usr/share/doc/mpfr/FAQ.html - toolchains/quantenna - Git at Google

 <?xml version="1.0" encoding="iso-8859-1"?>
 <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">

 <!--
 Copyright 2000-2016 Free Software Foundation, Inc.
 Contributed by the AriC and Caramba projects, INRIA.

 This file is part of the GNU MPFR Library.

 The GNU MPFR Library is free software; you can redistribute it and/or modify
 it under the terms of the GNU Lesser General Public License as published by
 the Free Software Foundation; either version 3 of the License, or (at your
 option) any later version.

 The GNU MPFR Library is distributed in the hope that it will be useful, but
 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
 License for more details.

 You should have received a copy of the GNU Lesser General Public License
 along with the GNU MPFR Library; see the file COPYING.LESSER.  If not, see
 http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA.
 -->

 <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">

 <head><meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1" />
 <title>Frequently Asked Questions about GNU MPFR</title>
 <style type="text/css">/*<![CDATA[*/
 /* Global stylesheet for visual media */

 html, body
 {
   background: white;
   color: black;
 }

 div.logo { float: right }
 div.logo img { border: 0 }

 div.footer img { border: 0 }

 dt
 {
   margin-top: 2ex;
   margin-bottom: 1ex;
   font-weight: bolder;
 }

 /* For testing: dd { background: #ddddff } */

 table { margin: 0.5ex auto }

 li { margin-top: 0.5ex; margin-bottom: 0.5ex }

 dd + dd
 {
   margin-top: 0;
   margin-bottom: 0;
   padding-top: 0.5ex;
   padding-bottom: 0;
 }

 li > p, dd > p
 {
   margin-top: 0;
   margin-bottom: 0;
   padding-top: 0.5ex;
   padding-bottom: 0.5ex;
 }

 .block-code code, code.block-code,
 .block-code samp, samp.block-code
 {
   display: block;
   padding: 0.5ex 0;
   margin-left: 2em;
 }

 .nowrap { white-space: nowrap }

 /*
 dl.faq { counter-reset: faq }

 dl.faq dt:before
 {
   counter-increment: faq;
   content: counter(faq) ". ";
 }
 */

 dl.faq dt { background: #dddddd }

 dl.faq dd
 {
   border-left: 4px solid;
   border-color: transparent;
   margin-left: 0em;
   padding-left: 1.5em;
 }

 dl.faq dt:target + dd
 {
   border-left-color: #aaaaaa;
 }

 var.env { font-style: normal }
 /*]]>*/</style>
 </head>

 <body>

 <h1>Frequently Asked Questions about <cite><acronym>GNU</acronym> <acronym>MPFR</acronym></cite></h1>

 <p><strong>Important notice: Problems with a particular version of
 <cite><acronym>MPFR</acronym></cite> are discussed in the corresponding
 bugs page.</strong></p>

 <p>The latest version of this <acronym>FAQ</acronym> is available at
 <a href="http://www.mpfr.org/faq.html">http://www.mpfr.org/faq.html</a>.
 Please look at this version if possible.</p>

 <ol>
 <li><a href="#mpfr_vs_mpf">What are the differences between
 <cite><acronym>MPF</acronym></cite> from <cite><acronym>GMP</acronym></cite>
 and <cite><acronym>MPFR</acronym></cite>?</a></li>
 <li><a href="#mpf2mpfr">How to convert my program written using
 <cite><acronym>MPF</acronym></cite> to
 <cite><acronym>MPFR</acronym></cite>?</a></li>
 <li><a href="#no_libgmp">At configure time, I get the error: <q>libgmp not found or uses a different ABI.</q></a></li>
 <li><a href="#undef_ref1">I get undefined reference to <code>__gmp_get_memory_functions</code>.</a></li>
 <li><a href="#undef_ref2">When I link my program with
 <cite><acronym>MPFR</acronym></cite>, I get undefined reference
 to <code>__gmpXXXX</code>.</a></li>
 <li><a href="#crash_high_prec">My program crashes with high precisions.</a></li>
 <li><a href="#accuracy">Though I have increased the precision, the results
 are not more accurate.</a></li>
 <li><a href="#detect_mpfr">How can I detect <cite><acronym>MPFR</acronym></cite>
 installation using <cite>autoconf</cite> or <cite>pkg-config</cite>?</a></li>
 <li><a href="#cite">How to cite <cite><acronym>MPFR</acronym></cite> in a
 scientific publication?</a></li>
 <li><a href="#fpic">When I build <cite><acronym>MPFR</acronym></cite>, I get
 an error asking me to recompile with <samp>-fPIC</samp>.</a></li>
 </ol>

 <dl class="faq">

 <dt id="mpfr_vs_mpf">1. What are the differences between
 <cite><acronym>MPF</acronym></cite> from <cite><acronym>GMP</acronym></cite>
 and <cite><acronym>MPFR</acronym></cite>?</dt>

