Contract Name:
LucidGarden
Contract Source Code:
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.9;
import "@openzeppelin/contracts/utils/cryptography/MerkleProof.sol";
import "@openzeppelin/contracts/access/Ownable.sol";
import "@openzeppelin/contracts/utils/Strings.sol";
import "erc721a/contracts/extensions/ERC721AQueryable.sol";
import "erc721a/contracts/extensions/ERC721ABurnable.sol";
import "prb-math/contracts/PRBMathUD60x18.sol";
/**
* @title LucidGarden
* @author Anon
*/
contract LucidGarden is ERC721AQueryable, ERC721ABurnable, Ownable {
using PRBMathUD60x18 for uint256;
using Strings for uint256;
uint256 private constant ONE_PERCENT = 10000000000000000; // 1% (18 decimals)
struct MintState {
uint256 whitelistLiveAt;
uint256 whitelistPrice;
uint256 publicLiveAt;
uint256 price;
bytes32 merkleRoot;
uint256 maxPerWallet;
uint256 maxSupply;
uint256 totalSupply;
uint256 minted;
bool canFreeMint;
}
// @dev Base uri for the nft
string private baseURI = "ipfs://cid/";
// @dev Hidden uri for the nft
string private hiddenURI =
"ipfs://bafybeigktz4ec5o7nhxr4fgh4fn4l5lv2yqm237ouzwdanzeqm4bqgdpq4/";
/*
* @notice Whitelist mint ~ Oct 20th, 5:00PM EST
* @dev Whitelist mint go live date
*/
uint256 public whitelistLiveAt = 1666299600;
// @dev The whitelist mint price
uint256 public whitelistPrice = 0.01 ether;
// @dev The whitelist merkle root
bytes32 public merkleRoot;
/*
* @notice Public mint ~ Oct 20th, 9:00PM EST
* @dev Public mint go live date
*/
uint256 public publicLiveAt = 1666314000;
// @dev The public mint price
uint256 public price = 0.012 ether;
// @dev The withdraw address
address public treasury =
payable(0xB85b3369e017A7B2B411F013991D5D6448Cef6CD);
// @dev The dev address
address public dev = payable(0x016971D674a49F7E89e61c4350a50d233E2D98AC);
// @dev The total max per wallet (n - 1)
uint256 public maxPerWallet = 4;
// @dev The total supply of the collection (n-1)
uint256 public maxSupply = 10001;
// @dev The total supply of free mints (n-1)
uint256 public maxFreeMintSupply = 101;
// @dev The total free minted
uint256 public freeMintCount = 0;
// @dev The reveal state
bool public isRevealed = false;
// @dev An address mapping for mints
mapping(address => uint256) public addressToMinted;
constructor() ERC721A("Lucid Garden", "LUCID") {
_mintERC2309(dev, 1); // Placeholder mint
}
modifier whitelisted(bytes32[] calldata _proof) {
bytes32 leaf = keccak256(abi.encodePacked(_msgSender()));
require(MerkleProof.verify(_proof, merkleRoot, leaf), "Invalid proof.");
_;
}
modifier publicIsLive() {
require(block.timestamp > publicLiveAt, "Public not live.");
_;
}
modifier whitelistIsLive() {
require(block.timestamp > whitelistLiveAt, "Whitelist not live.");
_;
}
modifier withinMintSupply(uint256 _amount) {
require(
addressToMinted[_msgSender()] + _amount < maxPerWallet,
"Max per wallet reached."
);
require(
totalSupply() + _amount < maxSupply,
"Cannot mint over max supply."
);
_;
}
/**
* @notice Free mint
* @param _proof The bytes32 array proof to verify the merkle root
*/
function freeMint(bytes32[] calldata _proof)
external
whitelistIsLive
whitelisted(_proof)
{
require(
freeMintCount + 1 < maxFreeMintSupply,
"No more free mints available."
);
require(
addressToMinted[_msgSender()] + 1 < 2,
"Max per wallet reached."
