Pyewacket 0.0.1b7

Drop-in Replacement for the Python Random Library.

Pyewacket

Fast, fault-tolerant, drop-in replacement for the Python3 random module

Built atop the RNG Storm Engine for proven stability and performance. While Storm is a high quality random engine, Pyewacket is not appropriate for cryptography of any kind. Pyewacket is meant for games, data science, A.I. and experimental programming, not security.

Recommended Installation: $ pip install Pyewacket

Pyewacket serves three main goals:

1. Provide a feature rich and familiar API for generating random numbers and values.
   • Faithful to the random module API, but not a slave to it.
2. Go fast!
   • The RNG Storm Engine. An order of magnitude faster on average.
3. Fix things. Random.random is NOT broken, however it is not fault tolerant either.
   • Exceptions that can be avoided with balance, symmetry and sound mathematics, will be avoided. New behavior will be implemented as needed, but new math will not be invented.
   • Do or do not, there is no try/except. Alright, sometimes try: is useful, but it's only needed in truly exceptional cases where lambda calculus fails.
   • All class methods will be implemented as free functions when possible.

Random Integers

• Pyewacket.randbelow(n: int) -> int
  • Back by popular demand. While randrange(a, b, c) is handy when you need it, it's more complex than needed most of the time. Mathematically, randbelow(n) is equivalent to randrange(n).
  • Pyewacket.randbelow is 10x - 12x faster than Random._randbelow().
  • @param n :: expanded acceptable input domain to include non-positive values of n.
  • @return :: random integer in range (n, 0] or [0, n)
  • Analytic Continuation about zero to achieve full input domain coverage for a function that normally only takes positive, non-zero values as input. I think this lambda is beautiful in every sense of the word. Let it wash over you like poetry.
  • lambda f, n: f(n) if n > 0 else -f(-n) if n < 0 else 0
  • This lambda is not part of the actual implementation, but it represents the idea of AC pretty well. AC will invert the meaning of a function for negative input. Thus turning randbelow into randabove for all negative input n.

from Pyewacket import randbelow


""" Standard """
randbelow(10)       # -> [0, 10)

""" Extras """
randbelow(0)        # -> [0, 0) => 0
randbelow(-10)      # -> (-10, 0]

• Pyewacket.randint(a: int, b: int) -> int
  • @param a, b :: both are required,
  • @return :: random integer in range [a, b] or [b, a]
  • Inclusive on both sides, for a == b returns a
  • Removed the asymmetric requirement of a < b

from Pyewacket import randint


""" Standard """
randint(1, 10)      # -> [1, 10]

""" Extras """
randint(10, 1)      # -> [1, 10]
randint(10, 10)     # -> [10, 10] => 10

• Pyewacket.randrange(start: int, stop: int = 0, step: int = 1) -> int
  • Fault tolerant and about 20x faster than random.randrange()
  • @param start :: required
  • @param stop :: optional, default=0
  • @parma step :: optional, default=1
  • @return :: random integer in range (stop, start] or [start, stop) by |step|
  • Removed the requirements of start < stop, and step > 0
  • Always returns start for start == stop or step == 0
  • Always inclusive on the side closer to zero and exclusive on the other side. Because zero is always the most natural place to start no matter what direction you're going. This matches the symmetry of the analytic continuation of Pyewacket.randbelow(). Also, the unit vector, no matter what direction it's pointing, always includes and points away from zero.
  • Ignores sign of step, but it could be a trigger for reversing the inclusivity rule.

from Pyewacket import randrange


""" Standard """
randrange(10)           # -> [0, 10) by whole numbers
randrange(1, 10)        # -> [1, 10) by whole numbers
randrange(1, 10, 2)     # -> [1, 10) by 2, odd numbers

""" Extras """
randrange(0)            # -> [0, 0) -> 0
randrange(-10)          # -> (-10, 0] by 1
randrange(10, 1)        # -> [1, 10) by 1
randrange(10, 0, 2)     # -> [0, 10) by 2, even numbers
randrange(10, 10, 0)    # -> [10, 10) => 10

