RNG 1.3.2

Python API for the C++ Random library

Random Number Generator: RNG Storm Engine

Python API for the C++ Random library.

RNG is not suitable for cryptography, but it could be perfect for other random stuff like data science, experimental programming, A.I. and games.

Recommended Installation: $ pip install RNG

Support this project: https://www.patreon.com/brokencode

Number Types, Precision & Size:

• Float: Python float -> double at the C++ layer.

  • Min Float: -1.7976931348623157e+308
  • Max Float: 1.7976931348623157e+308
  • Min Below Zero: -5e-324
  • Min Above Zero: 5e-324

• Integer: Python int -> long long at the C++ layer.

  • Input & Output Range: (-2**63, 2**63) or approximately +/- 9.2 billion billion.
  • Min Integer: -9223372036854775807
  • Max Integer: 9223372036854775807

Random Binary Function

• bernoulli(ratio_of_truth: float) -> bool
  • Bernoulli distribution.
  • @param ratio_of_truth :: the probability of True as a decimal. Expected input range: [0.0, 1.0], clamped.
  • @return :: True or False

Random Integer Functions

• random_int(left_limit: int, right_limit: int) -> int
  • Flat uniform distribution.
  • 20x faster than random.randint()
  • @param left_limit :: input A.
  • @param right_limit :: input B.
  • @return :: random integer in the inclusive range [A, B] or [B, A] if B < A
• random_below(upper_bound: int) -> int
  • Flat uniform distribution.
  • @param upper_bound :: inout A
  • @return :: random integer in exclusive range [0, A) or (A, 0] if A < 0
• binomial(number_of_trials: int, probability: float) -> int
  • Based on the idea of flipping a coin and counting how many heads come up after some number of flips.
  • @param number_of_trials :: how many times to flip a coin.
  • @param probability :: how likely heads will be flipped. 0.5 is a fair coin. 1.0 is a double headed coin.
  • @return :: count of how many heads came up.
• negative_binomial(trial_successes: int, probability: float) -> int
  • Based on the idea of flipping a coin as long as it takes to succeed.
  • @param trial_successes :: the required number of heads flipped to succeed.
  • @param probability :: how likely heads will be flipped. 0.50 is a fair coin.
  • @return :: the count of how many tails came up before the required number of heads.
• geometric(probability: float) -> int
  • Same as random_negative_binomial(1, probability).
• poisson(mean: float) -> int
  • @param mean :: sets the average output of the function.
  • @return :: random integer, poisson distribution centered on the mean.

Random Floating Point Functions

• generate_canonical() -> float
  • Evenly distributes real values of maximum precision.
  • @return :: random Float in range {0.0, 1.0} biclusive. The spec defines the output range to be [0.0, 1.0).
    • biclusive: feature/bug rendering the exclusivity of this function a bit more mysterious than desired. This is a known compiler bug.
• random_float(left_limit: float, right_limit: float) -> float
  • Suffers from the same biclusive feature/bug noted for generate_canonical().
  • @param left_limit :: input A
  • @param right_limit :: input B
  • @return :: random Float in range {A, B} biclusive. The spec defines the output range to be [A, B).
• normalvariate(mean: float, std_dev: float) -> float
  • @param mean :: sets the average output of the function.
  • @param std_dev :: standard deviation. Specifies spread of data from the mean.
• lognormvariate(log_mean: float, log_deviation: float) -> float
  • @param log_mean :: sets the log of the mean of the function.
  • @param log_deviation :: log of the standard deviation. Specifies spread of data from the mean.
• exponential(lambda_rate: float) -> float
  • Produces random non-negative floating-point values, distributed according to probability density function.
  • @param lambda_rate :: λ constant rate of a random event per unit of time/distance.
  • @return :: The time/distance until the next random event. For example, this distribution describes the time between the clicks of a Geiger counter or the distance between point mutations in a DNA strand.
• gammavariate(shape: float, scale: float) -> float
  • Generalization of the exponential distribution.
  • Produces random positive floating-point values, distributed according to probability density function.
  • @param shape :: α the number of independent exponentially distributed random variables.
  • @param scale :: β the scale factor or the mean of each of the distributed random variables.
  • @return :: the sum of α independent exponentially distributed random variables, each of which has a mean of β.
• weibullvariate(shape: float, scale: float) -> float
  • Generalization of the exponential distribution.
  • Similar to the gamma distribution but uses a closed form distribution function.
  • Popular in reliability and survival analysis.
• extreme_value(location: float, scale: float) -> float
  • Based on Extreme Value Theory.
  • Used for statistical models of the magnitude of earthquakes and volcanoes.
• chi_squared(degrees_of_freedom: float) -> float
  • Used with the Chi Squared Test and Null Hypotheses to test if sample data fits an expected distribution.
• cauchy(location: float, scale: float) -> float
  • @param location :: It specifies the location of the peak. The default value is 0.0.
  • @param scale :: It represents the half-width at half-maximum. The default value is 1.0.
  • @return :: Continuous Distribution.
• fisher_f(degrees_of_freedom_1: float, degrees_of_freedom_2: float) -> float
  • F distributions often arise when comparing ratios of variances.
• student_t(degrees_of_freedom: float) -> float
  • T distribution. Same as a normal distribution except it uses the sample standard deviation rather than the population standard deviation.
  • As degrees_of_freedom goes to infinity it converges with the normal distribution.

