Pyewacket 0.0.1b5

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)
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]

""" Extra """
randint(10, 1)      # -> [1, 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

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 v0.0.1b5

• 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: 468ns
Raw Samples: 0.33998096656068333, 0.03824705683337104, 0.43903726442372515, 0.398803413180975, 0.9753099220329432
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 4.795755933961754e-05
 Median: (0.5018945866869721, 0.5019761085559419)
 Maximum: 0.9996932166808268
 Mean: 0.4993705787082727
 Std Deviation: 0.2895083321879852
Post-processor Distribution using lambda1 method:
 0: 10.38%
 1: 9.79%
 2: 9.81%
 3: 10.14%
 4: 9.6%
 5: 9.98%
 6: 10.52%
 7: 9.99%
 8: 9.76%
 9: 10.03%

Output Distribution: random()
Approximate Single Execution Time: Min: 31ns, Mid: 46ns, Max: 125ns
Raw Samples: 0.2124361313066671, 0.9481471365690445, 0.5391108794585697, 0.2950395343522406, 0.4370737692584957
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 5.8027228788259813e-05
 Median: (0.5028637378283466, 0.5031367800451703)
 Maximum: 0.9999301871479003
 Mean: 0.501189889333633
 Std Deviation: 0.28957684283589546
Post-processor Distribution using lambda2 method:
 0: 10.46%
 1: 9.29%
 2: 10.1%
 3: 10.08%
 4: 9.78%
 5: 10.02%
 6: 10.12%
 7: 10.14%
 8: 9.88%
 9: 10.13%

Output Distribution: Random.uniform(0.0, 10.0)
Approximate Single Execution Time: Min: 218ns, Mid: 234ns, Max: 1375ns
Raw Samples: 0.4326179289235865, 2.899678611477822, 4.008489435431713, 1.0684114323879845, 2.011079340084189
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.0007916263821405867
 Median: (5.045839451542293, 5.049629868995088)
 Maximum: 9.99835505889272
 Mean: 5.00843223256577
 Std Deviation: 2.8845963364682983
Post-processor Distribution using floor method:
 0: 10.03%
 1: 9.92%
 2: 9.97%
 3: 9.75%
 4: 9.91%
 5: 10.21%
 6: 10.28%
 7: 9.83%
 8: 10.04%
 9: 10.06%

Output Distribution: uniform(0.0, 10.0)
Approximate Single Execution Time: Min: 31ns, Mid: 46ns, Max: 93ns
Raw Samples: 4.33594318266003, 4.625033359017187, 9.127412906945366, 4.936957727692714, 8.51850449095233
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.00015430148050690176
 Median: (5.017877934244143, 5.018254114806144)
 Maximum: 9.996460143805594
 Mean: 5.050044975862397
 Std Deviation: 2.8920194241084225
Post-processor Distribution using floor method:
 0: 9.61%
 1: 9.77%
 2: 9.94%
 3: 10.15%
 4: 10.32%
 5: 9.57%
 6: 9.61%
 7: 10.52%
 8: 9.87%
 9: 10.64%

Output Distribution: Random.triangular(0.0, 10.0, 0.0)
Approximate Single Execution Time: Min: 531ns, Mid: 531ns, Max: 781ns
Raw Samples: 3.553845942870046, 5.94428544380859, 4.443662456040607, 3.0147774266713547, 3.420580207065198
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.0004320489008993178
 Median: (2.9089726939197726, 2.9094710554433263)
 Maximum: 9.991697138221088
 Mean: 3.3187067625928144
 Std Deviation: 2.35315316491313
Post-processor Distribution using floor method:
 0: 19.26%
 1: 17.15%
 2: 14.85%
 3: 12.53%
 4: 10.92%
 5: 9.58%
 6: 6.87%
 7: 5.26%
 8: 2.69%
 9: 0.89%

