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// SPDX-License-Identifier: ISC
pragma solidity 0.8.23;

// ====================================================================
// |     ______                   _______                             |
// |    / _____________ __  __   / ____(_____  ____ _____  ________   |
// |   / /_  / ___/ __ `| |/_/  / /_  / / __ \/ __ `/ __ \/ ___/ _ \  |
// |  / __/ / /  / /_/ _>  <   / __/ / / / / / /_/ / / / / /__/  __/  |
// | /_/   /_/   \__,_/_/|_|  /_/   /_/_/ /_/\__,_/_/ /_/\___/\___/   |
// |                                                                  |
// ====================================================================
// ====================== VariableInterestRate ========================
// ====================================================================

import { Strings } from "@openzeppelin/contracts/utils/Strings.sol";
import { IVariableInterestRate } from "./interfaces/IVariableInterestRate.sol";

/// @title A formula for calculating interest rates as a function of utilization and time
/// @author Frax Finance (https://github.com/FraxFinance)
/// @notice A Contract for calculating interest rates as a function of utilization and time
contract VariableInterestRate is IVariableInterestRate {
    using Strings for uint256;

    /// @notice The name suffix for the interest rate calculator
    string public suffix;

    // Utilization Settings
    /// @notice The minimum utilization wherein no adjustment to full utilization and vertex rates occurs
    uint256 public immutable MIN_TARGET_UTIL;
    /// @notice The maximum utilization wherein no adjustment to full utilization and vertex rates occurs
    uint256 public immutable MAX_TARGET_UTIL;
    /// @notice The utilization at which the slope increases
    uint256 public immutable VERTEX_UTILIZATION;
    /// @notice The second utilization at which the slope increases
    uint256 public immutable VERTEX_2_UTILIZATION;
    /// @notice precision of utilization calculations
    uint256 public constant UTIL_PREC = 1e5; // 5 decimals

    // Interest Rate Settings (all rates are per second), 365.24 days per year
    /// @notice The minimum interest rate (per second) when utilization is 100%
    uint256 public immutable MIN_FULL_UTIL_RATE; // 18 decimals
    /// @notice The maximum interest rate (per second) when utilization is 100%
    uint256 public immutable MAX_FULL_UTIL_RATE; // 18 decimals
    /// @notice The interest rate (per second) when utilization is 0%
    uint256 public immutable ZERO_UTIL_RATE; // 18 decimals
    /// @notice The interest rate half life in seconds, determines rate of adjustments to rate curve
    uint256 public immutable RATE_HALF_LIFE; // 1 decimals
    /// @notice The percent of the delta between max and min at the first kink
    uint256 public immutable VERTEX_RATE_PERCENT; // 18 decimals
    /// @notice The percent of the delta between max and min at the second kink
    uint256 public immutable VERTEX_2_RATE_PERCENT; // 18 decimals
    /// @notice The precision of interest rate calculations
    uint256 public constant RATE_PREC = 1e18; // 18 decimals

    error MaxUtilizationTooLow();
    error MaxFullUtilizationTooLow();
    error DivideByZero();
    error VertexUtilizationTooHigh();
    error UtilizationRateTooHigh();
    error Vertex2UtilizationTooLow();

