what is the purpose to use 3 function to compare cost add_path/set_cheapest/get_cheapest_fractional_path

Hello Hackers:
I'm reading the code of optimizer and get confused about the 3
functions. add_path/set_cheapest/get_cheapest_fractional_path

add_(partial_)path:
For every relations, optimizer will build path for it and add then call
add_path to the rel->pathlist. during this stage, *it compare the current
rel->pathlist with the new one, then it may discard it or add it into the
pathlist. finally we may have multi path now. *

*set_cheapest*
after we finished the add_path for each relation, we will call
set_cheapest, *the cheapest is the one with the lowest total cost plus the
parameterized path. *

*get_cheapest_fractional_path*
*after we build the paths for all the relation, it calls
*get_cheapest_fractional_path
to get the best path and then build the plan.

so my question is why do we need to have the 3 cost compare function?

and i have another real case, and hope you can provide some hints:

select * from t1 where slow_func(t1.a, 3) == true; ==> parallel bitmap
index scan.

select * from t1, t2 where t2.pk = 1 and t1.b = t2.b and
slow_function(t1.a, t2.a) == true; ==> I get nest loop without parallel
scan. what I hope is after I get the t2.a (only 1 value), I want to go
with parallel index scan as well.

In this case, which part should I focus on to figure out the issue?

Thanks