Patchwork Improves __ieee754_exp() performance by 2x-5x on sparc/x86.

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Submitter Patrick McGehearty
Date Jan. 3, 2018, 7:28 p.m.
Message ID <1515007683-3161-1-git-send-email-patrick.mcgehearty@oracle.com>
Download mbox | patch
Permalink /patch/25197/
State New
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Patrick McGehearty - Jan. 3, 2018, 7:28 p.m.
Version 10 of proposed patch.

Add removal of sysdeps/i386/fpu/slowexp.c, sysdeps/ia64/fpu/slowexp.c
and sysdeps/m68k/m680x0/fpu/slowexp.c as building of slowexp.c no
longer needs to be overriden in these architectures.

Reverted eexp.tbl to 64 entries for scaling table and changed back to
invln2_64, ln2_64hi, ln2_64lo. Reduces L1 cache impact of table at
cost of increasing frequency of 1 ulp differences from old method.

Cleaned up trailing white space in e_exp.c

Performance gain for typical values is 2x on Sparc and 5x on x86.
SET_RESTORE_ROUND is particularly slow on Sparc.  Investigating the
root cause is out of scope for this patch, but worthy of later study
as the same issue may be seen elsewhere.  For those values which
triggered calls to "slowexp" in the previous algorithm, the speedup on
both Sparc and x86 is over 100x. Over a range of randomly generated
values, these slow cases are rare but have been reported to be notable
in some applications.

Version 9 of proposed patch.

Replaced get_rounding_mode and libc_fesetround() with SET_RESTORE_ROUND
to avoid Intel rounding mode issue which showed as test failures in
tgamma_upward. Adds noticable overhead for platforms that incur
significant cost when rounding mode is already FE_TONEAREST. Added
SET_RESTORE_ROUND to two more cases which resolved 1 ulp rounding
errors for cexp().

Expanded the scaling table from 64 entries to 128 entries, renaming
invln2_64 to invln2_256 as well as ln2_64hi and ln2_64lo to ln2_256hi
and ln2_256lo. That reduces the 1 ulp error rate per 1000 values from
1.6 to 0.6.

Even with all changes, performance gain is still quite dramatic.
Adding libc_fegetround, libc_fegetroundf and libc_fegetroundl to
the math_private and fenv_private.h macros would allow using
libc_fegetround and libc_fesetround as a future performance enhancement.

Version 8 of proposed patch.

Renamed ln2_32hi2 and ln2_32lo2 to be ln2_64hi and ln2_64lo.
Revised comments to more accurately describe these constants.
Revised constants t2, t3, t4, t5 to better match values of 1/n factorial.
Change eliminated 1 ulp error in 942 tests out 40 million values tested.

Version 7 of proposed patch.

Fixed formatting issue in sysdeps/ieee754/dbl-64/e_exp.c

Version 6 of proposed patch.

Fixed error in patch revision.
Cleaned up formatting of return () and location of '+' for line breaks.
Fixed comments in eexp.tbl. Adjusted 3 values in eexp.tbl to be correctly
rounded in ulp as computed by quad precision.

Modified e_exp.c and eexp.tbl to use table of 64 intervals instead of
32 intervals for computing exp(x). That change reduced the differences
from the prior ieee754 exp(x) to 16 in 10,000 from 29 in 10,000. Also
reduced the make check differences for exp to 1 from 3. No observed
change in performance for using the larger table on either x86 or Sparc.

Version 5 of proposed patch.

Cleaned up formatting of comments and braces.
Returned to single patch for submission.

Version 4 of proposed patch.

New comments revised to use GNU standard comment formating.
Limited comment added in eexp.tbl for TBL[]. The original src
used for porting to Linux did not have a comment about TBL[].
The new comment is limited to the current worker's level of
understanding.

The (-xx.x > threshold2) case is changed to return force_underflow.
For FE_TONEAREST, tiny*tiny will always be zero but for
FE_UPWARD, it will be the smallest representable value.

That change caused no change in the math test results for Sparc or x86.

Version 3 changes

All hex constants in version 2 replaced with C99 double hex constants,
allowing Big Endian and Little Endian versions to be merged.
Only e_exp.c and eexp.tbl changed from version 2.
Minor changes in performance results due to system noise.
No other changes from version 2.

Version 2 of proposed patch.
Revised copyright notice and formatting issues.
Removed slowexp.c and related references.
Replaced tables of double constants with hex constants, taking special
  attention to correctly handle little endian and big endian versions.
  Using hex initialization also required changing variables to be declared
  as unions.  Tables moved from e_exp.c to sysdeps/ieee754/dbl-64/eexp.tbl.
Replaced __fegetround(), __fesetround() with get_rounding_mode and
  libc_fesetround().
Removed use of "small". "inexact mode" now ignored.
Retested and rebenchmarked on sparc and x86 with the above changes.

These changes will be active for all platforms that don't provide
their own exp() routines. They will also be active for ieee754
versions of ccos, ccosh, cosh, csin, csinh, sinh, exp10, gamma, and
erf.

Typical performance gains is typically around 5x when measured on
Sparc s7 for common values between exp(1) and exp(40).

Using the glibc perf tests on sparc,
      sparc (nsec)    x86 (nsec)
      old     new     old     new
max   17629   395    5173     144
min     399    54      15      13
mean   5317   200    1349      23

The extreme max times for the old (ieee754) exp are due to the
multiprecision computation in the old algorithm when the true value is
very near 0.5 ulp away from an value representable in double
precision. The new algorithm does not take special measures for those
cases. The current glibc exp perf tests overrepresent those values.
Informal testing suggests approximately one in 200 cases might
invoke the high cost computation. The performance advantage of the new
algorithm for other values is still large but not as large as indicated
by the chart above.

Glibc correctness tests for exp() and expf() were run. Within the
test suite 3 input values were found to cause 1 bit differences (ulp)
when "FE_TONEAREST" rounding mode is set. No differences in exp() were
seen for the tested values for the other rounding modes.
Typical example:
exp(-0x1.760cd2p+0)  (-1.46113312244415283203125)
 new code:    2.31973271630014299393707e-01   0x1.db14cd799387ap-3
 old code:    2.31973271630014271638132e-01   0x1.db14cd7993879p-3
    exp    =  2.31973271630014285508337 (high precision)
Old delta: off by 0.49 ulp
New delta: off by 0.51 ulp

In addition, because ieee754_exp() is used by other routines, cexp()
showed test results with very small imaginary input values where the
imaginary portion of the result was off by 3 ulp when in upward
rounding mode, but not in the other rounding modes.  For x86, tgamma
showed a few values where the ulp increased to 6 (max ulp for tgamma
is 5). Sparc tgamma did not show these failures.  I presume the tgamma
differences are due to compiler optimization differences within the
gamma function.The gamma function is known to be difficult to compute
accurately.
---
 manual/probes.texi                          |   14 -
 math/Makefile                               |    2 +-
 sysdeps/generic/math_private.h              |    1 -
 sysdeps/i386/fpu/slowexp.c                  |    1 -
 sysdeps/ia64/fpu/slowexp.c                  |    1 -
 sysdeps/ieee754/dbl-64/e_exp.c              |  341 +++++++++++++--------------
 sysdeps/ieee754/dbl-64/e_pow.c              |    2 +-
 sysdeps/ieee754/dbl-64/eexp.tbl             |  255 ++++++++++++++++++++
 sysdeps/ieee754/dbl-64/slowexp.c            |   86 -------
 sysdeps/m68k/m680x0/fpu/slowexp.c           |    1 -
 sysdeps/powerpc/power4/fpu/Makefile         |    1 -
 sysdeps/x86_64/fpu/multiarch/Makefile       |    9 +-
 sysdeps/x86_64/fpu/multiarch/e_exp-avx.c    |    1 -
 sysdeps/x86_64/fpu/multiarch/e_exp-fma.c    |    1 -
 sysdeps/x86_64/fpu/multiarch/e_exp-fma4.c   |    1 -
 sysdeps/x86_64/fpu/multiarch/slowexp-avx.c  |    9 -
 sysdeps/x86_64/fpu/multiarch/slowexp-fma.c  |    9 -
 sysdeps/x86_64/fpu/multiarch/slowexp-fma4.c |    9 -
 18 files changed, 426 insertions(+), 318 deletions(-)
 delete mode 100644 sysdeps/i386/fpu/slowexp.c
 delete mode 100644 sysdeps/ia64/fpu/slowexp.c
 create mode 100644 sysdeps/ieee754/dbl-64/eexp.tbl
 delete mode 100644 sysdeps/ieee754/dbl-64/slowexp.c
 delete mode 100644 sysdeps/m68k/m680x0/fpu/slowexp.c
 delete mode 100644 sysdeps/x86_64/fpu/multiarch/slowexp-avx.c
 delete mode 100644 sysdeps/x86_64/fpu/multiarch/slowexp-fma.c
 delete mode 100644 sysdeps/x86_64/fpu/multiarch/slowexp-fma4.c
Joseph Myers - Jan. 3, 2018, 8:57 p.m.
On Wed, 3 Jan 2018, Patrick McGehearty wrote:

> Using the glibc perf tests on sparc,
>       sparc (nsec)    x86 (nsec)
>       old     new     old     new
> max   17629   395    5173     144
> min     399    54      15      13
> mean   5317   200    1349      23

These are exactly the same figures as in the previous version that was 
reverted.  Are you *sure* they are the correct results of retesting with 
this patch version?  Remember, the patch submission message must be 
correct for the patch version being submitted and there must be an 
unambiguous division between the content intended for the commit message 
(describing the current patch version) and any other content such as 
descriptions of differences from previous patch versions (which don't go 
in the commit message).

