1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
|
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values</title>
<link rel="stylesheet" href="../math.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
<link rel="up" href="../utils.html" title="Chapter 2. Floating Point Utilities">
<link rel="prev" href="fp_facets/rationale.html" title="Design Rationale">
<link rel="next" href="next_float/nextafter.html" title="Finding the Next Representable Value in a Specific Direction (nextafter)">
</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="fp_facets/rationale.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../utils.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="next_float/nextafter.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.next_float"></a><a class="link" href="next_float.html" title="Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values">Floating-Point Representation
Distance (ULP), and Finding Adjacent Floating-Point Values</a>
</h2></div></div></div>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="next_float/nextafter.html">Finding the Next Representable
Value in a Specific Direction (nextafter)</a></span></dt>
<dt><span class="section"><a href="next_float/float_next.html">Finding the Next
Greater Representable Value (float_next)</a></span></dt>
<dt><span class="section"><a href="next_float/float_prior.html">Finding the Next
Smaller Representable Value (float_prior)</a></span></dt>
<dt><span class="section"><a href="next_float/float_distance.html">Calculating the
Representation Distance Between Two Floating Point Values (ULP) float_distance</a></span></dt>
<dt><span class="section"><a href="next_float/float_advance.html">Advancing a Floating
Point Value by a Specific Representation Distance (ULP) float_advance</a></span></dt>
</dl></div>
<p>
<a href="http://en.wikipedia.org/wiki/Unit_in_the_last_place" target="_top">Unit of Least
Precision or Unit in the Last Place</a> is the gap between two different,
but as close as possible, floating-point numbers.
</p>
<p>
Most decimal values, for example 0.1, cannot be exactly represented as floating-point
values, but will be stored as the <a href="http://en.wikipedia.org/wiki/Floating_point#Representable_numbers.2C_conversion_and_rounding" target="_top">closest
representable floating-point</a>.
</p>
<p>
Functions are provided for finding adjacent greater and lesser floating-point
values, and estimating the number of gaps between any two floating-point values.
</p>
<p>
The floating-point type FPT must have has a fixed number of bits in the representation.
The number of bits may set at runtime, but must be the same for all numbers.
For example, <a href="http://shoup.net/ntl/doc/quad_float.txt" target="_top">NTL::quad_float</a>
type (fixed 128-bit representation) or <a href="http://shoup.net/ntl/doc/RR.txt" target="_top">NTL::RR</a>
type (arbitrary but fixed decimal digits, default 150) but <span class="bold"><strong>not</strong></span>
a type that extends the representation to provide an exact representation for
any number, for example <a href="http://keithbriggs.info/xrc.html" target="_top">XRC eXact
Real in C</a>.
</p>
</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 © 2006-2010, 2012-2014 Nikhar Agrawal,
Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
Holin, Bruno Lalande, John Maddock, Johan Råde, Gautam Sewani, Benjamin Sobotta,
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="fp_facets/rationale.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../utils.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="next_float/nextafter.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>
|