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<h3 class="section">4.6 Exceptions</h3>

<p>MPFR supports 6 exception types:

     <ul>
<li>Underflow:
An underflow occurs when the exact result of a function is a non-zero
real number and the result obtained after the rounding, assuming an
unbounded exponent range (for the rounding), has an exponent smaller
than the minimum value of the current exponent range. (In the round-to-nearest
mode, the halfway case is rounded toward zero.)

     <p>Note: This is not the single possible definition of the underflow. MPFR chooses
to consider the underflow <em>after</em> rounding. The underflow before rounding
can also be defined. For instance, consider a function that has the
exact result 7 multiplied by two to the power
<var>e</var>&minus;4, where <var>e</var> is the smallest exponent (for a
significand between 1/2 and 1),
with a 2-bit target precision and rounding toward plus infinity. 
The exact result has the exponent <var>e</var>&minus;1. With the underflow
before rounding, such a function call would yield an underflow, as
<var>e</var>&minus;1 is outside the current exponent range. However, MPFR
first considers the rounded result assuming an unbounded exponent range. 
The exact result cannot be represented exactly in precision 2, and here,
it is rounded to 0.5 times 2 to <var>e</var>, which is
representable in the current exponent range. As a consequence, this will
not yield an underflow in MPFR.

     <li>Overflow:
An overflow occurs when the exact result of a function is a non-zero
real number and the result obtained after the rounding, assuming an
unbounded exponent range (for the rounding), has an exponent larger
than the maximum value of the current exponent range. In the round-to-nearest
mode, the result is infinite. 
Note: unlike the underflow case, there is only one possible definition of
overflow here.

     <li>Divide-by-zero:
An exact infinite result is obtained from finite inputs.

     <li>NaN:
A NaN exception occurs when the result of a function is NaN. 
<!-- NaN is defined above. So, we don't say anything more. -->

     <li>Inexact:
An inexact exception occurs when the result of a function cannot be
represented exactly and must be rounded.

     <li>Range error:
A range exception occurs when a function that does not return a MPFR
number (such as comparisons and conversions to an integer) has an
invalid result (e.g., an argument is NaN in <code>mpfr_cmp</code>, or a
conversion to an integer cannot be represented in the target type).

   </ul>

   <p>MPFR has a global flag for each exception, which can be cleared, set
or tested by functions described in <a href="Exception-Related-Functions.html#Exception-Related-Functions">Exception Related Functions</a>.

   <p>Differences with the ISO C99 standard:

     <ul>
<li>In C, only quiet NaNs are specified, and a NaN propagation does not
raise an invalid exception. Unless explicitly stated otherwise, MPFR sets
the NaN flag whenever a NaN is generated, even when a NaN is propagated
(e.g., in NaN + NaN), as if all NaNs were signaling.

     <li>An invalid exception in C corresponds to either a NaN exception or
a range error in MPFR.

   </ul>

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