<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Literal Types and constexpr Support</title>
-<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css">
+<link rel="stylesheet" href="../../multiprecision.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision">
<link rel="up" href="../tut.html" title="Tutorial">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_multiprecision.tut.lits"></a><a class="link" href="lits.html" title="Literal Types and constexpr Support">Literal Types and <code class="computeroutput"><span class="keyword">constexpr</span></code> Support</a>
</h3></div></div></div>
-<div class="note"><table border="0" summary="Note">
-<tr>
-<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../doc/src/images/note.png"></td>
-<th align="left">Note</th>
-</tr>
-<tr><td align="left" valign="top"><p>
- The features described in this section make heavy use of C++11 language
- features, currently (as of May 2013) only GCC-4.7 and later, and Clang
- 3.3 and later have the support required to make these features work.
- </p></td></tr>
-</table></div>
<p>
- There is limited support for <code class="computeroutput"><span class="keyword">constexpr</span></code>
- and user-defined literals in the library, currently the <code class="computeroutput"><span class="identifier">number</span></code>
- front end supports <code class="computeroutput"><span class="keyword">constexpr</span></code>
- on default construction and all forwarding constructors, but not on any of
- the non-member operators. So if some type <code class="computeroutput"><span class="identifier">B</span></code>
- is a literal type, then <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">B</span><span class="special">></span></code>
- is also a literal type, and you will be able to compile-time-construct such
- a type from any literal that <code class="computeroutput"><span class="identifier">B</span></code>
- is compile-time-constructible from. However, you will not be able to perform
- compile-time arithmetic on such types.
+ There are two kinds of <code class="computeroutput"><span class="keyword">constexpr</span></code>
+ support in this library:
</p>
+<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
+<li class="listitem">
+ The more basic version requires only C++11 and allow the construction
+ of some number types as literals.
+ </li>
+<li class="listitem">
+ The more advanced support permits constexpr arithmetic and requires at
+ least C++14 constexpr support, and for many operations C++2a support
+ </li>
+</ul></div>
+<h5>
+<a name="boost_multiprecision.tut.lits.h0"></a>
+ <span class="phrase"><a name="boost_multiprecision.tut.lits.declaring_numeric_literals"></a></span><a class="link" href="lits.html#boost_multiprecision.tut.lits.declaring_numeric_literals">Declaring
+ numeric literals</a>
+ </h5>
<p>
- Currently the only backend type provided by the library that is also a literal
- type are instantiations of <code class="computeroutput"><span class="identifier">cpp_int_backend</span></code>
- where the Allocator parameter is type <code class="computeroutput"><span class="keyword">void</span></code>,
- and the Checked parameter is <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">unchecked</span></code>.
+ There are two backend types which are literals:
</p>
+<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
+<li class="listitem">
+ <a class="link" href="floats/float128.html" title="float128">float128</a>
+ (which requires GCC), and
+ </li>
+<li class="listitem">
+ Instantiations of <code class="computeroutput"><span class="identifier">cpp_int_backend</span></code>
+ where the Allocator parameter is type <code class="computeroutput"><span class="keyword">void</span></code>.
+ In addition, prior to C++14 the Checked parameter must be <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">unchecked</span></code>.
