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-<html lang="en">
-<head>
-<title>MPFR 2.3.2</title>
-<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
-<meta name="description" content="How to install and use MPFR, a library for reliable multiple precision floating-point arithmetic, version 2.3.2.">
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-This manual documents how to install and use the Multiple Precision
-Floating-Point Reliable Library, version 2.3.2.
-
-Copyright 1991, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008 Free Software Foundation, Inc.
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-Permission is granted to copy, distribute and/or modify this document under
-the terms of the GNU Free Documentation License, Version 1.2 or any later
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-<div class="node">
-<p><hr>
-<a name="Top"></a>
-Next: <a rel="next" accesskey="n" href="#Copying">Copying</a>,
-Previous: <a rel="previous" accesskey="p" href="#dir">(dir)</a>,
-Up: <a rel="up" accesskey="u" href="#dir">(dir)</a>
-
-</div>
-
-<h2 class="unnumbered">MPFR</h2>
-
- <p>This manual documents how to install and use the Multiple Precision
-Floating-Point Reliable Library, version 2.3.2.
-
- <p>Copyright 1991, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008 Free Software Foundation, Inc.
-
- <p>Permission is granted to copy, distribute and/or modify this document under
-the terms of the GNU Free Documentation License, Version 1.2 or any later
-version published by the Free Software Foundation; with no Invariant Sections,
-with no Front-Cover Texts, and with no Back-Cover Texts. A copy of the
-license is included in <a href="#GNU-Free-Documentation-License">GNU Free Documentation License</a>.
- <pre class="sp">
-
-</pre>
-
-<!-- Don't bother with contents for html, the menus seem adequate. -->
-<ul class="menu">
-<li><a accesskey="1" href="#Copying">Copying</a>: MPFR Copying Conditions (LGPL).
-<li><a accesskey="2" href="#Introduction-to-MPFR">Introduction to MPFR</a>: Brief introduction to MPFR.
-<li><a accesskey="3" href="#Installing-MPFR">Installing MPFR</a>: How to configure and compile the MPFR library.
-<li><a accesskey="4" href="#Reporting-Bugs">Reporting Bugs</a>: How to usefully report bugs.
-<li><a accesskey="5" href="#MPFR-Basics">MPFR Basics</a>: What every MPFR user should now.
-<li><a accesskey="6" href="#MPFR-Interface">MPFR Interface</a>: MPFR functions and macros.
-<li><a accesskey="7" href="#Contributors">Contributors</a>
-<li><a accesskey="8" href="#References">References</a>
-<li><a accesskey="9" href="#GNU-Free-Documentation-License">GNU Free Documentation License</a>
-<li><a href="#Concept-Index">Concept Index</a>
-<li><a href="#Function-Index">Function Index</a>
-</ul>
-
-<!-- @m{T,N} is $T$ in tex or @math{N} otherwise. This is an easy way to give -->
-<!-- different forms for math in tex and info. Commas in N or T don't work, -->
-<!-- but @C{} can be used instead. \, works in info but not in tex. -->
-<!-- Usage: @GMPabs{x} -->
-<!-- Give either |x| in tex, or abs(x) in info or html. -->
-<!-- Usage: @GMPtimes{} -->
-<!-- Give either \times or the word "times". -->
-<!-- New math operators. -->
-<!-- @abs{} can be used in both tex and info, or just \abs in tex. -->
-<!-- @times{} made available as a "*" in info and html (already works in tex). -->
-<!-- Math operators already available in tex, made available in info too. -->
-<!-- For example @log{} can be used in both tex and info. -->
-<!-- @pom{} definition -->
-<!-- The following macro have been copied from gmp.texi -->
-<!-- Usage: @MPFRpxreftop{info,title} -->
-<!-- Like @pxref{}, but designed for a reference to the top of a document, not -->
-<!-- a particular section. -->
-<!-- The texinfo manual recommends putting a likely section name in references -->
-<!-- like this, eg. "Introduction", but it seems better to just give the title. -->
-<div class="node">
-<p><hr>
-<a name="Copying"></a>
-Next: <a rel="next" accesskey="n" href="#Introduction-to-MPFR">Introduction to MPFR</a>,
-Previous: <a rel="previous" accesskey="p" href="#Top">Top</a>,
-Up: <a rel="up" accesskey="u" href="#Top">Top</a>
-
-</div>
-
-<!-- node-name, next, previous, up -->
-<h2 class="unnumbered">MPFR Copying Conditions</h2>
-
-<p><a name="index-Copying-conditions-1"></a><a name="index-Conditions-for-copying-MPFR-2"></a>
-This library is <dfn>free</dfn>; this means that everyone is free to use it and
-free to redistribute it on a free basis. The library is not in the public
-domain; it is copyrighted and there are restrictions on its distribution, but
-these restrictions are designed to permit everything that a good cooperating
-citizen would want to do. What is not allowed is to try to prevent others
-from further sharing any version of this library that they might get from
-you.
-
- <p>Specifically, we want to make sure that you have the right to give away copies
-of the library, that you receive source code or else can get it if you want
-it, that you can change this library or use pieces of it in new free programs,
-and that you know you can do these things.
-
- <p>To make sure that everyone has such rights, we have to forbid you to deprive
-anyone else of these rights. For example, if you distribute copies of the
-MPFR library, you must give the recipients all the rights that you have. You
-must make sure that they, too, receive or can get the source code. And you
-must tell them their rights.
-
- <p>Also, for our own protection, we must make certain that everyone finds out
-that there is no warranty for the MPFR library. If it is modified by
-someone else and passed on, we want their recipients to know that what they
-have is not what we distributed, so that any problems introduced by others
-will not reflect on our reputation.
-
- <p>The precise conditions of the license for the MPFR library are found in the
-Lesser General Public License that accompanies the source code.
-See the file COPYING.LIB.
-
-<div class="node">
-<p><hr>
-<a name="Introduction-to-MPFR"></a>
-Next: <a rel="next" accesskey="n" href="#Installing-MPFR">Installing MPFR</a>,
-Previous: <a rel="previous" accesskey="p" href="#Copying">Copying</a>,
-Up: <a rel="up" accesskey="u" href="#Top">Top</a>
-
-</div>
-
-<!-- node-name, next, previous, up -->
-<h2 class="chapter">1 Introduction to MPFR</h2>
-
-<p>MPFR is a portable library written in C for arbitrary precision arithmetic
-on floating-point numbers. It is based on the GNU MP library.
-It aims to extend the class of floating-point numbers provided by the
-GNU MP library by a precise semantics. The main differences
-with the <code>mpf</code> class from GNU MP are:
-
- <ul>
-<li>the MPFR code is portable, i.e. the result of any operation
-does not depend (or should not) on the machine word size
-<code>mp_bits_per_limb</code> (32 or 64 on most machines);
-<li>the precision in bits can be set exactly to any valid value
-for each variable (including very small precision);
-<li>MPFR provides the four rounding modes from the IEEE 754-1985
-standard.
-</ul>
-
- <p>In particular, with a precision of 53 bits, MPFR should be able to
-exactly reproduce all computations with double-precision machine
-floating-point numbers (e.g., <code>double</code> type in C, with a C
-implementation that rigorously follows Annex F of the ISO C99 standard
-and <code>FP_CONTRACT</code> pragma set to <code>OFF</code>) on the four arithmetic
-operations and the square root, except the default exponent range is much
-wider and subnormal numbers are not implemented (but can be emulated).
-
- <p>This version of MPFR is released under the GNU Lesser General Public
-License, Version 2.1 or any later version.
-It is permitted to link MPFR to most non-free programs, as long as when
-distributing them the MPFR source code and a means to re-link with a
-modified MPFR library is provided.
-
-<h3 class="section">1.1 How to Use This Manual</h3>
-
-<p>Everyone should read <a href="#MPFR-Basics">MPFR Basics</a>. If you need to install the library
-yourself, you need to read <a href="#Installing-MPFR">Installing MPFR</a>, too.
-
- <p>The rest of the manual can be used for later reference, although it is
-probably a good idea to glance through it.
-
-<div class="node">
-<p><hr>
-<a name="Installing-MPFR"></a>
-Next: <a rel="next" accesskey="n" href="#Reporting-Bugs">Reporting Bugs</a>,
-Previous: <a rel="previous" accesskey="p" href="#Introduction-to-MPFR">Introduction to MPFR</a>,
-Up: <a rel="up" accesskey="u" href="#Top">Top</a>
-
-</div>
-
-<!-- node-name, next, previous, up -->
-<h2 class="chapter">2 Installing MPFR</h2>
-
-<p><a name="index-Installation-3"></a>
-
-<h3 class="section">2.1 How to Install</h3>
-
-<p>Here are the steps needed to install the library on Unix systems
-(more details are provided in the <samp><span class="file">INSTALL</span></samp> file):
-
- <ol type=1 start=1>
-<li>To build MPFR, you first have to install GNU MP
-(version 4.1 or higher) on your computer.
-You need a C compiler, preferably GCC, but any reasonable compiler should
-work. And you need a standard Unix ‘<samp><span class="samp">make</span></samp>’ program, plus some other
-standard Unix utility programs.
-
- <li>In the MPFR build directory, type
-‘<samp><span class="samp">./configure</span></samp>’
-
- <p>This will prepare the build and setup the options according to your system.
-If you get error messages, you might check that you use the same compiler
-and compile options as for GNU MP (see the <samp><span class="file">INSTALL</span></samp> file).
-
- <li>‘<samp><span class="samp">make</span></samp>’
-
- <p>This will compile MPFR, and create a library archive file <samp><span class="file">libmpfr.a</span></samp>.
-A dynamic library may be produced too (see configure).
-
- <li>‘<samp><span class="samp">make check</span></samp>’
-
- <p>This will make sure MPFR was built correctly.
-If you get error messages, please
-report this to ‘<samp><span class="samp">[email protected]</span></samp>’. (See <a href="#Reporting-Bugs">Reporting Bugs</a>, for
-information on what to include in useful bug reports.)
-
- <li>‘<samp><span class="samp">make install</span></samp>’
-
- <p>This will copy the files <samp><span class="file">mpfr.h</span></samp> and <samp><span class="file">mpf2mpfr.h</span></samp> to the directory
-<samp><span class="file">/usr/local/include</span></samp>, the file <samp><span class="file">libmpfr.a</span></samp> to the directory
-<samp><span class="file">/usr/local/lib</span></samp>, and the file <samp><span class="file">mpfr.info</span></samp> to the directory
-<samp><span class="file">/usr/local/share/info</span></samp> (or if you passed the ‘<samp><span class="samp">--prefix</span></samp>’ option to
- <samp><span class="file">configure</span></samp>, using the prefix directory given as argument to
-‘<samp><span class="samp">--prefix</span></samp>’ instead of <samp><span class="file">/usr/local</span></samp>).
- </ol>
-
-<h3 class="section">2.2 Other `make' Targets</h3>
-
-<p>There are some other useful make targets:
-
- <ul>
-<li>‘<samp><span class="samp">mpfr.info</span></samp>’ or ‘<samp><span class="samp">info</span></samp>’
-
- <p>Create an info version of the manual, in <samp><span class="file">mpfr.info</span></samp>.
-
- <li>‘<samp><span class="samp">mpfr.pdf</span></samp>’ or ‘<samp><span class="samp">pdf</span></samp>’
-
- <p>Create a PDF version of the manual, in <samp><span class="file">mpfr.pdf</span></samp>.
-
- <li>‘<samp><span class="samp">mpfr.dvi</span></samp>’ or ‘<samp><span class="samp">dvi</span></samp>’
-
- <p>Create a DVI version of the manual, in <samp><span class="file">mpfr.dvi</span></samp>.
-
- <li>‘<samp><span class="samp">mpfr.ps</span></samp>’ or ‘<samp><span class="samp">ps</span></samp>’
-
- <p>Create a Postscript version of the manual, in <samp><span class="file">mpfr.ps</span></samp>.
-
- <li>‘<samp><span class="samp">mpfr.html</span></samp>’ or ‘<samp><span class="samp">html</span></samp>’
-
- <p>Create a HTML version of the manual, in several pages in the directory
-<samp><span class="file">mpfr.html</span></samp>; if you want only one output HTML file, then type
-‘<samp><span class="samp">makeinfo --html --no-split mpfr.texi</span></samp>’ instead.
-
- <li>‘<samp><span class="samp">clean</span></samp>’
-
- <p>Delete all object files and archive files, but not the configuration files.
-
- <li>‘<samp><span class="samp">distclean</span></samp>’
-
- <p>Delete all files not included in the distribution.
-
- <li>‘<samp><span class="samp">uninstall</span></samp>’
-
- <p>Delete all files copied by ‘<samp><span class="samp">make install</span></samp>’.
-</ul>
-
-<h3 class="section">2.3 Build Problems</h3>
-
-<p>In case of problem, please read the <samp><span class="file">INSTALL</span></samp> file carefully
-before reporting a bug, in particular section “In case of problem”.
-Some problems are due to bad configuration on the user side (not
-specific to MPFR). Problems are also mentioned in the FAQ
-<a href="http://www.mpfr.org/faq.html">http://www.mpfr.org/faq.html</a>.
-
-<!-- Warning! Do not split "MPFR ... @url{...}" across several lines -->
-<!-- as this needs to be updated with update-version. -->
- <p>Please report problems to ‘<samp><span class="samp">[email protected]</span></samp>’.
-See <a href="#Reporting-Bugs">Reporting Bugs</a>.
-Some bug fixes are available on the
-MPFR 2.3.2 web page <a href="http://www.mpfr.org/mpfr-2.3.2/">http://www.mpfr.org/mpfr-2.3.2/</a>.
-
-<h3 class="section">2.4 Getting the Latest Version of MPFR</h3>
-
-<p>The latest version of MPFR is available from <a href="http://www.mpfr.org/">http://www.mpfr.org/</a>.
-
-<div class="node">
-<p><hr>
-<a name="Reporting-Bugs"></a>
-Next: <a rel="next" accesskey="n" href="#MPFR-Basics">MPFR Basics</a>,
-Previous: <a rel="previous" accesskey="p" href="#Installing-MPFR">Installing MPFR</a>,
-Up: <a rel="up" accesskey="u" href="#Top">Top</a>
-
-</div>
-
-<!-- node-name, next, previous, up -->
-<h2 class="chapter">3 Reporting Bugs</h2>
-
-<p><a name="index-Reporting-bugs-4"></a>
-<!-- Warning! Do not split "MPFR ... @url{...}" across several lines -->
-<!-- as this needs to be updated with update-version. -->
-If you think you have found a bug in the MPFR library, first have a look
-on the MPFR 2.3.2 web page <a href="http://www.mpfr.org/mpfr-2.3.2/">http://www.mpfr.org/mpfr-2.3.2/</a> and the
-FAQ <a href="http://www.mpfr.org/faq.html">http://www.mpfr.org/faq.html</a>:
-perhaps this bug is already known, in which case you may find there
-a workaround for it. Otherwise, please investigate and report it.
-We have made this library available to you, and it is not to ask too
-much from you, to ask you to report the bugs that you find.
-
- <p>There are a few things you should think about when you put your bug report
-together.
-
- <p>You have to send us a test case that makes it possible for us to reproduce the
-bug. Include instructions on how to run the test case.
-
- <p>You also have to explain what is wrong; if you get a crash, or if the results
-printed are incorrect and in that case, in what way.
-
- <p>Please include compiler version information in your bug report. This can
-be extracted using ‘<samp><span class="samp">cc -V</span></samp>’ on some machines, or, if you're using gcc,
-‘<samp><span class="samp">gcc -v</span></samp>’. Also, include the output from ‘<samp><span class="samp">uname -a</span></samp>’ and the MPFR
-version (the GMP version may be useful too).
-
- <p>If your bug report is good, we will do our best to help you to get a corrected
-version of the library; if the bug report is poor, we won't do anything about
-it (aside of chiding you to send better bug reports).
-
- <p>Send your bug report to: ‘<samp><span class="samp">[email protected]</span></samp>’.
-
- <p>If you think something in this manual is unclear, or downright incorrect, or if
-the language needs to be improved, please send a note to the same address.
-
-<div class="node">
-<p><hr>
-<a name="MPFR-Basics"></a>
-Next: <a rel="next" accesskey="n" href="#MPFR-Interface">MPFR Interface</a>,
-Previous: <a rel="previous" accesskey="p" href="#Reporting-Bugs">Reporting Bugs</a>,
-Up: <a rel="up" accesskey="u" href="#Top">Top</a>
-
-</div>
-
-<!-- node-name, next, previous, up -->
-<h2 class="chapter">4 MPFR Basics</h2>
-
-<h3 class="section">4.1 Headers and Libraries</h3>
-
-<p><a name="index-g_t_0040file_007bmpfr_002eh_007d-5"></a>All declarations needed to use MPFR are collected in the include file
-<samp><span class="file">mpfr.h</span></samp>. It is designed to work with both C and C++ compilers.
-You should include that file in any program using the MPFR library:
-
-<pre class="example"> #include <mpfr.h>
-</pre>
- <p><a name="index-g_t_0040code_007bstdio_002eh_007d-6"></a>Note however that prototypes for MPFR functions with <code>FILE *</code> parameters
-are provided only if <code><stdio.h></code> is included too (before <samp><span class="file">mpfr.h</span></samp>).
-
-<pre class="example"> #include <stdio.h>
- #include <mpfr.h>
-</pre>
- <p>You can avoid the use of MPFR macros encapsulating functions by defining
-the ‘<samp><span class="samp">MPFR_USE_NO_MACRO</span></samp>’ macro before <samp><span class="file">mpfr.h</span></samp> is included. In
-general this should not be necessary, but this can be useful when debugging
-user code: with some macros, the compiler may emit spurious warnings with
-some warning options, and macros can prevent some prototype checking.
-
- <p><a name="index-Libraries-7"></a><a name="index-Linking-8"></a><a name="index-g_t_0040code_007blibmpfr_007d-9"></a>All programs using MPFR must link against both <samp><span class="file">libmpfr</span></samp> and
-<samp><span class="file">libgmp</span></samp> libraries. On a typical Unix-like system this can be
-done with ‘<samp><span class="samp">-lmpfr -lgmp</span></samp>’ (in that order), for example
-
-<pre class="example"> gcc myprogram.c -lmpfr -lgmp
-</pre>
- <p><a name="index-Libtool-10"></a>MPFR is built using Libtool and an application can use that to link if
-desired, see <cite>GNU Libtool</cite>.
-<!-- Note: Do not try the above cross reference without moving mpfr.info -->
-<!-- into some "safe" place first. Due to a poor design, "info" will not -->
-<!-- find the correct libtool info file because of the "libtool" script -->
-<!-- in MPFR's directory! -->
-
- <p>If MPFR has been installed to a non-standard location, then it may be
-necessary to set up environment variables such as ‘<samp><span class="samp">C_INCLUDE_PATH</span></samp>’
-and ‘<samp><span class="samp">LIBRARY_PATH</span></samp>’, or use ‘<samp><span class="samp">-I</span></samp>’ and ‘<samp><span class="samp">-L</span></samp>’ compiler options,
-in order to point to the right directories. For a shared library, it may
-also be necessary to set up some sort of run-time library path (e.g.,
-‘<samp><span class="samp">LD_LIBRARY_PATH</span></samp>’) on some systems. Please read the <samp><span class="file">INSTALL</span></samp>
-file for additional information.
-
-<h3 class="section">4.2 Nomenclature and Types</h3>
-
-<p><a name="index-Floating_002dpoint-number-11"></a><a name="index-g_t_0040code_007bmpfr_005ft_007d-12"></a>A <dfn>floating-point number</dfn> or <dfn>float</dfn> for short, is an arbitrary
-precision significand (also called mantissa) with a limited precision
-exponent. The C data type
-for such objects is <code>mpfr_t</code> (internally defined as a one-element
-array of a structure, and <code>mpfr_ptr</code> is the C data type representing
-a pointer to this structure). A floating-point number can have
-three special values: Not-a-Number (NaN) or plus or minus Infinity. NaN
-represents an uninitialized object, the result of an invalid operation
-(like 0 divided by 0), or a value that cannot be determined (like
-+Infinity minus +Infinity). Moreover, like in the IEEE 754-1985 standard,
-zero is signed, i.e. there are both +0 and −0; the behavior
-is the same as in the IEEE 754-1985 standard and it is generalized to
-the other functions supported by MPFR.
-
- <p><a name="index-Precision-13"></a><a name="index-g_t_0040code_007bmp_005fprec_005ft_007d-14"></a>The <dfn>precision</dfn> is the number of bits used to represent the significand
-of a floating-point number;
-the corresponding C data type is <code>mp_prec_t</code>.
-The precision can be any integer between <code>MPFR_PREC_MIN</code> and
-<code>MPFR_PREC_MAX</code>. In the current implementation, <code>MPFR_PREC_MIN</code>
-is equal to 2.
-
- <p>Warning! MPFR needs to increase the precision internally, in order to
-provide accurate results (and in particular, correct rounding). Do not
-attempt to set the precision to any value near <code>MPFR_PREC_MAX</code>,
-otherwise MPFR will abort due to an assertion failure. Moreover, you
-may reach some memory limit on your platform, in which case the program
-may abort, crash or have undefined behavior (depending on your C
-implementation).
-
- <p><a name="index-Rounding-Modes-15"></a><a name="index-g_t_0040code_007bmp_005frnd_005ft_007d-16"></a>The <dfn>rounding mode</dfn> specifies the way to round the result of a
-floating-point operation, in case the exact result can not be represented
-exactly in the destination significand;
-the corresponding C data type is <code>mp_rnd_t</code>.
-
- <p><a name="index-Limb-17"></a><!-- @tindex @code{mp_limb_t} -->
-A <dfn>limb</dfn> means the part of a multi-precision number that fits in a single
-word. (We chose this word because a limb of the human body is analogous to a
-digit, only larger, and containing several digits.) Normally a limb contains
-32 or 64 bits. The C data type for a limb is <code>mp_limb_t</code>.
-
-<h3 class="section">4.3 Function Classes</h3>
-
-<p>There is only one class of functions in the MPFR library:
-
- <ol type=1 start=1>
-<li>Functions for floating-point arithmetic, with names beginning with
-<code>mpfr_</code>. The associated type is <code>mpfr_t</code>.
- </ol>
-
-<h3 class="section">4.4 MPFR Variable Conventions</h3>
-
-<p>As a general rule, all MPFR functions expect output arguments before input
-arguments. This notation is based on an analogy with the assignment operator.
-
- <p>MPFR allows you to use the same variable for both input and output in the same
-expression. For example, the main function for floating-point multiplication,
-<code>mpfr_mul</code>, can be used like this: <code>mpfr_mul (x, x, x, rnd_mode)</code>.
-This
-computes the square of <var>x</var> with rounding mode <code>rnd_mode</code>
-and puts the result back in <var>x</var>.
-
- <p>Before you can assign to an MPFR variable, you need to initialize it by calling
-one of the special initialization functions. When you're done with a
-variable, you need to clear it out, using one of the functions for that
-purpose.
-
- <p>A variable should only be initialized once, or at least cleared out between
-each initialization. After a variable has been initialized, it may be
-assigned to any number of times.
-
- <p>For efficiency reasons, avoid to initialize and clear out a variable in loops.
-Instead, initialize it before entering the loop, and clear it out after the
-loop has exited.
-
- <p>You don't need to be concerned about allocating additional space for MPFR
-variables, since any variable has a significand of fixed size.
-Hence unless you change its precision, or clear and reinitialize it,
-a floating-point variable will have the same allocated space during all its
-life.
