Fortuna 2.1.1

Random Value Generator: RNG Storm Engine

Fortuna: Random Value Generator

Fortuna's main goal is to provide a quick and easy way to build custom random generators that don't suck.

The core functionality of Fortuna is based on the RNG Storm engine. While Storm is a high quality random engine, Fortuna is not appropriate for cryptography of any kind. Fortuna is meant for games, data science, A.I. and experimental programming, not security.

Suggested Installation: $ pip install Fortuna

Installation on platforms other than MacOS may require building from source files.

Documentation Table of Contents:

• Random Value Generators
  • TruffleShuffle(Sequence) -> Callable
  • QuantumMonty(Sequence) -> Callable
  • CumulativeWeightedChoice(Table) -> Callable
  • RelativeWeightedChoice(Table) -> Callable
  • FlexCat(Matrix) -> Callable
• Random Integer Functions
  • randbelow(number: int) -> int
  • randint(left_lmit: int, right_limit: int) -> int
  • randrange(start: int, stop: int, step: int) -> int
  • d(sides: int) -> int
  • dice(rolls: int, sides: int) -> int
  • plus_or_minus(number: int) -> int
  • plus_or_minus_linear(number: int) -> int
  • binomial(number_of_trials: int, probability: float) -> int
  • negative_binomial(trial_successes: int, probability: float) -> int
  • geometric(probability: float) -> int
  • poisson(mean: float) -> int
  • discrete(count: int, xmin: int, xmax: int) -> int
• Random Float Functions
  • random() -> float
  • uniform(a: float, b: float) -> float
  • expovariate(lambd: float) -> float
  • gammavariate(alpha, beta) -> float
  • weibullvariate(alpha, beta) -> float
  • betavariate(alpha, beta) -> float
  • paretovariate(alpha) -> float
  • gauss(mu: float, sigma: float) -> float
  • normalvariate(mu: float, sigma: float) -> float
  • lognormvariate(mu: float, sigma: float) -> float
  • vonmisesvariate(mu: float, kappa: float) -> float
  • triangular(low: float, high: float, mode: float = None)
  • extreme_value(location: float, scale: float) -> float
  • chi_squared(degrees_of_freedom: float) -> float
  • cauchy(location: float, scale: float) -> float
  • fisher_f(degrees_of_freedom_1: float, degrees_of_freedom_2: float) -> float
  • student_t(degrees_of_freedom: float) -> float
• Random Bool Function
  • percent_true(truth_factor: float) -> bool
• Random Shuffle Functions
  • shuffle(array: list) -> None
  • knuth(array: list) -> None
  • fisher_yates(array: list) -> None
• Test Suite Functions
  • distribution_timer(func: staticmethod, *args, **kwargs) -> None
  • quick_test()
• Test Suite Output
  • Distributions and performance data from the most recent build.
• Development Log
• Legal Information

Project Definitions:

• Integer: 64 bit signed long long int.
  • Input & Output Range: (-2**63, 2**63) or approximately +/- 9.2 billion billion.
  • Minimum: -9223372036854775807
  • Maximum: 9223372036854775807
• Float: 64 bit double precision real number.
  • Minimum: -1.7976931348623157e+308
  • Maximum: 1.7976931348623157e+308
  • Epsilon Below Zero: -5e-324
  • Epsilon Above Zero: 5e-324
• Value: Any python object that can be put inside a list: str, int, and lambda to name a few. Almost anything.
• Callable: Any function, method or lambda.
• Sequence: Any object that can be converted into a list.
  • List, Tuple, Set, etc...
  • Comprehensions and Generators that produce Sequences also qualify.
• Array: List or tuple.
  • Must be indexed like a list.
  • List comprehensions are ok, but sets and generators are not indexed.
  • All arrays are sequences but not all sequences are arrays.
  • Classes that wrap a list will take any Sequence or Array and copy it or convert it as needed.
  • Functions that operate on a list will require an Array.
• Pair: Sequence of two values.
• Table: Sequence of Pairs.
  • List of lists of two values each.
  • Tuple of tuples of two values each.
  • Generators that produce Tables also qualify.
  • The result of zip(list_1, list_2) also qualifies.
• Matrix: Dictionary of Sequences.
  • Generators that produce Matrices also qualify.

Random Value Classes

TruffleShuffle

TruffleShuffle(list_of_values: Sequence) -> callable

• The input Sequence can be any list like object (list, set, tuple or generator).
• The input Sequence must not be empty. Values can be any python object.
• The returned callable produces a random value from the list with a wide uniform distribution.

TruffleShuffle, Basic Use Case

from Fortuna import TruffleShuffle


list_of_values = [1, 2, 3, 4, 5, 6]

truffle_shuffle = TruffleShuffle(list_of_values)

print(truffle_shuffle())  # prints a random value from the list_of_values.

Wide Uniform Sequence: "Wide" refers to the average distance between consecutive occurrences of the same item in the output sequence. The goal of this type of distribution is to keep the output sequence free of clumps while maintaining randomness and the uniform probability of each value.

This is not the same as a flat uniform distribution. The two distributions will be statistically similar, but the output sequences are very different. For a more general solution that offers several statistical distributions, please refer to QuantumMonty. For a more custom solution featuring discrete rarity refer to RelativeWeightedChoice and its counterpart CumulativeWeightedChoice.

Micro-shuffle: This is the hallmark of TruffleShuffle and how it creates a wide uniform distribution efficiently. While adjacent duplicates are forbidden, nearly consecutive occurrences of the same item are also required to be extremely rare with respect to the size of the set. This gives rise to output sequences that seem less mechanical than other random sequences. Somehow more and less random at the same time, almost human-like?

Automatic Flattening: TruffleShuffle and all higher-order Fortuna classes will recursively unpack callable objects returned from the data set at call time. Automatic flattening is dynamic, lazy, fault tolerant and on by default. Un-callable objects or those that require arguments will be returned in an uncalled state without error. A callable object can be any class, function, method or lambda. Mixing callable objects with un-callable objects is fully supported. Nested callable objects are fully supported. It's lambda all the way down.

To disable automatic flattening, pass the optional argument flat=False during instantiation.

Please review the code examples of each section. If higher-order functions and lambdas make your head spin, concentrate only on the first example of each section. Because lambda(lambda) -> lambda fixes everything for arbitrary values of 'because', 'fixes' and 'everything'.

Flattening

from Fortuna import TruffleShuffle


flatted = TruffleShuffle([lambda: 1, lambda: 2])
print(flatted())  # will print the value 1 or 2

un_flat = TruffleShuffle([lambda: 1, lambda: 2], flat=False)
print(un_flat()())  # will print the value 1 or 2, mind the double-double parenthesis

auto_un_flat = TruffleShuffle([lambda x: x, lambda x: x + 1])
# flat=False is not required here because the lambdas can't be called without input x satisfied.
print(auto_un_flat()(1))  # will print the value 1 or 2, mind the double-double parenthesis

Mixing Static Objects with Callable Objects

from Fortuna import TruffleShuffle


mixed_flat = TruffleShuffle([1, lambda: 2])
print(mixed_flat())  # will print 1 or 2

mixed_un_flat = TruffleShuffle([1, lambda: 2], flat=False) # not recommended.
print(mixed_flat())  # will print 1 or <lambda at some_address>
# This pattern is not recommended because you wont know the nature of what you get back.
# This is almost always not what you want, and always messy.

Dynamic Strings

To successfully express a dynamic string, at least one level of indirection is required. Without an indirection the f-string would collapse into a static string too soon.

WARNING: The following example features a higher order function that takes a tuple of lambdas and returns a higher order function that returns a random lambda that returns a dynamic f-string.

from Fortuna import TruffleShuffle, d


# d is a simple dice function.
brainiac = TruffleShuffle((
    lambda: f"A{d(2)}",
    lambda: f"B{d(4)}",
    lambda: f"C{d(6)}",
))

print(brainiac())  # prints a random dynamic string.

QuantumMonty

QuantumMonty(some_list: Sequence) -> callable

• The input Sequence can be any list like object (list, set, tuple or generator).
• The input Sequence must not be empty. Values can be any python object.
• The returned callable will produce random values from the list using the selected distribution model or "monty".
• The default monty is the Quantum Monty Algorithm.

from Fortuna import QuantumMonty


list_of_values = [1, 2, 3, 4, 5, 6]
quantum_monty = QuantumMonty(list_of_values)

print(quantum_monty())          # prints a random value from the list_of_values.
                                # uses the default Quantum Monty Algorithm.

print(quantum_monty.uniform())  # prints a random value from the list_of_values.
                                # uses the "uniform" monty: a flat uniform distribution.
                                # equivalent to random.choice(list_of_values) but better.