+ </li>
+</ul></div>
<p>
For example:
</p>
<pre class="programlisting"><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="keyword">constexpr</span> <span class="identifier">float128</span> <span class="identifier">f</span> <span class="special">=</span> <span class="number">0.1</span><span class="identifier">Q</span> <span class="comment">// OK, float128's are always literals in C++11</span>
+
<span class="keyword">constexpr</span> <span class="identifier">int128_t</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="comment">// OK, fixed precision int128_t has no allocator.</span>
<span class="keyword">constexpr</span> <span class="identifier">uint1024_t</span> <span class="identifier">j</span> <span class="special">=</span> <span class="number">0</span><span class="identifier">xFFFFFFFF00000000uLL</span><span class="special">;</span> <span class="comment">// OK, fixed precision uint1024_t has no allocator.</span>
-<span class="keyword">constexpr</span> <span class="identifier">checked_uint128_t</span> <span class="identifier">k</span> <span class="special">=</span> <span class="special">-</span><span class="number">1</span><span class="special">;</span> <span class="comment">// Error, checked type is not a literal type as we need runtime error checking.</span>
+<span class="keyword">constexpr</span> <span class="identifier">checked_uint128_t</span> <span class="identifier">k</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> <span class="comment">// OK from C++14 and later, not supported for C++11.</span>
+<span class="keyword">constexpr</span> <span class="identifier">checked_uint128_t</span> <span class="identifier">k</span> <span class="special">=</span> <span class="special">-</span><span class="number">1</span><span class="special">;</span> <span class="comment">// Error, as this would normally lead to a runtime failure (exception).</span>
<span class="keyword">constexpr</span> <span class="identifier">cpp_int</span> <span class="identifier">l</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> <span class="comment">// Error, type is not a literal as it performs memory management.</span>
</pre>
<p>
- There is also limited support for user defined-literals - these are limited
- to unchecked, fixed precision <code class="computeroutput"><span class="identifier">cpp_int</span></code>'s
+ There is also support for user defined-literals with <a class="link" href="ints/cpp_int.html" title="cpp_int">cpp_int</a>
+ - these are limited to unchecked, fixed precision <code class="computeroutput"><span class="identifier">cpp_int</span></code>'s
which are specified in hexadecimal notation. The suffixes supported are:
</p>
<div class="informaltable"><table class="table">
<span class="comment">// Smaller values can be assigned to larger values:</span>
<span class="identifier">int256_t</span> <span class="identifier">c</span> <span class="special">=</span> <span class="number">0x1234</span><span class="identifier">_cppi</span><span class="special">;</span> <span class="comment">// OK</span>
<span class="comment">//</span>
-<span class="comment">// However, this does not currently work in constexpr contexts:</span>
-<span class="keyword">constexpr</span> <span class="identifier">int256_t</span> <span class="identifier">d</span> <span class="special">=</span> <span class="number">0x1</span><span class="identifier">_cppi</span><span class="special">;</span> <span class="comment">// Compiler error</span>
+<span class="comment">// However, this only works in constexpr contexts from C++14 onwards:</span>
+<span class="keyword">constexpr</span> <span class="identifier">int256_t</span> <span class="identifier">d</span> <span class="special">=</span> <span class="number">0x1</span><span class="identifier">_cppi</span><span class="special">;</span> <span class="comment">// Compiler error in C++11, requires C++14</span>
<span class="comment">//</span>
<span class="comment">// Constants can be padded out with leading zeros to generate wider types:</span>
<span class="keyword">constexpr</span> <span class="identifier">uint256_t</span> <span class="identifier">e</span> <span class="special">=</span> <span class="number">0</span><span class="identifier">x0000000000000000000000000000000000000000000FFFFFFFFFFFFFFFFFFFFF_cppui</span><span class="special">;</span> <span class="comment">// OK</span>
<span class="comment">// Which means this also works:</span>
<span class="keyword">constexpr</span> <span class="identifier">int1024_t</span> <span class="identifier">j</span> <span class="special">=</span> <span class="special">-</span><span class="identifier">g</span><span class="special">;</span> <span class="comment">// OK: unary minus operator is constexpr.</span>
</pre>
+<h5>
+<a name="boost_multiprecision.tut.lits.h1"></a>
+ <span class="phrase"><a name="boost_multiprecision.tut.lits.constexpr_arithmetic"></a></span><a class="link" href="lits.html#boost_multiprecision.tut.lits.constexpr_arithmetic">constexpr
+ arithmetic</a>
+ </h5>
+<p>
+ The front end of the library is all <code class="computeroutput"><span class="keyword">constexpr</span></code>
+ from C++14 and later. Currently there are only two back end types that are
+ <code class="computeroutput"><span class="keyword">constexpr</span></code> aware: <a class="link" href="floats/float128.html" title="float128">float128</a>
+ and <a class="link" href="ints/cpp_int.html" title="cpp_int">cpp_int</a>.
+ More backends will follow at a later date.
+ </p>
+<p>
+ Provided the compiler is GCC, type <a class="link" href="floats/float128.html" title="float128">float128</a>
+ support <code class="computeroutput"><span class="keyword">constexpr</span></code> operations
+ on all arithmetic operations from C++14, comparisons, <code class="computeroutput"><span class="identifier">abs</span></code>,
+ <code class="computeroutput"><span class="identifier">fabs</span></code>, <code class="computeroutput"><span class="identifier">fpclassify</span></code>,
+ <code class="computeroutput"><span class="identifier">isnan</span></code>, <code class="computeroutput"><span class="identifier">isinf</span></code>,
+ <code class="computeroutput"><span class="identifier">isfinite</span></code> and <code class="computeroutput"><span class="identifier">isnormal</span></code> are also fully supported, but
+ the transcendental functions are not.
