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<div class="titlepage"><div><div><h4 class="title">
<a name="boost_multiprecision.tut.floats.cpp_bin_float"></a><a class="link" href="cpp_bin_float.html" title="cpp_bin_float">cpp_bin_float</a>
</h4></div></div></div>
<p>
<code class="computeroutput"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">cpp_bin_float</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></code>
</p>
<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>
The <code class="computeroutput"><span class="identifier">cpp_bin_float</span></code> back-end
is used in conjunction with <code class="computeroutput"><span class="identifier">number</span></code>:
It acts as an entirely C++ (header only and dependency free) floating-point
number type that is a drop-in replacement for the native C++ floating-point
types, but with much greater precision.
</p>
<p>
Type <code class="computeroutput"><span class="identifier">cpp_bin_float</span></code> can
be used at fixed precision by specifying a non-zero <code class="computeroutput"><span class="identifier">Digits</span></code>
template parameter. The typedefs <code class="computeroutput"><span class="identifier">cpp_bin_float_50</span></code>
and <code class="computeroutput"><span class="identifier">cpp_bin_float_100</span></code> provide
arithmetic types at 50 and 100 decimal digits precision respectively.
</p>
<p>
Optionally, you can specify whether the precision is specified in decimal
digits or binary bits - for example to declare a <code class="computeroutput"><span class="identifier">cpp_bin_float</span></code>
with exactly the same precision as <code class="computeroutput"><span class="keyword">double</span></code>
one would use <code class="computeroutput"><span class="identifier">number</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">digit_base_2</span><span class="special">></span> <span class="special">></span></code>.
The typedefs <code class="computeroutput"><span class="identifier">cpp_bin_float_single</span></code>,
<code class="computeroutput"><span class="identifier">cpp_bin_float_double</span></code>,
<code class="computeroutput"><span class="identifier">cpp_bin_float_quad</span></code> and
<code class="computeroutput"><span class="identifier">cpp_bin_float_double_extended</span></code>
provide software analogues of the IEEE single, double and quad float data
types, plus the Intel-extended-double type respectively. Note that while
these types are functionally equivalent to the native IEEE types, but they
do not have the same size or bit-layout as true IEEE compatible types.
</p>
<p>
Normally <code class="computeroutput"><span class="identifier">cpp_bin_float</span></code>
allocates no memory: all of the space required for its digits are allocated
directly within the class. As a result care should be taken not to use
the class with too high a digit count as stack space requirements can grow
out of control. If that represents a problem then providing an allocator
as a template parameter causes <code class="computeroutput"><span class="identifier">cpp_bin_float</span></code>
to dynamically allocate the memory it needs: this significantly reduces
the size of <code class="computeroutput"><span class="identifier">cpp_bin_float</span></code>
and increases the viable upper limit on the number of digits at the expense
of performance. However, please bear in mind that arithmetic operations
rapidly become <span class="emphasis"><em>very</em></span> expensive as the digit count grows:
the current implementation really isn't optimized or designed for large
digit counts. Note that since the actual type of the objects allocated
is completely opaque, the suggestion would be to use an allocator with
<code class="computeroutput"><span class="keyword">void</span></code> <code class="computeroutput"><span class="identifier">value_type</span></code>,
for example: <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="number">1000</span><span class="special">,</span> <span class="identifier">digit_base_10</span><span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">allocator</span><span class="special"><</span><span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="special">></span></code>.
</p>
<p>
The final template parameters determine the type and range of the exponent:
parameter <code class="computeroutput"><span class="identifier">Exponent</span></code> can
be any signed integer type, but note that <code class="computeroutput"><span class="identifier">MinExponent</span></code>
and <code class="computeroutput"><span class="identifier">MaxExponent</span></code> can not
go right up to the limits of the <code class="computeroutput"><span class="identifier">Exponent</span></code>
type as there has to be a little extra headroom for internal calculations.
You will get a compile time error if this is the case. In addition if MinExponent
or MaxExponent are zero, then the library will choose suitable values that
are as large as possible given the constraints of the type and need for
extra headroom for internal calculations.
</p>
<p>
There is full standard library and <code class="computeroutput"><span class="identifier">numeric_limits</span></code>
support available for this type.
</p>
<p>
Things you should know when using this type:
</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
Default constructed <code class="computeroutput"><span class="identifier">cpp_bin_float</span></code>s
have a value of zero.
</li>
<li class="listitem">
The radix of this type is 2, even when the precision is specified as
decimal digits.
</li>
<li class="listitem">
The type supports both infinities and NaN's. An infinity is generated
whenever the result would overflow, and a NaN is generated for any
mathematically undefined operation.
</li>
<li class="listitem">
There is a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code> specialisation for
this type.
</li>
<li class="listitem">
Any <code class="computeroutput"><span class="identifier">number</span></code> instantiated
on this type, is convertible to any other <code class="computeroutput"><span class="identifier">number</span></code>
instantiated on this type - for example you can convert from <code class="computeroutput"><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></code> to <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="identifier">SomeOtherValue</span><span class="special">></span> <span class="special">></span></code>.
Narrowing conversions round to nearest and are <code class="computeroutput"><span class="keyword">explicit</span></code>.
</li>
<li class="listitem">
Conversion from a string results in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code>
being thrown if the string can not be interpreted as a valid floating
point number.
</li>
<li class="listitem">
All arithmetic operations are correctly rounded to nearest. String
conversions and the <code class="computeroutput"><span class="identifier">sqrt</span></code>
function are also correctly rounded, but transcendental functions (sin,
cos, pow, exp etc) are not.
</li>
</ul></div>
<h6>
<a name="boost_multiprecision.tut.floats.cpp_bin_float.h0"></a>
<span class="phrase"><a name="boost_multiprecision.tut.floats.cpp_bin_float.cpp_bin_float_example"></a></span><a class="link" href="cpp_bin_float.html#boost_multiprecision.tut.floats.cpp_bin_float.cpp_bin_float_example">cpp_bin_float
example:</a>
</h6>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">cpp_bin_float</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span>
<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
<span class="special">{</span>
<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span>
<span class="comment">// Operations at fixed precision and full numeric_limits support:</span>
<span class="identifier">cpp_bin_float_100</span> <span class="identifier">b</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">cpp_bin_float_100</span><span class="special">>::</span><span class="identifier">digits</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">cpp_bin_float_100</span><span class="special">>::</span><span class="identifier">digits10</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="comment">// We can use any C++ std lib function, lets print all the digits as well:</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">cpp_bin_float_100</span><span class="special">>::</span><span class="identifier">max_digits10</span><span class="special">)</span>
<span class="special"><<</span> <span class="identifier">log</span><span class="special">(</span><span class="identifier">b</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// print log(2)</span>
<span class="comment">// We can also use any function from Boost.Math:</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">b</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="comment">// These even work when the argument is an expression template:</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">b</span> <span class="special">*</span> <span class="identifier">b</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="comment">// And since we have an extended exponent range we can generate some really large </span>
<span class="comment">// numbers here (4.0238726007709377354370243e+2564):</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">cpp_bin_float_100</span><span class="special">(</span><span class="number">1000</span><span class="special">))</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
<span class="special">}</span>
</pre>
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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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