8360559: Optimize Math.sinh for x86 64 bit platforms

[missa-prime]

The goal of this PR is to implement an x86_64 intrinsic for java.lang.Math.sinh() using libm. There is a new set of micro-benchmarks are included to check the performance of specific input value ranges to help prevent regressions in the future.

The command to run all range specific micro-benchmarks is posted below.

make test TEST="micro:SinhPerf.SinhPerfRanges"

The results of all tests posted below were captured with an Intel® Xeon 8488C using OpenJDK v26-b4 as the baseline version.

For performance data collected with the new built in range micro-benchmark, see the table below. Each result is the mean of 8 individual runs, and the input ranges used match those from the original Java implementation. Overall, the intrinsic provides an an average uplift of 64% when input values fall into the middle three ranges where heavy computation is required. However, very small inputs and very large inputs show drops of 74% and 66% respectively.

Input range(s)	Baseline throughput (ops/ms)	Intrinsic throughput (ops/ms)	Speedup
[-2^(-28), 2^(-28)]	844160	216029	0.26x
[-22, -2^(-28)], [2^(-28), 22]	81662	157351	1.93x
[-709.78, -22], [22, 709.78]	119075	167635	1.41x
[-710.48, -709.78], [709.78, 710.48]	111636	177125	1.59x
(-INF, -710.48], [710.48, INF)	959296	313839	0.33x

Finally, the jtreg:test/jdk/java/lang/Math/HyperbolicTests.java test passed with the changes.

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• JDK-8360559: Optimize Math.sinh for x86 64 bit platforms (Enhancement - P4)

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[mlbridge]

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[fweimer-rh]

Isn't this effectively a libm benchmark (where the sinh implementation resides)? Please include the libm version for reference here. Thanks.

[jddarcy]

Are there plans for a cosh intrinsic as follow-up work? There was a previous effort to intrinsify tanh.

[jddarcy]

A large fraction of floating-point numbers are in the [-2^(-28), 2^(-28)] range where there is a performance degradation with the new implementation.

What is the expected distribution of arguments to sinh?

[missa-prime]

A large fraction of floating-point numbers are in the [-2^(-28), 2^(-28)] range where there is a performance degradation with the new implementation.

What is the expected distribution of arguments to sinh?

I don't know about an expected distribution of distribution of arguments to sinh. From glancing through research papers though, I get the sense that the [-2^(-28), 2^(-28)] range isn't used all that much. A couple of papers showing this are linked below.

1. An Analysis of the Hyperbolic Bid Stacking Technique's Use in Modeling Power Prices
2. Experimental Validation of a 3GPP compliant 5G-based Positioning System

I think the [-2^(-28), 2^(-28)] range isn't all that interesting for sinh anyway as it just returns the input itself. So, I doubt any applications are relying all that heavily on it.

[missa-prime]

Are there plans for a cosh intrinsic as follow-up work? There was a previous effort to intrinsify tanh.

Yes, the intention is to have cosh as next math intrinsic.

[missa-prime]

Isn't this effectively a libm benchmark (where the sinh implementation resides)? Please include the libm version for reference here. Thanks.

I'm not sure which libm version you're referring to. The only current sinh benchmark I'm aware of is in MathBench.java, and the benchmarks in SinhPerf.java didn't exist until now. Could you clarify?