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<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>
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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>
<dt><span class="section"><a href="next_float/ulp.html">Obtaining the Size of a
      Unit In the Last Place - ULP</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), <a href="http://shoup.net/ntl/doc/RR.txt" target="_top">NTL::RR</a>
      type (arbitrary but fixed decimal digits, default 150) or <a href="../../../../../libs/multiprecision/doc/html/index.html" target="_top">Boost.Multiprecision</a>
      <a href="../../../../../libs/multiprecision/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html" target="_top">cpp_dec_float</a>
      and<a href="../../../../../libs/multiprecision/doc/html/boost_multiprecision/tut/floats/cpp_bin_float.html" target="_top">cpp_bin_float</a>
      are fixed at runtime, 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>
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      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>)
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	4	<title>Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values</title>
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	6	<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
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	24	</div>
	25	<div class="section">
	26	<div class="titlepage"><div><div><h2 class="title" style="clear: both">
	27	<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
	28	Distance (ULP), and Finding Adjacent Floating-Point Values</a>
	29	</h2></div></div></div>
	30	<div class="toc"><dl>
	31	<dt><span class="section"><a href="next_float/nextafter.html">Finding the Next Representable
	32	Value in a Specific Direction (nextafter)</a></span></dt>
	33	<dt><span class="section"><a href="next_float/float_next.html">Finding the Next
	34	Greater Representable Value (float_next)</a></span></dt>
	35	<dt><span class="section"><a href="next_float/float_prior.html">Finding the Next
	36	Smaller Representable Value (float_prior)</a></span></dt>
	37	<dt><span class="section"><a href="next_float/float_distance.html">Calculating the
	38	Representation Distance Between Two floating-point Values (ULP) float_distance</a></span></dt>
	39	<dt><span class="section"><a href="next_float/float_advance.html">Advancing a floating-point
	40	Value by a Specific Representation Distance (ULP) float_advance</a></span></dt>
	41	<dt><span class="section"><a href="next_float/ulp.html">Obtaining the Size of a
	42	Unit In the Last Place - ULP</a></span></dt>
	43	</dl></div>
	44	<p>
	45	<a href="http://en.wikipedia.org/wiki/Unit_in_the_last_place" target="_top">Unit of Least
	46	Precision or Unit in the Last Place</a> is the gap between two different,
	47	but as close as possible, floating-point numbers.
	48	</p>
	49	<p>
	50	Most decimal values, for example 0.1, cannot be exactly represented as floating-point
	51	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
	52	representable floating-point</a>.
	53	</p>
	54	<p>
	55	Functions are provided for finding adjacent greater and lesser floating-point
	56	values, and estimating the number of gaps between any two floating-point values.
	57	</p>
	58	<p>
	59	The floating-point type (FPT) must have has a fixed number of bits in the representation.
	60	The number of bits may set at runtime, but must be the same for all numbers.
	61	For example, <a href="http://shoup.net/ntl/doc/quad_float.txt" target="_top">NTL::quad_float</a>
	62	type (fixed 128-bit representation), <a href="http://shoup.net/ntl/doc/RR.txt" target="_top">NTL::RR</a>
	63	type (arbitrary but fixed decimal digits, default 150) or <a href="../../../../../libs/multiprecision/doc/html/index.html" target="_top">Boost.Multiprecision</a>
	64	<a href="../../../../../libs/multiprecision/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html" target="_top">cpp_dec_float</a>
65	and<a href="../../../../../libs/multiprecision/doc/html/boost_multiprecision/tut/floats/cpp_bin_float.html" target="_top">cpp_bin_float</a>
66	are fixed at runtime, but <span class="bold"><strong>not</strong></span> a type that
67	extends the representation to provide an exact representation for any number,
68	for example <a href="http://keithbriggs.info/xrc.html" target="_top">XRC eXact Real in
69	C</a>.
70	</p>
71	</div>
72	<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
73	<td align="left"></td>
74	<td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal,
75	Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
76	Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani,
77	Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
78	Distributed under the Boost Software License, Version 1.0. (See accompanying
79	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>)
80	</p>
81	</div></td>
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