RFR: 8355992: Add unsignedMultiplyExact and *powExact methods to Math and StrictMath [v2]

[fabioromano1]

On Fri, 2 May 2025 16:45:28 GMT, Raffaello Giulietti <rgiulietti at openjdk.org> wrote:

> I don't think there's a quick, _precise_ pre-check that would ensure that the loop can just use simple, unchecked `*` multiplications.
> 
> Consider `unsignedPowExact(3L, 40)`, which does not overflow, versus `unsignedPowExact(3L, 41)`, which does. How would you pre-check these two cases using integer arithmetic?
> 
> IMO, you still need checked multiplications in the loop.
> 
> (Besides, the product in your checks can overflow, so you would have to add a guard.)

@rgiulietti

1. `BigInteger.bitLengthForLong(x) * n <= Long.SIZE` is a sufficient condition to ensure no overflow;

2. `(BigInteger.bitLengthForLong(x) - 1L) * n + 1L > Long.SIZE` is a sufficient condition to ensure the overflow.


Thus, there remain only the cases when ` Long.SIZE < BigInteger.bitLengthForLong(x) * n && (BigInteger.bitLengthForLong(x) - 1L) * n + 1L <= Long.SIZE`, in this cases checked multiplications in the loop are needed.
 
Moreover, `BigInteger.bitLengthForLong(x) - 1L` is a `long`, so the product does not overflow, so the condition at point 1 never overflows if it is evaluated only if the condition at point 2 is false.

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PR Review Comment: https://git.openjdk.org/jdk/pull/25003#discussion_r2071904898