# Price Calculation

The CoolDEX uses a constant product market maker (CPMM) formula for price calculations.

## Constant Product Formula

The core formula for the CoolDEX is:

```
k = x * y
```

Where:

* `x` is the amount of token X in the pool
* `y` is the amount of token Y in the pool
* `k` is a constant that must be maintained during trades

This formula ensures that the product of the two token reserves remains constant, which creates a hyperbolic price curve.

## Swap Base In Calculation

When a user specifies the input amount for a swap, the output amount is calculated as:

```
amount_out = (pool_out * amount_in) / (pool_in + amount_in)
```

Where:

* `pool_out` is the amount of output token in the pool
* `pool_in` is the amount of input token in the pool
* `amount_in` is the specified input amount

### Example Calculation

Let's say:

* Pool has 1,000,000 TOKEN and 1,000 SOL
* User wants to swap 10 SOL for TOKEN

The calculation would be:

```
amount_out = (1,000,000 * 10) / (1,000 + 10)
amount_out = 10,000,000 / 1,010
amount_out ≈ 9,900.99 TOKEN
```

## Swap Base Out Calculation

When a user specifies the output amount for a swap, the required input amount is calculated as:

```
amount_in = (pool_in * amount_out) / (pool_out - amount_out)
```

Where:

* `pool_in` is the amount of input token in the pool
* `pool_out` is the amount of output token in the pool
* `amount_out` is the specified output amount

### Example Calculation

Let's say:

* Pool has 1,000,000 TOKEN and 1,000 SOL
* User wants to receive exactly 10,000 TOKEN

The calculation would be:

```
amount_in = (1,000 * 10,000) / (1,000,000 - 10,000)
amount_in = 10,000,000 / 990,000
amount_in ≈ 10.10 SOL
```

## Fee Calculation

Fees are applied to the swap amounts. The exact fee calculation depends on the token type:

### Standard Tokens

For standard (non-SC Bonding Curve) tokens, a simple fee is applied:

```
fee_amount = amount_in * fee_numerator / fee_denominator
amount_in_after_fee = amount_in - fee_amount
```

### SC Bonding Curve Tokens

For SC Bonding Curve tokens, the fee calculation is more complex and depends on the token's specific parameters:

1. **For selling tokens (Coin2PC)**:

   ```
   taxable_amount = amount_in * swap_fee_numerator * (cooldex_team_fee_wsol_fee_denominator - cooldex_team_fee_wsol_fee_numerator) / (swap_fee_denominator * cooldex_team_fee_wsol_fee_denominator)
   amount_to_burn = taxable_amount * burn_rate / CURVE_BURN_RATE_DENOMINATOR
   cult_token = (taxable_amount - amount_to_burn) / 2
   ```
2. **For buying tokens (PC2Coin)**:

   ```
   taxable_amount = amount_in * swap_fee_numerator / swap_fee_denominator
   platform_tax = taxable_amount * cooldex_team_fee_wsol_fee_numerator / cooldex_team_fee_wsol_fee_denominator
   cult_wsol = (taxable_amount - platform_tax) * (CURVE_BURN_RATE_DENOMINATOR - burn_rate) / (2 * CURVE_BURN_RATE_DENOMINATOR)
   ```

## LP Token Calculation

### Adding Liquidity

When adding liquidity, the amount of LP tokens minted is proportional to the share of the pool being added:

```
mint_lp_amount = (deposit_amount / total_amount) * total_lp_supply
```

Where:

* `deposit_amount` is the amount of the base token being deposited
* `total_amount` is the total amount of that token in the pool
* `total_lp_supply` is the current total supply of LP tokens

### Removing Liquidity

When removing liquidity, the amounts of tokens received are proportional to the share of LP tokens being burned:

```
token_amount = (lp_amount / total_lp_supply) * total_token_amount
```

Where:

* `lp_amount` is the amount of LP tokens being burned
* `total_lp_supply` is the current total supply of LP tokens
* `total_token_amount` is the total amount of the token in the pool


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