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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> |
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<p><strong>Important notice: Problems with a particular version of |
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<cite><acronym>MPFR</acronym></cite> are discussed in the corresponding |
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bugs page.</strong></p> |
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<p>The latest version of this <acronym>FAQ</acronym> is available at |
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<a href="https://www.mpfr.org/faq.html">https://www.mpfr.org/faq.html</a>. |
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Please look at this version if possible.</p> |
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<ol> |
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<li><a href="#mpfr_vs_mpf">What are the differences between |
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<cite><acronym>MPF</acronym></cite> from <cite><acronym>GMP</acronym></cite> |
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and <cite><acronym>MPFR</acronym></cite>?</a></li> |
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<li><a href="#mpf2mpfr">How to convert my program written using |
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<cite><acronym>MPF</acronym></cite> to |
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<cite><acronym>MPFR</acronym></cite>?</a></li> |
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<li><a href="#no_libgmp">At configure time, I get the error: <q>libgmp not found or uses a different ABI.</q></a></li> |
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<li><a href="#undef_ref1">I get undefined reference to <code>__gmp_get_memory_functions</code>.</a></li> |
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<li><a href="#undef_ref2">When I link my program with |
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<cite><acronym>MPFR</acronym></cite>, I get undefined reference |
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to <code>__gmpXXXX</code>.</a></li> |
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<li><a href="#crash_high_prec">My program crashes with high precisions.</a></li> |
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<li><a href="#accuracy">Though I have increased the precision, the results |
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are not more accurate.</a></li> |
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<li><a href="#detect_mpfr">How can I detect <cite><acronym>MPFR</acronym></cite> |
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installation using <cite>autoconf</cite> or <cite>pkg-config</cite>?</a></li> |
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<li><a href="#cite">How to cite <cite><acronym>MPFR</acronym></cite> in a |
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scientific publication?</a></li> |
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<li><a href="#fpic">When I build <cite><acronym>MPFR</acronym></cite>, I get |
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an error asking me to recompile with <samp>-fPIC</samp>.</a></li> |
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</ol> |
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<dl class="faq"> |
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<dt id="mpfr_vs_mpf">1. What are the differences between |
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<cite><acronym>MPF</acronym></cite> from <cite><acronym>GMP</acronym></cite> |
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and <cite><acronym>MPFR</acronym></cite>?</dt> |
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<dd><p>The main differences are:</p> |
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<ul> |
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<li><p>The precision of a <cite><acronym>MPFR</acronym></cite> variable |
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is the <em>exact</em> number of bits used for its mantissa, whereas in |
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<cite><acronym>MPF</acronym></cite>, the precision requested by the user |
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is a minimum value (<cite><acronym>MPF</acronym></cite> generally uses a |
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higher precision). With the additional difference below, this implies that |
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the <cite><acronym>MPFR</acronym></cite> results do not depend on the |
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number of bits (16, 32, 64 or more) of the underlying architecture.</p></li> |
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<li><p>As a consequence, <cite><acronym>MPFR</acronym></cite> uses a |
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base-2 exponent, whereas in <cite><acronym>MPF</acronym></cite>, this |
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is a base-2<sup>32</sup> or base-2<sup>64</sup> exponent, depending on |
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the limb size. For this reason (and other internal ones), the maximum |
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exponent range in <cite><acronym>MPFR</acronym></cite> is different |
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(and smaller, if the exponent is represented by the same type as in |
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<cite><acronym>MPF</acronym></cite>).</p></li> |
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<li><p><cite><acronym>MPFR</acronym></cite> provides an additional rounding |
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mode argument to its functions; furthermore, it is guaranteed that the |
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result of any operation is the nearest possible floating-point value from |
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the exact result (considering the input variables as exact values), taking |
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into account the precision of the destination variable and the rounding |
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mode. <cite><acronym>MPFR</acronym></cite> also says whether the rounded |
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result is above or below the exact result.</p></li> |
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<li><p><cite><acronym>MPFR</acronym></cite> supports much more functions |
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(in particular transcendental functions such as exponentials, logarithms, |
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trigonometric functions and so on) and special values: signed zeros, |
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infinities, not-a-number (NaN).</p></li> |
