Begin stableswap spec #2873
Begin stableswap spec #2873
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| Suppose the existence of a function $\text{solve\_cfmm}(x, v, w, k) = y\text{ s.t. }g(x, y, v, w) = k$. | ||
| Then we can solve swaps by first computing $k = g(x_0, y_0, v, w)$. | ||
| Then suppose I want to swap $a$ units of $x$, and then want to find how many units $b$ of $y$ that we get out. | ||
| We do this by computing $y_f = \text{solve\_cfmm}(x_0 + a, v, w, k)$, and then $b = y_0 - y_f$ |
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This and all of the remaining expressions also do not render for me unfortunately
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Thoughts on throwing this into a hackmd so we can work on filling out the rest together? Or would you prefer to fill out the whole spec and then have others review? |
| upperbound = | ||
| ``` | ||
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| ### Spot Price |
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Are these considered as TODOs for future reference?
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Yeah, just things that should be filled in before stableswap has a full spec
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@p0mvn github rendering now fixed |
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@AlpinYukseloglu happy with either of the options you proposed. Feel free to commit to the branch, or move it to a hackmd. I also don't think we need to have the full spec written in one PR though. (e.g. I'm happy with this getting in its current form, I feel like it gives us a swap algorithm description we can iterate on for comparing against code) |
| The maximal upperbound is obviously unworkable, and in general binary searching around wide ranges is unfortunate, as we expect most trades to be centered around $y_0$. | ||
| This would suggest that we should do something smarter to iteratively approach the right value for the upperbound at least. | ||
| Notice that $h$ is super-linearly related in $y$, and at most cubically related to $y$. | ||
| This means that $ \forall c \in \R^+, c * h(x,y,w) < h(x,c*y,w) < c^3 * h(x,y,w)$. |
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ty. fixed! (Also apologies, last commit got cut off a bit early in the web editor) |
Co-authored-by: Roman <roman@osmosis.team>
What is the purpose of the change
WIP work on a spec for Solidly stableswap and description of equations used within it
Rendered URL: https://github.com/osmosis-labs/osmosis/blob/dev/stableswap_spec/x/gamm/pool-models/stableswap/README.md