Canto Dex Oracle contest - Bronicle's results

Low issue

Multiplication after division

1. Summary: Performing a multiplication after a division should be avoided as precision is lost in the division step.

2. Details: In order to minimize rounding errors, when performing mathematical operations, it is encouraged to leave the division step at the end of the expression.

3. Github Permalinks: https://github.com/code-423n4/2022-09-canto/blob/main/src/Swap/BaseV1-periphery.sol#L549-L593

4. Mitigation:

   The current implementation of the computation at lines 581 to 585 can be mathematically written as follows:

   $\text{LpPricesCumulative} = \sum_i \frac{\left(\text{token0TVL}+\text{token1TVL}\right)\cdot 10^{18}}{\text{supply}_i}$

   which is equivalent to

   $\text{LpPricesCumulative} = \sum_i \frac{\left(\text{assetReserves}_i\cdot\frac{\text{prices}_i}{\text{decimals}}+\text{token1TVL}\right)\cdot 10^{18}}{\text{supply}_i}$

   Note that we can extract $10^{18}$ from the summation because it is constant. Moreover, if multiplying both the denominator and the numerator by $\text{decimals}$, we can do the same. This results in:

   $\text{LpPricesCumulative} = \frac{10^{18}}{\text{decimals}} \sum_i \frac{\text{assetReserves}_i\cdot\text{prices}_i+\text{token1TVL}\cdot\text{decimals}}{\text{supply}_i}$

   Moreover, if one checks that the number of decimals (let's call it $z$, so that $\text{decimals} = 10^{z}$) is less or equal than $18$, the above expression can be simplified to:

   $\text{LpPricesCumulative} = 10^{18 - z} \sum_i \frac{\text{assetReserves}_i\cdot\text{prices}_i+\text{token1TVL}\cdot\text{decimals}}{\text{supply}_i}$

   With this expression, one can reduce the amount of divisions performed and will most likely have a better rounding precision.

   Moreover, at line 592, more simplifications can be done. The expression

   $\text{LpPrice}\cdot\frac{\text{getPriceNote(address(wcanto), false)}}{10^{18}}$

   can be rewritten as

   $\frac{\text{LpPricesCumulative}}{8}\cdot\frac{\text{getPriceNote(address(wcanto), false)}}{10^{18}}$

   which in turn equals

   $\frac{10^{18 - z}}{8} \sum_i \frac{\text{assetReserves}_i\cdot\text{prices}_i+\text{token1TVL}\cdot\text{decimals}}{\text{supply}_i}\cdot\frac{\text{getPriceNote(address(wcanto), false)}}{10^{18}}$

   having thus

   $\frac{1}{8\cdot 10^´z} \sum_i \frac{\text{assetReserves}_i\cdot\text{prices}_i+\text{token1TVL}\cdot\text{decimals}}{\text{supply}_i}\cdot\text{getPriceNote(address(wcanto), false)}$

   which might be a better implementation of the computations.