mev-beta/pkg/pricing/uniswap_v3.go

package pricing

import (
	"math"
	"math/big"
)

// Uniswap V3 Pricing Library
// Based on: https://github.com/t4sk/notes/tree/main/python/uniswap-v3
//
// Key concepts:
// - Prices are stored as sqrtPriceX96 (Q64.96 fixed-point format)
// - Ticks represent discrete 0.01% price movements
// - Each tick corresponds to price = 1.0001^tick

const (
	// Q96 is the scaling factor used in Uniswap V3 (2^96)
	Q96 = 96

	// TickBase is the constant representing each tick's 0.01% price change
	TickBase = 1.0001

	// MinTick is the minimum tick value in Uniswap V3
	MinTick = -887272

	// MaxTick is the maximum tick value in Uniswap V3
	MaxTick = 887272
)

var (
	// q96Big is 2^96 as a big.Int for calculations
	q96Big = new(big.Int).Lsh(big.NewInt(1), Q96)

	// q96Float is 2^96 as a big.Float for calculations
	q96Float = new(big.Float).SetInt(q96Big)
)

// SqrtPriceX96ToPrice converts Uniswap V3's sqrtPriceX96 to a human-readable price
//
// Formula: price = (sqrtPriceX96 / 2^96)^2 * (10^decimals0 / 10^decimals1)
//
// Example from Python notebook:
//   sqrt_price_x_96 = 3443439269043970780644209
//   price = (sqrt_price_x_96 / 2^96)^2 * (1e18 / 1e6) ≈ 1888.97 USDC per ETH
//
// Parameters:
//   - sqrtPriceX96: The sqrt price in Q64.96 format
//   - token0Decimals: Number of decimals for token0
//   - token1Decimals: Number of decimals for token1
//
// Returns: Price of token0 in terms of token1
func SqrtPriceX96ToPrice(sqrtPriceX96 *big.Int, token0Decimals, token1Decimals uint8) *big.Float {
	if sqrtPriceX96 == nil || sqrtPriceX96.Sign() == 0 {
		return big.NewFloat(0)
	}

	// Convert to float
	sqrtPriceFloat := new(big.Float).SetInt(sqrtPriceX96)

	// Divide by 2^96 to get the actual sqrt(price)
	sqrtPrice := new(big.Float).Quo(sqrtPriceFloat, q96Float)

	// Square to get price
	price := new(big.Float).Mul(sqrtPrice, sqrtPrice)

	// Adjust for decimal differences
	// price = price * (10^token0Decimals / 10^token1Decimals)
	if token0Decimals != token1Decimals {
		decimalAdjustment := new(big.Float).SetInt(
			new(big.Int).Exp(
				big.NewInt(10),
				big.NewInt(int64(token0Decimals)-int64(token1Decimals)),
				nil,
			),
		)
		price = new(big.Float).Mul(price, decimalAdjustment)
	}

	return price
}

// TickToPrice converts a Uniswap V3 tick to a price
//
// Formula: price = 1.0001^tick * (10^decimals0 / 10^decimals1)
//
// Example from Python notebook:
//   tick = -200963
//   price = 1.0001^(-200963) * (1e18 / 1e6) ≈ 1873.80 USDC per ETH
//
// Parameters:
//   - tick: The tick value (-887272 to 887272)
//   - token0Decimals: Number of decimals for token0
//   - token1Decimals: Number of decimals for token1
//
// Returns: Price of token0 in terms of token1
func TickToPrice(tick int32, token0Decimals, token1Decimals uint8) *big.Float {
	// Calculate price = 1.0001^tick
	price := math.Pow(TickBase, float64(tick))

	// Adjust for decimal differences
	decimalAdjustment := math.Pow10(int(token0Decimals) - int(token1Decimals))
	adjustedPrice := price * decimalAdjustment

	return big.NewFloat(adjustedPrice)
}

// SqrtPriceX96ToTick converts sqrtPriceX96 to a tick value
//
// Formula: tick = 2 * ln(sqrtPrice / 2^96) / ln(1.0001)
//
// Example from Python notebook:
//   sqrt_price = 3436899527919986964832931
//   tick = 2 * ln(sqrt_price / 2^96) / ln(1.0001) ≈ -200920.39
//
// Parameters:
//   - sqrtPriceX96: The sqrt price in Q64.96 format
//
// Returns: Tick value (rounded to nearest integer)
func SqrtPriceX96ToTick(sqrtPriceX96 *big.Int) int32 {
	if sqrtPriceX96 == nil || sqrtPriceX96.Sign() == 0 {
		return 0
	}

	// Convert to float64 for logarithm calculation
	sqrtPriceFloat := new(big.Float).SetInt(sqrtPriceX96)
	q96Float := new(big.Float).SetInt(q96Big)

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

	// Convert to float64
	ratioFloat64, _ := ratio.Float64()

	// Calculate tick = 2 * ln(ratio) / ln(1.0001)
	tick := 2.0 * math.Log(ratioFloat64) / math.Log(TickBase)

