diff --git a/test/SUMMARY.md b/test/SUMMARY.md index f86a75bc..96a35483 100644 --- a/test/SUMMARY.md +++ b/test/SUMMARY.md @@ -29,32 +29,32 @@ Additional properties from BNum were tested independently too (with severe limit # Notes The bmath corresponding equations are: -`Spot price:` -$\text{spotPrice} = \frac{\text{tokenBalanceIn}/\text{tokenWeightIn}}{\text{tokenBalanceOut}/\text{tokenWeightOut}} \cdot \frac{1}{1 - \text{swapFee}}$ +**Spot price:** +$$\text{spotPrice} = \frac{\text{tokenBalanceIn}/\text{tokenWeightIn}}{\text{tokenBalanceOut}/\text{tokenWeightOut}} \cdot \frac{1}{1 - \text{swapFee}}$$ -`Out given in:` -$\text{tokenAmountOut} = \text{tokenBalanceOut} \cdot \left( 1 - \left( \frac{\text{tokenBalanceIn}}{\text{tokenBalanceIn} + \left( \text{tokenAmountIn} \cdot \left(1 - \text{swapFee}\right)\right)} \right)^{\frac{\text{tokenWeightIn}}{\text{tokenWeightOut}}} \right)$ +**Out given in:** +$$\text{tokenAmountOut} = \text{tokenBalanceOut} \cdot \left( 1 - \left( \frac{\text{tokenBalanceIn}}{\text{tokenBalanceIn} + \left( \text{tokenAmountIn} \cdot \left(1 - \text{swapFee}\right)\right)} \right)^{\frac{\text{tokenWeightIn}}{\text{tokenWeightOut}}} \right)$$ -`In given out:` -$\text{tokenAmountIn} = \frac{\text{tokenBalanceIn} \cdot \left( \frac{\text{tokenBalanceOut}}{\text{tokenBalanceOut} - \text{tokenAmountOut}} \right)^{\frac{\text{tokenWeightOut}}{\text{tokenWeightIn}}} - 1}{1 - \text{swapFee}}$ +**In given out:** +$$\text{tokenAmountIn} = \frac{\text{tokenBalanceIn} \cdot \left( \frac{\text{tokenBalanceOut}}{\text{tokenBalanceOut} - \text{tokenAmountOut}} \right)^{\frac{\text{tokenWeightOut}}{\text{tokenWeightIn}}} - 1}{1 - \text{swapFee}}$$ -`Pool out given single in` -$\text{poolAmountOut} = \left(\frac{\text{tokenAmountIn} \cdot \left(1 - \left(1 - \frac{\text{tokenWeightIn}}{\text{totalWeight}}\right) \cdot \text{swapFee}\right) + \text{tokenBalanceIn}}{\text{tokenBalanceIn}}\right)^{\frac{\text{tokenWeightIn}}{\text{totalWeight}}} \cdot \text{poolSupply} - \text{poolSupply}$ +**Pool out given single in** +$$\text{poolAmountOut} = \left(\frac{\text{tokenAmountIn} \cdot \left(1 - \left(1 - \frac{\text{tokenWeightIn}}{\text{totalWeight}}\right) \cdot \text{swapFee}\right) + \text{tokenBalanceIn}}{\text{tokenBalanceIn}}\right)^{\frac{\text{tokenWeightIn}}{\text{totalWeight}}} \cdot \text{poolSupply} - \text{poolSupply}$$ -`Single in given pool out` -$\text{tokenAmountIn} = \frac{\left(\frac{\text{poolSupply} + \text{poolAmountOut}}{\text{poolSupply}}\right)^{\frac{1}{\frac{\text{weightIn}}{\text{totalWeight}}}} \cdot \text{balanceIn} - \text{balanceIn}}{\left(1 - \frac{\text{weightIn}}{\text{totalWeight}}\right) \cdot \text{swapFee}}$ +**Single in given pool out** +$$\text{tokenAmountIn} = \frac{\left(\frac{\text{poolSupply} + \text{poolAmountOut}}{\text{poolSupply}}\right)^{\frac{1}{\frac{\text{weightIn}}{\text{totalWeight}}}} \cdot \text{balanceIn} - \text{balanceIn}}{\left(1 - \frac{\text{weightIn}}{\text{totalWeight}}\right) \cdot \text{swapFee}}$$ -`Single out given pool in` -$\text{tokenAmountOut} = \left( \text{tokenBalanceOut} - \left( \frac{\text{poolSupply} - \left(\text{poolAmountIn} \cdot \left(1 - \text{exitFee}\right)\right)}{\text{poolSupply}} \right)^{\frac{1}{\frac{\text{tokenWeightOut}}{\text{totalWeight}}}} \cdot \text{tokenBalanceOut} \right) \cdot \left(1 - \left(1 - \frac{\text{tokenWeightOut}}{\text{totalWeight}}\right) \cdot \text{swapFee}\right)$ +**Single out given pool in** +$$\text{tokenAmountOut} = \left( \text{tokenBalanceOut} - \left( \frac{\text{poolSupply} - \left(\text{poolAmountIn} \cdot \left(1 - \text{exitFee}\right)\right)}{\text{poolSupply}} \right)^{\frac{1}{\frac{\text{tokenWeightOut}}{\text{totalWeight}}}} \cdot \text{tokenBalanceOut} \right) \cdot \left(1 - \left(1 - \frac{\text{tokenWeightOut}}{\text{totalWeight}}\right) \cdot \text{swapFee}\right)$$ -`Pool in given single out` -$\text{poolAmountIn} = \frac{\text{poolSupply} - \left( \frac{\text{tokenBalanceOut} - \frac{\text{tokenAmountOut}}{1 - \left(1 - \frac{\text{tokenWeightOut}}{\text{totalWeight}}\right) \cdot \text{swapFee}}}{\text{tokenBalanceOut}} \right)^{\frac{\text{tokenWeightOut}}{\text{totalWeight}}} \cdot \text{poolSupply}}{1 - \text{exitFee}}$ +**Pool in given single out** +$$\text{poolAmountIn} = \frac{\text{poolSupply} - \left( \frac{\text{tokenBalanceOut} - \frac{\text{tokenAmountOut}}{1 - \left(1 - \frac{\text{tokenWeightOut}}{\text{totalWeight}}\right) \cdot \text{swapFee}}}{\text{tokenBalanceOut}} \right)^{\frac{\text{tokenWeightOut}}{\text{totalWeight}}} \cdot \text{poolSupply}}{1 - \text{exitFee}}$$ BNum bpow is based on exponentiation by squaring and hold true because (see dapphub dsmath): https://github.com/dapphub/ds-math/blob/e70a364787804c1ded9801ed6c27b440a86ebd32/src/math.sol#L62