On Wed, 7 May 2025 09:25:30 GMT, Andrew Haley <[email protected]> wrote:
>> 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?
The idea is mainly that the _EXP_MSK2_ constant operates on the input to match
up with it's corresponding entries in the lookup tables: _rcp_table_,
_cbrt_table_, and _D_table_. The key part starts with computing the difference
(_r = x - x'_) shown in line 260 below.
```c++
__ subsd(xmm1, xmm3);
Here _x_ is essentially the input fraction with all bits while _x'_ is the
input fraction with _EXP_MSK2_ applied. This is then multiplied (_r = (x - x')
* rcp_table(x')_) with the corresponding lookup table entry (_-1 / 1.b1 b2 b3
b4 b5 b6_ where _b6=1_) as shown in line 264 below.
```c++
__ mulsd(xmm1, xmm4);
This value then gets used by subsequent steps that involve entries from
_cbrt_table_ and _D_table_. It won't necessarily round the final result up
though as those effects will depend on what the input is. However, the
polynomial coefficients will have a bigger impact on rounding. For a summary of
the approximations, please refer to the algorithm description comment block
near the beginning of the source file.
-------------
PR Review Comment: https://git.openjdk.org/jdk/pull/24470#discussion_r2087726049