Output Distribution: triangular(0.0, 10.0, 0.0)
Approximate Single Execution Time: Min: 31ns, Mid: 62ns, Max: 125ns
Raw Samples: 1.7423016325975937, 0.45171991486482765, 0.5635280776175577, 2.441211877485787, 0.29375725416494025
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 9.551196659129957e-06
 Median: (2.9087554044349795, 2.9102392525031364)
 Maximum: 9.825156407223533
 Mean: 3.3255059262054276
 Std Deviation: 2.357551316999739
Post-processor Distribution using floor method:
 0: 19.01%
 1: 17.24%
 2: 14.89%
 3: 12.82%
 4: 10.89%
 5: 9.42%
 6: 6.8%
 7: 4.95%
 8: 2.98%
 9: 1.0%

Output Distribution: Random._randbelow(10)
Approximate Single Execution Time: Min: 562ns, Mid: 625ns, Max: 1312ns
Raw Samples: 8, 2, 8, 3, 0
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 4
 Maximum: 9
 Mean: 4.4834
 Std Deviation: 2.9069519220220505
Sample Distribution:
 0: 10.57%
 1: 9.93%
 2: 10.36%
 3: 9.66%
 4: 9.83%
 5: 9.7%
 6: 9.85%
 7: 9.56%
 8: 9.99%
 9: 10.55%

Output Distribution: randbelow(10)
Approximate Single Execution Time: Min: 62ns, Mid: 62ns, Max: 156ns
Raw Samples: 4, 2, 0, 7, 3
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 5
 Maximum: 9
 Mean: 4.5144
 Std Deviation: 2.8735376040407377
Sample Distribution:
 0: 10.12%
 1: 9.94%
 2: 9.6%
 3: 9.72%
 4: 10.42%
 5: 10.15%
 6: 9.75%
 7: 10.18%
 8: 10.13%
 9: 9.99%

Output Distribution: Random.randint(1, 10)
Approximate Single Execution Time: Min: 1218ns, Mid: 1281ns, Max: 1875ns
Raw Samples: 5, 9, 9, 4, 9
Test Samples: 10000
Sample Statistics:
 Minimum: 1
 Median: 5
 Maximum: 10
 Mean: 5.4964
 Std Deviation: 2.873188570431138
Sample Distribution:
 1: 9.98%
 2: 10.18%
 3: 9.93%
 4: 9.75%
 5: 10.26%
 6: 9.87%
 7: 10.27%
 8: 9.93%
 9: 9.64%
 10: 10.19%

Output Distribution: randint(1, 10)
Approximate Single Execution Time: Min: 62ns, Mid: 62ns, Max: 125ns
Raw Samples: 10, 2, 1, 1, 2
Test Samples: 10000
Sample Statistics:
 Minimum: 1
 Median: 5
 Maximum: 10
 Mean: 5.5083
 Std Deviation: 2.8840532044829943
Sample Distribution:
 1: 10.13%
 2: 9.73%
 3: 9.89%
 4: 10.49%
 5: 10.19%
 6: 9.52%
 7: 9.53%
 8: 10.26%
 9: 9.85%
 10: 10.41%

Output Distribution: Random.randrange(10)
Approximate Single Execution Time: Min: 843ns, Mid: 968ns, Max: 2093ns
Raw Samples: 7, 2, 0, 9, 9
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 5
 Maximum: 9
 Mean: 4.4989
 Std Deviation: 2.8795881637482954
Sample Distribution:
 0: 9.95%
 1: 10.46%
 2: 9.87%
 3: 9.73%
 4: 9.94%
 5: 9.64%
 6: 10.26%
 7: 10.18%
 8: 10.01%
 9: 9.96%

Output Distribution: randrange(10)
Approximate Single Execution Time: Min: 62ns, Mid: 62ns, Max: 156ns
Raw Samples: 3, 0, 8, 5, 0
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 4
 Maximum: 9
 Mean: 4.4854
 Std Deviation: 2.8863506270018893
Sample Distribution:
 0: 10.12%
 1: 10.23%
 2: 10.09%
 3: 9.96%
 4: 10.1%
 5: 9.67%
 6: 9.43%
 7: 10.5%
 8: 9.68%
 9: 10.22%

