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Vincent Lefevre
06 янв 2022, 18:24
06 янв 2022, 18:24cfa33ad
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<title>Frequently Asked Questions about GNU MPFR</title>
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<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="https://www.mpfr.org/faq.html">https://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 positive infinity, <code>MPFR_RNDD</code> for rounding
toward negative 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 in any order inside a group:
<samp class="block-code">gcc link.c -Wl,--start-group libgmp.a libmpfr.a -Wl,--end-group</samp>
with the full path to the libraries, or
<samp class="block-code">gcc link.c -Wl,--start-group -l:libgmp.a -l:libmpfr.a -Wl,--end-group</samp>
to use the library path.
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.
Limited <cite>pkg-config</cite> support has been added for
<cite><acronym>MPFR</acronym></cite>�4.0.0; example:</p>
<pre style="margin-left: 2em">cc myprogram.c $(pkg-config --cflags --libs mpfr)</pre></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="https://doi.org/10.1145/1236463.1236468"><acronym title="Association for Computing Machinery">ACM</acronym>
<acronym title="Transactions on Mathematical Software">TOMS</acronym>
paper</a>
and/or the library web page
<a href="https://www.mpfr.org/">https://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>
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     in MPFR's configure.{ac,in} and acinclude.m4 -->

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