 <dd><p>The main differences are:</p>
 <ul>
 <li><p>The precision of a <cite><acronym>MPFR</acronym></cite> variable
 is the <em>exact</em> number of bits used for its mantissa, whereas in
 <cite><acronym>MPF</acronym></cite>, the precision requested by the user
 is a minimum value (<cite><acronym>MPF</acronym></cite> generally uses a
 higher precision). With the additional difference below, this implies that
 the <cite><acronym>MPFR</acronym></cite> results do not depend on the
 number of bits (16, 32, 64 or more) of the underlying architecture.</p></li>
 <li><p>As a consequence, <cite><acronym>MPFR</acronym></cite> uses a
 base-2 exponent, whereas in <cite><acronym>MPF</acronym></cite>, this
 is a base-2<sup>32</sup> or base-2<sup>64</sup> exponent, depending on
 the limb size. For this reason (and other internal ones), the maximum
 exponent range in <cite><acronym>MPFR</acronym></cite> is different
 (and smaller, if the exponent is represented by the same type as in
 <cite><acronym>MPF</acronym></cite>).</p></li>
 <li><p><cite><acronym>MPFR</acronym></cite> provides an additional rounding
 mode argument to its functions; furthermore, it is guaranteed that the
 result of any operation is the nearest possible floating-point value from
 the exact result (considering the input variables as exact values), taking
 into account the precision of the destination variable and the rounding
 mode. <cite><acronym>MPFR</acronym></cite> also says whether the rounded
 result is above or below the exact result.</p></li>
 <li><p><cite><acronym>MPFR</acronym></cite> supports much more functions
 (in particular transcendental functions such as exponentials, logarithms,
 trigonometric functions and so on) and special values: signed zeros,
 infinities, not-a-number (NaN).</p></li>
 </ul></dd>

 <dt id="mpf2mpfr">2. How to convert my program written using
 <cite><acronym>MPF</acronym></cite> to
 <cite><acronym>MPFR</acronym></cite>?</dt>

 <dd><p>You need to add <q><code>r</code></q> to the function names, and to
 specify the rounding mode (<code>MPFR_RNDN</code> for rounding to nearest,
 <code>MPFR_RNDZ</code> for rounding toward zero, <code>MPFR_RNDU</code>
 for rounding toward plus infinity, <code>MPFR_RNDD</code> for rounding
 toward minus infinity). You can also define macros as follows:
 <code class="block-code">#define mpf_add(a, b, c) mpfr_add(a, b, c, MPFR_RNDN)</code></p>
 <p>The header file <samp>mpf2mpfr.h</samp> from the
 <cite><acronym>MPFR</acronym></cite> distribution automatically
 redefines all <cite><acronym>MPF</acronym></cite> functions in this
 way, using the default <cite><acronym>MPFR</acronym></cite> rounding
 mode. Thus you simply need to add the following line in all your files
 using <cite><acronym>MPF</acronym></cite> functions:
 <code class="block-code">#include &lt;mpf2mpfr.h&gt;</code>
 just after the <samp>gmp.h</samp> and <samp>mpfr.h</samp>
 header files. If the program uses <cite><acronym>MPF</acronym></cite>
 internals (such as direct access to <code>__mpf_struct</code> members),
 additional changes will be needed.</p></dd>

 <dt id="no_libgmp">3. At configure time, I get the error: <q>libgmp not found or uses a different ABI.</q></dt>

 <dd><p>This test (<samp>checking for __gmpz_init in -lgmp</samp>) comes
 after the <samp>gmp.h</samp> detection. The failure occurs either because
 the <cite><acronym>GMP</acronym></cite> library could not be found
 (as it is not in the provided library search paths) or because the
 <cite><acronym>GMP</acronym></cite> library that was found does not have
 the expected <acronym title="Application Binary Interface">ABI</acronym>
 (<abbr>e.g.</abbr> 32-bit <abbr>vs</abbr> 64-bit). The former problem can be
 due to the fact that a static build of <cite><acronym>MPFR</acronym></cite>
 was requested while only a shared <cite><acronym>GMP</acronym></cite> library
 is installed (or the opposite, but another error can also show up in this
 case, see the <a href="#fpic">question about <samp>-fPIC</samp></a>). The
 latter problem can have several causes:</p>
 <ul>
 <li>A wrong libgmp library has been picked up. This can occur if you have
 several <cite><acronym>GMP</acronym></cite> versions installed on the
 machine and something is wrong with the provided library search paths.</li>
 <li>Wrong compiler options (<samp>CFLAGS</samp>) were given. In general, the
 presence or absence of the <samp>-m64</samp> compiler option must match the
 library <acronym title="Application Binary Interface">ABI</acronym>.</li>
 <li>A wrong <samp>gmp.h</samp> file has been picked up (if you have several
 <cite><acronym>GMP</acronym></cite> versions installed). Indeed, by default,
 <cite><acronym>MPFR</acronym></cite> gets the compiler options from the
 <samp>gmp.h</samp> file (with <cite><acronym>GMP</acronym></cite> 4.2.3
 or later); this is needed because <cite><acronym>GMP</acronym></cite> does
 not necessarily use the default <acronym>ABI</acronym>. The consequence is
 that if the <samp>gmp.h</samp> file is associated with a library using a
 different <acronym>ABI</acronym>, the <acronym>ABI</acronym>-related options
 will be incorrect. Hence the failure.</li>
 </ul>
 <p>Note: The <samp>config.log</samp> output gives more information
 than the error message. In particular, see the output of the test:
 <samp>checking for CC and CFLAGS in gmp.h</samp>; it should give you
 the default compiler options (from <samp>gmp.h</samp>).</p>