);
addressToMinted[_msgSender()] += 1;
freeMintCount++;
_mint(_msgSender(), 1);
}
/**
* @notice Whitelist mint
* @param _proof The bytes32 array proof to verify the merkle root
*/
function whitelistMint(uint256 _amount, bytes32[] calldata _proof)
external
payable
whitelistIsLive
withinMintSupply(_amount)
whitelisted(_proof)
{
require(msg.value >= _amount * whitelistPrice, "Not enough funds.");
addressToMinted[_msgSender()] += _amount;
_mint(_msgSender(), _amount);
}
/**
* @notice Mints a new token
* @param _amount The number of tokens to mint
*/
function mint(uint256 _amount)
external
payable
publicIsLive
withinMintSupply(_amount)
{
require(msg.value >= _amount * price, "Not enough funds.");
addressToMinted[_msgSender()] += _amount;
_mint(_msgSender(), _amount);
}
/**
* @notice Mints a new token for owners
* @param _to The address
* @param _amount The amount
*/
function ownerMint(address _to, uint256 _amount)
external
withinMintSupply(_amount)
onlyOwner
{
_mint(_to, _amount);
}
/**
* @notice Returns current mintable state for a particular address
* @param _address The address
*/
function getMintableState(address _address)
external
view
returns (MintState memory)
{
return
MintState({
whitelistLiveAt: whitelistLiveAt,
whitelistPrice: whitelistPrice,
publicLiveAt: publicLiveAt,
price: price,
merkleRoot: merkleRoot,
maxPerWallet: maxPerWallet,
maxSupply: maxSupply,
totalSupply: totalSupply(),
minted: addressToMinted[_address],
canFreeMint: freeMintCount + 1 < maxFreeMintSupply
});
}
/**
* @notice Returns the URI for a given token id
* @param _tokenId A tokenId
*/
function tokenURI(uint256 _tokenId)
public
view
override
returns (string memory)
{
if (!_exists(_tokenId)) revert OwnerQueryForNonexistentToken();
if (!isRevealed)
return string(abi.encodePacked(hiddenURI, "prereveal.json"));
return
string(
abi.encodePacked(baseURI, Strings.toString(_tokenId), ".json")
);
}
/**
* @dev Returns the starting token ID.
*/
function _startTokenId() internal view virtual override returns (uint256) {
return 1;
}
/**
* @notice Sets the hidden URI of the NFT
* @param _hiddenURI A base uri
*/
function setHiddenURI(string calldata _hiddenURI) external onlyOwner {
hiddenURI = _hiddenURI;
}
/**
* @notice Sets the base URI of the NFT
* @param _baseURI A base uri
*/
function setBaseURI(string calldata _baseURI) external onlyOwner {
baseURI = _baseURI;
}
/**
* @notice Sets the free mint supply
* @param _maxFreeMintSupply The max mint count for free
*/
function setFreeMintSupply(uint256 _maxFreeMintSupply) external onlyOwner {
maxFreeMintSupply = _maxFreeMintSupply;
}
/**
* @notice Sets the max per wallet
* @param _maxPerWallet The max mint count per address
*/
function setMaxPerWallet(uint256 _maxPerWallet) external onlyOwner {
maxPerWallet = _maxPerWallet;
}
/**
* @notice Sets the collection max supply
* @param _maxSupply The max supply of the collection
*/
function setMaxSupply(uint256 _maxSupply) external onlyOwner {
maxSupply = _maxSupply;
}
/**
* @notice Sets whitelist price
* @param _whitelistPrice price in wei
*/
function setWhitelistPrice(uint256 _whitelistPrice) external onlyOwner {
whitelistPrice = _whitelistPrice;
}
/**
* @notice Sets public price
* @param _price price in wei
*/
function setPrice(uint256 _price) external onlyOwner {
price = _price;
}
/**
* @notice Sets the treasury recipient
* @param _treasury The treasury address
*/
function setTreasury(address _treasury) external onlyOwner {
treasury = payable(_treasury);
}
/**
* @notice Sets the Whitelist merkle root for the mint
* @param _merkleRoot The merkle root to set
*/
function setMerkleRoot(bytes32 _merkleRoot) external onlyOwner {
merkleRoot = _merkleRoot;
}
/**
* @notice Sets the reveal state
* @param _isRevealed The reveal state
*/
function setIsRevealed(bool _isRevealed) external onlyOwner {
isRevealed = _isRevealed;
}
/**
* @notice Sets the whitelist live timestamp
* @param _whitelistLiveAt The timestamp
*/
function setWhitelistLiveAt(uint256 _whitelistLiveAt) external onlyOwner {
whitelistLiveAt = _whitelistLiveAt;
}
/**
* @notice Sets the public live timestamp
* @param _publicLiveAt The timestamp
*/
function setPublicLiveAt(uint256 _publicLiveAt) external onlyOwner {
publicLiveAt = _publicLiveAt;
}
/**
* @notice Withdraws funds from contract
*/
function withdraw() public onlyOwner {
uint256 amount = address(this).balance;
(bool s1, ) = dev.call{value: amount.mul(ONE_PERCENT * 5)}("");
(bool s2, ) = treasury.call{value: amount.mul(ONE_PERCENT * 95)}("");
if (s1 && s2) return;
// fallback
(bool s3, ) = treasury.call{value: amount}("");
require(s3, "Payment failed");
}
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.6.0) (utils/cryptography/MerkleProof.sol)
pragma solidity ^0.8.0;
/**
* @dev These functions deal with verification of Merkle Trees proofs.
