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<html>
<head>
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<title>Error Handling</title>
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<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.error_handling"></a><a class="link" href="error_handling.html" title="Error Handling">Error Handling</a>
</h2></div></div></div>
<h4>
<a name="math_toolkit.error_handling.h0"></a>
<span class="phrase"><a name="math_toolkit.error_handling.quick_reference"></a></span><a class="link" href="error_handling.html#math_toolkit.error_handling.quick_reference">Quick
Reference</a>
</h4>
<p>
Handling of errors by this library is split into two orthogonal parts:
</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
What kind of error has been raised?
</li>
<li class="listitem">
What should be done when the error is raised?
</li>
</ul></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>
The default error actions are to throw an exception with an informative error
message. If you do not try to catch the exception, you will not see the message!
</p></td></tr>
</table></div>
<p>
The kinds of errors that can be raised are:
</p>
<div class="variablelist">
<p class="title"><b></b></p>
<dl class="variablelist">
<dt><span class="term">Domain Error</span></dt>
<dd><p>
Occurs when one or more arguments to a function are out of range.
</p></dd>
<dt><span class="term">Pole Error</span></dt>
<dd><p>
Occurs when the particular arguments cause the function to be evaluated
at a pole with no well defined residual value. For example if <a class="link" href="sf_gamma/tgamma.html" title="Gamma">tgamma</a>
is evaluated at exactly -2, the function approaches different limiting
values depending upon whether you approach from just above or just below
-2. Hence the function has no well defined value at this point and a
Pole Error will be raised.
</p></dd>
<dt><span class="term">Overflow Error</span></dt>
<dd><p>
Occurs when the result is either infinite, or too large to represent
in the numeric type being returned by the function.
</p></dd>
<dt><span class="term">Underflow Error</span></dt>
<dd><p>
Occurs when the result is not zero, but is too small to be represented
by any other value in the type being returned by the function.
</p></dd>
<dt><span class="term">Denormalisation Error</span></dt>
<dd><p>
Occurs when the returned result would be a denormalised value.
</p></dd>
<dt><span class="term">Rounding Error</span></dt>
<dd><p>
Occurs when the argument to one of the rounding functions <a class="link" href="rounding/trunc.html" title="Truncation Functions">trunc</a>,
<a class="link" href="rounding/round.html" title="Rounding Functions">round</a> and <a class="link" href="rounding/modf.html" title="Integer and Fractional Part Splitting (modf)">modf</a>
can not be represented as an integer type, is outside the range of the
result type.
</p></dd>
<dt><span class="term">Evaluation Error</span></dt>
<dd><p>
Occurs if no method of evaluation is known, or when an internal error
occurred that prevented the result from being evaluated: this should
never occur, but if it does, then it's likely to be due to an iterative
method not converging fast enough.
</p></dd>
<dt><span class="term">Indeterminate Result Error</span></dt>
<dd><p>
Occurs when the result of a function is not defined for the values that
were passed to it.
</p></dd>
</dl>
</div>
<p>
The action undertaken by each error condition is determined by the current
<a class="link" href="../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc">Policy</a> in effect. This can be changed program-wide
by setting some configuration macros, or at namespace scope, or at the call
site (by specifying a specific policy in the function call).
</p>
<p>
The available actions are:
</p>
<div class="variablelist">
<p class="title"><b></b></p>
<dl class="variablelist">
<dt><span class="term">throw_on_error</span></dt>
<dd><p>
Throws the exception most appropriate to the error condition.
</p></dd>
<dt><span class="term">errno_on_error</span></dt>
<dd><p>
Sets ::errno to an appropriate value, and then returns the most appropriate
result
</p></dd>
<dt><span class="term">ignore_error</span></dt>
<dd><p>
Ignores the error and simply the returns the most appropriate result.
</p></dd>
<dt><span class="term">user_error</span></dt>
<dd><p>
Calls a <a class="link" href="pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">user-supplied
error handler</a>.