-
-<h3 class="section">4.5 Rounding Modes</h3>
-
-<p>The following four rounding modes are supported:
-
- <ul>
-<li><code>GMP_RNDN</code>: round to nearest
-<li><code>GMP_RNDZ</code>: round toward zero
-<li><code>GMP_RNDU</code>: round toward plus infinity
-<li><code>GMP_RNDD</code>: round toward minus infinity
-</ul>
-
- <p>The ‘<samp><span class="samp">round to nearest</span></samp>’ mode works as in the IEEE 754-1985 standard: in
-case the number to be rounded lies exactly in the middle of two representable
-numbers, it is rounded to the one with the least significant bit set to zero.
-For example, the number 5/2, which is represented by (10.1) in binary, is
-rounded to (10.0)=2 with a precision of two bits, and not to (11.0)=3.
-This rule avoids the <dfn>drift</dfn> phenomenon mentioned by Knuth in volume 2
-of The Art of Computer Programming (Section 4.2.2).
-
- <p>Most MPFR functions take as first argument the destination variable, as
-second and following arguments the input variables, as last argument a
-rounding mode, and have a return value of type <code>int</code>, called the
-<dfn>ternary value</dfn>. The value stored in the destination variable is
-correctly rounded, i.e. MPFR behaves as if it computed the result with
-an infinite precision, then rounded it to the precision of this variable.
-The input variables are regarded as exact (in particular, their precision
-does not affect the result).
-
- <p>As a consequence, in case of a non-zero real rounded result, the error
-on the result is less or equal to 1/2 ulp (unit in the last place) of
-the target in the rounding to nearest mode, and less than 1 ulp of the
-target in the directed rounding modes (a ulp is the weight of the least
-significant represented bit of the target after rounding).
-<!-- Since subnormals are not supported, we must take into account the ulp of -->
-<!-- the rounded result, not the one of the exact result, for full generality. -->
-
- <p>Unless documented otherwise, functions returning an <code>int</code> return
-a ternary value.
-If the ternary value is zero, it means that the value stored in the
-destination variable is the exact result of the corresponding mathematical
-function. If the ternary value is positive (resp. negative), it means
-the value stored in the destination variable is greater (resp. lower)
-than the exact result. For example with the <code>GMP_RNDU</code> rounding mode,
-the ternary value is usually positive, except when the result is exact, in
-which case it is zero. In the case of an infinite result, it is considered
-as inexact when it was obtained by overflow, and exact otherwise. A NaN
-result (Not-a-Number) always corresponds to an exact return value.
-The opposite of a returned ternary value is guaranteed to be representable
-in an <code>int</code>.
-
- <p>Unless documented otherwise, functions returning a <code>1</code>
-(or any other value specified in this manual)
-for special cases (like <code>acos(0)</code>) should return an overflow or
-an underflow if <code>1</code> is not representable in the current exponent range.
-
-<h3 class="section">4.6 Floating-Point Values on Special Numbers</h3>
-
-<p>This section specifies the floating-point values (of type <code>mpfr_t</code>)
-returned by MPFR functions. For functions returning several values (like
-<code>mpfr_sin_cos</code>), the rules apply to each result separately.
-
- <p>Functions can have one or several input arguments. An input point is
-a mapping from these input arguments to the set of the MPFR numbers.
-When none of its components are NaN, an input point can also be seen
-as a tuple in the extended real numbers (the set of the real numbers
-with both infinities).
-
- <p>When the input point is in the domain of the mathematical function, the
-result is rounded as described in Section “Rounding Modes” (but see
-below for the specification of the sign of an exact zero). Otherwise
-the general rules from this section apply unless stated otherwise in
-the description of the MPFR function (<a href="#MPFR-Interface">MPFR Interface</a>).
-
- <p>When the input point is not in the domain of the mathematical function
-but is in its closure in the extended real numbers and the function can
-be extended by continuity, the result is the obtained limit.
-Examples: <code>mpfr_hypot</code> on (+Inf,0) gives +Inf. But <code>mpfr_pow</code>
-cannot be defined on (1,+Inf) using this rule, as one can find
-sequences (<var>x</var>_<var>n</var>,<var>y</var>_<var>n</var>) such that
-<var>x</var>_<var>n</var> goes to 1, <var>y</var>_<var>n</var> goes to +Inf
-and <var>x</var>_<var>n</var> to the <var>y</var>_<var>n</var> goes to any
-positive value when <var>n</var> goes to the infinity.
-
- <p>When the input point is in the closure of the domain of the mathematical
-function and an input argument is +0 (resp. −0), one considers
-the limit when the corresponding argument approaches 0 from above
-(resp. below). If the limit is not defined (e.g., <code>mpfr_log</code> on
-−0), the behavior must be specified in the description of the
-MPFR function.
-
- <p>When the result is equal to 0, its sign is determined by considering the
-limit as if the input point were not in the domain: If one approaches 0
-from above (resp. below), the result is +0 (resp. −0). In the
-other cases, the sign must be specified in the description of the MPFR
-function. Example: <code>mpfr_sin</code> on +0 gives +0.
-
- <p>When the input point is not in the closure of the domain of the function,
-the result is NaN. Example: <code>mpfr_sqrt</code> on −17 gives NaN.
-
- <p>When an input argument is NaN, the result is NaN, possibly except when
-a partial function is constant on the finite floating-point numbers;
-such a case is always explicitly specified in <a href="#MPFR-Interface">MPFR Interface</a>.
-<!-- Said otherwise, if such a case is not specified, this is a bug, thus -->
-<!-- we may change the returned value after documenting it without having -->
-<!-- to change the libtool interface number (this would have more drawbacks -->
-<!-- that advantages in practice), like for any bug fix. -->
-Example: <code>mpfr_hypot</code> on (NaN,0) gives NaN, but <code>mpfr_hypot</code>
-on (NaN,+Inf) gives +Inf (as specified in <a href="#Special-Functions">Special Functions</a>),
-since for any finite input <var>x</var>, <code>mpfr_hypot</code> on (<var>x</var>,+Inf)
-gives +Inf.
-
-<h3 class="section">4.7 Exceptions</h3>
-
-<p>MPFR supports 5 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 exponent of the current range. In the round-to-nearest
-mode, the halfway case is rounded toward zero.
-
- <p>Note: This is not the single definition of the underflow. MPFR chooses
-to consider the underflow after 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>−4, where <var>e</var> is the smallest exponent (for a
-significand between 1/2 and 1) in the current
-range, with a 2-bit target precision and rounding toward plus infinity.
-The exact result has the exponent <var>e</var>−1. With the underflow
-before rounding, such a function call would yield an underflow, as
-<var>e</var>−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 exponent of the current range. In the round-to-nearest
-mode, the result is infinite.
-
- <li>NaN:
-A NaN exception occurs when the result of a function is a 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 in a
-conversion to an integer).
-
- </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">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>
-
-<h3 class="section">4.8 Memory Handling</h3>
-
-<p>MPFR functions may create caches, e.g. when computing constants such
-as Pi, either because the user has called a function like
-<code>mpfr_const_pi</code> directly or because such a function was called
-internally by the MPFR library itself to compute some other function.
-
- <p>At any time, the user can free the various caches with
-<code>mpfr_free_cache</code>. It is strongly advised to do that before
-terminating a thread, or before exiting when using tools like
-‘<samp><span class="samp">valgrind</span></samp>’ (to avoid memory leaks being reported).
-
- <p>MPFR internal data such as flags, the exponent range, the default
-precision and rounding mode, and caches (i.e., data that are not
-accessed via parameters) are either global (if MPFR has not been
-compiled as thread safe) or per-thread (thread local storage).
-
-<div class="node">
-<p><hr>
-<a name="MPFR-Interface"></a>
-Next: <a rel="next" accesskey="n" href="#Contributors">Contributors</a>,
-Previous: <a rel="previous" accesskey="p" href="#MPFR-Basics">MPFR Basics</a>,
-Up: <a rel="up" accesskey="u" href="#Top">Top</a>
-
-</div>
-
-<!-- node-name, next, previous, up -->
-<h2 class="chapter">5 MPFR Interface</h2>
-
-<p><a name="index-Floating_002dpoint-functions-18"></a><a name="index-Float-functions-19"></a>
-The floating-point functions expect arguments of type <code>mpfr_t</code>.
-
- <p>The MPFR floating-point functions have an interface that is similar to the
-GNU MP
-integer functions. The function prefix for floating-point operations is
-<code>mpfr_</code>.
-
- <p>There is one significant characteristic of floating-point numbers that has
-motivated a difference between this function class and other GNU MP function
-classes: the inherent inexactness of floating-point arithmetic. The user has
-to specify the precision for each variable. A computation that assigns a
-variable will take place with the precision of the assigned variable; the
-cost of that computation should not depend from the
-precision of variables used as input (on average).
-
- <p><a name="index-Precision-20"></a>The semantics of a calculation in MPFR is specified as follows: Compute the
-requested operation exactly (with “infinite accuracy”), and round the result
-to the precision of the destination variable, with the given rounding mode.
-The MPFR floating-point functions are intended to be a smooth extension
-of the IEEE 754-1985 arithmetic. The results obtained on one computer should
-not differ from the results obtained on a computer with a different word size.
-
- <p><a name="index-Accuracy-21"></a>MPFR does not keep track of the accuracy of a computation. This is left
-to the user or to a higher layer.
-As a consequence, if two variables are used to store
-only a few significant bits, and their product is stored in a variable with large
-precision, then MPFR will still compute the result with full precision.
-
- <p>The value of the standard C macro <code>errno</code> may be set to non-zero by
-any MPFR function or macro, whether or not there is an error.
-
-<ul class="menu">
-<li><a accesskey="1" href="#Initialization-Functions">Initialization Functions</a>
-<li><a accesskey="2" href="#Assignment-Functions">Assignment Functions</a>
-<li><a accesskey="3" href="#Combined-Initialization-and-Assignment-Functions">Combined Initialization and Assignment Functions</a>
-<li><a accesskey="4" href="#Conversion-Functions">Conversion Functions</a>
-<li><a accesskey="5" href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a>
-<li><a accesskey="6" href="#Comparison-Functions">Comparison Functions</a>
-<li><a accesskey="7" href="#Special-Functions">Special Functions</a>
-<li><a accesskey="8" href="#Input-and-Output-Functions">Input and Output Functions</a>
-<li><a accesskey="9" href="#Integer-Related-Functions">Integer Related Functions</a>
-<li><a href="#Miscellaneous-Functions">Miscellaneous Functions</a>
-<li><a href="#Rounding-Mode-Related-Functions">Rounding Mode Related Functions</a>
-<li><a href="#Exception-Related-Functions">Exception Related Functions</a>
-<li><a href="#Advanced-Functions">Advanced Functions</a>
-<li><a href="#Compatibility-with-MPF">Compatibility with MPF</a>
-<li><a href="#Custom-Interface">Custom Interface</a>
-<li><a href="#Internals">Internals</a>
-</ul>
-
-<div class="node">
-<p><hr>
-<a name="Initialization-Functions"></a>
-Next: <a rel="next" accesskey="n" href="#Assignment-Functions">Assignment Functions</a>,
-Previous: <a rel="previous" accesskey="p" href="#MPFR-Interface">MPFR Interface</a>,
-Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
-
-</div>
-
-<!-- node-name, next, previous, up -->
- <p><a name="index-Initialization-functions-22"></a>
-
-<h3 class="section">5.1 Initialization Functions</h3>
-
-<p>An <code>mpfr_t</code> object must be initialized before storing the first value in
-it. The functions <code>mpfr_init</code> and <code>mpfr_init2</code> are used for that
-purpose.
-
-<div class="defun">
-— Function: void <b>mpfr_init2</b> (<var>mpfr_t x, mp_prec_t prec</var>)<var><a name="index-mpfr_005finit2-23"></a></var><br>
-<blockquote><p>Initialize <var>x</var>, set its precision to be <strong>exactly</strong>
-<var>prec</var> bits and its value to NaN. (Warning: the corresponding
-<code>mpf</code> functions initialize to zero instead.)
-
- <p>Normally, a variable should be initialized once only or at
-least be cleared, using <code>mpfr_clear</code>, between initializations.
-To change the precision of a variable which has already been initialized,
-use <code>mpfr_set_prec</code>.
-The precision <var>prec</var> must be an integer between <code>MPFR_PREC_MIN</code> and
-<code>MPFR_PREC_MAX</code> (otherwise the behavior is undefined).
-</p></blockquote></div>
-
-<div class="defun">
-— Function: void <b>mpfr_clear</b> (<var>mpfr_t x</var>)<var><a name="index-mpfr_005fclear-24"></a></var><br>
-<blockquote><p>Free the space occupied by <var>x</var>. Make sure to call this function for all
-<code>mpfr_t</code> variables when you are done with them.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: void <b>mpfr_init</b> (<var>mpfr_t x</var>)<var><a name="index-mpfr_005finit-25"></a></var><br>
-<blockquote><p>Initialize <var>x</var> and set its value to NaN.
-
- <p>Normally, a variable should be initialized once only
-or at least be cleared, using <code>mpfr_clear</code>, between initializations. The
-precision of <var>x</var> is the default precision, which can be changed
-by a call to <code>mpfr_set_default_prec</code>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: void <b>mpfr_set_default_prec</b> (<var>mp_prec_t prec</var>)<var><a name="index-mpfr_005fset_005fdefault_005fprec-26"></a></var><br>
-<blockquote><p>Set the default precision to be <strong>exactly</strong> <var>prec</var> bits. The
-precision of a variable means the number of bits used to store its significand.
-All
-subsequent calls to <code>mpfr_init</code> will use this precision, but previously
-initialized variables are unaffected.
-This default precision is set to 53 bits initially.
-The precision can be any integer between <code>MPFR_PREC_MIN</code> and
-<code>MPFR_PREC_MAX</code>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: mp_prec_t <b>mpfr_get_default_prec</b> (<var>void</var>)<var><a name="index-mpfr_005fget_005fdefault_005fprec-27"></a></var><br>
-<blockquote><p>Return the default MPFR precision in bits.
-</p></blockquote></div>
-
- <p>Here is an example on how to initialize floating-point variables:
-
-<pre class="example"> {
- mpfr_t x, y;
- mpfr_init (x); /* use default precision */
- mpfr_init2 (y, 256); /* precision <em>exactly</em> 256 bits */
- ...
- /* When the program is about to exit, do ... */
- mpfr_clear (x);
- mpfr_clear (y);
- mpfr_free_cache ();
- }
-</pre>
- <p>The following functions are useful for changing the precision during a
-calculation. A typical use would be for adjusting the precision gradually in
-iterative algorithms like Newton-Raphson, making the computation precision
-closely match the actual accurate part of the numbers.
-
-<div class="defun">
-— Function: void <b>mpfr_set_prec</b> (<var>mpfr_t x, mp_prec_t prec</var>)<var><a name="index-mpfr_005fset_005fprec-28"></a></var><br>
-<blockquote><p>Reset the precision of <var>x</var> to be <strong>exactly</strong> <var>prec</var> bits,
-and set its value to NaN.
-The previous value stored in <var>x</var> is lost. It is equivalent to
-a call to <code>mpfr_clear(x)</code> followed by a call to
-<code>mpfr_init2(x, prec)</code>, but more efficient as no allocation is done in
-case the current allocated space for the significand of <var>x</var> is enough.
-The precision <var>prec</var> can be any integer between <code>MPFR_PREC_MIN</code> and
-<code>MPFR_PREC_MAX</code>.
-
- <p>In case you want to keep the previous value stored in <var>x</var>,
-use <code>mpfr_prec_round</code> instead.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: mp_prec_t <b>mpfr_get_prec</b> (<var>mpfr_t x</var>)<var><a name="index-mpfr_005fget_005fprec-29"></a></var><br>
-<blockquote><p>Return the precision actually used for assignments of <var>x</var>, i.e. the
-number of bits used to store its significand.
-</p></blockquote></div>
-
-<div class="node">
-<p><hr>
-<a name="Assignment-Functions"></a>
-Next: <a rel="next" accesskey="n" href="#Combined-Initialization-and-Assignment-Functions">Combined Initialization and Assignment Functions</a>,
-Previous: <a rel="previous" accesskey="p" href="#Initialization-Functions">Initialization Functions</a>,
-Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
-
-</div>
-
-<!-- node-name, next, previous, up -->
- <p><a name="index-Assignment-functions-30"></a>
-
-<h3 class="section">5.2 Assignment Functions</h3>
-
-<p>These functions assign new values to already initialized floats
-(see <a href="#Initialization-Functions">Initialization Functions</a>). When using any functions using
-<code>intmax_t</code>, you must include <code><stdint.h></code> or <code><inttypes.h></code>
-before <samp><span class="file">mpfr.h</span></samp>, to allow <samp><span class="file">mpfr.h</span></samp> to define prototypes for
-these functions.
-
-<div class="defun">
-— Function: int <b>mpfr_set</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset-31"></a></var><br>
-— Function: int <b>mpfr_set_ui</b> (<var>mpfr_t rop, unsigned long int op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005fui-32"></a></var><br>
-— Function: int <b>mpfr_set_si</b> (<var>mpfr_t rop, long int op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005fsi-33"></a></var><br>
-— Function: int <b>mpfr_set_uj</b> (<var>mpfr_t rop, uintmax_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005fuj-34"></a></var><br>
-— Function: int <b>mpfr_set_sj</b> (<var>mpfr_t rop, intmax_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005fsj-35"></a></var><br>
-— Function: int <b>mpfr_set_d</b> (<var>mpfr_t rop, double op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005fd-36"></a></var><br>
-— Function: int <b>mpfr_set_ld</b> (<var>mpfr_t rop, long double op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005fld-37"></a></var><br>
-— Function: int <b>mpfr_set_decimal64</b> (<var>mpfr_t rop, _Decimal64 op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005fdecimal64-38"></a></var><br>
-— Function: int <b>mpfr_set_z</b> (<var>mpfr_t rop, mpz_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005fz-39"></a></var><br>
-— Function: int <b>mpfr_set_q</b> (<var>mpfr_t rop, mpq_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005fq-40"></a></var><br>
-— Function: int <b>mpfr_set_f</b> (<var>mpfr_t rop, mpf_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005ff-41"></a></var><br>
-<blockquote><p>Set the value of <var>rop</var> from <var>op</var>, rounded
-toward the given direction <var>rnd</var>.
-Note that the input 0 is converted to +0 by <code>mpfr_set_ui</code>,
-<code>mpfr_set_si</code>, <code>mpfr_set_sj</code>, <code>mpfr_set_uj</code>,
-<code>mpfr_set_z</code>, <code>mpfr_set_q</code> and
-<code>mpfr_set_f</code>, regardless of the rounding mode.
-If the system doesn't support the IEEE-754 standard, <code>mpfr_set_d</code>,
-<code>mpfr_set_ld</code> and
-<code>mpfr_set_decimal64</code> might not preserve the signed zeros.
-The <code>mpfr_set_decimal64</code> function is built only with the configure
-option ‘<samp><span class="samp">--enable-decimal-float</span></samp>’, which also requires
-‘<samp><span class="samp">--with-gmp-build</span></samp>’, and when the compiler or
-system provides the ‘<samp><span class="samp">_Decimal64</span></samp>’ data type
-(GCC version 4.2.0 is known to support this data type,
-but only when configured with ‘<samp><span class="samp">--enable-decimal-float</span></samp>’ too).
-<code>mpfr_set_q</code> might not be able to work if the numerator (or the
-denominator) can not be representable as a <code>mpfr_t</code>.
-
- <p>Note: If you want to store a floating-point constant to a <code>mpfr_t</code>,
-you should use <code>mpfr_set_str</code> (or one of the MPFR constant functions,
-such as <code>mpfr_const_pi</code> for Pi) instead of <code>mpfr_set_d</code>,
-<code>mpfr_set_ld</code> or <code>mpfr_set_decimal64</code>.
-Otherwise the floating-point constant will be first
-converted into a reduced-precision (e.g., 53-bit) binary number before
-MPFR can work with it.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_set_ui_2exp</b> (<var>mpfr_t rop, unsigned long int op, mp_exp_t e, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005fui_005f2exp-42"></a></var><br>
-— Function: int <b>mpfr_set_si_2exp</b> (<var>mpfr_t rop, long int op, mp_exp_t e, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005fsi_005f2exp-43"></a></var><br>
-— Function: int <b>mpfr_set_uj_2exp</b> (<var>mpfr_t rop, uintmax_t op, intmax_t e, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005fuj_005f2exp-44"></a></var><br>
-— Function: int <b>mpfr_set_sj_2exp</b> (<var>mpfr_t rop, intmax_t op, intmax_t e, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005fsj_005f2exp-45"></a></var><br>
-<blockquote><p>Set the value of <var>rop</var> from <var>op</var> multiplied by
-two to the power <var>e</var>, rounded toward the given direction <var>rnd</var>.
-Note that the input 0 is converted to +0.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_set_str</b> (<var>mpfr_t rop, const char *s, int base, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005fstr-46"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the value of the whole string <var>s</var> in base <var>base</var>,
-rounded in the direction <var>rnd</var>.
-See the documentation of <code>mpfr_strtofr</code> for a detailed description
-of the valid string formats.
-<!-- Additionally, special values -->
-<!-- @code{@@NaN@@}, @code{@@Inf@@}, @code{+@@Inf@@} and @code{-@@Inf@@}, -->
-<!-- all case insensitive, without leading whitespace and possibly followed by -->
-<!-- other characters, are accepted too (it may change). -->
-This function returns 0 if the entire string up to the final null character
-is a valid number in base <var>base</var>; otherwise it returns −1, and
-<var>rop</var> may have changed.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_strtofr</b> (<var>mpfr_t rop, const char *nptr, char **endptr, int base, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fstrtofr-47"></a></var><br>
-<blockquote>
- <p>Read a floating-point number from a string <var>nptr</var> in base <var>base</var>,
-rounded in the direction <var>rnd</var>; <var>base</var> must be either 0 (to
-detect the base, as described below) or a number from 2 to 36 (otherwise
-the behavior is undefined). If <var>nptr</var> starts with valid data, the
-result is stored in <var>rop</var> and <code>*</code><var>endptr</var> points to the
-character just after the valid data (if <var>endptr</var> is not a null pointer);
-otherwise <var>rop</var> is set to zero and the value of <var>nptr</var> is stored
-in the location referenced by <var>endptr</var> (if <var>endptr</var> is not a null
-pointer). The usual ternary value is returned.
-
- <p>Parsing follows the standard C <code>strtod</code> function with some extensions.
-Case is ignored. After optional leading whitespace, one has a subject
-sequence consisting of an optional sign (<code>+</code> or <code>-</code>), and either
-numeric data or special data. The subject sequence is defined as the
-longest initial subsequence of the input string, starting with the first
-non-whitespace character, that is of the expected form.
-
- <p>The form of numeric data is a non-empty sequence of significand digits
-with an optional decimal point, and an optional exponent consisting of
-an exponent prefix followed by an optional sign and a non-empty sequence
-of decimal digits. A significand digit is either a decimal digit or a
-Latin letter (62 possible characters), with <code>a</code> = 10, <code>b</code> = 11,
-<small class="dots">...</small>, <code>z</code> = 36; its value must be strictly less than the base.
-The decimal point can be either the one defined by the current locale or
-the period (the first one is accepted for consistency with the C standard
-and the practice, the second one is accepted to allow the programmer to
-provide MPFR numbers from strings in a way that does not depend on the
-current locale).
-The exponent prefix can be <code>e</code> or <code>E</code> for bases up to 10, or
-<code>@</code> in any base; it indicates a multiplication by a power of the
-base. In bases 2 and 16, the exponent prefix can also be <code>p</code> or
-<code>P</code>, in which case it introduces a binary exponent: it indicates a
-multiplication by a power of 2 (there is a difference only for base 16).
-The value of an exponent is always written in base 10.
