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<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.using_udt.concepts"></a><a class="link" href="concepts.html" title="Conceptual Requirements for Real Number Types"> Conceptual Requirements
for Real Number Types</a>
</h3></div></div></div>
<p>
The functions, and statistical distributions in this library can be used
with any type <span class="emphasis"><em>RealType</em></span> that meets the conceptual requirements
given below. All the built in floating point types will meet these requirements.
User defined types that meet the requirements can also be used. For example,
with <a class="link" href="use_ntl.html" title="Using With NTL - a High-Precision Floating-Point Library">a thin wrapper class</a>
one of the types provided with <a href="http://shoup.net/ntl/" target="_top">NTL (RR)</a>
can be used. Submissions of binding to other extended precision types would
also be most welcome!
</p>
<p>
The guiding principal behind these requirements, is that a <span class="emphasis"><em>RealType</em></span>
behaves just like a built in floating point type.
</p>
<a name="math_toolkit.using_udt.concepts.basic_arithmetic_requirements"></a><h5>
<a name="id1229795"></a>
<a class="link" href="concepts.html#math_toolkit.using_udt.concepts.basic_arithmetic_requirements">Basic
Arithmetic Requirements</a>
</h5>
<p>
These requirements are common to all of the functions in this library.
</p>
<p>
In the following table <span class="emphasis"><em>r</em></span> is an object of type <code class="computeroutput"><span class="identifier">RealType</span></code>, <span class="emphasis"><em>cr</em></span> and
<span class="emphasis"><em>cr2</em></span> are objects of type <code class="computeroutput"><span class="keyword">const</span>
<span class="identifier">RealType</span></code>, and <span class="emphasis"><em>ca</em></span>
is an object of type <code class="computeroutput"><span class="keyword">const</span> <span class="identifier">arithmetic</span><span class="special">-</span><span class="identifier">type</span></code> (arithmetic types include all the
built in integers and floating point types).
</p>
<div class="informaltable"><table class="table">
<colgroup>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
Expression
</p>
</th>
<th>
<p>
Result Type
</p>
</th>
<th>
<p>
Notes
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">RealType</span><span class="special">(</span><span class="identifier">cr</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
<td>
<p>
RealType is copy constructible.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">RealType</span><span class="special">(</span><span class="identifier">ca</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
<td>
<p>
RealType is copy constructible from the arithmetic types.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">r</span> <span class="special">=</span>
<span class="identifier">cr</span></code>
</p>
</td>
<td>
<p>
RealType&amp;
</p>
</td>
<td>
<p>
Assignment operator.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">r</span> <span class="special">=</span>
<span class="identifier">ca</span></code>
</p>
</td>
<td>
<p>
RealType&amp;
</p>
</td>
<td>
<p>
Assignment operator from the arithmetic types.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">r</span> <span class="special">+=</span>
<span class="identifier">cr</span></code>
</p>
</td>
<td>
<p>
RealType&amp;
</p>
</td>
<td>
<p>
Adds cr to r.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">r</span> <span class="special">+=</span>
<span class="identifier">ca</span></code>
</p>
</td>
<td>
<p>
RealType&amp;
</p>
</td>
<td>
<p>
Adds ar to r.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">r</span> <span class="special">-=</span>
<span class="identifier">cr</span></code>
</p>
</td>
<td>
<p>
RealType&amp;
</p>
</td>
<td>
<p>
Subtracts cr from r.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">r</span> <span class="special">-=</span>
<span class="identifier">ca</span></code>
</p>
</td>
<td>
<p>
RealType&amp;
</p>
</td>
<td>
<p>
Subtracts ca from r.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">r</span> <span class="special">*=</span>
<span class="identifier">cr</span></code>
</p>
</td>
<td>
<p>
RealType&amp;
</p>
</td>
<td>
<p>
Multiplies r by cr.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">r</span> <span class="special">*=</span>
<span class="identifier">ca</span></code>
</p>
</td>
<td>
<p>
RealType&amp;
</p>
</td>
<td>
<p>
Multiplies r by ca.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">r</span> <span class="special">/=</span>
<span class="identifier">cr</span></code>
</p>
</td>
<td>
<p>
RealType&amp;
</p>
</td>
<td>
<p>
Divides r by cr.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">r</span> <span class="special">/=</span>
<span class="identifier">ca</span></code>
</p>
</td>
<td>
<p>
RealType&amp;
</p>
</td>
<td>
<p>
Divides r by ca.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="special">-</span><span class="identifier">r</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
<td>
<p>
Unary Negation.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="special">+</span><span class="identifier">r</span></code>
