lib/msun: Cleanup after $FreeBSD$ removal

Remove no longer needed explicit inclusion of sys/cdefs.h.

PR: 276669
MFC after: 1 week

Remove $FreeBSD$: one-line .c pattern

Remove /^[\s*]*__FBSDID\("\$FreeBSD\$"\);?\s*\n/

Merge from head

IFC @ r254014

IFC @253398

Merge fresh head.

Fix some regressions caused by the switch from gcc to clang. The fixes
are workarounds for various symptoms of the problem described in clang
bugs 3929, 8100, 8241, 10409, and 12958.

The regression

Fix some regressions caused by the switch from gcc to clang. The fixes
are workarounds for various symptoms of the problem described in clang
bugs 3929, 8100, 8241, 10409, and 12958.

The regression tests did their job: they failed, someone brought it
up on the mailing lists, and then the issue got ignored for 6 months.
Oops. There may still be some regressions for functions we don't have
test coverage for yet.

show more ...

Fix some rather obscene code that has ambiguous if...if...else...
constructs in it.

Fix cutoffs. This is just a cleanup and an optimization for unusual
cases which are used mainly by regression tests.

As usual, the cutoff for tiny args was not correctly translated to
float precisi

Fix cutoffs. This is just a cleanup and an optimization for unusual
cases which are used mainly by regression tests.

As usual, the cutoff for tiny args was not correctly translated to
float precision. It was 2**-54 but 2**-24 works. It must be about
2**-precision, since the error from approximating log(1+x) by x is
about the same as |x|. Exhaustive testing shows that 2**-24 gives
perfect rounding in round-to-nearest mode.

Similarly for the cutoff for being small, except this is not used by
so many other functions. It was 2**-29 but 2**-15 works. It must be
a bit smaller than sqrt(2**-precision), since the error from
approximating log(1+x) by x-x*x/2 is about the same as x*x. Exhaustive
testing shows that 2**-15 gives a maximum error of 0.5052 ulps in
round-to-nearest-mode. The algorithm for the general case is only good
for 0.8388 ulps, so this is sufficient (but it loses slightly on i386 --
then extra precision gives 0.5032 ulps for the general case).

While investigating this, I noticed that optimizing the usual case by
falling into a middle case involving a simple polynomial evaluation
(return x-x*x/2 instead of x here) is not such a good idea since it
gives an enormous pessimization of tinier args on machines for which
denormals are slow. Float x*x/2 is denormal when |x| ~< 2**-64 and
x*x/2 is evaluated in float precision, so it can easily be denormal
for normal x. This is even more interesting for general polynomial
evaluations. Multiplying out large powers of x is normally a good
optimization since it reduces dependencies, but it creates denormals
starting with quite large x.

show more ...

Use STRICT_ASSIGN() for log1pf() and log1p() instead of a volatile cast
hack for log1pf() only. The cast hack broke with gcc-4, resulting in
~1 million errors of more than 1 ulp, with a maximum erro

Use STRICT_ASSIGN() for log1pf() and log1p() instead of a volatile cast
hack for log1pf() only. The cast hack broke with gcc-4, resulting in
~1 million errors of more than 1 ulp, with a maximum error of ~1.5 ulps.
Now the maximum error for log1pf() on i386 is 0.5034 ulps again (this
depends on extra precision), and log1p() has a chance of working with
extra precision.

See s_log1pf.c 1.8 for the original hack. (It claims only 62343 large
errors).

Convert to _FBSDID(). Another thing broken with gcc-4 is the static
const hack used for rcsids.

show more ...

For log1pf(), fixed the approximations to sqrt(2), sqrt(2)-1 and
sqrt(2)/2-1. For log1p(), fixed the approximation to sqrt(2)/2-1.

The end result is to fix an error of 1.293 ulps in
log1pf(0.41

For log1pf(), fixed the approximations to sqrt(2), sqrt(2)-1 and
sqrt(2)/2-1. For log1p(), fixed the approximation to sqrt(2)/2-1.

