doubledouble.html

很好用的库

<title>The doubledouble homepage</title>
<IMG SRC="updated.gif" ALIGN="TOP">1998 February 03<br>
<H1>The doubledouble homepage</H1>
<hr>
<H2>Overview</H2>
This page describes my C++ software package `doubledouble' which 
implements approximately 30 decimal place floating point arithmetic.
This code does NOT use multiple-precision or arbitrary-precision methods,
which always have a significant speed penalty.  Rather, the intention is to increase
precision beyond double, while maintaining efficiency.   The speed penalty
is about a 10-25 times slowdown compared to double precision.  Hardware strictly conforming to IEEE 754 is essential,
though the Pentium is also acceptable since the control word is manipulated to override
the effect of double rounding.
<p>
This is the probably the simplest way to increase the precision of 
existing double-precision C or C++ code.   For a quick conversion of simple 
programs, all that may be required to convert to doubledouble is the addition of two lines:<p>
#include "doubledouble.h"<br>
#define double doubledouble<p>
and the linking of the doubledouble library.<br>
(This is NOT the recommended method, though. See the file trydd.cc for more
sophisticated examples of usage.)

<hr>
<H2>Internals</H2>
The techniques used are the well-known ones due to Dekker, Linnainmaa, Kahan, Knuth and Priest; that is, the same methods normally used for software implementations
of real*16 in Fortran compilers.
I credit Kahan with the addition algorithm (the simplification
which permits the elimination of the tests and branches is due to Knuth);
Dekker and Linnainmaa with the multiply, divide, and square root routines,
and Priest for an initial transcription into C++.
<p>
Included is a fairly complete math library, which borrows some ideas
from David Bailey's <a href="http://science.nas.nasa.gov/Groups/AAA/db.webpage/mpdist/mpdist.html">MPFUN</a> fortran package.
<p>
Except where otherwise indicated by comments in the code, this software
is covered by the GNU Public License, as described in the included COPYLEFT notice.
<p>
The current version is 2.2.  This version includes many improvements suggested
by Stefan Bauberger, Roger Schlafly, Wayne Hayes, Victor Shoup, Tony Dixon, and Alan
Miller.  These include new operators, more transcendental functions, 
portability enhancements, and improvements to many details.  
In particular, I am grateful to Wayne Hayes for writing new output formatting
code, more overloaded operators, modf, and a new test program.  Victor Shoup supplied
a fix for the non-IEEE Pentium problem.
<p>
Warning: the representable numbers in this system have a strange distribution.
For example, numbers like 1+1e-300 can be represented.   This makes the concept
of machine epsilon rather ambiguous.   For more information on the theory, see
<a href="http://HTTP.CS.Berkeley.EDU/~wkahan/ieee754status/ieee754.ps">this paper by Kahan</a>.
<p>
This is a development of code formerly released as `Quad version 2.0'.
The name Quad has been dropped as the code does NOT implement the 
IEEE quadruple precision format.   The name `doubledouble' was chosen instead
since it is distinctive and reminds one that an unusual data type is being
used, and it describes the format of two adjacent doubles. 
<p>
The code was developed with g++ 2.7.2.1 and egcs-1.0 
(See <A HREF="http://www.cygnus.com/egcs/">egcs project home page</A>
or <A HREF="ftp://sunsite.doc.ic.ac.uk/packages/gnu/cygnus/egcs/releases/egcs-1.0.1/">UK mirror</A>).
<br>
To use doubledouble precision complex numbers,<br>
#include &lt;std/complext.h&gt;<br>
#include &lt;std/complext.cc&gt;<br>
typedef complex&lt;doubledouble&gt; dd_complex;
<br><br>
The code has been tested on:<br>
x86-unknown-linux with gcc 2.7.2.1<br>
mips*-sgi-irix6 with ecgs-1.0<br>
sparc-sun-solaris2.4 with ecgs-1.0<br>
x86-unknown-windows95 with Microsoft C++ 5.0.<br>
<hr>

<H2>Applications</H2>
This code has been used for:<br>
<p>
Studies of Feigenbaum scaling in discrete dynamical systems.<br>
Two-loop integral for radiative corrections in muon decay.<br>
Number theory research, e.g. in LLL algorithms.<br>
Coefficient generation and checking of double-precision algorithms for transcendental functions.<br>
Testing sensitivity to rounding errors of existing double-precision code.
<p>
An earlier version of this code is also used in the C++ libraries 
<a href="http://www.informatik.th-darmstadt.de/TI/LiDIA/">LiDIA</a>
(as xdouble) and 
<a href="http://www.cs.wisc.edu/~shoup/ntl/">NTL</a>
(as quad_float).<br>
These libraries also implement arbitrary-precision arithmetic.
<hr>

<H2>Download the current version</H2>
as a gzipped tar file: <a href="doubledouble.tgz">shift-click here</a><br>
as a shar file: <a href="doubledouble.shar">click here</a><br>
<p>
The sources (not necessarily the current version) may be browsed here:<br>
<A HREF="doubledouble.h.html">doubledouble.h</a><br>
<A HREF="doubledouble.cc.html">doubledouble.cc</a><br>
<A HREF="inline.h.html">inline.h</a><br>
<A HREF="math.cc.html">math.cc</a><br>
<hr>

<H2>Installation</H2>
0. Unpack shar or tar file.
   Typical location: ~/math++/2.2/
<br>
1. Edit top part of `Makefile' to suit your hardware and compiler
<br>
2. make
<br>
User programs should:<br>
   (a) #include "doubledouble.h"<br>
   (b) compile with -DDD_INLINE<br>
   (c) compile with -Dx86 on x86 hardware (including Pentium)<br>
   (d) link libdoubledouble.a<br>
   See trydd.cc for examples of usage.
<hr>
<H2>Screenshot</H2>
<img src="ss.gif">
<hr>
<H2>Bugs</H2>
There is not much documentation apart from this webpage.
<hr>
Feedback is very welcome, especially reports of success or failure on other platforms.<p>
Please send reports to <A HREF="mailto:[e-mail]">Keith Briggs</A>,
not forgetting to clean up the processed meat first.<P>
Department of Plant Sciences,
University of Cambridge, Downing Street, Cambridge CB2 3EA.<br>
<hr>