 <p>See also the answer to the <a href="#undef_ref1">next question</a>.</p></dd>

 <dt id="undef_ref1">4. I get undefined reference to <code>__gmp_get_memory_functions</code>.</dt>

 <dd><p>Note: this was mainly a problem when upgrading from
 <cite><acronym>GMP</acronym></cite> 4.1.4 to a later version,
 but information given below may still be useful in other cases,
 when several <cite><acronym>GMP</acronym></cite> libraries are
 installed on the same machine.</p>

 <p>If you get such an error, in particular when running
 <samp>make check</samp>, then this probably means that you are using
 the header file from <cite><acronym>GMP</acronym></cite> 4.2.x but the
 <cite><acronym>GMP</acronym></cite> 4.1.4 library. This can happen if
 several <cite><acronym>GMP</acronym></cite> versions are installed on
 your machine (<abbr>e.g.</abbr>, one provided by the system in
 <samp>/usr/{include,lib}</samp> and a new one installed by the owner or
 administrator of the machine in <samp>/usr/local/{include,lib}</samp>)
 and your include and library search paths are inconsistent. On various
 <acronym>GNU</acronym>/Linux machines, this is unfortunately the case
 by default (<samp>/usr/local/include</samp> is in the default include
 search path, but <samp>/usr/local/lib</samp> is <em>not</em> in the
 default library search path). Typical errors are:
 <samp class="block-code">undefined reference to `__gmp_get_memory_functions'</samp>
 in <samp>make check</samp>. The best solution is to add
 <samp>/usr/local/include</samp> to your <var class="env">C_INCLUDE_PATH</var>
 environment variable and to add <samp>/usr/local/lib</samp> to your
 <var class="env">LIBRARY_PATH</var> and <var class="env">LD_LIBRARY_PATH</var>
 environment variables (and/or <var class="env">LD_RUN_PATH</var>).
 Alternatively, you can use <samp>--with-gmp*</samp> configure options,
 <abbr>e.g.</abbr> <samp>--with-gmp=/usr/local</samp>, but <strong>this is
 not guaranteed to work</strong> (in particular with <samp>gcc</samp> and
 system directories such as <samp>/usr</samp> or <samp>/usr/local</samp>),
 and other software that uses <cite><acronym>GMP</acronym></cite> and/or
 <cite><acronym>MPFR</acronym></cite> will need correct paths too;
 environment variables allow you to set them in a global way.</p>
 <p>Other information can be given in the <samp>INSTALL</samp> file and
 <samp>ld</samp> manual. Please look at them for more details. See also
 the <a href="#undef_ref2">next question</a>.</p></dd>

 <dt id="undef_ref2">5. When I link my program with
 <cite><acronym>MPFR</acronym></cite>, I get undefined reference
 to <code>__gmpXXXX</code>.</dt>

 <dd><p>Link your program with <cite><acronym>GMP</acronym></cite>. Assuming
 that your program is <samp>foo.c</samp>, you should link it using:
 <samp class="block-code">cc link.c -lmpfr -lgmp</samp>
 <cite><acronym>MPFR</acronym></cite> library reference (<samp>-lmpfr</samp>)
 should be before <cite><acronym>GMP</acronym></cite>'s one
 (<samp>-lgmp</samp>). Another solution is, with <acronym>GNU</acronym>
 <samp>ld</samp>, to give all the libraries inside a group:
 <samp class="block-code">gcc link.c -Wl,--start-group libgmp.a libmpfr.a -Wl,--end-group</samp>
 See <samp>INSTALL</samp> file and <samp>ld</samp> manual for more
 details.</p>
 <p>If you used correct link options, but still get an error, this may mean
 that your include and library search paths are inconsistent. Please see the
 <a href="#undef_ref1">previous question</a>.</p></dd>

