author | Misaki Miyashita <Misaki.Miyashita@Oracle.COM> |
Thu, 16 Oct 2014 16:50:39 -0700 | |
branch | s11-update |
changeset 3396 | 2865c45ffb48 |
parent 219 | 22d9e175d379 |
permissions | -rw-r--r-- |
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<title>MPFR 2.3.2</title> |
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<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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<meta name="generator" content="makeinfo 4.11"> |
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<link title="Top" rel="top" href="#Top"> |
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<link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage"> |
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<!-- |
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This manual documents how to install and use the Multiple Precision |
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Floating-Point Reliable Library, version 2.3.2. |
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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 |
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the terms of the GNU Free Documentation License, Version 1.2 or any later |
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version published by the Free Software Foundation; with no Invariant Sections, |
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with no Front-Cover Texts, and with no Back-Cover Texts. A copy of the |
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license is included in *note GNU Free Documentation License::.--> |
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<meta http-equiv="Content-Style-Type" content="text/css"> |
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<style type="text/css"><!-- |
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span.sansserif { font-family:sans-serif; font-weight:normal; } |
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--></style> |
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</head> |
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<body> |
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<a name="Top"></a> |
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Next: <a rel="next" accesskey="n" href="#Copying">Copying</a>, |
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Previous: <a rel="previous" accesskey="p" href="#dir">(dir)</a>, |
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Up: <a rel="up" accesskey="u" href="#dir">(dir)</a> |
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</div> |
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<h2 class="unnumbered">MPFR</h2> |
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<p>This manual documents how to install and use the Multiple Precision |
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Floating-Point Reliable Library, version 2.3.2. |
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<p>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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<p>Permission is granted to copy, distribute and/or modify this document under |
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the terms of the GNU Free Documentation License, Version 1.2 or any later |
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version published by the Free Software Foundation; with no Invariant Sections, |
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with no Front-Cover Texts, and with no Back-Cover Texts. A copy of the |
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license is included in <a href="#GNU-Free-Documentation-License">GNU Free Documentation License</a>. |
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<pre class="sp"> |
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</pre> |
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<!-- Don't bother with contents for html, the menus seem adequate. --> |
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<ul class="menu"> |
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<li><a accesskey="1" href="#Copying">Copying</a>: MPFR Copying Conditions (LGPL). |
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<li><a accesskey="2" href="#Introduction-to-MPFR">Introduction to MPFR</a>: Brief introduction to MPFR. |
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<li><a accesskey="3" href="#Installing-MPFR">Installing MPFR</a>: How to configure and compile the MPFR library. |
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<li><a accesskey="4" href="#Reporting-Bugs">Reporting Bugs</a>: How to usefully report bugs. |
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<li><a accesskey="5" href="#MPFR-Basics">MPFR Basics</a>: What every MPFR user should now. |
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<li><a accesskey="6" href="#MPFR-Interface">MPFR Interface</a>: MPFR functions and macros. |
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<li><a accesskey="7" href="#Contributors">Contributors</a> |
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<li><a accesskey="8" href="#References">References</a> |
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<li><a accesskey="9" href="#GNU-Free-Documentation-License">GNU Free Documentation License</a> |
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<li><a href="#Concept-Index">Concept Index</a> |
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<li><a href="#Function-Index">Function Index</a> |
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</ul> |
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<!-- @m{T,N} is $T$ in tex or @math{N} otherwise. This is an easy way to give --> |
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<!-- different forms for math in tex and info. Commas in N or T don't work, --> |
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<!-- but @C{} can be used instead. \, works in info but not in tex. --> |
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<!-- Usage: @GMPabs{x} --> |
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<!-- Give either |x| in tex, or abs(x) in info or html. --> |
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<!-- Usage: @GMPtimes{} --> |
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<!-- Give either \times or the word "times". --> |
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<!-- New math operators. --> |
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<!-- @abs{} can be used in both tex and info, or just \abs in tex. --> |
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<!-- @times{} made available as a "*" in info and html (already works in tex). --> |
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<!-- Math operators already available in tex, made available in info too. --> |
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<!-- For example @log{} can be used in both tex and info. --> |
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<!-- @pom{} definition --> |
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<!-- The following macro have been copied from gmp.texi --> |
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<!-- Usage: @MPFRpxreftop{info,title} --> |
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<!-- Like @pxref{}, but designed for a reference to the top of a document, not --> |
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<!-- a particular section. --> |
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<!-- The texinfo manual recommends putting a likely section name in references --> |
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<!-- like this, eg. "Introduction", but it seems better to just give the title. --> |
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<div class="node"> |
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<p><hr> |
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<a name="Copying"></a> |
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Next: <a rel="next" accesskey="n" href="#Introduction-to-MPFR">Introduction to MPFR</a>, |
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Previous: <a rel="previous" accesskey="p" href="#Top">Top</a>, |
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Up: <a rel="up" accesskey="u" href="#Top">Top</a> |
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</div> |
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<!-- node-name, next, previous, up --> |
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<h2 class="unnumbered">MPFR Copying Conditions</h2> |
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<p><a name="index-Copying-conditions-1"></a><a name="index-Conditions-for-copying-MPFR-2"></a> |
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This library is <dfn>free</dfn>; this means that everyone is free to use it and |
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free to redistribute it on a free basis. The library is not in the public |
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domain; it is copyrighted and there are restrictions on its distribution, but |
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these restrictions are designed to permit everything that a good cooperating |
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citizen would want to do. What is not allowed is to try to prevent others |
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from further sharing any version of this library that they might get from |
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you. |
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|
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<p>Specifically, we want to make sure that you have the right to give away copies |
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of the library, that you receive source code or else can get it if you want |
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it, that you can change this library or use pieces of it in new free programs, |
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and that you know you can do these things. |
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|
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<p>To make sure that everyone has such rights, we have to forbid you to deprive |
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anyone else of these rights. For example, if you distribute copies of the |
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MPFR library, you must give the recipients all the rights that you have. You |
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must make sure that they, too, receive or can get the source code. And you |
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must tell them their rights. |
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|
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<p>Also, for our own protection, we must make certain that everyone finds out |
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that there is no warranty for the MPFR library. If it is modified by |
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someone else and passed on, we want their recipients to know that what they |
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have is not what we distributed, so that any problems introduced by others |
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will not reflect on our reputation. |
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|
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<p>The precise conditions of the license for the MPFR library are found in the |
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Lesser General Public License that accompanies the source code. |
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See the file COPYING.LIB. |
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135 |
<div class="node"> |
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<p><hr> |
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<a name="Introduction-to-MPFR"></a> |
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Next: <a rel="next" accesskey="n" href="#Installing-MPFR">Installing MPFR</a>, |
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Previous: <a rel="previous" accesskey="p" href="#Copying">Copying</a>, |
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Up: <a rel="up" accesskey="u" href="#Top">Top</a> |
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141 |
|
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</div> |
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|
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144 |
<!-- node-name, next, previous, up --> |
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<h2 class="chapter">1 Introduction to MPFR</h2> |
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146 |
|
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<p>MPFR is a portable library written in C for arbitrary precision arithmetic |
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on floating-point numbers. It is based on the GNU MP library. |
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It aims to extend the class of floating-point numbers provided by the |
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GNU MP library by a precise semantics. The main differences |
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with the <code>mpf</code> class from GNU MP are: |
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|
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<ul> |
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<li>the MPFR code is portable, i.e. the result of any operation |
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does not depend (or should not) on the machine word size |
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<code>mp_bits_per_limb</code> (32 or 64 on most machines); |
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<li>the precision in bits can be set exactly to any valid value |
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for each variable (including very small precision); |
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<li>MPFR provides the four rounding modes from the IEEE 754-1985 |
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standard. |
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</ul> |
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162 |
|
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<p>In particular, with a precision of 53 bits, MPFR should be able to |
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exactly reproduce all computations with double-precision machine |
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floating-point numbers (e.g., <code>double</code> type in C, with a C |
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implementation that rigorously follows Annex F of the ISO C99 standard |
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and <code>FP_CONTRACT</code> pragma set to <code>OFF</code>) on the four arithmetic |
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operations and the square root, except the default exponent range is much |
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wider and subnormal numbers are not implemented (but can be emulated). |
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|
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<p>This version of MPFR is released under the GNU Lesser General Public |
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License, Version 2.1 or any later version. |
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It is permitted to link MPFR to most non-free programs, as long as when |
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distributing them the MPFR source code and a means to re-link with a |
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modified MPFR library is provided. |
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|
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<h3 class="section">1.1 How to Use This Manual</h3> |
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|
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<p>Everyone should read <a href="#MPFR-Basics">MPFR Basics</a>. If you need to install the library |
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yourself, you need to read <a href="#Installing-MPFR">Installing MPFR</a>, too. |
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181 |
|
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<p>The rest of the manual can be used for later reference, although it is |
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probably a good idea to glance through it. |
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184 |
|
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185 |
<div class="node"> |
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186 |
<p><hr> |
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187 |
<a name="Installing-MPFR"></a> |
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188 |
Next: <a rel="next" accesskey="n" href="#Reporting-Bugs">Reporting Bugs</a>, |
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189 |
Previous: <a rel="previous" accesskey="p" href="#Introduction-to-MPFR">Introduction to MPFR</a>, |
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190 |
Up: <a rel="up" accesskey="u" href="#Top">Top</a> |
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191 |
|
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</div> |
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193 |
|
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194 |
<!-- node-name, next, previous, up --> |
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<h2 class="chapter">2 Installing MPFR</h2> |
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|
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<p><a name="index-Installation-3"></a> |
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198 |
|
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<h3 class="section">2.1 How to Install</h3> |
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200 |
|
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<p>Here are the steps needed to install the library on Unix systems |
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(more details are provided in the <samp><span class="file">INSTALL</span></samp> file): |
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|
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<ol type=1 start=1> |
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<li>To build MPFR, you first have to install GNU MP |
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(version 4.1 or higher) on your computer. |
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You need a C compiler, preferably GCC, but any reasonable compiler should |
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work. And you need a standard Unix ‘<samp><span class="samp">make</span></samp>’ program, plus some other |
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standard Unix utility programs. |
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|
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<li>In the MPFR build directory, type |
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‘<samp><span class="samp">./configure</span></samp>’ |
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|
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<p>This will prepare the build and setup the options according to your system. |
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If you get error messages, you might check that you use the same compiler |
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and compile options as for GNU MP (see the <samp><span class="file">INSTALL</span></samp> file). |
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|
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<li>‘<samp><span class="samp">make</span></samp>’ |
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|
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<p>This will compile MPFR, and create a library archive file <samp><span class="file">libmpfr.a</span></samp>. |
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A dynamic library may be produced too (see configure). |
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|
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<li>‘<samp><span class="samp">make check</span></samp>’ |
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|
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<p>This will make sure MPFR was built correctly. |
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226 |
If you get error messages, please |
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report this to ‘<samp><span class="samp">[email protected]</span></samp>’. (See <a href="#Reporting-Bugs">Reporting Bugs</a>, for |
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information on what to include in useful bug reports.) |
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|
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<li>‘<samp><span class="samp">make install</span></samp>’ |
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<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 |
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<samp><span class="file">/usr/local/include</span></samp>, the file <samp><span class="file">libmpfr.a</span></samp> to the directory |
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<samp><span class="file">/usr/local/lib</span></samp>, and the file <samp><span class="file">mpfr.info</span></samp> to the directory |
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<samp><span class="file">/usr/local/share/info</span></samp> (or if you passed the ‘<samp><span class="samp">--prefix</span></samp>’ option to |
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<samp><span class="file">configure</span></samp>, using the prefix directory given as argument to |
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‘<samp><span class="samp">--prefix</span></samp>’ instead of <samp><span class="file">/usr/local</span></samp>). |
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</ol> |
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<h3 class="section">2.2 Other `make' Targets</h3> |
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<p>There are some other useful make targets: |
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<ul> |
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<li>‘<samp><span class="samp">mpfr.info</span></samp>’ or ‘<samp><span class="samp">info</span></samp>’ |
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<p>Create an info version of the manual, in <samp><span class="file">mpfr.info</span></samp>. |
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<li>‘<samp><span class="samp">mpfr.pdf</span></samp>’ or ‘<samp><span class="samp">pdf</span></samp>’ |
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<p>Create a PDF version of the manual, in <samp><span class="file">mpfr.pdf</span></samp>. |
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<li>‘<samp><span class="samp">mpfr.dvi</span></samp>’ or ‘<samp><span class="samp">dvi</span></samp>’ |
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<p>Create a DVI version of the manual, in <samp><span class="file">mpfr.dvi</span></samp>. |
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<li>‘<samp><span class="samp">mpfr.ps</span></samp>’ or ‘<samp><span class="samp">ps</span></samp>’ |
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<p>Create a Postscript version of the manual, in <samp><span class="file">mpfr.ps</span></samp>. |
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<li>‘<samp><span class="samp">mpfr.html</span></samp>’ or ‘<samp><span class="samp">html</span></samp>’ |
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<p>Create a HTML version of the manual, in several pages in the directory |
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<samp><span class="file">mpfr.html</span></samp>; if you want only one output HTML file, then type |
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‘<samp><span class="samp">makeinfo --html --no-split mpfr.texi</span></samp>’ instead. |
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<li>‘<samp><span class="samp">clean</span></samp>’ |
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<p>Delete all object files and archive files, but not the configuration files. |
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<li>‘<samp><span class="samp">distclean</span></samp>’ |
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<p>Delete all files not included in the distribution. |
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<li>‘<samp><span class="samp">uninstall</span></samp>’ |
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<p>Delete all files copied by ‘<samp><span class="samp">make install</span></samp>’. |
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</ul> |
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<h3 class="section">2.3 Build Problems</h3> |
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<p>In case of problem, please read the <samp><span class="file">INSTALL</span></samp> file carefully |
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before reporting a bug, in particular section “In case of problem”. |
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Some problems are due to bad configuration on the user side (not |
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specific to MPFR). Problems are also mentioned in the FAQ |
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<a href="http://www.mpfr.org/faq.html">http://www.mpfr.org/faq.html</a>. |
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<!-- Warning! Do not split "MPFR ... @url{...}" across several lines --> |
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<!-- as this needs to be updated with update-version. --> |
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<p>Please report problems to ‘<samp><span class="samp">[email protected]</span></samp>’. |
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See <a href="#Reporting-Bugs">Reporting Bugs</a>. |
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Some bug fixes are available on the |
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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>. |
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|
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<h3 class="section">2.4 Getting the Latest Version of MPFR</h3> |
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|
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<p>The latest version of MPFR is available from <a href="http://www.mpfr.org/">http://www.mpfr.org/</a>. |
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<div class="node"> |
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<p><hr> |
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<a name="Reporting-Bugs"></a> |
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Next: <a rel="next" accesskey="n" href="#MPFR-Basics">MPFR Basics</a>, |
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Previous: <a rel="previous" accesskey="p" href="#Installing-MPFR">Installing MPFR</a>, |
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Up: <a rel="up" accesskey="u" href="#Top">Top</a> |
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|
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</div> |
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|
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<!-- node-name, next, previous, up --> |
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<h2 class="chapter">3 Reporting Bugs</h2> |
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<p><a name="index-Reporting-bugs-4"></a> |
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<!-- Warning! Do not split "MPFR ... @url{...}" across several lines --> |
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<!-- as this needs to be updated with update-version. --> |
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If you think you have found a bug in the MPFR library, first have a look |
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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 |
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FAQ <a href="http://www.mpfr.org/faq.html">http://www.mpfr.org/faq.html</a>: |
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perhaps this bug is already known, in which case you may find there |
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a workaround for it. Otherwise, please investigate and report it. |
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We have made this library available to you, and it is not to ask too |
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much from you, to ask you to report the bugs that you find. |
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|
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<p>There are a few things you should think about when you put your bug report |
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together. |
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|
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<p>You have to send us a test case that makes it possible for us to reproduce the |
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bug. Include instructions on how to run the test case. |
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|
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<p>You also have to explain what is wrong; if you get a crash, or if the results |
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printed are incorrect and in that case, in what way. |
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|
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<p>Please include compiler version information in your bug report. This can |
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be extracted using ‘<samp><span class="samp">cc -V</span></samp>’ on some machines, or, if you're using gcc, |
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‘<samp><span class="samp">gcc -v</span></samp>’. Also, include the output from ‘<samp><span class="samp">uname -a</span></samp>’ and the MPFR |
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version (the GMP version may be useful too). |
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|
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<p>If your bug report is good, we will do our best to help you to get a corrected |
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version of the library; if the bug report is poor, we won't do anything about |
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it (aside of chiding you to send better bug reports). |
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|
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340 |
<p>Send your bug report to: ‘<samp><span class="samp">[email protected]</span></samp>’. |
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341 |
|
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342 |
<p>If you think something in this manual is unclear, or downright incorrect, or if |
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343 |
the language needs to be improved, please send a note to the same address. |
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344 |
|
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345 |
<div class="node"> |
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346 |
<p><hr> |
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347 |
<a name="MPFR-Basics"></a> |
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348 |
Next: <a rel="next" accesskey="n" href="#MPFR-Interface">MPFR Interface</a>, |
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349 |
Previous: <a rel="previous" accesskey="p" href="#Reporting-Bugs">Reporting Bugs</a>, |
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350 |
Up: <a rel="up" accesskey="u" href="#Top">Top</a> |
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351 |
|
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352 |
</div> |
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353 |
|
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354 |
<!-- node-name, next, previous, up --> |
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355 |
<h2 class="chapter">4 MPFR Basics</h2> |
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356 |
|
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357 |
<h3 class="section">4.1 Headers and Libraries</h3> |
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358 |
|
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359 |
<p><a name="index-g_t_0040file_007bmpfr_002eh_007d-5"></a>All declarations needed to use MPFR are collected in the include file |
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360 |
<samp><span class="file">mpfr.h</span></samp>. It is designed to work with both C and C++ compilers. |
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361 |
You should include that file in any program using the MPFR library: |
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362 |
|
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363 |
<pre class="example"> #include <mpfr.h> |
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364 |
</pre> |
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365 |
<p><a name="index-g_t_0040code_007bstdio_002eh_007d-6"></a>Note however that prototypes for MPFR functions with <code>FILE *</code> parameters |
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366 |
are provided only if <code><stdio.h></code> is included too (before <samp><span class="file">mpfr.h</span></samp>). |
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367 |
|
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368 |
<pre class="example"> #include <stdio.h> |
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369 |
#include <mpfr.h> |
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370 |
</pre> |
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371 |
<p>You can avoid the use of MPFR macros encapsulating functions by defining |
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372 |
the ‘<samp><span class="samp">MPFR_USE_NO_MACRO</span></samp>’ macro before <samp><span class="file">mpfr.h</span></samp> is included. In |
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373 |
general this should not be necessary, but this can be useful when debugging |
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374 |
user code: with some macros, the compiler may emit spurious warnings with |
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375 |
some warning options, and macros can prevent some prototype checking. |
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376 |
|
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377 |
<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 |
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378 |
<samp><span class="file">libgmp</span></samp> libraries. On a typical Unix-like system this can be |
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379 |
done with ‘<samp><span class="samp">-lmpfr -lgmp</span></samp>’ (in that order), for example |
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380 |
|
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381 |
<pre class="example"> gcc myprogram.c -lmpfr -lgmp |
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382 |
</pre> |
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383 |
<p><a name="index-Libtool-10"></a>MPFR is built using Libtool and an application can use that to link if |
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384 |
desired, see <cite>GNU Libtool</cite>. |
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385 |
<!-- Note: Do not try the above cross reference without moving mpfr.info --> |
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386 |
<!-- into some "safe" place first. Due to a poor design, "info" will not --> |
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387 |
<!-- find the correct libtool info file because of the "libtool" script --> |
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388 |
<!-- in MPFR's directory! --> |
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389 |
|
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390 |
<p>If MPFR has been installed to a non-standard location, then it may be |
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391 |
necessary to set up environment variables such as ‘<samp><span class="samp">C_INCLUDE_PATH</span></samp>’ |
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392 |
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, |
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393 |
in order to point to the right directories. For a shared library, it may |
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394 |
also be necessary to set up some sort of run-time library path (e.g., |
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395 |
‘<samp><span class="samp">LD_LIBRARY_PATH</span></samp>’) on some systems. Please read the <samp><span class="file">INSTALL</span></samp> |
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396 |
file for additional information. |
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397 |
|
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398 |
<h3 class="section">4.2 Nomenclature and Types</h3> |
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399 |
|
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400 |
<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 |
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401 |
precision significand (also called mantissa) with a limited precision |
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402 |
exponent. The C data type |
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403 |
for such objects is <code>mpfr_t</code> (internally defined as a one-element |
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404 |
array of a structure, and <code>mpfr_ptr</code> is the C data type representing |
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405 |
a pointer to this structure). A floating-point number can have |
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406 |
three special values: Not-a-Number (NaN) or plus or minus Infinity. NaN |
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407 |
represents an uninitialized object, the result of an invalid operation |
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408 |
(like 0 divided by 0), or a value that cannot be determined (like |
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409 |
+Infinity minus +Infinity). Moreover, like in the IEEE 754-1985 standard, |
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410 |
zero is signed, i.e. there are both +0 and −0; the behavior |
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411 |
is the same as in the IEEE 754-1985 standard and it is generalized to |
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412 |
the other functions supported by MPFR. |
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413 |
|
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414 |
<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 |
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415 |
of a floating-point number; |
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416 |
the corresponding C data type is <code>mp_prec_t</code>. |
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417 |
The precision can be any integer between <code>MPFR_PREC_MIN</code> and |
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418 |
<code>MPFR_PREC_MAX</code>. In the current implementation, <code>MPFR_PREC_MIN</code> |
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419 |
is equal to 2. |
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420 |
|
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421 |
<p>Warning! MPFR needs to increase the precision internally, in order to |
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422 |
provide accurate results (and in particular, correct rounding). Do not |
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423 |
attempt to set the precision to any value near <code>MPFR_PREC_MAX</code>, |
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424 |
otherwise MPFR will abort due to an assertion failure. Moreover, you |
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425 |
may reach some memory limit on your platform, in which case the program |
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426 |
may abort, crash or have undefined behavior (depending on your C |
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427 |
implementation). |
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428 |
|
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429 |
<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 |
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430 |
floating-point operation, in case the exact result can not be represented |
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431 |
exactly in the destination significand; |
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432 |
the corresponding C data type is <code>mp_rnd_t</code>. |
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433 |
|
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434 |
<p><a name="index-Limb-17"></a><!-- @tindex @code{mp_limb_t} --> |
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435 |
A <dfn>limb</dfn> means the part of a multi-precision number that fits in a single |
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436 |
word. (We chose this word because a limb of the human body is analogous to a |
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437 |
digit, only larger, and containing several digits.) Normally a limb contains |
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438 |
32 or 64 bits. The C data type for a limb is <code>mp_limb_t</code>. |
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439 |
|
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440 |
<h3 class="section">4.3 Function Classes</h3> |
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441 |
|
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442 |
<p>There is only one class of functions in the MPFR library: |
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443 |
|
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444 |
<ol type=1 start=1> |
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445 |
<li>Functions for floating-point arithmetic, with names beginning with |
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446 |
<code>mpfr_</code>. The associated type is <code>mpfr_t</code>. |
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447 |
</ol> |
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448 |
|
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449 |
<h3 class="section">4.4 MPFR Variable Conventions</h3> |
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450 |
|
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451 |
<p>As a general rule, all MPFR functions expect output arguments before input |
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452 |
arguments. This notation is based on an analogy with the assignment operator. |
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453 |
|
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454 |
<p>MPFR allows you to use the same variable for both input and output in the same |
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455 |
expression. For example, the main function for floating-point multiplication, |
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456 |
<code>mpfr_mul</code>, can be used like this: <code>mpfr_mul (x, x, x, rnd_mode)</code>. |
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|
457 |
This |
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458 |
computes the square of <var>x</var> with rounding mode <code>rnd_mode</code> |
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459 |
and puts the result back in <var>x</var>. |
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460 |
|
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461 |
<p>Before you can assign to an MPFR variable, you need to initialize it by calling |
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462 |
one of the special initialization functions. When you're done with a |
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463 |
variable, you need to clear it out, using one of the functions for that |
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464 |
purpose. |
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|
465 |
|
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466 |
<p>A variable should only be initialized once, or at least cleared out between |
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467 |
each initialization. After a variable has been initialized, it may be |
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468 |
assigned to any number of times. |
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|
469 |
|
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470 |
<p>For efficiency reasons, avoid to initialize and clear out a variable in loops. |
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471 |
Instead, initialize it before entering the loop, and clear it out after the |
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472 |
loop has exited. |
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|
473 |
|
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474 |
<p>You don't need to be concerned about allocating additional space for MPFR |
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|
475 |
variables, since any variable has a significand of fixed size. |
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476 |
Hence unless you change its precision, or clear and reinitialize it, |
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|
477 |
a floating-point variable will have the same allocated space during all its |
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|
478 |
life. |
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|
479 |
|
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|
480 |
<h3 class="section">4.5 Rounding Modes</h3> |
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|
481 |
|
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|
482 |
<p>The following four rounding modes are supported: |
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changeset
|
483 |
|
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|
484 |
<ul> |
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|
485 |
<li><code>GMP_RNDN</code>: round to nearest |
