MinterGateway.updateIndex

$MinterGateway.updateIndex()$

• Calculates and updates $minterIndex$ AND $earnerIndex$ to their current values

  • Distributes excess M, claimable by ZERO holders, in Distribution Vault $excessM = totalOwedM - totalSupply\; of\; M Token,\; if\; totalOwedM > totalSupply\; of\;M$

  • Calculates and updates $minterIndex$: $minterIndex_{now} =fn(minter_{IndexminterIndexLastUpdatedlTimestamp}, rate, now - minterIndexLastUpdatedTimestamp)$

  • Sets $latestMinterRate = minterInterestRateModel.getRate()$

  • Sets $minterIndexLastUpdatedTimestamp = now$

  • Calculates and updates $earnerIndex$ : $earnerIndex_{now}=fn( earnerIndex_{earnerIndexLastUpdatedTimestamp}, rate, now - earnerIndexLastUpdatedTimestamp)$

  • Sets $latestEarnerRate = earnerInterestRateModel.getRate()$

  • Sets $earnerIndexLastUpdatedlTimestamp = now$

NOTE: $index2 = index1 * e(rate *timeElapsed),$ using Pade(4, 4) approximation $timeElapsed = now - indexLastUpdatedTimestamp$, $e(x) = (1 + x/2 + 3(x^2)/28 + x^3/84 + x^4/1680) / (1 - x/2 + 3(x^2)/28 - x^3/84 + x^4/1680)$