9e8da7bd21
This fix for k_tan.c is a copy from fdlibm version 5.3 (see also http://www.netlib.org/fdlibm/readme), adjusted to use the macros available in newlib (SET_LOW_WORD). This fix reduces the ULP error of the value shown in the fdlibm readme (tan(1.7765241907548024E+269)) to 0.45 (thereby reducing the error by 1). This issue only happens for large numbers that get reduced by the range reduction to a value smaller in magnitude than 2^-28, that is also reduced an uneven number of times. This seems rather unlikely given that one ULP is (much) larger than 2^-28 for the values that may cause an issue. Although given the sheer number of values a double can represent, it is still possible that there are more affected values, finding them however will be quite hard, if not impossible. We also took a look at how another library (libm in FreeBSD) handles the issue: In FreeBSD the complete if branch which checks for values smaller than 2^-28 (or rather 2^-27, another change done by FreeBSD) is moved out of the kernel function and into the external function. This means that the value that gets checked for this condition is the unreduced value. Therefore the input value which caused a problem in the fdlibm/newlib kernel tan will run through the full polynomial, including the careful calculation of -1/(x+r). So the difference is really whether r or y is used. r = y + p with p being the result of the polynomial with 1/3*x^3 being the largest (and magnitude defining) value. With x being <2^-27 we therefore know that p is smaller than y (y has to be at least the size of the value of x last mantissa bit divided by 2, which is at least x*2^-51 for doubles) by enough to warrant saying that r ~ y. So we can conclude that the general implementation of this special case is the same, FreeBSD simply has a different philosophy on when to handle especially small numbers. |
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README
README for GNU development tools This directory contains various GNU compilers, assemblers, linkers, debuggers, etc., plus their support routines, definitions, and documentation. If you are receiving this as part of a GDB release, see the file gdb/README. If with a binutils release, see binutils/README; if with a libg++ release, see libg++/README, etc. That'll give you info about this package -- supported targets, how to use it, how to report bugs, etc. It is now possible to automatically configure and build a variety of tools with one command. To build all of the tools contained herein, run the ``configure'' script here, e.g.: ./configure make To install them (by default in /usr/local/bin, /usr/local/lib, etc), then do: make install (If the configure script can't determine your type of computer, give it the name as an argument, for instance ``./configure sun4''. You can use the script ``config.sub'' to test whether a name is recognized; if it is, config.sub translates it to a triplet specifying CPU, vendor, and OS.) If you have more than one compiler on your system, it is often best to explicitly set CC in the environment before running configure, and to also set CC when running make. For example (assuming sh/bash/ksh): CC=gcc ./configure make A similar example using csh: setenv CC gcc ./configure make Much of the code and documentation enclosed is copyright by the Free Software Foundation, Inc. See the file COPYING or COPYING.LIB in the various directories, for a description of the GNU General Public License terms under which you can copy the files. REPORTING BUGS: Again, see gdb/README, binutils/README, etc., for info on where and how to report problems.