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Cosmetics. 

Signed-off-by: Daira Hopwood <daira@jacaranda.org>
This commit is contained in:
Daira Hopwood 2019-02-24 02:05:58 +00:00
parent 4284a49a20
commit 5cf59663d9
1 changed files with 26 additions and 15 deletions
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41
protocol/protocol.tex
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@ -9028,7 +9028,7 @@ Define:
\item $\BlossomPoWTargetSpacingRatio := \hfrac{\PreBlossomPoWTargetSpacing}{\PostBlossomPoWTargetSpacing}$ \item $\BlossomPoWTargetSpacingRatio := \hfrac{\PreBlossomPoWTargetSpacing}{\PostBlossomPoWTargetSpacing}$
\item $\PostBlossomHalvingInterval := \floor{\PreBlossomHalvingInterval \mult \BlossomPoWTargetSpacingRatio}$ \item $\PostBlossomHalvingInterval := \floor{\PreBlossomHalvingInterval \mult \BlossomPoWTargetSpacingRatio}$
\item $\PoWTargetSpacingFunc(\BlockHeight) := \begin{cases} \item $\PoWTargetSpacingFunc(\BlockHeight) := \begin{cases}
\PreBlossomPoWTargetSpacing,&\caseif \text{not} \IsBlossomActivated(\BlockHeight) \\ \PreBlossomPoWTargetSpacing,&\caseif \text{not } \IsBlossomActivated(\BlockHeight) \\
\PostBlossomPoWTargetSpacing,&\caseotherwise \PostBlossomPoWTargetSpacing,&\caseotherwise
\end{cases}$ \end{cases}$
} %blossom } %blossom
@ -9039,8 +9039,9 @@ Define:
\item $\MedianTime(\BlockHeight) := \median(\listcomp{\nTime(i) \for i \from \item $\MedianTime(\BlockHeight) := \median(\listcomp{\nTime(i) \for i \from
\maximum(0, \BlockHeight - \PoWMedianBlockSpan) \upto \BlockHeight - 1})$ \maximum(0, \BlockHeight - \PoWMedianBlockSpan) \upto \BlockHeight - 1})$
\item $\ActualTimespan(\BlockHeight) := \MedianTime(\BlockHeight) - \MedianTime(\BlockHeight - \PoWAveragingWindow)$ \item $\ActualTimespan(\BlockHeight) := \MedianTime(\BlockHeight) - \MedianTime(\BlockHeight - \PoWAveragingWindow)$
\item $\ActualTimespanDamped(\BlockHeight) := \\ \item $\ActualTimespanDamped(\BlockHeight) :=$
\AveragingWindowTimespan\blossom{(\BlockHeight)} + \trunc{\scalebox{0.98}{\hfrac{\ActualTimespan(\BlockHeight) - \AveragingWindowTimespan\blossom{(\BlockHeight)}}{\PoWDampingFactor}}}$ \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 $\ActualTimespanBounded(\BlockHeight) := \bound{\MinActualTimespan\blossom{(\BlockHeight)}}{\MaxActualTimespan\blossom{(\BlockHeight)}}(\ActualTimespanDamped(\BlockHeight))$
\item $\MeanTarget(\BlockHeight) := \begin{cases} \item $\MeanTarget(\BlockHeight) := \begin{cases}
\PoWLimit, \hspace{16em}\text{if } \BlockHeight \leq \PoWAveragingWindow \\ \PoWLimit, \hspace{16em}\text{if } \BlockHeight \leq \PoWAveragingWindow \\
@ -9111,20 +9112,24 @@ in its \blockHeader is defined as $\floor{\hfrac{2^{256}}{\ToTarget(\nBits) + 1}
\crossref{subsidyconcepts} defines the \blockSubsidy, \minerSubsidy,\blossom{ \fundingStreams,} and \crossref{subsidyconcepts} defines the \blockSubsidy, \minerSubsidy,\blossom{ \fundingStreams,} and
\foundersReward. Their amounts in \zatoshi are calculated from the \blockHeight using \foundersReward. Their amounts in \zatoshi are calculated from the \blockHeight using
the formulae below. The constants $\SlowStartInterval$, $\PreBlossomHalvingInterval$, the formulae below.\notbeforeblossom{
\blossom{$\PostBlossomHalvingInterval$, $\BlossomActivationHeight$, }$\MaxBlockSubsidy$,
and $\FoundersFraction$ are instantiated in \crossref{constants}. }The constants $\SlowStartInterval$, $\MaxBlockSubsidy$, $\FoundersFraction$,\notblossom{ and} $\PreBlossomHalvingInterval$,
\blossom{The per-\fundingStream constants $\FundingStreamFraction{i}$, $\FundingStreamStartHeight{i}$, \blossom{$\MaxFundingStreams$, $\PostBlossomHalvingInterval$, and $\BlossomActivationHeight$} are instantiated in \crossref{constants}.
