Copy stable/10@r272459 to releng/10.1 as part of
the 10.1-RELEASE process.

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

MFC r257770 r257818 r257823 r260066 r260067 r260089 r260145 r268587 r268588
r268589 r268590 r268593 r268597 r269758 r270845 r270847 r270893 r270932
r270947 r271147

Merge libm work by kargl, bde and das from the past few months.
Besides optimisations and small bug fixes this includes new implementations
for C99 functions expl, coshl, sinhl, tanhl, erfl and erfcl.

Approved by: re (kib)

Copy head (r256279) to stable/10 as part of the 10.0-RELEASE cycle.

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

Change a comma to a semicolon.

Remove a blank line that crept into the declarations.

Fix a comment to show a sign on a NaN.

ld80 and ld128 implementations of expm1l(). This code started life
as a fairly faithful implementation of the algorithm found in

PTP Tang, "Table-driven implementation of the Expm1 function
in IEEE floating-point arithmetic," ACM Trans. Math. Soft., 18,
211-222 (1992).

Over the last 18-24 months, the code has under gone significant
optimization and testing.

Reviewed by: bde
Obtained from: bde (most of the optimizations)

Fix two comments that got lost in the disentanglement of the larger diff.

ld80/s_expl.c:

* Use integral numerical constants, and let the compiler do the
conversion to long double.

ld128/s_expl.c:

* Use integral numerical constants, and let the compiler do the
conversion to long double.
* Use the ENTERI/RETURNI macros, which are no-ops on ld128. This
however makes the ld80 and ld128 identical.

Reviewed by: bde (as part of larger diff)

Micro-optimization: move the unary mius operator to operate
on a literal constant.

Obtained from: bde

Add a comment to note that bde supplied most, if not all,
of the optimizations.

ld80/s_expl.c:

* In the special case x = -Inf or -NaN, use a micro-optimization
to eliminate the need to access u.xbits.man.

* Fix an off-by-one for small arguments |x| < 0x1p-65.

ld128/s_expl.c:

* In the special case x = -Inf or -NaN, use a micro-optimization
to eliminate the need to access u.xbits.manh and u.xbits.manl.

* Fix an off-by-one for small arguments |x| < 0x1p-114.

Obtained from: bde

ld80/s_expl.c:

* Update the evaluation of the polynomial. This allows the removal
of the now unused variables t23 and t45.

ld128/s_expl.c:

* Update the evaluation of the polynomial and the intermediate
result t. This update allows several numerical constants to be
written as double rather than long double constants. Update
the constants as appropriate.

Obtained from: bde

Update a comment to reflect that we are using an endpoint of
an interval instead of a midpoint.

Introduce the macro LOG2_INTERVAL, which is log2(number of intervals).
Use the macroi as a micro-optimization to convert a subtraction and
division to a shift.

Obtained from: bde

Whitespace.

* Rename the polynomial coefficients from P2, P3, ... to A2, A3, ....
The names now coincide with the name used in PTP Tang's paper.

* Rename the variable from s to tbl to better reflect that
this is a table, and to be consistent with the naming scheme
in s_exp2l.c

Reviewed by: bde (as part of larger diff)

ld80/s_expl.c:

* Update Copyright years to include 2013.

ld128/s_expl.c:

* Correct and update Copyright years. This code originated from
the ld80 version, so it should reflect the same time period.

Reviewed by: bde (as part of larger diff)

Add logl, log2l, log10l, and log1pl.

Submitted by: bde

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.

* ld80/s_expl.c:
. Fix the threshold for expl(x) where |x| is small.
. Also update the previously incorrect comment to match the
new threshold.

* ld128/s_expl.c:
. Re-order logic in exceptional cases to match the logic used in
other long double functions.
. Fix the threshold for expl(x) where is |x| is small.
. Also update the previously incorrect comment to match the
new threshold.

Submitted by: bde
Approved by: das (mentor)

* ld80/s_expl.c:
. Guard a comment from reformatting by indent(1).
. Re-order variables in declarations to alphabetical order.
. Remove a banal comment.

* ld128/s_expl.c:
. Add a comment to point to ld80/s_expl.c for implementation details.
. Move the #define of INTERVAL to reduce the diff with ld80/s_expl.c.
. twom10000 does not need to be volatile, so move its declaration.
. Re-order variables in declarations to alphabetical order.
. Add a comment that describes the argument reduction.
. Remove the same banal comment found in ld80/s_expl.c.

Reviewed by: bde
Approved by: das (mentor)

Whitespace.

Submitted by: bde
Approved by: das (pre-approved)

Replace the macro name NUM with INTERVALS. This change provides
compatibility with the INTERVALS macro used in the soon-to-be-commmitted
expm1l() and someday-to-be-committed log*l() functions.

Add a comment into ld128/s_expl.c noting at gcc issue that was
deleted when rewriting ld80/e_expl.c as ld128/s_expl.c.

