There are different approaches to the issue of not having a value to return.
</p>
<p>
A typical approach is to consider the existence of a valid return value as
a postcondition, so that if the function cannot compute the value to return,
it has either undefined behavior (and can use assert in a debug build) or uses
a runtime check and throws an exception if the postcondition is violated. This
is a reasonable choice for example, for function (A), because the lack of a
proper return value is directly related to an invalid parameter (out of domain
argument), so it is appropriate to require the callee to supply only parameters
in a valid domain for execution to continue normally.
</p>
<p>
However, function (B), because of its asynchronous nature, does not fail just
because it can't find a value to return; so it is incorrect to consider such
a situation an error and assert or throw an exception. This function must return,
and somehow, must tell the callee that it is not returning a meaningful value.
</p>
<p>
A similar situation occurs with function (C): it is conceptually an error to
ask a <spanclass="emphasis"><em>null-area</em></span> polygon to return a point inside itself,
but in many applications, it is just impractical for performance reasons to
treat this as an error (because detecting that the polygon has no area might
be too expensive to be required to be tested previously), and either an arbitrary
point (typically at infinity) is returned, or some efficient way to tell the
callee that there is no such point is used.
</p>
<p>
There are various mechanisms to let functions communicate that the returned
value is not valid. One such mechanism, which is quite common since it has
zero or negligible overhead, is to use a special value which is reserved to
communicate this. Classical examples of such special values are <codeclass="computeroutput"><spanclass="identifier">EOF</span></code>, <codeclass="computeroutput"><spanclass="identifier">string</span><spanclass="special">::</span><spanclass="identifier">npos</span></code>, points
at infinity, etc...
</p>
<p>
When those values exist, i.e. the return type can hold all meaningful values
<spanclass="emphasis"><em>plus</em></span> the <spanclass="emphasis"><em>signal</em></span> value, this mechanism
is quite appropriate and well known. Unfortunately, there are cases when such
values do not exist. In these cases, the usual alternative is either to use
a wider type, such as <codeclass="computeroutput"><spanclass="keyword">int</span></code> in place
of <codeclass="computeroutput"><spanclass="keyword">char</span></code>; or a compound type, such
as <codeclass="computeroutput"><spanclass="identifier">std</span><spanclass="special">::</span><spanclass="identifier">pair</span><spanclass="special"><</span><spanclass="identifier">point</span><spanclass="special">,</span><spanclass="keyword">bool</span><spanclass="special">></span></code>.
</p>
<p>
Returning a <codeclass="computeroutput"><spanclass="identifier">std</span><spanclass="special">::</span><spanclass="identifier">pair</span><spanclass="special"><</span><spanclass="identifier">T</span><spanclass="special">,</span><spanclass="keyword">bool</span><spanclass="special">></span></code>, thus attaching a boolean flag to the result
which indicates if the result is meaningful, has the advantage that can be
turned into a consistent idiom since the first element of the pair can be whatever
the function would conceptually return. For example, the last two functions