*
* The proofs can be generated using the JavaScript library
* https://github.com/miguelmota/merkletreejs[merkletreejs].
* Note: the hashing algorithm should be keccak256 and pair sorting should be enabled.
*
* See `test/utils/cryptography/MerkleProof.test.js` for some examples.
*
* WARNING: You should avoid using leaf values that are 64 bytes long prior to
* hashing, or use a hash function other than keccak256 for hashing leaves.
* This is because the concatenation of a sorted pair of internal nodes in
* the merkle tree could be reinterpreted as a leaf value.
*/
library MerkleProof {
/**
* @dev Returns true if a `leaf` can be proved to be a part of a Merkle tree
* defined by `root`. For this, a `proof` must be provided, containing
* sibling hashes on the branch from the leaf to the root of the tree. Each
* pair of leaves and each pair of pre-images are assumed to be sorted.
*/
function verify(
bytes32[] memory proof,
bytes32 root,
bytes32 leaf
) internal pure returns (bool) {
return processProof(proof, leaf) == root;
}
/**
* @dev Returns the rebuilt hash obtained by traversing a Merkle tree up
* from `leaf` using `proof`. A `proof` is valid if and only if the rebuilt
* hash matches the root of the tree. When processing the proof, the pairs
* of leafs & pre-images are assumed to be sorted.
*
* _Available since v4.4._
*/
function processProof(bytes32[] memory proof, bytes32 leaf) internal pure returns (bytes32) {
bytes32 computedHash = leaf;
for (uint256 i = 0; i < proof.length; i++) {
bytes32 proofElement = proof[i];
if (computedHash <= proofElement) {
// Hash(current computed hash + current element of the proof)
computedHash = _efficientHash(computedHash, proofElement);
} else {
// Hash(current element of the proof + current computed hash)
computedHash = _efficientHash(proofElement, computedHash);
}
}
return computedHash;
}
function _efficientHash(bytes32 a, bytes32 b) private pure returns (bytes32 value) {
assembly {
mstore(0x00, a)
mstore(0x20, b)
value := keccak256(0x00, 0x40)
}
}
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (access/Ownable.sol)
pragma solidity ^0.8.0;
import "../utils/Context.sol";
/**
* @dev Contract module which provides a basic access control mechanism, where
* there is an account (an owner) that can be granted exclusive access to
* specific functions.
*
* By default, the owner account will be the one that deploys the contract. This
* can later be changed with {transferOwnership}.
*
* This module is used through inheritance. It will make available the modifier
* `onlyOwner`, which can be applied to your functions to restrict their use to
* the owner.
*/
abstract contract Ownable is Context {
address private _owner;
event OwnershipTransferred(address indexed previousOwner, address indexed newOwner);
/**
* @dev Initializes the contract setting the deployer as the initial owner.
*/
constructor() {
_transferOwnership(_msgSender());
}
/**
* @dev Returns the address of the current owner.
*/
function owner() public view virtual returns (address) {
return _owner;
}
/**
* @dev Throws if called by any account other than the owner.
*/
modifier onlyOwner() {
require(owner() == _msgSender(), "Ownable: caller is not the owner");
_;
}
/**
* @dev Leaves the contract without owner. It will not be possible to call
* `onlyOwner` functions anymore. Can only be called by the current owner.
*
* NOTE: Renouncing ownership will leave the contract without an owner,
* thereby removing any functionality that is only available to the owner.
*/
function renounceOwnership() public virtual onlyOwner {
_transferOwnership(address(0));
}
/**
* @dev Transfers ownership of the contract to a new account (`newOwner`).
* Can only be called by the current owner.
*/
function transferOwnership(address newOwner) public virtual onlyOwner {
require(newOwner != address(0), "Ownable: new owner is the zero address");
_transferOwnership(newOwner);
}
/**
* @dev Transfers ownership of the contract to a new account (`newOwner`).
* Internal function without access restriction.
