{"language":"Solidity","sources":{"@openzeppelin/contracts/interfaces/IERC165.sol":{"content":"// SPDX-License-Identifier: MIT\n// OpenZeppelin Contracts (last updated v5.0.0) (interfaces/IERC165.sol)\n\npragma solidity ^0.8.20;\n\nimport {IERC165} from \"../utils/introspection/IERC165.sol\";\n"},"@openzeppelin/contracts/interfaces/IERC4906.sol":{"content":"// SPDX-License-Identifier: MIT\n// OpenZeppelin Contracts (last updated v5.0.0) (interfaces/IERC4906.sol)\n\npragma solidity ^0.8.20;\n\nimport {IERC165} from \"./IERC165.sol\";\nimport {IERC721} from \"./IERC721.sol\";\n\n/// @title EIP-721 Metadata Update Extension\ninterface IERC4906 is IERC165, IERC721 {\n /// @dev This event emits when the metadata of a token is changed.\n /// So that the third-party platforms such as NFT market could\n /// timely update the images and related attributes of the NFT.\n event MetadataUpdate(uint256 _tokenId);\n\n /// @dev This event emits when the metadata of a range of tokens is changed.\n /// So that the third-party platforms such as NFT market could\n /// timely update the images and related attributes of the NFTs.\n event BatchMetadataUpdate(uint256 _fromTokenId, uint256 _toTokenId);\n}\n"},"@openzeppelin/contracts/interfaces/IERC721.sol":{"content":"// SPDX-License-Identifier: MIT\n// OpenZeppelin Contracts (last updated v5.0.0) (interfaces/IERC721.sol)\n\npragma solidity ^0.8.20;\n\nimport {IERC721} from \"../token/ERC721/IERC721.sol\";\n"},"@openzeppelin/contracts/token/ERC20/extensions/IERC20Metadata.sol":{"content":"// SPDX-License-Identifier: MIT\n// OpenZeppelin Contracts (last updated v5.0.0) (token/ERC20/extensions/IERC20Metadata.sol)\n\npragma solidity ^0.8.20;\n\nimport {IERC20} from \"../IERC20.sol\";\n\n/**\n * @dev Interface for the optional metadata functions from the ERC20 standard.\n */\ninterface IERC20Metadata is IERC20 {\n /**\n * @dev Returns the name of the token.\n */\n function name() external view returns (string memory);\n\n /**\n * @dev Returns the symbol of the token.\n */\n function symbol() external view returns (string memory);\n\n /**\n * @dev Returns the decimals places of the token.\n */\n function decimals() external view returns (uint8);\n}\n"},"@openzeppelin/contracts/token/ERC20/IERC20.sol":{"content":"// SPDX-License-Identifier: MIT\n// OpenZeppelin Contracts (last updated v5.0.0) (token/ERC20/IERC20.sol)\n\npragma solidity ^0.8.20;\n\n/**\n * @dev Interface of the ERC20 standard as defined in the EIP.\n */\ninterface IERC20 {\n /**\n * @dev Emitted when `value` tokens are moved from one account (`from`) to\n * another (`to`).\n *\n * Note that `value` may be zero.\n */\n event Transfer(address indexed from, address indexed to, uint256 value);\n\n /**\n * @dev Emitted when the allowance of a `spender` for an `owner` is set by\n * a call to {approve}. `value` is the new allowance.\n */\n event Approval(address indexed owner, address indexed spender, uint256 value);\n\n /**\n * @dev Returns the value of tokens in existence.\n */\n function totalSupply() external view returns (uint256);\n\n /**\n * @dev Returns the value of tokens owned by `account`.\n */\n function balanceOf(address account) external view returns (uint256);\n\n /**\n * @dev Moves a `value` amount of tokens from the caller's account to `to`.\n *\n * Returns a boolean value indicating whether the operation succeeded.\n *\n * Emits a {Transfer} event.\n */\n function transfer(address to, uint256 value) external returns (bool);\n\n /**\n * @dev Returns the remaining number of tokens that `spender` will be\n * allowed to spend on behalf of `owner` through {transferFrom}. This is\n * zero by default.\n *\n * This value changes when {approve} or {transferFrom} are called.\n */\n function allowance(address owner, address spender) external view returns (uint256);\n\n /**\n * @dev Sets a `value` amount of tokens as the allowance of `spender` over the\n * caller's tokens.\n *\n * Returns a boolean value indicating whether the operation succeeded.\n *\n * IMPORTANT: Beware that changing an allowance with this method brings the risk\n * that someone may use both the old and the new allowance by unfortunate\n * transaction ordering. One possible solution to mitigate this race\n * condition is to first reduce the spender's allowance to 0 and set the\n * desired value afterwards:\n * https://github.com/ethereum/EIPs/issues/20#issuecomment-263524729\n *\n * Emits an {Approval} event.\n */\n function approve(address spender, uint256 value) external returns (bool);\n\n /**\n * @dev Moves a `value` amount of tokens from `from` to `to` using the\n * allowance mechanism. `value` is then deducted from the caller's\n * allowance.\n *\n * Returns a boolean value indicating whether the operation succeeded.\n *\n * Emits a {Transfer} event.\n */\n function transferFrom(address from, address to, uint256 value) external returns (bool);\n}\n"},"@openzeppelin/contracts/token/ERC721/extensions/IERC721Metadata.sol":{"content":"// SPDX-License-Identifier: MIT\n// OpenZeppelin Contracts (last updated v5.0.0) (token/ERC721/extensions/IERC721Metadata.sol)\n\npragma solidity ^0.8.20;\n\nimport {IERC721} from \"../IERC721.sol\";\n\n/**\n * @title ERC-721 Non-Fungible Token Standard, optional metadata extension\n * @dev See https://eips.ethereum.org/EIPS/eip-721\n */\ninterface IERC721Metadata is IERC721 {\n /**\n * @dev Returns the token collection name.\n */\n function name() external view returns (string memory);\n\n /**\n * @dev Returns the token collection symbol.\n */\n function symbol() external view returns (string memory);\n\n /**\n * @dev Returns the Uniform Resource Identifier (URI) for `tokenId` token.\n */\n function tokenURI(uint256 tokenId) external view returns (string memory);\n}\n"},"@openzeppelin/contracts/token/ERC721/IERC721.sol":{"content":"// SPDX-License-Identifier: MIT\n// OpenZeppelin Contracts (last updated v5.0.0) (token/ERC721/IERC721.sol)\n\npragma solidity ^0.8.20;\n\nimport {IERC165} from \"../../utils/introspection/IERC165.sol\";\n\n/**\n * @dev Required interface of an ERC721 compliant contract.\n */\ninterface IERC721 is IERC165 {\n /**\n * @dev Emitted when `tokenId` token is transferred from `from` to `to`.\n */\n event Transfer(address indexed from, address indexed to, uint256 indexed tokenId);\n\n /**\n * @dev Emitted when `owner` enables `approved` to manage the `tokenId` token.\n */\n event Approval(address indexed owner, address indexed approved, uint256 indexed tokenId);\n\n /**\n * @dev Emitted when `owner` enables or disables (`approved`) `operator` to manage all of its assets.\n */\n event ApprovalForAll(address indexed owner, address indexed operator, bool approved);\n\n /**\n * @dev Returns the number of tokens in ``owner``'s account.\n */\n function balanceOf(address owner) external view returns (uint256 balance);\n\n /**\n * @dev Returns the owner of the `tokenId` token.\n *\n * Requirements:\n *\n * - `tokenId` must exist.\n */\n function ownerOf(uint256 tokenId) external view returns (address owner);\n\n /**\n * @dev Safely transfers `tokenId` token from `from` to `to`.\n *\n * Requirements:\n *\n * - `from` cannot be the zero address.\n * - `to` cannot be the zero address.\n * - `tokenId` token must exist and be owned by `from`.\n * - If the caller is not `from`, it must be approved to move this token by either {approve} or {setApprovalForAll}.\n * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon\n * a safe transfer.\n *\n * Emits a {Transfer} event.\n */\n function safeTransferFrom(address from, address to, uint256 tokenId, bytes calldata data) external;\n\n /**\n * @dev Safely transfers `tokenId` token from `from` to `to`, checking first that contract recipients\n * are aware of the ERC721 protocol to prevent tokens from being forever locked.\n *\n * Requirements:\n *\n * - `from` cannot be the zero address.\n * - `to` cannot be the zero address.\n * - `tokenId` token must exist and be owned by `from`.\n * - If the caller is not `from`, it must have been allowed to move this token by either {approve} or\n * {setApprovalForAll}.\n * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon\n * a safe transfer.\n *\n * Emits a {Transfer} event.\n */\n function safeTransferFrom(address from, address to, uint256 tokenId) external;\n\n /**\n * @dev Transfers `tokenId` token from `from` to `to`.\n *\n * WARNING: Note that the caller is responsible to confirm that the recipient is capable of receiving ERC721\n * or else they may be permanently lost. Usage of {safeTransferFrom} prevents loss, though the caller must\n * understand this adds an external call which potentially creates a reentrancy vulnerability.\n *\n * Requirements:\n *\n * - `from` cannot be the zero address.\n * - `to` cannot be the zero address.\n * - `tokenId` token must be owned by `from`.\n * - If the caller is not `from`, it must be approved to move this token by either {approve} or {setApprovalForAll}.\n *\n * Emits a {Transfer} event.\n */\n function transferFrom(address from, address to, uint256 tokenId) external;\n\n /**\n * @dev Gives permission to `to` to transfer `tokenId` token to another account.\n * The approval is cleared when the token is transferred.\n *\n * Only a single account can be approved at a time, so approving the zero address clears previous approvals.\n *\n * Requirements:\n *\n * - The caller must own the token or be an approved operator.\n * - `tokenId` must exist.\n *\n * Emits an {Approval} event.\n */\n function approve(address to, uint256 tokenId) external;\n\n /**\n * @dev Approve or remove `operator` as an operator for the caller.\n * Operators can call {transferFrom} or {safeTransferFrom} for any token owned by the caller.\n *\n * Requirements:\n *\n * - The `operator` cannot be the address zero.\n *\n * Emits an {ApprovalForAll} event.\n */\n function setApprovalForAll(address operator, bool approved) external;\n\n /**\n * @dev Returns the account approved for `tokenId` token.\n *\n * Requirements:\n *\n * - `tokenId` must exist.\n */\n function getApproved(uint256 tokenId) external view returns (address operator);\n\n /**\n * @dev Returns if the `operator` is allowed to manage all of the assets of `owner`.\n *\n * See {setApprovalForAll}\n */\n function isApprovedForAll(address owner, address operator) external view returns (bool);\n}\n"},"@openzeppelin/contracts/utils/Base64.sol":{"content":"// SPDX-License-Identifier: MIT\n// OpenZeppelin Contracts (last updated v5.0.2) (utils/Base64.sol)\n\npragma solidity ^0.8.20;\n\n/**\n * @dev Provides a set of functions to operate with Base64 strings.\n */\nlibrary Base64 {\n /**\n * @dev Base64 Encoding/Decoding Table\n */\n string internal constant _TABLE = \"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/\";\n\n /**\n * @dev Converts a `bytes` to its Bytes64 `string` representation.\n */\n function encode(bytes memory data) internal pure returns (string memory) {\n /**\n * Inspired by Brecht Devos (Brechtpd) implementation - MIT licence\n * https://github.com/Brechtpd/base64/blob/e78d9fd951e7b0977ddca77d92dc85183770daf4/base64.sol\n */\n if (data.length == 0) return \"\";\n\n // Loads the table into memory\n string memory table = _TABLE;\n\n // Encoding takes 3 bytes chunks of binary data from `bytes` data parameter\n // and split into 4 numbers of 6 bits.\n // The final Base64 length should be `bytes` data length multiplied by 4/3 rounded up\n // - `data.length + 2` -> Round up\n // - `/ 3` -> Number of 3-bytes chunks\n // - `4 *` -> 4 characters for each chunk\n string memory result = new string(4 * ((data.length + 2) / 3));\n\n /// @solidity memory-safe-assembly\n assembly {\n // Prepare the lookup table (skip the first \"length\" byte)\n let tablePtr := add(table, 1)\n\n // Prepare result pointer, jump over length\n let resultPtr := add(result, 0x20)\n let dataPtr := data\n let endPtr := add(data, mload(data))\n\n // In some cases, the last iteration will read bytes after the end of the data. We cache the value, and\n // set it to zero to make sure no dirty bytes are read in that section.\n let afterPtr := add(endPtr, 0x20)\n let afterCache := mload(afterPtr)\n mstore(afterPtr, 0x00)\n\n // Run over the input, 3 bytes at a time\n for {\n\n } lt(dataPtr, endPtr) {\n\n } {\n // Advance 3 bytes\n dataPtr := add(dataPtr, 3)\n let input := mload(dataPtr)\n\n // To write each character, shift the 3 byte (24 bits) chunk\n // 4 times in blocks of 6 bits for each character (18, 12, 6, 0)\n // and apply logical AND with 0x3F to bitmask the least significant 6 bits.\n // Use this as an index into the lookup table, mload an entire word\n // so the desired character is in the least significant byte, and\n // mstore8 this least significant byte into the result and continue.\n\n mstore8(resultPtr, mload(add(tablePtr, and(shr(18, input), 0x3F))))\n resultPtr := add(resultPtr, 1) // Advance\n\n mstore8(resultPtr, mload(add(tablePtr, and(shr(12, input), 0x3F))))\n resultPtr := add(resultPtr, 1) // Advance\n\n mstore8(resultPtr, mload(add(tablePtr, and(shr(6, input), 0x3F))))\n resultPtr := add(resultPtr, 1) // Advance\n\n mstore8(resultPtr, mload(add(tablePtr, and(input, 0x3F))))\n resultPtr := add(resultPtr, 1) // Advance\n }\n\n // Reset the value that was cached\n mstore(afterPtr, afterCache)\n\n // When data `bytes` is not exactly 3 bytes long\n // it is padded with `=` characters at the end\n switch mod(mload(data), 3)\n case 1 {\n mstore8(sub(resultPtr, 1), 0x3d)\n mstore8(sub(resultPtr, 2), 0x3d)\n }\n case 2 {\n mstore8(sub(resultPtr, 1), 0x3d)\n }\n }\n\n return result;\n }\n}\n"},"@openzeppelin/contracts/utils/introspection/IERC165.sol":{"content":"// SPDX-License-Identifier: MIT\n// OpenZeppelin Contracts (last updated v5.0.0) (utils/introspection/IERC165.sol)\n\npragma solidity ^0.8.20;\n\n/**\n * @dev Interface of the ERC165 standard, as defined in the\n * https://eips.ethereum.org/EIPS/eip-165[EIP].\n *\n * Implementers can declare support of contract interfaces, which can then be\n * queried by others ({ERC165Checker}).\n *\n * For an implementation, see {ERC165}.\n */\ninterface IERC165 {\n /**\n * @dev Returns true if this contract implements the interface defined by\n * `interfaceId`. See the corresponding\n * https://eips.ethereum.org/EIPS/eip-165#how-interfaces-are-identified[EIP section]\n * to learn more about how these ids are created.\n *\n * This function call must use less than 30 000 gas.\n */\n function supportsInterface(bytes4 interfaceId) external view returns (bool);\n}\n"},"@openzeppelin/contracts/utils/math/Math.sol":{"content":"// SPDX-License-Identifier: MIT\n// OpenZeppelin Contracts (last updated v5.0.0) (utils/math/Math.sol)\n\npragma solidity ^0.8.20;\n\n/**\n * @dev Standard math utilities missing in the Solidity language.\n */\nlibrary Math {\n /**\n * @dev Muldiv operation overflow.\n */\n error MathOverflowedMulDiv();\n\n enum Rounding {\n Floor, // Toward negative infinity\n Ceil, // Toward positive infinity\n Trunc, // Toward zero\n Expand // Away from zero\n }\n\n /**\n * @dev Returns the addition of two unsigned integers, with an overflow flag.\n */\n function tryAdd(uint256 a, uint256 b) internal pure returns (bool, uint256) {\n unchecked {\n uint256 c = a + b;\n if (c < a) return (false, 0);\n return (true, c);\n }\n }\n\n /**\n * @dev Returns the subtraction of two unsigned integers, with an overflow flag.\n */\n function trySub(uint256 a, uint256 b) internal pure returns (bool, uint256) {\n unchecked {\n if (b > a) return (false, 0);\n return (true, a - b);\n }\n }\n\n /**\n * @dev Returns the multiplication of two unsigned integers, with an overflow flag.\n */\n function tryMul(uint256 a, uint256 b) internal pure returns (bool, uint256) {\n unchecked {\n // Gas optimization: this is cheaper than requiring 'a' not being zero, but the\n // benefit is lost if 'b' is also tested.\n // See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522\n if (a == 0) return (true, 0);\n uint256 c = a * b;\n if (c / a != b) return (false, 0);\n return (true, c);\n }\n }\n\n /**\n * @dev Returns the division of two unsigned integers, with a division by zero flag.\n */\n function tryDiv(uint256 a, uint256 b) internal pure returns (bool, uint256) {\n unchecked {\n if (b == 0) return (false, 0);\n return (true, a / b);\n }\n }\n\n /**\n * @dev Returns the remainder of dividing two unsigned integers, with a division by zero flag.\n */\n function tryMod(uint256 a, uint256 b) internal pure returns (bool, uint256) {\n unchecked {\n if (b == 0) return (false, 0);\n return (true, a % b);\n }\n }\n\n /**\n * @dev Returns the largest of two numbers.\n */\n function max(uint256 a, uint256 b) internal pure returns (uint256) {\n return a > b ? a : b;\n }\n\n /**\n * @dev Returns the smallest of two numbers.\n */\n function min(uint256 a, uint256 b) internal pure returns (uint256) {\n return a < b ? a : b;\n }\n\n /**\n * @dev Returns the average of two numbers. The result is rounded towards\n * zero.\n */\n function average(uint256 a, uint256 b) internal pure returns (uint256) {\n // (a + b) / 2 can overflow.\n return (a & b) + (a ^ b) / 2;\n }\n\n /**\n * @dev Returns the ceiling of the division of two numbers.\n *\n * This differs from standard division with `/` in that it rounds towards infinity instead\n * of rounding towards zero.\n */\n function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {\n if (b == 0) {\n // Guarantee the same behavior as in a regular Solidity division.\n return a / b;\n }\n\n // (a + b - 1) / b can overflow on addition, so we distribute.\n return a == 0 ? 0 : (a - 1) / b + 1;\n }\n\n /**\n * @notice Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or\n * denominator == 0.\n * @dev Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv) with further edits by\n * Uniswap Labs also under MIT license.\n */\n function mulDiv(uint256 x, uint256 y, uint256 denominator) internal pure returns (uint256 result) {\n unchecked {\n // 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use\n // use the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256\n // variables such that product = prod1 * 2^256 + prod0.\n uint256 prod0 = x * y; // Least significant 256 bits of the product\n uint256 prod1; // Most significant 256 bits of the product\n assembly {\n let mm := mulmod(x, y, not(0))\n prod1 := sub(sub(mm, prod0), lt(mm, prod0))\n }\n\n // Handle non-overflow cases, 256 by 256 division.\n if (prod1 == 0) {\n // Solidity will revert if denominator == 0, unlike the div opcode on its own.\n // The surrounding unchecked block does not change this fact.\n // See https://docs.soliditylang.org/en/latest/control-structures.html#checked-or-unchecked-arithmetic.\n return prod0 / denominator;\n }\n\n // Make sure the result is less than 2^256. Also prevents denominator == 0.\n if (denominator <= prod1) {\n revert MathOverflowedMulDiv();\n }\n\n ///////////////////////////////////////////////\n // 512 by 256 division.\n ///////////////////////////////////////////////\n\n // Make division exact by subtracting the remainder from [prod1 prod0].\n uint256 remainder;\n assembly {\n // Compute remainder using mulmod.\n remainder := mulmod(x, y, denominator)\n\n // Subtract 256 bit number from 512 bit number.\n prod1 := sub(prod1, gt(remainder, prod0))\n prod0 := sub(prod0, remainder)\n }\n\n // Factor powers of two out of denominator and compute largest power of two divisor of denominator.\n // Always >= 1. See https://cs.stackexchange.com/q/138556/92363.\n\n uint256 twos = denominator & (0 - denominator);\n assembly {\n // Divide denominator by twos.\n denominator := div(denominator, twos)\n\n // Divide [prod1 prod0] by twos.\n prod0 := div(prod0, twos)\n\n // Flip twos such that it is 2^256 / twos. If twos is zero, then it becomes one.\n twos := add(div(sub(0, twos), twos), 1)\n }\n\n // Shift in bits from prod1 into prod0.\n prod0 |= prod1 * twos;\n\n // Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such\n // that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for\n // four bits. That is, denominator * inv = 1 mod 2^4.\n uint256 inverse = (3 * denominator) ^ 2;\n\n // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also\n // works in modular arithmetic, doubling the correct bits in each step.\n inverse *= 2 - denominator * inverse; // inverse mod 2^8\n inverse *= 2 - denominator * inverse; // inverse mod 2^16\n inverse *= 2 - denominator * inverse; // inverse mod 2^32\n inverse *= 2 - denominator * inverse; // inverse mod 2^64\n inverse *= 2 - denominator * inverse; // inverse mod 2^128\n inverse *= 2 - denominator * inverse; // inverse mod 2^256\n\n // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.\n // This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is\n // less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1\n // is no longer required.\n result = prod0 * inverse;\n return result;\n }\n }\n\n /**\n * @notice Calculates x * y / denominator with full precision, following the selected rounding direction.\n */\n function mulDiv(uint256 x, uint256 y, uint256 denominator, Rounding rounding) internal pure returns (uint256) {\n uint256 result = mulDiv(x, y, denominator);\n if (unsignedRoundsUp(rounding) && mulmod(x, y, denominator) > 0) {\n result += 1;\n }\n return result;\n }\n\n /**\n * @dev Returns the square root of a number. If the number is not a perfect square, the value is rounded\n * towards zero.\n *\n * Inspired by Henry S. Warren, Jr.'s \"Hacker's Delight\" (Chapter 11).\n */\n function sqrt(uint256 a) internal pure returns (uint256) {\n if (a == 0) {\n return 0;\n }\n\n // For our first guess, we get the biggest power of 2 which is smaller than the square root of the target.\n //\n // We know that the \"msb\" (most significant bit) of our target number `a` is a power of 2 such that we have\n // `msb(a) <= a < 2*msb(a)`. This value can be written `msb(a)=2**k` with `k=log2(a)`.\n //\n // This can be rewritten `2**log2(a) <= a < 2**(log2(a) + 1)`\n // → `sqrt(2**k) <= sqrt(a) < sqrt(2**(k+1))`\n // → `2**(k/2) <= sqrt(a) < 2**((k+1)/2) <= 2**(k/2 + 1)`\n //\n // Consequently, `2**(log2(a) / 2)` is a good first approximation of `sqrt(a)` with at least 1 correct bit.\n uint256 result = 1 << (log2(a) >> 1);\n\n // At this point `result` is an estimation with one bit of precision. We know the true value is a uint128,\n // since it is the square root of a uint256. Newton's method converges quadratically (precision doubles at\n // every iteration). We thus need at most 7 iteration to turn our partial result with one bit of precision\n // into the expected uint128 result.\n unchecked {\n result = (result + a / result) >> 1;\n result = (result + a / result) >> 1;\n result = (result + a / result) >> 1;\n result = (result + a / result) >> 1;\n result = (result + a / result) >> 1;\n result = (result + a / result) >> 1;\n result = (result + a / result) >> 1;\n return min(result, a / result);\n }\n }\n\n /**\n * @notice Calculates sqrt(a), following the selected rounding direction.\n */\n function sqrt(uint256 a, Rounding rounding) internal pure returns (uint256) {\n unchecked {\n uint256 result = sqrt(a);\n return result + (unsignedRoundsUp(rounding) && result * result < a ? 1 : 0);\n }\n }\n\n /**\n * @dev Return the log in base 2 of a positive value rounded towards zero.\n * Returns 0 if given 0.\n */\n function log2(uint256 value) internal pure returns (uint256) {\n uint256 result = 0;\n unchecked {\n if (value >> 128 > 0) {\n value >>= 128;\n result += 128;\n }\n if (value >> 64 > 0) {\n value >>= 64;\n result += 64;\n }\n if (value >> 32 > 0) {\n value >>= 32;\n result += 32;\n }\n if (value >> 16 > 0) {\n value >>= 16;\n result += 16;\n }\n if (value >> 8 > 0) {\n value >>= 8;\n result += 8;\n }\n if (value >> 4 > 0) {\n value >>= 4;\n result += 4;\n }\n if (value >> 2 > 0) {\n value >>= 2;\n result += 2;\n }\n if (value >> 1 > 0) {\n result += 1;\n }\n }\n return result;\n }\n\n /**\n * @dev Return the log in base 2, following the selected rounding direction, of a positive value.\n * Returns 0 if given 0.\n */\n function log2(uint256 value, Rounding rounding) internal pure returns (uint256) {\n unchecked {\n uint256 result = log2(value);\n return result + (unsignedRoundsUp(rounding) && 1 << result < value ? 1 : 0);\n }\n }\n\n /**\n * @dev Return the log in base 10 of a positive value rounded towards zero.\n * Returns 0 if given 0.\n */\n function log10(uint256 value) internal pure returns (uint256) {\n uint256 result = 0;\n unchecked {\n if (value >= 10 ** 64) {\n value /= 10 ** 64;\n result += 64;\n }\n if (value >= 10 ** 32) {\n value /= 10 ** 32;\n result += 32;\n }\n if (value >= 10 ** 16) {\n value /= 10 ** 16;\n result += 16;\n }\n if (value >= 10 ** 8) {\n value /= 10 ** 8;\n result += 8;\n }\n if (value >= 10 ** 4) {\n value /= 10 ** 4;\n result += 4;\n }\n if (value >= 10 ** 2) {\n value /= 10 ** 2;\n result += 2;\n }\n if (value >= 10 ** 1) {\n result += 1;\n }\n }\n return result;\n }\n\n /**\n * @dev Return the log in base 10, following the selected rounding direction, of a positive value.\n * Returns 0 if given 0.\n */\n function log10(uint256 value, Rounding rounding) internal pure returns (uint256) {\n unchecked {\n uint256 result = log10(value);\n return result + (unsignedRoundsUp(rounding) && 10 ** result < value ? 1 : 0);\n }\n }\n\n /**\n * @dev Return the log in base 256 of a positive value rounded towards zero.\n * Returns 0 if given 0.\n *\n * Adding one to the result gives the number of pairs of hex symbols needed to represent `value` as a hex string.\n */\n function log256(uint256 value) internal pure returns (uint256) {\n uint256 result = 0;\n unchecked {\n if (value >> 128 > 0) {\n value >>= 128;\n result += 16;\n }\n if (value >> 64 > 0) {\n value >>= 64;\n result += 8;\n }\n if (value >> 32 > 0) {\n value >>= 32;\n result += 4;\n }\n if (value >> 16 > 0) {\n value >>= 16;\n result += 2;\n }\n if (value >> 8 > 0) {\n result += 1;\n }\n }\n return result;\n }\n\n /**\n * @dev Return the log in base 256, following the selected rounding direction, of a positive value.\n * Returns 0 if given 0.\n */\n function log256(uint256 value, Rounding rounding) internal pure returns (uint256) {\n unchecked {\n uint256 result = log256(value);\n return result + (unsignedRoundsUp(rounding) && 1 << (result << 3) < value ? 1 : 0);\n }\n }\n\n /**\n * @dev Returns whether a provided rounding mode is considered rounding up for unsigned integers.\n */\n function unsignedRoundsUp(Rounding rounding) internal pure returns (bool) {\n return uint8(rounding) % 2 == 1;\n }\n}\n"},"@openzeppelin/contracts/utils/math/SignedMath.sol":{"content":"// SPDX-License-Identifier: MIT\n// OpenZeppelin Contracts (last updated v5.0.0) (utils/math/SignedMath.sol)\n\npragma solidity ^0.8.20;\n\n/**\n * @dev Standard signed math utilities missing in the Solidity language.