.assertRaises(OverflowError, func, 65)
        self.assertRaises(OverflowError, func, 9999999)
        self.assertRaises(OverflowError, func, -1)

    @tag('important')
    def test_random_getrandbits(self):
        self._check_getrandbits(jit_unary("random.getrandbits"), get_py_state_ptr())

    # Explanation for the large ulps value: on 32-bit platforms, our
    # LLVM-compiled functions use SSE but they are compared against
    # C functions which use x87.
    # On some distributions, the errors seem to accumulate dramatically.

    def _check_dist(self, func, pyfunc, argslist, niters=3,
                    prec='double', ulps=12, pydtype=None):
        assert len(argslist)
        for args in argslist:
            results = [func(*args) for i in range(niters)]
            pyresults = [(pyfunc(*args, dtype=pydtype) if pydtype else pyfunc(*args))
                         for i in range(niters)]
            self.assertPreciseEqual(results, pyresults, prec=prec, ulps=ulps,
                                    msg="for arguments %s" % (args,))

    def _check_gauss(self, func2, func1, func0, ptr):
        """
        Check a gauss()-like function.
        """
        # Our implementation follows Numpy's.
        r = self._follow_numpy(ptr)
        if func2 is not None:
            self._check_dist(func2, r.normal,
                             [(1.0, 1.0), (2.0, 0.5), (-2.0, 0.5)],
                             niters=N // 2 + 10)
        if func1 is not None:
            self._check_dist(func1, r.normal, [(0.5,)])
        if func0 is not None:
            self._check_dist(func0, r.normal, [()])

    @tag('important')
    def test_random_gauss(self):
        self._check_gauss(jit_binary("random.gauss"), None, None, get_py_state_ptr())

    def test_random_normalvariate(self):
        # normalvariate() is really an alias to gauss() in Numba
        # (not in Python, though - they use different algorithms)
        self._check_gauss(jit_binary("random.normalvariate"), None, None,
                          get_py_state_ptr())

    @tag('important')
    def test_numpy_normal(self):
        self._check_gauss(jit_binary("np.random.normal"),
                          jit_unary("np.random.normal"),
                          jit_nullary("np.random.normal"),
                          get_np_state_ptr())

    @tag('important')
    def test_numpy_standard_normal(self):
        self._check_gauss(None, None, jit_nullary("np.random.standard_normal"),
                          get_np_state_ptr())

    @tag('important')
    def test_numpy_randn(self):
        self._check_gauss(None, None, jit_nullary("np.random.randn"),
                          get_np_state_ptr())

    def _check_lognormvariate(self, func2, func1, func0, ptr):
        """
        Check a lognormvariate()-like function.
        """
        # Our implementation follows Numpy's.
        r = self._follow_numpy(ptr)
        if func2 is not None:
            self._check_dist(func2, r.lognormal,
                             [(1.0, 1.0), (2.0, 0.5), (-2.0, 0.5)],
                             niters=N // 2 + 10)
        if func1 is not None:
            self._check_dist(func1, r.lognormal, [(0.5,)])
        if func0 is not None:
            self._check_dist(func0, r.lognormal, [()])

    def test_random_lognormvariate(self):
        self._check_lognormvariate(jit_binary("random.lognormvariate"),
                                   None, None, get_py_state_ptr())

    def test_numpy_lognormal(self):
        self._check_lognormvariate(jit_binary("np.random.lognormal"),
                                   jit_unary("np.random.lognormal"),
                                   jit_nullary("np.random.lognormal"),
                                   get_np_state_ptr())

    def _check_randrange(self, func1, func2, func3, ptr, max_width, is_numpy, tp=None):
        """
        Check a randrange()-like function.
        """
        # Sanity check
        ints = []
        for i in range(10):
            ints.append(func1(500000000))
            ints.append(func2(5, 500000000))
            if func3 is not None:
                ints.append(func3(5, 500000000, 3))
        self.assertEqual(len(ints), len(set(ints)), ints)
        # Our implementation follows Python 3's.
        if sys.version_info >= (3,):
            if is_numpy:
                rr = self._follow_numpy(ptr).randint
            else:
                rr = self._follow_cpython(ptr).randrange
            widths = [w for w in [1, 5, 8, 5000, 2**40, 2**62 + 2**61] if w < max_width]
            pydtype = tp if is_numpy and np.__version__ >= '1.11.0' else None
            for width in widths:
                self._check_dist(func1, rr, [(width,)], niters=10,
                                 pydtype=pydtype)
                self._check_dist(func2, rr, [(-2, 2 +width)], niters=10,
                                 pydtype=pydtype)
                if func3 is not None:
                    self.assertPreciseEqual(func3(-2, 2 + width, 6),
                                            rr(-2, 2 + width, 6))
                    self.assertPreciseEqual(func3(2 + width, 2, -3),
                                            rr(2 + width, 2, -3))
        # Empty ranges
        self.assertRaises(ValueError, func1, 0)
        self.assertRaises(ValueError, func1, -5)
        self.assertRaises(ValueError, func2, 5, 5)
        self.assertRaises(ValueError, func2, 5, 2)
        if func3 is not None:
            self.assertRaises(ValueError, func3, 5, 7, -1)
            self.assertRaises(ValueError, func3, 7, 5, 1)

    @tag('important')
    def test_random_randrange(self):
        for tp, max_width in [(types.int64, 2**63), (types.int32, 2**31)]:
            cr1 = compile_isolated(random_randrange1, (tp,))
            cr2 = compile_isolated(random_randrange2, (tp, tp))
            cr3 = compile_isolated(random_randrange3, (tp, tp, tp))
            self._check_randrange(cr1.entry_point, cr2.entry_point,
                                  cr3.entry_point, get_py_state_ptr(),
                                  max_width, False)

