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I've added a small C program to test the effect of the contraction to FMA on my computer arithmetic pages. It shows that under some conditions, one can have expressions like 1.1 × 1.1 - 1.1 × 1.1 whose evaluation does not return 0, which can give subtle bugs, in particular if the result is a negative number and one takes its square root...
On a similar subject (but only on constant expressions and without an example of failure in practice), see Defect Report #300.
The MPFR 2.3.2 library has been released. The changes from the 2.3.1 version:
Bug fixes; see the MPFR 2.3.1 page.
Improved MPFR manual.
Behavior of mpfr_check_range changed: if the value is an inexact infinity, the overflow flag is set (in case it was lost).
Function mpfr_init_gmp_rand (only defined when building MPFR without the --with-gmp-build configure option) is no longer defined at all. This function was private and not documented, and was used only in the MPFR test suite. User code that calls it is regarded as broken and may fail as a consequence. Running the old test suite against MPFR 2.3.2 may also fail.
The IEEE Standards Revision Committee (RevCom) approved P754 (revision of the IEEE-754 standard) unanimously, which was then approved by the IEEE-SA Standards Board on 12 June 2008.
Arith'19 (19th IEEE Symposium on Computer Arithmetic) call for papers. Deadline: 2008-10-15. Conference: 8-10 June 2009, Portland, Oregon, USA.
Patch 1 of MPFR 2.3.1 is available in the bugs section of the MPFR 2.3.1 page. It fixes a bug in the thread-safe configure test (enabled when the --enable-thread-safe option is given): this test always fails when the build directory is different from the source directory. Note that if you could already build MPFR 2.3.1, then you don't need this patch.
The MPFR 2.3.1 library has been released. The changes from the 2.3.0 version:
Changes in the behavior of mpfr_strtofr and in its documentation concerning particular cases where the code and the documentation did not match.
Bug fixes; see the MPFR 2.3.0 page.
Configure test for TLS support.
Improved MPFR manual.
MPFR 2.3.1 Release Candidate 2 is available.
MPFR 2.3.1 Release Candidate is available.
GNU C library (glibc): printf doesn't take the rounding mode into account opened on 2007-09-19.
Perl: floating-point binary-decimal conversion bugs opened on 2007-11-19.
Debian / GNU C library (glibc): libc6: strtod("-0", 0) returns +0.0 instead of -0.0 fixed in Debian on 2007-11-23.
Debian / zsh: zsh: printf %g -0 outputs 0 instead of -0 fixed in Debian on 2007-11-25.
FreeBSD: output of long double subnormals (with printf) is wrong by a factor 2 fixed in HEAD on 2007-12-09.
A short note about the next events related to computer arithmetic.
Dagstuhl Seminar 08021: Numerical Validation in Current Hardware Architectures, January 6-11, 2008.
8th Conference on Real Numbers and Computers (RNC8), July 7-9, 2008, Santiago de Compostela, Spain. Submission deadline: February 8, 2008 February 22, 2008 (extended deadline).
First challenge in the forecast of solar power, friendly competition part of RNC8.
2es Rencontres Arithmétique de l'Informatique Mathématique (RAIM) du GDR Informatique Mathématique, 3-5 juin 2008, Lille.
Patches 1 to 4 are available in the bugs section of the MPFR 2.3.0 page.
The first patch is necessary when the build directory is different from the source directory. The second patch fixes an assertion failure in mpfr_acosh on arguments that are slightly larger than 1 (this bug can occur only if the precision of the destination is strictly smaller than the precision of the input argument), but I'm not sure about the error analysis; a better patch will published later. The third patch fixes an important bug in mpfr_atan2, which occurs when the underflow flag is set before the function call. The fourth patch fixes various bugs in mpfr_subnormalize.
A bug in Microsoft Excel 2007 has recently been found, which has the effect of giving 100,000 instead of 65,535 and 100,001 instead of 65,536 after some calculations. In fact, it is only a display bug, because of an incorrect conversion from base 2 to base 10 (the value stored internally is correct). Details about this bug on the blog for Microsoft Excel.
