RFR: 8077587: BigInteger Roots [v52]

[fabioromano1]

On Tue, 29 Jul 2025 13:03:59 GMT, Raffaello Giulietti <rgiulietti at openjdk.org> wrote:

>>> To the above, we can also add
>>> 
>>> ```
>>>                  * 
>>>                  * Noting that x ≥ 2^(bl-1) and ex ≥ 0, similarly to the above we further get
>>>                  *      x 2^(-sh') ≥ 2^(ex+P-1) ≥ 2^(P-1)
>>>                  * which shows that ⌊x / 2^sh'⌋ has at least P bits of precision.
>>> ```
>> 
>> And this should follow by the fact that `bl - (sh - ex) =  bl - (bl - P - ex) = P + ex`, since `ex ≥ 0`.
>
> My point is that this should be done, not the exact form it takes. Mine or yours are both better than nothing.
> 
> Another point I wanted to make is that the `if` condition bl - (sh - ex) ≤ ME can be replaced with the simpler ex ≤ ME - P, whose right-hand side is a compile time constant.
> 
>> And this should follow by the fact that bl - (sh - ex) =  bl - (bl - P - ex) = P + ex, since ex ≥ 0.
> 
> To show that ⌊x / 2^sh'⌋ has at least P bits of precision, I think you need to make use of x ≥ 2^(bl-1).
> 
> Anyway, I hope I made my point clear: it is better to write proofs rather than relying on readers to reverse-engineer them from the code. Surely, there's no need to be pedantic in every single detail.

@rgiulietti Are there other points that are still not clear?

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PR Review Comment: https://git.openjdk.org/jdk/pull/24898#discussion_r2239834907