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+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 independent of the target
+platform and the specific real floating type and format and contains
+placeholder test "templates" for math functions defined in libm.
+The file, along with a generated file named "auto-libm-test-out",
+is 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.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.c", "test-float.c", and "test-ldouble.c"
+test the normal double, float and long double implementation of libm.
+The test drivers with an 'i' in their name ("test-idouble.c",
+"test-ifloat.c", and "test-ildoubl.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.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" file contains sets of test cases to exercise,
+the conditions under which to exercise each, and the expected results.
+The file is 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
+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)
+
+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.