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simulation package for Exponent CLMM (Concentrated Liquidity Market Maker) markets.","maintainers":[{"name":"8bitpen","email":"8bitpen@gmail.com"},{"name":"valentin-exponent","email":"valentin@incility.com"}],"readme":"# @exponent-labs/market-three-math\n\nMathematical simulation package for Exponent CLMM (Concentrated Liquidity Market Maker) markets.\n\n## Overview\n\nThis package provides TypeScript implementations of the CLMM mathematical functions from the Exponent protocol. It enables client-side simulation of:\n\n- **Swap operations**: Simulate PT ↔ SY trades with accurate pricing and fee calculations\n- **Liquidity deposits**: Calculate required token amounts for concentrated liquidity positions\n- **Price calculations**: Convert between effective prices, implied rates, and tick indices\n\nThe implementations are direct ports from the Rust on-chain program code in `solana/programs/exponent_clmm`.\n\n## Installation\n\n```bash\nyarn add @exponent-labs/market-three-math\n```\n\n## Usage\n\n### Simulating a Swap\n\n```typescript\nimport { MarketThreeState, SwapDirection, simulateSwap } from \"@exponent-labs/market-three-math\"\n\n// Prepare market state\nconst marketState: MarketThreeState = {\n  financials: {\n    expirationTs: Date.now() / 1000 + 86400, // 1 day from now\n    ptBalance: 1000000,\n    syBalance: 1000000,\n    liquidityBalance: 1000000,\n  },\n  configurationOptions: {\n    lnFeeRateRoot: 0.001,\n    rateScalarRoot: 5.0,\n    treasuryFeeBps: 2000, // 20%\n    lastLnImpliedRate: 0.05,\n    epsilonClamp: 0.000001,\n    minLpTickAmount: 1000,\n    maxLpSupply: 10000000000,\n    tickSpace: 100,\n    priceDecimals: 4,\n  },\n  ticks: {\n    currentTick: 500,\n    currentSpotPrice: 0.05,\n    feeGrowthIndexGlobalPt: 0,\n    feeGrowthIndexGlobalSy: 0,\n    ticks: [\n      // ... tick data\n    ],\n    market: \"marketAddress\",\n  },\n  currentSyExchangeRate: 1.0,\n}\n\n// Simulate buying PT with SY\nconst swapResult = simulateSwap(marketState, {\n  direction: SwapDirection.SyToPt,\n  amountIn: 100000, // 100k SY\n  syExchangeRate: 1.0,\n  isCurrentFlashSwap: false,\n  priceSpotLimit: 0.06, // Maximum price willing to pay\n})\n\nconsole.log(\"PT received:\", swapResult.amountOut)\nconsole.log(\"Fees paid:\", swapResult.lpFeeChargedOutToken + swapResult.protocolFeeChargedOutToken)\nconsole.log(\"Final price:\", swapResult.finalSpotPrice)\n```\n\n### Simulating Liquidity Deposit\n\n```typescript\nimport { estimateBalancedDeposit, simulateAddLiquidity } from \"@exponent-labs/market-three-math\"\n\n// Estimate balanced amounts for a target liquidity\nconst { ptNeeded, syNeeded } = estimateBalancedDeposit(\n  marketState,\n  100000, // Target liquidity\n  4.5, // Lower tick APY (%)\n  5.5, // Upper tick APY (%)\n)\n\n// Simulate the actual deposit\nconst depositResult = simulateAddLiquidity(marketState, {\n  lowerTick: 45000, // 4.5% in basis points\n  upperTick: 55000, // 5.5% in basis points\n  maxSy: syNeeded,\n  maxPt: ptNeeded,\n  syExchangeRate: 1.0,\n})\n\nconsole.log(\"Liquidity added:\", depositResult.deltaL)\nconsole.log(\"PT spent:\", depositResult.ptSpent)\nconsole.log(\"SY spent:\", depositResult.sySpent)\n```\n\n### Working with Effective Prices\n\n```typescript\nimport { EffSnap, normalizedTimeRemaining } from \"@exponent-labs/market-three-math\"\n\nconst secondsRemaining = 86400 // 1 day\nconst syExchangeRate = 1.0\n\nconst snap = new EffSnap(normalizedTimeRemaining(secondsRemaining), syExchangeRate)\n\n// Convert ln implied rate to effective price\nconst lnImpliedRate = 0.05 // 5%\nconst effectivePrice = snap.getEffectivePrice(lnImpliedRate)\n\n// Convert back from effective price to implied rate\nconst recoveredRate = snap.impliedRateFromEffectivePrice(effectivePrice)\n```\n\n## Key Concepts\n\n### Effective Price Model\n\nThe CLMM uses an effective price model where:\n\n```\nC = e^(-τ * u) / r\n```\n\nWhere:\n\n- `C` = effective price (PT per SY)\n- `τ` = time factor (normalized time to expiry)\n- `u` = ln implied rate (spot price)\n- `r` = SY exchange rate\n\n### Tick-Based Liquidity\n\nLiquidity is concentrated in tick ranges, similar to Uniswap v3:\n\n- Each tick represents a specific implied rate\n- Liquidity is active only when the current price is within the tick range\n- Ticks store principal PT and SY for accurate accounting\n\n### Fee Structure\n\nFees are calculated as:\n\n- LP fee: Retained by liquidity providers\n- Protocol fee: Sent to treasury (typically 20% of total fee)\n- Total fee rate increases as expiration approaches\n\n## API Reference\n\n### Types\n\n- `MarketThreeState`: Complete market state required for simulations\n- `SwapArgs`: Arguments for swap simulation\n- `SwapOutcome`: Results of a swap simulation\n- `AddLiquidityArgs`: Arguments for liquidity deposit simulation\n- `AddLiquidityOutcome`: Results of liquidity deposit simulation\n- `Tick`: Individual tick data structure\n- `Ticks`: Complete ticks array with metadata\n\n### Functions\n\n#### Swap Functions\n\n- `simulateSwap(marketState, args)`: Simulate a swap operation\n- `getSwapQuote(marketState, amountIn, direction)`: Quick quote for a swap\n\n#### Liquidity Functions\n\n- `simulateAddLiquidity(marketState, args)`: Simulate liquidity deposit\n- `estimateBalancedDeposit(marketState, targetLiquidity, lowerTickApy, upperTickApy)`: Estimate balanced PT/SY amounts\n- `computeLiquidityTargetAndTokenNeeds(...)`: Low-level liquidity calculation\n\n#### Utility Functions\n\n- `EffSnap`: Effective price snapshot class\n- `calculateFeeRate(lnFeeRateRoot, secondsRemaining)`: Calculate current fee rate\n- `normalizedTimeRemaining(secondsRemaining)`: Normalize time to [0,1]\n- `getLnImpliedRate(tickKey)`: Convert tick key to implied rate\n- `convertApyToApyBp(apyPercent)` / `convertApyBpToApy(apyBp)`: APY conversion utilities\n\n## Relationship to On-Chain Code\n\nThis package is a direct port of the Rust implementations from:\n\n- `solana/programs/exponent_clmm/src/state/market_three/helpers/swap.rs`\n- `solana/programs/exponent_clmm/src/state/market_three/helpers/add_liquidity.rs`\n- `solana/programs/exponent_clmm/src/utils/math.rs`\n\nThe TypeScript implementations maintain mathematical equivalence with the on-chain code to ensure accurate simulations.\n\n## License\n\nAGPL-3.0\n","readmeFilename":"README.md"}