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25 | <div class="section"> | |
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> | |
31 | ||
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> | |
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 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>. | |
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 | > 0</em></span> and <span class="emphasis"><em>x > 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 * ε   >= 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> | |
74 | </div> | |
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77 | <td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal, | |
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80 | Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p> | |
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