ECIP 1039: Monetary policy rounding specification

Abstract

This ECIP proposes a precise specification for eventual rounding issues around ECIP-1017 Monetary Policy calculation, particularly around

• block winner reward calculation
• block winner reward for including uncles
• block uncle miner reward for having uncles included in the winning block

The content of the proposal deals exclusively with reward calculation beginning with Era 2.

Motivation

[@rtkacyk] In its current form, [ambiguity in the specification] may lead to different interpretations and implementations that may result in a network split in further eras. See these issues for details:

• https://github.com/ethereumproject/go-ethereum/issues/352
• https://github.com/paritytech/parity/issues/6523

Solution

Definitions

• In this document, the mathematic and code symbol / should be understood as a “floor divide,” and any fractions using / (eg. 1/32) should not be interpreted as floating points.

Block winner reward calculation.

Block winner reward calculation for a given era should be rounded down only once. This can be accomplished using exponentiation. In the following specifications around uncles, use of this strategy will be assumed as well.

eg.

eraBlockReward * 4^era / 5^era

Reasoning: a block reward in this case is always singular, and era number is an essentially arbitrary constant (for any given bock). If the block reward for a given era n is rounded n times, the iterative rounding will eventually cause the final reward to atrophy. I see no reason for magnitude of era to “degrade” the singular block reward.

This, as opposed to the example below (which should NOT be used):

rewardReductionConstant = 4/5
maxBlockReward = 5
eraBlockReward = maxBlockReward # Modified below from initial max reward per era

# Here, rounding would happen n times for n eras
for (era in eras) {
    eraBlockReward = eraBlockReward * depreciationConstant
}

See Block winner comparison table for expected rewards. Note that the discrepency would begin in era 22, where a single rounding will yield 46116860184273879, and iterative rounding will yield 46116860184273878.

Uncle rewards

• Rewards for both the winning block miner for including and uncles and the miner of the included uncle(s) should round down the winning block reward prior to division by 32 in the calculation of the uncle(s) “bonus” reward.
• The reward for uncles inclusion should reflect rounding per uncle, as opposed to rounding per “magnitude of uncles,” which to say that an uncles inclusion reward is calculated using 1/32’s (rounded down) of the block winner reward.

Block winner reward for including uncle(s).

• Uncle(s) inclusion reward should be calculated and rounded down prior to addition with the block winner reward.

eg.

blockWinnerReward = blockWinnerRewardAtEra(n) # Block winner reward rounds down once prior to division
uncleInclusionReward = blockWinnerReward / 32 # Block uncle inclusion reward rounds down per uncle

And then either:

for (uncle in includedUncles) {
     blockWinnerReward = blockWinnerReward + uncleInclusionReward
}

Or:

blockWinnerReward = blockWinnerReward + (nIncludedUncles * uncleInlusionReward)

Reasoning: rounding down happens per uncle, since the reward in this case may be for one or two uncles. Otherwise, far in the future when rounding becomes an issue, a winning block with 2 uncles would get a proportionally higher per-uncle reward than a block with just one uncle. Since I don’t see any reason to incentivize including 2 uncles over 1, I think calculation should be done per uncle.

This, as opposed to the example below (which should NOT be used):

uncleInclusionReward = nIncludedUncles/32 * blockWinnerReward

blockWinnerReward = blockWinnerReward + uncleInclusionReward

See Block winner uncles inclusion reward comparison table for expected rewards. Note, for example, that era 22 yields a correct maximum block winner reward 48999163945790995 of 48999163945790996.

Block uncle miner reward for having an uncle(s) included in the winning block.

• Uses uncle(s) inclusion reward calculation as described in Uncle rewards.

Reasoning: Like Block winner reward for including uncles, without rounding per uncle reward calculation, an uncle miner rewarded for 2 included blocks would receive a proportionally higher per-uncle reward than for having only 1 uncle included. There is no reason for such asymmetry.

See Uncle miner inclusion reward comparison table for expected rewards. Note, for example, that era 22 yields a correct maximum uncles miner reward of 2882303761517116, while an incorrect calculation yields 2882303761517117.

Reward tables

Expected overview

Block winner reward comparison

Block winner uncles inclusion reward comparison

This table and the next deal exclusively with the reward for 2 uncles, since that’s the only case where rounding discrepencies will happen. These numbers assume use of the CORRECT block winner reward calculation.

Uncle miner inclusion reward comparison

Like above, this table deals exclusively with the reward for a miner of 2 uncles having those 2 uncles included in the winning block. Inclusion of 2 uncles is the only case where alternate rounding strategies can produce a discrepency, given constant block winner reward rounding.