RFR: 8265768 [aarch64] Use glibc libm impl for dlog, dlog10, dexp iff 2.29 or greater on AArch64.

[Andrew Dinn]

On Thu, 15 Apr 2021 08:33:47 GMT, gregcawthorne <github.com+73799211+gregcawthorne at openjdk.org> wrote:

> Glibc 2.29 onwards provides optimised versions of log,log10,exp.
> These functions have an accuracy of 0.9ulp or better in glibc
> 2.29.
> 
> Therefore this patch adds code to parse, store and check
> the runtime glibcs version in os_linux.cpp/hpp.
> This is then used to select the glibcs implementation of
> log, log10, exp at runtime for c1 and c2, iff we have
> glibc 2.29 or greater.
> 
> This will ensure OpenJDK can benefit from future improvements
> to glibc.
> 
> Glibc adheres to the ieee754 standard, unless stated otherwise
> in its spec.
> 
> As there are no stated exceptions in the current glibc spec
> for dlog, dlog10 and dexp, we can assume they currently follow
> ieee754 (which testing confirms). As such, future version of
> glibc are unlikely to lose this compliance with ieee754 in
> future.
> 
> W.r.t performance this patch sees ~15-30% performance improvements for
> log and log10, with ~50-80% performance improvements for exp for the
> common input ranged (which output real numbers). However for the NaN
> and inf output ranges we see a slow down of up to a factor of 2 for
> some functions and architectures.
> 
> Due to this being the uncommon case we assert that this is a
> worthwhile tradeoff.

> [ One thing: Java uses the term "semi-monotonic" to
> mean "whenever the mathematical function is non-decreasing, so is
> the floating-point approximation, likewise, whenever the
> mathematical function is non-increasing, so is the floating-point
> approximation." I don't really understand what distinction means. ]

I believe this is to allow for the fact that the function is continuous and the floating-point approximation is discrete.

Let F be the actual function and f the floating point approximation.  Assume we have two successive floating point values x, x'  and, without loss of generality, F(x) <= F(x'). What are the circumstances under which we require f(x) =< f(x')? Semi-monotonicity says that is only needed when F is non-decreasing on the interval [x, x']. Expressed more precisely, the condition that F is non-decreasing is

  for all y such that x =< y =< x' : F(x) <= F(y) <= F(x').

In other words:

  if the graph only ever stays level or increases across the interval [x, x'] then we must have f(x) =< f(x')

  If the graph wiggles *up* and *down* across the interval [x, x'] we can allow f(x) > f(x').

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PR: https://git.openjdk.java.net/jdk/pull/3510