</p>
</td>
<td>
<p>
RealType&amp;
</p>
</td>
<td>
<p>
Identity Operation.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">+</span>
<span class="identifier">cr2</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
<td>
<p>
Binary Addition
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">+</span>
<span class="identifier">ca</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
<td>
<p>
Binary Addition
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">ca</span> <span class="special">+</span>
<span class="identifier">cr</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
<td>
<p>
Binary Addition
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">-</span>
<span class="identifier">cr2</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
<td>
<p>
Binary Subtraction
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">-</span>
<span class="identifier">ca</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
<td>
<p>
Binary Subtraction
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">ca</span> <span class="special">-</span>
<span class="identifier">cr</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
<td>
<p>
Binary Subtraction
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">*</span>
<span class="identifier">cr2</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
<td>
<p>
Binary Multiplication
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">*</span>
<span class="identifier">ca</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
<td>
<p>
Binary Multiplication
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">ca</span> <span class="special">*</span>
<span class="identifier">cr</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
<td>
<p>
Binary Multiplication
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">/</span>
<span class="identifier">cr2</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
<td>
<p>
Binary Subtraction
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">/</span>
<span class="identifier">ca</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
<td>
<p>
Binary Subtraction
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">ca</span> <span class="special">/</span>
<span class="identifier">cr</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
<td>
<p>
Binary Subtraction
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">==</span>
<span class="identifier">cr2</span></code>
</p>
</td>
<td>
<p>
bool
</p>
</td>
<td>
<p>
Equality Comparison
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">==</span>
<span class="identifier">ca</span></code>
</p>
</td>
<td>
<p>
bool
</p>
</td>
<td>
<p>
Equality Comparison
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">ca</span> <span class="special">==</span>
<span class="identifier">cr</span></code>
</p>
</td>
<td>
<p>
bool
</p>
</td>
<td>
<p>
Equality Comparison
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">!=</span>
<span class="identifier">cr2</span></code>
</p>
</td>
<td>
<p>
bool
</p>
</td>
<td>
<p>
Inequality Comparison
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">!=</span>
<span class="identifier">ca</span></code>
</p>
</td>
<td>
<p>
bool
</p>
</td>
<td>
<p>
Inequality Comparison
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">ca</span> <span class="special">!=</span>
<span class="identifier">cr</span></code>
</p>
</td>
<td>
<p>
bool
</p>
</td>
<td>
<p>
Inequality Comparison
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">&lt;=</span>
<span class="identifier">cr2</span></code>
</p>
</td>
<td>
<p>
bool
</p>
</td>
<td>
<p>
Less than equal to.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">&lt;=</span>
<span class="identifier">ca</span></code>
</p>
</td>
<td>
<p>
bool
</p>
</td>
<td>
<p>
Less than equal to.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">ca</span> <span class="special">&lt;=</span>
<span class="identifier">cr</span></code>
</p>
</td>
<td>
<p>
bool
</p>
</td>
<td>
<p>
Less than equal to.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">&gt;=</span>
<span class="identifier">cr2</span></code>
</p>
</td>
<td>
<p>
bool
</p>
</td>
<td>
<p>
Greater than equal to.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">&gt;=</span>
<span class="identifier">ca</span></code>
</p>
</td>
<td>
<p>
bool
</p>
</td>
<td>
<p>
Greater than equal to.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">ca</span> <span class="special">&gt;=</span>
<span class="identifier">cr</span></code>
</p>
</td>
<td>
<p>
bool
</p>
</td>
<td>
<p>
Greater than equal to.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">&lt;</span>
<span class="identifier">cr2</span></code>
</p>
</td>
<td>
<p>
bool
</p>
</td>
<td>
<p>
Less than comparison.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">&lt;</span>
<span class="identifier">ca</span></code>
</p>
</td>
<td>
<p>
bool
</p>
</td>
<td>
<p>
Less than comparison.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">ca</span> <span class="special">&lt;</span>
<span class="identifier">cr</span></code>
</p>
</td>
<td>
<p>
bool
</p>
</td>
<td>
<p>
Less than comparison.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">&gt;</span>
<span class="identifier">cr2</span></code>
</p>
</td>
<td>
<p>
bool