Requested by: bde
Approved by: das (mentor)

* ld80/expl.c:
. Remove a few #ifdefs that should have been removed in the initial
commit.
. Sort fpmath.h to its rightful place.

* ld128/s_expl.c:
. Replace EXPMASK with its actual value.
. Sort fpmath.h to its rightful place.

Requested by: bde
Approved by: das (mentor)

Compute the exponential of x for Intel 80-bit format and IEEE 128-bit
format. These implementations are based on

PTP Tang, "Table-driven implementation of the exponential function
in IEEE floating-point arithmetic," ACM Trans. Math. Soft., 15,
144-157 (1989).

PR: standards/152415
Submitted by: kargl
Reviewed by: bde, das
Approved by: das (mentor)

Clean up the unneeded cpp macro INLINE_REM_PIO2L.

Reviewed by: das
Approved by: das (mentor)

Improve the accuracy from a max ULP of ~2000 to max ULP < 0.79
on i386-class hardware for sinl and cosl. The hand-rolled argument
reduction have been replaced by e_rem_pio2l() implementations. To
preserve history the following commands have been executed:

svn cp src/e_rem_pio2.c ld80/e_rem_pio2l.h
mv ${HOME}/bde/ld80/e_rem_pio2l.c ld80/e_rem_pio2l.h

svn cp src/e_rem_pio2.c ld128/e_rem_pio2l.h
mv ${HOME}/bde/ld128/e_rem_pio2l.c ld128/e_rem_pio2l.h

The ld80 version has been tested by bde, das, and kargl over the
last few years (bde, das) and few months (kargl). An older ld128
version was tested by das. The committed version has only been
compiled tested via 'make universe'.

Approved by: das (mentor)
Obtained from: bde

Add implementations of acosl(), asinl(), atanl(), atan2l(),
and cargl().

Reviewed by: bde
sparc64 testing resources from: remko

1 << 47 needs to be written 1ULL << 47.

Add kernel functions for 128-bit long doubles. These could be improved
a bit, but access to a freebsd/sparc64 machine is needed.

Submitted by: bde and Steve Kargl <sgk@apl.washington.edu> (earlier version)

Fix exp2*(x) on signaling NaNs by returning x+x as usual.

This has the side effect of confusing gcc-4.2.1's optimizer into more
often doing the right thing. When it does the wrong thing here, it
seems to be mainly making too many copies of x with dependency chains.
This effect is tiny on amd64, but in some cases on i386 it is enormous.
E.g., on i386 (A64) with -O1, the current version of exp2() should
take about 50 cycles, but took 83 cycles before this change and 66
cycles after this change. exp2f() with -O1 only speeded up from 51
to 47 cycles. (exp2f() should take about 40 cycles, on an Athlon in
either i386 or amd64 mode, and now takes 42 on amd64). exp2l() with
-O1 slowed down from 155 cycles to 123 for some args; this is unimportant
since the i386 exp2l() is a fake; the wrong thing for it seems to
involve branch misprediction.

Use a better method of scaling by 2**k. Instead of adding to the
exponent bits of the reduced result, construct 2**k (hopefully in
parallel with the construction of the reduced result) and multiply by
it. This tends to be much faster if the construction of 2**k is
actually in parallel, and might be faster even with no parallelism
since adjustment of the exponent requires a read-modify-wrtite at an
unfortunate time for pipelines.

In some cases involving exp2* on amd64 (A64), this change saves about
40 cycles or 30%. I think it is inherently only about 12 cycles faster
in these cases and the rest of the speedup is from partly-accidentally
avoiding compiler pessimizations (the construction of 2**k is now
manually scheduled for good results, and -O2 doesn't always mess this
up). In most cases on amd64 (A64) and i386 (A64) the speedup is about
20 cycles. The worst case that I found is expf on ia64 where this
change is a pessimization of about 10 cycles or 5%. The manual
scheduling for plain exp[f] is harder and not as tuned.

This change ld128/s_exp2l.c has not been tested.

Implement exp2l(). There is one version for machines with 80-bit
long doubles (i386, amd64, ia64) and one for machines with 128-bit
long doubles (sparc64). Other platforms use the double version.
I've only done runtime testing on i386.

Thanks to bde@ for helpful discussions and bugfixes.

Since nan() is supposed to work the same as strtod("nan(...)", NULL),
my original implementation made both use the same code. Unfortunately,
this meant libm depended on a vendor header at compile time and previously-
unexposed vendor bits in libc at runtime.

Hence, I just wrote my own version of the relevant vendor routine. As it
turns out, mine has a factor of 8 fewer of lines of code, and is a bit more
readable anyway. The strtod() and *scanf() routines still use vendor code.

Reviewed by: bde

Implement and document nan(), nanf(), and nanl(). This commit
adds two new directories in msun: ld80 and ld128. These are for
long double functions specific to the 80-bit long double format
used on x86-derived architectures, and the 128-bit format used on
sparc64, respectively.