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  <header>
    <copyright>
      <year>2015</year>
      <holder>Ericsson AB. All Rights Reserved.</holder>
    </copyright>
    <legalnotice>
      Licensed under the Apache License, Version 2.0 (the "License");
      you may not use this file except in compliance with the License.
      You may obtain a copy of the License at
 
          http://www.apache.org/licenses/LICENSE-2.0

      Unless required by applicable law or agreed to in writing, software
      distributed under the License is distributed on an "AS IS" BASIS,
      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
      See the License for the specific language governing permissions and
      limitations under the License.

    </legalnotice>

    <title>rand</title>
    <prepared></prepared>
    <responsible></responsible>
    <docno>1</docno>
    <approved></approved>
    <checked></checked>
    <date></date>
    <rev>A</rev>
    <file>rand.xml</file>
  </header>
  <module>rand</module>
  <modulesummary>Pseudo random number generation</modulesummary>
  <description>
    <p>Random number generator.</p>

    <p>The module contains several different algorithms and can be
    extended with more in the future.  The current uniform
    distribution algorithms uses the
    <url href="http://xorshift.di.unimi.it">
    scrambled Xorshift algorithms by Sebastiano Vigna</url> and the
    normal distribution algorithm uses the
    <url href="http://www.jstatsoft.org/v05/i08">
      Ziggurat Method by Marsaglia and Tsang</url>.
    </p>

    <p>The implemented algorithms are:</p>
    <taglist>
      <tag><c>exsplus</c></tag> <item>Xorshift116+, 58 bits precision and period of 2^116-1.</item>
      <tag><c>exs64</c></tag> <item>Xorshift64*, 64 bits precision and a period of 2^64-1.</item>
      <tag><c>exs1024</c></tag> <item>Xorshift1024*, 64 bits precision and a period of 2^1024-1.</item>
    </taglist>

    <p>The current default algorithm is <c>exsplus</c>. The default
    may change in future. If a specific algorithm is required make
    sure to always use <seealso marker="#seed-1">seed/1</seealso>
    to initialize the state.
    </p>

    <p>Every time a random number is requested, a state is used to
    calculate it and a new state produced. The state can either be
    implicit or it can be an explicit argument and return value.
    </p>

    <p>The functions with implicit state use the process dictionary
    variable <c>rand_seed</c> to remember the current state.</p>

    <p>If a process calls <seealso marker="#uniform-0">uniform/0</seealso> or
    <seealso marker="#uniform-1">uniform/1</seealso> without
    setting a seed first, <seealso marker="#seed-1">seed/1</seealso>
    is called automatically with the default algorithm and creates a
    non-constant seed.</p>

    <p>The functions with explicit state never use the process
    dictionary.</p>

    <p>Examples:</p>
    <pre>
      %% Simple usage. Creates and seeds the default algorithm
      %% with a non-constant seed if not already done.
      R0 = rand:uniform(),
      R1 = rand:uniform(),

      %% Use a given algorithm.
      _ = rand:seed(exs1024),
      R2 = rand:uniform(),

      %% Use a given algorithm with a constant seed.
      _ = rand:seed(exs1024, {123, 123534, 345345}),
      R3 = rand:uniform(),

      %% Use the functional api with non-constant seed.
      S0 = rand:seed_s(exsplus),
      {R4, S1} = rand:uniform_s(S0),

      %% Create a standard normal deviate.
      {SND0, S2} = rand:normal_s(S1),
    </pre>

    <note><p>This random number generator is not cryptographically
    strong. If a strong cryptographic random number generator is
    needed, use one of functions in the
    <seealso marker="crypto:crypto">crypto</seealso>
    module, for example <c>crypto:strong_rand_bytes/1</c>.</p></note>
  </description>
  <datatypes>
    <datatype>
      <name name="alg"/>
    </datatype>

    <datatype>
      <name name="state"/>
      <desc><p>Algorithm dependent state.</p></desc>
    </datatype>

    <datatype>
      <name name="export_state"/>
      <desc><p>Algorithm dependent state which can be printed or saved to file.</p></desc>
    </datatype>
  </datatypes>

