#!/usr/bin/env python

import unittest

import random

import time

import pickle

import warnings

from math import log, exp, sqrt, pi, fsum as msum

from test import test_support

class TestBasicOps(unittest.TestCase):

    # 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 xrange(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):

        for arg in [None, 0, 0L, 1, 1L, -1, -1L, 10**20, -(10**20),

                    3.14, 1+2j, 'a', tuple('abc')]:

            self.gen.seed(arg)

        for arg in [range(3), dict(one=1)]:

            self.assertRaises(TypeError, self.gen.seed, arg)

        self.assertRaises(TypeError, self.gen.seed, 1, 2)

        self.assertRaises(TypeError, type(self.gen), [])

    def test_jumpahead(self):

        self.gen.seed()

        state1 = self.gen.getstate()

        self.gen.jumpahead(100)

        state2 = self.gen.getstate()    # s/b distinct from state1

        self.assertNotEqual(state1, state2)

        self.gen.jumpahead(100)

        state3 = self.gen.getstate()    # s/b distinct from state2

        self.assertNotEqual(state2, state3)

        self.assertRaises(TypeError, self.gen.jumpahead)  # needs an arg

        self.assertRaises(TypeError, self.gen.jumpahead, "ick")  # wrong type

        self.assertRaises(TypeError, self.gen.jumpahead, 2.3)  # wrong type

        self.assertRaises(TypeError, self.gen.jumpahead, 2, 3)  # too many

    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 = xrange(N)

        for k in xrange(N+1):

            s = self.gen.sample(population, k)

            self.assertEqual(len(s), k)

            uniq = set(s)

            self.assertEqual(len(uniq), k)

            self.failUnless(uniq <= set(population))

        self.assertEqual(self.gen.sample([], 0), [])  # test edge case N==k==0

    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):

            return reduce(int.__mul__, xrange(1, n), 1)

        for k in xrange(n):

            expected = factorial(n) // factorial(n-k)

            perms = {}

            for i in xrange(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(xrange(20), 2)

        self.gen.sample(str('abcdefghijklmnopqrst'), 2)

        self.gen.sample(tuple('abcdefghijklmnopqrst'), 2)

    def test_sample_on_dicts(self):

        self.gen.sample(dict.fromkeys('abcdefghijklmnopqrst'), 2)

        # SF bug #1460340 -- random.sample can raise KeyError

        a = dict.fromkeys(range(10)+range(10,100,2)+range(100,110))

        self.gen.sample(a, 3)

        # A followup to bug #1460340:  sampling from a dict could return

        # a subset of its keys or of its values, depending on the size of

        # the subset requested.

        N = 30

        d = dict((i, complex(i, i)) for i in xrange(N))

        for k in xrange(N+1):

            samp = self.gen.sample(d, k)

            # Verify that we got ints back (keys); the values are complex.

            for x in samp:

                self.assert_(type(x) is int)

        samp.sort()

        self.assertEqual(samp, range(N))

    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):

        state = pickle.dumps(self.gen)

        origseq = [self.gen.random() for i in xrange(10)]

        newgen = pickle.loads(state)

        restoredseq = [newgen.random() for i in xrange(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(test_support.findfile(file),"rb")

            r = pickle.load(f)

            f.close()

            self.assertEqual(r.randrange(1000), value)

class WichmannHill_TestBasicOps(TestBasicOps):

    gen = random.WichmannHill()

    def test_setstate_first_arg(self):

        self.assertRaises(ValueError, self.gen.setstate, (2, None, None))

    def test_strong_jumpahead(self):

        # tests that jumpahead(n) semantics correspond to n calls to random()

        N = 1000

        s = self.gen.getstate()

        self.gen.jumpahead(N)

        r1 = self.gen.random()

        # now do it the slow way

        self.gen.setstate(s)

        for i in xrange(N):

            self.gen.random()

        r2 = self.gen.random()

        self.assertEqual(r1, r2)

    def test_gauss_with_whseed(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.whseed(seed)

            x1 = self.gen.random()

            y1 = self.gen.gauss(0, 1)

            self.gen.whseed(seed)

            x2 = self.gen.random()

            y2 = self.gen.gauss(0, 1)

            self.assertEqual(x1, x2)

            self.assertEqual(y1, y2)

    def test_bigrand(self):