The QuantumMonty class represents a diverse collection of strategies for producing random values from a sequence where the output distribution is based on the method you choose. Generally speaking, each value in the sequence will have a probability that is based on its position in the sequence. For example: the "front" monty produces random values where the beginning of the sequence is geometrically more common than the back. Given enough samples the "front" monty will always converge to a 45 degree slope down for any list of unique values.

There are three primary method families: geometric, gaussian, and poisson. Each family has three base methods; 'front', 'middle', 'back', plus a 'quantum' method that incorporates all three base methods. The quantum algorithms for each family produce distributions by overlapping the probability waves of the other methods in their family. The Quantum Monty Algorithm incorporates all nine base methods.

In addition to the thirteen positional methods that are core to QuantumMonty, it also implements a uniform distribution as a simple base case.

Automatic Flattening: All higher-order Fortuna classes will recursively unpack callable objects returned from the data set at call time. Automatic flattening is dynamic, lazy, fault tolerant and on by default. Un-callable objects or those that require arguments will be returned in an uncalled state without error.

import Fortuna


quantum_monty = Fortuna.QuantumMonty(
    ["Alpha", "Beta", "Delta", "Eta", "Gamma", "Kappa", "Zeta"]
)

""" Each of the following methods will return a random value from the sequence.
Each method has its own unique distribution model for the same data set. """

""" Flat Base Case """
quantum_monty.uniform()             # Flat Uniform Distribution

""" Geometric Positional """
quantum_monty.front()               # Geometric Descending, Triangle
quantum_monty.middle()              # Geometric Median Peak, Equilateral Triangle
quantum_monty.back()                # Geometric Ascending, Triangle
quantum_monty.quantum()             # Geometric Overlay, Saw Tooth

""" Gaussian Positional """
quantum_monty.front_gauss()         # Exponential Gamma
quantum_monty.middle_gauss()        # Scaled Gaussian
quantum_monty.back_gauss()          # Reversed Gamma
quantum_monty.quantum_gauss()       # Gaussian Overlay

""" Poisson Positional """
quantum_monty.front_poisson()       # 1/3 Mean Poisson
quantum_monty.middle_poisson()      # 1/2 Mean Poisson
quantum_monty.back_poisson()        # 2/3 Mean Poisson
quantum_monty.quantum_poisson()     # Poisson Overlay

""" Quantum Monty Algorithm """
quantum_monty.quantum_monty()       # Quantum Monty Algorithm

Weighted Choice: Custom Rarity

Weighted Choice offers two strategies for selecting random values from a sequence where programmable rarity is desired. Both produce a custom distribution of values based on the weights of the values.

Flatten: Both will recursively unpack callable objects returned from the data set. Callable objects that require arguments are returned in an uncalled state. To disable this behavior pass the optional argument flat=False during instantiation. By default flat=True.

• Constructor takes a copy of a sequence of weighted value pairs... [(weight, value), ... ]
• Automatically optimizes the sequence for correctness and optimal call performance for large data sets.
• The sequence must not be empty, and each pair must contain a weight and a value.
• Weights must be positive integers.
• Values can be any Python object that can be passed around... string, int, list, function etc.
• Performance scales by some fraction of the length of the sequence.

Automatic Flattening: All higher-order Fortuna classes will recursively unpack callable objects returned from the data set at call time. Automatic flattening is dynamic, lazy, fault tolerant and on by default. Un-callable objects or those that require arguments will be returned in an uncalled state without error.

The following examples produce equivalent distributions with comparable performance. The choice to use one strategy over the other is purely about which one suits you or your data best. Relative weights are easier to understand at a glance. However, many RPG Treasure Tables map rather nicely to a cumulative weighted strategy.

Cumulative Weight Strategy

CumulativeWeightedChoice(weighted_table: Table) -> callable

Note: Logic dictates Cumulative Weights must be unique!

from Fortuna import CumulativeWeightedChoice


cum_weighted_choice = CumulativeWeightedChoice([
    (7, "Apple"),
    (11, "Banana"),
    (13, "Cherry"),
    (23, "Grape"),
    (26, "Lime"),
    (30, "Orange"),  # same as rel weight 4 because 30 - 26 = 4
])

print(cum_weighted_choice())  # prints a weighted random value

Relative Weight Strategy

RelativeWeightedChoice(weighted_table: Table) -> callable

from Fortuna import RelativeWeightedChoice


population = ["Apple", "Banana", "Cherry", "Grape", "Lime", "Orange"]
rel_weights = [7, 4, 2, 10, 3, 4]  # Alternate zip setup.
rel_weighted_choice = RelativeWeightedChoice(zip(rel_weights, population))

print(rel_weighted_choice())  # prints a weighted random value

FlexCat

FlexCat(dict_of_lists: Matrix) -> callable

FlexCat is a 2d QuantumMonty.

Rather than taking a sequence, FlexCat takes a Matrix: a dictionary of sequences. When the the instance is called it returns a random value from a random sequence.

The constructor takes two optional keyword arguments to specify the algorithms to be used to make random selections. The algorithm specified for selecting a key need not be the same as the one for selecting values. An optional key may be provided at call time to bypass the random key selection and select a random value from that category. Keys passed in this way must match a key in the Matrix.

By default, FlexCat will use key_bias="front" and val_bias="truffle_shuffle", this will make the top of the data structure geometrically more common than the bottom and it will truffle shuffle the sequence values. This config is known as Top Cat, it produces a descending-step distribution. Many other combinations are available.

Automatic Flattening: All higher-order Fortuna classes will recursively unpack callable objects returned from the data set at call time. Automatic flattening is dynamic, lazy, fault tolerant and on by default. Un-callable objects or those that require arguments will be returned in an uncalled state without error.

Algorithm Options: See QuantumMonty & TruffleShuffle for more details.

• 'front', Geometric Descending
• 'middle', Geometric Median Peak
• 'back', Geometric Ascending
• 'quantum', Geometric Overlay
• 'front_gauss', Exponential Gamma
• 'middle_gauss', Scaled Gaussian
• 'back_gauss', Reversed Gamma
• 'quantum_gauss', Gaussian Overlay
• 'front_poisson', 1/3 Mean Poisson
• 'middle_poisson', 1/2 Mean Poisson
• 'back_poisson', 2/3 Mean Poisson
• 'quantum_poisson', Poisson Overlay
• 'quantum_monty', Quantum Monty Algorithm
• 'uniform', uniform flat distribution
• 'truffle_shuffle', TruffleShuffle, wide uniform distribution

from Fortuna import FlexCat

matrix_data = {
    "Cat_A": ("A1", "A2", "A3", "A4", "A5"),
    "Cat_B": ("B1", "B2", "B3", "B4", "B5"),
    "Cat_C": ("C1", "C2", "C3", "C4", "C5"),
}
flex_cat = FlexCat(matrix_data, key_bias="front", val_bias="back")

flex_cat()          # returns a random "back" value from a random "front" category
flex_cat("Cat_B")   # returns a random "back" value specifically from "Cat_B"

Fortuna Functions

Random Numbers

• Fortuna.randbelow(number: int) -> int

  • Returns a random integer in the exclusive range:
    • [0, number) for positive values.
    • (number, 0] for negative values.
    • Always returns zero when the input is zero
  • Flat uniform distribution.

• Fortuna.randint(left_limit: int, right_limit: int) -> int

  • Fault-tolerant, efficient version of random.randint()
  • Returns a random integer in the range [left_limit, right_limit]
  • randint(1, 10) -> [1, 10]
  • randint(10, 1) -> [1, 10] same as above.
  • Flat uniform distribution.

• Fortuna.randrange(start: int, stop: int = 0, step: int = 1) -> int

  • Fault-tolerant, efficient version of random.randrange()
  • Returns a random integer in the range [A, B) by increments of C.
  • randrange(2, 11, 2) -> [2, 10] by 2 even numbers from 2 to 10.
  • randrange(10, 1, 0) -> [10] a step size or range size of zero always returns the first parameter.
  • Flat uniform distribution.

• Fortuna.d(sides: int) -> int

  • Represents a single die roll of a given size die.
  • Returns a random integer in the range [1, sides].
  • Flat uniform distribution.