    @tag('important')
    def test_numpy_randint(self):
        for tp, np_tp, max_width in [(types.int64, np.int64, 2**63),
                                     (types.int32, np.int32, 2**31)]:
            cr1 = compile_isolated(numpy_randint1, (tp,))
            cr2 = compile_isolated(numpy_randint2, (tp, tp))
            self._check_randrange(cr1.entry_point, cr2.entry_point,
                                  None, get_np_state_ptr(), max_width, True, np_tp)

    def _check_randint(self, func, ptr, max_width):
        """
        Check a randint()-like function.
        """
        # Sanity check
        ints = []
        for i in range(10):
            ints.append(func(5, 500000000))
        self.assertEqual(len(ints), len(set(ints)), ints)
        # Our implementation follows Python 3's.
        if sys.version_info >= (3,):
            r = self._follow_cpython(ptr)
            for args in [(1, 5), (13, 5000), (20, 2**62 + 2**61)]:
                if args[1] > max_width:
                    continue
                self._check_dist(func, r.randint, [args], niters=10)
        # Empty ranges
        self.assertRaises(ValueError, func, 5, 4)
        self.assertRaises(ValueError, func, 5, 2)

    @tag('important')
    def test_random_randint(self):
        for tp, max_width in [(types.int64, 2**63), (types.int32, 2**31)]:
            cr = compile_isolated(random_randint, (tp, tp))
            self._check_randint(cr.entry_point, get_py_state_ptr(), max_width)

    def _check_uniform(self, func, ptr):
        """
        Check a uniform()-like function.
        """
        # Our implementation follows Python's.
        r = self._follow_cpython(ptr)
        self._check_dist(func, r.uniform,
                         [(1.5, 1e6), (-2.5, 1e3), (1.5, -2.5)])

    @tag('important')
    def test_random_uniform(self):
        self._check_uniform(jit_binary("random.uniform"), get_py_state_ptr())

    @tag('important')
    def test_numpy_uniform(self):
        self._check_uniform(jit_binary("np.random.uniform"), get_np_state_ptr())

    def _check_triangular(self, func2, func3, ptr):
        """
        Check a triangular()-like function.
        """
        # Our implementation follows Python's.
        r = self._follow_cpython(ptr)
        if func2 is not None:
            self._check_dist(func2, r.triangular,
                             [(1.5, 3.5), (-2.5, 1.5), (1.5, 1.5)])
        self._check_dist(func3, r.triangular, [(1.5, 3.5, 2.2)])

    def test_random_triangular(self):
        self._check_triangular(jit_binary("random.triangular"),
                               jit_ternary("random.triangular"),
                               get_py_state_ptr())

    def test_numpy_triangular(self):
        triangular = jit_ternary("np.random.triangular")
        fixed_triangular = lambda l, r, m: triangular(l, m, r)
        self._check_triangular(None, fixed_triangular, get_np_state_ptr())

    def _check_gammavariate(self, func2, func1, ptr):
        """
        Check a gammavariate()-like function.
        """
        # Our implementation follows Python's.
        r = self._follow_cpython(ptr)
        if func2 is not None:
            self._check_dist(func2, r.gammavariate,
                             [(0.5, 2.5), (1.0, 1.5), (1.5, 3.5)])
        if func1 is not None:
            self.assertPreciseEqual(func1(1.5), r.gammavariate(1.5, 1.0))
        # Invalid inputs
        if func2 is not None:
            self.assertRaises(ValueError, func2, 0.0, 1.0)
            self.assertRaises(ValueError, func2, 1.0, 0.0)
            self.assertRaises(ValueError, func2, -0.5, 1.0)
            self.assertRaises(ValueError, func2, 1.0, -0.5)
        if func1 is not None:
            self.assertRaises(ValueError, func1, 0.0)
            self.assertRaises(ValueError, func1, -0.5)

    def test_random_gammavariate(self):
        self._check_gammavariate(jit_binary("random.gammavariate"), None,
                                 get_py_state_ptr())

    def test_numpy_gamma(self):
        self._check_gammavariate(jit_binary("np.random.gamma"),
                                 jit_unary("np.random.gamma"),
                                 get_np_state_ptr())
        self._check_gammavariate(None,
                                 jit_unary("np.random.standard_gamma"),
                                 get_np_state_ptr())

    def _check_betavariate(self, func, ptr):
        """
        Check a betavariate()-like function.
        """
        # Our implementation follows Python's.
        r = self._follow_cpython(ptr)
        self._check_dist(func, r.betavariate, [(0.5, 2.5)])
        # Invalid inputs
        self.assertRaises(ValueError, func, 0.0, 1.0)
        self.assertRaises(ValueError, func, 1.0, 0.0)
        self.assertRaises(ValueError, func, -0.5, 1.0)
        self.assertRaises(ValueError, func, 1.0, -0.5)

    def test_random_betavariate(self):
        self._check_betavariate(jit_binary("random.betavariate"), get_py_state_ptr())

    def test_numpy_beta(self):
        self._check_betavariate(jit_binary("np.random.beta"), get_np_state_ptr())

    def _check_vonmisesvariate(self, func, ptr):
        """
        Check a vonmisesvariate()-like function.
        """
        # Our implementation follows Python 2.7+'s.
        r = self._follow_cpython(ptr)
        self._check_dist(func, r.vonmisesvariate, [(0.5, 2.5)])

    def test_random_vonmisesvariate(self):
        self._check_vonmisesvariate(jit_binary("random.vonmisesvariate"),
                                    get_py_state_ptr())

    def test_numpy_vonmises(self):
        self._check_vonmisesvariate(jit_binary("np.random.vonmises"),
                                    get_np_state_ptr())