        # Verify warnings are raised when randrange is too large for random()

        with warnings.catch_warnings():

            warnings.filterwarnings("error", "Underlying random")

            self.assertRaises(UserWarning, self.gen.randrange, 2**60)

class SystemRandom_TestBasicOps(TestBasicOps):

    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_jumpahead(self):

        # Doesn't need to do anything except not fail

        self.gen.jumpahead(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):

        self.assertRaises(NotImplementedError, pickle.dumps, self.gen)

    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 xrange(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 xrange(100):

            r = self.gen.randrange(span)

            self.assert_(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)

            stop = self.gen.randrange(2 ** (i-2))

            if stop <= start:

                return

            self.assert_(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 xrange(100)]))

    def test_genrandbits(self):

        # Verify ranges

        for k in xrange(1, 1000):

            self.assert_(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 xrange(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 xrange(1, 1000):

            n = 1L << i # check an exact power of two

            numbits = i+1

            k = int(1.00001 + _log(n, 2))

            self.assertEqual(k, numbits)

            self.assert_(n == 2**(k-1))

            n += n - 1      # check 1 below the next power of two

            k = int(1.00001 + _log(n, 2))

            self.assert_(k in [numbits, numbits+1])

            self.assert_(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.assert_(2**k > n > 2**(k-1))   # note the stronger assertion

class MersenneTwister_TestBasicOps(TestBasicOps):

    gen = random.Random()

    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))

    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(61731L + (24903L<<32) + (614L<<64) + (42143L<<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 = [0x0eab3258d2231fL,

                    0x1b89db315277a5L,

                    0x1db622a5518016L,

                    0x0b7f9af0d575bfL,

                    0x029e4c4db82240L,

                    0x04961892f5d673L,

                    0x02b291598e4589L,

                    0x11388382c15694L,

                    0x02dad977c9e1feL,

                    0x191d96d4d334c6L]

        self.gen.seed(61731L + (24903L<<32) + (614L<<64) + (42143L<<96))

        actual = self.randomlist(2000)[-10:]

        for a, e in zip(actual, expected):

            self.assertEqual(long(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 = (1L << (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 xrange(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 xrange(100):

            r = self.gen.randrange(span)

            self.assert_(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)

            stop = self.gen.randrange(2 ** (i-2))

            if stop <= start:

                return

            self.assert_(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 xrange(100)]))

    def test_genrandbits(self):

        # Verify cross-platform repeatability

        self.gen.seed(1234567)

        self.assertEqual(self.gen.getrandbits(100),

                         97904845777343510404718956115L)

        # Verify ranges

        for k in xrange(1, 1000):

            self.assert_(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 xrange(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 xrange(1, 1000):

            n = 1L << i # check an exact power of two

            numbits = i+1

            k = int(1.00001 + _log(n, 2))

            self.assertEqual(k, numbits)

            self.assert_(n == 2**(k-1))

            n += n - 1      # check 1 below the next power of two

            k = int(1.00001 + _log(n, 2))

            self.assert_(k in [numbits, numbits+1])

            self.assert_(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.assert_(2**k > n > 2**(k-1))   # note the stronger assertion

    def test_randrange_bug_1590891(self):

        start = 1000000000000

        stop = -100000000000000000000

        step = -200

        x = self.gen.randrange(start, stop, step)

        self.assert_(stop < x <= start)

        self.assertEqual((x+stop)%step, 0)

_gammacoeff = (0.9999999999995183, 676.5203681218835, -1259.139216722289,

              771.3234287757674,  -176.6150291498386, 12.50734324009056,

              -0.1385710331296526, 0.9934937113930748e-05, 0.1659470187408462e-06)

def gamma(z, cof=_gammacoeff, g=7):

    z -= 1.0

    s = msum([cof[0]] + [cof[i] / (z+i) for i in range(1,len(cof))])

    z += 0.5

    return (z+g)**z / exp(z+g) * sqrt(2.0*pi) * s

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 xrange(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.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 xrange(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.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 xrange(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, 2)

            self.assertAlmostEqual(s2/(N-1), sigmasqrd, 2)

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