floating-point arithmetic on i386. Now I'm going to make excuses
for why this code is kinda scary:
- To avoid breaking the ABI with 5.3-RELEASE, we can't change
sizeof(fenv_t). I stuck the saved mxcsr in some discontiguous
reserved bits in the existing structure.
- Attempting to access the mxcsr on older processors results
in an illegal instruction exception, so support for SSE must
be detected at runtime. (The extra baggage is optimized away
if either the application or libm is compiled with -msse{,2}.)
I didn't run tests to ensure that this doesn't SIGILL on older 486's
lacking the cpuid instruction or on other processors lacking SSE.
Results from running the fenv regression test on these processors
would be appreciated. (You'll need to compile the test with
-DNO_STRICT_DFL_ENV.) If you have an 80386, or if your processor
supports SSE but the kernel didn't enable it, then you're probably out
of luck.
Also, I un-inlined some of the functions that grew larger as a result
of this change, moving them from fenv.h to fenv.c.
fedisableexcept(), and fegetexcept(). These two sets of routines
provide the same functionality. I implemented the former as an
undocumented internal interface to make the regression test easier to
write. However, fe(enable|disable|get)except() is already part of
glibc, and I would like to avoid gratuitous differences. The only
major flaw in the glibc API is that there's no good way to report
errors on processors that don't support all the unmasked exceptions.
particularly good reason to do this, except that __strong_reference
does type checking, whereas __weak_reference does not.
On Alpha, the compiler won't accept a 'long double' parameter in
place of a 'double' parameter even thought the two types are
identical.
an invalid exception and return an NaN.
- If a long double has 113 bits of precision, implement fma in terms
of simple long double arithmetic instead of complicated double arithmetic.
- If a long double is the same as a double, alias fma as fmal.
identical to scalbnf, which is now aliased as ldexpf. Note that the
old implementations made the mistake of setting errno and were the
only libm routines to do so.
- Add nexttoward{,f,l} and nextafterl. On all platforms,
nexttowardl is an alias for nextafterl.
- Add fmal.
- Add man pages for new routines: fmal, nextafterl,
nexttoward{,f,l}, scalb{,l}nl.
Note that on platforms where long double is the same as double, we
generally just alias the double versions of the routines, since doing
so avoids extra work on the source code level and redundant code in
the binary. In particular:
ldbl53 ldbl64/113
fmal s_fma.c s_fmal.c
ldexpl s_scalbn.c s_scalbnl.c
nextafterl s_nextafter.c s_nextafterl.c
nexttoward s_nextafter.c s_nexttoward.c
nexttowardf s_nexttowardf.c s_nexttowardf.c
nexttowardl s_nextafter.c s_nextafterl.c
scalbnl s_scalbn.c s_scalbnl.c
sparc64's 128-bit long doubles.
- Define FP_FAST_FMAL for ia64.
- Prototypes for fmal, frexpl, ldexpl, nextafterl, nexttoward{,f,l},
scalblnl, and scalbnl.
- In scalbln and scalblnf, check the bounds of the second argument.
This is probably unnecessary, but strictly speaking, we should
report an error if someone tries to compute scalbln(x, INT_MAX + 1ll).
nexttowardl. These are not needed on machines where long doubles
look like IEEE-754 doubles, so the implementation only supports
the usual long double formats with 15-bit exponents.
Anything bizarre, such as machines where floating-point and integer
data have different endianness, will cause problems. This is the case
with big endian ia64 according to libc/ia64/_fpmath.h. Please contact
me if you managed to get a machine running this way.
that are intended to raise underflow and inexact exceptions.
- On systems where long double is the same as double, nextafter
should be aliased as nexttoward, nexttowardl, and nextafterl.
Symptoms of the problem included assembler warnings and
nondeterministic runtime behavior when a fe*() call that affects the
fpsr is closely followed by a float point op.
The bug (at least, I think it's a bug) is that gcc does not insert a
break between a volatile asm and a dependent instruction if the
volatile asm came from an inlined function. Volatile asms seem to be
fine in other circumstances, even without -mvolatile-asm-stop, so
perhaps the compiler adds the stop bits before inlining takes place.
The problem does not occur at -O0 because inlining is disabled, and it
doesn't happen at -O2 because -fschedule-insns2 knows better.
inputs. The trouble with replacing two floats with a double is that
the latter has 6 extra bits of precision, which actually hurts
accuracy in many cases. All of the constants are optimal when float
arithmetic is used, and would need to be recomputed to do this right.
Noticed by: bde (ucbtest)
results in a performance gain on the order of 10% for amd64 (sledge),
ia64 (pluto1), i386+SSE (Pentium 4), and sparc64 (panther), and a
negligible improvement for i386 without SSE. (The i386 port still
uses the hardware instruction, though.)
manpages. They are not very related, so separating them makes it
easier to add meaningful cross-references and extend some of the
descriptions.
- Move the part of math(3) that discusses IEEE 754 to the ieee(3)
manpage.
- Rearrange the list of functions into categories.
- Remove the ulps column. It was appropriate for only some
of the functions in the list, and correct for even fewer
of them.
- Add some new paragraphs, and remove some old ones about
NaNs that may do more harm than good.
- Document precisions other than double-precision.
