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