DeFi 核心协议与流动性挖矿

// 核心公式：x * y = k
// x = 代币 A 的储备量
// y = 代币 B 的储备量
// k = 常数（仅在添加/移除流动性时变化）

function getAmountOut(uint amountIn, uint reserveIn, uint reserveOut) 
    internal pure returns (uint amountOut) 
{
    require(amountIn > 0, "INSUFFICIENT_INPUT_AMOUNT");
    require(reserveIn > 0 && reserveOut > 0, "INSUFFICIENT_LIQUIDITY");
    
    uint amountInWithFee = amountIn * 997;  // 0.3% 手续费
    uint numerator = amountInWithFee * reserveOut;
    uint denominator = reserveIn * 1000 + amountInWithFee;
    amountOut = numerator / denominator;
}

def impermanent_loss(price_ratio):
    """
    price_ratio = 新价格 / 原始价格
    返回无常损失百分比
    """
    r = price_ratio
    il = 2 * (r ** 0.5) / (1 + r) - 1
    return il * 100

# 价格变化 vs 无常损失
# 价格 ×1.5  → IL = -2.0%
# 价格 ×2    → IL = -5.7%
# 价格 ×3    → IL = -13.4%
# 价格 ×5    → IL = -25.5%

// Compound 的跳跃利率模型
function getBorrowRate(uint cash, uint borrows, uint reserves) public view returns (uint) {
    uint ur = utilizationRate(cash, borrows, reserves);  // 资金利用率
    
    if (ur <= kink) {
        // 低利用率：线性增长
        return multiplierPerBlock * ur / BASE + baseRatePerBlock;
    } else {
        // 高利用率：跳跃增长，激励还款
        uint normalRate = multiplierPerBlock * kink / BASE + baseRatePerBlock;
        uint excessUtil = ur - kink;
        return excessUtil * jumpMultiplierPerBlock / BASE + normalRate;
    }
}

function liquidate(address borrower, address repayToken, address seizeToken) external {
    // 1. 检查借款人的健康因子 < 1
    // 健康因子 = (抵押品价值 × 折扣) / 借款总额
    require(healthFactor(borrower) < 1e18, "Account is healthy");
    
    // 2. 清算人偿还借款人的债务
    uint repayAmount = min(borrowBalance, maxCloseFactor);
    
    // 3. 清算人获得抵押品（通常有 5-10% 折扣激励）
    uint seizeTokens = repayAmount * liquidationIncentive / priceOfSeizeToken;
    
    // 4. 执行转移
    transferCollateral(borrower, msg.sender, seizeTokens);
}

contract YieldCalculator {
    function calculateAPY(
        uint dailyRewardPerLP,     // 每日代币奖励 / LP 总量
        uint tokenPrice,           // 奖励代币价格（USD）
        uint lpTokenPrice,         // LP token 价格（USD）
        uint tradingFeeAPR,        // 年交易手续费率
        uint daysPerYear           // 365
    ) public pure returns (uint totalAPY) {
        uint rewardAPR = dailyRewardPerLP * tokenPrice * daysPerYear / lpTokenPrice;
        totalAPY = rewardAPR + tradingFeeAPR;
    }
    
    // 考虑复利的精确计算
    function calculateAPYCompounded(
        uint rewardPerBlock,       // 每区块奖励代币数
        uint blocksPerYear,        // 年区块数（ETH: ~2.6M）
        uint tokenPrice,
        uint lpValue
    ) public pure returns (uint apy) {
        uint yearlyRewardUSD = rewardPerBlock * blocksPerYear * tokenPrice;
        // 简单 APR
        apy = yearlyRewardUSD * 10000 / lpValue;  // 基点，10000=100%
    }
}