New Paper Accurate Complex Multiplication in Floating-Point Arithmetic

I have a new paper, written with Jean-Michel Muller: Accurate Complex Multiplication in Floating-Point Arithmetic. It has been accepted at the 26th IEEE Symposium on Computer Arithmetic (ARITH 26), which will take place on 10–12 June 2019 in Kyoto, Japan. Abstract:

We deal with accurate complex multiplication in binary floating-point arithmetic, with an emphasis on the case where one of the operands in a

double-wordnumber. We provide an algorithm that returns a complex product with normwise relative error bound close to the best possible one, i.e., the rounding unitu.

For testing, comparisons have been done with the naive algorithm in the binary64 (double precision) and binary128 (quadruple precision) formats, and with implementations based on GNU MPFR, on x86_64 and POWER9 machines (the latter is currently the only processor with hardware binary128 support).

GNU MPFR 4.0.2 is Released

The GNU MPFR 4.0.2 library (dinde aux marrons, patch level 2) has been released. In addition to bug fixes, this version corrects the `mpfr_get_str`

description in the manual in order to follow the historical behavior and GMP's `mpf_get_str`

function.

GNU MPFR 4.0.2 Release Candidate

The GNU MPFR 4.0.2 release candidate is available.

Patch 14 for GNU MPFR 4.0.1

Patch 14 of GNU MPFR 4.0.1 is available in the bugs section of the MPFR 4.0.1 page. It fixes a bug affecting the `mpfr_fmma`

and `mpfr_fmms`

functions in particular cases: in the round-to-nearest mode (`MPFR_RNDN`

), these functions can round in the wrong direction due to a double rounding in the computation.

Patches 12 and 13 for GNU MPFR 4.0.1

Patches 12 and 13 of GNU MPFR 4.0.1 are available in the bugs section of the MPFR 4.0.1 page. They fix bugs in the formatted output functions (`mpfr_*printf`

):

Patch 12: Possible undefined behavior in case of error: store to null pointer, free of bad pointer, and

`<stdarg.h>`related undefined behavior.Patch 13: The flags for the

`P`length modifier (`mpfr_prec_t`argument) are ignored; this includes the sign of the field width when the value is provided in argument (by using an asterisk`*`in the format string).

Patches 10 and 11 for GNU MPFR 4.0.1

Patches 10 and 11 of GNU MPFR 4.0.1 are available in the bugs section of the MPFR 4.0.1 page.

The main issue is that the `mpfr_erf`

and `mpfr_erfc`

functions can yield an assertion failure due to the fact that the error bound is computed with the `double` type and can overflow. This is fixed by patch 11.

Patches 7 to 9 for GNU MPFR 4.0.1

Patches 7 to 9 of GNU MPFR 4.0.1 are available in the bugs section of the MPFR 4.0.1 page.

The main issue can occur with the formatted output functions (`mpfr_*printf`

) when the `'` flag is used in a locale where the thousands separator is not empty. In some specific cases (that is, when the integer part is rounded upward to 10 or 100), the generated string can be incorrect and since it is shorter than expected, an incorrect buffer size may be provided to the free

function of the current GMP memory allocator. By default, this size is ignored, but it may matter if the memory allocators have been changed with the `mp_set_memory_functions`

GMP function, in which case a possible consequence could be memory corruption.

Patches 1 to 6 for GNU MPFR 4.0.1

Patches 1 to 6 of GNU MPFR 4.0.1 are available in the bugs section of the MPFR 4.0.1 page. The first one fixes a major bug introduced in MPFR 4.0.0 (in a particular case of addition/subtraction), though most applications are probably not affected. The other ones fix minor bugs, with probably no consequences in practice.

For the users of the `Math::MPFR` Perl module, note that patch 6 makes a bug appear in version 4.03 of this module (current version at the time of writing – **[Update 2018-05-08]** A new version of the module is now available).

GNU MPFR 4.0.1 is Released

The GNU MPFR 4.0.1 library (dinde aux marrons, patch level 1) has been released. It fixes some problems of version 4.0.0, which I did not announce here: in particular, a bug in the `mpfr_div_ui`

function, which was present since the introduction of `mpfr_div_ui`

at the very beginning of the development of MPFR in 1999. But as of version 4.0.0, this bug was also affecting the `mpfr_div`

function.

These versions 4.0.* contain many changes compared to versions 3.1.* (GNU MPFR 3.1.0 had been released in October 2011).

GNU MPFR 4.0.0 Release Candidate

The GNU MPFR 4.0.0 release candidate is available.

By the way, I did my first MPFR commit 17 years ago.

Patch 1 for GNU MPFR 3.1.6

Patch 1 of GNU MPFR 3.1.6 is available in the bugs section of the MPFR 3.1.6 page. It fixes the conversion functions `mpfr_get_ld`

, `mpfr_get_si`

, `mpfr_get_ui`

, `mpfr_get_sj`

, `mpfr_get_uj`

and `mpfr_get_z`

when called with a very reduced exponent range.

GNU MPFR 3.1.6 is Released

The GNU MPFR 3.1.6 library (canard à l'orange, patch level 6) has been released. The changes from version 3.1.5:

Improved MPFR manual.

Bug fixes (detailed list on the MPFR 3.1.5 page and

`ChangeLog`file).Autotools: Under Linux, make sure that the old dtags (when supported) are used if the

`LD_LIBRARY_PATH`environment variable is defined; otherwise

would check an installed, compatible MPFR library found in`make check``LD_LIBRARY_PATH`instead of the one that has been built with

.`make`

GNU MPFR 3.1.6 Release Candidate

The GNU MPFR 3.1.6 release candidate has been available for a few days.

Patch 10 for GNU MPFR 3.1.5

Patch 10 of GNU MPFR 3.1.5 is available in the bugs section of the MPFR 3.1.5 page. It fixes incorrect header inclusion introduced by patch 8, in order to get the correct definition of symbols and avoid a link-time error under Microsoft Windows with DLL.

Patch 9 for GNU MPFR 3.1.5

Patch 9 of GNU MPFR 3.1.5 is available in the bugs section of the MPFR 3.1.5 page. It fixes a very important bug for users of platforms with a 32-bit `unsigned long` (32-bit ABI or Microsoft Windows) for very high precisions: computations in `sin_cos.c` suffer from overflows in such precisions (more than about 1,000,000 bits) due to the limited size of the `unsigned long` type. In practice, this introduces an error of up to 2^{−1019574} approximately, so that the trigonometric functions (`mpfr_sin`

, `mpfr_cos`

, `mpfr_tan`

) and functions that call them can be very inaccurate (limiting the overall accuracy to about one million bits for these functions on such platforms).

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