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AMM keeper swap Refactor (#740)
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* refactor math

* factor out normalizedWeight

* unify into SolveConstantFunctionInvariant

* test in progress

* add randomized test

* Update x/gamm/keeper/math.go

Co-authored-by: Dev Ojha <[email protected]>

Co-authored-by: Dev Ojha <[email protected]>
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@mconcat @ValarDragon
mconcat and ValarDragon committed Jan 19, 2022
1 parent bd1c71b commit 0b52b47
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Showing 4 changed files with 451 additions and 171 deletions.
171 changes: 87 additions & 84 deletions x/gamm/keeper/math.go
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Original file line number Diff line number Diff line change
Expand Up @@ -54,7 +54,35 @@ func calcSpotPriceWithSwapFee(
return spotPrice.Mul(scale)
}

// aO
// solveConstantFunctionInvariant solves the constant function of an AMM
// that determines the relationship between the differences of two sides
// of assets inside the pool.
// For fixed balanceXBefore, balanceXAfter, weightX, balanceY, weightY,
// we could deduce the balanceYDelta, calculated by:
// balanceYDelta = balanceY * (1 - (balanceXBefore/balanceXAfter)^(weightX/weightY))
// balanceYDelta is positive when the balance liquidity decreases.
// balanceYDelta is negative when the balance liquidity increases.
func solveConstantFunctionInvariant(
tokenBalanceFixedBefore,
tokenBalanceFixedAfter,
tokenWeightFixed,
tokenBalanceUnknownBefore,
tokenWeightUnknown sdk.Dec,
) sdk.Dec {
// weightRatio = (weightX/weightY)
weightRatio := tokenWeightFixed.Quo(tokenWeightUnknown)

// y = balanceXBefore/balanceYAfter
y := tokenBalanceFixedBefore.Quo(tokenBalanceFixedAfter)

// amountY = balanceY * (1 - (y ^ weightRatio))
foo := osmomath.Pow(y, weightRatio)
multiplier := sdk.OneDec().Sub(foo)
return tokenBalanceUnknownBefore.Mul(multiplier)
}

// calcOutGivenIn calculates token to be swapped out given
// the provided amount, fee deducted, using solveConstantFunctionInvariant
func calcOutGivenIn(
tokenBalanceIn,
tokenWeightIn,
Expand All @@ -63,16 +91,15 @@ func calcOutGivenIn(
tokenAmountIn,
swapFee sdk.Dec,
) sdk.Dec {
weightRatio := tokenWeightIn.Quo(tokenWeightOut)
adjustedIn := sdk.OneDec().Sub(swapFee)
adjustedIn = tokenAmountIn.Mul(adjustedIn)
y := tokenBalanceIn.Quo(tokenBalanceIn.Add(adjustedIn))
foo := osmomath.Pow(y, weightRatio)
bar := sdk.OneDec().Sub(foo)
return tokenBalanceOut.Mul(bar)
// deduct swapfee on the in asset
tokenAmountInAfterFee := tokenAmountIn.Mul(sdk.OneDec().Sub(swapFee))
// delta balanceOut is positive(tokens inside the pool decreases)
tokenAmountOut := solveConstantFunctionInvariant(tokenBalanceIn, tokenBalanceIn.Add(tokenAmountInAfterFee), tokenWeightIn, tokenBalanceOut, tokenWeightOut)
return tokenAmountOut
}

// aI
// calcInGivenOut calculates token to be provided, fee added,
// given the swapped out amount, using solveConstantFunctionInvariant
func calcInGivenOut(
tokenBalanceIn,
tokenWeightIn,
Expand All @@ -81,120 +108,96 @@ func calcInGivenOut(
tokenAmountOut,
swapFee sdk.Dec,
) sdk.Dec {
weightRatio := tokenWeightOut.Quo(tokenWeightIn)
diff := tokenBalanceOut.Sub(tokenAmountOut)
y := tokenBalanceOut.Quo(diff)
foo := osmomath.Pow(y, weightRatio)
foo = foo.Sub(one)
tokenAmountIn := sdk.OneDec().Sub(swapFee)
return (tokenBalanceIn.Mul(foo)).Quo(tokenAmountIn)
// delta balanceIn is negative(amount of tokens inside the pool increases)
tokenAmountIn := solveConstantFunctionInvariant(tokenBalanceOut, tokenBalanceOut.Sub(tokenAmountOut), tokenWeightOut, tokenBalanceIn, tokenWeightIn).Neg()
// We deduct a swap fee on the input asset. The swap happens by following the invariant curve on the input * (1 - swap fee)
// and then the swap fee is added to the pool.
// Thus in order to give X amount out, we solve the invariant for the invariant input. However invariant input = (1 - swapfee) * trade input.
// Therefore we divide by (1 - swapfee) here
tokenAmountInBeforeFee := tokenAmountIn.Quo(sdk.OneDec().Sub(swapFee))
return tokenAmountInBeforeFee