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</ul></dd> |
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<dt id="mpf2mpfr">2. How to convert my program written using |
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<cite><acronym>MPF</acronym></cite> to |
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<cite><acronym>MPFR</acronym></cite>?</dt> |
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<dd><p>You need to add <q><code>r</code></q> to the function names, and to |
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specify the rounding mode (<code>MPFR_RNDN</code> for rounding to nearest, |
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<code>MPFR_RNDZ</code> for rounding toward zero, <code>MPFR_RNDU</code> |
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for rounding toward positive infinity, <code>MPFR_RNDD</code> for rounding |
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toward negative infinity). You can also define macros as follows: |
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<code class="block-code">#define mpf_add(a, b, c) mpfr_add(a, b, c, MPFR_RNDN)</code></p> |
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<p>The header file <samp>mpf2mpfr.h</samp> from the |
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<cite><acronym>MPFR</acronym></cite> distribution automatically |
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redefines all <cite><acronym>MPF</acronym></cite> functions in this |
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way, using the default <cite><acronym>MPFR</acronym></cite> rounding |
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mode. Thus you simply need to add the following line in all your files |
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using <cite><acronym>MPF</acronym></cite> functions: |
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<code class="block-code">#include <mpf2mpfr.h></code> |
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just after the <samp>gmp.h</samp> and <samp>mpfr.h</samp> |
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header files. If the program uses <cite><acronym>MPF</acronym></cite> |
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internals (such as direct access to <code>__mpf_struct</code> members), |
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additional changes will be needed.</p></dd> |
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<dt id="no_libgmp">3. At configure time, I get the error: <q>libgmp not found or uses a different ABI.</q></dt> |
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<dd><p>This test (<samp>checking for __gmpz_init in -lgmp</samp>) comes |
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after the <samp>gmp.h</samp> detection. The failure occurs either because |
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the <cite><acronym>GMP</acronym></cite> library could not be found |
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(as it is not in the provided library search paths) or because the |
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<cite><acronym>GMP</acronym></cite> library that was found does not have |
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the expected <acronym title="Application Binary Interface">ABI</acronym> |
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(<abbr>e.g.</abbr> 32-bit <abbr>vs</abbr> 64-bit). The former problem can be |
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due to the fact that a static build of <cite><acronym>MPFR</acronym></cite> |
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was requested while only a shared <cite><acronym>GMP</acronym></cite> library |
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is installed (or the opposite, but another error can also show up in this |
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case, see the <a href="#fpic">question about <samp>-fPIC</samp></a>). The |
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latter problem can have several causes:</p> |
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<ul> |
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<li>A wrong libgmp library has been picked up. This can occur if you have |
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several <cite><acronym>GMP</acronym></cite> versions installed on the |
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machine and something is wrong with the provided library search paths.</li> |
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<li>Wrong compiler options (<samp>CFLAGS</samp>) were given. In general, the |
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presence or absence of the <samp>-m64</samp> compiler option must match the |
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library <acronym title="Application Binary Interface">ABI</acronym>.</li> |
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<li>A wrong <samp>gmp.h</samp> file has been picked up (if you have several |
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<cite><acronym>GMP</acronym></cite> versions installed). Indeed, by default, |
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<cite><acronym>MPFR</acronym></cite> gets the compiler options from the |
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<samp>gmp.h</samp> file (with <cite><acronym>GMP</acronym></cite> 4.2.3 |
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or later); this is needed because <cite><acronym>GMP</acronym></cite> does |
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not necessarily use the default <acronym>ABI</acronym>. The consequence is |
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that if the <samp>gmp.h</samp> file is associated with a library using a |
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different <acronym>ABI</acronym>, the <acronym>ABI</acronym>-related options |
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will be incorrect. Hence the failure.</li> |
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</ul> |
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<p>Note: The <samp>config.log</samp> output gives more information |
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than the error message. In particular, see the output of the test: |
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<samp>checking for CC and CFLAGS in gmp.h</samp>; it should give you |
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the default compiler options (from <samp>gmp.h</samp>).</p> |
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<p>See also the answer to the <a href="#undef_ref1">next question</a>.</p></dd> |
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<dt id="undef_ref1">4. I get undefined reference to <code>__gmp_get_memory_functions</code>.</dt> |
