Pyewacket 0.0.1b6

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. 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

While there are still a number of optimizations to be made, Pyewacket is functional and passing all tests for everything implemented so far. See todo list for details about what isn't done yet.

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!
   • RNG Storm Engine.
3. Fix things
   • Exceptions that can be avoided with balance, symmetry and sound mathematics, will be.
   • Do or do not, there is no try/except. Alright, sometimes try is unavoidable, but only in truly exceptional cases where calculus fails.

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 much of the time. Mathematically, randbelow(n) is equivalent to randrange(n).
  • Pyewacket.randbelow is 10x - 12x faster than Random._randbelow() and it's fault tolerant by default.
  • @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 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) by whole numbers

""" 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 randbelow, randint, 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, this is 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, 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 2x performance gain for this algorithm so far.
  • See Weighted Choice in Fortuna for a better 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.
  • 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.
  • Fisher-Yates Shuffle Algorithm. Used in random.shuffle().
  • Walks backward and rotates forward, into oncoming traffic.
• Pyewacket.sample(population: List, k: int)
  • @param population :: list or tuple.
  • @param k :: number of unique samples to get.
  • @return :: size k list of 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 statistical analysis of a non-deterministic function.
  • @param func :: Function method or lambda to analyze. func(*args, **kwargs)
  • @optional_kw num_cycles=10000 :: Total number of samples for distribution 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 v0.0.1b6

• 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.random()
Approximate Single Execution Time: Min: 31ns, Mid: 62ns, Max: 125ns
Raw Samples: 0.012998264145302474, 0.0840767830247312, 0.4035154582140005, 0.5083781217502346, 0.9674115450047303
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 1.6926437449771292e-05
 Median: (0.49635181638724457, 0.49663199475829534)
 Maximum: 0.9999668017181624
 Mean: 0.4981160180563525
 Std Deviation: 0.2897393796641115
Post-processor Distribution using lambda1 method:
 0: 10.19%
 1: 10.14%
 2: 9.66%
 3: 10.58%
 4: 9.66%
 5: 9.93%
 6: 9.93%
 7: 9.79%
 8: 10.3%
 9: 9.82%

Output Distribution: random()
Approximate Single Execution Time: Min: 31ns, Mid: 31ns, Max: 125ns
Raw Samples: 0.8154939905188263, 0.10413073604111953, 0.23089703665109368, 0.8614967013102615, 0.49283619983849797
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 9.055289542758964e-06
 Median: (0.5025908337529288, 0.5026308472664768)
 Maximum: 0.9999523608695805
 Mean: 0.5050614080633075
 Std Deviation: 0.2877023055748328
Post-processor Distribution using lambda2 method:
 0: 9.44%
 1: 9.73%
 2: 10.18%
 3: 10.05%
 4: 10.31%
 5: 9.66%
 6: 10.24%
 7: 10.21%
 8: 9.52%
 9: 10.66%

Output Distribution: Random.uniform(0.0, 10.0)
Approximate Single Execution Time: Min: 218ns, Mid: 250ns, Max: 718ns
Raw Samples: 5.553911945894895, 4.396392437391059, 4.094062084619532, 4.87631314834873, 5.565805393915991
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.0005493010123713837
 Median: (5.079519756301797, 5.079722416235946)
 Maximum: 9.99948149707751
 Mean: 5.046116581845691
 Std Deviation: 2.869515701259223
Post-processor Distribution using floor method:
 0: 9.66%
 1: 9.45%
 2: 10.04%
 3: 9.95%
 4: 10.03%
 5: 10.58%
 6: 10.12%
 7: 9.85%
 8: 10.26%
 9: 10.06%

Output Distribution: uniform(0.0, 10.0)
Approximate Single Execution Time: Min: 31ns, Mid: 62ns, Max: 187ns
Raw Samples: 4.392951162912716, 7.172049027123219, 1.8694972976688373, 4.386492036321314, 7.090666834137275
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.000692974966366114
 Median: (5.000438583644794, 5.000581313872885)
 Maximum: 9.999870079253789
 Mean: 5.016534976099465
 Std Deviation: 2.863563426403059
Post-processor Distribution using floor method:
 0: 9.42%
 1: 10.04%
 2: 10.01%
 3: 10.13%
 4: 10.39%
 5: 9.73%
 6: 10.39%
 7: 10.04%
 8: 9.9%
 9: 9.95%

