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<div class="section" lang="en">
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.main_overview.error_handling"></a><a class="link" href="error_handling.html" title="Error Handling"> Error Handling</a>
</h3></div></div></div>
<a name="math_toolkit.main_overview.error_handling.quick_reference"></a><h5>
<a name="id913298"></a>
<a class="link" href="error_handling.html#math_toolkit.main_overview.error_handling.quick_reference">Quick
Reference</a>
</h5>
<p>
Handling of errors by this library is split into two orthogonal parts:
</p>
<div class="itemizedlist"><ul type="disc">
<li>
What kind of error has been raised?
</li>
<li>
What should be done when the error is raised?
</li>
</ul></div>
<p>
The kinds of errors that can be raised are:
</p>
<div class="variablelist">
<p class="title"><b></b></p>
<dl>
<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="../special/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="../utils/rounding/trunc.html" title="Truncation Functions">trunc</a>,
<a class="link" href="../utils/rounding/round.html" title="Rounding Functions">round</a> and
<a class="link" href="../utils/rounding/modf.html" title="Integer and Fractional Part Splitting (modf)">modf</a> can not
be represented as an integer type, is outide the range of the result
type.
</p></dd>
<dt><span class="term">Evaluation Error</span></dt>
<dd><p>
Occurs when an internal error occured 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="Policies">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>
<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="../policy/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 default action for each error shown in bold:
</p>
<div class="table">
<a name="id913562"></a><p class="title"><b>Table 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="../policy/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="id913808"></a><p class="title"><b>Table 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="../policy/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="id914054"></a><p class="title"><b>Table 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="../policy/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="id914300"></a><p class="title"><b>Table 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="../policy/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="id914487"></a><p class="title"><b>Table 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="../policy/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="id914670"></a><p class="title"><b>Table 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
an unspecified value.
</p>
</td>
</tr>
<tr>
<td>
<p>
ignore_error
</p>
</td>
<td>
<p>
<span class="bold"><strong>Returns the an unspecified 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_rounding_error</span></code>:
<a class="link" href="../policy/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="id914859"></a><p class="title"><b>Table 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="../policy/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="id915048"></a><p class="title"><b>Table 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="../policy/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"><a name="math_toolkit.main_overview.error_handling.rationale"></a><h5>
<a name="id915241"></a>
<a class="link" href="error_handling.html#math_toolkit.main_overview.error_handling.rationale">Rationale</a>
</h5>
<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 type="disc">
<li>
Genuine errors should be flagged with exceptions rather than following
C-compatible behaviour and setting ::errno.
</li>
<li>
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>
</ul></div>
<a name="math_toolkit.main_overview.error_handling.finding_more_information"></a><h5>
<a name="id915276"></a>
<a class="link" href="error_handling.html#math_toolkit.main_overview.error_handling.finding_more_information">Finding
More Information</a>
</h5>
<p>
There are some pre-processor macro defines that can be used to <a class="link" href="../policy/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="Policies">policy
section</a>.
</p>
<p>
An example is at the Policy tutorial in <a class="link" href="../policy/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="../dist/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>
<a name="domain_error"></a><a name="math_toolkit.main_overview.error_handling.domain_errors"></a><h5>
<a name="id915328"></a>
<a class="link" href="error_handling.html#math_toolkit.main_overview.error_handling.domain_errors">Domain
Errors</a>
</h5>
<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="Policies">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="Policies">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="Policies">Policy</a>
is to ignore the error, or set global ::errno, 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>
<a name="pole_error"></a><a name="math_toolkit.main_overview.error_handling.evaluation_at_a_pole"></a><h5>
<a name="id915577"></a>
<a class="link" href="error_handling.html#math_toolkit.main_overview.error_handling.evaluation_at_a_pole">Evaluation
at a pole</a>
</h5>
<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="Policies">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="Policies">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="../policy/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>
<a name="overflow_error"></a><a name="math_toolkit.main_overview.error_handling.numeric_overflow"></a><h5>
<a name="id915784"></a>
<a class="link" href="error_handling.html#math_toolkit.main_overview.error_handling.numeric_overflow">Numeric
Overflow</a>
</h5>
<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="Policies">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="Policies">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>
<a name="underflow_error"></a><a name="math_toolkit.main_overview.error_handling.numeric_underflow"></a><h5>
<a name="id915973"></a>
<a class="link" href="error_handling.html#math_toolkit.main_overview.error_handling.numeric_underflow">Numeric
Underflow</a>
</h5>
<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="Policies">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="Policies">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>
<a name="denorm_error"></a><a name="math_toolkit.main_overview.error_handling.denormalisation_errors"></a><h5>
<a name="id916118"></a>
<a class="link" href="error_handling.html#math_toolkit.main_overview.error_handling.denormalisation_errors">Denormalisation
Errors</a>
</h5>
<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="Policies">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="Policies">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>
<a name="evaluation_error"></a><a name="math_toolkit.main_overview.error_handling.evaluation_errors"></a><h5>
<a name="id916280"></a>
<a class="link" href="error_handling.html#math_toolkit.main_overview.error_handling.evaluation_errors">Evaluation
Errors</a>
</h5>
<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="Policies">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="Policies">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>
<a name="indeterminate_result_error"></a><a name="math_toolkit.main_overview.error_handling.indeterminate_result_errors"></a><h5>
<a name="id916495"></a>
<a class="link" href="error_handling.html#math_toolkit.main_overview.error_handling.indeterminate_result_errors">Indeterminate
Result Errors</a>
</h5>
<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="Policies">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 ignore_error and errno_on_error policies, and <a class="link" href="../policy.html" title="Policies">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>
<a name="rounding_error"></a><a name="math_toolkit.main_overview.error_handling.rounding_errors"></a><h5>
<a name="id916645"></a>
<a class="link" href="error_handling.html#math_toolkit.main_overview.error_handling.rounding_errors">Rounding
Errors</a>
</h5>
<p>
When one of the rounding functions <a class="link" href="../utils/rounding/round.html" title="Rounding Functions">round</a>,
<a class="link" href="../utils/rounding/trunc.html" title="Truncation Functions">trunc</a> or <a class="link" href="../utils/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="Policies">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="Policies">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>
<a name="checked_narrowing_cast"></a><a name="math_toolkit.main_overview.error_handling.errors_from_typecasts"></a><h5>
<a name="id917982"></a>
<a class="link" href="error_handling.html#math_toolkit.main_overview.error_handling.errors_from_typecasts">Errors
from typecasts</a>
</h5>
<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="Policies">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#overflow_error">overflow</a>, <a class="link" href="error_handling.html#underflow_error">underflow</a>
or <a class="link" href="error_handling.html#denorm_error">denormalisation</a>.
</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 © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, 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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