}

// pAo
func calcPoolOutGivenSingleIn(
tokenBalanceIn,
tokenWeightIn,
poolSupply,
totalWeight,
tokenAmountIn,
func feeRatio(
normalizedWeight,
swapFee sdk.Dec,
) sdk.Dec {
normalizedWeight := tokenWeightIn.Quo(totalWeight)
zaz := (sdk.OneDec().Sub(normalizedWeight)).Mul(swapFee)
tokenAmountInAfterFee := tokenAmountIn.Mul(sdk.OneDec().Sub(zaz))

newTokenBalanceIn := tokenBalanceIn.Add(tokenAmountInAfterFee)
tokenInRatio := newTokenBalanceIn.Quo(tokenBalanceIn)

// uint newPoolSupply = (ratioTi ^ weightTi) * poolSupply;
poolRatio := osmomath.Pow(tokenInRatio, normalizedWeight)
newPoolSupply := poolRatio.Mul(poolSupply)
return newPoolSupply.Sub(poolSupply)
zar := (sdk.OneDec().Sub(normalizedWeight)).Mul(swapFee)
return sdk.OneDec().Sub(zar)
}

//tAi
// calcSingleInGivenPoolOut calculates token to be provided, fee added,
// given the swapped out shares amount, using solveConstantFunctionInvariant
func calcSingleInGivenPoolOut(
tokenBalanceIn,
tokenWeightIn,
normalizedTokenWeightIn,
poolSupply,
totalWeight,
poolAmountOut,
swapFee sdk.Dec,
) sdk.Dec {
normalizedWeight := tokenWeightIn.Quo(totalWeight)
newPoolSupply := poolSupply.Add(poolAmountOut)
poolRatio := newPoolSupply.Quo(poolSupply)

//uint newBalTi = poolRatio^(1/weightTi) * balTi;
boo := sdk.OneDec().Quo(normalizedWeight)
tokenInRatio := osmomath.Pow(poolRatio, boo)
newTokenBalanceIn := tokenInRatio.Mul(tokenBalanceIn)
tokenAmountInAfterFee := newTokenBalanceIn.Sub(tokenBalanceIn)
// Do reverse order of fees charged in joinswap_ExternAmountIn, this way
// ``` pAo == joinswap_ExternAmountIn(Ti, joinswap_PoolAmountOut(pAo, Ti)) ```
//uint tAi = tAiAfterFee / (1 - (1-weightTi) * swapFee) ;
zar := (sdk.OneDec().Sub(normalizedWeight)).Mul(swapFee)
return tokenAmountInAfterFee.Quo(sdk.OneDec().Sub(zar))
// delta balanceIn is negative(tokens inside the pool increases)
// pool weight is always 1
tokenAmountIn := solveConstantFunctionInvariant(poolSupply.Add(poolAmountOut), poolSupply, sdk.OneDec(), tokenBalanceIn, normalizedTokenWeightIn).Neg()
// deduct swapfee on the in asset
tokenAmountInBeforeFee := tokenAmountIn.Quo(feeRatio(normalizedTokenWeightIn, swapFee))
return tokenAmountInBeforeFee
}

// pAo
func calcPoolOutGivenSingleIn(
tokenBalanceIn,
normalizedTokenWeightIn,
poolSupply,
tokenAmountIn,
swapFee sdk.Dec,
) sdk.Dec {
// deduct swapfee on the in asset
tokenAmountInAfterFee := tokenAmountIn.Mul(feeRatio(normalizedTokenWeightIn, swapFee))
// delta poolSupply is negative(total pool shares increases)
// pool weight is always 1
poolAmountOut := solveConstantFunctionInvariant(tokenBalanceIn.Add(tokenAmountInAfterFee), tokenBalanceIn, normalizedTokenWeightIn, poolSupply, sdk.OneDec()).Neg()
return poolAmountOut
}

