https://github.com/pma/lfsr

Elixir implementation of a binary Galois LFSR
https://github.com/pma/lfsr

Last synced: 2 months ago
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Elixir implementation of a binary Galois LFSR

• Host: GitHub
• URL: https://github.com/pma/lfsr
• Owner: pma
• License: mit
• Created: 2014-09-06T19:17:37.000Z (over 10 years ago)
• Default Branch: master
• Last Pushed: 2016-11-28T13:21:30.000Z (about 8 years ago)
• Last Synced: 2024-10-11T03:50:05.796Z (3 months ago)
• Language: Elixir
• Size: 14.6 KB
• Stars: 8
• Watchers: 3
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# LFSR

Elixir implementation of a binary Galois Linear Feedback Shift Register.

It can be used to generate out-of-order counters, since a LFSR of size n can

generate a sequence of length 2n-1 (without repetitions).

## Usage

Add LFSR as a dependency in your `mix.exs` file.

```elixir

def deps do

  [{:lfsr, "~> 0.0.2"}]

end

```

After you are done, run `mix deps.get` in your shell to fetch and compile LFSR. Start an interactive Elixir shell with `iex -S mix`.

```iex

iex> lfsr = LFSR.new(1, 16)

%LFSR{mask: 46080, state: 1}

iex> lfsr = lfsr |> LFSR.next |> LFSR.next

%LFSR{mask: 46080, state: 23040}

iex> LFSR.state(lfsr)

23040

```

### Usage with Streams

Let's generate a pseudo-random sequence of numbers between 1_000_000 and 9_999_999.

We need a 24-bit LFSR, since with a 23-bit we can only produce a sequence with length 8_388_607.

```iex

iex> LFSR.new(5_345_234, 24) \

...> |> Stream.iterate(&LFSR.next/1) \

...> |> Stream.map(&LFSR.state/1) \

...> |> Stream.filter(&(&1 in 1_000_000..9_999_999)) \

...> |> Enum.take(100)

[5345234, 2672617, 6697466, 3348733, 6342207, 9312455, 9930289, 9683736,

 4841868, 2420934, 1210467, 5787404, 2893702, 1446851, 5816952, 2908476,

 1454238, 8610569, 5036226, 2518113, 6658840, 3329420, 1664710, 6002284,

 3001142, 1500571, 5823667, 5315478, 2657739, 6230457, 8111214, 4055607,

 8764486, 4382243, 5397444, 2698722, 1349361, 6890940, 3445470, 1722735,

 8472877, 5001803, 5474889, 7922322, 3961161, 6495314, 3247657, 6316938,

 3158469, 6294641, ...]

```

### Usage with Agents

```elixir

defmodule PRNG do

  def start_link do

    Agent.start_link(fn -> LFSR.new(5_345_234, 24) end, name: __MODULE__)

  end

  def next do

    Agent.get_and_update(__MODULE__, fn lfsr ->

      lfsr = next_valid(lfsr)

      {lfsr.state, lfsr}

    end)

  end

  defp next_valid(%LFSR{} = lfsr) do

    lfsr = LFSR.next(lfsr)

    if lfsr.state in 1_000_000..9_999_999, do: lfsr, else: next_valid(lfsr)

  end

end

```

```iex

iex> PRNG.start_link

{:ok, #PID<0.101.0>}

iex> PRNG.next

2672617

iex> PRNG.next

6697466

```

## References

* http://en.wikipedia.org/wiki/Maximum_length_sequence

* http://en.wikipedia.org/wiki/Linear_feedback_shift_register#Galois_LFSRs

* http://www.eej.ulst.ac.uk/~ian/modules/EEE515/files/old_files/lfsr/lfsr_table.pdf