• Fortuna.dice(rolls: int, sides: int) -> int

  • Returns a random integer in range [X, Y] where X = rolls and Y = rolls * sides.
  • The return value represents the sum of multiple rolls of the same size die.
  • Geometric distribution based on the number and size of the dice rolled.
  • Complexity scales primarily with the number of rolls, not the size of the dice.

• Fortuna.plus_or_minus(number: int) -> int

  • Returns a random integer in range [-number, number].
  • Flat uniform distribution.

• Fortuna.plus_or_minus_linear(number: int) -> int

  • Returns a random integer in range [-number, number].
  • Linear geometric, triangle distribution.

• binomial(number_of_trials: int, probability: float) -> int

• negative_binomial(trial_successes: int, probability: float) -> int

• geometric(probability: float) -> int

• poisson(mean: float) -> int

• discrete(count: int, xmin: int, xmax: int) -> int

Random Float Functions

• random() -> float
• uniform(a: float, b: float) -> float
• expovariate(lambd: float) -> float
• gammavariate(alpha, beta) -> float
• weibullvariate(alpha, beta) -> float
• betavariate(alpha, beta) -> float
• paretovariate(alpha) -> float
• gauss(mu: float, sigma: float) -> float
• normalvariate(mu: float, sigma: float) -> float
• lognormvariate(mu: float, sigma: float) -> float
• vonmisesvariate(mu: float, kappa: float) -> float
• triangular(low: float, high: float, mode: float = None)
• extreme_value(location: float, scale: float) -> float
• chi_squared(degrees_of_freedom: float) -> float
• cauchy(location: float, scale: float) -> float
• fisher_f(degrees_of_freedom_1: float, degrees_of_freedom_2: float) -> float
• student_t(degrees_of_freedom: float) -> float

Random Truth

• Fortuna.percent_true(truth_factor: float = 50.0) -> bool
  • Always returns False if num is 0.0 or less
  • Always returns True if num is 100.0 or more.
  • Produces True or False based truth_factor: the probability of True as a percentage.

Random Shuffle Functions

• shuffle(array: list) -> None
• knuth(array: list) -> None
• fisher_yates(array: list) -> None

Test Suite Functions

• distribution_timer(func: staticmethod, *args, **kwargs) -> None
• quick_test()

Fortuna Distribution and Performance Test Suite

Fortuna Test Suite: RNG Storm Engine

TruffleShuffle
Output Analysis: TruffleShuffle([4, 8, 5, 0, 3, 9, 6, 2, 1, 7], flat=True)()
Approximate Single Execution Time: Min: 406ns, Mid: 437ns, Max: 1031ns
Raw Samples: 3, 0, 1, 8, 6
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 5
 Maximum: 9
 Mean: 4.514
 Std Deviation: 2.8800405315457516
Sample Distribution:
 0: 9.98%
 1: 10.27%
 2: 9.69%
 3: 9.98%
 4: 9.53%
 5: 10.11%
 6: 10.17%
 7: 10.1%
 8: 10.11%
 9: 10.06%


QuantumMonty([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
Output Distribution: QuantumMonty.uniform()
Approximate Single Execution Time: Min: 156ns, Mid: 187ns, Max: 593ns
Raw Samples: 3, 8, 9, 8, 4
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 5
 Maximum: 9
 Mean: 4.5303
 Std Deviation: 2.854382010114618
Sample Distribution:
 0: 9.29%
 1: 10.17%
 2: 9.89%
 3: 10.18%
 4: 10.33%
 5: 9.72%
 6: 10.57%
 7: 9.84%
 8: 9.77%
 9: 10.24%

Output Distribution: QuantumMonty.front()
Approximate Single Execution Time: Min: 250ns, Mid: 281ns, Max: 1125ns
Raw Samples: 9, 0, 4, 0, 0
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 3
 Maximum: 9
 Mean: 2.9621
 Std Deviation: 2.4628175200395384
Sample Distribution:
 0: 19.14%
 1: 16.62%
 2: 13.89%
 3: 12.66%
 4: 10.75%
 5: 8.91%
 6: 7.35%
 7: 5.16%
 8: 3.62%
 9: 1.9%

Output Distribution: QuantumMonty.back()
Approximate Single Execution Time: Min: 250ns, Mid: 281ns, Max: 1062ns
Raw Samples: 4, 2, 5, 7, 8
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 6
 Maximum: 9
 Mean: 5.9948
 Std Deviation: 2.4601581652039735
Sample Distribution:
 0: 1.9%
 1: 3.49%
 2: 5.56%
 3: 7.51%
 4: 9.12%
 5: 10.73%
 6: 12.89%
 7: 14.11%
 8: 16.11%
 9: 18.58%

Output Distribution: QuantumMonty.middle()
Approximate Single Execution Time: Min: 250ns, Mid: 281ns, Max: 406ns
Raw Samples: 5, 4, 7, 9, 6
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 4
 Maximum: 9
 Mean: 4.4764
 Std Deviation: 2.2352052823544923
Sample Distribution:
 0: 3.52%
 1: 6.45%
 2: 10.68%
 3: 13.64%
 4: 16.31%
 5: 16.49%
 6: 12.98%
 7: 9.57%
 8: 6.89%
 9: 3.47%

Output Distribution: QuantumMonty.quantum()
Approximate Single Execution Time: Min: 250ns, Mid: 312ns, Max: 937ns
Raw Samples: 4, 3, 3, 1, 6
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 5
 Maximum: 9
 Mean: 4.5274
 Std Deviation: 2.696956914312827
Sample Distribution:
 0: 7.85%
 1: 8.9%
 2: 9.87%
 3: 11.05%
 4: 11.96%
 5: 12.27%
 6: 10.73%
 7: 9.99%
 8: 8.97%
 9: 8.41%

Output Distribution: QuantumMonty.front_gauss()
Approximate Single Execution Time: Min: 187ns, Mid: 187ns, Max: 562ns
Raw Samples: 0, 0, 0, 0, 2
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 0
 Maximum: 8
 Mean: 0.5855
 Std Deviation: 0.9393497686159186
Sample Distribution:
 0: 62.56%
 1: 23.63%
 2: 8.94%
 3: 3.2%
 4: 1.19%
 5: 0.29%
 6: 0.11%
 7: 0.07%
 8: 0.01%

Output Distribution: QuantumMonty.back_gauss()
Approximate Single Execution Time: Min: 187ns, Mid: 187ns, Max: 625ns
Raw Samples: 9, 9, 8, 9, 6
Test Samples: 10000
Sample Statistics:
 Minimum: 1
 Median: 9
 Maximum: 9
 Mean: 8.427
 Std Deviation: 0.9391268263230436
Sample Distribution:
 1: 0.02%
 2: 0.05%
 3: 0.11%
 4: 0.4%
 5: 1.08%
 6: 3.16%
 7: 8.64%
 8: 23.05%
 9: 63.49%

Output Distribution: QuantumMonty.middle_gauss()
Approximate Single Execution Time: Min: 187ns, Mid: 250ns, Max: 406ns
Raw Samples: 6, 3, 4, 4, 3
Test Samples: 10000
Sample Statistics:
 Minimum: 1
 Median: 5
 Maximum: 8
 Mean: 4.5004
 Std Deviation: 1.043124465663176
Sample Distribution:
 1: 0.17%
 2: 2.03%
 3: 13.92%
 4: 33.65%
 5: 34.37%
 6: 13.55%
 7: 2.18%
 8: 0.13%

Output Distribution: QuantumMonty.quantum_gauss()
Approximate Single Execution Time: Min: 187ns, Mid: 218ns, Max: 625ns
Raw Samples: 8, 0, 9, 0, 9
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 5
 Maximum: 9
 Mean: 4.5356
 Std Deviation: 3.359116104885422
Sample Distribution:
 0: 21.07%
 1: 7.58%
 2: 3.68%
 3: 5.5%
 4: 11.57%
 5: 11.64%
 6: 5.95%
 7: 3.52%
 8: 8.11%
 9: 21.38%

Output Distribution: QuantumMonty.front_poisson()
Approximate Single Execution Time: Min: 218ns, Mid: 250ns, Max: 625ns
Raw Samples: 6, 3, 2, 1, 3
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 3
 Maximum: 9
 Mean: 3.1899
 Std Deviation: 1.7746979870655542
Sample Distribution:
 0: 4.1%
 1: 13.3%
 2: 20.61%
 3: 22.25%
 4: 17.89%
 5: 11.45%
 6: 5.9%
 7: 2.96%
 8: 1.07%
 9: 0.47%

