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C23 adds various <math.h> function families originally defined in TS 18661-4. Add the powr functions, which are like pow, but with simpler handling of special cases (based on exp(y*log(x)), so negative x and 0^0 are domain errors, powers of -0 are always +0 or +Inf never -0 or -Inf, and 1^+-Inf and Inf^0 are also domain errors, while NaN^0 and 1^NaN are NaN). The test inputs are taken from those for pow, with appropriate adjustments (including removing all tests that would be domain errors from those in auto-libm-test-in and adding some more such tests in libm-test-powr.inc). The underlying implementation uses __ieee754_pow functions after dealing with all special cases that need to be handled differently. It might be a little faster (avoiding a wrapper and redundant checks for special cases) to have an underlying implementation built separately for both pow and powr with compile-time conditionals for special-case handling, but I expect the benefit of that would be limited given that both functions will end up needing to use the same logic for computing pow outside of special cases. My understanding is that powr(negative, qNaN) should raise "invalid": that the rule on "invalid" for an argument outside the domain of the function takes precedence over a quiet NaN argument producing a quiet NaN result with no exceptions raised (for rootn it's explicit that the 0th root of qNaN raises "invalid"). I've raised this on the WG14 reflector to confirm the intent. Tested for x86_64 and x86, and with build-many-glibcs.py.
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.