    def _check_expovariate(self, func, ptr):
        """
        Check a expovariate()-like function.  Note the second argument
        is inversed compared to np.random.exponential().
        """
        # Our implementation follows Numpy's (and Python 2.7+'s).
        r = self._follow_numpy(ptr)
        for lambd in (0.2, 0.5, 1.5):
            for i in range(3):
                self.assertPreciseEqual(func(lambd), r.exponential(1 / lambd),
                                        prec='double')

    def test_random_expovariate(self):
        self._check_expovariate(jit_unary("random.expovariate"), get_py_state_ptr())

    def _check_exponential(self, func1, func0, ptr):
        """
        Check a exponential()-like function.
        """
        # Our implementation follows Numpy's (and Python 2.7+'s).
        r = self._follow_numpy(ptr)
        if func1 is not None:
            self._check_dist(func1, r.exponential, [(0.5,), (1.0,), (1.5,)])
        if func0 is not None:
            self._check_dist(func0, r.exponential, [()])

    def test_numpy_exponential(self):
        self._check_exponential(jit_unary("np.random.exponential"),
                                jit_nullary("np.random.exponential"),
                                get_np_state_ptr())

    def test_numpy_standard_exponential(self):
        self._check_exponential(None,
                                jit_nullary("np.random.standard_exponential"),
                                get_np_state_ptr())

    def _check_paretovariate(self, func, ptr):
        """
        Check a paretovariate()-like function.
        """
        # Our implementation follows Python's.
        r = self._follow_cpython(ptr)
        self._check_dist(func, r.paretovariate, [(0.5,), (3.5,)])

    def test_random_paretovariate(self):
        self._check_paretovariate(jit_unary("random.paretovariate"), get_py_state_ptr())

    def test_numpy_pareto(self):
        pareto = jit_unary("np.random.pareto")
        fixed_pareto = lambda a: pareto(a) + 1.0
        self._check_paretovariate(fixed_pareto, get_np_state_ptr())

    def _check_weibullvariate(self, func2, func1, ptr):
        """
        Check a weibullvariate()-like function.
        """
        # Our implementation follows Python's.
        r = self._follow_cpython(ptr)
        if func2 is not None:
            self._check_dist(func2, r.weibullvariate, [(0.5, 2.5)])
        if func1 is not None:
            for i in range(3):
                self.assertPreciseEqual(func1(2.5),
                                        r.weibullvariate(1.0, 2.5))

    def test_random_weibullvariate(self):
        self._check_weibullvariate(jit_binary("random.weibullvariate"),
                                   None, get_py_state_ptr())

    def test_numpy_weibull(self):
        self._check_weibullvariate(None, jit_unary("np.random.weibull"),
                                   get_np_state_ptr())

    @tag('important')
    def test_numpy_binomial(self):
        # We follow Numpy's algorithm up to n*p == 30
        binomial = jit_binary("np.random.binomial")
        r = self._follow_numpy(get_np_state_ptr(), 0)
        self._check_dist(binomial, r.binomial, [(18, 0.25)])
        # Sanity check many values
        for n in (100, 1000, 10000):
            self.assertEqual(binomial(n, 0.0), 0)
            self.assertEqual(binomial(n, 1.0), n)
            for p in (0.0001, 0.1, 0.4, 0.49999, 0.5, 0.50001, 0.8, 0.9, 0.9999):
                r = binomial(n, p)
                if p > 0.5:
                    r = n - r
                    p = 1 - p
                self.assertGreaterEqual(r, 0)
                self.assertLessEqual(r, n)
                expected = p * n
                tol = 3 * n / math.sqrt(n)
                self.assertGreaterEqual(r, expected - tol, (p, n, r))
                self.assertLessEqual(r, expected + tol, (p, n, r))
        # Invalid values
        self.assertRaises(ValueError, binomial, -1, 0.5)
        self.assertRaises(ValueError, binomial, 10, -0.1)
        self.assertRaises(ValueError, binomial, 10, 1.1)

    @tag('important')
    def test_numpy_chisquare(self):
        chisquare = jit_unary("np.random.chisquare")
        r = self._follow_cpython(get_np_state_ptr())
        self._check_dist(chisquare,
                         functools.partial(py_chisquare, r),
                         [(1.5,), (2.5,)])

    def test_numpy_f(self):
        f = jit_binary("np.random.f")
        r = self._follow_cpython(get_np_state_ptr())
        self._check_dist(f, functools.partial(py_f, r),
                         [(0.5, 1.5), (1.5, 0.8)])

    def test_numpy_geometric(self):
        geom = jit_unary("np.random.geometric")
        # p out of domain
        self.assertRaises(ValueError, geom, -1.0)
        self.assertRaises(ValueError, geom, 0.0)
        self.assertRaises(ValueError, geom, 1.001)
        # Some basic checks
        N = 200
        r = [geom(1.0) for i in range(N)]
        self.assertPreciseEqual(r, [1] * N)
        r = [geom(0.9) for i in range(N)]
        n = r.count(1)
        self.assertGreaterEqual(n, N // 2)
        self.assertLess(n, N)
        self.assertFalse([i for i in r if i > 1000])  # unlikely
        r = [geom(0.4) for i in range(N)]
        self.assertTrue([i for i in r if i > 4])  # likely
        r = [geom(0.01) for i in range(N)]
        self.assertTrue([i for i in r if i > 50])  # likely
        r = [geom(1e-15) for i in range(N)]
        self.assertTrue([i for i in r if i > 2**32])  # likely

    def test_numpy_gumbel(self):
        gumbel = jit_binary("np.random.gumbel")
        r = self._follow_numpy(get_np_state_ptr())
        self._check_dist(gumbel, r.gumbel, [(0.0, 1.0), (-1.5, 3.5)])

