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Compound RateModel Contract analysis

RateModel The contract is used to calculate Compound A contract with a specific token lending rate , By analyzing it, we can know how to calculate the loan interest rate .

Demonstrate the code warehouse ：https://github.com/33357/compound-protocol

WhitePaperInterestRateModel.sol

Linear interest rate model

Contract initialization

• Public function （ Both inside and outside the contract can call ）
  • constructor
    • Code overview

      constructor(uint baseRatePerYear, uint multiplierPerYear) public {
                
          baseRatePerBlock = baseRatePerYear.div(blocksPerYear);
          multiplierPerBlock = multiplierPerYear.div(blocksPerYear);
          emit NewInterestParams(baseRatePerBlock, multiplierPerBlock);
      }
      

    • Parametric analysis
      function constructor The input parameters are 2 individual , Out of ginseng 0 individual , The corresponding explanation is as follows ：

      constructor(
          uint baseRatePerYear, //  Annual benchmark interest rate 
          uint multiplierPerYear //  Annual interest rate multiplier 
      ) public {
                
          ...
      }
      

    • Implementation analysis

      ...
      {
                
          //  Block benchmark interest rate  =  Annual benchmark interest rate  /  Number of blocks per year 
          baseRatePerBlock = baseRatePerYear.div(blocksPerYear);
          //  Block rate multiplier  =  Annual interest rate multiplier  /  Number of blocks per year 
          multiplierPerBlock = multiplierPerYear.div(blocksPerYear);
          //  Triggering event  NewInterestParams
          emit NewInterestParams(baseRatePerBlock, multiplierPerBlock);
      }
      

    • summary
      The contract needs to be block Calculate interest rates as time units , Therefore, it is necessary to baseRatePerYear and multiplierPerYear Convert to baseRatePerBlock and multiplierPerBlock. there blocksPerYear by 2102400, Is on average 15 second One block Calculated .

Lending rate of funds

• Public function （ Both inside and outside the contract can call ）
  • utilizationRate
    • Code overview

      function utilizationRate(uint cash, uint borrows, uint reserves) public pure returns (uint) {
                
          if (borrows == 0) {
                
              return 0;
          }
          return borrows.mul(1e18).div(cash.add(borrows).sub(reserves));
      }
      

    • Parametric analysis
      function utilizationRate The input parameters are 3 individual , Out of ginseng 1 individual , The corresponding explanation is as follows ：

      constructor(
          uint cash, //  Token balance 
          uint borrows, //  Total number of tokens lent by users 
          uint reserves //  Total number of reserve tokens 
      ) public view returns (
          uint //  Lending rate of funds 
      ){
                
          ...
      }
      

    • Implementation analysis

      ...
      {
                
          //  If the total number of tokens lent is  0, The lending rate is also  0
          if (borrows == 0) {
                
              return 0;
          }
          // borrows * 1e18 / (cash + borrows - reserves)
          return borrows.mul(1e18).div(cash.add(borrows).sub(reserves));
      }
      

    • summary
      utilizationRate Used to calculate tokens Lending rate of funds , Lending rate of funds The calculation formula of is Lending rate of funds = Total number of tokens lent / ( Token balance + Total number of tokens lent - Total number of reserve tokens ). Due to the use of unsigned integers Lending rate of funds It's not accurate enough , So it needs to be multiplied by 1e18, Expand the accuracy range .

Capital interest rate

• Public function （ Both inside and outside the contract can call ）
  • getBorrowRate
    • Code overview

      function getBorrowRate(uint cash, uint borrows, uint reserves) public view returns (uint) {
                
          uint ur = utilizationRate(cash, borrows, reserves);
          return ur.mul(multiplierPerBlock).div(1e18).add(baseRatePerBlock);
      }
      

    • Parametric analysis
      function getBorrowRate The input parameters are 3 individual , Out of ginseng 1 individual , The corresponding explanation is as follows ：

      function getBorrowRate(
          uint cash, //  Token balance 
          uint borrows, //  Total number of tokens lent by users 
          uint reserves //  Total number of reserve tokens 
      ) public view returns (
          uint //  Block lending rate 
      ) {
                