I'd suggest following the conventions used by the Linux kernel, of the 
description of the current patch version for the commit message going 
*first*, then a line "---", then any other text not for the commit message 
(such as information about differences from previous patch versions), then 
the diff itself.

> In addition, because ieee754_exp() is used by other routines, cexp()
> showed test results with very small imaginary input values where the
> imaginary portion of the result was off by 3 ulp when in upward
> rounding mode, but not in the other rounding modes.  For x86, tgamma
> showed a few values where the ulp increased to 6 (max ulp for tgamma
> is 5). Sparc tgamma did not show these failures.  I presume the tgamma
> differences are due to compiler optimization differences within the
> gamma function.The gamma function is known to be difficult to compute
> accurately.

Is this still accurate for the current patch version?

If you tested on a platform requiring ulps updates, you should include the 
updates from "make regen-ulps" as part of the patch, and explicitly 
confirm that, given the patch applied including those ulps updates, all 
the math/ tests PASS on platforms that you specify in the patch submission 
message.
Patrick McGehearty - Jan. 3, 2018, 10:22 p.m.
On 1/3/2018 2:57 PM, Joseph Myers wrote:
> On Wed, 3 Jan 2018, Patrick McGehearty wrote:
>
>> Using the glibc perf tests on sparc,
>>        sparc (nsec)    x86 (nsec)
>>        old     new     old     new
>> max   17629   395    5173     144
>> min     399    54      15      13
>> mean   5317   200    1349      23
> These are exactly the same figures as in the previous version that was
> reverted.  Are you *sure* they are the correct results of retesting with
> this patch version?  Remember, the patch submission message must be
> correct for the patch version being submitted and there must be an
> unambiguous division between the content intended for the commit message
> (describing the current patch version) and any other content such as
> descriptions of differences from previous patch versions (which don't go
> in the commit message).
>
> I'd suggest following the conventions used by the Linux kernel, of the
> description of the current patch version for the commit message going
> *first*, then a line "---", then any other text not for the commit message
> (such as information about differences from previous patch versions), then
> the diff itself.
>
>> In addition, because ieee754_exp() is used by other routines, cexp()
>> showed test results with very small imaginary input values where the
>> imaginary portion of the result was off by 3 ulp when in upward
>> rounding mode, but not in the other rounding modes.  For x86, tgamma
>> showed a few values where the ulp increased to 6 (max ulp for tgamma
>> is 5). Sparc tgamma did not show these failures.  I presume the tgamma
>> differences are due to compiler optimization differences within the
>> gamma function.The gamma function is known to be difficult to compute
>> accurately.
> Is this still accurate for the current patch version?
>
> If you tested on a platform requiring ulps updates, you should include the
> updates from "make regen-ulps" as part of the patch, and explicitly
> confirm that, given the patch applied including those ulps updates, all
> the math/ tests PASS on platforms that you specify in the patch submission
> message.
>
I have not been updating any of the earlier comments when I responded
to the later comments. I just added the newest comment to the top of
the earlier patch comments to allow easy access to this PATCH history.
If we need another patch, I'll rework the comments as you suggest.

Here is the latest update for the performance tables:

All numbers rerun with the Jan 2, 2018 src code base:
       sparc (nsec)    x86 (nsec)
       old     new     old     new
max   17584   873    5158    1380
min     399    96      15      16
mean   5497   419    1333      24

Modest increases on x86 but roughly doubling on Sparc makes me think
that SET_RESTORE_ROUND has an opportunity for improvement on Sparc.

For the accuracy issue, we no longer see any failures on cexp() or
tgamma(). The tgamma() failure went away with the SET_RESTORE_ROUND
fix. As part of the SET_RESTORE_ROUND fix, I realized I had missed
handling rounding for a special case. When I fixed that, the cexp()
errors went away.

There only test value that fails now is:
Failure: Test: exp (-0x2.c469ep+8)
Result:
  is:          2.1872267636802106e-308   0x0.fba54632dddc0p-1022
  should be:   2.1872267636802101e-308   0x0.fba54632dddbfp-1022
  difference:  4.9406564584124654e-324   0x0.0000000000001p-1022
  ulp       :  1.0000
  max.ulp   :  0.0000

[Side note: this diff is still present with the 256 size table.]

I'm not clear about how "make regen-ulps" is part of the patch process.
I've not seen any discussion of that before.
Do I need to include the changes to the ulp test data as part
of the patch? I had assumed that was handled as a separate
patch after the code changes were merged.

Also, when I run "make check" on the base code for Sparc, I'm getting
some additional ulp failures for cpow, ctan, ctanh and a few others.
These did not occur with my 8th patch submission but did with my
9th patch. They do not occur on the x86 tests.
These ulp failures are unchanged by my exp() code, so I've
concluded they are not related to my work.

- patrick
Patrick McGehearty - Jan. 3, 2018, 10:30 p.m.
On 1/3/2018 1:28 PM, Patrick McGehearty wrote:
> Version 10 of proposed patch.
>
> Add removal of sysdeps/i386/fpu/slowexp.c, sysdeps/ia64/fpu/slowexp.c
> and sysdeps/m68k/m680x0/fpu/slowexp.c as building of slowexp.c no
> longer needs to be overriden in these architectures.
>
> Reverted eexp.tbl to 64 entries for scaling table and changed back to
> invln2_64, ln2_64hi, ln2_64lo. Reduces L1 cache impact of table at
> cost of increasing frequency of 1 ulp differences from old method.
>
> Cleaned up trailing white space in e_exp.c
>
> Performance gain for typical values is 2x on Sparc and 5x on x86.
> SET_RESTORE_ROUND is particularly slow on Sparc.  Investigating the
> root cause is out of scope for this patch, but worthy of later study
> as the same issue may be seen elsewhere.  For those values which
> triggered calls to "slowexp" in the previous algorithm, the speedup on
> both Sparc and x86 is over 100x. Over a range of randomly generated
> values, these slow cases are rare but have been reported to be notable
> in some applications.
>
>
Here is the proposed change log to go with patch version 10.
It includes the files overlooked in patch version 8.

2017-12-19  Patrick McGehearty <patrick.mcgehearty@oracle.com>

         * sysdeps/ieee754/dbl-64/e_exp.c: 5x faster __ieee754_exp() 
routine.
         * sysdeps/ieee754/dbl-64/eexp.tbl: New file for e_exp.
         * sysdeps/ieee754/dbl-64/slowexp.c: Removed.
         * sysdeps/i386/fpu/slowexp.c: Removed.
         * sysdeps/ia64/fpu/slowexp.c: Removed.
         * sysdeps/m68k/m680x0/fpu/slowexp.c: Removed.
         * sysdeps/x86_64/fpu/multiarch/slowexp-avx.c: Removed.
         * sysdeps/x86_64/fpu/multiarch/slowexp-fma.c: Removed.
         * sysdeps/x86_64/fpu/multiarch/slowexp-fma4.c: Removed.
         * sysdeps/generic/math_private.h: Remove slowexp.
         * sysdeps/ieee754/dbl-64/e_pow.c: Likewise.
         * sysdeps/powerpc/power4/fpu/Makefile: Likewise.
         * sysdeps/x86_64/fpu/multiarch/Makefile: Likewise.
         * sysdeps/x86_64/fpu/multiarch/e_exp-avx.c: Likewise.
         * sysdeps/x86_64/fpu/multiarch/e_exp-fma.c: Likewise.
         * sysdeps/x86_64/fpu/multiarch/e_exp-fma4.c: Likewise.
         * math/Makefile: Likewise.
         * manual/probes.texi: Remove slowexp documentation.
Joseph Myers - Jan. 4, 2018, 1:18 p.m.
On Wed, 3 Jan 2018, Patrick McGehearty wrote:

> Here is the proposed change log to go with patch version 10.
> It includes the files overlooked in patch version 8.

Please start from the rewritten ChangeLog entry I used when committing 
your previous patch.  It's likely the only change needed to the ChangeLog 
entry is to add the ulps regeneration.
Joseph Myers - Jan. 4, 2018, 1:29 p.m.
On Wed, 3 Jan 2018, Patrick McGehearty wrote:

> I have not been updating any of the earlier comments when I responded
> to the later comments. I just added the newest comment to the top of
> the earlier patch comments to allow easy access to this PATCH history.
> If we need another patch, I'll rework the comments as you suggest.

