gno.land/p/gnoswap/gnsmath/v1⧉

1// Package gnsmath provides core mathematical operations for GnoSwap's concentrated liquidity AMM.2//3// ## Overview4//5// This package provides the fundamental calculations for concentrated liquidity,6// including tick conversion, liquidity math calculations, sqrt price math, swap7// calculations, and bit manipulation utilities. All operations use Q64.96,8// Q128.128, and Q160 fixed-point arithmetic where appropriate.9//10// The implementation follows Uniswap V3's mathematical model.11//12// ## Features13//14//   - Bit Math: MSB/LSB calculations for tick bitmap operations15//   - Tick Math: tick and Q64.96 sqrt-price conversions16//   - Liquidity Math: liquidity and token amount math for price ranges17//   - Sqrt Price Math: token amount conversions using Q64.96 format18//   - Swap Math: single-step swap calculations with fee handling19//   - Overflow Protection: explicit int256/uint256 overflow checks20//   - Rounding Control: configurable rounding for AMM safety21//22// ## Core Concepts23//24// ### Q64.96 Fixed-Point Format25//26// Square root prices use Q64.96 representation:27//   - sqrtPriceX96 = sqrt(token1/token0) * 2^9628//   - Enables precise integer arithmetic without floating-point29//30// ### Rounding Directions31//32//   - Round UP: amounts owed TO pool (deposits, exact input)33//   - Round DOWN: amounts owed FROM pool (withdrawals, exact output)34//35// ## API36//37// ### Bit Math38//39//   - BitMathMostSignificantBit(x *u256.Uint) uint840//   - BitMathLeastSignificantBit(x *u256.Uint) uint841//42// ### Tick Math43//44//   - TickMathGetSqrtRatioAtTick(tick int32) *u256.Uint45//   - TickMathGetTickAtSqrtRatio(sqrtPriceX96 *u256.Uint) int32; accepts46//     `[MinSqrtRatio, MaxSqrtRatio)` (the upper bound is exclusive)47//48// ### Liquidity Math49//50//   - GetLiquidityForAmounts(sqrtRatioX96, sqrtRatioAX96, sqrtRatioBX96, amount0, amount1 *u256.Uint) *u256.Uint51//   - GetAmountsForLiquidity(sqrtRatioX96, sqrtRatioAX96, sqrtRatioBX96, liquidity *u256.Uint) (*u256.Uint, *u256.Uint)52//   - LiquidityMathAddDelta(x *u256.Uint, y *i256.Int) *u256.Uint53//54// ### Sqrt Price Math55//56//   - GetAmount0Delta(sqrtRatioAX96, sqrtRatioBX96 *u256.Uint, liquidity *i256.Int) *i256.Int57//   - GetAmount1Delta(sqrtRatioAX96, sqrtRatioBX96 *u256.Uint, liquidity *i256.Int) *i256.Int58//59// ### Swap Math60//61//   - SwapMathComputeSwapStep(sqrtRatioCurrentX96, sqrtRatioTargetX96, liquidity *u256.Uint, amountRemaining *i256.Int, feePips uint64) (*u256.Uint, *u256.Uint, *u256.Uint, *u256.Uint)62package gnsmath63