If you are mining Grin, supported only in the very latest Bminer release, it uses some variation of Cuckoo Cycle that will require "cuckaroo29" as you point out.
I suppose this will be yet another algorithm to add. To make it even more complex it looks like Grin supports GPU mining via CuckaRoo29, but also ASIC mining via CuckaToo31.
Green will not support asik, and a fork is scheduled for a turn every 6 months.
C29 ~ 5.5-6 gb Ram GPU
C31 ~ 10.5-11 gb ram GPU
C32, C33 and so on
https://www.grin-forum.org/t/what-to-mine-choosing-between-cuckatoo31-and-cuckaroo29/1732