Let us recall that in the past, Microsoft Excel already had a similar bug, but when a number was entered (incorrect conversion from base 10 to base 2) instead of displayed: entering 1.40737488355328 in Excel 3.0 to 7.0 was giving 0.64 (see also Microsoft support and via Google).
Powers of two are involved in both cases: 65536 = 216 and 1.40737488355328 = 247 / 1014.
After the discovery of this new bug, some people lost no time to recommend the switch to OpenOffice. But OpenOffice also has its problems, such as trying to correct the rounding errors, which can give surprising results and hide user-side bugs (see a discussion on the users-fr list, in French). Now, I don't know if Excel does the same kind of things. There are reasons to switch to OpenOffice, but they are very different.
The MPFR 2.3.0 library has been released. The main changes from the 2.2.* versions:
The mpfr.info file is now installed in the share subdirectory (as required by the Filesystem Hierarchy Standard); see output of ./configure --help.
The shared library is now enabled by default. If the MPFR build fails on your platform, try the --disable-shared configure option to disable the shared library.
Thread-safe support with Microsoft Visual compiler.
New functions mpfr_j0, mpfr_j1, mpfr_jn, mpfr_y0, mpfr_y1, mpfr_yn, mpfr_lgamma, mpfr_remainder, mpfr_remquo, mpfr_fms, mpfr_signbit, mpfr_setsign, mpfr_copysign, mpfr_get_patches.
Functions mpfr_sin, mpfr_cos and mpfr_sin_cos improved (argument reduction).
More detailed MPFR manual.
Improved tests (make check).
Bug fixes.
MPFR 2.3.0 Release Candidate 2 is available.
A CEA-EDF-INRIA school on the certified numerical computation theme will be held at the Loria (Nancy) on October 25-26, 2007.
The goal of this school is to make evidence of the problems arising with numerical computations using floating-point arithmetic (round-off error, limited precision, underflow or overflow, etc.) and to propose some new tools on this topic, in particular an initial formation to the MPFR library for floating-point computation in arbitrary precision.
Audience: engineers or researchers, either from public institutions or private companies. Warning! The number of attendees is limited.
My most recent papers:
Worst cases of a periodic function for large arguments, written with Guillaume Hanrot, Damien Stehlé and Paul Zimmermann. To appear in the Arith-18 proceedings in June 2007.
Abstract: One considers the problem of finding hard to round cases of a periodic function for large floating-point inputs, more precisely when the function cannot be efficiently approximated by a polynomial. This is one of the last few issues that prevents from guaranteeing an efficient computation of correctly rounded transcendentals for the whole IEEE-754 double precision format. The first non-naive algorithm for that problem is presented, with an heuristic complexity of O(20.676 p) for a precision of p bits. The efficiency of the algorithm is shown on the largest IEEE-754 double precision binade for the sine function, and some corresponding bad cases are given. We can hope that all the worst cases of the trigonometric functions in their whole domain will be found within a few years, a task that was considered out of reach until now.
Some notes on the possible under/overflow of the most common elementary functions, written with Jean-Michel Muller. May 2007.
Abstract: The purpose of this short note is not to describe when underflow or overflow must be signalled (it is quite clear that the rules are the same as for the basic arithmetic operations). We just want to show that for some of the most common functions and floating-point formats, in many cases, we can know in advance that the results will always lie in the range of the numbers that are representable by normal floating-point numbers, so that in these cases there is no need to worry about underflow or overflow. Note that when it is not the case, an implementation is still possible using a run-time test.
Computing integer powers in floating-point arithmetic, written with Peter Kornerup and Jean-Michel Muller. May 2007.
Abstract: We introduce two algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a fused multiply-add (fma) instruction is available. We show that our log-time algorithm always produce faithfully-rounded results, discuss the possibility of getting correctly rounded results, and show that results correctly rounded in double precision can be obtained if extended-precision is available with the possibility to round into double precision (with a single rounding).
ARITH18 - 18th IEEE Symposium on Computer Arithmetic, June 25-27, 2007, Montpellier, France. Early registration deadline: May 25, 2007.
Of course, I'll be there!
I've added a new category: Lyon, about the city of Lyon, France (events...). Four old blog items have been classified in this category.