The entirety of any proposed commit is subject to review.  This includes 
the commit message as well as the patch itself.  That means it must be 
unambiguous exactly what the proposed commit message is - and that message 
must all be in one place, not needing composing from pieces in multiple 
messages, and must correspond to the patch sent with that message.  Again, 
I recommend the same format used by the Linux kernel, of having the commit 
message first, with anything about changes between different patch 
versions afterwards, following a "---" line.  That's also what "git am" 
expects (though we can't quite use git am for glibc because of the need to 
update the ChangeLog file at commit time).

> I'm not clear about how "make regen-ulps" is part of the patch process.
> I've not seen any discussion of that before.
> Do I need to include the changes to the ulp test data as part
> of the patch? I had assumed that was handled as a separate
> patch after the code changes were merged.

Any patch submission should have non-regressing test results, on at least 
one platform that is explicitly named in the commit message as a platform 
on which the patch was tested.

This means that if a patch needs ulps updates to avoid FAILs of math/ 
tests, those ulps updates (on at least one named platform used for 
testing) must be included in the patch, and the patch as posted, complete 
with the ulps updates, must have been tested without resulting 
regressions.  It should be obvious from the problems with the previous 
patch version that it's *not* sufficient simply to eyeball the logs for 
failing tests - you need actually to update ulps and to confirm that FAILs 
don't appear given the ulps updates, because there are other ways those 
tests can fail that are not fixed by such updates.

If you test on more than one platform, including the ulps updates for all 
those platforms in the patch is a good idea.

> Also, when I run "make check" on the base code for Sparc, I'm getting
> some additional ulp failures for cpow, ctan, ctanh and a few others.
> These did not occur with my 8th patch submission but did with my
> 9th patch. They do not occur on the x86 tests.
> These ulp failures are unchanged by my exp() code, so I've
> concluded they are not related to my work.

If there are preexisting ulps failures, that means you need to send two 
patches.  The first one would be the results of "make regen-ulps" for 
current glibc, to fix the preexisting failures (and such a patch could be 
committed as obvious without prior review).  The second one would be 
relative to a tree with the first one applied, and would include whatever 
further ulps updates the exp patch requires.

Architecture maintainers should update ulps files as needed during the 
release freeze, and they or others may also do updates at other times as 
and when convenient.

Patch

diff --git a/manual/probes.texi b/manual/probes.texi
index 8ab6756..f8ae64b 100644
--- a/manual/probes.texi
+++ b/manual/probes.texi
@@ -258,20 +258,6 @@  Unless explicitly mentioned otherwise, a precision of 1 implies 24 bits of
 precision in the mantissa of the multiple precision number.  Hence, a precision
 level of 32 implies 768 bits of precision in the mantissa.
 
-@deftp Probe slowexp_p6 (double @var{$arg1}, double @var{$arg2})
-This probe is triggered when the @code{exp} function is called with an
-input that results in multiple precision computation with precision
-6.  Argument @var{$arg1} is the input value and @var{$arg2} is the
-computed output.
-@end deftp
-
-@deftp Probe slowexp_p32 (double @var{$arg1}, double @var{$arg2})
-This probe is triggered when the @code{exp} function is called with an
-input that results in multiple precision computation with precision
-32.  Argument @var{$arg1} is the input value and @var{$arg2} is the
-computed output.
-@end deftp
-
 @deftp Probe slowpow_p10 (double @var{$arg1}, double @var{$arg2}, double @var{$arg3}, double @var{$arg4})
 This probe is triggered when the @code{pow} function is called with
 inputs that result in multiple precision computation with precision
diff --git a/math/Makefile b/math/Makefile
index 4c8703c..46e33a6 100644
--- a/math/Makefile
+++ b/math/Makefile
@@ -114,7 +114,7 @@  type-ldouble-yes := ldouble
 # double support
 type-double-suffix :=
 type-double-routines := branred doasin dosincos halfulp mpa mpatan2	\
-		       mpatan mpexp mplog mpsqrt mptan sincos32 slowexp	\
+		       mpatan mpexp mplog mpsqrt mptan sincos32	\
 		       slowpow sincostab k_rem_pio2
 
 # float support
diff --git a/sysdeps/generic/math_private.h b/sysdeps/generic/math_private.h
index f29898c..689dc54 100644
--- a/sysdeps/generic/math_private.h
+++ b/sysdeps/generic/math_private.h
@@ -262,7 +262,6 @@  extern double __sin32 (double __x, double __res, double __res1);
 extern double __cos32 (double __x, double __res, double __res1);
 extern double __mpsin (double __x, double __dx, bool __range_reduce);
 extern double __mpcos (double __x, double __dx, bool __range_reduce);
-extern double __slowexp (double __x);
 extern double __slowpow (double __x, double __y, double __z);
 extern void __docos (double __x, double __dx, double __v[]);
 
diff --git a/sysdeps/i386/fpu/slowexp.c b/sysdeps/i386/fpu/slowexp.c
deleted file mode 100644
index 1cc8931..0000000
--- a/sysdeps/i386/fpu/slowexp.c
+++ /dev/null
@@ -1 +0,0 @@ 
-/* Not needed.  */
diff --git a/sysdeps/ia64/fpu/slowexp.c b/sysdeps/ia64/fpu/slowexp.c
deleted file mode 100644
index 1cc8931..0000000
--- a/sysdeps/ia64/fpu/slowexp.c
+++ /dev/null
@@ -1 +0,0 @@ 
-/* Not needed.  */
diff --git a/sysdeps/ieee754/dbl-64/e_exp.c b/sysdeps/ieee754/dbl-64/e_exp.c
index 3d2560c..5ba4411 100644
--- a/sysdeps/ieee754/dbl-64/e_exp.c
+++ b/sysdeps/ieee754/dbl-64/e_exp.c
@@ -1,3 +1,4 @@ 
+/* EXP function - Compute double precision exponential */
 /*
  * IBM Accurate Mathematical Library
  * written by International Business Machines Corp.
@@ -23,7 +24,7 @@ 
 /*           exp1                                                          */
 /*                                                                         */
 /* FILES NEEDED:dla.h endian.h mpa.h mydefs.h uexp.h                       */
-/*              mpa.c mpexp.x slowexp.c                                    */
+/*              mpa.c mpexp.x                                              */
 /*                                                                         */
 /* An ultimate exp routine. Given an IEEE double machine number x          */
 /* it computes the correctly rounded (to nearest) value of e^x             */
@@ -32,207 +33,197 @@ 
 /*                                                                         */
 /***************************************************************************/
 
+/*  IBM exp(x) replaced by following exp(x) in 2018. IBM exp1(x,xx) remains.  */
+/* exp(x)
+   Hybrid algorithm of Peter Tang's Table driven method (for large
+   arguments) and an accurate table (for small arguments).
+   Written by K.C. Ng, November 1988.
+   Revised by Patrick McGehearty, Jan 2018 to use j/64 instead of j/32
+   and to round with FE_TONEAREST if another rounding mode is set on entry.
+   Method (large arguments):
+	1. Argument Reduction: given the input x, find r and integer k
+	   and j such that
+	             x = (k+j/64)*(ln2) + r,  |r| <= (1/128)*ln2
+
+	2. exp(x) = 2^k * (2^(j/64) + 2^(j/64)*expm1(r))
+	   a. expm1(r) is approximated by a polynomial:
+	      expm1(r) ~ r + t1*r^2 + t2*r^3 + ... + t5*r^6
+	      Here t1 = 1/2 exactly.
+	   b. 2^(j/64) is represented to twice double precision
+	      as TBL[2j]+TBL[2j+1].
+
+   Note: If divide were fast enough, we could use another approximation
+	 in 2.a:
+	      expm1(r) ~ (2r)/(2-R), R = r - r^2*(t1 + t2*r^2)
+	      (for the same t1 and t2 as above)
+
+   Special cases:
+	exp(INF) is INF, exp(NaN) is NaN;
+	exp(-INF)=  0;
+	for finite argument, only exp(0)=1 is exact.
+
+   Accuracy:
+	According to an error analysis, the error is always less than
+	an ulp (unit in the last place).  The largest errors observed
+	are less than 0.55 ulp for normal results and less than 0.75 ulp
+	for subnormal results.
+
+   Misc. info.
+	For IEEE double
+		if x >  7.09782712893383973096e+02 then exp(x) overflow
+		if x < -7.45133219101941108420e+02 then exp(x) underflow.  */
+
 #include <math.h>
+#include <math-svid-compat.h>
+#include <math_private.h>
+#include <errno.h>
 #include "endian.h"
 #include "uexp.h"
+#include "uexp.tbl"
 #include "mydefs.h"
 #include "MathLib.h"
-#include "uexp.tbl"
-#include <math_private.h>
 #include <fenv.h>
 #include <float.h>
 