Output Distribution: Random.triangular(0.0, 10.0, 0.0)
Approximate Single Execution Time: Min: 468ns, Mid: 531ns, Max: 812ns
Raw Samples: 4.67576895476117, 5.9345664114119785, 6.443773916966315, 6.765152783396465, 2.8220879021376275
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.0013051461701767408
 Median: (2.9581599592868093, 2.958975837030998)
 Maximum: 9.946873014067227
 Mean: 3.3556226989097193
 Std Deviation: 2.3581082371131115
Post-processor Distribution using floor method:
 0: 18.82%
 1: 16.71%
 2: 15.04%
 3: 13.09%
 4: 10.76%
 5: 9.59%
 6: 6.8%
 7: 5.25%
 8: 2.94%
 9: 1.0%

Output Distribution: triangular(0.0, 10.0, 0.0)
Approximate Single Execution Time: Min: 31ns, Mid: 62ns, Max: 125ns
Raw Samples: 4.631125222225638, 6.675759584909944, 5.013757429265398, 3.328625168270128, 0.8089960699475951
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.00011516248837994958
 Median: (2.9284965443733246, 2.929286211729023)
 Maximum: 9.913305100944871
 Mean: 3.325284909237705
 Std Deviation: 2.364534513540724
Post-processor Distribution using floor method:
 0: 19.53%
 1: 17.03%
 2: 14.23%
 3: 13.24%
 4: 10.53%
 5: 9.44%
 6: 7.06%
 7: 5.0%
 8: 2.97%
 9: 0.97%

Output Distribution: Random._randbelow(10)
Approximate Single Execution Time: Min: 562ns, Mid: 593ns, Max: 1843ns
Raw Samples: 3, 4, 5, 7, 6
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 4
 Maximum: 9
 Mean: 4.473
 Std Deviation: 2.8841121355247314
Sample Distribution:
 0: 10.09%
 1: 10.38%
 2: 10.12%
 3: 10.09%
 4: 9.83%
 5: 9.74%
 6: 9.84%
 7: 10.19%
 8: 9.46%
 9: 10.26%

Output Distribution: randbelow(10)
Approximate Single Execution Time: Min: 31ns, Mid: 62ns, Max: 156ns
Raw Samples: 9, 2, 5, 1, 2
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 5
 Maximum: 9
 Mean: 4.5724
 Std Deviation: 2.8706066045746885
Sample Distribution:
 0: 9.22%
 1: 10.01%
 2: 10.14%
 3: 9.92%
 4: 9.82%
 5: 9.68%
 6: 10.05%
 7: 10.41%
 8: 10.41%
 9: 10.34%

Output Distribution: Random.randint(1, 10)
Approximate Single Execution Time: Min: 1187ns, Mid: 1250ns, Max: 1593ns
Raw Samples: 10, 9, 10, 5, 6
Test Samples: 10000
Sample Statistics:
 Minimum: 1
 Median: 5
 Maximum: 10
 Mean: 5.5008
 Std Deviation: 2.8742695598273755
Sample Distribution:
 1: 9.94%
 2: 10.2%
 3: 9.87%
 4: 9.81%
 5: 10.32%
 6: 9.64%
 7: 10.46%
 8: 9.93%
 9: 9.51%
 10: 10.32%

Output Distribution: randint(1, 10)
Approximate Single Execution Time: Min: 62ns, Mid: 62ns, Max: 218ns
Raw Samples: 10, 2, 1, 4, 3
Test Samples: 10000
Sample Statistics:
 Minimum: 1
 Median: 6
 Maximum: 10
 Mean: 5.5301
 Std Deviation: 2.8920806356393842
Sample Distribution:
 1: 10.1%
 2: 9.96%
 3: 9.91%
 4: 9.95%
 5: 9.6%
 6: 9.44%
 7: 10.44%
 8: 9.87%
 9: 10.52%
 10: 10.21%

Output Distribution: Random.randrange(10)
Approximate Single Execution Time: Min: 875ns, Mid: 1031ns, Max: 1500ns
Raw Samples: 3, 4, 5, 7, 1
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 5
 Maximum: 9
 Mean: 4.5139
 Std Deviation: 2.87061506180876
Sample Distribution:
 0: 10.03%
 1: 9.97%
 2: 9.8%
 3: 9.63%
 4: 10.39%
 5: 9.9%
 6: 10.05%
 7: 9.99%
 8: 10.52%
 9: 9.72%

