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>ForSyDe-3.1.1: ForSyDe's Haskell-embedded Domain Specific Language.</TD
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><A HREF="src/ForSyDe-Shallow-StochasticLib.html"
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><FONT SIZE="6"
>ForSyDe.Shallow.StochasticLib</FONT
></TD
><TD ALIGN="right"
><TABLE CLASS="narrow" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="infohead"
>Portability</TD
><TD CLASS="infoval"
>portable</TD
></TR
><TR
><TD CLASS="infohead"
>Stability</TD
><TD CLASS="infoval"
>experimental</TD
></TR
><TR
><TD CLASS="infohead"
>Maintainer</TD
><TD CLASS="infoval"
>forsyde-dev@ict.kth.se</TD
></TR
></TABLE
></TD
></TR
></TABLE
></TD
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><TR
><TD CLASS="s15"
></TD
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><TD
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="section4"
><B
>Contents</B
></TD
></TR
><TR
><TD
><DL
><DT
><A HREF="#1"
>Select based synchronous process constructors
</A
></DT
><DT
><A HREF="#2"
>Elementary stochastic processes
</A
></DT
></DL
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
>Description</TD
></TR
><TR
><TD CLASS="doc"
><P
>The stochastic library provides a few stochastic skeletons, which are
 relatives to the skeletons of the synchronous library. These skeletons are
 based on two elementary functions, <TT
><A HREF="ForSyDe-Shallow-StochasticLib.html#v%3AsigmaUn"
>sigmaUn</A
></TT
> and <TT
><A HREF="ForSyDe-Shallow-StochasticLib.html#v%3AsigmaGe"
>sigmaGe</A
></TT
>
 which provide stochastic signals. The background and motivation for this
 approach is described in the paper 
</P
><P
>Axel Jantsch, Ingo Sander, and Wenbiao Wu,
 &quot;The usage of stochastic processes in embedded system specifications&quot;,
 In <EM
>Proceedings of the Ninth International Symposium on Hardware and Software Codesign</EM
>, 
 April 2001 (<A HREF="http://web.it.kth.se/~axel/papers/2001/codes-2001.pdf"
>http://web.it.kth.se/~axel/papers/2001/codes-2001.pdf</A
>). 
</P
><P
>Unfortunately, not all of the suggested skeletons are
 implemented. In particular, consolidation-based process
 constructors and all constructors for the untimed and the discrete
 timed MoCs are missing.
</P
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
>Synopsis</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A HREF="#v%3AselMapSY"
>selMapSY</A
> ::  <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Int.html#t%3AInt"
>Int</A
> -&gt; (a -&gt; b) -&gt; (a -&gt; b) -&gt; <A HREF="ForSyDe-Shallow-Signal.html#t%3ASignal"
>Signal</A
> a -&gt; <A HREF="ForSyDe-Shallow-Signal.html#t%3ASignal"
>Signal</A
> b</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AselScanlSY"
>selScanlSY</A
> ::  <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Int.html#t%3AInt"
>Int</A
> -&gt; (a -&gt; b -&gt; a) -&gt; (a -&gt; b -&gt; a) -&gt; a -&gt; <A HREF="ForSyDe-Shallow-Signal.html#t%3ASignal"
>Signal</A
> b -&gt; <A HREF="ForSyDe-Shallow-Signal.html#t%3ASignal"
>Signal</A
> a</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AselMealySY"
>selMealySY</A
> ::  <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Int.html#t%3AInt"
>Int</A
> -&gt; <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Int.html#t%3AInt"
>Int</A
> -&gt; (a -&gt; b -&gt; a) -&gt; (a -&gt; b -&gt; a) -&gt; (a -&gt; b -&gt; c) -&gt; (a -&gt; b -&gt; c) -&gt; a -&gt; <A HREF="ForSyDe-Shallow-Signal.html#t%3ASignal"
>Signal</A
> b -&gt; <A HREF="ForSyDe-Shallow-Signal.html#t%3ASignal"
>Signal</A
> c</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AselMooreSY"
>selMooreSY</A
> ::  <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Int.html#t%3AInt"
>Int</A
> -&gt; <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Int.html#t%3AInt"
>Int</A
> -&gt; (a -&gt; b -&gt; a) -&gt; (a -&gt; b -&gt; a) -&gt; (a -&gt; c) -&gt; (a -&gt; c) -&gt; a -&gt; <A HREF="ForSyDe-Shallow-Signal.html#t%3ASignal"
>Signal</A
> b -&gt; <A HREF="ForSyDe-Shallow-Signal.html#t%3ASignal"
>Signal</A
> c</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AsigmaUn"