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|
486 |
<li><code>GMP_RNDZ</code>: round toward zero |
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|
487 |
<li><code>GMP_RNDU</code>: round toward plus infinity |
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|
488 |
<li><code>GMP_RNDD</code>: round toward minus infinity |
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|
489 |
</ul> |
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changeset
|
490 |
|
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|
491 |
<p>The ‘<samp><span class="samp">round to nearest</span></samp>’ mode works as in the IEEE 754-1985 standard: in |
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|
492 |
case the number to be rounded lies exactly in the middle of two representable |
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|
493 |
numbers, it is rounded to the one with the least significant bit set to zero. |
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|
494 |
For example, the number 5/2, which is represented by (10.1) in binary, is |
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|
495 |
rounded to (10.0)=2 with a precision of two bits, and not to (11.0)=3. |
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|
496 |
This rule avoids the <dfn>drift</dfn> phenomenon mentioned by Knuth in volume 2 |
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parents:
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|
497 |
of The Art of Computer Programming (Section 4.2.2). |
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|
498 |
|
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|
499 |
<p>Most MPFR functions take as first argument the destination variable, as |
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|
500 |
second and following arguments the input variables, as last argument a |
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|
501 |
rounding mode, and have a return value of type <code>int</code>, called the |
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parents:
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|
502 |
<dfn>ternary value</dfn>. The value stored in the destination variable is |
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parents:
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|
503 |
correctly rounded, i.e. MPFR behaves as if it computed the result with |
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parents:
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|
504 |
an infinite precision, then rounded it to the precision of this variable. |
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parents:
diff
changeset
|
505 |
The input variables are regarded as exact (in particular, their precision |
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parents:
diff
changeset
|
506 |
does not affect the result). |
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parents:
diff
changeset
|
507 |
|
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parents:
diff
changeset
|
508 |
<p>As a consequence, in case of a non-zero real rounded result, the error |
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parents:
diff
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|
509 |
on the result is less or equal to 1/2 ulp (unit in the last place) of |
22d9e175d379
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parents:
diff
changeset
|
510 |
the target in the rounding to nearest mode, and less than 1 ulp of the |
22d9e175d379
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parents:
diff
changeset
|
511 |
target in the directed rounding modes (a ulp is the weight of the least |
22d9e175d379
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parents:
diff
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|
512 |
significant represented bit of the target after rounding). |
22d9e175d379
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parents:
diff
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|
513 |
<!-- Since subnormals are not supported, we must take into account the ulp of --> |
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|
514 |
<!-- the rounded result, not the one of the exact result, for full generality. --> |
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parents:
diff
changeset
|
515 |
|
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parents:
diff
changeset
|
516 |
<p>Unless documented otherwise, functions returning an <code>int</code> return |
22d9e175d379
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
517 |
a ternary value. |
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parents:
diff
changeset
|
518 |
If the ternary value is zero, it means that the value stored in the |
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parents:
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changeset
|
519 |
destination variable is the exact result of the corresponding mathematical |
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parents:
diff
changeset
|
520 |
function. If the ternary value is positive (resp. negative), it means |
22d9e175d379
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parents:
diff
changeset
|
521 |
the value stored in the destination variable is greater (resp. lower) |
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parents:
diff
changeset
|
522 |
than the exact result. For example with the <code>GMP_RNDU</code> rounding mode, |
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parents:
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|
523 |
the ternary value is usually positive, except when the result is exact, in |
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parents:
diff
changeset
|
524 |
which case it is zero. In the case of an infinite result, it is considered |
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parents:
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|
525 |
as inexact when it was obtained by overflow, and exact otherwise. A NaN |
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parents:
diff
changeset
|
526 |
result (Not-a-Number) always corresponds to an exact return value. |
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parents:
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changeset
|
527 |
The opposite of a returned ternary value is guaranteed to be representable |
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parents:
diff
changeset
|
528 |
in an <code>int</code>. |
22d9e175d379
7041521 GNU MP to Userland
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parents:
diff
changeset
|
529 |
|
22d9e175d379
7041521 GNU MP to Userland
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diff
changeset
|
530 |
<p>Unless documented otherwise, functions returning a <code>1</code> |
22d9e175d379
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parents:
diff
changeset
|
531 |
(or any other value specified in this manual) |
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parents:
diff
changeset
|
532 |
for special cases (like <code>acos(0)</code>) should return an overflow or |
22d9e175d379
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parents:
diff
changeset
|
533 |
an underflow if <code>1</code> is not representable in the current exponent range. |
22d9e175d379
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parents:
diff
changeset
|
534 |
|
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7041521 GNU MP to Userland
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parents:
diff
changeset
|
535 |
<h3 class="section">4.6 Floating-Point Values on Special Numbers</h3> |
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parents:
diff
changeset
|
536 |
|
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parents:
diff
changeset
|
537 |
<p>This section specifies the floating-point values (of type <code>mpfr_t</code>) |
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parents:
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|
538 |
returned by MPFR functions. For functions returning several values (like |
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parents:
diff
changeset
|
539 |
<code>mpfr_sin_cos</code>), the rules apply to each result separately. |
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parents:
diff
changeset
|
540 |
|
22d9e175d379
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parents:
diff
changeset
|
541 |
<p>Functions can have one or several input arguments. An input point is |
22d9e175d379
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parents:
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changeset
|
542 |
a mapping from these input arguments to the set of the MPFR numbers. |
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parents:
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changeset
|
543 |
When none of its components are NaN, an input point can also be seen |
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parents:
diff
changeset
|
544 |
as a tuple in the extended real numbers (the set of the real numbers |
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parents:
diff
changeset
|
545 |
with both infinities). |
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parents:
diff
changeset
|
546 |
|
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parents:
diff
changeset
|
547 |
<p>When the input point is in the domain of the mathematical function, the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
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|
548 |
result is rounded as described in Section “Rounding Modes” (but see |
22d9e175d379
7041521 GNU MP to Userland
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parents:
diff
changeset
|
549 |
below for the specification of the sign of an exact zero). Otherwise |
22d9e175d379
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parents:
diff
changeset
|
550 |
the general rules from this section apply unless stated otherwise in |
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parents:
diff
changeset
|
551 |
the description of the MPFR function (<a href="#MPFR-Interface">MPFR Interface</a>). |
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parents:
diff
changeset
|
552 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
553 |
<p>When the input point is not in the domain of the mathematical function |
22d9e175d379
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parents:
diff
changeset
|
554 |
but is in its closure in the extended real numbers and the function can |
22d9e175d379
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parents:
diff
changeset
|
555 |
be extended by continuity, the result is the obtained limit. |
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parents:
diff
changeset
|
556 |
Examples: <code>mpfr_hypot</code> on (+Inf,0) gives +Inf. But <code>mpfr_pow</code> |
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parents:
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|
557 |
cannot be defined on (1,+Inf) using this rule, as one can find |
22d9e175d379
7041521 GNU MP to Userland
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parents:
diff
changeset
|
558 |
sequences (<var>x</var>_<var>n</var>,<var>y</var>_<var>n</var>) such that |
22d9e175d379
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parents:
diff
changeset
|
559 |
<var>x</var>_<var>n</var> goes to 1, <var>y</var>_<var>n</var> goes to +Inf |
22d9e175d379
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parents:
diff
changeset
|
560 |
and <var>x</var>_<var>n</var> to the <var>y</var>_<var>n</var> goes to any |
22d9e175d379
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parents:
diff
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|
561 |
positive value when <var>n</var> goes to the infinity. |
22d9e175d379
7041521 GNU MP to Userland
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parents:
diff
changeset
|
562 |
|
22d9e175d379
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parents:
diff
changeset
|
563 |
<p>When the input point is in the closure of the domain of the mathematical |
22d9e175d379
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
564 |
function and an input argument is +0 (resp. −0), one considers |
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parents:
diff
changeset
|
565 |
the limit when the corresponding argument approaches 0 from above |
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parents:
diff
changeset
|
566 |
(resp. below). If the limit is not defined (e.g., <code>mpfr_log</code> on |
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parents:
diff
changeset
|
567 |
−0), the behavior must be specified in the description of the |
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
568 |
MPFR function. |
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
569 |
|
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7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
570 |
<p>When the result is equal to 0, its sign is determined by considering the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
571 |
limit as if the input point were not in the domain: If one approaches 0 |
22d9e175d379
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
572 |
from above (resp. below), the result is +0 (resp. −0). In the |
22d9e175d379
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
573 |
other cases, the sign must be specified in the description of the MPFR |
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
574 |
function. Example: <code>mpfr_sin</code> on +0 gives +0. |
22d9e175d379
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
575 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
576 |
<p>When the input point is not in the closure of the domain of the function, |
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
577 |
the result is NaN. Example: <code>mpfr_sqrt</code> on −17 gives NaN. |
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
578 |
|
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7041521 GNU MP to Userland
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parents:
diff
changeset
|
579 |
<p>When an input argument is NaN, the result is NaN, possibly except when |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
580 |
a partial function is constant on the finite floating-point numbers; |
22d9e175d379
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parents:
diff
changeset
|
581 |
such a case is always explicitly specified in <a href="#MPFR-Interface">MPFR Interface</a>. |
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parents:
diff
changeset
|
582 |
<!-- Said otherwise, if such a case is not specified, this is a bug, thus --> |
22d9e175d379
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
583 |
<!-- we may change the returned value after documenting it without having --> |
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
584 |
<!-- to change the libtool interface number (this would have more drawbacks --> |
22d9e175d379
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
585 |
<!-- that advantages in practice), like for any bug fix. --> |
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parents:
diff
changeset
|
586 |
Example: <code>mpfr_hypot</code> on (NaN,0) gives NaN, but <code>mpfr_hypot</code> |
22d9e175d379
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
587 |
on (NaN,+Inf) gives +Inf (as specified in <a href="#Special-Functions">Special Functions</a>), |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
588 |
since for any finite input <var>x</var>, <code>mpfr_hypot</code> on (<var>x</var>,+Inf) |
22d9e175d379
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
589 |
gives +Inf. |
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parents:
diff
changeset
|
590 |
|
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7041521 GNU MP to Userland
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parents:
diff
changeset
|
591 |
<h3 class="section">4.7 Exceptions</h3> |
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parents:
diff
changeset
|
592 |
|
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7041521 GNU MP to Userland
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parents:
diff
changeset
|
593 |
<p>MPFR supports 5 exception types: |
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7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
594 |
|
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7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
595 |
<ul> |
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parents:
diff
changeset
|
596 |
<li>Underflow: |
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7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
597 |
An underflow occurs when the exact result of a function is a non-zero |
22d9e175d379
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
598 |
real number and the result obtained after the rounding, assuming an |
22d9e175d379
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
599 |
unbounded exponent range (for the rounding), has an exponent smaller |
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
600 |
than the minimum exponent of the current range. In the round-to-nearest |
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7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
601 |
mode, the halfway case is rounded toward zero. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
602 |
|
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7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
603 |
<p>Note: This is not the single definition of the underflow. MPFR chooses |
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
604 |
to consider the underflow after rounding. The underflow before rounding |
22d9e175d379
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
605 |
can also be defined. For instance, consider a function that has the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
606 |
exact result 7 multiplied by two to the power |
22d9e175d379
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
607 |
<var>e</var>−4, where <var>e</var> is the smallest exponent (for a |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
608 |
significand between 1/2 and 1) in the current |
22d9e175d379
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
609 |
range, with a 2-bit target precision and rounding toward plus infinity. |
22d9e175d379
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
610 |
The exact result has the exponent <var>e</var>−1. With the underflow |
22d9e175d379
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
611 |
before rounding, such a function call would yield an underflow, as |
22d9e175d379
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
612 |
<var>e</var>−1 is outside the current exponent range. However, MPFR |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
613 |
first considers the rounded result assuming an unbounded exponent range. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
614 |
The exact result cannot be represented exactly in precision 2, and here, |
22d9e175d379
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
615 |
it is rounded to 0.5 times 2 to <var>e</var>, which is |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
616 |
representable in the current exponent range. As a consequence, this will |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
617 |
not yield an underflow in MPFR. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
618 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
619 |
<li>Overflow: |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
620 |
An overflow occurs when the exact result of a function is a non-zero |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
621 |
real number and the result obtained after the rounding, assuming an |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
622 |
unbounded exponent range (for the rounding), has an exponent larger |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
623 |
than the maximum exponent of the current range. In the round-to-nearest |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
624 |
mode, the result is infinite. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
625 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
626 |
<li>NaN: |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
627 |
A NaN exception occurs when the result of a function is a NaN. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
628 |
<!-- NaN is defined above. So, we don't say anything more. --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
629 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
630 |
<li>Inexact: |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
631 |
An inexact exception occurs when the result of a function cannot be |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
632 |
represented exactly and must be rounded. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
633 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
634 |
<li>Range error: |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
635 |
A range exception occurs when a function that does not return a MPFR |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
636 |
number (such as comparisons and conversions to an integer) has an |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
637 |
invalid result (e.g. an argument is NaN in <code>mpfr_cmp</code> or in a |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
638 |
conversion to an integer). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
639 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
640 |
</ul> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
641 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
642 |
<p>MPFR has a global flag for each exception, which can be cleared, set |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
643 |
or tested by functions described in <a href="#Exception-Related-Functions">Exception Related Functions</a>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
644 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
645 |
<p>Differences with the ISO C99 standard: |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
646 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
647 |
<ul> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
648 |
<li>In C, only quiet NaNs are specified, and a NaN propagation does not |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
649 |
raise an invalid exception. Unless explicitly stated otherwise, MPFR sets |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
650 |
the NaN flag whenever a NaN is generated, even when a NaN is propagated |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
651 |
(e.g. in NaN + NaN), as if all NaNs were signaling. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
652 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
653 |
<li>An invalid exception in C corresponds to either a NaN exception or |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
654 |
a range error in MPFR. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
655 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
656 |
</ul> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
657 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
658 |
<h3 class="section">4.8 Memory Handling</h3> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
659 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
660 |
<p>MPFR functions may create caches, e.g. when computing constants such |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
661 |
as Pi, either because the user has called a function like |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
662 |
<code>mpfr_const_pi</code> directly or because such a function was called |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
663 |
internally by the MPFR library itself to compute some other function. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
664 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
665 |
<p>At any time, the user can free the various caches with |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
666 |
<code>mpfr_free_cache</code>. It is strongly advised to do that before |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
667 |
terminating a thread, or before exiting when using tools like |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
668 |
‘<samp><span class="samp">valgrind</span></samp>’ (to avoid memory leaks being reported). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
669 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
670 |
<p>MPFR internal data such as flags, the exponent range, the default |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
671 |
precision and rounding mode, and caches (i.e., data that are not |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
672 |
accessed via parameters) are either global (if MPFR has not been |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
673 |
compiled as thread safe) or per-thread (thread local storage). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
674 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
675 |
<div class="node"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
676 |
<p><hr> |
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7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
677 |
<a name="MPFR-Interface"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
678 |
Next: <a rel="next" accesskey="n" href="#Contributors">Contributors</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
679 |
Previous: <a rel="previous" accesskey="p" href="#MPFR-Basics">MPFR Basics</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
680 |
Up: <a rel="up" accesskey="u" href="#Top">Top</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
681 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
682 |
</div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
683 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
684 |
<!-- node-name, next, previous, up --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
685 |
<h2 class="chapter">5 MPFR Interface</h2> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
686 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
687 |
<p><a name="index-Floating_002dpoint-functions-18"></a><a name="index-Float-functions-19"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
688 |
The floating-point functions expect arguments of type <code>mpfr_t</code>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
689 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
690 |
<p>The MPFR floating-point functions have an interface that is similar to the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
691 |
GNU MP |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
692 |
integer functions. The function prefix for floating-point operations is |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
693 |
<code>mpfr_</code>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
694 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
695 |
<p>There is one significant characteristic of floating-point numbers that has |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
696 |
motivated a difference between this function class and other GNU MP function |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
697 |
classes: the inherent inexactness of floating-point arithmetic. The user has |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
698 |
to specify the precision for each variable. A computation that assigns a |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
699 |
variable will take place with the precision of the assigned variable; the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
700 |
cost of that computation should not depend from the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
701 |
precision of variables used as input (on average). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
702 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
703 |
<p><a name="index-Precision-20"></a>The semantics of a calculation in MPFR is specified as follows: Compute the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
704 |
requested operation exactly (with “infinite accuracy”), and round the result |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
705 |
to the precision of the destination variable, with the given rounding mode. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
706 |
The MPFR floating-point functions are intended to be a smooth extension |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
707 |
of the IEEE 754-1985 arithmetic. The results obtained on one computer should |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
708 |
not differ from the results obtained on a computer with a different word size. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
709 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
710 |
<p><a name="index-Accuracy-21"></a>MPFR does not keep track of the accuracy of a computation. This is left |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
711 |
to the user or to a higher layer. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
712 |
As a consequence, if two variables are used to store |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
713 |
only a few significant bits, and their product is stored in a variable with large |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
714 |
precision, then MPFR will still compute the result with full precision. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
715 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
716 |
<p>The value of the standard C macro <code>errno</code> may be set to non-zero by |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
717 |
any MPFR function or macro, whether or not there is an error. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
718 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
719 |
<ul class="menu"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
720 |
<li><a accesskey="1" href="#Initialization-Functions">Initialization Functions</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
721 |
<li><a accesskey="2" href="#Assignment-Functions">Assignment Functions</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
722 |
<li><a accesskey="3" href="#Combined-Initialization-and-Assignment-Functions">Combined Initialization and Assignment Functions</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
723 |
<li><a accesskey="4" href="#Conversion-Functions">Conversion Functions</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
724 |
<li><a accesskey="5" href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
725 |
<li><a accesskey="6" href="#Comparison-Functions">Comparison Functions</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
726 |
<li><a accesskey="7" href="#Special-Functions">Special Functions</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
727 |
<li><a accesskey="8" href="#Input-and-Output-Functions">Input and Output Functions</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
728 |
<li><a accesskey="9" href="#Integer-Related-Functions">Integer Related Functions</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
729 |
<li><a href="#Miscellaneous-Functions">Miscellaneous Functions</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
730 |
<li><a href="#Rounding-Mode-Related-Functions">Rounding Mode Related Functions</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
731 |
<li><a href="#Exception-Related-Functions">Exception Related Functions</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
732 |
<li><a href="#Advanced-Functions">Advanced Functions</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
733 |
<li><a href="#Compatibility-with-MPF">Compatibility with MPF</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
734 |
<li><a href="#Custom-Interface">Custom Interface</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
735 |
<li><a href="#Internals">Internals</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
736 |
</ul> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
737 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
738 |
<div class="node"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
739 |
<p><hr> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
740 |
<a name="Initialization-Functions"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
741 |
Next: <a rel="next" accesskey="n" href="#Assignment-Functions">Assignment Functions</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
742 |
Previous: <a rel="previous" accesskey="p" href="#MPFR-Interface">MPFR Interface</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
743 |
Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
744 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
745 |
</div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
746 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
747 |
<!-- node-name, next, previous, up --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
748 |
<p><a name="index-Initialization-functions-22"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
749 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
750 |
<h3 class="section">5.1 Initialization Functions</h3> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
751 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
752 |
<p>An <code>mpfr_t</code> object must be initialized before storing the first value in |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
753 |
it. The functions <code>mpfr_init</code> and <code>mpfr_init2</code> are used for that |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
754 |
purpose. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
755 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
756 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
757 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
758 |
<blockquote><p>Initialize <var>x</var>, set its precision to be <strong>exactly</strong> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
759 |
<var>prec</var> bits and its value to NaN. (Warning: the corresponding |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
760 |
<code>mpf</code> functions initialize to zero instead.) |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
761 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
762 |
<p>Normally, a variable should be initialized once only or at |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
763 |
least be cleared, using <code>mpfr_clear</code>, between initializations. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
764 |
To change the precision of a variable which has already been initialized, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
765 |
use <code>mpfr_set_prec</code>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
766 |
The precision <var>prec</var> must be an integer between <code>MPFR_PREC_MIN</code> and |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
767 |
<code>MPFR_PREC_MAX</code> (otherwise the behavior is undefined). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
768 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
769 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
770 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
771 |
— Function: void <b>mpfr_clear</b> (<var>mpfr_t x</var>)<var><a name="index-mpfr_005fclear-24"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
772 |
<blockquote><p>Free the space occupied by <var>x</var>. Make sure to call this function for all |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
773 |
<code>mpfr_t</code> variables when you are done with them. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
774 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
775 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
776 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
777 |
— Function: void <b>mpfr_init</b> (<var>mpfr_t x</var>)<var><a name="index-mpfr_005finit-25"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
778 |
<blockquote><p>Initialize <var>x</var> and set its value to NaN. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
779 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
780 |
<p>Normally, a variable should be initialized once only |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
781 |
or at least be cleared, using <code>mpfr_clear</code>, between initializations. The |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
782 |
precision of <var>x</var> is the default precision, which can be changed |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
783 |
by a call to <code>mpfr_set_default_prec</code>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
784 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
785 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
786 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
787 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
788 |
<blockquote><p>Set the default precision to be <strong>exactly</strong> <var>prec</var> bits. The |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
789 |
precision of a variable means the number of bits used to store its significand. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
790 |
All |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
791 |
subsequent calls to <code>mpfr_init</code> will use this precision, but previously |
22d9e175d379
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
792 |
initialized variables are unaffected. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
793 |
This default precision is set to 53 bits initially. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
794 |
The precision can be any integer between <code>MPFR_PREC_MIN</code> and |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
795 |
<code>MPFR_PREC_MAX</code>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
796 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
797 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
798 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
799 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
800 |
<blockquote><p>Return the default MPFR precision in bits. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
801 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
802 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
803 |
<p>Here is an example on how to initialize floating-point variables: |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
804 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
805 |
<pre class="example"> { |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
806 |
mpfr_t x, y; |
22d9e175d379
7041521 GNU MP to Userland
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parents:
diff
changeset
|
807 |
mpfr_init (x); /* use default precision */ |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
808 |
mpfr_init2 (y, 256); /* precision <em>exactly</em> 256 bits */ |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
809 |
... |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
810 |
/* When the program is about to exit, do ... */ |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
811 |
mpfr_clear (x); |
22d9e175d379
7041521 GNU MP to Userland
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parents:
diff
changeset
|
812 |
mpfr_clear (y); |
22d9e175d379
7041521 GNU MP to Userland
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parents:
diff
changeset
|
813 |
mpfr_free_cache (); |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
814 |
} |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
815 |
</pre> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
816 |
<p>The following functions are useful for changing the precision during a |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
817 |
calculation. A typical use would be for adjusting the precision gradually in |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
818 |
iterative algorithms like Newton-Raphson, making the computation precision |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
819 |
closely match the actual accurate part of the numbers. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
820 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
821 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
822 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
823 |
<blockquote><p>Reset the precision of <var>x</var> to be <strong>exactly</strong> <var>prec</var> bits, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
824 |
and set its value to NaN. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
825 |
The previous value stored in <var>x</var> is lost. It is equivalent to |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
826 |
a call to <code>mpfr_clear(x)</code> followed by a call to |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
827 |
<code>mpfr_init2(x, prec)</code>, but more efficient as no allocation is done in |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
828 |
case the current allocated space for the significand of <var>x</var> is enough. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
829 |
The precision <var>prec</var> can be any integer between <code>MPFR_PREC_MIN</code> and |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
830 |
<code>MPFR_PREC_MAX</code>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
831 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
832 |
<p>In case you want to keep the previous value stored in <var>x</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
833 |
use <code>mpfr_prec_round</code> instead. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
834 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
835 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
836 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
837 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
838 |
<blockquote><p>Return the precision actually used for assignments of <var>x</var>, i.e. the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
839 |
number of bits used to store its significand. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
840 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
841 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
842 |
<div class="node"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
843 |
<p><hr> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
844 |
<a name="Assignment-Functions"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
845 |
Next: <a rel="next" accesskey="n" href="#Combined-Initialization-and-Assignment-Functions">Combined Initialization and Assignment Functions</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
846 |
Previous: <a rel="previous" accesskey="p" href="#Initialization-Functions">Initialization Functions</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
847 |
Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
848 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
849 |
</div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
850 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
851 |
<!-- node-name, next, previous, up --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
852 |
<p><a name="index-Assignment-functions-30"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
853 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
854 |
<h3 class="section">5.2 Assignment Functions</h3> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
855 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
856 |
<p>These functions assign new values to already initialized floats |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
857 |
(see <a href="#Initialization-Functions">Initialization Functions</a>). When using any functions using |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
858 |
<code>intmax_t</code>, you must include <code><stdint.h></code> or <code><inttypes.h></code> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
859 |
before <samp><span class="file">mpfr.h</span></samp>, to allow <samp><span class="file">mpfr.h</span></samp> to define prototypes for |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
860 |
these functions. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
861 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
862 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
863 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
864 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
865 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
866 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
867 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
868 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
869 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
870 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
871 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
872 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
873 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
874 |
<blockquote><p>Set the value of <var>rop</var> from <var>op</var>, rounded |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
875 |
toward the given direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
876 |
Note that the input 0 is converted to +0 by <code>mpfr_set_ui</code>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
877 |
<code>mpfr_set_si</code>, <code>mpfr_set_sj</code>, <code>mpfr_set_uj</code>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
878 |
<code>mpfr_set_z</code>, <code>mpfr_set_q</code> and |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
879 |
<code>mpfr_set_f</code>, regardless of the rounding mode. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
880 |
If the system doesn't support the IEEE-754 standard, <code>mpfr_set_d</code>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
881 |
<code>mpfr_set_ld</code> and |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
882 |
<code>mpfr_set_decimal64</code> might not preserve the signed zeros. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
883 |
The <code>mpfr_set_decimal64</code> function is built only with the configure |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
884 |
option ‘<samp><span class="samp">--enable-decimal-float</span></samp>’, which also requires |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
885 |
‘<samp><span class="samp">--with-gmp-build</span></samp>’, and when the compiler or |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
886 |
system provides the ‘<samp><span class="samp">_Decimal64</span></samp>’ data type |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
887 |
(GCC version 4.2.0 is known to support this data type, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
888 |
but only when configured with ‘<samp><span class="samp">--enable-decimal-float</span></samp>’ too). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
889 |
<code>mpfr_set_q</code> might not be able to work if the numerator (or the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
890 |