\n */\nlibrary SignedMath {\n /**\n * @dev Returns the largest of two signed numbers.\n */\n function max(int256 a, int256 b) internal pure returns (int256) {\n return a > b ? a : b;\n }\n\n /**\n * @dev Returns the smallest of two signed numbers.\n */\n function min(int256 a, int256 b) internal pure returns (int256) {\n return a < b ? a : b;\n }\n\n /**\n * @dev Returns the average of two signed numbers without overflow.\n * The result is rounded towards zero.\n */\n function average(int256 a, int256 b) internal pure returns (int256) {\n // Formula from the book \"Hacker's Delight\"\n int256 x = (a & b) + ((a ^ b) >> 1);\n return x + (int256(uint256(x) >> 255) & (a ^ b));\n }\n\n /**\n * @dev Returns the absolute unsigned value of a signed value.\n */\n function abs(int256 n) internal pure returns (uint256) {\n unchecked {\n // must be unchecked in order to support `n = type(int256).min`\n return uint256(n >= 0 ? n : -n);\n }\n }\n}\n"},"@openzeppelin/contracts/utils/Strings.sol":{"content":"// SPDX-License-Identifier: MIT\n// OpenZeppelin Contracts (last updated v5.0.0) (utils/Strings.sol)\n\npragma solidity ^0.8.20;\n\nimport {Math} from \"./math/Math.sol\";\nimport {SignedMath} from \"./math/SignedMath.sol\";\n\n/**\n * @dev String operations.\n */\nlibrary Strings {\n bytes16 private constant HEX_DIGITS = \"0123456789abcdef\";\n uint8 private constant ADDRESS_LENGTH = 20;\n\n /**\n * @dev The `value` string doesn't fit in the specified `length`.\n */\n error StringsInsufficientHexLength(uint256 value, uint256 length);\n\n /**\n * @dev Converts a `uint256` to its ASCII `string` decimal representation.\n */\n function toString(uint256 value) internal pure returns (string memory) {\n unchecked {\n uint256 length = Math.log10(value) + 1;\n string memory buffer = new string(length);\n uint256 ptr;\n /// @solidity memory-safe-assembly\n assembly {\n ptr := add(buffer, add(32, length))\n }\n while (true) {\n ptr--;\n /// @solidity memory-safe-assembly\n assembly {\n mstore8(ptr, byte(mod(value, 10), HEX_DIGITS))\n }\n value /= 10;\n if (value == 0) break;\n }\n return buffer;\n }\n }\n\n /**\n * @dev Converts a `int256` to its ASCII `string` decimal representation.\n */\n function toStringSigned(int256 value) internal pure returns (string memory) {\n return string.concat(value < 0 ? \"-\" : \"\", toString(SignedMath.abs(value)));\n }\n\n /**\n * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.\n */\n function toHexString(uint256 value) internal pure returns (string memory) {\n unchecked {\n return toHexString(value, Math.log256(value) + 1);\n }\n }\n\n /**\n * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation with fixed length.\n */\n function toHexString(uint256 value, uint256 length) internal pure returns (string memory) {\n uint256 localValue = value;\n bytes memory buffer = new bytes(2 * length + 2);\n buffer[0] = \"0\";\n buffer[1] = \"x\";\n for (uint256 i = 2 * length + 1; i > 1; --i) {\n buffer[i] = HEX_DIGITS[localValue & 0xf];\n localValue >>= 4;\n }\n if (localValue != 0) {\n revert StringsInsufficientHexLength(value, length);\n }\n return string(buffer);\n }\n\n /**\n * @dev Converts an `address` with fixed length of 20 bytes to its not checksummed ASCII `string` hexadecimal\n * representation.\n */\n function toHexString(address addr) internal pure returns (string memory) {\n return toHexString(uint256(uint160(addr)), ADDRESS_LENGTH);\n }\n\n /**\n * @dev Returns true if the two strings are equal.\n */\n function equal(string memory a, string memory b) internal pure returns (bool) {\n return bytes(a).length == bytes(b).length && keccak256(bytes(a)) == keccak256(bytes(b));\n }\n}\n"},"@prb/math/src/Common.sol":{"content":"// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\n// Common.sol\n//\n// Common mathematical functions used in both SD59x18 and UD60x18. Note that these global functions do not\n// always operate with SD59x18 and UD60x18 numbers.\n\n/*//////////////////////////////////////////////////////////////////////////\n CUSTOM ERRORS\n//////////////////////////////////////////////////////////////////////////*/\n\n/// @notice Thrown when the resultant value in {mulDiv} overflows uint256.\nerror PRBMath_MulDiv_Overflow(uint256 x, uint256 y, uint256 denominator);\n\n/// @notice Thrown when the resultant value in {mulDiv18} overflows uint256.\nerror PRBMath_MulDiv18_Overflow(uint256 x, uint256 y);\n\n/// @notice Thrown when one of the inputs passed to {mulDivSigned} is `type(int256).min`.\nerror PRBMath_MulDivSigned_InputTooSmall();\n\n/// @notice Thrown when the resultant value in {mulDivSigned} overflows int256.\nerror PRBMath_MulDivSigned_Overflow(int256 x, int256 y);\n\n/*//////////////////////////////////////////////////////////////////////////\n CONSTANTS\n//////////////////////////////////////////////////////////////////////////*/\n\n/// @dev The maximum value a uint128 number can have.\nuint128 constant MAX_UINT128 = type(uint128).max;\n\n/// @dev The maximum value a uint40 number can have.\nuint40 constant MAX_UINT40 = type(uint40).max;\n\n/// @dev The unit number, which the decimal precision of the fixed-point types.\nuint256 constant UNIT = 1e18;\n\n/// @dev The unit number inverted mod 2^256.\nuint256 constant UNIT_INVERSE = 78156646155174841979727994598816262306175212592076161876661_508869554232690281;\n\n/// @dev The the largest power of two that divides the decimal value of `UNIT`. The logarithm of this value is the least significant\n/// bit in the binary representation of `UNIT`.\nuint256 constant UNIT_LPOTD = 262144;\n\n/*//////////////////////////////////////////////////////////////////////////\n FUNCTIONS\n//////////////////////////////////////////////////////////////////////////*/\n\n/// @notice Calculates the binary exponent of x using the binary fraction method.\n/// @dev Has to use 192.64-bit fixed-point numbers. See https://ethereum.stackexchange.com/a/96594/24693.\n/// @param x The exponent as an unsigned 192.64-bit fixed-point number.\n/// @return result The result as an unsigned 60.18-decimal fixed-point number.\n/// @custom:smtchecker abstract-function-nondet\nfunction exp2(uint256 x) pure returns (uint256 result) {\n unchecked {\n // Start from 0.5 in the 192.64-bit fixed-point format.\n result = 0x800000000000000000000000000000000000000000000000;\n\n // The following logic multiplies the result by $\\sqrt{2^{-i}}$ when the bit at position i is 1. Key points:\n //\n // 1. Intermediate results will not overflow, as the starting point is 2^191 and all magic factors are under 2^65.\n // 2. The rationale for organizing the if statements into groups of 8 is gas savings. If the result of performing\n // a bitwise AND operation between x and any value in the array [0x80; 0x40; 0x20; 0x10; 0x08; 0x04; 0x02; 0x01] is 1,\n // we know that `x & 0xFF` is also 1.\n if (x & 0xFF00000000000000 > 0) {\n if (x & 0x8000000000000000 > 0) {\n result = (result * 0x16A09E667F3BCC909) >> 64;\n }\n if (x & 0x4000000000000000 > 0) {\n result = (result * 0x1306FE0A31B7152DF) >> 64;\n }\n if (x & 0x2000000000000000 > 0) {\n result = (result * 0x1172B83C7D517ADCE) >> 64;\n }\n if (x & 0x1000000000000000 > 0) {\n result = (result * 0x10B5586CF9890F62A) >> 64;\n }\n if (x & 0x800000000000000 > 0) {\n result = (result * 0x1059B0D31585743AE) >> 64;\n }\n if (x & 0x400000000000000 > 0) {\n result = (result * 0x102C9A3E778060EE7) >> 64;\n }\n if (x & 0x200000000000000 > 0) {\n result = (result * 0x10163DA9FB33356D8) >> 64;\n }\n if (x & 0x100000000000000 > 0) {\n result = (result * 0x100B1AFA5ABCBED61) >> 64;\n }\n }\n\n if (x & 0xFF000000000000 > 0) {\n if (x & 0x80000000000000 > 0) {\n result = (result * 0x10058C86DA1C09EA2) >> 64;\n }\n if (x & 0x40000000000000 > 0) {\n result = (result * 0x1002C605E2E8CEC50) >> 64;\n }\n if (x & 0x20000000000000 > 0) {\n result = (result * 0x100162F3904051FA1) >> 64;\n }\n if (x & 0x10000000000000 > 0) {\n result = (result * 0x1000B175EFFDC76BA) >> 64;\n }\n if (x & 0x8000000000000 > 0) {\n result = (result * 0x100058BA01FB9F96D) >> 64;\n }\n if (x & 0x4000000000000 > 0) {\n result = (result * 0x10002C5CC37DA9492) >> 64;\n }\n if (x & 0x2000000000000 > 0) {\n result = (result * 0x1000162E525EE0547) >> 64;\n }\n if (x & 0x1000000000000 > 0) {\n result = (result * 0x10000B17255775C04) >> 64;\n }\n }\n\n if (x & 0xFF0000000000 > 0) {\n if (x & 0x800000000000 > 0) {\n result = (result * 0x1000058B91B5BC9AE) >> 64;\n }\n if (x & 0x400000000000 > 0) {\n result = (result * 0x100002C5C89D5EC6D) >> 64;\n }\n if (x & 0x200000000000 > 0) {\n result = (result * 0x10000162E43F4F831) >> 64;\n }\n if (x & 0x100000000000 > 0) {\n result = (result * 0x100000B1721BCFC9A) >> 64;\n }\n if (x & 0x80000000000 > 0) {\n result = (result * 0x10000058B90CF1E6E) >> 64;\n }\n if (x & 0x40000000000 > 0) {\n result = (result * 0x1000002C5C863B73F) >> 64;\n }\n if (x & 0x20000000000 > 0) {\n result = (result * 0x100000162E430E5A2) >> 64;\n }\n if (x & 0x10000000000 > 0) {\n result = (result * 0x1000000B172183551) >> 64;\n }\n }\n\n if (x & 0xFF00000000 > 0) {\n if (x & 0x8000000000 > 0) {\n result = (result * 0x100000058B90C0B49) >> 64;\n }\n if (x & 0x4000000000 > 0) {\n result = (result * 0x10000002C5C8601CC) >> 64;\n }\n if (x & 0x2000000000 > 0) {\n result = (result * 0x1000000162E42FFF0) >> 64;\n }\n if (x & 0x1000000000 > 0) {\n result = (result * 0x10000000B17217FBB) >> 64;\n }\n if (x & 0x800000000 > 0) {\n result = (result * 0x1000000058B90BFCE) >> 64;\n }\n if (x & 0x400000000 > 0) {\n result = (result * 0x100000002C5C85FE3) >> 64;\n }\n if (x & 0x200000000 > 0) {\n result = (result * 0x10000000162E42FF1) >> 64;\n }\n if (x & 0x100000000 > 0) {\n result = (result * 0x100000000B17217F8) >> 64;\n }\n }\n\n if (x & 0xFF000000 > 0) {\n if (x & 0x80000000 > 0) {\n result = (result * 0x10000000058B90BFC) >> 64;\n }\n if (x & 0x40000000 > 0) {\n result = (result * 0x1000000002C5C85FE) >> 64;\n }\n if (x & 0x20000000 > 0) {\n result = (result * 0x100000000162E42FF) >> 64;\n }\n if (x & 0x10000000 > 0) {\n result = (result * 0x1000000000B17217F) >> 64;\n }\n if (x & 0x8000000 > 0) {\n result = (result * 0x100000000058B90C0) >> 64;\n }\n if (x & 0x4000000 > 0) {\n result = (result * 0x10000000002C5C860) >> 64;\n }\n if (x & 0x2000000 > 0) {\n result = (result * 0x1000000000162E430) >> 64;\n }\n if (x & 0x1000000 > 0) {\n result = (result * 0x10000000000B17218) >> 64;\n }\n }\n\n if (x & 0xFF0000 > 0) {\n if (x & 0x800000 > 0) {\n result = (result * 0x1000000000058B90C) >> 64;\n }\n if (x & 0x400000 > 0) {\n result = (result * 0x100000000002C5C86) >> 64;\n }\n if (x & 0x200000 > 0) {\n result = (result * 0x10000000000162E43) >> 64;\n }\n if (x & 0x100000 > 0) {\n result = (result * 0x100000000000B1721) >> 64;\n }\n if (x & 0x80000 > 0) {\n result = (result * 0x10000000000058B91) >> 64;\n }\n if (x & 0x40000 > 0) {\n result = (result * 0x1000000000002C5C8) >> 64;\n }\n if (x & 0x20000 > 0) {\n result = (result * 0x100000000000162E4) >> 64;\n }\n if (x & 0x10000 > 0) {\n result = (result * 0x1000000000000B172) >> 64;\n }\n }\n\n if (x & 0xFF00 > 0) {\n if (x & 0x8000 > 0) {\n result = (result * 0x100000000000058B9) >> 64;\n }\n if (x & 0x4000 > 0) {\n result = (result * 0x10000000000002C5D) >> 64;\n }\n if (x & 0x2000 > 0) {\n result = (result * 0x1000000000000162E) >> 64;\n }\n if (x & 0x1000 > 0) {\n result = (result * 0x10000000000000B17) >> 64;\n }\n if (x & 0x800 > 0) {\n result = (result * 0x1000000000000058C) >> 64;\n }\n if (x & 0x400 > 0) {\n result = (result * 0x100000000000002C6) >> 64;\n }\n if (x & 0x200 > 0) {\n result = (result * 0x10000000000000163) >> 64;\n }\n if (x & 0x100 > 0) {\n result = (result * 0x100000000000000B1) >> 64;\n }\n }\n\n if (x & 0xFF > 0) {\n if (x & 0x80 > 0) {\n result = (result * 0x10000000000000059) >> 64;\n }\n if (x & 0x40 > 0) {\n result = (result * 0x1000000000000002C) >> 64;\n }\n if (x & 0x20 > 0) {\n result = (result * 0x10000000000000016) >> 64;\n }\n if (x & 0x10 > 0) {\n result = (result * 0x1000000000000000B) >> 64;\n }\n if (x & 0x8 > 0) {\n result = (result * 0x10000000000000006) >> 64;\n }\n if (x & 0x4 > 0) {\n result = (result * 0x10000000000000003) >> 64;\n }\n if (x & 0x2 > 0) {\n result = (result * 0x10000000000000001) >> 64;\n }\n if (x & 0x1 > 0) {\n result = (result * 0x10000000000000001) >> 64;\n }\n }\n\n // In the code snippet below, two operations are executed simultaneously:\n //\n // 1. The result is multiplied by $(2^n + 1)$, where $2^n$ represents the integer part, and the additional 1\n // accounts for the initial guess of 0.5. This is achieved by subtracting from 191 instead of 192.\n // 2. The result is then converted to an unsigned 60.18-decimal fixed-point format.\n //\n // The underlying logic is based on the relationship $2^{191-ip} = 2^{ip} / 2^{191}$, where $ip$ denotes the,\n // integer part, $2^n$.\n result *= UNIT;\n result >>= (191 - (x >> 64));\n }\n}\n\n/// @notice Finds the zero-based index of the first 1 in the binary representation of x.\n///\n/// @dev See the note on \"msb\" in this Wikipedia article: https://en.wikipedia.org/wiki/Find_first_set\n///\n/// Each step in this implementation is equivalent to this high-level code:\n///\n/// ```solidity\n/// if (x >= 2 ** 128) {\n/// x >>= 128;\n/// result += 128;\n/// }\n/// ```\n///\n/// Where 128 is replaced with each respective power of two factor. See the full high-level implementation here:\n/// https://gist.github.com/PaulRBerg/f932f8693f2733e30c4d479e8e980948\n///\n/// The Yul instructions used below are:\n///\n/// - \"gt\" is \"greater than\"\n/// - \"or\" is the OR bitwise operator\n/// - \"shl\" is \"shift left\"\n/// - \"shr\" is \"shift right\"\n///\n/// @param x The uint256 number for which to find the index of the most significant bit.\n/// @return result The index of the most significant bit as a uint256.\n/// @custom:smtchecker abstract-function-nondet\nfunction msb(uint256 x) pure returns (uint256 result) {\n // 2^128\n assembly (\"memory-safe\") {\n let factor := shl(7, gt(x, 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF))\n x := shr(factor, x)\n result := or(result, factor)\n }\n // 2^64\n assembly (\"memory-safe\") {\n let factor := shl(6, gt(x, 0xFFFFFFFFFFFFFFFF))\n x := shr(factor, x)\n result := or(result, factor)\n }\n // 2^32\n assembly (\"memory-safe\") {\n let factor := shl(5, gt(x, 0xFFFFFFFF))\n x := shr(factor, x)\n result := or(result, factor)\n }\n // 2^16\n assembly (\"memory-safe\") {\n let factor := shl(4, gt(x, 0xFFFF))\n x := shr(factor, x)\n result := or(result, factor)\n }\n // 2^8\n assembly (\"memory-safe\") {\n let factor := shl(3, gt(x, 0xFF))\n x := shr(factor, x)\n result := or(result, factor)\n }\n // 2^4\n assembly (\"memory-safe\") {\n let factor := shl(2, gt(x, 0xF))\n x := shr(factor, x)\n result := or(result, factor)\n }\n // 2^2\n assembly (\"memory-safe\") {\n let factor := shl(1, gt(x, 0x3))\n x := shr(factor, x)\n result := or(result, factor)\n }\n // 2^1\n // No need to shift x any more.\n assembly (\"memory-safe\") {\n let factor := gt(x, 0x1)\n result := or(result, factor)\n }\n}\n\n/// @notice Calculates x*y÷denominator with 512-bit precision.\n///\n/// @dev Credits to Remco Bloemen under MIT license https://xn--2-umb.com/21/muldiv.\n///\n/// Notes:\n/// - The result is rounded toward zero.\n///\n/// Requirements:\n/// - The denominator must not be zero.\n/// - The result must fit in uint256.\n///\n/// @param x The multiplicand as a uint256.\n/// @param y The multiplier as a uint256.\n/// @param denominator The divisor as a uint256.\n/// @return result The result as a uint256.\n/// @custom:smtchecker abstract-function-nondet\nfunction mulDiv(uint256 x, uint256 y, uint256 denominator) pure returns (uint256 result) {\n // 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use\n // use the Chinese Remainder Theorem to reconstruct the 512-bit result. The result is stored in two 256\n // variables such that product = prod1 * 2^256 + prod0.\n uint256 prod0; // Least significant 256 bits of the product\n uint256 prod1; // Most significant 256 bits of the product\n assembly (\"memory-safe\") {\n let mm := mulmod(x, y, not(0))\n prod0 := mul(x, y)\n prod1 := sub(sub(mm, prod0), lt(mm, prod0))\n }\n\n // Handle non-overflow cases, 256 by 256 division.\n if (prod1 == 0) {\n unchecked {\n return prod0 / denominator;\n }\n }\n\n // Make sure the result is less than 2^256. Also prevents denominator == 0.\n if (prod1 >= denominator) {\n revert PRBMath_MulDiv_Overflow(x, y, denominator);\n }\n\n ////////////////////////////////////////////////////////////////////////////\n // 512 by 256 division\n ////////////////////////////////////////////////////////////////////////////\n\n // Make division exact by subtracting the remainder from [prod1 prod0].\n uint256 remainder;\n assembly (\"memory-safe\") {\n // Compute remainder using the mulmod Yul instruction.\n remainder := mulmod(x, y, denominator)\n\n // Subtract 256 bit number from 512-bit number.\n prod1 := sub(prod1, gt(remainder, prod0))\n prod0 := sub(prod0, remainder)\n }\n\n unchecked {\n // Calculate the largest power of two divisor of the denominator using the unary operator ~. This operation cannot overflow\n // because the denominator cannot be zero at this point in the function execution. The result is always >= 1.\n // For more detail, see https://cs.stackexchange.com/q/138556/92363.\n uint256 lpotdod = denominator & (~denominator + 1);\n uint256 flippedLpotdod;\n\n assembly (\"memory-safe\") {\n // Factor powers of two out of denominator.\n denominator := div(denominator, lpotdod)\n\n // Divide [prod1 prod0] by lpotdod.\n prod0 := div(prod0, lpotdod)\n\n // Get the flipped value `2^256 / lpotdod`. If the `lpotdod` is zero, the flipped value is one.\n // `sub(0, lpotdod)` produces the two's complement version of `lpotdod`, which is equivalent to flipping all the bits.\n // However, `div` interprets this value as an unsigned value: https://ethereum.stackexchange.com/q/147168/24693\n flippedLpotdod := add(div(sub(0, lpotdod), lpotdod), 1)\n }\n\n // Shift in bits from prod1 into prod0.\n prod0 |= prod1 * flippedLpotdod;\n\n // Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such\n // that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for\n // four bits. That is, denominator * inv = 1 mod 2^4.\n uint256 inverse = (3 * denominator) ^ 2;\n\n // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also works\n // in modular arithmetic, doubling the correct bits in each step.\n inverse *= 2 - denominator * inverse; // inverse mod 2^8\n inverse *= 2 - denominator * inverse; // inverse mod 2^16\n inverse *= 2 - denominator * inverse; // inverse mod 2^32\n inverse *= 2 - denominator * inverse; // inverse mod 2^64\n inverse *= 2 - denominator * inverse; // inverse mod 2^128\n inverse *= 2 - denominator * inverse; // inverse mod 2^256\n\n // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.\n // This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is\n // less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1\n // is no longer required.\n result = prod0 * inverse;\n }\n}\n\n/// @notice Calculates x*y÷1e18 with 512-bit precision.\n///\n/// @dev A variant of {mulDiv} with constant folding, i.e. in which the denominator is hard coded to 1e18.\n///\n/// Notes:\n/// - The body is purposely left uncommented; to understand how this works, see the documentation in {mulDiv}.\n/// - The result is rounded toward zero.\n/// - We take as an axiom that the result cannot be `MAX_UINT256` when x and y solve the following system of equations:\n///\n/// $$\n/// \\begin{cases}\n/// x * y = MAX\\_UINT256 * UNIT \\\\\n/// (x * y) \\% UNIT \\geq \\frac{UNIT}{2}\n/// \\end{cases}\n/// $$\n///\n/// Requirements:\n/// - Refer to the requirements in {mulDiv}.\n/// - The result must fit in uint256.\n///\n/// @param x The multiplicand as an unsigned 60.18-decimal fixed-point number.\n/// @param y The multiplier as an unsigned 60.18-decimal fixed-point number.\n/// @return result The result as an unsigned 60.18-decimal fixed-point number.\n/// @custom:smtchecker abstract-function-nondet\nfunction mulDiv18(uint256 x, uint256 y) pure returns (uint256 result) {\n uint256 prod0;\n uint256 prod1;\n assembly (\"memory-safe\") {\n let mm := mulmod(x, y, not(0))\n prod0 := mul(x, y)\n prod1 := sub(sub(mm, prod0), lt(mm, prod0))\n }\n\n if (prod1 == 0) {\n unchecked {\n return prod0 / UNIT;\n }\n }\n\n if (prod1 >= UNIT) {\n revert PRBMath_MulDiv18_Overflow(x, y);\n }\n\n uint256 remainder;\n assembly (\"memory-safe\") {\n remainder := mulmod(x, y, UNIT)\n result :=\n mul(\n or(\n div(sub(prod0, remainder), UNIT_LPOTD),\n mul(sub(prod1, gt(remainder, prod0)), add(div(sub(0, UNIT_LPOTD), UNIT_LPOTD), 1))\n ),\n UNIT_INVERSE\n )\n }\n}\n\n/// @notice Calculates x*y÷denominator with 512-bit precision.\n///\n/// @dev This is an extension of {mulDiv} for signed numbers, which works by computing the signs and the absolute values separately.\n///\n/// Notes:\n/// - The result is rounded toward zero.\n///\n/// Requirements:\n/// - Refer to the requirements in {mulDiv}.\n/// - None of the inputs can be `type(int256).min`.\n/// - The result must fit in int256.\n///\n/// @param x The multiplicand as an int256.\n/// @param y The multiplier as an int256.\n/// @param denominator The divisor as an int256.\n/// @return result The result as an int256.\n/// @custom:smtchecker abstract-function-nondet\nfunction mulDivSigned(int256 x, int256 y, int256 denominator) pure returns (int256 result) {\n if (x == type(int256).min || y == type(int256).min || denominator == type(int256).min) {\n revert PRBMath_MulDivSigned_InputTooSmall();\n }\n\n // Get hold of the absolute values of x, y and the denominator.\n uint256 xAbs;\n uint256 yAbs;\n uint256 dAbs;\n unchecked {\n xAbs = x < 0 ? uint256(-x) : uint256(x);\n yAbs = y < 0 ? uint256(-y) : uint256(y);\n dAbs = denominator < 0 ? uint256(-denominator) : uint256(denominator);\n }\n\n // Compute the absolute value of x*y÷denominator. The result must fit in int256.\n uint256 resultAbs = mulDiv(xAbs, yAbs, dAbs);\n if (resultAbs > uint256(type(int256).max)) {\n revert PRBMath_MulDivSigned_Overflow(x, y);\n }\n\n // Get the signs of x, y and the denominator.\n uint256 sx;\n uint256 sy;\n uint256 sd;\n assembly (\"memory-safe\") {\n // \"sgt\" is the \"signed greater than\" assembly instruction and \"sub(0,1)\" is -1 in two's complement.\n sx := sgt(x, sub(0, 1))\n sy := sgt(y, sub(0, 1))\n sd := sgt(denominator, sub(0, 1))\n }\n\n // XOR over sx, sy and sd. What this does is to check whether there are 1 or 3 negative signs in the inputs.\n // If there are, the result should be negative. Otherwise, it should be positive.\n unchecked {\n result = sx ^ sy ^ sd == 0 ? -int256(resultAbs) : int256(resultAbs);\n }\n}\n\n/// @notice Calculates the square root of x using the Babylonian method.\n///\n/// @dev See https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.\n///\n/// Notes:\n/// - If x is not a perfect square, the result is rounded down.\n/// - Credits to OpenZeppelin for the explanations in comments below.\n///\n/// @param x The uint256 number for which to calculate the square root.\n/// @return result The result as a uint256.\n/// @custom:smtchecker abstract-function-nondet\nfunction sqrt(uint256 x) pure returns (uint256 result) {\n if (x == 0) {\n return 0;\n }\n\n // For our first guess, we calculate the biggest power of 2 which is smaller than the square root of x.\n //\n // We know that the \"msb\" (most significant bit) of x is a power of 2 such that we have:\n //\n // $$\n // msb(x) <= x <= 2*msb(x)$\n // $$\n //\n // We write $msb(x)$ as $2^k$, and we get:\n //\n // $$\n // k = log_2(x)\n // $$\n //\n // Thus, we can write the initial inequality as:\n //\n // $$\n // 2^{log_2(x)} <= x <= 2*2^{log_2(x)+1} \\\\\n // sqrt(2^k) <= sqrt(x) < sqrt(2^{k+1}) \\\\\n // 2^{k/2} <= sqrt(x) < 2^{(k+1)/2} <= 2^{(k/2)+1}\n // $$\n //\n // Consequently, $2^{log_2(x) /2} is a good first approximation of sqrt(x) with at least one correct bit.\n uint256 xAux = uint256(x);\n result = 1;\n if (xAux >= 2 ** 128) {\n xAux >>= 128;\n result <<= 64;\n }\n if (xAux >= 2 ** 64) {\n xAux >>= 64;\n result <<= 32;\n }\n if (xAux >= 2 ** 32) {\n xAux >>= 32;\n result <<= 16;\n }\n if (xAux >= 2 ** 16) {\n xAux >>= 16;\n result <<= 8;\n }\n if (xAux >= 2 ** 8) {\n xAux >>= 8;\n result <<= 4;\n }\n if (xAux >= 2 ** 4) {\n xAux >>= 4;\n result <<= 2;\n }\n if (xAux >= 2 ** 2) {\n result <<= 1;\n }\n\n // At this point, `result` is an estimation with at least one bit of precision. We know the true value has at\n // most 128 bits, since it is the square root of a uint256. Newton's method converges quadratically (precision\n // doubles at every iteration). We thus need at most 7 iteration to turn our partial result with one bit of\n // precision into the expected uint128 result.\n unchecked {\n result = (result + x / result) >> 1;\n result = (result + x / result) >> 1;\n result = (result + x / result) >> 1;\n result = (result + x / result) >> 1;\n result = (result + x / result) >> 1;\n result = (result + x / result) >> 1;\n result = (result + x / result) >> 1;\n\n // If x is not a perfect square, round the result toward zero.\n uint256 roundedResult = x / result;\n if (result >= roundedResult) {\n result = roundedResult;\n }\n }\n}\n"},"@prb/math/src/sd1x18/Casting.sol":{"content":"// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport \"../Common.sol\" as Common;\nimport \"./Errors.sol\" as CastingErrors;\nimport { SD59x18 } from \"../sd59x18/ValueType.sol\";\nimport { UD2x18 } from \"../ud2x18/ValueType.sol\";\nimport { UD60x18 } from \"../ud60x18/ValueType.sol\";\nimport { SD1x18 } from \"./ValueType.sol\";\n\n/// @notice Casts an SD1x18 number into SD59x18.\n/// @dev There is no overflow check because the domain of SD1x18 is a subset of SD59x18.\nfunction intoSD59x18(SD1x18 x) pure returns (SD59x18 result) {\n result = SD59x18.wrap(int256(SD1x18.unwrap(x)));\n}\n\n/// @notice Casts an SD1x18 number into UD2x18.\n/// - x must be positive.\nfunction intoUD2x18(SD1x18 x) pure returns (UD2x18 result) {\n int64 xInt = SD1x18.unwrap(x);\n if (xInt < 0) {\n revert CastingErrors.PRBMath_SD1x18_ToUD2x18_Underflow(x);\n }\n result = UD2x18.wrap(uint64(xInt));\n}\n\n/// @notice Casts an SD1x18 number into UD60x18.\n/// @dev Requirements:\n/// - x must be positive.