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<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.powers.hypot"></a><a class="link" href="hypot.html" title="hypot">hypot</a>
</h3></div></div></div>
<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</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">hypot</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">);</span>
<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter 14. 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">hypot</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</span>
</pre>
<p>
<span class="bold"><strong>Effects: </strong></span> computes <span class="inlinemediaobject"><img src="../../../equations/hypot.png"></span>
in such a way
as to avoid undue underflow and overflow.
</p>
<p>
The return type of this function is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
type calculation rules</em></span></a> when T1 and T2 are of different
types.
</p>
<p>
The final <a class="link" href="../../policy.html" title="Chapter 14. 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 14. Policies: Controlling Precision, Error Handling etc">policy
documentation for more details</a>.
</p>
<p>
When calculating <span class="inlinemediaobject"><img src="../../../equations/hypot.png"></span> it's quite easy for the intermediate terms to
either overflow or underflow, even though the result is in fact perfectly
representable.
</p>
<h5>
<a name="math_toolkit.powers.hypot.h0"></a>
<span class="phrase"><a name="math_toolkit.powers.hypot.implementation"></a></span><a class="link" href="hypot.html#math_toolkit.powers.hypot.implementation">Implementation</a>
</h5>
<p>
The function is even and symmetric in x and y, so first take assume <span class="emphasis"><em>x,y
> 0</em></span> and <span class="emphasis"><em>x > y</em></span> (we can permute the arguments
if this is not the case).
</p>
<p>
Then if <span class="emphasis"><em>x * ε   >= y</em></span> we can simply return <span class="emphasis"><em>x</em></span>.
</p>
<p>
Otherwise the result is given by:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../equations/hypot2.png"></span>
</p>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal,
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Holin, Bruno Lalande, John Maddock, Johan Råde, Gautam Sewani, Benjamin Sobotta,
Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
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