mev-beta/pkg/uniswap/pricing.go

package uniswap

import (
	"math"
	"math/big"

	"github.com/holiman/uint256"
)

const (
	// Q96 represents 2^96 used in Uniswap V3 sqrtPriceX96 calculations
	Q96 = "79228162514264337593543950336" // 2^96 as string to avoid overflow

	// Tick spacing for different fee tiers
	LowTickSpacing    = 10
	MediumTickSpacing = 60
	HighTickSpacing   = 200
)

// SqrtPriceX96ToPrice converts sqrtPriceX96 to a price
// Price is represented as token1/token0
func SqrtPriceX96ToPrice(sqrtPriceX96 *big.Int) *big.Float {
	// price = (sqrtPriceX96 / 2^96)^2
	// price = sqrtPriceX96^2 / 2^192

	// Initialize global cached constants
	initConstants()

	// Validate input
	if sqrtPriceX96 == nil || sqrtPriceX96.Sign() <= 0 {
		return new(big.Float).SetFloat64(0.0)
	}

	// Convert to big.Float for precision
	sqrtPrice := new(big.Float).SetPrec(256).SetInt(sqrtPriceX96)

	// Calculate sqrtPrice^2
	price := new(big.Float).SetPrec(256)
	price.Mul(sqrtPrice, sqrtPrice)

	// Divide by 2^192 using global cached constant
	denominator := new(big.Float).SetPrec(256).SetInt(GetQ192())
	price.Quo(price, denominator)

	return price
}

// PriceToSqrtPriceX96 converts a price to sqrtPriceX96
func PriceToSqrtPriceX96(price *big.Float) *big.Int {
	// sqrtPriceX96 = sqrt(price) * 2^96

	// Initialize global cached constants
	initConstants()

	// Calculate sqrt(price)
	input := new(big.Float).SetPrec(256).Copy(price)
	sqrtPrice := new(big.Float).SetPrec(256).Sqrt(input)

	// Multiply by 2^96 using global cached constant
	multiplier := new(big.Float).SetPrec(256).SetInt(GetQ96())
	sqrtPrice.Mul(sqrtPrice, multiplier)

	// Convert to big.Int
	sqrtPriceX96 := new(big.Int)
	sqrtPrice.Int(sqrtPriceX96)

	return sqrtPriceX96
}

// TickToSqrtPriceX96 converts a tick to sqrtPriceX96
func TickToSqrtPriceX96(tick int) *big.Int {
	// sqrtPriceX96 = 1.0001^(tick/2) * 2^96

	// Initialize global cached constants
	initConstants()

	// Calculate 1.0001^(tick/2)
	// For better precision, especially for large tick values, we use logarithms
	// 1.0001^(tick/2) = e^(ln(1.0001) * tick/2)
	lnBase := GetLnBase() // ln(1.0001) ≈ 9.999500016666e-05
	logResult := lnBase * float64(tick) / 2.0
	result := math.Exp(logResult)

	// Convert to big.Float
	price := new(big.Float).SetFloat64(result)

	// Multiply by 2^96 using global cached constant
	price.Mul(price, GetQ96Float())

	// Convert to big.Int
	sqrtPriceX96 := new(big.Int)
	price.Int(sqrtPriceX96)

	return sqrtPriceX96
}

// SqrtPriceX96ToTick converts sqrtPriceX96 to a tick
func SqrtPriceX96ToTick(sqrtPriceX96 *big.Int) int {
	// tick = log_1.0001(sqrtPriceX96 / 2^96)^2
	// tick = log_1.0001(price)
	// tick = 2 * log_1.0001(sqrtPriceX96 / 2^96)

	if sqrtPriceX96.Cmp(big.NewInt(0)) <= 0 {
		return 0 // Invalid input
	}

	// Initialize cached constants
	initConstants()

	// Convert to big.Float
	sqrtPrice := new(big.Float).SetInt(sqrtPriceX96)
	q96Float := GetQ96Float()

	// Calculate sqrtPriceX96 / 2^96
	ratio := new(big.Float).Quo(sqrtPrice, q96Float)

	// Calculate ln(sqrtPriceX96 / 2^96) to avoid potential overflow
	// tick = 2 * ln(sqrtPriceX96 / 2^96) / ln(1.0001)
	lnRatio, _ := ratio.Float64()
	lnValue := math.Log(lnRatio)

	// Calculate tick
	tick := int(2.0 * lnValue * GetInvLnBase())

	return tick
}

// GetTickAtSqrtPrice calculates the tick for a given sqrtPriceX96 using uint256
func GetTickAtSqrtPrice(sqrtPriceX96 *uint256.Int) int {
	// This is a simplified implementation
	// In practice, you would use a more precise logarithmic calculation

	// Convert to big.Int for calculation
	sqrtPriceBig := sqrtPriceX96.ToBig()
	return SqrtPriceX96ToTick(sqrtPriceBig)
}

// GetNextTick calculates the next initialized tick
func GetNextTick(currentTick int, tickSpacing int) int {
	// Round down to nearest tick spacing
	tick := ((currentTick / tickSpacing) + 1) * tickSpacing
	return tick
}

// GetPreviousTick calculates the previous initialized tick
func GetPreviousTick(currentTick int, tickSpacing int) int {
	// Round down to nearest tick spacing
	tick := (currentTick / tickSpacing) * tickSpacing
	return tick
}