Long ago static startup did not parse the auxiliary vector and therefore
could not get at any `AT_FPUCW' tag to check whether upon FPU context
allocation the kernel would use a FPU control word setting different to
that provided by the `__fpu_control' variable. Static startup therefore
always initialized the FPU control word, forcing immediate FPU context
allocation even for binaries that otherwise never used the FPU.
As from GIT commit f8f900ecb9 static
startup supports parsing the auxiliary vector, so now it can avoid
explicit initialization of the FPU control word, just as can dynamic
startup, in the usual case where the setting written to the FPU control
word would be the same as the kernel uses. This defers FPU context
allocation until the binary itself actually pokes at the FPU.
Note that the `AT_FPUCW' tag is usually absent from the auxiliary vector
in which case _FPU_DEFAULT is assumed to be the kernel default.
These have helped me find and fix type conversion issues in QEMU's MIPS
hardware emulation. While certainly glibc is not the best place for such
tests, they're just an enhancement of tests already present.
In 128-bit IBM long double the precision of the type
decreases as you approach subnormal numbers, equaling
that of a double for subnormal numbers. Therefore
adjust the computation in ulp to use 2^(MIN_EXP - MANT_DIG)
which is correct for FP_SUBNORMAL for all types.
The current value used for ulp near zero is wrong,
and this commit fixes it such that ulp(0) is the smallest
subnormal value nearest to zero, which makes the most
sense for testing values near zero. Note that this is not
what Java does; they use the nearest normal value, which
is less accurate than what we want for glibc. Note that
there is no correct implementation of ulp since there
is no strict mathmatical definition that is accepted by
all groups using IEEE 754.
Previously with the large ulp values near zero there
were tests that previously passed, but were in fact
billions of ulp away from the precise answer. With this
commit we now need to disable one of the cpow tests which
is revealed to be inaccurate (bug 14473).
---
2013-05-24 Carlos O'Donell <carlos@redhat.com>
* math/libm-test.inc (MAX_EXP): Define.
(ULPDIFF): Define.
(ulp): New function.
(check_float_internal): Use ULPDIFF.
(cpow_test): Disable failing test.
(check_ulp): Test ulp() implemetnation.
(main): Call check_ulp before starting tests.
