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0.8.19+commit.7dd6d404
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Solidity
// SPDX-License-Identifier: MIT
// File: @openzeppelin/contracts/utils/Strings.sol
pragma solidity ^0.8.0;
/**
* @dev String operations.
*/
library Strings {
bytes16 private constant _HEX_SYMBOLS = "0123456789abcdef";
/**
* @dev Converts a `uint256` to its ASCII `string` decimal representation.
*/
function toString(uint256 value) internal pure returns (string memory) {
// Inspired by OraclizeAPI's implementation - MIT licence
// https://github.com/oraclize/ethereum-api/blob/b42146b063c7d6ee1358846c198246239e9360e8/oraclizeAPI_0.4.25.sol
if (value == 0) {
return "0";
}
uint256 temp = value;
uint256 digits;
while (temp != 0) {
digits++;
temp /= 10;
}
bytes memory buffer = new bytes(digits);
while (value != 0) {
digits -= 1;
buffer[digits] = bytes1(uint8(48 + uint256(value % 10)));
value /= 10;
}
return string(buffer);
}
/**
* @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.
*/
function toHexString(uint256 value) internal pure returns (string memory) {
if (value == 0) {
return "0x00";
}
uint256 temp = value;
uint256 length = 0;
while (temp != 0) {
length++;
temp >>= 8;
}
return toHexString(value, length);
}
/**
* @dev Converts a `uint256` to its ASCII `string` hexadecimal representation with fixed length.
*/
function toHexString(uint256 value, uint256 length) internal pure returns (string memory) {
bytes memory buffer = new bytes(2 * length + 2);
buffer[0] = "0";
buffer[1] = "x";
for (uint256 i = 2 * length + 1; i > 1; --i) {
buffer[i] = _HEX_SYMBOLS[value & 0xf];
value >>= 4;
}
require(value == 0, "Strings: hex length insufficient");
return string(buffer);
}
}
// File: @openzeppelin/contracts/utils/Context.sol
pragma solidity ^0.8.0;
/**
* @dev Provides information about the current execution context, including the
* sender of the transaction and its data. While these are generally available
* via msg.sender and msg.data, they should not be accessed in such a direct
* manner, since when dealing with meta-transactions the account sending and
* paying for execution may not be the actual sender (as far as an application
* is concerned).
*
* This contract is only required for intermediate, library-like contracts.
*/
abstract contract Context {
function _msgSender() internal view virtual returns (address) {
return msg.sender;
}
function _msgData() internal view virtual returns (bytes calldata) {
return msg.data;
}
}
// File: @openzeppelin/contracts/utils/Address.sol
pragma solidity ^0.8.0;
/**
* @dev Collection of functions related to the address type
*/
library Address {
/**
* @dev Returns true if `account` is a contract.
*
* [IMPORTANT]
* ====
* It is unsafe to assume that an address for which this function returns
* false is an externally-owned account (EOA) and not a contract.
*
* Among others, `isContract` will return false for the following
* types of addresses:
*
* - an externally-owned account
* - a contract in construction
* - an address where a contract will be created
* - an address where a contract lived, but was destroyed
* ====
*/
function isContract(address account) internal view returns (bool) {
// This method relies on extcodesize, which returns 0 for contracts in
// construction, since the code is only stored at the end of the
// constructor execution.
uint256 size;
assembly {
size := extcodesize(account)
}
return size > 0;
}
/**
* @dev Replacement for Solidity's `transfer`: sends `amount` wei to
* `recipient`, forwarding all available gas and reverting on errors.
*
* https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
* of certain opcodes, possibly making contracts go over the 2300 gas limit
* imposed by `transfer`, making them unable to receive funds via
* `transfer`. {sendValue} removes this limitation.
*
* https://diligence.consensys.net/posts/2019/09/stop-using-soliditys-transfer-now/[Learn more].
*
* IMPORTANT: because control is transferred to `recipient`, care must be
* taken to not create reentrancy vulnerabilities. Consider using
* {ReentrancyGuard} or the
* https://solidity.readthedocs.io/en/v0.5.11/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
*/
function sendValue(address payable recipient, uint256 amount) internal {
require(address(this).balance >= amount, "Address: insufficient balance");
(bool success, ) = recipient.call{value: amount}("");
require(success, "Address: unable to send value, recipient may have reverted");
}
/**
* @dev Performs a Solidity function call using a low level `call`. A
* plain `call` is an unsafe replacement for a function call: use this
* function instead.
*
* If `target` reverts with a revert reason, it is bubbled up by this
* function (like regular Solidity function calls).
*
* Returns the raw returned data. To convert to the expected return value,
* use https://solidity.readthedocs.io/en/latest/units-and-global-variables.html?highlight=abi.decode#abi-encoding-and-decoding-functions[`abi.decode`].
*
* Requirements:
*
* - `target` must be a contract.
* - calling `target` with `data` must not revert.
*
* _Available since v3.1._
*/
function functionCall(address target, bytes memory data) internal returns (bytes memory) {
return functionCall(target, data, "Address: low-level call failed");
}
/**
* @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], but with
* `errorMessage` as a fallback revert reason when `target` reverts.
*
* _Available since v3.1._
*/
function functionCall(
address target,
bytes memory data,
string memory errorMessage
) internal returns (bytes memory) {
return functionCallWithValue(target, data, 0, errorMessage);
}
/**
* @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
* but also transferring `value` wei to `target`.
*
* Requirements:
*
* - the calling contract must have an ETH balance of at least `value`.
* - the called Solidity function must be `payable`.
*
* _Available since v3.1._
*/
function functionCallWithValue(
address target,
bytes memory data,
uint256 value
) internal returns (bytes memory) {
return functionCallWithValue(target, data, value, "Address: low-level call with value failed");
}
/**
* @dev Same as {xref-Address-functionCallWithValue-address-bytes-uint256-}[`functionCallWithValue`], but
* with `errorMessage` as a fallback revert reason when `target` reverts.
*
* _Available since v3.1._
*/
function functionCallWithValue(
address target,
bytes memory data,
uint256 value,
string memory errorMessage
) internal returns (bytes memory) {
require(address(this).balance >= value, "Address: insufficient balance for call");
require(isContract(target), "Address: call to non-contract");
(bool success, bytes memory returndata) = target.call{value: value}(data);
return verifyCallResult(success, returndata, errorMessage);
}
/**
* @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
* but performing a static call.
*
* _Available since v3.3._
*/
function functionStaticCall(address target, bytes memory data) internal view returns (bytes memory) {
return functionStaticCall(target, data, "Address: low-level static call failed");
}
/**
* @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
* but performing a static call.
*
* _Available since v3.3._
*/
function functionStaticCall(
address target,
bytes memory data,
string memory errorMessage
) internal view returns (bytes memory) {
require(isContract(target), "Address: static call to non-contract");
(bool success, bytes memory returndata) = target.staticcall(data);
return verifyCallResult(success, returndata, errorMessage);
}
/**
* @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
* but performing a delegate call.
*
* _Available since v3.4._
*/
function functionDelegateCall(address target, bytes memory data) internal returns (bytes memory) {
return functionDelegateCall(target, data, "Address: low-level delegate call failed");
}
/**
* @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
* but performing a delegate call.
*
* _Available since v3.4._
*/
function functionDelegateCall(
address target,
bytes memory data,
string memory errorMessage
) internal returns (bytes memory) {
require(isContract(target), "Address: delegate call to non-contract");
(bool success, bytes memory returndata) = target.delegatecall(data);
return verifyCallResult(success, returndata, errorMessage);
}
/**
* @dev Tool to verifies that a low level call was successful, and revert if it wasn't, either by bubbling the
* revert reason using the provided one.
*
* _Available since v4.3._
*/
function verifyCallResult(
bool success,
bytes memory returndata,
string memory errorMessage
) internal pure returns (bytes memory) {
if (success) {
return returndata;
} else {
// Look for revert reason and bubble it up if present
if (returndata.length > 0) {
// The easiest way to bubble the revert reason is using memory via assembly
assembly {
let returndata_size := mload(returndata)
revert(add(32, returndata), returndata_size)
}
} else {
revert(errorMessage);
}
}
}
}
// File: @openzeppelin/contracts/token/ERC721/IERC721Receiver.sol
pragma solidity ^0.8.0;
/**
* @title ERC721 token receiver interface
* @dev Interface for any contract that wants to support safeTransfers
* from ERC721 asset contracts.
*/
interface IERC721Receiver {
/**
* @dev Whenever an {IERC721} `tokenId` token is transferred to this contract via {IERC721-safeTransferFrom}
* by `operator` from `from`, this function is called.
*
* It must return its Solidity selector to confirm the token transfer.
* If any other value is returned or the interface is not implemented by the recipient, the transfer will be reverted.
*
* The selector can be obtained in Solidity with `IERC721.onERC721Received.selector`.
*/
function onERC721Received(
address operator,
address from,
uint256 tokenId,
bytes calldata data
) external returns (bytes4);
}
// File: @openzeppelin/contracts/utils/introspection/IERC165.sol
pragma solidity ^0.8.0;
/**
* @dev Interface of the ERC165 standard, as defined in the
* https://eips.ethereum.org/EIPS/eip-165[EIP].
*
* Implementers can declare support of contract interfaces, which can then be
* queried by others ({ERC165Checker}).
*
* For an implementation, see {ERC165}.
*/
interface IERC165 {
/**
* @dev Returns true if this contract implements the interface defined by
* `interfaceId`. See the corresponding
* https://eips.ethereum.org/EIPS/eip-165#how-interfaces-are-identified[EIP section]
* to learn more about how these ids are created.
*
* This function call must use less than 30 000 gas.
*/
function supportsInterface(bytes4 interfaceId) external view returns (bool);
}
// File: @openzeppelin/contracts/utils/introspection/ERC165.sol
pragma solidity ^0.8.0;
/**
* @dev Implementation of the {IERC165} interface.
*
* Contracts that want to implement ERC165 should inherit from this contract and override {supportsInterface} to check
* for the additional interface id that will be supported. For example:
*
* ```solidity
* function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
* return interfaceId == type(MyInterface).interfaceId || super.supportsInterface(interfaceId);
* }
* ```
*
* Alternatively, {ERC165Storage} provides an easier to use but more expensive implementation.
*/
abstract contract ERC165 is IERC165 {
/**
* @dev See {IERC165-supportsInterface}.
*/
function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
return interfaceId == type(IERC165).interfaceId;
}
}
// File: @openzeppelin/contracts/token/ERC721/IERC721.sol
pragma solidity ^0.8.0;
/**
* @dev Required interface of an ERC721 compliant contract.
*/
interface IERC721 is IERC165 {
/**
* @dev Emitted when `tokenId` token is transferred from `from` to `to`.
*/
event Transfer(address indexed from, address indexed to, uint256 indexed tokenId);
/**
* @dev Emitted when `owner` enables `approved` to manage the `tokenId` token.
*/
event Approval(address indexed owner, address indexed approved, uint256 indexed tokenId);
/**
* @dev Emitted when `owner` enables or disables (`approved`) `operator` to manage all of its assets.
*/
event ApprovalForAll(address indexed owner, address indexed operator, bool approved);
/**
* @dev Returns the number of tokens in ``owner``'s account.
*/
function balanceOf(address owner) external view returns (uint256 balance);
/**
* @dev Returns the owner of the `tokenId` token.
*
* Requirements:
*
* - `tokenId` must exist.
*/
function ownerOf(uint256 tokenId) external view returns (address owner);
/**
* @dev Safely transfers `tokenId` token from `from` to `to`, checking first that contract recipients
* are aware of the ERC721 protocol to prevent tokens from being forever locked.
*
* Requirements:
*
* - `from` cannot be the zero address.
* - `to` cannot be the zero address.
* - `tokenId` token must exist and be owned by `from`.
* - If the caller is not `from`, it must be have been allowed to move this token by either {approve} or {setApprovalForAll}.
* - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
*
* Emits a {Transfer} event.
