ceph/src/boost/libs/math/doc/html/math_toolkit/powers/hypot.html

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  26 <div class="titlepage"><div><div><h3 class="title">
  27 <a name="math_toolkit.powers.hypot"></a><a class="link" href="hypot.html" title="hypot">hypot</a>
  28 </h3></div></div></div>
  29 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</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">&gt;</span>
  30 <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>
  31
  32 <span class="keyword">template</span> <span class="special">&lt;</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&#160;15.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
  33 <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&#160;15.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
  34 </pre>
  35 <p>
  36         <span class="bold"><strong>Effects: </strong></span> computes <span class="inlinemediaobject"><img src="../../../equations/hypot.svg"></span>
  37 in such a way
  38         as to avoid undue underflow and overflow.
  39       </p>
  40 <p>
  41         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
  42         type calculation rules</em></span></a> when T1 and T2 are of different
  43         types.
  44       </p>
  45 <p>
  46         The final <a class="link" href="../../policy.html" title="Chapter&#160;15.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
  47         be used to control the behaviour of the function: how it handles errors,
  48         what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter&#160;15.&#160;Policies: Controlling Precision, Error Handling etc">policy
  49         documentation for more details</a>.
  50       </p>
  51 <p>
  52         When calculating <span class="inlinemediaobject"><img src="../../../equations/hypot.svg"></span> it's quite easy for the intermediate terms to
  53         either overflow or underflow, even though the result is in fact perfectly
  54         representable.
  55       </p>
  56 <h5>
  57 <a name="math_toolkit.powers.hypot.h0"></a>
  58         <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>
  59       </h5>
  60 <p>
  61         The function is even and symmetric in x and y, so first take assume <span class="emphasis"><em>x,y
  62         &gt; 0</em></span> and <span class="emphasis"><em>x &gt; y</em></span> (we can permute the arguments
  63         if this is not the case).
  64       </p>
  65 <p>
  66         Then if <span class="emphasis"><em>x * &#949; &#160; &gt;= y</em></span> we can simply return <span class="emphasis"><em>x</em></span>.
  67       </p>
  68 <p>
  69         Otherwise the result is given by:
  70       </p>
  71 <p>
  72         <span class="inlinemediaobject"><img src="../../../equations/hypot2.svg"></span>
  73       </p>
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  77 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
  78       Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
  79       Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam Sewani,
  80       Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
  81         Distributed under the Boost Software License, Version 1.0. (See accompanying
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