</p></dd>
</dl>
</div>
<p>
The following tables show all the permutations of errors and actions, with
the <span class="bold"><strong>default action for each error shown in bold</strong></span>:
</p>
<div class="table">
<a name="math_toolkit.error_handling.possible_actions_for_domain_erro"></a><p class="title"><b>Table 1.1. Possible Actions for Domain Errors</b></p>
<div class="table-contents"><table class="table" summary="Possible Actions for Domain Errors">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
Action
</p>
</th>
<th>
<p>
Behaviour
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
throw_on_error
</p>
</td>
<td>
<p>
<span class="bold"><strong>Throws <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">domain_error</span></code></strong></span>
</p>
</td>
</tr>
<tr>
<td>
<p>
errno_on_error
</p>
</td>
<td>
<p>
Sets <code class="computeroutput"><span class="special">::</span><span class="identifier">errno</span></code>
to <code class="computeroutput"><span class="identifier">EDOM</span></code> and returns
<code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">quiet_NaN</span><span class="special">()</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
ignore_error
</p>
</td>
<td>
<p>
Returns <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">quiet_NaN</span><span class="special">()</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
user_error
</p>
</td>
<td>
<p>
Returns the result of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">user_domain_error</span></code>:
<a class="link" href="pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">this function
must be defined by the user</a>.
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.error_handling.possible_actions_for_pole_errors"></a><p class="title"><b>Table 1.2. Possible Actions for Pole Errors</b></p>
<div class="table-contents"><table class="table" summary="Possible Actions for Pole Errors">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
Action
</p>
</th>
<th>
<p>
Behaviour
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
throw_on_error
</p>
</td>
<td>
<p>
<span class="bold"><strong>Throws <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">domain_error</span></code></strong></span>
</p>
</td>
</tr>
<tr>
<td>
<p>
errno_on_error
</p>
</td>
<td>
<p>
Sets <code class="computeroutput"><span class="special">::</span><span class="identifier">errno</span></code>
to <code class="computeroutput"><span class="identifier">EDOM</span></code> and returns
<code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">quiet_NaN</span><span class="special">()</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
ignore_error
</p>
</td>
<td>
<p>
Returns <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">quiet_NaN</span><span class="special">()</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
user_error
</p>
</td>
<td>
<p>
Returns the result of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">user_pole_error</span></code>:
<a class="link" href="pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">this function
must be defined by the user</a>.
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.error_handling.possible_actions_for_overflow_er"></a><p class="title"><b>Table 1.3. Possible Actions for Overflow Errors</b></p>
<div class="table-contents"><table class="table" summary="Possible Actions for Overflow Errors">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
Action
</p>
</th>
<th>
<p>
Behaviour
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
throw_on_error
</p>
</td>
<td>
<p>
<span class="bold"><strong>Throws <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code></strong></span>
</p>
</td>
</tr>
<tr>
<td>
<p>
errno_on_error
</p>
</td>
<td>
<p>
Sets <code class="computeroutput"><span class="special">::</span><span class="identifier">errno</span></code>
to <code class="computeroutput"><span class="identifier">ERANGE</span></code> and returns
<code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">infinity</span><span class="special">()</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
ignore_error
</p>
</td>
<td>
<p>
Returns <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">infinity</span><span class="special">()</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
user_error
</p>
</td>
<td>
<p>
Returns the result of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">user_overflow_error</span></code>:
<a class="link" href="pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">this function
must be defined by the user</a>.
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.error_handling.possible_actions_for_underflow_e"></a><p class="title"><b>Table 1.4. Possible Actions for Underflow Errors</b></p>
<div class="table-contents"><table class="table" summary="Possible Actions for Underflow Errors">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
Action
</p>
</th>
<th>
<p>
Behaviour
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
throw_on_error
</p>
</td>
<td>
<p>
Throws <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">underflow_error</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
errno_on_error
</p>
</td>
<td>
<p>
Sets <code class="computeroutput"><span class="special">::</span><span class="identifier">errno</span></code>
to <code class="computeroutput"><span class="identifier">ERANGE</span></code> and returns
0.