Output Distribution: QuantumMonty.back_poisson()
Approximate Single Execution Time: Min: 218ns, Mid: 250ns, Max: 1656ns
Raw Samples: 6, 9, 4, 6, 8
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 6
 Maximum: 9
 Mean: 5.8557
 Std Deviation: 1.7515662443741153
Sample Distribution:
 0: 0.29%
 1: 1.0%
 2: 2.62%
 3: 5.81%
 4: 11.64%
 5: 18.06%
 6: 21.36%
 7: 21.05%
 8: 14.0%
 9: 4.17%

Output Distribution: QuantumMonty.middle_poisson()
Approximate Single Execution Time: Min: 218ns, Mid: 250ns, Max: 375ns
Raw Samples: 4, 8, 2, 3, 2
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 5
 Maximum: 9
 Mean: 4.5386
 Std Deviation: 2.220270929481362
Sample Distribution:
 0: 2.28%
 1: 7.27%
 2: 11.35%
 3: 14.0%
 4: 14.33%
 5: 14.23%
 6: 14.54%
 7: 12.3%
 8: 7.22%
 9: 2.48%

Output Distribution: QuantumMonty.quantum_poisson()
Approximate Single Execution Time: Min: 250ns, Mid: 250ns, Max: 437ns
Raw Samples: 2, 6, 4, 6, 8
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 4
 Maximum: 9
 Mean: 4.4762
 Std Deviation: 2.197069928706677
Sample Distribution:
 0: 2.19%
 1: 7.3%
 2: 12.22%
 3: 14.23%
 4: 14.08%
 5: 14.93%
 6: 14.35%
 7: 11.64%
 8: 6.9%
 9: 2.16%

Output Distribution: QuantumMonty.quantum_monty()
Approximate Single Execution Time: Min: 250ns, Mid: 281ns, Max: 562ns
Raw Samples: 5, 2, 2, 3, 6
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 4
 Maximum: 9
 Mean: 4.4721
 Std Deviation: 2.808417759349756
Sample Distribution:
 0: 10.7%
 1: 8.29%
 2: 8.6%
 3: 10.45%
 4: 12.5%
 5: 12.4%
 6: 10.14%
 7: 8.53%
 8: 7.69%
 9: 10.7%


Weighted Choice
Base Case
Output Distribution: Random.choices([36, 30, 24, 18], cum_weights=[1, 10, 100, 1000])
Approximate Single Execution Time: Min: 1687ns, Mid: 1859ns, Max: 2906ns
Raw Samples: [18], [18], [18], [18], [18]
Test Samples: 10000
Sample Statistics:
 Minimum: 18
 Median: 18
 Maximum: 36
 Mean: 18.6684
 Std Deviation: 2.107720495836404
Sample Distribution:
 18: 89.98%
 24: 9.0%
 30: 0.92%
 36: 0.1%

Output Analysis: CumulativeWeightedChoice([(1, 36), (10, 30), (100, 24), (1000, 18)], flat=True)()
Approximate Single Execution Time: Min: 281ns, Mid: 312ns, Max: 468ns
Raw Samples: 18, 18, 18, 18, 18
Test Samples: 10000
Sample Statistics:
 Minimum: 18
 Median: 18
 Maximum: 36
 Mean: 18.6642
 Std Deviation: 2.0910465340495787
Sample Distribution:
 18: 89.97%
 24: 9.1%
 30: 0.82%
 36: 0.11%

Base Case
Output Distribution: Random.choices([36, 30, 24, 18], weights=[1, 9, 90, 900])
Approximate Single Execution Time: Min: 2125ns, Mid: 2156ns, Max: 2562ns
Raw Samples: [18], [18], [18], [18], [24]
Test Samples: 10000
Sample Statistics:
 Minimum: 18
 Median: 18
 Maximum: 36
 Mean: 18.66
 Std Deviation: 2.069016211344967
Sample Distribution:
 18: 89.97%
 24: 9.14%
 30: 0.81%
 36: 0.08%

Output Analysis: RelativeWeightedChoice([(1, 36), (9, 30), (90, 24), (900, 18)], flat=True)()
Approximate Single Execution Time: Min: 281ns, Mid: 312ns, Max: 468ns
Raw Samples: 18, 18, 18, 18, 18
Test Samples: 10000
Sample Statistics:
 Minimum: 18
 Median: 18
 Maximum: 36
 Mean: 18.6966
 Std Deviation: 2.163611924920032
Sample Distribution:
 18: 89.66%
 24: 9.17%
 30: 1.07%
 36: 0.1%

Output Distribution: cumulative_weighted_choice([(1, 36), (10, 30), (100, 24), (1000, 18)])
Approximate Single Execution Time: Min: 187ns, Mid: 218ns, Max: 562ns
Raw Samples: 18, 18, 18, 18, 24
Test Samples: 10000
Sample Statistics:
 Minimum: 18
 Median: 18
 Maximum: 36
 Mean: 18.6378
 Std Deviation: 2.0330333205454956
Sample Distribution:
 18: 90.3%
 24: 8.83%
 30: 0.81%
 36: 0.06%


FlexCat
Output Analysis: FlexCat({1: [1, 2, 3], 2: [10, 20, 30], 3: [100, 200, 300]}, key_bias='front', val_bias='truffle_shuffle', flat=True)()
Approximate Single Execution Time: Min: 781ns, Mid: 812ns, Max: 1093ns
Raw Samples: 200, 20, 100, 3, 1
Test Samples: 10000
Sample Statistics:
 Minimum: 1
 Median: 10
 Maximum: 300
 Mean: 41.4995
 Std Deviation: 79.2849141357355
Sample Distribution:
 1: 16.21%
 2: 16.69%
 3: 16.42%
 10: 11.22%
 20: 10.96%
 30: 11.59%
 100: 5.66%
 200: 5.69%
 300: 5.56%


Random Integers
Base Case
Output Distribution: Random.randrange(10)
Approximate Single Execution Time: Min: 843ns, Mid: 906ns, Max: 2531ns
Raw Samples: 5, 6, 7, 9, 3
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 5
 Maximum: 9
 Mean: 4.4852
 Std Deviation: 2.877604736738889
Sample Distribution:
 0: 10.15%
 1: 10.13%
 2: 10.08%
 3: 10.22%
 4: 9.31%
 5: 10.05%
 6: 9.95%
 7: 10.15%
 8: 10.31%
 9: 9.65%

Output Distribution: randbelow(10)
Approximate Single Execution Time: Min: 31ns, Mid: 62ns, Max: 812ns
Raw Samples: 8, 0, 4, 8, 5
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 4
 Maximum: 9
 Mean: 4.4767
 Std Deviation: 2.89044850832149
Sample Distribution:
 0: 10.29%
 1: 10.25%
 2: 9.93%
 3: 10.39%
 4: 9.4%
 5: 9.98%
 6: 9.54%
 7: 10.22%
 8: 9.89%
 9: 10.11%

Base Case
Output Distribution: Random.randint(-5, 5)
Approximate Single Execution Time: Min: 1156ns, Mid: 1187ns, Max: 2562ns
Raw Samples: -3, -1, 2, -1, 1
Test Samples: 10000
Sample Statistics:
 Minimum: -5
 Median: 0
 Maximum: 5
 Mean: 0.0101
 Std Deviation: 3.182862084838913
Sample Distribution:
 -5: 8.96%
 -4: 9.34%
 -3: 9.24%
 -2: 9.05%
 -1: 9.06%
 0: 8.98%
 1: 8.79%
 2: 8.75%
 3: 9.04%
 4: 9.31%
 5: 9.48%

Output Distribution: randint(-5, 5)
Approximate Single Execution Time: Min: 62ns, Mid: 62ns, Max: 156ns
Raw Samples: -5, -5, 0, -2, -5
Test Samples: 10000
Sample Statistics:
 Minimum: -5
 Median: 0
 Maximum: 5
 Mean: -0.0136
 Std Deviation: 3.1388533384068777
Sample Distribution:
 -5: 8.79%
 -4: 9.29%
 -3: 9.54%
 -2: 8.58%
 -1: 9.2%
 0: 9.03%
 1: 9.12%
 2: 9.57%
 3: 9.68%
 4: 8.57%
 5: 8.63%

