Fortuna 0.15.3

Fast & Flexible Random Value Generator

Fortuna

Fast & Flexible Random Value Generator, or Adventures in Non-determinism

Copyright (c) 2018 Robert Sharp aka Broken


More than just a high performance random number generator...
Fortuna can help you build rarefied treasure tables and more.
Examples coming soon.

Suggested Installation Method:

• Open your favorite Unix terminal and type pip install Fortuna

Primary Functions

• Note: All ranges are inclusive unless stated otherwise.

Fortuna.random_range(int A, int B) -> int
Inputs must be in range (-1,000,000,000..1,000,000,000).
Input order is ignored.
Returns a random integer in range (A..B), uniform distribution.
Ten to fifteen times faster than random.randrange() or random.randint().

Fortuna.d(int sides) -> int
Input must be in range (1..1,000,000,000).
Returns a random integer in the range (1, sides), uniform distribution.
Represents a single die roll.

Fortuna.dice(int rolls, int sides) -> int
Rolls must be in range (1..1,000,000).
Sides must be in range (1..1,000,000,000).
Maximum output (rolls * sides) must be in range (1..2,000,000,000).
Returns a random integer in range (rolls..(sides * rolls)) Returns a geometric distribution based on number and size of the dice rolled.
Represents the sum of multiple die rolls.
Complexity scales with the number of dice rolls.

Fortuna.plus_or_minus(int N) -> int
Input must be in range (-1,000,000,000..1,000,000,000).
Negative or positive input will produce an equivalent distribution.
Returns random integer in the range (-N, N), inclusive uniform distribution.

Fortuna.plus_or_minus_linear(int N) -> int
Input must be in range (-1,000,000,000..1,000,000,000).
Negative or positive input will produce an equivalent distribution.
Returns random integer in the range (-N, N), inclusive zero peak geometric distribution.

Fortuna.plus_or_minus_curve(int N) -> int
Input must be in range (-1,000,000,000..1,000,000,000).
Negative or positive input will produce an equivalent distribution.
Returns random integer in the range (-N, N), inclusive zero peak gaussian distribution.

Fortuna.percent_true(int N) -> bool
Input range: (0..100).
N=zero always returns False, N=100 always returns True.
Any value of N in range (1..99) will produce True or False. Returns a random Bool based on N: the probability of True as a percentage.

Fortuna.random_value(list) -> value
Input sequence length must be in range (1..1,000,000,000).
Returns a random value from a sequence (list or tuple), uniform distribution, non-destructive.
Replaces random.choice(). Up to 4x faster.

Class Abstractions

Mostly: The Quantum Monty

• Constructor takes a sequence (list or tuple) of arbitrary values.
• Sequence length must be in range (3..1,000,000,000).
• Values can be any Python object that can be passed around... string, int, list, function etc.
• Provides a variety of methods for choosing a random value based on position in the sequence.
• 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, Quantum Monty Algorithm (complex overlapped probability waves)

Random Cycle: The Truffle Shuffle

• Constructor takes a sequence (list or tuple) of arbitrary values.
• Sequence length must be in range (3..1,000,000,000).
• Values can be 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 from the sequence. Produces uniform distributions with no consecutive duplicates and relatively few nearby duplicates. This behavior gives rise to output sequences that seem much less mechanical when compared to output from other random_value algorithms.

Weighted Choice: Custom Rarity

• Constructors take a 2d sequence (list or tuple) of weighted values... [(weight, value), ... ]
• Sequence length must be in range (1..1,000,000,000).
• Weights must be integers. A future release may allow weights to be floats.
• Values can be any Python object that can be passed around... string, int, list, function etc.
• Returns a random value and produces 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 best. Relative weights are easier to understand at a glance, while RPG Treasure Tables map nicely to cumulative weights. Cumulative weights are slightly easier for humans to get wrong. Relative weights can be compared directly while cumulative weights can not.

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

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

Fortuna 0.15.3 Sample Distribution and Performance Test Suite

$ /usr/local/bin/python3.7 .../site-packages/fortuna_extras/fortuna_tests.py
Running 100,000 cycles of each...