\nfunction intoUD60x18(SD1x18 x) pure returns (UD60x18 result) {\n int64 xInt = SD1x18.unwrap(x);\n if (xInt < 0) {\n revert CastingErrors.PRBMath_SD1x18_ToUD60x18_Underflow(x);\n }\n result = UD60x18.wrap(uint64(xInt));\n}\n\n/// @notice Casts an SD1x18 number into uint256.\n/// @dev Requirements:\n/// - x must be positive.\nfunction intoUint256(SD1x18 x) pure returns (uint256 result) {\n int64 xInt = SD1x18.unwrap(x);\n if (xInt < 0) {\n revert CastingErrors.PRBMath_SD1x18_ToUint256_Underflow(x);\n }\n result = uint256(uint64(xInt));\n}\n\n/// @notice Casts an SD1x18 number into uint128.\n/// @dev Requirements:\n/// - x must be positive.\nfunction intoUint128(SD1x18 x) pure returns (uint128 result) {\n int64 xInt = SD1x18.unwrap(x);\n if (xInt < 0) {\n revert CastingErrors.PRBMath_SD1x18_ToUint128_Underflow(x);\n }\n result = uint128(uint64(xInt));\n}\n\n/// @notice Casts an SD1x18 number into uint40.\n/// @dev Requirements:\n/// - x must be positive.\n/// - x must be less than or equal to `MAX_UINT40`.\nfunction intoUint40(SD1x18 x) pure returns (uint40 result) {\n int64 xInt = SD1x18.unwrap(x);\n if (xInt < 0) {\n revert CastingErrors.PRBMath_SD1x18_ToUint40_Underflow(x);\n }\n if (xInt > int64(uint64(Common.MAX_UINT40))) {\n revert CastingErrors.PRBMath_SD1x18_ToUint40_Overflow(x);\n }\n result = uint40(uint64(xInt));\n}\n\n/// @notice Alias for {wrap}.\nfunction sd1x18(int64 x) pure returns (SD1x18 result) {\n result = SD1x18.wrap(x);\n}\n\n/// @notice Unwraps an SD1x18 number into int64.\nfunction unwrap(SD1x18 x) pure returns (int64 result) {\n result = SD1x18.unwrap(x);\n}\n\n/// @notice Wraps an int64 number into SD1x18.\nfunction wrap(int64 x) pure returns (SD1x18 result) {\n result = SD1x18.wrap(x);\n}\n"},"@prb/math/src/sd1x18/Constants.sol":{"content":"// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport { SD1x18 } from \"./ValueType.sol\";\n\n/// @dev Euler's number as an SD1x18 number.\nSD1x18 constant E = SD1x18.wrap(2_718281828459045235);\n\n/// @dev The maximum value an SD1x18 number can have.\nint64 constant uMAX_SD1x18 = 9_223372036854775807;\nSD1x18 constant MAX_SD1x18 = SD1x18.wrap(uMAX_SD1x18);\n\n/// @dev The maximum value an SD1x18 number can have.\nint64 constant uMIN_SD1x18 = -9_223372036854775808;\nSD1x18 constant MIN_SD1x18 = SD1x18.wrap(uMIN_SD1x18);\n\n/// @dev PI as an SD1x18 number.\nSD1x18 constant PI = SD1x18.wrap(3_141592653589793238);\n\n/// @dev The unit number, which gives the decimal precision of SD1x18.\nSD1x18 constant UNIT = SD1x18.wrap(1e18);\nint64 constant uUNIT = 1e18;\n"},"@prb/math/src/sd1x18/Errors.sol":{"content":"// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport { SD1x18 } from \"./ValueType.sol\";\n\n/// @notice Thrown when trying to cast a SD1x18 number that doesn't fit in UD2x18.\nerror PRBMath_SD1x18_ToUD2x18_Underflow(SD1x18 x);\n\n/// @notice Thrown when trying to cast a SD1x18 number that doesn't fit in UD60x18.\nerror PRBMath_SD1x18_ToUD60x18_Underflow(SD1x18 x);\n\n/// @notice Thrown when trying to cast a SD1x18 number that doesn't fit in uint128.\nerror PRBMath_SD1x18_ToUint128_Underflow(SD1x18 x);\n\n/// @notice Thrown when trying to cast a SD1x18 number that doesn't fit in uint256.\nerror PRBMath_SD1x18_ToUint256_Underflow(SD1x18 x);\n\n/// @notice Thrown when trying to cast a SD1x18 number that doesn't fit in uint40.\nerror PRBMath_SD1x18_ToUint40_Overflow(SD1x18 x);\n\n/// @notice Thrown when trying to cast a SD1x18 number that doesn't fit in uint40.\nerror PRBMath_SD1x18_ToUint40_Underflow(SD1x18 x);\n"},"@prb/math/src/sd1x18/ValueType.sol":{"content":"// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport \"./Casting.sol\" as Casting;\n\n/// @notice The signed 1.18-decimal fixed-point number representation, which can have up to 1 digit and up to 18\n/// decimals. The values of this are bound by the minimum and the maximum values permitted by the underlying Solidity\n/// type int64. This is useful when end users want to use int64 to save gas, e.g. with tight variable packing in contract\n/// storage.\ntype SD1x18 is int64;\n\n/*//////////////////////////////////////////////////////////////////////////\n CASTING\n//////////////////////////////////////////////////////////////////////////*/\n\nusing {\n Casting.intoSD59x18,\n Casting.intoUD2x18,\n Casting.intoUD60x18,\n Casting.intoUint256,\n Casting.intoUint128,\n Casting.intoUint40,\n Casting.unwrap\n} for SD1x18 global;\n"},"@prb/math/src/sd59x18/Casting.sol":{"content":"// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport \"./Errors.sol\" as CastingErrors;\nimport { MAX_UINT128, MAX_UINT40 } from \"../Common.sol\";\nimport { uMAX_SD1x18, uMIN_SD1x18 } from \"../sd1x18/Constants.sol\";\nimport { SD1x18 } from \"../sd1x18/ValueType.sol\";\nimport { uMAX_UD2x18 } from \"../ud2x18/Constants.sol\";\nimport { UD2x18 } from \"../ud2x18/ValueType.sol\";\nimport { UD60x18 } from \"../ud60x18/ValueType.sol\";\nimport { SD59x18 } from \"./ValueType.sol\";\n\n/// @notice Casts an SD59x18 number into int256.\n/// @dev This is basically a functional alias for {unwrap}.\nfunction intoInt256(SD59x18 x) pure returns (int256 result) {\n result = SD59x18.unwrap(x);\n}\n\n/// @notice Casts an SD59x18 number into SD1x18.\n/// @dev Requirements:\n/// - x must be greater than or equal to `uMIN_SD1x18`.\n/// - x must be less than or equal to `uMAX_SD1x18`.\nfunction intoSD1x18(SD59x18 x) pure returns (SD1x18 result) {\n int256 xInt = SD59x18.unwrap(x);\n if (xInt < uMIN_SD1x18) {\n revert CastingErrors.PRBMath_SD59x18_IntoSD1x18_Underflow(x);\n }\n if (xInt > uMAX_SD1x18) {\n revert CastingErrors.PRBMath_SD59x18_IntoSD1x18_Overflow(x);\n }\n result = SD1x18.wrap(int64(xInt));\n}\n\n/// @notice Casts an SD59x18 number into UD2x18.\n/// @dev Requirements:\n/// - x must be positive.\n/// - x must be less than or equal to `uMAX_UD2x18`.\nfunction intoUD2x18(SD59x18 x) pure returns (UD2x18 result) {\n int256 xInt = SD59x18.unwrap(x);\n if (xInt < 0) {\n revert CastingErrors.PRBMath_SD59x18_IntoUD2x18_Underflow(x);\n }\n if (xInt > int256(uint256(uMAX_UD2x18))) {\n revert CastingErrors.PRBMath_SD59x18_IntoUD2x18_Overflow(x);\n }\n result = UD2x18.wrap(uint64(uint256(xInt)));\n}\n\n/// @notice Casts an SD59x18 number into UD60x18.\n/// @dev Requirements:\n/// - x must be positive.\nfunction intoUD60x18(SD59x18 x) pure returns (UD60x18 result) {\n int256 xInt = SD59x18.unwrap(x);\n if (xInt < 0) {\n revert CastingErrors.PRBMath_SD59x18_IntoUD60x18_Underflow(x);\n }\n result = UD60x18.wrap(uint256(xInt));\n}\n\n/// @notice Casts an SD59x18 number into uint256.\n/// @dev Requirements:\n/// - x must be positive.\nfunction intoUint256(SD59x18 x) pure returns (uint256 result) {\n int256 xInt = SD59x18.unwrap(x);\n if (xInt < 0) {\n revert CastingErrors.PRBMath_SD59x18_IntoUint256_Underflow(x);\n }\n result = uint256(xInt);\n}\n\n/// @notice Casts an SD59x18 number into uint128.\n/// @dev Requirements:\n/// - x must be positive.\n/// - x must be less than or equal to `uMAX_UINT128`.\nfunction intoUint128(SD59x18 x) pure returns (uint128 result) {\n int256 xInt = SD59x18.unwrap(x);\n if (xInt < 0) {\n revert CastingErrors.PRBMath_SD59x18_IntoUint128_Underflow(x);\n }\n if (xInt > int256(uint256(MAX_UINT128))) {\n revert CastingErrors.PRBMath_SD59x18_IntoUint128_Overflow(x);\n }\n result = uint128(uint256(xInt));\n}\n\n/// @notice Casts an SD59x18 number into uint40.\n/// @dev Requirements:\n/// - x must be positive.\n/// - x must be less than or equal to `MAX_UINT40`.\nfunction intoUint40(SD59x18 x) pure returns (uint40 result) {\n int256 xInt = SD59x18.unwrap(x);\n if (xInt < 0) {\n revert CastingErrors.PRBMath_SD59x18_IntoUint40_Underflow(x);\n }\n if (xInt > int256(uint256(MAX_UINT40))) {\n revert CastingErrors.PRBMath_SD59x18_IntoUint40_Overflow(x);\n }\n result = uint40(uint256(xInt));\n}\n\n/// @notice Alias for {wrap}.\nfunction sd(int256 x) pure returns (SD59x18 result) {\n result = SD59x18.wrap(x);\n}\n\n/// @notice Alias for {wrap}.\nfunction sd59x18(int256 x) pure returns (SD59x18 result) {\n result = SD59x18.wrap(x);\n}\n\n/// @notice Unwraps an SD59x18 number into int256.\nfunction unwrap(SD59x18 x) pure returns (int256 result) {\n result = SD59x18.unwrap(x);\n}\n\n/// @notice Wraps an int256 number into SD59x18.\nfunction wrap(int256 x) pure returns (SD59x18 result) {\n result = SD59x18.wrap(x);\n}\n"},"@prb/math/src/sd59x18/Constants.sol":{"content":"// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport { SD59x18 } from \"./ValueType.sol\";\n\n// NOTICE: the \"u\" prefix stands for \"unwrapped\".\n\n/// @dev Euler's number as an SD59x18 number.\nSD59x18 constant E = SD59x18.wrap(2_718281828459045235);\n\n/// @dev The maximum input permitted in {exp}.\nint256 constant uEXP_MAX_INPUT = 133_084258667509499440;\nSD59x18 constant EXP_MAX_INPUT = SD59x18.wrap(uEXP_MAX_INPUT);\n\n/// @dev Any value less than this returns 0 in {exp}.\nint256 constant uEXP_MIN_THRESHOLD = -41_446531673892822322;\nSD59x18 constant EXP_MIN_THRESHOLD = SD59x18.wrap(uEXP_MIN_THRESHOLD);\n\n/// @dev The maximum input permitted in {exp2}.\nint256 constant uEXP2_MAX_INPUT = 192e18 - 1;\nSD59x18 constant EXP2_MAX_INPUT = SD59x18.wrap(uEXP2_MAX_INPUT);\n\n/// @dev Any value less than this returns 0 in {exp2}.\nint256 constant uEXP2_MIN_THRESHOLD = -59_794705707972522261;\nSD59x18 constant EXP2_MIN_THRESHOLD = SD59x18.wrap(uEXP2_MIN_THRESHOLD);\n\n/// @dev Half the UNIT number.\nint256 constant uHALF_UNIT = 0.5e18;\nSD59x18 constant HALF_UNIT = SD59x18.wrap(uHALF_UNIT);\n\n/// @dev $log_2(10)$ as an SD59x18 number.\nint256 constant uLOG2_10 = 3_321928094887362347;\nSD59x18 constant LOG2_10 = SD59x18.wrap(uLOG2_10);\n\n/// @dev $log_2(e)$ as an SD59x18 number.\nint256 constant uLOG2_E = 1_442695040888963407;\nSD59x18 constant LOG2_E = SD59x18.wrap(uLOG2_E);\n\n/// @dev The maximum value an SD59x18 number can have.\nint256 constant uMAX_SD59x18 = 57896044618658097711785492504343953926634992332820282019728_792003956564819967;\nSD59x18 constant MAX_SD59x18 = SD59x18.wrap(uMAX_SD59x18);\n\n/// @dev The maximum whole value an SD59x18 number can have.\nint256 constant uMAX_WHOLE_SD59x18 = 57896044618658097711785492504343953926634992332820282019728_000000000000000000;\nSD59x18 constant MAX_WHOLE_SD59x18 = SD59x18.wrap(uMAX_WHOLE_SD59x18);\n\n/// @dev The minimum value an SD59x18 number can have.\nint256 constant uMIN_SD59x18 = -57896044618658097711785492504343953926634992332820282019728_792003956564819968;\nSD59x18 constant MIN_SD59x18 = SD59x18.wrap(uMIN_SD59x18);\n\n/// @dev The minimum whole value an SD59x18 number can have.\nint256 constant uMIN_WHOLE_SD59x18 = -57896044618658097711785492504343953926634992332820282019728_000000000000000000;\nSD59x18 constant MIN_WHOLE_SD59x18 = SD59x18.wrap(uMIN_WHOLE_SD59x18);\n\n/// @dev PI as an SD59x18 number.\nSD59x18 constant PI = SD59x18.wrap(3_141592653589793238);\n\n/// @dev The unit number, which gives the decimal precision of SD59x18.\nint256 constant uUNIT = 1e18;\nSD59x18 constant UNIT = SD59x18.wrap(1e18);\n\n/// @dev The unit number squared.\nint256 constant uUNIT_SQUARED = 1e36;\nSD59x18 constant UNIT_SQUARED = SD59x18.wrap(uUNIT_SQUARED);\n\n/// @dev Zero as an SD59x18 number.\nSD59x18 constant ZERO = SD59x18.wrap(0);\n"},"@prb/math/src/sd59x18/Errors.sol":{"content":"// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport { SD59x18 } from \"./ValueType.sol\";\n\n/// @notice Thrown when taking the absolute value of `MIN_SD59x18`.\nerror PRBMath_SD59x18_Abs_MinSD59x18();\n\n/// @notice Thrown when ceiling a number overflows SD59x18.\nerror PRBMath_SD59x18_Ceil_Overflow(SD59x18 x);\n\n/// @notice Thrown when converting a basic integer to the fixed-point format overflows SD59x18.\nerror PRBMath_SD59x18_Convert_Overflow(int256 x);\n\n/// @notice Thrown when converting a basic integer to the fixed-point format underflows SD59x18.\nerror PRBMath_SD59x18_Convert_Underflow(int256 x);\n\n/// @notice Thrown when dividing two numbers and one of them is `MIN_SD59x18`.\nerror PRBMath_SD59x18_Div_InputTooSmall();\n\n/// @notice Thrown when dividing two numbers and one of the intermediary unsigned results overflows SD59x18.\nerror PRBMath_SD59x18_Div_Overflow(SD59x18 x, SD59x18 y);\n\n/// @notice Thrown when taking the natural exponent of a base greater than 133_084258667509499441.\nerror PRBMath_SD59x18_Exp_InputTooBig(SD59x18 x);\n\n/// @notice Thrown when taking the binary exponent of a base greater than 192e18.\nerror PRBMath_SD59x18_Exp2_InputTooBig(SD59x18 x);\n\n/// @notice Thrown when flooring a number underflows SD59x18.\nerror PRBMath_SD59x18_Floor_Underflow(SD59x18 x);\n\n/// @notice Thrown when taking the geometric mean of two numbers and their product is negative.\nerror PRBMath_SD59x18_Gm_NegativeProduct(SD59x18 x, SD59x18 y);\n\n/// @notice Thrown when taking the geometric mean of two numbers and multiplying them overflows SD59x18.\nerror PRBMath_SD59x18_Gm_Overflow(SD59x18 x, SD59x18 y);\n\n/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in SD1x18.\nerror PRBMath_SD59x18_IntoSD1x18_Overflow(SD59x18 x);\n\n/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in SD1x18.\nerror PRBMath_SD59x18_IntoSD1x18_Underflow(SD59x18 x);\n\n/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in UD2x18.\nerror PRBMath_SD59x18_IntoUD2x18_Overflow(SD59x18 x);\n\n/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in UD2x18.\nerror PRBMath_SD59x18_IntoUD2x18_Underflow(SD59x18 x);\n\n/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in UD60x18.\nerror PRBMath_SD59x18_IntoUD60x18_Underflow(SD59x18 x);\n\n/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint128.\nerror PRBMath_SD59x18_IntoUint128_Overflow(SD59x18 x);\n\n/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint128.\nerror PRBMath_SD59x18_IntoUint128_Underflow(SD59x18 x);\n\n/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint256.\nerror PRBMath_SD59x18_IntoUint256_Underflow(SD59x18 x);\n\n/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint40.\nerror PRBMath_SD59x18_IntoUint40_Overflow(SD59x18 x);\n\n/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint40.\nerror PRBMath_SD59x18_IntoUint40_Underflow(SD59x18 x);\n\n/// @notice Thrown when taking the logarithm of a number less than or equal to zero.\nerror PRBMath_SD59x18_Log_InputTooSmall(SD59x18 x);\n\n/// @notice Thrown when multiplying two numbers and one of the inputs is `MIN_SD59x18`.\nerror PRBMath_SD59x18_Mul_InputTooSmall();\n\n/// @notice Thrown when multiplying two numbers and the intermediary absolute result overflows SD59x18.\nerror PRBMath_SD59x18_Mul_Overflow(SD59x18 x, SD59x18 y);\n\n/// @notice Thrown when raising a number to a power and the intermediary absolute result overflows SD59x18.\nerror PRBMath_SD59x18_Powu_Overflow(SD59x18 x, uint256 y);\n\n/// @notice Thrown when taking the square root of a negative number.\nerror PRBMath_SD59x18_Sqrt_NegativeInput(SD59x18 x);\n\n/// @notice Thrown when the calculating the square root overflows SD59x18.\nerror PRBMath_SD59x18_Sqrt_Overflow(SD59x18 x);\n"},"@prb/math/src/sd59x18/Helpers.sol":{"content":"// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport { wrap } from \"./Casting.sol\";\nimport { SD59x18 } from \"./ValueType.sol\";\n\n/// @notice Implements the checked addition operation (+) in the SD59x18 type.\nfunction add(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {\n return wrap(x.unwrap() + y.unwrap());\n}\n\n/// @notice Implements the AND (&) bitwise operation in the SD59x18 type.\nfunction and(SD59x18 x, int256 bits) pure returns (SD59x18 result) {\n return wrap(x.unwrap() & bits);\n}\n\n/// @notice Implements the AND (&) bitwise operation in the SD59x18 type.\nfunction and2(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {\n return wrap(x.unwrap() & y.unwrap());\n}\n\n/// @notice Implements the equal (=) operation in the SD59x18 type.\nfunction eq(SD59x18 x, SD59x18 y) pure returns (bool result) {\n result = x.unwrap() == y.unwrap();\n}\n\n/// @notice Implements the greater than operation (>) in the SD59x18 type.\nfunction gt(SD59x18 x, SD59x18 y) pure returns (bool result) {\n result = x.unwrap() > y.unwrap();\n}\n\n/// @notice Implements the greater than or equal to operation (>=) in the SD59x18 type.\nfunction gte(SD59x18 x, SD59x18 y) pure returns (bool result) {\n result = x.unwrap() >= y.unwrap();\n}\n\n/// @notice Implements a zero comparison check function in the SD59x18 type.\nfunction isZero(SD59x18 x) pure returns (bool result) {\n result = x.unwrap() == 0;\n}\n\n/// @notice Implements the left shift operation (<<) in the SD59x18 type.\nfunction lshift(SD59x18 x, uint256 bits) pure returns (SD59x18 result) {\n result = wrap(x.unwrap() << bits);\n}\n\n/// @notice Implements the lower than operation (<) in the SD59x18 type.\nfunction lt(SD59x18 x, SD59x18 y) pure returns (bool result) {\n result = x.unwrap() < y.unwrap();\n}\n\n/// @notice Implements the lower than or equal to operation (<=) in the SD59x18 type.\nfunction lte(SD59x18 x, SD59x18 y) pure returns (bool result) {\n result = x.unwrap() <= y.unwrap();\n}\n\n/// @notice Implements the unchecked modulo operation (%) in the SD59x18 type.\nfunction mod(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {\n result = wrap(x.unwrap() % y.unwrap());\n}\n\n/// @notice Implements the not equal operation (!=) in the SD59x18 type.\nfunction neq(SD59x18 x, SD59x18 y) pure returns (bool result) {\n result = x.unwrap() != y.unwrap();\n}\n\n/// @notice Implements the NOT (~) bitwise operation in the SD59x18 type.\nfunction not(SD59x18 x) pure returns (SD59x18 result) {\n result = wrap(~x.unwrap());\n}\n\n/// @notice Implements the OR (|) bitwise operation in the SD59x18 type.\nfunction or(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {\n result = wrap(x.unwrap() | y.unwrap());\n}\n\n/// @notice Implements the right shift operation (>>) in the SD59x18 type.\nfunction rshift(SD59x18 x, uint256 bits) pure returns (SD59x18 result) {\n result = wrap(x.unwrap() >> bits);\n}\n\n/// @notice Implements the checked subtraction operation (-) in the SD59x18 type.\nfunction sub(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {\n result = wrap(x.unwrap() - y.unwrap());\n}\n\n/// @notice Implements the checked unary minus operation (-) in the SD59x18 type.\nfunction unary(SD59x18 x) pure returns (SD59x18 result) {\n result = wrap(-x.unwrap());\n}\n\n/// @notice Implements the unchecked addition operation (+) in the SD59x18 type.\nfunction uncheckedAdd(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {\n unchecked {\n result = wrap(x.unwrap() + y.unwrap());\n }\n}\n\n/// @notice Implements the unchecked subtraction operation (-) in the SD59x18 type.\nfunction uncheckedSub(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {\n unchecked {\n result = wrap(x.unwrap() - y.unwrap());\n }\n}\n\n/// @notice Implements the unchecked unary minus operation (-) in the SD59x18 type.\nfunction uncheckedUnary(SD59x18 x) pure returns (SD59x18 result) {\n unchecked {\n result = wrap(-x.unwrap());\n }\n}\n\n/// @notice Implements the XOR (^) bitwise operation in the SD59x18 type.\nfunction xor(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {\n result = wrap(x.unwrap() ^ y.unwrap());\n}\n"},"@prb/math/src/sd59x18/Math.sol":{"content":"// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport \"../Common.sol\" as Common;\nimport \"./Errors.sol\" as Errors;\nimport {\n uEXP_MAX_INPUT,\n uEXP2_MAX_INPUT,\n uEXP_MIN_THRESHOLD,\n uEXP2_MIN_THRESHOLD,\n uHALF_UNIT,\n uLOG2_10,\n uLOG2_E,\n uMAX_SD59x18,\n uMAX_WHOLE_SD59x18,\n uMIN_SD59x18,\n uMIN_WHOLE_SD59x18,\n UNIT,\n uUNIT,\n uUNIT_SQUARED,\n ZERO\n} from \"./Constants.sol\";\nimport { wrap } from \"./Helpers.sol\";\nimport { SD59x18 } from \"./ValueType.sol\";\n\n/// @notice Calculates the absolute value of x.\n///\n/// @dev Requirements:\n/// - x must be greater than `MIN_SD59x18`.\n///\n/// @param x The SD59x18 number for which to calculate the absolute value.\n/// @param result The absolute value of x as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction abs(SD59x18 x) pure returns (SD59x18 result) {\n int256 xInt = x.unwrap();\n if (xInt == uMIN_SD59x18) {\n revert Errors.PRBMath_SD59x18_Abs_MinSD59x18();\n }\n result = xInt < 0 ? wrap(-xInt) : x;\n}\n\n/// @notice Calculates the arithmetic average of x and y.\n///\n/// @dev Notes:\n/// - The result is rounded toward zero.\n///\n/// @param x The first operand as an SD59x18 number.\n/// @param y The second operand as an SD59x18 number.\n/// @return result The arithmetic average as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction avg(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {\n int256 xInt = x.unwrap();\n int256 yInt = y.unwrap();\n\n unchecked {\n // This operation is equivalent to `x / 2 + y / 2`, and it can never overflow.\n int256 sum = (xInt >> 1) + (yInt >> 1);\n\n if (sum < 0) {\n // If at least one of x and y is odd, add 1 to the result, because shifting negative numbers to the right\n // rounds toward negative infinity. The right part is equivalent to `sum + (x % 2 == 1 || y % 2 == 1)`.\n assembly (\"memory-safe\") {\n result := add(sum, and(or(xInt, yInt), 1))\n }\n } else {\n // Add 1 if both x and y are odd to account for the double 0.5 remainder truncated after shifting.\n result = wrap(sum + (xInt & yInt & 1));\n }\n }\n}\n\n/// @notice Yields the smallest whole number greater than or equal to x.\n///\n/// @dev Optimized for fractional value inputs, because every whole value has (1e18 - 1) fractional counterparts.\n/// See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.\n///\n/// Requirements:\n/// - x must be less than or equal to `MAX_WHOLE_SD59x18`.\n///\n/// @param x The SD59x18 number to ceil.\n/// @param result The smallest whole number greater than or equal to x, as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction ceil(SD59x18 x) pure returns (SD59x18 result) {\n int256 xInt = x.unwrap();\n if (xInt > uMAX_WHOLE_SD59x18) {\n revert Errors.PRBMath_SD59x18_Ceil_Overflow(x);\n }\n\n int256 remainder = xInt % uUNIT;\n if (remainder == 0) {\n result = x;\n } else {\n unchecked {\n // Solidity uses C fmod style, which returns a modulus with the same sign as x.\n int256 resultInt = xInt - remainder;\n if (xInt > 0) {\n resultInt += uUNIT;\n }\n result = wrap(resultInt);\n }\n }\n}\n\n/// @notice Divides two SD59x18 numbers, returning a new SD59x18 number.\n///\n/// @dev This is an extension of {Common.mulDiv} for signed numbers, which works by computing the signs and the absolute\n/// values separately.\n///\n/// Notes:\n/// - Refer to the notes in {Common.mulDiv}.\n/// - The result is rounded toward zero.\n///\n/// Requirements:\n/// - Refer to the requirements in {Common.mulDiv}.\n/// - None of the inputs can be `MIN_SD59x18`.\n/// - The denominator must not be zero.\n/// - The result must fit in SD59x18.\n///\n/// @param x The numerator as an SD59x18 number.\n/// @param y The denominator as an SD59x18 number.\n/// @param result The quotient as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction div(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {\n int256 xInt = x.unwrap();\n int256 yInt = y.unwrap();\n if (xInt == uMIN_SD59x18 || yInt == uMIN_SD59x18) {\n revert Errors.PRBMath_SD59x18_Div_InputTooSmall();\n }\n\n // Get hold of the absolute values of x and y.\n uint256 xAbs;\n uint256 yAbs;\n unchecked {\n xAbs = xInt < 0 ? uint256(-xInt) : uint256(xInt);\n yAbs = yInt < 0 ? uint256(-yInt) : uint256(yInt);\n }\n\n // Compute the absolute value (x*UNIT÷y). The resulting value must fit in SD59x18.\n uint256 resultAbs = Common.mulDiv(xAbs, uint256(uUNIT), yAbs);\n if (resultAbs > uint256(uMAX_SD59x18)) {\n revert Errors.PRBMath_SD59x18_Div_Overflow(x, y);\n }\n\n // Check if x and y have the same sign using two's complement representation. The left-most bit represents the sign (1 for\n // negative, 0 for positive or zero).\n bool sameSign = (xInt ^ yInt) > -1;\n\n // If the inputs have the same sign, the result should be positive. Otherwise, it should be negative.\n unchecked {\n result = wrap(sameSign ? int256(resultAbs) : -int256(resultAbs));\n }\n}\n\n/// @notice Calculates the natural exponent of x using the following formula:\n///\n/// $$\n/// e^x = 2^{x * log_2{e}}\n/// $$\n///\n/// @dev Notes:\n/// - Refer to the notes in {exp2}.\n///\n/// Requirements:\n/// - Refer to the requirements in {exp2}.\n/// - x must be less than 133_084258667509499441.\n///\n/// @param x The exponent as an SD59x18 number.\n/// @return result The result as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction exp(SD59x18 x) pure returns (SD59x18 result) {\n int256 xInt = x.unwrap();\n\n // Any input less than the threshold returns zero.\n // This check also prevents an overflow for very small numbers.\n if (xInt < uEXP_MIN_THRESHOLD) {\n return ZERO;\n }\n\n // This check prevents values greater than 192e18 from being passed to {exp2}.\n if (xInt > uEXP_MAX_INPUT) {\n revert Errors.PRBMath_SD59x18_Exp_InputTooBig(x);\n }\n\n unchecked {\n // Inline the fixed-point multiplication to save gas.\n int256 doubleUnitProduct = xInt * uLOG2_E;\n result = exp2(wrap(doubleUnitProduct / uUNIT));\n }\n}\n\n/// @notice Calculates the binary exponent of x using the binary fraction method using the following formula:\n///\n/// $$\n/// 2^{-x} = \\frac{1}{2^x}\n/// $$\n///\n/// @dev See https://ethereum.stackexchange.com/q/79903/24693.\n///\n/// Notes:\n/// - If x is less than -59_794705707972522261, the result is zero.\n///\n/// Requirements:\n/// - x must be less than 192e18.\n/// - The result must fit in SD59x18.\n///\n/// @param x The exponent as an SD59x18 number.\n/// @return result The result as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction exp2(SD59x18 x) pure returns (SD59x18 result) {\n int256 xInt = x.unwrap();\n if (xInt < 0) {\n // The inverse of any number less than the threshold is truncated to zero.\n if (xInt < uEXP2_MIN_THRESHOLD) {\n return ZERO;\n }\n\n unchecked {\n // Inline the fixed-point inversion to save gas.\n result = wrap(uUNIT_SQUARED / exp2(wrap(-xInt)).unwrap());\n }\n } else {\n // Numbers greater than or equal to 192e18 don't fit in the 192.64-bit format.\n if (xInt > uEXP2_MAX_INPUT) {\n revert Errors.PRBMath_SD59x18_Exp2_InputTooBig(x);\n }\n\n unchecked {\n // Convert x to the 192.64-bit fixed-point format.\n uint256 x_192x64 = uint256((xInt << 64) / uUNIT);\n\n // It is safe to cast the result to int256 due to the checks above.\n result = wrap(int256(Common.exp2(x_192x64)));\n }\n }\n}\n\n/// @notice Yields the greatest whole number less than or equal to x.\n///\n/// @dev Optimized for fractional value inputs, because for every whole value there are (1e18 - 1) fractional\n/// counterparts. See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.