From b3634449f898bc7a4e024081ac199670cfa5fa5d Mon Sep 17 00:00:00 2001 From: algoidan Date: Thu, 4 Aug 2022 23:09:50 +0300 Subject: [PATCH] fix comment --- dev/ledger.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/dev/ledger.md b/dev/ledger.md index 4b6260d..5ea94a0 100644 --- a/dev/ledger.md +++ b/dev/ledger.md @@ -619,19 +619,19 @@ specific fashion: computing the top $N_{SP}$ accounts by their algo balance is difficult in the presence of pending rewards. Thus, to make this top-$N_{SP}$ calculation more efficient, we choose the top accounts based on a - normalized balance. normalized balance, denoted below by $n_I$. + normalized balance, denoted below by $n_I$. The normalized balance is a hypothetical balance: Consider an account $I$ with current balance $a_I$. If an account had balance $n_I$ in the genesis block, and did not perform any transactions since then, then its balance by the current round (when rewards are included) will be $a_I$, except perhaps due to rounding effects. In more detail, let $r$ be the last round in which a transaction touched account $I$ (and therefore all pending rewards were added to it). Consider the following quantities, as defined in the [Account State](#account-state): - - The raw balance $a_I$ of account $I$ at round $r$ is its total balance. + - The raw balance $a_I$ of account $I$ at round $r$ is its total balance on that round. - The rewards base $a'_I$ is meant to capture the total rewards that were allocated to all accounts upto round $r$, expressed as a fraction of the total stake (with limited precision as described below). Given these two quantities, the normalized balance of an online account $I$ is $a_I/(1+a'_I)$. For example, if the total amount of rewards distributed upto round $r$ is 20% of the total stake, then the normalized balance is $a_I/1.2$. To limit the required precision in this calculation, the system uses a parameter $ru$ that specifies the rewards-earning unit, namely accounts only earn rewards for a whole number of $ru$ microAlgos. (Currently $ru=1,000,000$, so the rewards-earning unit is one Algo.) - The parameter $a'_I$ above is an integer such that $a'_I/ru$ is the desired fraction, rounded down to precision of $1/ru$. The normalized balance is them computed as $n_I = \lfloor a_I \cdot ru / (a'_I + ru) \rfloor$. + The parameter $a'_I$ above is an integer such that $a'_I/ru$ is the desired fraction, rounded down to precision of $1/ru$. The normalized balance is computed as $n_I = \lfloor a_I \cdot ru / (a'_I + ru) \rfloor$. # Transactions