-In base 2, the significand can start with <code>0b</code> or <code>0B</code>, and
-in base 16, it can start with <code>0x</code> or <code>0X</code>.
-
- <p>If the argument <var>base</var> is 0, then the base is automatically detected
-as follows. If the significand starts with <code>0b</code> or <code>0B</code>, base 2
-is assumed. If the significand starts with <code>0x</code> or <code>0X</code>, base 16
-is assumed. Otherwise base 10 is assumed.
-
- <p>Note: The exponent must contain at least a digit. Otherwise the possible
-exponent prefix and sign are not part of the number (which ends with the
-significand). Similarly, if <code>0b</code>, <code>0B</code>, <code>0x</code> or <code>0X</code>
-is not followed by a binary/hexadecimal digit, then the subject sequence
-stops at the character <code>0</code>.
-
- <p>Special data (for infinities and NaN) can be <code>@inf@</code> or
-<code>@nan@(n-char-sequence)</code>, and if <var>base</var> <= 16,
-it can also be <code>infinity</code>, <code>inf</code>, <code>nan</code> or
-<code>nan(n-char-sequence)</code>, all case insensitive.
-A <code>n-char-sequence</code> is a non-empty string containing only digits,
-Latin letters and the underscore (0, 1, 2, <small class="dots">...</small>, 9, a, b, <small class="dots">...</small>, z,
-A, B, <small class="dots">...</small>, Z, _). Note: one has an optional sign for all data, even
-NaN.
-
- </blockquote></div>
-
-<div class="defun">
-— Function: void <b>mpfr_set_inf</b> (<var>mpfr_t x, int sign</var>)<var><a name="index-mpfr_005fset_005finf-48"></a></var><br>
-— Function: void <b>mpfr_set_nan</b> (<var>mpfr_t x</var>)<var><a name="index-mpfr_005fset_005fnan-49"></a></var><br>
-<blockquote><p>Set the variable <var>x</var> to infinity or NaN (Not-a-Number) respectively.
-In <code>mpfr_set_inf</code>, <var>x</var> is set to plus infinity iff <var>sign</var> is
-nonnegative.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: void <b>mpfr_swap</b> (<var>mpfr_t x, mpfr_t y</var>)<var><a name="index-mpfr_005fswap-50"></a></var><br>
-<blockquote><p>Swap the values <var>x</var> and <var>y</var> efficiently. Warning: the
-precisions are exchanged too; in case the precisions are different,
-<code>mpfr_swap</code> is thus not equivalent to three <code>mpfr_set</code> calls
-using a third auxiliary variable.
-</p></blockquote></div>
-
-<div class="node">
-<p><hr>
-<a name="Combined-Initialization-and-Assignment-Functions"></a>
-Next: <a rel="next" accesskey="n" href="#Conversion-Functions">Conversion Functions</a>,
-Previous: <a rel="previous" accesskey="p" href="#Assignment-Functions">Assignment Functions</a>,
-Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
-
-</div>
-
-<!-- node-name, next, previous, up -->
- <p><a name="index-Combined-initialization-and-assignment-functions-51"></a>
-
-<h3 class="section">5.3 Combined Initialization and Assignment Functions</h3>
-
-<div class="defun">
-— Macro: int <b>mpfr_init_set</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005finit_005fset-52"></a></var><br>
-— Macro: int <b>mpfr_init_set_ui</b> (<var>mpfr_t rop, unsigned long int op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005finit_005fset_005fui-53"></a></var><br>
-— Macro: int <b>mpfr_init_set_si</b> (<var>mpfr_t rop, signed long int op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005finit_005fset_005fsi-54"></a></var><br>
-— Macro: int <b>mpfr_init_set_d</b> (<var>mpfr_t rop, double op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005finit_005fset_005fd-55"></a></var><br>
-— Macro: int <b>mpfr_init_set_ld</b> (<var>mpfr_t rop, long double op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005finit_005fset_005fld-56"></a></var><br>
-— Macro: int <b>mpfr_init_set_z</b> (<var>mpfr_t rop, mpz_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005finit_005fset_005fz-57"></a></var><br>
-— Macro: int <b>mpfr_init_set_q</b> (<var>mpfr_t rop, mpq_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005finit_005fset_005fq-58"></a></var><br>
-— Macro: int <b>mpfr_init_set_f</b> (<var>mpfr_t rop, mpf_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005finit_005fset_005ff-59"></a></var><br>
-<blockquote><p>Initialize <var>rop</var> and set its value from <var>op</var>, rounded in the direction
-<var>rnd</var>.
-The precision of <var>rop</var> will be taken from the active default precision,
-as set by <code>mpfr_set_default_prec</code>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_init_set_str</b> (<var>mpfr_t x, const char *s, int base, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005finit_005fset_005fstr-60"></a></var><br>
-<blockquote><p>Initialize <var>x</var> and set its value from
-the string <var>s</var> in base <var>base</var>,
-rounded in the direction <var>rnd</var>.
-See <code>mpfr_set_str</code>.
-</p></blockquote></div>
-
-<div class="node">
-<p><hr>
-<a name="Conversion-Functions"></a>
-Next: <a rel="next" accesskey="n" href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a>,
-Previous: <a rel="previous" accesskey="p" href="#Combined-Initialization-and-Assignment-Functions">Combined Initialization and Assignment Functions</a>,
-Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
-
-</div>
-
-<!-- node-name, next, previous, up -->
- <p><a name="index-Conversion-functions-61"></a>
-
-<h3 class="section">5.4 Conversion Functions</h3>
-
-<div class="defun">
-— Function: double <b>mpfr_get_d</b> (<var>mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fget_005fd-62"></a></var><br>
-— Function: long double <b>mpfr_get_ld</b> (<var>mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fget_005fld-63"></a></var><br>
-— Function: _Decimal64 <b>mpfr_get_decimal64</b> (<var>mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fget_005fdecimal64-64"></a></var><br>
-<blockquote><p>Convert <var>op</var> to a <code>double</code> (respectively <code>_Decimal64</code> or
-<code>long double</code>), using the rounding mode <var>rnd</var>.
-If <var>op</var> is NaN, some fixed NaN (either quiet or signaling) or the result
-of 0.0/0.0 is returned. If <var>op</var> is �Inf, an infinity of the same
-sign or the result of �1.0/0.0 is returned. If <var>op</var> is zero, these
-functions return a zero, trying to preserve its sign, if possible.
-The <code>mpfr_get_decimal64</code> function is built only under some conditions:
-see the documentation of <code>mpfr_set_decimal64</code>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: double <b>mpfr_get_d_2exp</b> (<var>long *exp, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fget_005fd_005f2exp-65"></a></var><br>
-— Function: long double <b>mpfr_get_ld_2exp</b> (<var>long *exp, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fget_005fld_005f2exp-66"></a></var><br>
-<blockquote><p>Return <var>d</var> and set <var>exp</var> such that 0.5<=abs(<var>d</var>)<1
-and <var>d</var> times 2 raised to <var>exp</var> equals
-<var>op</var> rounded to double (resp. long double)
-precision, using the given rounding mode.
-<!-- See ISO C standard, frexp function. -->
-If <var>op</var> is zero, then a zero of the same sign (or an unsigned zero,
-if the implementation does not have signed zeros) is returned, and
-<var>exp</var> is set to 0.
-If <var>op</var> is NaN or an infinity, then the corresponding double precision
-(resp. long-double precision)
-value is returned, and <var>exp</var> is undefined.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: long <b>mpfr_get_si</b> (<var>mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fget_005fsi-67"></a></var><br>
-— Function: unsigned long <b>mpfr_get_ui</b> (<var>mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fget_005fui-68"></a></var><br>
-— Function: intmax_t <b>mpfr_get_sj</b> (<var>mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fget_005fsj-69"></a></var><br>
-— Function: uintmax_t <b>mpfr_get_uj</b> (<var>mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fget_005fuj-70"></a></var><br>
-<blockquote><p>Convert <var>op</var> to a <code>long</code>, an <code>unsigned long</code>,
-an <code>intmax_t</code> or an <code>uintmax_t</code> (respectively) after rounding
-it with respect to <var>rnd</var>.
-If <var>op</var> is NaN, the result is undefined.
-If <var>op</var> is too big for the return type, it returns the maximum
-or the minimum of the corresponding C type, depending on the direction
-of the overflow. The flag erange is set too.
-See also <code>mpfr_fits_slong_p</code>, <code>mpfr_fits_ulong_p</code>,
-<code>mpfr_fits_intmax_p</code> and <code>mpfr_fits_uintmax_p</code>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: mp_exp_t <b>mpfr_get_z_exp</b> (<var>mpz_t rop, mpfr_t op</var>)<var><a name="index-mpfr_005fget_005fz_005fexp-71"></a></var><br>
-<blockquote><p>Put the scaled significand of <var>op</var> (regarded as an integer, with the
-precision of <var>op</var>) into <var>rop</var>, and return the exponent <var>exp</var>
-(which may be outside the current exponent range) such that <var>op</var>
-exactly equals
-<var>rop</var> multiplied by two exponent <var>exp</var>.
-If the exponent is not representable in the <code>mp_exp_t</code> type, the
-behavior is undefined.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: void <b>mpfr_get_z</b> (<var>mpz_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fget_005fz-72"></a></var><br>
-<blockquote><p>Convert <var>op</var> to a <code>mpz_t</code>, after rounding it with respect to
-<var>rnd</var>. If <var>op</var> is NaN or Inf, the result is undefined.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_get_f</b> (<var>mpf_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fget_005ff-73"></a></var><br>
-<blockquote><p>Convert <var>op</var> to a <code>mpf_t</code>, after rounding it with respect to
-<var>rnd</var>. Return zero iff no error occurred,
-in particular a non-zero value is returned if
-<var>op</var> is NaN or Inf, which do not exist in <code>mpf</code>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: char * <b>mpfr_get_str</b> (<var>char *str, mp_exp_t *expptr, int b, size_t n, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fget_005fstr-74"></a></var><br>
-<blockquote><p>Convert <var>op</var> to a string of digits in base <var>b</var>, with rounding in
-the direction <var>rnd</var>, where <var>n</var> is either zero (see below) or the
-number of significant digits; in the latter case, <var>n</var> must be greater
-or equal to 2. The base may vary from 2 to 36.
-
- <p>The generated string is a fraction, with an implicit radix point immediately
-to the left of the first digit. For example, the number −3.1416 would
-be returned as "−31416" in the string and 1 written at <var>expptr</var>.
-If <var>rnd</var> is to nearest, and <var>op</var> is exactly in the middle of two
-possible outputs, the one with an even last digit is chosen
-(for an odd base, this may not correspond to an even significand).
-
- <p>If <var>n</var> is zero, the number of digits of the significand is chosen
-large enough so that re-reading the printed value with the same precision,
-assuming both output and input use rounding to nearest, will recover
-the original value of <var>op</var>.
-More precisely, in most cases, the chosen precision of <var>str</var> is
-the minimal precision depending on <var>n</var> and <var>b</var> only that
-satisfies the above property, i.e.,
-m = 1 + ceil(<var>n</var>*log(2)/log(<var>b</var>)),
-but in some very rare cases, it might be m+1.
-
- <p>If <var>str</var> is a null pointer, space for the significand is allocated using
-the current allocation function, and a pointer to the string is returned.
-To free the returned string, you must use <code>mpfr_free_str</code>.
-
- <p>If <var>str</var> is not a null pointer, it should point to a block of storage
-large enough for the significand, i.e., at least <code>max(</code><var>n</var><code> + 2, 7)</code>.
-The extra two bytes are for a possible minus sign, and for the terminating null
-character.
-
- <p>If the input number is an ordinary number, the exponent is written through
-the pointer <var>expptr</var> (the current minimal exponent for 0).
-
- <p>A pointer to the string is returned, unless there is an error, in which
-case a null pointer is returned.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: void <b>mpfr_free_str</b> (<var>char *str</var>)<var><a name="index-mpfr_005ffree_005fstr-75"></a></var><br>
-<blockquote><p>Free a string allocated by <code>mpfr_get_str</code> using the current unallocation
-function (preliminary interface).
-The block is assumed to be <code>strlen(</code><var>str</var><code>)+1</code> bytes.
-For more information about how it is done:
-see section “Custom Allocation” in <cite>GNU MP</cite>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_fits_ulong_p</b> (<var>mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ffits_005fulong_005fp-76"></a></var><br>
-— Function: int <b>mpfr_fits_slong_p</b> (<var>mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ffits_005fslong_005fp-77"></a></var><br>
-— Function: int <b>mpfr_fits_uint_p</b> (<var>mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ffits_005fuint_005fp-78"></a></var><br>
-— Function: int <b>mpfr_fits_sint_p</b> (<var>mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ffits_005fsint_005fp-79"></a></var><br>
-— Function: int <b>mpfr_fits_ushort_p</b> (<var>mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ffits_005fushort_005fp-80"></a></var><br>
-— Function: int <b>mpfr_fits_sshort_p</b> (<var>mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ffits_005fsshort_005fp-81"></a></var><br>
-— Function: int <b>mpfr_fits_intmax_p</b> (<var>mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ffits_005fintmax_005fp-82"></a></var><br>
-— Function: int <b>mpfr_fits_uintmax_p</b> (<var>mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ffits_005fuintmax_005fp-83"></a></var><br>
-<blockquote><p>Return non-zero if <var>op</var> would fit in the respective C data type, when
-rounded to an integer in the direction <var>rnd</var>.
-</p></blockquote></div>
-
-<div class="node">
-<p><hr>
-<a name="Basic-Arithmetic-Functions"></a>
-Next: <a rel="next" accesskey="n" href="#Comparison-Functions">Comparison Functions</a>,
-Previous: <a rel="previous" accesskey="p" href="#Conversion-Functions">Conversion Functions</a>,
-Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
-
-</div>
-
-<!-- node-name, next, previous, up -->
- <p><a name="index-Basic-arithmetic-functions-84"></a><a name="index-Float-arithmetic-functions-85"></a><a name="index-Arithmetic-functions-86"></a>
-
-<h3 class="section">5.5 Basic Arithmetic Functions</h3>
-
-<div class="defun">
-— Function: int <b>mpfr_add</b> (<var>mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fadd-87"></a></var><br>
-— Function: int <b>mpfr_add_ui</b> (<var>mpfr_t rop, mpfr_t op1, unsigned long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fadd_005fui-88"></a></var><br>
-— Function: int <b>mpfr_add_si</b> (<var>mpfr_t rop, mpfr_t op1, long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fadd_005fsi-89"></a></var><br>
-— Function: int <b>mpfr_add_z</b> (<var>mpfr_t rop, mpfr_t op1, mpz_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fadd_005fz-90"></a></var><br>
-— Function: int <b>mpfr_add_q</b> (<var>mpfr_t rop, mpfr_t op1, mpq_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fadd_005fq-91"></a></var><br>
-<blockquote><p>Set <var>rop</var> to <var>op1</var> + <var>op2</var> rounded in the direction
-<var>rnd</var>. For types having no signed zero, it is considered unsigned
-(i.e. (+0) + 0 = (+0) and (−0) + 0 = (−0)).
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_sub</b> (<var>mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsub-92"></a></var><br>
-— Function: int <b>mpfr_ui_sub</b> (<var>mpfr_t rop, unsigned long int op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fui_005fsub-93"></a></var><br>
-— Function: int <b>mpfr_sub_ui</b> (<var>mpfr_t rop, mpfr_t op1, unsigned long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsub_005fui-94"></a></var><br>
-— Function: int <b>mpfr_si_sub</b> (<var>mpfr_t rop, long int op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsi_005fsub-95"></a></var><br>
-— Function: int <b>mpfr_sub_si</b> (<var>mpfr_t rop, mpfr_t op1, long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsub_005fsi-96"></a></var><br>
-— Function: int <b>mpfr_sub_z</b> (<var>mpfr_t rop, mpfr_t op1, mpz_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsub_005fz-97"></a></var><br>
-— Function: int <b>mpfr_sub_q</b> (<var>mpfr_t rop, mpfr_t op1, mpq_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsub_005fq-98"></a></var><br>
-<blockquote><p>Set <var>rop</var> to <var>op1</var> - <var>op2</var> rounded in the direction
-<var>rnd</var>. For types having no signed zero, it is considered unsigned
-(i.e. (+0) − 0 = (+0), (−0) − 0 = (−0),
-0 − (+0) = (−0) and 0 − (−0) = (+0)).
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_mul</b> (<var>mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fmul-99"></a></var><br>
-— Function: int <b>mpfr_mul_ui</b> (<var>mpfr_t rop, mpfr_t op1, unsigned long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fmul_005fui-100"></a></var><br>
-— Function: int <b>mpfr_mul_si</b> (<var>mpfr_t rop, mpfr_t op1, long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fmul_005fsi-101"></a></var><br>
-— Function: int <b>mpfr_mul_z</b> (<var>mpfr_t rop, mpfr_t op1, mpz_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fmul_005fz-102"></a></var><br>
-— Function: int <b>mpfr_mul_q</b> (<var>mpfr_t rop, mpfr_t op1, mpq_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fmul_005fq-103"></a></var><br>
-<blockquote><p>Set <var>rop</var> to <var>op1</var> times <var>op2</var> rounded in the
-direction <var>rnd</var>.
-When a result is zero, its sign is the product of the signs of the operands
-(for types having no signed zero, it is considered positive).
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_sqr</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsqr-104"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the square of <var>op</var>
-rounded in the direction <var>rnd</var>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_div</b> (<var>mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fdiv-105"></a></var><br>
-— Function: int <b>mpfr_ui_div</b> (<var>mpfr_t rop, unsigned long int op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fui_005fdiv-106"></a></var><br>
-— Function: int <b>mpfr_div_ui</b> (<var>mpfr_t rop, mpfr_t op1, unsigned long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fdiv_005fui-107"></a></var><br>
-— Function: int <b>mpfr_si_div</b> (<var>mpfr_t rop, long int op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsi_005fdiv-108"></a></var><br>
-— Function: int <b>mpfr_div_si</b> (<var>mpfr_t rop, mpfr_t op1, long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fdiv_005fsi-109"></a></var><br>
-— Function: int <b>mpfr_div_z</b> (<var>mpfr_t rop, mpfr_t op1, mpz_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fdiv_005fz-110"></a></var><br>
-— Function: int <b>mpfr_div_q</b> (<var>mpfr_t rop, mpfr_t op1, mpq_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fdiv_005fq-111"></a></var><br>
-<blockquote><p>Set <var>rop</var> to <var>op1</var>/<var>op2</var> rounded in the direction <var>rnd</var>.
-When a result is zero, its sign is the product of the signs of the operands
-(for types having no signed zero, it is considered positive).
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_sqrt</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsqrt-112"></a></var><br>
-— Function: int <b>mpfr_sqrt_ui</b> (<var>mpfr_t rop, unsigned long int op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsqrt_005fui-113"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the square root of <var>op</var>
-rounded in the direction <var>rnd</var>. Return −0 if <var>op</var> is
-−0 (to be consistent with the IEEE 754-1985 standard).
-Set <var>rop</var> to NaN if <var>op</var> is negative.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_cbrt</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fcbrt-114"></a></var><br>
-— Function: int <b>mpfr_root</b> (<var>mpfr_t rop, mpfr_t op, unsigned long int k, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005froot-115"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the cubic root (resp. the <var>k</var>th root)
-of <var>op</var> rounded in the direction <var>rnd</var>.
-An odd (resp. even) root of a negative number (including −Inf)
-returns a negative number (resp. NaN).
-The <var>k</var>th root of −0 is defined to be −0,
-whatever the parity of <var>k</var>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_pow</b> (<var>mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fpow-116"></a></var><br>
-— Function: int <b>mpfr_pow_ui</b> (<var>mpfr_t rop, mpfr_t op1, unsigned long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fpow_005fui-117"></a></var><br>
-— Function: int <b>mpfr_pow_si</b> (<var>mpfr_t rop, mpfr_t op1, long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fpow_005fsi-118"></a></var><br>
-— Function: int <b>mpfr_pow_z</b> (<var>mpfr_t rop, mpfr_t op1, mpz_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fpow_005fz-119"></a></var><br>
-— Function: int <b>mpfr_ui_pow_ui</b> (<var>mpfr_t rop, unsigned long int op1, unsigned long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fui_005fpow_005fui-120"></a></var><br>
-— Function: int <b>mpfr_ui_pow</b> (<var>mpfr_t rop, unsigned long int op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fui_005fpow-121"></a></var><br>
-<blockquote><p>Set <var>rop</var> to <var>op1</var> raised to <var>op2</var>,
-rounded in the direction <var>rnd</var>.
-Special values are currently handled as described in the ISO C99 standard
-for the <code>pow</code> function (note this may change in future versions):
- <ul>
-<li><code>pow(�0, </code><var>y</var><code>)</code> returns plus or minus infinity for <var>y</var> a negative odd integer.
-<li><code>pow(�0, </code><var>y</var><code>)</code> returns plus infinity for <var>y</var> negative and not an odd integer.
-<li><code>pow(�0, </code><var>y</var><code>)</code> returns plus or minus zero for <var>y</var> a positive odd integer.
-<li><code>pow(�0, </code><var>y</var><code>)</code> returns plus zero for <var>y</var> positive and not an odd integer.
-<li><code>pow(-1, �Inf)</code> returns 1.
-<li><code>pow(+1, </code><var>y</var><code>)</code> returns 1 for any <var>y</var>, even a NaN.
-<li><code>pow(</code><var>x</var><code>, �0)</code> returns 1 for any <var>x</var>, even a NaN.
-<li><code>pow(</code><var>x</var><code>, </code><var>y</var><code>)</code> returns NaN for finite negative <var>x</var> and finite non-integer <var>y</var>.
-<li><code>pow(</code><var>x</var><code>, -Inf)</code> returns plus infinity for 0 < abs(x) < 1, and plus zero for abs(x) > 1.
-<li><code>pow(</code><var>x</var><code>, +Inf)</code> returns plus zero for 0 < abs(x) < 1, and plus infinity for abs(x) > 1.
-<li><code>pow(-Inf, </code><var>y</var><code>)</code> returns minus zero for <var>y</var> a negative odd integer.
-<li><code>pow(-Inf, </code><var>y</var><code>)</code> returns plus zero for <var>y</var> negative and not an odd integer.
-<li><code>pow(-Inf, </code><var>y</var><code>)</code> returns minus infinity for <var>y</var> a positive odd integer.
-<li><code>pow(-Inf, </code><var>y</var><code>)</code> returns plus infinity for <var>y</var> positive and not an odd integer.
-<li><code>pow(+Inf, </code><var>y</var><code>)</code> returns plus zero for <var>y</var> negative, and plus infinity for <var>y</var> positive.
-</ul>
- </p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_neg</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fneg-122"></a></var><br>
-<blockquote><p>Set <var>rop</var> to -<var>op</var> rounded in the direction <var>rnd</var>.
-Just changes the sign if <var>rop</var> and <var>op</var> are the same variable.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_abs</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fabs-123"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the absolute value of <var>op</var>,
-rounded in the direction <var>rnd</var>.
-Just changes the sign if <var>rop</var> and <var>op</var> are the same variable.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_dim</b> (<var>mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fdim-124"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the positive difference of <var>op1</var> and <var>op2</var>, i.e.,
-<var>op1</var> - <var>op2</var> rounded in the direction <var>rnd</var>
-if <var>op1</var> > <var>op2</var>, and +0 otherwise.