Engines

• mersenne_twister_engine: internal only
  • Implements 64 bit Mersenne twister algorithm. Default engine on most systems.
• linear_congruential_engine: internal only
  • Implements linear congruential algorithm.
• subtract_with_carry_engine: internal only
  • Implements a subtract-with-carry (lagged Fibonacci) algorithm.
• storm_engine: internal only
  • RNG: Custom Engine
  • Default Standard

Engine Adaptors

Engine adaptors generate pseudo-random numbers using another random number engine as entropy source. They are generally used to alter the spectral characteristics of the underlying engine.

• discard_block_engine: internal only
  • Discards some output of a random number engine.
• independent_bits_engine: internal only
  • Packs the output of a random number engine into blocks of a specified number of bits.
• shuffle_order_engine: internal only
  • Delivers the output of a random number engine in a different order.

Seeds & Entropy Source

• random_device: internal only
  • Non-deterministic uniform random bit generator, although implementations are allowed to implement random_device using a pseudo-random number engine if there is no support for non-deterministic random number generation.
• seed_seq: internal only
  • General-purpose bias-eliminating scrambled seed sequence generator.

Distribution & Performance Test Suite

• distribution_timer(func: staticmethod, *args, **kwargs) -> None
  • For statistical analysis of non-deterministic numeric functions.
  • @param func :: Function method or lambda to analyze. func(*args, **kwargs)
  • @optional_kw num_cycles :: Total number of samples for distribution analysis.
  • @optional_kw post_processor :: Used to scale a large set of data into a smaller set of groupings.
• quick_test(n=10000) -> None
  • Runs a battery of tests for every random distribution function in the module.
  • @param n :: the total number of samples to collect for each test. Default: 10,000

Development Log

RNG 1.3.1

• Test Update

RNG 1.3.1

• Fixed Typos

RNG 1.3.0

• Storm Update

RNG 1.2.5

• Low level clean up

RNG 1.2.4

• Minor Typos Fixed

RNG 1.2.3

• Documentation Update
• Test Update
• Bug Fixes

RNG 1.0.0 - 1.2.2, internal

• API Changes:
  • randint changed to random_int
  • randbelow changed to random_below
  • random changed to generate_canonical
  • uniform changed to random_float

RNG 0.2.3

• Bug Fixes

RNG 0.2.2

• discrete() removed.

RNG 0.2.1

• minor typos
• discrete() depreciated.

RNG 0.2.0

• Major Rebuild.

RNG 0.1.22

• The RNG Storm Engine is now the default standard.
• Experimental Vortex Engine added for testing.

RNG 0.1.21 beta

• Small update to the testing suite.

RNG 0.1.20 beta

• Changed default inputs for random_int and random_below to sane values.
  • random_int(left_limit=1, right_limit=20) down from -2**63, 2**63 - 1
  • random_below(upper_bound=10) down from 2**63 - 1

RNG 0.1.19 beta

• Broke some fixed typos, for a change of pace.

RNG 0.1.18 beta

• Fixed some typos.

RNG 0.1.17 beta

• Major Refactoring.
• New primary engine: Hurricane.
• Experimental engine Typhoon added: random_below() only.

RNG 0.1.16 beta

• Internal Engine Performance Tuning.

RNG 0.1.15 beta

• Engine Testing.

RNG 0.1.14 beta

• Fixed a few typos.

RNG 0.1.13 beta

• Fixed a few typos.

