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/

Clean up libm use of the __ieee754_ prefix

This removes the __ieee754_ prefix from a number of the math functions.
msun/src/math_private.h contains the statement that

/*
* ieee style elementar

Clean up libm use of the __ieee754_ prefix

This removes the __ieee754_ prefix from a number of the math functions.
msun/src/math_private.h contains the statement that

/*
* ieee style elementary functions
*
* We rename functions here to improve other sources' diffability
* against fdlibm.
*/
#define __ieee754_sqrt sqrt
...

Here, fdlibm refers to https://netlib.org/fdlibm. It is seen from
https://netlib.org/fdlibm/readme that this prefix was used to
differentiate between different standards:

Wrapper functions will twist the result of the ieee754
function to comply to the standard specified by the value
of _LIB_VERSION
if _LIB_VERSION = _IEEE_, return the ieee754 result;
if _LIB_VERSION = _SVID_, return SVID result;
if _LIB_VERSION = _XOPEN_, return XOPEN result;
if _LIB_VERSION = _POSIX_, return POSIX/ANSI result.
(These are macros, see fdlibm.h for their definition.)

AFAICT, FreeBSD has never supported these wrappers. In addition, as C99,
principally the long double, functions were added to libm, this
convention was not maintained. Given that only 148 of 324 files under
lib/msun contain a "Copyright (C) 1993 by Sun Microsystems" statement,
the removal of the __ieee754_ prefix provides consistency across all
source files.

The last time someone compared lib/msun to fdlibm appears to be

commit 3f70824172feb82ea3dcdb3866b54fe0eb7cd890
Author: David Schultz <das@FreeBSD.org>
Date: Fri Feb 4 18:26:06 2005 +0000

Reduce diffs against vendor source (Sun fdlibm 5.3).

The most recent fdlibm RCS string that appears in a Sun Microsystem
copyrighted file is date "95/01/18". With Oracle Corporation's
acquisition of Sun Microsystems in 2009, it is unlikely that fdlibm will
ever be updated. A search for fdlibm at https://opensource.oracle.com/
yields no hits.

Finally, OpenBSD removed the use of this prefix over 21 years ago. pSee
revision 1.6 of OpenBSD's math_private.h.

Note: this does not drop the __ieee754_ prefix from the trigonometric
argument reduction functions, e.g., __ieee754_rem_pio2. These functions
are internal to the libm and exported through Symbol.map; and thus,
reserved for the implementation.

PR: 272783
MFC after: 1 week

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libm: remove unused variables

Sponsored by: The FreeBSD Foundation

The value small=2**-(p+3), where p is the precision, can be determine from
lgamma(x) = -log(x) - log(1+x) + x*(1-g) + x**2*P(x) with g = 0.57...
being the Euler constant and P(x) a polynomial. Subst

The value small=2**-(p+3), where p is the precision, can be determine from
lgamma(x) = -log(x) - log(1+x) + x*(1-g) + x**2*P(x) with g = 0.57...
being the Euler constant and P(x) a polynomial. Substitution of small
into the RHS shows that the last 3 terms are negligible in comparison to
the leading term. The choice of 3 may be conservative.

The value large=2**(p+3) is detemined from Stirling's approximation
lgamma(x) = x*(log(x)-1) - log(x)/2 + log(2*pi)/2 + P(1/x)/x
Again, substitution of large into the RHS reveals the last 3 terms
are negligible in comparison to the leading term.

Move the x=+-0 special case into the |x|<small block.

In the ld80 and ld128 implementaion, use fdlibm compatible comparisons
involving ix, lx, and llx. This replaces several floating point
comparisons (some involving fabsl()) and also fixes the special cases
x=1 and x=2.

While here
. Remove unnecessary parentheses.
. Fix/improve comments due to the above changes.
. Fix nearby whitespace.

* src/e_lgamma_r.c:
. Sort declaration.
. Remove unneeded explicit cast for type conversion.
. Replace a double literal constant by an integer literal constant.

* src/e_lgammaf_r.c:
. Sort declaration.