\n///\n/// Requirements:\n/// - x must be greater than or equal to `MIN_WHOLE_SD59x18`.\n///\n/// @param x The SD59x18 number to floor.\n/// @param result The greatest whole number less than or equal to x, as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction floor(SD59x18 x) pure returns (SD59x18 result) {\n int256 xInt = x.unwrap();\n if (xInt < uMIN_WHOLE_SD59x18) {\n revert Errors.PRBMath_SD59x18_Floor_Underflow(x);\n }\n\n int256 remainder = xInt % uUNIT;\n if (remainder == 0) {\n result = x;\n } else {\n unchecked {\n // Solidity uses C fmod style, which returns a modulus with the same sign as x.\n int256 resultInt = xInt - remainder;\n if (xInt < 0) {\n resultInt -= uUNIT;\n }\n result = wrap(resultInt);\n }\n }\n}\n\n/// @notice Yields the excess beyond the floor of x for positive numbers and the part of the number to the right.\n/// of the radix point for negative numbers.\n/// @dev Based on the odd function definition. https://en.wikipedia.org/wiki/Fractional_part\n/// @param x The SD59x18 number to get the fractional part of.\n/// @param result The fractional part of x as an SD59x18 number.\nfunction frac(SD59x18 x) pure returns (SD59x18 result) {\n result = wrap(x.unwrap() % uUNIT);\n}\n\n/// @notice Calculates the geometric mean of x and y, i.e. $\\sqrt{x * y}$.\n///\n/// @dev Notes:\n/// - The result is rounded toward zero.\n///\n/// Requirements:\n/// - x * y must fit in SD59x18.\n/// - x * y must not be negative, since complex numbers are not supported.\n///\n/// @param x The first operand as an SD59x18 number.\n/// @param y The second operand as an SD59x18 number.\n/// @return result The result as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction gm(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {\n int256 xInt = x.unwrap();\n int256 yInt = y.unwrap();\n if (xInt == 0 || yInt == 0) {\n return ZERO;\n }\n\n unchecked {\n // Equivalent to `xy / x != y`. Checking for overflow this way is faster than letting Solidity do it.\n int256 xyInt = xInt * yInt;\n if (xyInt / xInt != yInt) {\n revert Errors.PRBMath_SD59x18_Gm_Overflow(x, y);\n }\n\n // The product must not be negative, since complex numbers are not supported.\n if (xyInt < 0) {\n revert Errors.PRBMath_SD59x18_Gm_NegativeProduct(x, y);\n }\n\n // We don't need to multiply the result by `UNIT` here because the x*y product picked up a factor of `UNIT`\n // during multiplication. See the comments in {Common.sqrt}.\n uint256 resultUint = Common.sqrt(uint256(xyInt));\n result = wrap(int256(resultUint));\n }\n}\n\n/// @notice Calculates the inverse of x.\n///\n/// @dev Notes:\n/// - The result is rounded toward zero.\n///\n/// Requirements:\n/// - x must not be zero.\n///\n/// @param x The SD59x18 number for which to calculate the inverse.\n/// @return result The inverse as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction inv(SD59x18 x) pure returns (SD59x18 result) {\n result = wrap(uUNIT_SQUARED / x.unwrap());\n}\n\n/// @notice Calculates the natural logarithm of x using the following formula:\n///\n/// $$\n/// ln{x} = log_2{x} / log_2{e}\n/// $$\n///\n/// @dev Notes:\n/// - Refer to the notes in {log2}.\n/// - The precision isn't sufficiently fine-grained to return exactly `UNIT` when the input is `E`.\n///\n/// Requirements:\n/// - Refer to the requirements in {log2}.\n///\n/// @param x The SD59x18 number for which to calculate the natural logarithm.\n/// @return result The natural logarithm as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction ln(SD59x18 x) pure returns (SD59x18 result) {\n // Inline the fixed-point multiplication to save gas. This is overflow-safe because the maximum value that\n // {log2} can return is ~195_205294292027477728.\n result = wrap(log2(x).unwrap() * uUNIT / uLOG2_E);\n}\n\n/// @notice Calculates the common logarithm of x using the following formula:\n///\n/// $$\n/// log_{10}{x} = log_2{x} / log_2{10}\n/// $$\n///\n/// However, if x is an exact power of ten, a hard coded value is returned.\n///\n/// @dev Notes:\n/// - Refer to the notes in {log2}.\n///\n/// Requirements:\n/// - Refer to the requirements in {log2}.\n///\n/// @param x The SD59x18 number for which to calculate the common logarithm.\n/// @return result The common logarithm as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction log10(SD59x18 x) pure returns (SD59x18 result) {\n int256 xInt = x.unwrap();\n if (xInt < 0) {\n revert Errors.PRBMath_SD59x18_Log_InputTooSmall(x);\n }\n\n // Note that the `mul` in this block is the standard multiplication operation, not {SD59x18.mul}.\n // prettier-ignore\n assembly (\"memory-safe\") {\n switch x\n case 1 { result := mul(uUNIT, sub(0, 18)) }\n case 10 { result := mul(uUNIT, sub(1, 18)) }\n case 100 { result := mul(uUNIT, sub(2, 18)) }\n case 1000 { result := mul(uUNIT, sub(3, 18)) }\n case 10000 { result := mul(uUNIT, sub(4, 18)) }\n case 100000 { result := mul(uUNIT, sub(5, 18)) }\n case 1000000 { result := mul(uUNIT, sub(6, 18)) }\n case 10000000 { result := mul(uUNIT, sub(7, 18)) }\n case 100000000 { result := mul(uUNIT, sub(8, 18)) }\n case 1000000000 { result := mul(uUNIT, sub(9, 18)) }\n case 10000000000 { result := mul(uUNIT, sub(10, 18)) }\n case 100000000000 { result := mul(uUNIT, sub(11, 18)) }\n case 1000000000000 { result := mul(uUNIT, sub(12, 18)) }\n case 10000000000000 { result := mul(uUNIT, sub(13, 18)) }\n case 100000000000000 { result := mul(uUNIT, sub(14, 18)) }\n case 1000000000000000 { result := mul(uUNIT, sub(15, 18)) }\n case 10000000000000000 { result := mul(uUNIT, sub(16, 18)) }\n case 100000000000000000 { result := mul(uUNIT, sub(17, 18)) }\n case 1000000000000000000 { result := 0 }\n case 10000000000000000000 { result := uUNIT }\n case 100000000000000000000 { result := mul(uUNIT, 2) }\n case 1000000000000000000000 { result := mul(uUNIT, 3) }\n case 10000000000000000000000 { result := mul(uUNIT, 4) }\n case 100000000000000000000000 { result := mul(uUNIT, 5) }\n case 1000000000000000000000000 { result := mul(uUNIT, 6) }\n case 10000000000000000000000000 { result := mul(uUNIT, 7) }\n case 100000000000000000000000000 { result := mul(uUNIT, 8) }\n case 1000000000000000000000000000 { result := mul(uUNIT, 9) }\n case 10000000000000000000000000000 { result := mul(uUNIT, 10) }\n case 100000000000000000000000000000 { result := mul(uUNIT, 11) }\n case 1000000000000000000000000000000 { result := mul(uUNIT, 12) }\n case 10000000000000000000000000000000 { result := mul(uUNIT, 13) }\n case 100000000000000000000000000000000 { result := mul(uUNIT, 14) }\n case 1000000000000000000000000000000000 { result := mul(uUNIT, 15) }\n case 10000000000000000000000000000000000 { result := mul(uUNIT, 16) }\n case 100000000000000000000000000000000000 { result := mul(uUNIT, 17) }\n case 1000000000000000000000000000000000000 { result := mul(uUNIT, 18) }\n case 10000000000000000000000000000000000000 { result := mul(uUNIT, 19) }\n case 100000000000000000000000000000000000000 { result := mul(uUNIT, 20) }\n case 1000000000000000000000000000000000000000 { result := mul(uUNIT, 21) }\n case 10000000000000000000000000000000000000000 { result := mul(uUNIT, 22) }\n case 100000000000000000000000000000000000000000 { result := mul(uUNIT, 23) }\n case 1000000000000000000000000000000000000000000 { result := mul(uUNIT, 24) }\n case 10000000000000000000000000000000000000000000 { result := mul(uUNIT, 25) }\n case 100000000000000000000000000000000000000000000 { result := mul(uUNIT, 26) }\n case 1000000000000000000000000000000000000000000000 { result := mul(uUNIT, 27) }\n case 10000000000000000000000000000000000000000000000 { result := mul(uUNIT, 28) }\n case 100000000000000000000000000000000000000000000000 { result := mul(uUNIT, 29) }\n case 1000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 30) }\n case 10000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 31) }\n case 100000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 32) }\n case 1000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 33) }\n case 10000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 34) }\n case 100000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 35) }\n case 1000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 36) }\n case 10000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 37) }\n case 100000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 38) }\n case 1000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 39) }\n case 10000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 40) }\n case 100000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 41) }\n case 1000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 42) }\n case 10000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 43) }\n case 100000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 44) }\n case 1000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 45) }\n case 10000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 46) }\n case 100000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 47) }\n case 1000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 48) }\n case 10000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 49) }\n case 100000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 50) }\n case 1000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 51) }\n case 10000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 52) }\n case 100000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 53) }\n case 1000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 54) }\n case 10000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 55) }\n case 100000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 56) }\n case 1000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 57) }\n case 10000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 58) }\n default { result := uMAX_SD59x18 }\n }\n\n if (result.unwrap() == uMAX_SD59x18) {\n unchecked {\n // Inline the fixed-point division to save gas.\n result = wrap(log2(x).unwrap() * uUNIT / uLOG2_10);\n }\n }\n}\n\n/// @notice Calculates the binary logarithm of x using the iterative approximation algorithm:\n///\n/// $$\n/// log_2{x} = n + log_2{y}, \\text{ where } y = x*2^{-n}, \\ y \\in [1, 2)\n/// $$\n///\n/// For $0 \\leq x \\lt 1$, the input is inverted:\n///\n/// $$\n/// log_2{x} = -log_2{\\frac{1}{x}}\n/// $$\n///\n/// @dev See https://en.wikipedia.org/wiki/Binary_logarithm#Iterative_approximation.\n///\n/// Notes:\n/// - Due to the lossy precision of the iterative approximation, the results are not perfectly accurate to the last decimal.\n///\n/// Requirements:\n/// - x must be greater than zero.\n///\n/// @param x The SD59x18 number for which to calculate the binary logarithm.\n/// @return result The binary logarithm as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction log2(SD59x18 x) pure returns (SD59x18 result) {\n int256 xInt = x.unwrap();\n if (xInt <= 0) {\n revert Errors.PRBMath_SD59x18_Log_InputTooSmall(x);\n }\n\n unchecked {\n int256 sign;\n if (xInt >= uUNIT) {\n sign = 1;\n } else {\n sign = -1;\n // Inline the fixed-point inversion to save gas.\n xInt = uUNIT_SQUARED / xInt;\n }\n\n // Calculate the integer part of the logarithm.\n uint256 n = Common.msb(uint256(xInt / uUNIT));\n\n // This is the integer part of the logarithm as an SD59x18 number. The operation can't overflow\n // because n is at most 255, `UNIT` is 1e18, and the sign is either 1 or -1.\n int256 resultInt = int256(n) * uUNIT;\n\n // Calculate $y = x * 2^{-n}$.\n int256 y = xInt >> n;\n\n // If y is the unit number, the fractional part is zero.\n if (y == uUNIT) {\n return wrap(resultInt * sign);\n }\n\n // Calculate the fractional part via the iterative approximation.\n // The `delta >>= 1` part is equivalent to `delta /= 2`, but shifting bits is more gas efficient.\n int256 DOUBLE_UNIT = 2e18;\n for (int256 delta = uHALF_UNIT; delta > 0; delta >>= 1) {\n y = (y * y) / uUNIT;\n\n // Is y^2 >= 2e18 and so in the range [2e18, 4e18)?\n if (y >= DOUBLE_UNIT) {\n // Add the 2^{-m} factor to the logarithm.\n resultInt = resultInt + delta;\n\n // Halve y, which corresponds to z/2 in the Wikipedia article.\n y >>= 1;\n }\n }\n resultInt *= sign;\n result = wrap(resultInt);\n }\n}\n\n/// @notice Multiplies two SD59x18 numbers together, returning a new SD59x18 number.\n///\n/// @dev Notes:\n/// - Refer to the notes in {Common.mulDiv18}.\n///\n/// Requirements:\n/// - Refer to the requirements in {Common.mulDiv18}.\n/// - None of the inputs can be `MIN_SD59x18`.\n/// - The result must fit in SD59x18.\n///\n/// @param x The multiplicand as an SD59x18 number.\n/// @param y The multiplier as an SD59x18 number.\n/// @return result The product as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction mul(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {\n int256 xInt = x.unwrap();\n int256 yInt = y.unwrap();\n if (xInt == uMIN_SD59x18 || yInt == uMIN_SD59x18) {\n revert Errors.PRBMath_SD59x18_Mul_InputTooSmall();\n }\n\n // Get hold of the absolute values of x and y.\n uint256 xAbs;\n uint256 yAbs;\n unchecked {\n xAbs = xInt < 0 ? uint256(-xInt) : uint256(xInt);\n yAbs = yInt < 0 ? uint256(-yInt) : uint256(yInt);\n }\n\n // Compute the absolute value (x*y÷UNIT). The resulting value must fit in SD59x18.\n uint256 resultAbs = Common.mulDiv18(xAbs, yAbs);\n if (resultAbs > uint256(uMAX_SD59x18)) {\n revert Errors.PRBMath_SD59x18_Mul_Overflow(x, y);\n }\n\n // Check if x and y have the same sign using two's complement representation. The left-most bit represents the sign (1 for\n // negative, 0 for positive or zero).\n bool sameSign = (xInt ^ yInt) > -1;\n\n // If the inputs have the same sign, the result should be positive. Otherwise, it should be negative.\n unchecked {\n result = wrap(sameSign ? int256(resultAbs) : -int256(resultAbs));\n }\n}\n\n/// @notice Raises x to the power of y using the following formula:\n///\n/// $$\n/// x^y = 2^{log_2{x} * y}\n/// $$\n///\n/// @dev Notes:\n/// - Refer to the notes in {exp2}, {log2}, and {mul}.\n/// - Returns `UNIT` for 0^0.\n///\n/// Requirements:\n/// - Refer to the requirements in {exp2}, {log2}, and {mul}.\n///\n/// @param x The base as an SD59x18 number.\n/// @param y Exponent to raise x to, as an SD59x18 number\n/// @return result x raised to power y, as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction pow(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {\n int256 xInt = x.unwrap();\n int256 yInt = y.unwrap();\n\n // If both x and y are zero, the result is `UNIT`. If just x is zero, the result is always zero.\n if (xInt == 0) {\n return yInt == 0 ? UNIT : ZERO;\n }\n // If x is `UNIT`, the result is always `UNIT`.\n else if (xInt == uUNIT) {\n return UNIT;\n }\n\n // If y is zero, the result is always `UNIT`.\n if (yInt == 0) {\n return UNIT;\n }\n // If y is `UNIT`, the result is always x.\n else if (yInt == uUNIT) {\n return x;\n }\n\n // Calculate the result using the formula.\n result = exp2(mul(log2(x), y));\n}\n\n/// @notice Raises x (an SD59x18 number) to the power y (an unsigned basic integer) using the well-known\n/// algorithm \"exponentiation by squaring\".\n///\n/// @dev See https://en.wikipedia.org/wiki/Exponentiation_by_squaring.\n///\n/// Notes:\n/// - Refer to the notes in {Common.mulDiv18}.\n/// - Returns `UNIT` for 0^0.\n///\n/// Requirements:\n/// - Refer to the requirements in {abs} and {Common.mulDiv18}.\n/// - The result must fit in SD59x18.\n///\n/// @param x The base as an SD59x18 number.\n/// @param y The exponent as a uint256.\n/// @return result The result as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction powu(SD59x18 x, uint256 y) pure returns (SD59x18 result) {\n uint256 xAbs = uint256(abs(x).unwrap());\n\n // Calculate the first iteration of the loop in advance.\n uint256 resultAbs = y & 1 > 0 ? xAbs : uint256(uUNIT);\n\n // Equivalent to `for(y /= 2; y > 0; y /= 2)`.\n uint256 yAux = y;\n for (yAux >>= 1; yAux > 0; yAux >>= 1) {\n xAbs = Common.mulDiv18(xAbs, xAbs);\n\n // Equivalent to `y % 2 == 1`.\n if (yAux & 1 > 0) {\n resultAbs = Common.mulDiv18(resultAbs, xAbs);\n }\n }\n\n // The result must fit in SD59x18.\n if (resultAbs > uint256(uMAX_SD59x18)) {\n revert Errors.PRBMath_SD59x18_Powu_Overflow(x, y);\n }\n\n unchecked {\n // Is the base negative and the exponent odd? If yes, the result should be negative.\n int256 resultInt = int256(resultAbs);\n bool isNegative = x.unwrap() < 0 && y & 1 == 1;\n if (isNegative) {\n resultInt = -resultInt;\n }\n result = wrap(resultInt);\n }\n}\n\n/// @notice Calculates the square root of x using the Babylonian method.\n///\n/// @dev See https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.\n///\n/// Notes:\n/// - Only the positive root is returned.\n/// - The result is rounded toward zero.\n///\n/// Requirements:\n/// - x cannot be negative, since complex numbers are not supported.\n/// - x must be less than `MAX_SD59x18 / UNIT`.\n///\n/// @param x The SD59x18 number for which to calculate the square root.\n/// @return result The result as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction sqrt(SD59x18 x) pure returns (SD59x18 result) {\n int256 xInt = x.unwrap();\n if (xInt < 0) {\n revert Errors.PRBMath_SD59x18_Sqrt_NegativeInput(x);\n }\n if (xInt > uMAX_SD59x18 / uUNIT) {\n revert Errors.PRBMath_SD59x18_Sqrt_Overflow(x);\n }\n\n unchecked {\n // Multiply x by `UNIT` to account for the factor of `UNIT` picked up when multiplying two SD59x18 numbers.\n // In this case, the two numbers are both the square root.\n uint256 resultUint = Common.sqrt(uint256(xInt * uUNIT));\n result = wrap(int256(resultUint));\n }\n}\n"},"@prb/math/src/sd59x18/ValueType.sol":{"content":"// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport \"./Casting.sol\" as Casting;\nimport \"./Helpers.sol\" as Helpers;\nimport \"./Math.sol\" as Math;\n\n/// @notice The signed 59.18-decimal fixed-point number representation, which can have up to 59 digits and up to 18\n/// decimals. The values of this are bound by the minimum and the maximum values permitted by the underlying Solidity\n/// type int256.\ntype SD59x18 is int256;\n\n/*//////////////////////////////////////////////////////////////////////////\n CASTING\n//////////////////////////////////////////////////////////////////////////*/\n\nusing {\n Casting.intoInt256,\n Casting.intoSD1x18,\n Casting.intoUD2x18,\n Casting.intoUD60x18,\n Casting.intoUint256,\n Casting.intoUint128,\n Casting.intoUint40,\n Casting.unwrap\n} for SD59x18 global;\n\n/*//////////////////////////////////////////////////////////////////////////\n MATHEMATICAL FUNCTIONS\n//////////////////////////////////////////////////////////////////////////*/\n\nusing {\n Math.abs,\n Math.avg,\n Math.ceil,\n Math.div,\n Math.exp,\n Math.exp2,\n Math.floor,\n Math.frac,\n Math.gm,\n Math.inv,\n Math.log10,\n Math.log2,\n Math.ln,\n Math.mul,\n Math.pow,\n Math.powu,\n Math.sqrt\n} for SD59x18 global;\n\n/*//////////////////////////////////////////////////////////////////////////\n HELPER FUNCTIONS\n//////////////////////////////////////////////////////////////////////////*/\n\nusing {\n Helpers.add,\n Helpers.and,\n Helpers.eq,\n Helpers.gt,\n Helpers.gte,\n Helpers.isZero,\n Helpers.lshift,\n Helpers.lt,\n Helpers.lte,\n Helpers.mod,\n Helpers.neq,\n Helpers.not,\n Helpers.or,\n Helpers.rshift,\n Helpers.sub,\n Helpers.uncheckedAdd,\n Helpers.uncheckedSub,\n Helpers.uncheckedUnary,\n Helpers.xor\n} for SD59x18 global;\n\n/*//////////////////////////////////////////////////////////////////////////\n OPERATORS\n//////////////////////////////////////////////////////////////////////////*/\n\n// The global \"using for\" directive makes it possible to use these operators on the SD59x18 type.\nusing {\n Helpers.add as +,\n Helpers.and2 as &,\n Math.div as /,\n Helpers.eq as ==,\n Helpers.gt as >,\n Helpers.gte as >=,\n Helpers.lt as <,\n Helpers.lte as <=,\n Helpers.mod as %,\n Math.mul as *,\n Helpers.neq as !=,\n Helpers.not as ~,\n Helpers.or as |,\n Helpers.sub as -,\n Helpers.unary as -,\n Helpers.xor as ^\n} for SD59x18 global;\n"},"@prb/math/src/UD2x18.sol":{"content":"// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\n/*\n\n██████╗ ██████╗ ██████╗ ███╗ ███╗ █████╗ ████████╗██╗ ██╗\n██╔══██╗██╔══██╗██╔══██╗████╗ ████║██╔══██╗╚══██╔══╝██║ ██║\n██████╔╝██████╔╝██████╔╝██╔████╔██║███████║ ██║ ███████║\n██╔═══╝ ██╔══██╗██╔══██╗██║╚██╔╝██║██╔══██║ ██║ ██╔══██║\n██║ ██║ ██║██████╔╝██║ ╚═╝ ██║██║ ██║ ██║ ██║ ██║\n╚═╝ ╚═╝ ╚═╝╚═════╝ ╚═╝ ╚═╝╚═╝ ╚═╝ ╚═╝ ╚═╝ ╚═╝\n\n██╗ ██╗██████╗ ██████╗ ██╗ ██╗ ██╗ █████╗\n██║ ██║██╔══██╗╚════██╗╚██╗██╔╝███║██╔══██╗\n██║ ██║██║ ██║ █████╔╝ ╚███╔╝ ╚██║╚█████╔╝\n██║ ██║██║ ██║██╔═══╝ ██╔██╗ ██║██╔══██╗\n╚██████╔╝██████╔╝███████╗██╔╝ ██╗ ██║╚█████╔╝\n ╚═════╝ ╚═════╝ ╚══════╝╚═╝ ╚═╝ ╚═╝ ╚════╝\n\n*/\n\nimport \"./ud2x18/Casting.sol\";\nimport \"./ud2x18/Constants.sol\";\nimport \"./ud2x18/Errors.sol\";\nimport \"./ud2x18/ValueType.sol\";\n"},"@prb/math/src/ud2x18/Casting.sol":{"content":"// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport \"../Common.sol\" as Common;\nimport \"./Errors.sol\" as Errors;\nimport { uMAX_SD1x18 } from \"../sd1x18/Constants.sol\";\nimport { SD1x18 } from \"../sd1x18/ValueType.sol\";\nimport { SD59x18 } from \"../sd59x18/ValueType.sol\";\nimport { UD60x18 } from \"../ud60x18/ValueType.sol\";\nimport { UD2x18 } from \"./ValueType.sol\";\n\n/// @notice Casts a UD2x18 number into SD1x18.\n/// - x must be less than or equal to `uMAX_SD1x18`.\nfunction intoSD1x18(UD2x18 x) pure returns (SD1x18 result) {\n uint64 xUint = UD2x18.unwrap(x);\n if (xUint > uint64(uMAX_SD1x18)) {\n revert Errors.PRBMath_UD2x18_IntoSD1x18_Overflow(x);\n }\n result = SD1x18.wrap(int64(xUint));\n}\n\n/// @notice Casts a UD2x18 number into SD59x18.\n/// @dev There is no overflow check because the domain of UD2x18 is a subset of SD59x18.\nfunction intoSD59x18(UD2x18 x) pure returns (SD59x18 result) {\n result = SD59x18.wrap(int256(uint256(UD2x18.unwrap(x))));\n}\n\n/// @notice Casts a UD2x18 number into UD60x18.\n/// @dev There is no overflow check because the domain of UD2x18 is a subset of UD60x18.\nfunction intoUD60x18(UD2x18 x) pure returns (UD60x18 result) {\n result = UD60x18.wrap(UD2x18.unwrap(x));\n}\n\n/// @notice Casts a UD2x18 number into uint128.\n/// @dev There is no overflow check because the domain of UD2x18 is a subset of uint128.\nfunction intoUint128(UD2x18 x) pure returns (uint128 result) {\n result = uint128(UD2x18.unwrap(x));\n}\n\n/// @notice Casts a UD2x18 number into uint256.\n/// @dev There is no overflow check because the domain of UD2x18 is a subset of uint256.\nfunction intoUint256(UD2x18 x) pure returns (uint256 result) {\n result = uint256(UD2x18.unwrap(x));\n}\n\n/// @notice Casts a UD2x18 number into uint40.\n/// @dev Requirements:\n/// - x must be less than or equal to `MAX_UINT40`.\nfunction intoUint40(UD2x18 x) pure returns (uint40 result) {\n uint64 xUint = UD2x18.unwrap(x);\n if (xUint > uint64(Common.MAX_UINT40)) {\n revert Errors.PRBMath_UD2x18_IntoUint40_Overflow(x);\n }\n result = uint40(xUint);\n}\n\n/// @notice Alias for {wrap}.\nfunction ud2x18(uint64 x) pure returns (UD2x18 result) {\n result = UD2x18.wrap(x);\n}\n\n/// @notice Unwrap a UD2x18 number into uint64.\nfunction unwrap(UD2x18 x) pure returns (uint64 result) {\n result = UD2x18.unwrap(x);\n}\n\n/// @notice Wraps a uint64 number into UD2x18.\nfunction wrap(uint64 x) pure returns (UD2x18 result) {\n result = UD2x18.wrap(x);\n}\n"},"@prb/math/src/ud2x18/Constants.sol":{"content":"// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport { UD2x18 } from \"./ValueType.sol\";\n\n/// @dev Euler's number as a UD2x18 number.\nUD2x18 constant E = UD2x18.wrap(2_718281828459045235);\n\n/// @dev The maximum value a UD2x18 number can have.\nuint64 constant uMAX_UD2x18 = 18_446744073709551615;\nUD2x18 constant MAX_UD2x18 = UD2x18.wrap(uMAX_UD2x18);\n\n/// @dev PI as a UD2x18 number.\nUD2x18 constant PI = UD2x18.wrap(3_141592653589793238);\n\n/// @dev The unit number, which gives the decimal precision of UD2x18.\nUD2x18 constant UNIT = UD2x18.wrap(1e18);\nuint64 constant uUNIT = 1e18;\n"},"@prb/math/src/ud2x18/Errors.sol":{"content":"// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport { UD2x18 } from \"./ValueType.sol\";\n\n/// @notice Thrown when trying to cast a UD2x18 number that doesn't fit in SD1x18.\nerror PRBMath_UD2x18_IntoSD1x18_Overflow(UD2x18 x);\n\n/// @notice Thrown when trying to cast a UD2x18 number that doesn't fit in uint40.\nerror PRBMath_UD2x18_IntoUint40_Overflow(UD2x18 x);\n"},"@prb/math/src/ud2x18/ValueType.sol":{"content":"// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport \"./Casting.sol\" as Casting;\n\n/// @notice The unsigned 2.18-decimal fixed-point number representation, which can have up to 2 digits and up to 18\n/// decimals. The values of this are bound by the minimum and the maximum values permitted by the underlying Solidity\n/// type uint64. This is useful when end users want to use uint64 to save gas, e.g. with tight variable packing in contract\n/// storage.\ntype UD2x18 is uint64;\n\n/*//////////////////////////////////////////////////////////////////////////\n CASTING\n//////////////////////////////////////////////////////////////////////////*/\n\nusing {\n Casting.intoSD1x18,\n Casting.intoSD59x18,\n Casting.intoUD60x18,\n Casting.intoUint256,\n Casting.intoUint128,\n Casting.intoUint40,\n Casting.unwrap\n} for UD2x18 global;\n"},"@prb/math/src/UD60x18.sol":{"content":"// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\n/*\n\n██████╗ ██████╗ ██████╗ ███╗ ███╗ █████╗ ████████╗██╗ ██╗\n██╔══██╗██╔══██╗██╔══██╗████╗ ████║██╔══██╗╚══██╔══╝██║ ██║\n██████╔╝██████╔╝██████╔╝██╔████╔██║███████║ ██║ ███████║\n██╔═══╝ ██╔══██╗██╔══██╗██║╚██╔╝██║██╔══██║ ██║ ██╔══██║\n██║ ██║ ██║██████╔╝██║ ╚═╝ ██║██║ ██║ ██║ ██║ ██║\n╚═╝ ╚═╝ ╚═╝╚═════╝ ╚═╝ ╚═╝╚═╝ ╚═╝ ╚═╝ ╚═╝ ╚═╝\n\n██╗ ██╗██████╗ ██████╗ ██████╗ ██╗ ██╗ ██╗ █████╗\n██║ ██║██╔══██╗██╔════╝ ██╔═████╗╚██╗██╔╝███║██╔══██╗\n██║ ██║██║ ██║███████╗ ██║██╔██║ ╚███╔╝ ╚██║╚█████╔╝\n██║ ██║██║ ██║██╔═══██╗████╔╝██║ ██╔██╗ ██║██╔══██╗\n╚██████╔╝██████╔╝╚██████╔╝╚██████╔╝██╔╝ ██╗ ██║╚█████╔╝\n ╚═════╝ ╚═════╝ ╚═════╝ ╚═════╝ ╚═╝ ╚═╝ ╚═╝ ╚════╝\n\n*/\n\nimport \"./ud60x18/Casting.sol\";\nimport \"./ud60x18/Constants.sol\";\nimport \"./ud60x18/Conversions.sol\";\nimport \"./ud60x18/Errors.sol\";\nimport \"./ud60x18/Helpers.sol\";\nimport \"./ud60x18/Math.sol\";\nimport \"./ud60x18/ValueType.sol\";\n"},"@prb/math/src/ud60x18/Casting.sol":{"content":"// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport \"./Errors.sol\" as CastingErrors;\nimport { MAX_UINT128, MAX_UINT40 } from \"../Common.sol\";\nimport { uMAX_SD1x18 } from \"../sd1x18/Constants.sol\";\nimport { SD1x18 } from \"../sd1x18/ValueType.sol\";\nimport { uMAX_SD59x18 } from \"../sd59x18/Constants.sol\";\nimport { SD59x18 } from \"../sd59x18/ValueType.sol\";\nimport { uMAX_UD2x18 } from \"../ud2x18/Constants.sol\";\nimport { UD2x18 } from \"../ud2x18/ValueType.sol\";\nimport { UD60x18 } from \"./ValueType.sol\";\n\n/// @notice Casts a UD60x18 number into SD1x18.