RNG 0.1.12 beta

• Major Test Suite Upgrade.
• Major Bug Fixes.
  • Removed several 'foot-guns' in prep for fuzz testing in future releases.

RNG 0.1.11 beta

• Fixed small bug in the install script.

RNG 0.1.10 beta

• Fixed some typos.

RNG 0.1.9 beta

• Fixed some typos.

RNG 0.1.8 beta

• Fixed some typos.
• More documentation added.

RNG 0.1.7 beta

• The random_floating_point function renamed to random_float.
• The function c_rand() has been removed as well as all the cruft it required.
• Major Documentation Upgrade.
• Fixed an issue where keyword arguments would fail to propagate. Both, positional args and kwargs now work as intended.
• Added this Dev Log.

RNG 0.0.6 alpha

• Minor ABI changes.

RNG 0.0.5 alpha

• Tests redesigned slightly for Float functions.

RNG 0.0.4 alpha

• Random Float Functions Implemented.

RNG 0.0.3 alpha

• Random Integer Functions Implemented.

RNG 0.0.2 alpha

• Random Bool Function Implemented.

RNG 0.0.1 pre-alpha

• Planning & Design.

Distribution and Performance Test Suite

Quick Test: RNG Storm Engine

Round Trip Numeric Limits:
 Min Integer: -9223372036854775808
 Max Integer:  9223372036854775807
 Min Float: -1.7976931348623157e+308
 Max Float:  1.7976931348623157e+308
 Min Below Zero: -5e-324
 Min Above Zero:  5e-324


Binary Tests

Output Analysis: bernoulli(0.3333333333333333)
Typical Timing: 63 ± 1 ns
Statistics of 1000 Samples:
 Minimum: False
 Median: False
 Maximum: True
 Mean: 0.334
 Std Deviation: 0.47187568984497036
Distribution of 10000 Samples:
 False: 66.82%
 True: 33.18%


Integer Tests

Base Case
Output Analysis: Random.randint(1, 6)
Typical Timing: 1125 ± 11 ns
Statistics of 1000 Samples:
 Minimum: 1
 Median: 3
 Maximum: 6
 Mean: 3.494
 Std Deviation: 1.7154902817873692
Distribution of 10000 Samples:
 1: 16.75%
 2: 16.57%
 3: 16.09%
 4: 16.47%
 5: 17.27%
 6: 16.85%

Output Analysis: random_int(1, 6)
Typical Timing: 63 ± 1 ns
Statistics of 1000 Samples:
 Minimum: 1
 Median: 4
 Maximum: 6
 Mean: 3.513
 Std Deviation: 1.6872100277314848
Distribution of 10000 Samples:
 1: 16.5%
 2: 16.7%
 3: 16.81%
 4: 16.64%
 5: 16.28%
 6: 17.07%

Base Case
Output Analysis: Random.randrange(6)
Typical Timing: 813 ± 10 ns
Statistics of 1000 Samples:
 Minimum: 0
 Median: 2
 Maximum: 5
 Mean: 2.466
 Std Deviation: 1.7209897750439442
Distribution of 10000 Samples:
 0: 16.84%
 1: 16.34%
 2: 16.75%
 3: 16.76%
 4: 16.67%
 5: 16.64%

Output Analysis: random_below(6)
Typical Timing: 32 ± 3 ns
Statistics of 1000 Samples:
 Minimum: 0
 Median: 3
 Maximum: 5
 Mean: 2.507
 Std Deviation: 1.7300127005152142
Distribution of 10000 Samples:
 0: 16.65%
 1: 17.38%
 2: 16.21%
 3: 17.18%
 4: 16.46%
 5: 16.12%

Output Analysis: binomial(4, 0.5)
Typical Timing: 157 ± 6 ns
Statistics of 1000 Samples:
 Minimum: 0
 Median: 2
 Maximum: 4
 Mean: 2.02
 Std Deviation: 1.0259886220873273
Distribution of 10000 Samples:
 0: 6.23%
 1: 25.37%
 2: 37.35%
 3: 24.81%
 4: 6.24%

Output Analysis: negative_binomial(5, 0.75)
Typical Timing: 94 ± 4 ns
Statistics of 1000 Samples:
 Minimum: 0
 Median: 1
 Maximum: 8
 Mean: 1.649
 Std Deviation: 1.4859364074572663
Distribution of 10000 Samples:
 0: 23.98%
 1: 30.21%
 2: 21.79%
 3: 12.8%
 4: 6.52%
 5: 2.86%
 6: 1.15%
 7: 0.38%
 8: 0.21%
 9: 0.06%
 10: 0.03%
 11: 0.01%