    /// @param _params Abi Encoding of the following schema:
    /// param _suffix The suffix of the contract name
    /// param _vertexUtilization The utilization at which the slope increases
    /// param _vertex2Utilization The utilization at which the slope increases
    /// param _vertexRatePercentOfDelta The percent of the delta between max and min, defines vertex rate
    /// param _vertex2RatePercentOfDelta The percent of delta between the
    /// param _minUtil The minimum utilization wherein no adjustment to full utilization and vertex rates occurs
    /// param _maxUtil The maximum utilization wherein no adjustment to full utilization and vertex rates occurs
    /// param _zeroUtilizationRate The interest rate (per second) when utilization is 0%
    /// param _minFullUtilizationRate The minimum interest rate at 100% utilization
    /// param _maxFullUtilizationRate The maximum interest rate at 100% utilization
    /// param _rateHalfLife The half life parameter for interest rate adjustments
    constructor(bytes memory _params) {
        (
            suffix,
            VERTEX_UTILIZATION,
            VERTEX_2_UTILIZATION,
            VERTEX_RATE_PERCENT,
            VERTEX_2_RATE_PERCENT,
            MIN_TARGET_UTIL,
            MAX_TARGET_UTIL,
            ZERO_UTIL_RATE,
            MIN_FULL_UTIL_RATE,
            MAX_FULL_UTIL_RATE,
            RATE_HALF_LIFE
        ) = abi.decode(
            _params,
            (string, uint256, uint256, uint256, uint256, uint256, uint256, uint256, uint256, uint256, uint256)
        );
        if (MAX_TARGET_UTIL <= MIN_TARGET_UTIL) {
            revert MaxUtilizationTooLow();
        }
        if (MAX_FULL_UTIL_RATE <= MIN_FULL_UTIL_RATE) {
            revert MaxFullUtilizationTooLow();
        }

        if (VERTEX_UTILIZATION > UTIL_PREC) {
            revert VertexUtilizationTooHigh();
        }

        if (VERTEX_2_UTILIZATION > UTIL_PREC) {
            revert VertexUtilizationTooHigh();
        }

        if (VERTEX_2_UTILIZATION <= VERTEX_UTILIZATION) {
            revert Vertex2UtilizationTooLow();
        }

        if (
            MAX_TARGET_UTIL == 0 ||
            RATE_HALF_LIFE == 0 ||
            VERTEX_UTILIZATION == 0 ||
            VERTEX_UTILIZATION == UTIL_PREC ||
            VERTEX_2_UTILIZATION == 0 ||
            VERTEX_2_UTILIZATION == UTIL_PREC ||
            MAX_TARGET_UTIL == UTIL_PREC
        ) {
            revert DivideByZero();
        }

        if (MAX_TARGET_UTIL > UTIL_PREC || MAX_FULL_UTIL_RATE > RATE_PREC) {
            revert UtilizationRateTooHigh();
        }
    }

    /// @notice The ```name``` function returns the name of the rate contract
    /// @return memory name of contract
    function name() external view returns (string memory) {
        return string.concat("Variable Rate V3 ", suffix);
    }

    /// @notice The ```version``` function returns the semantic version of the rate contract
    /// @dev Follows semantic versioning
    /// @return _major Major version
    /// @return _minor Minor version
    /// @return _patch Patch version
    function version() external pure returns (uint256 _major, uint256 _minor, uint256 _patch) {
        _major = 3;
        _minor = 0;
        _patch = 1;
    }

    /// @notice The ```getFullUtilizationInterest``` function calculate the new maximum interest rate, i.e. rate when utilization is 100%
    /// @dev Given in interest per second
    /// @param _deltaTime The elapsed time since last update given in seconds
    /// @param _utilization The utilization %, given with 5 decimals of precision
    /// @param _fullUtilizationInterest The interest value when utilization is 100%, given with 18 decimals of precision
    /// @return _newFullUtilizationInterest The new maximum interest rate
    function getFullUtilizationInterest(
        uint256 _deltaTime,
        uint256 _utilization,
        uint64 _fullUtilizationInterest
    ) internal view returns (uint64 _newFullUtilizationInterest) {
        if (_utilization < MIN_TARGET_UTIL) {
            // 18 decimals
            uint256 _deltaUtilization = ((MIN_TARGET_UTIL - _utilization) * 1e18) / MIN_TARGET_UTIL;
            // 36 decimals
            uint256 _decayGrowth = (RATE_HALF_LIFE * 1e36) + (_deltaUtilization * _deltaUtilization * _deltaTime);
            // 18 decimals
            _newFullUtilizationInterest = uint64((_fullUtilizationInterest * (RATE_HALF_LIFE * 1e36)) / _decayGrowth);
        } else if (_utilization > MAX_TARGET_UTIL) {
            // 18 decimals
            uint256 _deltaUtilization = ((_utilization - MAX_TARGET_UTIL) * 1e18) / (UTIL_PREC - MAX_TARGET_UTIL);
            // 36 decimals
            uint256 _decayGrowth = (RATE_HALF_LIFE * 1e36) + (_deltaUtilization * _deltaUtilization * _deltaTime);
            // 18 decimals
            _newFullUtilizationInterest = uint64((_fullUtilizationInterest * _decayGrowth) / (RATE_HALF_LIFE * 1e36));
        } else {
            _newFullUtilizationInterest = _fullUtilizationInterest;
        }
        if (_newFullUtilizationInterest > MAX_FULL_UTIL_RATE) {
            _newFullUtilizationInterest = uint64(MAX_FULL_UTIL_RATE);
        } else if (_newFullUtilizationInterest < MIN_FULL_UTIL_RATE) {
            _newFullUtilizationInterest = uint64(MIN_FULL_UTIL_RATE);
        }
    }

