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formula.go
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formula.go
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package formula
import (
"github.com/MinterTeam/minter-go-node/math"
"math/big"
)
const (
precision = 100
)
// CalculatePurchaseReturn calculates amount of coin that user will receive by depositing given amount of BIP
// Return = supply * ((1 + deposit / reserve) ^ (crr / 100) - 1)
func CalculatePurchaseReturn(supply *big.Int, reserve *big.Int, crr uint32, deposit *big.Int) *big.Int {
if deposit.Sign() == 0 {
return big.NewInt(0)
}
if crr == 100 {
result := big.NewInt(0).Mul(supply, deposit)
return result.Div(result, reserve)
}
tSupply := newFloat(0).SetInt(supply)
tReserve := newFloat(0).SetInt(reserve)
tDeposit := newFloat(0).SetInt(deposit)
res := newFloat(0).Quo(tDeposit, tReserve) // deposit / reserve
res.Add(res, newFloat(1)) // 1 + (deposit / reserve)
res = math.Pow(res, newFloat(float64(crr)/100)) // (1 + deposit / reserve) ^ (crr / 100)
res.Sub(res, newFloat(1)) // ((1 + deposit / reserve) ^ (crr / 100) - 1)
res.Mul(res, tSupply) // supply * ((1 + deposit / reserve) ^ (crr / 100) - 1)
result, _ := res.Int(nil)
return result
}
// CalculatePurchaseAmount is the reversed version of function CalculatePurchaseReturn
// Deposit = reserve * (((wantReceive + supply) / supply)^(100/c) - 1)
func CalculatePurchaseAmount(supply *big.Int, reserve *big.Int, crr uint32, wantReceive *big.Int) *big.Int {
if wantReceive.Sign() == 0 {
return big.NewInt(0)
}
if crr == 100 {
result := big.NewInt(0).Mul(wantReceive, reserve)
return result.Div(result, supply)
}
tSupply := newFloat(0).SetInt(supply)
tReserve := newFloat(0).SetInt(reserve)
tWantReceive := newFloat(0).SetInt(wantReceive)
res := newFloat(0).Add(tWantReceive, tSupply) // reserve + supply
res.Quo(res, tSupply) // (reserve + supply) / supply
res = math.Pow(res, newFloat(100/float64(crr))) // ((reserve + supply) / supply)^(100/c)
res.Sub(res, newFloat(1)) // (((reserve + supply) / supply)^(100/c) - 1)
res.Mul(res, tReserve) // reserve * (((reserve + supply) / supply)^(100/c) - 1)
result, _ := res.Int(nil)
return result
}
// CalculateSaleReturn returns amount of BIP user will receive by depositing given amount of coins
// Return = reserve * (1 - (1 - sellAmount / supply) ^ (100 / crr))
func CalculateSaleReturn(supply *big.Int, reserve *big.Int, crr uint32, sellAmount *big.Int) *big.Int {
// special case for 0 sell amount
if sellAmount.Sign() == 0 {
return big.NewInt(0)
}
// special case for selling the entire supply
if sellAmount.Cmp(supply) == 0 {
return big.NewInt(0).Set(reserve)
}
if crr == 100 {
ret := big.NewInt(0).Mul(reserve, sellAmount)
ret.Div(ret, supply)
return ret
}
tSupply := newFloat(0).SetInt(supply)
tReserve := newFloat(0).SetInt(reserve)
tSellAmount := newFloat(0).SetInt(sellAmount)
res := newFloat(0).Quo(tSellAmount, tSupply) // sellAmount / supply
res.Sub(newFloat(1), res) // (1 - sellAmount / supply)
res = math.Pow(res, newFloat(100/(float64(crr)))) // (1 - sellAmount / supply) ^ (100 / crr)
res.Sub(newFloat(1), res) // (1 - (1 - sellAmount / supply) ^ (1 / (crr / 100)))
res.Mul(res, tReserve) // reserve * (1 - (1 - sellAmount / supply) ^ (1 / (crr / 100)))
result, _ := res.Int(nil)
return result
}
// CalculateSaleAmount is the reversed version of function CalculateSaleReturn
// Deposit = -(-1 + (-(wantReceive - reserve)/reserve)^(1/crr)) * supply
func CalculateSaleAmount(supply *big.Int, reserve *big.Int, crr uint32, wantReceive *big.Int) *big.Int {
if wantReceive.Sign() == 0 {
return big.NewInt(0)
}
if crr == 100 {
ret := big.NewInt(0).Mul(wantReceive, supply)
ret.Div(ret, reserve)
return ret
}
tSupply := newFloat(0).SetInt(supply)
tReserve := newFloat(0).SetInt(reserve)
tWantReceive := newFloat(0).SetInt(wantReceive)
res := newFloat(0).Sub(tWantReceive, tReserve) // (wantReceive - reserve)
res.Neg(res) // -(wantReceive - reserve)
res.Quo(res, tReserve) // -(wantReceive - reserve)/reserve
res = math.Pow(res, newFloat(float64(crr)/100)) // (-(wantReceive - reserve)/reserve)^(1/crr)
res.Add(res, newFloat(-1)) // -1 + (-(wantReceive - reserve)/reserve)^(1/crr)
res.Neg(res) // -(-1 + (-(wantReceive - reserve)/reserve)^(1/crr))
res.Mul(res, tSupply) // -(-1 + (-(wantReceive - reserve)/reserve)^(1/crr)) * supply
result, _ := res.Int(nil)
return result
}
func newFloat(x float64) *big.Float {
return big.NewFloat(x).SetPrec(precision)
}