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<title>Frequently Asked Questions about MPFR</title>
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<h1>Frequently Asked Questions about <cite><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>.</p>
<dl>
<dt>What are the differences between <cite><acronym>MPF</acronym></cite>
from <cite><acronym>GMP</acronym></cite> and
<cite><acronym>MPFR</acronym></cite>?</dt>
<dd>Unlike <cite><acronym>MPF</acronym></cite>, the precision of a
<cite><acronym>MPFR</acronym></cite> variable is the <em>exact</em>
number of bits used for its mantissa. This implies that
<cite><acronym>MPFR</acronym></cite> results do not depend on the
number of bits (16, 32, 64 or more) of the underlying architecture.
Also, <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.</dd>
<dt>How to convert my program written using
<cite><acronym>MPF</acronym></cite> to
<cite><acronym>MPFR</acronym></cite>?</dt>
<dd>You need to add <q><code>r</code></q> to the function names, and to
specify the rounding mode (<code>GMP_RNDN</code> for rounding to nearest,
<code>GMP_RNDZ</code> for rounding towards zero, <code>GMP_RNDU</code>
for rounding towards plus infinity, <code>GMP_RNDD</code> for rounding
towards minus infinity). You can also define macros as follows:
<pre>#define mpf_add(a, b, c) mpfr_add(a, b, c, GMP_RNDN)</pre>
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:
<pre>#include <mpf2mpfr.h></pre>
just after the <samp>gmp.h</samp> and <samp>mpfr.h</samp> header files.</dd>
<dt>When I link my program with <cite><acronym>MPFR</acronym></cite>,
I get undefined reference to <code>__gmpz_XXXX</code>,
<code>__gmpn_XXXX</code>.</dt>
<dd>Link your program with <cite><acronym>GMP</acronym></cite>. Assuming
that your program is <samp>foo.c</samp>, you should link it using:
<pre> cc link.c -lmpfr -lgmp</pre>
<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:
<pre> gcc link.c -Wl,--start-group libgmp.a libmpfr.a -Wl,--end-group</pre>
See <samp>ld</samp> manual for more details.</dd>
<dt>My program crashes with high precisions.</dt>
<dd>Your stack size limit may be too small; indeed, by default,
<cite><acronym>GMP</acronym></cite> currently allocates all
temporary results on the stack, and in very high precisions,
this limit may be reached. You can increase it with the
<samp>limit</samp>, <samp>unlimit</samp> or <samp>ulimit</samp> command,
depending on your shell. Alternatively, <abbr>e.g.</abbr> if your
system does not allow you to increase it further, you can rebuild
<cite><acronym>GMP</acronym></cite> and <cite><acronym>MPFR</acronym></cite>
to use another allocation method.</dd>
<dt>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, GMP_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>
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