+ </p>
+<p>
+ The <a class="link" href="ints/cpp_int.html" title="cpp_int">cpp_int</a>
+ types support constexpr arithmetic, provided it is a fixed precision type
+ with no allocator. It may also be a checked integer: in which case a compiler
+ error will be generated on overflow or undefined behaviour. In addition the
+ free functions <code class="computeroutput"><span class="identifier">abs</span></code>, <code class="computeroutput"><span class="identifier">swap</span></code>, <code class="computeroutput"><span class="identifier">multiply</span></code>,
+ <code class="computeroutput"><span class="identifier">add</span></code>, <code class="computeroutput"><span class="identifier">subtract</span></code>,
+ <code class="computeroutput"><span class="identifier">divide_qr</span></code>, <code class="computeroutput"><span class="identifier">integer_modulus</span></code>, <code class="computeroutput"><span class="identifier">powm</span></code>,
+ <code class="computeroutput"><span class="identifier">lsb</span></code>, <code class="computeroutput"><span class="identifier">msb</span></code>,
+ <code class="computeroutput"><span class="identifier">bit_test</span></code>, <code class="computeroutput"><span class="identifier">bit_set</span></code>,
+ <code class="computeroutput"><span class="identifier">bit_unset</span></code>, <code class="computeroutput"><span class="identifier">bit_flip</span></code>, <code class="computeroutput"><span class="identifier">sqrt</span></code>,
+ <code class="computeroutput"><span class="identifier">gcd</span></code>, <code class="computeroutput"><span class="identifier">lcm</span></code>
+ are all supported. Use of <a class="link" href="ints/cpp_int.html" title="cpp_int">cpp_int</a>
+ in this way requires either a C++2a compiler (one which supports <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">is_constant_evaluated</span><span class="special">()</span></code> - currently only gcc-9 or clang-9 or later),
+ or GCC-6 or later in C++14 mode. Compilers other than GCC and without <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">is_constant_evaluated</span><span class="special">()</span></code> will support a very limited set of operations:
+ expect to hit roadblocks rather easily.
+ </p>
+<p>
+ For example given:
+ </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span>
+<span class="keyword">inline</span> <span class="keyword">constexpr</span> <span class="identifier">T</span> <span class="identifier">circumference</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">radius</span><span class="special">)</span>
+<span class="special">{</span>
+ <span class="keyword">return</span> <span class="number">2</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">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special"><</span><span class="identifier">T</span><span class="special">>()</span> <span class="special">*</span> <span class="identifier">radius</span><span class="special">;</span>
+<span class="special">}</span>
+
+<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span>
+<span class="keyword">inline</span> <span class="keyword">constexpr</span> <span class="identifier">T</span> <span class="identifier">area</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">radius</span><span class="special">)</span>
+<span class="special">{</span>
+ <span class="keyword">return</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special"><</span><span class="identifier">T</span><span class="special">>()</span> <span class="special">*</span> <span class="identifier">radius</span> <span class="special">*</span> <span class="identifier">radius</span><span class="special">;</span>
+<span class="special">}</span>
+</pre>
+<p>
+ We can now calculate areas and circumferences using all constexpr arithmetic:
+ </p>
+<pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">float128</span><span class="special">;</span>
+
+<span class="keyword">constexpr</span> <span class="identifier">float128</span> <span class="identifier">radius</span> <span class="special">=</span> <span class="number">2.25</span><span class="special">;</span>
+<span class="keyword">constexpr</span> <span class="identifier">float128</span> <span class="identifier">c</span> <span class="special">=</span> <span class="identifier">circumference</span><span class="special">(</span><span class="identifier">radius</span><span class="special">);</span>
+<span class="keyword">constexpr</span> <span class="identifier">float128</span> <span class="identifier">a</span> <span class="special">=</span> <span class="identifier">area</span><span class="special">(</span><span class="identifier">radius</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="string">"Circumference = "</span> <span class="special"><<</span> <span class="identifier">c</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="string">"Area = "</span> <span class="special"><<</span> <span class="identifier">a</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+</pre>
+<p>
+ Note that these make use of the numeric constants from the Math library,
+ which also happen to be <code class="computeroutput"><span class="keyword">constexpr</span></code>.