Output Analysis: geometric(0.75)
Typical Timing: 63 ± 1 ns
Statistics of 1000 Samples:
 Minimum: 0
 Median: 0
 Maximum: 5
 Mean: 0.321
 Std Deviation: 0.6545130918380375
Distribution of 10000 Samples:
 0: 75.48%
 1: 18.74%
 2: 4.29%
 3: 1.07%
 4: 0.37%
 5: 0.05%

Output Analysis: poisson(4.5)
Typical Timing: 94 ± 8 ns
Statistics of 1000 Samples:
 Minimum: 0
 Median: 4
 Maximum: 13
 Mean: 4.47
 Std Deviation: 2.1282926560108293
Distribution of 10000 Samples:
 0: 0.94%
 1: 5.21%
 2: 11.16%
 3: 16.82%
 4: 19.44%
 5: 16.87%
 6: 13.06%
 7: 8.14%
 8: 4.52%
 9: 2.27%
 10: 1.0%
 11: 0.33%
 12: 0.14%
 13: 0.07%
 14: 0.02%
 15: 0.01%


Floating Point Tests

Base Case
Output Analysis: Random.random()
Typical Timing: 32 ± 8 ns
Statistics of 1000 Samples:
 Minimum: 0.0018642861079508632
 Median: (0.4865522788422926, 0.48694668495861426)
 Maximum: 0.9985633134556822
 Mean: 0.48901738537454814
 Std Deviation: 0.28748684142665426
Post-processor Distribution of 10000 Samples using round method:
 0: 49.55%
 1: 50.45%

Output Analysis: generate_canonical()
Typical Timing: 32 ± 8 ns
Statistics of 1000 Samples:
 Minimum: 0.002359750132155993
 Median: (0.48431349416875374, 0.48573568810722473)
 Maximum: 0.9999435036254807
 Mean: 0.4943137436415561
 Std Deviation: 0.2900488178192246
Post-processor Distribution of 10000 Samples using round method:
 0: 51.21%
 1: 48.79%

Output Analysis: random_float(0.0, 10.0)
Typical Timing: 32 ± 8 ns
Statistics of 1000 Samples:
 Minimum: 0.004522243792486171
 Median: (4.921505459005925, 4.924210379552047)
 Maximum: 9.995787333576851
 Mean: 4.896222634165114
 Std Deviation: 2.916193866609588
Post-processor Distribution of 10000 Samples using floor method:
 0: 9.95%
 1: 10.21%
 2: 10.28%
 3: 9.7%
 4: 10.07%
 5: 10.16%
 6: 10.24%
 7: 10.04%
 8: 9.53%
 9: 9.82%

Base Case
Output Analysis: Random.expovariate(1.0)
Typical Timing: 313 ± 8 ns
Statistics of 1000 Samples:
 Minimum: 0.002216150797450532
 Median: (0.65490187439184, 0.6570304361976486)
 Maximum: 6.8602232620425925
 Mean: 0.9662768540796546
 Std Deviation: 0.9718578350843132
Post-processor Distribution of 10000 Samples using floor_mod_10 method:
 0: 63.81%
 1: 23.15%
 2: 8.24%
 3: 3.1%
 4: 1.06%
 5: 0.45%
 6: 0.1%
 7: 0.07%
 8: 0.01%
 9: 0.01%

Output Analysis: expovariate(1.0)
Typical Timing: 32 ± 3 ns
Statistics of 1000 Samples:
 Minimum: 0.0001443232661739669
 Median: (0.604609619919764, 0.6058374269792876)
 Maximum: 7.523762627178045
 Mean: 0.950007897809117
 Std Deviation: 0.9903508341192871
Post-processor Distribution of 10000 Samples using floor_mod_10 method:
 0: 63.47%
 1: 22.79%
 2: 8.69%
 3: 3.26%
 4: 1.1%
 5: 0.37%
 6: 0.2%
 7: 0.08%
 8: 0.02%
 9: 0.02%

