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).

Patches 3 to 8 for GNU MPFR 3.1.5

Patches 3 to 8 of GNU MPFR 3.1.5 are available in the bugs section of the MPFR 3.1.5 page. The first five fix minor issues and patch 8 fixes some `mpf2mpfr.h` macros (only users of this header file, used to build GMP/mpf programs with MPFR instead of mpf, may be affected).

My Latest Publications

I have two new papers that have just been accepted, both related to GNU MPFR.

Correctly Rounded Arbitrary-Precision Floating-Point Summation, to be published in IEEE Transactions on Computers. DOI: 10.1109/TC.2017.2690632 (official link). PDF file on my personal web site (freely downloadable, © IEEE). Abstract:

We present a fast algorithm together with its low-level implementation of correctly rounded arbitrary-precision floating-point summation. The arithmetic is the one used by the GNU MPFR library: radix 2; no subnormals; each variable (each input and the output) has its own precision. We also give a worst-case complexity of this algorithm and describe how the implementation is tested.

Optimized Binary64 and Binary128 Arithmetic with GNU MPFR, written with Paul Zimmermann. Accepted at the 24th IEEE Symposium on Computer Arithmetic (ARITH 24), which will take place on 24–26 July 2017 in London, England. Abstract:

We describe algorithms used to optimize the GNU MPFR library when the operands fit into one or two words. On modern processors, a correctly rounded addition of two quadruple precision numbers is now performed in 22 cycles, a subtraction in 24 cycles, a multiplication in 32 cycles, a division in 64 cycles, and a square root in 69 cycles. We also introduce a new

*faithful*rounding mode, which enables even faster computations. Those optimizations will be available in version 4 of MPFR.

Status of the GNU MPFR Trunk

For those who test the GNU MPFR trunk via Subversion on InriaForge:

The

`tzeta`test should no longer fail on most platforms (IEEE 754 machines with default IEEE exception handling).The

`tsprintf`test still fails (fix in progress). The cause is a major efficiency issue in particular cases (huge precision requested).

Note: Both problems are also present in the released versions, but they have no tests that trigger them.

Patch 2 for GNU MPFR 3.1.5

Patch 2 of GNU MPFR 3.1.5 is available in the bugs section of the MPFR 3.1.5 page. It fixes the following bug. The `mpfr_strtofr`

function can return an incorrect ternary value in the round-to-nearest mode (`MPFR_RNDN`

).

Patch 1 for GNU MPFR 3.1.5

Patch 1 of GNU MPFR 3.1.5 is available in the bugs section of the MPFR 3.1.5 page. It fixes the following bug. The formatted output functions (`mpfr_*printf`

) yield an undefined behavior or assertion failure when a precision less than −1 is given as an argument for the `f` or `F` conversion specifier (the given precision should have been ignored).

GNU MPFR 3.1.5 is Released

The GNU MPFR 3.1.5 library (canard à l'orange, patch level 5) has been released. The changes from version 3.1.4:

C++11 compatibility.

Bug fixes (detailed list on the MPFR 3.1.4 page and

`ChangeLog`file).More tests.

Patches 5 and 6 for GNU MPFR 3.1.4

Patches 5 and 6 of GNU MPFR 3.1.4 are available in the bugs section of the MPFR 3.1.4 page. Patch 5 fixes bugs in the `mpfr_can_round_raw`

internal rounding-test function, used by the `mpfr_can_round`

public function (in particular, the few MPFR math functions that use this rounding test might be rounded incorrectly). Patch 6 fixes the `mpfr_get_ld`

function, which did not round correctly in the subnormal range on x86 platforms.

Patch 4 for GNU MPFR 3.1.4

Patch 4 of GNU MPFR 3.1.4 is available in the bugs section of the MPFR 3.1.4 page. It fixes an incompatibility of some programs of the test suite with the C++11 standard (used by default with `g++` from GCC 6) and is useful only for those who compile MPFR with such a C++ compiler (instead of a C compiler).

My ARITH-23 Article and Slides: Correctly Rounded Arbitrary-Precision Floating-Point Summation

A few days ago, I presented my paper Correctly Rounded Arbitrary-Precision Floating-Point Summation at the 23rd IEEE Symposium on Computer Arithmetic (ARITH 23), which took place from July 10 to July 13, 2016, in Santa Clara, California, USA. The goal of this work was a complete rewrite of the `mpfr_sum`

function for the next GNU MPFR release (version 4.0.0). Here are links to my article and my slides.

Note that I did some improvements since I wrote the article. The slides are more up-to-date, covering the current `mpfr_sum`

function (r10503) at this time. The current `sum.txt` file (r10523) contains more details, but it is still not up-to-date (like the article).

Patch 3 for GNU MPFR 3.1.4

Patch 3 of GNU MPFR 3.1.4 is available in the bugs section of the MPFR 3.1.4 page. It fixes a bug in the subtraction code (addition of two numbers of different signs or subtraction of two numbers of the same sign), which can give an overflow on some very particular case while it should not (see the link for details). It is very unlikely that an application would be affected by the bug.

I discovered this bug while I was reviewing a part of the code to implement *unbounded-float* support (floating-point numbers with an unbounded exponent range) in order to avoid intermediate overflows for functions like `mpfr_fmma`

(which computes `a`·`b` + `c`·`d`) or possibly in the future, polynomial evaluation with correct rounding.

Patches 1 and 2 for GNU MPFR 3.1.4

Patches 1 and 2 of GNU MPFR 3.1.4 are available in the bugs section of the MPFR 3.1.4 page. The first one concerns users of the 32-bit Cygwin (under Microsoft Windows). The second one fixes flags setting in functions `mpfr_add_ui`

and `mpfr_sub_ui`

; in practice, the only issue is that the NaN flag is not set with a NaN input.

I take the opportunity to point out that it was decided at the MPFR developer meeting of May 23-24 that the next MPFR release will be 4.0.

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