-Returns NaN when <var>op1</var> or <var>op2</var> is NaN.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_mul_2ui</b> (<var>mpfr_t rop, mpfr_t op1, unsigned long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fmul_005f2ui-125"></a></var><br>
-— Function: int <b>mpfr_mul_2si</b> (<var>mpfr_t rop, mpfr_t op1, long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fmul_005f2si-126"></a></var><br>
-<blockquote><p>Set <var>rop</var> to <var>op1</var> times 2 raised
-to <var>op2</var>
-rounded in the direction <var>rnd</var>. Just increases the exponent by <var>op2</var>
-when <var>rop</var> and <var>op1</var> are identical.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_div_2ui</b> (<var>mpfr_t rop, mpfr_t op1, unsigned long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fdiv_005f2ui-127"></a></var><br>
-— Function: int <b>mpfr_div_2si</b> (<var>mpfr_t rop, mpfr_t op1, long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fdiv_005f2si-128"></a></var><br>
-<blockquote><p>Set <var>rop</var> to <var>op1</var> divided by 2 raised
-to <var>op2</var>
-rounded in the direction <var>rnd</var>. Just decreases the exponent by <var>op2</var>
-when <var>rop</var> and <var>op1</var> are identical.
-</p></blockquote></div>
-
-<div class="node">
-<p><hr>
-<a name="Comparison-Functions"></a>
-Next: <a rel="next" accesskey="n" href="#Special-Functions">Special Functions</a>,
-Previous: <a rel="previous" accesskey="p" href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a>,
-Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
-
-</div>
-
-<!-- node-name, next, previous, up -->
- <p><a name="index-Float-comparisons-functions-129"></a><a name="index-Comparison-functions-130"></a>
-
-<h3 class="section">5.6 Comparison Functions</h3>
-
-<div class="defun">
-— Function: int <b>mpfr_cmp</b> (<var>mpfr_t op1, mpfr_t op2</var>)<var><a name="index-mpfr_005fcmp-131"></a></var><br>
-— Function: int <b>mpfr_cmp_ui</b> (<var>mpfr_t op1, unsigned long int op2</var>)<var><a name="index-mpfr_005fcmp_005fui-132"></a></var><br>
-— Function: int <b>mpfr_cmp_si</b> (<var>mpfr_t op1, signed long int op2</var>)<var><a name="index-mpfr_005fcmp_005fsi-133"></a></var><br>
-— Function: int <b>mpfr_cmp_d</b> (<var>mpfr_t op1, double op2</var>)<var><a name="index-mpfr_005fcmp_005fd-134"></a></var><br>
-— Function: int <b>mpfr_cmp_ld</b> (<var>mpfr_t op1, long double op2</var>)<var><a name="index-mpfr_005fcmp_005fld-135"></a></var><br>
-— Function: int <b>mpfr_cmp_z</b> (<var>mpfr_t op1, mpz_t op2</var>)<var><a name="index-mpfr_005fcmp_005fz-136"></a></var><br>
-— Function: int <b>mpfr_cmp_q</b> (<var>mpfr_t op1, mpq_t op2</var>)<var><a name="index-mpfr_005fcmp_005fq-137"></a></var><br>
-— Function: int <b>mpfr_cmp_f</b> (<var>mpfr_t op1, mpf_t op2</var>)<var><a name="index-mpfr_005fcmp_005ff-138"></a></var><br>
-<blockquote><p>Compare <var>op1</var> and <var>op2</var>. Return a positive value if <var>op1</var> >
-<var>op2</var>, zero if <var>op1</var> = <var>op2</var>, and a negative value if
-<var>op1</var> < <var>op2</var>.
-Both <var>op1</var> and <var>op2</var> are considered to their full own precision,
-which may differ.
-If one of the operands is NaN, set the erange flag and return zero.
-
- <p>Note: These functions may be useful to distinguish the three possible cases.
-If you need to distinguish two cases only, it is recommended to use the
-predicate functions (e.g., <code>mpfr_equal_p</code> for the equality) described
-below; they behave like the IEEE-754 comparisons, in particular when one
-or both arguments are NaN. But only floating-point numbers can be compared
-(you may need to do a conversion first).
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_cmp_ui_2exp</b> (<var>mpfr_t op1, unsigned long int op2, mp_exp_t e</var>)<var><a name="index-mpfr_005fcmp_005fui_005f2exp-139"></a></var><br>
-— Function: int <b>mpfr_cmp_si_2exp</b> (<var>mpfr_t op1, long int op2, mp_exp_t e</var>)<var><a name="index-mpfr_005fcmp_005fsi_005f2exp-140"></a></var><br>
-<blockquote><p>Compare <var>op1</var> and <var>op2</var> multiplied by two to
-the power <var>e</var>. Similar as above.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_cmpabs</b> (<var>mpfr_t op1, mpfr_t op2</var>)<var><a name="index-mpfr_005fcmpabs-141"></a></var><br>
-<blockquote><p>Compare |<var>op1</var>| and |<var>op2</var>|. Return a positive value if
-|<var>op1</var>| > |<var>op2</var>|, zero if |<var>op1</var>| = |<var>op2</var>|, and
-a negative value if |<var>op1</var>| < |<var>op2</var>|.
-If one of the operands is NaN, set the erange flag and return zero.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_nan_p</b> (<var>mpfr_t op</var>)<var><a name="index-mpfr_005fnan_005fp-142"></a></var><br>
-— Function: int <b>mpfr_inf_p</b> (<var>mpfr_t op</var>)<var><a name="index-mpfr_005finf_005fp-143"></a></var><br>
-— Function: int <b>mpfr_number_p</b> (<var>mpfr_t op</var>)<var><a name="index-mpfr_005fnumber_005fp-144"></a></var><br>
-— Function: int <b>mpfr_zero_p</b> (<var>mpfr_t op</var>)<var><a name="index-mpfr_005fzero_005fp-145"></a></var><br>
-<blockquote><p>Return non-zero if <var>op</var> is respectively NaN, an infinity, an ordinary
-number (i.e. neither NaN nor an infinity) or zero. Return zero otherwise.
-</p></blockquote></div>
-
-<div class="defun">
-— Macro: int <b>mpfr_sgn</b> (<var>mpfr_t op</var>)<var><a name="index-mpfr_005fsgn-146"></a></var><br>
-<blockquote><p>Return a positive value if <var>op</var> > 0, zero if <var>op</var> = 0,
-and a negative value if <var>op</var> < 0.
-If the operand is NaN, set the erange flag and return zero.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_greater_p</b> (<var>mpfr_t op1, mpfr_t op2</var>)<var><a name="index-mpfr_005fgreater_005fp-147"></a></var><br>
-<blockquote><p>Return non-zero if <var>op1</var> > <var>op2</var>, zero otherwise.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_greaterequal_p</b> (<var>mpfr_t op1, mpfr_t op2</var>)<var><a name="index-mpfr_005fgreaterequal_005fp-148"></a></var><br>
-<blockquote><p>Return non-zero if <var>op1</var> >= <var>op2</var>, zero otherwise.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_less_p</b> (<var>mpfr_t op1, mpfr_t op2</var>)<var><a name="index-mpfr_005fless_005fp-149"></a></var><br>
-<blockquote><p>Return non-zero if <var>op1</var> < <var>op2</var>, zero otherwise.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_lessequal_p</b> (<var>mpfr_t op1, mpfr_t op2</var>)<var><a name="index-mpfr_005flessequal_005fp-150"></a></var><br>
-<blockquote><p>Return non-zero if <var>op1</var> <= <var>op2</var>, zero otherwise.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_lessgreater_p</b> (<var>mpfr_t op1, mpfr_t op2</var>)<var><a name="index-mpfr_005flessgreater_005fp-151"></a></var><br>
-<blockquote><p>Return non-zero if <var>op1</var> < <var>op2</var> or
-<var>op1</var> > <var>op2</var> (i.e. neither <var>op1</var>, nor <var>op2</var> is
-NaN, and <var>op1</var> <> <var>op2</var>), zero otherwise (i.e. <var>op1</var>
-and/or <var>op2</var> are NaN, or <var>op1</var> = <var>op2</var>).
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_equal_p</b> (<var>mpfr_t op1, mpfr_t op2</var>)<var><a name="index-mpfr_005fequal_005fp-152"></a></var><br>
-<blockquote><p>Return non-zero if <var>op1</var> = <var>op2</var>, zero otherwise
-(i.e. <var>op1</var> and/or <var>op2</var> are NaN, or
-<var>op1</var> <> <var>op2</var>).
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_unordered_p</b> (<var>mpfr_t op1, mpfr_t op2</var>)<var><a name="index-mpfr_005funordered_005fp-153"></a></var><br>
-<blockquote><p>Return non-zero if <var>op1</var> or <var>op2</var> is a NaN (i.e. they cannot be
-compared), zero otherwise.
-</p></blockquote></div>
-
-<div class="node">
-<p><hr>
-<a name="Special-Functions"></a>
-Next: <a rel="next" accesskey="n" href="#Input-and-Output-Functions">Input and Output Functions</a>,
-Previous: <a rel="previous" accesskey="p" href="#Comparison-Functions">Comparison Functions</a>,
-Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
-
-</div>
-
- <p><a name="index-Special-functions-154"></a>
-
-<h3 class="section">5.7 Special Functions</h3>
-
-<p>All those functions, except explicitly stated, return zero for an
-exact return value, a positive value for a return value larger than the
-exact result, and a negative value otherwise.
-
- <p>Important note: in some domains, computing special functions (either with
-correct or incorrect rounding) is expensive, even for small precision,
-for example the trigonometric and Bessel functions for large argument.
-
-<div class="defun">
-— Function: int <b>mpfr_log</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005flog-155"></a></var><br>
-— Function: int <b>mpfr_log2</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005flog2-156"></a></var><br>
-— Function: int <b>mpfr_log10</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005flog10-157"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the natural logarithm of <var>op</var>,
-log2(<var>op</var>) or
-log10(<var>op</var>), respectively,
-rounded in the direction <var>rnd</var>.
-Return −Inf if <var>op</var> is −0 (i.e. the sign of the zero
-has no influence on the result).
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_exp</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fexp-158"></a></var><br>
-— Function: int <b>mpfr_exp2</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fexp2-159"></a></var><br>
-— Function: int <b>mpfr_exp10</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fexp10-160"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the exponential of <var>op</var>,
- to 2 power of <var>op</var>
-or to 10 power of <var>op</var>, respectively,
-rounded in the direction <var>rnd</var>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_cos</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fcos-161"></a></var><br>
-— Function: int <b>mpfr_sin</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsin-162"></a></var><br>
-— Function: int <b>mpfr_tan</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ftan-163"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the cosine of <var>op</var>, sine of <var>op</var>,
-tangent of <var>op</var>, rounded in the direction <var>rnd</var>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_sec</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsec-164"></a></var><br>
-— Function: int <b>mpfr_csc</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fcsc-165"></a></var><br>
-— Function: int <b>mpfr_cot</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fcot-166"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the secant of <var>op</var>, cosecant of <var>op</var>,
-cotangent of <var>op</var>, rounded in the direction <var>rnd</var>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_sin_cos</b> (<var>mpfr_t sop, mpfr_t cop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsin_005fcos-167"></a></var><br>
-<blockquote><p>Set simultaneously <var>sop</var> to the sine of <var>op</var> and
- <var>cop</var> to the cosine of <var>op</var>,
-rounded in the direction <var>rnd</var> with the corresponding precisions of
-<var>sop</var> and <var>cop</var>, which must be different variables.
-Return 0 iff both results are exact.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_acos</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005facos-168"></a></var><br>
-— Function: int <b>mpfr_asin</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fasin-169"></a></var><br>
-— Function: int <b>mpfr_atan</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fatan-170"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the arc-cosine, arc-sine or arc-tangent of <var>op</var>,
-rounded in the direction <var>rnd</var>.
-Note that since <code>acos(-1)</code> returns the floating-point number closest to
-Pi according to the given rounding mode, this number might not be
-in the output range 0 <= <var>rop</var> < \pi
-of the arc-cosine function;
-still, the result lies in the image of the output range
-by the rounding function.
-The same holds for <code>asin(-1)</code>, <code>asin(1)</code>, <code>atan(-Inf)</code>,
-<code>atan(+Inf)</code>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_atan2</b> (<var>mpfr_t rop, mpfr_t y, mpfr_t x, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fatan2-171"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the arc-tangent2 of <var>y</var> and <var>x</var>,
-rounded in the direction <var>rnd</var>:
-if <code>x > 0</code>, <code>atan2(y, x) = atan (y/x)</code>;
-if <code>x < 0</code>, <code>atan2(y, x) = sign(y)*(Pi - atan (abs(y/x)))</code>.
-As for <code>atan</code>, in case the exact mathematical result is +Pi or
--Pi, its rounded result might be outside the function output range.
-
- <p><code>atan2(y, 0)</code> does not raise any floating-point exception.
-Special values are currently handled as described in the ISO C99 standard
-for the <code>atan2</code> function (note this may change in future versions):
- <ul>
-<li><code>atan2(+0, -0)</code> returns +Pi.
-<li><code>atan2(-0, -0)</code> returns -Pi.
-<li><code>atan2(+0, +0)</code> returns +0.
-<li><code>atan2(-0, +0)</code> returns −0.
-<li><code>atan2(+0, x)</code> returns +Pi for x < 0.
-<li><code>atan2(-0, x)</code> returns -Pi for x < 0.
-<li><code>atan2(+0, x)</code> returns +0 for x > 0.
-<li><code>atan2(-0, x)</code> returns −0 for x > 0.
-<li><code>atan2(y, 0)</code> returns -Pi/2 for y < 0.
-<li><code>atan2(y, 0)</code> returns +Pi/2 for y > 0.
-<li><code>atan2(+Inf, -Inf)</code> returns +3*Pi/4.
-<li><code>atan2(-Inf, -Inf)</code> returns -3*Pi/4.
-<li><code>atan2(+Inf, +Inf)</code> returns +Pi/4.
-<li><code>atan2(-Inf, +Inf)</code> returns -Pi/4.
-<li><code>atan2(+Inf, x)</code> returns +Pi/2 for finite x.
-<li><code>atan2(-Inf, x)</code> returns -Pi/2 for finite x.
-<li><code>atan2(y, -Inf)</code> returns +Pi for finite y > 0.
-<li><code>atan2(y, -Inf)</code> returns -Pi for finite y < 0.
-<li><code>atan2(y, +Inf)</code> returns +0 for finite y > 0.
-<li><code>atan2(y, +Inf)</code> returns −0 for finite y < 0.
-</ul>
- </p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_cosh</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fcosh-172"></a></var><br>
-— Function: int <b>mpfr_sinh</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsinh-173"></a></var><br>
-— Function: int <b>mpfr_tanh</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ftanh-174"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the hyperbolic cosine, sine or tangent of <var>op</var>,
-rounded in the direction <var>rnd</var>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_sech</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsech-175"></a></var><br>
-— Function: int <b>mpfr_csch</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fcsch-176"></a></var><br>
-— Function: int <b>mpfr_coth</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fcoth-177"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the hyperbolic secant of <var>op</var>, cosecant of <var>op</var>,
-cotangent of <var>op</var>, rounded in the direction <var>rnd</var>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_acosh</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005facosh-178"></a></var><br>
-— Function: int <b>mpfr_asinh</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fasinh-179"></a></var><br>
-— Function: int <b>mpfr_atanh</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fatanh-180"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the inverse hyperbolic cosine, sine or tangent of <var>op</var>,
-rounded in the direction <var>rnd</var>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_fac_ui</b> (<var>mpfr_t rop, unsigned long int op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ffac_005fui-181"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the factorial of the <code>unsigned long int</code> <var>op</var>,
-rounded in the direction <var>rnd</var>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_log1p</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005flog1p-182"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the logarithm of one plus <var>op</var>,
-rounded in the direction <var>rnd</var>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_expm1</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fexpm1-183"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the exponential of <var>op</var> minus one,
-rounded in the direction <var>rnd</var>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_eint</b> (<var>mpfr_t y, mpfr_t x, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005feint-184"></a></var><br>
-<blockquote><p>Set <var>y</var> to the exponential integral of <var>x</var>,
-rounded in the direction <var>rnd</var>.
-For positive <var>x</var>,
-the exponential integral is the sum of Euler's constant, of the logarithm
-of <var>x</var>, and of the sum for k from 1 to infinity of
-<var>x</var> to the power k, divided by k and factorial(k).
-For negative <var>x</var>, the returned value is NaN.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_gamma</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fgamma-185"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the value of the Gamma function on <var>op</var>, rounded in the
-direction <var>rnd</var>. When <var>op</var> is a negative integer, NaN is returned.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_lngamma</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005flngamma-186"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the value of the logarithm of the Gamma function on <var>op</var>,
-rounded in the direction <var>rnd</var>.
-When −2<var>k</var>−1 <= <var>x</var> <= −2<var>k</var>,
-<var>k</var> being a non-negative integer, NaN is returned.
-See also <code>mpfr_lgamma</code>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_lgamma</b> (<var>mpfr_t rop, int *signp, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005flgamma-187"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the value of the logarithm of the absolute value of the
-Gamma function on <var>op</var>, rounded in the direction <var>rnd</var>. The sign
-(1 or −1) of Gamma(<var>op</var>) is returned in the object pointed to
-by <var>signp</var>. When <var>op</var> is an infinity or a non-positive integer,
-+Inf is returned. When <var>op</var> is NaN, −Inf or a negative integer,
-*<var>signp</var> is undefined, and when <var>op</var> is �0, *<var>signp</var> is
-the sign of the zero.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_zeta</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fzeta-188"></a></var><br>
-— Function: int <b>mpfr_zeta_ui</b> (<var>mpfr_t rop, unsigned long op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fzeta_005fui-189"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the value of the Riemann Zeta function on <var>op</var>,
-rounded in the direction <var>rnd</var>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_erf</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ferf-190"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the value of the error function on <var>op</var>,
-rounded in the direction <var>rnd</var>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_erfc</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ferfc-191"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the value of the complementary error function on <var>op</var>,
-rounded in the direction <var>rnd</var>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_j0</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fj0-192"></a></var><br>
-— Function: int <b>mpfr_j1</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fj1-193"></a></var><br>
-— Function: int <b>mpfr_jn</b> (<var>mpfr_t rop, long n, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fjn-194"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the value of the first order Bessel function of order 0, 1
-and <var>n</var> on <var>op</var>, rounded in the direction <var>rnd</var>. When <var>op</var> is
-NaN, <var>rop</var> is always set to NaN. When <var>op</var> is plus or minus Infinity,
-<var>rop</var> is set to +0. When <var>op</var> is zero, and <var>n</var> is not zero,
-<var>rop</var> is +0 or −0 depending on the parity and sign of <var>n</var>,
-and the sign of <var>op</var>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_y0</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fy0-195"></a></var><br>
-— Function: int <b>mpfr_y1</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fy1-196"></a></var><br>
-— Function: int <b>mpfr_yn</b> (<var>mpfr_t rop, long n, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fyn-197"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the value of the second order Bessel function of order 0, 1
-and <var>n</var> on <var>op</var>, rounded in the direction <var>rnd</var>. When <var>op</var> is
-NaN or negative,
-<var>rop</var> is always set to NaN. When <var>op</var> is +Inf,
-<var>rop</var> is +0. When <var>op</var> is zero,
-<var>rop</var> is +Inf or −Inf depending on the parity and sign of <var>n</var>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_fma</b> (<var>mpfr_t rop, mpfr_t op1, mpfr_t op2, mpfr_t op3, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ffma-198"></a></var><br>
-<blockquote><p>Set <var>rop</var> to (<var>op1</var> times <var>op2</var>) + <var>op3</var>,
-rounded in the direction <var>rnd</var>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_fms</b> (<var>mpfr_t rop, mpfr_t op1, mpfr_t op2, mpfr_t op3, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ffms-199"></a></var><br>
-<blockquote><p>Set <var>rop</var> to (<var>op1</var> times <var>op2</var>) - <var>op3</var>,
-rounded in the direction <var>rnd</var>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_agm</b> (<var>mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fagm-200"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the arithmetic-geometric mean of <var>op1</var> and <var>op2</var>,
-rounded in the direction <var>rnd</var>.
-The arithmetic-geometric mean is the common limit of the sequences
-u[n] and v[n], where u[0]=<var>op1</var>, v[0]=<var>op2</var>, u[n+1] is the
-arithmetic mean of u[n] and v[n], and v[n+1] is the geometric mean of
-u[n] and v[n].
-If any operand is negative, the return value is NaN.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_hypot</b> (<var>mpfr_t rop, mpfr_t x, mpfr_t y, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fhypot-201"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the Euclidean norm of <var>x</var> and <var>y</var>,
-i.e. the square root of the sum of the squares of <var>x</var> and <var>y</var>,
-rounded in the direction <var>rnd</var>.
-Special values are currently handled as described in Section F.9.4.3 of
-the ISO C99 standard, for the <code>hypot</code> function (note this may change
-in future versions): If <var>x</var> or <var>y</var> is an infinity, then plus
-infinity is returned in <var>rop</var>, even if the other number is NaN.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_const_log2</b> (<var>mpfr_t rop, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fconst_005flog2-202"></a></var><br>
-— Function: int <b>mpfr_const_pi</b> (<var>mpfr_t rop, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fconst_005fpi-203"></a></var><br>
-— Function: int <b>mpfr_const_euler</b> (<var>mpfr_t rop, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fconst_005feuler-204"></a></var><br>
-— Function: int <b>mpfr_const_catalan</b> (<var>mpfr_t rop, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fconst_005fcatalan-205"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the logarithm of 2, the value of Pi,
-of Euler's constant 0.577<small class="dots">...</small>, of Catalan's constant 0.915<small class="dots">...</small>,
-respectively, rounded in the direction
-<var>rnd</var>. These functions cache the computed values to avoid other
-calculations if a lower or equal precision is requested. To free these caches,
-use <code>mpfr_free_cache</code>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: void <b>mpfr_free_cache</b> (<var>void</var>)<var><a name="index-mpfr_005ffree_005fcache-206"></a></var><br>
-<blockquote><p>Free various caches used by MPFR internally, in particular the
-caches used by the functions computing constants (currently
-<code>mpfr_const_log2</code>, <code>mpfr_const_pi</code>,
-<code>mpfr_const_euler</code> and <code>mpfr_const_catalan</code>).
-You should call this function before terminating a thread, even if you did
-not call these functions directly (they could have been called internally).
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_sum</b> (<var>mpfr_t rop, mpfr_ptr const tab</var>[]<var>, unsigned long n, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsum-207"></a></var><br>
-<blockquote><p>Set <var>ret</var> to the sum of all elements of <var>tab</var> whose size is <var>n</var>,
-rounded in the direction <var>rnd</var>. Warning, <var>tab</var> is a table of pointers
-to mpfr_t, not a table of mpfr_t (preliminary interface). The returned
-<code>int</code> value is zero when the computed value is the exact value,
-and non-zero when this cannot be guaranteed, without giving the
-direction of the error as the other functions do.
-</p></blockquote></div>
-
-<div class="node">
-<p><hr>
-<a name="Input-and-Output-Functions"></a>
-Next: <a rel="next" accesskey="n" href="#Integer-Related-Functions">Integer Related Functions</a>,
-Previous: <a rel="previous" accesskey="p" href="#Special-Functions">Special Functions</a>,
-Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
-
-</div>
-
-<!-- node-name, next, previous, up -->
- <p><a name="index-Float-input-and-output-functions-208"></a><a name="index-Input-functions-209"></a><a name="index-Output-functions-210"></a><a name="index-I_002fO-functions-211"></a>
-
-<h3 class="section">5.8 Input and Output Functions</h3>
-
-<p>This section describes functions that perform input from an input/output
-stream, and functions that output to an input/output stream.
-Passing a null pointer for a <var>stream</var> argument to any of
-these functions will make them read from <code>stdin</code> and write to
-<code>stdout</code>, respectively.
-
- <p>When using any of these functions, you must include the <code><stdio.h></code>
-standard header before <samp><span class="file">mpfr.h</span></samp>, to allow <samp><span class="file">mpfr.h</span></samp> to define
-prototypes for these functions.