+ </p>
+<p>
+ For a more interesting example, in <a href="../../../../example/constexpr_float_arithmetic_examples.cpp" target="_top">constexpr_float_arithmetic_examples.cpp</a>
+ we define a simple class for <code class="computeroutput"><span class="keyword">constexpr</span></code>
+ polynomial arithmetic:
+ </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">Order</span><span class="special">></span>
+<span class="keyword">struct</span> <span class="identifier">const_polynomial</span><span class="special">;</span>
+</pre>
+<p>
+ Given this, we can use recurrence relations to calculate the coefficients
+ for various orthogonal polynomials - in the example we use the Hermite polynomials,
+ only the constructor does any work - it uses the recurrence relations to
+ calculate the coefficient array:
+ </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">Order</span><span class="special">></span>
+<span class="keyword">class</span> <span class="identifier">hermite_polynomial</span>
+<span class="special">{</span>
+ <span class="identifier">const_polynomial</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">Order</span><span class="special">></span> <span class="identifier">m_data</span><span class="special">;</span>
+
+ <span class="keyword">public</span><span class="special">:</span>
+ <span class="keyword">constexpr</span> <span class="identifier">hermite_polynomial</span><span class="special">()</span> <span class="special">:</span> <span class="identifier">m_data</span><span class="special">(</span><span class="identifier">hermite_polynomial</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">Order</span> <span class="special">-</span> <span class="number">1</span><span class="special">>().</span><span class="identifier">data</span><span class="special">()</span> <span class="special">*</span> <span class="identifier">const_polynomial</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="number">1</span><span class="special">>{</span><span class="number">0</span><span class="special">,</span> <span class="number">2</span><span class="special">}</span> <span class="special">-</span> <span class="identifier">hermite_polynomial</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">Order</span> <span class="special">-</span> <span class="number">1</span><span class="special">>().</span><span class="identifier">data</span><span class="special">().</span><span class="identifier">derivative</span><span class="special">())</span>
+ <span class="special">{</span>
+ <span class="special">}</span>
+ <span class="keyword">constexpr</span> <span class="keyword">const</span> <span class="identifier">const_polynomial</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">Order</span><span class="special">>&</span> <span class="identifier">data</span><span class="special">()</span> <span class="keyword">const</span>
+ <span class="special">{</span>
+ <span class="keyword">return</span> <span class="identifier">m_data</span><span class="special">;</span>
+ <span class="special">}</span>
+ <span class="keyword">constexpr</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">[](</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">N</span><span class="special">)</span><span class="keyword">const</span>
+ <span class="special">{</span>
+ <span class="keyword">return</span> <span class="identifier">m_data</span><span class="special">[</span><span class="identifier">N</span><span class="special">];</span>
+ <span class="special">}</span>
+ <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">U</span><span class="special">></span>
+ <span class="keyword">constexpr</span> <span class="identifier">T</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">U</span> <span class="identifier">val</span><span class="special">)</span><span class="keyword">const</span>
+ <span class="special">{</span>
+ <span class="keyword">return</span> <span class="identifier">m_data</span><span class="special">(</span><span class="identifier">val</span><span class="special">);</span>
+ <span class="special">}</span>
+<span class="special">};</span>
+</pre>
+<p>
+ Now we just need to define H<sub>0</sub> and H<sub>1</sub> as termination conditions for the recurrence:
+ </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span>
+<span class="keyword">class</span> <span class="identifier">hermite_polynomial</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="number">0</span><span class="special">></span>
+<span class="special">{</span>
+ <span class="identifier">const_polynomial</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="number">0</span><span class="special">></span> <span class="identifier">m_data</span><span class="special">;</span>
+
+ <span class="keyword">public</span><span class="special">:</span>
+ <span class="keyword">constexpr</span> <span class="identifier">hermite_polynomial</span><span class="special">()</span> <span class="special">:</span> <span class="identifier">m_data</span><span class="special">{</span><span class="number">1</span><span class="special">}</span> <span class="special">{}</span>
