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<!DOCTYPE erlref SYSTEM "erlref.dtd">
<erlref>
<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.
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distributed under the License is distributed on an "AS IS" BASIS,
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<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>For some algorithms, jump functions are provided for generating
non-overlapping sequences for parallel computations.
The jump functions perform calculations
equivalent to perform a large number of repeated calls
for calculating new states. </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>
<p>Jump function: equivalent to 2^64 calls</p>
</item>
<tag><c>exs64</c></tag>
<item>
<p>Xorshift64*, 64 bits precision and a period of 2^64-1</p>
<p>Jump function: not available</p>
</item>
<tag><c>exs1024</c></tag>
<item>
<p>Xorshift1024*, 64 bits precision and a period of 2^1024-1</p>
<p>Jump function: equivalent to 2^512 calls</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="jump" arity="0"/>
<fsummary>Return the seed after performing jump calculation
to the state in the process dictionary.</fsummary>
<desc><marker id="jump-0" />
<p>Returns the state
after performing jump calculation
to the state in the process dictionary.</p>
<p>This function generates a <c>not_implemented</c> error exception
when the jump function is not implemented for
the algorithm specified in the state
in the process dictionary.</p>
</desc>
</func>
<func>
<name name="jump" arity="1"/>
<fsummary>Return the seed after performing jump calculation.</fsummary>
<desc><marker id="jump-1" />
<p>Returns the state after performing jump calculation
to the given state. </p>
<p>This function generates a <c>not_implemented</c> error exception
when the jump function is not implemented for
the algorithm specified in the 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>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 < <anno>X</anno> < 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 <= <anno>X</anno> <= <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 <
<anno>X</anno> < 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 <= <anno>X</anno> <= <anno>N</anno></c> and a
new state.</p>
</desc>
</func>
</funcs>
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