Fortuna 0.14.0

Fast & Flexible Random Value Generator

Fortuna

Fast & Flexible Random Value Generator

Copyright (c) 2018 Robert Sharp

Primary Functions

Fortuna.random_range(int A, int B) -> int
Returns a random integer within the range (A, B), inclusive uniform distribution.
Nearly ten times faster than random.randrange() or random.randint().

Fortuna.d(int sides) -> int
Returns a random integer in the range (1, sides), inclusive uniform distribution.
Represents a single die roll.

Fortuna.dice(int rolls, int sides) -> int
Returns a geometric distribution based on number and size of dice rolled.
Represents the sum of multiple die rolls.

Fortuna.plus_or_minus(int N) -> int
Returns random integer in the range (-N, N), inclusive uniform distribution.

Fortuna.plus_or_minus_linear(int N) -> int
Returns random integer in the range (-N, N), inclusive zero peak geometric distribution.

Fortuna.plus_or_minus_curve(int N) -> int
Returns random integer in the range (-N, N), inclusive zero peak gaussian distribution.

Fortuna.percent_true(int N) -> bool
Returns a random Bool based on N: the probability of True as a percentage.

Fortuna.random_value(list) -> value
Returns a random value from a list or tuple, non-destructive. Replaces random.choice().

Abstractions

Mostly: Random Patterns

• Constructor takes a sequence of unique values.
• Sequence must have 3 or more items, works best with 10 or more.
• Values can be any object, not just strings as in the example below.
• Provides a variety of methods for choosing a random value based on position in the list.
• Performance scales by some tiny fraction of the length of the sequence.

some_sequence = ["Alpha", "Beta", "Delta", "Eta", "Gamma", "Kappa", "Zeta"]
random_monty = Fortuna.Mostly(some_sequence)

random_monty.mostly_front() -> value
Returns a random value, mostly from the front of the list (geometric)

random_monty.mostly_middle() -> value
Returns a random value, mostly from the middle of the list (geometric)

random_monty.mostly_back() -> value
Returns a random value, mostly from the back of the list (geometric)

random_monty.mostly_first() -> value
Returns a random value, mostly from the very front of the list (gaussian)

random_monty.mostly_center() -> value
Returns a random value, mostly from the very center of the list (gaussian)

random_monty.mostly_last() -> value
Returns a random value, mostly from the very back of the list (gaussian)

random_monty() -> value
Returns a random value, calls a random method above (complex)

Random Cycle: The Truffle Shuffle variant

• Constructors take a sequence (list or tuple) of unique arbitrary values.
• Sequence must have 3 or more items. Works best with 10 or more.
• Values can be virtually any Python object that can be passed around... string, int, list, function etc.
• Features continuous smart micro-shuffling: The Truffle Shuffle.
• Performance scales by some small fraction of the length of the sequence.

some_sequence = ["Alpha", "Beta", "Delta", "Eta", "Gamma", "Kappa", "Zeta"]
random_cycle = Fortuna.RandomCycle(some_sequence)
random_cycle() -> value

Returns a random value, produces uniform distributions with no consecutive duplicates and relatively few nearby duplicates. This "fuzzy" behavior gives rise to output sequences that seem much less mechanical compared to the output of other random_value algorithms.

Weighted Choice: Custom Rarity

• Constructors will take a 2d sequence (list or tuple) of weighted values... [(weight, value), ... ]
• Sequence must not be empty.
• Weights must be integers.
• Values can be any Python object that can be passed around... string, int, list, function etc.
• Each returns a random value, and produce custom distributions based on weighting.
• Performance scales by some fraction of the length of the sequence.

The following examples produce equivalent distributions with comparable performance. The choice to use one over the other is purely about which strategy suits you or the data. Relative weights are easier to understand at a glance,

Relative Weight Strategy:

relative_weighted_table = (
    (7, "Apple"),
    (4, "Banana"),
    (2, "Cherry"),
    (10, "Grape"),
    (3, "Lime"),
    (4, "Orange"),
)
relative_weighted_choice = Fortuna.RelativeWeightedChoice(relative_weighted_table)
relative_weighted_choice() -> value

Cumulative Weight Strategy:

Note: Logic dictates Cumulative Weights must be unique!

cumulative_weighted_table = (
    (7, "Apple"),
    (11, "Banana"),
    (13, "Cherry"),
    (23, "Grape"),
    (26, "Lime"),
    (30, "Orange"),
)
cumulative_weighted_choice = Fortuna.CumulativeWeightedChoice(cumulative_weighted_table)
cumulative_weighted_choice() -> value

Sample Distribution and Performance Test Suite

.../fortuna_extras/fortuna_tests.py

Running 100,000 cycles of each...