          ...
      }
      

    • Implementation analysis

      ...
      {
                
          //  Calculate the lending rate 
          uint ur = utilizationRate(cash, borrows, reserves);
          // ur * multiplierPerBlock / 1e18 + baseRatePerBlock
          return ur.mul(multiplierPerBlock).div(1e18).add(baseRatePerBlock);
      }
      

    • summary
      getBorrowRate Used to calculate tokens Block lending rate , Block lending rate The calculation formula of is Block lending rate = Lending rate of funds * Block rate multiplier + Block benchmark interest rate . because Lending rate of funds The accuracy range is expanded , It needs to be divided by 1e18 Get the actual value .
  • getSupplyRate
    • Code overview

      function getSupplyRate(uint cash, uint borrows, uint reserves, uint reserveFactorMantissa) public view returns (uint) {
                
          uint oneMinusReserveFactor = uint(1e18).sub(reserveFactorMantissa);
          uint borrowRate = getBorrowRate(cash, borrows, reserves);
          uint rateToPool = borrowRate.mul(oneMinusReserveFactor).div(1e18);
          return utilizationRate(cash, borrows, reserves).mul(rateToPool).div(1e18);
      }
      

    • Parametric analysis
      function getSupplyRate The input parameters are 4 individual , Out of ginseng 1 individual , The corresponding explanation is as follows ：

      getSupplyRate(
          uint cash, //  Token balance 
          uint borrows, //  Total number of tokens lent by users 
          uint reserves, //  Total number of reserve tokens 
          uint reserveFactorMantissa //  Reserve ratio 
      ) public view returns (
          uint //  Block pledge interest rate 
      ) {
                
          ...
      }
      

    • Implementation analysis

      ...
      {
                
          // 1 - reserveFactorMantissa
          uint oneMinusReserveFactor = uint(1e18).sub(reserveFactorMantissa);
          //  Get the loan interest rate  borrowRate
          uint borrowRate = getBorrowRate(cash, borrows, reserves);
          // borrowRate * (1 - reserveFactorMantissa)
          uint rateToPool = borrowRate.mul(oneMinusReserveFactor).div(1e18);
          // utilizationRate * borrowRate * (1 - reserveFactorMantissa)
          return utilizationRate(cash, borrows, reserves).mul(rateToPool).div(1e18);
      }
      

    • summary
      getSupplyRate Used to calculate tokens Block pledge interest rate , Block pledge interest rate The calculation formula of is Block pledge interest rate = Lending rate of funds * The interest rate for borrowing * (1 - Reserve ratio ) = The interest rate for borrowing * Lending rate of funds * (1 - Reserve ratio ). because Lending rate of funds The accuracy range is expanded , It needs to be divided by 1e18 Get the actual value .

BaseJumpRateModelV2.sol

Inflection point interest rate model

Contract initialization

• Internal function （ Can only be called within the contract ）
  • constructor
    • Code overview

      constructor(uint baseRatePerYear, uint multiplierPerYear, uint jumpMultiplierPerYear, uint kink_, address owner_) internal {
                
          owner = owner_;
          updateJumpRateModelInternal(baseRatePerYear,  multiplierPerYear, jumpMultiplierPerYear, kink_);
      }
      

    • Parametric analysis
      function constructor The input parameters are 5 individual , Out of ginseng 0 individual , The corresponding explanation is as follows ：

      constructor(
          uint baseRatePerYear, //  Annual benchmark interest rate 
          uint multiplierPerYear //  Annual interest rate multiplier 
          uint jumpMultiplierPerYear, //  Inflection point annual interest rate multiplier 
          uint kink_, //  Inflection point capital lending rate 
          address owner_ //  owner 
      ) internal {
                
          ...
      }
      

    • Implementation analysis

      ...
      {
                
          //  Record owner 
          owner = owner_;
          //  Update inflection point interest rate model parameters 
          updateJumpRateModelInternal(baseRatePerYear,  multiplierPerYear, jumpMultiplierPerYear, kink_);
      }
      

