33 lines
1.2 KiB
Markdown
33 lines
1.2 KiB
Markdown
---
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# katex
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title: running average
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...
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The running average $a_n$ of a series $R_n$
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$$a_n =\frac{a\_{n-1}\times u+R_n\times v}{u+v}$$
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The larger $u$ and the smaller $v$, the longer the period over which the running average is taken.
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We don’t want to do floating point arithmetic, because different peers
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might get different answers.
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It is probably harmless if they get different answers, provided that this
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happens rarely, but easier to ensure that this never happens than to try to
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think about all the possible circumstances where this could become a
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problem, where malicious people could contrive inputs to make sure it
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becomes a problem.
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Unsigned integer arithmetic is guaranteed to give the same answers on all
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hardware under all compilers. So, when we can, use unsigned integers.
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$R_n$is a very small integer where we are worried about very small
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differences, so we rescale to represent arithmetic with eight or so bits after
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the binary point in integer arithmetic.
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$\widetilde {a_n}$represents the rescaled running average $a_n$
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$$\widetilde {a_n}=\frac{u\widetilde{a_{n-1}} +v{R_n}\times 2^8}{u+v}$$
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$$a_n = \bigg\lfloor\frac{{\widetilde {a_n}}+2^7}{2^8}\bigg\rfloor$$
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