Output Distribution: randrange(10)
Approximate Single Execution Time: Min: 125ns, Mid: 125ns, Max: 781ns
Raw Samples: 5, 4, 5, 1, 1
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 4
 Maximum: 9
 Mean: 4.4852
 Std Deviation: 2.8772224107427093
Sample Distribution:
 0: 10.22%
 1: 9.89%
 2: 9.96%
 3: 10.33%
 4: 10.05%
 5: 9.81%
 6: 9.68%
 7: 9.96%
 8: 10.23%
 9: 9.87%

Output Distribution: Random.randrange(0, 10)
Approximate Single Execution Time: Min: 1031ns, Mid: 1125ns, Max: 1375ns
Raw Samples: 6, 9, 5, 3, 5
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 5
 Maximum: 9
 Mean: 4.5293
 Std Deviation: 2.83847621175878
Sample Distribution:
 0: 9.56%
 1: 9.7%
 2: 9.68%
 3: 10.16%
 4: 10.24%
 5: 10.69%
 6: 10.21%
 7: 10.02%
 8: 10.08%
 9: 9.66%

Output Distribution: randrange(0, 10)
Approximate Single Execution Time: Min: 62ns, Mid: 62ns, Max: 156ns
Raw Samples: 1, 1, 8, 1, 0
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 5
 Maximum: 9
 Mean: 4.4997
 Std Deviation: 2.868139210752021
Sample Distribution:
 0: 10.17%
 1: 9.83%
 2: 9.79%
 3: 10.15%
 4: 9.86%
 5: 10.11%
 6: 10.14%
 7: 10.01%
 8: 10.25%
 9: 9.69%

Output Distribution: Random.randrange(0, 10, 2)
Approximate Single Execution Time: Min: 1437ns, Mid: 1687ns, Max: 3031ns
Raw Samples: 2, 6, 2, 8, 4
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 4
 Maximum: 8
 Mean: 3.9422
 Std Deviation: 2.837510230189601
Sample Distribution:
 0: 20.71%
 2: 20.37%
 4: 19.64%
 6: 19.66%
 8: 19.62%

Output Distribution: randrange(0, 10, 2)
Approximate Single Execution Time: Min: 62ns, Mid: 93ns, Max: 156ns
Raw Samples: 0, 6, 8, 8, 0
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 4
 Maximum: 8
 Mean: 3.9978
 Std Deviation: 2.8299109525919643
Sample Distribution:
 0: 19.62%
 2: 21.04%
 4: 19.42%
 6: 19.67%
 8: 20.25%

Output Distribution: Random.choice([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
Approximate Single Execution Time: Min: 750ns, Mid: 812ns, Max: 937ns
Raw Samples: 4, 1, 7, 0, 5
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 5
 Maximum: 9
 Mean: 4.5585
 Std Deviation: 2.8800706989105445
Sample Distribution:
 0: 9.62%
 1: 9.89%
 2: 9.8%
 3: 9.91%
 4: 10.19%
 5: 9.99%
 6: 9.95%
 7: 9.59%
 8: 10.45%
 9: 10.61%

Output Distribution: choice([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
Approximate Single Execution Time: Min: 62ns, Mid: 62ns, Max: 125ns
Raw Samples: 1, 8, 8, 8, 6
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 4
 Maximum: 9
 Mean: 4.4757
 Std Deviation: 2.888086497035959
Sample Distribution:
 0: 10.17%
 1: 10.29%
 2: 10.06%
 3: 10.09%
 4: 9.87%
 5: 9.96%
 6: 9.86%
 7: 9.37%
 8: 10.11%
 9: 10.22%

Output Distribution: Random.sample([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], k=3)
Approximate Single Execution Time: Min: 4593ns, Mid: 4750ns, Max: 8906ns
Raw Samples: [2, 3, 5], [6, 0, 4], [9, 3, 4], [3, 7, 2], [2, 1, 3]
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 4
 Maximum: 9
 Mean: 4.4753
 Std Deviation: 2.8720749975373465
Sample Distribution:
 0: 10.15%
 1: 10.19%
 2: 10.04%
 3: 9.8%
 4: 10.19%
 5: 9.9%
 6: 9.94%
 7: 10.13%
 8: 9.89%
 9: 9.77%