denominator) can not be representable as a <code>mpfr_t</code>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
891 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
892 |
<p>Note: If you want to store a floating-point constant to a <code>mpfr_t</code>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
893 |
you should use <code>mpfr_set_str</code> (or one of the MPFR constant functions, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
894 |
such as <code>mpfr_const_pi</code> for Pi) instead of <code>mpfr_set_d</code>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
895 |
<code>mpfr_set_ld</code> or <code>mpfr_set_decimal64</code>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
896 |
Otherwise the floating-point constant will be first |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
897 |
converted into a reduced-precision (e.g., 53-bit) binary number before |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
898 |
MPFR can work with it. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
899 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
900 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
901 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
902 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
903 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
904 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
905 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
906 |
<blockquote><p>Set the value of <var>rop</var> from <var>op</var> multiplied by |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
907 |
two to the power <var>e</var>, rounded toward the given direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
908 |
Note that the input 0 is converted to +0. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
909 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
910 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
911 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
912 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
913 |
<blockquote><p>Set <var>rop</var> to the value of the whole string <var>s</var> in base <var>base</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
914 |
rounded in the direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
915 |
See the documentation of <code>mpfr_strtofr</code> for a detailed description |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
916 |
of the valid string formats. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
917 |
<!-- Additionally, special values --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
918 |
<!-- @code{@@NaN@@}, @code{@@Inf@@}, @code{+@@Inf@@} and @code{-@@Inf@@}, --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
919 |
<!-- all case insensitive, without leading whitespace and possibly followed by --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
920 |
<!-- other characters, are accepted too (it may change). --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
921 |
This function returns 0 if the entire string up to the final null character |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
922 |
is a valid number in base <var>base</var>; otherwise it returns −1, and |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
923 |
<var>rop</var> may have changed. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
924 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
925 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
926 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
927 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
928 |
<blockquote> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
929 |
<p>Read a floating-point number from a string <var>nptr</var> in base <var>base</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
930 |
rounded in the direction <var>rnd</var>; <var>base</var> must be either 0 (to |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
931 |
detect the base, as described below) or a number from 2 to 36 (otherwise |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
932 |
the behavior is undefined). If <var>nptr</var> starts with valid data, the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
933 |
result is stored in <var>rop</var> and <code>*</code><var>endptr</var> points to the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
934 |
character just after the valid data (if <var>endptr</var> is not a null pointer); |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
935 |
otherwise <var>rop</var> is set to zero and the value of <var>nptr</var> is stored |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
936 |
in the location referenced by <var>endptr</var> (if <var>endptr</var> is not a null |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
937 |
pointer). The usual ternary value is returned. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
938 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
939 |
<p>Parsing follows the standard C <code>strtod</code> function with some extensions. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
940 |
Case is ignored. After optional leading whitespace, one has a subject |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
941 |
sequence consisting of an optional sign (<code>+</code> or <code>-</code>), and either |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
942 |
numeric data or special data. The subject sequence is defined as the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
943 |
longest initial subsequence of the input string, starting with the first |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
944 |
non-whitespace character, that is of the expected form. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
945 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
946 |
<p>The form of numeric data is a non-empty sequence of significand digits |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
947 |
with an optional decimal point, and an optional exponent consisting of |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
948 |
an exponent prefix followed by an optional sign and a non-empty sequence |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
949 |
of decimal digits. A significand digit is either a decimal digit or a |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
950 |
Latin letter (62 possible characters), with <code>a</code> = 10, <code>b</code> = 11, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
951 |
<small class="dots">...</small>, <code>z</code> = 36; its value must be strictly less than the base. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
952 |
The decimal point can be either the one defined by the current locale or |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
953 |
the period (the first one is accepted for consistency with the C standard |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
954 |
and the practice, the second one is accepted to allow the programmer to |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
955 |
provide MPFR numbers from strings in a way that does not depend on the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
956 |
current locale). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
957 |
The exponent prefix can be <code>e</code> or <code>E</code> for bases up to 10, or |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
958 |
<code>@</code> in any base; it indicates a multiplication by a power of the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
959 |
base. In bases 2 and 16, the exponent prefix can also be <code>p</code> or |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
960 |
<code>P</code>, in which case it introduces a binary exponent: it indicates a |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
961 |
multiplication by a power of 2 (there is a difference only for base 16). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
962 |
The value of an exponent is always written in base 10. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
963 |
In base 2, the significand can start with <code>0b</code> or <code>0B</code>, and |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
964 |
in base 16, it can start with <code>0x</code> or <code>0X</code>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
965 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
966 |
<p>If the argument <var>base</var> is 0, then the base is automatically detected |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
967 |
as follows. If the significand starts with <code>0b</code> or <code>0B</code>, base 2 |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
968 |
is assumed. If the significand starts with <code>0x</code> or <code>0X</code>, base 16 |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
969 |
is assumed. Otherwise base 10 is assumed. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
970 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
971 |
<p>Note: The exponent must contain at least a digit. Otherwise the possible |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
972 |
exponent prefix and sign are not part of the number (which ends with the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
973 |
significand). Similarly, if <code>0b</code>, <code>0B</code>, <code>0x</code> or <code>0X</code> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
974 |
is not followed by a binary/hexadecimal digit, then the subject sequence |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
975 |
stops at the character <code>0</code>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
976 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
977 |
<p>Special data (for infinities and NaN) can be <code>@inf@</code> or |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
978 |
<code>@nan@(n-char-sequence)</code>, and if <var>base</var> <= 16, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
979 |
it can also be <code>infinity</code>, <code>inf</code>, <code>nan</code> or |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
980 |
<code>nan(n-char-sequence)</code>, all case insensitive. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
981 |
A <code>n-char-sequence</code> is a non-empty string containing only digits, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
982 |
Latin letters and the underscore (0, 1, 2, <small class="dots">...</small>, 9, a, b, <small class="dots">...</small>, z, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
983 |
A, B, <small class="dots">...</small>, Z, _). Note: one has an optional sign for all data, even |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
984 |
NaN. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
985 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
986 |
</blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
987 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
988 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
989 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
990 |
— Function: void <b>mpfr_set_nan</b> (<var>mpfr_t x</var>)<var><a name="index-mpfr_005fset_005fnan-49"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
991 |
<blockquote><p>Set the variable <var>x</var> to infinity or NaN (Not-a-Number) respectively. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
992 |
In <code>mpfr_set_inf</code>, <var>x</var> is set to plus infinity iff <var>sign</var> is |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
993 |
nonnegative. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
994 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
995 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
996 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
997 |
— Function: void <b>mpfr_swap</b> (<var>mpfr_t x, mpfr_t y</var>)<var><a name="index-mpfr_005fswap-50"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
998 |
<blockquote><p>Swap the values <var>x</var> and <var>y</var> efficiently. Warning: the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
999 |
precisions are exchanged too; in case the precisions are different, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1000 |
<code>mpfr_swap</code> is thus not equivalent to three <code>mpfr_set</code> calls |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1001 |
using a third auxiliary variable. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1002 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1003 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1004 |
<div class="node"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1005 |
<p><hr> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1006 |
<a name="Combined-Initialization-and-Assignment-Functions"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1007 |
Next: <a rel="next" accesskey="n" href="#Conversion-Functions">Conversion Functions</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1008 |
Previous: <a rel="previous" accesskey="p" href="#Assignment-Functions">Assignment Functions</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1009 |
Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1010 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1011 |
</div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1012 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1013 |
<!-- node-name, next, previous, up --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1014 |
<p><a name="index-Combined-initialization-and-assignment-functions-51"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1015 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1016 |
<h3 class="section">5.3 Combined Initialization and Assignment Functions</h3> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1017 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1018 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1019 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1020 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1021 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1022 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1023 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1024 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1025 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1026 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1027 |
<blockquote><p>Initialize <var>rop</var> and set its value from <var>op</var>, rounded in the direction |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1028 |
<var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1029 |
The precision of <var>rop</var> will be taken from the active default precision, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1030 |
as set by <code>mpfr_set_default_prec</code>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1031 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1032 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1033 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1034 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1035 |
<blockquote><p>Initialize <var>x</var> and set its value from |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1036 |
the string <var>s</var> in base <var>base</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1037 |
rounded in the direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1038 |
See <code>mpfr_set_str</code>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1039 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1040 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1041 |
<div class="node"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1042 |
<p><hr> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1043 |
<a name="Conversion-Functions"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1044 |
Next: <a rel="next" accesskey="n" href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1045 |
Previous: <a rel="previous" accesskey="p" href="#Combined-Initialization-and-Assignment-Functions">Combined Initialization and Assignment Functions</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1046 |
Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1047 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1048 |
</div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1049 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1050 |
<!-- node-name, next, previous, up --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1051 |
<p><a name="index-Conversion-functions-61"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1052 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1053 |
<h3 class="section">5.4 Conversion Functions</h3> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1054 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1055 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1056 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1057 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1058 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1059 |
<blockquote><p>Convert <var>op</var> to a <code>double</code> (respectively <code>_Decimal64</code> or |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1060 |
<code>long double</code>), using the rounding mode <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1061 |
If <var>op</var> is NaN, some fixed NaN (either quiet or signaling) or the result |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1062 |
of 0.0/0.0 is returned. If <var>op</var> is �Inf, an infinity of the same |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1063 |
sign or the result of �1.0/0.0 is returned. If <var>op</var> is zero, these |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1064 |
functions return a zero, trying to preserve its sign, if possible. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1065 |
The <code>mpfr_get_decimal64</code> function is built only under some conditions: |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1066 |
see the documentation of <code>mpfr_set_decimal64</code>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1067 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1068 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1069 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1070 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1071 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1072 |
<blockquote><p>Return <var>d</var> and set <var>exp</var> such that 0.5<=abs(<var>d</var>)<1 |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1073 |
and <var>d</var> times 2 raised to <var>exp</var> equals |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1074 |
<var>op</var> rounded to double (resp. long double) |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1075 |
precision, using the given rounding mode. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1076 |
<!-- See ISO C standard, frexp function. --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1077 |
If <var>op</var> is zero, then a zero of the same sign (or an unsigned zero, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1078 |
if the implementation does not have signed zeros) is returned, and |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1079 |
<var>exp</var> is set to 0. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1080 |
If <var>op</var> is NaN or an infinity, then the corresponding double precision |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1081 |
(resp. long-double precision) |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1082 |
value is returned, and <var>exp</var> is undefined. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1083 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1084 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1085 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1086 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1087 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1088 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1089 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1090 |
<blockquote><p>Convert <var>op</var> to a <code>long</code>, an <code>unsigned long</code>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1091 |
an <code>intmax_t</code> or an <code>uintmax_t</code> (respectively) after rounding |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1092 |
it with respect to <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1093 |
If <var>op</var> is NaN, the result is undefined. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1094 |
If <var>op</var> is too big for the return type, it returns the maximum |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1095 |
or the minimum of the corresponding C type, depending on the direction |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1096 |
of the overflow. The flag erange is set too. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1097 |
See also <code>mpfr_fits_slong_p</code>, <code>mpfr_fits_ulong_p</code>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1098 |
<code>mpfr_fits_intmax_p</code> and <code>mpfr_fits_uintmax_p</code>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1099 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1100 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1101 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1102 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1103 |
<blockquote><p>Put the scaled significand of <var>op</var> (regarded as an integer, with the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1104 |
precision of <var>op</var>) into <var>rop</var>, and return the exponent <var>exp</var> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1105 |
(which may be outside the current exponent range) such that <var>op</var> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1106 |
exactly equals |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1107 |
<var>rop</var> multiplied by two exponent <var>exp</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1108 |
If the exponent is not representable in the <code>mp_exp_t</code> type, the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1109 |
behavior is undefined. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1110 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1111 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1112 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1113 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1114 |
<blockquote><p>Convert <var>op</var> to a <code>mpz_t</code>, after rounding it with respect to |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1115 |
<var>rnd</var>. If <var>op</var> is NaN or Inf, the result is undefined. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1116 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1117 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1118 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1119 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1120 |
<blockquote><p>Convert <var>op</var> to a <code>mpf_t</code>, after rounding it with respect to |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1121 |
<var>rnd</var>. Return zero iff no error occurred, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1122 |
in particular a non-zero value is returned if |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1123 |
<var>op</var> is NaN or Inf, which do not exist in <code>mpf</code>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1124 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1125 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1126 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1127 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1128 |
<blockquote><p>Convert <var>op</var> to a string of digits in base <var>b</var>, with rounding in |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1129 |
the direction <var>rnd</var>, where <var>n</var> is either zero (see below) or the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1130 |
number of significant digits; in the latter case, <var>n</var> must be greater |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1131 |
or equal to 2. The base may vary from 2 to 36. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1132 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1133 |
<p>The generated string is a fraction, with an implicit radix point immediately |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1134 |
to the left of the first digit. For example, the number −3.1416 would |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1135 |
be returned as "−31416" in the string and 1 written at <var>expptr</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1136 |
If <var>rnd</var> is to nearest, and <var>op</var> is exactly in the middle of two |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1137 |
possible outputs, the one with an even last digit is chosen |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1138 |
(for an odd base, this may not correspond to an even significand). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1139 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1140 |
<p>If <var>n</var> is zero, the number of digits of the significand is chosen |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1141 |
large enough so that re-reading the printed value with the same precision, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1142 |
assuming both output and input use rounding to nearest, will recover |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1143 |
the original value of <var>op</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1144 |
More precisely, in most cases, the chosen precision of <var>str</var> is |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1145 |
the minimal precision depending on <var>n</var> and <var>b</var> only that |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1146 |
satisfies the above property, i.e., |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1147 |
m = 1 + ceil(<var>n</var>*log(2)/log(<var>b</var>)), |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1148 |
but in some very rare cases, it might be m+1. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1149 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1150 |
<p>If <var>str</var> is a null pointer, space for the significand is allocated using |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1151 |
the current allocation function, and a pointer to the string is returned. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1152 |
To free the returned string, you must use <code>mpfr_free_str</code>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1153 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1154 |
<p>If <var>str</var> is not a null pointer, it should point to a block of storage |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1155 |
large enough for the significand, i.e., at least <code>max(</code><var>n</var><code> + 2, 7)</code>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1156 |
The extra two bytes are for a possible minus sign, and for the terminating null |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1157 |
character. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1158 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1159 |
<p>If the input number is an ordinary number, the exponent is written through |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1160 |
the pointer <var>expptr</var> (the current minimal exponent for 0). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1161 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1162 |
<p>A pointer to the string is returned, unless there is an error, in which |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1163 |
case a null pointer is returned. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1164 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1165 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1166 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1167 |
— Function: void <b>mpfr_free_str</b> (<var>char *str</var>)<var><a name="index-mpfr_005ffree_005fstr-75"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1168 |
<blockquote><p>Free a string allocated by <code>mpfr_get_str</code> using the current unallocation |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1169 |
function (preliminary interface). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1170 |
The block is assumed to be <code>strlen(</code><var>str</var><code>)+1</code> bytes. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1171 |
For more information about how it is done: |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1172 |
see section “Custom Allocation” in <cite>GNU MP</cite>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1173 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1174 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1175 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1176 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1177 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1178 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1179 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1180 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1181 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1182 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1183 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1184 |
<blockquote><p>Return non-zero if <var>op</var> would fit in the respective C data type, when |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1185 |
rounded to an integer in the direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1186 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1187 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1188 |
<div class="node"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1189 |
<p><hr> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1190 |
<a name="Basic-Arithmetic-Functions"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1191 |
Next: <a rel="next" accesskey="n" href="#Comparison-Functions">Comparison Functions</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1192 |
Previous: <a rel="previous" accesskey="p" href="#Conversion-Functions">Conversion Functions</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1193 |
Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1194 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1195 |
</div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1196 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1197 |
<!-- node-name, next, previous, up --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1198 |
<p><a name="index-Basic-arithmetic-functions-84"></a><a name="index-Float-arithmetic-functions-85"></a><a name="index-Arithmetic-functions-86"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1199 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1200 |
<h3 class="section">5.5 Basic Arithmetic Functions</h3> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1201 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1202 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1203 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1204 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1205 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1206 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1207 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1208 |
<blockquote><p>Set <var>rop</var> to <var>op1</var> + <var>op2</var> rounded in the direction |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1209 |
<var>rnd</var>. For types having no signed zero, it is considered unsigned |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1210 |
(i.e. (+0) + 0 = (+0) and (−0) + 0 = (−0)). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1211 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1212 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1213 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1214 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1215 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1216 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1217 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1218 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1219 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1220 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1221 |
<blockquote><p>Set <var>rop</var> to <var>op1</var> - <var>op2</var> rounded in the direction |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1222 |
<var>rnd</var>. For types having no signed zero, it is considered unsigned |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1223 |
(i.e. (+0) − 0 = (+0), (−0) − 0 = (−0), |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1224 |
0 − (+0) = (−0) and 0 − (−0) = (+0)). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1225 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1226 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1227 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1228 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1229 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1230 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1231 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1232 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1233 |
<blockquote><p>Set <var>rop</var> to <var>op1</var> times <var>op2</var> rounded in the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1234 |
direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1235 |
When a result is zero, its sign is the product of the signs of the operands |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1236 |
(for types having no signed zero, it is considered positive). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1237 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1238 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1239 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1240 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1241 |
<blockquote><p>Set <var>rop</var> to the square of <var>op</var> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1242 |
rounded in the direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1243 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1244 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1245 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1246 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1247 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1248 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1249 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1250 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1251 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1252 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1253 |
<blockquote><p>Set <var>rop</var> to <var>op1</var>/<var>op2</var> rounded in the direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1254 |
When a result is zero, its sign is the product of the signs of the operands |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1255 |
(for types having no signed zero, it is considered positive). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1256 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1257 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1258 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1259 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1260 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1261 |
<blockquote><p>Set <var>rop</var> to the square root of <var>op</var> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1262 |
rounded in the direction <var>rnd</var>. Return −0 if <var>op</var> is |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1263 |
−0 (to be consistent with the IEEE 754-1985 standard). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1264 |
Set <var>rop</var> to NaN if <var>op</var> is negative. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1265 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1266 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1267 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1268 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1269 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1270 |
<blockquote><p>Set <var>rop</var> to the cubic root (resp. the <var>k</var>th root) |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1271 |
of <var>op</var> rounded in the direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1272 |
An odd (resp. even) root of a negative number (including −Inf) |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1273 |
returns a negative number (resp. NaN). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1274 |
The <var>k</var>th root of −0 is defined to be −0, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1275 |
whatever the parity of <var>k</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1276 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1277 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1278 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1279 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1280 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1281 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1282 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1283 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1284 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1285 |
<blockquote><p>Set <var>rop</var> to <var>op1</var> raised to <var>op2</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1286 |
rounded in the direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1287 |
Special values are currently handled as described in the ISO C99 standard |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1288 |
for the <code>pow</code> function (note this may change in future versions): |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1289 |
<ul> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1290 |
<li><code>pow(�0, </code><var>y</var><code>)</code> returns plus or minus infinity for <var>y</var> a negative odd integer. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1291 |
<li><code>pow(�0, </code><var>y</var><code>)</code> returns plus infinity for <var>y</var> negative and not an odd integer. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1292 |
<li><code>pow(�0, </code><var>y</var><code>)</code> returns plus or minus zero for <var>y</var> a positive odd integer. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1293 |
<li><code>pow(�0, </code><var>y</var><code>)</code> returns plus zero for <var>y</var> positive and not an odd integer. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1294 |
<li><code>pow(-1, �Inf)</code> returns 1. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1295 |
<li><code>pow(+1, </code><var>y</var><code>)</code> returns 1 for any <var>y</var>, even a NaN. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1296 |
<li><code>pow(</code><var>x</var><code>, �0)</code> returns 1 for any <var>x</var>, even a NaN. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1297 |
<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>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1298 |
<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. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1299 |
<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. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1300 |
<li><code>pow(-Inf, </code><var>y</var><code>)</code> returns minus zero for <var>y</var> a negative odd integer. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1301 |
<li><code>pow(-Inf, </code><var>y</var><code>)</code> returns plus zero for <var>y</var> negative and not an odd integer. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1302 |
<li><code>pow(-Inf, </code><var>y</var><code>)</code> returns minus infinity for <var>y</var> a positive odd integer. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1303 |
<li><code>pow(-Inf, </code><var>y</var><code>)</code> returns plus infinity for <var>y</var> positive and not an odd integer. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1304 |
<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. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1305 |
</ul> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1306 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1307 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1308 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1309 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1310 |
<blockquote><p>Set <var>rop</var> to -<var>op</var> rounded in the direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1311 |
Just changes the sign if <var>rop</var> and <var>op</var> are the same variable. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1312 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1313 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1314 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1315 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1316 |
<blockquote><p>Set <var>rop</var> to the absolute value of <var>op</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1317 |
rounded in the direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1318 |
Just changes the sign if <var>rop</var> and <var>op</var> are the same variable. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1319 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1320 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1321 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1322 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1323 |
<blockquote><p>Set <var>rop</var> to the positive difference of <var>op1</var> and <var>op2</var>, i.e., |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1324 |
<var>op1</var> - <var>op2</var> rounded in the direction <var>rnd</var> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1325 |
if <var>op1</var> > <var>op2</var>, and +0 otherwise. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1326 |
Returns NaN when <var>op1</var> or <var>op2</var> is NaN. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1327 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1328 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1329 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1330 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1331 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1332 |
<blockquote><p>Set <var>rop</var> to <var>op1</var> times 2 raised |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1333 |
to <var>op2</var> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1334 |
rounded in the direction <var>rnd</var>. Just increases the exponent by <var>op2</var> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1335 |
when <var>rop</var> and <var>op1</var> are identical. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1336 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1337 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1338 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1339 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1340 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1341 |
<blockquote><p>Set <var>rop</var> to <var>op1</var> divided by 2 raised |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1342 |
to <var>op2</var> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1343 |
rounded in the direction <var>rnd</var>. Just decreases the exponent by <var>op2</var> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1344 |
when <var>rop</var> and <var>op1</var> are identical. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1345 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1346 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1347 |
<div class="node"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1348 |
<p><hr> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1349 |
<a name="Comparison-Functions"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1350 |
Next: <a rel="next" accesskey="n" href="#Special-Functions">Special Functions</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1351 |
Previous: <a rel="previous" accesskey="p" href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1352 |
Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1353 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1354 |
</div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1355 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1356 |
<!-- node-name, next, previous, up --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1357 |
<p><a name="index-Float-comparisons-functions-129"></a><a name="index-Comparison-functions-130"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1358 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1359 |
<h3 class="section">5.6 Comparison Functions</h3> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1360 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1361 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1362 |
— Function: int <b>mpfr_cmp</b> (<var>mpfr_t op1, mpfr_t op2</var>)<var><a name="index-mpfr_005fcmp-131"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1363 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1364 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1365 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1366 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1367 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1368 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1369 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1370 |
<blockquote><p>Compare <var>op1</var> and <var>op2</var>. Return a positive value if <var>op1</var> > |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1371 |
<var>op2</var>, zero if <var>op1</var> = <var>op2</var>, and a negative value if |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1372 |
<var>op1</var> < <var>op2</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1373 |
Both <var>op1</var> and <var>op2</var> are considered to their full own precision, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1374 |
which may differ. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1375 |
If one of the operands is NaN, set the erange flag and return zero. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1376 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1377 |
<p>Note: These functions may be useful to distinguish the three possible cases. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1378 |
If you need to distinguish two cases only, it is recommended to use the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1379 |
predicate functions (e.g., <code>mpfr_equal_p</code> for the equality) described |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1380 |
below; they behave like the IEEE-754 comparisons, in particular when one |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1381 |
or both arguments are NaN. But only floating-point numbers can be compared |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1382 |
