glibc/math

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 Python
script "gen-libm-test.py" have some options.  A full list of options
is available with --help (for the test drivers) and -h for
"gen-libm-test.py".


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 files are "libm-test-<func>.inc".  They are independent of
the target platform and the specific real floating type and format and
contain placeholder test "templates" for math functions defined in
libm.  These files, along with generated files named
"auto-libm-test-out-<func>", are preprocessed by the Python script
"gen-libm-test.py" to expand the templates and produce a set of test
cases for each math function that are specific to the target platform
but still independent of the real floating type.  The results of the
processing are "libm-test-<func>.c" and a file "libm-test-ulps.h" with
specific math results that can be either generic for the floating
type or platform specific.

The test drivers "test-double-<func>.c", "test-float-<func>.c", and
"test-ldouble-<func>.c", generated by the Makefile, test the normal
double, float and long double implementation of libm.  Each driver
selects the desired real floating type to exercise the math functions
to test with (float, double, or long double) by defining a small set
of macros just before including the generic "libm-test.c" file. Each
driver is compiled into a single executable test program with the
corresponding name.

The math tests do not report up to 9 Units of Least Precision (ULP)
(13 for IBM long double format) difference between the obtained
result and the expected one as a regression.  The "gen-libm-test.py"
script looks for files named "libm-test-ulps" in the sysdep directories
to generate the "libm-test-ulps.h" file.

The "auto-libm-test-out-<func>" files contain sets of test cases to
exercise, the conditions under which to exercise each, and the
expected results.  The files are generated by the
"gen-auto-libm-tests" program from the "auto-libm-test-in" file.  See
the comments in gen-auto-libm-tests.c for details about the content
and format of the -in and -out files.

How can I use "libm-test-ulps"?
====================================

A "libm-test-ulps" is required only to test for extra constraints in
the math tests.  The file contains lines for maximal errors of single
functions, like:

Function "yn":
float: 2
double: 6

It means that if the "yn" shows error larger than 2 ULP for float
or 6 ULP for double, the related test for "symbol" will fail.  It can
be useful to check for correctly rounded implementation, where the
expected ULP is 0.

The function is tested with default FE_TONEAREST rounding mode.  To
check with a different one, the function definition name should be
prepended with an underline plus the rounding mode 'downward' (FE_DOWNWARD),
'towardzero' (FE_TOWARDZERO), or 'upward' (FE_UPWARD).  For instance,

Function "yn_downward":
float: 3
double: 7

It means that 'yn' will be checked with FE_DOWNWARD rounding mode
and any error larger than 3 ULPs for float or 7 ULPs for double will be
reported as a regression.

The keywords are float, double, ldouble, and float128.

Also, multiple "libm-test-ulps" can be added, "gen-libm-test.py" will
merge the input in only one table.

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.py" has an option to generate a pretty-printed and
sorted new ULPs file from the output of the test drivers.


Adding tests to libm-test-<func>.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
- "j" for long double.
- "a" for ARG_FLOAT, the argument type for narrowing functions.
- "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.
- "u" for unsigned int.
- "M" for intmax_t.
- "U" for uintmax_t.
- "p" for an argument (described in the previous character) passed
  through a pointer rather than directly.
- "F" for the address of a FLOAT (only as input parameter)
- "I" for the address of an int (only as input parameter)
- "1" for an additional output (either output through a pointer passed
  as an argument, or to a global variable such as signgam).

How to read the test output
===========================

Running each test on its own at the default level of verbosity will
print on stdout a line describing the implementation of math functions
exercised by the test (float, double, or long double).  This is then
followed by the details of test failures (if any).  The output concludes
by a summary listing the number of test cases exercised and the number
of test failures uncovered.

For each test failure (and for each test case at higher levels of
verbosity), the output contains the name of the function under test
and its arguments or conditions that triggered the failure.  Note
that the name of the function in the output need not correspond
exactly to the name of the math function actually invoked. For example,
the output will refer to the "acos" function even if the actual function
under test is acosf (for the float version) or acosl (for the long
double version).  Also note that the function arguments may be shown
in either the decimal or the  hexadecimal floating point format which
may or may not correspond to the format used in the auto-libm-test-in
file. Besides the name of the function, for each test failure the
output contains the actual and expected results and the difference
between the two, printed in both the decimal and hexadecimal
floating point format, and the ULP and maximum ULP for the test
case.