Base Case
Output Distribution: Random.randrange(1, 21, 2)
Approximate Single Execution Time: Min: 1312ns, Mid: 1375ns, Max: 2625ns
Raw Samples: 3, 5, 3, 7, 3
Test Samples: 10000
Sample Statistics:
 Minimum: 1
 Median: 11
 Maximum: 19
 Mean: 10.0916
 Std Deviation: 5.728009291983115
Sample Distribution:
 1: 9.76%
 3: 9.78%
 5: 9.86%
 7: 9.84%
 9: 9.62%
 11: 10.42%
 13: 9.98%
 15: 10.85%
 17: 9.86%
 19: 10.03%

Output Distribution: randrange(1, 21, 2)
Approximate Single Execution Time: Min: 62ns, Mid: 93ns, Max: 156ns
Raw Samples: 9, 13, 13, 13, 15
Test Samples: 10000
Sample Statistics:
 Minimum: 1
 Median: 11
 Maximum: 19
 Mean: 10.013
 Std Deviation: 5.758467417177896
Sample Distribution:
 1: 10.33%
 3: 9.41%
 5: 10.2%
 7: 10.0%
 9: 10.05%
 11: 9.94%
 13: 9.99%
 15: 9.69%
 17: 10.34%
 19: 10.05%

Output Distribution: d(10)
Approximate Single Execution Time: Min: 62ns, Mid: 62ns, Max: 500ns
Raw Samples: 9, 2, 10, 6, 3
Test Samples: 10000
Sample Statistics:
 Minimum: 1
 Median: 5
 Maximum: 10
 Mean: 5.4937
 Std Deviation: 2.8975506708233763
Sample Distribution:
 1: 10.08%
 2: 10.35%
 3: 10.11%
 4: 9.98%
 5: 9.58%
 6: 10.33%
 7: 9.19%
 8: 9.73%
 9: 10.21%
 10: 10.44%

Output Distribution: dice(2, 6)
Approximate Single Execution Time: Min: 62ns, Mid: 93ns, Max: 656ns
Raw Samples: 7, 7, 3, 7, 7
Test Samples: 10000
Sample Statistics:
 Minimum: 2
 Median: 7
 Maximum: 12
 Mean: 7.0092
 Std Deviation: 2.4034751983956335
Sample Distribution:
 2: 2.56%
 3: 5.54%
 4: 8.21%
 5: 11.45%
 6: 13.83%
 7: 16.91%
 8: 13.67%
 9: 10.89%
 10: 8.46%
 11: 5.99%
 12: 2.49%

Output Distribution: plus_or_minus(5)
Approximate Single Execution Time: Min: 62ns, Mid: 62ns, Max: 781ns
Raw Samples: -1, -4, 1, 2, 2
Test Samples: 10000
Sample Statistics:
 Minimum: -5
 Median: 0
 Maximum: 5
 Mean: -0.0197
 Std Deviation: 3.166783030375802
Sample Distribution:
 -5: 8.97%
 -4: 9.44%
 -3: 9.39%
 -2: 9.2%
 -1: 8.63%
 0: 9.08%
 1: 9.02%
 2: 9.13%
 3: 8.89%
 4: 9.36%
 5: 8.89%

Output Distribution: binomial(4, 0.5)
Approximate Single Execution Time: Min: 156ns, Mid: 156ns, Max: 281ns
Raw Samples: 3, 3, 2, 1, 3
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 2
 Maximum: 4
 Mean: 2.005
 Std Deviation: 0.9870523933625429
Sample Distribution:
 0: 5.86%
 1: 24.88%
 2: 38.16%
 3: 25.1%
 4: 6.0%

Output Distribution: negative_binomial(5, 0.75)
Approximate Single Execution Time: Min: 93ns, Mid: 125ns, Max: 312ns
Raw Samples: 1, 3, 3, 1, 2
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 1
 Maximum: 10
 Mean: 1.655
 Std Deviation: 1.4750568054342603
Sample Distribution:
 0: 23.77%
 1: 29.91%
 2: 22.03%
 3: 13.21%
 4: 6.45%
 5: 2.7%
 6: 1.32%
 7: 0.32%
 8: 0.19%
 9: 0.08%
 10: 0.02%

Output Distribution: geometric(0.75)
Approximate Single Execution Time: Min: 31ns, Mid: 62ns, Max: 406ns
Raw Samples: 0, 0, 0, 0, 0
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 0
 Maximum: 6
 Mean: 0.3302
 Std Deviation: 0.6551418785943307
Sample Distribution:
 0: 74.94%
 1: 19.08%
 2: 4.41%
 3: 1.2%
 4: 0.34%
 5: 0.02%
 6: 0.01%

Output Distribution: poisson(4.5)
Approximate Single Execution Time: Min: 93ns, Mid: 125ns, Max: 718ns
Raw Samples: 5, 1, 1, 6, 2
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 4
 Maximum: 15
 Mean: 4.5301
 Std Deviation: 2.143024322149549
Sample Distribution:
 0: 1.15%
 1: 5.03%
 2: 11.03%
 3: 16.83%
 4: 18.66%
 5: 16.8%
 6: 12.69%
 7: 8.79%
 8: 4.95%
 9: 2.3%
 10: 1.03%
 11: 0.46%
 12: 0.21%
 13: 0.05%
 14: 0.01%
 15: 0.01%

Output Distribution: discrete(7, 1, 30, 1)
Approximate Single Execution Time: Min: 406ns, Mid: 406ns, Max: 1312ns
Raw Samples: 5, 3, 3, 3, 6
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 4
 Maximum: 6
 Mean: 4.013
 Std Deviation: 1.7209088159211898
Sample Distribution:
 0: 3.62%
 1: 6.68%
 2: 10.32%
 3: 14.95%
 4: 18.25%
 5: 20.95%
 6: 25.23%


Random Floats
Output Distribution: random()
Approximate Single Execution Time: Min: 31ns, Mid: 62ns, Max: 93ns
Raw Samples: 0.5800464922493787, 0.043488866632812775, 0.3859588768371167, 0.9483497804889398, 0.5306540070010375
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 8.867019995467186e-05
 Median: (0.502485454928805, 0.5025552828547625)
 Maximum: 0.9999692057231605
 Mean: 0.49917873810390834
 Std Deviation: 0.29107651583413235
Post-processor Distribution using round method:
 0: 49.73%
 1: 50.27%

Output Distribution: uniform(0.0, 10.0)
Approximate Single Execution Time: Min: 31ns, Mid: 62ns, Max: 750ns
Raw Samples: 7.683740476726002, 9.112257793602874, 6.261677200248692, 2.68161504518201, 3.0361560487097154
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.0006271204327472748
 Median: (5.062511102027736, 5.0630253511783705)
 Maximum: 9.999646485915989
 Mean: 5.049980179323852
 Std Deviation: 2.901416912289138
Post-processor Distribution using floor method:
 0: 10.09%
 1: 9.29%
 2: 10.08%
 3: 10.26%
 4: 9.73%
 5: 10.36%
 6: 9.39%
 7: 9.97%
 8: 10.0%
 9: 10.83%

Output Distribution: expovariate(1.0)
Approximate Single Execution Time: Min: 31ns, Mid: 62ns, Max: 750ns
Raw Samples: 2.044791422815635, 1.0386588628457503, 0.30526375253255594, 0.17130910168862182, 1.006102205522561
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 4.973385005531503e-06
 Median: (0.6873287191294839, 0.6873564642122496)
 Maximum: 10.917165422193088
 Mean: 0.9950001220827994
 Std Deviation: 0.9904648080651394
Post-processor Distribution using floor method:
 0: 62.81%
 1: 24.13%
 2: 8.14%
 3: 3.11%
 4: 1.18%
 5: 0.44%
 6: 0.09%
 7: 0.07%
 8: 0.01%
 10: 0.02%

Output Distribution: gammavariate(2.0, 1.0)
Approximate Single Execution Time: Min: 93ns, Mid: 125ns, Max: 218ns
Raw Samples: 1.926573565330512, 1.428510478433571, 2.7330389786756197, 3.006561883726166, 1.0901161121027156
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.001191091237989772
 Median: (1.6869925853483823, 1.6871907479781751)
 Maximum: 11.439663216059733
 Mean: 2.005584879431955
 Std Deviation: 1.395623425106559
Post-processor Distribution using round method:
 0: 8.92%
 1: 34.73%
 2: 27.09%
 3: 15.43%
 4: 7.71%
 5: 3.64%
 6: 1.51%
 7: 0.6%
 8: 0.24%
 9: 0.08%
 10: 0.04%
 11: 0.01%