*/
function safeTransferFrom(
address from,
address to,
uint256 tokenId
) external;
/**
* @dev Transfers `tokenId` token from `from` to `to`.
*
* WARNING: Usage of this method is discouraged, use {safeTransferFrom} whenever possible.
*
* Requirements:
*
* - `from` cannot be the zero address.
* - `to` cannot be the zero address.
* - `tokenId` token must be owned by `from`.
* - If the caller is not `from`, it must be approved to move this token by either {approve} or {setApprovalForAll}.
*
* Emits a {Transfer} event.
*/
function transferFrom(
address from,
address to,
uint256 tokenId
) external;
/**
* @dev Gives permission to `to` to transfer `tokenId` token to another account.
* The approval is cleared when the token is transferred.
*
* Only a single account can be approved at a time, so approving the zero address clears previous approvals.
*
* Requirements:
*
* - The caller must own the token or be an approved operator.
* - `tokenId` must exist.
*
* Emits an {Approval} event.
*/
function approve(address to, uint256 tokenId) external;
/**
* @dev Returns the account approved for `tokenId` token.
*
* Requirements:
*
* - `tokenId` must exist.
*/
function getApproved(uint256 tokenId) external view returns (address operator);
/**
* @dev Approve or remove `operator` as an operator for the caller.
* Operators can call {transferFrom} or {safeTransferFrom} for any token owned by the caller.
*
* Requirements:
*
* - The `operator` cannot be the caller.
*
* Emits an {ApprovalForAll} event.
*/
function setApprovalForAll(address operator, bool _approved) external;
/**
* @dev Returns if the `operator` is allowed to manage all of the assets of `owner`.
*
* See {setApprovalForAll}
*/
function isApprovedForAll(address owner, address operator) external view returns (bool);
/**
* @dev Safely transfers `tokenId` token from `from` to `to`.
*
* Requirements:
*
* - `from` cannot be the zero address.
* - `to` cannot be the zero address.
* - `tokenId` token must exist and be owned by `from`.
* - If the caller is not `from`, it must be approved to move this token by either {approve} or {setApprovalForAll}.
* - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
*
* Emits a {Transfer} event.
*/
function safeTransferFrom(
address from,
address to,
uint256 tokenId,
bytes calldata data
) external;
}
// File: @openzeppelin/contracts/token/ERC721/extensions/IERC721Enumerable.sol
pragma solidity ^0.8.0;
/**
* @title ERC-721 Non-Fungible Token Standard, optional enumeration extension
* @dev See https://eips.ethereum.org/EIPS/eip-721
*/
interface IERC721Enumerable is IERC721 {
/**
* @dev Returns the total amount of tokens stored by the contract.
*/
function totalSupply() external view returns (uint256);
/**
* @dev Returns a token ID owned by `owner` at a given `index` of its token list.
* Use along with {balanceOf} to enumerate all of ``owner``'s tokens.
*/
function tokenOfOwnerByIndex(address owner, uint256 index) external view returns (uint256 tokenId);
/**
* @dev Returns a token ID at a given `index` of all the tokens stored by the contract.
* Use along with {totalSupply} to enumerate all tokens.
*/
function tokenByIndex(uint256 index) external view returns (uint256);
}
// File: @openzeppelin/contracts/token/ERC721/extensions/IERC721Metadata.sol
pragma solidity ^0.8.0;
/**
* @title ERC-721 Non-Fungible Token Standard, optional metadata extension
* @dev See https://eips.ethereum.org/EIPS/eip-721
*/
interface IERC721Metadata is IERC721 {
/**
* @dev Returns the token collection name.
*/
function name() external view returns (string memory);
/**
* @dev Returns the token collection symbol.
*/
function symbol() external view returns (string memory);
/**
* @dev Returns the Uniform Resource Identifier (URI) for `tokenId` token.
*/
function tokenURI(uint256 tokenId) external view returns (string memory);
}
// File: @openzeppelin/contracts/token/ERC721/ERC721.sol
pragma solidity ^0.8.0;
/**
* @dev Implementation of https://eips.ethereum.org/EIPS/eip-721[ERC721] Non-Fungible Token Standard, including
* the Metadata extension, but not including the Enumerable extension, which is available separately as
* {ERC721Enumerable}.
*/
contract ERC721 is Context, ERC165, IERC721, IERC721Metadata {
using Address for address;
using Strings for uint256;
// Token name
string private _name;
// Token symbol
string private _symbol;
// Mapping from token ID to owner address
mapping(uint256 => address) private _owners;
// Mapping owner address to token count
mapping(address => uint256) private _balances;
// Mapping from token ID to approved address
mapping(uint256 => address) private _tokenApprovals;
// Mapping from owner to operator approvals
mapping(address => mapping(address => bool)) private _operatorApprovals;
/**
* @dev Initializes the contract by setting a `name` and a `symbol` to the token collection.
*/
constructor(string memory name_, string memory symbol_) {
_name = name_;
_symbol = symbol_;
}
/**
* @dev See {IERC165-supportsInterface}.
*/
function supportsInterface(bytes4 interfaceId) public view virtual override(ERC165, IERC165) returns (bool) {
return
interfaceId == type(IERC721).interfaceId ||
interfaceId == type(IERC721Metadata).interfaceId ||
super.supportsInterface(interfaceId);
}
/**
* @dev See {IERC721-balanceOf}.
*/
function balanceOf(address owner) public view virtual override returns (uint256) {
require(owner != address(0), "ERC721: balance query for the zero address");
return _balances[owner];
}
/**
* @dev See {IERC721-ownerOf}.
*/
function ownerOf(uint256 tokenId) public view virtual override returns (address) {
address owner = _owners[tokenId];
require(owner != address(0), "ERC721: owner query for nonexistent token");
return owner;
}
/**
* @dev See {IERC721Metadata-name}.
*/
function name() public view virtual override returns (string memory) {
return _name;
}
/**
* @dev See {IERC721Metadata-symbol}.
*/
function symbol() public view virtual override returns (string memory) {
return _symbol;
}
/**
* @dev See {IERC721Metadata-tokenURI}.
*/
function tokenURI(uint256 tokenId) public view virtual override returns (string memory) {
require(_exists(tokenId), "ERC721Metadata: URI query for nonexistent token");
string memory baseURI = _baseURI();
return bytes(baseURI).length > 0 ? string(abi.encodePacked(baseURI, tokenId.toString())) : "";
}
/**
* @dev Base URI for computing {tokenURI}. If set, the resulting URI for each
* token will be the concatenation of the `baseURI` and the `tokenId`. Empty
* by default, can be overriden in child contracts.
*/
function _baseURI() internal view virtual returns (string memory) {
return "";
}
/**
* @dev See {IERC721-approve}.
*/
function approve(address to, uint256 tokenId) public virtual override {
address owner = ERC721.ownerOf(tokenId);
require(to != owner, "ERC721: approval to current owner");
require(
_msgSender() == owner || isApprovedForAll(owner, _msgSender()),
"ERC721: approve caller is not owner nor approved for all"
);
_approve(to, tokenId);
}
/**
* @dev See {IERC721-getApproved}.
*/
function getApproved(uint256 tokenId) public view virtual override returns (address) {
require(_exists(tokenId), "ERC721: approved query for nonexistent token");
return _tokenApprovals[tokenId];
}
/**
* @dev See {IERC721-setApprovalForAll}.
*/
function setApprovalForAll(address operator, bool approved) public virtual override {
require(operator != _msgSender(), "ERC721: approve to caller");
_operatorApprovals[_msgSender()][operator] = approved;
emit ApprovalForAll(_msgSender(), operator, approved);
}
/**
* @dev See {IERC721-isApprovedForAll}.
*/
function isApprovedForAll(address owner, address operator) public view virtual override returns (bool) {
return _operatorApprovals[owner][operator];
}
/**
* @dev See {IERC721-transferFrom}.
*/
function transferFrom(
address from,
address to,
uint256 tokenId
) public virtual override {
//solhint-disable-next-line max-line-length
require(_isApprovedOrOwner(_msgSender(), tokenId), "ERC721: transfer caller is not owner nor approved");
_transfer(from, to, tokenId);
}
/**
* @dev See {IERC721-safeTransferFrom}.
*/
function safeTransferFrom(
address from,
address to,
uint256 tokenId
) public virtual override {
safeTransferFrom(from, to, tokenId, "");
}
/**
* @dev See {IERC721-safeTransferFrom}.
*/
function safeTransferFrom(
address from,
address to,
uint256 tokenId,
bytes memory _data
) public virtual override {
require(_isApprovedOrOwner(_msgSender(), tokenId), "ERC721: transfer caller is not owner nor approved");
_safeTransfer(from, to, tokenId, _data);
}
/**
* @dev Safely transfers `tokenId` token from `from` to `to`, checking first that contract recipients
* are aware of the ERC721 protocol to prevent tokens from being forever locked.
*
* `_data` is additional data, it has no specified format and it is sent in call to `to`.
*
* This internal function is equivalent to {safeTransferFrom}, and can be used to e.g.
* implement alternative mechanisms to perform token transfer, such as signature-based.
*
* Requirements:
*
* - `from` cannot be the zero address.
* - `to` cannot be the zero address.
* - `tokenId` token must exist and be owned by `from`.
* - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
*
* Emits a {Transfer} event.
*/
function _safeTransfer(
address from,
address to,
uint256 tokenId,
bytes memory _data
) internal virtual {
_transfer(from, to, tokenId);
require(_checkOnERC721Received(from, to, tokenId, _data), "ERC721: transfer to non ERC721Receiver implementer");
}
/**
* @dev Returns whether `tokenId` exists.
*
* Tokens can be managed by their owner or approved accounts via {approve} or {setApprovalForAll}.
*
* Tokens start existing when they are minted (`_mint`),
* and stop existing when they are burned (`_burn`).
*/
function _exists(uint256 tokenId) internal view virtual returns (bool) {
return _owners[tokenId] != address(0);
}
/**
* @dev Returns whether `spender` is allowed to manage `tokenId`.
*
* Requirements:
*
* - `tokenId` must exist.
*/
function _isApprovedOrOwner(address spender, uint256 tokenId) internal view virtual returns (bool) {
require(_exists(tokenId), "ERC721: operator query for nonexistent token");
address owner = ERC721.ownerOf(tokenId);
return (spender == owner || getApproved(tokenId) == spender || isApprovedForAll(owner, spender));
}
/**
* @dev Safely mints `tokenId` and transfers it to `to`.
*
* Requirements:
*
* - `tokenId` must not exist.
* - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
*
* Emits a {Transfer} event.
*/
function _safeMint(address to, uint256 tokenId) internal virtual {
_safeMint(to, tokenId, "");
}
/**
* @dev Same as {xref-ERC721-_safeMint-address-uint256-}[`_safeMint`], with an additional `data` parameter which is
* forwarded in {IERC721Receiver-onERC721Received} to contract recipients.
*/
function _safeMint(
address to,
uint256 tokenId,
bytes memory _data
) internal virtual {
_mint(to, tokenId);
require(
_checkOnERC721Received(address(0), to, tokenId, _data),
"ERC721: transfer to non ERC721Receiver implementer"
);
}
/**
* @dev Mints `tokenId` and transfers it to `to`.
*
* WARNING: Usage of this method is discouraged, use {_safeMint} whenever possible
*
* Requirements:
*
* - `tokenId` must not exist.
* - `to` cannot be the zero address.
*
* Emits a {Transfer} event.
*/
function _mint(address to, uint256 tokenId) internal virtual {
require(to != address(0), "ERC721: mint to the zero address");
require(!_exists(tokenId), "ERC721: token already minted");
_beforeTokenTransfer(address(0), to, tokenId);
_balances[to] += 1;
_owners[tokenId] = to;
emit Transfer(address(0), to, tokenId);
}
/**
* @dev Destroys `tokenId`.
* The approval is cleared when the token is burned.
*
* Requirements:
*
* - `tokenId` must exist.
*
* Emits a {Transfer} event.