+ <span class="keyword">constexpr</span> <span class="keyword">const</span> <span class="identifier">const_polynomial</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="number">0</span><span class="special">>&</span> <span class="identifier">data</span><span class="special">()</span> <span class="keyword">const</span>
+ <span class="special">{</span>
+ <span class="keyword">return</span> <span class="identifier">m_data</span><span class="special">;</span>
+ <span class="special">}</span>
+ <span class="keyword">constexpr</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">[](</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">N</span><span class="special">)</span> <span class="keyword">const</span>
+ <span class="special">{</span>
+ <span class="keyword">return</span> <span class="identifier">m_data</span><span class="special">[</span><span class="identifier">N</span><span class="special">];</span>
+ <span class="special">}</span>
+ <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">U</span><span class="special">></span>
+ <span class="keyword">constexpr</span> <span class="identifier">T</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">U</span> <span class="identifier">val</span><span class="special">)</span>
+ <span class="special">{</span>
+ <span class="keyword">return</span> <span class="identifier">m_data</span><span class="special">(</span><span class="identifier">val</span><span class="special">);</span>
+ <span class="special">}</span>
+<span class="special">};</span>
+
+<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span>
+<span class="keyword">class</span> <span class="identifier">hermite_polynomial</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="number">1</span><span class="special">></span>
+<span class="special">{</span>
+ <span class="identifier">const_polynomial</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="number">1</span><span class="special">></span> <span class="identifier">m_data</span><span class="special">;</span>
+
+ <span class="keyword">public</span><span class="special">:</span>
+ <span class="keyword">constexpr</span> <span class="identifier">hermite_polynomial</span><span class="special">()</span> <span class="special">:</span> <span class="identifier">m_data</span><span class="special">{</span><span class="number">0</span><span class="special">,</span> <span class="number">2</span><span class="special">}</span> <span class="special">{}</span>
+ <span class="keyword">constexpr</span> <span class="keyword">const</span> <span class="identifier">const_polynomial</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="number">1</span><span class="special">>&</span> <span class="identifier">data</span><span class="special">()</span> <span class="keyword">const</span>
+ <span class="special">{</span>
+ <span class="keyword">return</span> <span class="identifier">m_data</span><span class="special">;</span>
+ <span class="special">}</span>
+ <span class="keyword">constexpr</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">[](</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">N</span><span class="special">)</span> <span class="keyword">const</span>
+ <span class="special">{</span>
+ <span class="keyword">return</span> <span class="identifier">m_data</span><span class="special">[</span><span class="identifier">N</span><span class="special">];</span>
+ <span class="special">}</span>
+ <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">U</span><span class="special">></span>
+ <span class="keyword">constexpr</span> <span class="identifier">T</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">U</span> <span class="identifier">val</span><span class="special">)</span>
+ <span class="special">{</span>
+ <span class="keyword">return</span> <span class="identifier">m_data</span><span class="special">(</span><span class="identifier">val</span><span class="special">);</span>
+ <span class="special">}</span>
+<span class="special">};</span>
+</pre>
+<p>
+ We can now declare H<sub>9</sub> as a constexpr object, access the coefficients, and
+ evaluate at an abscissa value, all using <code class="computeroutput"><span class="keyword">constexpr</span></code>
+ arithmetic:
+ </p>
+<pre class="programlisting"><span class="keyword">constexpr</span> <span class="identifier">hermite_polynomial</span><span class="special"><</span><span class="identifier">float128</span><span class="special">,</span> <span class="number">9</span><span class="special">></span> <span class="identifier">h9</span><span class="special">;</span>
+<span class="comment">//</span>
+<span class="comment">// Verify that the polynomial's coefficients match the known values:</span>
+<span class="comment">//</span>
+<span class="keyword">static_assert</span><span class="special">(</span><span class="identifier">h9</span><span class="special">[</span><span class="number">0</span><span class="special">]</span> <span class="special">==</span> <span class="number">0</span><span class="special">);</span>
+<span class="keyword">static_assert</span><span class="special">(</span><span class="identifier">h9</span><span class="special">[</span><span class="number">1</span><span class="special">]</span> <span class="special">==</span> <span class="number">30240</span><span class="special">);</span>
