changed the algorithm: large input is not special cased
(when exp(-x) is small compared to exp(x))
and the threshold values are reevaluated
(fdlibm code had a log(2)/2 cutoff for which i could not find
justification, log(2) seems to be a better threshold and this
was verified empirically)
the new code is simpler, makes smaller binaries and should be
faster for common cases
the old comments were removed as they are no longer true for the
new algorithm and the fdlibm copyright was dropped as well
because there is no common code or idea with the original anymore
except for trivial ones.
with naive exp2l(x*log2e) the last 12bits of the result was incorrect
for x with large absolute value
with hi + lo = x*log2e is caluclated to 128 bits precision and then
expl(x) = exp2l(hi) + exp2l(hi) * f2xm1(lo)
this gives <1.5ulp measured error everywhere in nearest rounding mode
uses the lanczos approximation method with the usual tweaks.
same parameters were selected as in boost and python.
(avoides some extra work and special casing found in boost
so the precision is not that good: measured error is <5ulp for
positive x and <10ulp for negative)
an alternative lgamma_r implementation is also given in the same
file which is simpler and smaller than the current one, but less
precise so it's ifdefed out for now.
modifications:
* avoid unsigned->signed conversions
* removed various volatile hacks
* use FORCE_EVAL when evaluating only for side-effects
* factor out R() rational approximation instead of manual inline
* __invtrigl.h now only provides __invtrigl_R, __pio2_hi and __pio2_lo
* use 2*pio2_hi, 2*pio2_lo instead of pi_hi, pi_lo
otherwise the logic is not changed, long double versions will
need a revisit when a genaral long double cleanup happens
modifications:
* avoid unsigned->signed integer conversion
* do not handle special cases when they work correctly anyway
* more strict threshold values (0x1p26 instead of 0x1p28 etc)
* smaller code, cleaner branching logic
* same precision as the old code:
acosh(x) has up to 2ulp error in [1,1.125]
asinh(x) has up to 1.6ulp error in [0.125,0.5], [-0.5,-0.125]
atanh(x) has up to 1.7ulp error in [0.125,0.5], [-0.5,-0.125]
this change fixes an obscure issue with some nonstandard kernels,
where the initial brk syscall returns a pointer just past the end of
bss rather than the beginning of a new page. in that case, the dynamic
linker has already reclaimed the space between the end of bss and the
page end for use by malloc, and memory corruption (allocating the same
memory twice) will occur when malloc again claims it on the first call
to brk.
if there's evidence of any use for it, we can add it back later. as
far as I can tell, glibc has it only for internal use (and musl uses a
direct syscall in that case rather than a function call), not for
exposing it to applications.
in case of mmap-obtained chunks, end points past the end of the
mapping and reading it may fault. since the value is not needed until
after the conditional, move the access to prevent invalid reads.
the issue is identical to the recent commit fixing the mips versions:
despite other implementations doing this, it conflicts with the
requirements of ISO C and it's a waste of time and code size.
nothing in the standard requires or even allows the fenv state to be
restored by longjmp. restoring the exception flags is not such a big
deal since it's probably valid to clobber them completely, but
restoring the rounding mode yields an observable side effect not
sanctioned by ISO C. saving/restoring it also wastes a few cycles and
16 bytes of code.
as for historical behavior, reportedly SGI IRIX did save/restore fenv,
and this is where glibc and uClibc got the behavior from. a few other
systems save/restore it too (on archs other than mips), even though
this is apparently wrong. further details are documented here:
http://www-personal.umich.edu/~williams/archive/computation/setjmp-fpmode.html
as musl aims for standards conformance rather than coddling historical
programs expecting non-conforming behavior, and as it's unlikely that
any historical programs actually depend on the incorrect behavior
(such programs would break on other archs, anyway), I'm making the
change not to save/restore fenv on mips.
for some reason I have not been able to determine, gcc 3.2 rejects the
array notation. this seems to be a gcc bug, but since it's easy to
work around, let's do the workaround and avoid gratuitously requiring
newer compilers.
previously, shared library constructors were being called before
important internal things like the environment (extern char **environ)
and hwcap flags (needed for sjlj to work right with float on arm) were
initialized in __libc_start_main. rather than trying to have to
dynamic linker make sure this stuff all gets initialized right, I've
opted to just defer calling shared library constructors until after
the main program's entry point is reached. this also fixes the order
of ctors to be the exact reverse of dtors, which is a desirable
property and possibly even mandated by some languages.
the main practical effect of this change is that shared libraries
calling getenv from ctors will no longer fail.
it's essential to decrement the stack pointer before writing to new
stack space, rather than afterwards. otherwise there is a race
condition during which asynchronous code (signals) could clobber the
data being stored.
it may be possible to optimize the code further using stwu, but I
wanted to avoid making any changes to the actual stack layout in this
commit. further improvements can be made separately if desired.
based on proposal by Isaac Dunham. nonexistance of bits/io.h will
cause inclusion of sys/io.h to produce an error on archs that are not
supposed to have it. this is probably the desired behavior, but the
error message may be a bit unusual.
similar to exp.c cleanup: use scalbnf, don't return excess precision,
drop some optimizatoins.
exp.c was changed to be more consistent with expf.c code.
fortunately the memory corruption could not hurt anything, but it
prevented clearing the final newline and thus prevented the last path
element from working.
priority inheritance is not yet supported, and priority protection
probably will not be supported ever unless there's serious demand for
it (it's a fairly heavy-weight feature).
per-thread cpu clocks would be nice to have, but to my knowledge linux
is still not capable of supporting them. glibc fakes them by using the
_process_ cpu-time clock and subtracting the thread creation time,
which gives seriously incorrect semantics (worse than not supporting
the feature at all), so until there's a way to do it right, it will
remain as a stub that always fails.
overflow and underflow was incorrect when the result was not stored.
an optimization for the 0.5*ln2 < |x| < 1.5*ln2 domain was removed.
did various cleanups around static constants and made the comments
consistent with the code.
incomplete but at least partly working. requires all files to be
compiled in the new "secure" plt model, not the old one that put plt
code in the data segment. TLS is untested but may work. invoking the
dynamic linker explicitly to load a program does not yet handle argv
correctly.
