Bug 16516 reports spurious underflows from erf (for all floating-point
types), when the result is close to underflowing but does not actually
underflow.
erf (x) is about (2/sqrt(pi))*x for x close to 0, so there are
subnormal arguments for which it does not underflow. The various
implementations do (x + efx*x) (for efx = 2/sqrt(pi) - 1), for greater
accuracy than if just using a single multiplication by an
approximation to 2/sqrt(pi) (effectively, this way there are a few
more bits in the approximation to 2/sqrt(pi)). This can introduce
underflows when efx*x underflows even though the final result does
not, so a scaled calculation with 8*efx is done in these cases - but 8
is not a big enough scale factor to avoid all such underflows. 16 is
(any underflows with a scale factor of 16 would only occur when the
final result underflows), so this patch changes the code to use that
factor. Rather than recomputing all the values of the efx8 variable,
it is removed, leaving it to the compiler's constant folding to
compute 16*efx. As such scaling can also lose underflows when the
final scaling down happens to be exact, appropriate checks are added
to ensure underflow exceptions occur when required in such cases.
Tested x86_64 and x86; no ulps updates needed. Also spot-checked for
powerpc32 and mips64 to verify the changes to the ldbl-128ibm and
ldbl-128 implementations.
[BZ #16516]
* sysdeps/ieee754/dbl-64/s_erf.c (efx8): Remove variable.
(__erf): Scale by 16 instead of 8 in potentially underflowing
case. Ensure exception if result actually underflows.
* sysdeps/ieee754/flt-32/s_erff.c (efx8): Remove variable.
(__erff): Scale by 16 instead of 8 in potentially underflowing
case. Ensure exception if result actually underflows.
* sysdeps/ieee754/ldbl-128/s_erfl.c: Include <float.h>.
(efx8): Remove variable.
(__erfl): Scale by 16 instead of 8 in potentially underflowing
case. Ensure exception if result actually underflows.
* sysdeps/ieee754/ldbl-128ibm/s_erfl.c: Include <float.h>.
(efx8): Remove variable.
(__erfl): Scale by 16 instead of 8 in potentially underflowing
case. Ensure exception if result actually underflows.
* sysdeps/ieee754/ldbl-96/s_erfl.c: Include <float.h>.
(efx8): Remove variable.
(__erfl): Scale by 16 instead of 8 in potentially underflowing
case. Ensure exception if result actually underflows.
* math/auto-libm-test-in: Add more tests of erf.
* math/auto-libm-test-out: Regenerated.
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 maximal errors of single functions, like:
Function "yn":
idouble: 6
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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