    def test_numpy_hypergeometric(self):
        # Our implementation follows Numpy's up to nsamples = 10.
        hg = jit_ternary("np.random.hypergeometric")
        r = self._follow_numpy(get_np_state_ptr())
        self._check_dist(hg, r.hypergeometric,
                         [(1000, 5000, 10), (5000, 1000, 10)],
                         niters=30)
        # Sanity checks
        r = [hg(1000, 1000, 100) for i in range(100)]
        self.assertTrue(all(x >= 0 and x <= 100 for x in r), r)
        self.assertGreaterEqual(np.mean(r), 40.0)
        self.assertLessEqual(np.mean(r), 60.0)
        r = [hg(1000, 100000, 100) for i in range(100)]
        self.assertTrue(all(x >= 0 and x <= 100 for x in r), r)
        self.assertLessEqual(np.mean(r), 10.0)
        r = [hg(100000, 1000, 100) for i in range(100)]
        self.assertTrue(all(x >= 0 and x <= 100 for x in r), r)
        self.assertGreaterEqual(np.mean(r), 90.0)

    def test_numpy_laplace(self):
        r = self._follow_numpy(get_np_state_ptr())
        self._check_dist(jit_binary("np.random.laplace"), r.laplace,
                         [(0.0, 1.0), (-1.5, 3.5)])
        self._check_dist(jit_unary("np.random.laplace"), r.laplace,
                         [(0.0,), (-1.5,)])
        self._check_dist(jit_nullary("np.random.laplace"), r.laplace, [()])

    @tag('important')
    def test_numpy_logistic(self):
        r = self._follow_numpy(get_np_state_ptr())
        self._check_dist(jit_binary("np.random.logistic"), r.logistic,
                         [(0.0, 1.0), (-1.5, 3.5)])
        self._check_dist(jit_unary("np.random.logistic"), r.logistic,
                         [(0.0,), (-1.5,)])
        self._check_dist(jit_nullary("np.random.logistic"), r.logistic, [()])

    def test_numpy_logseries(self):
        r = self._follow_numpy(get_np_state_ptr())
        logseries = jit_unary("np.random.logseries")
        self._check_dist(logseries, r.logseries,
                         [(0.1,), (0.99,), (0.9999,)],
                         niters=50)
        # Numpy's logseries overflows on 32-bit builds, so instead
        # hardcode Numpy's (correct) output on 64-bit builds.
        r = self._follow_numpy(get_np_state_ptr(), seed=1)
        self.assertEqual([logseries(0.9999999999999) for i in range(10)],
                         [2022733531, 77296, 30, 52204, 9341294, 703057324,
                          413147702918, 1870715907, 16009330, 738])
        self.assertRaises(ValueError, logseries, 0.0)
        self.assertRaises(ValueError, logseries, -0.1)
        self.assertRaises(ValueError, logseries, 1.1)

    def test_numpy_poisson(self):
        r = self._follow_numpy(get_np_state_ptr())
        poisson = jit_unary("np.random.poisson")
        # Our implementation follows Numpy's.
        self._check_dist(poisson, r.poisson,
                         [(0.0,), (0.5,), (2.0,), (10.0,), (900.5,)],
                         niters=50)
        self.assertRaises(ValueError, poisson, -0.1)

    def test_numpy_negative_binomial(self):
        self._follow_numpy(get_np_state_ptr(), 0)
        negbin = jit_binary("np.random.negative_binomial")
        self.assertEqual([negbin(10, 0.9) for i in range(10)],
                         [2, 3, 1, 5, 2, 1, 0, 1, 0, 0])
        self.assertEqual([negbin(10, 0.1) for i in range(10)],
                         [55, 71, 56, 57, 56, 56, 34, 55, 101, 67])
        self.assertEqual([negbin(1000, 0.1) for i in range(10)],
                         [9203, 8640, 9081, 9292, 8938,
                          9165, 9149, 8774, 8886, 9117])
        m = np.mean([negbin(1000000000, 0.1)
                     for i in range(50)])
        self.assertGreater(m, 9e9 * 0.99)
        self.assertLess(m, 9e9 * 1.01)
        self.assertRaises(ValueError, negbin, 0, 0.5)
        self.assertRaises(ValueError, negbin, -1, 0.5)
        self.assertRaises(ValueError, negbin, 10, -0.1)
        self.assertRaises(ValueError, negbin, 10, 1.1)

    @tag('important')
    def test_numpy_power(self):
        r = self._follow_numpy(get_np_state_ptr())
        power = jit_unary("np.random.power")
        self._check_dist(power, r.power,
                         [(0.1,), (0.5,), (0.9,), (6.0,)])
        self.assertRaises(ValueError, power, 0.0)
        self.assertRaises(ValueError, power, -0.1)

    def test_numpy_rayleigh(self):
        r = self._follow_numpy(get_np_state_ptr())
        rayleigh1 = jit_unary("np.random.rayleigh")
        rayleigh0 = jit_nullary("np.random.rayleigh")
        self._check_dist(rayleigh1, r.rayleigh,
                         [(0.1,), (0.8,), (25.,), (1e3,)])
        self._check_dist(rayleigh0, r.rayleigh, [()])
        self.assertRaises(ValueError, rayleigh1, 0.0)
        self.assertRaises(ValueError, rayleigh1, -0.1)

    def test_numpy_standard_cauchy(self):
        r = self._follow_numpy(get_np_state_ptr())
        cauchy = jit_nullary("np.random.standard_cauchy")
        self._check_dist(cauchy, r.standard_cauchy, [()])