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

Base Case:
random.randrange(10) x 100000: 125.37 ms
 0: 10.0%
 1: 10.03%
 2: 10.0%
 3: 9.96%
 4: 10.16%
 5: 10.23%
 6: 9.86%
 7: 9.97%
 8: 9.81%
 9: 9.99%

Fortuna.random_below(10) x 100000: 11.9 ms
 0: 10.04%
 1: 10.0%
 2: 9.96%
 3: 9.9%
 4: 10.09%
 5: 10.06%
 6: 9.96%
 7: 10.11%
 8: 9.98%
 9: 9.88%

Base Case:
random.randint(1, 10) x 100000: 159.45 ms
 1: 9.91%
 2: 10.08%
 3: 10.13%
 4: 10.22%
 5: 10.0%
 6: 9.79%
 7: 9.99%
 8: 9.86%
 9: 10.03%
 10: 10.0%

Fortuna.random_range(1, 10) x 100000: 11.16 ms
 1: 10.02%
 2: 10.0%
 3: 9.98%
 4: 10.07%
 5: 9.95%
 6: 9.93%
 7: 10.08%
 8: 10.07%
 9: 9.91%
 10: 9.99%

Fortuna.d(10) x 100000: 9.76 ms
 1: 10.05%
 2: 10.12%
 3: 9.86%
 4: 10.01%
 5: 10.01%
 6: 10.2%
 7: 9.97%
 8: 9.77%
 9: 10.07%
 10: 9.94%

Fortuna.dice(1, 10) x 100000: 9.76 ms
 1: 9.9%
 2: 10.08%
 3: 10.08%
 4: 9.99%
 5: 9.91%
 6: 10.02%
 7: 9.96%
 8: 10.01%
 9: 10.0%
 10: 10.05%

Fortuna.plus_or_minus(5) x 100000: 9.32 ms
 -5: 9.1%
 -4: 9.03%
 -3: 9.09%
 -2: 8.97%
 -1: 9.15%
 0: 8.82%
 1: 9.18%
 2: 9.02%
 3: 9.21%
 4: 9.24%
 5: 9.19%

Fortuna.plus_or_minus_linear(5) x 100000: 11.97 ms
 -5: 2.79%
 -4: 5.65%
 -3: 8.38%
 -2: 11.23%
 -1: 13.76%
 0: 16.75%
 1: 13.8%
 2: 11.06%
 3: 8.34%
 4: 5.48%
 5: 2.76%

Fortuna.plus_or_minus_curve(5) x 100000: 14.51 ms
 -5: 0.23%
 -4: 1.2%
 -3: 4.39%
 -2: 11.4%
 -1: 20.47%
 0: 24.75%
 1: 20.39%
 2: 11.44%
 3: 4.38%
 4: 1.13%
 5: 0.2%


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

Fortuna.percent_true(25) x 100000: 8.72 ms
 False: 75.03%
 True: 24.97%


Random Values from a Sequence
-------------------------------------------------------------------------

some_list = ['Alpha', 'Beta', 'Delta', 'Eta', 'Gamma', 'Kappa', 'Zeta']

Base Case:
random.choice(some_list) x 100000: 103.75 ms
 Alpha: 14.3%
 Beta: 14.19%
 Delta: 14.37%
 Eta: 14.22%
 Gamma: 14.38%
 Kappa: 14.29%
 Zeta: 14.26%