Random Floating Point

• Pyewacket.random() -> float
  • random float in range [0.0, 1.0] or [0.0, 1.0) depending on rounding.
  • This is the only function that doesn't show a performance increase, as expected.
  • Roughly the same speed as random.random()
• Pyewacket.uniform(a: float, b: float) -> float
  • random float in [a, b] or [a, b) depending on rounding
  • 4x faster
• Pyewacket.expovariate(lambd: float) -> float
  • 5x faster
• Pyewacket.gammavariate(alpha, beta) -> float
  • 10x faster
• Pyewacket.weibullvariate(alpha, beta) -> float
  • 4x faster
• Pyewacket.betavariate(alpha, beta) -> float
  • 16x faster
• Pyewacket.paretovariate(alpha) -> float
  • 4x faster
• Pyewacket.gauss(mu: float, sigma: float) -> float
  • 10x faster
• Pyewacket.normalvariate(mu: float, sigma: float) -> float
  • 10x faster
• Pyewacket.lognormvariate(mu: float, sigma: float) -> float
  • 10x faster
• Pyewacket.vonmisesvariate(mu: float, kappa: float) -> float
  • 4x faster
• Pyewacket.triangular(low: float, high: float, mode: float = None)
  • 10x faster

Random Sequence Values

• Pyewacket.choice(seq: List) -> Value
  • An order of magnitude faster than random.choice().
  • @param seq :: any zero indexed object like a list or tuple.
  • @return :: random value from the list, can be any object type that can be put into a list.
• Pyewacket.choices(population, weights=None, *, cum_weights=None, k=1)
  • Only seeing a 2x performance gain for this algorithm so far.
  • See Weighted Choice in Fortuna for another approach. https://pypi.org/project/Fortuna/
• Pyewacket.shuffle(array: list) -> None
  • Shuffles a list in place.
  • @param array :: must be a mutable list.
  • Approximately 20 times faster than random.shuffle().
  • Implements Knuth 2 Shuffle Algorithm. Knuth 2 is twice as fast as Knuth 1 or Fisher-Yates for every test case. This is likely due to the combination of walking backward and rotating backward into the back side of the list. With this combination it can never modify the data it still needs to walk through. Fresh snow all the way home, aka very low probability for cache misses.
• Pyewacket.knuth(array: list) -> None, shuffle alternate.
  • Shuffles a list in place.
  • @param array :: must be a mutable list.
  • Approximately 10 times faster than random.shuffle().
  • Original Knuth Shuffle Algorithm.
  • Walks forward and rotates backward, but to the front side of the list.
• Pyewacket.fisher_yates(array: list) -> None, shuffle alternate.
  • Shuffles a list in place.
  • @param array :: must be a mutable list.
  • Approximately 10 times faster than random.shuffle().
  • Fisher-Yates Shuffle Algorithm. Used in random.shuffle().
  • Walks backward and rotates forward, into oncoming traffic.
• Pyewacket.sample(population: List, k: int) -> list
  • @param population :: list or tuple.
  • @param k :: number of unique samples to get.
  • @return :: size k list of unique random samples.
  • Performance gains range (5x to 20x) depending on len(population) and the ratio of k to len(population). Higher performance gains are seen when k ~= pop size.

Testing Suite

• distribution_timer(func: staticmethod, *args, **kwargs) -> None
  • For the statistical analysis of a non-deterministic numeric output function.
  • @param func :: function, method or lambda to analyze. func(*args, **kwargs)
  • @optional_kw num_cycles=10000 :: Total number of samples to use for analysis.
  • @optional_kw post_processor=None :: Used to scale a large set of data into a smaller set of groupings for better visualization of the data, esp. useful for distributions of floats. For many functions in quick_test(), math.floor() is used, for others round() is more appropriate. For more complex post processing - lambdas work nicely. Post processing only affects the distribution, the statistics and performance results are unaffected.
• quick_test()
  • Runs a battery of tests for every random distribution function in the module.

Development Log

• ToDo:
  • seed()
  • getrandbits()

Pyewacket v0.0.1b7

• Engine Fine Tuning
• Fixed some typos.

Pyewacket v0.0.1b6

• Rearranged tests to be more consistant and match the documentation.

Pyewacket v0.0.1b5

• Documentation Upgrade
• Minor Performance Tweaks

Pyewacket v0.0.1b4

• Public Beta

Pyewacket v0.0.1b3

• quick_test()
• Extended Functionality
  • sample()
  • expovariate()
  • gammavariate()
  • weibullvariate()
  • betavariate()
  • paretovariate()
  • gauss()
  • normalvariate()
  • lognormvariate()
  • vonmisesvariate()
  • triangular()

Pyewacket v0.0.1b2

• Basic Functionality
  • random()
  • uniform()
  • randbelow()
  • randint()
  • randrange()
  • choice()
  • choices()
  • shuffle()

Pyewacket v0.0.1b1

• Initial Design & Planning

Pywacket Distribution and Performance Test Suite

>>> from Pyewacket import quick_test
>>> quick_test()