\n/// @dev Requirements:\n/// - x must be less than or equal to `uMAX_SD1x18`.\nfunction intoSD1x18(UD60x18 x) pure returns (SD1x18 result) {\n uint256 xUint = UD60x18.unwrap(x);\n if (xUint > uint256(int256(uMAX_SD1x18))) {\n revert CastingErrors.PRBMath_UD60x18_IntoSD1x18_Overflow(x);\n }\n result = SD1x18.wrap(int64(uint64(xUint)));\n}\n\n/// @notice Casts a UD60x18 number into UD2x18.\n/// @dev Requirements:\n/// - x must be less than or equal to `uMAX_UD2x18`.\nfunction intoUD2x18(UD60x18 x) pure returns (UD2x18 result) {\n uint256 xUint = UD60x18.unwrap(x);\n if (xUint > uMAX_UD2x18) {\n revert CastingErrors.PRBMath_UD60x18_IntoUD2x18_Overflow(x);\n }\n result = UD2x18.wrap(uint64(xUint));\n}\n\n/// @notice Casts a UD60x18 number into SD59x18.\n/// @dev Requirements:\n/// - x must be less than or equal to `uMAX_SD59x18`.\nfunction intoSD59x18(UD60x18 x) pure returns (SD59x18 result) {\n uint256 xUint = UD60x18.unwrap(x);\n if (xUint > uint256(uMAX_SD59x18)) {\n revert CastingErrors.PRBMath_UD60x18_IntoSD59x18_Overflow(x);\n }\n result = SD59x18.wrap(int256(xUint));\n}\n\n/// @notice Casts a UD60x18 number into uint128.\n/// @dev This is basically an alias for {unwrap}.\nfunction intoUint256(UD60x18 x) pure returns (uint256 result) {\n result = UD60x18.unwrap(x);\n}\n\n/// @notice Casts a UD60x18 number into uint128.\n/// @dev Requirements:\n/// - x must be less than or equal to `MAX_UINT128`.\nfunction intoUint128(UD60x18 x) pure returns (uint128 result) {\n uint256 xUint = UD60x18.unwrap(x);\n if (xUint > MAX_UINT128) {\n revert CastingErrors.PRBMath_UD60x18_IntoUint128_Overflow(x);\n }\n result = uint128(xUint);\n}\n\n/// @notice Casts a UD60x18 number into uint40.\n/// @dev Requirements:\n/// - x must be less than or equal to `MAX_UINT40`.\nfunction intoUint40(UD60x18 x) pure returns (uint40 result) {\n uint256 xUint = UD60x18.unwrap(x);\n if (xUint > MAX_UINT40) {\n revert CastingErrors.PRBMath_UD60x18_IntoUint40_Overflow(x);\n }\n result = uint40(xUint);\n}\n\n/// @notice Alias for {wrap}.\nfunction ud(uint256 x) pure returns (UD60x18 result) {\n result = UD60x18.wrap(x);\n}\n\n/// @notice Alias for {wrap}.\nfunction ud60x18(uint256 x) pure returns (UD60x18 result) {\n result = UD60x18.wrap(x);\n}\n\n/// @notice Unwraps a UD60x18 number into uint256.\nfunction unwrap(UD60x18 x) pure returns (uint256 result) {\n result = UD60x18.unwrap(x);\n}\n\n/// @notice Wraps a uint256 number into the UD60x18 value type.\nfunction wrap(uint256 x) pure returns (UD60x18 result) {\n result = UD60x18.wrap(x);\n}\n"},"@prb/math/src/ud60x18/Constants.sol":{"content":"// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport { UD60x18 } from \"./ValueType.sol\";\n\n// NOTICE: the \"u\" prefix stands for \"unwrapped\".\n\n/// @dev Euler's number as a UD60x18 number.\nUD60x18 constant E = UD60x18.wrap(2_718281828459045235);\n\n/// @dev The maximum input permitted in {exp}.\nuint256 constant uEXP_MAX_INPUT = 133_084258667509499440;\nUD60x18 constant EXP_MAX_INPUT = UD60x18.wrap(uEXP_MAX_INPUT);\n\n/// @dev The maximum input permitted in {exp2}.\nuint256 constant uEXP2_MAX_INPUT = 192e18 - 1;\nUD60x18 constant EXP2_MAX_INPUT = UD60x18.wrap(uEXP2_MAX_INPUT);\n\n/// @dev Half the UNIT number.\nuint256 constant uHALF_UNIT = 0.5e18;\nUD60x18 constant HALF_UNIT = UD60x18.wrap(uHALF_UNIT);\n\n/// @dev $log_2(10)$ as a UD60x18 number.\nuint256 constant uLOG2_10 = 3_321928094887362347;\nUD60x18 constant LOG2_10 = UD60x18.wrap(uLOG2_10);\n\n/// @dev $log_2(e)$ as a UD60x18 number.\nuint256 constant uLOG2_E = 1_442695040888963407;\nUD60x18 constant LOG2_E = UD60x18.wrap(uLOG2_E);\n\n/// @dev The maximum value a UD60x18 number can have.\nuint256 constant uMAX_UD60x18 = 115792089237316195423570985008687907853269984665640564039457_584007913129639935;\nUD60x18 constant MAX_UD60x18 = UD60x18.wrap(uMAX_UD60x18);\n\n/// @dev The maximum whole value a UD60x18 number can have.\nuint256 constant uMAX_WHOLE_UD60x18 = 115792089237316195423570985008687907853269984665640564039457_000000000000000000;\nUD60x18 constant MAX_WHOLE_UD60x18 = UD60x18.wrap(uMAX_WHOLE_UD60x18);\n\n/// @dev PI as a UD60x18 number.\nUD60x18 constant PI = UD60x18.wrap(3_141592653589793238);\n\n/// @dev The unit number, which gives the decimal precision of UD60x18.\nuint256 constant uUNIT = 1e18;\nUD60x18 constant UNIT = UD60x18.wrap(uUNIT);\n\n/// @dev The unit number squared.\nuint256 constant uUNIT_SQUARED = 1e36;\nUD60x18 constant UNIT_SQUARED = UD60x18.wrap(uUNIT_SQUARED);\n\n/// @dev Zero as a UD60x18 number.\nUD60x18 constant ZERO = UD60x18.wrap(0);\n"},"@prb/math/src/ud60x18/Conversions.sol":{"content":"// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport { uMAX_UD60x18, uUNIT } from \"./Constants.sol\";\nimport { PRBMath_UD60x18_Convert_Overflow } from \"./Errors.sol\";\nimport { UD60x18 } from \"./ValueType.sol\";\n\n/// @notice Converts a UD60x18 number to a simple integer by dividing it by `UNIT`.\n/// @dev The result is rounded toward zero.\n/// @param x The UD60x18 number to convert.\n/// @return result The same number in basic integer form.\nfunction convert(UD60x18 x) pure returns (uint256 result) {\n result = UD60x18.unwrap(x) / uUNIT;\n}\n\n/// @notice Converts a simple integer to UD60x18 by multiplying it by `UNIT`.\n///\n/// @dev Requirements:\n/// - x must be less than or equal to `MAX_UD60x18 / UNIT`.\n///\n/// @param x The basic integer to convert.\n/// @param result The same number converted to UD60x18.\nfunction convert(uint256 x) pure returns (UD60x18 result) {\n if (x > uMAX_UD60x18 / uUNIT) {\n revert PRBMath_UD60x18_Convert_Overflow(x);\n }\n unchecked {\n result = UD60x18.wrap(x * uUNIT);\n }\n}\n"},"@prb/math/src/ud60x18/Errors.sol":{"content":"// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport { UD60x18 } from \"./ValueType.sol\";\n\n/// @notice Thrown when ceiling a number overflows UD60x18.\nerror PRBMath_UD60x18_Ceil_Overflow(UD60x18 x);\n\n/// @notice Thrown when converting a basic integer to the fixed-point format overflows UD60x18.\nerror PRBMath_UD60x18_Convert_Overflow(uint256 x);\n\n/// @notice Thrown when taking the natural exponent of a base greater than 133_084258667509499441.\nerror PRBMath_UD60x18_Exp_InputTooBig(UD60x18 x);\n\n/// @notice Thrown when taking the binary exponent of a base greater than 192e18.\nerror PRBMath_UD60x18_Exp2_InputTooBig(UD60x18 x);\n\n/// @notice Thrown when taking the geometric mean of two numbers and multiplying them overflows UD60x18.\nerror PRBMath_UD60x18_Gm_Overflow(UD60x18 x, UD60x18 y);\n\n/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in SD1x18.\nerror PRBMath_UD60x18_IntoSD1x18_Overflow(UD60x18 x);\n\n/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in SD59x18.\nerror PRBMath_UD60x18_IntoSD59x18_Overflow(UD60x18 x);\n\n/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in UD2x18.\nerror PRBMath_UD60x18_IntoUD2x18_Overflow(UD60x18 x);\n\n/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint128.\nerror PRBMath_UD60x18_IntoUint128_Overflow(UD60x18 x);\n\n/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint40.\nerror PRBMath_UD60x18_IntoUint40_Overflow(UD60x18 x);\n\n/// @notice Thrown when taking the logarithm of a number less than 1.\nerror PRBMath_UD60x18_Log_InputTooSmall(UD60x18 x);\n\n/// @notice Thrown when calculating the square root overflows UD60x18.\nerror PRBMath_UD60x18_Sqrt_Overflow(UD60x18 x);\n"},"@prb/math/src/ud60x18/Helpers.sol":{"content":"// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport { wrap } from \"./Casting.sol\";\nimport { UD60x18 } from \"./ValueType.sol\";\n\n/// @notice Implements the checked addition operation (+) in the UD60x18 type.\nfunction add(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {\n result = wrap(x.unwrap() + y.unwrap());\n}\n\n/// @notice Implements the AND (&) bitwise operation in the UD60x18 type.\nfunction and(UD60x18 x, uint256 bits) pure returns (UD60x18 result) {\n result = wrap(x.unwrap() & bits);\n}\n\n/// @notice Implements the AND (&) bitwise operation in the UD60x18 type.\nfunction and2(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {\n result = wrap(x.unwrap() & y.unwrap());\n}\n\n/// @notice Implements the equal operation (==) in the UD60x18 type.\nfunction eq(UD60x18 x, UD60x18 y) pure returns (bool result) {\n result = x.unwrap() == y.unwrap();\n}\n\n/// @notice Implements the greater than operation (>) in the UD60x18 type.\nfunction gt(UD60x18 x, UD60x18 y) pure returns (bool result) {\n result = x.unwrap() > y.unwrap();\n}\n\n/// @notice Implements the greater than or equal to operation (>=) in the UD60x18 type.\nfunction gte(UD60x18 x, UD60x18 y) pure returns (bool result) {\n result = x.unwrap() >= y.unwrap();\n}\n\n/// @notice Implements a zero comparison check function in the UD60x18 type.\nfunction isZero(UD60x18 x) pure returns (bool result) {\n // This wouldn't work if x could be negative.\n result = x.unwrap() == 0;\n}\n\n/// @notice Implements the left shift operation (<<) in the UD60x18 type.\nfunction lshift(UD60x18 x, uint256 bits) pure returns (UD60x18 result) {\n result = wrap(x.unwrap() << bits);\n}\n\n/// @notice Implements the lower than operation (<) in the UD60x18 type.\nfunction lt(UD60x18 x, UD60x18 y) pure returns (bool result) {\n result = x.unwrap() < y.unwrap();\n}\n\n/// @notice Implements the lower than or equal to operation (<=) in the UD60x18 type.\nfunction lte(UD60x18 x, UD60x18 y) pure returns (bool result) {\n result = x.unwrap() <= y.unwrap();\n}\n\n/// @notice Implements the checked modulo operation (%) in the UD60x18 type.\nfunction mod(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {\n result = wrap(x.unwrap() % y.unwrap());\n}\n\n/// @notice Implements the not equal operation (!=) in the UD60x18 type.\nfunction neq(UD60x18 x, UD60x18 y) pure returns (bool result) {\n result = x.unwrap() != y.unwrap();\n}\n\n/// @notice Implements the NOT (~) bitwise operation in the UD60x18 type.\nfunction not(UD60x18 x) pure returns (UD60x18 result) {\n result = wrap(~x.unwrap());\n}\n\n/// @notice Implements the OR (|) bitwise operation in the UD60x18 type.\nfunction or(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {\n result = wrap(x.unwrap() | y.unwrap());\n}\n\n/// @notice Implements the right shift operation (>>) in the UD60x18 type.\nfunction rshift(UD60x18 x, uint256 bits) pure returns (UD60x18 result) {\n result = wrap(x.unwrap() >> bits);\n}\n\n/// @notice Implements the checked subtraction operation (-) in the UD60x18 type.\nfunction sub(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {\n result = wrap(x.unwrap() - y.unwrap());\n}\n\n/// @notice Implements the unchecked addition operation (+) in the UD60x18 type.\nfunction uncheckedAdd(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {\n unchecked {\n result = wrap(x.unwrap() + y.unwrap());\n }\n}\n\n/// @notice Implements the unchecked subtraction operation (-) in the UD60x18 type.\nfunction uncheckedSub(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {\n unchecked {\n result = wrap(x.unwrap() - y.unwrap());\n }\n}\n\n/// @notice Implements the XOR (^) bitwise operation in the UD60x18 type.\nfunction xor(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {\n result = wrap(x.unwrap() ^ y.unwrap());\n}\n"},"@prb/math/src/ud60x18/Math.sol":{"content":"// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport \"../Common.sol\" as Common;\nimport \"./Errors.sol\" as Errors;\nimport { wrap } from \"./Casting.sol\";\nimport {\n uEXP_MAX_INPUT,\n uEXP2_MAX_INPUT,\n uHALF_UNIT,\n uLOG2_10,\n uLOG2_E,\n uMAX_UD60x18,\n uMAX_WHOLE_UD60x18,\n UNIT,\n uUNIT,\n uUNIT_SQUARED,\n ZERO\n} from \"./Constants.sol\";\nimport { UD60x18 } from \"./ValueType.sol\";\n\n/*//////////////////////////////////////////////////////////////////////////\n MATHEMATICAL FUNCTIONS\n//////////////////////////////////////////////////////////////////////////*/\n\n/// @notice Calculates the arithmetic average of x and y using the following formula:\n///\n/// $$\n/// avg(x, y) = (x & y) + ((xUint ^ yUint) / 2)\n/// $$\n///\n/// In English, this is what this formula does:\n///\n/// 1. AND x and y.\n/// 2. Calculate half of XOR x and y.\n/// 3. Add the two results together.\n///\n/// This technique is known as SWAR, which stands for \"SIMD within a register\". You can read more about it here:\n/// https://devblogs.microsoft.com/oldnewthing/20220207-00/?p=106223\n///\n/// @dev Notes:\n/// - The result is rounded toward zero.\n///\n/// @param x The first operand as a UD60x18 number.\n/// @param y The second operand as a UD60x18 number.\n/// @return result The arithmetic average as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction avg(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {\n uint256 xUint = x.unwrap();\n uint256 yUint = y.unwrap();\n unchecked {\n result = wrap((xUint & yUint) + ((xUint ^ yUint) >> 1));\n }\n}\n\n/// @notice Yields the smallest whole number greater than or equal to x.\n///\n/// @dev This is optimized for fractional value inputs, because for every whole value there are (1e18 - 1) fractional\n/// counterparts. See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.\n///\n/// Requirements:\n/// - x must be less than or equal to `MAX_WHOLE_UD60x18`.\n///\n/// @param x The UD60x18 number to ceil.\n/// @param result The smallest whole number greater than or equal to x, as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction ceil(UD60x18 x) pure returns (UD60x18 result) {\n uint256 xUint = x.unwrap();\n if (xUint > uMAX_WHOLE_UD60x18) {\n revert Errors.PRBMath_UD60x18_Ceil_Overflow(x);\n }\n\n assembly (\"memory-safe\") {\n // Equivalent to `x % UNIT`.\n let remainder := mod(x, uUNIT)\n\n // Equivalent to `UNIT - remainder`.\n let delta := sub(uUNIT, remainder)\n\n // Equivalent to `x + remainder > 0 ? delta : 0`.\n result := add(x, mul(delta, gt(remainder, 0)))\n }\n}\n\n/// @notice Divides two UD60x18 numbers, returning a new UD60x18 number.\n///\n/// @dev Uses {Common.mulDiv} to enable overflow-safe multiplication and division.\n///\n/// Notes:\n/// - Refer to the notes in {Common.mulDiv}.\n///\n/// Requirements:\n/// - Refer to the requirements in {Common.mulDiv}.\n///\n/// @param x The numerator as a UD60x18 number.\n/// @param y The denominator as a UD60x18 number.\n/// @param result The quotient as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction div(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {\n result = wrap(Common.mulDiv(x.unwrap(), uUNIT, y.unwrap()));\n}\n\n/// @notice Calculates the natural exponent of x using the following formula:\n///\n/// $$\n/// e^x = 2^{x * log_2{e}}\n/// $$\n///\n/// @dev Requirements:\n/// - x must be less than 133_084258667509499441.\n///\n/// @param x The exponent as a UD60x18 number.\n/// @return result The result as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction exp(UD60x18 x) pure returns (UD60x18 result) {\n uint256 xUint = x.unwrap();\n\n // This check prevents values greater than 192e18 from being passed to {exp2}.\n if (xUint > uEXP_MAX_INPUT) {\n revert Errors.PRBMath_UD60x18_Exp_InputTooBig(x);\n }\n\n unchecked {\n // Inline the fixed-point multiplication to save gas.\n uint256 doubleUnitProduct = xUint * uLOG2_E;\n result = exp2(wrap(doubleUnitProduct / uUNIT));\n }\n}\n\n/// @notice Calculates the binary exponent of x using the binary fraction method.\n///\n/// @dev See https://ethereum.stackexchange.com/q/79903/24693\n///\n/// Requirements:\n/// - x must be less than 192e18.\n/// - The result must fit in UD60x18.\n///\n/// @param x The exponent as a UD60x18 number.\n/// @return result The result as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction exp2(UD60x18 x) pure returns (UD60x18 result) {\n uint256 xUint = x.unwrap();\n\n // Numbers greater than or equal to 192e18 don't fit in the 192.64-bit format.\n if (xUint > uEXP2_MAX_INPUT) {\n revert Errors.PRBMath_UD60x18_Exp2_InputTooBig(x);\n }\n\n // Convert x to the 192.64-bit fixed-point format.\n uint256 x_192x64 = (xUint << 64) / uUNIT;\n\n // Pass x to the {Common.exp2} function, which uses the 192.64-bit fixed-point number representation.\n result = wrap(Common.exp2(x_192x64));\n}\n\n/// @notice Yields the greatest whole number less than or equal to x.\n/// @dev Optimized for fractional value inputs, because every whole value has (1e18 - 1) fractional counterparts.\n/// See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.\n/// @param x The UD60x18 number to floor.\n/// @param result The greatest whole number less than or equal to x, as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction floor(UD60x18 x) pure returns (UD60x18 result) {\n assembly (\"memory-safe\") {\n // Equivalent to `x % UNIT`.\n let remainder := mod(x, uUNIT)\n\n // Equivalent to `x - remainder > 0 ? remainder : 0)`.\n result := sub(x, mul(remainder, gt(remainder, 0)))\n }\n}\n\n/// @notice Yields the excess beyond the floor of x using the odd function definition.\n/// @dev See https://en.wikipedia.org/wiki/Fractional_part.\n/// @param x The UD60x18 number to get the fractional part of.\n/// @param result The fractional part of x as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction frac(UD60x18 x) pure returns (UD60x18 result) {\n assembly (\"memory-safe\") {\n result := mod(x, uUNIT)\n }\n}\n\n/// @notice Calculates the geometric mean of x and y, i.e. $\\sqrt{x * y}$, rounding down.\n///\n/// @dev Requirements:\n/// - x * y must fit in UD60x18.\n///\n/// @param x The first operand as a UD60x18 number.\n/// @param y The second operand as a UD60x18 number.\n/// @return result The result as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction gm(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {\n uint256 xUint = x.unwrap();\n uint256 yUint = y.unwrap();\n if (xUint == 0 || yUint == 0) {\n return ZERO;\n }\n\n unchecked {\n // Checking for overflow this way is faster than letting Solidity do it.\n uint256 xyUint = xUint * yUint;\n if (xyUint / xUint != yUint) {\n revert Errors.PRBMath_UD60x18_Gm_Overflow(x, y);\n }\n\n // We don't need to multiply the result by `UNIT` here because the x*y product picked up a factor of `UNIT`\n // during multiplication. See the comments in {Common.sqrt}.\n result = wrap(Common.sqrt(xyUint));\n }\n}\n\n/// @notice Calculates the inverse of x.\n///\n/// @dev Notes:\n/// - The result is rounded toward zero.\n///\n/// Requirements:\n/// - x must not be zero.\n///\n/// @param x The UD60x18 number for which to calculate the inverse.\n/// @return result The inverse as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction inv(UD60x18 x) pure returns (UD60x18 result) {\n unchecked {\n result = wrap(uUNIT_SQUARED / x.unwrap());\n }\n}\n\n/// @notice Calculates the natural logarithm of x using the following formula:\n///\n/// $$\n/// ln{x} = log_2{x} / log_2{e}\n/// $$\n///\n/// @dev Notes:\n/// - Refer to the notes in {log2}.\n/// - The precision isn't sufficiently fine-grained to return exactly `UNIT` when the input is `E`.\n///\n/// Requirements:\n/// - Refer to the requirements in {log2}.\n///\n/// @param x The UD60x18 number for which to calculate the natural logarithm.\n/// @return result The natural logarithm as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction ln(UD60x18 x) pure returns (UD60x18 result) {\n unchecked {\n // Inline the fixed-point multiplication to save gas. This is overflow-safe because the maximum value that\n // {log2} can return is ~196_205294292027477728.\n result = wrap(log2(x).unwrap() * uUNIT / uLOG2_E);\n }\n}\n\n/// @notice Calculates the common logarithm of x using the following formula:\n///\n/// $$\n/// log_{10}{x} = log_2{x} / log_2{10}\n/// $$\n///\n/// However, if x is an exact power of ten, a hard coded value is returned.\n///\n/// @dev Notes:\n/// - Refer to the notes in {log2}.\n///\n/// Requirements:\n/// - Refer to the requirements in {log2}.\n///\n/// @param x The UD60x18 number for which to calculate the common logarithm.\n/// @return result The common logarithm as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction log10(UD60x18 x) pure returns (UD60x18 result) {\n uint256 xUint = x.unwrap();\n if (xUint < uUNIT) {\n revert Errors.PRBMath_UD60x18_Log_InputTooSmall(x);\n }\n\n // Note that the `mul` in this assembly block is the standard multiplication operation, not {UD60x18.mul}.\n // prettier-ignore\n assembly (\"memory-safe\") {\n switch x\n case 1 { result := mul(uUNIT, sub(0, 18)) }\n case 10 { result := mul(uUNIT, sub(1, 18)) }\n case 100 { result := mul(uUNIT, sub(2, 18)) }\n case 1000 { result := mul(uUNIT, sub(3, 18)) }\n case 10000 { result := mul(uUNIT, sub(4, 18)) }\n case 100000 { result := mul(uUNIT, sub(5, 18)) }\n case 1000000 { result := mul(uUNIT, sub(6, 18)) }\n case 10000000 { result := mul(uUNIT, sub(7, 18)) }\n case 100000000 { result := mul(uUNIT, sub(8, 18)) }\n case 1000000000 { result := mul(uUNIT, sub(9, 18)) }\n case 10000000000 { result := mul(uUNIT, sub(10, 18)) }\n case 100000000000 { result := mul(uUNIT, sub(11, 18)) }\n case 1000000000000 { result := mul(uUNIT, sub(12, 18)) }\n case 10000000000000 { result := mul(uUNIT, sub(13, 18)) }\n case 100000000000000 { result := mul(uUNIT, sub(14, 18)) }\n case 1000000000000000 { result := mul(uUNIT, sub(15, 18)) }\n case 10000000000000000 { result := mul(uUNIT, sub(16, 18)) }\n case 100000000000000000 { result := mul(uUNIT, sub(17, 18)) }\n case 1000000000000000000 { result := 0 }\n case 10000000000000000000 { result := uUNIT }\n case 100000000000000000000 { result := mul(uUNIT, 2) }\n case 1000000000000000000000 { result := mul(uUNIT, 3) }\n case 10000000000000000000000 { result := mul(uUNIT, 4) }\n case 100000000000000000000000 { result := mul(uUNIT, 5) }\n case 1000000000000000000000000 { result := mul(uUNIT, 6) }\n case 10000000000000000000000000 { result := mul(uUNIT, 7) }\n case 100000000000000000000000000 { result := mul(uUNIT, 8) }\n case 1000000000000000000000000000 { result := mul(uUNIT, 9) }\n case 10000000000000000000000000000 { result := mul(uUNIT, 10) }\n case 100000000000000000000000000000 { result := mul(uUNIT, 11) }\n case 1000000000000000000000000000000 { result := mul(uUNIT, 12) }\n case 10000000000000000000000000000000 { result := mul(uUNIT, 13) }\n case 100000000000000000000000000000000 { result := mul(uUNIT, 14) }\n case 1000000000000000000000000000000000 { result := mul(uUNIT, 15) }\n case 10000000000000000000000000000000000 { result := mul(uUNIT, 16) }\n case 100000000000000000000000000000000000 { result := mul(uUNIT, 17) }\n case 1000000000000000000000000000000000000 { result := mul(uUNIT, 18) }\n case 10000000000000000000000000000000000000 { result := mul(uUNIT, 19) }\n case 100000000000000000000000000000000000000 { result := mul(uUNIT, 20) }\n case 1000000000000000000000000000000000000000 { result := mul(uUNIT, 21) }\n case 10000000000000000000000000000000000000000 { result := mul(uUNIT, 22) }\n case 100000000000000000000000000000000000000000 { result := mul(uUNIT, 23) }\n case 1000000000000000000000000000000000000000000 { result := mul(uUNIT, 24) }\n case 10000000000000000000000000000000000000000000 { result := mul(uUNIT, 25) }\n case 100000000000000000000000000000000000000000000 { result := mul(uUNIT, 26) }\n case 1000000000000000000000000000000000000000000000 { result := mul(uUNIT, 27) }\n case 10000000000000000000000000000000000000000000000 { result := mul(uUNIT, 28) }\n case 100000000000000000000000000000000000000000000000 { result := mul(uUNIT, 29) }\n case 1000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 30) }\n case 10000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 31) }\n case 100000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 32) }\n case 1000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 33) }\n case 10000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 34) }\n case 100000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 35) }\n case 1000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 36) }\n case 10000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 37) }\n case 100000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 38) }\n case 1000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 39) }\n case 10000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 40) }\n case 100000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 41) }\n case 1000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 42) }\n case 10000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 43) }\n case 100000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 44) }\n case 1000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 45) }\n case 10000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 46) }\n case 100000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 47) }\n case 1000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 48) }\n case 10000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 49) }\n case 100000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 50) }\n case 1000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 51) }\n case 10000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 52) }\n case 100000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 53) }\n case 1000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 54) }\n case 10000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 55) }\n case 100000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 56) }\n case 1000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 57) }\n case 10000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 58) }\n case 100000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 59) }\n default { result := uMAX_UD60x18 }\n }\n\n if (result.unwrap() == uMAX_UD60x18) {\n unchecked {\n // Inline the fixed-point division to save gas.\n result = wrap(log2(x).unwrap() * uUNIT / uLOG2_10);\n }\n }\n}\n\n/// @notice Calculates the binary logarithm of x using the iterative approximation algorithm:\n///\n/// $$\n/// log_2{x} = n + log_2{y}, \\text{ where } y = x*2^{-n}, \\ y \\in [1, 2)\n/// $$\n///\n/// For $0 \\leq x \\lt 1$, the input is inverted:\n///\n/// $$\n/// log_2{x} = -log_2{\\frac{1}{x}}\n/// $$\n///\n/// @dev See https://en.wikipedia.org/wiki/Binary_logarithm#Iterative_approximation\n///\n/// Notes:\n/// - Due to the lossy precision of the iterative approximation, the results are not perfectly accurate to the last decimal.