previously 0x1p-1000 and 0x1p1000 was used for raising inexact
exception like x+tiny (when x is big) or x+huge (when x is small)
the rational is that these float consts are large enough
(0x1p-120 + 1 raises inexact even on ld128 which has 113 mant bits)
and float consts maybe smaller or easier to load on some platforms
(on i386 this reduced the object file size by 4bytes in some cases)
this is not a full rewrite just fixes to the special case logic:
+-0 and non-integer x<INT_MIN inputs incorrectly raised invalid
exception and for +-0 the return value was wrong
so integer test and odd/even test for negative inputs are changed
and a useless overflow test was removed
comments are kept in the double version of the function
compared to fdlibm/freebsd we partition the domain into one
more part and select different threshold points:
now the [log(5/3)/2,log(3)/2] and [log(3)/2,inf] domains
should have <1.5ulp error
(so only the last bit may be wrong, assuming good exp, expm1)
(note that log(3)/2 and log(5/3)/2 are the points where tanh
changes resolution: tanh(log(3)/2)=0.5, tanh(log(5/3)/2)=0.25)
for some x < log(5/3)/2 (~=0.2554) the error can be >1.5ulp
but it should be <2ulp
(the freebsd code had some >2ulp errors in [0.255,1])
even with the extra logic the new code produces smaller
object files
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
in tgmath.h the return values are casted to the appropriate
floating-point type (if the compiler supports gcc __typeof__),
this is wrong in case of ilogb, lrint, llrint, lround, llround
which do not need such cast
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]
j0l,j1l,jnl,y0l,j1l,jnl are gnu extensions, bsd and posix do not
have them.
noone seems to use them and there is no plan to implement them any
time soon so we shouldn't declare them in math.h.
despite glibc using __key and __seq rather than key and seq, some
applications, notably busybox, assume the names are key and seq unless
glibc is being used. and the names key and seq are really the ones
that _should_ be exposed when not attempting to present a
standards-conforming namespace; apps should not be using names that
begin with double-underscore. thus, the optimal fix is to use key and
seq as the actual names of the members when in bsd/gnu source profile,
and define macros for __key and __seq that redirect to plain key and
seq.
traditionally, both BSD and GNU systems have it this way.
sys/syscall.h is purely syscall number macros. presently glibc exposes
the syscall declaration in unistd.h only with _GNU_SOURCE, but that
does not reflect historical practice.
a while back, gcc switched from using the old _init/_fini fragments
method for calling ctors and dtors on arm to the __init_array and
__fini_array method. unfortunately, on glibc this depends on ugly
hacks involving making libc.so a linker script and pulling parts of
libc into the main program binary. so I cheat a little bit, and just
write asm to iterate over the init/fini arrays from the _init/_fini
asm. the same approach could be used on any arch it's needed on, but
for now arm is the only one.
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.
they were accidentally exposed under just baseline POSIX, which is a
big namespace pollution issue. thankfully glibc only exposes them
under _GNU_SOURCE, not under any of its other options, so omitting
the pollution in the default _BSD_SOURCE profile does not hurt
application compatibility at all.
previously the names were exposed as key/seq with _GNU_SOURCE and
__ipc_perm_key/__ipc_perm/seq otherwise, whereas glibc always uses
__key and __seq for the names. thus, the old behavior never matched
glibc, and the new behavior always does, regardless of feature test
macros.
for now, i'm leaving the renaming here in sys/ipc.h where it's easy to
change globally for all archs, in case something turns out to be
wrong, but eventually the names could just be incorporated directly
into the bits headers for each arch and the renaming removed.
Szabolcs Nagy
Rich Felker
rofl0r