RFR: 8295010: Reduce if required in EC limbs operations [v4]

[Xue-Lei Andrew Fan]

On Wed, 9 Nov 2022 16:38:38 GMT, Xue-Lei Andrew Fan <xuelei at openjdk.org> wrote:

> > The way I see it is this: as limbs are 64-bit wide, the only place where they can possibly overflow (during the computations they are used for) is the multiplication (including multiply by int and squaring). So I would first try to change the mult() and square() methods only in IntegerPolynomialP256.java (well, in the generator that creates it).
> 
> I agreed. The addition and subtraction operations are limited as well. Each limb cannot exceed 32 bits, otherwise the carry/reduce may not work as far as I can see. It would be good the addition and subtraction was placed in IntegerPolynomialP256.java as well. Otherwise, we have to check the the limits in the caller level, which is error-prone.
> 
> I will think about how to make this suggestion right. It may be another PR for the restructure.
> 

I had a further look at the current code structure.  The addition counter status is maintained in the caller level (IntegerPolynomial.java).  It is possible to re-org the code (the generator), but we may not like the scale of the update. It may not be the purpose of this update. I would like to defer to a separated PR later and keep this PR focus on performance improvement.

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PR: https://git.openjdk.org/jdk/pull/10624