(you may need to do a conversion first). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1383 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1384 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1385 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1386 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1387 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1388 |
<blockquote><p>Compare <var>op1</var> and <var>op2</var> multiplied by two to |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1389 |
the power <var>e</var>. Similar as above. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1390 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1391 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1392 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1393 |
— Function: int <b>mpfr_cmpabs</b> (<var>mpfr_t op1, mpfr_t op2</var>)<var><a name="index-mpfr_005fcmpabs-141"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1394 |
<blockquote><p>Compare |<var>op1</var>| and |<var>op2</var>|. Return a positive value if |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1395 |
|<var>op1</var>| > |<var>op2</var>|, zero if |<var>op1</var>| = |<var>op2</var>|, and |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1396 |
a negative value if |<var>op1</var>| < |<var>op2</var>|. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1397 |
If one of the operands is NaN, set the erange flag and return zero. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1398 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1399 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1400 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1401 |
— Function: int <b>mpfr_nan_p</b> (<var>mpfr_t op</var>)<var><a name="index-mpfr_005fnan_005fp-142"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1402 |
— Function: int <b>mpfr_inf_p</b> (<var>mpfr_t op</var>)<var><a name="index-mpfr_005finf_005fp-143"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1403 |
— Function: int <b>mpfr_number_p</b> (<var>mpfr_t op</var>)<var><a name="index-mpfr_005fnumber_005fp-144"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1404 |
— Function: int <b>mpfr_zero_p</b> (<var>mpfr_t op</var>)<var><a name="index-mpfr_005fzero_005fp-145"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1405 |
<blockquote><p>Return non-zero if <var>op</var> is respectively NaN, an infinity, an ordinary |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1406 |
number (i.e. neither NaN nor an infinity) or zero. Return zero otherwise. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1407 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1408 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1409 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1410 |
— Macro: int <b>mpfr_sgn</b> (<var>mpfr_t op</var>)<var><a name="index-mpfr_005fsgn-146"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1411 |
<blockquote><p>Return a positive value if <var>op</var> > 0, zero if <var>op</var> = 0, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1412 |
and a negative value if <var>op</var> < 0. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1413 |
If the operand is NaN, set the erange flag and return zero. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1414 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1415 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1416 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1417 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1418 |
<blockquote><p>Return non-zero if <var>op1</var> > <var>op2</var>, zero otherwise. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1419 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1420 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1421 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1422 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1423 |
<blockquote><p>Return non-zero if <var>op1</var> >= <var>op2</var>, zero otherwise. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1424 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1425 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1426 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1427 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1428 |
<blockquote><p>Return non-zero if <var>op1</var> < <var>op2</var>, zero otherwise. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1429 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1430 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1431 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1432 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1433 |
<blockquote><p>Return non-zero if <var>op1</var> <= <var>op2</var>, zero otherwise. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1434 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1435 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1436 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1437 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1438 |
<blockquote><p>Return non-zero if <var>op1</var> < <var>op2</var> or |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1439 |
<var>op1</var> > <var>op2</var> (i.e. neither <var>op1</var>, nor <var>op2</var> is |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1440 |
NaN, and <var>op1</var> <> <var>op2</var>), zero otherwise (i.e. <var>op1</var> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1441 |
and/or <var>op2</var> are NaN, or <var>op1</var> = <var>op2</var>). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1442 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1443 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1444 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1445 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1446 |
<blockquote><p>Return non-zero if <var>op1</var> = <var>op2</var>, zero otherwise |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1447 |
(i.e. <var>op1</var> and/or <var>op2</var> are NaN, or |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1448 |
<var>op1</var> <> <var>op2</var>). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1449 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1450 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1451 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1452 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1453 |
<blockquote><p>Return non-zero if <var>op1</var> or <var>op2</var> is a NaN (i.e. they cannot be |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1454 |
compared), zero otherwise. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1455 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1456 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1457 |
<div class="node"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1458 |
<p><hr> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1459 |
<a name="Special-Functions"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1460 |
Next: <a rel="next" accesskey="n" href="#Input-and-Output-Functions">Input and Output Functions</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1461 |
Previous: <a rel="previous" accesskey="p" href="#Comparison-Functions">Comparison Functions</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1462 |
Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1463 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1464 |
</div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1465 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1466 |
<p><a name="index-Special-functions-154"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1467 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1468 |
<h3 class="section">5.7 Special Functions</h3> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1469 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1470 |
<p>All those functions, except explicitly stated, return zero for an |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1471 |
exact return value, a positive value for a return value larger than the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1472 |
exact result, and a negative value otherwise. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1473 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1474 |
<p>Important note: in some domains, computing special functions (either with |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1475 |
correct or incorrect rounding) is expensive, even for small precision, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1476 |
for example the trigonometric and Bessel functions for large argument. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1477 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1478 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1479 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1480 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1481 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1482 |
<blockquote><p>Set <var>rop</var> to the natural logarithm of <var>op</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1483 |
log2(<var>op</var>) or |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1484 |
log10(<var>op</var>), respectively, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1485 |
rounded in the direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1486 |
Return −Inf if <var>op</var> is −0 (i.e. the sign of the zero |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1487 |
has no influence on the result). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1488 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1489 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1490 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1491 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1492 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1493 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1494 |
<blockquote><p>Set <var>rop</var> to the exponential of <var>op</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1495 |
to 2 power of <var>op</var> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1496 |
or to 10 power of <var>op</var>, respectively, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1497 |
rounded in the direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1498 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1499 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1500 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1501 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1502 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1503 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1504 |
<blockquote><p>Set <var>rop</var> to the cosine of <var>op</var>, sine of <var>op</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1505 |
tangent of <var>op</var>, rounded in the direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1506 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1507 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1508 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1509 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1510 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1511 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1512 |
<blockquote><p>Set <var>rop</var> to the secant of <var>op</var>, cosecant of <var>op</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1513 |
cotangent of <var>op</var>, rounded in the direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1514 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1515 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1516 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1517 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1518 |
<blockquote><p>Set simultaneously <var>sop</var> to the sine of <var>op</var> and |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1519 |
<var>cop</var> to the cosine of <var>op</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1520 |
rounded in the direction <var>rnd</var> with the corresponding precisions of |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1521 |
<var>sop</var> and <var>cop</var>, which must be different variables. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1522 |
Return 0 iff both results are exact. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1523 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1524 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1525 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1526 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1527 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1528 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1529 |
<blockquote><p>Set <var>rop</var> to the arc-cosine, arc-sine or arc-tangent of <var>op</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1530 |
rounded in the direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1531 |
Note that since <code>acos(-1)</code> returns the floating-point number closest to |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1532 |
Pi according to the given rounding mode, this number might not be |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1533 |
in the output range 0 <= <var>rop</var> < \pi |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1534 |
of the arc-cosine function; |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1535 |
still, the result lies in the image of the output range |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1536 |
by the rounding function. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1537 |
The same holds for <code>asin(-1)</code>, <code>asin(1)</code>, <code>atan(-Inf)</code>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1538 |
<code>atan(+Inf)</code>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1539 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1540 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1541 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1542 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1543 |
<blockquote><p>Set <var>rop</var> to the arc-tangent2 of <var>y</var> and <var>x</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1544 |
rounded in the direction <var>rnd</var>: |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1545 |
if <code>x > 0</code>, <code>atan2(y, x) = atan (y/x)</code>; |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1546 |
if <code>x < 0</code>, <code>atan2(y, x) = sign(y)*(Pi - atan (abs(y/x)))</code>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1547 |
As for <code>atan</code>, in case the exact mathematical result is +Pi or |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1548 |
-Pi, its rounded result might be outside the function output range. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1549 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1550 |
<p><code>atan2(y, 0)</code> does not raise any floating-point exception. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1551 |
Special values are currently handled as described in the ISO C99 standard |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1552 |
for the <code>atan2</code> function (note this may change in future versions): |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1553 |
<ul> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1554 |
<li><code>atan2(+0, -0)</code> returns +Pi. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1555 |
<li><code>atan2(-0, -0)</code> returns -Pi. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1556 |
<li><code>atan2(+0, +0)</code> returns +0. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1557 |
<li><code>atan2(-0, +0)</code> returns −0. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1558 |
<li><code>atan2(+0, x)</code> returns +Pi for x < 0. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1559 |
<li><code>atan2(-0, x)</code> returns -Pi for x < 0. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1560 |
<li><code>atan2(+0, x)</code> returns +0 for x > 0. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1561 |
<li><code>atan2(-0, x)</code> returns −0 for x > 0. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1562 |
<li><code>atan2(y, 0)</code> returns -Pi/2 for y < 0. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1563 |
<li><code>atan2(y, 0)</code> returns +Pi/2 for y > 0. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1564 |
<li><code>atan2(+Inf, -Inf)</code> returns +3*Pi/4. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1565 |
<li><code>atan2(-Inf, -Inf)</code> returns -3*Pi/4. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1566 |
<li><code>atan2(+Inf, +Inf)</code> returns +Pi/4. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1567 |
<li><code>atan2(-Inf, +Inf)</code> returns -Pi/4. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1568 |
<li><code>atan2(+Inf, x)</code> returns +Pi/2 for finite x. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1569 |
<li><code>atan2(-Inf, x)</code> returns -Pi/2 for finite x. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1570 |
<li><code>atan2(y, -Inf)</code> returns +Pi for finite y > 0. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1571 |
<li><code>atan2(y, -Inf)</code> returns -Pi for finite y < 0. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1572 |
<li><code>atan2(y, +Inf)</code> returns +0 for finite y > 0. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1573 |
<li><code>atan2(y, +Inf)</code> returns −0 for finite y < 0. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1574 |
</ul> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1575 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1576 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1577 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1578 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1579 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1580 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1581 |
<blockquote><p>Set <var>rop</var> to the hyperbolic cosine, sine or tangent of <var>op</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1582 |
rounded in the direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1583 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1584 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1585 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1586 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1587 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1588 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1589 |
<blockquote><p>Set <var>rop</var> to the hyperbolic secant of <var>op</var>, cosecant of <var>op</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1590 |
cotangent of <var>op</var>, rounded in the direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1591 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1592 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1593 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1594 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1595 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1596 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1597 |
<blockquote><p>Set <var>rop</var> to the inverse hyperbolic cosine, sine or tangent of <var>op</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1598 |
rounded in the direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1599 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1600 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1601 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1602 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1603 |
<blockquote><p>Set <var>rop</var> to the factorial of the <code>unsigned long int</code> <var>op</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1604 |
rounded in the direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1605 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1606 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1607 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1608 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1609 |
<blockquote><p>Set <var>rop</var> to the logarithm of one plus <var>op</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1610 |
rounded in the direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1611 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1612 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1613 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1614 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1615 |
<blockquote><p>Set <var>rop</var> to the exponential of <var>op</var> minus one, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1616 |
rounded in the direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1617 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1618 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1619 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1620 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1621 |
<blockquote><p>Set <var>y</var> to the exponential integral of <var>x</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1622 |
rounded in the direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1623 |
For positive <var>x</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1624 |
the exponential integral is the sum of Euler's constant, of the logarithm |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1625 |
of <var>x</var>, and of the sum for k from 1 to infinity of |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1626 |
<var>x</var> to the power k, divided by k and factorial(k). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1627 |
For negative <var>x</var>, the returned value is NaN. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1628 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1629 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1630 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1631 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1632 |
<blockquote><p>Set <var>rop</var> to the value of the Gamma function on <var>op</var>, rounded in the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1633 |
direction <var>rnd</var>. When <var>op</var> is a negative integer, NaN is returned. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1634 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1635 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1636 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1637 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1638 |
<blockquote><p>Set <var>rop</var> to the value of the logarithm of the Gamma function on <var>op</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1639 |
rounded in the direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1640 |
When −2<var>k</var>−1 <= <var>x</var> <= −2<var>k</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1641 |
<var>k</var> being a non-negative integer, NaN is returned. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1642 |
See also <code>mpfr_lgamma</code>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1643 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1644 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1645 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1646 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1647 |
<blockquote><p>Set <var>rop</var> to the value of the logarithm of the absolute value of the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1648 |
Gamma function on <var>op</var>, rounded in the direction <var>rnd</var>. The sign |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1649 |
(1 or −1) of Gamma(<var>op</var>) is returned in the object pointed to |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1650 |
by <var>signp</var>. When <var>op</var> is an infinity or a non-positive integer, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1651 |
+Inf is returned. When <var>op</var> is NaN, −Inf or a negative integer, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1652 |
*<var>signp</var> is undefined, and when <var>op</var> is �0, *<var>signp</var> is |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1653 |
the sign of the zero. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1654 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1655 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1656 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1657 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1658 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1659 |
<blockquote><p>Set <var>rop</var> to the value of the Riemann Zeta function on <var>op</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1660 |
rounded in the direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1661 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1662 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1663 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1664 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1665 |
<blockquote><p>Set <var>rop</var> to the value of the error function on <var>op</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1666 |
rounded in the direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1667 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1668 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1669 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1670 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1671 |
<blockquote><p>Set <var>rop</var> to the value of the complementary error function on <var>op</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1672 |
rounded in the direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1673 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1674 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1675 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1676 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1677 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1678 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1679 |
<blockquote><p>Set <var>rop</var> to the value of the first order Bessel function of order 0, 1 |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1680 |
and <var>n</var> on <var>op</var>, rounded in the direction <var>rnd</var>. When <var>op</var> is |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1681 |
NaN, <var>rop</var> is always set to NaN. When <var>op</var> is plus or minus Infinity, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1682 |
<var>rop</var> is set to +0. When <var>op</var> is zero, and <var>n</var> is not zero, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1683 |
<var>rop</var> is +0 or −0 depending on the parity and sign of <var>n</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1684 |
and the sign of <var>op</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1685 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1686 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1687 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1688 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1689 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1690 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1691 |
<blockquote><p>Set <var>rop</var> to the value of the second order Bessel function of order 0, 1 |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1692 |
and <var>n</var> on <var>op</var>, rounded in the direction <var>rnd</var>. When <var>op</var> is |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1693 |
NaN or negative, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1694 |
<var>rop</var> is always set to NaN. When <var>op</var> is +Inf, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1695 |
<var>rop</var> is +0. When <var>op</var> is zero, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1696 |
<var>rop</var> is +Inf or −Inf depending on the parity and sign of <var>n</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1697 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1698 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1699 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1700 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1701 |
<blockquote><p>Set <var>rop</var> to (<var>op1</var> times <var>op2</var>) + <var>op3</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1702 |
rounded in the direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1703 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1704 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1705 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1706 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1707 |
<blockquote><p>Set <var>rop</var> to (<var>op1</var> times <var>op2</var>) - <var>op3</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1708 |
rounded in the direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1709 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1710 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1711 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1712 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1713 |
<blockquote><p>Set <var>rop</var> to the arithmetic-geometric mean of <var>op1</var> and <var>op2</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1714 |
rounded in the direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1715 |
The arithmetic-geometric mean is the common limit of the sequences |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1716 |
u[n] and v[n], where u[0]=<var>op1</var>, v[0]=<var>op2</var>, u[n+1] is the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1717 |
arithmetic mean of u[n] and v[n], and v[n+1] is the geometric mean of |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1718 |
u[n] and v[n]. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1719 |
If any operand is negative, the return value is NaN. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1720 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1721 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1722 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1723 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1724 |
<blockquote><p>Set <var>rop</var> to the Euclidean norm of <var>x</var> and <var>y</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1725 |
i.e. the square root of the sum of the squares of <var>x</var> and <var>y</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1726 |
rounded in the direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1727 |
Special values are currently handled as described in Section F.9.4.3 of |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1728 |
the ISO C99 standard, for the <code>hypot</code> function (note this may change |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1729 |
in future versions): If <var>x</var> or <var>y</var> is an infinity, then plus |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1730 |
infinity is returned in <var>rop</var>, even if the other number is NaN. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1731 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1732 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1733 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1734 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1735 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1736 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1737 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1738 |
<blockquote><p>Set <var>rop</var> to the logarithm of 2, the value of Pi, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1739 |
of Euler's constant 0.577<small class="dots">...</small>, of Catalan's constant 0.915<small class="dots">...</small>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1740 |
respectively, rounded in the direction |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1741 |
<var>rnd</var>. These functions cache the computed values to avoid other |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1742 |
calculations if a lower or equal precision is requested. To free these caches, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1743 |
use <code>mpfr_free_cache</code>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1744 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1745 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1746 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1747 |
— Function: void <b>mpfr_free_cache</b> (<var>void</var>)<var><a name="index-mpfr_005ffree_005fcache-206"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1748 |
<blockquote><p>Free various caches used by MPFR internally, in particular the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1749 |
caches used by the functions computing constants (currently |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1750 |
<code>mpfr_const_log2</code>, <code>mpfr_const_pi</code>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1751 |
<code>mpfr_const_euler</code> and <code>mpfr_const_catalan</code>). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1752 |
You should call this function before terminating a thread, even if you did |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1753 |
not call these functions directly (they could have been called internally). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1754 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1755 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1756 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1757 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1758 |
<blockquote><p>Set <var>ret</var> to the sum of all elements of <var>tab</var> whose size is <var>n</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1759 |
rounded in the direction <var>rnd</var>. Warning, <var>tab</var> is a table of pointers |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1760 |
to mpfr_t, not a table of mpfr_t (preliminary interface). The returned |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1761 |
<code>int</code> value is zero when the computed value is the exact value, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1762 |
and non-zero when this cannot be guaranteed, without giving the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1763 |
direction of the error as the other functions do. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1764 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1765 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1766 |
<div class="node"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1767 |
<p><hr> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1768 |
<a name="Input-and-Output-Functions"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1769 |
Next: <a rel="next" accesskey="n" href="#Integer-Related-Functions">Integer Related Functions</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1770 |
Previous: <a rel="previous" accesskey="p" href="#Special-Functions">Special Functions</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1771 |
Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1772 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1773 |
</div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1774 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1775 |
<!-- node-name, next, previous, up --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1776 |
<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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1777 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1778 |
<h3 class="section">5.8 Input and Output Functions</h3> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1779 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1780 |
<p>This section describes functions that perform input from an input/output |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1781 |
stream, and functions that output to an input/output stream. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1782 |
Passing a null pointer for a <var>stream</var> argument to any of |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1783 |
these functions will make them read from <code>stdin</code> and write to |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1784 |
<code>stdout</code>, respectively. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1785 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1786 |
<p>When using any of these functions, you must include the <code><stdio.h></code> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1787 |
standard header before <samp><span class="file">mpfr.h</span></samp>, to allow <samp><span class="file">mpfr.h</span></samp> to define |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1788 |
prototypes for these functions. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1789 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1790 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1791 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1792 |
<blockquote><p>Output <var>op</var> on stream <var>stream</var>, as a string of digits in |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1793 |
base <var>base</var>, rounded in the direction <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1794 |
The base may vary from 2 to 36. Print <var>n</var> significant digits exactly, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1795 |
or if <var>n</var> is 0, enough digits so that <var>op</var> can be read back |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1796 |
exactly (see <code>mpfr_get_str</code>). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1797 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1798 |
<p>In addition to the significant digits, a decimal point (defined by the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1799 |
current locale) at the right of the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1800 |
first digit and a trailing exponent in base 10, in the form ‘<samp><span class="samp">eNNN</span></samp>’, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1801 |
are printed. If <var>base</var> is greater than 10, ‘<samp><span class="samp">@</span></samp>’ will be used |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1802 |
instead of ‘<samp><span class="samp">e</span></samp>’ as exponent delimiter. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1803 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1804 |
<p>Return the number of bytes written, or if an error occurred, return 0. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1805 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1806 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1807 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1808 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1809 |
<blockquote><p>Input a string in base <var>base</var> from stream <var>stream</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1810 |
rounded in the direction <var>rnd</var>, and put the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1811 |
read float in <var>rop</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1812 |
<!-- The argument @var{base} must be in the range 2 to 36. --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1813 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1814 |
<!-- The string is of the form @samp{M@@N} or, if the --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1815 |
<!-- base is 10 or less, alternatively @samp{MeN} or @samp{MEN}, or, if the base --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1816 |
<!-- is 16, alternatively @samp{MpB} or @samp{MPB}. --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1817 |
<!-- @samp{M} is the significand in the specified base, @samp{N} is the exponent --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1818 |
<!-- written in decimal for the specified base, and in base 16, @samp{B} is the --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1819 |
<!-- binary exponent written in decimal (i.e.@: it indicates the power of 2 by --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1820 |
<!-- which the significand is to be scaled). --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1821 |
<p>This function reads a word (defined as a sequence of characters between |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1822 |
whitespace) and parses it using <code>mpfr_set_str</code> (it may change). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1823 |
See the documentation of <code>mpfr_strtofr</code> for a detailed description |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1824 |
of the valid string formats. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1825 |
<!-- Special values can be read as follows (the case does not matter): --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1826 |
<!-- @code{@@NaN@@}, @code{@@Inf@@}, @code{+@@Inf@@} and @code{-@@Inf@@}, --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1827 |
<!-- possibly followed by other characters; if the base is smaller or equal --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1828 |
<!-- to 16, the following strings are accepted too: @code{NaN}, @code{Inf}, --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1829 |
<!-- @code{+Inf} and @code{-Inf}. --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1830 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1831 |
<p>Return the number of bytes read, or if an error occurred, return 0. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1832 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1833 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1834 |
<!-- @deftypefun void mpfr_inp_raw (mpfr_t @var{float}, FILE *@var{stream}) --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1835 |
<!-- Input from stdio stream @var{stream} in the format written by --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1836 |
<!-- @code{mpfr_out_raw}, and put the result in @var{float}. --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1837 |
<!-- @end deftypefun --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1838 |
<div class="node"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1839 |
<p><hr> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1840 |
<a name="Integer-Related-Functions"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1841 |
Next: <a rel="next" accesskey="n" href="#Miscellaneous-Functions">Miscellaneous Functions</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1842 |
Previous: <a rel="previous" accesskey="p" href="#Input-and-Output-Functions">Input and Output Functions</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1843 |
Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1844 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1845 |
</div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1846 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1847 |
<!-- node-name, next, previous, up --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1848 |
<p><a name="index-Integer-related-functions-214"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1849 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1850 |
<h3 class="section">5.9 Integer Related Functions</h3> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1851 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1852 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1853 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1854 |
— Function: int <b>mpfr_ceil</b> (<var>mpfr_t rop, mpfr_t op</var>)<var><a name="index-mpfr_005fceil-216"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1855 |
— Function: int <b>mpfr_floor</b> (<var>mpfr_t rop, mpfr_t op</var>)<var><a name="index-mpfr_005ffloor-217"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1856 |
— Function: int <b>mpfr_round</b> (<var>mpfr_t rop, mpfr_t op</var>)<var><a name="index-mpfr_005fround-218"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1857 |
— Function: int <b>mpfr_trunc</b> (<var>mpfr_t rop, mpfr_t op</var>)<var><a name="index-mpfr_005ftrunc-219"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1858 |
<blockquote><p>Set <var>rop</var> to <var>op</var> rounded to an integer. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1859 |
<code>mpfr_rint</code> rounds to the nearest representable integer in the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1860 |
given rounding mode, <code>mpfr_ceil</code> rounds |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1861 |
to the next higher or equal representable integer, <code>mpfr_floor</code> to |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1862 |
the next lower or equal representable integer, <code>mpfr_round</code> to the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1863 |
nearest representable integer, rounding halfway cases away from zero, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1864 |
and <code>mpfr_trunc</code> to the next representable integer toward zero. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1865 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1866 |
<p>The returned value is zero when the result is exact, positive when it is |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1867 |
greater than the original value of <var>op</var>, and negative when it is smaller. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1868 |
More precisely, the returned value is 0 when <var>op</var> is an integer |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1869 |
representable in <var>rop</var>, 1 or −1 when <var>op</var> is an integer |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1870 |
that is not representable in <var>rop</var>, 2 or −2 when <var>op</var> is |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1871 |
not an integer. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1872 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1873 |
<p>Note that <code>mpfr_round</code> is different from <code>mpfr_rint</code> called with |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1874 |
the rounding to nearest mode (where halfway cases are rounded to an even |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1875 |
integer or significand). Note also that no double rounding is performed; for |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1876 |
instance, 4.5 (100.1 in binary) is rounded by <code>mpfr_round</code> to 4 (100 |
22d9e175d379
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parents:
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|
1877 |
in binary) in 2-bit precision, though <code>round(4.5)</code> is equal to 5 and |
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parents:
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changeset
|
1878 |
5 (101 in binary) is rounded to 6 (110 in binary) in 2-bit precision. |
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parents:
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|
1879 |
</p></blockquote></div> |
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changeset
|
1880 |
|
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|
1881 |
<div class="defun"> |
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|
