// SPDX-License-Identifier: BUSL-1.1
pragma solidity ^0.8.13;

library Math {
    // Taken from https://github.com/usmfum/USM/blob/master/src/WadMath.sol
    /// @dev Multiply an amount by a fixed point factor with 18 decimals, rounds down.
    function wmul(uint256 x, uint256 y) internal pure returns (uint256 z) {
        z = x * y;
        unchecked {
            z /= 1e18;
        }
    }

    // Taken from https://github.com/usmfum/USM/blob/master/src/WadMath.sol
    /// @dev Multiply x and y, with y being fixed point. If both are integers, the result is a fixed point factor. Rounds up.
    function wmulup(uint256 x, uint256 y) internal pure returns (uint256 z) {
        z = x * y + 1e18 - 1; // Rounds up.  So (again imagining 2 decimal places):
        unchecked {
            z /= 1e18;
        } // 383 (3.83) * 235 (2.35) -> 90005 (9.0005), + 99 (0.0099) -> 90104, / 100 -> 901 (9.01).
    }

    // Taken from https://github.com/usmfum/USM/blob/master/src/WadMath.sol
    /// @dev Divide an amount by a fixed point factor with 18 decimals
    function wdiv(uint256 x, uint256 y) internal pure returns (uint256 z) {
        z = (x * 1e18) / y;
    }

    // Taken from https://github.com/usmfum/USM/blob/master/src/WadMath.sol
    /// @dev Divide x and y, with y being fixed point. If both are integers, the result is a fixed point factor. Rounds up.
    function wdivup(uint256 x, uint256 y) internal pure returns (uint256 z) {
        z = x * 1e18 + y; // 101 (1.01) / 1000 (10) -> (101 * 100 + 1000 - 1) / 1000 -> 11 (0.11 = 0.101 rounded up).
        unchecked {
            z -= 1;
        } // Can do unchecked subtraction since division in next line will catch y = 0 case anyway
        z /= y;
    }

    // Taken from https://github.com/Rari-Capital/solmate/blob/main/src/utils/FixedPointMathLib.sol
    /// @dev $x ^ $n; $x is 18-decimals fixed point number
    function wpow(uint256 x, uint256 n) internal pure returns (uint256 z) {
        uint256 baseUnit = 1e18;
        assembly {
            switch x
            case 0 {
                switch n
                case 0 {
                    // 0 ** 0 = 1
                    z := baseUnit
                }
                default {
                    // 0 ** n = 0
                    z := 0
                }
            }
            default {
                switch mod(n, 2)
                case 0 {
                    // If n is even, store baseUnit in z for now.
                    z := baseUnit
                }
                default {
                    // If n is odd, store x in z for now.
                    z := x
                }

                // Shifting right by 1 is like dividing by 2.
                let half := shr(1, baseUnit)

                for {
                    // Shift n right by 1 before looping to halve it.
                    n := shr(1, n)
                } n {
                    // Shift n right by 1 each iteration to halve it.
                    n := shr(1, n)
                } {
                    // Revert immediately if x ** 2 would overflow.
                    // Equivalent to iszero(eq(div(xx, x), x)) here.
                    if shr(128, x) { revert(0, 0) }

                    // Store x squared.
                    let xx := mul(x, x)

                    // Round to the nearest number.
                    let xxRound := add(xx, half)

                    // Revert if xx + half overflowed.
                    if lt(xxRound, xx) { revert(0, 0) }

                    // Set x to scaled xxRound.
                    x := div(xxRound, baseUnit)

                    // If n is even:
                    if mod(n, 2) {
                        // Compute z * x.
                        let zx := mul(z, x)

                        // If z * x overflowed:
                        if iszero(eq(div(zx, x), z)) {
                            // Revert if x is non-zero.
                            if iszero(iszero(x)) { revert(0, 0) }
                        }

                        // Round to the nearest number.
                        let zxRound := add(zx, half)

                        // Revert if zx + half overflowed.
                        if lt(zxRound, zx) { revert(0, 0) }

                        // Return properly scaled zxRound.
                        z := div(zxRound, baseUnit)
                    }
                }
            }
        }
    }

    /// @dev Divide an amount by a fixed point factor with 27 decimals
    function rdiv(uint256 x, uint256 y) internal pure returns (uint256 z) {
        z = (x * 1e27) / y;
    }
}