// SPDX-License-Identifier: agpl-3.0
pragma solidity 0.8.4;
 
import {Errors} from "../helpers/Errors.sol";
 
/**
 * @title WadRayMath library
 * @author Bend
 * @dev Provides mul and div function for wads (decimal numbers with 18 digits precision) and rays (decimals with 27 digits)
 **/
 
library WadRayMath {
  uint256 internal constant WAD = 1e18;
  uint256 internal constant HALF_WAD = WAD / 2;
 
  uint256 internal constant RAY = 1e27;
  uint256 internal constant HALF_RAY = RAY / 2;
 
  uint256 internal constant WAD_RAY_RATIO = 1e9;
 
  /**
   * @return One ray, 1e27
   **/
  function ray() internal pure returns (uint256) {
    return RAY;
  }
 
  /**
   * @return One wad, 1e18
   **/
 
  function wad() internal pure returns (uint256) {
    return WAD;
  }
 
  /**
   * @return Half ray, 1e27/2
   **/
  function halfRay() internal pure returns (uint256) {
    return HALF_RAY;
  }
 
  /**
   * @return Half ray, 1e18/2
   **/
  function halfWad() internal pure returns (uint256) {
    return HALF_WAD;
  }
 
  /**
   * @dev Multiplies two wad, rounding half up to the nearest wad
   * @param a Wad
   * @param b Wad
   * @return The result of a*b, in wad
   **/
  function wadMul(uint256 a, uint256 b) internal pure returns (uint256) {
    if (a == 0 || b == 0) {
      return 0;
    }
 
    require(a <= (type(uint256).max - HALF_WAD) / b, Errors.MATH_MULTIPLICATION_OVERFLOW);
 
    return (a * b + HALF_WAD) / WAD;
  }
 
  /**
   * @dev Divides two wad, rounding half up to the nearest wad
   * @param a Wad
   * @param b Wad
   * @return The result of a/b, in wad
   **/
  function wadDiv(uint256 a, uint256 b) internal pure returns (uint256) {
    require(b != 0, Errors.MATH_DIVISION_BY_ZERO);
    uint256 halfB = b / 2;
 
    require(a <= (type(uint256).max - halfB) / WAD, Errors.MATH_MULTIPLICATION_OVERFLOW);
 
    return (a * WAD + halfB) / b;
  }
 
  /**
   * @dev Multiplies two ray, rounding half up to the nearest ray
   * @param a Ray
   * @param b Ray
   * @return The result of a*b, in ray
   **/
  function rayMul(uint256 a, uint256 b) internal pure returns (uint256) {
    if (a == 0 || b == 0) {
      return 0;
    }
 
    require(a <= (type(uint256).max - HALF_RAY) / b, Errors.MATH_MULTIPLICATION_OVERFLOW);
 
    return (a * b + HALF_RAY) / RAY;
  }
 
  /**
   * @dev Divides two ray, rounding half up to the nearest ray
   * @param a Ray
   * @param b Ray
   * @return The result of a/b, in ray
   **/
  function rayDiv(uint256 a, uint256 b) internal pure returns (uint256) {
    require(b != 0, Errors.MATH_DIVISION_BY_ZERO);
    uint256 halfB = b / 2;
 
    require(a <= (type(uint256).max - halfB) / RAY, Errors.MATH_MULTIPLICATION_OVERFLOW);
 
    return (a * RAY + halfB) / b;
  }
 
  /**
   * @dev Casts ray down to wad
   * @param a Ray
   * @return a casted to wad, rounded half up to the nearest wad
   **/
  function rayToWad(uint256 a) internal pure returns (uint256) {
    uint256 halfRatio = WAD_RAY_RATIO / 2;
    uint256 result = halfRatio + a;
    require(result >= halfRatio, Errors.MATH_ADDITION_OVERFLOW);
 
    return result / WAD_RAY_RATIO;
  }
 
  /**
   * @dev Converts wad up to ray
   * @param a Wad
   * @return a converted in ray
   **/
  function wadToRay(uint256 a) internal pure returns (uint256) {
    uint256 result = a * WAD_RAY_RATIO;
    require(result / WAD_RAY_RATIO == a, Errors.MATH_MULTIPLICATION_OVERFLOW);
    return result;
  }
}