For the flat-curve CFMM swap, the LP tokens are created by this simple formula:
LP_token_amount = amount_token_A + amount_token_B
The weekly reward amount gets distributed to stakers in the farm. Depending on the farm there can be different reward types with different distribution formulas.
|1||Flat incentive||The rewards are allocated over time, proportionally to the user's stake in the farm and the weekly reward. This is how most farms work.|
|2||Long-term inventive||The the weight of a user's stake is are growing over time, up to the maximum at 180 days age of the stake. More details below. The goal is to incentivise long term staking.|
Farms have a defined reward distribution per period. this can be weeks, days and for calculation purposes typically seconds.
rewards_per_week rewards_per_day = rewards_per_week / 7 rewards_per_second = rewards_per_day / (24 * 60 *60)
At any time a user's
token_fraction is equal to
token_fraction = number_staked_LP_tokens_of_user / number_LP_tokens_total
The calculation of a user's rewards
reward_payout is straightforward for any time period
time_period_in_seconds where the
rewards_per_second stay constant.
period_reward_payout[i] = token_fraction[i] * time_period_in_seconds[i] * rewards_per_second[i]
aggregated_reward_payout is just the sum of the
aggregated_reward_payout[i] = aggregated_reward_payout[i-1] + period_reward_payout[i]
Whenever either of
rewards_per_second need to be recalculated, the above formula can be re-applied.
The unweighted reward payout
aggregated_reward_payout is as in the flat incentive case above.
now and timestamp
ts_applied have seconds as units.
now is expressed as the current Unix Epoch time.
max_release_days = 180max_release_seconds = max_release_days * 24 * 60 *60 = 15,552,000
To calculate the age at a given time
age_current, the formula is as follows:
age_current = MIN(max_release_seconds, now - ts_applied)
The weight at a given time
weight_current = age_current/max_release_seconds
The number of LP tokens a user has in the pool at a given moment are called
Upon adding more LP tokens to the pool, the applied age
number_LP_tokens_current get updated.
age_applied = (number_LP_tokens_current * age_current + number_LP_tokens_added * 0) / (number_LP_tokens_current + number_LP_tokens_added)number_LP_tokens_current = number_LP_tokens_current + number_LP_tokens_added
As a consequence the applied timestamp
ts_applied is updated as follows:
ts_applied = now - age_applied
number_LP_tokens_current previously was 0, then
age_applied = 0
ts_applied = now
When claiming rewards, the claim which gets paid out is
weighted_aggregate_reward_payout. It is calculated as:
weighted_aggregate_reward_payout = aggregated_reward_payout * weight_current
Furthermore, the residual of
aggregated_reward_payout - weighted_aggregate_reward_payout is distributed to the ongoing participants in the farm, proportional to their
Finally the claiming user's
aggregated_reward_payout gets reset.
aggregated_reward_payout = 0
When claiming without withdrawing LP tokens, the applied timestamp
ts_applied remains unchanged.
A user's stake of LP tokens can only be withdrawn in full and upon withdrawing, the
aggregated_reward_payout is calculated and the rewards are automatically claimed and the residual rewards are distributed to the farm.