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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;20.&#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;20.&#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
  37       </p>
  38 <div class="blockquote"><blockquote class="blockquote"><p>
  39           <span class="inlinemediaobject"><img src="../../../equations/hypot.svg"></span>
  40
  41         </p></blockquote></div>
  42 <p>
  43         in such a way as to avoid undue underflow and overflow.
  44       </p>
  45 <p>
  46         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
  47         type calculation rules</em></span></a> when T1 and T2 are of different
  48         types.
  49       </p>
  50 <p>
  51         The final <a class="link" href="../../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
  52         be used to control the behaviour of the function: how it handles errors,
  53         what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">policy
  54         documentation for more details</a>.
  55       </p>
  56 <p>
  57         When calculating
  58       </p>
  59 <div class="blockquote"><blockquote class="blockquote"><p>
  60           <span class="inlinemediaobject"><img src="../../../equations/hypot.svg"></span>
  61
  62         </p></blockquote></div>
  63 <p>
  64         it's quite easy for the intermediate terms to either overflow or underflow,
  65         even though the result is in fact perfectly representable.
  66       </p>
  67 <h5>
  68 <a name="math_toolkit.powers.hypot.h0"></a>
  69         <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>
  70       </h5>
  71 <p>
  72         The function is even and symmetric in <span class="emphasis"><em>x</em></span> and <span class="emphasis"><em>y</em></span>,
  73         so first take assume <span class="emphasis"><em>x,y &gt; 0</em></span> and <span class="emphasis"><em>x &gt;
  74         y</em></span> (we can permute the arguments if this is not the case).
  75       </p>
  76 <p>
  77         Then if <span class="emphasis"><em>x * &#949; &gt;= y</em></span> we can simply return <span class="emphasis"><em>x</em></span>.
  78       </p>
  79 <p>
  80         Otherwise the result is given by:
  81       </p>
  82 <div class="blockquote"><blockquote class="blockquote"><p>
  83           <span class="inlinemediaobject"><img src="../../../equations/hypot2.svg"></span>
  84
  85         </p></blockquote></div>
  86 </div>
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