</p>
</td>
</tr>
<tr>
<td>
<p>
ignore_error
</p>
</td>
<td>
<p>
<span class="bold"><strong>Returns 0</strong></span>
</p>
</td>
</tr>
<tr>
<td>
<p>
user_error
</p>
</td>
<td>
<p>
Returns the result of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">user_underflow_error</span></code>:
<a class="link" href="pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">this function
must be defined by the user</a>.
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.error_handling.possible_actions_for_denorm_erro"></a><p class="title"><b>Table 1.5. Possible Actions for Denorm Errors</b></p>
<div class="table-contents"><table class="table" summary="Possible Actions for Denorm Errors">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
Action
</p>
</th>
<th>
<p>
Behaviour
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
throw_on_error
</p>
</td>
<td>
<p>
Throws <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">underflow_error</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
errno_on_error
</p>
</td>
<td>
<p>
Sets <code class="computeroutput"><span class="special">::</span><span class="identifier">errno</span></code>
to <code class="computeroutput"><span class="identifier">ERANGE</span></code> and returns
the denormalised value.
</p>
</td>
</tr>
<tr>
<td>
<p>
ignore_error
</p>
</td>
<td>
<p>
<span class="bold"><strong>Returns the denormalised value.</strong></span>
</p>
</td>
</tr>
<tr>
<td>
<p>
user_error
</p>
</td>
<td>
<p>
Returns the result of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">user_denorm_error</span></code>:
<a class="link" href="pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">this function
must be defined by the user</a>.
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.error_handling.possible_actions_for_rounding_er"></a><p class="title"><b>Table 1.6. Possible Actions for Rounding Errors</b></p>
<div class="table-contents"><table class="table" summary="Possible Actions for Rounding Errors">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
Action
</p>
</th>
<th>
<p>
Behaviour
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
throw_on_error
</p>
</td>
<td>
<p>
Throws <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">rounding_error</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
errno_on_error
</p>
</td>
<td>
<p>
Sets <code class="computeroutput"><span class="special">::</span><span class="identifier">errno</span></code>
to <code class="computeroutput"><span class="identifier">ERANGE</span></code> and returns
the largest representable value of the target integer type (or the
most negative value if the argument to the function was less than
zero).
</p>
</td>
</tr>
<tr>
<td>
<p>
ignore_error
</p>
</td>
<td>
<p>
<span class="bold"><strong>Returns the largest representable value of
the target integer type (or the most negative value if the argument
to the function was less than zero).</strong></span>
</p>
</td>
</tr>
<tr>
<td>
<p>
user_error
</p>
</td>
<td>
<p>
Returns the result of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">user_rounding_error</span></code>:
<a class="link" href="pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">this function
must be defined by the user</a>.
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.error_handling.possible_actions_for_internal_ev"></a><p class="title"><b>Table 1.7. Possible Actions for Internal Evaluation Errors</b></p>
<div class="table-contents"><table class="table" summary="Possible Actions for Internal Evaluation Errors">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
Action
</p>
</th>
<th>
<p>
Behaviour
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
throw_on_error
</p>
</td>
<td>
<p>
<span class="bold"><strong>Throws <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">evaluation_error</span></code></strong></span>
</p>
</td>
</tr>
<tr>
<td>
<p>
errno_on_error
</p>
</td>
<td>
<p>
Sets <code class="computeroutput"><span class="special">::</span><span class="identifier">errno</span></code>
to <code class="computeroutput"><span class="identifier">EDOM</span></code> and returns
the closest approximation found.
</p>
</td>
</tr>
<tr>
<td>
<p>
ignore_error
</p>
</td>
<td>
<p>
Returns the closest approximation found.
</p>
</td>
</tr>
<tr>
<td>
<p>
user_error
</p>
</td>
<td>
<p>
Returns the result of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">user_evaluation_error</span></code>:
<a class="link" href="pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">this function
must be defined by the user</a>.