Output Distribution: weibullvariate(1.0, 1.0)
Approximate Single Execution Time: Min: 93ns, Mid: 93ns, Max: 250ns
Raw Samples: 2.5733534061575347, 0.0014765045026283606, 0.22121842103841668, 0.35362623203448945, 0.39939185217450446
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 1.6268418852022657e-05
 Median: (0.6847523818807449, 0.6847852460602326)
 Maximum: 8.235654817179471
 Mean: 0.9901923773201728
 Std Deviation: 0.9901515528423851
Post-processor Distribution using floor method:
 0: 64.03%
 1: 22.73%
 2: 8.49%
 3: 2.96%
 4: 1.05%
 5: 0.41%
 6: 0.26%
 7: 0.06%
 8: 0.01%

Output Distribution: betavariate(3.0, 3.0)
Approximate Single Execution Time: Min: 156ns, Mid: 187ns, Max: 1000ns
Raw Samples: 0.8917331579916562, 0.4636264518663151, 0.6508654934417588, 0.22319725992278755, 0.6254231021374439
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.023898932338302068
 Median: (0.49780200401673536, 0.4978118297934674)
 Maximum: 0.9803148496362412
 Mean: 0.49923547491357523
 Std Deviation: 0.18915337211317368
Post-processor Distribution using round method:
 0: 50.51%
 1: 49.49%

Output Distribution: paretovariate(4.0)
Approximate Single Execution Time: Min: 62ns, Mid: 93ns, Max: 312ns
Raw Samples: 1.627480878980606, 1.3487554529406793, 1.1821544411961245, 1.1373384120690586, 1.1457859805595632
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 1.0000015211597575
 Median: (1.1857605069832788, 1.1858898510877436)
 Maximum: 9.56685975652894
 Mean: 1.326264669119937
 Std Deviation: 0.4630862614994137
Post-processor Distribution using floor method:
 1: 93.89%
 2: 5.08%
 3: 0.61%
 4: 0.2%
 5: 0.07%
 6: 0.08%
 7: 0.06%
 9: 0.01%

Output Distribution: gauss(0.0, 1.0)
Approximate Single Execution Time: Min: 62ns, Mid: 93ns, Max: 812ns
Raw Samples: -1.6689154253827059, 2.24335243002752, -1.187248264616695, -0.2777899861560098, -0.31456910558065837
Test Samples: 10000
Pre-processor Statistics:
 Minimum: -3.5006094315128915
 Median: (0.021185934410276126, 0.021619492456612224)
 Maximum: 3.3266350559345987
 Mean: 0.006178195950939541
 Std Deviation: 0.9917787223515085
Post-processor Distribution using round method:
 -4: 0.01%
 -3: 0.53%
 -2: 5.69%
 -1: 24.36%
 0: 37.95%
 1: 25.04%
 2: 5.9%
 3: 0.52%

Output Distribution: normalvariate(0.0, 1.0)
Approximate Single Execution Time: Min: 62ns, Mid: 93ns, Max: 187ns
Raw Samples: -0.5735329587129836, -0.6672135228213479, 2.0602826184684746, -1.3282234609194108, 1.4696925734480908
Test Samples: 10000
Pre-processor Statistics:
 Minimum: -3.6135859002824002
 Median: (-0.011302420369202431, -0.011002550434201605)
 Maximum: 4.252040575161474
 Mean: -0.01941086513686669
 Std Deviation: 0.9936380155911713
Post-processor Distribution using round method:
 -4: 0.02%
 -3: 0.52%
 -2: 6.38%
 -1: 24.98%
 0: 37.97%
 1: 23.87%
 2: 5.72%
 3: 0.52%
 4: 0.02%

Output Distribution: lognormvariate(0.0, 0.5)
Approximate Single Execution Time: Min: 93ns, Mid: 93ns, Max: 718ns
Raw Samples: 3.7293729665455264, 1.9389746959485228, 0.9688237961464069, 1.0599587039817806, 0.7060794671167071
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.15155327939751997
 Median: (1.0066568125923447, 1.0066638044408405)
 Maximum: 6.574290056206128
 Mean: 1.1350491576201573
 Std Deviation: 0.6048203380048177
Post-processor Distribution using round method:
 0: 8.04%
 1: 71.25%
 2: 17.36%
 3: 2.74%
 4: 0.47%
 5: 0.09%
 6: 0.03%
 7: 0.02%

Output Distribution: vonmisesvariate(0, 0)
Approximate Single Execution Time: Min: 62ns, Mid: 93ns, Max: 187ns
Raw Samples: 0.020552987454550725, 3.180714221545409, 4.659009367442065, 5.564254519032381, 3.5595833122959752
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.0008371474004456611
 Median: (3.171370489150539, 3.1722657149837343)
 Maximum: 6.2822693775643215
 Mean: 3.144364752655393
 Std Deviation: 1.8096549638134425
Post-processor Distribution using floor method:
 0: 15.66%
 1: 16.52%
 2: 15.27%
 3: 15.73%
 4: 16.73%
 5: 15.44%
 6: 4.65%

Output Distribution: triangular(0.0, 10.0, 0.0)
Approximate Single Execution Time: Min: 31ns, Mid: 62ns, Max: 125ns
Raw Samples: 2.4700412929536952, 3.672628737609809, 3.338539978803998, 2.8700398961344584, 1.5870282689381543
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.0003708367176968874
 Median: (2.9276846793106714, 2.9277153654471078)
 Maximum: 9.869549682620763
 Mean: 3.33398171116572
 Std Deviation: 2.3701354758766024
Post-processor Distribution using floor method:
 0: 19.07%
 1: 17.56%
 2: 14.48%
 3: 12.72%
 4: 11.08%
 5: 8.74%
 6: 7.05%
 7: 5.41%
 8: 2.82%
 9: 1.07%

Output Distribution: extreme_value(0.0, 1.0)
Approximate Single Execution Time: Min: 62ns, Mid: 93ns, Max: 187ns
Raw Samples: 0.7056514468735201, -0.916581536106132, 0.22913636245854976, -1.5236394821687687, -0.3642494086593194
Test Samples: 10000
Pre-processor Statistics:
 Minimum: -2.2004522079539828
 Median: (0.3704415824039264, 0.37076007265322025)
 Maximum: 8.094561618952314
 Mean: 0.5834155760886909
 Std Deviation: 1.2850277722861412
Post-processor Distribution using round method:
 -2: 1.08%
 -1: 18.28%
 0: 35.21%
 1: 25.14%
 2: 12.08%
 3: 5.0%
 4: 2.07%
 5: 0.76%
 6: 0.27%
 7: 0.1%
 8: 0.01%

Output Distribution: chi_squared(1.0)
Approximate Single Execution Time: Min: 93ns, Mid: 125ns, Max: 281ns
Raw Samples: 1.0129768119802582, 4.914557707629436, 0.20114125166589553, 0.305603882224802, 2.4030352963677726
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 1.805332135790612e-09
 Median: (0.44174970712423706, 0.4420126089195971)
 Maximum: 14.458205846412724
 Mean: 0.9982183984548565
 Std Deviation: 1.436369503804896
Post-processor Distribution using <lambda> method:
 0: 68.53%
 1: 16.09%
 2: 7.55%
 3: 3.62%
 4: 1.83%
 5: 1.12%
 6: 0.59%
 7: 0.4%
 8: 0.2%
 9: 0.07%

Output Distribution: cauchy(0.0, 1.0)
Approximate Single Execution Time: Min: 62ns, Mid: 93ns, Max: 562ns
Raw Samples: -2.921281686246588, -1.0500628980385103, 1.1006468989825988, 0.632063201222543, -0.5649399556174318
Test Samples: 10000
Pre-processor Statistics:
 Minimum: -15450.41368191262
 Median: (0.030410924768096138, 0.03061868442733929)
 Maximum: 4591.941813716859
 Mean: -0.9362604103563443
 Std Deviation: 163.37592157494655
Post-processor Distribution using <lambda> method:
 0: 26.32%
 1: 11.44%
 2: 5.89%
 3: 3.81%
 4: 3.23%
 5: 3.07%
 6: 3.82%
 7: 5.76%
 8: 10.9%
 9: 25.76%