\n///\n/// Requirements:\n/// - x must be greater than zero.\n///\n/// @param x The UD60x18 number for which to calculate the binary logarithm.\n/// @return result The binary logarithm as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction log2(UD60x18 x) pure returns (UD60x18 result) {\n uint256 xUint = x.unwrap();\n\n if (xUint < uUNIT) {\n revert Errors.PRBMath_UD60x18_Log_InputTooSmall(x);\n }\n\n unchecked {\n // Calculate the integer part of the logarithm.\n uint256 n = Common.msb(xUint / uUNIT);\n\n // This is the integer part of the logarithm as a UD60x18 number. The operation can't overflow because n\n // n is at most 255 and UNIT is 1e18.\n uint256 resultUint = n * uUNIT;\n\n // Calculate $y = x * 2^{-n}$.\n uint256 y = xUint >> n;\n\n // If y is the unit number, the fractional part is zero.\n if (y == uUNIT) {\n return wrap(resultUint);\n }\n\n // Calculate the fractional part via the iterative approximation.\n // The `delta >>= 1` part is equivalent to `delta /= 2`, but shifting bits is more gas efficient.\n uint256 DOUBLE_UNIT = 2e18;\n for (uint256 delta = uHALF_UNIT; delta > 0; delta >>= 1) {\n y = (y * y) / uUNIT;\n\n // Is y^2 >= 2e18 and so in the range [2e18, 4e18)?\n if (y >= DOUBLE_UNIT) {\n // Add the 2^{-m} factor to the logarithm.\n resultUint += delta;\n\n // Halve y, which corresponds to z/2 in the Wikipedia article.\n y >>= 1;\n }\n }\n result = wrap(resultUint);\n }\n}\n\n/// @notice Multiplies two UD60x18 numbers together, returning a new UD60x18 number.\n///\n/// @dev Uses {Common.mulDiv} to enable overflow-safe multiplication and division.\n///\n/// Notes:\n/// - Refer to the notes in {Common.mulDiv}.\n///\n/// Requirements:\n/// - Refer to the requirements in {Common.mulDiv}.\n///\n/// @dev See the documentation in {Common.mulDiv18}.\n/// @param x The multiplicand as a UD60x18 number.\n/// @param y The multiplier as a UD60x18 number.\n/// @return result The product as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction mul(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {\n result = wrap(Common.mulDiv18(x.unwrap(), y.unwrap()));\n}\n\n/// @notice Raises x to the power of y.\n///\n/// For $1 \\leq x \\leq \\infty$, the following standard formula is used:\n///\n/// $$\n/// x^y = 2^{log_2{x} * y}\n/// $$\n///\n/// For $0 \\leq x \\lt 1$, since the unsigned {log2} is undefined, an equivalent formula is used:\n///\n/// $$\n/// i = \\frac{1}{x}\n/// w = 2^{log_2{i} * y}\n/// x^y = \\frac{1}{w}\n/// $$\n///\n/// @dev Notes:\n/// - Refer to the notes in {log2} and {mul}.\n/// - Returns `UNIT` for 0^0.\n/// - It may not perform well with very small values of x. Consider using SD59x18 as an alternative.\n///\n/// Requirements:\n/// - Refer to the requirements in {exp2}, {log2}, and {mul}.\n///\n/// @param x The base as a UD60x18 number.\n/// @param y The exponent as a UD60x18 number.\n/// @return result The result as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction pow(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {\n uint256 xUint = x.unwrap();\n uint256 yUint = y.unwrap();\n\n // If both x and y are zero, the result is `UNIT`. If just x is zero, the result is always zero.\n if (xUint == 0) {\n return yUint == 0 ? UNIT : ZERO;\n }\n // If x is `UNIT`, the result is always `UNIT`.\n else if (xUint == uUNIT) {\n return UNIT;\n }\n\n // If y is zero, the result is always `UNIT`.\n if (yUint == 0) {\n return UNIT;\n }\n // If y is `UNIT`, the result is always x.\n else if (yUint == uUNIT) {\n return x;\n }\n\n // If x is greater than `UNIT`, use the standard formula.\n if (xUint > uUNIT) {\n result = exp2(mul(log2(x), y));\n }\n // Conversely, if x is less than `UNIT`, use the equivalent formula.\n else {\n UD60x18 i = wrap(uUNIT_SQUARED / xUint);\n UD60x18 w = exp2(mul(log2(i), y));\n result = wrap(uUNIT_SQUARED / w.unwrap());\n }\n}\n\n/// @notice Raises x (a UD60x18 number) to the power y (an unsigned basic integer) using the well-known\n/// algorithm \"exponentiation by squaring\".\n///\n/// @dev See https://en.wikipedia.org/wiki/Exponentiation_by_squaring.\n///\n/// Notes:\n/// - Refer to the notes in {Common.mulDiv18}.\n/// - Returns `UNIT` for 0^0.\n///\n/// Requirements:\n/// - The result must fit in UD60x18.\n///\n/// @param x The base as a UD60x18 number.\n/// @param y The exponent as a uint256.\n/// @return result The result as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction powu(UD60x18 x, uint256 y) pure returns (UD60x18 result) {\n // Calculate the first iteration of the loop in advance.\n uint256 xUint = x.unwrap();\n uint256 resultUint = y & 1 > 0 ? xUint : uUNIT;\n\n // Equivalent to `for(y /= 2; y > 0; y /= 2)`.\n for (y >>= 1; y > 0; y >>= 1) {\n xUint = Common.mulDiv18(xUint, xUint);\n\n // Equivalent to `y % 2 == 1`.\n if (y & 1 > 0) {\n resultUint = Common.mulDiv18(resultUint, xUint);\n }\n }\n result = wrap(resultUint);\n}\n\n/// @notice Calculates the square root of x using the Babylonian method.\n///\n/// @dev See https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.\n///\n/// Notes:\n/// - The result is rounded toward zero.\n///\n/// Requirements:\n/// - x must be less than `MAX_UD60x18 / UNIT`.\n///\n/// @param x The UD60x18 number for which to calculate the square root.\n/// @return result The result as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction sqrt(UD60x18 x) pure returns (UD60x18 result) {\n uint256 xUint = x.unwrap();\n\n unchecked {\n if (xUint > uMAX_UD60x18 / uUNIT) {\n revert Errors.PRBMath_UD60x18_Sqrt_Overflow(x);\n }\n // Multiply x by `UNIT` to account for the factor of `UNIT` picked up when multiplying two UD60x18 numbers.\n // In this case, the two numbers are both the square root.\n result = wrap(Common.sqrt(xUint * uUNIT));\n }\n}\n"},"@prb/math/src/ud60x18/ValueType.sol":{"content":"// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport \"./Casting.sol\" as Casting;\nimport \"./Helpers.sol\" as Helpers;\nimport \"./Math.sol\" as Math;\n\n/// @notice The unsigned 60.18-decimal fixed-point number representation, which can have up to 60 digits and up to 18\n/// decimals. The values of this are bound by the minimum and the maximum values permitted by the Solidity type uint256.\n/// @dev The value type is defined here so it can be imported in all other files.\ntype UD60x18 is uint256;\n\n/*//////////////////////////////////////////////////////////////////////////\n CASTING\n//////////////////////////////////////////////////////////////////////////*/\n\nusing {\n Casting.intoSD1x18,\n Casting.intoUD2x18,\n Casting.intoSD59x18,\n Casting.intoUint128,\n Casting.intoUint256,\n Casting.intoUint40,\n Casting.unwrap\n} for UD60x18 global;\n\n/*//////////////////////////////////////////////////////////////////////////\n MATHEMATICAL FUNCTIONS\n//////////////////////////////////////////////////////////////////////////*/\n\n// The global \"using for\" directive makes the functions in this library callable on the UD60x18 type.\nusing {\n Math.avg,\n Math.ceil,\n Math.div,\n Math.exp,\n Math.exp2,\n Math.floor,\n Math.frac,\n Math.gm,\n Math.inv,\n Math.ln,\n Math.log10,\n Math.log2,\n Math.mul,\n Math.pow,\n Math.powu,\n Math.sqrt\n} for UD60x18 global;\n\n/*//////////////////////////////////////////////////////////////////////////\n HELPER FUNCTIONS\n//////////////////////////////////////////////////////////////////////////*/\n\n// The global \"using for\" directive makes the functions in this library callable on the UD60x18 type.\nusing {\n Helpers.add,\n Helpers.and,\n Helpers.eq,\n Helpers.gt,\n Helpers.gte,\n Helpers.isZero,\n Helpers.lshift,\n Helpers.lt,\n Helpers.lte,\n Helpers.mod,\n Helpers.neq,\n Helpers.not,\n Helpers.or,\n Helpers.rshift,\n Helpers.sub,\n Helpers.uncheckedAdd,\n Helpers.uncheckedSub,\n Helpers.xor\n} for UD60x18 global;\n\n/*//////////////////////////////////////////////////////////////////////////\n OPERATORS\n//////////////////////////////////////////////////////////////////////////*/\n\n// The global \"using for\" directive makes it possible to use these operators on the UD60x18 type.\nusing {\n Helpers.add as +,\n Helpers.and2 as &,\n Math.div as /,\n Helpers.eq as ==,\n Helpers.gt as >,\n Helpers.gte as >=,\n Helpers.lt as <,\n Helpers.lte as <=,\n Helpers.or as |,\n Helpers.mod as %,\n Math.mul as *,\n Helpers.neq as !=,\n Helpers.not as ~,\n Helpers.sub as -,\n Helpers.xor as ^\n} for UD60x18 global;\n"},"contracts/interfaces/IAdminable.sol":{"content":"// SPDX-License-Identifier: GPL-3.0-or-later\npragma solidity >=0.8.20;\n\n/// @title IAdminable\n/// @notice Contract module that provides a basic access control mechanism, with an admin that can be\n/// granted exclusive access to specific functions. The inheriting contract must set the initial admin\n/// in the constructor.\ninterface IAdminable {\n /*//////////////////////////////////////////////////////////////////////////\n EVENTS\n //////////////////////////////////////////////////////////////////////////*/\n\n /// @notice Emitted when the admin is transferred.\n /// @param oldAdmin The address of the old admin.\n /// @param newAdmin The address of the new admin.\n event TransferAdmin(address indexed oldAdmin, address indexed newAdmin);\n\n /*//////////////////////////////////////////////////////////////////////////\n CONSTANT FUNCTIONS\n //////////////////////////////////////////////////////////////////////////*/\n\n /// @notice The address of the admin account or contract.\n function admin() external view returns (address);\n\n /*//////////////////////////////////////////////////////////////////////////\n NON-CONSTANT FUNCTIONS\n //////////////////////////////////////////////////////////////////////////*/\n\n /// @notice Transfers the contract admin to a new address.\n ///\n /// @dev Notes:\n /// - Does not revert if the admin is the same.\n /// - This function can potentially leave the contract without an admin, thereby removing any\n /// functionality that is only available to the admin.\n ///\n /// Requirements:\n /// - `msg.sender` must be the contract admin.\n ///\n /// @param newAdmin The address of the new admin.\n function transferAdmin(address newAdmin) external;\n}\n"},"contracts/interfaces/ISablierV2Lockup.sol":{"content":"// SPDX-License-Identifier: GPL-3.0-or-later\npragma solidity >=0.8.20;\n\nimport { IERC4906 } from \"@openzeppelin/contracts/interfaces/IERC4906.sol\";\nimport { IERC20 } from \"@openzeppelin/contracts/token/ERC20/IERC20.sol\";\nimport { IERC721Metadata } from \"@openzeppelin/contracts/token/ERC721/extensions/IERC721Metadata.sol\";\nimport { UD60x18 } from \"@prb/math/src/UD60x18.sol\";\n\nimport { Lockup } from \"../types/DataTypes.sol\";\nimport { IAdminable } from \"./IAdminable.sol\";\nimport { ISablierV2NFTDescriptor } from \"./ISablierV2NFTDescriptor.sol\";\n\n/// @title ISablierV2Lockup\n/// @notice Common logic between all Sablier V2 Lockup contracts.\ninterface ISablierV2Lockup is\n IAdminable, // 0 inherited components\n IERC4906, // 2 inherited components\n IERC721Metadata // 2 inherited components\n{\n /*//////////////////////////////////////////////////////////////////////////\n EVENTS\n //////////////////////////////////////////////////////////////////////////*/\n\n /// @notice Emitted when the admin allows a new recipient contract to hook to Sablier.\n /// @param admin The address of the current contract admin.\n /// @param recipient The address of the recipient contract put on the allowlist.\n event AllowToHook(address indexed admin, address recipient);\n\n /// @notice Emitted when a stream is canceled.\n /// @param streamId The ID of the stream.\n /// @param sender The address of the stream's sender.\n /// @param recipient The address of the stream's recipient.\n /// @param asset The contract address of the ERC-20 asset to be distributed.\n /// @param senderAmount The amount of assets refunded to the stream's sender, denoted in units of the asset's\n /// decimals.\n /// @param recipientAmount The amount of assets left for the stream's recipient to withdraw, denoted in units of the\n /// asset's decimals.\n event CancelLockupStream(\n uint256 streamId,\n address indexed sender,\n address indexed recipient,\n IERC20 indexed asset,\n uint128 senderAmount,\n uint128 recipientAmount\n );\n\n /// @notice Emitted when a sender gives up the right to cancel a stream.\n /// @param streamId The ID of the stream.\n event RenounceLockupStream(uint256 indexed streamId);\n\n /// @notice Emitted when the admin sets a new NFT descriptor contract.\n /// @param admin The address of the current contract admin.\n /// @param oldNFTDescriptor The address of the old NFT descriptor contract.\n /// @param newNFTDescriptor The address of the new NFT descriptor contract.\n event SetNFTDescriptor(\n address indexed admin, ISablierV2NFTDescriptor oldNFTDescriptor, ISablierV2NFTDescriptor newNFTDescriptor\n );\n\n /// @notice Emitted when assets are withdrawn from a stream.\n /// @param streamId The ID of the stream.\n /// @param to The address that has received the withdrawn assets.\n /// @param asset The contract address of the ERC-20 asset to be distributed.\n /// @param amount The amount of assets withdrawn, denoted in units of the asset's decimals.\n event WithdrawFromLockupStream(uint256 indexed streamId, address indexed to, IERC20 indexed asset, uint128 amount);\n\n /*//////////////////////////////////////////////////////////////////////////\n CONSTANT FUNCTIONS\n //////////////////////////////////////////////////////////////////////////*/\n\n /// @notice Retrieves the address of the ERC-20 asset to be distributed.\n /// @dev Reverts if `streamId` references a null stream.\n /// @param streamId The stream ID for the query.\n function getAsset(uint256 streamId) external view returns (IERC20 asset);\n\n /// @notice Retrieves the amount deposited in the stream, denoted in units of the asset's decimals.\n /// @dev Reverts if `streamId` references a null stream.\n /// @param streamId The stream ID for the query.\n function getDepositedAmount(uint256 streamId) external view returns (uint128 depositedAmount);\n\n /// @notice Retrieves the stream's end time, which is a Unix timestamp.\n /// @dev Reverts if `streamId` references a null stream.\n /// @param streamId The stream ID for the query.\n function getEndTime(uint256 streamId) external view returns (uint40 endTime);\n\n /// @notice Retrieves the stream's recipient.\n /// @dev Reverts if the NFT has been burned.\n /// @param streamId The stream ID for the query.\n function getRecipient(uint256 streamId) external view returns (address recipient);\n\n /// @notice Retrieves the amount refunded to the sender after a cancellation, denoted in units of the asset's\n /// decimals. This amount is always zero unless the stream was canceled.\n /// @dev Reverts if `streamId` references a null stream.\n /// @param streamId The stream ID for the query.\n function getRefundedAmount(uint256 streamId) external view returns (uint128 refundedAmount);\n\n /// @notice Retrieves the stream's sender.\n /// @dev Reverts if `streamId` references a null stream.\n /// @param streamId The stream ID for the query.\n function getSender(uint256 streamId) external view returns (address sender);\n\n /// @notice Retrieves the stream's start time, which is a Unix timestamp.\n /// @dev Reverts if `streamId` references a null stream.\n /// @param streamId The stream ID for the query.\n function getStartTime(uint256 streamId) external view returns (uint40 startTime);\n\n /// @notice Retrieves the amount withdrawn from the stream, denoted in units of the asset's decimals.\n /// @dev Reverts if `streamId` references a null stream.\n /// @param streamId The stream ID for the query.\n function getWithdrawnAmount(uint256 streamId) external view returns (uint128 withdrawnAmount);\n\n /// @notice Retrieves a flag indicating whether the provided address is a contract allowed to hook to Sablier\n /// when a stream is canceled or when assets are withdrawn.\n /// @dev See {ISablierLockupRecipient} for more information.\n function isAllowedToHook(address recipient) external view returns (bool result);\n\n /// @notice Retrieves a flag indicating whether the stream can be canceled. When the stream is cold, this\n /// flag is always `false`.\n /// @dev Reverts if `streamId` references a null stream.\n /// @param streamId The stream ID for the query.\n function isCancelable(uint256 streamId) external view returns (bool result);\n\n /// @notice Retrieves a flag indicating whether the stream is cold, i.e. settled, canceled, or depleted.\n /// @dev Reverts if `streamId` references a null stream.\n /// @param streamId The stream ID for the query.\n function isCold(uint256 streamId) external view returns (bool result);\n\n /// @notice Retrieves a flag indicating whether the stream is depleted.\n /// @dev Reverts if `streamId` references a null stream.\n /// @param streamId The stream ID for the query.\n function isDepleted(uint256 streamId) external view returns (bool result);\n\n /// @notice Retrieves a flag indicating whether the stream exists.\n /// @dev Does not revert if `streamId` references a null stream.\n /// @param streamId The stream ID for the query.\n function isStream(uint256 streamId) external view returns (bool result);\n\n /// @notice Retrieves a flag indicating whether the stream NFT can be transferred.\n /// @dev Reverts if `streamId` references a null stream.\n /// @param streamId The stream ID for the query.\n function isTransferable(uint256 streamId) external view returns (bool result);\n\n /// @notice Retrieves a flag indicating whether the stream is warm, i.e. either pending or streaming.\n /// @dev Reverts if `streamId` references a null stream.\n /// @param streamId The stream ID for the query.\n function isWarm(uint256 streamId) external view returns (bool result);\n\n /// @notice Retrieves the maximum broker fee that can be charged by the broker, denoted as a fixed-point\n /// number where 1e18 is 100%.\n /// @dev This value is hard coded as a constant.\n function MAX_BROKER_FEE() external view returns (UD60x18);\n\n /// @notice Counter for stream IDs, used in the create functions.\n function nextStreamId() external view returns (uint256);\n\n /// @notice Contract that generates the non-fungible token URI.\n function nftDescriptor() external view returns (ISablierV2NFTDescriptor);\n\n /// @notice Calculates the amount that the sender would be refunded if the stream were canceled, denoted in units\n /// of the asset's decimals.\n /// @dev Reverts if `streamId` references a null stream.\n /// @param streamId The stream ID for the query.\n function refundableAmountOf(uint256 streamId) external view returns (uint128 refundableAmount);\n\n /// @notice Retrieves the stream's status.\n /// @dev Reverts if `streamId` references a null stream.\n /// @param streamId The stream ID for the query.\n function statusOf(uint256 streamId) external view returns (Lockup.Status status);\n\n /// @notice Calculates the amount streamed to the recipient, denoted in units of the asset's decimals.\n /// @dev Reverts if `streamId` references a null stream.\n ///\n /// Notes:\n /// - Upon cancellation of the stream, the amount streamed is calculated as the difference between the deposited\n /// amount and the refunded amount. Ultimately, when the stream becomes depleted, the streamed amount is equivalent\n /// to the total amount withdrawn.\n ///\n /// @param streamId The stream ID for the query.\n function streamedAmountOf(uint256 streamId) external view returns (uint128 streamedAmount);\n\n /// @notice Retrieves a flag indicating whether the stream was canceled.\n /// @dev Reverts if `streamId` references a null stream.\n /// @param streamId The stream ID for the query.\n function wasCanceled(uint256 streamId) external view returns (bool result);\n\n /// @notice Calculates the amount that the recipient can withdraw from the stream, denoted in units of the asset's\n /// decimals.\n /// @dev Reverts if `streamId` references a null stream.\n /// @param streamId The stream ID for the query.\n function withdrawableAmountOf(uint256 streamId) external view returns (uint128 withdrawableAmount);\n\n /*//////////////////////////////////////////////////////////////////////////\n NON-CONSTANT FUNCTIONS\n //////////////////////////////////////////////////////////////////////////*/\n\n /// @notice Allows a recipient contract to hook to Sablier when a stream is canceled or when assets are withdrawn.\n /// Useful for implementing contracts that hold streams on behalf of users, such as vaults or staking contracts.\n ///\n /// @dev Emits an {AllowToHook} event.\n ///\n /// Notes:\n /// - Does not revert if the contract is already on the allowlist.\n /// - This is an irreversible operation. The contract cannot be removed from the allowlist.\n ///\n /// Requirements:\n /// - `msg.sender` must be the contract admin.\n /// - `recipient` must have a non-zero code size.\n /// - `recipient` must implement {ISablierLockupRecipient}.\n ///\n /// @param recipient The address of the contract to allow for hooks.\n function allowToHook(address recipient) external;\n\n /// @notice Burns the NFT associated with the stream.\n ///\n /// @dev Emits a {Transfer} event.\n ///\n /// Requirements:\n /// - Must not be delegate called.\n /// - `streamId` must reference a depleted stream.\n /// - The NFT must exist.\n /// - `msg.sender` must be either the NFT owner or an approved third party.\n ///\n /// @param streamId The ID of the stream NFT to burn.\n function burn(uint256 streamId) external;\n\n /// @notice Cancels the stream and refunds any remaining assets to the sender.\n ///\n /// @dev Emits a {Transfer}, {CancelLockupStream}, and {MetadataUpdate} event.\n ///\n /// Notes:\n /// - If there any assets left for the recipient to withdraw, the stream is marked as canceled. Otherwise, the\n /// stream is marked as depleted.\n /// - This function attempts to invoke a hook on the recipient, if the resolved address is a contract.\n ///\n /// Requirements:\n /// - Must not be delegate called.\n /// - The stream must be warm and cancelable.\n /// - `msg.sender` must be the stream's sender.\n ///\n /// @param streamId The ID of the stream to cancel.\n function cancel(uint256 streamId) external;\n\n /// @notice Cancels multiple streams and refunds any remaining assets to the sender.\n ///\n /// @dev Emits multiple {Transfer}, {CancelLockupStream}, and {MetadataUpdate} events.\n ///\n /// Notes:\n /// - Refer to the notes in {cancel}.\n ///\n /// Requirements:\n /// - All requirements from {cancel} must be met for each stream.\n ///\n /// @param streamIds The IDs of the streams to cancel.\n function cancelMultiple(uint256[] calldata streamIds) external;\n\n /// @notice Removes the right of the stream's sender to cancel the stream.\n ///\n /// @dev Emits a {RenounceLockupStream} and {MetadataUpdate} event.\n ///\n /// Notes:\n /// - This is an irreversible operation.\n ///\n /// Requirements:\n /// - Must not be delegate called.\n /// - `streamId` must reference a warm stream.\n /// - `msg.sender` must be the stream's sender.\n /// - The stream must be cancelable.\n ///\n /// @param streamId The ID of the stream to renounce.\n function renounce(uint256 streamId) external;\n\n /// @notice Sets a new NFT descriptor contract, which produces the URI describing the Sablier stream NFTs.\n ///\n /// @dev Emits a {SetNFTDescriptor} and {BatchMetadataUpdate} event.\n ///\n /// Notes:\n /// - Does not revert if the NFT descriptor is the same.\n ///\n /// Requirements:\n /// - `msg.sender` must be the contract admin.\n ///\n /// @param newNFTDescriptor The address of the new NFT descriptor contract.\n function setNFTDescriptor(ISablierV2NFTDescriptor newNFTDescriptor) external;\n\n /// @notice Withdraws the provided amount of assets from the stream to the `to` address.\n ///\n /// @dev Emits a {Transfer}, {WithdrawFromLockupStream}, and {MetadataUpdate} event.\n ///\n /// Notes:\n /// - This function attempts to call a hook on the recipient of the stream, unless `msg.sender` is the recipient.\n ///\n /// Requirements:\n /// - Must not be delegate called.\n /// - `streamId` must not reference a null or depleted stream.\n /// - `to` must not be the zero address.\n /// - `amount` must be greater than zero and must not exceed the withdrawable amount.\n /// - `to` must be the recipient if `msg.sender` is not the stream's recipient or an approved third party.\n ///\n /// @param streamId The ID of the stream to withdraw from.\n /// @param to The address receiving the withdrawn assets.\n /// @param amount The amount to withdraw, denoted in units of the asset's decimals.\n function withdraw(uint256 streamId, address to, uint128 amount) external;\n\n /// @notice Withdraws the maximum withdrawable amount from the stream to the provided address `to`.\n ///\n /// @dev Emits a {Transfer}, {WithdrawFromLockupStream}, and {MetadataUpdate} event.\n ///\n /// Notes:\n /// - Refer to the notes in {withdraw}.\n ///\n /// Requirements:\n /// - Refer to the requirements in {withdraw}.\n ///\n /// @param streamId The ID of the stream to withdraw from.\n /// @param to The address receiving the withdrawn assets.\n /// @return withdrawnAmount The amount withdrawn, denoted in units of the asset's decimals.\n function withdrawMax(uint256 streamId, address to) external returns (uint128 withdrawnAmount);\n\n /// @notice Withdraws the maximum withdrawable amount from the stream to the current recipient, and transfers the\n /// NFT to `newRecipient`.\n ///\n /// @dev Emits a {WithdrawFromLockupStream} and a {Transfer} event.\n ///\n /// Notes:\n /// - If the withdrawable amount is zero, the withdrawal is skipped.\n /// - Refer to the notes in {withdraw}.\n ///\n /// Requirements:\n /// - `msg.sender` must be the stream's recipient.\n /// - Refer to the requirements in {withdraw}.\n /// - Refer to the requirements in {IERC721.transferFrom}.\n ///\n /// @param streamId The ID of the stream NFT to transfer.\n /// @param newRecipient The address of the new owner of the stream NFT.\n /// @return withdrawnAmount The amount withdrawn, denoted in units of the asset's decimals.\n function withdrawMaxAndTransfer(\n uint256 streamId,\n address newRecipient\n )\n external\n returns (uint128 withdrawnAmount);\n\n /// @notice Withdraws assets from streams to the recipient of each stream.\n ///\n /// @dev Emits multiple {Transfer}, {WithdrawFromLockupStream}, and {MetadataUpdate} events.\n ///\n /// Notes:\n /// - This function attempts to call a hook on the recipient of each stream, unless `msg.sender` is the recipient.