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26 <div class=
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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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"left"></td>
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"right"><div class=
"copyright-footer">Copyright
© 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
åde, 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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