Note: It is not possible to do category-based filtering at the server level yet, but I may add that one day...
Patches 2 to 5 are available in the bugs section of the MPFR 2.2.1 page. The first three fix various problems related to exceptions, and patch 5 updates the MPFR manual: The default install directory for the info file has changed and this patch updates it in the manual, and it adds a new section Exceptions and the missing description of the mpfr_dim function (that was added to MPFR 2.0.1).
The MPFR 2.2.0 to 2.2.1 changes didn't mention the following change:
The mpfr.info file is now installed in the share subdirectory (as required by the Filesystem Hierarchy Standard); see output of ./configure --help.
I've updated the MPFR web page, the NEWS files and fixed the mpfr.texi files (in both the trunk and 2.2 branch). Users should make sure that their INFOPATH environment variable has a correct value, e.g. /usr/local/share/info:/usr/local/info (in this order, in case old files remain in /usr/local/info).
It was a change in autoconf 2.59c (more information in autoconf's NEWS file).
As this was requested, the supplied patches for MPFR now modify the version string by adding a suffix (-p1, -p2, and so on), so that one can know what patches have been applied. For practical reasons, not all the files where the version appears are patched, but the updated version string is available with the MPFR_VERSION_STRING macro (mpfr.h header file) and the mpfr_get_version function (library).
Patch 1 is available in the bugs section of the MPFR 2.2.1 page. It adds the mpfr_init_set_ld macro, which is documented in the MPFR manual.
L'École Jeunes Chercheurs Informatique Mathématique (ex École Jeunes Chercheurs en Algorithmique et Calcul Formel) se tiendra cette année à Nancy, au LORIA, du 19 au 23 mars 2007. Date limite d'inscription et de soumission d'un exposé: 2 mars 2007.
The presentations of the Rencontres Arithmétique de l'Informatique Mathématique (which took place in Montpellier, France, on January 22-25) are now available, mainly in French.
INT_MIN % -1This is apparently a well-known GCC bug, but it has just been reported on GCC's BTS (bug 30484), following a discussion on this subject in the GCC development mailing-list. According to the ISO C standard, INT_MIN % -1
Floating-point exception under Linux/x86, with gcc 4.1.2 (prerelease).
2147483647 under Linux/PowerPC (G4), with gcc 4.1.2 (prerelease).
-2147483648 under Mac OS X PowerPC G5, with gcc 4.0.1 from Apple (Xcode 2.4.1).
But on my Zaurus (Linux/ARM), I obtain the correct value 0. I have used the following program:
#include <limits.h>
#include <stdio.h>
int main (void)
{
volatile int i = INT_MIN, j = -1;
printf ("%d\n", i % j);
return 0;
}
Whe one gets an incorrect behavior in C, it is the same with Perl, using the following script:
#!/usr/bin/env perl use integer; $x = -2147483648; $y = -1; print "$x % $y = ", $x % $y, "\n";
If someone has a real code that can fail due to this bug, let him signal it! For MPFR, we had to face bugs on other particular cases (e.g. on 0 + , LONG_MINLONG_MIN / 1LONG_MIN / (-2)
New page: my analysis of the Debian bug 153548 in glibc. I explain why only a few values are (completely) wrong.
The MPFR 2.2.1 library has been released. The main changes from the 2.2.0 version:
Many bug fixes (see the MPFR 2.2.0 page for the list).
Updated mpfr-longlong.h from the GMP 4.2 longlong.h file.
Moved some internal declarations from mpfr.h to mpfr-impl.h.
Use -search_paths_first on Darwin (Mac OS X) to fix linking behavior.
Improved make check: much more complete generic tests.
Improved INSTALL file and MPFR manual.
After 17 years, Jean-Michel Muller's book Arithmétique des ordinateurs is now freely available, as scanned pages (as Jean-Michel used proprietary word processing software at that time instead of TeX).
Patch 16 is available on the MPFR 2.2.0 page. It fixes the failure of the texp2 test.
Patch 15 is available on the MPFR 2.2.0 page. It fixes several bugs, mainly related to particular cases, exceptions and global flags.
Patches 13 and 14 are available on the MPFR 2.2.0 page. They fix problems concerning include and library paths.
