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<a name="mtwist-calling-conventions-1"></a>
<h3 class="subsection">D.12.1 <code>mtwist</code> calling conventions</h3>

<p>All of the functions in this library simulate a random draw from a
distribution. There is a choice of distribution statistics depending
on the function used.
</p>
<dl compact="compact">
<dt> <code>bern</code></dt>
<dd><p>takes a floating point number <var>p</var> between 0 and 1, encoded as in
<a href="math.html#math"><code>math</code></a>, and returns a boolean value, either <code>(nil,nil)</code> for
true or <code>nil</code> for false. A true value is returned only if a
random draw from a uniform distribution ranging from 0 to 1 is less
than <var>p</var>.  This function therefore simulates a draw from a
Bernoulli distribution. A <code>nil</code> value of <var>p</var> is treated as
1/2.
</p></dd>
<dt> <code>u_cont</code></dt>
<dd><p>takes a floating point number <var>x</var> as an
argument, and returns a random draw from a continuous uniform
distribution ranging from 0 to <var>x</var>. A <code>nil</code> value of <var>x</var>
is treated as unity.
</p></dd>
<dt> <code>u_disc</code></dt>
<dd><p>simulates a draw from a uniform discrete distribution whose domain
is the set of natural numbers from 0 to <var>n</var> - 1. The number <var>n</var>
is given as a parameter to this function, and the retuned value
is the draw.
</p>
<ul>
<li>
The returned value will have at most 64 bits regardless of <var>n</var>.
</li><li>
Natural numbers are encoded as described in
<a href="Representation-of-Numeric-and-Textual-Data.html#Representation-of-Numeric-and-Textual-Data">Representation of Numeric and Textual Data</a>.
</li><li>
If a value of 0 is passed for <var>n</var>, the full 64 bit range is
used.
</li></ul>
</dd>
<dt> <code>u_path</code></dt>
<dd><p>takes a pair of natural numbers <code>(<var>n</var>,<var>m</var>)</code> and returns a
randomly chosen tree (<a href="Raw-Material.html#Raw-Material">Raw Material</a>) with 1 leaf and <var>n</var>
non-leaves each having either a left or a right descendent but not
both. The number <var>m</var> constrains the result to fall within the
first <var>m</var> - 1 trees of this form enumerated by exhausting all
possibilities at lower levels before admitting a right descendent at a
higher level. Within these criteria, all possible results are equally
probable. Both numbers are masked to 64 bits, but if <var>m</var> is zero,
it is treated as 2^<var>n</var>.
</p></dd>
<dt> <code>u_enum</code></dt>
<dd><p>simulates a random draw from a uniform discrete distribution whose
domain is enumerated. The argument to the function is a non-empty list,
and the result is an item selected from the list, with all choices
being equally probable.
</p></dd>
<dt> <code>w_disc</code></dt>
<dd><p>simulates a random draw from a non-uniform, or &ldquo;weighted&rdquo; discrete
distribution whose domain is a set of consecutive natural numbers
starting from zero. The argument to the function is a list giving the
probability of each outcome starting from zero as a floating point
number. Probabilities must be non-negative but needn&rsquo;t be normalized.
</p></dd>
<dt> <code>w_enum</code></dt>
<dd><p>simulates a random draw from a non-uniform, or &ldquo;weighted&rdquo; discrete
distribution with an arbitrary domain enumerated in the argument. The
argument is a list of pairs <code>&lt;(<var>x</var>,<var>p</var>)..&gt;</code>, where
<var>x</var> is a possible outcome and <var>p</var> is its probability. The
result returned is one of the values of <var>x</var> from the input list
chosen at random according to the associated
probability. Probabilities must be non-negative but needn&rsquo;t be
normalized.
</p></dd>
</dl>

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