Random Numbers
------------------------------------------------------------------------

Base Case:
random.randrange(10) x 100000: 150.65 ms
 0: 9.95%
 1: 10.22%
 2: 10.12%
 3: 10.0%
 4: 9.84%
 5: 10.09%
 6: 10.13%
 7: 9.89%
 8: 9.85%
 9: 9.93%

Base Case:
random.randint(1, 10) x 100000: 161.54 ms
 1: 10.2%
 2: 9.93%
 3: 10.0%
 4: 9.99%
 5: 9.96%
 6: 10.06%
 7: 10.02%
 8: 10.0%
 9: 9.98%
 10: 9.85%

random_range(1, 10) x 100000: 10.39 ms
 1: 9.89%
 2: 9.94%
 3: 10.05%
 4: 10.12%
 5: 9.98%
 6: 10.12%
 7: 9.96%
 8: 9.95%
 9: 9.93%
 10: 10.07%

d(6) x 100000: 8.9 ms
 1: 16.75%
 2: 16.66%
 3: 16.69%
 4: 16.69%
 5: 16.66%
 6: 16.56%

dice(2, 6) x 100000: 11.45 ms
 2: 2.71%
 3: 5.53%
 4: 8.29%
 5: 11.13%
 6: 13.9%
 7: 16.65%
 8: 13.84%
 9: 11.22%
 10: 8.36%
 11: 5.61%
 12: 2.77%

plus_or_minus(5) x 100000: 9.07 ms
 -5: 9.32%
 -4: 9.03%
 -3: 9.17%
 -2: 9.03%
 -1: 8.95%
 0: 9.13%
 1: 8.98%
 2: 9.18%
 3: 9.2%
 4: 9.04%
 5: 8.96%

plus_or_minus_linear(5) x 100000: 11.61 ms
 -5: 2.8%
 -4: 5.61%
 -3: 8.34%
 -2: 11.07%
 -1: 14.02%
 0: 16.57%
 1: 13.89%
 2: 11.25%
 3: 8.22%
 4: 5.51%
 5: 2.72%

plus_or_minus_curve(5) x 100000: 13.61 ms
 -5: 0.2%
 -4: 1.1%
 -3: 4.32%
 -2: 11.51%
 -1: 20.42%
 0: 24.81%
 1: 20.18%
 2: 11.69%
 3: 4.44%
 4: 1.13%
 5: 0.2%


Random Truth
------------------------------------------------------------------------

percent_true(25) x 100000: 8.42 ms
 False: 75.02%
 True: 24.98%


Random List Values
------------------------------------------------------------------------

Base Case:
random.choice(some_list) x 100000: 116.49 ms
 Alpha: 14.32%
 Beta: 14.24%
 Delta: 14.5%
 Eta: 14.26%
 Gamma: 14.32%
 Kappa: 14.19%
 Zeta: 14.16%

random_value(some_list) x 100000: 17.9 ms
 Alpha: 14.29%
 Beta: 14.24%
 Delta: 14.21%
 Eta: 14.27%
 Gamma: 14.39%
 Kappa: 14.23%
 Zeta: 14.36%

Mostly.mostly_front() x 100000: 35.7 ms
 Alpha: 24.81%
 Beta: 21.5%
 Delta: 17.98%
 Eta: 14.2%
 Gamma: 10.71%
 Kappa: 7.25%
 Zeta: 3.54%

Mostly.mostly_middle() x 100000: 30.47 ms
 Alpha: 6.35%
 Beta: 12.53%
 Delta: 18.82%
 Eta: 24.8%
 Gamma: 18.78%
 Kappa: 12.4%
 Zeta: 6.32%

Mostly.mostly_back() x 100000: 38.3 ms
 Alpha: 3.58%
 Beta: 7.02%
 Delta: 10.69%
 Eta: 14.1%
 Gamma: 18.11%
 Kappa: 21.39%
 Zeta: 25.11%

Mostly.mostly_first() x 100000: 51.04 ms
 Alpha: 34.44%
 Beta: 29.81%
 Delta: 19.97%
 Eta: 10.33%
 Gamma: 4.03%
 Kappa: 1.16%
 Zeta: 0.27%

Mostly.mostly_center() x 100000: 40.63 ms
 Alpha: 0.41%
 Beta: 5.41%
 Delta: 24.17%
 Eta: 39.98%
 Gamma: 24.14%
 Kappa: 5.44%
 Zeta: 0.45%

Mostly.mostly_last() x 100000: 35.56 ms
 Alpha: 0.28%
 Beta: 1.16%
 Delta: 4.01%
 Eta: 10.34%
 Gamma: 19.97%
 Kappa: 30.03%
 Zeta: 34.21%

Mostly() x 100000: 92.47 ms
 Alpha: 11.03%
 Beta: 12.78%
 Delta: 16.44%
 Eta: 19.64%
 Gamma: 16.37%
 Kappa: 12.94%
 Zeta: 10.81%

RandomCycle() x 100000: 86.44 ms
 Alpha: 14.22%
 Beta: 14.28%
 Delta: 14.31%
 Eta: 14.3%
 Gamma: 14.28%
 Kappa: 14.22%
 Zeta: 14.39%


Random Values by Weight
------------------------------------------------------------------------

RelativeWeightedChoice() x 100000: 31.85 ms
 Apple: 23.41%
 Banana: 13.24%
 Cherry: 6.61%
 Grape: 33.52%
 Lime: 9.95%
 Orange: 13.27%

CumulativeWeightedChoice() x 100000: 31.96 ms
 Apple: 23.47%
 Banana: 13.21%
 Cherry: 6.61%
 Grape: 33.29%
 Lime: 9.99%
 Orange: 13.42%


------------------------------------------------------------------------
Total Test Time: 1.38 sec

Process finished with exit code 0

Update History

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