Patches 11 and 12 are available on the MPFR 2.2.0 page. They fix miscellaneous problems with the division and the mpfr_get_f function.
Moreover directories may be added in an inconsistent order to CPPFLAGS and LDFLAGS, which may yield an incorrect library in some cases. This problem is fixed in the Subversion repository. But you may still get a warning saying that gmp.h and libgmp seems to have different versions or you cannot run a program linked with GMP. The test is not reliable enough in practice and the warning may be confusing; therefore the related code should be changed or removed. The MPFR library should still be built correctly, though.
I've written a small Perl module that provides a Perl interface to Maple and masks most of the problems with Maple I had to face. It is available from my Maple page, which gives a few explanations.
A friendly competition of exact real arithmetic software will be held in Nancy during the RNC7 conference. The goal is to measure the performance of various numerical computing packages on a set of challenging problems, with a strong emphasis on accuracy. All packages with arbitrary precision capabilities are welcome to compete...
The MPFR web site will be unavailable from 2006-04-20 16:00 UTC for a few hours, due to an upgrade of the network where the web site is hosted (Loria). The project web site on InriaGforge and the Subversion repository are not concerned by this network interruption.
I've added a new page on Maple. For the moment, it contains only a section on how to use Maple with the Perl language under Unix (Linux or Solaris), by using either pipes or a pseudo-terminal (pty).
This is one-week old, but I forgot to announce it here... Patch 9 is available on the MPFR 2.2.0 page. It fixes a small bug in the mpfr_random2 function. In practice, this bug has probably no effect.
Patch 8 is available on the MPFR 2.2.0 page. It fixes bugs in the mpfr_get_f and mpfr_set_f conversion functions with the mpf layer of GMP: mpfr_get_f gives a wrong value when the result has a negative exponent and mpfr_set_f does not support overflows. If you do not use mpf, this patch will probably be useless to you.
Une page web Recrutements sur des postes scientifiques au Loria a été ouverte.
Patch 7 is available on the MPFR 2.2.0 page. It fixes a rounding bug in the mpfr_sin function for some worst cases (as those used to test the standard C library).
Patch 6 is available on the MPFR 2.2.0 page. It fixes an important efficiency problem in mpfr_div when the divisor has a much smaller precision than the dividend; this problem was introduced after the rewrite of the division code for MPFR 2.2.0, so that previous MPFR versions are not affected.
I've received Loria's medal, with the other members of the MPFR team, after we won the Many Digits Friendly Competition.
We've just published a research report on MPFR (link on HAL).
Patch 5 for MPFR 2.2.0 is available. This patch fixes various problems (see the web page for the details).
A new MPFI version (1.3.4-RC1) is available. This is the first version supporting MPFR 2.2.0. Thanks Fabrice for this update!
The old CVS repository of MPFR is closed. The MPFR library is now hosted on InriaGforge. At the same time, the repository has been converted to Subversion.
See the information about InriaGforge, MPFR and Subversion on the MPFR web site.
The DPE library provides floating-point numbers with large exponents. A DPE number is represented by a pair (d, e), where d is a floating-point number in [1/2, 1), and e is the corresponding exponent (int type), representing d × 2e.
DPE is developed by Patrick Pélissier and Paul Zimmermann in the SPACES project (Loria / INRIA Lorraine).
The MPFR team, which I belong to, has won the Many Digits Friendly Competition, that took place on 3 and 4 October 2005 at Radboud University, Nijmegen, The Netherlands.
The results and the detailed final timings and rankings.
For the problem 20, the formula giving cos(π/17), which I knew since it is in my list of 17's, was very useful. I was also interested in the problem 17, for which I could pass from N = 4 to N = 5 by hacking the zeta_ui function written by Paul, to calculate ζ(3) and ζ(5) at the same time and avoid in this way to do some identical computations twice.
For the users of Darwin (Mac OS X) who wish to build a dynamic library, a new patch is available on the MPFR 2.2.0 page. At the time of the MPFR 2.2.0 release, there was a bug in the libtool used to generate the MPFR configure script, preventing the creation of shared libraries on Darwin. This script can be fixed by this patch (thanks to Dave Morrison); alternatively, users can run autoreconf if they have the necessary tools.