    def test_numpy_standard_t(self):
        # We use CPython's algorithm for the gamma dist and numpy's
        # for the normal dist.  Standard T calls both so we can't check
        # against either generator's output.
        r = self._follow_cpython(get_np_state_ptr())
        standard_t = jit_unary("np.random.standard_t")
        avg = np.mean([standard_t(5) for i in range(5000)])
        # Sanity check
        self.assertLess(abs(avg), 0.5)

    def test_numpy_wald(self):
        r = self._follow_numpy(get_np_state_ptr())
        wald = jit_binary("np.random.wald")
        self._check_dist(wald, r.wald, [(1.0, 1.0), (2.0, 5.0)])
        self.assertRaises(ValueError, wald, 0.0, 1.0)
        self.assertRaises(ValueError, wald, -0.1, 1.0)
        self.assertRaises(ValueError, wald, 1.0, 0.0)
        self.assertRaises(ValueError, wald, 1.0, -0.1)

    def test_numpy_zipf(self):
        r = self._follow_numpy(get_np_state_ptr())
        zipf = jit_unary("np.random.zipf")
        self._check_dist(zipf, r.zipf, [(1.5,), (2.5,)], niters=100)
        for val in (1.0, 0.5, 0.0, -0.1):
            self.assertRaises(ValueError, zipf, val)

    def _check_shuffle(self, func, ptr, is_numpy):
        """
        Check a shuffle()-like function for arrays.
        """
        # Our implementation follows Python 3's.
        arrs = [np.arange(20), np.arange(32).reshape((8, 4))]
        if sys.version_info >= (3,):
            if is_numpy:
                r = self._follow_numpy(ptr)
            else:
                r = self._follow_cpython(ptr)
            for a in arrs:
                for i in range(3):
                    got = a.copy()
                    expected = a.copy()
                    func(got)
                    if is_numpy or len(a.shape) == 1:
                        r.shuffle(expected)
                        self.assertPreciseEqual(got, expected)
        else:
            # Sanity check
            for a in arrs:
                for i in range(3):
                    b = a.copy()
                    func(b)
                    self.assertFalse(np.array_equal(a, b))
                    self.assertTrue(np.array_equal(np.sort(a, axis=0),
                                                   np.sort(b, axis=0)))
                    a = b
        # Test with an arbitrary buffer-providing object
        a = arrs[0]
        b = a.copy()
        func(memoryview(b))
        self.assertNotEqual(list(a), list(b))
        self.assertEqual(sorted(a), sorted(b))
        # Read-only object
        with self.assertTypingError():
            func(memoryview(b"xyz"))

    @tag('important')
    def test_random_shuffle(self):
        self._check_shuffle(jit_unary("random.shuffle"), get_py_state_ptr(), False)

    @tag('important')
    def test_numpy_shuffle(self):
        self._check_shuffle(jit_unary("np.random.shuffle"), get_np_state_ptr(), True)

    def _check_startup_randomness(self, func_name, func_args):
        """
        Check that the state is properly randomized at startup.
        """
        code = """if 1:
            from numba.tests import test_random
            func = getattr(test_random, %(func_name)r)
            print(func(*%(func_args)r))
            """ % (locals())
        numbers = set()
        for i in range(3):
            popen = subprocess.Popen([sys.executable, "-c", code],
                                     stdout=subprocess.PIPE, stderr=subprocess.PIPE)
            out, err = popen.communicate()
            if popen.returncode != 0:
                raise AssertionError("process failed with code %s: stderr follows\n%s\n"
                                     % (popen.returncode, err.decode()))
            numbers.add(float(out.strip()))
        self.assertEqual(len(numbers), 3, numbers)

    def test_random_random_startup(self):
        self._check_startup_randomness("random_random", ())

    def test_random_gauss_startup(self):
        self._check_startup_randomness("random_gauss", (1.0, 1.0))

    def test_numpy_random_startup(self):
        self._check_startup_randomness("numpy_random", ())

    def test_numpy_gauss_startup(self):
        self._check_startup_randomness("numpy_normal", (1.0, 1.0))

    def test_numpy_random_permutation(self):
        # Our implementation follows Python 3's.
        func = jit_unary("np.random.permutation")
        if sys.version_info >= (3,):
            r = self._follow_numpy(get_np_state_ptr())
            for s in [5, 10, 15, 20]:
                a = np.arange(s)
                b = a.copy()
                # Test array version
                self.assertPreciseEqual(func(a), r.permutation(a))
                # Test int version
                self.assertPreciseEqual(func(s), r.permutation(s))
                # Permutation should not modify its argument
                self.assertPreciseEqual(a, b)
            # Check multi-dimensional arrays
            arrs = [np.arange(10).reshape(2, 5),
                    np.arange(27).reshape(3, 3, 3),
                    np.arange(36).reshape(2, 3, 3, 2)]
            for a in arrs:
                b = a.copy()
                self.assertPreciseEqual(func(a), r.permutation(a))
                self.assertPreciseEqual(a, b)
        else:
            # Sanity check
            arrs = [np.arange(20), np.arange(20).reshape(5, 2, 2)]
            for a in arrs:
                checked = 0
                while checked < 3:
                    b = func(a)
                    # check that permuted arrays are equal when sorted
                    # account for the possibility of the identity permutation
                    if not np.array_equal(a, b):
                        self.assertTrue(np.array_equal(np.sort(a, axis=0),
                                                       np.sort(b, axis=0)))
                        checked += 1


class TestRandomArrays(BaseTest):
    """
    Test array-producing variants of np.random.* functions.
    """

    def _compile_array_dist(self, funcname, nargs):
        qualname = "np.random.%s" % (funcname,)
        argstring = ', '.join('abcd'[:nargs])
        return jit_with_args(qualname, argstring)