Output Distribution: Random._randbelow(10)
Approximate Single Execution Time: Min: 531ns, Mid: 593ns, Max: 1625ns
Raw Samples: 4, 2, 6, 0, 7
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 5
 Maximum: 9
 Mean: 4.5317
 Std Deviation: 2.869253974788078
Sample Distribution:
 0: 10.01%
 1: 9.33%
 2: 10.53%
 3: 9.71%
 4: 9.74%
 5: 9.87%
 6: 10.59%
 7: 9.69%
 8: 10.8%
 9: 9.73%

Output Distribution: randbelow(10)
Approximate Single Execution Time: Min: 62ns, Mid: 62ns, Max: 593ns
Raw Samples: 8, 1, 5, 4, 6
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 5
 Maximum: 9
 Mean: 4.5
 Std Deviation: 2.860003140172433
Sample Distribution:
 0: 9.74%
 1: 10.33%
 2: 9.9%
 3: 9.54%
 4: 10.27%
 5: 10.55%
 6: 9.91%
 7: 9.83%
 8: 10.22%
 9: 9.71%

Output Distribution: Random.randint(1, 10)
Approximate Single Execution Time: Min: 1156ns, Mid: 1187ns, Max: 2437ns
Raw Samples: 10, 4, 1, 1, 6
Test Samples: 10000
Sample Statistics:
 Minimum: 1
 Median: 6
 Maximum: 10
 Mean: 5.5225
 Std Deviation: 2.859774743079971
Sample Distribution:
 1: 9.83%
 2: 9.39%
 3: 10.11%
 4: 10.56%
 5: 9.8%
 6: 10.25%
 7: 10.24%
 8: 9.67%
 9: 9.97%
 10: 10.18%

Output Distribution: randint(1, 10)
Approximate Single Execution Time: Min: 62ns, Mid: 62ns, Max: 125ns
Raw Samples: 3, 10, 9, 2, 9
Test Samples: 10000
Sample Statistics:
 Minimum: 1
 Median: (5, 6)
 Maximum: 10
 Mean: 5.5015
 Std Deviation: 2.8729815788332567
Sample Distribution:
 1: 9.55%
 2: 10.08%
 3: 11.06%
 4: 9.78%
 5: 9.53%
 6: 9.82%
 7: 10.09%
 8: 10.07%
 9: 9.82%
 10: 10.2%

Output Distribution: Random.randrange(0, 10, 2)
Approximate Single Execution Time: Min: 1312ns, Mid: 1375ns, Max: 1750ns
Raw Samples: 4, 8, 0, 8, 0
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 4
 Maximum: 8
 Mean: 3.9526
 Std Deviation: 2.8230037504434
Sample Distribution:
 0: 20.05%
 2: 21.11%
 4: 19.56%
 6: 19.72%
 8: 19.56%

Output Distribution: randrange(0, 10, 2)
Approximate Single Execution Time: Min: 62ns, Mid: 93ns, Max: 125ns
Raw Samples: 4, 0, 8, 6, 0
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 4
 Maximum: 8
 Mean: 4.0218
 Std Deviation: 2.8470221835334115
Sample Distribution:
 0: 20.05%
 2: 20.11%
 4: 19.05%
 6: 20.28%
 8: 20.51%

Output Distribution: Random.random()
Approximate Single Execution Time: Min: 31ns, Mid: 46ns, Max: 781ns
Raw Samples: 0.6941940430301239, 0.17485400098448722, 0.32270460855316896, 0.7617370603786612, 0.6379199365060996
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 4.812423009470379e-05
 Median: (0.4932608117252698, 0.4933548448219319)
 Maximum: 0.999980425138994
 Mean: 0.49762903521995966
 Std Deviation: 0.2901183334227781
Post-processor Distribution using floor method:
 0: 100.0%

Output Distribution: random()
Approximate Single Execution Time: Min: 31ns, Mid: 31ns, Max: 93ns
Raw Samples: 0.45733502271957777, 0.5460840273003155, 0.7634811973233878, 0.8057744592450823, 0.088528400978526
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 5.7318118912210695e-05
 Median: (0.5025142163768245, 0.5025857566862206)
 Maximum: 0.999945311629445
 Mean: 0.5014876034570467
 Std Deviation: 0.28925939171313575
Post-processor Distribution using floor method:
 0: 100.0%