\blossom{The per \fundingStream constants $\FundingStreamFraction{i}$, $\FundingStreamStartHeight{i}$,
and $\FundingStreamEndHeight{i}$ are instantiated in \crossref{fundingstreams}.} and $\FundingStreamEndHeight{i}$ are instantiated in \crossref{fundingstreams}.}
\vspace{1ex}
\begin{formulae} \begin{formulae}
\item $\SlowStartShift \typecolon \Nat := \hfrac{\SlowStartInterval}{2}$ \item $\SlowStartShift \typecolon \Nat := \hfrac{\SlowStartInterval}{2}$
\item $\SlowStartRate \typecolon \Nat := \hfrac{\MaxBlockSubsidy}{\SlowStartInterval}$ \item $\SlowStartRate \typecolon \Nat := \hfrac{\MaxBlockSubsidy}{\SlowStartInterval}$
\vspace{0.5ex}
\item $\Halving(\BlockHeight) := \notblossom{\floor{\hfrac{\BlockHeight - \SlowStartShift}{\PreBlossomHalvingInterval}}} \item $\Halving(\BlockHeight) := \notblossom{\floor{\hfrac{\BlockHeight - \SlowStartShift}{\PreBlossomHalvingInterval}}}
\notbeforeblossom{\begin{cases} \notbeforeblossom{\begin{cases}
\floor{\hfrac{\BlockHeight - \SlowStartShift}{\PreBlossomHalvingInterval}},\hspace{1em}\blossom{\caseif \text{ not } \IsBlossomActivated(\BlockHeight}) \\ \floor{\hfrac{\BlockHeight - \SlowStartShift}{\PreBlossomHalvingInterval}},\hspace{1em}\blossom{\caseif \text{not } \IsBlossomActivated(\BlockHeight)} \\[1.4ex]
\blossom{\floor{\hfrac{\BlossomActivationHeight - \SlowStartShift}{\PreBlossomHalvingInterval} + \hfrac{\BlockHeight - \BlossomActivationHeight}{\PostBlossomHalvingInterval}},}&\blossom{\caseotherwise} \blossom{\floor{\hfrac{\BlossomActivationHeight - \SlowStartShift}{\PreBlossomHalvingInterval} + \hfrac{\BlockHeight - \BlossomActivationHeight}{\PostBlossomHalvingInterval}},}&\blossom{\caseotherwise}
\end{cases}}$ \end{cases}}$
\vspace{0.5ex}
\item $\BlockSubsidy(\BlockHeight) := \begin{cases} \item $\BlockSubsidy(\BlockHeight) := \begin{cases}
\SlowStartRate \mult \BlockHeight,&\caseif \BlockHeight < \hfrac{\SlowStartInterval}{2} \\[1.4ex] \SlowStartRate \mult \BlockHeight,&\caseif \BlockHeight < \hfrac{\SlowStartInterval}{2} \\[1.4ex]
\SlowStartRate \mult (\BlockHeight + 1),&\caseif \hfrac{\SlowStartInterval}{2} \leq \BlockHeight \\[1.4ex] \SlowStartRate \mult (\BlockHeight + 1),&\caseif \hfrac{\SlowStartInterval}{2} \leq \BlockHeight \\[1.4ex]
@ -9137,8 +9142,10 @@ and $\FundingStreamEndHeight{i}$ are instantiated in \crossref{fundingstreams}.}
\end{cases}$ \end{cases}$
\blossom { \blossom {
\item $\FundingStreamValue{i}(\BlockHeight) := \\[1.4ex] \vspace{0.5ex}
\begin{cases} \item $\FundingStreamValue{i}(\BlockHeight) :=$
\vspace{-0.5ex}
\item \tab $\begin{cases}
0,&\caseif \BlockHeight < \BlossomActivationHeight \\ 0,&\caseif \BlockHeight < \BlossomActivationHeight \\
\floor{\BlockSubsidy(\BlockHeight) \mult \FundingStreamFraction{i}},&\caseif \FundingStreamStartHeight{i} \leq \BlockHeight \\ \floor{\BlockSubsidy(\BlockHeight) \mult \FundingStreamFraction{i}},&\caseif \FundingStreamStartHeight{i} \leq \BlockHeight \\
&\text{ and } \BlockHeight < \FundingStreamEndHeight{i} \\ &\text{ and } \BlockHeight < \FundingStreamEndHeight{i} \\
@ -9154,7 +9161,10 @@ and $\FundingStreamEndHeight{i}$ are instantiated in \crossref{fundingstreams}.}
0,&\caseotherwise 0,&\caseotherwise
\end{cases}$ \end{cases}$
\item $\MinerSubsidy(\BlockHeight) := \BlockSubsidy(\BlockHeight) - \FoundersReward(\BlockHeight) \blossom{- \sum_{i = 0}^\text{streams} \FundingStreamValue{i}(\BlockHeight)}$. \item $\MinerSubsidy(\BlockHeight) :=$
\vspace{-1.5ex}
\item \tab $\BlockSubsidy(\BlockHeight) - \FoundersReward(\BlockHeight)
\blossom{\,- \ssum{i = 1}{\MaxFundingStreams} \FundingStreamValue{i}(\BlockHeight)}$.