Fortuna.random_value(some_list) x 100000: 15.87 ms
 Alpha: 14.34%
 Beta: 14.39%
 Delta: 14.37%
 Eta: 14.26%
 Gamma: 14.25%
 Kappa: 14.11%
 Zeta: 14.29%

monty = Mostly(some_list)

monty.mostly_front() x 100000: 29.86 ms
 Alpha: 25.0%
 Beta: 21.5%
 Delta: 17.87%
 Eta: 14.28%
 Gamma: 10.65%
 Kappa: 7.15%
 Zeta: 3.56%

monty.mostly_middle() x 100000: 26.06 ms
 Alpha: 6.26%
 Beta: 12.46%
 Delta: 18.57%
 Eta: 25.11%
 Gamma: 18.82%
 Kappa: 12.56%
 Zeta: 6.21%

monty.mostly_back() x 100000: 40.02 ms
 Alpha: 3.6%
 Beta: 7.23%
 Delta: 10.65%
 Eta: 14.39%
 Gamma: 17.87%
 Kappa: 21.55%
 Zeta: 24.71%

monty.mostly_first() x 100000: 45.4 ms
 Alpha: 34.47%
 Beta: 29.66%
 Delta: 20.11%
 Eta: 10.26%
 Gamma: 3.99%
 Kappa: 1.25%
 Zeta: 0.26%

monty.mostly_center() x 100000: 30.24 ms
 Alpha: 0.46%
 Beta: 5.4%
 Delta: 24.26%
 Eta: 39.99%
 Gamma: 24.32%
 Kappa: 5.16%
 Zeta: 0.41%

monty.mostly_last() x 100000: 35.41 ms
 Alpha: 0.26%
 Beta: 1.2%
 Delta: 3.97%
 Eta: 10.16%
 Gamma: 19.85%
 Kappa: 30.06%
 Zeta: 34.5%

monty() x 100000: 74.09 ms
 Alpha: 11.1%
 Beta: 12.88%
 Delta: 16.4%
 Eta: 19.79%
 Gamma: 16.44%
 Kappa: 12.71%
 Zeta: 10.68%

truffle_shuffle = RandomCycle(some_list)

truffle_shuffle() x 100000: 76.6 ms
 Alpha: 14.39%
 Beta: 14.22%
 Delta: 14.3%
 Eta: 14.25%
 Gamma: 14.29%
 Kappa: 14.26%
 Zeta: 14.29%


Random Values by Weighted Table
-------------------------------------------------------------------------

cumulative_weighted_table = [(7, "Apple"), (11, "Banana"), (13, "Cherry"), (23, "Grape"), (26, "Lime"), (30, "Orange")]
cumulative_weighted_choice = CumulativeWeightedChoice(cumulative_weighted_table)

cumulative_weighted_choice() x 100000: 37.18 ms
 Apple: 23.33%
 Banana: 13.36%
 Cherry: 6.65%
 Grape: 33.37%
 Lime: 9.86%
 Orange: 13.43%

relative_weighted_table = [(7, "Apple"), (4, "Banana"), (2, "Cherry"), (10, "Grape"), (3, "Lime"), (4, "Orange")]
relative_weighted_choice = RelativeWeightedChoice(relative_weighted_table)

relative_weighted_choice() x 100000: 42.24 ms
 Apple: 23.48%
 Banana: 13.19%
 Cherry: 6.64%
 Grape: 33.63%
 Lime: 10.0%
 Orange: 13.06%


Multi Dice: 10d10
-------------------------------------------------------------------------

Base Case:
randrange_dice(10, 10) x 100000: 1252.45 ms

Base Case:
floor_dice(10, 10) x 100000: 381.88 ms

Fortuna.dice(10, 10) x 100000: 41.31 ms


-------------------------------------------------------------------------
Total Test Time: 2.95 sec


Process finished with exit code 0

Update History

Fortuna 0.15.3

Reworked the MultiCat example to include all three random abstractions working in concert. Added Multi Dice 10d10 performance tests

Fortuna 0.15.2

Fixed: Linux installation failure. Added: complete source files to distribution (.cpp .hpp .pyx). The distribution_timer in fortuna_tests.py now uses kwarg: call_sig="f(x)" and no longer attempts to discover the function's name automatically.

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

Minor performance tweaks. \ Readme updated, added some details.

Fortuna 0.14.1

Readme updated, fixed some typos.

Fortuna 0.14.0

Fortuna now requires Python 3.7
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

Legal Stuff

Fortuna :: Copyright (c) 2018 Robert Sharp aka Broken

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.