Output Distribution: Random.uniform(0.0, 10.0)
Approximate Single Execution Time: Min: 218ns, Mid: 250ns, Max: 375ns
Raw Samples: 9.668704812681328, 4.7417797999685085, 7.518017552469133, 8.91016915242336, 8.774374863574796
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.0018064338880463549
 Median: (4.978623941011841, 4.978694358831093)
 Maximum: 9.996018939535697
 Mean: 5.004917192930529
 Std Deviation: 2.8953188299401607
Post-processor Distribution using floor method:
 0: 10.0%
 1: 9.97%
 2: 10.13%
 3: 9.82%
 4: 10.31%
 5: 9.98%
 6: 9.64%
 7: 9.93%
 8: 9.95%
 9: 10.27%

Output Distribution: uniform(0.0, 10.0)
Approximate Single Execution Time: Min: 31ns, Mid: 62ns, Max: 156ns
Raw Samples: 5.9496742688673745, 9.979688437526802, 2.023108367905618, 6.867501571245822, 5.982608579920515
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.0011906789387196466
 Median: (4.978753944070585, 4.980402269440451)
 Maximum: 9.998755767134211
 Mean: 4.990382250003069
 Std Deviation: 2.8804886096342
Post-processor Distribution using floor method:
 0: 10.32%
 1: 9.66%
 2: 9.98%
 3: 9.81%
 4: 10.44%
 5: 9.66%
 6: 10.16%
 7: 10.6%
 8: 9.58%
 9: 9.79%

Output Distribution: Random.expovariate(1.0)
Approximate Single Execution Time: Min: 312ns, Mid: 343ns, Max: 1000ns
Raw Samples: 0.2549771968592414, 0.9723047007891543, 3.545732671080762, 0.7135224471578017, 0.19147636717280797
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 6.473824300838516e-05
 Median: (0.6902274673865786, 0.6902606148835126)
 Maximum: 9.624857069156732
 Mean: 1.013422141990842
 Std Deviation: 1.0267170284571334
Post-processor Distribution using floor method:
 0: 62.92%
 1: 23.05%
 2: 8.65%
 3: 3.34%
 4: 1.28%
 5: 0.47%
 6: 0.15%
 7: 0.09%
 8: 0.02%
 9: 0.03%

Output Distribution: expovariate(1.0)
Approximate Single Execution Time: Min: 62ns, Mid: 62ns, Max: 531ns
Raw Samples: 0.7330125819249081, 0.15440590526420866, 0.5392437726225944, 0.27684117471206476, 0.4697070589087616
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 7.050043143252826e-05
 Median: (0.6705658631946525, 0.670614401314085)
 Maximum: 10.124910984085856
 Mean: 0.9826254615050338
 Std Deviation: 1.000362917434349
Post-processor Distribution using floor method:
 0: 64.15%
 1: 22.7%
 2: 8.17%
 3: 3.22%
 4: 1.14%
 5: 0.33%
 6: 0.19%
 7: 0.05%
 8: 0.03%
 9: 0.01%
 10: 0.01%

Output Distribution: Random.gammavariate(2.0, 1.0)
Approximate Single Execution Time: Min: 1218ns, Mid: 1343ns, Max: 1843ns
Raw Samples: 0.6744365050223298, 2.584159676984, 6.6296547438971825, 4.380738900029027, 0.8333716384062827
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.00855195094000188
 Median: (1.7112071279358414, 1.7114054634967995)
 Maximum: 14.480464289498236
 Mean: 2.0345668925336025
 Std Deviation: 1.4374004583148943
Post-processor Distribution using round method:
 0: 8.8%
 1: 34.5%
 2: 26.89%
 3: 15.61%
 4: 8.01%
 5: 3.41%
 6: 1.5%
 7: 0.68%
 8: 0.32%
 9: 0.22%
 10: 0.04%
 13: 0.01%
 14: 0.01%

Output Distribution: gammavariate(2.0, 1.0)
Approximate Single Execution Time: Min: 93ns, Mid: 125ns, Max: 187ns
Raw Samples: 1.0197525644334242, 1.0857362968603943, 1.4499936264397992, 2.506905910664416, 1.836976558199616
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.010221107157393994
 Median: (1.6953686633806437, 1.695445546110932)
 Maximum: 12.17631095960002
 Mean: 2.0107238512492698
 Std Deviation: 1.418923121067204
Post-processor Distribution using round method:
 0: 8.79%
 1: 35.2%
 2: 26.85%
 3: 15.6%
 4: 7.26%
 5: 3.61%
 6: 1.54%
 7: 0.74%
 8: 0.21%
 9: 0.1%
 10: 0.05%
 11: 0.04%
 12: 0.01%