Output Distribution: Random.randrange(0, 10)
Approximate Single Execution Time: Min: 1062ns, Mid: 1093ns, Max: 2031ns
Raw Samples: 3, 5, 6, 0, 9
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 5
 Maximum: 9
 Mean: 4.5263
 Std Deviation: 2.8708417725901096
Sample Distribution:
 0: 9.69%
 1: 10.02%
 2: 10.22%
 3: 9.66%
 4: 10.11%
 5: 9.77%
 6: 10.04%
 7: 10.3%
 8: 10.15%
 9: 10.04%

Output Distribution: randrange(0, 10)
Approximate Single Execution Time: Min: 62ns, Mid: 62ns, Max: 156ns
Raw Samples: 6, 7, 7, 1, 2
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 4
 Maximum: 9
 Mean: 4.4813
 Std Deviation: 2.8833455703692223
Sample Distribution:
 0: 10.2%
 1: 9.84%
 2: 10.25%
 3: 10.56%
 4: 9.7%
 5: 9.49%
 6: 10.14%
 7: 9.91%
 8: 9.54%
 9: 10.37%

Output Distribution: Random.randrange(0, 10, 2)
Approximate Single Execution Time: Min: 1343ns, Mid: 1359ns, Max: 1750ns
Raw Samples: 6, 8, 4, 4, 0
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 4
 Maximum: 8
 Mean: 4.0188
 Std Deviation: 2.828788921902175
Sample Distribution:
 0: 19.9%
 2: 19.83%
 4: 19.72%
 6: 20.53%
 8: 20.02%

Output Distribution: randrange(0, 10, 2)
Approximate Single Execution Time: Min: 62ns, Mid: 93ns, Max: 125ns
Raw Samples: 6, 6, 8, 2, 4
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 4
 Maximum: 8
 Mean: 3.9824
 Std Deviation: 2.815045770190749
Sample Distribution:
 0: 19.98%
 2: 20.12%
 4: 20.13%
 6: 20.34%
 8: 19.43%

Output Distribution: Random.choice([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
Approximate Single Execution Time: Min: 750ns, Mid: 812ns, Max: 1062ns
Raw Samples: 7, 5, 9, 4, 3
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 5
 Maximum: 9
 Mean: 4.5124
 Std Deviation: 2.8799089616796496
Sample Distribution:
 0: 10.19%
 1: 9.55%
 2: 10.38%
 3: 9.64%
 4: 10.07%
 5: 9.88%
 6: 10.19%
 7: 9.83%
 8: 10.05%
 9: 10.22%

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: 6, 9, 2, 2, 6
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 4
 Maximum: 9
 Mean: 4.4611
 Std Deviation: 2.851894128471813
Sample Distribution:
 0: 9.82%
 1: 10.28%
 2: 10.04%
 3: 10.12%
 4: 10.41%
 5: 10.55%
 6: 9.39%
 7: 10.19%
 8: 9.47%
 9: 9.73%

Output Distribution: Random.sample([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], k=3)
Approximate Single Execution Time: Min: 4125ns, Mid: 4250ns, Max: 7281ns
Raw Samples: [9, 2, 3], [4, 3, 8], [7, 0, 1], [7, 8, 4], [8, 2, 4]
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 5
 Maximum: 9
 Mean: 4.4977
 Std Deviation: 2.8931007091304854
Sample Distribution:
 0: 10.8%
 1: 9.45%
 2: 9.9%
 3: 10.19%
 4: 9.26%
 5: 9.89%
 6: 10.16%
 7: 10.31%
 8: 10.03%
 9: 10.01%

Output Distribution: sample([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], k=3)
Approximate Single Execution Time: Min: 875ns, Mid: 906ns, Max: 1250ns
Raw Samples: [5, 8, 9], [1, 5, 4], [2, 3, 4], [6, 7, 9], [7, 8, 1]
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 5
 Maximum: 9
 Mean: 4.4874
 Std Deviation: 2.865285714588097
Sample Distribution:
 0: 9.82%
 1: 9.96%
 2: 10.86%
 3: 9.51%
 4: 9.73%
 5: 10.52%
 6: 9.82%
 7: 10.01%
 8: 9.91%
 9: 9.86%

Timer only: _random.shuffle(some_list) of size 10:
Approximate Single Execution Time: Min: 7031ns, Mid: 7187ns, Max: 8906ns

