Add Liquidity

Add Liquidity
The event of adding liquidity requires the following information from the user:
1. AduA_{du}Adu​
 Amount of token A to be added
2. BduB_{du}Bdu​
 Amount of token B to be added
3. Owner
 After the information was supplied, the add liquidity function will perform the following activities:
1. Calculate factors
1.1 Calculate Option Price 
This happens if i≠0i≠0i=0
. If i=0i=0i=0
 , it is not required to calculate the option price in the very first liquidity provision in a pool. 
For simplicity, let's acknowledge that the option price is a function that required a MarketData{MarketData}MarketData
 and an internal vector (IVIVIV
) as input.
​Pi=fp(IVi−1,MarketDatai)P_i=f_p({IV_{i-1}},{MarketData_i})Pi​=fp​(IVi−1​,MarketDatai​)
 
For more details about the pricing formula or its contract implementation for pricing the options, check this section. 
ABPrice variable on _addLiquidity at AMM.sol
1.2 Calculate the Pool's Value Factor (FviF_{v_{i}}Fvi​​
) 
If i=0i=0i=0
 , Fvi=1F_{v_{i}}=1Fvi​​=1
 
If i≠0i≠0i=0
 , Fvi=TBAi−1⋅Pi+TBBi−1DBAi−1⋅Pi+DBBi−1\displaystyle F_{v_{i}}= \frac{TB_{A_{i-1}}\cdot P_i+TB_{B_{i-1}}}{DB_{A_{i-1}} \cdot P_i+DB_{B_{i-1}}}Fvi​​=DBAi−1​​⋅Pi​+DBBi−1​​TBAi−1​​⋅Pi​+TBBi−1​​​
 
Since this is the first liquidity provision of the pool, this is i=0i=0i=0
 and therefore, Fvi=1F_{v_{i}}=1Fvi​​=1
.
PoolValue factor variable on _addLiquidity at AMM.sol
FImp function at AMM.sol
2. Updates
2.1 Update Deamortized Balance of the pool for each token
By the time the pool is created (i=0i=0i=0
) , the DBAiDB_{A_i}DBAi​​
and DBBiDB_{B_i}DBBi​​
 will be equal to the AduA_{du}Adu​
 and BduB_{du}Bdu​
 since:
 Fvi=1F_{v_{i}} = 1Fvi​​=1

DBAi−1=0\displaystyle DB_{A_{i-1}}=0DBAi−1​​=0

DBBi−1=0\displaystyle DB_{B_{i-1}}=0DBBi−1​​=0
​
​DBAi=DBAi−1+AduFvi\displaystyle DB_{A_{i}}=DB_{A_{i-1}} +\frac{A_{du}}{F_{v_{i}}}DBAi​​=DBAi−1​​+Fvi​​Adu​​
​
​DBBi=DBBi−1+BduFvi\displaystyle DB_{B_{i}}=DB_{B_{i-1}} +\frac{B_{du}}{F_{v_{i}}}DBBi​​=DBBi−1​​+Fvi​​Bdu​​
​
deamortizedBalance on _addLiquidity at AMM.sol 
2.2 Update the User Balances for each token and the Pool Factor previously calculated
Updating this factor is essential, especially when there is a re-add liquidity event. 
​UBAu=AduUB_{A_{u}}=A_{du}UBAu​​=Adu​
 
​UBBu=BduUB_{B_{u}}=B_{du}UBBu​​=Bdu​
​
The UBfuUB_{f_{u}}UBfu​​
 works as if it was a snapshot of the pool's factor at the moment of this user's deposit. This factor will be updated in the case of re-add liquidity by the user. 
​UBFu=FvduUB_{F_{u}}=F{v_{du}}UBFu​​=Fvdu​
 
Updating User Balance (userDepositSnapshot) at _addLiquidity on AMM.sol
2.3 Update Total Balance of the pool for each token
​TBAi=TBAi−1+AduTB_{A_{i}}=TB_{A_{i-1}} +A_{du}TBAi​​=TBAi−1​​+Adu​
 
​TBBi=TBBi−1+BduTB_{B_{i}}=TB_{B_{i-1}} +B_{du}TBBi​​=TBBi−1​​+Bdu​
 
At the contract level, an ERC20 transfer is happening. Total balance (TB) is just a mathematical representation. The Total balance is checked by consulting the balanceOf() of the pool contract of the respective token (tokenA or tokenB)
Add liquidity ✅