Output Distribution: Random.weibullvariate(1.0, 1.0)
Approximate Single Execution Time: Min: 406ns, Mid: 531ns, Max: 3125ns
Raw Samples: 2.746502283547922, 1.0068708396697563, 1.3954276256727072, 0.04106859835977052, 1.6587014746388393
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 5.733209225437167e-06
 Median: (0.6888536013153301, 0.6889679643195677)
 Maximum: 9.137764803301023
 Mean: 0.98784543209998
 Std Deviation: 0.9782754322004967
Post-processor Distribution using floor method:
 0: 63.34%
 1: 23.5%
 2: 8.42%
 3: 2.97%
 4: 1.17%
 5: 0.42%
 6: 0.11%
 7: 0.02%
 8: 0.03%
 9: 0.02%

Output Distribution: weibullvariate(1.0, 1.0)
Approximate Single Execution Time: Min: 93ns, Mid: 93ns, Max: 218ns
Raw Samples: 4.184450458884846, 3.3116806766243228, 0.055698997588411216, 0.18547470500373348, 0.9911780315126322
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 5.857687320418934e-05
 Median: (0.691383539427008, 0.6916661984559255)
 Maximum: 9.976677205033512
 Mean: 0.9940158344159216
 Std Deviation: 0.9826116791510814
Post-processor Distribution using floor method:
 0: 63.36%
 1: 23.46%
 2: 8.1%
 3: 3.44%
 4: 1.04%
 5: 0.42%
 6: 0.11%
 7: 0.04%
 8: 0.02%
 9: 0.01%

Output Distribution: Random.betavariate(3.0, 3.0)
Approximate Single Execution Time: Min: 2468ns, Mid: 2827ns, Max: 3750ns
Raw Samples: 0.32844406180852403, 0.6115502460232568, 0.3082939588831324, 0.3757784313356038, 0.5581558269044338
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.025162086920439797
 Median: (0.5032143601507688, 0.5033113379973247)
 Maximum: 0.9749694339601178
 Mean: 0.5014647638694397
 Std Deviation: 0.1892074953805759
Post-processor Distribution using round method:
 0: 49.46%
 1: 50.54%

Output Distribution: betavariate(3.0, 3.0)
Approximate Single Execution Time: Min: 156ns, Mid: 187ns, Max: 843ns
Raw Samples: 0.49997423011890246, 0.4904004391772204, 0.49074958702527066, 0.7522246124304496, 0.42429391368407987
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.01258593902045308
 Median: (0.4951685364590418, 0.4952682569098579)
 Maximum: 0.9802874949305062
 Mean: 0.49680347472160036
 Std Deviation: 0.1908469868540003
Post-processor Distribution using round method:
 0: 50.85%
 1: 49.15%

Output Distribution: Random.paretovariate(4.0)
Approximate Single Execution Time: Min: 281ns, Mid: 281ns, Max: 500ns
Raw Samples: 1.4085882614468865, 1.2057356999761197, 1.213622181737407, 1.2733769209344357, 1.612486363121649
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 1.0000189672392448
 Median: (1.1873031541895127, 1.1873145067194437)
 Maximum: 13.805626908097038
 Mean: 1.3270483653341174
 Std Deviation: 0.4565062335633648
Post-processor Distribution using floor method:
 1: 94.08%
 2: 4.77%
 3: 0.77%
 4: 0.26%
 5: 0.08%
 6: 0.02%
 10: 0.01%
 13: 0.01%

Output Distribution: paretovariate(4.0)
Approximate Single Execution Time: Min: 62ns, Mid: 93ns, Max: 750ns
Raw Samples: 1.1838169546280912, 1.1193023237881206, 1.653160764521429, 1.045790519143321, 2.071923553335483
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 1.0000528579057941
 Median: (1.1878877892523834, 1.1879471971063735)
 Maximum: 13.506919571071949
 Mean: 1.3352180555952093
 Std Deviation: 0.48919334495218686
Post-processor Distribution using floor method:
 1: 93.8%
 2: 4.78%
 3: 0.96%
 4: 0.27%
 5: 0.09%
 6: 0.04%
 7: 0.03%
 8: 0.01%
 11: 0.01%
 13: 0.01%

