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<!-- This manual documents how to install and use the Multiple Precision
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Floating-Point Reliable Library, version 3.1.4.
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Copyright 1991, 1993-2016 Free Software Foundation, Inc.
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Permission is granted to copy, distribute and/or modify this document under
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the terms of the GNU Free Documentation License, Version 1.2 or any later
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with no Front-Cover Texts, and with no Back-Cover Texts. A copy of the
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<head>
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<title>Exceptions (GNU MPFR 3.1.4)</title>
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<meta name="description" content="How to install and use GNU MPFR, a library for reliable multiple precision
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floating-point arithmetic, version 3.1.4.">
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<meta name="keywords" content="Exceptions (GNU MPFR 3.1.4)">
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<link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index">
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<link href="MPFR-Basics.html#MPFR-Basics" rel="up" title="MPFR Basics">
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<link href="Memory-Handling.html#Memory-Handling" rel="next" title="Memory Handling">
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<link href="Floating_002dPoint-Values-on-Special-Numbers.html#Floating_002dPoint-Values-on-Special-Numbers" rel="prev" title="Floating-Point Values on Special Numbers">
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<a name="Exceptions"></a>
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<div class="header">
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<p>
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Next: <a href="Memory-Handling.html#Memory-Handling" accesskey="n" rel="next">Memory Handling</a>, Previous: <a href="Floating_002dPoint-Values-on-Special-Numbers.html#Floating_002dPoint-Values-on-Special-Numbers" accesskey="p" rel="prev">Floating-Point Values on Special Numbers</a>, Up: <a href="MPFR-Basics.html#MPFR-Basics" accesskey="u" rel="up">MPFR Basics</a> [<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
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</div>
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<hr>
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<a name="Exceptions-1"></a>
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<h3 class="section">4.6 Exceptions</h3>
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<p>MPFR supports 6 exception types:
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</p>
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<ul>
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<li> Underflow:
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An underflow occurs when the exact result of a function is a non-zero
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real number and the result obtained after the rounding, assuming an
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unbounded exponent range (for the rounding), has an exponent smaller
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than the minimum value of the current exponent range. (In the round-to-nearest
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mode, the halfway case is rounded toward zero.)
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<p>Note: This is not the single possible definition of the underflow. MPFR chooses
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to consider the underflow <em>after</em> rounding. The underflow before rounding
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can also be defined. For instance, consider a function that has the
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exact result <em>7 multiplied by two to the power
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<var>e</var>−4</em>, where <var>e</var> is the smallest exponent (for a
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significand between 1/2 and 1),
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with a 2-bit target precision and rounding toward plus infinity.
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The exact result has the exponent <var>e</var>−1. With the underflow
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before rounding, such a function call would yield an underflow, as
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<var>e</var>−1 is outside the current exponent range. However, MPFR
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first considers the rounded result assuming an unbounded exponent range.
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The exact result cannot be represented exactly in precision 2, and here,
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it is rounded to <em>0.5 times 2 to <var>e</var></em>, which is
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representable in the current exponent range. As a consequence, this will
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not yield an underflow in MPFR.
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</p>
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</li><li> Overflow:
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An overflow occurs when the exact result of a function is a non-zero
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real number and the result obtained after the rounding, assuming an
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unbounded exponent range (for the rounding), has an exponent larger
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than the maximum value of the current exponent range. In the round-to-nearest
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mode, the result is infinite.
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Note: unlike the underflow case, there is only one possible definition of
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overflow here.
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</li><li> Divide-by-zero:
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An exact infinite result is obtained from finite inputs.
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</li><li> NaN:
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A NaN exception occurs when the result of a function is NaN.
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</li><li> Inexact:
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An inexact exception occurs when the result of a function cannot be
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represented exactly and must be rounded.
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</li><li> Range error:
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A range exception occurs when a function that does not return a MPFR
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number (such as comparisons and conversions to an integer) has an
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invalid result (e.g., an argument is NaN in <code>mpfr_cmp</code>, or a
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conversion to an integer cannot be represented in the target type).
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</li></ul>
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<p>MPFR has a global flag for each exception, which can be cleared, set
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or tested by functions described in <a href="Exception-Related-Functions.html#Exception-Related-Functions">Exception Related Functions</a>.
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</p>
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<p>Differences with the ISO C99 standard:
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</p>
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<ul>
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<li> In C, only quiet NaNs are specified, and a NaN propagation does not
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raise an invalid exception. Unless explicitly stated otherwise, MPFR sets
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the NaN flag whenever a NaN is generated, even when a NaN is propagated
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(e.g., in NaN + NaN), as if all NaNs were signaling.
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</li><li> An invalid exception in C corresponds to either a NaN exception or
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a range error in MPFR.
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</li></ul>
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<hr>
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<div class="header">
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<p>
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Next: <a href="Memory-Handling.html#Memory-Handling" accesskey="n" rel="next">Memory Handling</a>, Previous: <a href="Floating_002dPoint-Values-on-Special-Numbers.html#Floating_002dPoint-Values-on-Special-Numbers" accesskey="p" rel="prev">Floating-Point Values on Special Numbers</a>, Up: <a href="MPFR-Basics.html#MPFR-Basics" accesskey="u" rel="up">MPFR Basics</a> [<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
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