Round off error when using in the EMA

[zawy12]

When converting to and from bits field (aka target) to difficulty, it is important to not make a consistently wrong round off error. For example, if previous difficulty was 100,000, it is important that nothing in the code make it consistently +50 more or consistently -50 less (0.05% error). That would cause the EMA at N=70 to have 3.5% error in solvetime. At 0.5% error per block, there is 35% error in the solvetimes (difficulty is 30% too high or low). The error that develops from 0.5% and using N=70 seems to be based on about 1.005^70 = 41%. Larger N means larger error from "round off". If half the time it is +1,000 too high and the other half -1,000 too low, then it's OK. just don't be consistently wrong in the same direction. Error in the value for e=2.7183 does not hurt it.

In an simple average (SMA), a multiplicative error like this only causes a proportional error in solvetime, not a compounded error. The error in EMA only compounds for N, not for the number of blocks.

There is a T/solvetime ratio in two places. It must be the same in both places. I don't know how it would be coded to give something different, but I want to keep an eye out for anything fragile in it.