*/
function _burn(uint256 tokenId) internal virtual {
address owner = ERC721.ownerOf(tokenId);
_beforeTokenTransfer(owner, address(0), tokenId);
// Clear approvals
_approve(address(0), tokenId);
_balances[owner] -= 1;
delete _owners[tokenId];
emit Transfer(owner, address(0), tokenId);
}
/**
* @dev Transfers `tokenId` from `from` to `to`.
* As opposed to {transferFrom}, this imposes no restrictions on msg.sender.
*
* Requirements:
*
* - `to` cannot be the zero address.
* - `tokenId` token must be owned by `from`.
*
* Emits a {Transfer} event.
*/
function _transfer(
address from,
address to,
uint256 tokenId
) internal virtual {
require(ERC721.ownerOf(tokenId) == from, "ERC721: transfer of token that is not own");
require(to != address(0), "ERC721: transfer to the zero address");
_beforeTokenTransfer(from, to, tokenId);
// Clear approvals from the previous owner
_approve(address(0), tokenId);
_balances[from] -= 1;
_balances[to] += 1;
_owners[tokenId] = to;
emit Transfer(from, to, tokenId);
}
/**
* @dev Approve `to` to operate on `tokenId`
*
* Emits a {Approval} event.
*/
function _approve(address to, uint256 tokenId) internal virtual {
_tokenApprovals[tokenId] = to;
emit Approval(ERC721.ownerOf(tokenId), to, tokenId);
}
/**
* @dev Internal function to invoke {IERC721Receiver-onERC721Received} on a target address.
* The call is not executed if the target address is not a contract.
*
* @param from address representing the previous owner of the given token ID
* @param to target address that will receive the tokens
* @param tokenId uint256 ID of the token to be transferred
* @param _data bytes optional data to send along with the call
* @return bool whether the call correctly returned the expected magic value
*/
function _checkOnERC721Received(
address from,
address to,
uint256 tokenId,
bytes memory _data
) private returns (bool) {
if (to.isContract()) {
try IERC721Receiver(to).onERC721Received(_msgSender(), from, tokenId, _data) returns (bytes4 retval) {
return retval == IERC721Receiver.onERC721Received.selector;
} catch (bytes memory reason) {
if (reason.length == 0) {
revert("ERC721: transfer to non ERC721Receiver implementer");
} else {
assembly {
revert(add(32, reason), mload(reason))
}
}
}
} else {
return true;
}
}
/**
* @dev Hook that is called before any token transfer. This includes minting
* and burning.
*
* Calling conditions:
*
* - When `from` and `to` are both non-zero, ``from``'s `tokenId` will be
* transferred to `to`.
* - When `from` is zero, `tokenId` will be minted for `to`.
* - When `to` is zero, ``from``'s `tokenId` will be burned.
* - `from` and `to` are never both zero.
*
* To learn more about hooks, head to xref:ROOT:extending-contracts.adoc#using-hooks[Using Hooks].
*/
function _beforeTokenTransfer(
address from,
address to,
uint256 tokenId
) internal virtual {}
}
// File: @openzeppelin/contracts/token/ERC721/extensions/ERC721Enumerable.sol
pragma solidity ^0.8.0;
/**
* @dev This implements an optional extension of {ERC721} defined in the EIP that adds
* enumerability of all the token ids in the contract as well as all token ids owned by each
* account.
*/
abstract contract ERC721Enumerable is ERC721, IERC721Enumerable {
// Mapping from owner to list of owned token IDs
mapping(address => mapping(uint256 => uint256)) private _ownedTokens;
// Mapping from token ID to index of the owner tokens list
mapping(uint256 => uint256) private _ownedTokensIndex;
// Array with all token ids, used for enumeration
uint256[] private _allTokens;
// Mapping from token id to position in the allTokens array
mapping(uint256 => uint256) private _allTokensIndex;
/**
* @dev See {IERC165-supportsInterface}.
*/
function supportsInterface(bytes4 interfaceId) public view virtual override(IERC165, ERC721) returns (bool) {
return interfaceId == type(IERC721Enumerable).interfaceId || super.supportsInterface(interfaceId);
}
/**
* @dev See {IERC721Enumerable-tokenOfOwnerByIndex}.
*/
function tokenOfOwnerByIndex(address owner, uint256 index) public view virtual override returns (uint256) {
require(index < ERC721.balanceOf(owner), "ERC721Enumerable: owner index out of bounds");
return _ownedTokens[owner][index];
}
/**
* @dev See {IERC721Enumerable-totalSupply}.
*/
function totalSupply() public view virtual override returns (uint256) {
return _allTokens.length;
}
/**
* @dev See {IERC721Enumerable-tokenByIndex}.
*/
function tokenByIndex(uint256 index) public view virtual override returns (uint256) {
require(index < ERC721Enumerable.totalSupply(), "ERC721Enumerable: global index out of bounds");
return _allTokens[index];
}
/**
* @dev Hook that is called before any token transfer. This includes minting
* and burning.
*
* Calling conditions:
*
* - When `from` and `to` are both non-zero, ``from``'s `tokenId` will be
* transferred to `to`.
* - When `from` is zero, `tokenId` will be minted for `to`.
* - When `to` is zero, ``from``'s `tokenId` will be burned.
* - `from` cannot be the zero address.
* - `to` cannot be the zero address.
*
* To learn more about hooks, head to xref:ROOT:extending-contracts.adoc#using-hooks[Using Hooks].
*/
function _beforeTokenTransfer(
address from,
address to,
uint256 tokenId
) internal virtual override {
super._beforeTokenTransfer(from, to, tokenId);
if (from == address(0)) {
_addTokenToAllTokensEnumeration(tokenId);
} else if (from != to) {
_removeTokenFromOwnerEnumeration(from, tokenId);
}
if (to == address(0)) {
_removeTokenFromAllTokensEnumeration(tokenId);
} else if (to != from) {
_addTokenToOwnerEnumeration(to, tokenId);
}
}
/**
* @dev Private function to add a token to this extension's ownership-tracking data structures.
* @param to address representing the new owner of the given token ID
* @param tokenId uint256 ID of the token to be added to the tokens list of the given address
*/
function _addTokenToOwnerEnumeration(address to, uint256 tokenId) private {
uint256 length = ERC721.balanceOf(to);
_ownedTokens[to][length] = tokenId;
_ownedTokensIndex[tokenId] = length;
}
/**
* @dev Private function to add a token to this extension's token tracking data structures.
* @param tokenId uint256 ID of the token to be added to the tokens list
*/
function _addTokenToAllTokensEnumeration(uint256 tokenId) private {
_allTokensIndex[tokenId] = _allTokens.length;
_allTokens.push(tokenId);
}
/**
* @dev Private function to remove a token from this extension's ownership-tracking data structures. Note that
* while the token is not assigned a new owner, the `_ownedTokensIndex` mapping is _not_ updated: this allows for
* gas optimizations e.g. when performing a transfer operation (avoiding double writes).
* This has O(1) time complexity, but alters the order of the _ownedTokens array.
* @param from address representing the previous owner of the given token ID
* @param tokenId uint256 ID of the token to be removed from the tokens list of the given address
*/
function _removeTokenFromOwnerEnumeration(address from, uint256 tokenId) private {
// To prevent a gap in from's tokens array, we store the last token in the index of the token to delete, and
// then delete the last slot (swap and pop).
uint256 lastTokenIndex = ERC721.balanceOf(from) - 1;
uint256 tokenIndex = _ownedTokensIndex[tokenId];
// When the token to delete is the last token, the swap operation is unnecessary
if (tokenIndex != lastTokenIndex) {
uint256 lastTokenId = _ownedTokens[from][lastTokenIndex];
_ownedTokens[from][tokenIndex] = lastTokenId; // Move the last token to the slot of the to-delete token
_ownedTokensIndex[lastTokenId] = tokenIndex; // Update the moved token's index
}
// This also deletes the contents at the last position of the array
delete _ownedTokensIndex[tokenId];
delete _ownedTokens[from][lastTokenIndex];
}
/**
* @dev Private function to remove a token from this extension's token tracking data structures.
* This has O(1) time complexity, but alters the order of the _allTokens array.
* @param tokenId uint256 ID of the token to be removed from the tokens list
*/
function _removeTokenFromAllTokensEnumeration(uint256 tokenId) private {
// To prevent a gap in the tokens array, we store the last token in the index of the token to delete, and
// then delete the last slot (swap and pop).
uint256 lastTokenIndex = _allTokens.length - 1;
uint256 tokenIndex = _allTokensIndex[tokenId];
// When the token to delete is the last token, the swap operation is unnecessary. However, since this occurs so
// rarely (when the last minted token is burnt) that we still do the swap here to avoid the gas cost of adding
// an 'if' statement (like in _removeTokenFromOwnerEnumeration)
uint256 lastTokenId = _allTokens[lastTokenIndex];
_allTokens[tokenIndex] = lastTokenId; // Move the last token to the slot of the to-delete token
_allTokensIndex[lastTokenId] = tokenIndex; // Update the moved token's index
// This also deletes the contents at the last position of the array
delete _allTokensIndex[tokenId];
_allTokens.pop();
}
}
// File: prb-math/contracts/PRBMath.sol
pragma solidity >=0.8.4;
/// @notice Emitted when the result overflows uint256.
error PRBMath__MulDivFixedPointOverflow(uint256 prod1);
/// @notice Emitted when the result overflows uint256.
error PRBMath__MulDivOverflow(uint256 prod1, uint256 denominator);
/// @notice Emitted when one of the inputs is type(int256).min.
error PRBMath__MulDivSignedInputTooSmall();
/// @notice Emitted when the intermediary absolute result overflows int256.
error PRBMath__MulDivSignedOverflow(uint256 rAbs);
/// @notice Emitted when the input is MIN_SD59x18.
error PRBMathSD59x18__AbsInputTooSmall();
/// @notice Emitted when ceiling a number overflows SD59x18.
error PRBMathSD59x18__CeilOverflow(int256 x);
/// @notice Emitted when one of the inputs is MIN_SD59x18.
error PRBMathSD59x18__DivInputTooSmall();
/// @notice Emitted when one of the intermediary unsigned results overflows SD59x18.
error PRBMathSD59x18__DivOverflow(uint256 rAbs);
/// @notice Emitted when the input is greater than 133.084258667509499441.
error PRBMathSD59x18__ExpInputTooBig(int256 x);
/// @notice Emitted when the input is greater than 192.
error PRBMathSD59x18__Exp2InputTooBig(int256 x);
/// @notice Emitted when flooring a number underflows SD59x18.
error PRBMathSD59x18__FloorUnderflow(int256 x);
/// @notice Emitted when converting a basic integer to the fixed-point format overflows SD59x18.
error PRBMathSD59x18__FromIntOverflow(int256 x);
/// @notice Emitted when converting a basic integer to the fixed-point format underflows SD59x18.
error PRBMathSD59x18__FromIntUnderflow(int256 x);
/// @notice Emitted when the product of the inputs is negative.
error PRBMathSD59x18__GmNegativeProduct(int256 x, int256 y);
/// @notice Emitted when multiplying the inputs overflows SD59x18.
error PRBMathSD59x18__GmOverflow(int256 x, int256 y);
/// @notice Emitted when the input is less than or equal to zero.
error PRBMathSD59x18__LogInputTooSmall(int256 x);
/// @notice Emitted when one of the inputs is MIN_SD59x18.
error PRBMathSD59x18__MulInputTooSmall();
/// @notice Emitted when the intermediary absolute result overflows SD59x18.
error PRBMathSD59x18__MulOverflow(uint256 rAbs);
/// @notice Emitted when the intermediary absolute result overflows SD59x18.
error PRBMathSD59x18__PowuOverflow(uint256 rAbs);
/// @notice Emitted when the input is negative.
error PRBMathSD59x18__SqrtNegativeInput(int256 x);
/// @notice Emitted when the calculating the square root overflows SD59x18.
error PRBMathSD59x18__SqrtOverflow(int256 x);
/// @notice Emitted when addition overflows UD60x18.
