lib/msun: Cleanup after $FreeBSD$ removal

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

PR: 276669
MFC after: 1 week

lib: Remove ancient SCCS tags.

Remove ancient SCCS tags from the tree, automated scripting, with two
minor fixup to keep things compiling. All the common forms in the tree
were removed with a perl s

lib: Remove ancient SCCS tags.

Remove ancient SCCS tags from the tree, automated scripting, with two
minor fixup to keep things compiling. All the common forms in the tree
were removed with a perl script.

Sponsored by: Netflix

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Remove $FreeBSD$: one-line .c pattern

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

Rearrange the polynomial evaluation for better parallelism. This
saves an average of about 8 cycles or 5% on A64 (amd64 and i386 --
more in cycles but about the same percentage on i386, and more wit

Rearrange the polynomial evaluation for better parallelism. This
saves an average of about 8 cycles or 5% on A64 (amd64 and i386 --
more in cycles but about the same percentage on i386, and more with
old versions of gcc) with good CFLAGS and some parallelism in the
caller. As usual, it takes a couple more multiplications so it will
be slower on old machines.

Convert to __FBSDID().

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Fix a harmless type error in 1.9.

Use a better algorithm for reducing the error in __kernel_cos[f]().
This supersedes the fix for the old algorithm in rev.1.8 of k_cosf.c.

I want this change mainly because it is an optimization. It

Use a better algorithm for reducing the error in __kernel_cos[f]().
This supersedes the fix for the old algorithm in rev.1.8 of k_cosf.c.

I want this change mainly because it is an optimization. It helps
make software cos[f](x) and sin[f](x) faster than the i387 hardware
versions for small x. It is also a simplification, and reduces the
maximum relative error for cosf() and sinf() on machines like amd64
from about 0.87 ulps to about 0.80 ulps. It was validated for cosf()
and sinf() by exhaustive testing. Exhaustive testing is not possible
for cos() and sin(), but ucbtest reports a similar reduction for the
worst case found by non-exhaustive testing. ucbtest's non-exhaustive
testing seems to be good enough to find problems in algorithms but not
maximum relative errors when there are spikes. E.g., short runs of
it find only 3 ulp error where the i387 hardware cos() has an error
of about 2**40 ulps near pi/2.

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Moved the optimization for tiny x from __kernel_{cos,sin}[f](x) to
{cos_sin}[f](x) so that x doesn't need to be reclassified in the
"kernel" functions to determine if it is tiny (it still needs to be

Moved the optimization for tiny x from __kernel_{cos,sin}[f](x) to
{cos_sin}[f](x) so that x doesn't need to be reclassified in the
"kernel" functions to determine if it is tiny (it still needs to be
reclassified in the cosine case for other reasons that will go away).

This optimization is quite large for exponentially distributed x, since
x is tiny for almost half of the domain, but it is a pessimization for
uniformally distributed x since it takes a little time for all cases
but rarely applies. Arg reduction on exponentially distributed x
rarely gives a tiny x unless the reduction is null, so it is best to
only do the optimization if the initial x is tiny, which is what this
commit arranges. The imediate result is an average optimization of
1.4% relative to the previous version in a case that doesn't favour
the optimization (double cos(x) on all float x) and a large
pessimization for the relatively unimportant cases of lgamma[f][_r](x)
on tiny, negative, exponentially distributed x. The optimization should
be recovered for lgamma*() as part of fixing lgamma*()'s low-quality
arg reduction.

Fixed various wrong constants for the cutoff for "tiny". For cosine,
the cutoff is when x**2/2! == {FLT or DBL}_EPSILON/2. We round down
to an integral power of 2 (and for cos() reduce the power by another
1) because the exact cutoff doesn't matter and would take more work
to determine. For sine, the exact cutoff is larger due to the ration
of terms being x**2/3! instead of x**2/2!, but we use the same cutoff
as for cosine. We now use a cutoff of 2**-27 for double precision and
2**-12 for single precision. 2**-27 was used in all cases but was
misspelled 2**27 in comments. Wrong and sloppy cutoffs just cause
missed optimizations (provided the rounding mode is to nearest --
other modes just aren't supported).

