both jn and yn functions had integer overflow issues for large
and small n
to handle these issues nm1 (== |n|-1) is used instead of n and -n
in the code and some loops are changed to make sure the iteration
counter does not overflow
(another solution could be to use larger integer type or even double
but that has more size and runtime cost, on x87 loading int64_t or
even uint32_t into an fpu register is more than two times slower than
loading int32_t, and using double for n slows down iteration logic)
yn(-1,0) now returns inf
posix2008 specifies that on overflow and at +-0 all y0,y1,yn functions
return -inf, this is not consistent with math when n<0 odd integer in yn
(eg. when x->0, yn(-1,x)->inf, but historically yn(-1,0) seems to be
special cased and returned -inf)
some threshold values in jnf and ynf were fixed that seems to be
incorrectly copy-pasted from the double version
a common code path in j1 and y1 was factored out so the resulting
object code is a bit smaller
unsigned int arithmetics is used for bit manipulation
j1(-inf) now returns 0 instead of -0
an incorrect threshold in the common code of j1f and y1f got fixed
(this caused spurious overflow and underflow exceptions)
the else branch in pone and pzero functions are fixed
(so code analyzers dont warn about uninitialized values)
a common code path in j0 and y0 was factored out so the resulting
object code is smaller
unsigned int arithmetics is used for bit manipulation
the logic of j0 got a bit simplified (x < 1 case was handled
separately with a bit higher precision than now, but there are large
errors in other domains anyway so that branch has been removed)
some threshold values were adjusted in j0f and y0f
libc is the macro, __libc is the internal symbol, but under some
configurations on old/broken compilers, the symbol might not actually
exist and the libc macro might instead use __libc_loc() to obtain
access to the object.
the previous logic was assuming the kernel would give EINVAL when
passed an invalid address, but instead with MAP_FIXED it was giving
EPERM, as it considered this an attempt to map over kernel memory.
instead of trying to get the kernel to do the rigth thing, the new
code just handles the error in userspace.
I have also cleaned up the code to use a single mask to check for
invalid low bits and unsupported high bits, so it's simpler and more
clearly correct. the old code was actually wrong for sizeof(long)
smaller than sizeof(off_t) but not equal to 4; now it should be
correct for all possibilities.
for 64-bit systems, the low-bits test is new and extraneous (the
kernel should catch the error anyway when the mmap2 syscall is not
used), but it's cheap anyway. if this is an issue, the OFF_MASK
definition could be tweaked to omit the low bits when SYS_mmap2 is not
defined.
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
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.
Szabolcs Nagy
Rich Felker
rofl0r