Output Distribution: sample([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], k=3)
Approximate Single Execution Time: Min: 843ns, Mid: 875ns, Max: 1062ns
Raw Samples: [3, 8, 9], [0, 6, 9], [7, 6, 8], [1, 5, 3], [7, 4, 5]
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 5
 Maximum: 9
 Mean: 4.5266
 Std Deviation: 2.8683994163158575
Sample Distribution:
 0: 9.78%
 1: 9.99%
 2: 9.55%
 3: 10.25%
 4: 10.09%
 5: 10.3%
 6: 9.77%
 7: 10.13%
 8: 9.83%
 9: 10.31%

Timer only: _random.shuffle(some_list) of size 10:
Approximate Single Execution Time: Min: 7062ns, Mid: 7406ns, Max: 11312ns

Timer only: shuffle(some_list) of size 10:
Approximate Single Execution Time: Min: 531ns, Mid: 562ns, Max: 656ns

Timer only: knuth(some_list) of size 10:
Approximate Single Execution Time: Min: 968ns, Mid: 1000ns, Max: 1031ns

Timer only: fisher_yates(some_list) of size 10:
Approximate Single Execution Time: Min: 968ns, Mid: 1000ns, Max: 2312ns

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: 3156ns, Mid: 3218ns, Max: 5687ns
Raw Samples: [9, 4, 0], [2, 1, 4], [0, 0, 0], [5, 8, 1], [1, 5, 0]
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 3
 Maximum: 9
 Mean: 3.0171
 Std Deviation: 2.458457238025327
Sample Distribution:
 0: 17.76%
 1: 16.6%
 2: 14.6%
 3: 12.78%
 4: 11.08%
 5: 8.62%
 6: 7.52%
 7: 5.24%
 8: 3.85%
 9: 1.95%

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: 2156ns, Max: 3812ns
Raw Samples: [1, 2, 6], [2, 8, 1], [1, 3, 2], [0, 3, 4], [3, 7, 4]
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 3
 Maximum: 9
 Mean: 3.019
 Std Deviation: 2.472620145723662
Sample Distribution:
 0: 17.97%
 1: 16.71%
 2: 14.5%
 3: 12.49%
 4: 10.84%
 5: 8.84%
 6: 7.18%
 7: 5.6%
 8: 3.95%
 9: 1.92%

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: 2718ns, Mid: 2812ns, Max: 4437ns
Raw Samples: [5, 0, 5], [4, 8, 0], [1, 7, 8], [0, 5, 1], [3, 1, 3]
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 3
 Maximum: 9
 Mean: 3.0291
 Std Deviation: 2.461799999172068
Sample Distribution:
 0: 17.91%
 1: 16.22%
 2: 14.32%
 3: 13.2%
 4: 10.69%
 5: 9.23%
 6: 7.17%
 7: 5.6%
 8: 3.62%
 9: 2.04%

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: 1437ns, Mid: 1515ns, Max: 3125ns
Raw Samples: [3, 2, 4], [5, 4, 7], [1, 0, 1], [6, 0, 5], [4, 1, 2]
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 3
 Maximum: 9
 Mean: 2.9752
 Std Deviation: 2.4424130482270634
Sample Distribution:
 0: 18.35%
 1: 16.49%
 2: 14.83%
 3: 12.63%
 4: 10.9%
 5: 8.67%
 6: 7.41%
 7: 5.46%
 8: 3.49%
 9: 1.77%

Output Distribution: Random.normalvariate(0.0, 2.8)
Approximate Single Execution Time: Min: 656ns, Mid: 718ns, Max: 906ns
Raw Samples: 0.5930272777209413, -0.47797300789432534, -2.1019380237834957, -0.4723026100350704, -0.4496695044655188
Test Samples: 10000
Pre-processor Statistics:
 Minimum: -12.088179925409266
 Median: (-0.012324637099808482, -0.012044945973750774)
 Maximum: 9.955174998304587
 Mean: -0.0070620004893537525
 Std Deviation: 2.8132845189363174
Post-processor Distribution using round method:
 -12: 0.01%
 -10: 0.06%
 -9: 0.07%
 -8: 0.22%
 -7: 0.7%
 -6: 1.52%
 -5: 2.83%
 -4: 5.16%
 -3: 8.15%
 -2: 11.34%
 -1: 13.17%
 0: 13.55%
 1: 13.76%
 2: 11.09%
 3: 7.84%
 4: 5.1%
 5: 2.83%
 6: 1.41%
 7: 0.74%
 8: 0.29%
 9: 0.14%
 10: 0.02%