 <dt id="crash_high_prec">6. My program crashes with high precisions.</dt>

 <dd><p>Your stack size limit may be too small; indeed, by default,
 <cite><acronym>GMP</acronym></cite> 4.1.4 and below allocates all
 temporary results on the stack, and in very high precisions, this
 limit may be reached. You can solve this problem in different ways:</p>
 <ul>
 <li><p>You can upgrade to <cite><acronym>GMP</acronym></cite> 4.2 (or above),
 which now makes temporary allocations on the stack only when they are
 small.</p></li>
 <li><p>You can increase the stack size limit with the <samp>limit</samp>,
 <samp>unlimit</samp> or <samp>ulimit</samp> command, depending on your
 shell. This may fail on some systems, where the maximum stack size cannot
 be increased above some value.</p></li>
 <li><p>You can rebuild both <cite><acronym>GMP</acronym></cite> and
 <cite><acronym>MPFR</acronym></cite> to use another allocation method.</p></li>
 </ul></dd>

 <dt id="accuracy">7. Though I have increased the precision, the results
 are not more accurate.</dt>

 <dd><p>The reason may be the use of C floating-point numbers. 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 <cite><acronym>MPFR</acronym></cite>
 constant functions, such as <code>mpfr_const_pi</code> for &#960;) instead
 of <code>mpfr_set_d</code> or <code>mpfr_set_ld</code>. Otherwise the
 floating-point constant will be first converted into a reduced-precision
 (<abbr>e.g.</abbr>, 53-bit) binary number before
 <cite><acronym>MPFR</acronym></cite> can work with it. This is the case
 in particular for most exact decimal numbers, such as 0.17, which are
 not exactly representable in binary.</p>
 <p>Also remember that <cite><acronym>MPFR</acronym></cite> does not track
 the accuracy of the results: copying a value <var>x</var> to <var>y</var>
 with <code>mpfr_set (y, x, MPFR_RNDN)</code> where the variable <var>y</var>
 is more precise than the variable <var>x</var> will not make it more
 accurate; the (binary) value will remain unchanged.</p></dd>

 <dt id="detect_mpfr">8. How can I detect <cite><acronym>MPFR</acronym></cite>
 installation using <cite>autoconf</cite> or <cite>pkg-config</cite>?</dt>

 <dd><p>The <cite><acronym>MPFR</acronym></cite> team does not currently
 recommend any <cite>autoconf</cite> code, but a section will later
 be added to the <cite><acronym>MPFR</acronym></cite> manual. The
 <cite><acronym>MPFR</acronym></cite> team does not wish to support
 <cite>pkg-config</cite> yet.</p></dd>

 <dt id="cite">9. How to cite <cite><acronym>MPFR</acronym></cite> in a
 scientific publication?</dt>

 <dd><p>To properly cite <cite><acronym>MPFR</acronym></cite> in a scientific
 publication, please cite the
 <a href="http://doi.acm.org/10.1145/1236463.1236468"><acronym title="Association for Computing Machinery">ACM</acronym>
 <acronym title="Transactions on Mathematical Software">TOMS</acronym>
 paper</a>
 (<a href="http://toms.acm.org/cgi/TOMSbibget.cgi?Fousse:2007:MMP">BibTeX</a>)
 and/or the library web page
 <a href="http://www.mpfr.org/">http://www.mpfr.org</a>. If your publication
 is related to a particular release of <cite><acronym>MPFR</acronym></cite>,
 for example if you report timings, please also indicate the release number
 for future reference.</p></dd>

 <dt id="fpic">10. When I build <cite><acronym>MPFR</acronym></cite>, I get
 an error asking me to recompile with <samp>-fPIC</samp>.</dt>

 <dd><p>A typical error looks like:</p>
 <p><tt>/usr/bin/ld: <em>/path/to/</em>libgmp.a(realloc.o): relocation
 R_X86_64_32 against `.rodata.str1.1' can not be used when making a
 shared object; recompile with -fPIC<br />
 <em>/path/to/</em>libgmp.a: could not read symbols: Bad value<br />
 collect2: ld returned 1 exit status</tt></p>
 <p>The probable reason is that you tried to build
 <cite><acronym>MPFR</acronym></cite> with the shared library enabled (this
 is the default), while only a static <cite><acronym>GMP</acronym></cite>
 library could be found. To solve this problem, either rebuild and reinstall
 <cite><acronym>GMP</acronym></cite> without the <samp>--disable-shared</samp>
 configure option, or configure <cite><acronym>MPFR</acronym></cite> with
 <samp>--disable-shared</samp>. If you did this and still get the above
 error, the cause may be conflicting <cite><acronym>GMP</acronym></cite>
 versions installed on your system; please check that your search path
 settings are correct.</p>
 <p>Additional note about the last sentence: Under <acronym>GNU</acronym>/Linux
 (for instance), the linker takes the first library found in the library search
 path, whether it is dynamic or static. The default behavior under darwin is
 different, but <cite><acronym>MPFR</acronym></cite> will change it.</p></dd>
 <!-- Reference concerning darwin: see MPFR_LD_SEARCH_PATHS_FIRST
      in MPFR's configure.{ac,in} and acinclude.m4 -->

 </dl>

 </body>

 </html>
	<?xml version="1.0" encoding="iso-8859-1"?>
	<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">

	<!--
	Copyright 2000-2016 Free Software Foundation, Inc.
	Contributed by the AriC and Caramba projects, INRIA.