+<span class="keyword">static_assert</span><span class="special">(</span><span class="identifier">h9</span><span class="special">[</span><span class="number">2</span><span class="special">]</span> <span class="special">==</span> <span class="number">0</span><span class="special">);</span>
+<span class="keyword">static_assert</span><span class="special">(</span><span class="identifier">h9</span><span class="special">[</span><span class="number">3</span><span class="special">]</span> <span class="special">==</span> <span class="special">-</span><span class="number">80640</span><span class="special">);</span>
+<span class="keyword">static_assert</span><span class="special">(</span><span class="identifier">h9</span><span class="special">[</span><span class="number">4</span><span class="special">]</span> <span class="special">==</span> <span class="number">0</span><span class="special">);</span>
+<span class="keyword">static_assert</span><span class="special">(</span><span class="identifier">h9</span><span class="special">[</span><span class="number">5</span><span class="special">]</span> <span class="special">==</span> <span class="number">48384</span><span class="special">);</span>
+<span class="keyword">static_assert</span><span class="special">(</span><span class="identifier">h9</span><span class="special">[</span><span class="number">6</span><span class="special">]</span> <span class="special">==</span> <span class="number">0</span><span class="special">);</span>
+<span class="keyword">static_assert</span><span class="special">(</span><span class="identifier">h9</span><span class="special">[</span><span class="number">7</span><span class="special">]</span> <span class="special">==</span> <span class="special">-</span><span class="number">9216</span><span class="special">);</span>
+<span class="keyword">static_assert</span><span class="special">(</span><span class="identifier">h9</span><span class="special">[</span><span class="number">8</span><span class="special">]</span> <span class="special">==</span> <span class="number">0</span><span class="special">);</span>
+<span class="keyword">static_assert</span><span class="special">(</span><span class="identifier">h9</span><span class="special">[</span><span class="number">9</span><span class="special">]</span> <span class="special">==</span> <span class="number">512</span><span class="special">);</span>
+<span class="comment">//</span>
+<span class="comment">// Define an abscissa value to evaluate at:</span>
+<span class="comment">//</span>
+<span class="keyword">constexpr</span> <span class="identifier">float128</span> <span class="identifier">abscissa</span><span class="special">(</span><span class="number">0.5</span><span class="special">);</span>
+<span class="comment">//</span>
+<span class="comment">// Evaluate H_9(0.5) using all constexpr arithmetic:</span>
+<span class="comment">//</span>
+<span class="keyword">static_assert</span><span class="special">(</span><span class="identifier">h9</span><span class="special">(</span><span class="identifier">abscissa</span><span class="special">)</span> <span class="special">==</span> <span class="number">6481</span><span class="special">);</span>
+</pre>
+<p>
+ Also since the coefficients to the Hermite polynomials are integers, we can
+ also generate the Hermite coefficients using (fixed precision) cpp_int's:
+ see <a href="../../../../test/constexpr_test_cpp_int_6.cpp" target="_top">constexpr_test_cpp_int_6.cpp</a>.
+ </p>
+<p>
+ We can also generate factorials (and validate the result) like so:
+ </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span>
+<span class="keyword">constexpr</span> <span class="identifier">T</span> <span class="identifier">factorial</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">a</span><span class="special">)</span>
+<span class="special">{</span>
+ <span class="keyword">return</span> <span class="identifier">a</span> <span class="special">?</span> <span class="identifier">a</span> <span class="special">*</span> <span class="identifier">factorial</span><span class="special">(</span><span class="identifier">a</span> <span class="special">-</span> <span class="number">1</span><span class="special">)</span> <span class="special">:</span> <span class="number">1</span><span class="special">;</span>
+<span class="special">}</span>
+</pre>
+<pre class="programlisting"><span class="keyword">constexpr</span> <span class="identifier">uint1024_t</span> <span class="identifier">f1</span> <span class="special">=</span> <span class="identifier">factorial</span><span class="special">(</span><span class="identifier">uint1024_t</span><span class="special">(</span><span class="number">31</span><span class="special">));</span>
+<span class="keyword">static_assert</span><span class="special">(</span><span class="identifier">f1</span> <span class="special">==</span> <span class="number">0</span><span class="identifier">x1956ad0aae33a4560c5cd2c000000_cppi</span><span class="special">);</span>
+</pre>
+<p>
+ Another example in <a href="../../../../test/constexpr_test_cpp_int_7.cpp" target="_top">constexpr_test_cpp_int_7.cpp</a>
+ generates a fresh multiprecision random number each time the file is compiled.
+ </p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
projects / platform / upstream / boost.git / blobdiff