Users of the CVS tree are not affected by this problem since they need to run these tools on their own machine.
Two patches are available on the MPFR 2.2.0 page.
The Debian package libmpfr-dev 2.2.0.dfsg.1-1 has been uploaded; it contains these two patches, but no longer contains the documentation due to the Debian policy concerning the documentation license.
Under Linux/x86, like some other JVMs, the Kaffe Virtual Machine was computing internally in extended precision, though this is not allowed by the Java specification. This problem has been fixed in the 1.1.6-2 Debian package (I don't know anything about the other Linux distributions).
For more information on this bug and the problems related to extended precision under Linux/x86, please see my page Linux and the Extended Precision on x86 Processors. I've also just added a reference to my paper The Euclidean division implemented with a floating-point division and a floor, which gives an example particularly useful for programs written in ECMAScript (often referred to as Javascript) or using XPath.
The MPFR 2.2.0 library has been released. The main changes from the 2.1.* versions:
Bug fixes.
New functions: mpfr_set_overflow, mpfr_set_underflow, mpfr_set_inexflag, mpfr_set_erangeflag, mpfr_set_nanflag, mpfr_erfc, mpfr_atan2, mpfr_pow_z, mpfr_subnormalize, mpfr_const_catalan, mpfr_sec, mpfr_csc, mpfr_cot, mpfr_root, mpfr_eint, mpfr_get_f, mpfr_sech, mpfr_csch, mpfr_coth, mpfr_lngamma.
New macro: MPFR_VERSION_STRING.
The exported MPFR variables have been removed from mpfr.h (they were undocumented, so programs which respect the API still work).
The mathematical functions are faster (both average and worst cases).
Better support for the long double type.
Shared library support.
Thread safe (if built with the --enable-thread-safe configure option).
Logging facility.
Change in the semantics of mpfr_out_str and mpfr_get_str when the number-of-digits parameter is 0.
Better locale support.
This version is binary compatible with previous versions if you do not use undocumented features.
The Arith'17 slides are available on the conference web site and mirrored here.
The MPFR 2.1.2 library has been released. This is a bug-fix release, including the 12 patches to the 2.1.1 version.
You can download it in one of the following three archive formats:
mpfr-2.1.2.tar.bz2 (signature, MD5: 4e2b64fe2263d093bd809820221289a8),
mpfr-2.1.2.tar.gz (signature, MD5: d3bf773894478bf71af87f681b6819a1),
mpfr-2.1.2.zip (signature, MD5: 2f29793940d782e313d4eb8ba2f30e8d).
This new version will appear soon as a Debian package.
Many DigitsFriendly Competition
A friendly competition/benchmark session for investigating the state of the art in the various implementations of exact real arithmetic will be held at Radboud University, Nijmegen, The Netherlands, on 4 October 2005.
All the interactive software packages capable of handling arbitrary precision arithmetic on elementary functions are invited to participate. Moreover all libraries for handling arbitrary precision arithmetic in any programming language are welcome to participate provided that the participant writes a suitable interface/program.
A remote participation is possible. See the call for participation (registration deadline: 26 August).
The blog index pages are now reduced to 15 items. The whole set of items is now available on a new page. New improvements will come later...
A new patch is available on the MPFR 2.1.1 page. It fixes a bug that may occur with some locales, e.g. with the Turkish locale tr_TR.ISO8859-9, where the ASCII characters I and i do not match (the lowercase version of I is the dotless i).
I discovered this bug after reading a development file from Mutt, where similar problems may occur if developers do not take care. As often, while doing tests, I discovered another bug, in zsh.
Three new patches (since 2005-05-12) are available on the MPFR 2.1.1 page.
Since the last few months:
[March] Test of mathematical functions of the standard C library: two new tested functions (cube and cube root).
[May] Linux/x86 and the extended precision: various updates.
[June] New test program overflow.c.
[June] My slides for the Arith'17 conference are available.
Miscellaneous announces I've received in my mailbox...
2005-06-15: Call For Papers Real Numbers, special issue of Theoretical Informatics and Applications (dead-line postponed to June 15).