-#ifndef SECTION
-# define SECTION
-#endif
+extern double __ieee754_exp (double);
+
+#include "eexp.tbl"
+
+static const double
+  half = 0.5,
+  one = 1.0;
 
-double __slowexp (double);
 
-/* An ultimate exp routine. Given an IEEE double machine number x it computes
-   the correctly rounded (to nearest) value of e^x.  */
 double
-SECTION
-__ieee754_exp (double x)
+__ieee754_exp (double x_arg)
 {
-  double bexp, t, eps, del, base, y, al, bet, res, rem, cor;
-  mynumber junk1, junk2, binexp = {{0, 0}};
-  int4 i, j, m, n, ex;
+  double z, t;
   double retval;
-
+  int hx, ix, k, j, m;
+  union
   {
-    SET_RESTORE_ROUND (FE_TONEAREST);
-
-    junk1.x = x;
-    m = junk1.i[HIGH_HALF];
-    n = m & hugeint;
-
-    if (n > smallint && n < bigint)
-      {
-	y = x * log2e.x + three51.x;
-	bexp = y - three51.x;	/*  multiply the result by 2**bexp        */
-
-	junk1.x = y;
-
-	eps = bexp * ln_two2.x;	/* x = bexp*ln(2) + t - eps               */
-	t = x - bexp * ln_two1.x;
-
-	y = t + three33.x;
-	base = y - three33.x;	/* t rounded to a multiple of 2**-18      */
-	junk2.x = y;
-	del = (t - base) - eps;	/*  x = bexp*ln(2) + base + del           */
-	eps = del + del * del * (p3.x * del + p2.x);
-
-	binexp.i[HIGH_HALF] = (junk1.i[LOW_HALF] + 1023) << 20;
-
-	i = ((junk2.i[LOW_HALF] >> 8) & 0xfffffffe) + 356;
-	j = (junk2.i[LOW_HALF] & 511) << 1;
-
-	al = coar.x[i] * fine.x[j];
-	bet = ((coar.x[i] * fine.x[j + 1] + coar.x[i + 1] * fine.x[j])
-	       + coar.x[i + 1] * fine.x[j + 1]);
-
-	rem = (bet + bet * eps) + al * eps;
-	res = al + rem;
-	cor = (al - res) + rem;
-	if (res == (res + cor * err_0))
+    int i_part[2];
+    double x;
+  } xx;
+  union
+  {
+    int y_part[2];
+    double y;
+  } yy;
+  xx.x = x_arg;
+
+  ix = xx.i_part[HIGH_HALF];
+  hx = ix & ~0x80000000;
+
+  if (hx < 0x3ff0a2b2)
+    {				/* |x| < 3/2 ln 2 */
+      if (hx < 0x3f862e42)
+	{			/* |x| < 1/64 ln 2 */
+	  if (hx < 0x3ed00000)
+	    {			/* |x| < 2^-18 */
+	      if (hx < 0x3e300000)
+		{
+		  {
+		    SET_RESTORE_ROUND (FE_TONEAREST);
+		    retval = one + xx.x;
+		  }
+		  return retval;
+		}
+	      {
+		SET_RESTORE_ROUND (FE_TONEAREST);
+		retval = one + xx.x * (one + half * xx.x);
+	      }
+	      return retval;
+	    }
 	  {
-	    retval = res * binexp.x;
-	    goto ret;
+	    SET_RESTORE_ROUND (FE_TONEAREST);
+	    t = xx.x * xx.x;
+	    yy.y = xx.x + (t * (half + xx.x * t2)
+			     + (t * t) * (t3 + xx.x * t4 + t * t5));
+	    retval = one + yy.y;
 	  }
-	else
-	  {
-	    retval = __slowexp (x);
-	    goto ret;
-	  }			/*if error is over bound */
-      }
+	  return retval;
+	}
 
-    if (n <= smallint)
+      /* Find the multiple of 2^-6 nearest x.  */
+      k = hx >> 20;
+      j = (0x00100000 | (hx & 0x000fffff)) >> (0x40c - k);
+      j = (j - 1) & ~1;
+      if (ix < 0)
+	j += 134;
       {
-	retval = 1.0;
-	goto ret;
+	SET_RESTORE_ROUND (FE_TONEAREST);
+	z = xx.x - TBL2[j];
+	t = z * z;
+	yy.y = z + (t * (half + (z * t2))
+		    + (t * t) * (t3 + z * t4 + t * t5));
+	retval = TBL2[j + 1] + TBL2[j + 1] * yy.y;
       }
+      return retval;
+    }
 
-    if (n >= badint)
-      {
-	if (n > infint)
-	  {
-	    retval = x + x;
-	    goto ret;
-	  }			/* x is NaN */
-	if (n < infint)
-	  {
-	    if (x > 0)
-	      goto ret_huge;
-	    else
-	      goto ret_tiny;
-	  }
-	/* x is finite,  cause either overflow or underflow  */
-	if (junk1.i[LOW_HALF] != 0)
-	  {
-	    retval = x + x;
-	    goto ret;
-	  }			/*  x is NaN  */
-	retval = (x > 0) ? inf.x : zero;	/* |x| = inf;  return either inf or 0 */
-	goto ret;
-      }
+  if (hx >= 0x40862e42)
+    {				/* x is large, infinite, or nan.  */
+      if (hx >= 0x7ff00000)
+	{
+	  if (ix == 0xfff00000 && xx.i_part[LOW_HALF] == 0)
+	    return zero;	/* exp(-inf) = 0.  */
+	  return (xx.x * xx.x);	/* exp(nan/inf) is nan or inf.  */
+	}
+      if (xx.x > threshold1)
+	{			/* Set overflow error condition.  */
+	  retval = hhuge * hhuge;
+	  return retval;
+	}
+      if (-xx.x > threshold2)
+	{			/* Set underflow error condition.  */
+	  double force_underflow = tiny * tiny;
+	  math_force_eval (force_underflow);
+	  retval = force_underflow;
+	  return retval;
+	}
+    }
 
-    y = x * log2e.x + three51.x;
-    bexp = y - three51.x;
-    junk1.x = y;
-    eps = bexp * ln_two2.x;
-    t = x - bexp * ln_two1.x;
-    y = t + three33.x;
-    base = y - three33.x;
-    junk2.x = y;
-    del = (t - base) - eps;
-    eps = del + del * del * (p3.x * del + p2.x);
-    i = ((junk2.i[LOW_HALF] >> 8) & 0xfffffffe) + 356;
-    j = (junk2.i[LOW_HALF] & 511) << 1;
-    al = coar.x[i] * fine.x[j];
-    bet = ((coar.x[i] * fine.x[j + 1] + coar.x[i + 1] * fine.x[j])
-	   + coar.x[i + 1] * fine.x[j + 1]);
-    rem = (bet + bet * eps) + al * eps;
-    res = al + rem;
-    cor = (al - res) + rem;
-    if (m >> 31)
-      {
-	ex = junk1.i[LOW_HALF];
-	if (res < 1.0)
-	  {
-	    res += res;
-	    cor += cor;
-	    ex -= 1;
-	  }
-	if (ex >= -1022)
-	  {
-	    binexp.i[HIGH_HALF] = (1023 + ex) << 20;
-	    if (res == (res + cor * err_0))
-	      {
-		retval = res * binexp.x;
-		goto ret;
-	      }
-	    else
-	      {
-		retval = __slowexp (x);
-		goto check_uflow_ret;
-	      }			/*if error is over bound */
-	  }
-	ex = -(1022 + ex);
-	binexp.i[HIGH_HALF] = (1023 - ex) << 20;
-	res *= binexp.x;
-	cor *= binexp.x;
-	eps = 1.0000000001 + err_0 * binexp.x;
-	t = 1.0 + res;
-	y = ((1.0 - t) + res) + cor;
-	res = t + y;
-	cor = (t - res) + y;
-	if (res == (res + eps * cor))
-	  {
-	    binexp.i[HIGH_HALF] = 0x00100000;
-	    retval = (res - 1.0) * binexp.x;
-	    goto check_uflow_ret;
-	  }
-	else
-	  {
-	    retval = __slowexp (x);
-	    goto check_uflow_ret;
-	  }			/*   if error is over bound    */
-      check_uflow_ret:
-	if (retval < DBL_MIN)
-	  {
-	    double force_underflow = tiny * tiny;
-	    math_force_eval (force_underflow);
-	  }
-	if (retval == 0)
-	  goto ret_tiny;
-	goto ret;
-      }
+  {
+    SET_RESTORE_ROUND (FE_TONEAREST);
+    t = invln2_64 * xx.x;
+    if (ix < 0)
+      t -= half;
     else
-      {
-	binexp.i[HIGH_HALF] = (junk1.i[LOW_HALF] + 767) << 20;
-	if (res == (res + cor * err_0))
-	  retval = res * binexp.x * t256.x;
-	else
-	  retval = __slowexp (x);
-	if (isinf (retval))
-	  goto ret_huge;
-	else
-	  goto ret;
-      }
+      t += half;
+    k = (int) t;
+    j = (k & 0x3f) << 1;
+    m = k >> 6;
+    z = (xx.x - k * ln2_64hi) - k * ln2_64lo;
+
+    /* z is now in primary range.  */
+    t = z * z;
+    yy.y = z + (t * (half + z * t2) + (t * t) * (t3 + z * t4 + t * t5));
+    yy.y = TBL[j] + (TBL[j + 1] + TBL[j] * yy.y);
   }
-ret:
-  return retval;
-
- ret_huge:
-  return hhuge * hhuge;
 
