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gnsmath

Core mathematical operations for GnoSwap's concentrated liquidity AMM.

Overview

This package provides the fundamental calculations for concentrated liquidity, including sqrt price math, swap calculations, and bit manipulation utilities. All operations use Q96 and Q160 fixed-point arithmetic for precision.

The implementation follows Uniswap V3's mathematical model, ensuring compatibility and correctness for cross-chain liquidity operations.

Features

  • Bit Math: MSB/LSB calculations for tick bitmap operations
  • Sqrt Price Math: Token amount conversions using Q64.96 format
  • Swap Math: Single-step swap calculations with fee handling
  • Overflow Protection: Built-in int256 overflow detection
  • Rounding Control: Configurable rounding for AMM safety

Core Concepts

Q96 Fixed-Point Format

Square root prices use Q64.96 representation:

  • sqrtPriceX96 = sqrt(token1/token0) * 2^96
  • Enables precise integer arithmetic without floating-point

Rounding Directions

  • Round UP: Amounts owed TO pool (deposits, exact input)
  • Round DOWN: Amounts owed FROM pool (withdrawals, exact output)

Usage

 1import (
 2    "gno.land/p/gnoswap/gnsmath"
 3    i256 "gno.land/p/gnoswap/int256"
 4    u256 "gno.land/p/gnoswap/uint256"
 5)
 6
 7// Calculate token amounts for liquidity change
 8sqrtPriceA := u256.MustFromDecimal("79228162514264337593543950336")
 9sqrtPriceB := u256.MustFromDecimal("79625275426524748796330556128")
10liquidity := i256.MustFromDecimal("1000000000000000000")
11
12amount0 := gnsmath.GetAmount0Delta(sqrtPriceA, sqrtPriceB, liquidity)
13amount1 := gnsmath.GetAmount1Delta(sqrtPriceA, sqrtPriceB, liquidity)
14
15// Compute swap step
16feePips := uint64(3000) // 0.3% fee
17sqrtPriceNext, amountIn, amountOut, feeAmount := gnsmath.SwapMathComputeSwapStep(
18    currentPrice,
19    targetPrice,
20    liquidity,
21    amountRemaining,
22    feePips,
23)
24
25// Bit operations for tick bitmap
26tickBitmap := u256.NewUint(0xFF00)
27msb := gnsmath.BitMathMostSignificantBit(tickBitmap)
28println(msb) // Output: 15
29
30lsb := gnsmath.BitMathLeastSignificantBit(tickBitmap)
31println(lsb) // Output: 8

API

Bit Math

  • BitMathMostSignificantBit(x *u256.Uint) uint8 - Find MSB position (0-255)
  • BitMathLeastSignificantBit(x *u256.Uint) uint8 - Find LSB position (0-255)

Sqrt Price Math

  • GetAmount0Delta(sqrtRatioAX96, sqrtRatioBX96 *u256.Uint, liquidity *i256.Int) *i256.Int
    • Calculate token0 amount: liquidity * (1/√Pb - 1/√Pa)
  • GetAmount1Delta(sqrtRatioAX96, sqrtRatioBX96 *u256.Uint, liquidity *i256.Int) *i256.Int
    • Calculate token1 amount: liquidity * (√Pb - √Pa)

Swap Math

  • SwapMathComputeSwapStep(sqrtRatioCurrentX96, sqrtRatioTargetX96, liquidity *u256.Uint, amountRemaining *i256.Int, feePips uint64) (*u256.Uint, *u256.Uint, *u256.Uint, *u256.Uint)
    • Returns: (nextSqrtPrice, amountIn, amountOut, feeAmount)
    • Handles both exact input and exact output swaps