Output Distribution: normalvariate(0.0, 2.8)
Approximate Single Execution Time: Min: 125ns, Mid: 156ns, Max: 312ns
Raw Samples: 3.1706278613491965, 3.6574720875994187, -2.275747864378095, 4.326414066173328, -3.135249595256448
Test Samples: 10000
Pre-processor Statistics:
 Minimum: -10.890423534384194
 Median: (0.0011985381998108058, 0.0027786871337978692)
 Maximum: 10.570000101216161
 Mean: 0.007342869674920708
 Std Deviation: 2.8144761726539627
Post-processor Distribution using round method:
 -11: 0.02%
 -10: 0.02%
 -9: 0.09%
 -8: 0.29%
 -7: 0.59%
 -6: 1.35%
 -5: 3.24%
 -4: 5.26%
 -3: 7.93%
 -2: 10.55%
 -1: 13.27%
 0: 14.45%
 1: 13.08%
 2: 10.88%
 3: 8.46%
 4: 5.08%
 5: 2.84%
 6: 1.49%
 7: 0.73%
 8: 0.24%
 9: 0.08%
 10: 0.05%
 11: 0.01%

Output Distribution: Random.gauss(1.0, 1.0)
Approximate Single Execution Time: Min: 593ns, Mid: 593ns, Max: 1156ns
Raw Samples: 0.7120070882580258, -0.29764540760410685, 2.033945496798204, -0.8503062310437042, 0.3692271865994241
Test Samples: 10000
Pre-processor Statistics:
 Minimum: -3.359576662673504
 Median: (0.9856090902210608, 0.9856546337914275)
 Maximum: 5.0914893111748745
 Mean: 0.9922302355809425
 Std Deviation: 1.0002759976973903
Post-processor Distribution using round method:
 -3: 0.02%
 -2: 0.58%
 -1: 6.08%
 0: 24.4%
 1: 39.01%
 2: 23.11%
 3: 6.04%
 4: 0.73%
 5: 0.03%

Output Distribution: gauss(1.0, 1.0)
Approximate Single Execution Time: Min: 62ns, Mid: 93ns, Max: 218ns
Raw Samples: 2.711161776385261, 2.143321491256298, 0.21163716799234947, 0.011365852520925266, 0.9892766413964316
Test Samples: 10000
Pre-processor Statistics:
 Minimum: -2.9312711186170617
 Median: (0.9855366681561074, 0.9864120767687009)
 Maximum: 5.541341474708732
 Mean: 0.9959291857563403
 Std Deviation: 1.0056627222736383
Post-processor Distribution using round method:
 -3: 0.04%
 -2: 0.5%
 -1: 6.16%
 0: 24.85%
 1: 37.93%
 2: 23.47%
 3: 6.32%
 4: 0.71%
 5: 0.01%
 6: 0.01%

Output Distribution: Random.lognormvariate(0.0, 0.5)
Approximate Single Execution Time: Min: 781ns, Mid: 890ns, Max: 1531ns
Raw Samples: 0.6160287409271726, 1.8324509183774187, 0.955163626280501, 0.578895009812598, 0.6169501996251227
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.1633912190376701
 Median: (0.9864841594111071, 0.9865734176720258)
 Maximum: 8.448200224941578
 Mean: 1.1249521005904621
 Std Deviation: 0.6063635270568627
Post-processor Distribution using round method:
 0: 8.74%
 1: 70.45%
 2: 17.45%
 3: 2.81%
 4: 0.42%
 5: 0.09%
 6: 0.02%
 7: 0.01%
 8: 0.01%

Output Distribution: lognormvariate(0.0, 0.5)
Approximate Single Execution Time: Min: 93ns, Mid: 125ns, Max: 250ns
Raw Samples: 0.4862130391635644, 1.3691871282475665, 1.077423752814334, 1.3414434768983654, 1.9015404617981928
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.15493218776862422
 Median: (1.000836226276059, 1.0009285118982114)
 Maximum: 6.535897327159081
 Mean: 1.1374168325024776
 Std Deviation: 0.6119312852435634
Post-processor Distribution using round method:
 0: 8.18%
 1: 70.58%
 2: 17.83%
 3: 2.81%
 4: 0.44%
 5: 0.11%
 6: 0.04%
 7: 0.01%