Output Distribution: Random.gauss(1.0, 1.0)
Approximate Single Execution Time: Min: 562ns, Mid: 593ns, Max: 2093ns
Raw Samples: 1.729515983988858, 0.23572361378443019, 2.4702827427697294, -0.03844099322285888, 1.3438146760704852
Test Samples: 10000
Pre-processor Statistics:
 Minimum: -2.870401720739052
 Median: (1.0101449724171718, 1.0103081945922343)
 Maximum: 4.873846782557925
 Mean: 1.0153640548623994
 Std Deviation: 1.0064192355183734
Post-processor Distribution using round method:
 -3: 0.02%
 -2: 0.71%
 -1: 5.52%
 0: 24.29%
 1: 38.29%
 2: 24.03%
 3: 6.33%
 4: 0.78%
 5: 0.03%

Output Distribution: gauss(1.0, 1.0)
Approximate Single Execution Time: Min: 62ns, Mid: 93ns, Max: 625ns
Raw Samples: 0.7668496245308872, 0.49690527402256857, 1.804399570815262, 0.624710345349967, 1.9567402144067607
Test Samples: 10000
Pre-processor Statistics:
 Minimum: -2.5897656238988094
 Median: (0.9804781259961777, 0.9807921702428998)
 Maximum: 5.200128168225341
 Mean: 0.9861964583785982
 Std Deviation: 1.0026460371413002
Post-processor Distribution using round method:
 -3: 0.01%
 -2: 0.56%
 -1: 6.48%
 0: 24.29%
 1: 38.08%
 2: 23.8%
 3: 6.3%
 4: 0.45%
 5: 0.03%

Output Distribution: Random.normalvariate(0.0, 2.8)
Approximate Single Execution Time: Min: 687ns, Mid: 781ns, Max: 1093ns
Raw Samples: -1.6314559923142005, -0.8546000793653936, -4.865280275228334, -4.176907812343894, -3.758077898620468
Test Samples: 10000
Pre-processor Statistics:
 Minimum: -10.281990288718138
 Median: (-0.0677765646050498, -0.06769976542589246)
 Maximum: 9.917287769757687
 Mean: -0.0363090297489825
 Std Deviation: 2.83545947068475
Post-processor Distribution using round method:
 -10: 0.02%
 -9: 0.1%
 -8: 0.27%
 -7: 0.78%
 -6: 1.63%
 -5: 3.04%
 -4: 5.27%
 -3: 8.21%
 -2: 11.06%
 -1: 13.0%
 0: 14.32%
 1: 12.72%
 2: 10.86%
 3: 8.29%
 4: 5.11%
 5: 2.71%
 6: 1.65%
 7: 0.57%
 8: 0.26%
 9: 0.12%
 10: 0.01%

Output Distribution: normalvariate(0.0, 2.8)
Approximate Single Execution Time: Min: 62ns, Mid: 93ns, Max: 687ns
Raw Samples: 0.3646201467703742, 2.685511008705458, 2.6567868851248444, 2.774365676115649, -6.338480083063179
Test Samples: 10000
Pre-processor Statistics:
 Minimum: -11.164374962611202
 Median: (0.005205853953496323, 0.006719893396189962)
 Maximum: 9.621235250928372
 Mean: -0.03972504530984834
 Std Deviation: 2.791697212649597
Post-processor Distribution using round method:
 -11: 0.01%
 -10: 0.02%
 -9: 0.07%
 -8: 0.2%
 -7: 0.65%
 -6: 1.48%
 -5: 3.08%
 -4: 5.32%
 -3: 8.68%
 -2: 10.47%
 -1: 13.16%
 0: 14.29%
 1: 13.88%
 2: 10.84%
 3: 7.49%
 4: 5.1%
 5: 2.76%
 6: 1.53%
 7: 0.61%
 8: 0.27%
 9: 0.07%
 10: 0.02%

Output Distribution: Random.lognormvariate(0.0, 0.5)
Approximate Single Execution Time: Min: 781ns, Mid: 890ns, Max: 2062ns
Raw Samples: 0.3708492778762383, 0.9248287029054568, 0.9911242998693577, 0.24725827288672472, 1.3225695530816808
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.1652851521928113
 Median: (1.0066085380137175, 1.0068087174846445)
 Maximum: 5.833166984019462
 Mean: 1.1344866918632812
 Std Deviation: 0.5943935475537597
Post-processor Distribution using round method:
 0: 8.01%
 1: 70.99%
 2: 17.75%
 3: 2.67%
 4: 0.46%
 5: 0.09%
 6: 0.03%