Timer only: shuffle(some_list) of size 10:
Approximate Single Execution Time: Min: 375ns, Mid: 375ns, Max: 468ns

Timer only: knuth(some_list) of size 10:
Approximate Single Execution Time: Min: 843ns, Mid: 875ns, Max: 1468ns

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

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: 3187ns, Max: 3625ns
Raw Samples: [3, 3, 0], [4, 0, 6], [3, 5, 0], [7, 0, 6], [3, 3, 1]
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 3
 Maximum: 9
 Mean: 2.9868
 Std Deviation: 2.445531398772512
Sample Distribution:
 0: 17.68%
 1: 17.06%
 2: 14.82%
 3: 12.95%
 4: 10.8%
 5: 8.84%
 6: 6.7%
 7: 5.5%
 8: 3.82%
 9: 1.83%

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: 1968ns, Max: 2781ns
Raw Samples: [3, 3, 2], [4, 4, 3], [7, 0, 5], [3, 3, 0], [5, 4, 0]
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 3
 Maximum: 9
 Mean: 2.9949
 Std Deviation: 2.4417760374411293
Sample Distribution:
 0: 18.11%
 1: 15.91%
 2: 14.87%
 3: 13.54%
 4: 10.72%
 5: 9.18%
 6: 6.85%
 7: 5.25%
 8: 3.54%
 9: 2.03%

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: 2562ns, Mid: 2593ns, Max: 2968ns
Raw Samples: [5, 4, 1], [6, 2, 6], [6, 5, 4], [0, 1, 1], [0, 4, 2]
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 3
 Maximum: 9
 Mean: 2.9771
 Std Deviation: 2.4556421986642896
Sample Distribution:
 0: 18.53%
 1: 16.74%
 2: 14.63%
 3: 12.07%
 4: 10.83%
 5: 9.09%
 6: 7.27%
 7: 5.37%
 8: 3.71%
 9: 1.76%

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: 1468ns, Mid: 1500ns, Max: 1718ns
Raw Samples: [0, 2, 0], [2, 4, 5], [4, 5, 1], [1, 4, 1], [3, 0, 8]
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 3
 Maximum: 9
 Mean: 3.0149
 Std Deviation: 2.4456238667484747
Sample Distribution:
 0: 18.3%
 1: 15.86%
 2: 14.49%
 3: 12.46%
 4: 11.21%
 5: 9.61%
 6: 7.14%
 7: 5.59%
 8: 3.65%
 9: 1.69%

Output Distribution: Random.normalvariate(0.0, 2.8)
Approximate Single Execution Time: Min: 656ns, Mid: 750ns, Max: 1125ns
Raw Samples: -0.9638329216563319, 0.7667922770184131, -0.29447773676806216, 2.1588780712269164, 1.919198907965857
Test Samples: 10000
Pre-processor Statistics:
 Minimum: -11.959693935832286
 Median: (-0.018184589112064158, -0.017703802380392868)
 Maximum: 10.518052604450656
 Mean: -0.010342977523360091
 Std Deviation: 2.7940237038161344
Post-processor Distribution using round method:
 -12: 0.02%
 -10: 0.05%
 -9: 0.12%
 -8: 0.19%
 -7: 0.55%
 -6: 1.69%
 -5: 2.85%
 -4: 5.01%
 -3: 7.99%
 -2: 10.72%
 -1: 14.01%
 0: 14.38%
 1: 12.98%
 2: 11.15%
 3: 7.85%
 4: 5.06%
 5: 3.03%
 6: 1.42%
 7: 0.51%
 8: 0.25%
 9: 0.13%
 10: 0.03%
 11: 0.01%