2005-09-01: Call For Papers More Accurate Computation: Methods and Software at SAC 2006.
I've written a page on the results of the search for worst cases (for the Table Maker's Dilemma) for the 2x function in x86 extended precision (64-bit mantissa), between 1/2 and 1.
A new patch is available on the MPFR 2.1.1 page. It fixes a bug in the mpfr_div_ui function.
Four new patches (since 2005-03-09) are available on the MPFR 2.1.1 page.
Due to a power downtime of the Loria, the MPFR web site is not accessible until April 20, at about 07:30 UTC. The e-mails to addresses at Loria will neither be lost nor rejected, but they will not be read before the servers are put back online.
The slides of my presentation (in French) at the Arinews workshop on 7-8 March 2005 are available on my research page.
I'm writing a research report on this subject, giving more details. The abstract:
We study conditions under which the Euclidean division can be implemented using a floating-point division followed by a
floorfunction. We show that under reasonable assumptions, the rounding downward mode can always be used, and the rounding to nearest mode can be used in most practical cases. These results may be useful for any language, but there is a particular benefit for languages, like ECMAScript, that do not have an integer division and that always round to nearest.
Two patches are available on the MPFR 2.1.1 page. They have been applied in the Debian package libmpfr-dev 2.1.1-2.
Under Linux/x86, like some other JVMs, JamVM was computing internally in extended precision, though this is not allowed by the Java specification. I've just learned that this problem had been fixed in the 1.2.1 release (2004-12-02). To my knowledge, it is the second free JVM implementation to be fixed and now computing correctly.
For more information on this bug and the problems related to extended precision under Linux/x86, please see my page Linux and the Extended Precision on x86 Processors.
The MPFR 2.1.1 library has been released. This is a bug-fix release, including the 17 patches to the 2.1.0 version.
You can download it in one of the following three archive formats:
mpfr-2.1.1.tar.bz2 (MD5: 843422d90349800ee721f6710d051c87),
mpfr-2.1.1.tar.gz (MD5: b7eb5932ab86c78d13ed0569ad26af38),
mpfr-2.1.1.zip (MD5: b999dea40758ea5fecf6afb1b65dacf4).
This new version will appear soon as a Debian package.
I've found a new bug in MPFR 2.1.0: the function mpfr_ui_sub applied to the integer 0 and the floating-point number +0 gives +0 instead of −0; this bug was introduced in MPFR 2.1.0, thus it is not present in previous versions. The patch is available on the MPFR 2.1.0 page.
Three new patches are available on the MPFR 2.1.0 page.
Miscellaneous announces I've received in my mailbox...
2005-03: Journées Arinews, March 7-8, 2005, ENS Lyon, France.
2005-04: École Jeunes Chercheurs en Algorithmique et Calcul Formel, April 4-8, 2005, Montpellier, France.
2005-07: SNC 2005: International Workshop on Symbolic-Numeric Computation, July 19-21, 2005, Xi'an, China (satellite conference of ISSAC 2005).
2005-09: CASC'2005: The 8th International Workshop on Computer Algebra in Scientific Computing, September 12-16, 2005, Kalamata, Greece. Deadline for submissions: April 1, 2005.
Postdoc opportunity, ENS Lyon, France.
A 13th patch is available on the MPFR 2.1.0 page.
I detected the bug thanks to the worst cases of the sine function in double precision, as some of them made the new code on the CVS trunk (future version 2.2.0) fail.
12 patches are available on the MPFR 2.1.0 page.
Several platforms added to the page of the tests of mathematical functions of the standard C library. I've also added the timings of the tests for each platform (except some old ones, that are not available any longer).
I noticed that the -ffloat-store option was necessary for gcc 3.4 under Linux/x86. Indeed the results of some functions of the mathematical library are and remain in extended precision after an assignment. This does not conform to the ISO/IEC 9899:1999 standard (C language); it is a bug in gcc (any version). This option is now systematically used with gcc.
I've added a new page on the formats of the electronic versions of my publications and slides. It deals with HTTP content negociation and some problems with the postscript/PDF viewer gv, in particular.
rint glibc Bug FixedThe glibc bug 602 powerpc rint() function is buggy in the rounding toward -inf and +inf modes has just been completely fixed in the CVS. Thanks!