Output Distribution: lognormvariate(0.0, 0.5)
Approximate Single Execution Time: Min: 93ns, Mid: 93ns, Max: 718ns
Raw Samples: 0.4599715207189707, 0.6789455297744604, 1.0135056209783908, 0.678214879134608, 1.3428800705211028
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.06459685218889291
 Median: (1.0060070999005202, 1.006018907893141)
 Maximum: 6.384560365616348
 Mean: 1.1354860466984218
 Std Deviation: 0.6033786741174197
Post-processor Distribution using round method:
 0: 8.45%
 1: 70.31%
 2: 18.11%
 3: 2.48%
 4: 0.51%
 5: 0.11%
 6: 0.03%

Output Distribution: Random.vonmisesvariate(0, 0)
Approximate Single Execution Time: Min: 250ns, Mid: 265ns, Max: 437ns
Raw Samples: 3.513562649483689, 4.176803500322518, 1.3673662845590548, 3.4348196176844827, 2.5579558694494553
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 2.126404009227571e-06
 Median: (3.1573522497065087, 3.1578254451516297)
 Maximum: 6.282245517191791
 Mean: 3.120011384830744
 Std Deviation: 1.8069530836247483
Post-processor Distribution using floor method:
 0: 16.44%
 1: 15.72%
 2: 15.56%
 3: 16.14%
 4: 16.37%
 5: 15.73%
 6: 4.04%

Output Distribution: vonmisesvariate(0, 0)
Approximate Single Execution Time: Min: 62ns, Mid: 77ns, Max: 187ns
Raw Samples: 4.168122790248578, 1.8979020289664212, 4.727619374097524, 3.869537488113744, 0.16210650146556146
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.0008064049020208305
 Median: (3.0965195613889844, 3.096593061614531)
 Maximum: 6.282889777259252
 Mean: 3.101329547309987
 Std Deviation: 1.8191907440628765
Post-processor Distribution using floor method:
 0: 16.58%
 1: 16.14%
 2: 15.6%
 3: 16.57%
 4: 15.27%
 5: 15.33%
 6: 4.51%

Output Distribution: Random.triangular(0.0, 10.0, 0.0)
Approximate Single Execution Time: Min: 500ns, Mid: 531ns, Max: 1750ns
Raw Samples: 6.908110261331436, 7.579643482009035, 1.9280134265280306, 2.793210240074875, 3.6184155179966018
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.0019892339812273008
 Median: (2.998329316569169, 2.99834508593639)
 Maximum: 9.926385317393363
 Mean: 3.374974569740504
 Std Deviation: 2.3761406449285416
Post-processor Distribution using floor method:
 0: 18.87%
 1: 16.35%
 2: 14.81%
 3: 13.26%
 4: 11.15%
 5: 8.92%
 6: 7.38%
 7: 4.96%
 8: 3.19%
 9: 1.11%

Output Distribution: triangular(0.0, 10.0, 0.0)
Approximate Single Execution Time: Min: 31ns, Mid: 62ns, Max: 718ns
Raw Samples: 6.081572531163487, 0.14110055703602797, 4.158523810564406, 2.8656277821350704, 6.092030170872266
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.0007764447546654285
 Median: (2.89777393153269, 2.8987369039171282)
 Maximum: 9.936099075543218
 Mean: 3.318166389705701
 Std Deviation: 2.345792369394541
Post-processor Distribution using floor method:
 0: 19.02%
 1: 16.8%
 2: 15.48%
 3: 12.88%
 4: 11.25%
 5: 8.74%
 6: 7.02%
 7: 5.04%
 8: 2.71%
 9: 1.06%

Output Distribution: Random.choice([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
Approximate Single Execution Time: Min: 750ns, Mid: 781ns, Max: 1843ns
Raw Samples: 2, 0, 8, 8, 1
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 4
 Maximum: 9
 Mean: 4.4936
 Std Deviation: 2.853554505757991
Sample Distribution:
 0: 9.81%
 1: 10.24%
 2: 9.65%
 3: 10.0%
 4: 10.41%
 5: 9.79%
 6: 10.57%
 7: 10.08%
 8: 9.8%
 9: 9.65%

Output Distribution: choice([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
Approximate Single Execution Time: Min: 62ns, Mid: 62ns, Max: 531ns
Raw Samples: 8, 4, 9, 5, 5
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 5
 Maximum: 9
 Mean: 4.5273
 Std Deviation: 2.8800146107990217
Sample Distribution:
 0: 9.95%
 1: 10.15%
 2: 9.66%
 3: 9.57%
 4: 10.28%
 5: 9.95%
 6: 10.11%
 7: 9.66%
 8: 10.63%
 9: 10.04%

