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

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

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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 inte

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

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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
th

* 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)

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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 per

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)

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MFC @ r241285

IFC @ r242684

Sync from head

* 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 except

* 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)

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* 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

* 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)

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Merge head r233826 through r239010.

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

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)

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* 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.

* 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)

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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-

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)

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