	This file is part of the GNU MPFR Library.

	The GNU MPFR Library is free software; you can redistribute it and/or modify
	it under the terms of the GNU Lesser General Public License as published by
	the Free Software Foundation; either version 3 of the License, or (at your
	option) any later version.

	The GNU MPFR Library is distributed in the hope that it will be useful, but
	WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
	or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
	License for more details.

	You should have received a copy of the GNU Lesser General Public License
	along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see
	http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
	51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA.
	-->

	<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">

	<head><meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1" />
	<title>Frequently Asked Questions about GNU MPFR</title>
	<style type="text/css">/<![CDATA[/
	/* Global stylesheet for visual media */

	html, body
	{
	background: white;
	color: black;
	}

	div.logo { float: right }
	div.logo img { border: 0 }

	div.footer img { border: 0 }

	dt
	{
	margin-top: 2ex;
	margin-bottom: 1ex;
	font-weight: bolder;
	}

	/* For testing: dd { background: #ddddff } */

	table { margin: 0.5ex auto }

	li { margin-top: 0.5ex; margin-bottom: 0.5ex }

	dd + dd
	{
	margin-top: 0;
	margin-bottom: 0;
	padding-top: 0.5ex;
	padding-bottom: 0;
	}

	li > p, dd > p
	{
	margin-top: 0;
	margin-bottom: 0;
	padding-top: 0.5ex;
	padding-bottom: 0.5ex;
	}

	.block-code code, code.block-code,
	.block-code samp, samp.block-code
	{
	display: block;
	padding: 0.5ex 0;
	margin-left: 2em;
	}

	.nowrap { white-space: nowrap }

	/*
	dl.faq { counter-reset: faq }

	dl.faq dt:before
	{
	counter-increment: faq;
	content: counter(faq) ". ";
	}
	*/

	dl.faq dt { background: #dddddd }

	dl.faq dd
	{
	border-left: 4px solid;
	border-color: transparent;
	margin-left: 0em;
	padding-left: 1.5em;
	}

	dl.faq dt:target + dd
	{
	border-left-color: #aaaaaa;
	}

	var.env { font-style: normal }
	/]]>/</style>
	</head>

	<body>

	<h1>Frequently Asked Questions about <cite><acronym>GNU</acronym> <acronym>MPFR</acronym></cite></h1>

	<p><strong>Important notice: Problems with a particular version of
	<cite><acronym>MPFR</acronym></cite> are discussed in the corresponding
	bugs page.</strong></p>

	<p>The latest version of this <acronym>FAQ</acronym> is available at
	<a href="http://www.mpfr.org/faq.html">http://www.mpfr.org/faq.html</a>.
	Please look at this version if possible.</p>

	<ol>
	<li><a href="#mpfr_vs_mpf">What are the differences between
	<cite><acronym>MPF</acronym></cite> from <cite><acronym>GMP</acronym></cite>
	and <cite><acronym>MPFR</acronym></cite>?</a></li>
	<li><a href="#mpf2mpfr">How to convert my program written using
	<cite><acronym>MPF</acronym></cite> to
	<cite><acronym>MPFR</acronym></cite>?</a></li>
	<li><a href="#no_libgmp">At configure time, I get the error: <q>libgmp not found or uses a different ABI.</q></a></li>
	<li><a href="#undef_ref1">I get undefined reference to <code>__gmp_get_memory_functions</code>.</a></li>
	<li><a href="#undef_ref2">When I link my program with
	<cite><acronym>MPFR</acronym></cite>, I get undefined reference
	to <code>__gmpXXXX</code>.</a></li>
	<li><a href="#crash_high_prec">My program crashes with high precisions.</a></li>
	<li><a href="#accuracy">Though I have increased the precision, the results
	are not more accurate.</a></li>
	<li><a href="#detect_mpfr">How can I detect <cite><acronym>MPFR</acronym></cite>
	installation using <cite>autoconf</cite> or <cite>pkg-config</cite>?</a></li>
	<li><a href="#cite">How to cite <cite><acronym>MPFR</acronym></cite> in a
	scientific publication?</a></li>
	<li><a href="#fpic">When I build <cite><acronym>MPFR</acronym></cite>, I get
	an error asking me to recompile with <samp>-fPIC</samp>.</a></li>
	</ol>

	<dl class="faq">

	<dt id="mpfr_vs_mpf">1. What are the differences between
	<cite><acronym>MPF</acronym></cite> from <cite><acronym>GMP</acronym></cite>
	and <cite><acronym>MPFR</acronym></cite>?</dt>

