Restored a cleanup in rev.1.9 tthat was lost in rev.1.10.

Moved all the optimizations for |x| <= 9pi/2 from
__ieee754_rem_pio2f() to its 3 callers and manually inline them.

On Athlons, with favourable compiler flags and optimizations and
favourable pipelin

Moved all the optimizations for |x| <= 9pi/2 from
__ieee754_rem_pio2f() to its 3 callers and manually inline them.

On Athlons, with favourable compiler flags and optimizations and
favourable pipeline conditions, this gives a speedup of 30-40 cycles
for cosf(), sinf() and tanf() on the range pi/4 < |x| <= 9pi/4, so
thes functions are now signifcantly faster than the hardware trig
functions in many cases. E.g., in a benchmark with uniformly distributed
x in [-2pi, 2pi], A64 hardware fcos took 72-129 cycles and cosf() took
37-55 cycles. Out-of-order execution is needed to get both of these
times. The optimizations in this commit apparently work more by
removing 1 serialization point than by reducing latency.

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Minor cleanups:

s_cosf.c and s_sinf.c:
Use a non-bogus magic constant for the threshold of pi/4. It was 2 ulps
smaller than pi/4 rounded down, but its value is not critical so it should
be the resu

Minor cleanups:

s_cosf.c and s_sinf.c:
Use a non-bogus magic constant for the threshold of pi/4. It was 2 ulps
smaller than pi/4 rounded down, but its value is not critical so it should
be the result of natural rounding.

s_cosf.c and s_tanf.c:
Use a literal 0.0 instead of an unnecessary variable initialized to
[(float)]0.0. Let the function prototype convert to 0.0F.

Improved wording in some comments.

Attempted to improve indentation of comments.

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Moved the optimization for tiny x from __kernel_tan[f](x) to tan[f](x)
so that it can be faster for tiny x and avoided for reduced x.

This improves things a little differently than for cosine and si

Moved the optimization for tiny x from __kernel_tan[f](x) to tan[f](x)
so that it can be faster for tiny x and avoided for reduced x.

This improves things a little differently than for cosine and sine.
We still need to reclassify x in the "kernel" functions, but we get
an extra optimization for tiny x, and an overall optimization since
tiny reduced x rarely happens. We also get optimizations for space
and style. A large block of poorly duplicated code to fix a special
case is no longer needed. This supersedes the fixes in k_sin.c revs
1.9 and 1.11 and k_sinf.c 1.8 and 1.10.

Fixed wrong constant for the cutoff for "tiny" in tanf(). It was
2**-28, but should be almost the same as the cutoff in sinf() (2**-12).
The incorrect cutoff protected us from the bugs fixed in k_sinf.c 1.8
and 1.10, except 4 cases of reduced args passed the cutoff and needed
special handling in theory although not in practice. Now we essentially
use a cutoff of 0 for the case of reduced args, so we now have 0 special
args instead of 4.

This change makes no difference to the results for sinf() (since it
only changes the algorithm for the 4 special args and the results for
those happen not to change), but it changes lots of results for sin().
Exhaustive testing is impossible for sin(), but exhaustive testing
for sinf() (relative to a version with the old algorithm and a fixed
cutoff) shows that the changes in the error are either reductions or
from 0.5-epsilon ulps to 0.5+epsilon ulps. The new method just uses
some extra terms in approximations so it tends to give more accurate
results, and there are apparently no problems from having extra
accuracy. On amd64 with -O1, on all float args the error range in ulps
is reduced from (0.500, 0.665] to [0.335, 0.500) in 24168 cases and
increased from 0.500-epsilon to 0.500+epsilon in 24 cases. Non-
exhaustive testing by ucbtest shows no differences.

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Fix formatting, this is hard to explain, so I'll show one example.

- float ynf(int n, float x) /* wrapper ynf */
+float
+ynf(int n, float x) /* wrapper ynf */

This is because the __S

Fix formatting, this is hard to explain, so I'll show one example.

- float ynf(int n, float x) /* wrapper ynf */
+float
+ynf(int n, float x) /* wrapper ynf */

This is because the __STDC__ stuff was indented.

Reviewed by: md5

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Assume __STDC__, remove non-__STDC__ code.

Reviewed by: md5

$Id$ -> $FreeBSD$

Revert $FreeBSD$ to $Id$

Make the long-awaited change from $Id$ to $FreeBSD$

This will make a number of things easier in the future, as well as (finally!)
avoiding the Id-smashing problem which has plagued developers for so

Make the long-awaited change from $Id$ to $FreeBSD$

This will make a number of things easier in the future, as well as (finally!)
avoiding the Id-smashing problem which has plagued developers for so long.

Boy, I'm glad we're not using sup anymore. This update would have been
insane otherwise.

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Remove trailing whitespace.

J.T. Conklin's latest version of the Sun math library.

-- Begin comments from J.T. Conklin:
The most significant improvement is the addition of "float" versions
of the math functions that take float

J.T. Conklin's latest version of the Sun math library.

-- Begin comments from J.T. Conklin:
The most significant improvement is the addition of "float" versions
of the math functions that take float arguments, return floats, and do
all operations in floating point. This doesn't help (performance)
much on the i386, but they are still nice to have.

The float versions were orginally done by Cygnus' Ian Taylor when
fdlibm was integrated into the libm we support for embedded systems.
I gave Ian a copy of my libm as a starting point since I had already
fixed a lot of bugs & problems in Sun's original code. After he was
done, I cleaned it up a bit and integrated the changes back into my
libm.
-- End comments

Reviewed by: jkh
Submitted by: jtc

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