- ret_tiny:
-  return tiny * tiny;
+  if (m < -1021)
+    {
+      yy.y_part[HIGH_HALF] += (m + 54) << 20;
+      retval = twom54 * yy.y;
+      if (retval < DBL_MIN)
+	{
+	  double force_underflow = tiny * tiny;
+	  math_force_eval (force_underflow);
+	}
+      return retval;
+    }
+  yy.y_part[HIGH_HALF] += m << 20;
+  return yy.y;
 }
 #ifndef __ieee754_exp
 strong_alias (__ieee754_exp, __exp_finite)
 #endif
 
+#ifndef SECTION
+# define SECTION
+#endif
+
 /* Compute e^(x+xx).  The routine also receives bound of error of previous
    calculation.  If after computing exp the error exceeds the allowed bounds,
    the routine returns a non-positive number.  Otherwise it returns the
diff --git a/sysdeps/ieee754/dbl-64/e_pow.c b/sysdeps/ieee754/dbl-64/e_pow.c
index f6e5fcd..c410b04 100644
--- a/sysdeps/ieee754/dbl-64/e_pow.c
+++ b/sysdeps/ieee754/dbl-64/e_pow.c
@@ -25,7 +25,7 @@ 
 /*             log1                                                        */
 /*             checkint                                                    */
 /* FILES NEEDED: dla.h endian.h mpa.h mydefs.h                             */
-/*               halfulp.c mpexp.c mplog.c slowexp.c slowpow.c mpa.c       */
+/*               halfulp.c mpexp.c mplog.c slowpow.c mpa.c                 */
 /*                          uexp.c  upow.c				   */
 /*               root.tbl uexp.tbl upow.tbl                                */
 /* An ultimate power routine. Given two IEEE double machine numbers y,x    */
diff --git a/sysdeps/ieee754/dbl-64/eexp.tbl b/sysdeps/ieee754/dbl-64/eexp.tbl
new file mode 100644
index 0000000..a4eef22
--- /dev/null
+++ b/sysdeps/ieee754/dbl-64/eexp.tbl
@@ -0,0 +1,255 @@ 
+/* EXP function tables - for use in computing double precision exponential
+   Copyright (C) 2018 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
+
+
+/*
+   TBL[2*j] is 2**(j/64), rounded to nearest.
+   TBL[2*j+1] is 2**(j/64) - TBL[2*j], rounded to nearest.
+   These values are used to approximate exp(x) using the formula
+   given in the comments for e_exp.c.  */
+
+static const double TBL[128] = {
+    0x1.0000000000000p+0,  0x0.0000000000000p+0,
+    0x1.02c9a3e778061p+0, -0x1.19083535b085dp-56,
+    0x1.059b0d3158574p+0,  0x1.d73e2a475b465p-55,
+    0x1.0874518759bc8p+0,  0x1.186be4bb284ffp-57,
+    0x1.0b5586cf9890fp+0,  0x1.8a62e4adc610bp-54,
+    0x1.0e3ec32d3d1a2p+0,  0x1.03a1727c57b52p-59,
+    0x1.11301d0125b51p+0, -0x1.6c51039449b3ap-54,
+    0x1.1429aaea92de0p+0, -0x1.32fbf9af1369ep-54,
+    0x1.172b83c7d517bp+0, -0x1.19041b9d78a76p-55,
+    0x1.1a35beb6fcb75p+0,  0x1.e5b4c7b4968e4p-55,
+    0x1.1d4873168b9aap+0,  0x1.e016e00a2643cp-54,
+    0x1.2063b88628cd6p+0,  0x1.dc775814a8495p-55,
+    0x1.2387a6e756238p+0,  0x1.9b07eb6c70573p-54,
+    0x1.26b4565e27cddp+0,  0x1.2bd339940e9d9p-55,
+    0x1.29e9df51fdee1p+0,  0x1.612e8afad1255p-55,
+    0x1.2d285a6e4030bp+0,  0x1.0024754db41d5p-54,
+    0x1.306fe0a31b715p+0,  0x1.6f46ad23182e4p-55,
+    0x1.33c08b26416ffp+0,  0x1.32721843659a6p-54,
+    0x1.371a7373aa9cbp+0, -0x1.63aeabf42eae2p-54,
+    0x1.3a7db34e59ff7p+0, -0x1.5e436d661f5e3p-56,
+    0x1.3dea64c123422p+0,  0x1.ada0911f09ebcp-55,
+    0x1.4160a21f72e2ap+0, -0x1.ef3691c309278p-58,
+    0x1.44e086061892dp+0,  0x1.89b7a04ef80d0p-59,
+    0x1.486a2b5c13cd0p+0,  0x1.3c1a3b69062f0p-56,
+    0x1.4bfdad5362a27p+0,  0x1.d4397afec42e2p-56,
+    0x1.4f9b2769d2ca7p+0, -0x1.4b309d25957e3p-54,
+    0x1.5342b569d4f82p+0, -0x1.07abe1db13cadp-55,
+    0x1.56f4736b527dap+0,  0x1.9bb2c011d93adp-54,
+    0x1.5ab07dd485429p+0,  0x1.6324c054647adp-54,
+    0x1.5e76f15ad2148p+0,  0x1.ba6f93080e65ep-54,
+    0x1.6247eb03a5585p+0, -0x1.383c17e40b497p-54,
+    0x1.6623882552225p+0, -0x1.bb60987591c34p-54,
+    0x1.6a09e667f3bcdp+0, -0x1.bdd3413b26456p-54,
+    0x1.6dfb23c651a2fp+0, -0x1.bbe3a683c88abp-57,
+    0x1.71f75e8ec5f74p+0, -0x1.16e4786887a99p-55,
+    0x1.75feb564267c9p+0, -0x1.0245957316dd3p-54,
+    0x1.7a11473eb0187p+0, -0x1.41577ee04992fp-55,
+    0x1.7e2f336cf4e62p+0,  0x1.05d02ba15797ep-56,
+    0x1.82589994cce13p+0, -0x1.d4c1dd41532d8p-54,
+    0x1.868d99b4492edp+0, -0x1.fc6f89bd4f6bap-54,
+    0x1.8ace5422aa0dbp+0,  0x1.6e9f156864b27p-54,
+    0x1.8f1ae99157736p+0,  0x1.5cc13a2e3976cp-55,
+    0x1.93737b0cdc5e5p+0, -0x1.75fc781b57ebcp-57,
+    0x1.97d829fde4e50p+0, -0x1.d185b7c1b85d1p-54,
+    0x1.9c49182a3f090p+0,  0x1.c7c46b071f2bep-56,
+    0x1.a0c667b5de565p+0, -0x1.359495d1cd533p-54,
+    0x1.a5503b23e255dp+0, -0x1.d2f6edb8d41e1p-54,
+    0x1.a9e6b5579fdbfp+0,  0x1.0fac90ef7fd31p-54,
+    0x1.ae89f995ad3adp+0,  0x1.7a1cd345dcc81p-54,
+    0x1.b33a2b84f15fbp+0, -0x1.2805e3084d708p-57,
+    0x1.b7f76f2fb5e47p+0, -0x1.5584f7e54ac3bp-56,
+    0x1.bcc1e904bc1d2p+0,  0x1.23dd07a2d9e84p-55,
+    0x1.c199bdd85529cp+0,  0x1.11065895048ddp-55,
+    0x1.c67f12e57d14bp+0,  0x1.2884dff483cadp-54,
+    0x1.cb720dcef9069p+0,  0x1.503cbd1e949dbp-56,
+    0x1.d072d4a07897cp+0, -0x1.cbc3743797a9cp-54,
+    0x1.d5818dcfba487p+0,  0x1.2ed02d75b3707p-55,
+    0x1.da9e603db3285p+0,  0x1.c2300696db532p-54,
+    0x1.dfc97337b9b5fp+0, -0x1.1a5cd4f184b5cp-54,
+    0x1.e502ee78b3ff6p+0,  0x1.39e8980a9cc8fp-55,
+    0x1.ea4afa2a490dap+0, -0x1.e9c23179c2893p-54,
+    0x1.efa1bee615a27p+0,  0x1.dc7f486a4b6b0p-54,
+    0x1.f50765b6e4540p+0,  0x1.9d3e12dd8a18bp-54,
+    0x1.fa7c1819e90d8p+0,  0x1.74853f3a5931ep-55};
+
+/* For i = 0, ..., 66,
+     TBL2[2*i] is a double precision number near (i+1)*2^-6, and
+     TBL2[2*i+1] = exp(TBL2[2*i]) to within a relative error less
+     than 2^-60.
+
+   For i = 67, ..., 133,
+     TBL2[2*i] is a double precision number near -(i+1)*2^-6, and
+     TBL2[2*i+1] = exp(TBL2[2*i]) to within a relative error less
+     than 2^-60.  */
+
+static const double TBL2[268] = {
+    0x1.ffffffffffc82p-7,   0x1.04080ab55de32p+0,
+    0x1.fffffffffffdbp-6,   0x1.08205601127ecp+0,
+    0x1.80000000000a0p-5,   0x1.0c49236829e91p+0,