Base Case
Output Analysis: Random.gammavariate(1.0, 1.0)
Typical Timing: 500 ± 6 ns
Statistics of 1000 Samples:
 Minimum: 0.0010388346856487658
 Median: (0.6843158205748362, 0.6844232963414119)
 Maximum: 7.0212957044378435
 Mean: 0.9905427667057285
 Std Deviation: 0.9861209526154319
Post-processor Distribution of 10000 Samples using floor_mod_10 method:
 0: 63.15%
 1: 22.99%
 2: 8.74%
 3: 3.25%
 4: 1.27%
 5: 0.35%
 6: 0.17%
 7: 0.07%
 8: 0.01%

Output Analysis: gammavariate(1.0, 1.0)
Typical Timing: 63 ± 3 ns
Statistics of 1000 Samples:
 Minimum: 0.0005345626996068837
 Median: (0.6973929491715651, 0.700809651289934)
 Maximum: 6.895658731396534
 Mean: 0.992240907792841
 Std Deviation: 0.9685063029877555
Post-processor Distribution of 10000 Samples using floor_mod_10 method:
 0: 62.5%
 1: 24.02%
 2: 8.59%
 3: 3.23%
 4: 1.08%
 5: 0.33%
 6: 0.16%
 7: 0.07%
 8: 0.01%
 9: 0.01%

Base Case
Output Analysis: Random.weibullvariate(1.0, 1.0)
Typical Timing: 407 ± 8 ns
Statistics of 1000 Samples:
 Minimum: 0.0005576390899240854
 Median: (0.7130756039405082, 0.7139022175371896)
 Maximum: 7.09116708798363
 Mean: 0.9649662155425063
 Std Deviation: 0.9043079942748469
Post-processor Distribution of 10000 Samples using floor_mod_10 method:
 0: 63.1%
 1: 23.67%
 2: 8.82%
 3: 2.87%
 4: 0.86%
 5: 0.54%
 6: 0.08%
 7: 0.04%
 8: 0.02%

Output Analysis: weibullvariate(1.0, 1.0)
Typical Timing: 94 ± 6 ns
Statistics of 1000 Samples:
 Minimum: 0.0013769198506304672
 Median: (0.6854759401451815, 0.6860935612996812)
 Maximum: 6.334333188852022
 Mean: 0.9927655215478188
 Std Deviation: 0.9904626429090108
Post-processor Distribution of 10000 Samples using floor_mod_10 method:
 0: 62.79%
 1: 23.72%
 2: 8.83%
 3: 3.09%
 4: 0.98%
 5: 0.4%
 6: 0.14%
 7: 0.03%
 8: 0.01%
 9: 0.01%

Output Analysis: extreme_value(0.0, 1.0)
Typical Timing: 63 ± 8 ns
Statistics of 1000 Samples:
 Minimum: -1.9168155334568997
 Median: (0.4202144360886349, 0.42021803685752834)
 Maximum: 7.534776672035387
 Mean: 0.6281455771570104
 Std Deviation: 1.2882972276403204
Post-processor Distribution of 10000 Samples using round method:
 -2: 1.16%
 -1: 17.89%
 0: 34.29%
 1: 26.1%
 2: 12.54%
 3: 4.94%
 4: 2.04%
 5: 0.76%
 6: 0.18%
 7: 0.08%
 8: 0.01%
 9: 0.01%

Base Case
Output Analysis: Random.gauss(5.0, 2.0)
Typical Timing: 563 ± 7 ns
Statistics of 1000 Samples:
 Minimum: -1.6634807888337688
 Median: (4.992411644420636, 4.999776377007621)
 Maximum: 11.690371059618943
 Mean: 5.010119985590884
 Std Deviation: 2.0205453733106298
Post-processor Distribution of 10000 Samples using round method:
 -3: 0.01%
 -2: 0.06%
 -1: 0.27%
 0: 1.06%
 1: 2.5%
 2: 6.61%
 3: 12.35%
 4: 17.78%
 5: 19.24%
 6: 17.32%
 7: 12.01%
 8: 6.64%
 9: 2.92%
 10: 0.93%
 11: 0.23%
 12: 0.06%
 13: 0.01%

Output Analysis: normalvariate(5.0, 2.0)
Typical Timing: 94 ± 1 ns
Statistics of 1000 Samples:
 Minimum: -0.4216081465400877
 Median: (4.957867873498797, 4.960525287092449)
 Maximum: 12.63349318909003
 Mean: 5.008923426162033
 Std Deviation: 1.9401326818290008
Post-processor Distribution of 10000 Samples using round method:
 -2: 0.05%
 -1: 0.21%
 0: 0.86%
 1: 2.78%
 2: 6.48%
 3: 12.26%
 4: 17.87%
 5: 19.34%
 6: 16.74%
 7: 12.33%
 8: 6.99%
 9: 2.7%
 10: 1.04%
 11: 0.28%
 12: 0.06%
 13: 0.01%