    • summary
      Inflection point interest rate model Than Linear interest rate model More Inflection point annual interest rate multiplier and Inflection point capital lending rate These two parameters .
  • updateJumpRateModelInternal
    • Code overview

      function updateJumpRateModelInternal(uint baseRatePerYear, uint multiplierPerYear, uint jumpMultiplierPerYear, uint kink_) internal {
                
          baseRatePerBlock = baseRatePerYear.div(blocksPerYear);
          multiplierPerBlock = (multiplierPerYear.mul(1e18)).div(blocksPerYear.mul(kink_));
          jumpMultiplierPerBlock = jumpMultiplierPerYear.div(blocksPerYear);
          kink = kink_;
          emit NewInterestParams(baseRatePerBlock, multiplierPerBlock, jumpMultiplierPerBlock, kink);
      }
      

    • Parametric analysis
      function updateJumpRateModelInternal The input parameters are 4 individual , Out of ginseng 0 individual , The corresponding explanation is as follows ：

      function updateJumpRateModelInternal(
          uint baseRatePerYear, //  Annual benchmark interest rate 
          uint multiplierPerYear //  Annual interest rate multiplier 
          uint jumpMultiplierPerYear, //  Inflection point annual interest rate multiplier 
          uint kink_, //  Inflection point capital lending rate 
      ) internal {
                
          ...
      }
      

    • Implementation analysis

      ...
      {
                
          //  Block benchmark interest rate  =  Annual benchmark interest rate  /  Number of blocks per year 
          baseRatePerBlock = baseRatePerYear.div(blocksPerYear);
          //  Block rate multiplier  =  Annual benchmark interest rate  / ( Number of blocks per year  *  Inflection point capital lending rate )
          multiplierPerBlock = (multiplierPerYear.mul(1e18)).div(blocksPerYear.mul(kink_));
          //  Inflection point block interest rate multiplier  =  Inflection point annual interest rate multiplier  /  Number of blocks per year 
          jumpMultiplierPerBlock = jumpMultiplierPerYear.div(blocksPerYear);
          //  Record the inflection point capital lending rate 
          kink = kink_;
          //  Triggering event  NewInterestParams
          emit NewInterestParams(baseRatePerBlock, multiplierPerBlock, jumpMultiplierPerBlock, kink);
      }
      

    • summary
      Inflection point interest rate model Middle computation Block rate multiplier when , Methods and Linear interest rate model Dissimilarity ： Inflection point capital lending rate The higher the , Block rate multiplier The lower the , I am not very clear about its purpose .( It may be that the deeper the token market is, the higher the capital lending rate at the inflection point is , The block rate multiplier can be set lower , You can discuss )

Lending rate of funds

• Public function （ Both inside and outside the contract can call ）
  • utilizationRate
    • Code overview

      function utilizationRate(uint cash, uint borrows, uint reserves) public pure returns (uint) {
                
          if (borrows == 0) {
                
              return 0;
          }
          return borrows.mul(1e18).div(cash.add(borrows).sub(reserves));
      }
      

    • Parametric analysis
      function utilizationRate The input parameters are 3 individual , Out of ginseng 1 individual , The corresponding explanation is as follows ：

      constructor(
          uint cash, //  Token balance 
          uint borrows, //  Total number of tokens lent by users 
          uint reserves //  Total number of reserve tokens 
      ) public view returns (
          uint //  Lending rate of funds 
      ){
                
          ...
      }
      

    • Implementation analysis

      ...
      {
                
          //  If the total number of tokens lent is  0, The lending rate is also  0
          if (borrows == 0) {
                
              return 0;
          }
          //  Lending rate of funds  = borrows * 1e18 / (cash + borrows - reserves)
          return borrows.mul(1e18).div(cash.add(borrows).sub(reserves));
      }
      

    • summary
      Inflection point interest rate model Middle computation Lending rate of funds and Linear interest rate model identical .

