glibc/math
Joseph Myers 7c84a5042f Add more tests of log2.
In testing for x86_64 on an AMD processor, I observed libm test
failures of the form:

testing long double (without inline functions)
Failure: Test: log2_downward (0x2.b7e151628aed4p+0)
Result:
 is:          1.44269504088896356633e+00   0xb.8aa3b295c17f67600000p-3
 should be:   1.44269504088896356622e+00   0xb.8aa3b295c17f67500000p-3
 difference:  1.08420217248550443400e-19   0x8.00000000000000000000p-66
 ulp       :  1.0000
 max.ulp   :  0.0000
Maximal error of `log2_downward'
 is      : 1 ulp
 accepted: 0 ulp

These issues arise because the maximum ulps when regenerating on one
processor are not the same as on another processor, so regeneration on
several processors may be needed when updating libm-test-ulps to avoid
failures for some users testing glibc - but such regeneration on
multiple processors is inconvenient.  Causes can be: on x86 and, for
x86_64, for long double, variation in results of x87 instructions for
transcendental operations between processors; on x86, variation in
compiler excess precision between compiler versions and
configurations; on any processor where the compiler may contract
expressions using fused multiply-add, variation in what contraction
occurs.

Although it's hard to be sure libm-test-ulps covers all ulps that may
be seen in any configuration for the given architecture, in practice
it helps simply to add wider test coverage to make it more likely
that, when testing on one processor, the ulps seen are the biggest
that can be seen for that function on that processor, and hopefully
they are also the biggest that can be seen for that function in other
configurations for that architecture.  Thus, this patch adds some
tests of log2 that increase the ulps I see on x86_64 on an Intel
processor, so that hopefully future from-scratch regenerations on that
processor will produce ulps big enough not to have errors from testing
on AMD processors.  These tests were found by randomly generating
inputs and seeing what produced ulps larger than those currently in
libm-test-ulps.  Of course such increases also improve the accuracy of
the empirical table of known ulps generated from libm-test-ulps files
that goes in the manual.

Tested for x86_64 and x86 and ulps updated accordingly.

	* math/auto-libm-test-in: Add more tests of log2.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-03-24 23:06:28 +00:00
..
bits Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
machine
atest-exp2.c Adjust timeouts for some tests, to accommodate slow processors, 2015-02-22 01:05:02 -08:00
atest-exp.c Adjust timeouts for some tests, to accommodate slow processors, 2015-02-22 01:05:02 -08:00
atest-sincos.c Adjust timeouts for some tests, to accommodate slow processors, 2015-02-22 01:05:02 -08:00
auto-libm-test-in Add more tests of log2. 2015-03-24 23:06:28 +00:00
auto-libm-test-out Add more tests of log2. 2015-03-24 23:06:28 +00:00
basic-test.c Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
bug-nextafter.c Make more libm tests condition exceptions tests with math-tests.h. 2013-06-12 12:41:25 +00:00
bug-nexttoward.c Make more libm tests condition exceptions tests with math-tests.h. 2013-06-12 12:41:25 +00:00
bug-tgmath1.c Update. 2004-05-07 02:14:18 +00:00
cabs.c Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
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e_acoshl.c [BZ #157] Remove include/stub-tag.h for good. 2012-11-04 19:59:40 +01:00
e_acosl.c [BZ #157] Remove include/stub-tag.h for good. 2012-11-04 19:59:40 +01:00
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e_coshl.c [BZ #157] Remove include/stub-tag.h for good. 2012-11-04 19:59:40 +01:00
e_exp2l.c Fix exp2 spurious underflows (bug 16560). 2015-02-12 19:02:45 +00:00
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fegetround.c Fix libm fegetround namespace (bug 17748). 2015-01-02 20:44:42 +00:00
feholdexcpt.c Fix libm feholdexcept namespace (bug 17748). 2015-01-05 23:06:14 +00:00
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ieee-math.c
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k_sincosl.c Moved to csu/errno-loc.c. 2005-12-14 15:06:39 +00:00
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k_tanl.c [BZ #157] Remove include/stub-tag.h for good. 2012-11-04 19:59:40 +01:00
libm-test.inc Fix ldbl-128ibm logbl near powers of 2 (bug 18030). 2015-02-26 15:14:58 +00:00
Makefile powerpc: Fix inline feraiseexcept, feclearexcept macros 2015-03-03 10:01:49 -05:00
math.h Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
multc3.c Update copyright dates with scripts/update-copyrights. 2015-01-02 16:29:47 +00:00
README.libm-test Clarify math/README.libm-test. Add "How to read the test output." 2015-01-28 21:07:01 -07:00
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s_ldexp.c Remove __STDC__ conditionals from libm. 2012-01-27 17:29:45 +00:00
s_ldexpf.c Don't use INTDEF with __ldexpf (bug 14132). 2014-10-21 23:11:49 +00:00
s_ldexpl.c Remove __STDC__ conditionals from libm. 2012-01-27 17:29:45 +00:00
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s_nextafter.c Fix nextafter overflow in non-default rounding modes (bug 16677). 2014-03-11 22:24:00 +00:00
s_nexttowardf.c Fix nexttoward bugs (bugs 2550, 2570). 2012-05-01 15:37:43 +00:00
s_nexttowardl.c Moved to csu/errno-loc.c. 2005-12-14 15:06:39 +00:00
s_significand.c Remove __STDC__ conditionals from libm. 2012-01-27 17:29:45 +00:00
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Versions New <math.h> macro named issignaling to check for a signaling NaN (sNaN). 2013-04-02 13:51:02 +02:00
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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.