@spec bits(non_neg_integer(), non_neg_integer()) :: float()

Entropy bits necessary to generate total number of puids with risk risk of repeat.

The total number of possible puids is 2^bits. Risk is expressed as a 1 in risk chance, so the probability of a repeat is 1/risk.

Example

iex> Puid.Entropy.bits(10.0e6, 1.0e12)
85.37013046707142

@spec bits_for_len(Puid.Chars.puid_chars(), non_neg_integer()) ::
  {:ok, non_neg_integer()} | {:error, String.t()}

Entropy bits for a binary of length len comprised of chars characters.

chars must be valid as per Chars.charlist/1.

Example

iex> Puid.Entropy.bits_for_len(:alphanum, 14)
{:ok, 83}

iex> Puid.Entropy.bits_for_len(~c'dingosky', 14)
{:ok, 42}

@spec bits_for_len!(Puid.Chars.puid_chars(), non_neg_integer()) :: non_neg_integer()

Same as Puid.Entropy.bits_for_len/2 but either returns bits or raises a Puid.Error

Example

iex> Puid.Entropy.bits_for_len!(:alphanum, 14)
83

iex> Puid.Entropy.bits_for_len!("dingosky", 14)
42

@spec bits_per_char(Puid.Chars.puid_chars()) :: {:ok, float()} | {:error, String.t()}

Entropy bits per chars character.

chars must be valid as per Chars.charlist/1.

Example

iex> Puid.Entropy.bits_per_char(:alphanum)
{:ok, 5.954196310386875}

iex> Puid.Entropy.bits_per_char("dingosky")
{:ok, 3.0}

@spec bits_per_char!(Puid.Chars.puid_chars()) :: float()

Same as bits_per_char/1 but either returns bits or raises a Puid.Error

Example

iex> Puid.Entropy.bits_per_char!(:alphanum)
5.954196310386875

Puid.Entropy.bits_per_char!("dingosky")
3.0

@spec len_for_bits(Puid.Chars.puid_chars(), non_neg_integer()) ::
  {:ok, non_neg_integer()} | {:error, String.t()}

Length needed for a string generated from chars to have entropy bits.

chars must be valid as per Chars.charlist/1.

Example

iex> Puid.Entropy.len_for_bits(:alphanum, 128)
{:ok, 22}

iex> Puid.Entropy.len_for_bits("dingosky", 128)
{:ok, 43}

@spec len_for_bits!(Puid.Chars.puid_chars(), non_neg_integer()) :: non_neg_integer()

Same as Puid.Entropy.len_for_bits/2 but either returns len or raises a Puid.Error

Example

iex> Puid.Entropy.len_for_bits!(:alphanum, 128)
22

iex> Puid.Entropy.len_for_bits!(~c'dingosky', 128)
43

@spec risk(bits :: float(), total :: float()) :: integer()

Risk of repeat in total number of events with bits bits entropy.

The total number of possible puids is 2^bits. Risk is expressed as a 1 in risk chance, so the probability of a repeat is 1/risk.

This approximation is conservative and will understate the true risk.

Example

iex> bits = 96
iex> total = 1.0e7
iex> Puid.Entropy.risk(bits, total)
1584563250285288
iex> 1.0 / 1584563250285288
6.31088724176809e-16

@spec total(bits :: float(), risk :: float()) :: integer()

Approximate total number of puids which can be generated using bits bits entropy at a risk risk of repeat.

The total number of possible puids is 2^bits. Risk is expressed as a 1 in risk chance, so the probability of a repeat is 1/risk.

This approximation is conservative and will understate the true total.

Example

iex> bits = 64
iex> risk = 1.0e9
iex> Puid.Entropy.total(bits, risk)
192077