\end{formulae} \end{formulae}
\introsection \introsection
@ -9249,7 +9259,7 @@ Define:
\end{formulae} \end{formulae}
Let $\RedeemScriptHash(\BlockHeight)$ be the standard redeem script hash, as defined in Let $\RedeemScriptHash(\BlockHeight)$ be the standard redeem script hash, as defined in
\cite{Bitcoin-Multisig}, for the P2SH multisig address with Base58Check representation \cite{Bitcoin-Multisig}, for the P2SH multisig address with Base58Check form
given by $\FounderAddressList_{\,\FounderAddressIndex(\BlockHeight)}$. given by $\FounderAddressList_{\,\FounderAddressIndex(\BlockHeight)}$.
\consensusrule{ \consensusrule{
@ -9293,8 +9303,9 @@ Define:
\begin{formulae} \begin{formulae}
\item $\FundingStreamAddressChangeInterval := \PostBlossomHalvingInterval / 48$ \item $\FundingStreamAddressChangeInterval := \PostBlossomHalvingInterval / 48$
\item $\FundingStreamAddressPeriod(\BlockHeight) := \floor{\hfrac{\BlockHeight + \PostBlossomHalvingInterval - \HeightForHalving(1)}{\FundingStreamAddressChangeInterval}}$ \item $\FundingStreamAddressPeriod(\BlockHeight) := \floor{\hfrac{\BlockHeight + \PostBlossomHalvingInterval - \HeightForHalving(1)}{\FundingStreamAddressChangeInterval}}$
\item $\FundingStreamAddressIndex{i}(\BlockHeight) := \\ \item $\FundingStreamAddressIndex{i}(\BlockHeight) :=$
1 + \FundingStreamAddressPeriod(\BlockHeight) - \FundingStreamAddressPeriod(\FundingStreamStartHeight{i})$. \vspace{-0.5ex}
\item \tab $1 + \FundingStreamAddressPeriod(\BlockHeight) - \FundingStreamAddressPeriod(\FundingStreamStartHeight{i})$.
\end{formulae} \end{formulae}
The number of \transparent addresses per \fundingStream is therefore: The number of \transparent addresses per \fundingStream is therefore:
@ -9308,7 +9319,7 @@ Each address representation in $\FundingStreamAddressList{i}_{\oneto{\FundingStr
denotes a \transparent P2SH multisig address. denotes a \transparent P2SH multisig address.
Let $\RedeemScriptHash_i(\BlockHeight)$ be the standard redeem script hash, as defined in Let $\RedeemScriptHash_i(\BlockHeight)$ be the standard redeem script hash, as defined in
\cite{Bitcoin-Multisig}, for the P2SH multisig address with Base58Check representation \cite{Bitcoin-Multisig}, for the P2SH multisig address with Base58Check form
given by $\FundingStreamAddressList{i}_{\,\FundingStreamAddressIndex{i}(\BlockHeight)}$. given by $\FundingStreamAddressList{i}_{\,\FundingStreamAddressIndex{i}(\BlockHeight)}$.
Recall from \crossref{subsidies} the definition of $\FundingStreamValue{i}$. Recall from \crossref{subsidies} the definition of $\FundingStreamValue{i}$.