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       1                 :             : // SPDX-License-Identifier: BUSL-1.1
       2                 :             : pragma solidity ^0.8.0;
       3                 :             : 
       4                 :             : /**
       5                 :             :  * @title PercentageMath library
       6                 :             :  * @author Aave
       7                 :             :  * @notice Provides functions to perform percentage calculations
       8                 :             :  * @dev Percentages are defined by default with 2 decimals of precision (100.00). The precision is indicated by PERCENTAGE_FACTOR
       9                 :             :  * @dev Operations are rounded. If a value is >=.5, will be rounded up, otherwise rounded down.
      10                 :             :  */
      11                 :             : library PercentageMath {
      12                 :             :   // Maximum percentage factor (100.00%)
      13                 :             :   uint256 internal constant PERCENTAGE_FACTOR = 1e4;
      14                 :             : 
      15                 :             :   // Half percentage factor (50.00%)
      16                 :             :   uint256 internal constant HALF_PERCENTAGE_FACTOR = 0.5e4;
      17                 :             : 
      18                 :             :   /**
      19                 :             :    * @notice Executes a percentage multiplication
      20                 :             :    * @dev assembly optimized for improved gas savings, see https://twitter.com/transmissions11/status/1451131036377571328
      21                 :             :    * @param value The value of which the percentage needs to be calculated
      22                 :             :    * @param percentage The percentage of the value to be calculated
      23                 :             :    * @return result value percentmul percentage
      24                 :             :    */
      25                 :             :   function percentMul(uint256 value, uint256 percentage) internal pure returns (uint256 result) {
      26                 :             :     // to avoid overflow, value <= (type(uint256).max - HALF_PERCENTAGE_FACTOR) / percentage
      27                 :             :     assembly {
      28                 :      158440 :       if iszero(
      29                 :             :         or(
      30                 :             :           iszero(percentage),
      31                 :             :           iszero(gt(value, div(sub(not(0), HALF_PERCENTAGE_FACTOR), percentage)))
      32                 :             :         )
      33                 :             :       ) {
      34                 :         303 :         revert(0, 0)
      35                 :             :       }
      36                 :             : 
      37                 :      158137 :       result := div(add(mul(value, percentage), HALF_PERCENTAGE_FACTOR), PERCENTAGE_FACTOR)
      38                 :             :     }
      39                 :             :   }
      40                 :             : 
      41                 :             :   /**
      42                 :             :    * @notice Executes a percentage division
      43                 :             :    * @dev assembly optimized for improved gas savings, see https://twitter.com/transmissions11/status/1451131036377571328
      44                 :             :    * @param value The value of which the percentage needs to be calculated
      45                 :             :    * @param percentage The percentage of the value to be calculated
      46                 :             :    * @return result value percentdiv percentage
      47                 :             :    */
      48                 :             :   function percentDiv(uint256 value, uint256 percentage) internal pure returns (uint256 result) {
      49                 :             :     // to avoid overflow, value <= (type(uint256).max - halfPercentage) / PERCENTAGE_FACTOR
      50                 :             :     assembly {
      51                 :       30126 :       if or(
      52                 :             :         iszero(percentage),
      53                 :             :         iszero(iszero(gt(value, div(sub(not(0), div(percentage, 2)), PERCENTAGE_FACTOR))))
      54                 :             :       ) {
      55                 :          74 :         revert(0, 0)
      56                 :             :       }
      57                 :             : 
      58                 :       30052 :       result := div(add(mul(value, PERCENTAGE_FACTOR), div(percentage, 2)), percentage)
      59                 :             :     }
      60                 :             :   }
      61                 :             : }