Output Distribution: Random.choices([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], k=3)
Approximate Single Execution Time: Min: 3125ns, Mid: 3625ns, Max: 7218ns
Raw Samples: [2, 6, 0], [4, 6, 6], [0, 4, 0], [7, 7, 0], [2, 4, 6]
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 3
 Maximum: 9
 Mean: 3.028
 Std Deviation: 2.4655676633161456
Sample Distribution:
 0: 18.13%
 1: 16.03%
 2: 14.45%
 3: 12.75%
 4: 11.02%
 5: 9.23%
 6: 7.03%
 7: 5.67%
 8: 3.69%
 9: 2.0%

Output Distribution: choices([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], k=3)
Approximate Single Execution Time: Min: 1906ns, Mid: 1937ns, Max: 2218ns
Raw Samples: [4, 7, 9], [6, 4, 5], [3, 2, 4], [3, 3, 1], [0, 2, 5]
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 3
 Maximum: 9
 Mean: 2.9812
 Std Deviation: 2.4229390465635605
Sample Distribution:
 0: 18.09%
 1: 16.08%
 2: 14.87%
 3: 12.9%
 4: 11.76%
 5: 8.86%
 6: 6.86%
 7: 5.27%
 8: 3.58%
 9: 1.73%

Output Distribution: Random.choices([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], cum_weights=[10, 19, 27, 34, 40, 45, 49, 52, 54, 55], k=3)
Approximate Single Execution Time: Min: 2593ns, Mid: 2625ns, Max: 3062ns
Raw Samples: [5, 3, 2], [2, 0, 1], [4, 2, 5], [0, 1, 7], [0, 2, 2]
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 3
 Maximum: 9
 Mean: 3.054
 Std Deviation: 2.4431702576960963
Sample Distribution:
 0: 17.11%
 1: 15.98%
 2: 15.18%
 3: 12.92%
 4: 10.95%
 5: 9.38%
 6: 7.08%
 7: 5.87%
 8: 3.74%
 9: 1.79%

Output Distribution: choices([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], cum_weights=[10, 19, 27, 34, 40, 45, 49, 52, 54, 55], k=3)
Approximate Single Execution Time: Min: 1406ns, Mid: 1468ns, Max: 2968ns
Raw Samples: [0, 3, 3], [4, 6, 1], [1, 2, 2], [3, 4, 0], [3, 3, 2]
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 3
 Maximum: 9
 Mean: 3.0008
 Std Deviation: 2.4517749652135703
Sample Distribution:
 0: 18.38%
 1: 15.89%
 2: 14.64%
 3: 13.0%
 4: 11.12%
 5: 8.81%
 6: 7.21%
 7: 5.36%
 8: 3.71%
 9: 1.88%

Timer only: _random.shuffle(some_list) of size 10:
Approximate Single Execution Time: Min: 6750ns, Mid: 6937ns, Max: 11875ns

Timer only: shuffle(some_list) of size 10:
Approximate Single Execution Time: Min: 375ns, Mid: 375ns, Max: 906ns

Timer only: knuth(some_list) of size 10:
Approximate Single Execution Time: Min: 843ns, Mid: 875ns, Max: 1343ns

Timer only: fisher_yates(some_list) of size 10:
Approximate Single Execution Time: Min: 937ns, Mid: 968ns, Max: 1031ns

Output Distribution: Random.sample([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], k=3)
Approximate Single Execution Time: Min: 4093ns, Mid: 4202ns, Max: 6000ns
Raw Samples: [5, 2, 9], [9, 1, 7], [8, 9, 5], [5, 4, 0], [3, 0, 8]
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 4
 Maximum: 9
 Mean: 4.4766
 Std Deviation: 2.87615710071039
Sample Distribution:
 0: 10.54%
 1: 9.75%
 2: 9.61%
 3: 10.46%
 4: 9.89%
 5: 10.07%
 6: 10.01%
 7: 9.96%
 8: 9.77%
 9: 9.94%

Output Distribution: sample([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], k=3)
Approximate Single Execution Time: Min: 812ns, Mid: 843ns, Max: 2406ns
Raw Samples: [1, 4, 7], [2, 4, 9], [4, 2, 9], [0, 3, 5], [2, 9, 7]
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 4
 Maximum: 9
 Mean: 4.5021
 Std Deviation: 2.863951084006352
Sample Distribution:
 0: 10.0%
 1: 9.61%
 2: 10.14%
 3: 10.29%
 4: 10.15%
 5: 9.86%
 6: 9.87%
 7: 10.09%
 8: 10.21%
 9: 9.78%


Total Test Time: 1.6283 sec