    def _check_array_dist(self, funcname, scalar_args):
        """
        Check returning an array according to a given distribution.
        """
        cfunc = self._compile_array_dist(funcname, len(scalar_args) + 1)
        r = self._follow_numpy(get_np_state_ptr())
        pyfunc = getattr(r, funcname)
        for size in (8, (2, 3)):
            args = scalar_args + (size,)
            expected = pyfunc(*args)
            got = cfunc(*args)
            # Numpy may return int32s where we return int64s, adjust
            if (expected.dtype == np.dtype('int32')
                and got.dtype == np.dtype('int64')):
                expected = expected.astype(got.dtype)
            self.assertPreciseEqual(expected, got, prec='double', ulps=5)

    def test_numpy_randint(self):
        cfunc = self._compile_array_dist("randint", 3)
        low, high = 1000, 10000
        size = (30, 30)
        res = cfunc(low, high, size)
        self.assertIsInstance(res, np.ndarray)
        self.assertEqual(res.shape, size)
        self.assertIn(res.dtype, (np.dtype('int32'), np.dtype('int64')))
        self.assertTrue(np.all(res >= low))
        self.assertTrue(np.all(res < high))
        # Crude statistical tests
        mean = (low + high) / 2
        tol = (high - low) / 20
        self.assertGreaterEqual(res.mean(), mean - tol)
        self.assertLessEqual(res.mean(), mean + tol)

    def test_numpy_random_random(self):
        cfunc = self._compile_array_dist("random", 1)
        size = (30, 30)
        res = cfunc(size)
        self.assertIsInstance(res, np.ndarray)
        self.assertEqual(res.shape, size)
        self.assertEqual(res.dtype, np.dtype('float64'))
        # Results are within expected bounds
        self.assertTrue(np.all(res >= 0.0))
        self.assertTrue(np.all(res < 1.0))
        # Crude statistical tests
        self.assertTrue(np.any(res <= 0.1))
        self.assertTrue(np.any(res >= 0.9))
        mean = res.mean()
        self.assertGreaterEqual(mean, 0.45)
        self.assertLessEqual(mean, 0.55)

    # Sanity-check various distributions.  For convenience, we only check
    # those distributions that produce the exact same values as Numpy's.

    def test_numpy_binomial(self):
        self._check_array_dist("binomial", (20, 0.5))

    def test_numpy_exponential(self):
        self._check_array_dist("exponential", (1.5,))

    def test_numpy_gumbel(self):
        self._check_array_dist("gumbel", (1.5, 0.5))

    def test_numpy_laplace(self):
        self._check_array_dist("laplace", (1.5, 0.5))

    def test_numpy_logistic(self):
        self._check_array_dist("logistic", (1.5, 0.5))

    def test_numpy_lognormal(self):
        self._check_array_dist("lognormal", (1.5, 2.0))

    def test_numpy_logseries(self):
        self._check_array_dist("logseries", (0.8,))

    @tag('important')
    def test_numpy_normal(self):
        self._check_array_dist("normal", (0.5, 2.0))

    def test_numpy_poisson(self):
        self._check_array_dist("poisson", (0.8,))

    def test_numpy_power(self):
        self._check_array_dist("power", (0.8,))

    @tag('important')
    def test_numpy_rand(self):
        cfunc = jit(nopython=True)(numpy_check_rand)
        expected, got = cfunc(42, 2, 3)
        self.assertEqual(got.shape, (2, 3))
        self.assertPreciseEqual(expected, got)

    @tag('important')
    def test_numpy_randn(self):
        cfunc = jit(nopython=True)(numpy_check_randn)
        expected, got = cfunc(42, 2, 3)
        self.assertEqual(got.shape, (2, 3))
        self.assertPreciseEqual(expected, got)

    def test_numpy_rayleigh(self):
        self._check_array_dist("rayleigh", (0.8,))

    def test_numpy_standard_cauchy(self):
        self._check_array_dist("standard_cauchy", ())

    def test_numpy_standard_exponential(self):
        self._check_array_dist("standard_exponential", ())

    def test_numpy_standard_normal(self):
        self._check_array_dist("standard_normal", ())

    def test_numpy_uniform(self):
        self._check_array_dist("uniform", (0.1, 0.4))

    def test_numpy_wald(self):
        self._check_array_dist("wald", (0.1, 0.4))

    def test_numpy_zipf(self):
        self._check_array_dist("zipf", (2.5,))


class TestRandomChoice(BaseTest):
    """
    Test np.random.choice.
    """

    def _check_results(self, pop, res, replace=True):
        """
        Check basic expectations about a batch of samples.
        """
        spop = set(pop)
        sres = set(res)
        # All results are in the population
        self.assertLessEqual(sres, spop)
        # Sorted results are unlikely
        self.assertNotEqual(sorted(res), list(res))
        if replace:
            # Duplicates are likely
            self.assertLess(len(sres), len(res), res)
        else:
            # No duplicates
            self.assertEqual(len(sres), len(res), res)

    def _check_dist(self, pop, samples):
        """
        Check distribution of some samples.
        """
        # Sanity check that we have enough samples
        self.assertGreaterEqual(len(samples), len(pop) * 100)
        # Check equidistribution of samples
        expected_frequency = len(samples) / len(pop)
        c = collections.Counter(samples)
        for value in pop:
            n = c[value]
            self.assertGreaterEqual(n, expected_frequency * 0.5)
            self.assertLessEqual(n, expected_frequency * 2.0)

    def _accumulate_array_results(self, func, nresults):
        """
        Accumulate array results produced by *func* until they reach
        *nresults* elements.
        """
        res = []
        while len(res) < nresults:
            res += list(func().flat)
        return res[:nresults]

    def _check_choice_1(self, a, pop):
        """
        Check choice(a) against pop.
        """
        cfunc = jit(nopython=True)(numpy_choice1)
        n = len(pop)
        res = [cfunc(a) for i in range(n)]
        self._check_results(pop, res)
        dist = [cfunc(a) for i in range(n * 100)]
        self._check_dist(pop, dist)

