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<?xml version='1.0'?>
<html xmlns='http://www.w3.org/1999/xhtml'
      xmlns:math='http://www.w3.org/1998/Math/MathML'
>
<head>
<title>exp_eps: Implementation</title>
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<center><b><big><big>exp_eps: Implementation</big></big></b></center>
<code><font color="blue"><pre style='display:inline'> 
template &lt;class Type&gt;
Type exp_eps(const Type &amp;x, const Type &amp;epsilon)
{	// abs_x = |x|
	Type abs_x = x;
	if( Type(0) &gt; x )
		abs_x = - x;
	// initialize
	int  k    = 0;          // initial order 
	Type term = 1.;         // term = |x|^k / k !
	Type sum  = term;       // initial sum
	while(term &gt; epsilon)
	{	k         = k + 1;          // order for next term
		Type temp = term * abs_x;   // term = |x|^k / (k-1)!
		term      = temp / Type(k); // term = |x|^k / k !
		sum       = sum + term;     // sum  = 1 + ... + |x|^k / k !
	}
	// In the case where x is negative, use exp(x) = 1 / exp(-|x|)
	if( Type(0) &gt; x ) 
		sum = Type(1) / sum;
	return sum;
}
</pre>

</font></code>


<hr/>Input File: introduction/exp_apx/exp_eps.omh

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