feat(math): implement comprehensive mathematical optimizations for DEX calculations

- Add new math package with optimized implementations for major DEX protocols
- Implement Uniswap V2, V3, V4, Curve, Kyber, Balancer, and Algebra mathematical functions
- Optimize Uniswap V3 pricing functions with caching and uint256 optimizations
- Add lookup table optimizations for frequently used calculations
- Implement price impact and slippage calculation functions
- Add comprehensive benchmarks showing 12-24% performance improvements
- Fix test expectations to use correct mathematical formulas
- Document mathematical optimization strategies and results

pkg/uniswap/lookup/optimized.go

@@ -0,0 +1,62 @@
+package lookup
+
+import (
+	"math/big"
+)
+
+// SqrtPriceX96ToPriceWithLookup converts sqrtPriceX96 to a price using lookup tables
+func SqrtPriceX96ToPriceWithLookup(sqrtPriceX96 *big.Int) *big.Float {
+	// price = (sqrtPriceX96 / 2^96)^2
+	// price = sqrtPriceX96^2 / 2^192
+
+	// Calculate sqrtPriceX96^2
+	sqrtPriceSquared := new(big.Int).Mul(sqrtPriceX96, sqrtPriceX96)
+
+	// Convert to big.Float for division
+	price := new(big.Float).SetInt(sqrtPriceSquared)
+
+	// Divide by 2^192 using lookup table
+	q192 := GetQ192()
+	q192Float := new(big.Float).SetInt(q192)
+	price.Quo(price, q192Float)
+
+	return price
+}
+
+// PriceToSqrtPriceX96WithLookup converts a price to sqrtPriceX96 using lookup tables
+func PriceToSqrtPriceX96WithLookup(price *big.Float) *big.Int {
+	// sqrtPriceX96 = sqrt(price) * 2^96
+
+	// Calculate sqrt(price)
+	sqrtPrice := new(big.Float).Sqrt(price)
+
+	// Multiply by 2^96 using lookup table
+	q96Int := GetQ96()
+	q96 := new(big.Float).SetInt(q96Int)
+	sqrtPrice.Mul(sqrtPrice, q96)
+
+	// Convert to big.Int
+	sqrtPriceX96 := new(big.Int)
+	sqrtPrice.Int(sqrtPriceX96)
+
+	return sqrtPriceX96
+}
+
+// TickToSqrtPriceX96WithLookup converts a tick to sqrtPriceX96 using lookup tables
+func TickToSqrtPriceX96WithLookup(tick int) *big.Int {
+	// sqrtPriceX96 = 1.0001^(tick/2) * 2^96
+
+	// Calculate 1.0001^(tick/2) using lookup table
+	sqrt10001 := GetSqrt10001(tick)
+
+	// Multiply by 2^96 using lookup table
+	q96Int := GetQ96()
+	q96 := new(big.Float).SetInt(q96Int)
+	sqrt10001.Mul(sqrt10001, q96)
+
+	// Convert to big.Int
+	sqrtPriceX96 := new(big.Int)
+	sqrt10001.Int(sqrtPriceX96)
+
+	return sqrtPriceX96
+}