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| <div class="section"> |
| <div class="titlepage"><div><div><h3 class="title"> |
| <a name="boost_multiprecision.ref.cpp_bin_float_ref"></a><a class="link" href="cpp_bin_float_ref.html" title="cpp_bin_float">cpp_bin_float</a> |
| </h3></div></div></div> |
| <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span> |
| |
| <span class="keyword">enum</span> <span class="identifier">digit_base_type</span> |
| <span class="special">{</span> |
| <span class="identifier">digit_base_2</span> <span class="special">=</span> <span class="number">2</span><span class="special">,</span> |
| <span class="identifier">digit_base_10</span> <span class="special">=</span> <span class="number">10</span> |
| <span class="special">};</span> |
| |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits</span><span class="special">,</span> <span class="identifier">digit_base_type</span> <span class="identifier">base</span> <span class="special">=</span> <span class="identifier">digit_base_10</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Allocator</span> <span class="special">=</span> <span class="keyword">void</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Exponent</span> <span class="special">=</span> <span class="keyword">int</span><span class="special">,</span> <span class="identifier">ExponentMin</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">ExponentMax</span> <span class="special">=</span> <span class="number">0</span><span class="special">></span> |
| <span class="keyword">class</span> <span class="identifier">cpp_bin_float</span><span class="special">;</span> |
| |
| <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="number">50</span><span class="special">></span> <span class="special">></span> <span class="identifier">cpp_bin_float_50</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="number">100</span><span class="special">></span> <span class="special">></span> <span class="identifier">cpp_bin_float_100</span><span class="special">;</span> |
| |
| <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">backends</span><span class="special">::</span><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="number">24</span><span class="special">,</span> <span class="identifier">backends</span><span class="special">::</span><span class="identifier">digit_base_2</span><span class="special">,</span> <span class="keyword">void</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">int16_t</span><span class="special">,</span> <span class="special">-</span><span class="number">126</span><span class="special">,</span> <span class="number">127</span><span class="special">>,</span> <span class="identifier">et_off</span><span class="special">></span> <span class="identifier">cpp_bin_float_single</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">backends</span><span class="special">::</span><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="number">53</span><span class="special">,</span> <span class="identifier">backends</span><span class="special">::</span><span class="identifier">digit_base_2</span><span class="special">,</span> <span class="keyword">void</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">int16_t</span><span class="special">,</span> <span class="special">-</span><span class="number">1022</span><span class="special">,</span> <span class="number">1023</span><span class="special">>,</span> <span class="identifier">et_off</span><span class="special">></span> <span class="identifier">cpp_bin_float_double</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">backends</span><span class="special">::</span><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="number">64</span><span class="special">,</span> <span class="identifier">backends</span><span class="special">::</span><span class="identifier">digit_base_2</span><span class="special">,</span> <span class="keyword">void</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">int16_t</span><span class="special">,</span> <span class="special">-</span><span class="number">16382</span><span class="special">,</span> <span class="number">16383</span><span class="special">>,</span> <span class="identifier">et_off</span><span class="special">></span> <span class="identifier">cpp_bin_float_double_extended</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">backends</span><span class="special">::</span><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="number">113</span><span class="special">,</span> <span class="identifier">backends</span><span class="special">::</span><span class="identifier">digit_base_2</span><span class="special">,</span> <span class="keyword">void</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">int16_t</span><span class="special">,</span> <span class="special">-</span><span class="number">16382</span><span class="special">,</span> <span class="number">16383</span><span class="special">>,</span> <span class="identifier">et_off</span><span class="special">></span> <span class="identifier">cpp_bin_float_quad</span><span class="special">;</span> |
| |
| <span class="special">}}</span> <span class="comment">// namespaces</span> |
| </pre> |
| <p> |
| Class template <code class="computeroutput"><span class="identifier">cpp_bin_float</span></code> |
| fulfils all of the requirements for a <a class="link" href="backendconc.html" title="Backend Requirements">Backend</a> |
| type. Its members and non-member functions are deliberately not documented: |
| these are considered implementation details that are subject to change. |
| </p> |
| <p> |
| The class takes six template parameters: |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl class="variablelist"> |
| <dt><span class="term">Digits</span></dt> |
| <dd><p> |
| The number of digits precision the type should support. This is normally |
| expressed as base-10 digits, but that can be changed via the second |
| template parameter. |
| </p></dd> |
| <dt><span class="term">base</span></dt> |
| <dd><p> |
| An enumerated value (either <code class="computeroutput"><span class="identifier">digit_base_10</span></code> |
| or <code class="computeroutput"><span class="identifier">digit_base_2</span></code>) that |
