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Re: [PATCH] v11 Improves __ieee754_exp() performance by greater than 5x on sparc/x86.

On 2/2/2018 8:40 AM, Szabolcs Nagy wrote:
On 29/01/18 21:44, Patrick McGehearty wrote:
New with this version:
Adds updates sparc and x86_64 libm-test-ulps files (1 ulp for
various exp tests). Rewrite of full comment to reflect current
state of patch.

Summary of patch rationale

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

Typical performance gains are 2x on Sparc s7 and 5x on x86_64.
The former code included a slow path to assure no 1 ulp errors
that could be 50-200 times slower than the normal path.
Informal testing suggests perhaps 1 in 200 values might invoke
the slow path.

Using the glibc_perf tests:
       sparc (nsec)    x86 (nsec)
       old     new     old     new
max   18180   936    4863     275
min     399    96      15      15
mean   5499   419    1336      24

i tested this patch on aarch64 against the current code
with the slow path removed and the later was about 10%
faster on both my throughput and latency benchmarks.
(i also removed the rounding mode settings in both cases
as that can be avoided at least on aarch64)

Removing the rounding mode settings certainly makes a big
difference in performance. When I started, my base code did
not include the rounding mode changes. Unfortunately,
that also generated many more test failures in the non-round-to-nearest
settings, including failures in other ieee754 functions that used
ieee754_exp(). Most platforms do not have a way to avoid the
rounding mode settings, making that option unavailable
for most users of the generic IEEE754 code.

Has there been a serious discussion in the past of to what degree
of accuracy glibc/libm should support other rounding modes than
round-to-nearest?  If a concensus decision were made that
other rounding modes were allowed slightly greater ulp diffs,
we could remove all the rounding mode checks and get
faster code. Failing that concensus, I don't see how we
can bypass the rounding mode checks for the generic code.

so i suggest just removing the slow path first, which
should have good enough error rate and similar performance.

I'll look into comparing removing the slow path on Sparc and
x86, including running my own "10 million values" test to
get a sense of how frequently the slow path is triggered
and what the largest relative error that test observes.
I'll also run timing tests.

May be a little while before I have something to report.

i did some testing and i think it's possible to do the
common case >30% faster with similar table size and around
0.501 ulp error, with a slower path for values close to
overflow/underflow (at least on aarch64, which has
convert-to-nearest-int instruction that does not depend on
rounding mode, i'll see if it can be done in a generic way)

- patrick

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