Capital interest rate

• Internal function （ Can only be called inside the contract ）
  • getBorrowRate
    • Code overview

      function getBorrowRateInternal(uint cash, uint borrows, uint reserves) internal view returns (uint) {
                
          uint util = utilizationRate(cash, borrows, reserves);
          if (util <= kink) {
                
              return util.mul(multiplierPerBlock).div(1e18).add(baseRatePerBlock);
          } else {
                
              uint normalRate = kink.mul(multiplierPerBlock).div(1e18).add(baseRatePerBlock);
              uint excessUtil = util.sub(kink);
              return excessUtil.mul(jumpMultiplierPerBlock).div(1e18).add(normalRate);
          }
      }
      

    • Parametric analysis
      function getBorrowRateInternal The input parameters are 3 individual , Out of ginseng 1 individual , The corresponding explanation is as follows ：

      function getBorrowRate(
          uint cash, //  Token balance 
          uint borrows, //  Total number of tokens lent by users 
          uint reserves //  Total number of reserve tokens 
      ) internal view returns (
          uint //  Block lending rate 
      ) {
                
          ...
      }
      

    • Implementation analysis

      {
                
          //  Obtain the lending rate of funds  util
          uint util = utilizationRate(cash, borrows, reserves);
          //  If  util < kink
          if (util <= kink) {
                
              // return util * multiplierPerBlock + baseRatePerBlock
              return util.mul(multiplierPerBlock).div(1e18).add(baseRatePerBlock);
          } else {
                
              //  The lending rate before the inflection point  = kink * multiplierPerBlock + baseRatePerBlock
              uint normalRate = kink.mul(multiplierPerBlock).div(1e18).add(baseRatePerBlock);
              //  The lending rate of funds beyond the inflection point  = util - kink
              uint excessUtil = util.sub(kink);
              //  Block lending rate  = (util - kink) * jumpMultiplierPerBlock + kink * multiplierPerBlock + baseRatePerBlock
              return excessUtil.mul(jumpMultiplierPerBlock).div(1e18).add(normalRate);
          }
      }
      

    • summary
      Inflection point interest rate model Middle computation Block lending rate The calculation formula of is divided into two parts ： stay Lending rate of funds lower than Inflection point capital lending rate when , The formula is ： Block lending rate = Lending rate of funds * Block rate multiplier + Block benchmark interest rate ; stay Lending rate of funds higher than Inflection point capital lending rate when , The formula is ： Block lending rate = ( Lending rate of funds - Inflection point capital lending rate ) * Inflection point block interest rate multiplier + Inflection point capital lending rate * Block rate multiplier + Block benchmark interest rate .
  • getSupplyRate
    • Code overview

      function getSupplyRate(uint cash, uint borrows, uint reserves, uint reserveFactorMantissa) public view returns (uint) {
                
          uint oneMinusReserveFactor = uint(1e18).sub(reserveFactorMantissa);
          uint borrowRate = getBorrowRateInternal(cash, borrows, reserves);
          uint rateToPool = borrowRate.mul(oneMinusReserveFactor).div(1e18);
          return utilizationRate(cash, borrows, reserves).mul(rateToPool).div(1e18);
      }
      

    • Parametric analysis
      function getSupplyRate The input parameters are 4 individual , Out of ginseng 1 individual , The corresponding explanation is as follows ：

      getSupplyRate(
          uint cash, //  Token balance 
          uint borrows, //  Total number of tokens lent by users 
          uint reserves, //  Total number of reserve tokens 
          uint reserveFactorMantissa //  Reserve ratio 
      ) public view returns (
          uint //  Block pledge interest rate 
      ) {
                
          ...
      }
      

    • Implementation analysis

      ...
      {
                
          // 1 - reserveFactorMantissa
          uint oneMinusReserveFactor = uint(1e18).sub(reserveFactorMantissa);
          //  Get the loan interest rate  borrowRate
          uint borrowRate = getBorrowRateInternal(cash, borrows, reserves);
          // rateToPool = borrowRate * (1 - reserveFactorMantissa)
          uint rateToPool = borrowRate.mul(oneMinusReserveFactor).div(1e18);
          //  Block pledge interest rate  = utilizationRate * borrowRate * (1 - reserveFactorMantissa)
          return utilizationRate(cash, borrows, reserves).mul(rateToPool).div(1e18);
      }
      

    • summary
      Inflection point interest rate model Middle computation Capital pledge interest rate and Linear interest rate model identical .