+    0x1.fffffffffff79p-5,   0x1.1082b577d34e9p+0,
+    0x1.3fffffffffffcp-4,   0x1.14cd4fc989cd6p+0,
+    0x1.8000000000060p-4,   0x1.192937074e0d4p+0,
+    0x1.c000000000061p-4,   0x1.1d96b0eff0e80p+0,
+    0x1.fffffffffffd6p-4,   0x1.2216045b6f5cap+0,
+    0x1.1ffffffffff58p-3,   0x1.26a7793f6014cp+0,
+    0x1.3ffffffffff75p-3,   0x1.2b4b58b372c65p+0,
+    0x1.5ffffffffff00p-3,   0x1.3001ecf601ad1p+0,
+    0x1.8000000000020p-3,   0x1.34cb8170b583ap+0,
+    0x1.9ffffffffa629p-3,   0x1.39a862bd3b344p+0,
+    0x1.c00000000000fp-3,   0x1.3e98deaa11dcep+0,
+    0x1.e00000000007fp-3,   0x1.439d443f5f16dp+0,
+    0x1.0000000000072p-2,   0x1.48b5e3c3e81abp+0,
+    0x1.0fffffffffecap-2,   0x1.4de30ec211dfbp+0,
+    0x1.1ffffffffff8fp-2,   0x1.5325180cfacd2p+0,
+    0x1.300000000003bp-2,   0x1.587c53c5a7b04p+0,
+    0x1.4000000000034p-2,   0x1.5de9176046007p+0,
+    0x1.4ffffffffff89p-2,   0x1.636bb9a98322fp+0,
+    0x1.5ffffffffffe7p-2,   0x1.690492cbf942ap+0,
+    0x1.6ffffffffff78p-2,   0x1.6eb3fc55b1e45p+0,
+    0x1.7ffffffffff65p-2,   0x1.747a513dbef32p+0,
+    0x1.8ffffffffffd5p-2,   0x1.7a57ede9ea22ep+0,
+    0x1.9ffffffffff6ep-2,   0x1.804d30347b50fp+0,
+    0x1.affffffffffc3p-2,   0x1.865a7772164aep+0,
+    0x1.c000000000053p-2,   0x1.8c802477b0030p+0,
+    0x1.d00000000004dp-2,   0x1.92be99a09bf1ep+0,
+    0x1.e000000000096p-2,   0x1.99163ad4b1e08p+0,
+    0x1.efffffffffefap-2,   0x1.9f876d8e8c4fcp+0,
+    0x1.fffffffffffd0p-2,   0x1.a61298e1e0688p+0,
+    0x1.0800000000002p-1,   0x1.acb82581eee56p+0,
+    0x1.100000000001fp-1,   0x1.b3787dc80f979p+0,
+    0x1.17ffffffffff8p-1,   0x1.ba540dba56e4fp+0,
+    0x1.1fffffffffffap-1,   0x1.c14b431256441p+0,
+    0x1.27fffffffffc4p-1,   0x1.c85e8d43f7c9bp+0,
+    0x1.2fffffffffffdp-1,   0x1.cf8e5d84758a6p+0,
+    0x1.380000000001fp-1,   0x1.d6db26d16cd84p+0,
+    0x1.3ffffffffffd8p-1,   0x1.de455df80e39bp+0,
+    0x1.4800000000052p-1,   0x1.e5cd799c6a59cp+0,
+    0x1.4ffffffffffc8p-1,   0x1.ed73f240dc10cp+0,
+    0x1.5800000000013p-1,   0x1.f539424d90f71p+0,
+    0x1.5ffffffffffbcp-1,   0x1.fd1de6182f885p+0,
+    0x1.680000000002dp-1,   0x1.02912df5ce741p+1,
+    0x1.7000000000040p-1,   0x1.06a39207f0a2ap+1,
+    0x1.780000000004fp-1,   0x1.0ac660691652ap+1,
+    0x1.7ffffffffff6fp-1,   0x1.0ef9db467dcabp+1,
+    0x1.87fffffffffe5p-1,   0x1.133e45d82e943p+1,
+    0x1.9000000000035p-1,   0x1.1793e4652cc6dp+1,
+    0x1.97fffffffffb3p-1,   0x1.1bfafc47bda48p+1,
+    0x1.a000000000000p-1,   0x1.2073d3f1bd518p+1,
+    0x1.a80000000004ap-1,   0x1.24feb2f105ce2p+1,
+    0x1.affffffffffedp-1,   0x1.299be1f3e7f11p+1,
+    0x1.b7ffffffffffbp-1,   0x1.2e4baacdb6611p+1,
+    0x1.c00000000001dp-1,   0x1.330e587b62b39p+1,
+    0x1.c800000000079p-1,   0x1.37e437282d538p+1,
+    0x1.cffffffffff51p-1,   0x1.3ccd943268248p+1,
+    0x1.d7fffffffff74p-1,   0x1.41cabe304cadcp+1,
+    0x1.e000000000011p-1,   0x1.46dc04f4e5343p+1,
+    0x1.e80000000001ep-1,   0x1.4c01b9950a124p+1,
+    0x1.effffffffff9ep-1,   0x1.513c2e6c73196p+1,
+    0x1.f7fffffffffedp-1,   0x1.568bb722dd586p+1,
+    0x1.0000000000034p+0,   0x1.5bf0a8b1457b0p+1,
+    0x1.03fffffffffe2p+0,   0x1.616b5967376dfp+1,
+    0x1.07fffffffff4bp+0,   0x1.66fc20f0337a9p+1,
+    0x1.0bffffffffffdp+0,   0x1.6ca35859290f5p+1,
+   -0x1.fffffffffffe4p-7,   0x1.f80feabfeefa5p-1,
+   -0x1.ffffffffffb0bp-6,   0x1.f03f56a88b5fep-1,
+   -0x1.7ffffffffffa7p-5,   0x1.e88dc6afecfc5p-1,
+   -0x1.ffffffffffea8p-5,   0x1.e0fabfbc702b8p-1,
+   -0x1.3ffffffffffb3p-4,   0x1.d985c89d041acp-1,
+   -0x1.7ffffffffffe3p-4,   0x1.d22e6a0197c06p-1,
+   -0x1.bffffffffff9ap-4,   0x1.caf42e73a4c89p-1,
+   -0x1.fffffffffff98p-4,   0x1.c3d6a24ed822dp-1,
+   -0x1.1ffffffffffe9p-3,   0x1.bcd553b9d7b67p-1,
+   -0x1.3ffffffffffe0p-3,   0x1.b5efd29f24c2dp-1,
+   -0x1.5fffffffff553p-3,   0x1.af25b0a61a9f4p-1,
+   -0x1.7ffffffffff8bp-3,   0x1.a876812c08794p-1,
+   -0x1.9fffffffffe51p-3,   0x1.a1e1d93d68828p-1,
+   -0x1.bffffffffff6ep-3,   0x1.9b674f8f2f3f5p-1,
+   -0x1.dffffffffff7fp-3,   0x1.95067c7837a0cp-1,
+   -0x1.fffffffffff7ap-3,   0x1.8ebef9eac8225p-1,
+   -0x1.0fffffffffffep-2,   0x1.8890636e31f55p-1,
+   -0x1.1ffffffffff41p-2,   0x1.827a56188975ep-1,
+   -0x1.2ffffffffffbap-2,   0x1.7c7c708877656p-1,
+   -0x1.3fffffffffff8p-2,   0x1.769652df22f81p-1,
+   -0x1.4ffffffffff90p-2,   0x1.70c79eba33c2fp-1,
+   -0x1.5ffffffffffdbp-2,   0x1.6b0ff72deb8aap-1,
+   -0x1.6ffffffffff9ap-2,   0x1.656f00bf5798ep-1,
+   -0x1.7ffffffffff9fp-2,   0x1.5fe4615e98eb0p-1,
+   -0x1.8ffffffffffeep-2,   0x1.5a6fc061433cep-1,
+   -0x1.9fffffffffc4ap-2,   0x1.5510c67cd26cdp-1,
+   -0x1.affffffffff30p-2,   0x1.4fc71dc13566bp-1,
+   -0x1.bfffffffffff0p-2,   0x1.4a9271936fd0ep-1,
+   -0x1.cfffffffffff3p-2,   0x1.45726ea84fb8cp-1,
+   -0x1.dfffffffffff3p-2,   0x1.4066c2ff3912bp-1,
+   -0x1.effffffffff80p-2,   0x1.3b6f1ddd05ab9p-1,
+   -0x1.fffffffffffdfp-2,   0x1.368b2fc6f9614p-1,
+   -0x1.0800000000000p-1,   0x1.31baaa7dca843p-1,
+   -0x1.0ffffffffffa4p-1,   0x1.2cfd40f8bdce4p-1,
+   -0x1.17fffffffff0ap-1,   0x1.2852a760d5ce7p-1,
+   -0x1.2000000000000p-1,   0x1.23ba930c1568bp-1,
+   -0x1.27fffffffffbbp-1,   0x1.1f34ba78d568dp-1,
+   -0x1.2fffffffffe32p-1,   0x1.1ac0d5492c1dbp-1,
+   -0x1.37ffffffff042p-1,   0x1.165e9c3e67ef2p-1,
+   -0x1.3ffffffffff77p-1,   0x1.120dc93499431p-1,
+   -0x1.47fffffffff6bp-1,   0x1.0dce171e34ecep-1,
+   -0x1.4fffffffffff1p-1,   0x1.099f41ffbe588p-1,
+   -0x1.57ffffffffe02p-1,   0x1.058106eb8a7aep-1,
+   -0x1.5ffffffffffe5p-1,   0x1.017323fd9002ep-1,
+   -0x1.67fffffffffb0p-1,   0x1.faeab0ae9386cp-2,
+   -0x1.6ffffffffffb2p-1,   0x1.f30ec837503d7p-2,
+   -0x1.77fffffffff7fp-1,   0x1.eb5210d627133p-2,
+   -0x1.7ffffffffffe8p-1,   0x1.e3b40ebefcd95p-2,
+   -0x1.87fffffffffc8p-1,   0x1.dc3448110dae2p-2,
+   -0x1.8fffffffffb30p-1,   0x1.d4d244cf4ef06p-2,
+   -0x1.97fffffffffefp-1,   0x1.cd8d8ed8ee395p-2,