	<dd><p>The main differences are:</p>
	<ul>
	<li><p>The precision of a <cite><acronym>MPFR</acronym></cite> variable
	is the <em>exact</em> number of bits used for its mantissa, whereas in
	<cite><acronym>MPF</acronym></cite>, the precision requested by the user
	is a minimum value (<cite><acronym>MPF</acronym></cite> generally uses a
	higher precision). With the additional difference below, this implies that
	the <cite><acronym>MPFR</acronym></cite> results do not depend on the
	number of bits (16, 32, 64 or more) of the underlying architecture.</p></li>
	<li><p>As a consequence, <cite><acronym>MPFR</acronym></cite> uses a
	base-2 exponent, whereas in <cite><acronym>MPF</acronym></cite>, this
	is a base-2<sup>32</sup> or base-2<sup>64</sup> exponent, depending on
	the limb size. For this reason (and other internal ones), the maximum
	exponent range in <cite><acronym>MPFR</acronym></cite> is different
	(and smaller, if the exponent is represented by the same type as in
	<cite><acronym>MPF</acronym></cite>).</p></li>
	<li><p><cite><acronym>MPFR</acronym></cite> provides an additional rounding
	mode argument to its functions; furthermore, it is guaranteed that the
	result of any operation is the nearest possible floating-point value from
	the exact result (considering the input variables as exact values), taking
	into account the precision of the destination variable and the rounding
	mode. <cite><acronym>MPFR</acronym></cite> also says whether the rounded
	result is above or below the exact result.</p></li>
	<li><p><cite><acronym>MPFR</acronym></cite> supports much more functions
	(in particular transcendental functions such as exponentials, logarithms,
	trigonometric functions and so on) and special values: signed zeros,
	infinities, not-a-number (NaN).</p></li>
	</ul></dd>

	<dt id="mpf2mpfr">2. How to convert my program written using
	<cite><acronym>MPF</acronym></cite> to
	<cite><acronym>MPFR</acronym></cite>?</dt>

	<dd><p>You need to add <q><code>r</code></q> to the function names, and to
	specify the rounding mode (<code>MPFR_RNDN</code> for rounding to nearest,
	<code>MPFR_RNDZ</code> for rounding toward zero, <code>MPFR_RNDU</code>
	for rounding toward plus infinity, <code>MPFR_RNDD</code> for rounding
	toward minus infinity). You can also define macros as follows:
	<code class="block-code">#define mpf_add(a, b, c) mpfr_add(a, b, c, MPFR_RNDN)</code></p>
	<p>The header file <samp>mpf2mpfr.h</samp> from the
	<cite><acronym>MPFR</acronym></cite> distribution automatically
	redefines all <cite><acronym>MPF</acronym></cite> functions in this
	way, using the default <cite><acronym>MPFR</acronym></cite> rounding
	mode. Thus you simply need to add the following line in all your files
	using <cite><acronym>MPF</acronym></cite> functions:
	<code class="block-code">#include <mpf2mpfr.h></code>
	just after the <samp>gmp.h</samp> and <samp>mpfr.h</samp>
	header files. If the program uses <cite><acronym>MPF</acronym></cite>
	internals (such as direct access to <code>__mpf_struct</code> members),
	additional changes will be needed.</p></dd>

	<dt id="no_libgmp">3. At configure time, I get the error: <q>libgmp not found or uses a different ABI.</q></dt>

	<dd><p>This test (<samp>checking for __gmpz_init in -lgmp</samp>) comes
	after the <samp>gmp.h</samp> detection. The failure occurs either because
	the <cite><acronym>GMP</acronym></cite> library could not be found
	(as it is not in the provided library search paths) or because the
	<cite><acronym>GMP</acronym></cite> library that was found does not have
	the expected <acronym title="Application Binary Interface">ABI</acronym>
	(<abbr>e.g.</abbr> 32-bit <abbr>vs</abbr> 64-bit). The former problem can be
	due to the fact that a static build of <cite><acronym>MPFR</acronym></cite>
	was requested while only a shared <cite><acronym>GMP</acronym></cite> library
	is installed (or the opposite, but another error can also show up in this
	case, see the <a href="#fpic">question about <samp>-fPIC</samp></a>). The
	latter problem can have several causes:</p>
	<ul>
	<li>A wrong libgmp library has been picked up. This can occur if you have
	several <cite><acronym>GMP</acronym></cite> versions installed on the
	machine and something is wrong with the provided library search paths.</li>
	<li>Wrong compiler options (<samp>CFLAGS</samp>) were given. In general, the
	presence or absence of the <samp>-m64</samp> compiler option must match the
	library <acronym title="Application Binary Interface">ABI</acronym>.</li>
	<li>A wrong <samp>gmp.h</samp> file has been picked up (if you have several
	<cite><acronym>GMP</acronym></cite> versions installed). Indeed, by default,
	<cite><acronym>MPFR</acronym></cite> gets the compiler options from the
	<samp>gmp.h</samp> file (with <cite><acronym>GMP</acronym></cite> 4.2.3
	or later); this is needed because <cite><acronym>GMP</acronym></cite> does
	not necessarily use the default <acronym>ABI</acronym>. The consequence is
	that if the <samp>gmp.h</samp> file is associated with a library using a
	different <acronym>ABI</acronym>, the <acronym>ABI</acronym>-related options
	will be incorrect. Hence the failure.</li>
	</ul>
	<p>Note: The <samp>config.log</samp> output gives more information
	than the error message. In particular, see the output of the test:
	<samp>checking for CC and CFLAGS in gmp.h</samp>; it should give you
	the default compiler options (from <samp>gmp.h</samp>).</p>