\n ///\n /// Requirements:\n /// - Must not be delegate called.\n /// - There must be an equal number of `streamIds` and `amounts`.\n /// - Each stream ID in the array must not reference a null or depleted stream.\n /// - Each amount in the array must be greater than zero and must not exceed the withdrawable amount.\n ///\n /// @param streamIds The IDs of the streams to withdraw from.\n /// @param amounts The amounts to withdraw, denoted in units of the asset's decimals.\n function withdrawMultiple(uint256[] calldata streamIds, uint128[] calldata amounts) external;\n}\n"},"contracts/interfaces/ISablierV2NFTDescriptor.sol":{"content":"// SPDX-License-Identifier: GPL-3.0-or-later\npragma solidity >=0.8.20;\n\nimport { IERC721Metadata } from \"@openzeppelin/contracts/token/ERC721/extensions/IERC721Metadata.sol\";\n\n/// @title ISablierV2NFTDescriptor\n/// @notice This contract generates the URI describing the Sablier V2 stream NFTs.\n/// @dev Inspired by Uniswap V3 Positions NFTs.\ninterface ISablierV2NFTDescriptor {\n /// @notice Produces the URI describing a particular stream NFT.\n /// @dev This is a data URI with the JSON contents directly inlined.\n /// @param sablier The address of the Sablier contract the stream was created in.\n /// @param streamId The ID of the stream for which to produce a description.\n /// @return uri The URI of the ERC721-compliant metadata.\n function tokenURI(IERC721Metadata sablier, uint256 streamId) external view returns (string memory uri);\n}\n"},"contracts/libraries/Errors.sol":{"content":"// SPDX-License-Identifier: GPL-3.0-or-later\npragma solidity >=0.8.20;\n\nimport { IERC721Metadata } from \"@openzeppelin/contracts/token/ERC721/extensions/IERC721Metadata.sol\";\nimport { UD60x18 } from \"@prb/math/src/UD60x18.sol\";\n\n/// @title Errors\n/// @notice Library containing all custom errors the protocol may revert with.\nlibrary Errors {\n /*//////////////////////////////////////////////////////////////////////////\n GENERICS\n //////////////////////////////////////////////////////////////////////////*/\n\n /// @notice Thrown when `msg.sender` is not the admin.\n error CallerNotAdmin(address admin, address caller);\n\n /// @notice Thrown when trying to delegate call to a function that disallows delegate calls.\n error DelegateCall();\n\n /*//////////////////////////////////////////////////////////////////////////\n SABLIER-V2-LOCKUP\n //////////////////////////////////////////////////////////////////////////*/\n\n /// @notice Thrown when trying to allow to hook a contract that doesn't implement the interface correctly.\n error SablierV2Lockup_AllowToHookUnsupportedInterface(address recipient);\n\n /// @notice Thrown when trying to allow to hook an address with no code.\n error SablierV2Lockup_AllowToHookZeroCodeSize(address recipient);\n\n /// @notice Thrown when the broker fee exceeds the maximum allowed fee.\n error SablierV2Lockup_BrokerFeeTooHigh(UD60x18 brokerFee, UD60x18 maxBrokerFee);\n\n /// @notice Thrown when trying to create a stream with a zero deposit amount.\n error SablierV2Lockup_DepositAmountZero();\n\n /// @notice Thrown when trying to create a stream with an end time not in the future.\n error SablierV2Lockup_EndTimeNotInTheFuture(uint40 blockTimestamp, uint40 endTime);\n\n /// @notice Thrown when the hook does not return the correct selector.\n error SablierV2Lockup_InvalidHookSelector(address recipient);\n\n /// @notice Thrown when trying to transfer Stream NFT when transferability is disabled.\n error SablierV2Lockup_NotTransferable(uint256 tokenId);\n\n /// @notice Thrown when the ID references a null stream.\n error SablierV2Lockup_Null(uint256 streamId);\n\n /// @notice Thrown when trying to withdraw an amount greater than the withdrawable amount.\n error SablierV2Lockup_Overdraw(uint256 streamId, uint128 amount, uint128 withdrawableAmount);\n\n /// @notice Thrown when trying to create a stream with a zero start time.\n error SablierV2Lockup_StartTimeZero();\n\n /// @notice Thrown when trying to cancel or renounce a canceled stream.\n error SablierV2Lockup_StreamCanceled(uint256 streamId);\n\n /// @notice Thrown when trying to cancel, renounce, or withdraw from a depleted stream.\n error SablierV2Lockup_StreamDepleted(uint256 streamId);\n\n /// @notice Thrown when trying to cancel or renounce a stream that is not cancelable.\n error SablierV2Lockup_StreamNotCancelable(uint256 streamId);\n\n /// @notice Thrown when trying to burn a stream that is not depleted.\n error SablierV2Lockup_StreamNotDepleted(uint256 streamId);\n\n /// @notice Thrown when trying to cancel or renounce a settled stream.\n error SablierV2Lockup_StreamSettled(uint256 streamId);\n\n /// @notice Thrown when `msg.sender` lacks authorization to perform an action.\n error SablierV2Lockup_Unauthorized(uint256 streamId, address caller);\n\n /// @notice Thrown when trying to withdraw to an address other than the recipient's.\n error SablierV2Lockup_WithdrawalAddressNotRecipient(uint256 streamId, address caller, address to);\n\n /// @notice Thrown when trying to withdraw zero assets from a stream.\n error SablierV2Lockup_WithdrawAmountZero(uint256 streamId);\n\n /// @notice Thrown when trying to withdraw from multiple streams and the number of stream IDs does\n /// not match the number of withdraw amounts.\n error SablierV2Lockup_WithdrawArrayCountsNotEqual(uint256 streamIdsCount, uint256 amountsCount);\n\n /// @notice Thrown when trying to withdraw to the zero address.\n error SablierV2Lockup_WithdrawToZeroAddress(uint256 streamId);\n\n /*//////////////////////////////////////////////////////////////////////////\n SABLIER-V2-LOCKUP-DYNAMIC\n //////////////////////////////////////////////////////////////////////////*/\n\n /// @notice Thrown when trying to create a stream with a deposit amount not equal to the sum of the\n /// segment amounts.\n error SablierV2LockupDynamic_DepositAmountNotEqualToSegmentAmountsSum(\n uint128 depositAmount, uint128 segmentAmountsSum\n );\n\n /// @notice Thrown when trying to create a stream with more segments than the maximum allowed.\n error SablierV2LockupDynamic_SegmentCountTooHigh(uint256 count);\n\n /// @notice Thrown when trying to create a stream with no segments.\n error SablierV2LockupDynamic_SegmentCountZero();\n\n /// @notice Thrown when trying to create a stream with unordered segment timestamps.\n error SablierV2LockupDynamic_SegmentTimestampsNotOrdered(\n uint256 index, uint40 previousTimestamp, uint40 currentTimestamp\n );\n\n /// @notice Thrown when trying to create a stream with a start time not strictly less than the first\n /// segment timestamp.\n error SablierV2LockupDynamic_StartTimeNotLessThanFirstSegmentTimestamp(\n uint40 startTime, uint40 firstSegmentTimestamp\n );\n\n /*//////////////////////////////////////////////////////////////////////////\n SABLIER-V2-LOCKUP-LINEAR\n //////////////////////////////////////////////////////////////////////////*/\n\n /// @notice Thrown when trying to create a stream with a cliff time not strictly less than the end time.\n error SablierV2LockupLinear_CliffTimeNotLessThanEndTime(uint40 cliffTime, uint40 endTime);\n\n /// @notice Thrown when trying to create a stream with a start time not strictly less than the cliff time, when the\n /// cliff time does not have a zero value.\n error SablierV2LockupLinear_StartTimeNotLessThanCliffTime(uint40 startTime, uint40 cliffTime);\n\n /// @notice Thrown when trying to create a stream with a start time not strictly less than the end time.\n error SablierV2LockupLinear_StartTimeNotLessThanEndTime(uint40 startTime, uint40 endTime);\n\n /*//////////////////////////////////////////////////////////////////////////\n SABLIER-V2-NFT-DESCRIPTOR\n //////////////////////////////////////////////////////////////////////////*/\n\n /// @notice Thrown when trying to generate the token URI for an unknown ERC-721 NFT contract.\n error SablierV2NFTDescriptor_UnknownNFT(IERC721Metadata nft, string symbol);\n\n /*//////////////////////////////////////////////////////////////////////////\n SABLIER-V2-LOCKUP-TRANCHE\n //////////////////////////////////////////////////////////////////////////*/\n\n /// @notice Thrown when trying to create a stream with a deposit amount not equal to the sum of the\n /// tranche amounts.\n error SablierV2LockupTranched_DepositAmountNotEqualToTrancheAmountsSum(\n uint128 depositAmount, uint128 trancheAmountsSum\n );\n\n /// @notice Thrown when trying to create a stream with a start time not strictly less than the first\n /// tranche timestamp.\n error SablierV2LockupTranched_StartTimeNotLessThanFirstTrancheTimestamp(\n uint40 startTime, uint40 firstTrancheTimestamp\n );\n\n /// @notice Thrown when trying to create a stream with more tranches than the maximum allowed.\n error SablierV2LockupTranched_TrancheCountTooHigh(uint256 count);\n\n /// @notice Thrown when trying to create a stream with no tranches.\n error SablierV2LockupTranched_TrancheCountZero();\n\n /// @notice Thrown when trying to create a stream with unordered tranche timestamps.\n error SablierV2LockupTranched_TrancheTimestampsNotOrdered(\n uint256 index, uint40 previousTimestamp, uint40 currentTimestamp\n );\n}\n"},"contracts/libraries/NFTSVG.sol":{"content":"// SPDX-License-Identifier: GPL-3.0-or-later\n// solhint-disable quotes\npragma solidity >=0.8.20;\n\nimport { Strings } from \"@openzeppelin/contracts/utils/Strings.sol\";\n\nimport { SVGElements } from \"./SVGElements.sol\";\n\nlibrary NFTSVG {\n using Strings for uint256;\n\n uint256 internal constant CARD_MARGIN = 16;\n\n struct SVGParams {\n string accentColor;\n string amount;\n string assetAddress;\n string assetSymbol;\n string duration;\n string progress;\n uint256 progressNumerical;\n string sablierAddress;\n string sablierModel;\n string status;\n }\n\n struct SVGVars {\n string amountCard;\n uint256 amountWidth;\n uint256 amountXPosition;\n string cards;\n uint256 cardsWidth;\n string durationCard;\n uint256 durationWidth;\n uint256 durationXPosition;\n string progressCard;\n uint256 progressWidth;\n uint256 progressXPosition;\n string statusCard;\n uint256 statusWidth;\n uint256 statusXPosition;\n }\n\n function generateSVG(SVGParams memory params) internal pure returns (string memory) {\n SVGVars memory vars;\n\n // Generate the progress card.\n (vars.progressWidth, vars.progressCard) = SVGElements.card({\n cardType: SVGElements.CardType.PROGRESS,\n content: params.progress,\n circle: SVGElements.progressCircle({\n progressNumerical: params.progressNumerical,\n accentColor: params.accentColor\n })\n });\n\n // Generate the status card.\n (vars.statusWidth, vars.statusCard) =\n SVGElements.card({ cardType: SVGElements.CardType.STATUS, content: params.status });\n\n // Generate the deposit amount card.\n (vars.amountWidth, vars.amountCard) =\n SVGElements.card({ cardType: SVGElements.CardType.AMOUNT, content: params.amount });\n\n // Generate the duration card.\n (vars.durationWidth, vars.durationCard) =\n SVGElements.card({ cardType: SVGElements.CardType.DURATION, content: params.duration });\n\n unchecked {\n // Calculate the width of the row containing the cards and the margins between them.\n vars.cardsWidth =\n vars.amountWidth + vars.durationWidth + vars.progressWidth + vars.statusWidth + CARD_MARGIN * 3;\n\n // Calculate the positions on the X axis based on the following layout:\n //\n // ___________________________ SVG Width (1000px) ___________________________\n // | | | | | | | | | |\n // | <-> | Progress | 16px | Status | 16px | Amount | 16px | Duration | <-> |\n vars.progressXPosition = (1000 - vars.cardsWidth) / 2;\n vars.statusXPosition = vars.progressXPosition + vars.progressWidth + CARD_MARGIN;\n vars.amountXPosition = vars.statusXPosition + vars.statusWidth + CARD_MARGIN;\n vars.durationXPosition = vars.amountXPosition + vars.amountWidth + CARD_MARGIN;\n }\n\n // Concatenate all cards.\n vars.cards = string.concat(vars.progressCard, vars.statusCard, vars.amountCard, vars.durationCard);\n\n return string.concat(\n '\"\n );\n }\n\n function generateDefs(\n string memory accentColor,\n string memory status,\n string memory cards\n )\n internal\n pure\n returns (string memory)\n {\n return string.concat(\n \"\",\n SVGElements.GLOW,\n SVGElements.NOISE,\n SVGElements.LOGO,\n SVGElements.FLOATING_TEXT,\n SVGElements.gradients(accentColor),\n SVGElements.hourglass(status),\n cards,\n \"\"\n );\n }\n\n function generateFloatingText(\n string memory sablierAddress,\n string memory sablierModel,\n string memory assetAddress,\n string memory assetSymbol\n )\n internal\n pure\n returns (string memory)\n {\n return string.concat(\n '',\n SVGElements.floatingText({\n offset: \"-100%\",\n text: string.concat(sablierAddress, unicode\" • \", \"Sablier V2 \", sablierModel)\n }),\n SVGElements.floatingText({\n offset: \"0%\",\n text: string.concat(sablierAddress, unicode\" • \", \"Sablier V2 \", sablierModel)\n }),\n SVGElements.floatingText({ offset: \"-50%\", text: string.concat(assetAddress, unicode\" • \", assetSymbol) }),\n SVGElements.floatingText({ offset: \"50%\", text: string.concat(assetAddress, unicode\" • \", assetSymbol) }),\n \"\"\n );\n }\n\n function generateHrefs(\n uint256 progressXPosition,\n uint256 statusXPosition,\n uint256 amountXPosition,\n uint256 durationXPosition\n )\n internal\n pure\n returns (string memory)\n {\n return string.concat(\n '',\n '',\n ''\n '',\n '',\n '',\n '',\n ''\n );\n }\n}\n"},"contracts/libraries/SVGElements.sol":{"content":"// SPDX-License-Identifier: GPL-3.0-or-later\n// solhint-disable max-line-length,quotes\npragma solidity >=0.8.20;\n\nimport { Math } from \"@openzeppelin/contracts/utils/math/Math.sol\";\nimport { Strings } from \"@openzeppelin/contracts/utils/Strings.sol\";\n\nlibrary SVGElements {\n using Strings for string;\n using Strings for uint256;\n\n /*//////////////////////////////////////////////////////////////////////////\n CONSTANTS\n //////////////////////////////////////////////////////////////////////////*/\n\n string internal constant BACKGROUND =\n '';\n\n string internal constant BACKGROUND_COLOR = \"hsl(230,21%,11%)\";\n\n string internal constant FLOATING_TEXT =\n '';\n\n string internal constant GLOW = '';\n\n string internal constant LOGO =\n '';\n\n string internal constant HOURGLASS_BACKGROUND_CIRCLE =\n '';\n\n string internal constant HOURGLASS_FILL =\n '';\n\n string internal constant HOURGLASS_STROKE =\n '';\n\n string internal constant HOURGLASS_LOWER_BULB_LARGE =\n '';\n\n string internal constant HOURGLASS_LOWER_BULB_SMALL =\n '';\n\n string internal constant HOURGLASS_UPPER_BULB =\n '';\n\n string internal constant NOISE =\n '';\n\n /// @dev Escape character for \"≥\".\n string internal constant SIGN_GE = \"≥\";\n\n /// @dev Escape character for \">\".\n string internal constant SIGN_GT = \">\";\n\n /// @dev Escape character for \"<\".\n string internal constant SIGN_LT = \"<\";\n\n /*//////////////////////////////////////////////////////////////////////////\n DATA TYPES\n //////////////////////////////////////////////////////////////////////////*/\n\n enum CardType {\n PROGRESS,\n STATUS,\n AMOUNT,\n DURATION\n }\n\n /*//////////////////////////////////////////////////////////////////////////\n COMPONENTS\n //////////////////////////////////////////////////////////////////////////*/\n\n function card(CardType cardType, string memory content) internal pure returns (uint256, string memory) {\n return card({ cardType: cardType, content: content, circle: \"\" });\n }\n\n function card(\n CardType cardType,\n string memory content,\n string memory circle\n )\n internal\n pure\n returns (uint256 width, string memory card_)\n {\n string memory caption = stringifyCardType(cardType);\n\n // The progress card can have a fixed width because the content is never longer than the caption. The former\n // has 6 characters (at most, e.g. \"42.09%\"), whereas the latter has 8 characters (\"Progress\").\n if (cardType == CardType.PROGRESS) {\n // The progress can be 0%, in which case the circle is not rendered.\n if (circle.equal(\"\")) {\n width = 144; // 2 * 20 (margins) + 8 * 13 (charWidth)\n } else {\n width = 208; // 3 * 20 (margins) + 8 * 13 (charWidth) + 44 (diameter)\n }\n }\n // For the other cards, the width is calculated dynamically based on the number of characters.\n else {\n uint256 captionWidth = calculatePixelWidth({ text: caption, largeFont: false });\n uint256 contentWidth = calculatePixelWidth({ text: content, largeFont: true });\n\n // Use the greater of the two widths, and add the left and the right margin.\n unchecked {\n width = Math.max(captionWidth, contentWidth) + 40;\n }\n }\n\n card_ = string.concat(\n '',\n '',\n '',\n caption,\n \"\",\n '',\n content,\n \"\",\n circle,\n \"\"\n );\n }\n\n function floatingText(string memory offset, string memory text) internal pure returns (string memory) {\n return string.concat(\n '',\n '',\n text,\n \"\"\n );\n }\n\n function gradients(string memory accentColor) internal pure returns (string memory) {\n string memory radialGlow = string.concat(\n '',\n '',\n '',\n \"\"\n );\n string memory sandTop = string.concat(\n '',\n '',\n '',\n \"\"\n );\n string memory sandBottom = string.concat(\n '',\n '',\n '',\n '',\n \"\"\n );\n // Needs to be declared last so that the stroke is painted on top of the sand.\n string memory hourglassStroke = string.concat(\n '',\n '',\n '',\n \"\"\n );\n return string.concat(radialGlow, sandTop, sandBottom, hourglassStroke);\n }\n\n function hourglass(string memory status) internal pure returns (string memory) {\n bool settledOrDepleted = status.equal(\"Settled\") || status.equal(\"Depleted\");\n return string.concat(\n '',\n HOURGLASS_BACKGROUND_CIRCLE,\n HOURGLASS_FILL,\n settledOrDepleted ? \"\" : HOURGLASS_UPPER_BULB, // empty or filled\n settledOrDepleted ? HOURGLASS_LOWER_BULB_LARGE : HOURGLASS_LOWER_BULB_SMALL,\n HOURGLASS_STROKE, // needs to be declared last so that the stroke is painted on top of the sand\n \"\"\n );\n }\n\n function progressCircle(\n uint256 progressNumerical,\n string memory accentColor\n )\n internal\n pure\n returns (string memory)\n {\n if (progressNumerical == 0) {\n return \"\";\n }\n return string.concat(\n '',\n '',\n '',\n \"\"\n );\n }\n\n /*//////////////////////////////////////////////////////////////////////////\n HELPERS\n //////////////////////////////////////////////////////////////////////////*/\n\n /// @notice Calculates the pixel width of the provided string.\n /// @dev Notes:\n /// - A factor of ~0.6 is applied to the two font sizes used in the SVG (26px and 22px) to approximate the average\n /// character width.\n /// - It is assumed that escaped characters are placed at the beginning of `text`.\n /// - It is further assumed that there is no other semicolon in `text`.\n function calculatePixelWidth(string memory text, bool largeFont) internal pure returns (uint256 width) {\n uint256 length = bytes(text).length;\n if (length == 0) {\n return 0;\n }\n\n unchecked {\n uint256 charWidth = largeFont ? 16 : 13;\n uint256 semicolonIndex;\n for (uint256 i = 0; i < length; ++i) {\n if (bytes(text)[i] == \";\") {\n semicolonIndex = i;\n }\n width += charWidth;\n }\n\n // Account for escaped characters (such as ≥).\n width -= charWidth * semicolonIndex;\n }\n }\n\n /// @notice Retrieves the card type as a string.\n function stringifyCardType(CardType cardType) internal pure returns (string memory) {\n if (cardType == CardType.PROGRESS) {\n return \"Progress\";\n } else if (cardType == CardType.STATUS) {\n return \"Status\";\n } else if (cardType == CardType.AMOUNT) {\n return \"Amount\";\n } else {\n return \"Duration\";\n }\n }\n}\n"},"contracts/SablierV2NFTDescriptor.sol":{"content":"// SPDX-License-Identifier: GPL-3.0-or-later\n// solhint-disable max-line-length,quotes\npragma solidity >=0.8.20;\n\nimport { IERC20Metadata } from \"@openzeppelin/contracts/token/ERC20/extensions/IERC20Metadata.sol\";\nimport { IERC721Metadata } from \"@openzeppelin/contracts/token/ERC721/extensions/IERC721Metadata.sol\";\nimport { Base64 } from \"@openzeppelin/contracts/utils/Base64.sol\";\nimport { Strings } from \"@openzeppelin/contracts/utils/Strings.sol\";\n\nimport { ISablierV2Lockup } from \"./interfaces/ISablierV2Lockup.sol\";\nimport { ISablierV2NFTDescriptor } from \"./interfaces/ISablierV2NFTDescriptor.sol\";\nimport { Lockup } from \"./types/DataTypes.sol\";\n\nimport { Errors } from \"./libraries/Errors.sol\";\nimport { NFTSVG } from \"./libraries/NFTSVG.sol\";\nimport { SVGElements } from \"./libraries/SVGElements.sol\";\n\n/*\n\n███████╗ █████╗ ██████╗ ██╗ ██╗███████╗██████╗ ██╗ ██╗██████╗\n██╔════╝██╔══██╗██╔══██╗██║ ██║██╔════╝██╔══██╗ ██║ ██║╚════██╗\n███████╗███████║██████╔╝██║ ██║█████╗ ██████╔╝ ██║ ██║ █████╔╝\n╚════██║██╔══██║██╔══██╗██║ ██║██╔══╝ ██╔══██╗ ╚██╗ ██╔╝██╔═══╝\n███████║██║ ██║██████╔╝███████╗██║███████╗██║ ██║ ╚████╔╝ ███████╗\n╚══════╝╚═╝ ╚═╝╚═════╝ ╚══════╝╚═╝╚══════╝╚═╝ ╚═╝ ╚═══╝ ╚══════╝\n\n███╗ ██╗███████╗████████╗ ██████╗ ███████╗███████╗ ██████╗██████╗ ██╗██████╗ ████████╗ ██████╗ ██████╗\n████╗ ██║██╔════╝╚══██╔══╝ ██╔══██╗██╔════╝██╔════╝██╔════╝██╔══██╗██║██╔══██╗╚══██╔══╝██╔═══██╗██╔══██╗\n██╔██╗ ██║█████╗ ██║ ██║ ██║█████╗ ███████╗██║ ██████╔╝██║██████╔╝ ██║ ██║ ██║██████╔╝\n██║╚██╗██║██╔══╝ ██║ ██║ ██║██╔══╝ ╚════██║██║ ██╔══██╗██║██╔═══╝ ██║ ██║ ██║██╔══██╗\n██║ ╚████║██║ ██║ ██████╔╝███████╗███████║╚██████╗██║ ██║██║██║ ██║ ╚██████╔╝██║ ██║\n╚═╝ ╚═══╝╚═╝ ╚═╝ ╚═════╝ ╚══════╝╚══════╝ ╚═════╝╚═╝ ╚═╝╚═╝╚═╝ ╚═╝ ╚═════╝ ╚═╝ ╚═╝\n\n*/\n\n/// @title SablierV2NFTDescriptor\n/// @notice See the documentation in {ISablierV2NFTDescriptor}.\ncontract SablierV2NFTDescriptor is ISablierV2NFTDescriptor {\n using Strings for address;\n using Strings for string;\n using Strings for uint256;\n\n /*//////////////////////////////////////////////////////////////////////////\n USER-FACING CONSTANT FUNCTIONS\n //////////////////////////////////////////////////////////////////////////*/\n\n /// @dev Needed to avoid Stack Too Deep.\n struct TokenURIVars {\n address asset;\n string assetSymbol;\n uint128 depositedAmount;\n bool isTransferable;\n string json;\n bytes returnData;\n ISablierV2Lockup sablier;\n string sablierModel;\n string sablierStringified;\n string status;\n string svg;\n uint256 streamedPercentage;\n bool success;\n }\n\n /// @inheritdoc ISablierV2NFTDescriptor\n function tokenURI(IERC721Metadata sablier, uint256 streamId) external view override returns (string memory uri) {\n TokenURIVars memory vars;\n\n // Load the contracts.\n vars.sablier = ISablierV2Lockup(address(sablier));\n vars.sablierModel = mapSymbol(sablier);\n vars.sablierStringified = address(sablier).toHexString();\n vars.asset = address(vars.sablier.getAsset(streamId));\n vars.assetSymbol = safeAssetSymbol(vars.asset);\n vars.depositedAmount = vars.sablier.getDepositedAmount(streamId);\n\n // Load the stream's data.\n vars.status = stringifyStatus(vars.sablier.statusOf(streamId));\n vars.streamedPercentage = calculateStreamedPercentage({\n streamedAmount: vars.sablier.streamedAmountOf(streamId),\n depositedAmount: vars.depositedAmount\n });\n\n // Generate the SVG.\n vars.svg = NFTSVG.generateSVG(\n NFTSVG.SVGParams({\n accentColor: generateAccentColor(address(sablier), streamId),\n amount: abbreviateAmount({ amount: vars.depositedAmount, decimals: safeAssetDecimals(vars.asset) }),\n assetAddress: vars.asset.toHexString(),\n assetSymbol: vars.assetSymbol,\n duration: calculateDurationInDays({\n startTime: vars.sablier.getStartTime(streamId),\n endTime: vars.sablier.getEndTime(streamId)\n }),\n sablierAddress: vars.sablierStringified,\n progress: stringifyPercentage(vars.streamedPercentage),\n progressNumerical: vars.streamedPercentage,\n status: vars.status,\n sablierModel: vars.sablierModel\n })\n );\n\n // Performs a low-level call to handle older deployments that miss the `isTransferable` function.\n (vars.success, vars.returnData) =\n address(vars.sablier).staticcall(abi.encodeCall(ISablierV2Lockup.isTransferable, (streamId)));\n\n // When the call has failed, the stream NFT is assumed to be transferable.\n vars.isTransferable = vars.success ? abi.decode(vars.returnData, (bool)) : true;\n\n // Generate the JSON metadata.\n vars.json = string.concat(\n '{\"attributes\":',\n generateAttributes({\n assetSymbol: vars.assetSymbol,\n sender: vars.sablier.getSender(streamId).toHexString(),\n status: vars.status\n }),\n ',\"description\":\"',\n generateDescription({\n sablierModel: vars.sablierModel,\n assetSymbol: vars.assetSymbol,\n sablierStringified: vars.sablierStringified,\n assetAddress: vars.asset.toHexString(),\n streamId: streamId.toString(),\n isTransferable: vars.isTransferable\n }),\n '\",\"external_url\":\"https://sablier.com\",\"name\":\"',\n generateName({ sablierModel: vars.sablierModel, streamId: streamId.toString() }),\n '\",\"image\":\"data:image/svg+xml;base64,',\n Base64.encode(bytes(vars.svg)),\n '\"}'\n );\n\n // Encode the JSON metadata in Base64.\n uri = string.concat(\"data:application/json;base64,\", Base64.encode(bytes(vars.json)));\n }\n\n /*//////////////////////////////////////////////////////////////////////////\n INTERNAL CONSTANT FUNCTIONS\n //////////////////////////////////////////////////////////////////////////*/\n\n /// @notice Creates an abbreviated representation of the provided amount, rounded down and prefixed with \">= \".\n /// @dev The abbreviation uses these suffixes:\n /// - \"K\" for thousands\n /// - \"M\" for millions\n /// - \"B\" for billions\n /// - \"T\" for trillions\n /// For example, if the input is 1,234,567, the output is \">= 1.23M\".\n /// @param amount The amount to abbreviate, denoted in units of `decimals`.\n /// @param decimals The number of decimals to assume when abbreviating the amount.\n /// @return abbreviation The abbreviated representation of the provided amount, as a string.\n function abbreviateAmount(uint256 amount, uint256 decimals) internal pure returns (string memory) {\n if (amount == 0) {\n return \"0\";\n }\n\n uint256 truncatedAmount;\n unchecked {\n truncatedAmount = decimals == 0 ? amount : amount / 10 ** decimals;\n }\n\n // Return dummy values when the truncated amount is either very small or very big.\n if (truncatedAmount < 1) {\n return string.concat(SVGElements.SIGN_LT, \" 1\");\n } else if (truncatedAmount >= 1e15) {\n return string.concat(SVGElements.SIGN_GT, \" 999.99T\");\n }\n\n string[5] memory suffixes = [\"\", \"K\", \"M\", \"B\", \"T\"];\n uint256 fractionalAmount;\n uint256 suffixIndex = 0;\n\n // Truncate repeatedly until the amount is less than 1000.