+   -0x1.9ffffffffffa7p-1,   0x1.c665b1e1f1e5cp-2,
+   -0x1.a7fffffffffdcp-1,   0x1.bf5a3b6bf18d6p-2,
+   -0x1.affffffffff95p-1,   0x1.b86ababeef93bp-2,
+   -0x1.b7fffffffffcbp-1,   0x1.b196c0e24d256p-2,
+   -0x1.bffffffffff32p-1,   0x1.aadde095dadf7p-2,
+   -0x1.c7fffffffff6ap-1,   0x1.a43fae4b047c9p-2,
+   -0x1.cffffffffffb6p-1,   0x1.9dbbc01e182a4p-2,
+   -0x1.d7fffffffffcap-1,   0x1.9751adcfa81ecp-2,
+   -0x1.dffffffffffcdp-1,   0x1.910110be0699ep-2,
+   -0x1.e7ffffffffffbp-1,   0x1.8ac983dedbc69p-2,
+   -0x1.effffffffff88p-1,   0x1.84aaa3b8d51a9p-2,
+   -0x1.f7fffffffffbbp-1,   0x1.7ea40e5d6d92ep-2,
+   -0x1.fffffffffffdbp-1,   0x1.78b56362cef53p-2,
+   -0x1.03fffffffff00p+0,   0x1.72de43ddcb1f2p-2,
+   -0x1.07ffffffffe6fp+0,   0x1.6d1e525bed085p-2,
+   -0x1.0bfffffffffd6p+0,   0x1.677532dda1c57p-2};
+
+static const double
+/* invln2_64 = 64/ln2 - used to scale x to primary range. */
+  invln2_64 = 0x1.71547652b82fep+6,
+/* ln2_64hi = high 32 bits of log(2.)/64. */
+  ln2_64hi = 0x1.62e42fee00000p-7, 
+/* ln2_64lo = remainder bits for log(2.)/64 - ln2_64hi. */
+  ln2_64lo = 0x1.a39ef35793c76p-39,
+/* t2-t5 terms used for polynomial computation.  */
+  t2 = 0x1.5555555555555p-3, /* 1.6666666666526086527e-1 */
+  t3 = 0x1.5555555555555p-5, /* 4.1666666666226079285e-2 */
+  t4 = 0x1.1111111111111p-7, /* 8.3333679843421958056e-3 */
+  t5 = 0x1.6c16c16c16c17p-10, /* 1.3888949086377719040e-3 */
+/* Maximum value for x to not overflow.  */
+  threshold1 = 0x1.62e42fefa39efp+9, /* 7.09782712893383973096e+02 */
+/* Maximum value for -x to not underflow to zero in FE_TONEAREST mode.  */
+  threshold2 = 0x1.74910d52d3051p+9, /* 7.45133219101941108420e+02 */
+/* Scaling factor used when result near zero.  */
+  twom54 = 0x1.0000000000000p-54; /* 5.55111512312578270212e-17 */
diff --git a/sysdeps/ieee754/dbl-64/slowexp.c b/sysdeps/ieee754/dbl-64/slowexp.c
deleted file mode 100644
index ba56174..0000000
--- a/sysdeps/ieee754/dbl-64/slowexp.c
+++ /dev/null
@@ -1,86 +0,0 @@ 
-/*
- * IBM Accurate Mathematical Library
- * written by International Business Machines Corp.
- * Copyright (C) 2001-2018 Free Software Foundation, Inc.
- *
- * This program is free software; you can redistribute it and/or modify
- * it under the terms of the GNU Lesser General Public License as published by
- * the Free Software Foundation; either version 2.1 of the License, or
- * (at your option) any later version.
- *
- * This program is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
- * GNU Lesser General Public License for more details.
- *
- * You should have received a copy of the GNU Lesser General Public License
- * along with this program; if not, see <http://www.gnu.org/licenses/>.
- */
-/**************************************************************************/
-/*  MODULE_NAME:slowexp.c                                                 */
-/*                                                                        */
-/*  FUNCTION:slowexp                                                      */
-/*                                                                        */
-/*  FILES NEEDED:mpa.h                                                    */
-/*               mpa.c mpexp.c                                            */
-/*                                                                        */
-/*Converting from double precision to Multi-precision and calculating     */
-/* e^x                                                                    */
-/**************************************************************************/
-#include <math_private.h>
-
-#include <stap-probe.h>
-
-#ifndef USE_LONG_DOUBLE_FOR_MP
-# include "mpa.h"
-void __mpexp (mp_no *x, mp_no *y, int p);
-#endif
-
-#ifndef SECTION
-# define SECTION
-#endif
-
-/*Converting from double precision to Multi-precision and calculating  e^x */
-double
-SECTION
-__slowexp (double x)
-{
-#ifndef USE_LONG_DOUBLE_FOR_MP
-  double w, z, res, eps = 3.0e-26;
-  int p;
-  mp_no mpx, mpy, mpz, mpw, mpeps, mpcor;
-
-  /* Use the multiple precision __MPEXP function to compute the exponential
-     First at 144 bits and if it is not accurate enough, at 768 bits.  */
-  p = 6;
-  __dbl_mp (x, &mpx, p);
-  __mpexp (&mpx, &mpy, p);
-  __dbl_mp (eps, &mpeps, p);
-  __mul (&mpeps, &mpy, &mpcor, p);
-  __add (&mpy, &mpcor, &mpw, p);
-  __sub (&mpy, &mpcor, &mpz, p);
-  __mp_dbl (&mpw, &w, p);
-  __mp_dbl (&mpz, &z, p);
-  if (w == z)
-    {
-      /* Track how often we get to the slow exp code plus
-	 its input/output values.  */
-      LIBC_PROBE (slowexp_p6, 2, &x, &w);
-      return w;
-    }
-  else
-    {
-      p = 32;
-      __dbl_mp (x, &mpx, p);
-      __mpexp (&mpx, &mpy, p);
-      __mp_dbl (&mpy, &res, p);
-
-      /* Track how often we get to the uber-slow exp code plus
-	 its input/output values.  */
-      LIBC_PROBE (slowexp_p32, 2, &x, &res);
-      return res;
-    }
-#else
-  return (double) __ieee754_expl((long double)x);
-#endif
-}
diff --git a/sysdeps/m68k/m680x0/fpu/slowexp.c b/sysdeps/m68k/m680x0/fpu/slowexp.c
deleted file mode 100644
index 1cc8931..0000000
--- a/sysdeps/m68k/m680x0/fpu/slowexp.c
+++ /dev/null
@@ -1 +0,0 @@ 
-/* Not needed.  */
diff --git a/sysdeps/powerpc/power4/fpu/Makefile b/sysdeps/powerpc/power4/fpu/Makefile
index e17d32f..ded9976 100644
--- a/sysdeps/powerpc/power4/fpu/Makefile
+++ b/sysdeps/powerpc/power4/fpu/Makefile
@@ -3,5 +3,4 @@ 
 ifeq ($(subdir),math)
 CFLAGS-mpa.c += --param max-unroll-times=4 -funroll-loops -fpeel-loops
 CPPFLAGS-slowpow.c += -DUSE_LONG_DOUBLE_FOR_MP=1
-CPPFLAGS-slowexp.c += -DUSE_LONG_DOUBLE_FOR_MP=1
 endif
diff --git a/sysdeps/x86_64/fpu/multiarch/Makefile b/sysdeps/x86_64/fpu/multiarch/Makefile
index 0825340..bec45e0 100644
--- a/sysdeps/x86_64/fpu/multiarch/Makefile
+++ b/sysdeps/x86_64/fpu/multiarch/Makefile
@@ -10,7 +10,7 @@  libm-sysdep_routines += s_ceil-sse4_1 s_ceilf-sse4_1 s_floor-sse4_1 \
 