  <funcs>
    <func>
      <name name="seed" arity="1"/>
      <fsummary>Seed random number generator</fsummary>
      <desc>
	<marker id="seed-1"/>
	<p>Seeds random number generation with the given algorithm and time dependent
	data if <anno>AlgOrExpState</anno> is an algorithm.</p>
	<p>Otherwise recreates the exported seed in the process
	dictionary, and returns the state.
	<em>See also:</em> <seealso marker="#export_seed-0">export_seed/0</seealso>.</p>
      </desc>
    </func>
    <func>
      <name name="seed_s" arity="1"/>
      <fsummary>Seed random number generator</fsummary>
      <desc>
	<p>Seeds random number generation with the given algorithm and time dependent
	data if <anno>AlgOrExpState</anno> is an algorithm.</p>
	<p>Otherwise recreates the exported seed and returns the state.
	<em>See also:</em> <seealso marker="#export_seed-0">export_seed/0</seealso>.</p>
      </desc>
    </func>
    <func>
      <name name="seed" arity="2"/>
      <fsummary>Seed the random number generation</fsummary>
      <desc>
	<p>Seeds random number generation with the given algorithm and
	integers in the process dictionary and returns
	the state.</p>
      </desc>
    </func>
    <func>
      <name name="seed_s" arity="2"/>
      <fsummary>Seed the random number generation</fsummary>
      <desc>
	<p>Seeds random number generation with the given algorithm and
	integers and returns the state.</p>
      </desc>
    </func>

    <func>
      <name name="export_seed" arity="0"/>
      <fsummary>Export the random number generation state</fsummary>
      <desc><marker id="export_seed-0"/>
      <p>Returns the random number state in an external format.
      To be used with <seealso marker="#seed-1">seed/1</seealso>.</p>
      </desc>
    </func>

    <func>
      <name name="export_seed_s" arity="1"/>
      <fsummary>Export the random number generation state</fsummary>
      <desc><marker id="export_seed_s-1"/>
      <p>Returns the random number generator state in an external format.
      To be used with <seealso marker="#seed-1">seed/1</seealso>.</p>
      </desc>
    </func>

    <func>
      <name name="uniform" arity="0"/>
      <fsummary>Return a random float</fsummary>
      <desc>
	<marker id="uniform-0"/>
        <p>Returns a random float uniformly distributed in the value
        range <c>0.0 &lt; <anno>X</anno> &lt; 1.0 </c> and
        updates the state in the process dictionary.</p>
      </desc>
    </func>
    <func>
      <name name="uniform_s" arity="1"/>
      <fsummary>Return a random float</fsummary>
      <desc>
        <p>Given a state, <c>uniform_s/1</c> returns a random float
        uniformly distributed in the value range <c>0.0 &lt;
        <anno>X</anno> &lt; 1.0</c> and a new state.</p>
      </desc>
    </func>

    <func>
      <name name="uniform" arity="1"/>
      <fsummary>Return a random integer</fsummary>
      <desc>
	<marker id="uniform-1"/>
        <p>Given an integer <c><anno>N</anno> >= 1</c>,
        <c>uniform/1</c> returns a random integer uniformly
        distributed in the value range
	<c>1 &lt;= <anno>X</anno> &lt;= <anno>N</anno></c> and
        updates the state in the process dictionary.</p>
      </desc>
    </func>
    <func>
      <name name="uniform_s" arity="2"/>
      <fsummary>Return a random integer</fsummary>
      <desc>
        <p>Given an integer <c><anno>N</anno> >= 1</c> and a state,
        <c>uniform_s/2</c> returns a random integer uniformly
        distributed in the value range <c>1 &lt;= <anno>X</anno> &lt;=
        <anno>N</anno></c> and a new state.</p>
      </desc>
    </func>

    <func>
      <name name="normal" arity="0"/>
      <fsummary>Return a standard normal distributed random float</fsummary>
      <desc>
        <p>Returns a standard normal deviate float (that is, the mean
        is 0 and the standard deviation is 1) and updates the state in
        the process dictionary.</p>
      </desc>
    </func>
    <func>
      <name name="normal_s" arity="1"/>
      <fsummary>Return a standard normal distributed random float</fsummary>
      <desc>
        <p>Given a state, <c>normal_s/1</c> returns a standard normal
        deviate float (that is, the mean is 0 and the standard
        deviation is 1) and a new state.</p>
      </desc>
    </func>

  </funcs>
</erlref>