error PRBMathUD60x18__AddOverflow(uint256 x, uint256 y);
/// @notice Emitted when ceiling a number overflows UD60x18.
error PRBMathUD60x18__CeilOverflow(uint256 x);
/// @notice Emitted when the input is greater than 133.084258667509499441.
error PRBMathUD60x18__ExpInputTooBig(uint256 x);
/// @notice Emitted when the input is greater than 192.
error PRBMathUD60x18__Exp2InputTooBig(uint256 x);
/// @notice Emitted when converting a basic integer to the fixed-point format format overflows UD60x18.
error PRBMathUD60x18__FromUintOverflow(uint256 x);
/// @notice Emitted when multiplying the inputs overflows UD60x18.
error PRBMathUD60x18__GmOverflow(uint256 x, uint256 y);
/// @notice Emitted when the input is less than 1.
error PRBMathUD60x18__LogInputTooSmall(uint256 x);
/// @notice Emitted when the calculating the square root overflows UD60x18.
error PRBMathUD60x18__SqrtOverflow(uint256 x);
/// @notice Emitted when subtraction underflows UD60x18.
error PRBMathUD60x18__SubUnderflow(uint256 x, uint256 y);
/// @dev Common mathematical functions used in both PRBMathSD59x18 and PRBMathUD60x18. Note that this shared library
/// does not always assume the signed 59.18-decimal fixed-point or the unsigned 60.18-decimal fixed-point
/// representation. When it does not, it is explicitly mentioned in the NatSpec documentation.
library PRBMath {
/// STRUCTS ///
struct SD59x18 {
int256 value;
}
struct UD60x18 {
uint256 value;
}
/// STORAGE ///
/// @dev How many trailing decimals can be represented.
uint256 internal constant SCALE = 1e18;
/// @dev Largest power of two divisor of SCALE.
uint256 internal constant SCALE_LPOTD = 262144;
/// @dev SCALE inverted mod 2^256.
uint256 internal constant SCALE_INVERSE = 78156646155174841979727994598816262306175212592076161876661508869554232690281;
/// FUNCTIONS ///
/// @notice Calculates the binary exponent of x using the binary fraction method.
/// @dev Has to use 192.64-bit fixed-point numbers.
/// See https://ethereum.stackexchange.com/a/96594/24693.
/// @param x The exponent as an unsigned 192.64-bit fixed-point number.
/// @return result The result as an unsigned 60.18-decimal fixed-point number.
function exp2(uint256 x) internal pure returns (uint256 result) {
unchecked {
// Start from 0.5 in the 192.64-bit fixed-point format.
result = 0x800000000000000000000000000000000000000000000000;
// Multiply the result by root(2, 2^-i) when the bit at position i is 1. None of the intermediary results overflows
// because the initial result is 2^191 and all magic factors are less than 2^65.
if (x & 0x8000000000000000 > 0) {
result = (result * 0x16A09E667F3BCC909) >> 64;
}
if (x & 0x4000000000000000 > 0) {
result = (result * 0x1306FE0A31B7152DF) >> 64;
}
if (x & 0x2000000000000000 > 0) {
result = (result * 0x1172B83C7D517ADCE) >> 64;
}
if (x & 0x1000000000000000 > 0) {
result = (result * 0x10B5586CF9890F62A) >> 64;
}
if (x & 0x800000000000000 > 0) {
result = (result * 0x1059B0D31585743AE) >> 64;
}
if (x & 0x400000000000000 > 0) {
result = (result * 0x102C9A3E778060EE7) >> 64;
}
if (x & 0x200000000000000 > 0) {
result = (result * 0x10163DA9FB33356D8) >> 64;
}
if (x & 0x100000000000000 > 0) {
result = (result * 0x100B1AFA5ABCBED61) >> 64;
}
if (x & 0x80000000000000 > 0) {
result = (result * 0x10058C86DA1C09EA2) >> 64;
}
if (x & 0x40000000000000 > 0) {
result = (result * 0x1002C605E2E8CEC50) >> 64;
}
if (x & 0x20000000000000 > 0) {
result = (result * 0x100162F3904051FA1) >> 64;
}
if (x & 0x10000000000000 > 0) {
result = (result * 0x1000B175EFFDC76BA) >> 64;
}
if (x & 0x8000000000000 > 0) {
result = (result * 0x100058BA01FB9F96D) >> 64;
}
if (x & 0x4000000000000 > 0) {
result = (result * 0x10002C5CC37DA9492) >> 64;
}
if (x & 0x2000000000000 > 0) {
result = (result * 0x1000162E525EE0547) >> 64;
}
if (x & 0x1000000000000 > 0) {
result = (result * 0x10000B17255775C04) >> 64;
}
if (x & 0x800000000000 > 0) {
result = (result * 0x1000058B91B5BC9AE) >> 64;
}
if (x & 0x400000000000 > 0) {
result = (result * 0x100002C5C89D5EC6D) >> 64;
}
if (x & 0x200000000000 > 0) {
result = (result * 0x10000162E43F4F831) >> 64;
}
if (x & 0x100000000000 > 0) {
result = (result * 0x100000B1721BCFC9A) >> 64;
}
if (x & 0x80000000000 > 0) {
result = (result * 0x10000058B90CF1E6E) >> 64;
}
if (x & 0x40000000000 > 0) {
result = (result * 0x1000002C5C863B73F) >> 64;
}
if (x & 0x20000000000 > 0) {
result = (result * 0x100000162E430E5A2) >> 64;
}
if (x & 0x10000000000 > 0) {
result = (result * 0x1000000B172183551) >> 64;
}
if (x & 0x8000000000 > 0) {
result = (result * 0x100000058B90C0B49) >> 64;
}
if (x & 0x4000000000 > 0) {
result = (result * 0x10000002C5C8601CC) >> 64;
}
if (x & 0x2000000000 > 0) {
result = (result * 0x1000000162E42FFF0) >> 64;
}
if (x & 0x1000000000 > 0) {
result = (result * 0x10000000B17217FBB) >> 64;
}
if (x & 0x800000000 > 0) {
result = (result * 0x1000000058B90BFCE) >> 64;
}
if (x & 0x400000000 > 0) {
result = (result * 0x100000002C5C85FE3) >> 64;
}
if (x & 0x200000000 > 0) {
result = (result * 0x10000000162E42FF1) >> 64;
}
if (x & 0x100000000 > 0) {
result = (result * 0x100000000B17217F8) >> 64;
}
if (x & 0x80000000 > 0) {
result = (result * 0x10000000058B90BFC) >> 64;
}
if (x & 0x40000000 > 0) {
result = (result * 0x1000000002C5C85FE) >> 64;
}
if (x & 0x20000000 > 0) {
result = (result * 0x100000000162E42FF) >> 64;
}
if (x & 0x10000000 > 0) {
result = (result * 0x1000000000B17217F) >> 64;
}
if (x & 0x8000000 > 0) {
result = (result * 0x100000000058B90C0) >> 64;
}
if (x & 0x4000000 > 0) {
result = (result * 0x10000000002C5C860) >> 64;
}
if (x & 0x2000000 > 0) {
result = (result * 0x1000000000162E430) >> 64;
}
if (x & 0x1000000 > 0) {
result = (result * 0x10000000000B17218) >> 64;
}
if (x & 0x800000 > 0) {
result = (result * 0x1000000000058B90C) >> 64;
}
if (x & 0x400000 > 0) {
result = (result * 0x100000000002C5C86) >> 64;
}
if (x & 0x200000 > 0) {
result = (result * 0x10000000000162E43) >> 64;
}
if (x & 0x100000 > 0) {
result = (result * 0x100000000000B1721) >> 64;
}
if (x & 0x80000 > 0) {
result = (result * 0x10000000000058B91) >> 64;
}
if (x & 0x40000 > 0) {
result = (result * 0x1000000000002C5C8) >> 64;
}
if (x & 0x20000 > 0) {
result = (result * 0x100000000000162E4) >> 64;
}
if (x & 0x10000 > 0) {
result = (result * 0x1000000000000B172) >> 64;
}
if (x & 0x8000 > 0) {
result = (result * 0x100000000000058B9) >> 64;
}
if (x & 0x4000 > 0) {
result = (result * 0x10000000000002C5D) >> 64;
}
if (x & 0x2000 > 0) {
result = (result * 0x1000000000000162E) >> 64;
}
if (x & 0x1000 > 0) {
result = (result * 0x10000000000000B17) >> 64;
}
if (x & 0x800 > 0) {
result = (result * 0x1000000000000058C) >> 64;
}
if (x & 0x400 > 0) {
result = (result * 0x100000000000002C6) >> 64;
}
if (x & 0x200 > 0) {
result = (result * 0x10000000000000163) >> 64;
}
if (x & 0x100 > 0) {
result = (result * 0x100000000000000B1) >> 64;
}
if (x & 0x80 > 0) {
result = (result * 0x10000000000000059) >> 64;
}
if (x & 0x40 > 0) {
result = (result * 0x1000000000000002C) >> 64;
}
if (x & 0x20 > 0) {
result = (result * 0x10000000000000016) >> 64;
}
if (x & 0x10 > 0) {
result = (result * 0x1000000000000000B) >> 64;
}
if (x & 0x8 > 0) {
result = (result * 0x10000000000000006) >> 64;
}
if (x & 0x4 > 0) {
result = (result * 0x10000000000000003) >> 64;
}
if (x & 0x2 > 0) {
result = (result * 0x10000000000000001) >> 64;
}
if (x & 0x1 > 0) {
result = (result * 0x10000000000000001) >> 64;
}
// We're doing two things at the same time:
//
// 1. Multiply the result by 2^n + 1, where "2^n" is the integer part and the one is added to account for
// the fact that we initially set the result to 0.5. This is accomplished by subtracting from 191
// rather than 192.
// 2. Convert the result to the unsigned 60.18-decimal fixed-point format.
//
// This works because 2^(191-ip) = 2^ip / 2^191, where "ip" is the integer part "2^n".
result *= SCALE;
result >>= (191 - (x >> 64));
}
}
/// @notice Finds the zero-based index of the first one in the binary representation of x.
/// @dev See the note on msb in the "Find First Set" Wikipedia article https://en.wikipedia.org/wiki/Find_first_set
/// @param x The uint256 number for which to find the index of the most significant bit.
/// @return msb The index of the most significant bit as an uint256.
function mostSignificantBit(uint256 x) internal pure returns (uint256 msb) {
if (x >= 2**128) {
x >>= 128;
msb += 128;
}
if (x >= 2**64) {
x >>= 64;
msb += 64;
}
if (x >= 2**32) {
x >>= 32;
msb += 32;
}
if (x >= 2**16) {
x >>= 16;
msb += 16;
}
if (x >= 2**8) {
x >>= 8;
msb += 8;
}
if (x >= 2**4) {
x >>= 4;
msb += 4;
}
if (x >= 2**2) {
x >>= 2;
msb += 2;
}
if (x >= 2**1) {
// No need to shift x any more.
msb += 1;
}
}
/// @notice Calculates floor(x*y÷denominator) with full precision.
///
/// @dev Credit to Remco Bloemen under MIT license https://xn--2-umb.com/21/muldiv.
///
/// Requirements:
/// - The denominator cannot be zero.
/// - The result must fit within uint256.
///
/// Caveats:
/// - This function does not work with fixed-point numbers.
///
/// @param x The multiplicand as an uint256.
/// @param y The multiplier as an uint256.
/// @param denominator The divisor as an uint256.
/// @return result The result as an uint256.
function mulDiv(
uint256 x,
uint256 y,
uint256 denominator
) internal pure returns (uint256 result) {
// 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use
// use the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
// variables such that product = prod1 * 2^256 + prod0.
uint256 prod0; // Least significant 256 bits of the product
uint256 prod1; // Most significant 256 bits of the product
assembly {
let mm := mulmod(x, y, not(0))
prod0 := mul(x, y)
prod1 := sub(sub(mm, prod0), lt(mm, prod0))
}
// Handle non-overflow cases, 256 by 256 division.
if (prod1 == 0) {
unchecked {
result = prod0 / denominator;
}
return result;
}
// Make sure the result is less than 2^256. Also prevents denominator == 0.
if (prod1 >= denominator) {
revert PRBMath__MulDivOverflow(prod1, denominator);
}
///////////////////////////////////////////////
// 512 by 256 division.