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Reduce diffs against vendor source (Sun fdlibm 5.3).

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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Rearrange the polynomial evaluation for better parallelism. This
saves an average of about 8 cycles or 5% on A64 (amd64 and i386 --
more in cycles but about the same percentage on i386, and more wit

Rearrange the polynomial evaluation for better parallelism. This
saves an average of about 8 cycles or 5% on A64 (amd64 and i386 --
more in cycles but about the same percentage on i386, and more with
old versions of gcc) with good CFLAGS and some parallelism in the
caller. As usual, it takes a couple more multiplications so it will
be slower on old machines.

Convert to __FBSDID().

show more ...

Fix a harmless type error in 1.9.

Use a better algorithm for reducing the error in __kernel_cos[f]().
This supersedes the fix for the old algorithm in rev.1.8 of k_cosf.c.

I want this change mainly because it is an optimization. It

Use a better algorithm for reducing the error in __kernel_cos[f]().
This supersedes the fix for the old algorithm in rev.1.8 of k_cosf.c.

I want this change mainly because it is an optimization. It helps
make software cos[f](x) and sin[f](x) faster than the i387 hardware
versions for small x. It is also a simplification, and reduces the
maximum relative error for cosf() and sinf() on machines like amd64
from about 0.87 ulps to about 0.80 ulps. It was validated for cosf()
and sinf() by exhaustive testing. Exhaustive testing is not possible
for cos() and sin(), but ucbtest reports a similar reduction for the
worst case found by non-exhaustive testing. ucbtest's non-exhaustive
testing seems to be good enough to find problems in algorithms but not
maximum relative errors when there are spikes. E.g., short runs of
it find only 3 ulp error where the i387 hardware cos() has an error
of about 2**40 ulps near pi/2.

show more ...

Moved the optimization for tiny x from __kernel_{cos,sin}[f](x) to
{cos_sin}[f](x) so that x doesn't need to be reclassified in the
"kernel" functions to determine if it is tiny (it still needs to be

Moved the optimization for tiny x from __kernel_{cos,sin}[f](x) to
{cos_sin}[f](x) so that x doesn't need to be reclassified in the
"kernel" functions to determine if it is tiny (it still needs to be
reclassified in the cosine case for other reasons that will go away).

This optimization is quite large for exponentially distributed x, since
x is tiny for almost half of the domain, but it is a pessimization for
uniformally distributed x since it takes a little time for all cases
but rarely applies. Arg reduction on exponentially distributed x
rarely gives a tiny x unless the reduction is null, so it is best to
only do the optimization if the initial x is tiny, which is what this
commit arranges. The imediate result is an average optimization of
1.4% relative to the previous version in a case that doesn't favour
the optimization (double cos(x) on all float x) and a large
pessimization for the relatively unimportant cases of lgamma[f][_r](x)
on tiny, negative, exponentially distributed x. The optimization should
be recovered for lgamma*() as part of fixing lgamma*()'s low-quality
arg reduction.

Fixed various wrong constants for the cutoff for "tiny". For cosine,
the cutoff is when x**2/2! == {FLT or DBL}_EPSILON/2. We round down
to an integral power of 2 (and for cos() reduce the power by another
1) because the exact cutoff doesn't matter and would take more work
to determine. For sine, the exact cutoff is larger due to the ration
of terms being x**2/3! instead of x**2/2!, but we use the same cutoff
as for cosine. We now use a cutoff of 2**-27 for double precision and
2**-12 for single precision. 2**-27 was used in all cases but was
misspelled 2**27 in comments. Wrong and sloppy cutoffs just cause
missed optimizations (provided the rounding mode is to nearest --
other modes just aren't supported).

show more ...

Reduce diffs against vendor source (Sun fdlibm 5.3).

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 ...