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There was generally a 5-10% speed improvement for using a
string.  This is because the cost of recreating the string
by appending was less than the cost of creating an array,
appending the the array, and then joining it back together.

I would recommend trying leaving it as a string, but
changing this:
if readsize > self.min_readsize:
  self.min_readsize = int(self.min_readsize * 1.25)

(or some kind of scaling factor)