Output Distribution: normalvariate(0.0, 2.8)
Approximate Single Execution Time: Min: 62ns, Mid: 93ns, Max: 187ns
Raw Samples: 0.07648034507601031, 3.1874962129390148, -2.9944655674380183, -2.4068083939625913, 6.327590276260219
Test Samples: 10000
Pre-processor Statistics:
 Minimum: -10.617728007392088
 Median: (0.015637721695609973, 0.01643281293249203)
 Maximum: 12.106080756478752
 Mean: 0.009623605820333957
 Std Deviation: 2.761662760101235
Post-processor Distribution using round method:
 -11: 0.02%
 -10: 0.04%
 -9: 0.07%
 -8: 0.23%
 -7: 0.61%
 -6: 1.29%
 -5: 2.53%
 -4: 5.22%
 -3: 8.18%
 -2: 11.25%
 -1: 13.14%
 0: 14.45%
 1: 13.83%
 2: 11.07%
 3: 7.82%
 4: 5.23%
 5: 2.56%
 6: 1.37%
 7: 0.66%
 8: 0.34%
 9: 0.04%
 10: 0.02%
 11: 0.02%
 12: 0.01%

Output Distribution: Random.gauss(1.0, 1.0)
Approximate Single Execution Time: Min: 593ns, Mid: 593ns, Max: 1000ns
Raw Samples: 0.4012979060969205, 1.941884667070438, 0.010783596985095345, 2.085410052973379, 1.294574208029832
Test Samples: 10000
Pre-processor Statistics:
 Minimum: -2.5945571541165457
 Median: (0.9959211555342227, 0.9961219174198657)
 Maximum: 4.586676187560908
 Mean: 0.9958260185482738
 Std Deviation: 0.996215041734771
Post-processor Distribution using round method:
 -3: 0.02%
 -2: 0.6%
 -1: 6.03%
 0: 24.51%
 1: 38.25%
 2: 24.0%
 3: 6.05%
 4: 0.52%
 5: 0.02%

Output Distribution: gauss(1.0, 1.0)
Approximate Single Execution Time: Min: 62ns, Mid: 93ns, Max: 187ns
Raw Samples: 3.352782138849746, 2.137719065725252, 0.8075695174077778, 0.5888325563139997, 0.0011753209240200873
Test Samples: 10000
Pre-processor Statistics:
 Minimum: -3.1632083387363
 Median: (0.9979885673503398, 0.9981581838577753)
 Maximum: 5.6225198960213385
 Mean: 0.9986406865600903
 Std Deviation: 1.0084361593193223
Post-processor Distribution using round method:
 -3: 0.04%
 -2: 0.65%
 -1: 6.36%
 0: 23.95%
 1: 38.12%
 2: 24.18%
 3: 6.05%
 4: 0.62%
 5: 0.02%
 6: 0.01%

Output Distribution: Random.lognormvariate(0.0, 0.5)
Approximate Single Execution Time: Min: 843ns, Mid: 906ns, Max: 1187ns
Raw Samples: 0.406468231175951, 0.9984997874316827, 0.7765348332307658, 0.9775862113200185, 1.6805052181790299
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.17349585207840304
 Median: (0.9976090978679204, 0.9976462074077258)
 Maximum: 6.4831055321768885
 Mean: 1.1398075568786807
 Std Deviation: 0.614888622001397
Post-processor Distribution using round method:
 0: 8.17%
 1: 70.71%
 2: 17.61%
 3: 2.89%
 4: 0.48%
 5: 0.08%
 6: 0.06%

Output Distribution: lognormvariate(0.0, 0.5)
Approximate Single Execution Time: Min: 93ns, Mid: 125ns, Max: 218ns
Raw Samples: 0.548413152929361, 1.1227522064582198, 0.6922223334866964, 0.6960751793194666, 0.7555290300807609
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.14503727266474367
 Median: (1.0030855716815583, 1.0031422126156202)
 Maximum: 6.460159099769669
 Mean: 1.136213985440458
 Std Deviation: 0.6161283778075691
Post-processor Distribution using round method:
 0: 8.58%
 1: 70.32%
 2: 17.71%
 3: 2.68%
 4: 0.52%
 5: 0.11%
 6: 0.08%

Output Distribution: Random.expovariate(1.0)
Approximate Single Execution Time: Min: 312ns, Mid: 343ns, Max: 593ns
Raw Samples: 0.2422641167215338, 0.6178232719733873, 1.8114197496021816, 1.7456107809923975, 0.14067087586794608
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 4.527084174710029e-05
 Median: (0.6829261701146624, 0.6830257613750366)
 Maximum: 9.122340710020298
 Mean: 0.9924720251699817
 Std Deviation: 0.9978711867253676
Post-processor Distribution using floor method:
 0: 64.03%
 1: 22.57%
 2: 8.46%
 3: 3.23%
 4: 1.02%
 5: 0.46%
 6: 0.12%
 7: 0.07%
 8: 0.03%
 9: 0.01%