</p>
</td>
<td>
<p>
Greater than comparison.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">cr</span> <span class="special">&gt;</span>
<span class="identifier">ca</span></code>
</p>
</td>
<td>
<p>
bool
</p>
</td>
<td>
<p>
Greater than comparison.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">ca</span> <span class="special">&gt;</span>
<span class="identifier">cr</span></code>
</p>
</td>
<td>
<p>
bool
</p>
</td>
<td>
<p>
Greater than comparison.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">::</span><span class="identifier">digits</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;()</span></code>
</p>
</td>
<td>
<p>
int
</p>
</td>
<td>
<p>
The number of digits in the significand of RealType.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">::</span><span class="identifier">max_value</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;()</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
<td>
<p>
The largest representable number by type RealType.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">::</span><span class="identifier">min_value</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;()</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
<td>
<p>
The smallest representable number by type RealType.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">::</span><span class="identifier">log_max_value</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;()</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
<td>
<p>
The natural logarithm of the largest representable number by type
RealType.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">::</span><span class="identifier">log_min_value</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;()</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
<td>
<p>
The natural logarithm of the smallest representable number by type
RealType.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">::</span><span class="identifier">epsilon</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;()</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
<td>
<p>
The machine epsilon of RealType.
</p>
</td>
</tr>
</tbody>
</table></div>
<p>
Note that:
</p>
<div class="orderedlist"><ol type="1">
<li>
The functions <code class="computeroutput"><span class="identifier">log_max_value</span></code>
and <code class="computeroutput"><span class="identifier">log_min_value</span></code> can
be synthesised from the others, and so no explicit specialisation is
required.
</li>
<li>
The function <code class="computeroutput"><span class="identifier">epsilon</span></code>
can be synthesised from the others, so no explicit specialisation is
required provided the precision of RealType does not vary at runtime
(see the header <a href="../../../../../../../boost/math/bindings/rr.hpp" target="_top">boost/math/bindings/rr.hpp</a>
for an example where the precision does vary at runtime).
</li>
<li>
The functions <code class="computeroutput"><span class="identifier">digits</span></code>,
<code class="computeroutput"><span class="identifier">max_value</span></code> and <code class="computeroutput"><span class="identifier">min_value</span></code>, all get synthesised automatically
from <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code>. However, if <code class="computeroutput"><span class="identifier">numeric_limits</span></code> is not specialised for
type RealType, then you will get a compiler error when code tries to
use these functions, <span class="emphasis"><em>unless</em></span> you explicitly specialise
them. For example if the precision of RealType varies at runtime, then
<code class="computeroutput"><span class="identifier">numeric_limits</span></code> support
may not be appropriate, see <a href="../../../../../../../boost/math/bindings/rr.hpp" target="_top">boost/math/bindings/rr.hpp</a>
for examples.
</li>
</ol></div>
<div class="warning"><table border="0" summary="Warning">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Warning]" src="../../../../../../../doc/src/images/warning.png"></td>
<th align="left">Warning</th>
</tr>
<tr><td align="left" valign="top">
<p>
If <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;&gt;</span></code>
is <span class="bold"><strong>not specialized</strong></span> for type <span class="emphasis"><em>RealType</em></span>
then the default float precision of 6 decimal digits will be used by other
Boost programs including:
</p>
<p>
Boost.Test: giving misleading error messages like
</p>
<p>
<span class="emphasis"><em>"difference between {9.79796} and {9.79796} exceeds 5.42101e-19%".</em></span>
</p>
<p>
Boost.LexicalCast and Boost.Serialization when converting the number to
a string, causing potentially serious loss of accuracy on output.
</p>
<p>
Although it might seem obvious that RealType should require <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code> to be specialized, this
is not sensible for <code class="computeroutput"><span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span></code>
and similar classes where the number of digits is a runtime parameter (where
as for <code class="computeroutput"><span class="identifier">numeric_limits</span></code> it
has to be fixed at compile time).