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.error_handling.possible_actions_for_indetermina"></a><p class="title"><b>Table 1.8. Possible Actions for Indeterminate Result Errors</b></p>
<div class="table-contents"><table class="table" summary="Possible Actions for Indeterminate Result Errors">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
Action
</p>
</th>
<th>
<p>
Behaviour
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
throw_on_error
</p>
</td>
<td>
<p>
Throws <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">domain_error</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
errno_on_error
</p>
</td>
<td>
<p>
Sets <code class="computeroutput"><span class="special">::</span><span class="identifier">errno</span></code>
to <code class="computeroutput"><span class="identifier">EDOM</span></code> and returns
the same value as <code class="computeroutput"><span class="identifier">ignore_error</span></code>.
</p>
</td>
</tr>
<tr>
<td>
<p>
ignore_error
</p>
</td>
<td>
<p>
<span class="bold"><strong>Returns a default result that depends on the
function where the error occurred.</strong></span>
</p>
</td>
</tr>
<tr>
<td>
<p>
user_error
</p>
</td>
<td>
<p>
Returns the result of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">user_indeterminate_result_error</span></code>:
<a class="link" href="pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">this function
must be defined by the user</a>.
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><p>
All these error conditions are in namespace boost::math::policies, made available,
for example, a by namespace declaration using <code class="computeroutput"><span class="keyword">namespace</span>
<span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span></code> or individual using declarations <code class="computeroutput"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">overflow_error</span><span class="special">;</span></code>.
</p>
<h4>
<a name="math_toolkit.error_handling.h1"></a>
<span class="phrase"><a name="math_toolkit.error_handling.rationale"></a></span><a class="link" href="error_handling.html#math_toolkit.error_handling.rationale">Rationale</a>
</h4>
<p>
The flexibility of the current implementation should be reasonably obvious:
the default behaviours were chosen based on feedback during the formal review
of this library. It was felt that:
</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
Genuine errors should be flagged with exceptions rather than following
C-compatible behaviour and setting <code class="computeroutput"><span class="special">::</span><span class="identifier">errno</span></code>.
</li>
<li class="listitem">
Numeric underflow and denormalised results were not considered to be fatal
errors in most cases, so it was felt that these should be ignored.
</li>
<li class="listitem">
If there is more than one error, only the first detected will be reported
in the throw message.
</li>
</ul></div>
<h4>
<a name="math_toolkit.error_handling.h2"></a>
<span class="phrase"><a name="math_toolkit.error_handling.finding_more_information"></a></span><a class="link" href="error_handling.html#math_toolkit.error_handling.finding_more_information">Finding
More Information</a>
</h4>
<p>
There are some pre-processor macro defines that can be used to <a class="link" href="pol_ref/policy_defaults.html" title="Using Macros to Change the Policy Defaults">change
the policy defaults</a>. See also the <a class="link" href="../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc">policy section</a>.
</p>
<p>
An example is at the Policy tutorial in <a class="link" href="pol_tutorial/changing_policy_defaults.html" title="Changing the Policy Defaults">Changing
the Policy Defaults</a>.
</p>
<p>
Full source code of this typical example of passing a 'bad' argument (negative
degrees of freedom) to Student's t distribution is <a class="link" href="stat_tut/weg/error_eg.html" title="Error Handling Example">in
the error handling example</a>.
</p>
<p>
The various kind of errors are described in more detail below.
</p>
<h4>
<a name="math_toolkit.error_handling.h3"></a>
<span class="phrase"><a name="math_toolkit.error_handling.domain_error"></a></span><a class="link" href="error_handling.html#math_toolkit.error_handling.domain_error">Domain
Errors</a>
</h4>
<p>
When a special function is passed an argument that is outside the range of
values for which that function is defined, then the function returns the result
of:
</p>
<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">raise_domain_error</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">FunctionName</span><span class="special">,</span> <span class="identifier">Message</span><span class="special">,</span> <span class="identifier">Val</span><span class="special">,</span> <a class="link" href="../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">);</span>
</pre>
<p>
Where <code class="computeroutput"><span class="identifier">T</span></code> is the floating-point
type passed to the function, <code class="computeroutput"><span class="identifier">FunctionName</span></code>
is the name of the function, <code class="computeroutput"><span class="identifier">Message</span></code>
is an error message describing the problem, Val is the value that was out of
range, and <a class="link" href="../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc">Policy</a> is the current policy in use
for the function that was called.