Output Distribution: expovariate(1.0)
Approximate Single Execution Time: Min: 62ns, Mid: 62ns, Max: 406ns
Raw Samples: 0.7769179279542874, 0.24705758954690768, 0.14365249544142883, 0.3548105939454481, 0.037610302594385345
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 2.1476893125206156e-06
 Median: (0.7000265180486522, 0.7001994054538824)
 Maximum: 10.869381579298153
 Mean: 1.0171813711227444
 Std Deviation: 1.0329722622043969
Post-processor Distribution using floor method:
 0: 62.68%
 1: 23.43%
 2: 8.5%
 3: 3.32%
 4: 1.39%
 5: 0.31%
 6: 0.25%
 7: 0.04%
 8: 0.04%
 9: 0.03%
 10: 0.01%

Output Distribution: Random.vonmisesvariate(0, 0)
Approximate Single Execution Time: Min: 250ns, Mid: 281ns, Max: 875ns
Raw Samples: 3.6616575134737466, 1.278601461852809, 4.842380436994988, 4.725447781252801, 4.501638933627854
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.0005240443355247881
 Median: (3.154017370598905, 3.154376384003555)
 Maximum: 6.280982848689891
 Mean: 3.152353962633879
 Std Deviation: 1.8147839454947114
Post-processor Distribution using floor method:
 0: 15.71%
 1: 16.1%
 2: 15.92%
 3: 15.48%
 4: 16.11%
 5: 16.11%
 6: 4.57%

Output Distribution: vonmisesvariate(0, 0)
Approximate Single Execution Time: Min: 62ns, Mid: 93ns, Max: 156ns
Raw Samples: 0.10768012993869423, 3.0615889777237015, 1.766949736377321, 4.976557710891564, 1.0906991446227738
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.0004824859890636866
 Median: (3.1293536616763733, 3.1300208674605057)
 Maximum: 6.282767643051886
 Mean: 3.13273384048183
 Std Deviation: 1.8224314080675545
Post-processor Distribution using floor method:
 0: 16.19%
 1: 16.42%
 2: 15.41%
 3: 15.56%
 4: 15.83%
 5: 15.96%
 6: 4.63%

Output Distribution: Random.gammavariate(2.0, 1.0)
Approximate Single Execution Time: Min: 1125ns, Mid: 1312ns, Max: 1687ns
Raw Samples: 0.6455940353162938, 1.678922050314309, 1.6295014813140711, 3.2387598814048055, 1.7268874607351676
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.01501206668699291
 Median: (1.6842968113430863, 1.6843034119368456)
 Maximum: 10.442829537759236
 Mean: 2.0114759421371313
 Std Deviation: 1.410003609075263
Post-processor Distribution using round method:
 0: 8.67%
 1: 35.36%
 2: 26.95%
 3: 15.34%
 4: 7.47%
 5: 3.54%
 6: 1.5%
 7: 0.67%
 8: 0.4%
 9: 0.06%
 10: 0.04%

Output Distribution: gammavariate(2.0, 1.0)
Approximate Single Execution Time: Min: 93ns, Mid: 125ns, Max: 218ns
Raw Samples: 0.8279033851543924, 3.910511043413273, 1.8353230061816679, 1.292922687917721, 1.2362227604701521
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.03266478997680422
 Median: (1.6833483065908224, 1.6833695283322059)
 Maximum: 12.822934513250981
 Mean: 2.00735762710373
 Std Deviation: 1.4158722479130144
Post-processor Distribution using round method:
 0: 8.7%
 1: 35.24%
 2: 27.3%
 3: 15.33%
 4: 7.45%
 5: 3.27%
 6: 1.44%
 7: 0.77%
 8: 0.23%
 9: 0.2%
 10: 0.05%
 11: 0.01%
 13: 0.01%

