159 lines
7.3 KiB
Plaintext
159 lines
7.3 KiB
Plaintext
README for libm-test math test suite
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====================================
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The libm-test math test suite tests a number of function points of
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math functions in the GNU C library. The following sections contain a
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brief overview. Please note that the test drivers and the Python
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script "gen-libm-test.py" have some options. A full list of options
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is available with --help (for the test drivers) and -h for
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"gen-libm-test.py".
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What is tested?
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===============
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The tests just evaluate the functions at specified points and compare
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the results with precomputed values and the requirements of the ISO
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C99 standard.
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Besides testing the special values mandated by IEEE 754 (infinities,
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NaNs and minus zero), some more or less random values are tested.
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Files that are part of libm-test
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================================
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The main files are "libm-test-<func>.inc". They are independent of
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the target platform and the specific real floating type and format and
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contain placeholder test "templates" for math functions defined in
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libm. These files, along with generated files named
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"auto-libm-test-out-<func>", are preprocessed by the Python script
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"gen-libm-test.py" to expand the templates and produce a set of test
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cases for each math function that are specific to the target platform
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but still independent of the real floating type. The results of the
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processing are "libm-test-<func>.c" and a file "libm-test-ulps.h" with
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platform specific deltas by which the actual math function results may
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deviate from the expected results and still be considered correct.
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The test drivers "test-double-<func>.c", "test-float-<func>.c", and
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"test-ldouble-<func>.c", generated by the Makefile, test the normal
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double, float and long double implementation of libm. Each driver
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selects the desired real floating type to exercise the math functions
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to test with (float, double, or long double) by defining a small set
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of macros just before including the generic "libm-test.c" file. Each
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driver is compiled into a single executable test program with the
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corresponding name.
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As mentioned above, the "gen-libm-test.py" script looks for a file
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named "libm-test-ulps" in the platform specific sysdep directory (or
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its fpu or nofpu subdirectory) and for each variant (real floating
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type and rounding mode) of every tested function reads from it the
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maximum difference expressed as Units of Least Precision (ULP) the
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actual result of the function may deviate from the expected result
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before it's considered incorrect.
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The "auto-libm-test-out-<func>" files contain sets of test cases to
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exercise, the conditions under which to exercise each, and the
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expected results. The files are generated by the
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"gen-auto-libm-tests" program from the "auto-libm-test-in" file. See
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the comments in gen-auto-libm-tests.c for details about the content
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and format of the -in and -out files.
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How can I generate "libm-test-ulps"?
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====================================
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To automatically generate a new "libm-test-ulps" run "make regen-ulps".
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This generates the file "math/NewUlps" in the build directory. The file
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contains the sorted results of all the tests. You can use the "NewUlps"
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file as the machine's updated "libm-test-ulps" file. Copy "NewUlps" to
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"libm-test-ulps" in the appropriate machine sysdep directory. Verify
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the changes, post your patch, and check it in after review.
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To manually generate a new "libm-test-ulps" file, first remove "ULPs"
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file in the current directory, then you can execute for example:
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./testrun.sh math/test-double -u --ignore-max-ulp=yes
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This generates a file "ULPs" with all double ULPs in it, ignoring any
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previously calculated ULPs, and running with the newly built dynamic
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loader and math library (assumes you didn't install your build). Now
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generate the ULPs for all other formats, the tests will be appending the
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data to the "ULPs" file. As final step run "gen-libm-test.py" with the
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file as input and ask to generate a pretty printed output in the file
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"NewUlps":
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gen-libm-test.py -u ULPs -n NewUlps
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Copy "NewUlps" to "libm-test-ulps" in the appropriate machine sysdep
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directory.
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Note that the test drivers have an option "-u" to output an unsorted
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list of all epsilons that the functions have. The output can be read
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in directly but it's better to pretty print it first.
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"gen-libm-test.py" has an option to generate a pretty-printed and
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sorted new ULPs file from the output of the test drivers.
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Contents of libm-test-ulps
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==========================
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Since libm-test-ulps can be generated automatically, just a few notes.
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The file contains lines for maximal errors of single functions, like:
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Function "yn":
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double: 6
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The keywords are float, double, and ldouble.
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Adding tests to libm-test-<func>.inc
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====================================
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The tests are evaluated by a set of special test macros. The macros
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start with "TEST_" followed by a specification the input values, an
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underscore and a specification of the output values. As an example,
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the test macro for a function with input of type FLOAT (FLOAT is
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either float, double, long double) and output of type FLOAT is
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"TEST_f_f". The macro's parameter are the name of the function, the
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input parameter, output parameter and optionally one exception
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parameter.
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The accepted parameter types are:
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- "f" for FLOAT
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- "j" for long double.
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- "a" for ARG_FLOAT, the argument type for narrowing functions.
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- "b" for boolean - just tests if the output parameter evaluates to 0
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or 1 (only for output).
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- "c" for complex. This parameter needs two values, first the real,
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then the imaginary part.
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- "i" for int.
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- "l" for long int.
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- "L" for long long int.
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- "u" for unsigned int.
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- "M" for intmax_t.
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- "U" for uintmax_t.
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- "p" for an argument (described in the previous character) passed
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through a pointer rather than directly.
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- "F" for the address of a FLOAT (only as input parameter)
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- "I" for the address of an int (only as input parameter)
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- "1" for an additional output (either output through a pointer passed
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as an argument, or to a global variable such as signgam).
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How to read the test output
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===========================
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Running each test on its own at the default level of verbosity will
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print on stdout a line describing the implementation of math functions
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exercised by the test (float, double, or long double). This is then
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followed by the details of test failures (if any). The output concludes
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by a summary listing the number of test cases exercised and the number
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of test failures uncovered.
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For each test failure (and for each test case at higher levels of
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verbosity), the output contains the name of the function under test
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and its arguments or conditions that triggered the failure. Note
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that the name of the function in the output need not correspond
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exactly to the name of the math function actually invoked. For example,
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the output will refer to the "acos" function even if the actual function
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under test is acosf (for the float version) or acosl (for the long
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double version). Also note that the function arguments may be shown
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in either the decimal or the hexadecimal floating point format which
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may or may not correspond to the format used in the auto-libm-test-in
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file. Besides the name of the function, for each test failure the
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output contains the actual and expected results and the difference
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between the two, printed in both the decimal and hexadecimal
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floating point format, and the ULP and maximum ULP for the test
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case.
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