On Mon, 28 Jul 2025 14:03:16 GMT, fabioromano1 <d...@openjdk.org> wrote:
>> This PR implements nth root computation for BigIntegers using Newton method.
>
> fabioromano1 has updated the pull request incrementally with one additional
> commit since the last revision:
>
> Zimmermann suggestion
src/java.base/share/classes/java/math/MutableBigInteger.java line 2002:
> 2000: // Try to shift as many bits as possible
> 2001: // without losing precision in double's representation.
> 2002: if (bitLength - (sh - shExcess) <= Double.MAX_EXPONENT) {
Here's an example of what I mean by "documenting the details"
Suggestion:
if (bitLength - (sh - shExcess) <= Double.MAX_EXPONENT) {
/*
* Let x = this, P = Double.PRECISION, ME = Double.MAX_EXPONENT,
* bl = bitLength, ex = shExcess, sh' = sh - ex
*
* We have
* bl - (sh - ex) ≤ ME ⇔ bl - (bl - P - ex) ≤ ME ⇔ ex
≤ ME - P
* hence, recalling x < 2^bl
* x 2^(-sh') = x 2^(ex-sh) = x 2^(-bl+ex+P) = x 2^(-bl)
2^(ex+P)
* < 2^(ex+P) ≤ 2^ME < Double.MAX_VALUE
* Thus, x 2^(-sh') is in the range of finite doubles.
* All the more so, this holds for ⌊x / 2^sh'⌋ ≤ x 2^(-sh'),
* which is what is computed below.
*/
Without this, the reader has to reconstruct this "proof", which is arguably
harder than just verifying its correctness.
OTOH, the statement "Adjust shift to a multiple of n" in the comment below is
rather evident, and IMO does not need further explanations (but "mileage may
vary" depending on the reader).
-------------
PR Review Comment: https://git.openjdk.org/jdk/pull/24898#discussion_r2239411008