</p>
<p>
The default policy behaviour of this function is to throw a std::domain_error
C++ exception. But if the <a class="link" href="../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc">Policy</a> is to ignore
the error, or set global <code class="computeroutput"><span class="special">::</span><span class="identifier">errno</span></code>,
then a NaN will be returned.
</p>
<p>
This behaviour is chosen to assist compatibility with the behaviour of <span class="emphasis"><em>ISO/IEC
9899:1999 Programming languages - C</em></span> and with the <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2005/n1836.pdf" target="_top">Draft
Technical Report on C++ Library Extensions, 2005-06-24, section 5.2.1, paragraph
6</a>:
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="emphasis"><em>"Each of the functions declared above shall return a NaN (Not
a Number) if any argument value is a NaN, but it shall not report a domain
error. Otherwise, each of the functions declared above shall report a domain
error for just those argument values for which:</em></span>
</p></blockquote></div>
<div class="blockquote"><blockquote class="blockquote">
<p>
<span class="emphasis"><em>"the function description's Returns clause explicitly specifies
a domain, and those arguments fall outside the specified domain; or</em></span>
</p>
<p>
<span class="emphasis"><em>"the corresponding mathematical function value has a non-zero
imaginary component; or</em></span>
</p>
<p>
<span class="emphasis"><em>"the corresponding mathematical function is not mathematically
defined.</em></span>
</p>
</blockquote></div>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="emphasis"><em>"Note 2: A mathematical function is mathematically defined
for a given set of argument values if it is explicitly defined for that set
of argument values or if its limiting value exists and does not depend on
the direction of approach."</em></span>
</p></blockquote></div>
<p>
Note that in order to support information-rich error messages when throwing
exceptions, <code class="computeroutput"><span class="identifier">Message</span></code> must contain
a <a href="../../../../format/index.html" target="_top">Boost.Format</a> recognised format
specifier: the argument <code class="computeroutput"><span class="identifier">Val</span></code>
is inserted into the error message according to the specifier used.
</p>
<p>
For example if <code class="computeroutput"><span class="identifier">Message</span></code> contains
a "%1%" then it is replaced by the value of <code class="computeroutput"><span class="identifier">Val</span></code>
to the full precision of T, where as "%.3g" would contain the value
of <code class="computeroutput"><span class="identifier">Val</span></code> to 3 digits. See the
<a href="../../../../format/index.html" target="_top">Boost.Format</a> documentation
for more details.
</p>
<h4>
<a name="math_toolkit.error_handling.h4"></a>
<span class="phrase"><a name="math_toolkit.error_handling.pole_error"></a></span><a class="link" href="error_handling.html#math_toolkit.error_handling.pole_error">Evaluation
at a pole</a>
</h4>
<p>
When a special function is passed an argument that is at a pole without a well
defined residual value, then the function returns the result of:
</p>
<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">raise_pole_error</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">FunctionName</span><span class="special">,</span> <span class="identifier">Message</span><span class="special">,</span> <span class="identifier">Val</span><span class="special">,</span> <a class="link" href="../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">);</span>
</pre>
<p>
Where <code class="computeroutput"><span class="identifier">T</span></code> is the floating point
type passed to the function, <code class="computeroutput"><span class="identifier">FunctionName</span></code>
is the name of the function, <code class="computeroutput"><span class="identifier">Message</span></code>
is an error message describing the problem, <code class="computeroutput"><span class="identifier">Val</span></code>
is the value of the argument that is at a pole, and <a class="link" href="../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc">Policy</a>
is the current policy in use for the function that was called.
</p>
<p>
The default behaviour of this function is to throw a std::domain_error exception.
But <a class="link" href="pol_ref/error_handling_policies.html" title="Error Handling Policies">error handling
policies</a> can be used to change this, for example to <code class="computeroutput"><span class="identifier">ignore_error</span></code>
and return NaN.