>sigmaUn</A
> :: <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Int.html#t%3AInt"
>Int</A
> -&gt; (<A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Int.html#t%3AInt"
>Int</A
>, <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Int.html#t%3AInt"
>Int</A
>) -&gt; <A HREF="ForSyDe-Shallow-Signal.html#t%3ASignal"
>Signal</A
> <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Int.html#t%3AInt"
>Int</A
></TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AsigmaGe"
>sigmaGe</A
> :: (<A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Prelude.html#t%3AFloat"
>Float</A
> -&gt; <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Prelude.html#t%3AFloat"
>Float</A
>) -&gt; <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Int.html#t%3AInt"
>Int</A
> -&gt; (<A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Int.html#t%3AInt"
>Int</A
>, <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Int.html#t%3AInt"
>Int</A
>) -&gt; <A HREF="ForSyDe-Shallow-Signal.html#t%3ASignal"
>Signal</A
> <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Int.html#t%3AInt"
>Int</A
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
><A NAME="1"
><A NAME="1"
>Select based synchronous process constructors
</A
></A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="topdecl"
><TABLE CLASS="declbar"
><TR
><TD CLASS="declname"
><A NAME="v:selMapSY"
><A NAME="v%3AselMapSY"
></A
></A
><B
>selMapSY</B
></TD
><TD CLASS="declbut"
><A HREF="src/ForSyDe-Shallow-StochasticLib.html#selMapSY"
>Source</A
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="arg"
>:: <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Int.html#t%3AInt"
>Int</A
></TD
><TD CLASS="rdoc"
>The seed for the stochastic process
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; a -&gt; b</TD
><TD CLASS="rdoc"
>The first alternative function
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; a -&gt; b</TD
><TD CLASS="rdoc"
>The second alternative function
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; <A HREF="ForSyDe-Shallow-Signal.html#t%3ASignal"
>Signal</A
> a</TD
><TD CLASS="rdoc"
>The input signal
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; <A HREF="ForSyDe-Shallow-Signal.html#t%3ASignal"
>Signal</A
> b</TD
><TD CLASS="rdoc"
>The output signal of the process
</TD
></TR
><TR
><TD CLASS="ndoc" COLSPAN="2"
>The skeleton <TT
><A HREF="ForSyDe-Shallow-StochasticLib.html#v%3AselMapSY"
>selMapSY</A
></TT
> is a stochastic variant of
 <TT
><A HREF="ForSyDe-Shallow-SynchronousLib.html#v%3AmapSY"
>mapSY</A
></TT
>. It has an internal stochastic process and selects one
 out of two combinatorial functions depending on the output of the
 stochastic process.
</TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="topdecl"
><TABLE CLASS="declbar"
><TR
><TD CLASS="declname"
><A NAME="v:selScanlSY"
><A NAME="v%3AselScanlSY"
></A
></A
><B
>selScanlSY</B
></TD
><TD CLASS="declbut"
><A HREF="src/ForSyDe-Shallow-StochasticLib.html#selScanlSY"
>Source</A
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="arg"
>:: <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Int.html#t%3AInt"
>Int</A
></TD
><TD CLASS="rdoc"
>The seed
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; a -&gt; b -&gt; a</TD
><TD CLASS="rdoc"
>The first alternative next-state function
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; a -&gt; b -&gt; a</TD
><TD CLASS="rdoc"
>The second alternative function
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; a</TD
><TD CLASS="rdoc"
>The initial state
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; <A HREF="ForSyDe-Shallow-Signal.html#t%3ASignal"
>Signal</A
> b</TD
><TD CLASS="rdoc"
>The input signal
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; <A HREF="ForSyDe-Shallow-Signal.html#t%3ASignal"
>Signal</A
> a</TD
><TD CLASS="rdoc"
>The output signal
</TD
></TR
><TR
><TD CLASS="ndoc" COLSPAN="2"
>The skeleton <TT
><A HREF="ForSyDe-Shallow-StochasticLib.html#v%3AselScanlSY"
>selScanlSY</A
></TT
> is a stochastic variant of <TT
><A HREF="ForSyDe-Shallow-SynchronousLib.html#v%3AscanlSY"
>scanlSY</A
></TT
>.
</TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="topdecl"
><TABLE CLASS="declbar"
><TR
><TD CLASS="declname"
><A NAME="v:selMealySY"
><A NAME="v%3AselMealySY"
></A
></A
><B
>selMealySY</B
></TD
><TD CLASS="declbut"
><A HREF="src/ForSyDe-Shallow-StochasticLib.html#selMealySY"
>Source</A
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="arg"
>:: <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Int.html#t%3AInt"
>Int</A
></TD
><TD CLASS="rdoc"
>The seed for the next-state function
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Int.html#t%3AInt"
>Int</A
></TD
><TD CLASS="rdoc"
>The seed for the output function
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; a -&gt; b -&gt; a</TD
><TD CLASS="rdoc"
>First alternative for the next-state function
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; a -&gt; b -&gt; a</TD
><TD CLASS="rdoc"
>Second alternative for the next-state function
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; a -&gt; b -&gt; c</TD
><TD CLASS="rdoc"
>First alternative for the output function
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; a -&gt; b -&gt; c</TD
><TD CLASS="rdoc"
>Second alternative for the output function
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; a</TD
><TD CLASS="rdoc"
>The initial state
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; <A HREF="ForSyDe-Shallow-Signal.html#t%3ASignal"
>Signal</A
> b</TD
><TD CLASS="rdoc"
>The input signal
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; <A HREF="ForSyDe-Shallow-Signal.html#t%3ASignal"
>Signal</A
> c</TD
><TD CLASS="rdoc"
>The output signal
</TD
></TR
><TR
><TD CLASS="ndoc" COLSPAN="2"
><TT
><A HREF="ForSyDe-Shallow-StochasticLib.html#v%3AselMealySY"
>selMealySY</A
></TT
> is the stochastic variant of mealySY. Both the 
   next-state and the output function is randomly selected based on a 
   uniform distribution.
</TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="topdecl"
><TABLE CLASS="declbar"
><TR
><TD CLASS="declname"
><A NAME="v:selMooreSY"
><A NAME="v%3AselMooreSY"
></A
></A
><B
>selMooreSY</B
></TD
><TD CLASS="declbut"
><A HREF="src/ForSyDe-Shallow-StochasticLib.html#selMooreSY"
>Source</A
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="arg"
>:: <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Int.html#t%3AInt"
>Int</A
></TD
><TD CLASS="rdoc"
>The seed for the next-state function
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Int.html#t%3AInt"
>Int</A
></TD
><TD CLASS="rdoc"
>The seed for the output function
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; a -&gt; b -&gt; a</TD
><TD CLASS="rdoc"
>First alternative for the next-state function
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; a -&gt; b -&gt; a</TD
><TD CLASS="rdoc"
>Second alternative for the next-state function
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; a -&gt; c</TD
><TD CLASS="rdoc"
>First alternative for the output function
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; a -&gt; c</TD
><TD CLASS="rdoc"
>Second alternative for the output function
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; a</TD
><TD CLASS="rdoc"
>The initial state
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; <A HREF="ForSyDe-Shallow-Signal.html#t%3ASignal"
>Signal</A
> b</TD
><TD CLASS="rdoc"
>The input signal
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; <A HREF="ForSyDe-Shallow-Signal.html#t%3ASignal"
>Signal</A
> c</TD
><TD CLASS="rdoc"
>The output signal
</TD
></TR
><TR
><TD CLASS="ndoc" COLSPAN="2"
><TT
><A HREF="ForSyDe-Shallow-StochasticLib.html#v%3AselMooreSY"
>selMooreSY</A
></TT
> is the stochastic variant of mooreSY. Both the 
   next-state and the output function is randomly selected based on a 
   uniform distribution.
</TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
><A NAME="2"
><A NAME="2"
>Elementary stochastic processes
</A
></A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="topdecl"
><TABLE CLASS="declbar"
><TR
><TD CLASS="declname"
><A NAME="v:sigmaUn"
><A NAME="v%3AsigmaUn"
></A
></A
><B
>sigmaUn</B
></TD
><TD CLASS="declbut"
><A HREF="src/ForSyDe-Shallow-StochasticLib.html#sigmaUn"
>Source</A
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="arg"
>:: <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Int.html#t%3AInt"
>Int</A
></TD
><TD CLASS="rdoc"
>The seed
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; (<A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Int.html#t%3AInt"
>Int</A
>, <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Int.html#t%3AInt"
>Int</A
>)</TD
><TD CLASS="rdoc"
>The interval from which the stochastic values are 
  taken
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; <A HREF="ForSyDe-Shallow-Signal.html#t%3ASignal"
>Signal</A
> <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Int.html#t%3AInt"
>Int</A
></TD
><TD CLASS="rdoc"
>The sequence of stochastic values
</TD
></TR
><TR
><TD CLASS="ndoc" COLSPAN="2"
><TT
><A HREF="ForSyDe-Shallow-StochasticLib.html#v%3AsigmaUn"
>sigmaUn</A
></TT
> generates a signal list of uniformly distributed Int within
 the given range and with a given seed. 
</TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="topdecl"
><TABLE CLASS="declbar"
><TR
><TD CLASS="declname"
><A NAME="v:sigmaGe"
><A NAME="v%3AsigmaGe"
></A
></A
><B
>sigmaGe</B
></TD
><TD CLASS="declbut"
><A HREF="src/ForSyDe-Shallow-StochasticLib.html#sigmaGe"
>Source</A
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="arg"
>:: <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Prelude.html#t%3AFloat"
>Float</A
> -&gt; <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Prelude.html#t%3AFloat"
>Float</A
></TD
><TD CLASS="rdoc"
>The stochastic distribution
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Int.html#t%3AInt"
>Int</A
></TD
><TD CLASS="rdoc"
>The seed
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; (<A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Int.html#t%3AInt"
>Int</A
>, <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Int.html#t%3AInt"
>Int</A
>)</TD
><TD CLASS="rdoc"
>The range
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; <A HREF="ForSyDe-Shallow-Signal.html#t%3ASignal"
>Signal</A
> <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Int.html#t%3AInt"
>Int</A
></TD
><TD CLASS="rdoc"
>The sequence of stochastic values
</TD
></TR
><TR
><TD CLASS="ndoc" COLSPAN="2"
><P
><TT
><A HREF="ForSyDe-Shallow-StochasticLib.html#v%3AsigmaGe"
>sigmaGe</A
></TT
> is a more general stochastic process. The first argument is a
 function f which describes the distribution. For each value v in the
 given range (r1,r2), f(v) is the probability that v is generated.  
</P
><P
>Note, that the user has to make sure that sum(f(v))=1 for v in (r1,r2).
</P
><P
>For illustration consider the following example.
</P
><PRE
> pdist :: Float -&gt; Float
 pdist d = 1\/\(2**d\)
 pdistsum 1 = pdist 1
 pdistsum d = \(pdist d\) + \(pdistsum \(d-1\)\)
</PRE
><PRE
> pdistnorm :: Float -&gt; Float -&gt; Float
 pdistnorm dmax d = 1\/((pdistsum dmax) * (2**d))
</PRE
><P
><TT
>pdistnorm dmax d</TT
> gives the probability of a value &lt;= d;
</P
><P
><TT
>pdistnorm dmax dmax</TT
> is always 1.0
</P
><P
>Hence, using pdistnorm as a function in <TT
><A HREF="ForSyDe-Shallow-StochasticLib.html#v%3AsigmaGe"
>sigmaGe</A
></TT
> gives an exponantial
 distribution for values in the range [0, dmax].
</P
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