 libm-sysdep_routines += e_exp-fma e_log-fma e_pow-fma s_atan-fma \
 			e_asin-fma e_atan2-fma s_sin-fma s_tan-fma \
-			mplog-fma mpa-fma slowexp-fma slowpow-fma \
+			mplog-fma mpa-fma slowpow-fma \
 			sincos32-fma doasin-fma dosincos-fma \
 			halfulp-fma mpexp-fma \
 			mpatan2-fma mpatan-fma mpsqrt-fma mptan-fma
@@ -32,7 +32,6 @@  CFLAGS-mpsqrt-fma.c = -mfma -mavx2
 CFLAGS-mptan-fma.c = -mfma -mavx2
 CFLAGS-s_atan-fma.c = -mfma -mavx2
 CFLAGS-sincos32-fma.c = -mfma -mavx2
-CFLAGS-slowexp-fma.c = -mfma -mavx2
 CFLAGS-slowpow-fma.c = -mfma -mavx2
 CFLAGS-s_sin-fma.c = -mfma -mavx2
 CFLAGS-s_tan-fma.c = -mfma -mavx2
@@ -52,7 +51,7 @@  CFLAGS-s_cosf-fma.c = -mfma -mavx2
 
 libm-sysdep_routines += e_exp-fma4 e_log-fma4 e_pow-fma4 s_atan-fma4 \
 			e_asin-fma4 e_atan2-fma4 s_sin-fma4 s_tan-fma4 \
-			mplog-fma4 mpa-fma4 slowexp-fma4 slowpow-fma4 \
+			mplog-fma4 mpa-fma4 slowpow-fma4 \
 			sincos32-fma4 doasin-fma4 dosincos-fma4 \
 			halfulp-fma4 mpexp-fma4 \
 			mpatan2-fma4 mpatan-fma4 mpsqrt-fma4 mptan-fma4
@@ -74,14 +73,13 @@  CFLAGS-mpsqrt-fma4.c = -mfma4
 CFLAGS-mptan-fma4.c = -mfma4
 CFLAGS-s_atan-fma4.c = -mfma4
 CFLAGS-sincos32-fma4.c = -mfma4
-CFLAGS-slowexp-fma4.c = -mfma4
 CFLAGS-slowpow-fma4.c = -mfma4
 CFLAGS-s_sin-fma4.c = -mfma4
 CFLAGS-s_tan-fma4.c = -mfma4
 
 libm-sysdep_routines += e_exp-avx e_log-avx s_atan-avx \
 			e_atan2-avx s_sin-avx s_tan-avx \
-			mplog-avx mpa-avx slowexp-avx \
+			mplog-avx mpa-avx \
 			mpexp-avx
 
 CFLAGS-e_atan2-avx.c = -msse2avx -DSSE2AVX
@@ -92,7 +90,6 @@  CFLAGS-mpexp-avx.c = -msse2avx -DSSE2AVX
 CFLAGS-mplog-avx.c = -msse2avx -DSSE2AVX
 CFLAGS-s_atan-avx.c = -msse2avx -DSSE2AVX
 CFLAGS-s_sin-avx.c = -msse2avx -DSSE2AVX
-CFLAGS-slowexp-avx.c = -msse2avx -DSSE2AVX
 CFLAGS-s_tan-avx.c = -msse2avx -DSSE2AVX
 endif
 
diff --git a/sysdeps/x86_64/fpu/multiarch/e_exp-avx.c b/sysdeps/x86_64/fpu/multiarch/e_exp-avx.c
index ee5dd6d..afd9174 100644
--- a/sysdeps/x86_64/fpu/multiarch/e_exp-avx.c
+++ b/sysdeps/x86_64/fpu/multiarch/e_exp-avx.c
@@ -1,6 +1,5 @@ 
 #define __ieee754_exp __ieee754_exp_avx
 #define __exp1 __exp1_avx
-#define __slowexp __slowexp_avx
 #define SECTION __attribute__ ((section (".text.avx")))
 
 #include <sysdeps/ieee754/dbl-64/e_exp.c>
diff --git a/sysdeps/x86_64/fpu/multiarch/e_exp-fma.c b/sysdeps/x86_64/fpu/multiarch/e_exp-fma.c
index 6e0fdb7..765b1b9 100644
--- a/sysdeps/x86_64/fpu/multiarch/e_exp-fma.c
+++ b/sysdeps/x86_64/fpu/multiarch/e_exp-fma.c
@@ -1,6 +1,5 @@ 
 #define __ieee754_exp __ieee754_exp_fma
 #define __exp1 __exp1_fma
-#define __slowexp __slowexp_fma
 #define SECTION __attribute__ ((section (".text.fma")))
 
 #include <sysdeps/ieee754/dbl-64/e_exp.c>
diff --git a/sysdeps/x86_64/fpu/multiarch/e_exp-fma4.c b/sysdeps/x86_64/fpu/multiarch/e_exp-fma4.c
index ae6eb67..9ac7aca 100644
--- a/sysdeps/x86_64/fpu/multiarch/e_exp-fma4.c
+++ b/sysdeps/x86_64/fpu/multiarch/e_exp-fma4.c
@@ -1,6 +1,5 @@ 
 #define __ieee754_exp __ieee754_exp_fma4
 #define __exp1 __exp1_fma4
-#define __slowexp __slowexp_fma4
 #define SECTION __attribute__ ((section (".text.fma4")))
 
 #include <sysdeps/ieee754/dbl-64/e_exp.c>
diff --git a/sysdeps/x86_64/fpu/multiarch/slowexp-avx.c b/sysdeps/x86_64/fpu/multiarch/slowexp-avx.c
deleted file mode 100644
index d01c6d7..0000000
--- a/sysdeps/x86_64/fpu/multiarch/slowexp-avx.c
+++ /dev/null
@@ -1,9 +0,0 @@ 
-#define __slowexp __slowexp_avx
-#define __add __add_avx
-#define __dbl_mp __dbl_mp_avx
-#define __mpexp __mpexp_avx
-#define __mul __mul_avx
-#define __sub __sub_avx
-#define SECTION __attribute__ ((section (".text.avx")))
-
-#include <sysdeps/ieee754/dbl-64/slowexp.c>
diff --git a/sysdeps/x86_64/fpu/multiarch/slowexp-fma.c b/sysdeps/x86_64/fpu/multiarch/slowexp-fma.c
deleted file mode 100644
index 6fffca1..0000000
--- a/sysdeps/x86_64/fpu/multiarch/slowexp-fma.c
+++ /dev/null
@@ -1,9 +0,0 @@ 
-#define __slowexp __slowexp_fma
-#define __add __add_fma
-#define __dbl_mp __dbl_mp_fma
-#define __mpexp __mpexp_fma
-#define __mul __mul_fma
-#define __sub __sub_fma
-#define SECTION __attribute__ ((section (".text.fma")))
-
-#include <sysdeps/ieee754/dbl-64/slowexp.c>
diff --git a/sysdeps/x86_64/fpu/multiarch/slowexp-fma4.c b/sysdeps/x86_64/fpu/multiarch/slowexp-fma4.c
deleted file mode 100644
index 3bcde84..0000000
--- a/sysdeps/x86_64/fpu/multiarch/slowexp-fma4.c
+++ /dev/null
@@ -1,9 +0,0 @@ 
-#define __slowexp __slowexp_fma4
-#define __add __add_fma4
-#define __dbl_mp __dbl_mp_fma4
-#define __mpexp __mpexp_fma4
-#define __mul __mul_fma4
-#define __sub __sub_fma4
-#define SECTION __attribute__ ((section (".text.fma4")))
-
-#include <sysdeps/ieee754/dbl-64/slowexp.c>