1882 |
— 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> |
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|
1883 |
— 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> |
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|
1884 |
— 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> |
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parents:
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|
1885 |
— 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> |
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|
1886 |
<blockquote><p>Set <var>rop</var> to <var>op</var> rounded to an integer. |
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|
1887 |
<code>mpfr_rint_ceil</code> rounds to the next higher or equal integer, |
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parents:
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changeset
|
1888 |
<code>mpfr_rint_floor</code> to the next lower or equal integer, |
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parents:
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changeset
|
1889 |
<code>mpfr_rint_round</code> to the nearest integer, rounding halfway cases away |
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parents:
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changeset
|
1890 |
from zero, and <code>mpfr_rint_trunc</code> to the next integer toward zero. |
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|
1891 |
If the result is not representable, it is rounded in the direction <var>rnd</var>. |
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|
1892 |
The returned value is the ternary value associated with the considered |
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parents:
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|
1893 |
round-to-integer function (regarded in the same way as any other |
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|
1894 |
mathematical function). |
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parents:
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|
1895 |
</p></blockquote></div> |
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changeset
|
1896 |
|
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|
1897 |
<div class="defun"> |
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|
1898 |
— 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> |
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changeset
|
1899 |
<blockquote><p>Set <var>rop</var> to the fractional part of <var>op</var>, having the same sign as |
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|
1900 |
<var>op</var>, rounded in the direction <var>rnd</var> (unlike in <code>mpfr_rint</code>, |
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|
1901 |
<var>rnd</var> affects only how the exact fractional part is rounded, not how |
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|
1902 |
the fractional part is generated). |
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|
1903 |
</p></blockquote></div> |
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changeset
|
1904 |
|
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|
1905 |
<div class="defun"> |
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|
1906 |
— 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> |
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|
1907 |
— 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> |
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changeset
|
1908 |
<blockquote><p>Set <var>r</var> to the remainder of the division of <var>x</var> by <var>y</var>, with |
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parents:
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changeset
|
1909 |
quotient rounded to the nearest integer (ties rounded to even), and |
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parents:
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changeset
|
1910 |
<var>r</var> rounded according to the direction <var>rnd</var>. |
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changeset
|
1911 |
If <var>r</var> is zero, it has the sign of <var>x</var>. |
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|
1912 |
The return value is the ternary value corresponding to <var>r</var>. |
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|
1913 |
Additionally, <code>mpfr_remquo</code> stores |
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|
1914 |
the low significant bits from the quotient in <var>*q</var> |
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|
1915 |
(more precisely the number of bits in a <code>long</code> minus one), |
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parents:
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changeset
|
1916 |
with the sign of <var>x</var> divided by <var>y</var> |
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changeset
|
1917 |
(except if those low bits are all zero, in which case zero is returned). |
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parents:
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changeset
|
1918 |
Note that <var>x</var> may be so large in magnitude relative to <var>y</var> that an |
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parents:
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changeset
|
1919 |
exact representation of the quotient is not practical. |
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changeset
|
1920 |
These functions are useful for additive argument reduction. |
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changeset
|
1921 |
</p></blockquote></div> |
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parents:
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changeset
|
1922 |
|
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|
1923 |
<div class="defun"> |
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|
1924 |
— Function: int <b>mpfr_integer_p</b> (<var>mpfr_t op</var>)<var><a name="index-mpfr_005finteger_005fp-227"></a></var><br> |
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parents:
diff
changeset
|
1925 |
<blockquote><p>Return non-zero iff <var>op</var> is an integer. |
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parents:
diff
changeset
|
1926 |
</p></blockquote></div> |
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parents:
diff
changeset
|
1927 |
|
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parents:
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|
1928 |
<div class="node"> |
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parents:
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changeset
|
1929 |
<p><hr> |
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parents:
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changeset
|
1930 |
<a name="Miscellaneous-Functions"></a> |
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parents:
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changeset
|
1931 |
Next: <a rel="next" accesskey="n" href="#Rounding-Mode-Related-Functions">Rounding Mode Related Functions</a>, |
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parents:
diff
changeset
|
1932 |
Previous: <a rel="previous" accesskey="p" href="#Integer-Related-Functions">Integer Related Functions</a>, |
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parents:
diff
changeset
|
1933 |
Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a> |
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parents:
diff
changeset
|
1934 |
|
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parents:
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changeset
|
1935 |
</div> |
22d9e175d379
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parents:
diff
changeset
|
1936 |
|
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parents:
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changeset
|
1937 |
<!-- node-name, next, previous, up --> |
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changeset
|
1938 |
<p><a name="index-Miscellaneous-float-functions-228"></a> |
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parents:
diff
changeset
|
1939 |
|
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parents:
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changeset
|
1940 |
<h3 class="section">5.10 Miscellaneous Functions</h3> |
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parents:
diff
changeset
|
1941 |
|
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parents:
diff
changeset
|
1942 |
<div class="defun"> |
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changeset
|
1943 |
— Function: void <b>mpfr_nexttoward</b> (<var>mpfr_t x, mpfr_t y</var>)<var><a name="index-mpfr_005fnexttoward-229"></a></var><br> |
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parents:
diff
changeset
|
1944 |
<blockquote><p>If <var>x</var> or <var>y</var> is NaN, set <var>x</var> to NaN. Otherwise, if <var>x</var> |
22d9e175d379
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parents:
diff
changeset
|
1945 |
is different from <var>y</var>, replace <var>x</var> by the next floating-point |
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parents:
diff
changeset
|
1946 |
number (with the precision of <var>x</var> and the current exponent range) |
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parents:
diff
changeset
|
1947 |
in the direction of <var>y</var>, if there is one |
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parents:
diff
changeset
|
1948 |
(the infinite values are seen as the smallest and largest floating-point |
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parents:
diff
changeset
|
1949 |
numbers). If the result is zero, it keeps the same sign. No underflow or |
22d9e175d379
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parents:
diff
changeset
|
1950 |
overflow is generated. |
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parents:
diff
changeset
|
1951 |
</p></blockquote></div> |
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parents:
diff
changeset
|
1952 |
|
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parents:
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changeset
|
1953 |
<div class="defun"> |
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changeset
|
1954 |
— Function: void <b>mpfr_nextabove</b> (<var>mpfr_t x</var>)<var><a name="index-mpfr_005fnextabove-230"></a></var><br> |
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parents:
diff
changeset
|
1955 |
<blockquote><p>Equivalent to <code>mpfr_nexttoward</code> where <var>y</var> is plus infinity. |
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parents:
diff
changeset
|
1956 |
</p></blockquote></div> |
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parents:
diff
changeset
|
1957 |
|
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parents:
diff
changeset
|
1958 |
<div class="defun"> |
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parents:
diff
changeset
|
1959 |
— Function: void <b>mpfr_nextbelow</b> (<var>mpfr_t x</var>)<var><a name="index-mpfr_005fnextbelow-231"></a></var><br> |
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parents:
diff
changeset
|
1960 |
<blockquote><p>Equivalent to <code>mpfr_nexttoward</code> where <var>y</var> is minus infinity. |
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1961 |
</p></blockquote></div> |
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parents:
diff
changeset
|
1962 |
|
22d9e175d379
7041521 GNU MP to Userland
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parents:
diff
changeset
|
1963 |
<div class="defun"> |
22d9e175d379
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parents:
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changeset
|
1964 |
— 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> |
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parents:
diff
changeset
|
1965 |
<blockquote><p>Set <var>rop</var> to the minimum of <var>op1</var> and <var>op2</var>. If <var>op1</var> |
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parents:
diff
changeset
|
1966 |
and <var>op2</var> are both NaN, then <var>rop</var> is set to NaN. If <var>op1</var> |
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parents:
diff
changeset
|
1967 |
or <var>op2</var> is NaN, then <var>rop</var> is set to the numeric value. If |
22d9e175d379
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parents:
diff
changeset
|
1968 |
<var>op1</var> and <var>op2</var> are zeros of different signs, then <var>rop</var> |
22d9e175d379
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parents:
diff
changeset
|
1969 |
is set to −0. |
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parents:
diff
changeset
|
1970 |
</p></blockquote></div> |
22d9e175d379
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parents:
diff
changeset
|
1971 |
|
22d9e175d379
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parents:
diff
changeset
|
1972 |
<div class="defun"> |
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parents:
diff
changeset
|
1973 |
— 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> |
22d9e175d379
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parents:
diff
changeset
|
1974 |
<blockquote><p>Set <var>rop</var> to the maximum of <var>op1</var> and <var>op2</var>. If <var>op1</var> |
22d9e175d379
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parents:
diff
changeset
|
1975 |
and <var>op2</var> are both NaN, then <var>rop</var> is set to NaN. If <var>op1</var> |
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parents:
diff
changeset
|
1976 |
or <var>op2</var> is NaN, then <var>rop</var> is set to the numeric value. If |
22d9e175d379
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parents:
diff
changeset
|
1977 |
<var>op1</var> and <var>op2</var> are zeros of different signs, then <var>rop</var> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1978 |
is set to +0. |
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parents:
diff
changeset
|
1979 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1980 |
|
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7041521 GNU MP to Userland
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parents:
diff
changeset
|
1981 |
<div class="defun"> |
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parents:
diff
changeset
|
1982 |
— 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> |
22d9e175d379
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parents:
diff
changeset
|
1983 |
<blockquote><p>Generate a uniformly distributed random float in the interval |
22d9e175d379
7041521 GNU MP to Userland
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parents:
diff
changeset
|
1984 |
0 <= <var>rop</var> < 1. |
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parents:
diff
changeset
|
1985 |
Return 0, unless the exponent is not in the current exponent range, in |
22d9e175d379
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1986 |
which case <var>rop</var> is set to NaN and a non-zero value is returned. The |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1987 |
second argument is a <code>gmp_randstate_t</code> structure which should be |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1988 |
created using the GMP <code>gmp_randinit</code> function, see the GMP manual. |
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7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1989 |
</p></blockquote></div> |
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1990 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1991 |
<div class="defun"> |
22d9e175d379
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1992 |
— Function: void <b>mpfr_random</b> (<var>mpfr_t rop</var>)<var><a name="index-mpfr_005frandom-235"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
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parents:
diff
changeset
|
1993 |
<blockquote><p>Generate a uniformly distributed random float in the interval |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1994 |
0 <= <var>rop</var> < 1. |
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1995 |
This function is deprecated; <code>mpfr_urandomb</code> should be used instead. |
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1996 |
</p></blockquote></div> |
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1997 |
|
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7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
1998 |
<div class="defun"> |
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parents:
diff
changeset
|
1999 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2000 |
<blockquote><p>Generate a random float of at most <var>size</var> limbs, with long strings of |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2001 |
zeros and ones in the binary representation. The exponent of the number is in |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2002 |
the interval −<var>exp</var> to <var>exp</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2003 |
This function is useful for |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2004 |
testing functions and algorithms, since this kind of random numbers have |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2005 |
proven to be more likely to trigger corner-case bugs. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2006 |
Negative random numbers are generated when <var>size</var> is negative. |
22d9e175d379
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2007 |
Put +0 in <var>rop</var> when size if zero. The internal state of the default |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2008 |
pseudorandom number generator is modified by a call to this function (the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2009 |
same one as GMP if MPFR was built using ‘<samp><span class="samp">--with-gmp-build</span></samp>’). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2010 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2011 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2012 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2013 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2014 |
<blockquote><p>Get the exponent of <var>x</var>, assuming that <var>x</var> is a non-zero ordinary |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2015 |
number and the significand is chosen in [1/2,1). The behavior for NaN, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2016 |
infinity or zero is undefined. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2017 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2018 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2019 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2020 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2021 |
<blockquote><p>Set the exponent of <var>x</var> if <var>e</var> is in the current exponent range, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2022 |
and return 0 (even if <var>x</var> is not a non-zero ordinary number); |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2023 |
otherwise, return a non-zero value. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2024 |
The significand is assumed to be in [1/2,1). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2025 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2026 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2027 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2028 |
— Function: int <b>mpfr_signbit</b> (<var>mpfr_t op</var>)<var><a name="index-mpfr_005fsignbit-239"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2029 |
<blockquote><p>Return a non-zero value iff <var>op</var> has its sign bit set (i.e. if it is |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2030 |
negative, −0, or a NaN whose representation has its sign bit set). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2031 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2032 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2033 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2034 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2035 |
<blockquote><p>Set the value of <var>rop</var> from <var>op</var>, rounded toward the given |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2036 |
direction <var>rnd</var>, then set (resp. clear) its sign bit if <var>s</var> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2037 |
is non-zero (resp. zero), even when <var>op</var> is a NaN. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2038 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2039 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2040 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2041 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2042 |
<blockquote><p>Set the value of <var>rop</var> from <var>op1</var>, rounded toward the given |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2043 |
direction <var>rnd</var>, then set its sign bit to that of <var>op2</var> (even |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2044 |
when <var>op1</var> or <var>op2</var> is a NaN). This function is equivalent to |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2045 |
<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>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2046 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2047 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2048 |
<!-- By definition, a C string is always null-terminated, so that we --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2049 |
<!-- could just say "string" or "null-terminated character array", --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2050 |
<!-- but "null-terminated string" is not an error and probably better --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2051 |
<!-- for most users. --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2052 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2053 |
— Function: const char * <b>mpfr_get_version</b> (<var>void</var>)<var><a name="index-mpfr_005fget_005fversion-242"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2054 |
<blockquote><p>Return the MPFR version, as a null-terminated string. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2055 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2056 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2057 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2058 |
— Macro: <b>MPFR_VERSION</b><var><a name="index-MPFR_005fVERSION-243"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2059 |
— Macro: <b>MPFR_VERSION_MAJOR</b><var><a name="index-MPFR_005fVERSION_005fMAJOR-244"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2060 |
— Macro: <b>MPFR_VERSION_MINOR</b><var><a name="index-MPFR_005fVERSION_005fMINOR-245"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2061 |
— Macro: <b>MPFR_VERSION_PATCHLEVEL</b><var><a name="index-MPFR_005fVERSION_005fPATCHLEVEL-246"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2062 |
— Macro: <b>MPFR_VERSION_STRING</b><var><a name="index-MPFR_005fVERSION_005fSTRING-247"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2063 |
<blockquote><p><code>MPFR_VERSION</code> is the version of MPFR as a preprocessing constant. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2064 |
<code>MPFR_VERSION_MAJOR</code>, <code>MPFR_VERSION_MINOR</code> and |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2065 |
<code>MPFR_VERSION_PATCHLEVEL</code> are respectively the major, minor and patch |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2066 |
level of MPFR version, as preprocessing constants. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2067 |
<code>MPFR_VERSION_STRING</code> is the version (with an optional suffix, used |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2068 |
in development and pre-release versions) as a string constant, which can |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2069 |
be compared to the result of <code>mpfr_get_version</code> to check at run time |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2070 |
the header file and library used match: |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2071 |
<pre class="example"> if (strcmp (mpfr_get_version (), MPFR_VERSION_STRING)) |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2072 |
fprintf (stderr, "Warning: header and library do not match\n"); |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2073 |
</pre> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2074 |
<p>Note: Obtaining different strings is not necessarily an error, as |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2075 |
in general, a program compiled with some old MPFR version can be |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2076 |
dynamically linked with a newer MPFR library version (if allowed |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2077 |
by the library versioning system). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2078 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2079 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2080 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2081 |
— Macro: long <b>MPFR_VERSION_NUM</b> (<var>major, minor, patchlevel</var>)<var><a name="index-MPFR_005fVERSION_005fNUM-248"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2082 |
<blockquote><p>Create an integer in the same format as used by <code>MPFR_VERSION</code> from the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2083 |
given <var>major</var>, <var>minor</var> and <var>patchlevel</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2084 |
Here is an example of how to check the MPFR version at compile time: |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2085 |
<pre class="example"> #if (!defined(MPFR_VERSION) || (MPFR_VERSION<MPFR_VERSION_NUM(2,1,0))) |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2086 |
# error "Wrong MPFR version." |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2087 |
#endif |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2088 |
</pre> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2089 |
</blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2090 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2091 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2092 |
— Function: const char * <b>mpfr_get_patches</b> (<var>void</var>)<var><a name="index-mpfr_005fget_005fpatches-249"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2093 |
<blockquote><p>Return a null-terminated string containing the ids of the patches applied to |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2094 |
the MPFR library (contents of the <samp><span class="file">PATCHES</span></samp> file), separated by spaces. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2095 |
Note: If the program has been compiled with an older MPFR version and is |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2096 |
dynamically linked with a new MPFR library version, the ids of the patches |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2097 |
applied to the old (compile-time) MPFR version are not available (however |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2098 |
this information should not have much interest in general). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2099 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2100 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2101 |
<div class="node"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2102 |
<p><hr> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2103 |
<a name="Rounding-Mode-Related-Functions"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2104 |
Next: <a rel="next" accesskey="n" href="#Exception-Related-Functions">Exception Related Functions</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2105 |
Previous: <a rel="previous" accesskey="p" href="#Miscellaneous-Functions">Miscellaneous Functions</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2106 |
Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2107 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2108 |
</div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2109 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2110 |
<p><a name="index-Rounding-mode-related-functions-250"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2111 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2112 |
<h3 class="section">5.11 Rounding Mode Related Functions</h3> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2113 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2114 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2115 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2116 |
<blockquote><p>Set the default rounding mode to <var>rnd</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2117 |
The default rounding mode is to nearest initially. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2118 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2119 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2120 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2121 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2122 |
<blockquote><p>Get the default rounding mode. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2123 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2124 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2125 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2126 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2127 |
<blockquote><p>Round <var>x</var> according to <var>rnd</var> with precision <var>prec</var>, which |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2128 |
must be an integer between <code>MPFR_PREC_MIN</code> and <code>MPFR_PREC_MAX</code> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2129 |
(otherwise the behavior is undefined). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2130 |
If <var>prec</var> is greater or equal to the precision of <var>x</var>, then new |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2131 |
space is allocated for the significand, and it is filled with zeros. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2132 |
Otherwise, the significand is rounded to precision <var>prec</var> with the given |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2133 |
direction. In both cases, the precision of <var>x</var> is changed to <var>prec</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2134 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2135 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2136 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2137 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2138 |
<blockquote><p>[This function is obsolete. Please use <code>mpfr_prec_round</code> instead.] |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2139 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2140 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2141 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2142 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2143 |
<blockquote><p>Return the input string (GMP_RNDD, GMP_RNDU, GMP_RNDN, GMP_RNDZ) |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2144 |
corresponding to the rounding mode <var>rnd</var> or a null pointer if |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2145 |
<var>rnd</var> is an invalid rounding mode. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2146 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2147 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2148 |
<div class="node"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2149 |
<p><hr> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2150 |
<a name="Exception-Related-Functions"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2151 |
Next: <a rel="next" accesskey="n" href="#Advanced-Functions">Advanced Functions</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2152 |
Previous: <a rel="previous" accesskey="p" href="#Rounding-Mode-Related-Functions">Rounding Mode Related Functions</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2153 |
Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2154 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2155 |
</div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2156 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2157 |
<!-- node-name, next, previous, up --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2158 |
<p><a name="index-Exception-related-functions-256"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2159 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2160 |
<h3 class="section">5.12 Exception Related Functions</h3> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2161 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2162 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2163 |
— Function: mp_exp_t <b>mpfr_get_emin</b> (<var>void</var>)<var><a name="index-mpfr_005fget_005femin-257"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2164 |
— Function: mp_exp_t <b>mpfr_get_emax</b> (<var>void</var>)<var><a name="index-mpfr_005fget_005femax-258"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2165 |
<blockquote><p>Return the (current) smallest and largest exponents allowed for a |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2166 |
floating-point variable. The smallest positive value of a floating-point |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2167 |
variable is one half times 2 raised to the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2168 |
smallest exponent and the largest value has the form (1 - epsilon) times 2 raised to the largest exponent. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2169 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2170 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2171 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2172 |
— Function: int <b>mpfr_set_emin</b> (<var>mp_exp_t exp</var>)<var><a name="index-mpfr_005fset_005femin-259"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2173 |
— Function: int <b>mpfr_set_emax</b> (<var>mp_exp_t exp</var>)<var><a name="index-mpfr_005fset_005femax-260"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2174 |
<blockquote><p>Set the smallest and largest exponents allowed for a floating-point variable. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2175 |
Return a non-zero value when <var>exp</var> is not in the range accepted by the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2176 |
implementation (in that case the smallest or largest exponent is not changed), |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2177 |
and zero otherwise. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2178 |
If the user changes the exponent range, it is her/his responsibility to check |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2179 |
that all current floating-point variables are in the new allowed range |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2180 |
(for example using <code>mpfr_check_range</code>), otherwise the subsequent |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2181 |
behavior will be undefined, in the sense of the ISO C standard. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2182 |
<!-- It is also her/his responsibility to check that @m {emin <= emax}. --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2183 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2184 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2185 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2186 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2187 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2188 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2189 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2190 |
<blockquote><p>Return the minimum and maximum of the smallest and largest exponents |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2191 |
allowed for <code>mpfr_set_emin</code> and <code>mpfr_set_emax</code>. These values |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2192 |
are implementation dependent; it is possible to create a non |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2193 |
portable program by writing <code>mpfr_set_emax(mpfr_get_emax_max())</code> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2194 |
and <code>mpfr_set_emin(mpfr_get_emin_min())</code> since the values |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2195 |
of the smallest and largest exponents become implementation dependent. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2196 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2197 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2198 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2199 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2200 |
<blockquote><p>This function forces <var>x</var> to be in the current range of acceptable |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2201 |
values, <var>t</var> being the current ternary value: negative if <var>x</var> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2202 |
is smaller than the exact value, positive if <var>x</var> is larger than |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2203 |
the exact value and zero if <var>x</var> is exact (before the call). It |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2204 |
generates an underflow or an overflow if the exponent of <var>x</var> is |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2205 |
outside the current allowed range; the value of <var>t</var> may be used |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2206 |
to avoid a double rounding. This function returns zero if the rounded |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2207 |
result is equal to the exact one, a positive value if the rounded |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2208 |
result is larger than the exact one, a negative value if the rounded |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2209 |
result is smaller than the exact one. Note that unlike most functions, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2210 |
the result is compared to the exact one, not the input value <var>x</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2211 |
i.e. the ternary value is propagated. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2212 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2213 |
<p>Note: If <var>x</var> is an infinity and <var>t</var> is different from zero (i.e., |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2214 |
if the rounded result is an inexact infinity), then the overflow flag is |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2215 |
set. This is useful because <code>mpfr_check_range</code> is typically called |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2216 |
(at least in MPFR functions) after restoring the flags that could have |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2217 |
been set due to internal computations. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2218 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2219 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2220 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2221 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2222 |
<blockquote><p>This function rounds <var>x</var> emulating subnormal number arithmetic: |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2223 |
if <var>x</var> is outside the subnormal exponent range, it just propagates the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2224 |
ternary value <var>t</var>; otherwise, it rounds <var>x</var> to precision |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2225 |
<code>EXP(x)-emin+1</code> according to rounding mode <var>rnd</var> and previous |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2226 |
ternary value <var>t</var>, avoiding double rounding problems. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2227 |
More precisely in the subnormal domain, denoting by <var>e</var> the value of |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2228 |
<code>emin</code>, <var>x</var> is rounded in fixed-point |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2229 |
arithmetic to an integer multiple of two to the power |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2230 |
<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 |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2231 |
is rounded to two to the power <var>e</var> with rounding to nearest. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2232 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2233 |
<p><code>PREC(x)</code> is not modified by this function. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2234 |
<var>rnd</var> and <var>t</var> must be the used rounding mode for computing <var>x</var> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2235 |
and the returned ternary value when computing <var>x</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2236 |
The subnormal exponent range is from <code>emin</code> to <code>emin+PREC(x)-1</code>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2237 |
If the result cannot be represented in the current exponent range |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2238 |
(due to a too small <code>emax</code>), the behavior is undefined. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2239 |
Note that unlike most functions, the result is compared to the exact one, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2240 |
not the input value <var>x</var>, i.e. the ternary value is propagated. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2241 |
This is a preliminary interface. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2242 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2243 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2244 |
<p>This is an example of how to emulate double IEEE-754 arithmetic |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2245 |
using MPFR: |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2246 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2247 |
<pre class="example"> { |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2248 |
mpfr_t xa, xb; |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2249 |
int i; |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2250 |
volatile double a, b; |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2251 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2252 |
mpfr_set_default_prec (53); |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2253 |
mpfr_set_emin (-1073); |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2254 |
mpfr_set_emax (1024); |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2255 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2256 |
mpfr_init (xa); mpfr_init (xb); |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2257 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2258 |
b = 34.3; mpfr_set_d (xb, b, GMP_RNDN); |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2259 |
a = 0x1.1235P-1021; mpfr_set_d (xa, a, GMP_RNDN); |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2260 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2261 |
a /= b; |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2262 |
i = mpfr_div (xa, xa, xb, GMP_RNDN); |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2263 |
i = mpfr_subnormalize (xa, i, GMP_RNDN); |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2264 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2265 |
mpfr_clear (xa); mpfr_clear (xb); |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2266 |
} |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2267 |
</pre> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2268 |
<p>Warning: this emulates a double IEEE-754 arithmetic with correct rounding |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2269 |
in the subnormal range, which may not be the case for your hardware. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2270 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2271 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2272 |
— Function: void <b>mpfr_clear_underflow</b> (<var>void</var>)<var><a name="index-mpfr_005fclear_005funderflow-267"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2273 |
— Function: void <b>mpfr_clear_overflow</b> (<var>void</var>)<var><a name="index-mpfr_005fclear_005foverflow-268"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2274 |
— Function: void <b>mpfr_clear_nanflag</b> (<var>void</var>)<var><a name="index-mpfr_005fclear_005fnanflag-269"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2275 |
— Function: void <b>mpfr_clear_inexflag</b> (<var>void</var>)<var><a name="index-mpfr_005fclear_005finexflag-270"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2276 |
— Function: void <b>mpfr_clear_erangeflag</b> (<var>void</var>)<var><a name="index-mpfr_005fclear_005ferangeflag-271"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2277 |
<blockquote><p>Clear the underflow, overflow, invalid, inexact and erange flags. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2278 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2279 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2280 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2281 |
— Function: void <b>mpfr_set_underflow</b> (<var>void</var>)<var><a name="index-mpfr_005fset_005funderflow-272"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2282 |
— Function: void <b>mpfr_set_overflow</b> (<var>void</var>)<var><a name="index-mpfr_005fset_005foverflow-273"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2283 |
— Function: void <b>mpfr_set_nanflag</b> (<var>void</var>)<var><a name="index-mpfr_005fset_005fnanflag-274"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2284 |
— Function: void <b>mpfr_set_inexflag</b> (<var>void</var>)<var><a name="index-mpfr_005fset_005finexflag-275"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2285 |
— Function: void <b>mpfr_set_erangeflag</b> (<var>void</var>)<var><a name="index-mpfr_005fset_005ferangeflag-276"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2286 |
<blockquote><p>Set the underflow, overflow, invalid, inexact and erange flags. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2287 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2288 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2289 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2290 |
— Function: void <b>mpfr_clear_flags</b> (<var>void</var>)<var><a name="index-mpfr_005fclear_005fflags-277"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2291 |
<blockquote><p>Clear all global flags (underflow, overflow, inexact, invalid, erange). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2292 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2293 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2294 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2295 |
