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Add type declarations for height in difficulty adjustment functions. 

Signed-off-by: Daira Hopwood <daira@jacaranda.org>
This commit is contained in:
Daira Hopwood 2019-05-01 10:50:10 +01:00
parent 65d43bfac4
commit ea346eaca8
1 changed files with 15 additions and 15 deletions
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30
protocol/protocol.tex
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@ -9009,28 +9009,28 @@ Define:
-\floor{-x},&\caseotherwise
\end{cases}$
\blossom{
\item $\IsBlossomActivated(\BlockHeight) := (\BlockHeight \geq \BlossomActivationHeight)$
\item $\IsBlossomActivated(\BlockHeight \typecolon \Nat) := (\BlockHeight \geq \BlossomActivationHeight)$
\item $\BlossomPoWTargetSpacingRatio := \hfrac{\PreBlossomPoWTargetSpacing}{\PostBlossomPoWTargetSpacing}$
\item $\PostBlossomHalvingInterval := \floor{\PreBlossomHalvingInterval \mult \BlossomPoWTargetSpacingRatio}$
\item $\PoWTargetSpacingFunc(\BlockHeight) := \begin{cases}
\item $\PoWTargetSpacingFunc(\BlockHeight \typecolon \Nat) := \begin{cases}
\PreBlossomPoWTargetSpacing,&\caseif \text{not } \IsBlossomActivated(\BlockHeight) \\
\PostBlossomPoWTargetSpacing,&\caseotherwise
\end{cases}$
} %blossom
\item $\AveragingWindowTimespan\blossom{(\BlockHeight)} := \PoWAveragingWindow \mult \PoWTargetSpacingFunc\blossom{(\BlockHeight)}$
\item $\MinActualTimespan\blossom{(\BlockHeight)} := \floor{\AveragingWindowTimespan\blossom{(\BlockHeight)} \mult (1 - \PoWMaxAdjustUp)}$
\item $\MaxActualTimespan\blossom{(\BlockHeight)} := \floor{\AveragingWindowTimespan\blossom{(\BlockHeight)} \mult (1 + \PoWMaxAdjustDown)}$
\item $\MedianTime(\BlockHeight) := \median(\listcomp{\nTime(i) \for i \from
\maximum(0, \BlockHeight - \PoWMedianBlockSpan) \upto \BlockHeight - 1})$
\item $\ActualTimespan(\BlockHeight) := \MedianTime(\BlockHeight) - \MedianTime(\BlockHeight - \PoWAveragingWindow)$
\item $\ActualTimespanDamped(\BlockHeight) :=$
\item $\AveragingWindowTimespan\blossom{(\BlockHeight \typecolon \Nat)} := \PoWAveragingWindow \mult \PoWTargetSpacingFunc\blossom{(\BlockHeight)}$
\item $\MinActualTimespan\blossom{(\BlockHeight \typecolon \Nat)} := \floor{\AveragingWindowTimespan\blossom{(\BlockHeight)} \mult (1 - \PoWMaxAdjustUp)}$
\item $\MaxActualTimespan\blossom{(\BlockHeight \typecolon \Nat)} := \floor{\AveragingWindowTimespan\blossom{(\BlockHeight)} \mult (1 + \PoWMaxAdjustDown)}$
\item $\MedianTime(\BlockHeight \typecolon \Nat) :=
\median(\listcomp{\nTime(i) \for i \from \maximum(0, \BlockHeight - \PoWMedianBlockSpan) \upto \BlockHeight - 1})$
\item $\ActualTimespan(\BlockHeight \typecolon \Nat) := \MedianTime(\BlockHeight) - \MedianTime(\BlockHeight - \PoWAveragingWindow)$
\item $\ActualTimespanDamped(\BlockHeight \typecolon \Nat) :=$
\vspace{-0.5ex}
\item \tab $\AveragingWindowTimespan\blossom{(\BlockHeight)} + \trunc{\scalebox{0.98}{\hfrac{\ActualTimespan(\BlockHeight) - \AveragingWindowTimespan\blossom{(\BlockHeight)}}{\PoWDampingFactor}}}$
\item $\ActualTimespanBounded(\BlockHeight) := \bound{\MinActualTimespan\blossom{(\BlockHeight)}}{\MaxActualTimespan\blossom{(\BlockHeight)}}(\ActualTimespanDamped(\BlockHeight))$
\item $\MeanTarget(\BlockHeight) := \begin{cases}
\item \tab $\AveragingWindowTimespan\blossom{(\BlockHeight \typecolon \Nat)} + \trunc{\scalebox{0.98}{\hfrac{\ActualTimespan(\BlockHeight) - \AveragingWindowTimespan\blossom{(\BlockHeight)}}{\PoWDampingFactor}}}$
\item $\ActualTimespanBounded(\BlockHeight \typecolon \Nat) := \bound{\MinActualTimespan\blossom{(\BlockHeight)}}{\MaxActualTimespan\blossom{(\BlockHeight)}}(\ActualTimespanDamped(\BlockHeight))$
\item $\MeanTarget(\BlockHeight \typecolon \Nat) := \begin{cases}
\PoWLimit, \hspace{16em}\text{if } \BlockHeight \leq \PoWAveragingWindow \\
\mean(\listcomp{\ToTarget(\nBits(i)) \for i \from \BlockHeight - \PoWAveragingWindow \upto \BlockHeight - 1}),\\
\mean(\listcomp{\!\ToTarget(\nBits(i)) \for i \from \BlockHeight\!-\!\PoWAveragingWindow \upto \BlockHeight\!-\!1\!}),\\
\hspace{20.7em}\text{otherwise.}
\end{cases}$
\end{formulae}
@ -9039,13 +9039,13 @@ Define:
The \targetThreshold for a given \blockHeight $\BlockHeight$ is then calculated as:
\begin{formulae}
\item $\Threshold(\BlockHeight) \hspace{0.43em} := \hspace{0.43em} \begin{cases}
\item $\Threshold(\BlockHeight \typecolon \Nat) \hspace{0.43em} := \begin{cases}
\PoWLimit, \hspace{16em}\text{if } \BlockHeight = 0 \\
\minimum(\PoWLimit, \floor{\hfrac{\MeanTarget(\BlockHeight)}{\AveragingWindowTimespan}}
\mult \ActualTimespanBounded(\BlockHeight)),\\
\hspace{20.7em}\text{otherwise}
\end{cases}$
\item $\ThresholdBits(\BlockHeight) := \ToCompact(\Threshold(\BlockHeight))$.
\item $\ThresholdBits(\BlockHeight \typecolon \Nat) := \ToCompact(\Threshold(\BlockHeight))$.
\end{formulae}
\vspace{-2ex}