RFR: 8334755: Asymptotically faster implementation of square root algorithm [v23]

[fabioromano1]

On Fri, 12 Jul 2024 13:06:46 GMT, Raffaello Giulietti <rgiulietti at openjdk.org> wrote:

>> fabioromano1 has updated the pull request incrementally with one additional commit since the last revision:
>> 
>>   Added comment on normalization in MutableBigInteger.sqrtRemZimmermann()
>
> src/java.base/share/classes/java/math/MutableBigInteger.java line 1967:
> 
>> 1965:         MutableBigInteger[] sqrtRem = x.sqrtRemZimmermann(x.intLen, needRemainder);
>> 1966: 
>> 1967:         // Unnormalize
> 
> This unnormalization code, as well as the one in the next method, requires a full explanation, perhaps in abstract, mathematical terms, to help understanding.

The full explanation for the unnormalization is in the second paper, "A proof of GMP square root", par. 3.2 at page 11.

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PR Review Comment: https://git.openjdk.org/jdk/pull/19710#discussion_r1675961884