math/README.libm-test

   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.