-
-<div class="defun">
-— Function: size_t <b>mpfr_out_str</b> (<var>FILE *stream, int base, size_t n, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fout_005fstr-212"></a></var><br>
-<blockquote><p>Output <var>op</var> on stream <var>stream</var>, as a string of digits in
-base <var>base</var>, rounded in the direction <var>rnd</var>.
-The base may vary from 2 to 36. Print <var>n</var> significant digits exactly,
-or if <var>n</var> is 0, enough digits so that <var>op</var> can be read back
-exactly (see <code>mpfr_get_str</code>).
-
- <p>In addition to the significant digits, a decimal point (defined by the
-current locale) at the right of the
-first digit and a trailing exponent in base 10, in the form ‘<samp><span class="samp">eNNN</span></samp>’,
-are printed. If <var>base</var> is greater than 10, ‘<samp><span class="samp">@</span></samp>’ will be used
-instead of ‘<samp><span class="samp">e</span></samp>’ as exponent delimiter.
-
- <p>Return the number of bytes written, or if an error occurred, return 0.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: size_t <b>mpfr_inp_str</b> (<var>mpfr_t rop, FILE *stream, int base, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005finp_005fstr-213"></a></var><br>
-<blockquote><p>Input a string in base <var>base</var> from stream <var>stream</var>,
-rounded in the direction <var>rnd</var>, and put the
-read float in <var>rop</var>.
-<!-- The argument @var{base} must be in the range 2 to 36. -->
-
- <!-- The string is of the form @samp{M@@N} or, if the -->
- <!-- base is 10 or less, alternatively @samp{MeN} or @samp{MEN}, or, if the base -->
- <!-- is 16, alternatively @samp{MpB} or @samp{MPB}. -->
- <!-- @samp{M} is the significand in the specified base, @samp{N} is the exponent -->
- <!-- written in decimal for the specified base, and in base 16, @samp{B} is the -->
- <!-- binary exponent written in decimal (i.e.@: it indicates the power of 2 by -->
- <!-- which the significand is to be scaled). -->
- <p>This function reads a word (defined as a sequence of characters between
-whitespace) and parses it using <code>mpfr_set_str</code> (it may change).
-See the documentation of <code>mpfr_strtofr</code> for a detailed description
-of the valid string formats.
-<!-- Special values can be read as follows (the case does not matter): -->
-<!-- @code{@@NaN@@}, @code{@@Inf@@}, @code{+@@Inf@@} and @code{-@@Inf@@}, -->
-<!-- possibly followed by other characters; if the base is smaller or equal -->
-<!-- to 16, the following strings are accepted too: @code{NaN}, @code{Inf}, -->
-<!-- @code{+Inf} and @code{-Inf}. -->
-
- <p>Return the number of bytes read, or if an error occurred, return 0.
-</p></blockquote></div>
-
-<!-- @deftypefun void mpfr_inp_raw (mpfr_t @var{float}, FILE *@var{stream}) -->
-<!-- Input from stdio stream @var{stream} in the format written by -->
-<!-- @code{mpfr_out_raw}, and put the result in @var{float}. -->
-<!-- @end deftypefun -->
-<div class="node">
-<p><hr>
-<a name="Integer-Related-Functions"></a>
-Next: <a rel="next" accesskey="n" href="#Miscellaneous-Functions">Miscellaneous Functions</a>,
-Previous: <a rel="previous" accesskey="p" href="#Input-and-Output-Functions">Input and Output Functions</a>,
-Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
-
-</div>
-
-<!-- node-name, next, previous, up -->
- <p><a name="index-Integer-related-functions-214"></a>
-
-<h3 class="section">5.9 Integer Related Functions</h3>
-
-<div class="defun">
-— Function: int <b>mpfr_rint</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005frint-215"></a></var><br>
-— Function: int <b>mpfr_ceil</b> (<var>mpfr_t rop, mpfr_t op</var>)<var><a name="index-mpfr_005fceil-216"></a></var><br>
-— Function: int <b>mpfr_floor</b> (<var>mpfr_t rop, mpfr_t op</var>)<var><a name="index-mpfr_005ffloor-217"></a></var><br>
-— Function: int <b>mpfr_round</b> (<var>mpfr_t rop, mpfr_t op</var>)<var><a name="index-mpfr_005fround-218"></a></var><br>
-— Function: int <b>mpfr_trunc</b> (<var>mpfr_t rop, mpfr_t op</var>)<var><a name="index-mpfr_005ftrunc-219"></a></var><br>
-<blockquote><p>Set <var>rop</var> to <var>op</var> rounded to an integer.
-<code>mpfr_rint</code> rounds to the nearest representable integer in the
-given rounding mode, <code>mpfr_ceil</code> rounds
-to the next higher or equal representable integer, <code>mpfr_floor</code> to
-the next lower or equal representable integer, <code>mpfr_round</code> to the
-nearest representable integer, rounding halfway cases away from zero,
-and <code>mpfr_trunc</code> to the next representable integer toward zero.
-
- <p>The returned value is zero when the result is exact, positive when it is
-greater than the original value of <var>op</var>, and negative when it is smaller.
-More precisely, the returned value is 0 when <var>op</var> is an integer
-representable in <var>rop</var>, 1 or −1 when <var>op</var> is an integer
-that is not representable in <var>rop</var>, 2 or −2 when <var>op</var> is
-not an integer.
-
- <p>Note that <code>mpfr_round</code> is different from <code>mpfr_rint</code> called with
-the rounding to nearest mode (where halfway cases are rounded to an even
-integer or significand). Note also that no double rounding is performed; for
-instance, 4.5 (100.1 in binary) is rounded by <code>mpfr_round</code> to 4 (100
-in binary) in 2-bit precision, though <code>round(4.5)</code> is equal to 5 and
-5 (101 in binary) is rounded to 6 (110 in binary) in 2-bit precision.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_rint_ceil</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005frint_005fceil-220"></a></var><br>
-— Function: int <b>mpfr_rint_floor</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005frint_005ffloor-221"></a></var><br>
-— Function: int <b>mpfr_rint_round</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005frint_005fround-222"></a></var><br>
-— Function: int <b>mpfr_rint_trunc</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005frint_005ftrunc-223"></a></var><br>
-<blockquote><p>Set <var>rop</var> to <var>op</var> rounded to an integer.
-<code>mpfr_rint_ceil</code> rounds to the next higher or equal integer,
-<code>mpfr_rint_floor</code> to the next lower or equal integer,
-<code>mpfr_rint_round</code> to the nearest integer, rounding halfway cases away
-from zero, and <code>mpfr_rint_trunc</code> to the next integer toward zero.
-If the result is not representable, it is rounded in the direction <var>rnd</var>.
-The returned value is the ternary value associated with the considered
-round-to-integer function (regarded in the same way as any other
-mathematical function).
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_frac</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ffrac-224"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the fractional part of <var>op</var>, having the same sign as
-<var>op</var>, rounded in the direction <var>rnd</var> (unlike in <code>mpfr_rint</code>,
-<var>rnd</var> affects only how the exact fractional part is rounded, not how
-the fractional part is generated).
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_remainder</b> (<var>mpfr_t r, mpfr_t x, mpfr_t y, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fremainder-225"></a></var><br>
-— Function: int <b>mpfr_remquo</b> (<var>mpfr_t r, long* q, mpfr_t x, mpfr_t y, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fremquo-226"></a></var><br>
-<blockquote><p>Set <var>r</var> to the remainder of the division of <var>x</var> by <var>y</var>, with
-quotient rounded to the nearest integer (ties rounded to even), and
-<var>r</var> rounded according to the direction <var>rnd</var>.
-If <var>r</var> is zero, it has the sign of <var>x</var>.
-The return value is the ternary value corresponding to <var>r</var>.
-Additionally, <code>mpfr_remquo</code> stores
-the low significant bits from the quotient in <var>*q</var>
-(more precisely the number of bits in a <code>long</code> minus one),
-with the sign of <var>x</var> divided by <var>y</var>
-(except if those low bits are all zero, in which case zero is returned).
-Note that <var>x</var> may be so large in magnitude relative to <var>y</var> that an
-exact representation of the quotient is not practical.
-These functions are useful for additive argument reduction.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_integer_p</b> (<var>mpfr_t op</var>)<var><a name="index-mpfr_005finteger_005fp-227"></a></var><br>
-<blockquote><p>Return non-zero iff <var>op</var> is an integer.
-</p></blockquote></div>
-
-<div class="node">
-<p><hr>
-<a name="Miscellaneous-Functions"></a>
-Next: <a rel="next" accesskey="n" href="#Rounding-Mode-Related-Functions">Rounding Mode Related Functions</a>,
-Previous: <a rel="previous" accesskey="p" href="#Integer-Related-Functions">Integer Related Functions</a>,
-Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
-
-</div>
-
-<!-- node-name, next, previous, up -->
- <p><a name="index-Miscellaneous-float-functions-228"></a>
-
-<h3 class="section">5.10 Miscellaneous Functions</h3>
-
-<div class="defun">
-— Function: void <b>mpfr_nexttoward</b> (<var>mpfr_t x, mpfr_t y</var>)<var><a name="index-mpfr_005fnexttoward-229"></a></var><br>
-<blockquote><p>If <var>x</var> or <var>y</var> is NaN, set <var>x</var> to NaN. Otherwise, if <var>x</var>
-is different from <var>y</var>, replace <var>x</var> by the next floating-point
-number (with the precision of <var>x</var> and the current exponent range)
-in the direction of <var>y</var>, if there is one
-(the infinite values are seen as the smallest and largest floating-point
-numbers). If the result is zero, it keeps the same sign. No underflow or
-overflow is generated.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: void <b>mpfr_nextabove</b> (<var>mpfr_t x</var>)<var><a name="index-mpfr_005fnextabove-230"></a></var><br>
-<blockquote><p>Equivalent to <code>mpfr_nexttoward</code> where <var>y</var> is plus infinity.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: void <b>mpfr_nextbelow</b> (<var>mpfr_t x</var>)<var><a name="index-mpfr_005fnextbelow-231"></a></var><br>
-<blockquote><p>Equivalent to <code>mpfr_nexttoward</code> where <var>y</var> is minus infinity.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_min</b> (<var>mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fmin-232"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the minimum of <var>op1</var> and <var>op2</var>. If <var>op1</var>
-and <var>op2</var> are both NaN, then <var>rop</var> is set to NaN. If <var>op1</var>
-or <var>op2</var> is NaN, then <var>rop</var> is set to the numeric value. If
-<var>op1</var> and <var>op2</var> are zeros of different signs, then <var>rop</var>
-is set to −0.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_max</b> (<var>mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fmax-233"></a></var><br>
-<blockquote><p>Set <var>rop</var> to the maximum of <var>op1</var> and <var>op2</var>. If <var>op1</var>
-and <var>op2</var> are both NaN, then <var>rop</var> is set to NaN. If <var>op1</var>
-or <var>op2</var> is NaN, then <var>rop</var> is set to the numeric value. If
-<var>op1</var> and <var>op2</var> are zeros of different signs, then <var>rop</var>
-is set to +0.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_urandomb</b> (<var>mpfr_t rop, gmp_randstate_t state</var>)<var><a name="index-mpfr_005furandomb-234"></a></var><br>
-<blockquote><p>Generate a uniformly distributed random float in the interval
-0 <= <var>rop</var> < 1.
-Return 0, unless the exponent is not in the current exponent range, in
-which case <var>rop</var> is set to NaN and a non-zero value is returned. The
-second argument is a <code>gmp_randstate_t</code> structure which should be
-created using the GMP <code>gmp_randinit</code> function, see the GMP manual.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: void <b>mpfr_random</b> (<var>mpfr_t rop</var>)<var><a name="index-mpfr_005frandom-235"></a></var><br>
-<blockquote><p>Generate a uniformly distributed random float in the interval
-0 <= <var>rop</var> < 1.
-This function is deprecated; <code>mpfr_urandomb</code> should be used instead.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: void <b>mpfr_random2</b> (<var>mpfr_t rop, mp_size_t size, mp_exp_t exp</var>)<var><a name="index-mpfr_005frandom2-236"></a></var><br>
-<blockquote><p>Generate a random float of at most <var>size</var> limbs, with long strings of
-zeros and ones in the binary representation. The exponent of the number is in
-the interval −<var>exp</var> to <var>exp</var>.
-This function is useful for
-testing functions and algorithms, since this kind of random numbers have
-proven to be more likely to trigger corner-case bugs.
-Negative random numbers are generated when <var>size</var> is negative.
-Put +0 in <var>rop</var> when size if zero. The internal state of the default
-pseudorandom number generator is modified by a call to this function (the
-same one as GMP if MPFR was built using ‘<samp><span class="samp">--with-gmp-build</span></samp>’).
-</p></blockquote></div>
-
-<div class="defun">
-— Function: mp_exp_t <b>mpfr_get_exp</b> (<var>mpfr_t x</var>)<var><a name="index-mpfr_005fget_005fexp-237"></a></var><br>
-<blockquote><p>Get the exponent of <var>x</var>, assuming that <var>x</var> is a non-zero ordinary
-number and the significand is chosen in [1/2,1). The behavior for NaN,
-infinity or zero is undefined.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_set_exp</b> (<var>mpfr_t x, mp_exp_t e</var>)<var><a name="index-mpfr_005fset_005fexp-238"></a></var><br>
-<blockquote><p>Set the exponent of <var>x</var> if <var>e</var> is in the current exponent range,
-and return 0 (even if <var>x</var> is not a non-zero ordinary number);
-otherwise, return a non-zero value.
-The significand is assumed to be in [1/2,1).
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_signbit</b> (<var>mpfr_t op</var>)<var><a name="index-mpfr_005fsignbit-239"></a></var><br>
-<blockquote><p>Return a non-zero value iff <var>op</var> has its sign bit set (i.e. if it is
-negative, −0, or a NaN whose representation has its sign bit set).
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_setsign</b> (<var>mpfr_t rop, mpfr_t op, int s, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsetsign-240"></a></var><br>
-<blockquote><p>Set the value of <var>rop</var> from <var>op</var>, rounded toward the given
-direction <var>rnd</var>, then set (resp. clear) its sign bit if <var>s</var>
-is non-zero (resp. zero), even when <var>op</var> is a NaN.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_copysign</b> (<var>mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fcopysign-241"></a></var><br>
-<blockquote><p>Set the value of <var>rop</var> from <var>op1</var>, rounded toward the given
-direction <var>rnd</var>, then set its sign bit to that of <var>op2</var> (even
-when <var>op1</var> or <var>op2</var> is a NaN). This function is equivalent to
-<code>mpfr_setsign (</code><var>rop</var><code>, </code><var>op1</var><code>, mpfr_signbit (</code><var>op2</var><code>), </code><var>rnd</var><code>)</code>.
-</p></blockquote></div>
-
-<!-- By definition, a C string is always null-terminated, so that we -->
-<!-- could just say "string" or "null-terminated character array", -->
-<!-- but "null-terminated string" is not an error and probably better -->
-<!-- for most users. -->
-<div class="defun">
-— Function: const char * <b>mpfr_get_version</b> (<var>void</var>)<var><a name="index-mpfr_005fget_005fversion-242"></a></var><br>
-<blockquote><p>Return the MPFR version, as a null-terminated string.
-</p></blockquote></div>
-
-<div class="defun">
-— Macro: <b>MPFR_VERSION</b><var><a name="index-MPFR_005fVERSION-243"></a></var><br>
-— Macro: <b>MPFR_VERSION_MAJOR</b><var><a name="index-MPFR_005fVERSION_005fMAJOR-244"></a></var><br>
-— Macro: <b>MPFR_VERSION_MINOR</b><var><a name="index-MPFR_005fVERSION_005fMINOR-245"></a></var><br>
-— Macro: <b>MPFR_VERSION_PATCHLEVEL</b><var><a name="index-MPFR_005fVERSION_005fPATCHLEVEL-246"></a></var><br>
-— Macro: <b>MPFR_VERSION_STRING</b><var><a name="index-MPFR_005fVERSION_005fSTRING-247"></a></var><br>
-<blockquote><p><code>MPFR_VERSION</code> is the version of MPFR as a preprocessing constant.
-<code>MPFR_VERSION_MAJOR</code>, <code>MPFR_VERSION_MINOR</code> and
-<code>MPFR_VERSION_PATCHLEVEL</code> are respectively the major, minor and patch
-level of MPFR version, as preprocessing constants.
-<code>MPFR_VERSION_STRING</code> is the version (with an optional suffix, used
-in development and pre-release versions) as a string constant, which can
-be compared to the result of <code>mpfr_get_version</code> to check at run time
-the header file and library used match:
- <pre class="example"> if (strcmp (mpfr_get_version (), MPFR_VERSION_STRING))
- fprintf (stderr, "Warning: header and library do not match\n");
-</pre>
- <p>Note: Obtaining different strings is not necessarily an error, as
-in general, a program compiled with some old MPFR version can be
-dynamically linked with a newer MPFR library version (if allowed
-by the library versioning system).
-</p></blockquote></div>
-
-<div class="defun">
-— Macro: long <b>MPFR_VERSION_NUM</b> (<var>major, minor, patchlevel</var>)<var><a name="index-MPFR_005fVERSION_005fNUM-248"></a></var><br>
-<blockquote><p>Create an integer in the same format as used by <code>MPFR_VERSION</code> from the
-given <var>major</var>, <var>minor</var> and <var>patchlevel</var>.
-Here is an example of how to check the MPFR version at compile time:
- <pre class="example"> #if (!defined(MPFR_VERSION) || (MPFR_VERSION<MPFR_VERSION_NUM(2,1,0)))
- # error "Wrong MPFR version."
- #endif
-</pre>
- </blockquote></div>
-
-<div class="defun">
-— Function: const char * <b>mpfr_get_patches</b> (<var>void</var>)<var><a name="index-mpfr_005fget_005fpatches-249"></a></var><br>
-<blockquote><p>Return a null-terminated string containing the ids of the patches applied to
-the MPFR library (contents of the <samp><span class="file">PATCHES</span></samp> file), separated by spaces.
-Note: If the program has been compiled with an older MPFR version and is
-dynamically linked with a new MPFR library version, the ids of the patches
-applied to the old (compile-time) MPFR version are not available (however
-this information should not have much interest in general).
-</p></blockquote></div>
-
-<div class="node">
-<p><hr>
-<a name="Rounding-Mode-Related-Functions"></a>
-Next: <a rel="next" accesskey="n" href="#Exception-Related-Functions">Exception Related Functions</a>,
-Previous: <a rel="previous" accesskey="p" href="#Miscellaneous-Functions">Miscellaneous Functions</a>,
-Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
-
-</div>
-
- <p><a name="index-Rounding-mode-related-functions-250"></a>
-
-<h3 class="section">5.11 Rounding Mode Related Functions</h3>
-
-<div class="defun">
-— Function: void <b>mpfr_set_default_rounding_mode</b> (<var>mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005fdefault_005frounding_005fmode-251"></a></var><br>
-<blockquote><p>Set the default rounding mode to <var>rnd</var>.
-The default rounding mode is to nearest initially.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: mp_rnd_t <b>mpfr_get_default_rounding_mode</b> (<var>void</var>)<var><a name="index-mpfr_005fget_005fdefault_005frounding_005fmode-252"></a></var><br>
-<blockquote><p>Get the default rounding mode.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_prec_round</b> (<var>mpfr_t x, mp_prec_t prec, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fprec_005fround-253"></a></var><br>
-<blockquote><p>Round <var>x</var> according to <var>rnd</var> with precision <var>prec</var>, which
-must be an integer between <code>MPFR_PREC_MIN</code> and <code>MPFR_PREC_MAX</code>
-(otherwise the behavior is undefined).
-If <var>prec</var> is greater or equal to the precision of <var>x</var>, then new
-space is allocated for the significand, and it is filled with zeros.
-Otherwise, the significand is rounded to precision <var>prec</var> with the given
-direction. In both cases, the precision of <var>x</var> is changed to <var>prec</var>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_round_prec</b> (<var>mpfr_t x, mp_rnd_t rnd, mp_prec_t prec</var>)<var><a name="index-mpfr_005fround_005fprec-254"></a></var><br>
-<blockquote><p>[This function is obsolete. Please use <code>mpfr_prec_round</code> instead.]
-</p></blockquote></div>
-
-<div class="defun">
-— Function: const char * <b>mpfr_print_rnd_mode</b> (<var>mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fprint_005frnd_005fmode-255"></a></var><br>
-<blockquote><p>Return the input string (GMP_RNDD, GMP_RNDU, GMP_RNDN, GMP_RNDZ)
-corresponding to the rounding mode <var>rnd</var> or a null pointer if
-<var>rnd</var> is an invalid rounding mode.
-</p></blockquote></div>
-
-<div class="node">
-<p><hr>
-<a name="Exception-Related-Functions"></a>
-Next: <a rel="next" accesskey="n" href="#Advanced-Functions">Advanced Functions</a>,
-Previous: <a rel="previous" accesskey="p" href="#Rounding-Mode-Related-Functions">Rounding Mode Related Functions</a>,
-Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
-
-</div>
-
-<!-- node-name, next, previous, up -->
- <p><a name="index-Exception-related-functions-256"></a>
-
-<h3 class="section">5.12 Exception Related Functions</h3>
-
-<div class="defun">
-— Function: mp_exp_t <b>mpfr_get_emin</b> (<var>void</var>)<var><a name="index-mpfr_005fget_005femin-257"></a></var><br>
-— Function: mp_exp_t <b>mpfr_get_emax</b> (<var>void</var>)<var><a name="index-mpfr_005fget_005femax-258"></a></var><br>
-<blockquote><p>Return the (current) smallest and largest exponents allowed for a
-floating-point variable. The smallest positive value of a floating-point
-variable is one half times 2 raised to the
-smallest exponent and the largest value has the form (1 - epsilon) times 2 raised to the largest exponent.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_set_emin</b> (<var>mp_exp_t exp</var>)<var><a name="index-mpfr_005fset_005femin-259"></a></var><br>
-— Function: int <b>mpfr_set_emax</b> (<var>mp_exp_t exp</var>)<var><a name="index-mpfr_005fset_005femax-260"></a></var><br>
-<blockquote><p>Set the smallest and largest exponents allowed for a floating-point variable.
-Return a non-zero value when <var>exp</var> is not in the range accepted by the
-implementation (in that case the smallest or largest exponent is not changed),
-and zero otherwise.
-If the user changes the exponent range, it is her/his responsibility to check
-that all current floating-point variables are in the new allowed range
-(for example using <code>mpfr_check_range</code>), otherwise the subsequent
-behavior will be undefined, in the sense of the ISO C standard.
