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<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span>
<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">acosh</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
-<span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter 19. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></span>
-<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">acosh</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter 19. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</span>
+<span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter 20. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></span>
+<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">acosh</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter 20. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</span>
</pre>
<p>
Computes the reciprocal of (the restriction to the range of <code class="literal">[0;+∞[</code>)
type calculation rules</em></span></a>: the return type is <code class="computeroutput"><span class="keyword">double</span></code> when T is an integer type, and T otherwise.
</p>
<p>
- The final <a class="link" href="../../policy.html" title="Chapter 19. Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
+ The final <a class="link" href="../../policy.html" title="Chapter 20. Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
be used to control the behaviour of the function: how it handles errors,
- what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter 19. Policies: Controlling Precision, Error Handling etc">policy
+ what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter 20. Policies: Controlling Precision, Error Handling etc">policy
documentation for more details</a>.
</p>
-<p>
- <span class="inlinemediaobject"><img src="../../../graphs/acosh.svg" align="middle"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../graphs/acosh.svg" align="middle"></span>
+
+ </p></blockquote></div>
<h5>
<a name="math_toolkit.inv_hyper.acosh.h0"></a>
<span class="phrase"><a name="math_toolkit.inv_hyper.acosh.accuracy"></a></span><a class="link" href="acosh.html#math_toolkit.inv_hyper.acosh.accuracy">Accuracy</a>
</h5>
<p>
- Generally accuracy is to within 1 or 2 epsilon across all supported platforms.
+ Generally accuracy is to within 1 or 2 <a href="http://en.wikipedia.org/wiki/Machine_epsilon" target="_top">machine
+ epsilon</a> across all supported platforms.
</p>
<h5>
<a name="math_toolkit.inv_hyper.acosh.h1"></a>
to give full function coverage computed at high precision using the "naive"
formula:
</p>
-<p>
- <span class="inlinemediaobject"><img src="../../../equations/acosh1.svg"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../equations/acosh1.svg"></span>
+
+ </p></blockquote></div>
<p>
along with a selection of sanity check values computed using functions.wolfram.com
to at least 50 decimal digits.
<p>
For sufficiently large x, we can use the <a href="http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/06/01/0001/" target="_top">approximation</a>:
</p>
-<p>
- <span class="inlinemediaobject"><img src="../../../equations/acosh2.svg"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../equations/acosh2.svg"></span>
+
+ </p></blockquote></div>
<p>
For x sufficiently close to 1 we can use the <a href="http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/04/01/0001/" target="_top">approximation</a>:
</p>
-<p>
- <span class="inlinemediaobject"><img src="../../../equations/acosh4.svg"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../equations/acosh4.svg"></span>
+
+ </p></blockquote></div>
<p>
Otherwise for x close to 1 we can use the following rearrangement of the
primary definition to preserve accuracy:
</p>
-<p>
- <span class="inlinemediaobject"><img src="../../../equations/acosh3.svg"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../equations/acosh3.svg"></span>
+
+ </p></blockquote></div>
<p>
Otherwise the <a href="http://functions.wolfram.com/ElementaryFunctions/ArcCosh/02/" target="_top">primary
definition</a> is used:
</p>
-<p>
- <span class="inlinemediaobject"><img src="../../../equations/acosh1.svg"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../equations/acosh1.svg"></span>
+
+ </p></blockquote></div>
</div>
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