Output Distribution: Random.expovariate(1.0)
Approximate Single Execution Time: Min: 312ns, Mid: 375ns, Max: 875ns
Raw Samples: 2.171240626638392, 3.0070848861894484, 0.4691229312413158, 1.6779018548838955, 0.5178344741879356
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.0001108910312373615
 Median: (0.6971824775172758, 0.6972403354574873)
 Maximum: 9.442825975807686
 Mean: 1.0042423365395818
 Std Deviation: 1.0252041161684906
Post-processor Distribution using floor method:
 0: 63.47%
 1: 23.02%
 2: 8.46%
 3: 2.88%
 4: 1.39%
 5: 0.4%
 6: 0.22%
 7: 0.08%
 8: 0.05%
 9: 0.03%

Output Distribution: expovariate(1.0)
Approximate Single Execution Time: Min: 62ns, Mid: 62ns, Max: 187ns
Raw Samples: 0.9260325077887819, 0.036615327981158304, 0.9130273769161751, 1.300319104829159, 0.1914926336362293
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 8.553575385506888e-05
 Median: (0.7007296988092121, 0.7011433814823741)
 Maximum: 9.316857049510938
 Mean: 0.9941761901894112
 Std Deviation: 0.9794981381056284
Post-processor Distribution using floor method:
 0: 63.2%
 1: 23.4%
 2: 8.69%
 3: 3.11%
 4: 1.05%
 5: 0.36%
 6: 0.1%
 7: 0.04%
 8: 0.04%
 9: 0.01%

Output Distribution: Random.vonmisesvariate(0, 0)
Approximate Single Execution Time: Min: 281ns, Mid: 296ns, Max: 437ns
Raw Samples: 0.08577179899973336, 6.049940139440558, 0.5044318410628879, 2.5358999686789323, 6.113470730663246
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.0019618805490201224
 Median: (3.198524794137351, 3.198676926645815)
 Maximum: 6.279569304570442
 Mean: 3.1735089351626025
 Std Deviation: 1.8161931222391179
Post-processor Distribution using floor method:
 0: 15.56%
 1: 15.39%
 2: 16.06%
 3: 15.81%
 4: 16.46%
 5: 16.12%
 6: 4.6%

Output Distribution: vonmisesvariate(0, 0)
Approximate Single Execution Time: Min: 62ns, Mid: 77ns, Max: 156ns
Raw Samples: 4.669859381969691, 0.7979976849780615, 2.4717694896796267, 4.297595769372298, 3.4795232706688073
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.000183295698807474
 Median: (3.0886262864776435, 3.088920290854218)
 Maximum: 6.282533789310254
 Mean: 3.1181350830868175
 Std Deviation: 1.8307471757275202
Post-processor Distribution using floor method:
 0: 16.53%
 1: 15.97%
 2: 16.18%
 3: 15.7%
 4: 15.16%
 5: 15.55%
 6: 4.91%

Output Distribution: Random.gammavariate(2.0, 1.0)
Approximate Single Execution Time: Min: 1312ns, Mid: 1577ns, Max: 2218ns
Raw Samples: 4.796009051217658, 2.5588128532777596, 1.061423361078811, 1.7185771068277527, 5.646378113979173
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.015464898311536638
 Median: (1.6869050579053622, 1.6870713754806705)
 Maximum: 12.607644999191049
 Mean: 2.004733475293573
 Std Deviation: 1.4137920838699123
Post-processor Distribution using round method:
 0: 9.0%
 1: 34.77%
 2: 27.3%
 3: 15.19%
 4: 7.66%
 5: 3.45%
 6: 1.56%
 7: 0.66%
 8: 0.18%
 9: 0.13%
 10: 0.03%
 11: 0.06%
 13: 0.01%

Output Distribution: gammavariate(2.0, 1.0)
Approximate Single Execution Time: Min: 93ns, Mid: 125ns, Max: 218ns
Raw Samples: 1.400721481695334, 1.617580988927482, 1.2689662602473293, 2.2794879221091966, 4.507748832291918
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.014454491619661725
 Median: (1.6946287939179534, 1.6946538773921362)
 Maximum: 12.072731788570229
 Mean: 2.0071354843118594
 Std Deviation: 1.4157723677980187
Post-processor Distribution using round method:
 0: 9.11%
 1: 34.76%
 2: 26.97%
 3: 15.65%
 4: 7.21%
 5: 3.66%
 6: 1.61%
 7: 0.55%
 8: 0.26%
 9: 0.14%
 10: 0.04%
 11: 0.03%
 12: 0.01%