-<!-- It is also her/his responsibility to check that @m {emin <= emax}. -->
-</p></blockquote></div>
-
-<div class="defun">
-— Function: mp_exp_t <b>mpfr_get_emin_min</b> (<var>void</var>)<var><a name="index-mpfr_005fget_005femin_005fmin-261"></a></var><br>
-— Function: mp_exp_t <b>mpfr_get_emin_max</b> (<var>void</var>)<var><a name="index-mpfr_005fget_005femin_005fmax-262"></a></var><br>
-— Function: mp_exp_t <b>mpfr_get_emax_min</b> (<var>void</var>)<var><a name="index-mpfr_005fget_005femax_005fmin-263"></a></var><br>
-— Function: mp_exp_t <b>mpfr_get_emax_max</b> (<var>void</var>)<var><a name="index-mpfr_005fget_005femax_005fmax-264"></a></var><br>
-<blockquote><p>Return the minimum and maximum of the smallest and largest exponents
-allowed for <code>mpfr_set_emin</code> and <code>mpfr_set_emax</code>. These values
-are implementation dependent; it is possible to create a non
-portable program by writing <code>mpfr_set_emax(mpfr_get_emax_max())</code>
-and <code>mpfr_set_emin(mpfr_get_emin_min())</code> since the values
-of the smallest and largest exponents become implementation dependent.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_check_range</b> (<var>mpfr_t x, int t, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fcheck_005frange-265"></a></var><br>
-<blockquote><p>This function forces <var>x</var> to be in the current range of acceptable
-values, <var>t</var> being the current ternary value: negative if <var>x</var>
-is smaller than the exact value, positive if <var>x</var> is larger than
-the exact value and zero if <var>x</var> is exact (before the call). It
-generates an underflow or an overflow if the exponent of <var>x</var> is
-outside the current allowed range; the value of <var>t</var> may be used
-to avoid a double rounding. This function returns zero if the rounded
-result is equal to the exact one, a positive value if the rounded
-result is larger than the exact one, a negative value if the rounded
-result is smaller than the exact one. Note that unlike most functions,
-the result is compared to the exact one, not the input value <var>x</var>,
-i.e. the ternary value is propagated.
-
- <p>Note: If <var>x</var> is an infinity and <var>t</var> is different from zero (i.e.,
-if the rounded result is an inexact infinity), then the overflow flag is
-set. This is useful because <code>mpfr_check_range</code> is typically called
-(at least in MPFR functions) after restoring the flags that could have
-been set due to internal computations.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_subnormalize</b> (<var>mpfr_t x, int t, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsubnormalize-266"></a></var><br>
-<blockquote><p>This function rounds <var>x</var> emulating subnormal number arithmetic:
-if <var>x</var> is outside the subnormal exponent range, it just propagates the
-ternary value <var>t</var>; otherwise, it rounds <var>x</var> to precision
-<code>EXP(x)-emin+1</code> according to rounding mode <var>rnd</var> and previous
-ternary value <var>t</var>, avoiding double rounding problems.
-More precisely in the subnormal domain, denoting by <var>e</var> the value of
-<code>emin</code>, <var>x</var> is rounded in fixed-point
-arithmetic to an integer multiple of two to the power
-<var>e</var>−1; as a consequence, 1.5 multiplied by two to the power <var>e</var>−1 when <var>t</var> is zero
-is rounded to two to the power <var>e</var> with rounding to nearest.
-
- <p><code>PREC(x)</code> is not modified by this function.
-<var>rnd</var> and <var>t</var> must be the used rounding mode for computing <var>x</var>
-and the returned ternary value when computing <var>x</var>.
-The subnormal exponent range is from <code>emin</code> to <code>emin+PREC(x)-1</code>.
-If the result cannot be represented in the current exponent range
-(due to a too small <code>emax</code>), the behavior is undefined.
-Note that unlike most functions, the result is compared to the exact one,
-not the input value <var>x</var>, i.e. the ternary value is propagated.
-This is a preliminary interface.
-</p></blockquote></div>
-
- <p>This is an example of how to emulate double IEEE-754 arithmetic
-using MPFR:
-
-<pre class="example"> {
- mpfr_t xa, xb;
- int i;
- volatile double a, b;
-
- mpfr_set_default_prec (53);
- mpfr_set_emin (-1073);
- mpfr_set_emax (1024);
-
- mpfr_init (xa); mpfr_init (xb);
-
- b = 34.3; mpfr_set_d (xb, b, GMP_RNDN);
- a = 0x1.1235P-1021; mpfr_set_d (xa, a, GMP_RNDN);
-
- a /= b;
- i = mpfr_div (xa, xa, xb, GMP_RNDN);
- i = mpfr_subnormalize (xa, i, GMP_RNDN);
-
- mpfr_clear (xa); mpfr_clear (xb);
- }
-</pre>
- <p>Warning: this emulates a double IEEE-754 arithmetic with correct rounding
-in the subnormal range, which may not be the case for your hardware.
-
-<div class="defun">
-— Function: void <b>mpfr_clear_underflow</b> (<var>void</var>)<var><a name="index-mpfr_005fclear_005funderflow-267"></a></var><br>
-— Function: void <b>mpfr_clear_overflow</b> (<var>void</var>)<var><a name="index-mpfr_005fclear_005foverflow-268"></a></var><br>
-— Function: void <b>mpfr_clear_nanflag</b> (<var>void</var>)<var><a name="index-mpfr_005fclear_005fnanflag-269"></a></var><br>
-— Function: void <b>mpfr_clear_inexflag</b> (<var>void</var>)<var><a name="index-mpfr_005fclear_005finexflag-270"></a></var><br>
-— Function: void <b>mpfr_clear_erangeflag</b> (<var>void</var>)<var><a name="index-mpfr_005fclear_005ferangeflag-271"></a></var><br>
-<blockquote><p>Clear the underflow, overflow, invalid, inexact and erange flags.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: void <b>mpfr_set_underflow</b> (<var>void</var>)<var><a name="index-mpfr_005fset_005funderflow-272"></a></var><br>
-— Function: void <b>mpfr_set_overflow</b> (<var>void</var>)<var><a name="index-mpfr_005fset_005foverflow-273"></a></var><br>
-— Function: void <b>mpfr_set_nanflag</b> (<var>void</var>)<var><a name="index-mpfr_005fset_005fnanflag-274"></a></var><br>
-— Function: void <b>mpfr_set_inexflag</b> (<var>void</var>)<var><a name="index-mpfr_005fset_005finexflag-275"></a></var><br>
-— Function: void <b>mpfr_set_erangeflag</b> (<var>void</var>)<var><a name="index-mpfr_005fset_005ferangeflag-276"></a></var><br>
-<blockquote><p>Set the underflow, overflow, invalid, inexact and erange flags.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: void <b>mpfr_clear_flags</b> (<var>void</var>)<var><a name="index-mpfr_005fclear_005fflags-277"></a></var><br>
-<blockquote><p>Clear all global flags (underflow, overflow, inexact, invalid, erange).
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_underflow_p</b> (<var>void</var>)<var><a name="index-mpfr_005funderflow_005fp-278"></a></var><br>
-— Function: int <b>mpfr_overflow_p</b> (<var>void</var>)<var><a name="index-mpfr_005foverflow_005fp-279"></a></var><br>
-— Function: int <b>mpfr_nanflag_p</b> (<var>void</var>)<var><a name="index-mpfr_005fnanflag_005fp-280"></a></var><br>
-— Function: int <b>mpfr_inexflag_p</b> (<var>void</var>)<var><a name="index-mpfr_005finexflag_005fp-281"></a></var><br>
-— Function: int <b>mpfr_erangeflag_p</b> (<var>void</var>)<var><a name="index-mpfr_005ferangeflag_005fp-282"></a></var><br>
-<blockquote><p>Return the corresponding (underflow, overflow, invalid, inexact, erange)
-flag, which is non-zero iff the flag is set.
-</p></blockquote></div>
-
-<div class="node">
-<p><hr>
-<a name="Advanced-Functions"></a>
-Next: <a rel="next" accesskey="n" href="#Compatibility-with-MPF">Compatibility with MPF</a>,
-Previous: <a rel="previous" accesskey="p" href="#Exception-Related-Functions">Exception Related Functions</a>,
-Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
-
-</div>
-
-<!-- node-name, next, previous, up -->
- <p><a name="index-Advanced-functions-283"></a>
-
-<h3 class="section">5.13 Advanced Functions</h3>
-
-<p>All the given interfaces are preliminary. They might change incompatibly in
-future revisions.
-
-<div class="defun">
-— Macro: <b>MPFR_DECL_INIT</b> (<var>name, prec</var>)<var><a name="index-MPFR_005fDECL_005fINIT-284"></a></var><br>
-<blockquote><p>This macro declares <var>name</var> as an automatic variable of type <code>mpfr_t</code>,
-initializes it and sets its precision to be <strong>exactly</strong> <var>prec</var> bits
-and its value to NaN. <var>name</var> must be a valid identifier.
-You must use this macro in the declaration section.
-This macro is much faster than using <code>mpfr_init2</code> but has some
-drawbacks:
-
- <ul>
-<li>You <strong>must not</strong> call <code>mpfr_clear</code> with variables
-created with this macro (The storage is allocated at the point of declaration
-and deallocated when the brace-level is exited.).
-<li>You <strong>can not</strong> change their precision.
-<li>You <strong>should not</strong> create variables with huge precision with this macro.
-<li>Your compiler must support ‘<samp><span class="samp">Non-Constant Initializers</span></samp>’ (standard
-in C++ and ISO C99) and ‘<samp><span class="samp">Token Pasting</span></samp>’
-(standard in ISO C89). If <var>prec</var> is not a compiler constant, your compiler
-must support ‘<samp><span class="samp">Variable-length automatic arrays</span></samp>’ (standard in ISO C99).
-‘<samp><span class="samp">GCC 2.95.3</span></samp>’ supports all these features. If you compile your program
-with gcc in c89 mode and with ‘<samp><span class="samp">-pedantic</span></samp>’, you may want to define the
-<code>MPFR_USE_EXTENSION</code> macro to avoid warnings due to the
-<code>MPFR_DECL_INIT</code> implementation.
-</ul>
- </p></blockquote></div>
-
-<div class="defun">
-— Function: void <b>mpfr_inits</b> (<var>mpfr_t x, ...</var>)<var><a name="index-mpfr_005finits-285"></a></var><br>
-<blockquote><p>Initialize all the <code>mpfr_t</code> variables of the given <code>va_list</code>,
-set their precision to be the default precision and their value to NaN.
-See <code>mpfr_init</code> for more details.
-The <code>va_list</code> is assumed to be composed only of type <code>mpfr_t</code>
-(or equivalently <code>mpfr_ptr</code>).
-It begins from <var>x</var>. It ends when it encounters a null pointer (whose
-type must also be <code>mpfr_ptr</code>).
-</p></blockquote></div>
-
-<div class="defun">
-— Function: void <b>mpfr_inits2</b> (<var>mp_prec_t prec, mpfr_t x, ...</var>)<var><a name="index-mpfr_005finits2-286"></a></var><br>
-<blockquote><p>Initialize all the <code>mpfr_t</code> variables of the given <code>va_list</code>,
-set their precision to be <strong>exactly</strong>
-<var>prec</var> bits and their value to NaN.
-See <code>mpfr_init2</code> for more details.
-The <code>va_list</code> is assumed to be composed only of type <code>mpfr_t</code>
-(or equivalently <code>mpfr_ptr</code>).
-It begins from <var>x</var>. It ends when it encounters a null pointer (whose
-type must also be <code>mpfr_ptr</code>).
-</p></blockquote></div>
-
-<div class="defun">
-— Function: void <b>mpfr_clears</b> (<var>mpfr_t x, ...</var>)<var><a name="index-mpfr_005fclears-287"></a></var><br>
-<blockquote><p>Free the space occupied by all the <code>mpfr_t</code> variables of the given
-<code>va_list</code>. See <code>mpfr_clear</code> for more details.
-The <code>va_list</code> is assumed to be composed only of type <code>mpfr_t</code>
-(or equivalently <code>mpfr_ptr</code>).
-It begins from <var>x</var>. It ends when it encounters a null pointer (whose
-type must also be <code>mpfr_ptr</code>).
-</p></blockquote></div>
-
- <p>Here is an example of how to use multiple initialization functions:
-
-<pre class="example"> {
- mpfr_t x, y, z, t;
- mpfr_inits2 (256, x, y, z, t, (mpfr_ptr) 0);
- ...
- mpfr_clears (x, y, z, t, (mpfr_ptr) 0);
- }
-</pre>
- <div class="node">
-<p><hr>
-<a name="Compatibility-with-MPF"></a>
-Next: <a rel="next" accesskey="n" href="#Custom-Interface">Custom Interface</a>,
-Previous: <a rel="previous" accesskey="p" href="#Advanced-Functions">Advanced Functions</a>,
-Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
-
-</div>
-
- <p><a name="index-Compatibility-with-MPF-288"></a>
-
-<h3 class="section">5.14 Compatibility With MPF</h3>
-
-<p>A header file <samp><span class="file">mpf2mpfr.h</span></samp> is included in the distribution of MPFR for
-compatibility with the GNU MP class MPF.
-After inserting the following two lines after the <code>#include <gmp.h></code>
-line,
-<pre class="verbatim">
-#include <mpfr.h>
-#include <mpf2mpfr.h>
-</pre>
-any program written for
-MPF can be compiled directly with MPFR without any changes.
-All operations are then performed with the default MPFR rounding mode,
-which can be reset with <code>mpfr_set_default_rounding_mode</code>.
-
- <p>Warning: the <code>mpf_init</code> and <code>mpf_init2</code> functions initialize
-to zero, whereas the corresponding MPFR functions initialize to NaN:
-this is useful to detect uninitialized values, but is slightly incompatible
-with <code>mpf</code>.
-
-<div class="defun">
-— Function: void <b>mpfr_set_prec_raw</b> (<var>mpfr_t x, mp_prec_t prec</var>)<var><a name="index-mpfr_005fset_005fprec_005fraw-289"></a></var><br>
-<blockquote><p>Reset the precision of <var>x</var> to be <strong>exactly</strong> <var>prec</var> bits.
-The only difference with <code>mpfr_set_prec</code> is that <var>prec</var> is assumed to
-be small enough so that the significand fits into the current allocated memory
-space for <var>x</var>. Otherwise the behavior is undefined.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_eq</b> (<var>mpfr_t op1, mpfr_t op2, unsigned long int op3</var>)<var><a name="index-mpfr_005feq-290"></a></var><br>
-<blockquote><p>Return non-zero if <var>op1</var> and <var>op2</var> are both non-zero ordinary
-numbers with the same exponent and the same first <var>op3</var> bits, both
-zero, or both infinities of the same sign. Return zero otherwise. This
-function is defined for compatibility with <code>mpf</code>. Do not use it if
-you want to know whether two numbers are close to each other; for instance,
-1.011111 and 1.100000 are regarded as different for any value of <var>op3</var>
-larger than 1.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: void <b>mpfr_reldiff</b> (<var>mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005freldiff-291"></a></var><br>
-<blockquote><p>Compute the relative difference between <var>op1</var> and <var>op2</var>
-and store the result in <var>rop</var>.
-This function does not guarantee the correct rounding on the relative
-difference; it just computes |<var>op1</var>-<var>op2</var>|/<var>op1</var>, using the
-rounding mode <var>rnd</var> for all operations and the precision of <var>rop</var>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_mul_2exp</b> (<var>mpfr_t rop, mpfr_t op1, unsigned long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fmul_005f2exp-292"></a></var><br>
-— Function: int <b>mpfr_div_2exp</b> (<var>mpfr_t rop, mpfr_t op1, unsigned long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fdiv_005f2exp-293"></a></var><br>
-<blockquote><p>See <code>mpfr_mul_2ui</code> and <code>mpfr_div_2ui</code>. These functions are only kept
-for compatibility with MPF.
-</p></blockquote></div>
-
-<div class="node">
-<p><hr>
-<a name="Custom-Interface"></a>
-Next: <a rel="next" accesskey="n" href="#Internals">Internals</a>,
-Previous: <a rel="previous" accesskey="p" href="#Compatibility-with-MPF">Compatibility with MPF</a>,
-Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
-
-</div>
-
- <p><a name="index-Custom-interface-294"></a>
-
-<h3 class="section">5.15 Custom Interface</h3>
-
-<p>Some applications use a stack to handle the memory and their objects.
-However, the MPFR memory design is not well suited for such a thing. So that
-such applications are able to use MPFR, an auxiliary memory interface has
-been created: the Custom Interface.
-
- <p>The following interface allows them to use MPFR in two ways:
- <ul>
-<li>Either they directly store the MPFR FP number as a <code>mpfr_t</code>
-on the stack.
-<li>Either they store their own representation of a FP number on the
-stack and construct a new temporary <code>mpfr_t</code> each time it is needed.
-</ul>
- Nothing has to be done to destroy the FP numbers except garbaging the used
-memory: all the memory stuff (allocating, destroying, garbaging) is kept to
-the application.
-
- <p>Each function in this interface is also implemented as a macro for
-efficiency reasons: for example <code>mpfr_custom_init (s, p)</code>
-uses the macro, while <code>(mpfr_custom_init) (s, p)</code> uses the function.
-
- <p>Note 1: MPFR functions may still initialize temporary FP numbers
-using standard mpfr_init. See Custom Allocation (GNU MP).
-
- <p>Note 2: MPFR functions may use the cached functions (mpfr_const_pi for
-example), even if they are not explicitly called. You have to call
-<code>mpfr_free_cache</code> each time you garbage the memory iff mpfr_init, through
-GMP Custom Allocation, allocates its memory on the application stack.
-
- <p>Note 3: This interface is preliminary.
-
-<div class="defun">
-— Function: size_t <b>mpfr_custom_get_size</b> (<var>mp_prec_t prec</var>)<var><a name="index-mpfr_005fcustom_005fget_005fsize-295"></a></var><br>
-<blockquote><p>Return the needed size in bytes to store the significand of a FP number
-of precision <var>prec</var>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: void <b>mpfr_custom_init</b> (<var>void *significand, mp_prec_t prec</var>)<var><a name="index-mpfr_005fcustom_005finit-296"></a></var><br>
-<blockquote><p>Initialize a significand of precision <var>prec</var>.
-<var>significand</var> must be an area of <code>mpfr_custom_get_size (prec)</code> bytes
-at least and be suitably aligned for an array of <code>mp_limb_t</code>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: void <b>mpfr_custom_init_set</b> (<var>mpfr_t x, int kind, mp_exp_t exp, mp_prec_t prec, void *significand</var>)<var><a name="index-mpfr_005fcustom_005finit_005fset-297"></a></var><br>
-<blockquote><p>Perform a dummy initialization of a <code>mpfr_t</code> and set it to:
- <ul>
-<li>if <code>ABS(kind) == MPFR_NAN_KIND</code>, <var>x</var> is set to NaN;
-<li>if <code>ABS(kind) == MPFR_INF_KIND</code>, <var>x</var> is set to the infinity
-of sign <code>sign(kind)</code>;
-<li>if <code>ABS(kind) == MPFR_ZERO_KIND</code>, <var>x</var> is set to the zero of
-sign <code>sign(kind)</code>;
-<li>if <code>ABS(kind) == MPFR_REGULAR_KIND</code>, <var>x</var> is set to a regular
-number: <code>x = sign(kind)*significand*2^exp</code>
-</ul>
- In all cases, it uses <var>significand</var> directly for further computing
-involving <var>x</var>. It will not allocate anything.
-A FP number initialized with this function cannot be resized using
-<code>mpfr_set_prec</code>, or cleared using <code>mpfr_clear</code>!
-<var>significand</var> must have been initialized with <code>mpfr_custom_init</code>
-using the same precision <var>prec</var>.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: int <b>mpfr_custom_get_kind</b> (<var>mpfr_t x</var>)<var><a name="index-mpfr_005fcustom_005fget_005fkind-298"></a></var><br>
-<blockquote><p>Return the current kind of a <code>mpfr_t</code> as used by
-<code>mpfr_custom_init_set</code>.
-The behavior of this function for any <code>mpfr_t</code> not initialized
-with <code>mpfr_custom_init_set</code> is undefined.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: void * <b>mpfr_custom_get_mantissa</b> (<var>mpfr_t x</var>)<var><a name="index-mpfr_005fcustom_005fget_005fmantissa-299"></a></var><br>
-<blockquote><p>Return a pointer to the significand used by a <code>mpfr_t</code> initialized with
-<code>mpfr_custom_init_set</code>.
-The behavior of this function for any <code>mpfr_t</code> not initialized
-with <code>mpfr_custom_init_set</code> is undefined.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: mp_exp_t <b>mpfr_custom_get_exp</b> (<var>mpfr_t x</var>)<var><a name="index-mpfr_005fcustom_005fget_005fexp-300"></a></var><br>
-<blockquote><p>Return the exponent of <var>x</var>, assuming that <var>x</var> is a non-zero ordinary
-number. The return value for NaN, Infinity or Zero is unspecified but doesn't
-produce any trap.
-The behavior of this function for any <code>mpfr_t</code> not initialized
-with <code>mpfr_custom_init_set</code> is undefined.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: void <b>mpfr_custom_move</b> (<var>mpfr_t x, void *new_position</var>)<var><a name="index-mpfr_005fcustom_005fmove-301"></a></var><br>
-<blockquote><p>Inform MPFR that the significand has moved due to a garbage collect
-and update its new position to <code>new_position</code>.
-However the application has to move the significand and the <code>mpfr_t</code>
-itself.
-The behavior of this function for any <code>mpfr_t</code> not initialized
-with <code>mpfr_custom_init_set</code> is undefined.
-</p></blockquote></div>
-
- <p>See the test suite for examples.
-
-<div class="node">
-<p><hr>
-<a name="Internals"></a>
-Previous: <a rel="previous" accesskey="p" href="#Custom-Interface">Custom Interface</a>,
-Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
-
-</div>
-
- <p><a name="index-Internals-302"></a>
-
-<h3 class="section">5.16 Internals</h3>
-
-<p>The following types and
-functions were mainly designed for the implementation of MPFR,
-but may be useful for users too.
-However no upward compatibility is guaranteed.
-You may need to include <samp><span class="file">mpfr-impl.h</span></samp> to use them.
-
- <p>The <code>mpfr_t</code> type consists of four fields.
-
- <ul>
-<li>The <code>_mpfr_prec</code> field is used to store the precision of
-the variable (in bits); this is not less than <code>MPFR_PREC_MIN</code>.
-
- <li>The <code>_mpfr_sign</code> field is used to store the sign of the variable.
-
- <li>The <code>_mpfr_exp</code> field stores the exponent.
-An exponent of 0 means a radix point just above the most significant
-limb. Non-zero values n are a multiplier 2^n relative to that
-point.
-A NaN, an infinity and a zero are indicated by a special value of the exponent.
-
- <li>Finally, the <code>_mpfr_d</code> is a pointer to the limbs, least
-significant limbs stored first.
-The number of limbs in use is controlled by <code>_mpfr_prec</code>, namely
-ceil(<code>_mpfr_prec</code>/<code>mp_bits_per_limb</code>).
-Non-singular values always have the most significant bit of the most
-significant limb set to 1. When the precision does not correspond to a
-whole number of limbs, the excess bits at the low end of the data are zero.
-
- </ul>
-
-<!-- @deftypefun int mpfr_add_one_ulp (mpfr_t @var{x}, mp_rnd_t @var{rnd}) -->
-<!-- Add one unit in last place (ulp) to @var{x} if @var{x} is finite -->
-<!-- and positive, subtract one ulp if @var{x} is finite and negative; -->
-<!-- otherwise, @var{x} is not changed. -->
-<!-- The return value is zero unless an overflow occurs, in which case the -->
-<!-- @code{mpfr_add_one_ulp} function behaves like a conventional addition. -->
-<!-- @end deftypefun -->
-<!-- @deftypefun int mpfr_sub_one_ulp (mpfr_t @var{x}, mp_rnd_t @var{rnd}) -->
-<!-- Subtract one ulp to @var{x} if @var{x} is finite and positive, add one -->
-<!-- ulp if @var{x} is finite and negative; otherwise, @var{x} is not changed. -->
-<!-- The return value is zero unless an underflow occurs, in which case the -->
-<!-- @code{mpfr_sub_one_ulp} function behaves like a conventional subtraction. -->
-<!-- @end deftypefun -->
-<div class="defun">
-— Function: int <b>mpfr_can_round</b> (<var>mpfr_t b, mp_exp_t err, mp_rnd_t rnd1, mp_rnd_t rnd2, mp_prec_t prec</var>)<var><a name="index-mpfr_005fcan_005fround-303"></a></var><br>
-<blockquote><p>Assuming <var>b</var> is an approximation of an unknown number
-<var>x</var> in the direction <var>rnd1</var> with error at most two to the power
-E(b)-<var>err</var> where E(b) is the exponent of <var>b</var>, return a non-zero
-value if one is able to round correctly <var>x</var> to precision
-<var>prec</var> with the direction <var>rnd2</var>,
-and 0 otherwise (including for NaN and Inf).
