RFR: 8353686: Optimize Math.cbrt for x86 64 bit platforms [v3]

[Andrew Haley]

On Tue, 6 May 2025 21:45:34 GMT, Mohamed Issa <duke at openjdk.org> wrote:

>> The goal of this PR is to implement an x86_64 intrinsic for java.lang.Math.cbrt() 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 results of all tests posted below were captured with an [Intel® Xeon 6761P](https://www.intel.com/content/www/us/en/products/sku/241842/intel-xeon-6761p-processor-336m-cache-2-50-ghz/specifications.html) using [OpenJDK v25-b21](https://github.com/openjdk/jdk/releases/tag/jdk-25%2B21) 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 a major uplift of 169% when very small inputs are used and a more modest uplift of 45% for all other inputs.
>> 
>> | Input range(s)                                  | Throughput with baseline (op/s) | Throughput with intrinsic (op/s) | Speedup |
>> | :-------------------------------------: | :----------------------------------: | :----------------------------------: | :---------: |
>> | [-2^(-1022), 2^(-1022)]                   | 6568                                             | 17678                                          | 2.69x       |
>> | (-INF, -2^(-1022)], [2^(-1022), INF) | 138932                                         | 200897                                        | 1.45x       |
>> 
>> Finally, the `jtreg:test/jdk/java/lang/Math/CubeRootTests.java` test passed with the changes.
>
> Mohamed Issa has updated the pull request incrementally with one additional commit since the last revision:
> 
>   Add new set of cbrt micro-benchmarks

src/hotspot/cpu/x86/stubGenerator_x86_64_cbrt.cpp line 62:

> 60: {
> 61:     0, 3220193280
> 62: };

What is this constant?

Its value is 0xbff0400000000000, which is -ve bit set, bias (top bit of exponent) clear, but one of the bits in the fraction is set. So its value is -0x1.04p+0. As well as the exponent it also sets the 1 bit, just below the 5 most significant bits of the fraction. I guess this in effect rounds up the value that is added in the final rounding.

Is that right?

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PR Review Comment: https://git.openjdk.org/jdk/pull/24470#discussion_r2077214995