Added the page Floating-Point Arithmetic Test Programs. I've also updated tst-ieee754.c as the test of assignments in extended precision no longer showed a bug in gcc 3.4, probably because of a new optimization related to static functions; the test has been improved and the bug is still there in gcc.
Page of the tests of mathematical functions of the standard C library: I've added host dixsept.loria.fr (Pentium 4 model 3, i.e. Prescott), which gives the same results as the other Pentium 4 processors, as expected.
The MPFR 2.1.0 library has been released.
Download it (MD5: 9174f5e0cd43f2253b5779743368c8f2). MPFR 2.1.0 is also available as an official Debian package (unstable distribution only).
I've added results of 5 additional machines at testdrive.hp.com on the page of the tests of mathematical functions of the standard C library:
spe191 (PA-RISC 8800 under HP-UX).
spe145 (Alpha EV56 under OSF1 4.0).
spe206 (Alpha EV67 under OSF1 5.1).
spe176 (Intel Itanium 2 under HP-UX).
spe189 (AMD Opteron 248 under GNU/Linux). According to the results, this machine uses the mathematical functions (partly with exact rounding) from the glibc library.
Here's my new general blog. It doesn't have a particular subject, but for those who are interested only in some subjects, I'll add server-side filtering mechanisms on some categories. You can already set up a client-side filtering (with your RSS feed reader, or with CSS for the web version, for instance).
My already existing blog on computer arithmetic and my research pages is integrated to this general blog, but the old URLs remain valid and currently constitute the only server-side filtering.
Some entries will be written only in French and will appear untranslated in the English version of my blog; server-side filtering on the language is also planned.
The first call for participation for the 6th Conference on Real Numbers and Computers (RNC6), November 15-17, 2004, Schloß Dagstuhl, Germany, is on the conference web site.
Contents: introduction, publications, links to some implementations of the various algorithms. The web page...
Several modifications on my publication page:
Alternative links set up.
HTTP negociation on the format (postscript or PDF) to be used for the main links.
Translations in the French page.
Because of a bug concerning the pipes under OpenMosix (well, probably this one), my programs searching for worst cases for the exact rounding (see the introduction to the Table Maker's Dilemma) were sometimes giving incorrect results, that couldn't be detected a priori, on the ble.ens-lyon.fr cluster; I mentioned this problem in my slides (in French) of my presentation for the journées au vert SPACES 2004. It was probably due to a data loss in the communications by pipe between my programs and Maple. Most often, pipes (not only in my programs) were just freezing, without leading to incorrect results. After a new version of the kernel has been installed by the system administrators, new tests performed yesterday confirmed that these problems have completely disappeared.
Several years ago, a faulty memory of a file server caused errors in my programs, that were fortunately detected. As this kind of errors occur randomly, the tests will really have to be performed at least twice, on different machines.
Under Linux/x86, like some other JVMs, SableVM was computing internally in extended precision, though this is not allowed by the Java specification. Grzegorz B. Prokopski fixed this problem in the Debian package 1.1.6-4 by putting the FPU in double-precision rounding (in the right place in the C code). Thanks to him.
To my knowledge, SableVM is the first free JVM implementation to be fixed and now computing correctly.
For more information on this bug and the problems related to extended precision under Linux/x86, please see my page Linux and the Extended Precision on x86 Processors.
2004-06-30: Added the page Linux and the Extended Precision on x86 Processors.
2004-07-26: Added the Zaurus SL-C860 results on the page of the tests of mathematical functions of the standard C library.
2004-08-15: Added details for each machine for the page of the tests of mathematical functions of the standard C library.
Here's my blog on computer arithmetic and the research pages of my web site. I don't know yet how it will evolve... On a technical point of view, it is currently maintained with scripts and XSLT stylesheets. Concerning the contents, I may do a more general blog in the future, in which it will be integrated (with filtering by keywords). It should be both in English and in French.
Page generated from file research/blog/all.en.xml on 2008-11-18 by xsltproc (using libxml 20632, libxslt 10124 and libexslt 813).
Note: this DocBook conversion is still experimental; please report any problem.