methods for balancer sor

pricing_model.js

// calc_in_given_out (swap)
function _tokenInForExactTokenOut(amount, poolPairData) {
    let inReserves = poolPairData.balanceIn;
    let outReserves = poolPairData.balanceOut;
    let lpShares = poolPairData.lpShares;
    let inputToken = poolPairData.inputToken
    let outputToken = poolPairData.outputToken;
    let baseToken = poolPairData.baseToken;
    let principalToken = poolPairData.principalToken;
    let phi = poolPairData.swapFee;
    let t = poolPairData.time;
    if(inputToken == baseToken){
        outReserves += lpShares;
    } else if(inputToken == principalToken){
        inReserves += lpShares;
    }
    k=Math.pow(inReserves,1-t) + Math.pow(outReserves,1-t);
    withoutFee = Math.pow(k-Math.pow(outReserves-amount,1-t),1/(1-t)) - inReserves;
    fee = Math.abs(amount-withoutFee)*phi;
    return withoutFee+fee;
}

// calc_out_given_in (swap)
function _exactTokenInForTokenOut(amount, poolPairData) {
    let inReserves = poolPairData.balanceIn;
    let outReserves = poolPairData.balanceOut;
    let lpShares = poolPairData.lpShares;
    let inputToken = poolPairData.inputToken
    let outputToken = poolPairData.outputToken;
    let baseToken = poolPairData.baseToken;
    let principalToken = poolPairData.principalToken;
    let phi = poolPairData.swapFee;
    let t = poolPairData.time;
    if(outputToken == baseToken){
        inReserves += lpShares;
    } else if(outputToken == principalToken){
        outReserves += lpShares;
    }
    k=Math.pow(inReserves,1-t) + Math.pow(outReserves,1-t);
    withoutFee = outReserves - Math.pow(k-Math.pow(inReserves+amount,1-t),1/(1-t));
    fee = Math.abs(amount-withoutFee)*phi;
    return withoutFee-fee;
}


console.log("Case: _tokenInForExactTokenOut where inputToken = PT and outputToken = BT")
xReserves = 447689.0001456285
yReserves = 967438.5972366218
totalSupply = 265819.67027583614
phi = .05
t = 0.20475000000000002
amount = 2429.409437012756

var poolPairData = {}
poolPairData.balanceIn = yReserves
poolPairData.balanceOut = xReserves
poolPairData.lpShares = totalSupply
poolPairData.inputToken = "0x0P"
poolPairData.outputToken = "0x0B"
poolPairData.baseToken = "0x0B"
poolPairData.principalToken = "0x0P"
poolPairData.swapFee = phi
poolPairData.time = t
expectedAmountIn = 3020.089879734272

amountIn = _tokenInForExactTokenOut(amount, poolPairData)
console.log("Amount Out: " + amount + " -> Amount In: " + amountIn + " = " + expectedAmountIn)

console.log("Case: _tokenInForExactTokenOut where inputToken = BT and outputToken = PT")
xReserves = 227297.54091594956
yReserves = 230177.25143358269
totalSupply = 311863.7956289041
phi = .05
t = 0.12425
amount = 1690.739673346158

var poolPairData = {}
poolPairData.balanceIn = xReserves
poolPairData.balanceOut = yReserves
poolPairData.lpShares = totalSupply
poolPairData.inputToken = "0x0B"
poolPairData.outputToken = "0x0P"
poolPairData.baseToken = "0x0B"
poolPairData.principalToken = "0x0P"
poolPairData.swapFee = phi
poolPairData.time = t
expectedAmountIn = 1527.2097822578185

amountIn = _tokenInForExactTokenOut(amount, poolPairData)
console.log("Amount Out: " + amount + " -> Amount In: " + amountIn + " = " + expectedAmountIn)

console.log("Case: _exactTokenInForTokenOut where inputToken = BT and outputToken = PT")
xReserves = 674971.6048091053
yReserves = 252853.96590876798
totalSupply = 888791.4151192267
phi = .05
t = 0.127
amount = 2362.8991926827807

var poolPairData = {}
poolPairData.balanceIn = xReserves
poolPairData.balanceOut = yReserves
poolPairData.lpShares = totalSupply
poolPairData.inputToken = "0x0B"
poolPairData.outputToken = "0x0P"
poolPairData.baseToken = "0x0B"
poolPairData.principalToken = "0x0P"
poolPairData.swapFee = phi
poolPairData.time = t
expectedAmountOut = 2516.969797522765

amountOut = _exactTokenInForTokenOut(amount, poolPairData)
console.log("Amount In: " + amount + " -> Amount Out: " + amountOut + " = " + expectedAmountOut)


console.log("Case: _exactTokenInForTokenOut where inputToken = PT and outputToken = BT")
xReserves = 251639.14235585282
yReserves = 475364.5726183281
totalSupply = 203024.0527059632
phi = .05
t = 0.06075
amount = 2193.719312762269

var poolPairData = {}
poolPairData.balanceIn = yReserves
poolPairData.balanceOut = xReserves
poolPairData.lpShares = totalSupply
poolPairData.intputToken = "0x0P"
poolPairData.outputToken = "0x0B"
poolPairData.baseToken = "0x0B"
poolPairData.principalToken = "0x0P"
poolPairData.swapFee = phi
poolPairData.time = t
expectedAmountOut = 2058.2884734369927

amountOut = _exactTokenInForTokenOut(amount, poolPairData)
console.log("Amount In: " + amount + " -> Amount Out: " + amountOut + " = " + expectedAmountOut)