RFR: 8334755: Asymptotically faster implementation of square root algorithm [v28]

[Raffaello Giulietti]

On Wed, 17 Jul 2024 13:57:06 GMT, fabioromano1 <duke at openjdk.org> wrote:

>> In fact, if you run this code:
>> `long limit = 1L << 32;
>>  for (long n = 0; n < limit; n++) {
>>       long x = n * n;
>>       if (n != (long) Math.sqrt(x >= 0 ? x : x + 0x1p64)) {
>>           System.out.println(n);
>>       }
>> }`
>> 
>> now you find a lot of counterexamples. The question is: why, until recently, if I did run the same code I could not find a counterexample?
>
> I hope these errors are not due to an implementation change in the virtual machine instructions...

There are no counterexamples for perfect squares if you write `long s = (long) Math.rint(Math.sqrt(x >= 0 ? x : x + 0x1p64));`.

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PR Review Comment: https://git.openjdk.org/jdk/pull/19710#discussion_r1681105600