http://sourceware.org/ml/libc-alpha/2013-08/msg00084.html
Another batch of ieee854 macros and union replacement. These four
files also have bugs fixed with this patch. The fact that the two
doubles in an IBM long double may have different signs means that
negation and absolute value operations can't just twiddle one sign bit
as you can with ieee864 style extended double. fmodl, remainderl,
erfl and erfcl all had errors of this type. erfl also returned +1 for
large magnitude negative input where it should return -1. The hypotl
error is innocuous since the value adjusted twice is only used as a
flag. The e_hypotl.c tests for large "a" and small "b" are mutually
exclusive because we've already exited when x/y > 2**120. That allows
some further small simplifications.
[BZ #15734], [BZ #15735]
* sysdeps/ieee754/ldbl-128ibm/e_fmodl.c (__ieee754_fmodl): Rewrite
all uses of ieee875 long double macros and unions. Simplify test
for 0.0L. Correct |x|<|y| and |x|=|y| test. Use
ldbl_extract_mantissa value for ix,iy exponents. Properly
normalize after ldbl_extract_mantissa, and don't add hidden bit
already handled. Don't treat low word of ieee854 mantissa like
low word of IBM long double and mask off bit when testing for
zero.
* sysdeps/ieee754/ldbl-128ibm/e_hypotl.c (__ieee754_hypotl): Rewrite
all uses of ieee875 long double macros and unions. Simplify tests
for 0.0L and inf. Correct double adjustment of k. Delete dead code
adjusting ha,hb. Simplify code setting kld. Delete two600 and
two1022, instead use their values. Recognise that tests for large
"a" and small "b" are mutually exclusive. Rename vars. Comment.
* sysdeps/ieee754/ldbl-128ibm/e_remainderl.c (__ieee754_remainderl):
Rewrite all uses of ieee875 long double macros and unions. Simplify
test for 0.0L and nan. Correct negation.
* sysdeps/ieee754/ldbl-128ibm/s_erfl.c (__erfl): Rewrite all uses of
ieee875 long double macros and unions. Correct output for large
magnitude x. Correct absolute value calculation.
(__erfcl): Likewise.
* math/libm-test.inc: Add tests for errors discovered in IBM long
double versions of fmodl, remainderl, erfl and erfcl.
README for libm-test math test suite
====================================
The libm-test math test suite tests a number of function points of
math functions in the GNU C library. The following sections contain a
brief overview. Please note that the test drivers and the Perl script
"gen-libm-test.pl" have some options. A full list of options is
available with --help (for the test drivers) and -h for
"gen-libm-test.pl".
What is tested?
===============
The tests just evaluate the functions at specified points and compare
the results with precomputed values and the requirements of the ISO
C99 standard.
Besides testing the special values mandated by IEEE 754 (infinities,
NaNs and minus zero), some more or less random values are tested.
Files that are part of libm-test
================================
The main file is "libm-test.inc". It is platform and floating point
format independent. The file must be preprocessed by the Perl script
"gen-libm-test.pl". The results are "libm-test.c" and a file
"libm-test-ulps.h" with platform specific deltas.
The test drivers test-double.c, test-float.c, test-ldouble.c test the
normal double, float and long double implementation of libm. The test
drivers with an i in it (test-idouble.c, test-ifloat.c,
test-ildoubl.c) test the corresponding inline functions (where
available - otherwise they also test the real functions in libm).
"gen-libm-test.pl" needs a platform specific files with ULPs (Units of
Last Precision). The file is called "libm-test-ulps" and lives in
platform specific sysdep directory.
How can I generate "libm-test-ulps"?
====================================
To automatically generate a new "libm-test-ulps" run "make regen-ulps".
This generates the file "math/NewUlps" in the build directory. The file
contains the sorted results of all the tests. You can use the "NewUlps"
file as the machine's updated "libm-test-ulps" file. Copy "NewUlps" to
"libm-test-ulps" in the appropriate machine sysdep directory. Verify
the changes, post your patch, and check it in after review.
To manually generate a new "libm-test-ulps" file, first remove "ULPs"
file in the current directory, then you can execute for example:
./testrun.sh math/test-double -u --ignore-max-ulp=yes
This generates a file "ULPs" with all double ULPs in it, ignoring any
previously calculated ULPs, and running with the newly built dynamic
loader and math library (assumes you didn't install your build). Now
generate the ULPs for all other formats, the tests will be appending the
data to the "ULPs" file. As final step run "gen-libm-test.pl" with the
file as input and ask to generate a pretty printed output in the file
"NewUlps":
gen-libm-test.pl -u ULPs -n
Copy "NewUlps" to "libm-test-ulps" in the appropriate machine sysdep
directory.
Note that the test drivers have an option "-u" to output an unsorted
list of all epsilons that the functions have. The output can be read
in directly but it's better to pretty print it first.
"gen-libm-test.pl" has an option to generate a pretty-printed and
sorted new ULPs file from the output of the test drivers.
Contents of libm-test-ulps
==========================
Since libm-test-ulps can be generated automatically, just a few
notes. The file contains lines for single tests, like:
Test "cos (pi/2) == 0":
float: 1
and lines for maximal errors of single functions, like:
Function "yn":
idouble: 6.0000
The keywords are float, ifloat, double, idouble, ldouble and ildouble
(the prefix i stands for inline).
Adding tests to libm-test.inc
=============================
The tests are evaluated by a set of special test macros. The macros
start with "TEST_" followed by a specification the input values, an
underscore and a specification of the output values. As an example,
the test macro for a function with input of type FLOAT (FLOAT is
either float, double, long double) and output of type FLOAT is
"TEST_f_f". The macro's parameter are the name of the function, the
input parameter, output parameter and optionally one exception
parameter.
The accepted parameter types are:
- "f" for FLOAT
- "b" for boolean - just tests if the output parameter evaluates to 0
or 1 (only for output).
- "c" for complex. This parameter needs two values, first the real,
then the imaginary part.
- "i" for int.
- "l" for long int.
- "L" for long long int.
- "F" for the address of a FLOAT (only as input parameter)
- "I" for the address of an int (only as input parameter)
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