* ld128/e_lgammal_r.c:
. Replace a long double literal constant by a double literal constant.

* ld80/e_lgammal_r.c:
. Remove unused '#include float.h'
. Replace a long double literal constant by a double literal constant.

Requested by: bde

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For targets that have a signed zero, lgamma_r(-0, &signgamp) should
set signgamp = -1.

Submitted by: enh at google dot com (e_lgamma[f]_r.c)

* Makefile:
. Hook e_lgammal[_r].c to the build.
. Create man page links for lgammal[-r].3.

* Symbol.map:
. Sort lgammal to its rightful place.
. Add FBSD_1.4 section for the new lgamal_r sy

* Makefile:
. Hook e_lgammal[_r].c to the build.
. Create man page links for lgammal[-r].3.

* Symbol.map:
. Sort lgammal to its rightful place.
. Add FBSD_1.4 section for the new lgamal_r symbol.

* ld128/e_lgammal_r.c:
. 128-bit implementataion of lgammal_r().

* ld80/e_lgammal_r.c:
. Intel 80-bit format implementation of lgammal_r().

* src/e_lgamma.c:
. Expose lgammal as a weak reference to lgamma for platforms
where long double is mapped to double.

* src/e_lgamma_r.c:
. Use integer literal constants instead of real literal constants.
Let compiler(s) do the job of conversion to the appropriate type.
. Expose lgammal_r as a weak reference to lgamma_r for platforms
where long double is mapped to double.

* src/e_lgammaf_r.c:
. Fixed the Cygnus Support conversion of e_lgamma_r.c to float.
This includes the generation of new polynomial and rational
approximations with fewer terms. For each approximation, include
a comment on an estimate of the accuracy over the relevant domain.
. Use integer literal constants instead of real literal constants.
Let compiler(s) do the job of conversion to the appropriate type.
This allows the removal of several explicit casts of double values
to float.

* src/e_lgammal.c:
. Wrapper for lgammal() about lgammal_r().

* src/imprecise.c:
. Remove the lgamma.

* src/math.h:
. Add a prototype for lgammal_r().

* man/lgamma.3:
. Document the new functions.

Reviewed by: bde

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Remove an initialized, but otherwise, unused variable.

According to the ISO C standard, lgamma(-integer) returns
inf and raises the divided-by-zero exception. Compilers
constant fold one/zero to inf but do not raise the exception.
Introduce a volatile v

According to the ISO C standard, lgamma(-integer) returns
inf and raises the divided-by-zero exception. Compilers
constant fold one/zero to inf but do not raise the exception.
Introduce a volatile vzero to prevent the constant folding.

Move the declaration of zero into the main declaration block.

While here, fix a nearby disordering of 'lx,ix'

Discussed with: bde

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Fix a tab that somehow became 8 spaces.

Remove parentheses in a return statement to be consistent with the
rest of the file.

Rename sin_pi() in the float version to sin_pif().

Remove large comment

Fix a tab that somehow became 8 spaces.

Remove parentheses in a return statement to be consistent with the
rest of the file.

Rename sin_pi() in the float version to sin_pif().

Remove large comment that precedes sin_pif(). The comment
duplicates a comment in e_lgamma_r.c where the algorithm
is documented.

Requested by: bde

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Compute sin(pi*x) without actually doing the pi*x multiplication.
sin_pi(x) is only called for x < 0 and |x| < 2**(p-1) where p is
the precision of x. The new argument reduction is an optimization
c

Compute sin(pi*x) without actually doing the pi*x multiplication.
sin_pi(x) is only called for x < 0 and |x| < 2**(p-1) where p is
the precision of x. The new argument reduction is an optimization
compared to the old code, and it removes a chunk of dead code.
Accuracy tests in the intervals (-21,-20), (-20,-19), ... (-1,0)
show no differences between the old and new code.

Obtained from: bde

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Remove some unnecessary initializations.

Obtained from: DragonFlyBSD

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 be

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.

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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

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.

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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 l

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].

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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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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/