Output Distribution: Random.betavariate(3.0, 3.0)
Approximate Single Execution Time: Min: 2562ns, Mid: 2781ns, Max: 4750ns
Raw Samples: 0.47931615077792106, 0.7240379823243803, 0.45652108525038004, 0.30503815686335617, 0.49284646316045766
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.0066914414962923885
 Median: (0.5018831143105688, 0.5019774521951034)
 Maximum: 0.9841042667041499
 Mean: 0.5010755610854323
 Std Deviation: 0.1884985606931819
Post-processor Distribution using round method:
 0: 49.66%
 1: 50.34%

Output Distribution: betavariate(3.0, 3.0)
Approximate Single Execution Time: Min: 156ns, Mid: 187ns, Max: 281ns
Raw Samples: 0.7680664409465507, 0.3390177944214646, 0.5450482106505082, 0.37363960411292346, 0.1868484263916002
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.021051156006731284
 Median: (0.4958481167211107, 0.4958509632040114)
 Maximum: 0.9742586819712881
 Mean: 0.4989102190141408
 Std Deviation: 0.18794659961308374
Post-processor Distribution using round method:
 0: 50.96%
 1: 49.04%

Output Distribution: Random.paretovariate(4.0)
Approximate Single Execution Time: Min: 281ns, Mid: 312ns, Max: 468ns
Raw Samples: 1.0171076052975592, 1.0265328786941286, 1.3067474104394723, 1.0111933132937005, 1.7221949017413332
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 1.0000137370311148
 Median: (1.1886456368174607, 1.1887431874066272)
 Maximum: 7.928052700003265
 Mean: 1.329288041668601
 Std Deviation: 0.44921600547913065
Post-processor Distribution using floor method:
 1: 93.69%
 2: 5.19%
 3: 0.74%
 4: 0.22%
 5: 0.06%
 6: 0.07%
 7: 0.03%

Output Distribution: paretovariate(4.0)
Approximate Single Execution Time: Min: 62ns, Mid: 93ns, Max: 281ns
Raw Samples: 1.2354133742738347, 1.0849095830209727, 1.9355243112696066, 1.0750167510851978, 1.877247718066934
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 1.0000816555392331
 Median: (1.189139561596937, 1.1891917703960984)
 Maximum: 16.765728539036477
 Mean: 1.3357447741578463
 Std Deviation: 0.4968337794138987
Post-processor Distribution using floor method:
 1: 93.61%
 2: 5.22%
 3: 0.75%
 4: 0.2%
 5: 0.15%
 6: 0.03%
 9: 0.02%
 12: 0.01%
 16: 0.01%

Output Distribution: Random.weibullvariate(1.0, 1.0)
Approximate Single Execution Time: Min: 468ns, Mid: 468ns, Max: 812ns
Raw Samples: 0.3875296402873728, 3.578203404538266, 4.006832637656319, 0.29757989927915496, 1.2551929121819305
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 5.43719274496732e-05
 Median: (0.6936053648764988, 0.693783415891484)
 Maximum: 8.848302263195594
 Mean: 0.9977132202272788
 Std Deviation: 0.9947485618722824
Post-processor Distribution using floor method:
 0: 63.24%
 1: 23.13%
 2: 8.74%
 3: 3.13%
 4: 1.04%
 5: 0.48%
 6: 0.15%
 7: 0.06%
 8: 0.03%

Output Distribution: weibullvariate(1.0, 1.0)
Approximate Single Execution Time: Min: 93ns, Mid: 93ns, Max: 343ns
Raw Samples: 0.607271249451256, 0.1496417834877304, 0.007353003006799029, 0.3347005939515252, 0.5165337655771994
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 2.1026932063736618e-05
 Median: (0.7080966058468359, 0.7086468556180514)
 Maximum: 11.539519087393366
 Mean: 1.0145207034565435
 Std Deviation: 1.0284385151860722
Post-processor Distribution using floor method:
 0: 62.85%
 1: 23.59%
 2: 8.31%
 3: 3.2%
 4: 1.24%
 5: 0.53%
 6: 0.11%
 7: 0.1%
 8: 0.03%
 9: 0.03%
 11: 0.01%


Total Test Time: 1.8498 sec