This file is indexed.

/usr/lib/python2.7/test/test_random.py is in libpython2.7-testsuite 2.7.15~rc1-1.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
import unittest
import random
import time
import pickle
import warnings
from math import log, exp, pi, fsum, sin
from functools import reduce
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)

        with test_support.check_py3k_warnings(quiet=True):
            self.assertRaises(TypeError, self.gen.jumpahead)  # needs an arg
            self.assertRaises(TypeError, self.gen.jumpahead, 2, 3)  # too many

    def test_jumpahead_produces_valid_state(self):
        # From http://bugs.python.org/issue14591.
        self.gen.seed(199210368)
        self.gen.jumpahead(13550674232554645900)
        for i in range(500):
            val = self.gen.random()
            self.assertLess(val, 1.0)

    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.assertTrue(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.assertTrue(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):
        for proto in range(pickle.HIGHEST_PROTOCOL + 1):
            state = pickle.dumps(self.gen, proto)
            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):
        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 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.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 xrange(100)]))

    def test_genrandbits(self):
        # Verify ranges
        for k in xrange(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 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.assertTrue(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):
    gen = random.Random()

    @test_support.cpython_only
    def test_bug_31478(self):
        # _random.Random.seed() should ignore the __abs__() method of a
        # long/int subclass argument.
        class BadInt(int):
            def __abs__(self):
                1/0.0
        class BadLong(long):
            def __abs__(self):
                1/0.0
        self.gen.seed(42)
        expected_value = self.gen.random()
        for seed_arg in [42L, BadInt(42), BadLong(42)]:
            self.gen.seed(seed_arg)
            self.assertEqual(self.gen.random(), expected_value)

    def test_setstate_first_arg(self):
        self.assertRaises(ValueError, self.gen.setstate, (1, None, None))

    def test_setstate_middle_arg(self):
        start_state = self.gen.getstate()
        # 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))
        # Failed calls to setstate() should not have changed the state.
        bits100 = self.gen.getrandbits(100)
        self.gen.setstate(start_state)
        self.assertEqual(self.gen.getrandbits(100), bits100)

    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.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 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.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 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.assertTrue(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

    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 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.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 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.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 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, 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)


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)


def test_main(verbose=None):
    testclasses =    [WichmannHill_TestBasicOps,
                      MersenneTwister_TestBasicOps,
                      TestDistributions,
                      TestModule]

    try:
        random.SystemRandom().random()
    except NotImplementedError:
        pass
    else:
        testclasses.append(SystemRandom_TestBasicOps)

    test_support.run_unittest(*testclasses)

    # verify reference counting
    import sys
    if verbose and hasattr(sys, "gettotalrefcount"):
        counts = [None] * 5
        for i in xrange(len(counts)):
            test_support.run_unittest(*testclasses)
            counts[i] = sys.gettotalrefcount()
        print counts

if __name__ == "__main__":
    test_main(verbose=True)