# 沒有 input 時的數字顯示

# 先計算當 input 超級小的時候能拿到多少 localSP
localSP = sqrt(_input * _output) * premium
localSP = sqrt(_input * _input * fairPrice) * premium
localSP = _input * sqrt(price) * premium
localSP = (_input / decimal(input) * priceInput) * decimal(input) / priceInput * sqrt(fairPrice) * premium
localSP = inputUSD * decimal(input) / priceInput * sqrt(fairPrice) * premium

localSPMarginal = localSP/inputUSD = decimal(input) * sqrt(fairPrice)/priceInput * premium

> localSPMarginal = sqrt(decimal(baseToken)**2 * fairPrice)/baseTokenPrice * premium
# localSPMarginal 代表不會滑價的話，每投入 $1 會拿到多少 localSP
# fair price = quoteTokenReserve(1-baseTokenfee)/(baseTokenReserve(1-quoteTokenfee))
# premium 用最短期的 lock-up period 1 day 來計算

#read contract: get reserve
reserve = getCurrentPoolReserve(msg.sender)
pool = pools[msg.sender]

reserveDYSN = getCurrentGlobalReserve()
globalPool.weight

# localSP -> SP marginal
SPMarginal = reserve/pool.w * log(2)

# SP -> DYSN
DYSNMarginal = reserveDYSN/globalPool.weight * log(2)

# 投入一塊錢 input 可拿到多少 DYSN，再將單位轉換成 USD (govValue = DYSNValue)
DYSNValue = localSPMarginal * SPMarginal * DYSNMarginal * DYSNPrice

有以上資訊就可以計算 APR 了，假設 x = 1 (價值 1 美元的 input)
https://hackmd.io/nUqZ3rIJSDKUFh3-Qlw1bg