RFR: 8321939: [GenShen] ShenandoahOldEvacRatioPercent=100 fails with divide-by-zero [v2]

[Y. Srinivas Ramakrishna]

On Wed, 13 Dec 2023 21:43:52 GMT, Y. Srinivas Ramakrishna <ysr at openjdk.org> wrote:

>> src/hotspot/share/gc/shenandoah/shenandoahGeneration.cpp line 269:
>> 
>>> 267:   //            SOEP/100 = OE/TE
>>> 268:   //                     = OE/(OE+YE)
>>> 269:   //  => SOEP/(100-SOEP) = OE/((OE+YE)-OE)
>> 
>> I get lost at this step.  Here's how I see the algebra from this point forward:
>>   (OE + YE) * SOEP == 100 OE         (multiply both sides by 100 (OE + YE)
>>   YE * SOEP = 100 OE - SOEP * OE (subtract SOEP * OE from both sides)
>>   YE * SOEP = OE * (100 - SOEP)
>>   OE = YE * SOEP / (100 - SOEP)
>>   
>>   (we agree on final result.  I just don't follow the justification for step at line 269.  maybe you can explain that line better?)
>
> ah, yes, I used the so-called "componendo-dividendo" rule from middle school, in this instantiation of the more general schema:
> 
> If a/b = c/d, then a/(b-a) = c/(d-c)
> 
> It is perhaps not very well-known in modern ratio-proportion pedagogy in grade-school, but is very useful for quick arithemtic.
> 
> https://hsm.stackexchange.com/questions/7544/etymology-of-some-terms-used-in-ratio-and-proportion-in-old-algebra-textbooks

I'll add the justification in the comment.

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PR Review Comment: https://git.openjdk.org/shenandoah/pull/369#discussion_r1425924525