Base Case
Output Analysis: Random.lognormvariate(1.6, 0.25)
Typical Timing: 782 ± 23 ns
Statistics of 1000 Samples:
 Minimum: 2.100373404196032
 Median: (4.9760585202982925, 4.98628941430215)
 Maximum: 10.411691568142325
 Mean: 5.09383254093055
 Std Deviation: 1.2592170395705158
Post-processor Distribution of 10000 Samples using round method:
 2: 0.39%
 3: 7.53%
 4: 27.06%
 5: 31.19%
 6: 20.01%
 7: 8.56%
 8: 3.76%
 9: 0.97%
 10: 0.43%
 11: 0.07%
 12: 0.03%

Output Analysis: lognormvariate(1.6, 0.25)
Typical Timing: 94 ± 6 ns
Statistics of 1000 Samples:
 Minimum: 2.3102686193133475
 Median: (5.019794704716817, 5.022776860977586)
 Maximum: 12.469002534530496
 Mean: 5.11371929182671
 Std Deviation: 1.2248494106461876
Post-processor Distribution of 10000 Samples using round method:
 2: 0.18%
 3: 7.82%
 4: 26.79%
 5: 31.61%
 6: 19.92%
 7: 9.1%
 8: 3.08%
 9: 1.08%
 10: 0.3%
 11: 0.08%
 12: 0.04%

Output Analysis: chi_squared(1.0)
Typical Timing: 125 ± 5 ns
Statistics of 1000 Samples:
 Minimum: 3.085701168854021e-06
 Median: (0.48285661922698087, 0.48467165992763533)
 Maximum: 10.254473577411064
 Mean: 1.046383503767532
 Std Deviation: 1.4927844622805495
Post-processor Distribution of 10000 Samples using floor_mod_10 method:
 0: 68.1%
 1: 16.17%
 2: 7.23%
 3: 3.74%
 4: 2.09%
 5: 1.14%
 6: 0.71%
 7: 0.44%
 8: 0.25%
 9: 0.13%

Output Analysis: cauchy(0.0, 1.0)
Typical Timing: 63 ± 8 ns
Statistics of 1000 Samples:
 Minimum: -732.5261850485788
 Median: (-0.020055265859094697, -0.017184836963910936)
 Maximum: 306.47288939150184
 Mean: -0.6510962692967972
 Std Deviation: 35.35932237331378
Post-processor Distribution of 10000 Samples using floor_mod_10 method:
 0: 26.13%
 1: 11.46%
 2: 5.64%
 3: 3.76%
 4: 2.71%
 5: 3.2%
 6: 3.87%
 7: 6.02%
 8: 11.36%
 9: 25.85%

Output Analysis: fisher_f(8.0, 8.0)
Typical Timing: 188 ± 8 ns
Statistics of 1000 Samples:
 Minimum: 0.07352853206082759
 Median: (0.9890826680010241, 0.9912238450887711)
 Maximum: 31.86094635990357
 Mean: 1.3431530252093435
 Std Deviation: 1.4457616619997709
Post-processor Distribution of 10000 Samples using floor_mod_10 method:
 0: 49.96%
 1: 32.66%
 2: 10.12%
 3: 3.72%
 4: 1.75%
 5: 0.81%
 6: 0.49%
 7: 0.25%
 8: 0.13%
 9: 0.11%

Output Analysis: student_t(8.0)
Typical Timing: 157 ± 7 ns
Statistics of 1000 Samples:
 Minimum: -7.716646203378542
 Median: (-0.019686697570107447, -0.01893513978694138)
 Maximum: 5.106134947613407
 Mean: -0.05970990825645788
 Std Deviation: 1.16938035996734
Post-processor Distribution of 10000 Samples using round method:
 -9: 0.01%
 -8: 0.01%
 -7: 0.01%
 -6: 0.01%
 -5: 0.04%
 -4: 0.3%
 -3: 1.53%
 -2: 6.7%
 -1: 22.81%
 0: 36.51%
 1: 23.4%
 2: 6.79%
 3: 1.42%
 4: 0.34%
 5: 0.09%
 6: 0.02%
 18: 0.01%


=========================================================================
Total Test Time: 0.5868 seconds