</p>
</td></tr>
</table></div>
<a name="math_toolkit.using_udt.concepts.standard_library_support_requirements"></a><h5>
<a name="id1233610"></a>
<a class="link" href="concepts.html#math_toolkit.using_udt.concepts.standard_library_support_requirements">Standard
Library Support Requirements</a>
</h5>
<p>
Many (though not all) of the functions in this library make calls to standard
library functions, the following table summarises the requirements. Note
that most of the functions in this library will only call a small subset
of the functions listed here, so if in doubt whether a user defined type
has enough standard library support to be useable the best advise is to try
it and see!
</p>
<p>
In the following table <span class="emphasis"><em>r</em></span> is an object of type <code class="computeroutput"><span class="identifier">RealType</span></code>, <span class="emphasis"><em>cr1</em></span> and
<span class="emphasis"><em>cr2</em></span> are objects of type <code class="computeroutput"><span class="keyword">const</span>
<span class="identifier">RealType</span></code>, and <span class="emphasis"><em>i</em></span>
is an object of type <code class="computeroutput"><span class="keyword">int</span></code>.
</p>
<div class="informaltable"><table class="table">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
Expression
</p>
</th>
<th>
<p>
Result Type
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">fabs</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">abs</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">ceil</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">floor</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">exp</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">pow</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">,</span>
<span class="identifier">cr2</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">log</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">frexp</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">,</span>
<span class="special">&amp;</span><span class="identifier">i</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">ldexp</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">,</span>
<span class="identifier">i</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">cos</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">sin</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">asin</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">tan</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">atan</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">fmod</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">round</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">iround</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
int
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">trunc</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
RealType
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">itrunc</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
</p>
</td>
<td>
<p>
int
</p>
</td>
</tr>
</tbody>
</table></div>
<p>
Note that the table above lists only those standard library functions known
to be used (or likely to be used in the near future) by this library. The
following functions: <code class="computeroutput"><span class="identifier">acos</span></code>,
<code class="computeroutput"><span class="identifier">atan2</span></code>, <code class="computeroutput"><span class="identifier">fmod</span></code>,
<code class="computeroutput"><span class="identifier">cosh</span></code>, <code class="computeroutput"><span class="identifier">sinh</span></code>,
<code class="computeroutput"><span class="identifier">tanh</span></code>, <code class="computeroutput"><span class="identifier">log10</span></code>,
<code class="computeroutput"><span class="identifier">lround</span></code>, <code class="computeroutput"><span class="identifier">llround</span></code>,
ltrunc<code class="computeroutput"><span class="special">,</span> </code>lltrunc<code class="computeroutput"> <span class="keyword">and</span> </code>modf` are not currently used, but may
be if further special functions are added.
</p>
<p>
Note that the <code class="computeroutput"><span class="identifier">round</span></code>, <code class="computeroutput"><span class="identifier">trunc</span></code> and <code class="computeroutput"><span class="identifier">modf</span></code>
functions are not part of the current C++ standard: they are part of the
additions added to C99 which will likely be in the next C++ standard. There
are Boost versions of these provided as a backup, and the functions are always
called unqualified so that argument-dependent-lookup can take place.
</p>
<p>
In addition, for efficient and accurate results, a <a class="link" href="../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos
approximation</a> is highly desirable. You may be able to adapt an existing
approximation from <a href="../../../../../../../boost/math/special_functions/lanczos.hpp" target="_top">boost/math/special_functions/lanczos.hpp</a>
or <a href="../../../../../../../boost/math/bindings/detail/big_lanczos.hpp" target="_top">boost/math/bindings/detail/big_lanczos.hpp</a>:
in the former case you will need change static_cast's to lexical_cast's,
and the constants to <span class="emphasis"><em>strings</em></span> (in order to ensure the
coefficients aren't truncated to long double) and then specialise <code class="computeroutput"><span class="identifier">lanczos_traits</span></code> for type T. Otherwise you
may have to hack <a href="../../../../../tools/lanczos_generator.cpp" target="_top">libs/math/tools/lanczos_generator.cpp</a>
to find a suitable approximation for your RealType. The code will still compile
if you don't do this, but both accuracy and efficiency will be greatly compromised
in any function that makes use of the gamma/beta/erf family of functions.
</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 &#169; 2006 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan R&#229;de, 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>)
</p>
</div></td>
</tr></table>
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