A single polynomial approximation for tan(x) works in infinite precision
up to |x| < pi/2, but in finite precision, to restrict the accumulated
roundoff error to < 1 ulp, |x| must be restricted to less than about
sqrt(0.5/((1.5+1.5)/3)) ~= 0.707. We restricted it a bit more to
give a safety margin including some slop for optimizations. Now that
we use double precision for the calculations, the accumulated roundoff
error is in double-precision ulps so it can easily be made almost 2**29
times smaller than a single-precision ulp. Near x = pi/4 its maximum
is about 0.5+(1.5+1.5)*x**2/3 ~= 1.117 double-precision ulps.
The minimax polynomial needs to be different to work for the larger
interval. I didn't increase its degree the old degree is just large
enough to keep the final error less than 1 ulp and increasing the
degree would be a pessimization. The maximum error is now ~0.80
ulps instead of ~0.53 ulps.
The speedup from this optimization for uniformly distributed args in
[-2pi, 2pi] is 28-43% on athlons, depending on how badly gcc selected
and scheduled the instructions in the old version. The old version
has some int-to-float conversions that are apparently difficult to schedule
well, but gcc-3.3 somehow did everything ~10 cycles or ~10% faster than
gcc-3.4, with the difference especially large on AXPs. On A64s, the
problem seems to be related to documented penalties for moving single
precision data to undead xmm registers. With this version, the speed
is cycles is almost independent of the athlon and gcc version despite
the large differences in instruction selection to use the FPU on AXPs
and SSE on A64s.
directly. We need to copyin() the strings in the iovec before
we can strcmp() them. Also, when we want to send the errmsg back
to userspace, we need to copyout()/copystr() the string.
Add a small helper function vfs_getopt_pos() which takes in the
name of an option, and returns the array index of the name in the iovec,
or -1 if not found. This allows us to locate an option in
the iovec without actually manipulating the iovec members. directly via
strcmp().
Noticed by: kris on sparc64
- Add locked variants of start, init, and ifmedia_upd.
- Add a mutex to the softc and remove spl calls.
- Use callout(9) rather than timeout(9).
- Setup interrupt handler last in attach.
- Use M_ZERO rather than bzero.
MFC after: 1 week
Tested by: wpaul
- Improve panic message if we fail to read the PCI bus number from a bridge
device.
- Don't try to lookup a BIOS IRQ for a link unless the link is routed via
an ISA IRQ since BIOSen currently only route PCI link devices via ISA
IRQs.
Tested by: Mathieu Prevot bsdhack at club-internet dot fr
MFC after: 1 week
This is a minor interface change. The function is renamed from
__kernel_tanf() to __kernel_tandf() so that misues of it will cause
link errors and not crashes.
This version is a routine translation with no special optimizations
for accuracy or efficiency. It gives an unimportant increase in
accuracy, from ~0.9 ulps to 0.5285 ulps. Almost all of the error is
from the minimax polynomial (~0.03 ulps and the final rounding step
(< 0.5 ulps). It gives strange differences in efficiency in the -5
to +10% range, with -O1 fairly consistently becoming faster and -O2
slower on AXP and A64 with gcc-3.3 and gcc-3.4.
but not provide a panic(9) implementation. Thus, enable the sanity
checks under INVARIANTS only if _KERNEL is also defined.
Submitted by: jmallett
Approved by: rwatson (mentor)
arg to __kernel_rem_pio2() gives 53-bit (double) precision, not single
precision and/or the array dimension like I thought. prec == 2 is
used in e_rem_pio2.c for double precision although it is documented
to be for 64-bit (extended) precision, and I just reduced it by 1
thinking that this would give the value suitable for 24-bit (float)
precision. Reducing it 1 more to the documented value for float
precision doesn't actually work (it gives errors of ~0.75 ulps in the
reduced arg, but errors of much less than 0.5 ulps are needed; the bug
seems to be in kernel_rem_pio2.c). Keep using a value 1 larger than
the documented value but supply an array large enough hold the extra
unused result from this.
The bug can also be fixed quickly by increasing init_jk[0] in
k_rem_pio2.c from 2 to 3. This gives behaviour identical to using
prec == 1 except it doesn't create the extra result. It isn't clear
how the precision bug affects higher precisions. 113-bit (quad) is
the largest precision, so there is no way to use a large precision
to fix it.
Instead, re-evaluate _BIF only when we get a notify and use the cached
results. We also still evaluate _BIF once on boot. Also, optimize the
init loop a little by only querying for a particular info if it's not valid.
MFC after: 2 days
service name instead of channel number with -c command option. Supported
service names are: DUN (Dial-Up Networking), FAX (Fax) and SP (Serial Port).
MFC after: 1 week