Output Distribution: Random.betavariate(3.0, 3.0)
Approximate Single Execution Time: Min: 2531ns, Mid: 2718ns, Max: 3687ns
Raw Samples: 0.4977898556314353, 0.4971288838161344, 0.5733725414264217, 0.19737954691334925, 0.2765292072941526
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.0237041831053499
 Median: (0.49891246754560686, 0.49893143584434974)
 Maximum: 0.9754918093726632
 Mean: 0.5007690381018631
 Std Deviation: 0.18934773201644198
Post-processor Distribution using round method:
 0: 50.21%
 1: 49.79%

Output Distribution: betavariate(3.0, 3.0)
Approximate Single Execution Time: Min: 156ns, Mid: 187ns, Max: 281ns
Raw Samples: 0.5169473687657116, 0.5781426311186711, 0.22024564738280894, 0.38091398120760367, 0.6551665844999235
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.03295737359363762
 Median: (0.5012461277729405, 0.5012822149276874)
 Maximum: 0.9759112247297637
 Mean: 0.5000284851413378
 Std Deviation: 0.19023821573636202
Post-processor Distribution using round method:
 0: 49.75%
 1: 50.25%

Output Distribution: Random.paretovariate(4.0)
Approximate Single Execution Time: Min: 281ns, Mid: 312ns, Max: 593ns
Raw Samples: 1.0892032527310498, 1.4105408707014326, 1.4873303500425072, 1.5027745061826636, 1.692233618750214
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 1.0000135004910793
 Median: (1.1890585577199089, 1.1891239289847635)
 Maximum: 8.302549908370535
 Mean: 1.3332654313346441
 Std Deviation: 0.4577191932783395
Post-processor Distribution using floor method:
 1: 93.78%
 2: 4.91%
 3: 0.93%
 4: 0.21%
 5: 0.11%
 6: 0.04%
 8: 0.02%

Output Distribution: paretovariate(4.0)
Approximate Single Execution Time: Min: 62ns, Mid: 93ns, Max: 218ns
Raw Samples: 2.791180065930461, 1.299889349728669, 2.662567916648353, 1.3191328259663875, 1.292332821148301
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 1.0000261894615365
 Median: (1.18202615516677, 1.1820405416118565)
 Maximum: 8.9831793733239
 Mean: 1.3266626096990937
 Std Deviation: 0.4715200725588891
Post-processor Distribution using floor method:
 1: 93.95%
 2: 4.92%
 3: 0.79%
 4: 0.14%
 5: 0.07%
 6: 0.04%
 7: 0.04%
 8: 0.05%

Output Distribution: Random.weibullvariate(1.0, 1.0)
Approximate Single Execution Time: Min: 406ns, Mid: 437ns, Max: 750ns
Raw Samples: 3.7411829703274773, 0.47455282493769513, 0.6634974319650867, 1.0709168841581398, 0.8120412716184685
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.00019333851318390145
 Median: (0.700546407200361, 0.7007015040773169)
 Maximum: 10.138840175922857
 Mean: 1.017880166616793
 Std Deviation: 1.0202595019692828
Post-processor Distribution using floor method:
 0: 62.57%
 1: 23.41%
 2: 8.84%
 3: 3.22%
 4: 1.13%
 5: 0.52%
 6: 0.19%
 7: 0.1%
 8: 0.01%
 10: 0.01%

Output Distribution: weibullvariate(1.0, 1.0)
Approximate Single Execution Time: Min: 93ns, Mid: 93ns, Max: 218ns
Raw Samples: 0.8814977183035609, 0.19087829528785896, 0.07945466399893816, 0.24032517727942138, 0.6179726034535873
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 4.603387359685393e-05
 Median: (0.6910682929557863, 0.6911517931307695)
 Maximum: 10.576107686423642
 Mean: 1.0050384326448163
 Std Deviation: 1.0103523672737698
Post-processor Distribution using floor method:
 0: 63.69%
 1: 22.66%
 2: 8.5%
 3: 3.31%
 4: 1.22%
 5: 0.37%
 6: 0.15%
 7: 0.07%
 8: 0.01%
 10: 0.02%


Total Test Time: 1.7572 sec