<cbrt(x) in bits> ~= <x in bits>/3 + BIAS.
Keep the large comments only in the double version as usual.
Fixed some style bugs (mainly grammar and spelling errors in comments).
It was because I forgot to translate the part of the double precision
algorithm that chops t so that t*t is exact. Now the maximum error
is the same as for double precision (almost exactly 2.0/3 ulps).
The maximum error was 3.56 ulps.
The bug was another translation error. The double precision version
has a comment saying "new cbrt to 23 bits, may be implemented in
precision". This means exactly what it says -- that the 23 bit second
approximation for the double precision cbrt() may be implemented in
single (i.e., float) precision. It doesn't mean what the translation
assumed -- that this approximation, when implemented in float precision,
is good enough for the the final approximation in float precision.
First, float precision needs a 24 bit approximation. The "23 bit"
approximation is actually good to 24 bits on float precision args, but
only if it is evaluated in double precision. Second, the algorithm
requires a cleanup step to ensure its error bound.
In float precision, any reasonable algorithm works for the cleanup
step. Use the same algorithm as for double precision, although this
is much more than enough and is a significant pessimization, and don't
optimize or simplify anything using double precision to implement the
float case, so that the whole double precision algorithm can be verified
in float precision. A maximum error of 0.667 ulps is claimed for cbrt()
and the max for cbrtf() using the same algorithm shouldn't be different,
but the actual max for cbrtf() on amd64 is now 0.9834 ulps. (On i386
-O1 the max is 0.5006 (down from < 0.7) due to extra precision.)
The threshold for not being tiny was too small. Use the usual 2**-12
threshold. As for sinhf, use a different method (now the same as for
sinhf) to set the inexact flag for tiny nonzero x so that the larger
threshold works, although this method is imperfect. As for sinhf,
this change is not just an optimization, since the general code that
we fell into has accuracy problems even for tiny x. On amd64, avoiding
it fixes tanhf on 2*13495596 args with errors of between 1 and 1.3
ulps and thus reduces the total number of args with errors of >= 1 ulp
from 37533748 to 5271278; the maximum error is unchanged at 2.2 ulps.
The magic number 22 is log(DBL_MAX)/2 plus slop. This is bogus for
float precision. Use 9 (log(FLT_MAX)/2 plus less slop than for
double precision). Unlike for coshf and tanhf, this is just an
optimization, and MAX isn't misspelled EPSILON in the commit log.
I started testing with nonstandard rounding modes, and verified that
the chosen thresholds work for all modes modulo problems not related
to thresholds. The best thresholds are not very dependent on the mode,
at least for tanhf.
as part of rc. Doing this, and the sourcing of rc.subr after we have
determined if we are booting diskless (and correspondingly run
rc.initdiskless if necessary) are safe, and actually allow fewer files
to be needed on the diskless box. This also allows variables from
the configuration to be available to rc itself, such as ...
Add a variable to rc.conf, early_late_divider, which designates the
script which separates the early and late stages of the boot process.
Default this to mountcritlocal, and add text to etc/defaults/rc.conf,
rc.conf(5) and diskless(8) which describes how and why one might want
to change this.
Reviewed by: brooks
case. It seems entries are in reverse order when read from the kernel
memory but in the right order when read from a file (i.e. ALQ). Handle
both cases.
MFC after: 1 day
being hold by current thread or ignored by current process,
otherwise, it is very possible the thread will enter an infinite loop
and lead to an administrator's nightmare.
option is undocumented because it does nothing. It does nothing
because bsdtar never needs it. It is accepted because gnutar does
sometimes need it and many scripts use it.
Reported by: Pawel Jakub Dawidek
- number of read I/O requests,
- number of write I/O requests,
- number of read bytes,
- number of written bytes.
Add 'reset' subcommand for resetting statistics.
transmitted bits was between 8.6180us and 8.6200us when we used a RCLK
of 16.500MHz. This is a little low (should be 8.6805us). This error
is exactly the error one would expect if it actually had a 16.384MHz
watch oscillator (as suggested by garrett) instead of using the PCI
RCLK. Assume that the pci clock therefore wasn't really used, but
instead the cheap 16.384MH watch quartz oscillator. This gives bits
in the 8.6800us to 8.6810us ranage, which matches theoretical.
Submitted by: garrett