    /// @notice The ```getNewRate``` function calculates interest rates using two linear functions f(utilization)
    /// @param _deltaTime The elapsed time since last update, given in seconds
    /// @param _utilization The utilization %, given with 5 decimals of precision
    /// @param _oldFullUtilizationInterest The interest value when utilization is 100%, given with 18 decimals of precision
    /// @return _newRatePerSec The new interest rate, 18 decimals of precision
    /// @return _newFullUtilizationInterest The new max interest rate, 18 decimals of precision
    function getNewRate(
        uint256 _deltaTime,
        uint256 _utilization,
        uint64 _oldFullUtilizationInterest
    ) external view returns (uint64 _newRatePerSec, uint64 _newFullUtilizationInterest) {
        _newFullUtilizationInterest = getFullUtilizationInterest(_deltaTime, _utilization, _oldFullUtilizationInterest);

        // _vertexInterest is calculated as the percentage of the delta between min and max interest
        uint256 _vertexInterest = (((_newFullUtilizationInterest - ZERO_UTIL_RATE) * VERTEX_RATE_PERCENT) / RATE_PREC) +
            ZERO_UTIL_RATE;
        uint256 _vertex2Interest = (((_newFullUtilizationInterest - ZERO_UTIL_RATE) * VERTEX_2_RATE_PERCENT) /
            RATE_PREC) + ZERO_UTIL_RATE;
        if (_utilization < VERTEX_UTILIZATION) {
            // For readability, the following formula is equivalent to:
            // uint256 _slope = ((_vertexInterest - ZERO_UTIL_RATE) * UTIL_PREC) / VERTEX_UTILIZATION;
            // _newRatePerSec = uint64(ZERO_UTIL_RATE + ((_utilization * _slope) / UTIL_PREC));
            _newRatePerSec = uint64(
                ZERO_UTIL_RATE + (_utilization * (_vertexInterest - ZERO_UTIL_RATE)) / VERTEX_UTILIZATION
            );
        } else if (_utilization < VERTEX_2_UTILIZATION) {
            // For readability, the following formula is equivalent to:
            // uint256 _slope = (((_vertex2Interest - _vertexInterest) * UTIL_PREC) / (VERTEX_2_UTILIZATION - VERTEX_UTILIZATION));
            // _newRatePerSec = uint64(_vertexInterest + (((_utilization - VERTEX_UTILIZATION) * _slope) / UTIL_PREC));
            _newRatePerSec = uint64(
                _vertexInterest +
                    ((_utilization - VERTEX_UTILIZATION) * ((_vertex2Interest - _vertexInterest))) /
                    ((VERTEX_2_UTILIZATION - VERTEX_UTILIZATION))
            );
        } else {
            // For readability, the following formula is equivalent to:
            // uint256 _slope = (((_newFullUtilizationInterest - _vertex2Interest) * UTIL_PREC) / (UTIL_PREC - VERTEX_2_UTILIZATION));
            // _newRatePerSec = uint64(_vertex2Interest + (((_utilization - VERTEX_2_UTILIZATION) * _slope) / UTIL_PREC))
            _newRatePerSec = uint64(
                _vertex2Interest +
                    ((_utilization - VERTEX_2_UTILIZATION) * (_newFullUtilizationInterest - _vertex2Interest)) /
                    ((UTIL_PREC - VERTEX_2_UTILIZATION))
            );
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/Strings.sol)

