multi-asset swap / LP equations, and tests (#1383)

Closes: #1369 

## What is the purpose of the change

This change extends the CFMM equation we use for stableswap to multiple assets.

## Brief change log
 
  - Create multi-asset CFMM function
  - [wip] Create multi-asset CFMM solver
  - [wip] Create tests for new CFMM


## Testing and Verifying

This change added tests and can be verified as follows:

*(example:)*
  - [wip]

## Documentation and Release Note

  - Does this pull request introduce a new feature or user-facing behavior changes? (yes)
  - Is a relevant changelog entry added to the `Unreleased` section in `CHANGELOG.md`? (yes / no)
  - How is the feature or change documented? (not applicable   /   specification (`x/<module>/spec/`)  /  [Osmosis docs repo](https://github.com/osmosis-labs/docs)   /   not documented)

osmoutils/partialord/partialord_test.go

@@ -11,9 +11,11 @@ import (
 func TestAPI(t *testing.T) {
 	// begin block use case, we have a dozen modules, but only care about a couple orders.
 	// In practice this will be gotten from some API, e.g. app.AllModuleNames()
-	moduleNames := []string{"auth", "authz", "bank", "capabilities",
+	moduleNames := []string{
+		"auth", "authz", "bank", "capabilities",
 		"staking", "distribution", "epochs", "mint", "upgrades", "wasm", "ibc",
-		"ibctransfers", "bech32ibc"}
+		"ibctransfers", "bech32ibc",
+	}
 	beginBlockOrd := partialord.NewPartialOrdering(moduleNames)
 	beginBlockOrd.FirstElements("upgrades", "epochs", "capabilities")
 	beginBlockOrd.After("ibctransfers", "ibc")
@@ -23,9 +25,11 @@ func TestAPI(t *testing.T) {
 	beginBlockOrd.LastElements("auth", "authz", "wasm")
 
 	totalOrd := beginBlockOrd.TotalOrdering()
-	expTotalOrd := []string{"upgrades", "epochs", "capabilities",
+	expTotalOrd := []string{
+		"upgrades", "epochs", "capabilities",
 		"bank", "staking", "mint", "ibc", "distribution", "ibctransfers", "bech32ibc",
-		"auth", "authz", "wasm"}
+		"auth", "authz", "wasm",
+	}
 	require.Equal(t, expTotalOrd, totalOrd)
 }
 

tests/e2e/chain_init/main.go

@@ -34,7 +34,7 @@ func main() {
 
 	b, _ := json.Marshal(createdChain)
 	fileName := fmt.Sprintf("%v/%v-encode", dataDir, chainId)
-	if err = os.WriteFile(fileName, b, 0777); err != nil {
+	if err = os.WriteFile(fileName, b, 0o777); err != nil {
 		panic(err)
 	}
 }

tests/e2e/e2e_setup_test.go

@@ -306,7 +306,6 @@ func (s *IntegrationTestSuite) configureChain(chainId string) {
 		}
 	}
 	s.chains = append(s.chains, &newChain)
-
 }
 
 func (s *IntegrationTestSuite) configureDockerResources(chainIDOne, chainIDTwo string) {

x/gamm/pool-models/balancer/amm_test.go

@@ -292,7 +292,6 @@ func TestCalcSingleAssetInAndOut_InverseRelationship(t *testing.T) {
 	for _, tc := range testcases {
 		for _, swapFee := range swapFeeCases {
 			t.Run(getTestCaseName(tc, swapFee), func(t *testing.T) {
-
 				swapFeeDec, err := sdk.NewDecFromStr(swapFee)
 				require.NoError(t, err)
 

x/gamm/pool-models/stableswap/amm.go

@@ -15,6 +15,18 @@ func cfmmConstant(xReserve, yReserve sdk.Dec) sdk.Dec {
 	return xy.Mul(x2.Add(y2))
 }
 
+// multi-asset CFMM is xyu(x^2 + y^2 + v) = k,
+// where u is the product of the reserves of assets
+// outside of x and y (e.g. u = wz), and v is the sum
+// of their squares (e.g. v = w^2 + z^2).
+// When u = 1 and v = 0, this is equivalent to solidly's CFMM
+func cfmmConstantMulti(xReserve, yReserve, uReserve, vSumSquares sdk.Dec) sdk.Dec {
+	xyu := xReserve.Mul(yReserve.Mul(uReserve))
+	x2 := xReserve.Mul(xReserve)
+	y2 := yReserve.Mul(yReserve)
+	return xyu.Mul(x2.Add(y2).Add(vSumSquares))
+}
+
 // solidly CFMM is xy(x^2 + y^2) = k
 // So we want to solve for a given addition of `b` units of y into the pool,
 // how many units `a` of x do we get out.