	<p>See also the answer to the <a href="#undef_ref1">next question</a>.</p></dd>

	<dt id="undef_ref1">4. I get undefined reference to <code>__gmp_get_memory_functions</code>.</dt>

	<dd><p>Note: this was mainly a problem when upgrading from
	<cite><acronym>GMP</acronym></cite> 4.1.4 to a later version,
	but information given below may still be useful in other cases,
	when several <cite><acronym>GMP</acronym></cite> libraries are
	installed on the same machine.</p>

	<p>If you get such an error, in particular when running
	<samp>make check</samp>, then this probably means that you are using
	the header file from <cite><acronym>GMP</acronym></cite> 4.2.x but the
	<cite><acronym>GMP</acronym></cite> 4.1.4 library. This can happen if
	several <cite><acronym>GMP</acronym></cite> versions are installed on
	your machine (<abbr>e.g.</abbr>, one provided by the system in
	<samp>/usr/{include,lib}</samp> and a new one installed by the owner or
	administrator of the machine in <samp>/usr/local/{include,lib}</samp>)
	and your include and library search paths are inconsistent. On various
	<acronym>GNU</acronym>/Linux machines, this is unfortunately the case
	by default (<samp>/usr/local/include</samp> is in the default include
	search path, but <samp>/usr/local/lib</samp> is <em>not</em> in the
	default library search path). Typical errors are:
	<samp class="block-code">undefined reference to `__gmp_get_memory_functions'</samp>
	in <samp>make check</samp>. The best solution is to add
	<samp>/usr/local/include</samp> to your <var class="env">C_INCLUDE_PATH</var>
	environment variable and to add <samp>/usr/local/lib</samp> to your
	<var class="env">LIBRARY_PATH</var> and <var class="env">LD_LIBRARY_PATH</var>
	environment variables (and/or <var class="env">LD_RUN_PATH</var>).
	Alternatively, you can use <samp>--with-gmp*</samp> configure options,
	<abbr>e.g.</abbr> <samp>--with-gmp=/usr/local</samp>, but <strong>this is
	not guaranteed to work</strong> (in particular with <samp>gcc</samp> and
	system directories such as <samp>/usr</samp> or <samp>/usr/local</samp>),
	and other software that uses <cite><acronym>GMP</acronym></cite> and/or
	<cite><acronym>MPFR</acronym></cite> will need correct paths too;
	environment variables allow you to set them in a global way.</p>
	<p>Other information can be given in the <samp>INSTALL</samp> file and
	<samp>ld</samp> manual. Please look at them for more details. See also
	the <a href="#undef_ref2">next question</a>.</p></dd>

	<dt id="undef_ref2">5. When I link my program with
	<cite><acronym>MPFR</acronym></cite>, I get undefined reference
	to <code>__gmpXXXX</code>.</dt>

	<dd><p>Link your program with <cite><acronym>GMP</acronym></cite>. Assuming
	that your program is <samp>foo.c</samp>, you should link it using:
	<samp class="block-code">cc link.c -lmpfr -lgmp</samp>
	<cite><acronym>MPFR</acronym></cite> library reference (<samp>-lmpfr</samp>)
	should be before <cite><acronym>GMP</acronym></cite>'s one
	(<samp>-lgmp</samp>). Another solution is, with <acronym>GNU</acronym>
	<samp>ld</samp>, to give all the libraries inside a group:
	<samp class="block-code">gcc link.c -Wl,--start-group libgmp.a libmpfr.a -Wl,--end-group</samp>
	See <samp>INSTALL</samp> file and <samp>ld</samp> manual for more
	details.</p>
	<p>If you used correct link options, but still get an error, this may mean
	that your include and library search paths are inconsistent. Please see the
	<a href="#undef_ref1">previous question</a>.</p></dd>

