RFR: 8360559: Optimize Math.sinh for x86 64 bit platforms [v2]

[Srinivas Vamsi Parasa]

On Thu, 17 Jul 2025 18:46:06 GMT, Mohamed Issa <missa at openjdk.org> wrote:

>> 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](https://advisor.cloudzero.com/aws/ec2/r7i.metal-24xl) using [OpenJDK v26-b4](https://github.com/openjdk/jdk/releases/tag/jdk-26%2B4) 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.
>
> Mohamed Issa has updated the pull request incrementally with one additional commit since the last revision:
> 
>   Move error bound to separate section in comment header

I reviewed the code, ran the benchmarks and correctness test and verified that it's passing. This PR looks good to me.

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Marked as reviewed by sparasa (Author).

PR Review: https://git.openjdk.org/jdk/pull/26152#pullrequestreview-3064160746