// SPDX-License-Identifier: MIT

pragma solidity 0.8.19;

library PropelMath {
	uint256 internal constant DECIMAL_PRECISION = 1e18;

	/* Precision for Nominal ICR (independent of price). Rationale for the value:
	 *
	 * - Making it “too high” could lead to overflows.
	 * - Making it “too low” could lead to an ICR equal to zero, due to truncation from Solidity floor division.
	 *
	 * This value of 1e20 is chosen for safety: the NICR will only overflow for numerator > ~1e39,
	 * and will only truncate to 0 if the denominator is at least 1e20 times greater than the numerator.
	 *
	 */
	uint256 internal constant NICR_PRECISION = 1e20;

	function _min(uint256 _a, uint256 _b) internal pure returns (uint256) {
		return (_a < _b) ? _a : _b;
	}

	function _max(uint256 _a, uint256 _b) internal pure returns (uint256) {
		return (_a >= _b) ? _a : _b;
	}

	/*
	 * Multiply two decimal numbers and use normal rounding rules:
	 * -round product up if 19'th mantissa digit >= 5
	 * -round product down if 19'th mantissa digit < 5
	 *
	 * Used only inside the exponentiation, _decPow().
	 */
	function decMul(uint256 x, uint256 y) internal pure returns (uint256 decProd) {
		uint256 prod_xy = x * y;

		decProd = (prod_xy + (DECIMAL_PRECISION / 2)) / DECIMAL_PRECISION;
	}

	/*
	 * _decPow: Exponentiation function for 18-digit decimal base, and integer exponent n.
	 *
	 * Uses the efficient "exponentiation by squaring" algorithm. O(log(n)) complexity.
	 *
	 * TroveManager._calcDecayedBaseRate
	 *
	 * The exponent is capped to avoid reverting due to overflow. The cap 525600000 equals
	 * "minutes in 1000 years": 60 * 24 * 365 * 1000
	 *
	 * If a period of > 1000 years is ever used as an exponent in either of the above functions, the result will be
	 * negligibly different from just passing the cap, since:
	 *
	 * the decayed base rate will be 0 for 1000 years or > 1000 years
	 */
	function _decPow(uint256 _base, uint256 _minutes) internal pure returns (uint256) {
		if (_minutes > 525600000) {
			_minutes = 525600000;
		} // cap to avoid overflow

		if (_minutes == 0) {
			return DECIMAL_PRECISION;
		}

		uint256 y = DECIMAL_PRECISION;
		uint256 x = _base;
		uint256 n = _minutes;

		// Exponentiation-by-squaring
		while (n > 1) {
			if (n % 2 == 0) {
				x = decMul(x, x);
				n = n / 2;
			} else {
				// if (n % 2 != 0)
				y = decMul(x, y);
				x = decMul(x, x);
				n = (n - 1) / 2;
			}
		}

		return decMul(x, y);
	}

	function _getAbsoluteDifference(uint256 _a, uint256 _b) internal pure returns (uint256) {
		return (_a >= _b) ? _a - _b : _b - _a;
	}

	function _computeNominalCR(uint256 _coll, uint256 _debt) internal pure returns (uint256) {
		if (_debt > 0) {
			return (_coll * NICR_PRECISION) / _debt;
		}
		// Return the maximal value for uint256 if the Trove has a debt of 0. Represents "infinite" CR.
		else {
			// if (_debt == 0)
			return 2 ** 256 - 1;
		}
	}

	function _computeCR(uint256 _coll, uint256 _debt, uint256 _price) internal pure returns (uint256) {
		if (_debt > 0) {
			uint256 newCollRatio = (_coll * _price) / _debt;

			return newCollRatio;
		}
		// Return the maximal value for uint256 if the Trove has a debt of 0. Represents "infinite" CR.
		else {
			// if (_debt == 0)
			return type(uint256).max;
		}
	}

	function _computeCR(uint256 _coll, uint256 _debt) internal pure returns (uint256) {
		if (_debt > 0) {
			uint256 newCollRatio = (_coll) / _debt;

			return newCollRatio;
		}
		// Return the maximal value for uint256 if the Trove has a debt of 0. Represents "infinite" CR.
		else {
			// if (_debt == 0)
			return type(uint256).max;
		}
	}
}