    def test_choice_scalar_1(self):
        """
        Test choice(int)
        """
        n = 50
        pop = list(range(n))
        self._check_choice_1(n, pop)

    def test_choice_array_1(self):
        """
        Test choice(array)
        """
        pop = np.arange(50) * 2 + 100
        self._check_choice_1(pop, pop)

    def _check_array_results(self, func, pop, replace=True):
        """
        Check array results produced by *func* and their distribution.
        """
        n = len(pop)
        res = list(func().flat)
        self._check_results(pop, res, replace)
        dist = self._accumulate_array_results(func, n * 100)
        self._check_dist(pop, dist)

    def _check_choice_2(self, a, pop):
        """
        Check choice(a, size) against pop.
        """
        cfunc = jit(nopython=True)(numpy_choice2)
        n = len(pop)
        # Final sizes should be large enough, so as to stress
        # replacement
        sizes = [n - 10, (3, (n - 1) // 3), n * 10]

        for size in sizes:
            # Check result shape
            res = cfunc(a, size)
            expected_shape = size if isinstance(size, tuple) else (size,)
            self.assertEqual(res.shape, expected_shape)
            # Check results and their distribution
            self._check_array_results(lambda: cfunc(a, size), pop)

    def test_choice_scalar_2(self):
        """
        Test choice(int, size)
        """
        n = 50
        pop = np.arange(n)
        self._check_choice_2(n, pop)

    def test_choice_array_2(self):
        """
        Test choice(array, size)
        """
        pop = np.arange(50) * 2 + 100
        self._check_choice_2(pop, pop)

    def _check_choice_3(self, a, pop):
        """
        Check choice(a, size, replace) against pop.
        """
        cfunc = jit(nopython=True)(numpy_choice3)
        n = len(pop)
        # Final sizes should be close but slightly <= n, so as to stress
        # replacement (or not)
        sizes = [n - 10, (3, (n - 1) // 3)]
        replaces = [True, False]

        # Check result shapes
        for size in sizes:
            for replace in [True, False]:
                res = cfunc(a, size, replace)
                expected_shape = size if isinstance(size, tuple) else (size,)
                self.assertEqual(res.shape, expected_shape)

        # Check results for replace=True
        for size in sizes:
            self._check_array_results(lambda: cfunc(a, size, True), pop)
        # Check results for replace=False
        for size in sizes:
            self._check_array_results(lambda: cfunc(a, size, False), pop, False)

        # Can't ask for more samples than population size with replace=False
        for size in [n + 1, (3, n // 3 + 1)]:
            with self.assertRaises(ValueError):
                cfunc(a, size, False)

    def test_choice_scalar_3(self):
        """
        Test choice(int, size, replace)
        """
        n = 50
        pop = np.arange(n)
        self._check_choice_3(n, pop)

    def test_choice_array_3(self):
        """
        Test choice(array, size, replace)
        """
        pop = np.arange(50) * 2 + 100
        self._check_choice_3(pop, pop)


class TestRandomMultinomial(BaseTest):
    """
    Test np.random.multinomial.
    """
    # A biased dice
    pvals = np.array([1, 1, 1, 2, 3, 1], dtype=np.float64)
    pvals /= pvals.sum()

    def _check_sample(self, n, pvals, sample):
        """
        Check distribution of some samples.
        """
        self.assertIsInstance(sample, np.ndarray)
        self.assertEqual(sample.shape, (len(pvals),))
        self.assertIn(sample.dtype, (np.dtype('int32'), np.dtype('int64')))
        # Statistical properties
        self.assertEqual(sample.sum(), n)
        for p, nexp in zip(pvals, sample):
            self.assertGreaterEqual(nexp, 0)
            self.assertLessEqual(nexp, n)
            pexp = float(nexp) / n
            self.assertGreaterEqual(pexp, p * 0.5)
            self.assertLessEqual(pexp, p * 2.0)

    def test_multinomial_2(self):
        """
        Test multinomial(n, pvals)
        """
        cfunc = jit(nopython=True)(numpy_multinomial2)
        n, pvals = 1000, self.pvals
        res = cfunc(n, pvals)
        self._check_sample(n, pvals, res)
        # pvals as list
        pvals = list(pvals)
        res = cfunc(n, pvals)
        self._check_sample(n, pvals, res)
        # A case with extreme probabilities
        n = 1000000
        pvals = np.array([1, 0, n // 100, 1], dtype=np.float64)
        pvals /= pvals.sum()
        res = cfunc(n, pvals)
        self._check_sample(n, pvals, res)

    def test_multinomial_3_int(self):
        """
        Test multinomial(n, pvals, size: int)
        """
        cfunc = jit(nopython=True)(numpy_multinomial3)
        n, pvals = 1000, self.pvals
        k = 10
        res = cfunc(n, pvals, k)
        self.assertEqual(res.shape[0], k)
        for sample in res:
            self._check_sample(n, pvals, sample)

    def test_multinomial_3_tuple(self):
        """
        Test multinomial(n, pvals, size: tuple)
        """
        cfunc = jit(nopython=True)(numpy_multinomial3)
        n, pvals = 1000, self.pvals
        k = (3, 4)
        res = cfunc(n, pvals, k)
        self.assertEqual(res.shape[:-1], k)
        for sample in res.reshape((-1, res.shape[-1])):
            self._check_sample(n, pvals, sample)



@jit(nopython=True, nogil=True)
def py_extract_randomness(seed, out):
    if seed != 0:
        random.seed(seed)
    for i in range(out.size):
        out[i] = random.getrandbits(32)

