An experimental random number generator inspired by the famous Fibonacci number sequence.
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README.md

FibonacciRng

This gem implements a random number generator inspired by the famous Fibonacci number sequence. To be specific, it is a normalized, cyclic Fibonacci pseudo random number generator. So far, this generator has performed quite well when compared to the built-in Ruby random number generator when tested with:

  • A chi-squared test
  • An auto-correlation test
  • An X/Y scatter graph test

At this time I lack the mathematical skill to go beyond these rudimentary measures but they are enough to qualify this code for "light" duties.

Proving that this is indeed a good (or poor) RNG is left as an exercise for the reader! Hopefully one with greater knowledge of statistics than I.

Installation

Add this line to your application's Gemfile:

gem 'fibonacci_rng'

And then execute:

$ bundle

Or install it yourself as:

$ gem install fibonacci_rng

The fibonacci_rng gem itself is found at: ( https://rubygems.org/gems/fibonacci_rng )

A C++ version of this generator also exists and may be found at ( https://github.com/PeterCamilleri/Fibonacci_CPP )

Usage

require 'fibonacci_rng'

Then in an appropriate place in the code:

@my_rng = FibonacciRng.new(seed, depth, init)

Where:

  • depth is an optional integer value between 2 and 256. Defaults to 8.
  • seed is an optional number or string or other object that has a repeatable value and responds to the to_s method. Defaults to a value derived from system entropy.
  • init is the number of initial training cycles used to seed the generator. The allowed range is 1 to 1,000,000. By default the init value is 32*depth+768.

Here is an overview of the available options.

#Method #1
@my_rng = FibonacciRng.new                            # Random seed, depth = 8

#Method #2
@my_rng = FibonacciRng.new('seed')                    # Specified seed = 'seed', depth = 8

#Method #3
@my_rng = FibonacciRng.new('seed', 12)                # Specified seed = 'seed', depth = 12

#Method #4
@my_rng = FibonacciRng.new(FibonacciRng.new_seed, 12) # Random seed, depth = 12

#Method #5
@my_rng = FibonacciRng.new(FibonacciRng.new_seed, 12, 100) # Random seed, depth = 12 with 100 passes.

In addition, keyword arguments are emulated (as of Version 0.4.0) so these additional options also are available:

  • depth: value -- an integer value between 2 and 256. Defaults to 8.
  • seed: value -- a number or string or other object that has a repeatable value and responds to the to_s method. Defaults to a value derived from system entropy.
  • init: value -- the number of initial training cycles used to seed the generator. The allowed range is 1 to 1,000,000. By default the init value is 32*depth+768.

The following are examples of constructors with keyword arguments.

#Method #6
@my_rng = FibonacciRng.new(seed: 'seed')              # Specified seed = 'seed', depth = 8

#Method #7
@my_rng = FibonacciRng.new(seed: 'seed', depth: 12)   # Specified seed = 'seed', depth = 12

#Method #8
@my_rng = FibonacciRng.new(depth: 12)                 # Random seed, depth = 12

#Method #9
@my_rng = FibonacciRng.new(seed: 'seed', init: 2048)  # Specified seed = 'seed' with 2048 passes.

Note: Mixing positional and keyword arguments will not, in general, work. So don't do it!

Generating Pseudo Random Data

The Fibonacci generator class supports the classical rand method that emulates the behavior of the standard generator. It works like this:

@my_rng.rand          # A "random" float between 0.0 and less than 1.
@my_rng.rand(0)       # A "random" float between 0.0 and less than 1.
@my_rng.rand(100)     # A "random" integer between 0 and 99
@my_rng.rand(1..6)    # A "random" integer between 1 and 6

In addition, here are some other options:

@my_rng.dice(100)     # A "random" integer between 0 and 99
@my_rng.byte          # A "random" integer between 0 and 255
@my_rng.word          # A "random" integer between 0 and 65535
@my_rng.float         # A quick "random" float between 0 and less than 1.
@my_rng.double        # A better "random" float between 0 and less than 1.
@my_rng.string(10)    # A "random" string of 10 characters in length.

# A "random" string of 10 characters in length from the string 'abcdefg'.
@my_rng.string(10, 'abcdefg')

and also available are these helpful methods:

@my_rng.reseed(value) # Reseed the sequence with the new value.
@my_rng.reseed        # Reseed the sequence with a "random" seed.
@my_rng.spin(count)   # Spin the generator count times.
@my_rng.spin          # Spin the generator once.

Note: reseed is an alias of the srand method. The reseed method is preferred due to its clearer name.

If more than one stream of numbers is required, it is best to use multiple instances of FibonacciRng objects rather than rely on one. This will help avoid the two streams of data being correlated.

Hashing

As more as an experiment than anything else, it is also possible to use the generator as a primitive hash generator. To do so, create a new generator with a salt value, append data to it, and the retrieve the results as a (big) number or a string.

fib = FibonacciRng.new('salt')
fib << "The quick brown fox jumps over the lazy dog."
puts fib.hash_string
#displays: j5jqhk7ntrze02icv38gj28efa2qrctr6mi5ejbr2p4nj

Note that the length of the hash string is a function of the depth of the generator used to create it. This is about 5.5 characters per unit of depth.

