Just a comment w.r.t. rounding. The Python way is THE accepted way of rounding in Numerical Analysis! Always rounding n+0.5 (where n is integer) up is biased and makes problems. People have computed long time astronomical calculations and they experienced that our planets leave our solar system. After looking for the cause of the failure of their computations, after a lot of debugging, they found out that this biased rounding was the culprit. After they have changed their code to what is called "round half to even" (Wikipedia) the problem has gone. The rule applies to rounding a digit further right to the decimal point, as well. E.g. 1.005 is rounded down to 1.000 but 1.015 is rounded up to 1.020.
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