</p>
<p>
Note that in order to support information-rich error messages when throwing
exceptions, <code class="computeroutput"><span class="identifier">Message</span></code> must contain
a <a href="../../../../format/index.html" target="_top">Boost.Format</a> recognised format
specifier: the argument <code class="computeroutput"><span class="identifier">val</span></code>
is inserted into the error message according to the specifier used.
</p>
<p>
For example if <code class="computeroutput"><span class="identifier">Message</span></code> contains
a "%1%" then it is replaced by the value of <code class="computeroutput"><span class="identifier">val</span></code>
to the full precision of T, where as "%.3g" would contain the value
of <code class="computeroutput"><span class="identifier">val</span></code> to 3 digits. See the
<a href="../../../../format/index.html" target="_top">Boost.Format</a> documentation
for more details.
</p>
<h4>
<a name="math_toolkit.error_handling.h5"></a>
<span class="phrase"><a name="math_toolkit.error_handling.overflow_error"></a></span><a class="link" href="error_handling.html#math_toolkit.error_handling.overflow_error">Numeric
Overflow</a>
</h4>
<p>
When the result of a special function is too large to fit in the argument floating-point
type, then the function returns the result of:
</p>
<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">raise_overflow_error</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">FunctionName</span><span class="special">,</span> <span class="identifier">Message</span><span class="special">,</span> <a class="link" href="../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">);</span>
</pre>
<p>
Where <code class="computeroutput"><span class="identifier">T</span></code> is the floating-point
type passed to the function, <code class="computeroutput"><span class="identifier">FunctionName</span></code>
is the name of the function, <code class="computeroutput"><span class="identifier">Message</span></code>
is an error message describing the problem, and <a class="link" href="../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc">Policy</a>
is the current policy in use for the function that was called.
</p>
<p>
The default policy for this function is that <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code>
C++ exception is thrown. But if, for example, an <code class="computeroutput"><span class="identifier">ignore_error</span></code>
policy is used, then returns <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">infinity</span><span class="special">()</span></code>.
In this situation if the type <code class="computeroutput"><span class="identifier">T</span></code>
doesn't support infinities, the maximum value for the type is returned.
</p>
<h4>
<a name="math_toolkit.error_handling.h6"></a>
<span class="phrase"><a name="math_toolkit.error_handling.underflow_error"></a></span><a class="link" href="error_handling.html#math_toolkit.error_handling.underflow_error">Numeric
Underflow</a>
</h4>
<p>
If the result of a special function is known to be non-zero, but the calculated
result underflows to zero, then the function returns the result of:
</p>
<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">raise_underflow_error</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">FunctionName</span><span class="special">,</span> <span class="identifier">Message</span><span class="special">,</span> <a class="link" href="../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">);</span>
</pre>
<p>
Where <code class="computeroutput"><span class="identifier">T</span></code> is the floating point
type passed to the function, <code class="computeroutput"><span class="identifier">FunctionName</span></code>
is the name of the function, <code class="computeroutput"><span class="identifier">Message</span></code>
is an error message describing the problem, and <a class="link" href="../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc">Policy</a>
is the current policy in use for the called function.
</p>
<p>
The default version of this function returns zero. But with another policy,
like <code class="computeroutput"><span class="identifier">throw_on_error</span></code>, throws
an <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">underflow_error</span></code> C++ exception.
</p>
<h4>
<a name="math_toolkit.error_handling.h7"></a>
<span class="phrase"><a name="math_toolkit.error_handling.denorm_error"></a></span><a class="link" href="error_handling.html#math_toolkit.error_handling.denorm_error">Denormalisation
Errors</a>
</h4>
<p>
If the result of a special function is a denormalised value <span class="emphasis"><em>z</em></span>
then the function returns the result of:
</p>
<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">raise_denorm_error</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">z</span><span class="special">,</span> <span class="identifier">FunctionName</span><span class="special">,</span> <span class="identifier">Message</span><span class="special">,</span> <a class="link" href="../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">);</span>
</pre>
<p>
Where <code class="computeroutput"><span class="identifier">T</span></code> is the floating point
type passed to the function, <code class="computeroutput"><span class="identifier">FunctionName</span></code>
is the name of the function, <code class="computeroutput"><span class="identifier">Message</span></code>
is an error message describing the problem, and <a class="link" href="../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc">Policy</a>
is the current policy in use for the called function.