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<dd><p>Note: this was mainly a problem when upgrading from |
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<cite><acronym>GMP</acronym></cite> 4.1.4 to a later version, |
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but information given below may still be useful in other cases, |
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when several <cite><acronym>GMP</acronym></cite> libraries are |
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installed on the same machine.</p> |
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<p>If you get such an error, in particular when running |
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<samp>make check</samp>, then this probably means that you are using |
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the header file from <cite><acronym>GMP</acronym></cite> 4.2.x but the |
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<cite><acronym>GMP</acronym></cite> 4.1.4 library. This can happen if |
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several <cite><acronym>GMP</acronym></cite> versions are installed on |
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your machine (<abbr>e.g.</abbr>, one provided by the system in |
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<samp>/usr/{include,lib}</samp> and a new one installed by the owner or |
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administrator of the machine in <samp>/usr/local/{include,lib}</samp>) |
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and your include and library search paths are inconsistent. On various |
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<acronym>GNU</acronym>/Linux machines, this is unfortunately the case |
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by default (<samp>/usr/local/include</samp> is in the default include |
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search path, but <samp>/usr/local/lib</samp> is <em>not</em> in the |
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default library search path). Typical errors are: |
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<samp class="block-code">undefined reference to `__gmp_get_memory_functions'</samp> |
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in <samp>make check</samp>. The best solution is to add |
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<samp>/usr/local/include</samp> to your <var class="env">C_INCLUDE_PATH</var> |
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environment variable and to add <samp>/usr/local/lib</samp> to your |
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<var class="env">LIBRARY_PATH</var> and <var class="env">LD_LIBRARY_PATH</var> |
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environment variables (and/or <var class="env">LD_RUN_PATH</var>). |
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Alternatively, you can use <samp>--with-gmp*</samp> configure options, |
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<abbr>e.g.</abbr> <samp>--with-gmp=/usr/local</samp>, but <strong>this is |
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not guaranteed to work</strong> (in particular with <samp>gcc</samp> and |
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system directories such as <samp>/usr</samp> or <samp>/usr/local</samp>), |
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and other software that uses <cite><acronym>GMP</acronym></cite> and/or |
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<cite><acronym>MPFR</acronym></cite> will need correct paths too; |
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environment variables allow you to set them in a global way.</p> |
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<p>Other information can be given in the <samp>INSTALL</samp> file and |
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<samp>ld</samp> manual. Please look at them for more details. See also |
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the <a href="#undef_ref2">next question</a>.</p></dd> |
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<dt id="undef_ref2">5. When I link my program with |
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<cite><acronym>MPFR</acronym></cite>, I get undefined reference |
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to <code>__gmpXXXX</code>.</dt> |
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<dd><p>Link your program with <cite><acronym>GMP</acronym></cite>. Assuming |
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that your program is <samp>foo.c</samp>, you should link it using: |
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<samp class="block-code">cc link.c -lmpfr -lgmp</samp> |
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<cite><acronym>MPFR</acronym></cite> library reference (<samp>-lmpfr</samp>) |
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should be before <cite><acronym>GMP</acronym></cite>'s one |
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(<samp>-lgmp</samp>). Another solution is, with <acronym>GNU</acronym> |
|
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<samp>ld</samp>, to give all the libraries in any order inside a group: |
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<samp class="block-code">gcc link.c -Wl,--start-group libgmp.a libmpfr.a -Wl,--end-group</samp> |
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with the full path to the libraries, or |
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<samp class="block-code">gcc link.c -Wl,--start-group -l:libgmp.a -l:libmpfr.a -Wl,--end-group</samp> |
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to use the library path. |
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See <samp>INSTALL</samp> file and <samp>ld</samp> manual for more |
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details.</p> |
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<p>If you used correct link options, but still get an error, this may mean |
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that your include and library search paths are inconsistent. Please see the |
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<a href="#undef_ref1">previous question</a>.</p></dd> |
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<dt id="crash_high_prec">6. My program crashes with high precisions.</dt> |
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<dd><p>Your stack size limit may be too small; indeed, by default, |
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<cite><acronym>GMP</acronym></cite> 4.1.4 and below allocates all |
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temporary results on the stack, and in very high precisions, this |
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limit may be reached. You can solve this problem in different ways:</p> |
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<ul> |