	<dt id="crash_high_prec">6. My program crashes with high precisions.</dt>

	<dd><p>Your stack size limit may be too small; indeed, by default,
	<cite><acronym>GMP</acronym></cite> 4.1.4 and below allocates all
	temporary results on the stack, and in very high precisions, this
	limit may be reached. You can solve this problem in different ways:</p>
	<ul>
	<li><p>You can upgrade to <cite><acronym>GMP</acronym></cite> 4.2 (or above),
	which now makes temporary allocations on the stack only when they are
	small.</p></li>
	<li><p>You can increase the stack size limit with the <samp>limit</samp>,
	<samp>unlimit</samp> or <samp>ulimit</samp> command, depending on your
	shell. This may fail on some systems, where the maximum stack size cannot
	be increased above some value.</p></li>
	<li><p>You can rebuild both <cite><acronym>GMP</acronym></cite> and
	<cite><acronym>MPFR</acronym></cite> to use another allocation method.</p></li>
	</ul></dd>

	<dt id="accuracy">7. Though I have increased the precision, the results
	are not more accurate.</dt>

	<dd><p>The reason may be the use of C floating-point numbers. 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 <cite><acronym>MPFR</acronym></cite>
	constant functions, such as <code>mpfr_const_pi</code> for π) instead
	of <code>mpfr_set_d</code> or <code>mpfr_set_ld</code>. Otherwise the
	floating-point constant will be first converted into a reduced-precision
	(<abbr>e.g.</abbr>, 53-bit) binary number before
	<cite><acronym>MPFR</acronym></cite> can work with it. This is the case
	in particular for most exact decimal numbers, such as 0.17, which are
	not exactly representable in binary.</p>
	<p>Also remember that <cite><acronym>MPFR</acronym></cite> does not track
	the accuracy of the results: copying a value <var>x</var> to <var>y</var>
	with <code>mpfr_set (y, x, MPFR_RNDN)</code> where the variable <var>y</var>
	is more precise than the variable <var>x</var> will not make it more
	accurate; the (binary) value will remain unchanged.</p></dd>

	<dt id="detect_mpfr">8. How can I detect <cite><acronym>MPFR</acronym></cite>
	installation using <cite>autoconf</cite> or <cite>pkg-config</cite>?</dt>

	<dd><p>The <cite><acronym>MPFR</acronym></cite> team does not currently
	recommend any <cite>autoconf</cite> code, but a section will later
	be added to the <cite><acronym>MPFR</acronym></cite> manual. The
	<cite><acronym>MPFR</acronym></cite> team does not wish to support
	<cite>pkg-config</cite> yet.</p></dd>

	<dt id="cite">9. How to cite <cite><acronym>MPFR</acronym></cite> in a
	scientific publication?</dt>

	<dd><p>To properly cite <cite><acronym>MPFR</acronym></cite> in a scientific
	publication, please cite the
	<a href="http://doi.acm.org/10.1145/1236463.1236468"><acronym title="Association for Computing Machinery">ACM</acronym>
	<acronym title="Transactions on Mathematical Software">TOMS</acronym>
	paper</a>
	(<a href="http://toms.acm.org/cgi/TOMSbibget.cgi?Fousse:2007:MMP">BibTeX</a>)
	and/or the library web page
	<a href="http://www.mpfr.org/">http://www.mpfr.org</a>. If your publication
	is related to a particular release of <cite><acronym>MPFR</acronym></cite>,
	for example if you report timings, please also indicate the release number
	for future reference.</p></dd>

	<dt id="fpic">10. When I build <cite><acronym>MPFR</acronym></cite>, I get
	an error asking me to recompile with <samp>-fPIC</samp>.</dt>

	<dd><p>A typical error looks like:</p>
	<p><tt>/usr/bin/ld: <em>/path/to/</em>libgmp.a(realloc.o): relocation
	R_X86_64_32 against `.rodata.str1.1' can not be used when making a
	shared object; recompile with -fPIC<br />
	<em>/path/to/</em>libgmp.a: could not read symbols: Bad value<br />
	collect2: ld returned 1 exit status</tt></p>
	<p>The probable reason is that you tried to build
	<cite><acronym>MPFR</acronym></cite> with the shared library enabled (this
	is the default), while only a static <cite><acronym>GMP</acronym></cite>
	library could be found. To solve this problem, either rebuild and reinstall
	<cite><acronym>GMP</acronym></cite> without the <samp>--disable-shared</samp>
	configure option, or configure <cite><acronym>MPFR</acronym></cite> with
	<samp>--disable-shared</samp>. If you did this and still get the above
	error, the cause may be conflicting <cite><acronym>GMP</acronym></cite>
	versions installed on your system; please check that your search path
	settings are correct.</p>
	<p>Additional note about the last sentence: Under <acronym>GNU</acronym>/Linux
	(for instance), the linker takes the first library found in the library search
	path, whether it is dynamic or static. The default behavior under darwin is
	different, but <cite><acronym>MPFR</acronym></cite> will change it.</p></dd>
	<!-- Reference concerning darwin: see MPFR_LD_SEARCH_PATHS_FIRST
	in MPFR's configure.{ac,in} and acinclude.m4 -->

	</dl>

	</body>

	</html>