Copy stable/9 to releng/9.3 as part of the 9.3-RELEASE cycle.

Approved by: re (implicit)
Sponsored by: The FreeBSD Foundation

Copy head to stable/9 as part of 9.0-RELEASE release cycle.

Approved by: re (implicit)

s/rcsid/__FBSDID/

Don't assume that int is signed 32-bits in one place. Keep assuming
that ints have >= 31 value bits elsewhere. s/int/int32_t/ seems to
have been done too globally for all other files in msun/src before
msun/ was imported into FreeBSD.

Minor fixes in comments.

e_lgamma_r.c:
Describe special cases in more detail:
- exception for lgamma(0) and lgamma(neg.integer)
- lgamma(-Inf) = Inf. This is wrong but is required by C99 Annex F. I
hope to change this.

Fixed about 50 million errors of infinity ulps and about 3 million errors
of between 1.0 and 1.8509 ulps for lgammaf(x) with x between -2**-21 and
-2**-70.

As usual, the cutoff for tiny args was not correctly translated to
float precision. It was 2**-70 but 2**-21 works. Not as usual, having
a too-small threshold was worse than a pessimization. It was just a
pessimization for (positive) args between 2**-70 and 2**-21, but for
the first ~50 million (negative) args below -2**-70, the general code
overflowed and gave a result of infinity instead of correct (finite)
results near 70*log(2). For the remaining ~361 million negative args
above -2**21, the general code gave almost-acceptable errors (lgamma[f]()
is not very accurate in general) but the pessimization was larger than
for misclassified tiny positive args.

Now the max error for lgammaf(x) with |x| < 2**-21 is 0.7885 ulps, and
speed and accuracy are almost the same for positive and negative args
in this range. The maximum error overall is still infinity ulps.

A cutoff of 2**-70 is probably wastefully small for the double precision
case. Smaller cutoffs can be used to reduce the max error to nearly
0.5 ulps for tiny args, but this is useless since the general algrorithm
for nearly-tiny args is not nearly that accurate -- it has a max error of
about 1 ulp.

Use only double precision for "kernel" cosf and sinf (except for
returning float). The functions are renamed from __kernel_{cos,sin}f()
to __kernel_{cos,sin}df() so that misuses of them will cause link errors
and not crashes.

This version is an almost-routine translation with no special optimizations
for accuracy or efficiency. The not-quite-routine part is that in
__kernel_cosf(), regenerating the minimax polynomial with double
precision coefficients gives a coefficient for the x**2 term that is
not quite -0.5, so the literal 0.5 in the code and the related `hz'
variable need to be modified; also, the special code for reducing the
error in 1.0-x**2*0.5 is no longer needed, so it is convenient to
adjust all the logic for the x**2 term a little. Note that without
extra precision, it would be very bad to use a coefficient of other
than -0.5 for the x**2 term -- the old version depends on multiplication
by -0.5 being infinitely precise so as not to need even more special
code for reducing the error in 1-x**2*0.5.

This gives an unimportant increase in accuracy, from ~0.8 to ~0.501
ulps. Almost all of the error is from the final rounding step, since
the choice of the minimax polynomials so that their contribution to the
error is a bit less than 0.5 ulps just happens to give contributions that
are significantly less (~.001 ulps).

An Athlons, for uniformly distributed args in [-2pi, 2pi], this gives
overall speed increases in the 10-20% range, despite giving a speed
decrease of typically 19% (from 31 cycles up to 37) for sinf() on args
in [-pi/4, pi/4].

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

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 long.

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

Remove trailing whitespace.

This commit was generated by cvs2svn to compensate for changes in r2116,
which included commits to RCS files with non-trunk default branches.

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