pragma solidity ^0.8.20;

import {Math} from "./math/Math.sol";
import {SignedMath} from "./math/SignedMath.sol";

/**
 * @dev String operations.
 */
library Strings {
    bytes16 private constant HEX_DIGITS = "0123456789abcdef";
    uint8 private constant ADDRESS_LENGTH = 20;

    /**
     * @dev The `value` string doesn't fit in the specified `length`.
     */
    error StringsInsufficientHexLength(uint256 value, uint256 length);

    /**
     * @dev Converts a `uint256` to its ASCII `string` decimal representation.
     */
    function toString(uint256 value) internal pure returns (string memory) {
        unchecked {
            uint256 length = Math.log10(value) + 1;
            string memory buffer = new string(length);
            uint256 ptr;
            /// @solidity memory-safe-assembly
            assembly {
                ptr := add(buffer, add(32, length))
            }
            while (true) {
                ptr--;
                /// @solidity memory-safe-assembly
                assembly {
                    mstore8(ptr, byte(mod(value, 10), HEX_DIGITS))
                }
                value /= 10;
                if (value == 0) break;
            }
            return buffer;
        }
    }

    /**
     * @dev Converts a `int256` to its ASCII `string` decimal representation.
     */
    function toStringSigned(int256 value) internal pure returns (string memory) {
        return string.concat(value < 0 ? "-" : "", toString(SignedMath.abs(value)));
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.
     */
    function toHexString(uint256 value) internal pure returns (string memory) {
        unchecked {
            return toHexString(value, Math.log256(value) + 1);
        }
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation with fixed length.
     */
    function toHexString(uint256 value, uint256 length) internal pure returns (string memory) {
        uint256 localValue = value;
        bytes memory buffer = new bytes(2 * length + 2);
        buffer[0] = "0";
        buffer[1] = "x";
        for (uint256 i = 2 * length + 1; i > 1; --i) {
            buffer[i] = HEX_DIGITS[localValue & 0xf];
            localValue >>= 4;
        }
        if (localValue != 0) {
            revert StringsInsufficientHexLength(value, length);
        }
        return string(buffer);
    }

    /**
     * @dev Converts an `address` with fixed length of 20 bytes to its not checksummed ASCII `string` hexadecimal
     * representation.
     */
    function toHexString(address addr) internal pure returns (string memory) {
        return toHexString(uint256(uint160(addr)), ADDRESS_LENGTH);
    }

    /**
     * @dev Returns true if the two strings are equal.
     */
    function equal(string memory a, string memory b) internal pure returns (bool) {
        return bytes(a).length == bytes(b).length && keccak256(bytes(a)) == keccak256(bytes(b));
    }
}

// SPDX-License-Identifier: ISC
pragma solidity ^0.8.0;

interface IVariableInterestRate {
    function MAX_FULL_UTIL_RATE() external view returns (uint256);

    function MAX_TARGET_UTIL() external view returns (uint256);

    function MIN_FULL_UTIL_RATE() external view returns (uint256);

    function MIN_TARGET_UTIL() external view returns (uint256);

    function RATE_HALF_LIFE() external view returns (uint256);

    function RATE_PREC() external view returns (uint256);

    function UTIL_PREC() external view returns (uint256);

    function VERTEX_RATE_PERCENT() external view returns (uint256);

    function VERTEX_UTILIZATION() external view returns (uint256);

    function ZERO_UTIL_RATE() external view returns (uint256);

    function getNewRate(
        uint256 _deltaTime,
        uint256 _utilization,
        uint64 _oldFullUtilizationInterest
    ) external view returns (uint64 _newRatePerSec, uint64 _newFullUtilizationInterest);

    function name() external view returns (string memory);

    function version() external view returns (uint256 _major, uint256 _minor, uint256 _patch);

    function suffix() external view returns (string memory);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/math/Math.sol)

pragma solidity ^0.8.20;