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<li><p>You can upgrade to <cite><acronym>GMP</acronym></cite> 4.2 (or above), |
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which now makes temporary allocations on the stack only when they are |
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small.</p></li> |
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<li><p>You can increase the stack size limit with the <samp>limit</samp>, |
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<samp>unlimit</samp> or <samp>ulimit</samp> command, depending on your |
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shell. This may fail on some systems, where the maximum stack size cannot |
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be increased above some value.</p></li> |
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<li><p>You can rebuild both <cite><acronym>GMP</acronym></cite> and |
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|
<cite><acronym>MPFR</acronym></cite> to use another allocation method.</p></li> |
|
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</ul></dd> |
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<dt id="accuracy">7. Though I have increased the precision, the results |
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are not more accurate.</dt> |
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<dd><p>The reason may be the use of C floating-point numbers. If you want |
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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 |
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floating-point constant will be first converted into a reduced-precision |
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(<abbr>e.g.</abbr>, 53-bit) binary number before |
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|
<cite><acronym>MPFR</acronym></cite> can work with it. This is the case |
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in particular for most exact decimal numbers, such as 0.17, which are |
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not exactly representable in binary.</p> |
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|
<p>Also remember that <cite><acronym>MPFR</acronym></cite> does not track |
|
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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> |
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|
is more precise than the variable <var>x</var> will not make it more |
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accurate; the (binary) value will remain unchanged.</p></dd> |
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<dt id="detect_mpfr">8. How can I detect <cite><acronym>MPFR</acronym></cite> |
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installation using <cite>autoconf</cite> or <cite>pkg-config</cite>?</dt> |
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<dd><p>The <cite><acronym>MPFR</acronym></cite> team does not currently |
|
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recommend any <cite>autoconf</cite> code, but a section will later |
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|
be added to the <cite><acronym>MPFR</acronym></cite> manual. |
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|
Limited <cite>pkg-config</cite> support has been added for |
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|
<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> |
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<dt id="cite">9. How to cite <cite><acronym>MPFR</acronym></cite> in a |
|
|
scientific publication?</dt> |
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<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 |
|
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<a href="https://www.mpfr.org/">https://www.mpfr.org</a>. If your publication |
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is related to a particular release of <cite><acronym>MPFR</acronym></cite>, |
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for example if you report timings, please also indicate the release number |
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for future reference.</p></dd> |
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<dt id="fpic">10. When I build <cite><acronym>MPFR</acronym></cite>, I get |
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an error asking me to recompile with <samp>-fPIC</samp>.</dt> |
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<dd><p>A typical error looks like:</p> |
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<p><tt>/usr/bin/ld: <em>/path/to/</em>libgmp.a(realloc.o): relocation |
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R_X86_64_32 against `.rodata.str1.1' can not be used when making a |
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shared object; recompile with -fPIC<br /> |
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<em>/path/to/</em>libgmp.a: could not read symbols: Bad value<br /> |
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collect2: ld returned 1 exit status</tt></p> |
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<p>The probable reason is that you tried to build |
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<cite><acronym>MPFR</acronym></cite> with the shared library enabled (this |
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is the default), while only a static <cite><acronym>GMP</acronym></cite> |
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library could be found. To solve this problem, either rebuild and reinstall |
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<cite><acronym>GMP</acronym></cite> without the <samp>--disable-shared</samp> |
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configure option, or configure <cite><acronym>MPFR</acronym></cite> with |
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<samp>--disable-shared</samp>. If you did this and still get the above |
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error, the cause may be conflicting <cite><acronym>GMP</acronym></cite> |
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versions installed on your system; please check that your search path |
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settings are correct.</p> |
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<p>Additional note about the last sentence: Under <acronym>GNU</acronym>/Linux |
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(for instance), the linker takes the first library found in the library search |
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path, whether it is dynamic or static. The default behavior under darwin is |
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different, but <cite><acronym>MPFR</acronym></cite> will change it.</p></dd> |
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