///////////////////////////////////////////////
// Make division exact by subtracting the remainder from [prod1 prod0].
uint256 remainder;
assembly {
// Compute remainder using mulmod.
remainder := mulmod(x, y, denominator)
// Subtract 256 bit number from 512 bit number.
prod1 := sub(prod1, gt(remainder, prod0))
prod0 := sub(prod0, remainder)
}
// Factor powers of two out of denominator and compute largest power of two divisor of denominator. Always >= 1.
// See https://cs.stackexchange.com/q/138556/92363.
unchecked {
// Does not overflow because the denominator cannot be zero at this stage in the function.
uint256 lpotdod = denominator & (~denominator + 1);
assembly {
// Divide denominator by lpotdod.
denominator := div(denominator, lpotdod)
// Divide [prod1 prod0] by lpotdod.
prod0 := div(prod0, lpotdod)
// Flip lpotdod such that it is 2^256 / lpotdod. If lpotdod is zero, then it becomes one.
lpotdod := add(div(sub(0, lpotdod), lpotdod), 1)
}
// Shift in bits from prod1 into prod0.
prod0 |= prod1 * lpotdod;
// Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such
// that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for
// four bits. That is, denominator * inv = 1 mod 2^4.
uint256 inverse = (3 * denominator) ^ 2;
// Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also works
// in modular arithmetic, doubling the correct bits in each step.
inverse *= 2 - denominator * inverse; // inverse mod 2^8
inverse *= 2 - denominator * inverse; // inverse mod 2^16
inverse *= 2 - denominator * inverse; // inverse mod 2^32
inverse *= 2 - denominator * inverse; // inverse mod 2^64
inverse *= 2 - denominator * inverse; // inverse mod 2^128
inverse *= 2 - denominator * inverse; // inverse mod 2^256
// Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
// This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is
// less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1
// is no longer required.
result = prod0 * inverse;
return result;
}
}
/// @notice Calculates floor(x*y÷1e18) with full precision.
///
/// @dev Variant of "mulDiv" with constant folding, i.e. in which the denominator is always 1e18. Before returning the
/// final result, we add 1 if (x * y) % SCALE >= HALF_SCALE. Without this, 6.6e-19 would be truncated to 0 instead of
/// being rounded to 1e-18. See "Listing 6" and text above it at https://accu.org/index.php/journals/1717.
///
/// Requirements:
/// - The result must fit within uint256.
///
/// Caveats:
/// - The body is purposely left uncommented; see the NatSpec comments in "PRBMath.mulDiv" to understand how this works.
/// - It is assumed that the result can never be type(uint256).max when x and y solve the following two equations:
/// 1. x * y = type(uint256).max * SCALE
/// 2. (x * y) % SCALE >= SCALE / 2
///
/// @param x The multiplicand as an unsigned 60.18-decimal fixed-point number.
/// @param y The multiplier as an unsigned 60.18-decimal fixed-point number.
/// @return result The result as an unsigned 60.18-decimal fixed-point number.
function mulDivFixedPoint(uint256 x, uint256 y) internal pure returns (uint256 result) {
uint256 prod0;
uint256 prod1;
assembly {
let mm := mulmod(x, y, not(0))
prod0 := mul(x, y)
prod1 := sub(sub(mm, prod0), lt(mm, prod0))
}
if (prod1 >= SCALE) {
revert PRBMath__MulDivFixedPointOverflow(prod1);
}
uint256 remainder;
uint256 roundUpUnit;
assembly {
remainder := mulmod(x, y, SCALE)
roundUpUnit := gt(remainder, 499999999999999999)
}
if (prod1 == 0) {
unchecked {
result = (prod0 / SCALE) + roundUpUnit;
return result;
}
}
assembly {
result := add(
mul(
or(
div(sub(prod0, remainder), SCALE_LPOTD),
mul(sub(prod1, gt(remainder, prod0)), add(div(sub(0, SCALE_LPOTD), SCALE_LPOTD), 1))
),
SCALE_INVERSE
),
roundUpUnit
)
}
}
/// @notice Calculates floor(x*y÷denominator) with full precision.
///
/// @dev An extension of "mulDiv" for signed numbers. Works by computing the signs and the absolute values separately.
///
/// Requirements:
/// - None of the inputs can be type(int256).min.
/// - The result must fit within int256.
///
/// @param x The multiplicand as an int256.
/// @param y The multiplier as an int256.
/// @param denominator The divisor as an int256.
/// @return result The result as an int256.
function mulDivSigned(
int256 x,
int256 y,
int256 denominator
) internal pure returns (int256 result) {
if (x == type(int256).min || y == type(int256).min || denominator == type(int256).min) {
revert PRBMath__MulDivSignedInputTooSmall();
}
// Get hold of the absolute values of x, y and the denominator.
uint256 ax;
uint256 ay;
uint256 ad;
unchecked {
ax = x < 0 ? uint256(-x) : uint256(x);
ay = y < 0 ? uint256(-y) : uint256(y);
ad = denominator < 0 ? uint256(-denominator) : uint256(denominator);
}
// Compute the absolute value of (x*y)÷denominator. The result must fit within int256.
uint256 rAbs = mulDiv(ax, ay, ad);
if (rAbs > uint256(type(int256).max)) {
revert PRBMath__MulDivSignedOverflow(rAbs);
}
// Get the signs of x, y and the denominator.
uint256 sx;
uint256 sy;
uint256 sd;
assembly {
sx := sgt(x, sub(0, 1))
sy := sgt(y, sub(0, 1))
sd := sgt(denominator, sub(0, 1))
}
// XOR over sx, sy and sd. This is checking whether there are one or three negative signs in the inputs.
// If yes, the result should be negative.
result = sx ^ sy ^ sd == 0 ? -int256(rAbs) : int256(rAbs);
}
/// @notice Calculates the square root of x, rounding down.
/// @dev Uses the Babylonian method https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.
///
/// Caveats:
/// - This function does not work with fixed-point numbers.
///
/// @param x The uint256 number for which to calculate the square root.
/// @return result The result as an uint256.
function sqrt(uint256 x) internal pure returns (uint256 result) {
if (x == 0) {
return 0;
}
// Set the initial guess to the closest power of two that is higher than x.
uint256 xAux = uint256(x);
result = 1;
if (xAux >= 0x100000000000000000000000000000000) {
xAux >>= 128;
result <<= 64;
}
if (xAux >= 0x10000000000000000) {
xAux >>= 64;
result <<= 32;
}
if (xAux >= 0x100000000) {
xAux >>= 32;
result <<= 16;
}
if (xAux >= 0x10000) {
xAux >>= 16;
result <<= 8;
}
if (xAux >= 0x100) {
xAux >>= 8;
result <<= 4;
}
if (xAux >= 0x10) {
xAux >>= 4;
result <<= 2;
}
if (xAux >= 0x8) {
result <<= 1;
}
// The operations can never overflow because the result is max 2^127 when it enters this block.
unchecked {
result = (result + x / result) >> 1;
result = (result + x / result) >> 1;
result = (result + x / result) >> 1;
result = (result + x / result) >> 1;
result = (result + x / result) >> 1;
result = (result + x / result) >> 1;
result = (result + x / result) >> 1; // Seven iterations should be enough
uint256 roundedDownResult = x / result;
return result >= roundedDownResult ? roundedDownResult : result;
}
}
}
// File: prb-math/contracts/PRBMathUD60x18.sol
pragma solidity >=0.8.4;
/// @title PRBMathUD60x18
/// @author Paul Razvan Berg
/// @notice Smart contract library for advanced fixed-point math that works with uint256 numbers considered to have 18
/// trailing decimals. We call this number representation unsigned 60.18-decimal fixed-point, since there can be up to 60
/// digits in the integer part and up to 18 decimals in the fractional part. The numbers are bound by the minimum and the
/// maximum values permitted by the Solidity type uint256.
library PRBMathUD60x18 {
/// @dev Half the SCALE number.
uint256 internal constant HALF_SCALE = 5e17;
/// @dev log2(e) as an unsigned 60.18-decimal fixed-point number.
uint256 internal constant LOG2_E = 1442695040888963407;
/// @dev The maximum value an unsigned 60.18-decimal fixed-point number can have.
uint256 internal constant MAX_UD60x18 = 115792089237316195423570985008687907853269984665640564039457584007913129639935;
/// @dev The maximum whole value an unsigned 60.18-decimal fixed-point number can have.
uint256 internal constant MAX_WHOLE_UD60x18 = 115792089237316195423570985008687907853269984665640564039457000000000000000000;
/// @dev How many trailing decimals can be represented.
uint256 internal constant SCALE = 1e18;
/// @notice Calculates arithmetic average of x and y, rounding down.
/// @param x The first operand as an unsigned 60.18-decimal fixed-point number.
/// @param y The second operand as an unsigned 60.18-decimal fixed-point number.
/// @return result The arithmetic average as an unsigned 60.18-decimal fixed-point number.
function avg(uint256 x, uint256 y) internal pure returns (uint256 result) {
// The operations can never overflow.
unchecked {
// The last operand checks if both x and y are odd and if that is the case, we add 1 to the result. We need
// to do this because if both numbers are odd, the 0.5 remainder gets truncated twice.
result = (x >> 1) + (y >> 1) + (x & y & 1);
}
}
/// @notice Yields the least unsigned 60.18 decimal fixed-point number greater than or equal to x.
///
/// @dev Optimized for fractional value inputs, because for every whole value there are (1e18 - 1) fractional counterparts.
/// See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
///
/// Requirements:
/// - x must be less than or equal to MAX_WHOLE_UD60x18.
///
/// @param x The unsigned 60.18-decimal fixed-point number to ceil.
/// @param result The least integer greater than or equal to x, as an unsigned 60.18-decimal fixed-point number.
function ceil(uint256 x) internal pure returns (uint256 result) {
if (x > MAX_WHOLE_UD60x18) {
revert PRBMathUD60x18__CeilOverflow(x);
}
assembly {
// Equivalent to "x % SCALE" but faster.
let remainder := mod(x, SCALE)
// Equivalent to "SCALE - remainder" but faster.
let delta := sub(SCALE, remainder)
// Equivalent to "x + delta * (remainder > 0 ? 1 : 0)" but faster.
result := add(x, mul(delta, gt(remainder, 0)))
}
}
/// @notice Divides two unsigned 60.18-decimal fixed-point numbers, returning a new unsigned 60.18-decimal fixed-point number.
///
/// @dev Uses mulDiv to enable overflow-safe multiplication and division.
///
/// Requirements:
/// - The denominator cannot be zero.
///
/// @param x The numerator as an unsigned 60.18-decimal fixed-point number.
/// @param y The denominator as an unsigned 60.18-decimal fixed-point number.
/// @param result The quotient as an unsigned 60.18-decimal fixed-point number.
function div(uint256 x, uint256 y) internal pure returns (uint256 result) {
result = PRBMath.mulDiv(x, SCALE, y);
}
/// @notice Returns Euler's number as an unsigned 60.18-decimal fixed-point number.
/// @dev See https://en.wikipedia.org/wiki/E_(mathematical_constant).
function e() internal pure returns (uint256 result) {
result = 2718281828459045235;
}
/// @notice Calculates the natural exponent of x.
///
/// @dev Based on the insight that e^x = 2^(x * log2(e)).
///
/// Requirements:
/// - All from "log2".
/// - x must be less than 133.084258667509499441.
///
/// @param x The exponent as an unsigned 60.18-decimal fixed-point number.