/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library Math {
    /**
     * @dev Muldiv operation overflow.
     */
    error MathOverflowedMulDiv();

    enum Rounding {
        Floor, // Toward negative infinity
        Ceil, // Toward positive infinity
        Trunc, // Toward zero
        Expand // Away from zero
    }

    /**
     * @dev Returns the addition of two unsigned integers, with an overflow flag.
     */
    function tryAdd(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        unchecked {
            uint256 c = a + b;
            if (c < a) return (false, 0);
            return (true, c);
        }
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, with an overflow flag.
     */
    function trySub(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        unchecked {
            if (b > a) return (false, 0);
            return (true, a - b);
        }
    }

    /**
     * @dev Returns the multiplication of two unsigned integers, with an overflow flag.
     */
    function tryMul(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        unchecked {
            // Gas optimization: this is cheaper than requiring 'a' not being zero, but the
            // benefit is lost if 'b' is also tested.
            // See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522
            if (a == 0) return (true, 0);
            uint256 c = a * b;
            if (c / a != b) return (false, 0);
            return (true, c);
        }
    }

    /**
     * @dev Returns the division of two unsigned integers, with a division by zero flag.
     */
    function tryDiv(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        unchecked {
            if (b == 0) return (false, 0);
            return (true, a / b);
        }
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers, with a division by zero flag.
     */
    function tryMod(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        unchecked {
            if (b == 0) return (false, 0);
            return (true, a % b);
        }
    }

    /**
     * @dev Returns the largest of two numbers.
     */
    function max(uint256 a, uint256 b) internal pure returns (uint256) {
        return a > b ? a : b;
    }

    /**
     * @dev Returns the smallest of two numbers.
     */
    function min(uint256 a, uint256 b) internal pure returns (uint256) {
        return a < b ? a : b;
    }

    /**
     * @dev Returns the average of two numbers. The result is rounded towards
     * zero.
     */
    function average(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b) / 2 can overflow.
        return (a & b) + (a ^ b) / 2;
    }

    /**
     * @dev Returns the ceiling of the division of two numbers.
     *
     * This differs from standard division with `/` in that it rounds towards infinity instead
     * of rounding towards zero.
     */
    function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {
        if (b == 0) {
            // Guarantee the same behavior as in a regular Solidity division.
            return a / b;
        }

        // (a + b - 1) / b can overflow on addition, so we distribute.
        return a == 0 ? 0 : (a - 1) / b + 1;
    }

    /**
     * @notice Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or
     * denominator == 0.
     * @dev Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv) with further edits by
     * Uniswap Labs also under MIT license.
     */
    function mulDiv(uint256 x, uint256 y, uint256 denominator) internal pure returns (uint256 result) {
        unchecked {
            // 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use
            // use the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
            // variables such that product = prod1 * 2^256 + prod0.
            uint256 prod0 = x * y; // Least significant 256 bits of the product
            uint256 prod1; // Most significant 256 bits of the product
            assembly {
                let mm := mulmod(x, y, not(0))
                prod1 := sub(sub(mm, prod0), lt(mm, prod0))
            }

            // Handle non-overflow cases, 256 by 256 division.
            if (prod1 == 0) {
                // Solidity will revert if denominator == 0, unlike the div opcode on its own.
                // The surrounding unchecked block does not change this fact.
                // See https://docs.soliditylang.org/en/latest/control-structures.html#checked-or-unchecked-arithmetic.
                return prod0 / denominator;
            }

            // Make sure the result is less than 2^256. Also prevents denominator == 0.
            if (denominator <= prod1) {
                revert MathOverflowedMulDiv();
            }