</p>
<p>
The default version of this function returns <span class="emphasis"><em>z</em></span>. But with
another policy, like <code class="computeroutput"><span class="identifier">throw_on_error</span></code>
throws an <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">underflow_error</span></code> C++ exception.
</p>
<h4>
<a name="math_toolkit.error_handling.h8"></a>
<span class="phrase"><a name="math_toolkit.error_handling.evaluation_error"></a></span><a class="link" href="error_handling.html#math_toolkit.error_handling.evaluation_error">Evaluation
Errors</a>
</h4>
<p>
When a special function calculates a result that is known to be erroneous,
or where the result is incalculable then it calls:
</p>
<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">raise_evaluation_error</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">FunctionName</span><span class="special">,</span> <span class="identifier">Message</span><span class="special">,</span> <span class="identifier">Val</span><span class="special">,</span> <a class="link" href="../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">);</span>
</pre>
<p>
Where <code class="computeroutput"><span class="identifier">T</span></code> is the floating point
type passed to the function, <code class="computeroutput"><span class="identifier">FunctionName</span></code>
is the name of the function, <code class="computeroutput"><span class="identifier">Message</span></code>
is an error message describing the problem, <code class="computeroutput"><span class="identifier">Val</span></code>
is the erroneous value, and <a class="link" href="../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc">Policy</a> is the current
policy in use for the called function.
</p>
<p>
The default behaviour of this function is to throw a <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">evaluation_error</span></code>.
</p>
<p>
Note that in order to support information rich error messages when throwing
exceptions, <code class="computeroutput"><span class="identifier">Message</span></code> must contain
a <a href="../../../../format/index.html" target="_top">Boost.Format</a> recognised format
specifier: the argument <code class="computeroutput"><span class="identifier">val</span></code>
is inserted into the error message according to the specifier used.
</p>
<p>
For example if <code class="computeroutput"><span class="identifier">Message</span></code> contains
a "%1%" then it is replaced by the value of <code class="computeroutput"><span class="identifier">val</span></code>
to the full precision of T, where as "%.3g" would contain the value
of <code class="computeroutput"><span class="identifier">val</span></code> to 3 digits. See the
<a href="../../../../format/index.html" target="_top">Boost.Format</a> documentation
for more details.
</p>
<h4>
<a name="math_toolkit.error_handling.h9"></a>
<span class="phrase"><a name="math_toolkit.error_handling.indeterminate_result_error"></a></span><a class="link" href="error_handling.html#math_toolkit.error_handling.indeterminate_result_error">Indeterminate
Result Errors</a>
</h4>
<p>
When the result of a special function is indeterminate for the value that was
passed to it, then the function returns the result of:
</p>
<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">raise_overflow_error</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">FunctionName</span><span class="special">,</span> <span class="identifier">Message</span><span class="special">,</span> <span class="identifier">Val</span><span class="special">,</span> <span class="identifier">Default</span><span class="special">,</span> <a class="link" href="../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">);</span>
</pre>
<p>
Where <code class="computeroutput"><span class="identifier">T</span></code> is the floating-point
type passed to the function, <code class="computeroutput"><span class="identifier">FunctionName</span></code>
is the name of the function, <code class="computeroutput"><span class="identifier">Message</span></code>
is an error message describing the problem, Val is the value for which the
result is indeterminate, Default is an alternative default result that must
be returned for <code class="computeroutput"><span class="identifier">ignore_error</span></code>
and <code class="computeroutput"><span class="identifier">errno_on_erro</span></code> policies,
and <a class="link" href="../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc">Policy</a> is the current policy in use for the
function that was called.
