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<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.utils.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>
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<div class="toc"><dl>
<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>
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<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 closest representable floating-point.
</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>.
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<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<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>)
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