google3/third_party/grte/v5_src/glibc-2.27/math/README.libm-test - GRTEv5 - Git at Google

 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.
 - "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.
	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.
	- "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.