\n unchecked {\n while (truncatedAmount >= 1000) {\n fractionalAmount = (truncatedAmount / 10) % 100; // keep the first two digits after the decimal point\n truncatedAmount /= 1000;\n suffixIndex += 1;\n }\n }\n\n // Concatenate the calculated parts to form the final string.\n string memory prefix = string.concat(SVGElements.SIGN_GE, \" \");\n string memory wholePart = truncatedAmount.toString();\n string memory fractionalPart = stringifyFractionalAmount(fractionalAmount);\n return string.concat(prefix, wholePart, fractionalPart, suffixes[suffixIndex]);\n }\n\n /// @notice Calculates the stream's duration in days, rounding down.\n function calculateDurationInDays(uint256 startTime, uint256 endTime) internal pure returns (string memory) {\n uint256 durationInDays;\n unchecked {\n durationInDays = (endTime - startTime) / 1 days;\n }\n\n // Return dummy values when the duration is either very small or very big.\n if (durationInDays == 0) {\n return string.concat(SVGElements.SIGN_LT, \" 1 Day\");\n } else if (durationInDays > 9999) {\n return string.concat(SVGElements.SIGN_GT, \" 9999 Days\");\n }\n\n string memory suffix = durationInDays == 1 ? \" Day\" : \" Days\";\n return string.concat(durationInDays.toString(), suffix);\n }\n\n /// @notice Calculates how much of the deposited amount has been streamed so far, as a percentage with 4 implied\n /// decimals.\n function calculateStreamedPercentage(\n uint128 streamedAmount,\n uint128 depositedAmount\n )\n internal\n pure\n returns (uint256)\n {\n // This cannot overflow because both inputs are uint128s, and zero deposit amounts are not allowed in Sablier.\n unchecked {\n return streamedAmount * 10_000 / depositedAmount;\n }\n }\n\n /// @notice Generates a pseudo-random HSL color by hashing together the `chainid`, the `sablier` address,\n /// and the `streamId`. This will be used as the accent color for the SVG.\n function generateAccentColor(address sablier, uint256 streamId) internal view returns (string memory) {\n // The chain ID is part of the hash so that the generated color is different across chains.\n uint256 chainId = block.chainid;\n\n // Hash the parameters to generate a pseudo-random bit field, which will be used as entropy.\n // | Hue | Saturation | Lightness | -> Roles\n // | [31:16] | [15:8] | [7:0] | -> Bit positions\n uint32 bitField = uint32(uint256(keccak256(abi.encodePacked(chainId, sablier, streamId))));\n\n unchecked {\n // The hue is a degree on a color wheel, so its range is [0, 360).\n // Shifting 16 bits to the right means using the bits at positions [31:16].\n uint256 hue = (bitField >> 16) % 360;\n\n // The saturation is a percentage where 0% is grayscale and 100%, but here the range is bounded to [20,100]\n // to make the colors more lively.\n // Shifting 8 bits to the right and applying an 8-bit mask means using the bits at positions [15:8].\n uint256 saturation = ((bitField >> 8) & 0xFF) % 80 + 20;\n\n // The lightness is typically a percentage between 0% (black) and 100% (white), but here the range\n // is bounded to [30,100] to avoid dark colors.\n // Applying an 8-bit mask means using the bits at positions [7:0].\n uint256 lightness = (bitField & 0xFF) % 70 + 30;\n\n // Finally, concatenate the HSL values to form an SVG color string.\n return string.concat(\"hsl(\", hue.toString(), \",\", saturation.toString(), \"%,\", lightness.toString(), \"%)\");\n }\n }\n\n /// @notice Generates an array of JSON objects that represent the NFT's attributes:\n /// - Asset symbol\n /// - Sender address\n /// - Status\n /// @dev These attributes are useful for filtering and sorting the NFTs.\n function generateAttributes(\n string memory assetSymbol,\n string memory sender,\n string memory status\n )\n internal\n pure\n returns (string memory)\n {\n return string.concat(\n '[{\"trait_type\":\"Asset\",\"value\":\"',\n assetSymbol,\n '\"},{\"trait_type\":\"Sender\",\"value\":\"',\n sender,\n '\"},{\"trait_type\":\"Status\",\"value\":\"',\n status,\n '\"}]'\n );\n }\n\n /// @notice Generates a string with the NFT's JSON metadata description, which provides a high-level overview.\n function generateDescription(\n string memory sablierModel,\n string memory assetSymbol,\n string memory sablierStringified,\n string memory assetAddress,\n string memory streamId,\n bool isTransferable\n )\n internal\n pure\n returns (string memory)\n {\n // Depending on the transferability of the NFT, declare the relevant information.\n string memory info = isTransferable\n ?\n unicode\"⚠️ WARNING: Transferring the NFT makes the new owner the recipient of the stream. The funds are not automatically withdrawn for the previous recipient.\"\n : unicode\"❕INFO: This NFT is non-transferable. It cannot be sold or transferred to another account.\";\n\n return string.concat(\n \"This NFT represents a payment stream in a Sablier V2 \",\n sablierModel,\n \" contract. The owner of this NFT can withdraw the streamed assets, which are denominated in \",\n assetSymbol,\n \".\\\\n\\\\n- Stream ID: \",\n streamId,\n \"\\\\n- \",\n sablierModel,\n \" Address: \",\n sablierStringified,\n \"\\\\n- \",\n assetSymbol,\n \" Address: \",\n assetAddress,\n \"\\\\n\\\\n\",\n info\n );\n }\n\n /// @notice Generates a string with the NFT's JSON metadata name, which is unique for each stream.\n /// @dev The `streamId` is equivalent to the ERC-721 `tokenId`.\n function generateName(string memory sablierModel, string memory streamId) internal pure returns (string memory) {\n return string.concat(\"Sablier V2 \", sablierModel, \" #\", streamId);\n }\n\n /// @notice Checks whether the provided string contains only alphanumeric characters, spaces, and dashes.\n /// @dev Note that this returns true for empty strings.\n function isAllowedCharacter(string memory str) internal pure returns (bool) {\n // Convert the string to bytes to iterate over its characters.\n bytes memory b = bytes(str);\n\n uint256 length = b.length;\n for (uint256 i = 0; i < length; ++i) {\n bytes1 char = b[i];\n\n // Check if it's a space, dash, or an alphanumeric character.\n bool isSpace = char == 0x20; // space\n bool isDash = char == 0x2D; // dash\n bool isDigit = char >= 0x30 && char <= 0x39; // 0-9\n bool isUppercaseLetter = char >= 0x41 && char <= 0x5A; // A-Z\n bool isLowercaseLetter = char >= 0x61 && char <= 0x7A; // a-z\n if (!(isSpace || isDash || isDigit || isUppercaseLetter || isLowercaseLetter)) {\n return false;\n }\n }\n return true;\n }\n\n /// @notice Maps ERC-721 symbols to human-readable model names.\n /// @dev Reverts if the symbol is unknown.\n function mapSymbol(IERC721Metadata sablier) internal view returns (string memory) {\n string memory symbol = sablier.symbol();\n if (symbol.equal(\"SAB-V2-LOCKUP-LIN\")) {\n return \"Lockup Linear\";\n } else if (symbol.equal(\"SAB-V2-LOCKUP-DYN\")) {\n return \"Lockup Dynamic\";\n } else if (symbol.equal(\"SAB-V2-LOCKUP-TRA\")) {\n return \"Lockup Tranched\";\n } else {\n revert Errors.SablierV2NFTDescriptor_UnknownNFT(sablier, symbol);\n }\n }\n\n /// @notice Retrieves the asset's decimals safely, defaulting to \"0\" if an error occurs.\n /// @dev Performs a low-level call to handle assets in which the decimals are not implemented.\n function safeAssetDecimals(address asset) internal view returns (uint8) {\n (bool success, bytes memory returnData) = asset.staticcall(abi.encodeCall(IERC20Metadata.decimals, ()));\n if (success && returnData.length == 32) {\n return abi.decode(returnData, (uint8));\n } else {\n return 0;\n }\n }\n\n /// @notice Retrieves the asset's symbol safely, defaulting to a hard-coded value if an error occurs.\n /// @dev Performs a low-level call to handle assets in which the symbol is not implemented or it is a bytes32\n /// instead of a string.\n function safeAssetSymbol(address asset) internal view returns (string memory) {\n (bool success, bytes memory returnData) = asset.staticcall(abi.encodeCall(IERC20Metadata.symbol, ()));\n\n // Non-empty strings have a length greater than 64, and bytes32 has length 32.\n if (!success || returnData.length <= 64) {\n return \"ERC20\";\n }\n\n string memory symbol = abi.decode(returnData, (string));\n\n // Check if the symbol is too long or contains disallowed characters. This measure helps mitigate potential\n // security threats from malicious assets injecting scripts in the symbol string.\n if (bytes(symbol).length > 30) {\n return \"Long Symbol\";\n } else {\n if (!isAllowedCharacter(symbol)) {\n return \"Unsupported Symbol\";\n }\n return symbol;\n }\n }\n\n /// @notice Converts the provided fractional amount to a string prefixed by a dot.\n /// @param fractionalAmount A numerical value with 2 implied decimals.\n function stringifyFractionalAmount(uint256 fractionalAmount) internal pure returns (string memory) {\n // Return the empty string if the fractional amount is zero.\n if (fractionalAmount == 0) {\n return \"\";\n }\n // Add a leading zero if the fractional part is less than 10, e.g. for \"1\", this function returns \".01%\".\n else if (fractionalAmount < 10) {\n return string.concat(\".0\", fractionalAmount.toString());\n }\n // Otherwise, stringify the fractional amount simply.\n else {\n return string.concat(\".\", fractionalAmount.toString());\n }\n }\n\n /// @notice Converts the provided percentage to a string.\n /// @param percentage A numerical value with 4 implied decimals.\n function stringifyPercentage(uint256 percentage) internal pure returns (string memory) {\n // Extract the last two decimals.\n string memory fractionalPart = stringifyFractionalAmount(percentage % 100);\n\n // Remove the last two decimals.\n string memory wholePart = (percentage / 100).toString();\n\n // Concatenate the whole and fractional parts.\n return string.concat(wholePart, fractionalPart, \"%\");\n }\n\n /// @notice Retrieves the stream's status as a string.\n function stringifyStatus(Lockup.Status status) internal pure returns (string memory) {\n if (status == Lockup.Status.DEPLETED) {\n return \"Depleted\";\n } else if (status == Lockup.Status.CANCELED) {\n return \"Canceled\";\n } else if (status == Lockup.Status.STREAMING) {\n return \"Streaming\";\n } else if (status == Lockup.Status.SETTLED) {\n return \"Settled\";\n } else {\n return \"Pending\";\n }\n }\n}\n"},"contracts/types/DataTypes.sol":{"content":"// SPDX-License-Identifier: GPL-3.0-or-later\npragma solidity >=0.8.20;\n\nimport { IERC20 } from \"@openzeppelin/contracts/token/ERC20/IERC20.sol\";\nimport { UD2x18 } from \"@prb/math/src/UD2x18.sol\";\nimport { UD60x18 } from \"@prb/math/src/UD60x18.sol\";\n\n// DataTypes.sol\n//\n// This file defines all structs used in V2 Core, most of which are organized under three namespaces:\n//\n// - Lockup\n// - LockupDynamic\n// - LockupLinear\n// - LockupTranched\n//\n// You will notice that some structs contain \"slot\" annotations - they are used to indicate the\n// storage layout of the struct. It is more gas efficient to group small data types together so\n// that they fit in a single 32-byte slot.\n\n/// @notice Struct encapsulating the broker parameters passed to the create functions. Both can be set to zero.\n/// @param account The address receiving the broker's fee.\n/// @param fee The broker's percentage fee from the total amount, denoted as a fixed-point number where 1e18 is 100%.\nstruct Broker {\n address account;\n UD60x18 fee;\n}\n\n/// @notice Namespace for the structs used in both {SablierV2LockupLinear} and {SablierV2LockupDynamic}.\nlibrary Lockup {\n /// @notice Struct encapsulating the deposit, withdrawn, and refunded amounts, both denoted in units of the asset's\n /// decimals.\n /// @dev Because the deposited and the withdrawn amount are often read together, declaring them in the same slot\n /// saves gas.\n /// @param deposited The initial amount deposited in the stream, net of broker fee.\n /// @param withdrawn The cumulative amount withdrawn from the stream.\n /// @param refunded The amount refunded to the sender. Unless the stream was canceled, this is always zero.\n struct Amounts {\n // slot 0\n uint128 deposited;\n uint128 withdrawn;\n // slot 1\n uint128 refunded;\n }\n\n /// @notice Struct encapsulating the deposit amount and the broker fee amount, both denoted in units of the asset's\n /// decimals.\n /// @param deposit The amount to deposit in the stream.\n /// @param brokerFee The broker fee amount.\n struct CreateAmounts {\n uint128 deposit;\n uint128 brokerFee;\n }\n\n /// @notice Enum representing the different statuses of a stream.\n /// @custom:value0 PENDING Stream created but not started; assets are in a pending state.\n /// @custom:value1 STREAMING Active stream where assets are currently being streamed.\n /// @custom:value2 SETTLED All assets have been streamed; recipient is due to withdraw them.\n /// @custom:value3 CANCELED Canceled stream; remaining assets await recipient's withdrawal.\n /// @custom:value4 DEPLETED Depleted stream; all assets have been withdrawn and/or refunded.\n enum Status {\n PENDING,\n STREAMING,\n SETTLED,\n CANCELED,\n DEPLETED\n }\n\n /// @notice A common data structure to be stored in all {SablierV2Lockup} models.\n /// @dev The fields are arranged like this to save gas via tight variable packing.\n /// @param sender The address distributing the assets, with the ability to cancel the stream.\n /// @param startTime The Unix timestamp indicating the stream's start.\n /// @param endTime The Unix timestamp indicating the stream's end.\n /// @param isCancelable Boolean indicating if the stream is cancelable.\n /// @param wasCanceled Boolean indicating if the stream was canceled.\n /// @param asset The contract address of the ERC-20 asset to be distributed.\n /// @param isDepleted Boolean indicating if the stream is depleted.\n /// @param isStream Boolean indicating if the struct entity exists.\n /// @param isTransferable Boolean indicating if the stream NFT is transferable.\n /// @param amounts Struct containing the deposit, withdrawn, and refunded amounts, both denoted in units of the\n /// asset's decimals.\n struct Stream {\n // slot 0\n address sender;\n uint40 startTime;\n uint40 endTime;\n bool isCancelable;\n bool wasCanceled;\n // slot 1\n IERC20 asset;\n bool isDepleted;\n bool isStream;\n bool isTransferable;\n // slot 2 and 3\n Lockup.Amounts amounts;\n }\n}\n\n/// @notice Namespace for the structs used in {SablierV2LockupDynamic}.\nlibrary LockupDynamic {\n /// @notice Struct encapsulating the parameters of the {SablierV2LockupDynamic.createWithDurations} function.\n /// @param sender The address distributing the assets, with the ability to cancel the stream. It doesn't have to be\n /// the same as `msg.sender`.\n /// @param recipient The address receiving the assets.\n /// @param totalAmount The total amount of ERC-20 assets to be distributed, including the stream deposit and any\n /// broker fee, both denoted in units of the asset's decimals.\n /// @param asset The contract address of the ERC-20 asset to be distributed.\n /// @param cancelable Indicates if the stream is cancelable.\n /// @param transferable Indicates if the stream NFT is transferable.\n /// @param segments Segments with durations used to compose the dynamic distribution function. Timestamps are\n /// calculated by starting from `block.timestamp` and adding each duration to the previous timestamp.\n /// @param broker Struct containing (i) the address of the broker assisting in creating the stream, and (ii) the\n /// percentage fee paid to the broker from `totalAmount`, denoted as a fixed-point number. Both can be set to zero.\n struct CreateWithDurations {\n address sender;\n address recipient;\n uint128 totalAmount;\n IERC20 asset;\n bool cancelable;\n bool transferable;\n SegmentWithDuration[] segments;\n Broker broker;\n }\n\n /// @notice Struct encapsulating the parameters of the {SablierV2LockupDynamic.createWithTimestamps} function.\n /// @param sender The address distributing the assets, with the ability to cancel the stream. It doesn't have to be\n /// the same as `msg.sender`.\n /// @param recipient The address receiving the assets.\n /// @param totalAmount The total amount of ERC-20 assets to be distributed, including the stream deposit and any\n /// broker fee, both denoted in units of the asset's decimals.\n /// @param asset The contract address of the ERC-20 asset to be distributed.\n /// @param cancelable Indicates if the stream is cancelable.\n /// @param transferable Indicates if the stream NFT is transferable.\n /// @param startTime The Unix timestamp indicating the stream's start.\n /// @param segments Segments used to compose the dynamic distribution function.\n /// @param broker Struct containing (i) the address of the broker assisting in creating the stream, and (ii) the\n /// percentage fee paid to the broker from `totalAmount`, denoted as a fixed-point number. Both can be set to zero.\n struct CreateWithTimestamps {\n address sender;\n address recipient;\n uint128 totalAmount;\n IERC20 asset;\n bool cancelable;\n bool transferable;\n uint40 startTime;\n Segment[] segments;\n Broker broker;\n }\n\n /// @notice Segment struct used in the Lockup Dynamic stream.\n /// @param amount The amount of assets to be streamed in the segment, denoted in units of the asset's decimals.\n /// @param exponent The exponent of the segment, denoted as a fixed-point number.\n /// @param timestamp The Unix timestamp indicating the segment's end.\n struct Segment {\n // slot 0\n uint128 amount;\n UD2x18 exponent;\n uint40 timestamp;\n }\n\n /// @notice Segment struct used at runtime in {SablierV2LockupDynamic.createWithDurations}.\n /// @param amount The amount of assets to be streamed in the segment, denoted in units of the asset's decimals.\n /// @param exponent The exponent of the segment, denoted as a fixed-point number.\n /// @param duration The time difference in seconds between the segment and the previous one.\n struct SegmentWithDuration {\n uint128 amount;\n UD2x18 exponent;\n uint40 duration;\n }\n\n /// @notice Struct encapsulating the full details of a stream.\n /// @dev Extends `Lockup.Stream` by including the recipient and the segments.\n struct StreamLD {\n address sender;\n address recipient;\n uint40 startTime;\n uint40 endTime;\n bool isCancelable;\n bool wasCanceled;\n IERC20 asset;\n bool isDepleted;\n bool isStream;\n bool isTransferable;\n Lockup.Amounts amounts;\n Segment[] segments;\n }\n\n /// @notice Struct encapsulating the LockupDynamic timestamps.\n /// @param start The Unix timestamp indicating the stream's start.\n /// @param end The Unix timestamp indicating the stream's end.\n struct Timestamps {\n uint40 start;\n uint40 end;\n }\n}\n\n/// @notice Namespace for the structs used in {SablierV2LockupLinear}.\nlibrary LockupLinear {\n /// @notice Struct encapsulating the parameters of the {SablierV2LockupLinear.createWithDurations} function.\n /// @param sender The address distributing the assets, with the ability to cancel the stream. It doesn't have to be\n /// the same as `msg.sender`.\n /// @param recipient The address receiving the assets.\n /// @param totalAmount The total amount of ERC-20 assets to be distributed, including the stream deposit and any\n /// broker fee, both denoted in units of the asset's decimals.\n /// @param asset The contract address of the ERC-20 asset to be distributed.\n /// @param cancelable Indicates if the stream is cancelable.\n /// @param transferable Indicates if the stream NFT is transferable.\n /// @param durations Struct containing (i) cliff period duration and (ii) total stream duration, both in seconds.\n /// @param broker Struct containing (i) the address of the broker assisting in creating the stream, and (ii) the\n /// percentage fee paid to the broker from `totalAmount`, denoted as a fixed-point number. Both can be set to zero.\n struct CreateWithDurations {\n address sender;\n address recipient;\n uint128 totalAmount;\n IERC20 asset;\n bool cancelable;\n bool transferable;\n Durations durations;\n Broker broker;\n }\n\n /// @notice Struct encapsulating the parameters of the {SablierV2LockupLinear.createWithTimestamps} function.\n /// @param sender The address distributing the assets, with the ability to cancel the stream. It doesn't have to be\n /// the same as `msg.sender`.\n /// @param recipient The address receiving the assets.\n /// @param totalAmount The total amount of ERC-20 assets to be distributed, including the stream deposit and any\n /// broker fee, both denoted in units of the asset's decimals.\n /// @param asset The contract address of the ERC-20 asset to be distributed.\n /// @param cancelable Indicates if the stream is cancelable.\n /// @param transferable Indicates if the stream NFT is transferable.\n /// @param timestamps Struct containing (i) the stream's start time, (ii) cliff time, and (iii) end time, all as\n /// Unix timestamps.\n /// @param broker Struct containing (i) the address of the broker assisting in creating the stream, and (ii) the\n /// percentage fee paid to the broker from `totalAmount`, denoted as a fixed-point number. Both can be set to zero.\n struct CreateWithTimestamps {\n address sender;\n address recipient;\n uint128 totalAmount;\n IERC20 asset;\n bool cancelable;\n bool transferable;\n Timestamps timestamps;\n Broker broker;\n }\n\n /// @notice Struct encapsulating the cliff duration and the total duration.\n /// @param cliff The cliff duration in seconds.\n /// @param total The total duration in seconds.\n struct Durations {\n uint40 cliff;\n uint40 total;\n }\n\n /// @notice Struct encapsulating the full details of a stream.\n /// @dev Extends `Lockup.Stream` by including the recipient and the cliff time.\n struct StreamLL {\n address sender;\n address recipient;\n uint40 startTime;\n bool isCancelable;\n bool wasCanceled;\n IERC20 asset;\n uint40 endTime;\n bool isDepleted;\n bool isStream;\n bool isTransferable;\n Lockup.Amounts amounts;\n uint40 cliffTime;\n }\n\n /// @notice Struct encapsulating the LockupLinear timestamps.\n /// @param start The Unix timestamp for the stream's start.\n /// @param cliff The Unix timestamp for the cliff period's end. A value of zero means there is no cliff.\n /// @param end The Unix timestamp for the stream's end.\n struct Timestamps {\n uint40 start;\n uint40 cliff;\n uint40 end;\n }\n}\n\n/// @notice Namespace for the structs used in {SablierV2LockupTranched}.\nlibrary LockupTranched {\n /// @notice Struct encapsulating the parameters of the {SablierV2LockupTranched.createWithDurations} function.\n /// @param sender The address distributing the assets, with the ability to cancel the stream. It doesn't have to be\n /// the same as `msg.sender`.\n /// @param recipient The address receiving the assets.\n /// @param totalAmount The total amount of ERC-20 assets to be distributed, including the stream deposit and any\n /// broker fee, both denoted in units of the asset's decimals.\n /// @param asset The contract address of the ERC-20 asset to be distributed.\n /// @param cancelable Indicates if the stream is cancelable.\n /// @param transferable Indicates if the stream NFT is transferable.\n /// @param tranches Tranches with durations used to compose the tranched distribution function. Timestamps are\n /// calculated by starting from `block.timestamp` and adding each duration to the previous timestamp.\n /// @param broker Struct containing (i) the address of the broker assisting in creating the stream, and (ii) the\n /// percentage fee paid to the broker from `totalAmount`, denoted as a fixed-point number. Both can be set to zero.\n struct CreateWithDurations {\n address sender;\n address recipient;\n uint128 totalAmount;\n IERC20 asset;\n bool cancelable;\n bool transferable;\n TrancheWithDuration[] tranches;\n Broker broker;\n }\n\n /// @notice Struct encapsulating the parameters of the {SablierV2LockupTranched.createWithTimestamps} function.\n /// @param sender The address distributing the assets, with the ability to cancel the stream. It doesn't have to be\n /// the same as `msg.sender`.\n /// @param recipient The address receiving the assets.\n /// @param totalAmount The total amount of ERC-20 assets to be distributed, including the stream deposit and any\n /// broker fee, both denoted in units of the asset's decimals.\n /// @param asset The contract address of the ERC-20 asset to be distributed.\n /// @param cancelable Indicates if the stream is cancelable.\n /// @param transferable Indicates if the stream NFT is transferable.\n /// @param startTime The Unix timestamp indicating the stream's start.\n /// @param tranches Tranches used to compose the tranched distribution function.\n /// @param broker Struct containing (i) the address of the broker assisting in creating the stream, and (ii) the\n /// percentage fee paid to the broker from `totalAmount`, denoted as a fixed-point number. Both can be set to zero.\n struct CreateWithTimestamps {\n address sender;\n address recipient;\n uint128 totalAmount;\n IERC20 asset;\n bool cancelable;\n bool transferable;\n uint40 startTime;\n Tranche[] tranches;\n Broker broker;\n }\n\n /// @notice Struct encapsulating the full details of a stream.\n /// @dev Extends `Lockup.Stream` by including the recipient and the tranches.\n struct StreamLT {\n address sender;\n address recipient;\n uint40 startTime;\n uint40 endTime;\n bool isCancelable;\n bool wasCanceled;\n IERC20 asset;\n bool isDepleted;\n bool isStream;\n bool isTransferable;\n Lockup.Amounts amounts;\n Tranche[] tranches;\n }\n\n /// @notice Struct encapsulating the LockupTranched timestamps.\n /// @param start The Unix timestamp indicating the stream's start.\n /// @param end The Unix timestamp indicating the stream's end.\n struct Timestamps {\n uint40 start;\n uint40 end;\n }\n\n /// @notice Tranche struct used in the Lockup Tranched stream.\n /// @param amount The amount of assets to be unlocked in the tranche, denoted in units of the asset's decimals.\n /// @param timestamp The Unix timestamp indicating the tranche's end.\n struct Tranche {\n // slot 0\n uint128 amount;\n uint40 timestamp;\n }\n\n /// @notice Tranche struct used at runtime in {SablierV2LockupTranched.createWithDurations}.\n /// @param amount The amount of assets to be unlocked in the tranche, denoted in units of the asset's decimals.\n /// @param duration The time difference in seconds between the tranche and the previous one.\n struct TrancheWithDuration {\n uint128 amount;\n uint40 duration;\n }\n}\n"}},"settings":{"optimizer":{"enabled":true,"runs":500},"viaIR":true,"evmVersion":"paris","outputSelection":{"*":{"*":["abi","evm.bytecode","evm.deployedBytecode","evm.methodIdentifiers","metadata"],"":["ast"]}},"libraries":{}}}