> For the complete documentation index, see [llms.txt](https://calnix.gitbook.io/eth-dev/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://calnix.gitbook.io/eth-dev/fixed-point-math/amm-math.md).

# AMM Math

## Constant Product AMM

* <https://www.youtube.com/watch?v=QNPyFs8Wybk>
* If you have absolutely no background on this topic, the above video would be useful to set the stage.
* Else for quick reference:

<figure><img src="/files/ZVBsdnFq5vDaJgslqUxM" alt=""><figcaption></figcaption></figure>

### Swap - How many tokens to return in a trade?

<figure><img src="/files/89AyLTU1w53uRp3SQ9pb" alt=""><figcaption></figcaption></figure>

* The trick is to identify if we are calculating for the increasing or decreasing asset
* In the wild reference; buyQuote, sellQuote: <https://github.com/code-423n4/2023-04-caviar/blob/main/src/PrivatePool.sol#L699>


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