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  <header>
    <copyright>
      <year>2015</year><year>2016</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>This module provides a random number generator. The module contains
      a number of algorithms. The uniform distribution algorithms use the
      <url href="http://xorshift.di.unimi.it">scrambled Xorshift algorithms by
      Sebastiano Vigna</url>. The normal distribution algorithm uses the
      <url href="http://www.jstatsoft.org/v05/i08">Ziggurat Method by Marsaglia
      and Tsang</url>.</p>

    <p>The following algorithms are provided:</p>

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

    <p>The default algorithm is <c>exsplus</c>. If a specific algorithm is
      required, ensure to always use <seealso marker="#seed-1">
      <c>seed/1</c></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 is produced. The state can either be
      implicit or 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"><c>uniform/0</c></seealso> or
      <seealso marker="#uniform-1"><c>uniform/1</c></seealso> without
      setting a seed first, <seealso marker="#seed-1"><c>seed/1</c></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><em>Examples:</em></p>

    <p>Simple use; creates and seeds the default algorithm
      with a non-constant seed if not already done:</p>

    <pre>
R0 = rand:uniform(),
R1 = rand:uniform(),</pre>

    <p>Use a specified algorithm:</p>

    <pre>
_ = rand:seed(exs1024),
R2 = rand:uniform(),</pre>

    <p>Use a specified algorithm with a constant seed:</p>

    <pre>
_ = rand:seed(exs1024, {123, 123534, 345345}),
R3 = rand:uniform(),</pre>

   <p>Use the functional API with a non-constant seed:</p>

   <pre>
S0 = rand:seed_s(exsplus),
{R4, S1} = rand:uniform_s(S0),</pre>

   <p>Create a standard normal deviate:</p>

   <pre>
{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"><c>crypto</c></seealso>
        module, for example, <seealso marker="crypto:crypto">
        <c>crypto:strong_rand_bytes/1</c></seealso>.</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 that can be printed or saved to
        file.</p></desc>
    </datatype>
  </datatypes>

  <funcs>
    <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"><c>seed/1</c></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"><c>seed/1</c></seealso>.</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>Returns, for a specified state, a standard normal
          deviate float (that is, the mean is 0 and the standard
          deviation is 1) and a new state.</p>
      </desc>
    </func>

    <func>
      <name name="seed" arity="1"/>
      <fsummary>Seed random number generator.</fsummary>
      <desc>
        <marker id="seed-1"/>
        <p>Seeds random number generation with the specifed 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. See also
          <seealso marker="#export_seed-0"><c>export_seed/0</c></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 specified algorithm and
          integers in the process dictionary and returns the state.</p>
      </desc>
    </func>

    <func>
      <name name="seed_s" arity="1"/>
      <fsummary>Seed random number generator.</fsummary>
      <desc>
        <p>Seeds random number generation with the specifed algorithm and
          time-dependent data if <anno>AlgOrExpState</anno> is an algorithm.</p>
        <p>Otherwise recreates the exported seed and returns the state.
          See also <seealso marker="#export_seed-0">
          <c>export_seed/0</c></seealso>.</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 specified algorithm and
          integers and returns the state.</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" arity="1"/>
      <fsummary>Return a random integer.</fsummary>
      <desc><marker id="uniform-1"/>
        <p>Returns, for a specified integer <c><anno>N</anno> >= 1</c>,
          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="1"/>
      <fsummary>Return a random float.</fsummary>
      <desc>
        <p>Returns, for a specified state, 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_s" arity="2"/>
      <fsummary>Return a random integer.</fsummary>
      <desc>
        <p>Returns, for a specified integer <c><anno>N</anno> >= 1</c>
          and a state, 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>
  </funcs>
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