Apply and mint interest

[RickGriff]

We now have 3 aggregate trackers on the ActivePool, as per the simple compounding specification:

aggRecordedDebt (D)
recordedDebtSum (G)
weightedRecordedDebtSum (S)

G is the original ActivePool debt tracker from Liquity v1. We keep it for now as a) it may be useful for computing a size-weighted average interest rate on the front end, and b) would be needed if we decide to add an emergency base interest rate to every position.

Pseudocode for aggregate trackers in different operations

As in v1, we always apply any redistribution debt gain before handling interest accounting.
The redistribution gain is already included in G before we alter G from the specific operation.

The prefix “old” means the respective debt with no redistribution gains or interest applied, and “new” implies all debt changes (redist. gains, interest, debt drawn/repaid) are included.

openTrove:

D += agg_accrued_interest + trove_debt
S += weighted_trove_debt 
G += trove_debt

closeTrove:

D += (agg_accrued_interest - old_recorded_trove_debt - accrued_trove_interest) // Don’t remove redist. gain here since it was not already applied to D
S -= old_weighted_trove_debt
G -= (old_recorded_trove_debt + redistribution_gain)  // remove redist.gain here since it was already applied to G.

adjustTrove:

D+= agg_accrued_interest +trove_debt_change + redist_debt_gain
S+= (new_weighted_trove_debt - old_weighted_trove_debt)
G+= (new_recorded_trove_debt - old_recorded_trove_debt)

And for the individual Trove:
new_recorded_trove_debt = old_recorded_trove_debt + accrued_trove_interest + trove_debt_change

applyTroveInterestPermissionless:

D += agg_accrued_interest
S += (new_weighted_trove_debt - old_weighted_trove_debt)
G += (new_recorded_trove_debt - old_recorded_trove_debt)

adjustTroveInterestRate:

D+= agg_accrued_interest
S += (new_weighted_trove_debt - old_weighted_trove_debt)
G += (new_recorded_trove_debt - old_recorded_trove_debt)

SP deposit/withdrawal:
D += agg_accrued_interest

Liquidation - Normal Mode, offset

This is effectively the same as closing the Trove:

D+= agg_accrued_interest - old_recorded_trove_debt - accrued_trove_interest
S -= old_weighted_trove_debt
G -= (old_recorded_trove_debt + redist_debt_gain)

Liquidation - Normal Mode, redistribution:

This is effectively the same as closing the Trove, except we add the entire debt to the DefaultPool:

D+= (agg_accrued_interest - old_recorded_trove_debt - accrued_trove_interest)
S -= old_weighted_trove_debt
G -= (old_recorded_trove_debt + redist_debt_gain) 

Also:

DefaultPool.debt += (old_recorded_trove_debt + redistribution_gain + accrued_trove_interest)

TODOs:

** Liquidations in Recovery Mode**

Minting/applying interest has been implemented for RM liquidations to make tests pass, but if we keep RM we should double-check that minting/applying interest is correct for for every logical case of RM.

Redemption:

This is effectively a downward debt adjustment (since we will no longer close Troves on redemption):

D+= agg_accrued_interest - redeemed_debt + redist_debt_gain
S+= (new_weighted_recorded_debt - old_weighted_recorded_debt)
G+= (new_recorded_trove_debt - old_recorded_trove_debt)

This will be implemented in combination with #55 and #48, since these significantly change redemption logic anyway.

Testing TODOs:

• more thorough invariant test (i.e. D + S*delta_t == sum_individual_entire_trove_debts)

[bingen]

Closed in favour of #85