/// @return result The result as an unsigned 60.18-decimal fixed-point number.
function exp(uint256 x) internal pure returns (uint256 result) {
// Without this check, the value passed to "exp2" would be greater than 192.
if (x >= 133084258667509499441) {
revert PRBMathUD60x18__ExpInputTooBig(x);
}
// Do the fixed-point multiplication inline to save gas.
unchecked {
uint256 doubleScaleProduct = x * LOG2_E;
result = exp2((doubleScaleProduct + HALF_SCALE) / SCALE);
}
}
/// @notice Calculates the binary exponent of x using the binary fraction method.
///
/// @dev See https://ethereum.stackexchange.com/q/79903/24693.
///
/// Requirements:
/// - x must be 192 or less.
/// - The result must fit within MAX_UD60x18.
///
/// @param x The exponent as an unsigned 60.18-decimal fixed-point number.
/// @return result The result as an unsigned 60.18-decimal fixed-point number.
function exp2(uint256 x) internal pure returns (uint256 result) {
// 2^192 doesn't fit within the 192.64-bit format used internally in this function.
if (x >= 192e18) {
revert PRBMathUD60x18__Exp2InputTooBig(x);
}
unchecked {
// Convert x to the 192.64-bit fixed-point format.
uint256 x192x64 = (x << 64) / SCALE;
// Pass x to the PRBMath.exp2 function, which uses the 192.64-bit fixed-point number representation.
result = PRBMath.exp2(x192x64);
}
}
/// @notice Yields the greatest unsigned 60.18 decimal fixed-point number less than or equal to x.
/// @dev Optimized for fractional value inputs, because for every whole value there are (1e18 - 1) fractional counterparts.
/// See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
/// @param x The unsigned 60.18-decimal fixed-point number to floor.
/// @param result The greatest integer less than or equal to x, as an unsigned 60.18-decimal fixed-point number.
function floor(uint256 x) internal pure returns (uint256 result) {
assembly {
// Equivalent to "x % SCALE" but faster.
let remainder := mod(x, SCALE)
// Equivalent to "x - remainder * (remainder > 0 ? 1 : 0)" but faster.
result := sub(x, mul(remainder, gt(remainder, 0)))
}
}
/// @notice Yields the excess beyond the floor of x.
/// @dev Based on the odd function definition https://en.wikipedia.org/wiki/Fractional_part.
/// @param x The unsigned 60.18-decimal fixed-point number to get the fractional part of.
/// @param result The fractional part of x as an unsigned 60.18-decimal fixed-point number.
function frac(uint256 x) internal pure returns (uint256 result) {
assembly {
result := mod(x, SCALE)
}
}
/// @notice Converts a number from basic integer form to unsigned 60.18-decimal fixed-point representation.
///
/// @dev Requirements:
/// - x must be less than or equal to MAX_UD60x18 divided by SCALE.
///
/// @param x The basic integer to convert.
/// @param result The same number in unsigned 60.18-decimal fixed-point representation.
function fromUint(uint256 x) internal pure returns (uint256 result) {
unchecked {
if (x > MAX_UD60x18 / SCALE) {
revert PRBMathUD60x18__FromUintOverflow(x);
}
result = x * SCALE;
}
}
/// @notice Calculates geometric mean of x and y, i.e. sqrt(x * y), rounding down.
///
/// @dev Requirements:
/// - x * y must fit within MAX_UD60x18, lest it overflows.
///
/// @param x The first operand as an unsigned 60.18-decimal fixed-point number.
/// @param y The second operand as an unsigned 60.18-decimal fixed-point number.
/// @return result The result as an unsigned 60.18-decimal fixed-point number.
function gm(uint256 x, uint256 y) internal pure returns (uint256 result) {
if (x == 0) {
return 0;
}
unchecked {
// Checking for overflow this way is faster than letting Solidity do it.
uint256 xy = x * y;
if (xy / x != y) {
revert PRBMathUD60x18__GmOverflow(x, y);
}
// We don't need to multiply by the SCALE here because the x*y product had already picked up a factor of SCALE
// during multiplication. See the comments within the "sqrt" function.
result = PRBMath.sqrt(xy);
}
}
/// @notice Calculates 1 / x, rounding towards zero.
///
/// @dev Requirements:
/// - x cannot be zero.
///
/// @param x The unsigned 60.18-decimal fixed-point number for which to calculate the inverse.
/// @return result The inverse as an unsigned 60.18-decimal fixed-point number.
function inv(uint256 x) internal pure returns (uint256 result) {
unchecked {
// 1e36 is SCALE * SCALE.
result = 1e36 / x;
}
}
/// @notice Calculates the natural logarithm of x.
///
/// @dev Based on the insight that ln(x) = log2(x) / log2(e).
///
/// Requirements:
/// - All from "log2".
///
/// Caveats:
/// - All from "log2".
/// - This doesn't return exactly 1 for 2.718281828459045235, for that we would need more fine-grained precision.
///
/// @param x The unsigned 60.18-decimal fixed-point number for which to calculate the natural logarithm.
/// @return result The natural logarithm as an unsigned 60.18-decimal fixed-point number.
function ln(uint256 x) internal pure returns (uint256 result) {
// Do the fixed-point multiplication inline to save gas. This is overflow-safe because the maximum value that log2(x)
// can return is 196205294292027477728.
unchecked {
result = (log2(x) * SCALE) / LOG2_E;
}
}
/// @notice Calculates the common logarithm of x.
///
/// @dev First checks if x is an exact power of ten and it stops if yes. If it's not, calculates the common
/// logarithm based on the insight that log10(x) = log2(x) / log2(10).
///
/// Requirements:
/// - All from "log2".
///
/// Caveats:
/// - All from "log2".
///
/// @param x The unsigned 60.18-decimal fixed-point number for which to calculate the common logarithm.
/// @return result The common logarithm as an unsigned 60.18-decimal fixed-point number.
function log10(uint256 x) internal pure returns (uint256 result) {
if (x < SCALE) {
revert PRBMathUD60x18__LogInputTooSmall(x);
}
// Note that the "mul" in this block is the assembly multiplication operation, not the "mul" function defined
// in this contract.
// prettier-ignore
assembly {
switch x
case 1 { result := mul(SCALE, sub(0, 18)) }
case 10 { result := mul(SCALE, sub(1, 18)) }
case 100 { result := mul(SCALE, sub(2, 18)) }
case 1000 { result := mul(SCALE, sub(3, 18)) }
case 10000 { result := mul(SCALE, sub(4, 18)) }
case 100000 { result := mul(SCALE, sub(5, 18)) }
case 1000000 { result := mul(SCALE, sub(6, 18)) }
case 10000000 { result := mul(SCALE, sub(7, 18)) }
case 100000000 { result := mul(SCALE, sub(8, 18)) }
case 1000000000 { result := mul(SCALE, sub(9, 18)) }
case 10000000000 { result := mul(SCALE, sub(10, 18)) }
case 100000000000 { result := mul(SCALE, sub(11, 18)) }
case 1000000000000 { result := mul(SCALE, sub(12, 18)) }
case 10000000000000 { result := mul(SCALE, sub(13, 18)) }
case 100000000000000 { result := mul(SCALE, sub(14, 18)) }
case 1000000000000000 { result := mul(SCALE, sub(15, 18)) }
case 10000000000000000 { result := mul(SCALE, sub(16, 18)) }
case 100000000000000000 { result := mul(SCALE, sub(17, 18)) }
case 1000000000000000000 { result := 0 }
case 10000000000000000000 { result := SCALE }
case 100000000000000000000 { result := mul(SCALE, 2) }
case 1000000000000000000000 { result := mul(SCALE, 3) }
case 10000000000000000000000 { result := mul(SCALE, 4) }
case 100000000000000000000000 { result := mul(SCALE, 5) }
case 1000000000000000000000000 { result := mul(SCALE, 6) }
case 10000000000000000000000000 { result := mul(SCALE, 7) }
case 100000000000000000000000000 { result := mul(SCALE, 8) }
case 1000000000000000000000000000 { result := mul(SCALE, 9) }
case 10000000000000000000000000000 { result := mul(SCALE, 10) }
case 100000000000000000000000000000 { result := mul(SCALE, 11) }
case 1000000000000000000000000000000 { result := mul(SCALE, 12) }
case 10000000000000000000000000000000 { result := mul(SCALE, 13) }
case 100000000000000000000000000000000 { result := mul(SCALE, 14) }
case 1000000000000000000000000000000000 { result := mul(SCALE, 15) }
case 10000000000000000000000000000000000 { result := mul(SCALE, 16) }
case 100000000000000000000000000000000000 { result := mul(SCALE, 17) }
case 1000000000000000000000000000000000000 { result := mul(SCALE, 18) }
case 10000000000000000000000000000000000000 { result := mul(SCALE, 19) }
case 100000000000000000000000000000000000000 { result := mul(SCALE, 20) }
case 1000000000000000000000000000000000000000 { result := mul(SCALE, 21) }
case 10000000000000000000000000000000000000000 { result := mul(SCALE, 22) }
case 100000000000000000000000000000000000000000 { result := mul(SCALE, 23) }
case 1000000000000000000000000000000000000000000 { result := mul(SCALE, 24) }
case 10000000000000000000000000000000000000000000 { result := mul(SCALE, 25) }
case 100000000000000000000000000000000000000000000 { result := mul(SCALE, 26) }
case 1000000000000000000000000000000000000000000000 { result := mul(SCALE, 27) }
case 10000000000000000000000000000000000000000000000 { result := mul(SCALE, 28) }
case 100000000000000000000000000000000000000000000000 { result := mul(SCALE, 29) }
case 1000000000000000000000000000000000000000000000000 { result := mul(SCALE, 30) }
case 10000000000000000000000000000000000000000000000000 { result := mul(SCALE, 31) }
case 100000000000000000000000000000000000000000000000000 { result := mul(SCALE, 32) }
case 1000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 33) }
case 10000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 34) }
case 100000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 35) }
case 1000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 36) }
case 10000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 37) }
case 100000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 38) }
case 1000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 39) }
case 10000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 40) }
case 100000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 41) }
case 1000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 42) }
case 10000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 43) }
case 100000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 44) }
case 1000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 45) }
case 10000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 46) }
case 100000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 47) }
case 1000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 48) }
case 10000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 49) }
case 100000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 50) }
case 1000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 51) }
case 10000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 52) }
case 100000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 53) }
case 1000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 54) }
case 10000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 55) }
case 100000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 56) }
case 1000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 57) }
case 10000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 58) }
case 100000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 59) }
default {
result := MAX_UD60x18
}
}
if (result == MAX_UD60x18) {
// Do the fixed-point division inline to save gas. The denominator is log2(10).
unchecked {
result = (log2(x) * SCALE) / 3321928094887362347;
}
}
}
/// @notice Calculates the binary logarithm of x.
///
/// @dev Based on the iterative approximation algorithm.
/// https://en.wikipedia.org/wiki/Binary_logarithm#Iterative_approximation
///
/// Requirements:
/// - x must be greater than or equal to SCALE, otherwise the result would be negative.
///
/// Caveats:
/// - The results are nor perfectly accurate to the last decimal, due to the lossy precision of the iterative approximation.
///
/// @param x The unsigned 60.18-decimal fixed-point number for which to calculate the binary logarithm.
/// @return result The binary logarithm as an unsigned 60.18-decimal fixed-point number.
function log2(uint256 x) internal pure returns (uint256 result) {
if (x < SCALE) {
revert PRBMathUD60x18__LogInputTooSmall(x);
}
unchecked {
// Calculate the integer part of the logarithm and add it to the result and finally calculate y = x * 2^(-n).
uint256 n = PRBMath.mostSignificantBit(x / SCALE);
// The integer part of the logarithm as an unsigned 60.18-decimal fixed-point number. The operation can't overflow
// because n is maximum 255 and SCALE is 1e18.
result = n * SCALE;
// This is y = x * 2^(-n).
uint256 y = x >> n;
// If y = 1, the fractional part is zero.
if (y == SCALE) {
return result;
}
// Calculate the fractional part via the iterative approximation.
