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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> |
| </h3></div></div></div> |
| <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> |
| </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 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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| 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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