// tAo
func calcSingleOutGivenPoolIn(
tokenBalanceOut,
tokenWeightOut,
normalizedTokenWeightOut,
poolSupply,
totalWeight,
poolAmountIn,
swapFee sdk.Dec,
exitFee sdk.Dec,
) sdk.Dec {
normalizedWeight := tokenWeightOut.Quo(totalWeight)
// charge exit fee on the pool token side
// pAiAfterExitFee = pAi*(1-exitFee)
poolAmountInAfterExitFee := poolAmountIn.Mul(sdk.OneDec().Sub(exitFee))
newPoolSupply := poolSupply.Sub(poolAmountInAfterExitFee)
poolRatio := newPoolSupply.Quo(poolSupply)

// newBalTo = poolRatio^(1/weightTo) * balTo;

tokenOutRatio := osmomath.Pow(poolRatio, sdk.OneDec().Quo(normalizedWeight))
newTokenBalanceOut := tokenOutRatio.Mul(tokenBalanceOut)

tokenAmountOutBeforeSwapFee := tokenBalanceOut.Sub(newTokenBalanceOut)

// charge swap fee on the output token side
//uint tAo = tAoBeforeSwapFee * (1 - (1-weightTo) * swapFee)
zaz := (sdk.OneDec().Sub(normalizedWeight)).Mul(swapFee)
tokenAmountOut := tokenAmountOutBeforeSwapFee.Mul(sdk.OneDec().Sub(zaz))
return tokenAmountOut
// delta balanceOut is positive(tokens inside the pool decreases)
// pool weight is always 1
tokenAmountOut := solveConstantFunctionInvariant(poolSupply.Sub(poolAmountInAfterExitFee), poolSupply, sdk.OneDec(), tokenBalanceOut, normalizedTokenWeightOut)
// deduct
tokenAmountOutAfterFee := tokenAmountOut.Mul(feeRatio(normalizedTokenWeightOut, swapFee))
return tokenAmountOutAfterFee
}

// pAi
func calcPoolInGivenSingleOut(
tokenBalanceOut,
tokenWeightOut,
normalizedTokenWeightOut,
poolSupply,
totalWeight,
tokenAmountOut,
swapFee sdk.Dec,
exitFee sdk.Dec,
) sdk.Dec {
// charge swap fee on the output token side
normalizedWeight := tokenWeightOut.Quo(totalWeight)
//uint tAoBeforeSwapFee = tAo / (1 - (1-weightTo) * swapFee) ;
zoo := sdk.OneDec().Sub(normalizedWeight)
zar := zoo.Mul(swapFee)
tokenAmountOutBeforeSwapFee := tokenAmountOut.Quo(sdk.OneDec().Sub(zar))

newTokenBalanceOut := tokenBalanceOut.Sub(tokenAmountOutBeforeSwapFee)
tokenOutRatio := newTokenBalanceOut.Quo(tokenBalanceOut)
tokenAmountOutBeforeFee := tokenAmountOut.Quo(feeRatio(normalizedTokenWeightOut, swapFee))

//uint newPoolSupply = (ratioTo ^ weightTo) * poolSupply;
poolRatio := osmomath.Pow(tokenOutRatio, normalizedWeight)
newPoolSupply := poolRatio.Mul(poolSupply)
poolAmountInAfterExitFee := poolSupply.Sub(newPoolSupply)
// delta poolSupply is positive(total pool shares decreases)
// pool weight is always 1
poolAmountIn := solveConstantFunctionInvariant(tokenBalanceOut.Sub(tokenAmountOutBeforeFee), tokenBalanceOut, normalizedTokenWeightOut, poolSupply, sdk.OneDec())

// charge exit fee on the pool token side
// pAi = pAiAfterExitFee/(1-exitFee)
return poolAmountInAfterExitFee.Quo(sdk.OneDec().Sub(exitFee))
poolAmountInBeforeFee := poolAmountIn.Quo(sdk.OneDec().Sub(exitFee))
return poolAmountInBeforeFee
}
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