-This function <strong>does not modify</strong> its arguments.
-
- <p>Note: if one wants to also determine the correct ternary value when rounding
-<var>b</var> to precision <var>prec</var>, a useful trick is the following:
-<pre class="verbatim">
- if (mpfr_can_round (b, err, rnd1, GMP_RNDZ, prec + (rnd2 == GMP_RNDN)))
- ...
-</pre>
-Indeed, if <var>rnd2</var> is <code>GMP_RNDN</code>, this will check if one can
-round to <var>prec</var>+1 bits with a directed rounding:
-if so, one can surely round to nearest to <var>prec</var> bits,
-and in addition one can determine the correct ternary value, which would not
-be the case when <var>b</var> is near from a value exactly representable on
-<var>prec</var> bits.
-</p></blockquote></div>
-
-<div class="defun">
-— Function: double <b>mpfr_get_d1</b> (<var>mpfr_t op</var>)<var><a name="index-mpfr_005fget_005fd1-304"></a></var><br>
-<blockquote><p>Convert <var>op</var> to a <code>double</code>, using the default MPFR rounding mode
-(see function <code>mpfr_set_default_rounding_mode</code>). This function is
-obsolete.
-</p></blockquote></div>
-
-<!-- @deftypefun void mpfr_set_str_binary (mpfr_t @var{x}, const char *@var{s}) -->
-<!-- Set @var{x} to the value of the binary number in string @var{s}, which has to -->
-<!-- be of the -->
-<!-- form +/-xxxx.xxxxxxEyy. The exponent is read in decimal, but is interpreted -->
-<!-- as the power of two to be multiplied by the significand. -->
-<!-- The significand length of @var{s} has to be less or equal to the precision -->
-<!-- of @var{x}, otherwise an error occurs. -->
-<!-- If @var{s} starts with @code{N}, it is interpreted as NaN (Not-a-Number); -->
-<!-- if it starts with @code{I} after the sign, it is interpreted as infinity, -->
-<!-- with the corresponding sign. -->
-<!-- @end deftypefun -->
-<!-- @deftypefun void mpfr_print_binary (mpfr_t @var{float}) -->
-<!-- Output @var{float} on stdout -->
-<!-- in raw binary format (the exponent is written in decimal, yet). -->
-<!-- @end deftypefun -->
-<div class="node">
-<p><hr>
-<a name="Contributors"></a>
-Next: <a rel="next" accesskey="n" href="#References">References</a>,
-Previous: <a rel="previous" accesskey="p" href="#MPFR-Interface">MPFR Interface</a>,
-Up: <a rel="up" accesskey="u" href="#Top">Top</a>
-
-</div>
-
-<!-- node-name, next, previous, up -->
-<h2 class="unnumbered">Contributors</h2>
-
-<p>The main developers of MPFR are Guillaume Hanrot, Vincent Lefèvre,
-Patrick Pélissier, Philippe Théveny and Paul Zimmermann.
-
- <p>Sylvie Boldo from ENS-Lyon, France,
-contributed the functions <code>mpfr_agm</code> and <code>mpfr_log</code>.
-Emmanuel Jeandel, from ENS-Lyon too,
-contributed the generic hypergeometric code in
-<code>generic.c</code>, as well as the <code>mpfr_exp3</code>,
-a first implementation of the sine and cosine,
-and improved versions of
-<code>mpfr_const_log2</code> and <code>mpfr_const_pi</code>.
-Mathieu Dutour contributed the functions <code>mpfr_atan</code> and <code>mpfr_asin</code>,
-and a previous version of <code>mpfr_gamma</code>;
-David Daney contributed the hyperbolic and inverse hyperbolic functions,
-the base-2 exponential, and the factorial function. Fabrice Rouillier
-contributed the original version of <samp><span class="file">mul_ui.c</span></samp>, the <samp><span class="file">gmp_op.c</span></samp>
-file, and helped to the Microsoft Windows porting.
-Jean-Luc Rémy contributed the <code>mpfr_zeta</code> code.
-Ludovic Meunier helped in the design of the <code>mpfr_erf</code> code.
-Damien Stehlé contributed the <code>mpfr_get_ld_2exp</code> function.
-
- <p>We would like to thank Jean-Michel Muller and Joris van der Hoeven for very
-fruitful discussions at the beginning of that project, Torbjörn Granlund
-and Kevin Ryde for their help about design issues,
-and Nathalie Revol for her careful reading of a previous version of
-this documentation.
-Kevin Ryde did a tremendous job for the portability of MPFR in 2002-2004.
-
- <p>The development of the MPFR library would not have been possible without
-the continuous support of INRIA, and of the LORIA (Nancy, France) and LIP
-(Lyon, France) laboratories. In particular the main authors were or are
-members of the PolKA, Spaces, Cacao project-teams at LORIA and of the
-Arenaire project-team at LIP.
-This project was started during the Fiable (reliable in French) action
-supported by INRIA, and continued during the AOC action.
-The development of MPFR was also supported by a grant
-(202F0659 00 MPN 121) from the Conseil Régional de Lorraine in 2002,
-and from INRIA by an "associate engineer" grant (2003-2005)
-and an "opération de développement logiciel" grant (2007-2009).
-
-<div class="node">
-<p><hr>
-<a name="References"></a>
-Next: <a rel="next" accesskey="n" href="#GNU-Free-Documentation-License">GNU Free Documentation License</a>,
-Previous: <a rel="previous" accesskey="p" href="#Contributors">Contributors</a>,
-Up: <a rel="up" accesskey="u" href="#Top">Top</a>
-
-</div>
-
-<!-- node-name, next, previous, up -->
-<h2 class="unnumbered">References</h2>
-
- <ul>
-<li>Laurent Fousse, Guillaume Hanrot, Vincent Lefèvre,
-Patrick Pélissier and Paul Zimmermann,
-"MPFR: A Multiple-Precision Binary Floating-Point Library With Correct Rounding",
-ACM Transactions on Mathematical Software,
-volume 33, issue 2, article 13, 15 pages, 2007,
-<a href="http://doi.acm.org/10.1145/1236463.1236468">http://doi.acm.org/10.1145/1236463.1236468</a>.
-
- <li>Torbjörn Granlund, "GNU MP: The GNU Multiple Precision Arithmetic Library",
- version 4.2.2, 2007, <a href="http://gmplib.org">http://gmplib.org</a>.
-
- <li>IEEE standard for binary floating-point arithmetic, Technical Report
-ANSI-IEEE Standard 754-1985, New York, 1985.
-Approved March 21, 1985: IEEE Standards Board; approved July 26,
- 1985: American National Standards Institute, 18 pages.
-
- <li>Donald E. Knuth, "The Art of Computer Programming", vol 2,
-"Seminumerical Algorithms", 2nd edition, Addison-Wesley, 1981.
-
- <li>Jean-Michel Muller, "Elementary Functions, Algorithms and Implementation",
-Birkhauser, Boston, 2nd edition, 2006.
-
-</ul>
-
-<div class="node">
-<p><hr>
-<a name="GNU-Free-Documentation-License"></a>
-Next: <a rel="next" accesskey="n" href="#Concept-Index">Concept Index</a>,
-Previous: <a rel="previous" accesskey="p" href="#References">References</a>,
-Up: <a rel="up" accesskey="u" href="#Top">Top</a>
-
-</div>
-
-<h2 class="appendix">Appendix A GNU Free Documentation License</h2>
-
-<p><a name="index-GNU-Free-Documentation-License-305"></a>
-
-<!-- MPFR tweak: Have this in mpfr.texi to help texinfo-mode -->
-<!-- @node GNU Free Documentation License -->
-<!-- @appendixsec GNU Free Documentation License -->
- <p><a name="index-FDL_002c-GNU-Free-Documentation-License-306"></a><div align="center">Version 1.2, November 2002</div>
-
-<pre class="display"> Copyright © 2000,2001,2002 Free Software Foundation, Inc.
- 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA
-
- Everyone is permitted to copy and distribute verbatim copies
- of this license document, but changing it is not allowed.
-</pre>
- <ol type=1 start=0>
-<li>PREAMBLE
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-functional and useful document <dfn>free</dfn> in the sense of freedom: to
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-Secondarily, this License preserves for the author and publisher a way
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-for modifications made by others.
-
- <p>This License is a kind of “copyleft”, which means that derivative
-works of the document must themselves be free in the same sense. It
-complements the GNU General Public License, which is a copyleft
-license designed for free software.
-
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-program should come with manuals providing the same freedoms that the
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-you may not add another; but you may replace the old one, on explicit
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- <p>The author(s) and publisher(s) of the Document do not by this License
-give permission to use their names for publicity for or to assert or
-imply endorsement of any Modified Version.
-
- <li>COMBINING DOCUMENTS
-
- <p>You may combine the Document with other documents released under this
-License, under the terms defined in section 4 above for modified
-versions, provided that you include in the combination all of the
-Invariant Sections of all of the original documents, unmodified, and
-list them all as Invariant Sections of your combined work in its
-license notice, and that you preserve all their Warranty Disclaimers.
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-multiple identical Invariant Sections may be replaced with a single
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-different contents, make the title of each such section unique by
-adding at the end of it, in parentheses, the name of the original
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-Make the same adjustment to the section titles in the list of
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- <p>In the combination, you must combine any sections Entitled “History”
-in the various original documents, forming one section Entitled
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- <li>COLLECTIONS OF DOCUMENTS
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- <p>You may make a collection consisting of the Document and other documents
-released under this License, and replace the individual copies of this
-License in the various documents with a single copy that is included in
-the collection, provided that you follow the rules of this License for
-verbatim copying of each of the documents in all other respects.
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- <p>You may extract a single document from such a collection, and distribute
-it individually under this License, provided you insert a copy of this
-License into the extracted document, and follow this License in all
-other respects regarding verbatim copying of that document.
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- <li>AGGREGATION WITH INDEPENDENT WORKS
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- <p>A compilation of the Document or its derivatives with other separate
-and independent documents or works, in or on a volume of a storage or
-distribution medium, is called an “aggregate” if the copyright
-resulting from the compilation is not used to limit the legal rights
-of the compilation's users beyond what the individual works permit.
-When the Document is included in an aggregate, this License does not
-apply to the other works in the aggregate which are not themselves
-derivative works of the Document.
-
- <p>If the Cover Text requirement of section 3 is applicable to these
-copies of the Document, then if the Document is less than one half of
-the entire aggregate, the Document's Cover Texts may be placed on
-covers that bracket the Document within the aggregate, or the
-electronic equivalent of covers if the Document is in electronic form.
-Otherwise they must appear on printed covers that bracket the whole
-aggregate.
-
- <li>TRANSLATION
-
- <p>Translation is considered a kind of modification, so you may
-distribute translations of the Document under the terms of section 4.
-Replacing Invariant Sections with translations requires special
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-original versions of these Invariant Sections. You may include a
-translation of this License, and all the license notices in the
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-the original English version of this License and the original versions
-of those notices and disclaimers. In case of a disagreement between
-the translation and the original version of this License or a notice
-or disclaimer, the original version will prevail.
-
- <p>If a section in the Document is Entitled “Acknowledgements”,
-“Dedications”, or “History”, the requirement (section 4) to Preserve
-its Title (section 1) will typically require changing the actual
-title.
-
- <li>TERMINATION
-
- <p>You may not copy, modify, sublicense, or distribute the Document except
-as expressly provided for under this License. Any other attempt to
-copy, modify, sublicense or distribute the Document is void, and will
-automatically terminate your rights under this License. However,
-parties who have received copies, or rights, from you under this
-License will not have their licenses terminated so long as such
-parties remain in full compliance.
-
- <li>FUTURE REVISIONS OF THIS LICENSE
-
- <p>The Free Software Foundation may publish new, revised versions
-of the GNU Free Documentation License from time to time. Such new
-versions will be similar in spirit to the present version, but may
-differ in detail to address new problems or concerns. See
-<a href="http://www.gnu.org/copyleft/">http://www.gnu.org/copyleft/</a>.
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- <p>Each version of the License is given a distinguishing version number.
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-Free Software Foundation. If the Document does not specify a version
-number of this License, you may choose any version ever published (not
-as a draft) by the Free Software Foundation.
- </ol>
-
-<!-- MPFR tweak: Use @appendixsec -->
-<!-- @appendixsubsec ADDENDUM: How to use this License for your documents -->
-<h3 class="appendixsec">A.1 ADDENDUM: How to use this License for your documents</h3>
-
-<p>To use this License in a document you have written, include a copy of
-the License in the document and put the following copyright and
-license notices just after the title page:
-
-<pre class="smallexample"> Copyright (C) <var>year</var> <var>your name</var>.
- Permission is granted to copy, distribute and/or modify this document
- under the terms of the GNU Free Documentation License, Version 1.2
- or any later version published by the Free Software Foundation;
- with no Invariant Sections, no Front-Cover Texts, and no Back-Cover
- Texts. A copy of the license is included in the section entitled ``GNU
- Free Documentation License''.
-</pre>
- <p>If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts,
-replace the “with...Texts.” line with this:
-
-<pre class="smallexample"> with the Invariant Sections being <var>list their titles</var>, with
- the Front-Cover Texts being <var>list</var>, and with the Back-Cover Texts
- being <var>list</var>.
-</pre>
- <p>If you have Invariant Sections without Cover Texts, or some other
-combination of the three, merge those two alternatives to suit the
-situation.
-
- <p>If your document contains nontrivial examples of program code, we
-recommend releasing these examples in parallel under your choice of
-free software license, such as the GNU General Public License,
-to permit their use in free software.
-
-<!-- Local Variables: -->
-<!-- ispell-local-pdict: "ispell-dict" -->
-<!-- End: -->
-<div class="node">
-<p><hr>
-<a name="Concept-Index"></a>
-Next: <a rel="next" accesskey="n" href="#Function-Index">Function Index</a>,
-Previous: <a rel="previous" accesskey="p" href="#GNU-Free-Documentation-License">GNU Free Documentation License</a>,
-Up: <a rel="up" accesskey="u" href="#Top">Top</a>
-
-</div>
-
-<!-- node-name, next, previous, up -->
-<h2 class="unnumbered">Concept Index</h2>
-
-<ul class="index-cp" compact>
-<li><a href="#index-Accuracy-21">Accuracy</a>: <a href="#MPFR-Interface">MPFR Interface</a></li>
-<li><a href="#index-Advanced-functions-283">Advanced functions</a>: <a href="#Advanced-Functions">Advanced Functions</a></li>
-<li><a href="#index-Arithmetic-functions-86">Arithmetic functions</a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-Assignment-functions-30">Assignment functions</a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
-<li><a href="#index-Basic-arithmetic-functions-84">Basic arithmetic functions</a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-Combined-initialization-and-assignment-functions-51">Combined initialization and assignment functions</a>: <a href="#Combined-Initialization-and-Assignment-Functions">Combined Initialization and Assignment Functions</a></li>
-<li><a href="#index-Comparison-functions-130">Comparison functions</a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
-<li><a href="#index-Compatibility-with-MPF-288">Compatibility with MPF</a>: <a href="#Compatibility-with-MPF">Compatibility with MPF</a></li>
-<li><a href="#index-Conditions-for-copying-MPFR-2">Conditions for copying MPFR</a>: <a href="#Copying">Copying</a></li>
-<li><a href="#index-Conversion-functions-61">Conversion functions</a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
-<li><a href="#index-Copying-conditions-1">Copying conditions</a>: <a href="#Copying">Copying</a></li>
-<li><a href="#index-Custom-interface-294">Custom interface</a>: <a href="#Custom-Interface">Custom Interface</a></li>
-<li><a href="#index-Exception-related-functions-256">Exception related functions</a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
-<li><a href="#index-FDL_002c-GNU-Free-Documentation-License-306">FDL, GNU Free Documentation License</a>: <a href="#GNU-Free-Documentation-License">GNU Free Documentation License</a></li>
-<li><a href="#index-Float-arithmetic-functions-85">Float arithmetic functions</a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-Float-comparisons-functions-129">Float comparisons functions</a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
-<li><a href="#index-Float-functions-19">Float functions</a>: <a href="#MPFR-Interface">MPFR Interface</a></li>
-<li><a href="#index-Float-input-and-output-functions-208">Float input and output functions</a>: <a href="#Input-and-Output-Functions">Input and Output Functions</a></li>
-<li><a href="#index-Floating_002dpoint-functions-18">Floating-point functions</a>: <a href="#MPFR-Interface">MPFR Interface</a></li>
-<li><a href="#index-Floating_002dpoint-number-11">Floating-point number</a>: <a href="#MPFR-Basics">MPFR Basics</a></li>
-<li><a href="#index-GNU-Free-Documentation-License-305">GNU Free Documentation License</a>: <a href="#GNU-Free-Documentation-License">GNU Free Documentation License</a></li>
-<li><a href="#index-I_002fO-functions-211">I/O functions</a>: <a href="#Input-and-Output-Functions">Input and Output Functions</a></li>
-<li><a href="#index-Initialization-functions-22">Initialization functions</a>: <a href="#Initialization-Functions">Initialization Functions</a></li>
-<li><a href="#index-Input-functions-209">Input functions</a>: <a href="#Input-and-Output-Functions">Input and Output Functions</a></li>
-<li><a href="#index-Installation-3">Installation</a>: <a href="#Installing-MPFR">Installing MPFR</a></li>
-<li><a href="#index-Integer-related-functions-214">Integer related functions</a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li>
-<li><a href="#index-Internals-302">Internals</a>: <a href="#Internals">Internals</a></li>
-<li><a href="#index-g_t_0040code_007blibmpfr_007d-9"><code>libmpfr</code></a>: <a href="#MPFR-Basics">MPFR Basics</a></li>
-<li><a href="#index-Libraries-7">Libraries</a>: <a href="#MPFR-Basics">MPFR Basics</a></li>
-<li><a href="#index-Libtool-10">Libtool</a>: <a href="#MPFR-Basics">MPFR Basics</a></li>
-<li><a href="#index-Limb-17">Limb</a>: <a href="#MPFR-Basics">MPFR Basics</a></li>
-<li><a href="#index-Linking-8">Linking</a>: <a href="#MPFR-Basics">MPFR Basics</a></li>
-<li><a href="#index-Miscellaneous-float-functions-228">Miscellaneous float functions</a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
-<li><a href="#index-g_t_0040file_007bmpfr_002eh_007d-5"><samp><span class="file">mpfr.h</span></samp></a>: <a href="#MPFR-Basics">MPFR Basics</a></li>
-<li><a href="#index-Output-functions-210">Output functions</a>: <a href="#Input-and-Output-Functions">Input and Output Functions</a></li>
-<li><a href="#index-Precision-20">Precision</a>: <a href="#MPFR-Interface">MPFR Interface</a></li>
-<li><a href="#index-Precision-13">Precision</a>: <a href="#MPFR-Basics">MPFR Basics</a></li>
-<li><a href="#index-Reporting-bugs-4">Reporting bugs</a>: <a href="#Reporting-Bugs">Reporting Bugs</a></li>
-<li><a href="#index-Rounding-mode-related-functions-250">Rounding mode related functions</a>: <a href="#Rounding-Mode-Related-Functions">Rounding Mode Related Functions</a></li>
-<li><a href="#index-Rounding-Modes-15">Rounding Modes</a>: <a href="#MPFR-Basics">MPFR Basics</a></li>
-<li><a href="#index-Special-functions-154">Special functions</a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-g_t_0040code_007bstdio_002eh_007d-6"><code>stdio.h</code></a>: <a href="#MPFR-Basics">MPFR Basics</a></li>
-</ul><div class="node">
-<p><hr>
-<a name="Function-Index"></a>
-Previous: <a rel="previous" accesskey="p" href="#Concept-Index">Concept Index</a>,
-Up: <a rel="up" accesskey="u" href="#Top">Top</a>
-
-</div>
-
-<!-- node-name, next, previous, up -->
-<h2 class="unnumbered">Function and Type Index</h2>
-
-
-
-<ul class="index-fn" compact>
-<li><a href="#index-g_t_0040code_007bmp_005fprec_005ft_007d-14"><code>mp_prec_t</code></a>: <a href="#MPFR-Basics">MPFR Basics</a></li>
-<li><a href="#index-g_t_0040code_007bmp_005frnd_005ft_007d-16"><code>mp_rnd_t</code></a>: <a href="#MPFR-Basics">MPFR Basics</a></li>
-<li><a href="#index-mpfr_005fabs-123"><code>mpfr_abs</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005facos-168"><code>mpfr_acos</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005facosh-178"><code>mpfr_acosh</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fadd-87"><code>mpfr_add</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fadd_005fq-91"><code>mpfr_add_q</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fadd_005fsi-89"><code>mpfr_add_si</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fadd_005fui-88"><code>mpfr_add_ui</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fadd_005fz-90"><code>mpfr_add_z</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fagm-200"><code>mpfr_agm</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fasin-169"><code>mpfr_asin</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fasinh-179"><code>mpfr_asinh</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fatan-170"><code>mpfr_atan</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fatan2-171"><code>mpfr_atan2</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fatanh-180"><code>mpfr_atanh</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fcan_005fround-303"><code>mpfr_can_round</code></a>: <a href="#Internals">Internals</a></li>
-<li><a href="#index-mpfr_005fcbrt-114"><code>mpfr_cbrt</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fceil-216"><code>mpfr_ceil</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li>
-<li><a href="#index-mpfr_005fcheck_005frange-265"><code>mpfr_check_range</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
-<li><a href="#index-mpfr_005fclear-24"><code>mpfr_clear</code></a>: <a href="#Initialization-Functions">Initialization Functions</a></li>
-<li><a href="#index-mpfr_005fclear_005ferangeflag-271"><code>mpfr_clear_erangeflag</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
-<li><a href="#index-mpfr_005fclear_005fflags-277"><code>mpfr_clear_flags</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
-<li><a href="#index-mpfr_005fclear_005finexflag-270"><code>mpfr_clear_inexflag</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
-<li><a href="#index-mpfr_005fclear_005fnanflag-269"><code>mpfr_clear_nanflag</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
-<li><a href="#index-mpfr_005fclear_005foverflow-268"><code>mpfr_clear_overflow</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
-<li><a href="#index-mpfr_005fclear_005funderflow-267"><code>mpfr_clear_underflow</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
-<li><a href="#index-mpfr_005fclears-287"><code>mpfr_clears</code></a>: <a href="#Advanced-Functions">Advanced Functions</a></li>
-<li><a href="#index-mpfr_005fcmp-131"><code>mpfr_cmp</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
-<li><a href="#index-mpfr_005fcmp_005fd-134"><code>mpfr_cmp_d</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
-<li><a href="#index-mpfr_005fcmp_005ff-138"><code>mpfr_cmp_f</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
-<li><a href="#index-mpfr_005fcmp_005fld-135"><code>mpfr_cmp_ld</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
-<li><a href="#index-mpfr_005fcmp_005fq-137"><code>mpfr_cmp_q</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
-<li><a href="#index-mpfr_005fcmp_005fsi-133"><code>mpfr_cmp_si</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
-<li><a href="#index-mpfr_005fcmp_005fsi_005f2exp-140"><code>mpfr_cmp_si_2exp</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
-<li><a href="#index-mpfr_005fcmp_005fui-132"><code>mpfr_cmp_ui</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
-<li><a href="#index-mpfr_005fcmp_005fui_005f2exp-139"><code>mpfr_cmp_ui_2exp</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
-<li><a href="#index-mpfr_005fcmp_005fz-136"><code>mpfr_cmp_z</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
-<li><a href="#index-mpfr_005fcmpabs-141"><code>mpfr_cmpabs</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
-<li><a href="#index-mpfr_005fconst_005fcatalan-205"><code>mpfr_const_catalan</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fconst_005feuler-204"><code>mpfr_const_euler</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fconst_005flog2-202"><code>mpfr_const_log2</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fconst_005fpi-203"><code>mpfr_const_pi</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fcopysign-241"><code>mpfr_copysign</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