The end result is to fix an error of 1.293 ulps in
log1pf(0.41421395540 (hex 0x3ed413da))
and an error of 1.783 ulps in
log1p(-0.292893409729003961761) (hex 0x12bec4 00000001)).
The former was the only error of > 1 ulp for log1pf() and the latter
is the only such error that I know of for log1p().

The approximations don't need to be very accurate, but the last 2 need
to be related to the first and be rounded up a little (even more than
1 ulp for sqrt(2)/2-1) for the following implementation-detail reason:
when the arg (x) is not between (the approximations to) sqrt(2)/2-1
and sqrt(2)-1, we commit to using a correction term, but we only
actually use it if 1+x is between sqrt(2)/2 and sqrt(2) according to
the first approximation. Thus we must ensure that
!(sqrt(2)/2-1 < x < sqrt(2)-1) implies !(sqrt(2)/2 < x+1 < sqrt(2)),
where all the sqrt(2)'s are really slightly different approximations
to sqrt(2) and some of the "<"'s are really "<="'s. This was not done.

In log1pf(), the last 2 approximations were rounded up by about 6 ulps
more than needed relative to a good approximation to sqrt(2), but the
actual approximation to sqrt(2) was off by 3 ulps. The approximation
to sqrt(2)-1 ended up being 4 ulps too small, so the algoritm was
broken in 4 cases. The result happened to be broken in 1 case. This
is fixed by using a natural approximation to sqrt(2) and derived
approximations for the others.

In logf(), all the approximations made sense, but the approximation
to sqrt(2)/2-1 was 2 ulps too small (a tiny amount, since we compare
with a granularity of 2**32 ulps), so the algorithm was broken in 2
cases. The result was broken in 1 case. This is fixed by rounding
up the approximation to sqrt(2)/2-1 by 2**32 ulps, so 2**32 cases are
now handled a little differently (still correctly according to my
assertion that the approximations don't need to be very accurate, but
this has not been checked).

show more ...

Use the usual volatile hack to trick gcc into clipping any extra precision
on assignment.

Extra precision on i386's broke hi+lo decomposition in the usual way.
It caused all except 1 of the 62343 er

Use the usual volatile hack to trick gcc into clipping any extra precision
on assignment.

Extra precision on i386's broke hi+lo decomposition in the usual way.
It caused all except 1 of the 62343 errors of more than 1 ulp for
log1pf() on i386's with gcc -O [-fno-float-store].

show more ...

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

show more ...

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.

show more ...

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

show more ...

Fix some rather obscene code that has ambiguous if...if...else...
constructs in it.

Fix cutoffs. This is just a cleanup and an optimization for unusual
cases which are used mainly by regression tests.

As usual, the cutoff for tiny args was not correctly translated to
float precisi

Fix cutoffs. This is just a cleanup and an optimization for unusual
cases which are used mainly by regression tests.

As usual, the cutoff for tiny args was not correctly translated to
float precision. It was 2**-54 but 2**-24 works. It must be about
2**-precision, since the error from approximating log(1+x) by x is
about the same as |x|. Exhaustive testing shows that 2**-24 gives
perfect rounding in round-to-nearest mode.

Similarly for the cutoff for being small, except this is not used by
so many other functions. It was 2**-29 but 2**-15 works. It must be
a bit smaller than sqrt(2**-precision), since the error from
approximating log(1+x) by x-x*x/2 is about the same as x*x. Exhaustive
testing shows that 2**-15 gives a maximum error of 0.5052 ulps in
round-to-nearest-mode. The algorithm for the general case is only good
for 0.8388 ulps, so this is sufficient (but it loses slightly on i386 --
then extra precision gives 0.5032 ulps for the general case).

While investigating this, I noticed that optimizing the usual case by
falling into a middle case involving a simple polynomial evaluation
(return x-x*x/2 instead of x here) is not such a good idea since it
gives an enormous pessimization of tinier args on machines for which
denormals are slow. Float x*x/2 is denormal when |x| ~< 2**-64 and
x*x/2 is evaluated in float precision, so it can easily be denormal
for normal x. This is even more interesting for general polynomial
evaluations. Multiplying out large powers of x is normally a good
optimization since it reduces dependencies, but it creates denormals
starting with quite large x.

show more ...