            ///////////////////////////////////////////////
            // 512 by 256 division.
            ///////////////////////////////////////////////

            // Make division exact by subtracting the remainder from [prod1 prod0].
            uint256 remainder;
            assembly {
                // Compute remainder using mulmod.
                remainder := mulmod(x, y, denominator)

                // Subtract 256 bit number from 512 bit number.
                prod1 := sub(prod1, gt(remainder, prod0))
                prod0 := sub(prod0, remainder)
            }

            // Factor powers of two out of denominator and compute largest power of two divisor of denominator.
            // Always >= 1. See https://cs.stackexchange.com/q/138556/92363.

            uint256 twos = denominator & (0 - denominator);
            assembly {
                // Divide denominator by twos.
                denominator := div(denominator, twos)

                // Divide [prod1 prod0] by twos.
                prod0 := div(prod0, twos)

                // Flip twos such that it is 2^256 / twos. If twos is zero, then it becomes one.
                twos := add(div(sub(0, twos), twos), 1)
            }

            // Shift in bits from prod1 into prod0.
            prod0 |= prod1 * twos;

            // Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such
            // that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for
            // four bits. That is, denominator * inv = 1 mod 2^4.
            uint256 inverse = (3 * denominator) ^ 2;

            // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also
            // works in modular arithmetic, doubling the correct bits in each step.
            inverse *= 2 - denominator * inverse; // inverse mod 2^8
            inverse *= 2 - denominator * inverse; // inverse mod 2^16
            inverse *= 2 - denominator * inverse; // inverse mod 2^32
            inverse *= 2 - denominator * inverse; // inverse mod 2^64
            inverse *= 2 - denominator * inverse; // inverse mod 2^128
            inverse *= 2 - denominator * inverse; // inverse mod 2^256

            // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
            // This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is
            // less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1
            // is no longer required.
            result = prod0 * inverse;
            return result;
        }
    }

    /**
     * @notice Calculates x * y / denominator with full precision, following the selected rounding direction.
     */
    function mulDiv(uint256 x, uint256 y, uint256 denominator, Rounding rounding) internal pure returns (uint256) {
        uint256 result = mulDiv(x, y, denominator);
        if (unsignedRoundsUp(rounding) && mulmod(x, y, denominator) > 0) {
            result += 1;
        }
        return result;
    }

    /**
     * @dev Returns the square root of a number. If the number is not a perfect square, the value is rounded
     * towards zero.
     *
     * Inspired by Henry S. Warren, Jr.'s "Hacker's Delight" (Chapter 11).
     */
    function sqrt(uint256 a) internal pure returns (uint256) {
        if (a == 0) {
            return 0;
        }

        // For our first guess, we get the biggest power of 2 which is smaller than the square root of the target.
        //
        // We know that the "msb" (most significant bit) of our target number `a` is a power of 2 such that we have
        // `msb(a) <= a < 2*msb(a)`. This value can be written `msb(a)=2**k` with `k=log2(a)`.
        //
        // This can be rewritten `2**log2(a) <= a < 2**(log2(a) + 1)`
        // → `sqrt(2**k) <= sqrt(a) < sqrt(2**(k+1))`
        // → `2**(k/2) <= sqrt(a) < 2**((k+1)/2) <= 2**(k/2 + 1)`
        //
        // Consequently, `2**(log2(a) / 2)` is a good first approximation of `sqrt(a)` with at least 1 correct bit.
        uint256 result = 1 << (log2(a) >> 1);

        // At this point `result` is an estimation with one bit of precision. We know the true value is a uint128,
        // since it is the square root of a uint256. Newton's method converges quadratically (precision doubles at
        // every iteration). We thus need at most 7 iteration to turn our partial result with one bit of precision
        // into the expected uint128 result.
        unchecked {
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            return min(result, a / result);
        }
    }