-<li><a href="#index-mpfr_005fcos-161"><code>mpfr_cos</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fcosh-172"><code>mpfr_cosh</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fcot-166"><code>mpfr_cot</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fcoth-177"><code>mpfr_coth</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fcsc-165"><code>mpfr_csc</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fcsch-176"><code>mpfr_csch</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fcustom_005fget_005fexp-300"><code>mpfr_custom_get_exp</code></a>: <a href="#Custom-Interface">Custom Interface</a></li>
-<li><a href="#index-mpfr_005fcustom_005fget_005fkind-298"><code>mpfr_custom_get_kind</code></a>: <a href="#Custom-Interface">Custom Interface</a></li>
-<li><a href="#index-mpfr_005fcustom_005fget_005fmantissa-299"><code>mpfr_custom_get_mantissa</code></a>: <a href="#Custom-Interface">Custom Interface</a></li>
-<li><a href="#index-mpfr_005fcustom_005fget_005fsize-295"><code>mpfr_custom_get_size</code></a>: <a href="#Custom-Interface">Custom Interface</a></li>
-<li><a href="#index-mpfr_005fcustom_005finit-296"><code>mpfr_custom_init</code></a>: <a href="#Custom-Interface">Custom Interface</a></li>
-<li><a href="#index-mpfr_005fcustom_005finit_005fset-297"><code>mpfr_custom_init_set</code></a>: <a href="#Custom-Interface">Custom Interface</a></li>
-<li><a href="#index-mpfr_005fcustom_005fmove-301"><code>mpfr_custom_move</code></a>: <a href="#Custom-Interface">Custom Interface</a></li>
-<li><a href="#index-MPFR_005fDECL_005fINIT-284"><code>MPFR_DECL_INIT</code></a>: <a href="#Advanced-Functions">Advanced Functions</a></li>
-<li><a href="#index-mpfr_005fdim-124"><code>mpfr_dim</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fdiv-105"><code>mpfr_div</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fdiv_005f2exp-293"><code>mpfr_div_2exp</code></a>: <a href="#Compatibility-with-MPF">Compatibility with MPF</a></li>
-<li><a href="#index-mpfr_005fdiv_005f2si-128"><code>mpfr_div_2si</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fdiv_005f2ui-127"><code>mpfr_div_2ui</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fdiv_005fq-111"><code>mpfr_div_q</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fdiv_005fsi-109"><code>mpfr_div_si</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fdiv_005fui-107"><code>mpfr_div_ui</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fdiv_005fz-110"><code>mpfr_div_z</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005feint-184"><code>mpfr_eint</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005feq-290"><code>mpfr_eq</code></a>: <a href="#Compatibility-with-MPF">Compatibility with MPF</a></li>
-<li><a href="#index-mpfr_005fequal_005fp-152"><code>mpfr_equal_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
-<li><a href="#index-mpfr_005ferangeflag_005fp-282"><code>mpfr_erangeflag_p</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
-<li><a href="#index-mpfr_005ferf-190"><code>mpfr_erf</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005ferfc-191"><code>mpfr_erfc</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fexp-158"><code>mpfr_exp</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fexp10-160"><code>mpfr_exp10</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fexp2-159"><code>mpfr_exp2</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fexpm1-183"><code>mpfr_expm1</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005ffac_005fui-181"><code>mpfr_fac_ui</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005ffits_005fintmax_005fp-82"><code>mpfr_fits_intmax_p</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
-<li><a href="#index-mpfr_005ffits_005fsint_005fp-79"><code>mpfr_fits_sint_p</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
-<li><a href="#index-mpfr_005ffits_005fslong_005fp-77"><code>mpfr_fits_slong_p</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
-<li><a href="#index-mpfr_005ffits_005fsshort_005fp-81"><code>mpfr_fits_sshort_p</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
-<li><a href="#index-mpfr_005ffits_005fuint_005fp-78"><code>mpfr_fits_uint_p</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
-<li><a href="#index-mpfr_005ffits_005fuintmax_005fp-83"><code>mpfr_fits_uintmax_p</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
-<li><a href="#index-mpfr_005ffits_005fulong_005fp-76"><code>mpfr_fits_ulong_p</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
-<li><a href="#index-mpfr_005ffits_005fushort_005fp-80"><code>mpfr_fits_ushort_p</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
-<li><a href="#index-mpfr_005ffloor-217"><code>mpfr_floor</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li>
-<li><a href="#index-mpfr_005ffma-198"><code>mpfr_fma</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005ffms-199"><code>mpfr_fms</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005ffrac-224"><code>mpfr_frac</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li>
-<li><a href="#index-mpfr_005ffree_005fcache-206"><code>mpfr_free_cache</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005ffree_005fstr-75"><code>mpfr_free_str</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
-<li><a href="#index-mpfr_005fgamma-185"><code>mpfr_gamma</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fget_005fd-62"><code>mpfr_get_d</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
-<li><a href="#index-mpfr_005fget_005fd1-304"><code>mpfr_get_d1</code></a>: <a href="#Internals">Internals</a></li>
-<li><a href="#index-mpfr_005fget_005fd_005f2exp-65"><code>mpfr_get_d_2exp</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
-<li><a href="#index-mpfr_005fget_005fdecimal64-64"><code>mpfr_get_decimal64</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
-<li><a href="#index-mpfr_005fget_005fdefault_005fprec-27"><code>mpfr_get_default_prec</code></a>: <a href="#Initialization-Functions">Initialization Functions</a></li>
-<li><a href="#index-mpfr_005fget_005fdefault_005frounding_005fmode-252"><code>mpfr_get_default_rounding_mode</code></a>: <a href="#Rounding-Mode-Related-Functions">Rounding Mode Related Functions</a></li>
-<li><a href="#index-mpfr_005fget_005femax-258"><code>mpfr_get_emax</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
-<li><a href="#index-mpfr_005fget_005femax_005fmax-264"><code>mpfr_get_emax_max</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
-<li><a href="#index-mpfr_005fget_005femax_005fmin-263"><code>mpfr_get_emax_min</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
-<li><a href="#index-mpfr_005fget_005femin-257"><code>mpfr_get_emin</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
-<li><a href="#index-mpfr_005fget_005femin_005fmax-262"><code>mpfr_get_emin_max</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
-<li><a href="#index-mpfr_005fget_005femin_005fmin-261"><code>mpfr_get_emin_min</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
-<li><a href="#index-mpfr_005fget_005fexp-237"><code>mpfr_get_exp</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
-<li><a href="#index-mpfr_005fget_005ff-73"><code>mpfr_get_f</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
-<li><a href="#index-mpfr_005fget_005fld-63"><code>mpfr_get_ld</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
-<li><a href="#index-mpfr_005fget_005fld_005f2exp-66"><code>mpfr_get_ld_2exp</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
-<li><a href="#index-mpfr_005fget_005fpatches-249"><code>mpfr_get_patches</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
-<li><a href="#index-mpfr_005fget_005fprec-29"><code>mpfr_get_prec</code></a>: <a href="#Initialization-Functions">Initialization Functions</a></li>
-<li><a href="#index-mpfr_005fget_005fsi-67"><code>mpfr_get_si</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
-<li><a href="#index-mpfr_005fget_005fsj-69"><code>mpfr_get_sj</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
-<li><a href="#index-mpfr_005fget_005fstr-74"><code>mpfr_get_str</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
-<li><a href="#index-mpfr_005fget_005fui-68"><code>mpfr_get_ui</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
-<li><a href="#index-mpfr_005fget_005fuj-70"><code>mpfr_get_uj</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
-<li><a href="#index-mpfr_005fget_005fversion-242"><code>mpfr_get_version</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
-<li><a href="#index-mpfr_005fget_005fz-72"><code>mpfr_get_z</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
-<li><a href="#index-mpfr_005fget_005fz_005fexp-71"><code>mpfr_get_z_exp</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
-<li><a href="#index-mpfr_005fgreater_005fp-147"><code>mpfr_greater_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
-<li><a href="#index-mpfr_005fgreaterequal_005fp-148"><code>mpfr_greaterequal_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
-<li><a href="#index-mpfr_005fhypot-201"><code>mpfr_hypot</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005finexflag_005fp-281"><code>mpfr_inexflag_p</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
-<li><a href="#index-mpfr_005finf_005fp-143"><code>mpfr_inf_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
-<li><a href="#index-mpfr_005finit-25"><code>mpfr_init</code></a>: <a href="#Initialization-Functions">Initialization Functions</a></li>
-<li><a href="#index-mpfr_005finit2-23"><code>mpfr_init2</code></a>: <a href="#Initialization-Functions">Initialization Functions</a></li>
-<li><a href="#index-mpfr_005finit_005fset-52"><code>mpfr_init_set</code></a>: <a href="#Combined-Initialization-and-Assignment-Functions">Combined Initialization and Assignment Functions</a></li>
-<li><a href="#index-mpfr_005finit_005fset_005fd-55"><code>mpfr_init_set_d</code></a>: <a href="#Combined-Initialization-and-Assignment-Functions">Combined Initialization and Assignment Functions</a></li>
-<li><a href="#index-mpfr_005finit_005fset_005ff-59"><code>mpfr_init_set_f</code></a>: <a href="#Combined-Initialization-and-Assignment-Functions">Combined Initialization and Assignment Functions</a></li>
-<li><a href="#index-mpfr_005finit_005fset_005fld-56"><code>mpfr_init_set_ld</code></a>: <a href="#Combined-Initialization-and-Assignment-Functions">Combined Initialization and Assignment Functions</a></li>
-<li><a href="#index-mpfr_005finit_005fset_005fq-58"><code>mpfr_init_set_q</code></a>: <a href="#Combined-Initialization-and-Assignment-Functions">Combined Initialization and Assignment Functions</a></li>
-<li><a href="#index-mpfr_005finit_005fset_005fsi-54"><code>mpfr_init_set_si</code></a>: <a href="#Combined-Initialization-and-Assignment-Functions">Combined Initialization and Assignment Functions</a></li>
-<li><a href="#index-mpfr_005finit_005fset_005fstr-60"><code>mpfr_init_set_str</code></a>: <a href="#Combined-Initialization-and-Assignment-Functions">Combined Initialization and Assignment Functions</a></li>
-<li><a href="#index-mpfr_005finit_005fset_005fui-53"><code>mpfr_init_set_ui</code></a>: <a href="#Combined-Initialization-and-Assignment-Functions">Combined Initialization and Assignment Functions</a></li>
-<li><a href="#index-mpfr_005finit_005fset_005fz-57"><code>mpfr_init_set_z</code></a>: <a href="#Combined-Initialization-and-Assignment-Functions">Combined Initialization and Assignment Functions</a></li>
-<li><a href="#index-mpfr_005finits-285"><code>mpfr_inits</code></a>: <a href="#Advanced-Functions">Advanced Functions</a></li>
-<li><a href="#index-mpfr_005finits2-286"><code>mpfr_inits2</code></a>: <a href="#Advanced-Functions">Advanced Functions</a></li>
-<li><a href="#index-mpfr_005finp_005fstr-213"><code>mpfr_inp_str</code></a>: <a href="#Input-and-Output-Functions">Input and Output Functions</a></li>
-<li><a href="#index-mpfr_005finteger_005fp-227"><code>mpfr_integer_p</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li>
-<li><a href="#index-mpfr_005fj0-192"><code>mpfr_j0</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fj1-193"><code>mpfr_j1</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fjn-194"><code>mpfr_jn</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fless_005fp-149"><code>mpfr_less_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
-<li><a href="#index-mpfr_005flessequal_005fp-150"><code>mpfr_lessequal_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
-<li><a href="#index-mpfr_005flessgreater_005fp-151"><code>mpfr_lessgreater_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
-<li><a href="#index-mpfr_005flgamma-187"><code>mpfr_lgamma</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005flngamma-186"><code>mpfr_lngamma</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005flog-155"><code>mpfr_log</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005flog10-157"><code>mpfr_log10</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005flog1p-182"><code>mpfr_log1p</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005flog2-156"><code>mpfr_log2</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fmax-233"><code>mpfr_max</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
-<li><a href="#index-mpfr_005fmin-232"><code>mpfr_min</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
-<li><a href="#index-mpfr_005fmul-99"><code>mpfr_mul</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fmul_005f2exp-292"><code>mpfr_mul_2exp</code></a>: <a href="#Compatibility-with-MPF">Compatibility with MPF</a></li>
-<li><a href="#index-mpfr_005fmul_005f2si-126"><code>mpfr_mul_2si</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fmul_005f2ui-125"><code>mpfr_mul_2ui</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fmul_005fq-103"><code>mpfr_mul_q</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fmul_005fsi-101"><code>mpfr_mul_si</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fmul_005fui-100"><code>mpfr_mul_ui</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fmul_005fz-102"><code>mpfr_mul_z</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fnan_005fp-142"><code>mpfr_nan_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
-<li><a href="#index-mpfr_005fnanflag_005fp-280"><code>mpfr_nanflag_p</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
-<li><a href="#index-mpfr_005fneg-122"><code>mpfr_neg</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fnextabove-230"><code>mpfr_nextabove</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
-<li><a href="#index-mpfr_005fnextbelow-231"><code>mpfr_nextbelow</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
-<li><a href="#index-mpfr_005fnexttoward-229"><code>mpfr_nexttoward</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
-<li><a href="#index-mpfr_005fnumber_005fp-144"><code>mpfr_number_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
-<li><a href="#index-mpfr_005fout_005fstr-212"><code>mpfr_out_str</code></a>: <a href="#Input-and-Output-Functions">Input and Output Functions</a></li>
-<li><a href="#index-mpfr_005foverflow_005fp-279"><code>mpfr_overflow_p</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
-<li><a href="#index-mpfr_005fpow-116"><code>mpfr_pow</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fpow_005fsi-118"><code>mpfr_pow_si</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fpow_005fui-117"><code>mpfr_pow_ui</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fpow_005fz-119"><code>mpfr_pow_z</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fprec_005fround-253"><code>mpfr_prec_round</code></a>: <a href="#Rounding-Mode-Related-Functions">Rounding Mode Related Functions</a></li>
-<li><a href="#index-mpfr_005fprint_005frnd_005fmode-255"><code>mpfr_print_rnd_mode</code></a>: <a href="#Rounding-Mode-Related-Functions">Rounding Mode Related Functions</a></li>
-<li><a href="#index-mpfr_005frandom-235"><code>mpfr_random</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
-<li><a href="#index-mpfr_005frandom2-236"><code>mpfr_random2</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
-<li><a href="#index-mpfr_005freldiff-291"><code>mpfr_reldiff</code></a>: <a href="#Compatibility-with-MPF">Compatibility with MPF</a></li>
-<li><a href="#index-mpfr_005fremainder-225"><code>mpfr_remainder</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li>
-<li><a href="#index-mpfr_005fremquo-226"><code>mpfr_remquo</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li>
-<li><a href="#index-mpfr_005frint-215"><code>mpfr_rint</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li>
-<li><a href="#index-mpfr_005frint_005fceil-220"><code>mpfr_rint_ceil</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li>
-<li><a href="#index-mpfr_005frint_005ffloor-221"><code>mpfr_rint_floor</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li>
-<li><a href="#index-mpfr_005frint_005fround-222"><code>mpfr_rint_round</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li>
-<li><a href="#index-mpfr_005frint_005ftrunc-223"><code>mpfr_rint_trunc</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li>
-<li><a href="#index-mpfr_005froot-115"><code>mpfr_root</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fround-218"><code>mpfr_round</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li>
-<li><a href="#index-mpfr_005fround_005fprec-254"><code>mpfr_round_prec</code></a>: <a href="#Rounding-Mode-Related-Functions">Rounding Mode Related Functions</a></li>
-<li><a href="#index-mpfr_005fsec-164"><code>mpfr_sec</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fsech-175"><code>mpfr_sech</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fset-31"><code>mpfr_set</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
-<li><a href="#index-mpfr_005fset_005fd-36"><code>mpfr_set_d</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
-<li><a href="#index-mpfr_005fset_005fdecimal64-38"><code>mpfr_set_decimal64</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
-<li><a href="#index-mpfr_005fset_005fdefault_005fprec-26"><code>mpfr_set_default_prec</code></a>: <a href="#Initialization-Functions">Initialization Functions</a></li>
-<li><a href="#index-mpfr_005fset_005fdefault_005frounding_005fmode-251"><code>mpfr_set_default_rounding_mode</code></a>: <a href="#Rounding-Mode-Related-Functions">Rounding Mode Related Functions</a></li>
-<li><a href="#index-mpfr_005fset_005femax-260"><code>mpfr_set_emax</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
-<li><a href="#index-mpfr_005fset_005femin-259"><code>mpfr_set_emin</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
-<li><a href="#index-mpfr_005fset_005ferangeflag-276"><code>mpfr_set_erangeflag</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
-<li><a href="#index-mpfr_005fset_005fexp-238"><code>mpfr_set_exp</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
-<li><a href="#index-mpfr_005fset_005ff-41"><code>mpfr_set_f</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
-<li><a href="#index-mpfr_005fset_005finexflag-275"><code>mpfr_set_inexflag</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
-<li><a href="#index-mpfr_005fset_005finf-48"><code>mpfr_set_inf</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
-<li><a href="#index-mpfr_005fset_005fld-37"><code>mpfr_set_ld</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
-<li><a href="#index-mpfr_005fset_005fnan-49"><code>mpfr_set_nan</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
-<li><a href="#index-mpfr_005fset_005fnanflag-274"><code>mpfr_set_nanflag</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
-<li><a href="#index-mpfr_005fset_005foverflow-273"><code>mpfr_set_overflow</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
-<li><a href="#index-mpfr_005fset_005fprec-28"><code>mpfr_set_prec</code></a>: <a href="#Initialization-Functions">Initialization Functions</a></li>
-<li><a href="#index-mpfr_005fset_005fprec_005fraw-289"><code>mpfr_set_prec_raw</code></a>: <a href="#Compatibility-with-MPF">Compatibility with MPF</a></li>
-<li><a href="#index-mpfr_005fset_005fq-40"><code>mpfr_set_q</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
-<li><a href="#index-mpfr_005fset_005fsi-33"><code>mpfr_set_si</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
-<li><a href="#index-mpfr_005fset_005fsi_005f2exp-43"><code>mpfr_set_si_2exp</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
-<li><a href="#index-mpfr_005fset_005fsj-35"><code>mpfr_set_sj</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
-<li><a href="#index-mpfr_005fset_005fsj_005f2exp-45"><code>mpfr_set_sj_2exp</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
-<li><a href="#index-mpfr_005fset_005fstr-46"><code>mpfr_set_str</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
-<li><a href="#index-mpfr_005fset_005fui-32"><code>mpfr_set_ui</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
-<li><a href="#index-mpfr_005fset_005fui_005f2exp-42"><code>mpfr_set_ui_2exp</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
-<li><a href="#index-mpfr_005fset_005fuj-34"><code>mpfr_set_uj</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
-<li><a href="#index-mpfr_005fset_005fuj_005f2exp-44"><code>mpfr_set_uj_2exp</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
-<li><a href="#index-mpfr_005fset_005funderflow-272"><code>mpfr_set_underflow</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
-<li><a href="#index-mpfr_005fset_005fz-39"><code>mpfr_set_z</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
-<li><a href="#index-mpfr_005fsetsign-240"><code>mpfr_setsign</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
-<li><a href="#index-mpfr_005fsgn-146"><code>mpfr_sgn</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
-<li><a href="#index-mpfr_005fsi_005fdiv-108"><code>mpfr_si_div</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fsi_005fsub-95"><code>mpfr_si_sub</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fsignbit-239"><code>mpfr_signbit</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
-<li><a href="#index-mpfr_005fsin-162"><code>mpfr_sin</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fsin_005fcos-167"><code>mpfr_sin_cos</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fsinh-173"><code>mpfr_sinh</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fsqr-104"><code>mpfr_sqr</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fsqrt-112"><code>mpfr_sqrt</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fsqrt_005fui-113"><code>mpfr_sqrt_ui</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fstrtofr-47"><code>mpfr_strtofr</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
-<li><a href="#index-mpfr_005fsub-92"><code>mpfr_sub</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fsub_005fq-98"><code>mpfr_sub_q</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fsub_005fsi-96"><code>mpfr_sub_si</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fsub_005fui-94"><code>mpfr_sub_ui</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fsub_005fz-97"><code>mpfr_sub_z</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fsubnormalize-266"><code>mpfr_subnormalize</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
-<li><a href="#index-mpfr_005fsum-207"><code>mpfr_sum</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fswap-50"><code>mpfr_swap</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
-<li><a href="#index-g_t_0040code_007bmpfr_005ft_007d-12"><code>mpfr_t</code></a>: <a href="#MPFR-Basics">MPFR Basics</a></li>
-<li><a href="#index-mpfr_005ftan-163"><code>mpfr_tan</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005ftanh-174"><code>mpfr_tanh</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005ftrunc-219"><code>mpfr_trunc</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li>
-<li><a href="#index-mpfr_005fui_005fdiv-106"><code>mpfr_ui_div</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fui_005fpow-121"><code>mpfr_ui_pow</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fui_005fpow_005fui-120"><code>mpfr_ui_pow_ui</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005fui_005fsub-93"><code>mpfr_ui_sub</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
-<li><a href="#index-mpfr_005funderflow_005fp-278"><code>mpfr_underflow_p</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
-<li><a href="#index-mpfr_005funordered_005fp-153"><code>mpfr_unordered_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
-<li><a href="#index-mpfr_005furandomb-234"><code>mpfr_urandomb</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
-<li><a href="#index-MPFR_005fVERSION-243"><code>MPFR_VERSION</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
-<li><a href="#index-MPFR_005fVERSION_005fMAJOR-244"><code>MPFR_VERSION_MAJOR</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
-<li><a href="#index-MPFR_005fVERSION_005fMINOR-245"><code>MPFR_VERSION_MINOR</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
-<li><a href="#index-MPFR_005fVERSION_005fNUM-248"><code>MPFR_VERSION_NUM</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
-<li><a href="#index-MPFR_005fVERSION_005fPATCHLEVEL-246"><code>MPFR_VERSION_PATCHLEVEL</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
-<li><a href="#index-MPFR_005fVERSION_005fSTRING-247"><code>MPFR_VERSION_STRING</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
-<li><a href="#index-mpfr_005fy0-195"><code>mpfr_y0</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fy1-196"><code>mpfr_y1</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fyn-197"><code>mpfr_yn</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fzero_005fp-145"><code>mpfr_zero_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
-<li><a href="#index-mpfr_005fzeta-188"><code>mpfr_zeta</code></a>: <a href="#Special-Functions">Special Functions</a></li>
-<li><a href="#index-mpfr_005fzeta_005fui-189"><code>mpfr_zeta_ui</code></a>: <a href="#Special-Functions">Special Functions</a></li>
- </ul></body></html>
-
-<!--
-
-Local Variables:
-coding: iso-8859-1
-End:
-
--->
--- a/components/mpfr/mpfr.license Thu Mar 30 08:44:01 2017 -0700
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,902 +0,0 @@
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- GNU Free Documentation License
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-0. PREAMBLE
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-ADDENDUM: How to use this License for your documents
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