// The "delta >>= 1" part is equivalent to "delta /= 2", but shifting bits is faster.
for (uint256 delta = HALF_SCALE; delta > 0; delta >>= 1) {
y = (y * y) / SCALE;
// Is y^2 > 2 and so in the range [2,4)?
if (y >= 2 * SCALE) {
// Add the 2^(-m) factor to the logarithm.
result += delta;
// Corresponds to z/2 on Wikipedia.
y >>= 1;
}
}
}
}
/// @notice Multiplies two unsigned 60.18-decimal fixed-point numbers together, returning a new unsigned 60.18-decimal
/// fixed-point number.
/// @dev See the documentation for the "PRBMath.mulDivFixedPoint" function.
/// @param x The multiplicand as an unsigned 60.18-decimal fixed-point number.
/// @param y The multiplier as an unsigned 60.18-decimal fixed-point number.
/// @return result The product as an unsigned 60.18-decimal fixed-point number.
function mul(uint256 x, uint256 y) internal pure returns (uint256 result) {
result = PRBMath.mulDivFixedPoint(x, y);
}
/// @notice Returns PI as an unsigned 60.18-decimal fixed-point number.
function pi() internal pure returns (uint256 result) {
result = 3141592653589793238;
}
/// @notice Raises x to the power of y.
///
/// @dev Based on the insight that x^y = 2^(log2(x) * y).
///
/// Requirements:
/// - All from "exp2", "log2" and "mul".
///
/// Caveats:
/// - All from "exp2", "log2" and "mul".
/// - Assumes 0^0 is 1.
///
/// @param x Number to raise to given power y, as an unsigned 60.18-decimal fixed-point number.
/// @param y Exponent to raise x to, as an unsigned 60.18-decimal fixed-point number.
/// @return result x raised to power y, as an unsigned 60.18-decimal fixed-point number.
function pow(uint256 x, uint256 y) internal pure returns (uint256 result) {
if (x == 0) {
result = y == 0 ? SCALE : uint256(0);
} else {
result = exp2(mul(log2(x), y));
}
}
/// @notice Raises x (unsigned 60.18-decimal fixed-point number) to the power of y (basic unsigned integer) using the
/// famous algorithm "exponentiation by squaring".
///
/// @dev See https://en.wikipedia.org/wiki/Exponentiation_by_squaring
///
/// Requirements:
/// - The result must fit within MAX_UD60x18.
///
/// Caveats:
/// - All from "mul".
/// - Assumes 0^0 is 1.
///
/// @param x The base as an unsigned 60.18-decimal fixed-point number.
/// @param y The exponent as an uint256.
/// @return result The result as an unsigned 60.18-decimal fixed-point number.
function powu(uint256 x, uint256 y) internal pure returns (uint256 result) {
// Calculate the first iteration of the loop in advance.
result = y & 1 > 0 ? x : SCALE;
// Equivalent to "for(y /= 2; y > 0; y /= 2)" but faster.
for (y >>= 1; y > 0; y >>= 1) {
x = PRBMath.mulDivFixedPoint(x, x);
// Equivalent to "y % 2 == 1" but faster.
if (y & 1 > 0) {
result = PRBMath.mulDivFixedPoint(result, x);
}
}
}
/// @notice Returns 1 as an unsigned 60.18-decimal fixed-point number.
function scale() internal pure returns (uint256 result) {
result = SCALE;
}
/// @notice Calculates the square root of x, rounding down.
/// @dev Uses the Babylonian method https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.
///
/// Requirements:
/// - x must be less than MAX_UD60x18 / SCALE.
///
/// @param x The unsigned 60.18-decimal fixed-point number for which to calculate the square root.
/// @return result The result as an unsigned 60.18-decimal fixed-point .
function sqrt(uint256 x) internal pure returns (uint256 result) {
unchecked {
if (x > MAX_UD60x18 / SCALE) {
revert PRBMathUD60x18__SqrtOverflow(x);
}
// Multiply x by the SCALE to account for the factor of SCALE that is picked up when multiplying two unsigned
// 60.18-decimal fixed-point numbers together (in this case, those two numbers are both the square root).
result = PRBMath.sqrt(x * SCALE);
}
}
/// @notice Converts a unsigned 60.18-decimal fixed-point number to basic integer form, rounding down in the process.
/// @param x The unsigned 60.18-decimal fixed-point number to convert.
/// @return result The same number in basic integer form.
function toUint(uint256 x) internal pure returns (uint256 result) {
unchecked {
result = x / SCALE;
}
}
}
// File: contracts/MultyOwned.sol
pragma solidity >=0.5.0;
//import "hardhat/console.sol";
/// @title у контракта несколько владельцев
contract MultyOwned {
using PRBMathUD60x18 for uint256;
uint256 public constant OWNERS_COUNT = 3; // количество владельцев
uint256 constant OWNER_PART_0 = 425E15;
uint256 constant OWNER_PART_1 = 425E15;
uint256 constant OWNER_PART_2 = 150E15;
address OWNER_0 = address(0x1d3d6671a8A6650E60802613a3838865a4c260ef);
address OWNER_1 = address(0x79E551d8fF2eB3eC04e2d8B83c0714937cF00ECA);
address OWNER_2 = address(0xE102c1e0E0DB088ea15f9032b839E9C8cAf92cBC);
address[OWNERS_COUNT] _OwnerRequest; // кому предложено стать владельцем кошелька
// раскомментировать, перед выполнением тестов
/*constructor() {
OWNER_0 = msg.sender;
}*/
/// @dev модификатор метода, только для владельца контракта
modifier onlyOwner() {
require(IsOwner(msg.sender), "Only owner can call this function.");
_;
}
/// @dev определяет, является ли указанный адрес владельцем контракта
function IsOwner(address account) public view returns (bool) {
return account == OWNER_0 || account == OWNER_1 || account == OWNER_2;
}
/// @dev получает индекс владельца или индекс равный OWNERS_COUNT, если указанный адрес не владелец
function GetContractOwner(uint256 index) public view returns (address) {
if (index == 0) return OWNER_0;
if (index == 1) return OWNER_1;
if (index == 2) return OWNER_2;
return address(0);
}
/// @dev выводит владельца с указанным индексом
function GetContractOwnerIndex(address account)
public
view
returns (uint8)
{
if (account == OWNER_0) return 0;
if (account == OWNER_1) return 1;
if (account == OWNER_2) return 2;
return 4;
}
/// @dev предложить акку стать владельцем
function TransferOwnerRequest(address newOwner) public onlyOwner {
_OwnerRequest[GetContractOwnerIndex(msg.sender)] = newOwner;
}
/// @dev принимает запрос на получение права владения
function ApplyOwnerRequest() public {
if (_OwnerRequest[0] == msg.sender) {
OWNER_0 = msg.sender;
return;
}
if (_OwnerRequest[1] == msg.sender) {
OWNER_1 = msg.sender;
return;
}
if (_OwnerRequest[2] == msg.sender) {
OWNER_2 = msg.sender;
return;
}
}
/// @dev донатит разработчикам
function Donate() public payable {
uint256 sum; // сколько всего отправили
uint256 partSum;
// передаем 0 разработчику
partSum = PRBMathUD60x18.mul(OWNER_PART_0, msg.value);
payable(OWNER_0).transfer(partSum);
sum += partSum;
// передаем 1 разработчику
partSum = PRBMathUD60x18.mul(OWNER_PART_1, msg.value);
if (sum + partSum > msg.value) {
partSum = msg.value - sum;
if (partSum > 0) payable(OWNER_1).transfer(partSum);
return;
}
payable(OWNER_1).transfer(partSum);
sum += partSum;
// передаем 2 разработчику
partSum = PRBMathUD60x18.mul(OWNER_PART_2, msg.value);
if (sum + partSum > msg.value) {
partSum = msg.value - sum;
if (partSum > 0) payable(OWNER_2).transfer(partSum);
return;
}
payable(OWNER_2).transfer(partSum);
}
}
// File: contracts/OpenSeaMeta.sol
pragma solidity >=0.8.3;
/// @title описывает метаданные для Opensea
contract OpenSeaMeta is MultyOwned, ERC721Enumerable {
address _owner; // овнер - только для openSea и подобных систем
string public ContractURI = "https://musicracernft.org/api/globalmeta"; // мета контракта
string public BaseURI = "https://musicracernft.org/api/carsmeta/"; // базовый адрес для меты токенов
constructor(string memory name_, string memory symbol_)
ERC721(name_, symbol_)
{
_owner = msg.sender;
}
function owner() public view returns (address) {
return _owner;
}
function SetOwner(address newOwner) public onlyOwner {
_owner = newOwner;
}
/// @dev ссылка на метаданные уровня витрины
//function contractURI() public view returns (string memory) {
// return ContractURIInternal;
//}
/// @dev задает адрес меты контракта
function SetContractURI(string calldata newContractURI) public onlyOwner {
ContractURI = newContractURI;
}
/// @dev задает новый BaseURI
function SetBaseURI(string calldata newBaseURI) public onlyOwner {
BaseURI = newBaseURI;
}
/// @dev используется для вычисления адресов через
/// унаследованную функцию tokenURI(uint256 tokenId), который дописывает ID токена вконец
function _baseURI() internal view override returns (string memory) {
return BaseURI;
}
}
// File: contracts/Car.sol
pragma solidity >=0.8.3;
/// @title описание формирования начальной цены машины
struct PriceData {
/// @notice начальная цена 1=0.001 eth
uint256 StartPrice;
/// @notice конечная цена (когда все продано) 1=0.001 eth
uint256 EndPrice;
/// @notice тип формирования цены
/// 0 - только стартовая цена
/// 1 - линейная интерполяция от начальной цены к конечной
uint256 PriceType;
}
/// @title тип части машины
struct CarPartType {
/// @notice вероятность генерации не нуливого значения 100000=100%
uint256 Probability;
/// @notice сколько всего частей имеется
uint256 Count;
}
/// @title тип машины
struct CarType {
/// @notice все типы частей
CarPartType[] PartTypes;
/// @notice вероятности окрасок 100% будет окраска=100000
uint256[] Colors;
/// @notice сколько машин создано
uint256 Count;
/// @notice максимальное количество генерируемых машин
uint256 MaxCount;
/// @notice цена минта
PriceData Price;
/// @notice сколько машин зарезервировано для фабрики (это количество машин не может минтиться с контракта напрямую)
uint256 FactoryReserve;
/// @notice если истина, то минт машин этого типа возможен
bool Enable;
}
/// @title описание инстанции одной машины
struct Car {
/// @notice ID типа машины (больше 0, тк 0 это отсуствие типа)
uint256 TypeId;
/// @notice установленные части машины 0 - часть не задана
uint256[] Parts;
/// @notice какие цвета в машине включены, а какие нет
bool[] ColorsEnable;
/// @notice цвета машины
uint256[] Colors;
}
// File: contracts/CarFactory.sol
pragma solidity >=0.8.4;
/// @title порождает машины
contract CarFactory is OpenSeaMeta {
using PRBMathUD60x18 for uint256;
uint256 PriceMul = 1e15; // 1=0.001 эфира
mapping(uint256 => CarType) public CarsTypes; // все типы машин
uint256 public CarTypesCount = 0; // общее количество типов машин
uint256 _RandNonce = 0; // нонс рандома
event NewType(uint256 indexed carType); // когда создается новый тип машины
constructor(string memory name_, string memory symbol_)
OpenSeaMeta(name_, symbol_)
{
CarType storage ct = CarsTypes[1];
ct.PartTypes.push(CarPartType(50e3, 83));
ct.PartTypes.push(CarPartType(100e3, 28));
ct.PartTypes.push(CarPartType(50e3, 10));
ct.PartTypes.push(CarPartType(50e3, 11));
ct.PartTypes.push(CarPartType(100e3, 11));
ct.Colors = new uint256[](2);
ct.Colors[0] = 100e3;
ct.Colors[1] = 50e3;
ct.MaxCount = 333;
ct.Price = PriceData(132, 330, 1);
ct.FactoryReserve = 47;
ct.Enable = true;
CarTypesCount = 1;
emit NewType(CarTypesCount);
}
/// @dev порождает новую машину указанного типа
/// @param carTypeId ID типа машины
