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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"><</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>
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>
32 <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 15. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></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 15. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</span>
36 <span class="bold"><strong>Effects: </strong></span> computes <span class="inlinemediaobject"><img src="../../../equations/hypot.svg"></span>
38 as to avoid undue underflow and overflow.
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
46 The final <a class="link" href="../../policy.html" title="Chapter 15. 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 15. Policies: Controlling Precision, Error Handling etc">policy
49 documentation for more details</a>.
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
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>
61 The function is even and symmetric in x and y, so first take assume <span class="emphasis"><em>x,y
62 > 0</em></span> and <span class="emphasis"><em>x > y</em></span> (we can permute the arguments
63 if this is not the case).
66 Then if <span class="emphasis"><em>x * ε   >= y</em></span> we can simply return <span class="emphasis"><em>x</em></span>.
69 Otherwise the result is given by:
72 <span class="inlinemediaobject"><img src="../../../equations/hypot2.svg"></span>
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78 Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
79 Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, 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
82 file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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