Use STRICT_ASSIGN() for log1pf() and log1p() instead of a volatile cast
hack for log1pf() only. The cast hack broke with gcc-4, resulting in
~1 million errors of more than 1 ulp, with a maximum erro

Use STRICT_ASSIGN() for log1pf() and log1p() instead of a volatile cast
hack for log1pf() only. The cast hack broke with gcc-4, resulting in
~1 million errors of more than 1 ulp, with a maximum error of ~1.5 ulps.
Now the maximum error for log1pf() on i386 is 0.5034 ulps again (this
depends on extra precision), and log1p() has a chance of working with
extra precision.

See s_log1pf.c 1.8 for the original hack. (It claims only 62343 large
errors).

Convert to _FBSDID(). Another thing broken with gcc-4 is the static
const hack used for rcsids.

show more ...

For log1pf(), fixed the approximations to sqrt(2), sqrt(2)-1 and
sqrt(2)/2-1. For log1p(), fixed the approximation to sqrt(2)/2-1.

The end result is to fix an error of 1.293 ulps in
log1pf(0.41

For log1pf(), fixed the approximations to sqrt(2), sqrt(2)-1 and
sqrt(2)/2-1. For log1p(), fixed the approximation to sqrt(2)/2-1.

The end result is to fix an error of 1.293 ulps in
log1pf(0.41421395540 (hex 0x3ed413da))
and an error of 1.783 ulps in
log1p(-0.292893409729003961761) (hex 0x12bec4 00000001)).
The former was the only error of > 1 ulp for log1pf() and the latter
is the only such error that I know of for log1p().

The approximations don't need to be very accurate, but the last 2 need
to be related to the first and be rounded up a little (even more than
1 ulp for sqrt(2)/2-1) for the following implementation-detail reason:
when the arg (x) is not between (the approximations to) sqrt(2)/2-1
and sqrt(2)-1, we commit to using a correction term, but we only
actually use it if 1+x is between sqrt(2)/2 and sqrt(2) according to
the first approximation. Thus we must ensure that
!(sqrt(2)/2-1 < x < sqrt(2)-1) implies !(sqrt(2)/2 < x+1 < sqrt(2)),
where all the sqrt(2)'s are really slightly different approximations
to sqrt(2) and some of the "<"'s are really "<="'s. This was not done.

In log1pf(), the last 2 approximations were rounded up by about 6 ulps
more than needed relative to a good approximation to sqrt(2), but the
actual approximation to sqrt(2) was off by 3 ulps. The approximation
to sqrt(2)-1 ended up being 4 ulps too small, so the algoritm was
broken in 4 cases. The result happened to be broken in 1 case. This
is fixed by using a natural approximation to sqrt(2) and derived
approximations for the others.

In logf(), all the approximations made sense, but the approximation
to sqrt(2)/2-1 was 2 ulps too small (a tiny amount, since we compare
with a granularity of 2**32 ulps), so the algorithm was broken in 2
cases. The result was broken in 1 case. This is fixed by rounding
up the approximation to sqrt(2)/2-1 by 2**32 ulps, so 2**32 cases are
now handled a little differently (still correctly according to my
assertion that the approximations don't need to be very accurate, but
this has not been checked).

show more ...

Use the usual volatile hack to trick gcc into clipping any extra precision
on assignment.

Extra precision on i386's broke hi+lo decomposition in the usual way.
It caused all except 1 of the 62343 er

Use the usual volatile hack to trick gcc into clipping any extra precision
on assignment.

Extra precision on i386's broke hi+lo decomposition in the usual way.
It caused all except 1 of the 62343 errors of more than 1 ulp for
log1pf() on i386's with gcc -O [-fno-float-store].

show more ...

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

show more ...