/// @param carType тип машины
function CreateCar(uint256 carTypeId, CarType storage carType)
internal
returns (Car memory)
{
// генерируем части машины из ее типа
uint256[] memory parts = new uint256[](carType.PartTypes.length);
for (uint256 i = 0; i < carType.PartTypes.length; ++i) {
CarPartType memory partType = carType.PartTypes[i];
if ((_Random() % 100000) < partType.Probability)
parts[i] = 1 + (_Random() % partType.Count);
else parts[i] = 0;
}
// генерация цветов
bool[] memory colorsEnable = new bool[](carType.Colors.length);
uint256[] memory colors = new uint256[](carType.Colors.length);
for (uint256 i = 0; i < carType.Colors.length; ++i) {
colorsEnable[i] = (_Random() % 100000) < carType.Colors[i];
if (colorsEnable[i]) colors[i] = RandomColor();
}
// создаем машину
Car memory newCar = Car(carTypeId, parts, colorsEnable, colors);
// увеличиваем счетчик созданных машин
carType.Count++;
// вывод результата
return newCar;
}
/// @notice
function RandomColor() internal returns (uint256) {
uint256 r = _Random() % 256;
uint256 g = _Random() % 256;
uint256 b = _Random() % 256;
//uint256 a = _Random() % 256;
return b | (g << 8) | (r << 16); // & (a << 24);
}
function _Random() internal returns (uint256) {
uint256 res = uint256(
keccak256(abi.encodePacked(msg.sender, _RandNonce, block.timestamp))
);
_RandNonce++;
return res;
}
/// @dev добавляет новый тип машины
function AddCarType(CarType calldata newType) public onlyOwner {
require(
newType.Price.StartPrice <= newType.Price.EndPrice,
"car price is incorrect"
);
CarTypesCount++;
CarsTypes[CarTypesCount] = newType;
emit NewType(CarTypesCount);
}
/// @dev возвращает текущую цену машины
/// @param carTypeId Id типа машины
function GetPrice(uint256 carTypeId) public view returns (uint256) {
return GetPriceAlgorithm(carTypeId) * PriceMul;
}
/// @dev алгоритм получения ценника
function GetPriceAlgorithm(uint256 carTypeId)
private
view
returns (uint256)
{
CarType memory carType = CarsTypes[carTypeId];
if (carType.Price.PriceType == 0) return carType.Price.StartPrice;
if (carType.Price.PriceType == 1) {
uint256 f = PRBMathUD60x18.div(carType.Count, carType.MaxCount);
return
carType.Price.StartPrice +
PRBMathUD60x18.mul(
f,
carType.Price.EndPrice - carType.Price.StartPrice
);
} else return carType.Price.StartPrice;
}
/// @dev возвращает настройки ценообразования минта на определенный тип машин
function GetPriceData(uint256 carTypeId)
public
view
returns (PriceData memory)
{
return CarsTypes[carTypeId].Price;
}
/// @dev возвращает количество возможных частей машины указанного типа
/// @param carTypeId Id типа машины
function GetPartsCount(uint256 carTypeId) public view returns (uint256) {
return CarsTypes[carTypeId].PartTypes.length;
}
/// @dev возвращает тип части машины
/// @param carTypeId Id типа машины
/// @param partIndex индекс части машины
function GetPart(uint256 carTypeId, uint256 partIndex)
public
view
returns (CarPartType memory)
{
return CarsTypes[carTypeId].PartTypes[partIndex];
}
}
// File: contracts/MusicRacerNFT.sol
pragma solidity >=0.8.3;
//import "hardhat/console.sol";
/// @title определяет владение машинами
contract MusicRacerNFT is CarFactory {
mapping(uint256 => Car) public IdToCar; // кэш машин по ID
uint256 _CurMintId = 1; // текщий ID токена для минта
address public Factory; // фабрика, которая может минтить токены
mapping(uint256 => bool) public ChangeCarsBlock; // блоки изменений по типам машин (если true то гарантируется, что эту машину овнер изменить не может)
constructor() CarFactory("MusicRacerNFT", "MRCR") {}
/// @dev возвращает непосредственно данные машины для конкретного токена
function GetCar(uint256 tokenId) public view returns (Car memory) {
return IdToCar[tokenId];
}
/// @dev возвращает цвет в формате RGB
/// @param tokenId id токена
/// @param colorIndex индекс цвета
function GetCarColorRGB(uint256 tokenId, uint256 colorIndex)
public
view
returns (
bool, // имеется ли цвет
uint8, // r
uint8, // g
uint8 // b
)
{
Car memory car = GetCar(tokenId);
uint256 color = car.Colors[colorIndex];
uint8 b = (uint8)(color & 0xff);
color >>= 8;
uint8 g = (uint8)(color & 0xff);
color >>= 8;
uint8 r = (uint8)(color & 0xff);
return (car.ColorsEnable[colorIndex], r, g, b);
}
/// @dev задает адрес фабрики-краудсейла
function SetFactory(address newFactory) public onlyOwner {
Factory = newFactory;
}
/// @dev проверка возможности заминтить токен вызывающим адресом
function canMint(uint256 carTypeId) external view returns (bool) {
return canMintInternal(CarsTypes[carTypeId]);
}
function canMintInternal(CarType storage carType)
internal
view
returns (bool)
{
if (msg.sender == Factory) {
if (carType.Count >= carType.MaxCount) return false;
} else if (carType.Count + carType.FactoryReserve >= carType.MaxCount)
return false;
if (
msg.sender != address(this) &&
msg.sender != Factory &&
!IsOwner(msg.sender)
) return false;
return carType.Enable;
}
/// @dev минтит машину с указанным ID (метод для фабрики)
/// @param carTypeId id типа машины
/// @param _toAddress кому заминтить
function mint(uint256 carTypeId, address _toAddress) external {
CarType storage carType = CarsTypes[carTypeId];
require(canMintInternal(carType), "cannot mint car");
IdToCar[_CurMintId] = CreateCar(carTypeId, carType);
_mint(_toAddress, _CurMintId);
_CurMintId++;
if (msg.sender == Factory) --carType.FactoryReserve;
}
/// @dev производит изначальный минт машин
/// @param carTypeId ID типа машины, которую нужно заминтить
function MintCar(uint256 carTypeId) public payable {
require(msg.value >= GetPrice(carTypeId), "not enough eth");
Donate();
this.mint(carTypeId, msg.sender);
}
/// @dev изменяет машину
/// @param tokenId id токена
/// @param newCar новые данные машины
function ChangeCar(uint256 tokenId, Car calldata newCar) public onlyOwner {
uint256 carTypeId = IdToCar[tokenId].TypeId;
require(!ChangeCarsBlock[carTypeId], "cars changes blocked");
IdToCar[tokenId] = newCar;
IdToCar[tokenId].TypeId = carTypeId;
}
/// @dev изменяет настройки генерации машин определенного типа
function ChangeCarType(uint256 carTypeId, CarType calldata newTypeData)
public
onlyOwner
{
require(!ChangeCarsBlock[carTypeId], "cars changes blocked");
CarsTypes[carTypeId] = newTypeData;
}
/// @dev изменяет стоимость машины
function SetCarPrice(uint256 carTypeId, PriceData calldata newPrice)
public
onlyOwner
{
require(!ChangeCarsBlock[carTypeId], "cars changes blocked");
require(newPrice.StartPrice <= newPrice.EndPrice, "price is incorrect");
CarsTypes[carTypeId].Price = newPrice;
}
/// @dev блокирует изменения определенного типа машин
/// @param carTypeId тип машин
function BlockCarChanges(uint256 carTypeId) public onlyOwner {
ChangeCarsBlock[carTypeId] = true;
}
/// @dev задает возможность минтить машину указанного типа
/// @param carTypeId тип машин
/// @param mintEnable можно ли минтить машину
function SetMintEnable(uint256 carTypeId, bool mintEnable)
public
onlyOwner
{
CarsTypes[carTypeId].Enable = mintEnable;
}
/// @dev выводит список всех токенов указанного владельца
/// @param account на какого владельца выдать список
function GetTokensList(address account)
public
view
returns (uint256[] memory)
{
uint256 count = balanceOf(account);
uint256[] memory res = new uint256[](count);
for (uint256 i = 0; i < count; ++i) {
res[i] = tokenOfOwnerByIndex(account, i);
}
return res;
}
}{
"compilationTarget": {
"MusicRacerNFT.sol": "MusicRacerNFT"
},
"evmVersion": "london",
"libraries": {},
"metadata": {
"bytecodeHash": "ipfs"
},
"optimizer": {
"enabled": true,
"runs": 200
},
"remappings": []
}[{"inputs":[],"stateMutability":"nonpayable","type":"constructor"},{"inputs":[{"internalType":"uint256","name":"prod1","type":"uint256"}],"name":"PRBMath__MulDivFixedPointOverflow","type":"error"},{"inputs":[{"internalType":"uint256","name":"prod1","type":"uint256"},{"internalType":"uint256","name":"denominator","type":"uint256"}],"name":"PRBMath__MulDivOverflow","type":"error"},{"anonymous":false,"inputs":[{"indexed":true,"internalType":"address","name":"owner","type":"address"},{"indexed":true,"internalType":"address","name":"approved","type":"address"},{"indexed":true,"internalType":"uint256","name":"tokenId","type":"uint256"}],"name":"Approval","type":"event"},{"anonymous":false,"inputs":[{"indexed":true,"internalType":"address","name":"owner","type":"address"},{"indexed":true,"internalType":"address","name":"operator","type":"address"},{"indexed":false,"internalType":"bool","name":"approved","type":"bool"}],"name":"ApprovalForAll","type":"event"},{"anonymous":false,"inputs":[{"indexed":true,"internalType":"uint256","name":"carType","type":"uint256"}],"name":"NewType","type":"event"},{"anonymous":false,"inputs":[{"indexed":true,"internalType":"address","name":"from","type":"address"},{"indexed":true,"internalType":"address","name":"to","type":"address"},{"indexed":true,"internalType":"uint256","name":"tokenId","type":"uint256"}],"name":"Transfer","type":"event"},{"inputs":[{"components":[{"components":[{"internalType":"uint256","name":"Probability","type":"uint256"},{"internalType":"uint256","name":"Count","type":"uint256"}],"internalType":"struct CarPartType[]","name":"PartTypes","type":"tuple[]"},{"internalType":"uint256[]","name":"Colors","type":"uint256[]"},{"internalType":"uint256","name":"Count","type":"uint256"},{"internalType":"uint256","name":"MaxCount","type":"uint256"},{"components":[{"internalType":"uint256","name":"StartPrice","type":"uint256"},{"internalType":"uint256","name":"EndPrice","type":"uint256"},{"internalType":"uint256","name":"PriceType","type":"uint256"}],"internalType":"struct PriceData","name":"Price","type":"tuple"},{"internalType":"uint256","name":"FactoryReserve","type":"uint256"},{"internalType":"bool","name":"Enable","type":"bool"}],"internalType":"struct CarType","name":"newType","type":"tuple"}],"name":"AddCarType","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[],"name":"ApplyOwnerRequest","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[],"name":"BaseURI","outputs":[{"internalType":"string","name":"","type":"string"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"uint256","name":"carTypeId","type":"uint256"}],"name":"BlockCarChanges","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[],"name":"CarTypesCount","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"uint256","name":"","type":"uint256"}],"name":"CarsTypes","outputs":[{"internalType":"uint256","name":"Count","type":"uint256"},{"internalType":"uint256","name":"MaxCount","type":"uint256"},{"components":[{"internalType":"uint256","name":"StartPrice","type":"uint256"},{"internalType":"uint256","name":"EndPrice","type":"uint256"},{"internalType":"uint256","name":"PriceType","type":"uint256"}],"internalType":"struct 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