Output Distribution: fisher_f(8.0, 8.0)
Approximate Single Execution Time: Min: 156ns, Mid: 187ns, Max: 343ns
Raw Samples: 0.8098470368512319, 1.217651400724475, 0.6713018573996729, 1.5121908622540627, 0.9075475903089096
Test Samples: 10000
Pre-processor Statistics:
 Minimum: 0.03898416401414178
 Median: (0.9987218291088052, 0.9987333435378458)
 Maximum: 29.77068913546185
 Mean: 1.323288021228715
 Std Deviation: 1.234406249229726
Post-processor Distribution using <lambda> method:
 0: 50.15%
 1: 33.01%
 2: 10.34%
 3: 3.34%
 4: 1.59%
 5: 0.68%
 6: 0.44%
 7: 0.19%
 8: 0.13%
 9: 0.13%

Output Distribution: student_t(8.0)
Approximate Single Execution Time: Min: 125ns, Mid: 156ns, Max: 281ns
Raw Samples: 0.8317552688887871, -0.7070521826246058, -2.747842541211386e-05, -1.1209033294075401, 0.37818550316721766
Test Samples: 10000
Pre-processor Statistics:
 Minimum: -6.043268347043494
 Median: (0.018717718012266273, 0.018729300582745693)
 Maximum: 7.6827083627044335
 Mean: 0.02297590344939811
 Std Deviation: 1.1506335287280576
Post-processor Distribution using round method:
 -6: 0.04%
 -5: 0.09%
 -4: 0.25%
 -3: 1.25%
 -2: 6.36%
 -1: 23.04%
 0: 37.09%
 1: 22.9%
 2: 7.02%
 3: 1.53%
 4: 0.32%
 5: 0.08%
 6: 0.01%
 7: 0.01%
 8: 0.01%


Random Booleans
Output Distribution: percent_true(33.33)
Approximate Single Execution Time: Min: 31ns, Mid: 62ns, Max: 93ns
Raw Samples: False, False, False, True, True
Test Samples: 10000
Sample Statistics:
 Minimum: False
 Median: False
 Maximum: True
 Mean: 0.3361
 Std Deviation: 0.4723971908368963
Sample Distribution:
 False: 66.39%
 True: 33.61%


Random Shuffles
Base Case
Timer only: random.shuffle(some_list) of size 10:
Approximate Single Execution Time: Min: 6781ns, Mid: 6937ns, Max: 11281ns

Timer only: shuffle(some_list) of size 10:
Approximate Single Execution Time: Min: 343ns, Mid: 375ns, Max: 1187ns

Timer only: knuth(some_list) of size 10:
Approximate Single Execution Time: Min: 812ns, Mid: 843ns, Max: 1593ns

Timer only: fisher_yates(some_list) of size 10:
Approximate Single Execution Time: Min: 968ns, Mid: 1000ns, Max: 1687ns


Random Values
Base Case
Output Distribution: Random.choice([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
Approximate Single Execution Time: Min: 750ns, Mid: 812ns, Max: 2062ns
Raw Samples: 4, 3, 3, 8, 9
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 4
 Maximum: 9
 Mean: 4.4991
 Std Deviation: 2.8745130844279094
Sample Distribution:
 0: 9.87%
 1: 9.98%
 2: 10.38%
 3: 10.22%
 4: 9.59%
 5: 9.91%
 6: 9.85%
 7: 10.01%
 8: 10.28%
 9: 9.91%

Output Distribution: random_value([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
Approximate Single Execution Time: Min: 62ns, Mid: 62ns, Max: 156ns
Raw Samples: 5, 4, 1, 5, 0
Test Samples: 10000
Sample Statistics:
 Minimum: 0
 Median: 5
 Maximum: 9
 Mean: 4.5317
 Std Deviation: 2.8613657318464445
Sample Distribution:
 0: 9.81%
 1: 9.69%
 2: 10.0%
 3: 9.95%
 4: 9.71%
 5: 10.5%
 6: 10.03%
 7: 10.28%
 8: 10.12%
 9: 9.91%


-------------------------------------------------------------------------
Total Test Time: 1.942 seconds

Fortuna Development Log

Fortuna 2.1.1

• Small bug fixes.
• Test updates.

Fortuna 2.1.0, Major Feature Update

• Fortuna now includes the best of RNG and Pyewacket.

Fortuna 2.0.3

• Bug fix.

Fortuna 2.0.2

• Clarified some documentation.

Fortuna 2.0.1

• Fixed some typos.

Fortuna 2.0.0b1-10

• Total rebuild. New RNG Storm Engine.

Fortuna 1.26.7.1

• README updated.

Fortuna 1.26.7

• Small bug fix.

Fortuna 1.26.6

• Updated README to reflect recent changes to the test script.

Fortuna 1.26.5

• Fixed small bug in test script.

Fortuna 1.26.4

• Updated documentation for clarity.
• Fixed a minor typo in the test script.

Fortuna 1.26.3

• Clean build.

Fortuna 1.26.2

• Fixed some minor typos.

Fortuna 1.26.1

• Release.

Fortuna 1.26.0 beta 2

• Moved README and LICENSE files into fortuna_extras folder.

Fortuna 1.26.0 beta 1

• Dynamic version scheme implemented.
• The Fortuna Extension now requires the fortuna_extras package, previously it was optional.

Fortuna 1.25.4

• Fixed some minor typos in the test script.

Fortuna 1.25.3

• Since version 1.24 Fortuna requires Python 3.7 or higher. This patch corrects an issue where the setup script incorrectly reported requiring Python 3.6 or higher.

Fortuna 1.25.2

• Updated test suite.
• Major performance update for TruffleShuffle.
• Minor performance update for QuantumMonty & FlexCat: cycle monty.

Fortuna 1.25.1

• Important bug fix for TruffleShuffle, QuantumMonty and FlexCat.

Fortuna 1.25

• Full 64bit support.
• The Distribution & Performance Tests have been redesigned.
• Bloat Control: Two experimental features have been removed.
  • RandomWalk
  • CatWalk
• Bloat Control: Several utility functions have been removed from the top level API. These function remain in the Fortuna namespace for now, but may change in the future without warning.
  • stretch_bell, internal only.
  • min_max, not used anymore.
  • analytic_continuation, internal only.
  • flatten, internal only.

Fortuna 1.24.3

• Low level refactoring, non-breaking patch.

Fortuna 1.24.2

• Setup config updated to improve installation.

Fortuna 1.24.1

• Low level patch to avoid potential ADL issue. All low level function calls are now qualified.

Fortuna 1.24

• Documentation updated for even more clarity.
• Bloat Control: Two naïve utility functions that are no longer used in the module have been removed.
  • n_samples -> use a list comprehension instead. [f(x) for _ in range(n)]
  • bind -> use a lambda instead. lambda: f(x)

Fortuna 1.23.7

• Documentation updated for clarity.
• Minor bug fixes.
• TruffleShuffle has been redesigned slightly, it now uses a random rotate instead of swap.
• Custom __repr__ methods have been added to each class.

Fortuna 1.23.6

• New method for QuantumMonty: quantum_not_monty - produces the upside down quantum_monty.
• New bias option for FlexCat: not_monty.

Fortuna 1.23.5.1

• Fixed some small typos.

Fortuna 1.23.5

• Documentation updated for clarity.
• All sequence wrappers can now accept generators as input.
• Six new functions added:
  • random_float() -> float in range [0.0..1.0) exclusive, uniform flat distribution.
  • percent_true_float(num: float) -> bool, Like percent_true but with floating point precision.
  • plus_or_minus_linear_down(num: int) -> int in range [-num..num], upside down pyramid.
  • plus_or_minus_curve_down(num: int) -> int in range [-num..num], upside down bell curve.
  • mostly_not_middle(num: int) -> int in range [0..num], upside down pyramid.
  • mostly_not_center(num: int) -> int in range [0..num], upside down bell curve.
• Two new methods for QuantumMonty:
  • mostly_not_middle
  • mostly_not_center
• Two new bias options for FlexCat, either can be used to define x and/or y axis bias:
  • not_middle
  • not_center

Fortuna 1.23.4.2

• Fixed some minor typos in the README.md file.

Fortuna 1.23.4.1

• Fixed some minor typos in the test suite.

Fortuna 1.23.4

• Fortuna is now Production/Stable!
• Fortuna and Fortuna Pure now use the same test suite.

Fortuna 0.23.4, first release candidate.

• RandomCycle, BlockCycle and TruffleShuffle have been refactored and combined into one class: TruffleShuffle.
• QuantumMonty and FlexCat will now use the new TruffleShuffle for cycling.
• Minor refactoring across the module.