</p>
<p>
The default policy for this function is <code class="computeroutput"><span class="identifier">ignore_error</span></code>:
note that this error type is reserved for situations where the result is mathematically
undefined or indeterminate, but there is none the less a convention for what
the result should be: for example the C99 standard specifies that the result
of 0<sup>0</sup> is 1, even though the result is actually mathematically indeterminate.
</p>
<h4>
<a name="math_toolkit.error_handling.h10"></a>
<span class="phrase"><a name="math_toolkit.error_handling.rounding_error"></a></span><a class="link" href="error_handling.html#math_toolkit.error_handling.rounding_error">Rounding
Errors</a>
</h4>
<p>
When one of the rounding functions <a class="link" href="rounding/round.html" title="Rounding Functions">round</a>,
<a class="link" href="rounding/trunc.html" title="Truncation Functions">trunc</a> or <a class="link" href="rounding/modf.html" title="Integer and Fractional Part Splitting (modf)">modf</a>
is called with an argument that has no integer representation, or is too large
to be represented in the result type then the value returned is the result
of a call to:
</p>
<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">raise_rounding_error</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">FunctionName</span><span class="special">,</span> <span class="identifier">Message</span><span class="special">,</span> <span class="identifier">Val</span><span class="special">,</span> <a class="link" href="../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">);</span>
</pre>
<p>
Where <code class="computeroutput"><span class="identifier">T</span></code> is the floating point
type passed to the function, <code class="computeroutput"><span class="identifier">FunctionName</span></code>
is the name of the function, <code class="computeroutput"><span class="identifier">Message</span></code>
is an error message describing the problem, <code class="computeroutput"><span class="identifier">Val</span></code>
is the erroneous argument, and <a class="link" href="../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc">Policy</a> is the
current policy in use for the called function.
</p>
<p>
The default behaviour of this function is to throw a <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">rounding_error</span></code>.
</p>
<p>
Note that in order to support information rich error messages when throwing
exceptions, <code class="computeroutput"><span class="identifier">Message</span></code> must contain
a <a href="../../../../format/index.html" target="_top">Boost.Format</a> recognised format
specifier: the argument <code class="computeroutput"><span class="identifier">val</span></code>
is inserted into the error message according to the specifier used.
</p>
<p>
For example if <code class="computeroutput"><span class="identifier">Message</span></code> contains
a "%1%" then it is replaced by the value of <code class="computeroutput"><span class="identifier">val</span></code>
to the full precision of T, where as "%.3g" would contain the value
of <code class="computeroutput"><span class="identifier">val</span></code> to 3 digits. See the
<a href="../../../../format/index.html" target="_top">Boost.Format</a> documentation
for more details.
</p>
<h4>
<a name="math_toolkit.error_handling.h11"></a>
<span class="phrase"><a name="math_toolkit.error_handling.checked_narrowing_cast"></a></span><a class="link" href="error_handling.html#math_toolkit.error_handling.checked_narrowing_cast">Errors
from typecasts</a>
</h4>
<p>
Many special functions evaluate their results at a higher precision than their
arguments in order to ensure full machine precision in the result: for example,
a function passed a float argument may evaluate its result using double precision
internally. Many of the errors listed above may therefore occur not during
evaluation, but when converting the result to the narrower result type. The
function:
</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> <a class="link" href="../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">></span>
<span class="identifier">T</span> <span class="identifier">checked_narrowing_cast</span><span class="special">(</span><span class="identifier">U</span> <span class="keyword">const</span><span class="special">&</span> <span class="identifier">val</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">);</span>
</pre>
<p>
Is used to perform these conversions, and will call the error handlers listed
above on <a class="link" href="error_handling.html#math_toolkit.error_handling.overflow_error">overflow</a>,
<a class="link" href="error_handling.html#math_toolkit.error_handling.underflow_error">underflow</a>
or <a class="link" href="error_handling.html#math_toolkit.error_handling.denorm_error">denormalisation</a>.
</p>
</div>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal,
Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
Holin, Bruno Lalande, John Maddock, Johan Råde, Gautam Sewani, Benjamin Sobotta,
Thijs van den Berg, Daryle Walker and Xiaogang Zhang<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>
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