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| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="boost_multiprecision.tut.floats.cpp_dec_float"></a><a class="link" href="cpp_dec_float.html" title="cpp_dec_float">cpp_dec_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_dec_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">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">ExponentType</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">int32_t</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">cpp_dec_float</span><span class="special">;</span> |
| |
| <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_dec_float</span><span class="special"><</span><span class="number">50</span><span class="special">></span> <span class="special">></span> <span class="identifier">cpp_dec_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_dec_float</span><span class="special"><</span><span class="number">100</span><span class="special">></span> <span class="special">></span> <span class="identifier">cpp_dec_float_100</span><span class="special">;</span> |
| |
| <span class="special">}}</span> <span class="comment">// namespaces</span> |
| </pre> |
| <p> |
| The <code class="computeroutput"><span class="identifier">cpp_dec_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_dec_float</span></code> can |
| be used at fixed precision by specifying a non-zero <code class="computeroutput"><span class="identifier">Digits10</span></code> |
| template parameter. The typedefs <code class="computeroutput"><span class="identifier">cpp_dec_float_50</span></code> |
| and <code class="computeroutput"><span class="identifier">cpp_dec_float_100</span></code> provide |
| arithmetic types at 50 and 100 decimal digits precision respectively. Optionally, |
| you can specify an integer type to use for the exponent, this defaults |
| to a 32-bit integer type which is more than large enough for the vast majority |
| of use cases, but larger types such as <code class="computeroutput"><span class="keyword">long</span> |
| <span class="keyword">long</span></code> can also be specified if you |
| need a truly huge exponent range. In any case the ExponentType must be |
| a built in signed integer type at least 2 bytes and 16-bits wide. |
| </p> |
| <p> |
| Normally <code class="computeroutput"><span class="identifier">cpp_dec_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 the final template parameter causes <code class="computeroutput"><span class="identifier">cpp_dec_float</span></code> |
| to dynamically allocate the memory it needs: this significantly reduces |
| the size of <code class="computeroutput"><span class="identifier">cpp_dec_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. |
| </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_dec_float</span></code>s |
| have a value of zero. |
| </li> |
| <li class="listitem"> |
| The radix of this type is 10. As a result it can behave subtly differently |
| from base-2 types. |
| </li> |
| <li class="listitem"> |
| The type has a number of internal guard digits over and above those |
| specified in the template argument. Normally these should not be visible |
| to the user. |
| </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_dec_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_dec_float</span><span class="special"><</span><span class="identifier">SomeOtherValue</span><span class="special">></span> <span class="special">></span></code>. |
| Narrowing conversions are truncating and <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"> |
| The actual precision of a <code class="computeroutput"><span class="identifier">cpp_dec_float</span></code> |
| is always slightly higher than the number of digits specified in the |
| template parameter, actually how much higher is an implementation detail |
| but is always at least 8 decimal digits. |
| </li> |
| <li class="listitem"> |
| Operations involving <code class="computeroutput"><span class="identifier">cpp_dec_float</span></code> |
| are always truncating. However, note that since their are guard digits |
| in effect, in practice this has no real impact on accuracy for most |
| use cases. |
| </li> |
| </ul></div> |
| <h6> |
| <a name="boost_multiprecision.tut.floats.cpp_dec_float.h0"></a> |
| <span class="phrase"><a name="boost_multiprecision.tut.floats.cpp_dec_float.cpp_dec_float_example"></a></span><a class="link" href="cpp_dec_float.html#boost_multiprecision.tut.floats.cpp_dec_float.cpp_dec_float_example">cpp_dec_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_dec_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_dec_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_dec_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="comment">// Note that digits10 is the same as digits, since we're base 10! :</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_dec_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_dec_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_dec_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> |
| </div> |
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| 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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