_randint_limit = 1 << 32

@jit(nopython=True, nogil=True)
def np_extract_randomness(seed, out):
    if seed != 0:
        np.random.seed(seed)
    s = 0
    for i in range(out.size):
        out[i] = np.random.randint(_randint_limit)



class ConcurrencyBaseTest(TestCase):

    # Enough iterations for:
    # 1. Mersenne-Twister state shuffles to occur (once every 624)
    # 2. Race conditions to be plausible
    # 3. Nice statistical properties to emerge
    _extract_iterations = 100000

    def setUp(self):
        # Warm up, to avoid compiling in the threads
        args = (42, self._get_output(1))
        py_extract_randomness(*args)
        np_extract_randomness(*args)

    def _get_output(self, size):
        return np.zeros(size, dtype=np.uint32)

    def check_output(self, out):
        """
        Check statistical properties of output.
        """
        # Output should follow a uniform distribution in [0, 1<<32)
        expected_avg = 1 << 31
        expected_std = (1 << 32) / np.sqrt(12)
        rtol = 0.05  # given enough iterations
        np.testing.assert_allclose(out.mean(), expected_avg, rtol=rtol)
        np.testing.assert_allclose(out.std(), expected_std, rtol=rtol)

    def check_several_outputs(self, results, same_expected):
        # Outputs should have the expected statistical properties
        # (an unitialized PRNG or a PRNG whose internal state was
        #  corrupted by a race condition could produce bogus randomness)
        for out in results:
            self.check_output(out)

        # Check all threads gave either the same sequence or
        # distinct sequences
        if same_expected:
            expected_distinct = 1
        else:
            expected_distinct = len(results)

        heads = {tuple(out[:5]) for out in results}
        tails = {tuple(out[-5:]) for out in results}
        sums = {out.sum() for out in results}
        self.assertEqual(len(heads), expected_distinct, heads)
        self.assertEqual(len(tails), expected_distinct, tails)
        self.assertEqual(len(sums), expected_distinct, sums)


class TestThreads(ConcurrencyBaseTest):
    """
    Check the PRNG behaves well with threads.
    """

    def extract_in_threads(self, nthreads, extract_randomness, seed):
        """
        Run *nthreads* threads extracting randomness with the given *seed*
        (no seeding if 0).
        """
        results = [self._get_output(self._extract_iterations)
                   for i in range(nthreads + 1)]

        def target(i):
            # The PRNG will be seeded in thread
            extract_randomness(seed=seed, out=results[i])

        threads = [threading.Thread(target=target, args=(i,))
                   for i in range(nthreads)]

        for th in threads:
            th.start()
        # Exercise main thread as well
        target(nthreads)
        for th in threads:
            th.join()

        return results

    def check_thread_safety(self, extract_randomness):
        """
        When initializing the PRNG the same way, each thread
        should produce the same sequence of random numbers,
        using independent states, regardless of parallel
        execution.
        """
        # Note the seed value doesn't matter, as long as it's
        # the same for all threads
        results = self.extract_in_threads(15, extract_randomness, seed=42)

        # All threads gave the same sequence
        self.check_several_outputs(results, same_expected=True)

    def check_implicit_initialization(self, extract_randomness):
        """
        The PRNG in new threads should be implicitly initialized with
        system entropy, if seed() wasn't called.
        """
        results = self.extract_in_threads(4, extract_randomness, seed=0)

        # All threads gave a different, valid random sequence
        self.check_several_outputs(results, same_expected=False)

    def test_py_thread_safety(self):
        self.check_thread_safety(py_extract_randomness)

    def test_np_thread_safety(self):
        self.check_thread_safety(np_extract_randomness)

    def test_py_implicit_initialization(self):
        self.check_implicit_initialization(py_extract_randomness)

    def test_np_implicit_initialization(self):
        self.check_implicit_initialization(np_extract_randomness)


@unittest.skipIf(os.name == 'nt', "Windows is not affected by fork() issues")
class TestProcesses(ConcurrencyBaseTest):
    """
    Check the PRNG behaves well in child processes.
    """

    # Avoid nested multiprocessing AssertionError
    # ("daemonic processes are not allowed to have children")
    _numba_parallel_test_ = False


    def extract_in_processes(self, nprocs, extract_randomness):
        """
        Run *nprocs* processes extracting randomness
        without explicit seeding.
        """
        q = multiprocessing.Queue()
        results = []

        def target_inner():
            out = self._get_output(self._extract_iterations)
            extract_randomness(seed=0, out=out)
            return out

        def target():
            try:
                out = target_inner()
                q.put(out)
            except Exception as e:
                # Ensure an exception in a child gets reported
                # in the parent.
                q.put(e)
                raise

        procs = [multiprocessing.Process(target=target)
                 for i in range(nprocs)]
        for p in procs:
            p.start()
        # Need to dequeue before joining, otherwise the large size of the
        # enqueued objects will lead to deadlock.
        for i in range(nprocs):
            results.append(q.get(timeout=5))
        for p in procs:
            p.join()

        # Exercise parent process as well; this will detect if the
        # same state was reused for one of the children.
        results.append(target_inner())
        for res in results:
            if isinstance(res, Exception):
                self.fail("Exception in child: %s" % (res,))

        return results

    def check_implicit_initialization(self, extract_randomness):
        """
        The PRNG in new processes should be implicitly initialized
        with system entropy, to avoid reproducing the same sequences.
        """
        results = self.extract_in_processes(2, extract_randomness)

        # All processes gave a different, valid random sequence
        self.check_several_outputs(results, same_expected=False)

    def test_py_implicit_initialization(self):
        self.check_implicit_initialization(py_extract_randomness)

    def test_np_implicit_initialization(self):
        self.check_implicit_initialization(np_extract_randomness)


if __name__ == "__main__":
    unittest.main()