— Function: int <b>mpfr_underflow_p</b> (<var>void</var>)<var><a name="index-mpfr_005funderflow_005fp-278"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2296 |
— Function: int <b>mpfr_overflow_p</b> (<var>void</var>)<var><a name="index-mpfr_005foverflow_005fp-279"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2297 |
— Function: int <b>mpfr_nanflag_p</b> (<var>void</var>)<var><a name="index-mpfr_005fnanflag_005fp-280"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2298 |
— Function: int <b>mpfr_inexflag_p</b> (<var>void</var>)<var><a name="index-mpfr_005finexflag_005fp-281"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2299 |
— Function: int <b>mpfr_erangeflag_p</b> (<var>void</var>)<var><a name="index-mpfr_005ferangeflag_005fp-282"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2300 |
<blockquote><p>Return the corresponding (underflow, overflow, invalid, inexact, erange) |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2301 |
flag, which is non-zero iff the flag is set. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2302 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2303 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2304 |
<div class="node"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2305 |
<p><hr> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2306 |
<a name="Advanced-Functions"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2307 |
Next: <a rel="next" accesskey="n" href="#Compatibility-with-MPF">Compatibility with MPF</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2308 |
Previous: <a rel="previous" accesskey="p" href="#Exception-Related-Functions">Exception Related Functions</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2309 |
Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2310 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2311 |
</div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2312 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2313 |
<!-- node-name, next, previous, up --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2314 |
<p><a name="index-Advanced-functions-283"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2315 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2316 |
<h3 class="section">5.13 Advanced Functions</h3> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2317 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2318 |
<p>All the given interfaces are preliminary. They might change incompatibly in |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2319 |
future revisions. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2320 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2321 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2322 |
— Macro: <b>MPFR_DECL_INIT</b> (<var>name, prec</var>)<var><a name="index-MPFR_005fDECL_005fINIT-284"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2323 |
<blockquote><p>This macro declares <var>name</var> as an automatic variable of type <code>mpfr_t</code>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2324 |
initializes it and sets its precision to be <strong>exactly</strong> <var>prec</var> bits |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2325 |
and its value to NaN. <var>name</var> must be a valid identifier. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2326 |
You must use this macro in the declaration section. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2327 |
This macro is much faster than using <code>mpfr_init2</code> but has some |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2328 |
drawbacks: |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2329 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2330 |
<ul> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2331 |
<li>You <strong>must not</strong> call <code>mpfr_clear</code> with variables |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2332 |
created with this macro (The storage is allocated at the point of declaration |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2333 |
and deallocated when the brace-level is exited.). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2334 |
<li>You <strong>can not</strong> change their precision. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2335 |
<li>You <strong>should not</strong> create variables with huge precision with this macro. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2336 |
<li>Your compiler must support ‘<samp><span class="samp">Non-Constant Initializers</span></samp>’ (standard |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2337 |
in C++ and ISO C99) and ‘<samp><span class="samp">Token Pasting</span></samp>’ |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2338 |
(standard in ISO C89). If <var>prec</var> is not a compiler constant, your compiler |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2339 |
must support ‘<samp><span class="samp">Variable-length automatic arrays</span></samp>’ (standard in ISO C99). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2340 |
‘<samp><span class="samp">GCC 2.95.3</span></samp>’ supports all these features. If you compile your program |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2341 |
with gcc in c89 mode and with ‘<samp><span class="samp">-pedantic</span></samp>’, you may want to define the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2342 |
<code>MPFR_USE_EXTENSION</code> macro to avoid warnings due to the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2343 |
<code>MPFR_DECL_INIT</code> implementation. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2344 |
</ul> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2345 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2346 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2347 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2348 |
— Function: void <b>mpfr_inits</b> (<var>mpfr_t x, ...</var>)<var><a name="index-mpfr_005finits-285"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2349 |
<blockquote><p>Initialize all the <code>mpfr_t</code> variables of the given <code>va_list</code>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2350 |
set their precision to be the default precision and their value to NaN. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2351 |
See <code>mpfr_init</code> for more details. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2352 |
The <code>va_list</code> is assumed to be composed only of type <code>mpfr_t</code> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2353 |
(or equivalently <code>mpfr_ptr</code>). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2354 |
It begins from <var>x</var>. It ends when it encounters a null pointer (whose |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2355 |
type must also be <code>mpfr_ptr</code>). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2356 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2357 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2358 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2359 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2360 |
<blockquote><p>Initialize all the <code>mpfr_t</code> variables of the given <code>va_list</code>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2361 |
set their precision to be <strong>exactly</strong> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2362 |
<var>prec</var> bits and their value to NaN. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2363 |
See <code>mpfr_init2</code> for more details. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2364 |
The <code>va_list</code> is assumed to be composed only of type <code>mpfr_t</code> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2365 |
(or equivalently <code>mpfr_ptr</code>). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2366 |
It begins from <var>x</var>. It ends when it encounters a null pointer (whose |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2367 |
type must also be <code>mpfr_ptr</code>). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2368 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2369 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2370 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2371 |
— Function: void <b>mpfr_clears</b> (<var>mpfr_t x, ...</var>)<var><a name="index-mpfr_005fclears-287"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2372 |
<blockquote><p>Free the space occupied by all the <code>mpfr_t</code> variables of the given |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2373 |
<code>va_list</code>. See <code>mpfr_clear</code> for more details. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2374 |
The <code>va_list</code> is assumed to be composed only of type <code>mpfr_t</code> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2375 |
(or equivalently <code>mpfr_ptr</code>). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2376 |
It begins from <var>x</var>. It ends when it encounters a null pointer (whose |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2377 |
type must also be <code>mpfr_ptr</code>). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2378 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2379 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2380 |
<p>Here is an example of how to use multiple initialization functions: |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2381 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2382 |
<pre class="example"> { |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2383 |
mpfr_t x, y, z, t; |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2384 |
mpfr_inits2 (256, x, y, z, t, (mpfr_ptr) 0); |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2385 |
... |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2386 |
mpfr_clears (x, y, z, t, (mpfr_ptr) 0); |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2387 |
} |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2388 |
</pre> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2389 |
<div class="node"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2390 |
<p><hr> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2391 |
<a name="Compatibility-with-MPF"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2392 |
Next: <a rel="next" accesskey="n" href="#Custom-Interface">Custom Interface</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2393 |
Previous: <a rel="previous" accesskey="p" href="#Advanced-Functions">Advanced Functions</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2394 |
Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2395 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2396 |
</div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2397 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2398 |
<p><a name="index-Compatibility-with-MPF-288"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2399 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2400 |
<h3 class="section">5.14 Compatibility With MPF</h3> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2401 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2402 |
<p>A header file <samp><span class="file">mpf2mpfr.h</span></samp> is included in the distribution of MPFR for |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2403 |
compatibility with the GNU MP class MPF. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2404 |
After inserting the following two lines after the <code>#include <gmp.h></code> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2405 |
line, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2406 |
<pre class="verbatim"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2407 |
#include <mpfr.h> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2408 |
#include <mpf2mpfr.h> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2409 |
</pre> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2410 |
any program written for |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2411 |
MPF can be compiled directly with MPFR without any changes. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2412 |
All operations are then performed with the default MPFR rounding mode, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2413 |
which can be reset with <code>mpfr_set_default_rounding_mode</code>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2414 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2415 |
<p>Warning: the <code>mpf_init</code> and <code>mpf_init2</code> functions initialize |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2416 |
to zero, whereas the corresponding MPFR functions initialize to NaN: |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2417 |
this is useful to detect uninitialized values, but is slightly incompatible |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2418 |
with <code>mpf</code>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2419 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2420 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2421 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2422 |
<blockquote><p>Reset the precision of <var>x</var> to be <strong>exactly</strong> <var>prec</var> bits. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2423 |
The only difference with <code>mpfr_set_prec</code> is that <var>prec</var> is assumed to |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2424 |
be small enough so that the significand fits into the current allocated memory |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2425 |
space for <var>x</var>. Otherwise the behavior is undefined. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2426 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2427 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2428 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2429 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2430 |
<blockquote><p>Return non-zero if <var>op1</var> and <var>op2</var> are both non-zero ordinary |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2431 |
numbers with the same exponent and the same first <var>op3</var> bits, both |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2432 |
zero, or both infinities of the same sign. Return zero otherwise. This |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2433 |
function is defined for compatibility with <code>mpf</code>. Do not use it if |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2434 |
you want to know whether two numbers are close to each other; for instance, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2435 |
1.011111 and 1.100000 are regarded as different for any value of <var>op3</var> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2436 |
larger than 1. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2437 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2438 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2439 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2440 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2441 |
<blockquote><p>Compute the relative difference between <var>op1</var> and <var>op2</var> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2442 |
and store the result in <var>rop</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2443 |
This function does not guarantee the correct rounding on the relative |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2444 |
difference; it just computes |<var>op1</var>-<var>op2</var>|/<var>op1</var>, using the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2445 |
rounding mode <var>rnd</var> for all operations and the precision of <var>rop</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2446 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2447 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2448 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2449 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2450 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2451 |
<blockquote><p>See <code>mpfr_mul_2ui</code> and <code>mpfr_div_2ui</code>. These functions are only kept |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2452 |
for compatibility with MPF. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2453 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2454 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2455 |
<div class="node"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2456 |
<p><hr> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2457 |
<a name="Custom-Interface"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2458 |
Next: <a rel="next" accesskey="n" href="#Internals">Internals</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2459 |
Previous: <a rel="previous" accesskey="p" href="#Compatibility-with-MPF">Compatibility with MPF</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2460 |
Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2461 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2462 |
</div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2463 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2464 |
<p><a name="index-Custom-interface-294"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2465 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2466 |
<h3 class="section">5.15 Custom Interface</h3> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2467 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2468 |
<p>Some applications use a stack to handle the memory and their objects. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2469 |
However, the MPFR memory design is not well suited for such a thing. So that |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2470 |
such applications are able to use MPFR, an auxiliary memory interface has |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2471 |
been created: the Custom Interface. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2472 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2473 |
<p>The following interface allows them to use MPFR in two ways: |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2474 |
<ul> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2475 |
<li>Either they directly store the MPFR FP number as a <code>mpfr_t</code> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2476 |
on the stack. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2477 |
<li>Either they store their own representation of a FP number on the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2478 |
stack and construct a new temporary <code>mpfr_t</code> each time it is needed. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2479 |
</ul> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2480 |
Nothing has to be done to destroy the FP numbers except garbaging the used |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2481 |
memory: all the memory stuff (allocating, destroying, garbaging) is kept to |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2482 |
the application. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2483 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2484 |
<p>Each function in this interface is also implemented as a macro for |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2485 |
efficiency reasons: for example <code>mpfr_custom_init (s, p)</code> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2486 |
uses the macro, while <code>(mpfr_custom_init) (s, p)</code> uses the function. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2487 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2488 |
<p>Note 1: MPFR functions may still initialize temporary FP numbers |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2489 |
using standard mpfr_init. See Custom Allocation (GNU MP). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2490 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2491 |
<p>Note 2: MPFR functions may use the cached functions (mpfr_const_pi for |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2492 |
example), even if they are not explicitly called. You have to call |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2493 |
<code>mpfr_free_cache</code> each time you garbage the memory iff mpfr_init, through |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2494 |
GMP Custom Allocation, allocates its memory on the application stack. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2495 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2496 |
<p>Note 3: This interface is preliminary. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2497 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2498 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2499 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2500 |
<blockquote><p>Return the needed size in bytes to store the significand of a FP number |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2501 |
of precision <var>prec</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2502 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2503 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2504 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2505 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2506 |
<blockquote><p>Initialize a significand of precision <var>prec</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2507 |
<var>significand</var> must be an area of <code>mpfr_custom_get_size (prec)</code> bytes |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2508 |
at least and be suitably aligned for an array of <code>mp_limb_t</code>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2509 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2510 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2511 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2512 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2513 |
<blockquote><p>Perform a dummy initialization of a <code>mpfr_t</code> and set it to: |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2514 |
<ul> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2515 |
<li>if <code>ABS(kind) == MPFR_NAN_KIND</code>, <var>x</var> is set to NaN; |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2516 |
<li>if <code>ABS(kind) == MPFR_INF_KIND</code>, <var>x</var> is set to the infinity |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2517 |
of sign <code>sign(kind)</code>; |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2518 |
<li>if <code>ABS(kind) == MPFR_ZERO_KIND</code>, <var>x</var> is set to the zero of |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2519 |
sign <code>sign(kind)</code>; |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2520 |
<li>if <code>ABS(kind) == MPFR_REGULAR_KIND</code>, <var>x</var> is set to a regular |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2521 |
number: <code>x = sign(kind)*significand*2^exp</code> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2522 |
</ul> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2523 |
In all cases, it uses <var>significand</var> directly for further computing |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2524 |
involving <var>x</var>. It will not allocate anything. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2525 |
A FP number initialized with this function cannot be resized using |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2526 |
<code>mpfr_set_prec</code>, or cleared using <code>mpfr_clear</code>! |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2527 |
<var>significand</var> must have been initialized with <code>mpfr_custom_init</code> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2528 |
using the same precision <var>prec</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2529 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2530 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2531 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2532 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2533 |
<blockquote><p>Return the current kind of a <code>mpfr_t</code> as used by |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2534 |
<code>mpfr_custom_init_set</code>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2535 |
The behavior of this function for any <code>mpfr_t</code> not initialized |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2536 |
with <code>mpfr_custom_init_set</code> is undefined. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2537 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2538 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2539 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2540 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2541 |
<blockquote><p>Return a pointer to the significand used by a <code>mpfr_t</code> initialized with |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2542 |
<code>mpfr_custom_init_set</code>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2543 |
The behavior of this function for any <code>mpfr_t</code> not initialized |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2544 |
with <code>mpfr_custom_init_set</code> is undefined. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2545 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2546 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2547 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2548 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2549 |
<blockquote><p>Return the exponent of <var>x</var>, assuming that <var>x</var> is a non-zero ordinary |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2550 |
number. The return value for NaN, Infinity or Zero is unspecified but doesn't |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2551 |
produce any trap. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2552 |
The behavior of this function for any <code>mpfr_t</code> not initialized |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2553 |
with <code>mpfr_custom_init_set</code> is undefined. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2554 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2555 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2556 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2557 |
— 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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2558 |
<blockquote><p>Inform MPFR that the significand has moved due to a garbage collect |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2559 |
and update its new position to <code>new_position</code>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2560 |
However the application has to move the significand and the <code>mpfr_t</code> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2561 |
itself. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2562 |
The behavior of this function for any <code>mpfr_t</code> not initialized |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2563 |
with <code>mpfr_custom_init_set</code> is undefined. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2564 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2565 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2566 |
<p>See the test suite for examples. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2567 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2568 |
<div class="node"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2569 |
<p><hr> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2570 |
<a name="Internals"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2571 |
Previous: <a rel="previous" accesskey="p" href="#Custom-Interface">Custom Interface</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2572 |
Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2573 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2574 |
</div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2575 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2576 |
<p><a name="index-Internals-302"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2577 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2578 |
<h3 class="section">5.16 Internals</h3> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2579 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2580 |
<p>The following types and |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2581 |
functions were mainly designed for the implementation of MPFR, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2582 |
but may be useful for users too. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2583 |
However no upward compatibility is guaranteed. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2584 |
You may need to include <samp><span class="file">mpfr-impl.h</span></samp> to use them. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2585 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2586 |
<p>The <code>mpfr_t</code> type consists of four fields. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2587 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2588 |
<ul> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2589 |
<li>The <code>_mpfr_prec</code> field is used to store the precision of |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2590 |
the variable (in bits); this is not less than <code>MPFR_PREC_MIN</code>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2591 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2592 |
<li>The <code>_mpfr_sign</code> field is used to store the sign of the variable. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2593 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2594 |
<li>The <code>_mpfr_exp</code> field stores the exponent. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2595 |
An exponent of 0 means a radix point just above the most significant |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2596 |
limb. Non-zero values n are a multiplier 2^n relative to that |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2597 |
point. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2598 |
A NaN, an infinity and a zero are indicated by a special value of the exponent. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2599 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2600 |
<li>Finally, the <code>_mpfr_d</code> is a pointer to the limbs, least |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2601 |
significant limbs stored first. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2602 |
The number of limbs in use is controlled by <code>_mpfr_prec</code>, namely |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2603 |
ceil(<code>_mpfr_prec</code>/<code>mp_bits_per_limb</code>). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2604 |
Non-singular values always have the most significant bit of the most |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2605 |
significant limb set to 1. When the precision does not correspond to a |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2606 |
whole number of limbs, the excess bits at the low end of the data are zero. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2607 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2608 |
</ul> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2609 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2610 |
<!-- @deftypefun int mpfr_add_one_ulp (mpfr_t @var{x}, mp_rnd_t @var{rnd}) --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2611 |
<!-- Add one unit in last place (ulp) to @var{x} if @var{x} is finite --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2612 |
<!-- and positive, subtract one ulp if @var{x} is finite and negative; --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2613 |
<!-- otherwise, @var{x} is not changed. --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2614 |
<!-- The return value is zero unless an overflow occurs, in which case the --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2615 |
<!-- @code{mpfr_add_one_ulp} function behaves like a conventional addition. --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2616 |
<!-- @end deftypefun --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2617 |
<!-- @deftypefun int mpfr_sub_one_ulp (mpfr_t @var{x}, mp_rnd_t @var{rnd}) --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2618 |
<!-- Subtract one ulp to @var{x} if @var{x} is finite and positive, add one --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2619 |
<!-- ulp if @var{x} is finite and negative; otherwise, @var{x} is not changed. --> |
22d9e175d379
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2620 |
<!-- The return value is zero unless an underflow occurs, in which case the --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2621 |
<!-- @code{mpfr_sub_one_ulp} function behaves like a conventional subtraction. --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2622 |
<!-- @end deftypefun --> |
22d9e175d379
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parents:
diff
changeset
|
2623 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2624 |
— 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> |
22d9e175d379
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2625 |
<blockquote><p>Assuming <var>b</var> is an approximation of an unknown number |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2626 |
<var>x</var> in the direction <var>rnd1</var> with error at most two to the power |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2627 |
E(b)-<var>err</var> where E(b) is the exponent of <var>b</var>, return a non-zero |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2628 |
value if one is able to round correctly <var>x</var> to precision |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2629 |
<var>prec</var> with the direction <var>rnd2</var>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2630 |
and 0 otherwise (including for NaN and Inf). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2631 |
This function <strong>does not modify</strong> its arguments. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2632 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2633 |
<p>Note: if one wants to also determine the correct ternary value when rounding |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2634 |
<var>b</var> to precision <var>prec</var>, a useful trick is the following: |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2635 |
<pre class="verbatim"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2636 |
if (mpfr_can_round (b, err, rnd1, GMP_RNDZ, prec + (rnd2 == GMP_RNDN))) |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2637 |
... |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2638 |
</pre> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2639 |
Indeed, if <var>rnd2</var> is <code>GMP_RNDN</code>, this will check if one can |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2640 |
round to <var>prec</var>+1 bits with a directed rounding: |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2641 |
if so, one can surely round to nearest to <var>prec</var> bits, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2642 |
and in addition one can determine the correct ternary value, which would not |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2643 |
be the case when <var>b</var> is near from a value exactly representable on |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2644 |
<var>prec</var> bits. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2645 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2646 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2647 |
<div class="defun"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2648 |
— Function: double <b>mpfr_get_d1</b> (<var>mpfr_t op</var>)<var><a name="index-mpfr_005fget_005fd1-304"></a></var><br> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2649 |
<blockquote><p>Convert <var>op</var> to a <code>double</code>, using the default MPFR rounding mode |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2650 |
(see function <code>mpfr_set_default_rounding_mode</code>). This function is |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2651 |
obsolete. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2652 |
</p></blockquote></div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2653 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2654 |
<!-- @deftypefun void mpfr_set_str_binary (mpfr_t @var{x}, const char *@var{s}) --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2655 |
<!-- Set @var{x} to the value of the binary number in string @var{s}, which has to --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2656 |
<!-- be of the --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2657 |
<!-- form +/-xxxx.xxxxxxEyy. The exponent is read in decimal, but is interpreted --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2658 |
<!-- as the power of two to be multiplied by the significand. --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2659 |
<!-- The significand length of @var{s} has to be less or equal to the precision --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2660 |
<!-- of @var{x}, otherwise an error occurs. --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2661 |
<!-- If @var{s} starts with @code{N}, it is interpreted as NaN (Not-a-Number); --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2662 |
<!-- if it starts with @code{I} after the sign, it is interpreted as infinity, --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2663 |
<!-- with the corresponding sign. --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2664 |
<!-- @end deftypefun --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2665 |
<!-- @deftypefun void mpfr_print_binary (mpfr_t @var{float}) --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2666 |
<!-- Output @var{float} on stdout --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2667 |
<!-- in raw binary format (the exponent is written in decimal, yet). --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2668 |
<!-- @end deftypefun --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2669 |
<div class="node"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2670 |
<p><hr> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2671 |
<a name="Contributors"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2672 |
Next: <a rel="next" accesskey="n" href="#References">References</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2673 |
Previous: <a rel="previous" accesskey="p" href="#MPFR-Interface">MPFR Interface</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2674 |
Up: <a rel="up" accesskey="u" href="#Top">Top</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2675 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2676 |
</div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2677 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2678 |
<!-- node-name, next, previous, up --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2679 |
<h2 class="unnumbered">Contributors</h2> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2680 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2681 |
<p>The main developers of MPFR are Guillaume Hanrot, Vincent Lefèvre, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2682 |
Patrick Pélissier, Philippe Théveny and Paul Zimmermann. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2683 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2684 |
<p>Sylvie Boldo from ENS-Lyon, France, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2685 |
contributed the functions <code>mpfr_agm</code> and <code>mpfr_log</code>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2686 |
Emmanuel Jeandel, from ENS-Lyon too, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2687 |
contributed the generic hypergeometric code in |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2688 |
<code>generic.c</code>, as well as the <code>mpfr_exp3</code>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2689 |
a first implementation of the sine and cosine, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2690 |
and improved versions of |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2691 |
<code>mpfr_const_log2</code> and <code>mpfr_const_pi</code>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2692 |
Mathieu Dutour contributed the functions <code>mpfr_atan</code> and <code>mpfr_asin</code>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2693 |
and a previous version of <code>mpfr_gamma</code>; |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2694 |
David Daney contributed the hyperbolic and inverse hyperbolic functions, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2695 |
the base-2 exponential, and the factorial function. Fabrice Rouillier |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2696 |
contributed the original version of <samp><span class="file">mul_ui.c</span></samp>, the <samp><span class="file">gmp_op.c</span></samp> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2697 |
file, and helped to the Microsoft Windows porting. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2698 |
Jean-Luc Rémy contributed the <code>mpfr_zeta</code> code. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2699 |
Ludovic Meunier helped in the design of the <code>mpfr_erf</code> code. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2700 |
Damien Stehlé contributed the <code>mpfr_get_ld_2exp</code> function. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2701 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2702 |
<p>We would like to thank Jean-Michel Muller and Joris van der Hoeven for very |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2703 |
fruitful discussions at the beginning of that project, Torbjörn Granlund |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2704 |
and Kevin Ryde for their help about design issues, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2705 |
and Nathalie Revol for her careful reading of a previous version of |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2706 |
this documentation. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2707 |
Kevin Ryde did a tremendous job for the portability of MPFR in 2002-2004. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2708 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2709 |
<p>The development of the MPFR library would not have been possible without |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2710 |
the continuous support of INRIA, and of the LORIA (Nancy, France) and LIP |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2711 |
(Lyon, France) laboratories. In particular the main authors were or are |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2712 |
members of the PolKA, Spaces, Cacao project-teams at LORIA and of the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2713 |
Arenaire project-team at LIP. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2714 |
This project was started during the Fiable (reliable in French) action |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2715 |
supported by INRIA, and continued during the AOC action. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2716 |
The development of MPFR was also supported by a grant |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2717 |
(202F0659 00 MPN 121) from the Conseil Régional de Lorraine in 2002, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2718 |
and from INRIA by an "associate engineer" grant (2003-2005) |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2719 |
and an "opération de développement logiciel" grant (2007-2009). |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2720 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2721 |
<div class="node"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2722 |
<p><hr> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2723 |
<a name="References"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2724 |
Next: <a rel="next" accesskey="n" href="#GNU-Free-Documentation-License">GNU Free Documentation License</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2725 |
Previous: <a rel="previous" accesskey="p" href="#Contributors">Contributors</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2726 |
Up: <a rel="up" accesskey="u" href="#Top">Top</a> |
22d9e175d379
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2727 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2728 |
</div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2729 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2730 |
<!-- node-name, next, previous, up --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2731 |
<h2 class="unnumbered">References</h2> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2732 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2733 |
<ul> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2734 |
<li>Laurent Fousse, Guillaume Hanrot, Vincent Lefèvre, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2735 |
Patrick Pélissier and Paul Zimmermann, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2736 |
"MPFR: A Multiple-Precision Binary Floating-Point Library With Correct Rounding", |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2737 |
ACM Transactions on Mathematical Software, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2738 |
volume 33, issue 2, article 13, 15 pages, 2007, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2739 |
<a href="http://doi.acm.org/10.1145/1236463.1236468">http://doi.acm.org/10.1145/1236463.1236468</a>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2740 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2741 |
<li>Torbjörn Granlund, "GNU MP: The GNU Multiple Precision Arithmetic Library", |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2742 |
version 4.2.2, 2007, <a href="http://gmplib.org">http://gmplib.org</a>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2743 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2744 |
<li>IEEE standard for binary floating-point arithmetic, Technical Report |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2745 |
ANSI-IEEE Standard 754-1985, New York, 1985. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2746 |
Approved March 21, 1985: IEEE Standards Board; approved July 26, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2747 |
1985: American National Standards Institute, 18 pages. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2748 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2749 |
<li>Donald E. Knuth, "The Art of Computer Programming", vol 2, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2750 |
"Seminumerical Algorithms", 2nd edition, Addison-Wesley, 1981. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2751 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2752 |
<li>Jean-Michel Muller, "Elementary Functions, Algorithms and Implementation", |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2753 |
Birkhauser, Boston, 2nd edition, 2006. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2754 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2755 |