Fortuna 0.23.3, internal

• Function shuffle(arr: list) added.

Fortuna 0.23.2, internal

• Simplified the plus_or_minus_curve(num: int) function, output will now always be bounded to the range [-num..num].
• Function stretched_bell(num: int) added, this matches the previous behavior of an unbounded plus_or_minus_curve.

Fortuna 0.23.1, internal

• Small bug fixes and general clean up.

Fortuna 0.23.0

• The number of test cycles in the test suite has been reduced to 10,000 (down from 100,000). The performance of the pure python implementation and the c-extension are now directly comparable.
• Minor tweaks made to the examples in .../fortuna_extras/fortuna_examples.py

Fortuna 0.22.2, experimental features

• BlockCycle class added.
• RandomWalk class added.
• CatWalk class added.

Fortuna 0.22.1

• Fortuna classes no longer return lists of values, this behavior has been extracted to a free function called n_samples.

Fortuna 0.22.0, experimental features

• Function bind added.
• Function n_samples added.

Fortuna 0.21.3

• Flatten will no longer raise an error if passed a callable item that it can't call. It correctly returns such items in an uncalled state without error.
• Simplified .../fortuna_extras/fortuna_examples.py - removed unnecessary class structure.

Fortuna 0.21.2

• Fix some minor bugs.

Fortuna 0.21.1

• Fixed a bug in .../fortuna_extras/fortuna_examples.py

Fortuna 0.21.0

• Function flatten added.
• Flatten: The Fortuna classes will recursively unpack callable objects in the data set.

Fortuna 0.20.10

• Documentation updated.

Fortuna 0.20.9

• Minor bug fixes.

Fortuna 0.20.8, internal

• Testing cycle for potential new features.

Fortuna 0.20.7

• Documentation updated for clarity.

Fortuna 0.20.6

• Tests updated based on recent changes.

Fortuna 0.20.5, internal

• Documentation updated based on recent changes.

Fortuna 0.20.4, internal

• WeightedChoice (both types) can optionally return a list of samples rather than just one value, control the length of the list via the n_samples argument.

Fortuna 0.20.3, internal

• RandomCycle can optionally return a list of samples rather than just one value, control the length of the list via the n_samples argument.

Fortuna 0.20.2, internal

• QuantumMonty can optionally return a list of samples rather than just one value, control the length of the list via the n_samples argument.

Fortuna 0.20.1, internal

• FlexCat can optionally return a list of samples rather than just one value, control the length of the list via the n_samples argument.

Fortuna 0.20.0, internal

• FlexCat now accepts a standard dict as input. The ordered(ness) of dict is now part of the standard in Python 3.7.1. Previously FlexCat required an OrderedDict, now it accepts either and treats them the same.

Fortuna 0.19.7

• Fixed bug in .../fortuna_extras/fortuna_examples.py.

Fortuna 0.19.6

• Updated documentation formatting.
• Small performance tweak for QuantumMonty and FlexCat.

Fortuna 0.19.5

• Minor documentation update.

Fortuna 0.19.4

• Minor update to all classes for better debugging.

Fortuna 0.19.3

• Updated plus_or_minus_curve to allow unbounded output.

Fortuna 0.19.2

• Internal development cycle.
• Minor update to FlexCat for better debugging.

Fortuna 0.19.1

• Internal development cycle.

Fortuna 0.19.0

• Updated documentation for clarity.
• MultiCat has been removed, it is replaced by FlexCat.
• Mostly has been removed, it is replaced by QuantumMonty.

Fortuna 0.18.7

• Fixed some more README typos.

Fortuna 0.18.6

• Fixed some README typos.

Fortuna 0.18.5

• Updated documentation.
• Fixed another minor test bug.

Fortuna 0.18.4

• Updated documentation to reflect recent changes.
• Fixed some small test bugs.
• Reduced default number of test cycles to 10,000 - down from 100,000.

Fortuna 0.18.3

• Fixed some minor README typos.

Fortuna 0.18.2

• Fixed a bug with Fortuna Pure.

Fortuna 0.18.1

• Fixed some minor typos.
• Added tests for .../fortuna_extras/fortuna_pure.py

Fortuna 0.18.0

• Introduced new test format, now includes average call time in nanoseconds.
• Reduced default number of test cycles to 100,000 - down from 1,000,000.
• Added pure Python implementation of Fortuna: .../fortuna_extras/fortuna_pure.py
• Promoted several low level functions to top level.
  • zero_flat(num: int) -> int
  • zero_cool(num: int) -> int
  • zero_extreme(num: int) -> int
  • max_cool(num: int) -> int
  • max_extreme(num: int) -> int
  • analytic_continuation(func: staticmethod, num: int) -> int
  • min_max(num: int, lo: int, hi: int) -> int

Fortuna 0.17.3

• Internal development cycle.

Fortuna 0.17.2

• User Requested: dice() and d() functions now support negative numbers as input.

Fortuna 0.17.1

• Fixed some minor typos.

Fortuna 0.17.0

• Added QuantumMonty to replace Mostly, same default behavior with more options.
• Mostly is depreciated and may be removed in a future release.
• Added FlexCat to replace MultiCat, same default behavior with more options.
• MultiCat is depreciated and may be removed in a future release.
• Expanded the Treasure Table example in .../fortuna_extras/fortuna_examples.py

Fortuna 0.16.2

• Minor refactoring for WeightedChoice.

Fortuna 0.16.1

• Redesigned fortuna_examples.py to feature a dynamic random magic item generator.
• Raised cumulative_weighted_choice function to top level.
• Added test for cumulative_weighted_choice as free function.
• Updated MultiCat documentation for clarity.

Fortuna 0.16.0

• Pushed distribution_timer to the .pyx layer.
• Changed default number of iterations of tests to 1 million, up form 1 hundred thousand.
• Reordered tests to better match documentation.
• Added Base Case Fortuna.fast_rand_below.
• Added Base Case Fortuna.fast_d.
• Added Base Case Fortuna.fast_dice.

Fortuna 0.15.10

• Internal Development Cycle

Fortuna 0.15.9

• Added Base Cases for random.choices()
• Added Base Case for randint_dice()

Fortuna 0.15.8

• Clarified MultiCat Test

Fortuna 0.15.7

• Fixed minor typos.

Fortuna 0.15.6

• Fixed minor typos.
• Simplified MultiCat example.

Fortuna 0.15.5

• Added MultiCat test.
• Fixed some minor typos in docs.

Fortuna 0.15.4

• Performance optimization for both WeightedChoice() variants.
• Cython update provides small performance enhancement across the board.
• Compilation now leverages Python3 all the way down.
• MultiCat pushed to the .pyx layer for better performance.

Fortuna 0.15.3

• Reworked the MultiCat example to include several randomizing strategies working in concert.
• Added Multi Dice 10d10 performance tests.
• Updated sudo code in documentation to be more pythonic.

Fortuna 0.15.2

• Fixed: Linux installation failure.
• Added: complete source files to the distribution (.cpp .hpp .pyx).

Fortuna 0.15.1

• Updated & simplified distribution_timer in fortuna_tests.py
• Readme updated, fixed some typos.
• Known issue preventing successful installation on some linux platforms.

Fortuna 0.15.0

• Performance tweaks.
• Readme updated, added some details.

Fortuna 0.14.1

• Readme updated, fixed some typos.

Fortuna 0.14.0

• Fixed a bug where the analytic continuation algorithm caused a rare issue during compilation on some platforms.

Fortuna 0.13.3

• Fixed Test Bug: percent sign was missing in output distributions.
• Readme updated: added update history, fixed some typos.

Fortuna 0.13.2

• Readme updated for even more clarity.

Fortuna 0.13.1

• Readme updated for clarity.

Fortuna 0.13.0

• Minor Bug Fixes.
• Readme updated for aesthetics.
• Added Tests: .../fortuna_extras/fortuna_tests.py

Fortuna 0.12.0

• Internal test for future update.

Fortuna 0.11.0

• Initial Release: Public Beta

Fortuna 0.10.0

• Module name changed from Dice to Fortuna

Dice 0.1.x - 0.9.x

• Experimental Phase

Legal Information

Fortuna © 2019 Broken aka Robert W Sharp, all rights reserved.

Fortuna is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License.

See online version of this license here: http://creativecommons.org/licenses/by-nc/3.0/