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 ✅

Functions

Re-add Liquidity

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Add Liquidity

1. Calculate factors

1.1 Calculate Option Price

1.2 Calculate the Pool's Value Factor ()

2. Updates

2.1 Update Deamortized Balance of the pool for each token

2.2 Update the User Balances for each token and the Pool Factor previously calculated

2.3 Update Total Balance of the pool for each token

Add Liquidity

1. Calculate factors

1.1 Calculate Option Price

1.2 Calculate the Pool's Value Factor (FviF_{v_{i}}Fvi​​)

2. Updates

2.1 Update Deamortized Balance of the pool for each token

2.2 Update the User Balances for each token and the Pool Factor previously calculated

2.3 Update Total Balance of the pool for each token