Salting

Another (more practical) use for the Fibonacci generator is the creation of salting strings for use in more capable hashing schemes. Here are four possible ways that this can be done:

#Method #1
salt_string = FibonacciRng.new.hash_string  #Thread safe.

#Method #2
salt_string = FibonacciRng.new(depth: 12).hash_string  #Thread safe.

#Method #3
Thread.current[:salter] = FibonacciRng.new   #Need a separate generator for each thread.
# Much intervening code omitted.
salter = Thread.current[:salter]
salter << Time.now.to_s  # Note that unique time values are NOT needed.
salt_string = salter.hash_string

#Method #4
Thread.current[:salter] = FibonacciRng.new   #Need a separate generator for each thread.
# Much intervening code omitted.
salter = Thread.current[:salter]
salter.spin
salt_string = salter.hash_string

Each time any of these is run, a different salt string will be generated.

Methods back in Good Standing

  • bytes - This method would seem to generate an array of random bytes. It does not. However, it doesn't matter either. The bytes method was added to improve interoperability with the standard Random class. Thus deprecating it was a mistake. This note serves to announce that the bytes method is not going away.

Theory of Operation

The random number generator used in this gem is based on a modified, cyclic Fibonacci generator. This ring buffer design modifies the simple sequence so that it feeds back onto itself, which in turn gives the appearance of chaos. There is one further required modification however. Since the Fibonacci sequence uses additions, a mechanism for preventing zeros from "swamping" the data, is needed. This is accomplished by rotating one of the arguments to the right by one bit. The basic outline of the generational cycle operation, with depth of N is shown below: The Cycle Operation
Notes:

  • The last two elements are copies of the first two elements before the array was transformed.
  • The notation ror(x) above signifies a 29 bit rotate right of the argument.
  • Not shown above for brevity, the result of each addition is masked with the value 0x1FFFFFFF before being stored. This masks off any data beyond the low 29 bits.

29 bit Integers?

The random number generator masks the data in the ring buffer to 29 bit, unsigned values. To understand this, it is first necessary to under why masking is needed at all, and secondly, why this was done at 29 bits.

Masking at some level is required because it is needed to simulate the numeric overflow of more primitive systems of arithmetic. In most systems, when the limit of an integer is reached, overflow occurs with no error indication. Ruby does not permit this to occur. To avoid overflow, Ruby transparently converts from a simple integer (FIXNUM class) to a multiple-precision number (BIGNUM class). The random number generator requires the computations to overflow, so masking the results forces the computation to act as if they had.

So why 29 bits? Why not 32? or 64? The issue here is performance. Arithmetic with BIGNUM values is much slower than with FIXNUM values. Further, the conversion between FIXNUM and BIGNUM is also slow. The 29 bit size was chosen to ensure that all computations remain with FIXNUM values without ever reaching the threshold for the switch to BIGNUM values. In 32 bit Ruby systems, 29 bits is the largest value that meets this requirement.

Code

Enough with all these words and pictures. The best way to gain insight into ruby code is to study ruby code! What follows is the critical snippet of code that makes this random number generator spin:

private

#Cycle through the PRNG once.
def do_spin
  @buffer[-2] = @buffer[0]
  @buffer[-1] = @buffer[1]

  (0...@depth).each do |idx|
    tmp = @buffer[idx+2]
    @buffer[idx] = (@buffer[idx+1] + ((tmp >> 1)|(tmp.odd? ? TOP : 0))) & CHOP
  end
end

The above is found in the spinner.rb file. For completeness of understanding, the following constants are defined in the fibonacci_rng.rb file:

CHOP = 0x1FFFFFFF
TOP  = 0x10000000

Error Detection

Like all systems, the fibonacci random number generator has a failure mode. If it should happen that all the internal data registers have a value of zero, the generator will be trapped in an endless state of zero output. It will cease to operate as a pseudo random number generator.

While it is possible to show that this cannot occur in small generators, the case for larger ones is more difficult to analyze. To this end, the code now incorporates a test that at least one non-zero register is present. If this test should fail an exception "InvalidFibonacciRngState" is raised so that the application can take appropriate action.

To date, torture testing of the generator has yielded no failures, but this is not a proof that one cannot happen.

The test scans the registers until it finds a non-zero value. This means that it almost always only needs to look at one register, saving a great deal of execution time.

Contributing

Creating a good pseudo random number generator is quite an undertaking. For this reason, any input is most welcomed. There are two basic plans by which this can be accomplished.

Plan A

  1. Fork it ( https://github.com/PeterCamilleri/fibonacci_rng/fork )
  2. Create your feature branch (git checkout -b my-new-feature)
  3. Commit your changes (git commit -am 'Add some feature')
  4. Push to the branch (git push origin my-new-feature)
  5. Create new Pull Request

Plan B

Go to the GitHub repository and raise an issue calling attention to some aspect that could use some TLC or a suggestion or an idea.