| indicates whether <code class="computeroutput"><span class="identifier">Digits</span></code> |
| is base-10 or base-2 |
| </p></dd> |
| <dt><span class="term">Allocator</span></dt> |
| <dd><p> |
| The allocator used: defaults to type <code class="computeroutput"><span class="keyword">void</span></code>, |
| meaning all storage is within the class, and no dynamic allocation |
| is performed, but can be set to a standard library allocator if dynamic |
| allocation makes more sense. |
| </p></dd> |
| <dt><span class="term">Exponent</span></dt> |
| <dd><p> |
| A signed integer type to use as the type of the exponent - defaults |
| to <code class="computeroutput"><span class="keyword">int</span></code>. |
| </p></dd> |
| <dt><span class="term">ExponentMin</span></dt> |
| <dd><p> |
| The smallest (most negative) permitted exponent, defaults to zero, |
| meaning "define as small as possible given the limitations of |
| the type and our internal requirements". |
| </p></dd> |
| <dt><span class="term">ExponentMax</span></dt> |
| <dd><p> |
| The largest (most positive) permitted exponent, defaults to zero, meaning |
| "define as large as possible given the limitations of the type |
| and our internal requirements". |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| The type of <code class="computeroutput"><span class="identifier">number_category</span><span class="special"><</span><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="identifier">Args</span><span class="special">...></span> <span class="special">>::</span><span class="identifier">type</span></code> is <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special"><</span><span class="identifier">number_kind_floating_point</span><span class="special">></span></code>. |
| </p> |
| <p> |
| More information on this type can be found in the <a class="link" href="../tut/floats/cpp_bin_float.html" title="cpp_bin_float">tutorial</a>. |
| </p> |
| <h5> |
| <a name="boost_multiprecision.ref.cpp_bin_float_ref.h0"></a> |
| <span class="phrase"><a name="boost_multiprecision.ref.cpp_bin_float_ref.implementation_notes"></a></span><a class="link" href="cpp_bin_float_ref.html#boost_multiprecision.ref.cpp_bin_float_ref.implementation_notes">Implementation |
| Notes</a> |
| </h5> |
| <p> |
| Internally, an N-bit <code class="computeroutput"><span class="identifier">cpp_bin_float</span></code> |
| is represented as an N-bit unsigned integer along with an exponent and a |
| sign. The integer part is normalized so that it's most significant bit is |
| always 1. The decimal point is assumed to be directly after the most significant |
| bit of the integer part. The special values zero, infinity and NaN all have |
| the integer part set to zero, and the exponent to one of 3 special values |
| above the maximum permitted exponent. |
| </p> |
| <p> |
| Multiplication is trivial: multiply the two N-bit integer mantissa's to obtain |
| a 2N-bit number, then round and adjust the sign and exponent. |
| </p> |
| <p> |
| Addition and subtraction proceed similarly - if the exponents are such that |
| there is overlap between the two values, then left shift the larger value |
| to produce a number with between N and 2N bits, then perform integer addition |
| or subtraction, round, and adjust the exponent. |
| </p> |
| <p> |
| Division proceeds as follows: first scale the numerator by some power of |
| 2 so that integer division will produce either an N-bit or N+1 bit result |
| plus a remainder. If we get an N bit result then the size of twice the remainder |
| compared to the denominator gives us the rounding direction. Otherwise we |
| have one extra bit in the result which we can use to determine rounding (in |
| this case ties occur only if the remainder is zero and the extra bit is a |
| 1). |
| </p> |
| <p> |
| Square root uses integer square root in a manner analogous to division. |
| </p> |
| <p> |
| Decimal string to binary conversion proceeds as follows: first parse the |
| digits to produce an integer multiplied by a decimal exponent. Note that |
| we stop parsing digits once we have parsed as many as can possibly effect |
| the result - this stops the integer part growing too large when there are |
| a very large number of input digits provided. At this stage if the decimal |
| exponent is positive then the result is an integer and we can in principle |
| simply multiply by 10^N to get an exact integer result. In practice however, |
| that could produce some very large integers. We also need to be able to divide |
| by 10^N in the event that the exponent is negative. Therefore calculation |
| of the 10^N values plus the multiplication or division are performed using |
| limited precision integer arithmetic, plus an exponent, and a track of the |
| accumulated error. At the end of the calculation we will either be able to |
| round unambiguously, or the error will be such that we can't tell which way |
| to round. In the latter case we simply up the precision and try again until |
| we have an unambiguously rounded result. |
| </p> |
| <p> |
| Binary to decimal conversion proceeds very similarly to the above, our aim |
| is to calculate <code class="computeroutput"><span class="identifier">mantissa</span> <span class="special">*</span> <span class="number">2</span><span class="special">^</span><span class="identifier">shift</span> <span class="special">*</span> <span class="number">10</span><span class="special">^</span><span class="identifier">E</span></code> |
| where <code class="computeroutput"><span class="identifier">E</span></code> is the decimal exponent |
| and <code class="computeroutput"><span class="identifier">shift</span></code> is calculated so |
| that the result is an N bit integer assuming we want N digits printed in |
| the result. As before we use limited precision arithmetic to calculate the |
| result and up the precision as necessary until the result is unambiguously |
| correctly rounded. In addition our initial calculation of the decimal exponent |
| may be out by 1, so we have to correct that and loop as well in the that |
| case. |
| </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 © 2002-2013 John Maddock and Christopher Kormanyos<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> |
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