	// Round to nearest integer
	tickRounded := int32(math.Round(tick))

	// Clamp to valid range
	if tickRounded < MinTick {
		return MinTick
	}
	if tickRounded > MaxTick {
		return MaxTick
	}

	return tickRounded
}

// PriceToTick converts a price to a tick value
//
// Formula: tick = ln(price) / ln(1.0001)
//
// Note: Price should already be adjusted for decimal differences
//
// Parameters:
//   - price: The price ratio (token0/token1), adjusted for decimals
//
// Returns: Tick value (rounded to nearest integer)
func PriceToTick(price float64) int32 {
	if price <= 0 {
		return MinTick
	}

	// Calculate tick = ln(price) / ln(1.0001)
	tick := math.Log(price) / math.Log(TickBase)

	// Round to nearest integer
	tickRounded := int32(math.Round(tick))

	// Clamp to valid range
	if tickRounded < MinTick {
		return MinTick
	}
	if tickRounded > MaxTick {
		return MaxTick
	}

	return tickRounded
}

// TickToSqrtPriceX96 converts a tick to sqrtPriceX96
//
// Formula: sqrtPriceX96 = sqrt(1.0001^tick) * 2^96
//
// Parameters:
//   - tick: The tick value
//
// Returns: SqrtPriceX96 value
func TickToSqrtPriceX96(tick int32) *big.Int {
	// Calculate price = 1.0001^tick
	price := math.Pow(TickBase, float64(tick))

	// Calculate sqrtPrice = sqrt(price)
	sqrtPrice := math.Sqrt(price)

	// Calculate sqrtPriceX96 = sqrtPrice * 2^96
	sqrtPriceFloat := big.NewFloat(sqrtPrice)
	sqrtPriceX96Float := new(big.Float).Mul(sqrtPriceFloat, q96Float)

	// Convert to big.Int
	sqrtPriceX96Int, _ := sqrtPriceX96Float.Int(nil)

	return sqrtPriceX96Int
}

// GetPriceImpact calculates the price impact of a swap in basis points (BPS)
//
// Parameters:
//   - oldSqrtPriceX96: The sqrt price before the swap
//   - newSqrtPriceX96: The sqrt price after the swap
//   - token0Decimals: Number of decimals for token0
//   - token1Decimals: Number of decimals for token1
//
// Returns: Price impact in basis points (10000 BPS = 100%)
func GetPriceImpact(oldSqrtPriceX96, newSqrtPriceX96 *big.Int, token0Decimals, token1Decimals uint8) float64 {
	if oldSqrtPriceX96 == nil || newSqrtPriceX96 == nil ||
		oldSqrtPriceX96.Sign() == 0 || newSqrtPriceX96.Sign() == 0 {
		return 0
	}

	oldPrice := SqrtPriceX96ToPrice(oldSqrtPriceX96, token0Decimals, token1Decimals)
	newPrice := SqrtPriceX96ToPrice(newSqrtPriceX96, token0Decimals, token1Decimals)

	// Calculate percentage change
	priceDiff := new(big.Float).Sub(newPrice, oldPrice)
	percentChange := new(big.Float).Quo(priceDiff, oldPrice)

	// Convert to BPS (multiply by 10000)
	bps, _ := new(big.Float).Mul(percentChange, big.NewFloat(10000)).Float64()

	// Return absolute value
	if bps < 0 {
		return -bps
	}
	return bps
}

// GetTickSpacing returns the tick spacing for a given fee tier
//
// Uniswap V3 uses different tick spacings for different fee tiers:
//   - 0.01% fee (100): tick spacing = 1
//   - 0.05% fee (500): tick spacing = 10
//   - 0.30% fee (3000): tick spacing = 60
//   - 1.00% fee (10000): tick spacing = 200
//
// Parameters:
//   - feeBPS: The fee in basis points
//
// Returns: Tick spacing for the fee tier
func GetTickSpacing(feeBPS uint32) int32 {
	switch feeBPS {
	case 100: // 0.01%
		return 1
	case 500: // 0.05%
		return 10
	case 3000: // 0.30%
		return 60
	case 10000: // 1.00%
		return 200
	default:
		// Default to 60 (most common tier)
		return 60
	}
}

// GetNearestUsableTick returns the nearest usable tick for a given fee tier
//
// Ticks must be aligned to the tick spacing of the fee tier.
//
// Parameters:
//   - tick: The desired tick value
//   - tickSpacing: The tick spacing for the fee tier
//
// Returns: Nearest usable tick aligned to tick spacing
func GetNearestUsableTick(tick int32, tickSpacing int32) int32 {
	// Round to nearest multiple of tickSpacing
	rounded := (tick / tickSpacing) * tickSpacing

	// Clamp to valid range
	if rounded < MinTick {
		return MinTick
	}
	if rounded > MaxTick {
		return MaxTick
	}

	return rounded
}