Reserves

Reserves definition

A reserves mechanism was introduced to track increases in pool balances. Reserves reflect the last known pool balances - after the last major pool action has been performed ( mint/ burn/ swap/ collect/ flash). Immediately after interaction with the pool, under normal conditions, reserves should have the following values:

reserveToken0 = balanceToken0

reserveToken1 = balanceToken1

Synchronization of reserves and balances after interaction with the pool occurs based on the expected change in balances - using the number of tokens sent or requested by the pool. For example, sending tokens to a user (tokenAmount^{0,1}) causes the next change in the corresponding reserve:

$$reserveToken^{[0,1]}_{new} = reserveToken^{[0,1]}_{old} - tokenAmount^{[0,1]}$$

On the other hand, when (tokenAmount^[0,1]) is received, the reserve is increased accordingly:

$$reserveToke^{[0,1]}_{new} = reserveToken^{[0,1]}_{old} + tokenAmount^{[0,1]}$$

Thus, the value of the reserves at any given moment reflects the number of tokens the pool expects to have on its balance.

Reserves synchronization

At the beginning of the main pool interactions, it is checked whether the pool balances match the expected reserve values. In case of discrepancy, the corresponding token surplus (tokenDelta) is calculated and distributed among active liquidity positions as additional fees if the current liquidityLLis not zero:

$$token0Delta = balanceToken0−reserveToken0$$

$$token1Delta =balanceToken1 − reserveToken1$$

$$totalFeeGrowth1_{new} = totalFeeGrowth_{old} + token1Delta/L$$

$$totalFeeGrowth1_{new} = totalFeeGrowth_{old} + token1Delta/L$$

If current liquidity is zero (L=0), no synchronization occurs until liquidity becomes non-zero.

Thanks to this mechanism it became possible to support token rebase by the Algebra protocol - the pool is able to detect an increase in token balances due to external reasons and distribute the excess tokens among active liquidity providers.

In addition, tokens directly sent to the pool's contract for any reason will not be permanently blocked in the pool, and are distributed among active liquidity positions.

Another advantage of the reserve mechanism, is that it provides the ability to flashloan regardless of current liquidity - it is possible to use flashloan even if the current liquidity in the pool is zero, but there is some amount of tokens on the balance.

Limits

The reserve value for each of the tokens is limited to the maximum value of data type uint128: 2^128−1. This restriction allows us to minimize the cost of gas when interacting with the pool.

However, this restriction means that Algebra Integral does not guarantee full pooling performance when using tokens with totalSupply greater than the maximum value of uint128. For most pool interactions, if the pool interaction results in the reserve exceeding the maximum allowed value, the transaction will be reverted .

In case the maximum allowed reserve is exceeded for external reasons (sending tokens directly to the pool or overpaying in a flashloan), all excess tokens will be sent to AlgebraCommunityVault as communityFee.