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 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 Perl script

"gen-libm-test.pl" 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

platform specific deltas by which the actual math function results may

deviate from the expected results and still be considered correct.

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.  The test

drivers with an 'i' in their name ("test-idouble-<func>.c",

"test-ifloat-<func>.c", and "test-ildoubl-<func>.c") test the

corresponding inline functions (where available - otherwise they also

test the real functions in 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 also either

defines or undefines the __NO_MATH_INLINES macro just before including

"libm-test-<func>.c" to select either the real or inline functions,

respectively.  Each driver is compiled into a single executable test

program with the corresponding name.

As mentioned above, the "gen-libm-test.pl" script looks for a file

named "libm-test-ulps" in the platform specific sysdep directory (or

its fpu or nofpu subdirectory) and for each variant (real floating

type and rounding mode) of every tested function reads from it the

maximum difference expressed as Units of Least Precision (ULP) the

actual result of the function may deviate from the expected result

before it's considered incorrect.

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 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 NewUlps

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-<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), along with

whether the inline set has been selected, regardless of whether or

not any inline functions actually exist.  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.