</ul> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2756 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2757 |
<div class="node"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2758 |
<p><hr> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2759 |
<a name="GNU-Free-Documentation-License"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2760 |
Next: <a rel="next" accesskey="n" href="#Concept-Index">Concept Index</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2761 |
Previous: <a rel="previous" accesskey="p" href="#References">References</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2762 |
Up: <a rel="up" accesskey="u" href="#Top">Top</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2763 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2764 |
</div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2765 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2766 |
<h2 class="appendix">Appendix A GNU Free Documentation License</h2> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2767 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2768 |
<p><a name="index-GNU-Free-Documentation-License-305"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2769 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2770 |
<!-- MPFR tweak: Have this in mpfr.texi to help texinfo-mode --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2771 |
<!-- @node GNU Free Documentation License --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2772 |
<!-- @appendixsec GNU Free Documentation License --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2773 |
<p><a name="index-FDL_002c-GNU-Free-Documentation-License-306"></a><div align="center">Version 1.2, November 2002</div> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2774 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2775 |
<pre class="display"> Copyright © 2000,2001,2002 Free Software Foundation, Inc. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2776 |
51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2777 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2778 |
Everyone is permitted to copy and distribute verbatim copies |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2779 |
of this license document, but changing it is not allowed. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2780 |
</pre> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2781 |
<ol type=1 start=0> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2782 |
<li>PREAMBLE |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2783 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2784 |
<p>The purpose of this License is to make a manual, textbook, or other |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2785 |
functional and useful document <dfn>free</dfn> in the sense of freedom: to |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2786 |
assure everyone the effective freedom to copy and redistribute it, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2787 |
with or without modifying it, either commercially or noncommercially. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2788 |
Secondarily, this License preserves for the author and publisher a way |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2789 |
to get credit for their work, while not being considered responsible |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2790 |
for modifications made by others. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2791 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2792 |
<p>This License is a kind of “copyleft”, which means that derivative |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2793 |
works of the document must themselves be free in the same sense. It |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2794 |
complements the GNU General Public License, which is a copyleft |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2795 |
license designed for free software. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2796 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2797 |
<p>We have designed this License in order to use it for manuals for free |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2798 |
software, because free software needs free documentation: a free |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2799 |
program should come with manuals providing the same freedoms that the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2800 |
software does. But this License is not limited to software manuals; |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2801 |
it can be used for any textual work, regardless of subject matter or |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2802 |
whether it is published as a printed book. We recommend this License |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2803 |
principally for works whose purpose is instruction or reference. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2804 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2805 |
<li>APPLICABILITY AND DEFINITIONS |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2806 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2807 |
<p>This License applies to any manual or other work, in any medium, that |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2808 |
contains a notice placed by the copyright holder saying it can be |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2809 |
distributed under the terms of this License. Such a notice grants a |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2810 |
world-wide, royalty-free license, unlimited in duration, to use that |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2811 |
work under the conditions stated herein. The “Document”, below, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2812 |
refers to any such manual or work. Any member of the public is a |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2813 |
licensee, and is addressed as “you”. You accept the license if you |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2814 |
copy, modify or distribute the work in a way requiring permission |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2815 |
under copyright law. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2816 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2817 |
<p>A “Modified Version” of the Document means any work containing the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2818 |
Document or a portion of it, either copied verbatim, or with |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2819 |
modifications and/or translated into another language. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2820 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2821 |
<p>A “Secondary Section” is a named appendix or a front-matter section |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2822 |
of the Document that deals exclusively with the relationship of the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2823 |
publishers or authors of the Document to the Document's overall |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2824 |
subject (or to related matters) and contains nothing that could fall |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2825 |
directly within that overall subject. (Thus, if the Document is in |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2826 |
part a textbook of mathematics, a Secondary Section may not explain |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2827 |
any mathematics.) The relationship could be a matter of historical |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2828 |
connection with the subject or with related matters, or of legal, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2829 |
commercial, philosophical, ethical or political position regarding |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2830 |
them. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2831 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2832 |
<p>The “Invariant Sections” are certain Secondary Sections whose titles |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2833 |
are designated, as being those of Invariant Sections, in the notice |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2834 |
that says that the Document is released under this License. If a |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2835 |
section does not fit the above definition of Secondary then it is not |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2836 |
allowed to be designated as Invariant. The Document may contain zero |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2837 |
Invariant Sections. If the Document does not identify any Invariant |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2838 |
Sections then there are none. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2839 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2840 |
<p>The “Cover Texts” are certain short passages of text that are listed, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2841 |
as Front-Cover Texts or Back-Cover Texts, in the notice that says that |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2842 |
the Document is released under this License. A Front-Cover Text may |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2843 |
be at most 5 words, and a Back-Cover Text may be at most 25 words. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2844 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2845 |
<p>A “Transparent” copy of the Document means a machine-readable copy, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2846 |
represented in a format whose specification is available to the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2847 |
general public, that is suitable for revising the document |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2848 |
straightforwardly with generic text editors or (for images composed of |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2849 |
pixels) generic paint programs or (for drawings) some widely available |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2850 |
drawing editor, and that is suitable for input to text formatters or |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2851 |
for automatic translation to a variety of formats suitable for input |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2852 |
to text formatters. A copy made in an otherwise Transparent file |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2853 |
format whose markup, or absence of markup, has been arranged to thwart |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2854 |
or discourage subsequent modification by readers is not Transparent. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2855 |
An image format is not Transparent if used for any substantial amount |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2856 |
of text. A copy that is not “Transparent” is called “Opaque”. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2857 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2858 |
<p>Examples of suitable formats for Transparent copies include plain |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2859 |
<span class="sc">ascii</span> without markup, Texinfo input format, LaTeX input |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2860 |
format, <acronym>SGML</acronym> or <acronym>XML</acronym> using a publicly available |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2861 |
<acronym>DTD</acronym>, and standard-conforming simple <acronym>HTML</acronym>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2862 |
PostScript or <acronym>PDF</acronym> designed for human modification. Examples |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2863 |
of transparent image formats include <acronym>PNG</acronym>, <acronym>XCF</acronym> and |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2864 |
<acronym>JPG</acronym>. Opaque formats include proprietary formats that can be |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2865 |
read and edited only by proprietary word processors, <acronym>SGML</acronym> or |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2866 |
<acronym>XML</acronym> for which the <acronym>DTD</acronym> and/or processing tools are |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2867 |
not generally available, and the machine-generated <acronym>HTML</acronym>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2868 |
PostScript or <acronym>PDF</acronym> produced by some word processors for |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2869 |
output purposes only. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2870 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2871 |
<p>The “Title Page” means, for a printed book, the title page itself, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2872 |
plus such following pages as are needed to hold, legibly, the material |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2873 |
this License requires to appear in the title page. For works in |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2874 |
formats which do not have any title page as such, “Title Page” means |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2875 |
the text near the most prominent appearance of the work's title, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2876 |
preceding the beginning of the body of the text. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2877 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2878 |
<p>A section “Entitled XYZ” means a named subunit of the Document whose |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2879 |
title either is precisely XYZ or contains XYZ in parentheses following |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2880 |
text that translates XYZ in another language. (Here XYZ stands for a |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2881 |
specific section name mentioned below, such as “Acknowledgements”, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2882 |
“Dedications”, “Endorsements”, or “History”.) To “Preserve the Title” |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2883 |
of such a section when you modify the Document means that it remains a |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2884 |
section “Entitled XYZ” according to this definition. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2885 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2886 |
<p>The Document may include Warranty Disclaimers next to the notice which |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2887 |
states that this License applies to the Document. These Warranty |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2888 |
Disclaimers are considered to be included by reference in this |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2889 |
License, but only as regards disclaiming warranties: any other |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2890 |
implication that these Warranty Disclaimers may have is void and has |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2891 |
no effect on the meaning of this License. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2892 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2893 |
<li>VERBATIM COPYING |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2894 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2895 |
<p>You may copy and distribute the Document in any medium, either |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2896 |
commercially or noncommercially, provided that this License, the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2897 |
copyright notices, and the license notice saying this License applies |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2898 |
to the Document are reproduced in all copies, and that you add no other |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2899 |
conditions whatsoever to those of this License. You may not use |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2900 |
technical measures to obstruct or control the reading or further |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2901 |
copying of the copies you make or distribute. However, you may accept |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2902 |
compensation in exchange for copies. If you distribute a large enough |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2903 |
number of copies you must also follow the conditions in section 3. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2904 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2905 |
<p>You may also lend copies, under the same conditions stated above, and |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2906 |
you may publicly display copies. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2907 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2908 |
<li>COPYING IN QUANTITY |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2909 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2910 |
<p>If you publish printed copies (or copies in media that commonly have |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2911 |
printed covers) of the Document, numbering more than 100, and the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2912 |
Document's license notice requires Cover Texts, you must enclose the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2913 |
copies in covers that carry, clearly and legibly, all these Cover |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2914 |
Texts: Front-Cover Texts on the front cover, and Back-Cover Texts on |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2915 |
the back cover. Both covers must also clearly and legibly identify |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2916 |
you as the publisher of these copies. The front cover must present |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2917 |
the full title with all words of the title equally prominent and |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2918 |
visible. You may add other material on the covers in addition. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2919 |
Copying with changes limited to the covers, as long as they preserve |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2920 |
the title of the Document and satisfy these conditions, can be treated |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2921 |
as verbatim copying in other respects. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2922 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2923 |
<p>If the required texts for either cover are too voluminous to fit |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2924 |
legibly, you should put the first ones listed (as many as fit |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2925 |
reasonably) on the actual cover, and continue the rest onto adjacent |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2926 |
pages. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2927 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2928 |
<p>If you publish or distribute Opaque copies of the Document numbering |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2929 |
more than 100, you must either include a machine-readable Transparent |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2930 |
copy along with each Opaque copy, or state in or with each Opaque copy |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2931 |
a computer-network location from which the general network-using |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2932 |
public has access to download using public-standard network protocols |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2933 |
a complete Transparent copy of the Document, free of added material. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2934 |
If you use the latter option, you must take reasonably prudent steps, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2935 |
when you begin distribution of Opaque copies in quantity, to ensure |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2936 |
that this Transparent copy will remain thus accessible at the stated |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2937 |
location until at least one year after the last time you distribute an |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2938 |
Opaque copy (directly or through your agents or retailers) of that |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2939 |
edition to the public. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2940 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2941 |
<p>It is requested, but not required, that you contact the authors of the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2942 |
Document well before redistributing any large number of copies, to give |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2943 |
them a chance to provide you with an updated version of the Document. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2944 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2945 |
<li>MODIFICATIONS |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2946 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2947 |
<p>You may copy and distribute a Modified Version of the Document under |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2948 |
the conditions of sections 2 and 3 above, provided that you release |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2949 |
the Modified Version under precisely this License, with the Modified |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2950 |
Version filling the role of the Document, thus licensing distribution |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2951 |
and modification of the Modified Version to whoever possesses a copy |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2952 |
of it. In addition, you must do these things in the Modified Version: |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2953 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2954 |
<ol type=A start=1> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2955 |
<li>Use in the Title Page (and on the covers, if any) a title distinct |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2956 |
from that of the Document, and from those of previous versions |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2957 |
(which should, if there were any, be listed in the History section |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2958 |
of the Document). You may use the same title as a previous version |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2959 |
if the original publisher of that version gives permission. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2960 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2961 |
<li>List on the Title Page, as authors, one or more persons or entities |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2962 |
responsible for authorship of the modifications in the Modified |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2963 |
Version, together with at least five of the principal authors of the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2964 |
Document (all of its principal authors, if it has fewer than five), |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2965 |
unless they release you from this requirement. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2966 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2967 |
<li>State on the Title page the name of the publisher of the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2968 |
Modified Version, as the publisher. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2969 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2970 |
<li>Preserve all the copyright notices of the Document. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2971 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2972 |
<li>Add an appropriate copyright notice for your modifications |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2973 |
adjacent to the other copyright notices. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2974 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2975 |
<li>Include, immediately after the copyright notices, a license notice |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2976 |
giving the public permission to use the Modified Version under the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2977 |
terms of this License, in the form shown in the Addendum below. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2978 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2979 |
<li>Preserve in that license notice the full lists of Invariant Sections |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2980 |
and required Cover Texts given in the Document's license notice. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2981 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2982 |
<li>Include an unaltered copy of this License. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2983 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2984 |
<li>Preserve the section Entitled “History”, Preserve its Title, and add |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2985 |
to it an item stating at least the title, year, new authors, and |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2986 |
publisher of the Modified Version as given on the Title Page. If |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2987 |
there is no section Entitled “History” in the Document, create one |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2988 |
stating the title, year, authors, and publisher of the Document as |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2989 |
given on its Title Page, then add an item describing the Modified |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2990 |
Version as stated in the previous sentence. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2991 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2992 |
<li>Preserve the network location, if any, given in the Document for |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2993 |
public access to a Transparent copy of the Document, and likewise |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2994 |
the network locations given in the Document for previous versions |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2995 |
it was based on. These may be placed in the “History” section. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2996 |
You may omit a network location for a work that was published at |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2997 |
least four years before the Document itself, or if the original |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2998 |
publisher of the version it refers to gives permission. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
2999 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3000 |
<li>For any section Entitled “Acknowledgements” or “Dedications”, Preserve |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3001 |
the Title of the section, and preserve in the section all the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3002 |
substance and tone of each of the contributor acknowledgements and/or |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3003 |
dedications given therein. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3004 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3005 |
<li>Preserve all the Invariant Sections of the Document, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3006 |
unaltered in their text and in their titles. Section numbers |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3007 |
or the equivalent are not considered part of the section titles. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3008 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3009 |
<li>Delete any section Entitled “Endorsements”. Such a section |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3010 |
may not be included in the Modified Version. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3011 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3012 |
<li>Do not retitle any existing section to be Entitled “Endorsements” or |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3013 |
to conflict in title with any Invariant Section. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3014 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3015 |
<li>Preserve any Warranty Disclaimers. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3016 |
</ol> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3017 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3018 |
<p>If the Modified Version includes new front-matter sections or |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3019 |
appendices that qualify as Secondary Sections and contain no material |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3020 |
copied from the Document, you may at your option designate some or all |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3021 |
of these sections as invariant. To do this, add their titles to the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3022 |
list of Invariant Sections in the Modified Version's license notice. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3023 |
These titles must be distinct from any other section titles. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3024 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3025 |
<p>You may add a section Entitled “Endorsements”, provided it contains |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3026 |
nothing but endorsements of your Modified Version by various |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3027 |
parties—for example, statements of peer review or that the text has |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3028 |
been approved by an organization as the authoritative definition of a |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3029 |
standard. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3030 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3031 |
<p>You may add a passage of up to five words as a Front-Cover Text, and a |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3032 |
passage of up to 25 words as a Back-Cover Text, to the end of the list |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3033 |
of Cover Texts in the Modified Version. Only one passage of |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3034 |
Front-Cover Text and one of Back-Cover Text may be added by (or |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3035 |
through arrangements made by) any one entity. If the Document already |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3036 |
includes a cover text for the same cover, previously added by you or |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3037 |
by arrangement made by the same entity you are acting on behalf of, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3038 |
you may not add another; but you may replace the old one, on explicit |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3039 |
permission from the previous publisher that added the old one. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3040 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3041 |
<p>The author(s) and publisher(s) of the Document do not by this License |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3042 |
give permission to use their names for publicity for or to assert or |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3043 |
imply endorsement of any Modified Version. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3044 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3045 |
<li>COMBINING DOCUMENTS |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3046 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3047 |
<p>You may combine the Document with other documents released under this |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3048 |
License, under the terms defined in section 4 above for modified |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3049 |
versions, provided that you include in the combination all of the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3050 |
Invariant Sections of all of the original documents, unmodified, and |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3051 |
list them all as Invariant Sections of your combined work in its |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3052 |
license notice, and that you preserve all their Warranty Disclaimers. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3053 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3054 |
<p>The combined work need only contain one copy of this License, and |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3055 |
multiple identical Invariant Sections may be replaced with a single |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3056 |
copy. If there are multiple Invariant Sections with the same name but |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3057 |
different contents, make the title of each such section unique by |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3058 |
adding at the end of it, in parentheses, the name of the original |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3059 |
author or publisher of that section if known, or else a unique number. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3060 |
Make the same adjustment to the section titles in the list of |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3061 |
Invariant Sections in the license notice of the combined work. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3062 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3063 |
<p>In the combination, you must combine any sections Entitled “History” |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3064 |
in the various original documents, forming one section Entitled |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3065 |
“History”; likewise combine any sections Entitled “Acknowledgements”, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3066 |
and any sections Entitled “Dedications”. You must delete all |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3067 |
sections Entitled “Endorsements.” |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3068 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3069 |
<li>COLLECTIONS OF DOCUMENTS |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3070 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3071 |
<p>You may make a collection consisting of the Document and other documents |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3072 |
released under this License, and replace the individual copies of this |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3073 |
License in the various documents with a single copy that is included in |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3074 |
the collection, provided that you follow the rules of this License for |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3075 |
verbatim copying of each of the documents in all other respects. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3076 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3077 |
<p>You may extract a single document from such a collection, and distribute |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3078 |
it individually under this License, provided you insert a copy of this |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3079 |
License into the extracted document, and follow this License in all |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3080 |
other respects regarding verbatim copying of that document. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3081 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3082 |
<li>AGGREGATION WITH INDEPENDENT WORKS |
22d9e175d379
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3083 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3084 |
<p>A compilation of the Document or its derivatives with other separate |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3085 |
and independent documents or works, in or on a volume of a storage or |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3086 |
distribution medium, is called an “aggregate” if the copyright |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3087 |
resulting from the compilation is not used to limit the legal rights |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3088 |
of the compilation's users beyond what the individual works permit. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3089 |
When the Document is included in an aggregate, this License does not |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3090 |
apply to the other works in the aggregate which are not themselves |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3091 |
derivative works of the Document. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3092 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3093 |
<p>If the Cover Text requirement of section 3 is applicable to these |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3094 |
copies of the Document, then if the Document is less than one half of |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3095 |
the entire aggregate, the Document's Cover Texts may be placed on |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3096 |
covers that bracket the Document within the aggregate, or the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3097 |
electronic equivalent of covers if the Document is in electronic form. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3098 |
Otherwise they must appear on printed covers that bracket the whole |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3099 |
aggregate. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3100 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3101 |
<li>TRANSLATION |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3102 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3103 |
<p>Translation is considered a kind of modification, so you may |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3104 |
distribute translations of the Document under the terms of section 4. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3105 |
Replacing Invariant Sections with translations requires special |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3106 |
permission from their copyright holders, but you may include |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3107 |
translations of some or all Invariant Sections in addition to the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3108 |
original versions of these Invariant Sections. You may include a |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3109 |
translation of this License, and all the license notices in the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3110 |
Document, and any Warranty Disclaimers, provided that you also include |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3111 |
the original English version of this License and the original versions |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3112 |
of those notices and disclaimers. In case of a disagreement between |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3113 |
the translation and the original version of this License or a notice |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3114 |
or disclaimer, the original version will prevail. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3115 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3116 |
<p>If a section in the Document is Entitled “Acknowledgements”, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3117 |
“Dedications”, or “History”, the requirement (section 4) to Preserve |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3118 |
its Title (section 1) will typically require changing the actual |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3119 |
title. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3120 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3121 |
<li>TERMINATION |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3122 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3123 |
<p>You may not copy, modify, sublicense, or distribute the Document except |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3124 |
as expressly provided for under this License. Any other attempt to |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3125 |
copy, modify, sublicense or distribute the Document is void, and will |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3126 |
automatically terminate your rights under this License. However, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3127 |
parties who have received copies, or rights, from you under this |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3128 |
License will not have their licenses terminated so long as such |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3129 |
parties remain in full compliance. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3130 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3131 |
<li>FUTURE REVISIONS OF THIS LICENSE |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3132 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3133 |
<p>The Free Software Foundation may publish new, revised versions |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3134 |
of the GNU Free Documentation License from time to time. Such new |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3135 |
versions will be similar in spirit to the present version, but may |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3136 |
differ in detail to address new problems or concerns. See |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3137 |
<a href="http://www.gnu.org/copyleft/">http://www.gnu.org/copyleft/</a>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3138 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3139 |
<p>Each version of the License is given a distinguishing version number. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3140 |
If the Document specifies that a particular numbered version of this |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3141 |
License “or any later version” applies to it, you have the option of |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3142 |
following the terms and conditions either of that specified version or |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3143 |
of any later version that has been published (not as a draft) by the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3144 |
Free Software Foundation. If the Document does not specify a version |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3145 |
number of this License, you may choose any version ever published (not |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3146 |
as a draft) by the Free Software Foundation. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3147 |
</ol> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3148 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3149 |
<!-- MPFR tweak: Use @appendixsec --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3150 |
<!-- @appendixsubsec ADDENDUM: How to use this License for your documents --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3151 |
<h3 class="appendixsec">A.1 ADDENDUM: How to use this License for your documents</h3> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3152 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3153 |
<p>To use this License in a document you have written, include a copy of |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3154 |
the License in the document and put the following copyright and |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3155 |
license notices just after the title page: |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3156 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3157 |
<pre class="smallexample"> Copyright (C) <var>year</var> <var>your name</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3158 |
Permission is granted to copy, distribute and/or modify this document |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3159 |
under the terms of the GNU Free Documentation License, Version 1.2 |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3160 |
or any later version published by the Free Software Foundation; |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3161 |
with no Invariant Sections, no Front-Cover Texts, and no Back-Cover |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3162 |
Texts. A copy of the license is included in the section entitled ``GNU |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3163 |
Free Documentation License''. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3164 |
</pre> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3165 |
<p>If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3166 |
replace the “with...Texts.” line with this: |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3167 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3168 |
<pre class="smallexample"> with the Invariant Sections being <var>list their titles</var>, with |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3169 |
the Front-Cover Texts being <var>list</var>, and with the Back-Cover Texts |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3170 |
being <var>list</var>. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3171 |
</pre> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3172 |
<p>If you have Invariant Sections without Cover Texts, or some other |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3173 |
combination of the three, merge those two alternatives to suit the |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3174 |
situation. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3175 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3176 |
<p>If your document contains nontrivial examples of program code, we |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3177 |
recommend releasing these examples in parallel under your choice of |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3178 |
free software license, such as the GNU General Public License, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3179 |
to permit their use in free software. |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3180 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3181 |
<!-- Local Variables: --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3182 |
<!-- ispell-local-pdict: "ispell-dict" --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3183 |
<!-- End: --> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3184 |
<div class="node"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3185 |