    /**
     * @notice Calculates sqrt(a), following the selected rounding direction.
     */
    function sqrt(uint256 a, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = sqrt(a);
            return result + (unsignedRoundsUp(rounding) && result * result < a ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 2 of a positive value rounded towards zero.
     * Returns 0 if given 0.
     */
    function log2(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 128;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 64;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 32;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 16;
            }
            if (value >> 8 > 0) {
                value >>= 8;
                result += 8;
            }
            if (value >> 4 > 0) {
                value >>= 4;
                result += 4;
            }
            if (value >> 2 > 0) {
                value >>= 2;
                result += 2;
            }
            if (value >> 1 > 0) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 2, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log2(value);
            return result + (unsignedRoundsUp(rounding) && 1 << result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 10 of a positive value rounded towards zero.
     * Returns 0 if given 0.
     */
    function log10(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >= 10 ** 64) {
                value /= 10 ** 64;
                result += 64;
            }
            if (value >= 10 ** 32) {
                value /= 10 ** 32;
                result += 32;
            }
            if (value >= 10 ** 16) {
                value /= 10 ** 16;
                result += 16;
            }
            if (value >= 10 ** 8) {
                value /= 10 ** 8;
                result += 8;
            }
            if (value >= 10 ** 4) {
                value /= 10 ** 4;
                result += 4;
            }
            if (value >= 10 ** 2) {
                value /= 10 ** 2;
                result += 2;
            }
            if (value >= 10 ** 1) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 10, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log10(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log10(value);
            return result + (unsignedRoundsUp(rounding) && 10 ** result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 256 of a positive value rounded towards zero.
     * Returns 0 if given 0.
     *
     * Adding one to the result gives the number of pairs of hex symbols needed to represent `value` as a hex string.
     */
    function log256(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 16;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 8;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 4;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 2;
            }
            if (value >> 8 > 0) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 256, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log256(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log256(value);
            return result + (unsignedRoundsUp(rounding) && 1 << (result << 3) < value ? 1 : 0);
        }
    }

    /**
     * @dev Returns whether a provided rounding mode is considered rounding up for unsigned integers.
     */
    function unsignedRoundsUp(Rounding rounding) internal pure returns (bool) {
        return uint8(rounding) % 2 == 1;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/math/SignedMath.sol)

pragma solidity ^0.8.20;

/**
 * @dev Standard signed math utilities missing in the Solidity language.
 */
library SignedMath {
    /**
     * @dev Returns the largest of two signed numbers.
     */
    function max(int256 a, int256 b) internal pure returns (int256) {
        return a > b ? a : b;
    }

    /**
     * @dev Returns the smallest of two signed numbers.
     */
    function min(int256 a, int256 b) internal pure returns (int256) {
        return a < b ? a : b;
    }

    /**
     * @dev Returns the average of two signed numbers without overflow.
     * The result is rounded towards zero.
     */
    function average(int256 a, int256 b) internal pure returns (int256) {
        // Formula from the book "Hacker's Delight"
        int256 x = (a & b) + ((a ^ b) >> 1);
        return x + (int256(uint256(x) >> 255) & (a ^ b));
    }

    /**
     * @dev Returns the absolute unsigned value of a signed value.
     */
    function abs(int256 n) internal pure returns (uint256) {
        unchecked {
            // must be unchecked in order to support `n = type(int256).min`
            return uint256(n >= 0 ? n : -n);
        }
    }
}

{
  "remappings": [
    "frax-std/=node_modules/frax-standard-solidity/src/",
    "@prb/test/=node_modules/@prb/test/",
    "forge-std/=node_modules/forge-std/src/",
    "ds-test/=node_modules/ds-test/src/",
    "@openzeppelin/=node_modules/@openzeppelin/",
    "@uniswap/=node_modules/@uniswap/",
    "dev-fraxswap/=node_modules/dev-fraxswap/",
    "frax-standard-solidity/=node_modules/frax-standard-solidity/",
    "solidity-bytes-utils/=node_modules/solidity-bytes-utils/",
    "solmate/=node_modules/solmate/"
  ],
  "optimizer": {
    "enabled": true,
    "runs": 10000
  },
  "metadata": {
    "useLiteralContent": false,
    "bytecodeHash": "none",
    "appendCBOR": false
  },
  "outputSelection": {
    "*": {
      "*": [
        "evm.bytecode",
        "evm.deployedBytecode",
        "devdoc",
        "userdoc",
        "metadata",
        "abi"
      ]
    }
  },
  "evmVersion": "shanghai",
  "viaIR": false,
  "libraries": {}
}

