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    1 README for libm-test math test suite
    2 ====================================
    3 
    4 The libm-test math test suite tests a number of function points of
    5 math functions in the GNU C library.  The following sections contain a
    6 brief overview.  Please note that the test drivers and the Python
    7 script "gen-libm-test.py" have some options.  A full list of options
    8 is available with --help (for the test drivers) and -h for
    9 "gen-libm-test.py".
   10 
   11 
   12 What is tested?
   13 ===============
   14 The tests just evaluate the functions at specified points and compare
   15 the results with precomputed values and the requirements of the ISO
   16 C99 standard.
   17 
   18 Besides testing the special values mandated by IEEE 754 (infinities,
   19 NaNs and minus zero), some more or less random values are tested.
   20 
   21 Files that are part of libm-test
   22 ================================
   23 
   24 The main files are "libm-test-<func>.inc".  They are independent of
   25 the target platform and the specific real floating type and format and
   26 contain placeholder test "templates" for math functions defined in
   27 libm.  These files, along with generated files named
   28 "auto-libm-test-out-<func>", are preprocessed by the Python script
   29 "gen-libm-test.py" to expand the templates and produce a set of test
   30 cases for each math function that are specific to the target platform
   31 but still independent of the real floating type.  The results of the
   32 processing are "libm-test-<func>.c" and a file "libm-test-ulps.h" with
   33 platform specific deltas by which the actual math function results may
   34 deviate from the expected results and still be considered correct.
   35 
   36 The test drivers "test-double-<func>.c", "test-float-<func>.c", and
   37 "test-ldouble-<func>.c", generated by the Makefile, test the normal
   38 double, float and long double implementation of libm.  Each driver
   39 selects the desired real floating type to exercise the math functions
   40 to test with (float, double, or long double) by defining a small set
   41 of macros just before including the generic "libm-test.c" file. Each
   42 driver is compiled into a single executable test program with the
   43 corresponding name.
   44 
   45 As mentioned above, the "gen-libm-test.py" script looks for a file
   46 named "libm-test-ulps" in the platform specific sysdep directory (or
   47 its fpu or nofpu subdirectory) and for each variant (real floating
   48 type and rounding mode) of every tested function reads from it the
   49 maximum difference expressed as Units of Least Precision (ULP) the
   50 actual result of the function may deviate from the expected result
   51 before it's considered incorrect.
   52 
   53 The "auto-libm-test-out-<func>" files contain sets of test cases to
   54 exercise, the conditions under which to exercise each, and the
   55 expected results.  The files are generated by the
   56 "gen-auto-libm-tests" program from the "auto-libm-test-in" file.  See
   57 the comments in gen-auto-libm-tests.c for details about the content
   58 and format of the -in and -out files.
   59 
   60 How can I generate "libm-test-ulps"?
   61 ====================================
   62 
   63 To automatically generate a new "libm-test-ulps" run "make regen-ulps".
   64 This generates the file "math/NewUlps" in the build directory.  The file
   65 contains the sorted results of all the tests.  You can use the "NewUlps"
   66 file as the machine's updated "libm-test-ulps" file.  Copy "NewUlps" to
   67 "libm-test-ulps" in the appropriate machine sysdep directory.  Verify
   68 the changes, post your patch, and check it in after review.
   69 
   70 To manually generate a new "libm-test-ulps" file, first remove "ULPs"
   71 file in the current directory, then you can execute for example:
   72     ./testrun.sh math/test-double -u --ignore-max-ulp=yes
   73 This generates a file "ULPs" with all double ULPs in it, ignoring any
   74 previously calculated ULPs, and running with the newly built dynamic
   75 loader and math library (assumes you didn't install your build).  Now
   76 generate the ULPs for all other formats, the tests will be appending the
   77 data to the "ULPs" file.  As final step run "gen-libm-test.py" with the
   78 file as input and ask to generate a pretty printed output in the file
   79 "NewUlps":
   80   gen-libm-test.py -u ULPs -n NewUlps
   81 Copy "NewUlps" to "libm-test-ulps" in the appropriate machine sysdep
   82 directory.
   83 
   84 Note that the test drivers have an option "-u" to output an unsorted
   85 list of all epsilons that the functions have.  The output can be read
   86 in directly but it's better to pretty print it first.
   87 "gen-libm-test.py" has an option to generate a pretty-printed and
   88 sorted new ULPs file from the output of the test drivers.
   89 
   90 Contents of libm-test-ulps
   91 ==========================
   92 
   93 Since libm-test-ulps can be generated automatically, just a few notes.
   94 The file contains lines for maximal errors of single functions, like:
   95 
   96 Function "yn":
   97 double: 6
   98 
   99 The keywords are float, double, and ldouble.
  100 
  101 Adding tests to libm-test-<func>.inc
  102 ====================================
  103 
  104 The tests are evaluated by a set of special test macros.  The macros
  105 start with "TEST_" followed by a specification the input values, an
  106 underscore and a specification of the output values.  As an example,
  107 the test macro for a function with input of type FLOAT (FLOAT is
  108 either float, double, long double) and output of type FLOAT is
  109 "TEST_f_f".  The macro's parameter are the name of the function, the
  110 input parameter, output parameter and optionally one exception
  111 parameter.
  112 
  113 The accepted parameter types are:
  114 - "f" for FLOAT
  115 - "j" for long double.
  116 - "a" for ARG_FLOAT, the argument type for narrowing functions.
  117 - "b" for boolean - just tests if the output parameter evaluates to 0
  118   or 1 (only for output).
  119 - "c" for complex.  This parameter needs two values, first the real,
  120   then the imaginary part.
  121 - "i" for int.
  122 - "l" for long int.
  123 - "L" for long long int.
  124 - "u" for unsigned int.
  125 - "M" for intmax_t.
  126 - "U" for uintmax_t.
  127 - "p" for an argument (described in the previous character) passed
  128   through a pointer rather than directly.
  129 - "F" for the address of a FLOAT (only as input parameter)
  130 - "I" for the address of an int (only as input parameter)
  131 - "1" for an additional output (either output through a pointer passed
  132   as an argument, or to a global variable such as signgam).
  133 
  134 How to read the test output
  135 ===========================
  136 
  137 Running each test on its own at the default level of verbosity will
  138 print on stdout a line describing the implementation of math functions
  139 exercised by the test (float, double, or long double).  This is then
  140 followed by the details of test failures (if any).  The output concludes
  141 by a summary listing the number of test cases exercised and the number
  142 of test failures uncovered.
  143 
  144 For each test failure (and for each test case at higher levels of
  145 verbosity), the output contains the name of the function under test
  146 and its arguments or conditions that triggered the failure.  Note
  147 that the name of the function in the output need not correspond
  148 exactly to the name of the math function actually invoked. For example,
  149 the output will refer to the "acos" function even if the actual function
  150 under test is acosf (for the float version) or acosl (for the long
  151 double version).  Also note that the function arguments may be shown
  152 in either the decimal or the  hexadecimal floating point format which
  153 may or may not correspond to the format used in the auto-libm-test-in
  154 file. Besides the name of the function, for each test failure the
  155 output contains the actual and expected results and the difference
  156 between the two, printed in both the decimal and hexadecimal
  157 floating point format, and the ULP and maximum ULP for the test
  158 case.