105 lines
7.2 KiB
HTML
105 lines
7.2 KiB
HTML
<html>
|
||
<head>
|
||
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
|
||
<title>hypot</title>
|
||
<link rel="stylesheet" href="../../math.css" type="text/css">
|
||
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
|
||
<link rel="home" href="../../index.html" title="Math Toolkit 3.0.0">
|
||
<link rel="up" href="../powers.html" title="Basic Functions">
|
||
<link rel="prev" href="powm1.html" title="powm1">
|
||
<link rel="next" href="ct_pow.html" title="Compile Time Power of a Runtime Base">
|
||
</head>
|
||
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
|
||
<table cellpadding="2" width="100%"><tr>
|
||
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
|
||
<td align="center"><a href="../../../../../../index.html">Home</a></td>
|
||
<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td>
|
||
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
|
||
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
|
||
<td align="center"><a href="../../../../../../more/index.htm">More</a></td>
|
||
</tr></table>
|
||
<hr>
|
||
<div class="spirit-nav">
|
||
<a accesskey="p" href="powm1.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../powers.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="ct_pow.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="math_toolkit.powers.hypot"></a><a class="link" href="hypot.html" title="hypot">hypot</a>
|
||
</h3></div></div></div>
|
||
<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>
|
||
<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">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 21. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></span>
|
||
<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 21. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</span>
|
||
</pre>
|
||
<p>
|
||
<span class="bold"><strong>Effects: </strong></span> computes
|
||
</p>
|
||
<div class="blockquote"><blockquote class="blockquote"><p>
|
||
<span class="inlinemediaobject"><img src="../../../equations/hypot.svg"></span>
|
||
|
||
</p></blockquote></div>
|
||
<p>
|
||
in such a way as to avoid undue underflow and overflow.
|
||
</p>
|
||
<p>
|
||
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
|
||
type calculation rules</em></span></a> when T1 and T2 are of different
|
||
types.
|
||
</p>
|
||
<p>
|
||
The final <a class="link" href="../../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
|
||
be used to control the behaviour of the function: how it handles errors,
|
||
what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">policy
|
||
documentation for more details</a>.
|
||
</p>
|
||
<p>
|
||
When calculating
|
||
</p>
|
||
<div class="blockquote"><blockquote class="blockquote"><p>
|
||
<span class="inlinemediaobject"><img src="../../../equations/hypot.svg"></span>
|
||
|
||
</p></blockquote></div>
|
||
<p>
|
||
it's quite easy for the intermediate terms to either overflow or underflow,
|
||
even though the result is in fact perfectly representable.
|
||
</p>
|
||
<h5>
|
||
<a name="math_toolkit.powers.hypot.h0"></a>
|
||
<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>
|
||
</h5>
|
||
<p>
|
||
The function is even and symmetric in <span class="emphasis"><em>x</em></span> and <span class="emphasis"><em>y</em></span>,
|
||
so first take assume <span class="emphasis"><em>x,y > 0</em></span> and <span class="emphasis"><em>x >
|
||
y</em></span> (we can permute the arguments if this is not the case).
|
||
</p>
|
||
<p>
|
||
Then if <span class="emphasis"><em>x * ε >= y</em></span> we can simply return <span class="emphasis"><em>x</em></span>.
|
||
</p>
|
||
<p>
|
||
Otherwise the result is given by:
|
||
</p>
|
||
<div class="blockquote"><blockquote class="blockquote"><p>
|
||
<span class="inlinemediaobject"><img src="../../../equations/hypot2.svg"></span>
|
||
|
||
</p></blockquote></div>
|
||
</div>
|
||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||
<td align="left"></td>
|
||
<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
|
||
Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
|
||
Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||
Walker and Xiaogang Zhang<p>
|
||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||
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>)
|
||
</p>
|
||
</div></td>
|
||
</tr></table>
|
||
<hr>
|
||
<div class="spirit-nav">
|
||
<a accesskey="p" href="powm1.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../powers.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="ct_pow.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
|
||
</div>
|
||
</body>
|
||
</html>
|