<p><hr> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3186 |
<a name="Concept-Index"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3187 |
Next: <a rel="next" accesskey="n" href="#Function-Index">Function Index</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3188 |
Previous: <a rel="previous" accesskey="p" href="#GNU-Free-Documentation-License">GNU Free Documentation License</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3189 |
Up: <a rel="up" accesskey="u" href="#Top">Top</a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3190 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3191 |
</div> |
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diff
changeset
|
3192 |
|
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diff
changeset
|
3193 |
<!-- node-name, next, previous, up --> |
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diff
changeset
|
3194 |
<h2 class="unnumbered">Concept Index</h2> |
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diff
changeset
|
3195 |
|
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diff
changeset
|
3196 |
<ul class="index-cp" compact> |
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parents:
diff
changeset
|
3197 |
<li><a href="#index-Accuracy-21">Accuracy</a>: <a href="#MPFR-Interface">MPFR Interface</a></li> |
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parents:
diff
changeset
|
3198 |
<li><a href="#index-Advanced-functions-283">Advanced functions</a>: <a href="#Advanced-Functions">Advanced Functions</a></li> |
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3199 |
<li><a href="#index-Arithmetic-functions-86">Arithmetic functions</a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
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7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3200 |
<li><a href="#index-Assignment-functions-30">Assignment functions</a>: <a href="#Assignment-Functions">Assignment Functions</a></li> |
22d9e175d379
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3201 |
<li><a href="#index-Basic-arithmetic-functions-84">Basic arithmetic functions</a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3202 |
<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> |
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diff
changeset
|
3203 |
<li><a href="#index-Comparison-functions-130">Comparison functions</a>: <a href="#Comparison-Functions">Comparison Functions</a></li> |
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parents:
diff
changeset
|
3204 |
<li><a href="#index-Compatibility-with-MPF-288">Compatibility with MPF</a>: <a href="#Compatibility-with-MPF">Compatibility with MPF</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3205 |
<li><a href="#index-Conditions-for-copying-MPFR-2">Conditions for copying MPFR</a>: <a href="#Copying">Copying</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3206 |
<li><a href="#index-Conversion-functions-61">Conversion functions</a>: <a href="#Conversion-Functions">Conversion Functions</a></li> |
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3207 |
<li><a href="#index-Copying-conditions-1">Copying conditions</a>: <a href="#Copying">Copying</a></li> |
22d9e175d379
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parents:
diff
changeset
|
3208 |
<li><a href="#index-Custom-interface-294">Custom interface</a>: <a href="#Custom-Interface">Custom Interface</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3209 |
<li><a href="#index-Exception-related-functions-256">Exception related functions</a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3210 |
<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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3211 |
<li><a href="#index-Float-arithmetic-functions-85">Float arithmetic functions</a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3212 |
<li><a href="#index-Float-comparisons-functions-129">Float comparisons functions</a>: <a href="#Comparison-Functions">Comparison Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3213 |
<li><a href="#index-Float-functions-19">Float functions</a>: <a href="#MPFR-Interface">MPFR Interface</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3214 |
<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> |
22d9e175d379
7041521 GNU MP to Userland
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parents:
diff
changeset
|
3215 |
<li><a href="#index-Floating_002dpoint-functions-18">Floating-point functions</a>: <a href="#MPFR-Interface">MPFR Interface</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3216 |
<li><a href="#index-Floating_002dpoint-number-11">Floating-point number</a>: <a href="#MPFR-Basics">MPFR Basics</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3217 |
<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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3218 |
<li><a href="#index-I_002fO-functions-211">I/O functions</a>: <a href="#Input-and-Output-Functions">Input and Output Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3219 |
<li><a href="#index-Initialization-functions-22">Initialization functions</a>: <a href="#Initialization-Functions">Initialization Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3220 |
<li><a href="#index-Input-functions-209">Input functions</a>: <a href="#Input-and-Output-Functions">Input and Output Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3221 |
<li><a href="#index-Installation-3">Installation</a>: <a href="#Installing-MPFR">Installing MPFR</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3222 |
<li><a href="#index-Integer-related-functions-214">Integer related functions</a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3223 |
<li><a href="#index-Internals-302">Internals</a>: <a href="#Internals">Internals</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3224 |
<li><a href="#index-g_t_0040code_007blibmpfr_007d-9"><code>libmpfr</code></a>: <a href="#MPFR-Basics">MPFR Basics</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3225 |
<li><a href="#index-Libraries-7">Libraries</a>: <a href="#MPFR-Basics">MPFR Basics</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3226 |
<li><a href="#index-Libtool-10">Libtool</a>: <a href="#MPFR-Basics">MPFR Basics</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3227 |
<li><a href="#index-Limb-17">Limb</a>: <a href="#MPFR-Basics">MPFR Basics</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3228 |
<li><a href="#index-Linking-8">Linking</a>: <a href="#MPFR-Basics">MPFR Basics</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3229 |
<li><a href="#index-Miscellaneous-float-functions-228">Miscellaneous float functions</a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3230 |
<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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3231 |
<li><a href="#index-Output-functions-210">Output functions</a>: <a href="#Input-and-Output-Functions">Input and Output Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3232 |
<li><a href="#index-Precision-20">Precision</a>: <a href="#MPFR-Interface">MPFR Interface</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3233 |
<li><a href="#index-Precision-13">Precision</a>: <a href="#MPFR-Basics">MPFR Basics</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3234 |
<li><a href="#index-Reporting-bugs-4">Reporting bugs</a>: <a href="#Reporting-Bugs">Reporting Bugs</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3235 |
<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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3236 |
<li><a href="#index-Rounding-Modes-15">Rounding Modes</a>: <a href="#MPFR-Basics">MPFR Basics</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3237 |
<li><a href="#index-Special-functions-154">Special functions</a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3238 |
<li><a href="#index-g_t_0040code_007bstdio_002eh_007d-6"><code>stdio.h</code></a>: <a href="#MPFR-Basics">MPFR Basics</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3239 |
</ul><div class="node"> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3240 |
<p><hr> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3241 |
<a name="Function-Index"></a> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3242 |
Previous: <a rel="previous" accesskey="p" href="#Concept-Index">Concept Index</a>, |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3243 |
Up: <a rel="up" accesskey="u" href="#Top">Top</a> |
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7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3244 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
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diff
changeset
|
3245 |
</div> |
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7041521 GNU MP to Userland
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diff
changeset
|
3246 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3247 |
<!-- node-name, next, previous, up --> |
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7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
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diff
changeset
|
3248 |
<h2 class="unnumbered">Function and Type Index</h2> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3249 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3250 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3251 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3252 |
<ul class="index-fn" compact> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3253 |
<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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3254 |
<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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3255 |
<li><a href="#index-mpfr_005fabs-123"><code>mpfr_abs</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3256 |
<li><a href="#index-mpfr_005facos-168"><code>mpfr_acos</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3257 |
<li><a href="#index-mpfr_005facosh-178"><code>mpfr_acosh</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3258 |
<li><a href="#index-mpfr_005fadd-87"><code>mpfr_add</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3259 |
<li><a href="#index-mpfr_005fadd_005fq-91"><code>mpfr_add_q</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3260 |
<li><a href="#index-mpfr_005fadd_005fsi-89"><code>mpfr_add_si</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
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parents:
diff
changeset
|
3261 |
<li><a href="#index-mpfr_005fadd_005fui-88"><code>mpfr_add_ui</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
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parents:
diff
changeset
|
3262 |
<li><a href="#index-mpfr_005fadd_005fz-90"><code>mpfr_add_z</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3263 |
<li><a href="#index-mpfr_005fagm-200"><code>mpfr_agm</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3264 |
<li><a href="#index-mpfr_005fasin-169"><code>mpfr_asin</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
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parents:
diff
changeset
|
3265 |
<li><a href="#index-mpfr_005fasinh-179"><code>mpfr_asinh</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
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parents:
diff
changeset
|
3266 |
<li><a href="#index-mpfr_005fatan-170"><code>mpfr_atan</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3267 |
<li><a href="#index-mpfr_005fatan2-171"><code>mpfr_atan2</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
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parents:
diff
changeset
|
3268 |
<li><a href="#index-mpfr_005fatanh-180"><code>mpfr_atanh</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
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parents:
diff
changeset
|
3269 |
<li><a href="#index-mpfr_005fcan_005fround-303"><code>mpfr_can_round</code></a>: <a href="#Internals">Internals</a></li> |
22d9e175d379
7041521 GNU MP to Userland
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parents:
diff
changeset
|
3270 |
<li><a href="#index-mpfr_005fcbrt-114"><code>mpfr_cbrt</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
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parents:
diff
changeset
|
3271 |
<li><a href="#index-mpfr_005fceil-216"><code>mpfr_ceil</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li> |
22d9e175d379
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parents:
diff
changeset
|
3272 |
<li><a href="#index-mpfr_005fcheck_005frange-265"><code>mpfr_check_range</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li> |
22d9e175d379
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parents:
diff
changeset
|
3273 |
<li><a href="#index-mpfr_005fclear-24"><code>mpfr_clear</code></a>: <a href="#Initialization-Functions">Initialization Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
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parents:
diff
changeset
|
3274 |
<li><a href="#index-mpfr_005fclear_005ferangeflag-271"><code>mpfr_clear_erangeflag</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3275 |
<li><a href="#index-mpfr_005fclear_005fflags-277"><code>mpfr_clear_flags</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li> |
22d9e175d379
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parents:
diff
changeset
|
3276 |
<li><a href="#index-mpfr_005fclear_005finexflag-270"><code>mpfr_clear_inexflag</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li> |
22d9e175d379
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parents:
diff
changeset
|
3277 |
<li><a href="#index-mpfr_005fclear_005fnanflag-269"><code>mpfr_clear_nanflag</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3278 |
<li><a href="#index-mpfr_005fclear_005foverflow-268"><code>mpfr_clear_overflow</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3279 |
<li><a href="#index-mpfr_005fclear_005funderflow-267"><code>mpfr_clear_underflow</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3280 |
<li><a href="#index-mpfr_005fclears-287"><code>mpfr_clears</code></a>: <a href="#Advanced-Functions">Advanced Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3281 |
<li><a href="#index-mpfr_005fcmp-131"><code>mpfr_cmp</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3282 |
<li><a href="#index-mpfr_005fcmp_005fd-134"><code>mpfr_cmp_d</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3283 |
<li><a href="#index-mpfr_005fcmp_005ff-138"><code>mpfr_cmp_f</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3284 |
<li><a href="#index-mpfr_005fcmp_005fld-135"><code>mpfr_cmp_ld</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3285 |
<li><a href="#index-mpfr_005fcmp_005fq-137"><code>mpfr_cmp_q</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3286 |
<li><a href="#index-mpfr_005fcmp_005fsi-133"><code>mpfr_cmp_si</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3287 |
<li><a href="#index-mpfr_005fcmp_005fsi_005f2exp-140"><code>mpfr_cmp_si_2exp</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3288 |
<li><a href="#index-mpfr_005fcmp_005fui-132"><code>mpfr_cmp_ui</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3289 |
<li><a href="#index-mpfr_005fcmp_005fui_005f2exp-139"><code>mpfr_cmp_ui_2exp</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3290 |
<li><a href="#index-mpfr_005fcmp_005fz-136"><code>mpfr_cmp_z</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3291 |
<li><a href="#index-mpfr_005fcmpabs-141"><code>mpfr_cmpabs</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3292 |
<li><a href="#index-mpfr_005fconst_005fcatalan-205"><code>mpfr_const_catalan</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3293 |
<li><a href="#index-mpfr_005fconst_005feuler-204"><code>mpfr_const_euler</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3294 |
<li><a href="#index-mpfr_005fconst_005flog2-202"><code>mpfr_const_log2</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3295 |
<li><a href="#index-mpfr_005fconst_005fpi-203"><code>mpfr_const_pi</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3296 |
<li><a href="#index-mpfr_005fcopysign-241"><code>mpfr_copysign</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3297 |
<li><a href="#index-mpfr_005fcos-161"><code>mpfr_cos</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3298 |
<li><a href="#index-mpfr_005fcosh-172"><code>mpfr_cosh</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3299 |
<li><a href="#index-mpfr_005fcot-166"><code>mpfr_cot</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3300 |
<li><a href="#index-mpfr_005fcoth-177"><code>mpfr_coth</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3301 |
<li><a href="#index-mpfr_005fcsc-165"><code>mpfr_csc</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3302 |
<li><a href="#index-mpfr_005fcsch-176"><code>mpfr_csch</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3303 |
<li><a href="#index-mpfr_005fcustom_005fget_005fexp-300"><code>mpfr_custom_get_exp</code></a>: <a href="#Custom-Interface">Custom Interface</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3304 |
<li><a href="#index-mpfr_005fcustom_005fget_005fkind-298"><code>mpfr_custom_get_kind</code></a>: <a href="#Custom-Interface">Custom Interface</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3305 |
<li><a href="#index-mpfr_005fcustom_005fget_005fmantissa-299"><code>mpfr_custom_get_mantissa</code></a>: <a href="#Custom-Interface">Custom Interface</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3306 |
<li><a href="#index-mpfr_005fcustom_005fget_005fsize-295"><code>mpfr_custom_get_size</code></a>: <a href="#Custom-Interface">Custom Interface</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3307 |
<li><a href="#index-mpfr_005fcustom_005finit-296"><code>mpfr_custom_init</code></a>: <a href="#Custom-Interface">Custom Interface</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3308 |
<li><a href="#index-mpfr_005fcustom_005finit_005fset-297"><code>mpfr_custom_init_set</code></a>: <a href="#Custom-Interface">Custom Interface</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3309 |
<li><a href="#index-mpfr_005fcustom_005fmove-301"><code>mpfr_custom_move</code></a>: <a href="#Custom-Interface">Custom Interface</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3310 |
<li><a href="#index-MPFR_005fDECL_005fINIT-284"><code>MPFR_DECL_INIT</code></a>: <a href="#Advanced-Functions">Advanced Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3311 |
<li><a href="#index-mpfr_005fdim-124"><code>mpfr_dim</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3312 |
<li><a href="#index-mpfr_005fdiv-105"><code>mpfr_div</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3313 |
<li><a href="#index-mpfr_005fdiv_005f2exp-293"><code>mpfr_div_2exp</code></a>: <a href="#Compatibility-with-MPF">Compatibility with MPF</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3314 |
<li><a href="#index-mpfr_005fdiv_005f2si-128"><code>mpfr_div_2si</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3315 |
<li><a href="#index-mpfr_005fdiv_005f2ui-127"><code>mpfr_div_2ui</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3316 |
<li><a href="#index-mpfr_005fdiv_005fq-111"><code>mpfr_div_q</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3317 |
<li><a href="#index-mpfr_005fdiv_005fsi-109"><code>mpfr_div_si</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3318 |
<li><a href="#index-mpfr_005fdiv_005fui-107"><code>mpfr_div_ui</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3319 |
<li><a href="#index-mpfr_005fdiv_005fz-110"><code>mpfr_div_z</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3320 |
<li><a href="#index-mpfr_005feint-184"><code>mpfr_eint</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3321 |
<li><a href="#index-mpfr_005feq-290"><code>mpfr_eq</code></a>: <a href="#Compatibility-with-MPF">Compatibility with MPF</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3322 |
<li><a href="#index-mpfr_005fequal_005fp-152"><code>mpfr_equal_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3323 |
<li><a href="#index-mpfr_005ferangeflag_005fp-282"><code>mpfr_erangeflag_p</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3324 |
<li><a href="#index-mpfr_005ferf-190"><code>mpfr_erf</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3325 |
<li><a href="#index-mpfr_005ferfc-191"><code>mpfr_erfc</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3326 |
<li><a href="#index-mpfr_005fexp-158"><code>mpfr_exp</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3327 |
<li><a href="#index-mpfr_005fexp10-160"><code>mpfr_exp10</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3328 |
<li><a href="#index-mpfr_005fexp2-159"><code>mpfr_exp2</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3329 |
<li><a href="#index-mpfr_005fexpm1-183"><code>mpfr_expm1</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3330 |
<li><a href="#index-mpfr_005ffac_005fui-181"><code>mpfr_fac_ui</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3331 |
<li><a href="#index-mpfr_005ffits_005fintmax_005fp-82"><code>mpfr_fits_intmax_p</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3332 |
<li><a href="#index-mpfr_005ffits_005fsint_005fp-79"><code>mpfr_fits_sint_p</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3333 |
<li><a href="#index-mpfr_005ffits_005fslong_005fp-77"><code>mpfr_fits_slong_p</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3334 |
<li><a href="#index-mpfr_005ffits_005fsshort_005fp-81"><code>mpfr_fits_sshort_p</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3335 |
<li><a href="#index-mpfr_005ffits_005fuint_005fp-78"><code>mpfr_fits_uint_p</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3336 |
<li><a href="#index-mpfr_005ffits_005fuintmax_005fp-83"><code>mpfr_fits_uintmax_p</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3337 |
<li><a href="#index-mpfr_005ffits_005fulong_005fp-76"><code>mpfr_fits_ulong_p</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3338 |
<li><a href="#index-mpfr_005ffits_005fushort_005fp-80"><code>mpfr_fits_ushort_p</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3339 |
<li><a href="#index-mpfr_005ffloor-217"><code>mpfr_floor</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3340 |
<li><a href="#index-mpfr_005ffma-198"><code>mpfr_fma</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3341 |
<li><a href="#index-mpfr_005ffms-199"><code>mpfr_fms</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3342 |
<li><a href="#index-mpfr_005ffrac-224"><code>mpfr_frac</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3343 |
<li><a href="#index-mpfr_005ffree_005fcache-206"><code>mpfr_free_cache</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3344 |
<li><a href="#index-mpfr_005ffree_005fstr-75"><code>mpfr_free_str</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3345 |
<li><a href="#index-mpfr_005fgamma-185"><code>mpfr_gamma</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3346 |
<li><a href="#index-mpfr_005fget_005fd-62"><code>mpfr_get_d</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3347 |
<li><a href="#index-mpfr_005fget_005fd1-304"><code>mpfr_get_d1</code></a>: <a href="#Internals">Internals</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3348 |
<li><a href="#index-mpfr_005fget_005fd_005f2exp-65"><code>mpfr_get_d_2exp</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3349 |
<li><a href="#index-mpfr_005fget_005fdecimal64-64"><code>mpfr_get_decimal64</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3350 |
<li><a href="#index-mpfr_005fget_005fdefault_005fprec-27"><code>mpfr_get_default_prec</code></a>: <a href="#Initialization-Functions">Initialization Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3351 |
<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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3352 |
<li><a href="#index-mpfr_005fget_005femax-258"><code>mpfr_get_emax</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3353 |
<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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3354 |
<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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3355 |
<li><a href="#index-mpfr_005fget_005femin-257"><code>mpfr_get_emin</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3356 |
<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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3357 |
<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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3358 |
<li><a href="#index-mpfr_005fget_005fexp-237"><code>mpfr_get_exp</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3359 |
<li><a href="#index-mpfr_005fget_005ff-73"><code>mpfr_get_f</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3360 |
<li><a href="#index-mpfr_005fget_005fld-63"><code>mpfr_get_ld</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3361 |
<li><a href="#index-mpfr_005fget_005fld_005f2exp-66"><code>mpfr_get_ld_2exp</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3362 |
<li><a href="#index-mpfr_005fget_005fpatches-249"><code>mpfr_get_patches</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3363 |
<li><a href="#index-mpfr_005fget_005fprec-29"><code>mpfr_get_prec</code></a>: <a href="#Initialization-Functions">Initialization Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3364 |
<li><a href="#index-mpfr_005fget_005fsi-67"><code>mpfr_get_si</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3365 |
<li><a href="#index-mpfr_005fget_005fsj-69"><code>mpfr_get_sj</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3366 |
<li><a href="#index-mpfr_005fget_005fstr-74"><code>mpfr_get_str</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3367 |
<li><a href="#index-mpfr_005fget_005fui-68"><code>mpfr_get_ui</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3368 |
<li><a href="#index-mpfr_005fget_005fuj-70"><code>mpfr_get_uj</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3369 |
<li><a href="#index-mpfr_005fget_005fversion-242"><code>mpfr_get_version</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3370 |
<li><a href="#index-mpfr_005fget_005fz-72"><code>mpfr_get_z</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3371 |
<li><a href="#index-mpfr_005fget_005fz_005fexp-71"><code>mpfr_get_z_exp</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3372 |
<li><a href="#index-mpfr_005fgreater_005fp-147"><code>mpfr_greater_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3373 |
<li><a href="#index-mpfr_005fgreaterequal_005fp-148"><code>mpfr_greaterequal_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3374 |
<li><a href="#index-mpfr_005fhypot-201"><code>mpfr_hypot</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3375 |
<li><a href="#index-mpfr_005finexflag_005fp-281"><code>mpfr_inexflag_p</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3376 |
<li><a href="#index-mpfr_005finf_005fp-143"><code>mpfr_inf_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3377 |
<li><a href="#index-mpfr_005finit-25"><code>mpfr_init</code></a>: <a href="#Initialization-Functions">Initialization Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3378 |
<li><a href="#index-mpfr_005finit2-23"><code>mpfr_init2</code></a>: <a href="#Initialization-Functions">Initialization Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3379 |
<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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3380 |
<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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3381 |
<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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3382 |
<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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3383 |
<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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3384 |
<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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3385 |
<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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3386 |
<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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3387 |
<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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3388 |
<li><a href="#index-mpfr_005finits-285"><code>mpfr_inits</code></a>: <a href="#Advanced-Functions">Advanced Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3389 |
<li><a href="#index-mpfr_005finits2-286"><code>mpfr_inits2</code></a>: <a href="#Advanced-Functions">Advanced Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3390 |
<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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3391 |
<li><a href="#index-mpfr_005finteger_005fp-227"><code>mpfr_integer_p</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3392 |
<li><a href="#index-mpfr_005fj0-192"><code>mpfr_j0</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3393 |
<li><a href="#index-mpfr_005fj1-193"><code>mpfr_j1</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3394 |
<li><a href="#index-mpfr_005fjn-194"><code>mpfr_jn</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3395 |
<li><a href="#index-mpfr_005fless_005fp-149"><code>mpfr_less_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3396 |
<li><a href="#index-mpfr_005flessequal_005fp-150"><code>mpfr_lessequal_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3397 |
<li><a href="#index-mpfr_005flessgreater_005fp-151"><code>mpfr_lessgreater_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3398 |
<li><a href="#index-mpfr_005flgamma-187"><code>mpfr_lgamma</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3399 |
<li><a href="#index-mpfr_005flngamma-186"><code>mpfr_lngamma</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3400 |
<li><a href="#index-mpfr_005flog-155"><code>mpfr_log</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3401 |
<li><a href="#index-mpfr_005flog10-157"><code>mpfr_log10</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3402 |
<li><a href="#index-mpfr_005flog1p-182"><code>mpfr_log1p</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3403 |
<li><a href="#index-mpfr_005flog2-156"><code>mpfr_log2</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3404 |
<li><a href="#index-mpfr_005fmax-233"><code>mpfr_max</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3405 |
<li><a href="#index-mpfr_005fmin-232"><code>mpfr_min</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3406 |
<li><a href="#index-mpfr_005fmul-99"><code>mpfr_mul</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3407 |
<li><a href="#index-mpfr_005fmul_005f2exp-292"><code>mpfr_mul_2exp</code></a>: <a href="#Compatibility-with-MPF">Compatibility with MPF</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3408 |
<li><a href="#index-mpfr_005fmul_005f2si-126"><code>mpfr_mul_2si</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3409 |
<li><a href="#index-mpfr_005fmul_005f2ui-125"><code>mpfr_mul_2ui</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3410 |
<li><a href="#index-mpfr_005fmul_005fq-103"><code>mpfr_mul_q</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3411 |
<li><a href="#index-mpfr_005fmul_005fsi-101"><code>mpfr_mul_si</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3412 |
<li><a href="#index-mpfr_005fmul_005fui-100"><code>mpfr_mul_ui</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3413 |
<li><a href="#index-mpfr_005fmul_005fz-102"><code>mpfr_mul_z</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3414 |
<li><a href="#index-mpfr_005fnan_005fp-142"><code>mpfr_nan_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3415 |
<li><a href="#index-mpfr_005fnanflag_005fp-280"><code>mpfr_nanflag_p</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3416 |
<li><a href="#index-mpfr_005fneg-122"><code>mpfr_neg</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3417 |
<li><a href="#index-mpfr_005fnextabove-230"><code>mpfr_nextabove</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3418 |
<li><a href="#index-mpfr_005fnextbelow-231"><code>mpfr_nextbelow</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3419 |
<li><a href="#index-mpfr_005fnexttoward-229"><code>mpfr_nexttoward</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3420 |
<li><a href="#index-mpfr_005fnumber_005fp-144"><code>mpfr_number_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3421 |
<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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3422 |
<li><a href="#index-mpfr_005foverflow_005fp-279"><code>mpfr_overflow_p</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3423 |
<li><a href="#index-mpfr_005fpow-116"><code>mpfr_pow</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3424 |
<li><a href="#index-mpfr_005fpow_005fsi-118"><code>mpfr_pow_si</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3425 |
<li><a href="#index-mpfr_005fpow_005fui-117"><code>mpfr_pow_ui</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3426 |
<li><a href="#index-mpfr_005fpow_005fz-119"><code>mpfr_pow_z</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3427 |
<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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3428 |
<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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3429 |
<li><a href="#index-mpfr_005frandom-235"><code>mpfr_random</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3430 |
<li><a href="#index-mpfr_005frandom2-236"><code>mpfr_random2</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3431 |
<li><a href="#index-mpfr_005freldiff-291"><code>mpfr_reldiff</code></a>: <a href="#Compatibility-with-MPF">Compatibility with MPF</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3432 |
<li><a href="#index-mpfr_005fremainder-225"><code>mpfr_remainder</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3433 |
<li><a href="#index-mpfr_005fremquo-226"><code>mpfr_remquo</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3434 |
<li><a href="#index-mpfr_005frint-215"><code>mpfr_rint</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3435 |
<li><a href="#index-mpfr_005frint_005fceil-220"><code>mpfr_rint_ceil</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3436 |
<li><a href="#index-mpfr_005frint_005ffloor-221"><code>mpfr_rint_floor</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3437 |
<li><a href="#index-mpfr_005frint_005fround-222"><code>mpfr_rint_round</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3438 |
<li><a href="#index-mpfr_005frint_005ftrunc-223"><code>mpfr_rint_trunc</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3439 |
<li><a href="#index-mpfr_005froot-115"><code>mpfr_root</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3440 |
<li><a href="#index-mpfr_005fround-218"><code>mpfr_round</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3441 |
<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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3442 |
<li><a href="#index-mpfr_005fsec-164"><code>mpfr_sec</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3443 |
<li><a href="#index-mpfr_005fsech-175"><code>mpfr_sech</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3444 |
<li><a href="#index-mpfr_005fset-31"><code>mpfr_set</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3445 |
<li><a href="#index-mpfr_005fset_005fd-36"><code>mpfr_set_d</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3446 |
<li><a href="#index-mpfr_005fset_005fdecimal64-38"><code>mpfr_set_decimal64</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3447 |
<li><a href="#index-mpfr_005fset_005fdefault_005fprec-26"><code>mpfr_set_default_prec</code></a>: <a href="#Initialization-Functions">Initialization Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3448 |
<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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3449 |
<li><a href="#index-mpfr_005fset_005femax-260"><code>mpfr_set_emax</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3450 |
<li><a href="#index-mpfr_005fset_005femin-259"><code>mpfr_set_emin</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3451 |
<li><a href="#index-mpfr_005fset_005ferangeflag-276"><code>mpfr_set_erangeflag</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3452 |
<li><a href="#index-mpfr_005fset_005fexp-238"><code>mpfr_set_exp</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3453 |
<li><a href="#index-mpfr_005fset_005ff-41"><code>mpfr_set_f</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3454 |
<li><a href="#index-mpfr_005fset_005finexflag-275"><code>mpfr_set_inexflag</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3455 |
<li><a href="#index-mpfr_005fset_005finf-48"><code>mpfr_set_inf</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3456 |
<li><a href="#index-mpfr_005fset_005fld-37"><code>mpfr_set_ld</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3457 |
<li><a href="#index-mpfr_005fset_005fnan-49"><code>mpfr_set_nan</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3458 |
<li><a href="#index-mpfr_005fset_005fnanflag-274"><code>mpfr_set_nanflag</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3459 |
<li><a href="#index-mpfr_005fset_005foverflow-273"><code>mpfr_set_overflow</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3460 |
<li><a href="#index-mpfr_005fset_005fprec-28"><code>mpfr_set_prec</code></a>: <a href="#Initialization-Functions">Initialization Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3461 |
<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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3462 |
<li><a href="#index-mpfr_005fset_005fq-40"><code>mpfr_set_q</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3463 |
<li><a href="#index-mpfr_005fset_005fsi-33"><code>mpfr_set_si</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3464 |
<li><a href="#index-mpfr_005fset_005fsi_005f2exp-43"><code>mpfr_set_si_2exp</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3465 |
<li><a href="#index-mpfr_005fset_005fsj-35"><code>mpfr_set_sj</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3466 |
<li><a href="#index-mpfr_005fset_005fsj_005f2exp-45"><code>mpfr_set_sj_2exp</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3467 |
<li><a href="#index-mpfr_005fset_005fstr-46"><code>mpfr_set_str</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3468 |
<li><a href="#index-mpfr_005fset_005fui-32"><code>mpfr_set_ui</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3469 |
<li><a href="#index-mpfr_005fset_005fui_005f2exp-42"><code>mpfr_set_ui_2exp</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3470 |
<li><a href="#index-mpfr_005fset_005fuj-34"><code>mpfr_set_uj</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3471 |
<li><a href="#index-mpfr_005fset_005fuj_005f2exp-44"><code>mpfr_set_uj_2exp</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3472 |
<li><a href="#index-mpfr_005fset_005funderflow-272"><code>mpfr_set_underflow</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3473 |
<li><a href="#index-mpfr_005fset_005fz-39"><code>mpfr_set_z</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3474 |
<li><a href="#index-mpfr_005fsetsign-240"><code>mpfr_setsign</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3475 |
<li><a href="#index-mpfr_005fsgn-146"><code>mpfr_sgn</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3476 |
<li><a href="#index-mpfr_005fsi_005fdiv-108"><code>mpfr_si_div</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3477 |
<li><a href="#index-mpfr_005fsi_005fsub-95"><code>mpfr_si_sub</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3478 |
<li><a href="#index-mpfr_005fsignbit-239"><code>mpfr_signbit</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3479 |
<li><a href="#index-mpfr_005fsin-162"><code>mpfr_sin</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3480 |
<li><a href="#index-mpfr_005fsin_005fcos-167"><code>mpfr_sin_cos</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3481 |
<li><a href="#index-mpfr_005fsinh-173"><code>mpfr_sinh</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3482 |
<li><a href="#index-mpfr_005fsqr-104"><code>mpfr_sqr</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3483 |
<li><a href="#index-mpfr_005fsqrt-112"><code>mpfr_sqrt</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3484 |
<li><a href="#index-mpfr_005fsqrt_005fui-113"><code>mpfr_sqrt_ui</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3485 |
<li><a href="#index-mpfr_005fstrtofr-47"><code>mpfr_strtofr</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3486 |
<li><a href="#index-mpfr_005fsub-92"><code>mpfr_sub</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3487 |
<li><a href="#index-mpfr_005fsub_005fq-98"><code>mpfr_sub_q</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3488 |
<li><a href="#index-mpfr_005fsub_005fsi-96"><code>mpfr_sub_si</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3489 |
<li><a href="#index-mpfr_005fsub_005fui-94"><code>mpfr_sub_ui</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3490 |
<li><a href="#index-mpfr_005fsub_005fz-97"><code>mpfr_sub_z</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3491 |
<li><a href="#index-mpfr_005fsubnormalize-266"><code>mpfr_subnormalize</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3492 |
<li><a href="#index-mpfr_005fsum-207"><code>mpfr_sum</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3493 |
<li><a href="#index-mpfr_005fswap-50"><code>mpfr_swap</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3494 |
<li><a href="#index-g_t_0040code_007bmpfr_005ft_007d-12"><code>mpfr_t</code></a>: <a href="#MPFR-Basics">MPFR Basics</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3495 |
<li><a href="#index-mpfr_005ftan-163"><code>mpfr_tan</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3496 |
<li><a href="#index-mpfr_005ftanh-174"><code>mpfr_tanh</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3497 |
<li><a href="#index-mpfr_005ftrunc-219"><code>mpfr_trunc</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
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diff
changeset
|
3498 |
<li><a href="#index-mpfr_005fui_005fdiv-106"><code>mpfr_ui_div</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
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diff
changeset
|
3499 |
<li><a href="#index-mpfr_005fui_005fpow-121"><code>mpfr_ui_pow</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3500 |
<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> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3501 |
<li><a href="#index-mpfr_005fui_005fsub-93"><code>mpfr_ui_sub</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3502 |
<li><a href="#index-mpfr_005funderflow_005fp-278"><code>mpfr_underflow_p</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3503 |
<li><a href="#index-mpfr_005funordered_005fp-153"><code>mpfr_unordered_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3504 |
<li><a href="#index-mpfr_005furandomb-234"><code>mpfr_urandomb</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
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changeset
|
3505 |
<li><a href="#index-MPFR_005fVERSION-243"><code>MPFR_VERSION</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
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changeset
|
3506 |
<li><a href="#index-MPFR_005fVERSION_005fMAJOR-244"><code>MPFR_VERSION_MAJOR</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li> |
22d9e175d379
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diff
changeset
|
3507 |
<li><a href="#index-MPFR_005fVERSION_005fMINOR-245"><code>MPFR_VERSION_MINOR</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li> |
22d9e175d379
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Stefan Teleman <stefan.teleman@oracle.com>
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diff
changeset
|
3508 |
<li><a href="#index-MPFR_005fVERSION_005fNUM-248"><code>MPFR_VERSION_NUM</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li> |
22d9e175d379
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diff
changeset
|
3509 |
<li><a href="#index-MPFR_005fVERSION_005fPATCHLEVEL-246"><code>MPFR_VERSION_PATCHLEVEL</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
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diff
changeset
|
3510 |
<li><a href="#index-MPFR_005fVERSION_005fSTRING-247"><code>MPFR_VERSION_STRING</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li> |
22d9e175d379
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parents:
diff
changeset
|
3511 |
<li><a href="#index-mpfr_005fy0-195"><code>mpfr_y0</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3512 |
<li><a href="#index-mpfr_005fy1-196"><code>mpfr_y1</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
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Stefan Teleman <stefan.teleman@oracle.com>
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diff
changeset
|
3513 |
<li><a href="#index-mpfr_005fyn-197"><code>mpfr_yn</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
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Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3514 |
<li><a href="#index-mpfr_005fzero_005fp-145"><code>mpfr_zero_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3515 |
<li><a href="#index-mpfr_005fzeta-188"><code>mpfr_zeta</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3516 |
<li><a href="#index-mpfr_005fzeta_005fui-189"><code>mpfr_zeta_ui</code></a>: <a href="#Special-Functions">Special Functions</a></li> |
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7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
diff
changeset
|
3517 |
</ul></body></html> |
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changeset
|
3518 |
|
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
parents:
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changeset
|
3519 |
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Stefan Teleman <stefan.teleman@oracle.com>
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|
3520 |
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22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
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|
3521 |
Local Variables: |
22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
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|
3522 |
coding: iso-8859-1 |
22d9e175d379
7041521 GNU MP to Userland
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3523 |
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22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
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|
3524 |
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22d9e175d379
7041521 GNU MP to Userland
Stefan Teleman <stefan.teleman@oracle.com>
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3525 |
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