• No Contract Security Audit Submitted- Submit Audit Here

[{"inputs":[{"internalType":"bytes","name":"_params","type":"bytes"}],"stateMutability":"nonpayable","type":"constructor"},{"inputs":[],"name":"DivideByZero","type":"error"},{"inputs":[],"name":"MaxFullUtilizationTooLow","type":"error"},{"inputs":[],"name":"MaxUtilizationTooLow","type":"error"},{"inputs":[],"name":"UtilizationRateTooHigh","type":"error"},{"inputs":[],"name":"Vertex2UtilizationTooLow","type":"error"},{"inputs":[],"name":"VertexUtilizationTooHigh","type":"error"},{"inputs":[],"name":"MAX_FULL_UTIL_RATE","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"MAX_TARGET_UTIL","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"MIN_FULL_UTIL_RATE","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"MIN_TARGET_UTIL","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"RATE_HALF_LIFE","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"RATE_PREC","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"UTIL_PREC","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"VERTEX_2_RATE_PERCENT","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"VERTEX_2_UTILIZATION","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"VERTEX_RATE_PERCENT","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"VERTEX_UTILIZATION","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"ZERO_UTIL_RATE","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"uint256","name":"_deltaTime","type":"uint256"},{"internalType":"uint256","name":"_utilization","type":"uint256"},{"internalType":"uint64","name":"_oldFullUtilizationInterest","type":"uint64"}],"name":"getNewRate","outputs":[{"internalType":"uint64","name":"_newRatePerSec","type":"uint64"},{"internalType":"uint64","name":"_newFullUtilizationInterest","type":"uint64"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"name","outputs":[{"internalType":"string","name":"","type":"string"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"suffix","outputs":[{"internalType":"string","name":"","type":"string"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"version","outputs":[{"internalType":"uint256","name":"_major","type":"uint256"},{"internalType":"uint256","name":"_minor","type":"uint256"},{"internalType":"uint256","name":"_patch","type":"uint256"}],"stateMutability":"pure","type":"function"}]

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-----Decoded View---------------
Arg [0] : _params (bytes): 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

-----Encoded View---------------
16 Constructor Arguments found :
Arg [0] : 0000000000000000000000000000000000000000000000000000000000000020
Arg [1] : 00000000000000000000000000000000000000000000000000000000000001c0
Arg [2] : 0000000000000000000000000000000000000000000000000000000000000160
Arg [3] : 0000000000000000000000000000000000000000000000000000000000013880
Arg [4] : 0000000000000000000000000000000000000000000000000000000000015f90
Arg [5] : 00000000000000000000000000000000000000000000000002c68af0bb140000
Arg [6] : 0000000000000000000000000000000000000000000000000429d069189e0000
Arg [7] : 0000000000000000000000000000000000000000000000000000000000011b34
Arg [8] : 0000000000000000000000000000000000000000000000000000000000014244
Arg [9] : 0000000000000000000000000000000000000000000000000000000001e2ee81
Arg [10] : 000000000000000000000000000000000000000000000000000000005e52953c
Arg [11] : 00000000000000000000000000000000000000000000000000000035cb191c38
Arg [12] : 000000000000000000000000000000000000000000000000000000000002a300
Arg [13] : 0000000000000000000000000000000000000000000000000000000000000022
Arg [14] : 42616d6d205b2e30352d372e33305d2032206461797320282e3732352d2e3832
Arg [15] : 3529000000000000000000000000000000000000000000000000000000000000