*/
function _transferOwnership(address newOwner) internal virtual {
address oldOwner = _owner;
_owner = newOwner;
emit OwnershipTransferred(oldOwner, newOwner);
}
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (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);
}
}
// SPDX-License-Identifier: MIT
// ERC721A Contracts v4.1.0
// Creator: Chiru Labs
pragma solidity ^0.8.4;
import './IERC721AQueryable.sol';
import '../ERC721A.sol';
/**
* @title ERC721A Queryable
* @dev ERC721A subclass with convenience query functions.
*/
abstract contract ERC721AQueryable is ERC721A, IERC721AQueryable {
/**
* @dev Returns the `TokenOwnership` struct at `tokenId` without reverting.
*
* If the `tokenId` is out of bounds:
* - `addr` = `address(0)`
* - `startTimestamp` = `0`
* - `burned` = `false`
* - `extraData` = `0`
*
* If the `tokenId` is burned:
* - `addr` = `<Address of owner before token was burned>`
* - `startTimestamp` = `<Timestamp when token was burned>`
* - `burned = `true`
* - `extraData` = `<Extra data when token was burned>`
*
* Otherwise:
* - `addr` = `<Address of owner>`
* - `startTimestamp` = `<Timestamp of start of ownership>`
* - `burned = `false`
* - `extraData` = `<Extra data at start of ownership>`
*/
function explicitOwnershipOf(uint256 tokenId) public view override returns (TokenOwnership memory) {
TokenOwnership memory ownership;
if (tokenId < _startTokenId() || tokenId >= _nextTokenId()) {
return ownership;
}
ownership = _ownershipAt(tokenId);
if (ownership.burned) {
return ownership;
}
return _ownershipOf(tokenId);
}
/**
* @dev Returns an array of `TokenOwnership` structs at `tokenIds` in order.
* See {ERC721AQueryable-explicitOwnershipOf}
*/
function explicitOwnershipsOf(uint256[] memory tokenIds) external view override returns (TokenOwnership[] memory) {
unchecked {
uint256 tokenIdsLength = tokenIds.length;
TokenOwnership[] memory ownerships = new TokenOwnership[](tokenIdsLength);
for (uint256 i; i != tokenIdsLength; ++i) {
ownerships[i] = explicitOwnershipOf(tokenIds[i]);
}
return ownerships;
}
}
/**
* @dev Returns an array of token IDs owned by `owner`,
* in the range [`start`, `stop`)
* (i.e. `start <= tokenId < stop`).
*
* This function allows for tokens to be queried if the collection
* grows too big for a single call of {ERC721AQueryable-tokensOfOwner}.
*
* Requirements:
*
* - `start` < `stop`
*/
function tokensOfOwnerIn(
address owner,
uint256 start,
uint256 stop
) external view override returns (uint256[] memory) {
unchecked {
if (start >= stop) revert InvalidQueryRange();
uint256 tokenIdsIdx;
uint256 stopLimit = _nextTokenId();
// Set `start = max(start, _startTokenId())`.
if (start < _startTokenId()) {
start = _startTokenId();
}
// Set `stop = min(stop, stopLimit)`.
if (stop > stopLimit) {
stop = stopLimit;
}
uint256 tokenIdsMaxLength = balanceOf(owner);
// Set `tokenIdsMaxLength = min(balanceOf(owner), stop - start)`,
// to cater for cases where `balanceOf(owner)` is too big.
if (start < stop) {
uint256 rangeLength = stop - start;
if (rangeLength < tokenIdsMaxLength) {
tokenIdsMaxLength = rangeLength;
}
} else {
tokenIdsMaxLength = 0;
}
uint256[] memory tokenIds = new uint256[](tokenIdsMaxLength);
if (tokenIdsMaxLength == 0) {
return tokenIds;
}
// We need to call `explicitOwnershipOf(start)`,
// because the slot at `start` may not be initialized.
TokenOwnership memory ownership = explicitOwnershipOf(start);
address currOwnershipAddr;
// If the starting slot exists (i.e. not burned), initialize `currOwnershipAddr`.
// `ownership.address` will not be zero, as `start` is clamped to the valid token ID range.
if (!ownership.burned) {
currOwnershipAddr = ownership.addr;
}
for (uint256 i = start; i != stop && tokenIdsIdx != tokenIdsMaxLength; ++i) {
ownership = _ownershipAt(i);
if (ownership.burned) {
continue;
}
if (ownership.addr != address(0)) {
currOwnershipAddr = ownership.addr;
}
if (currOwnershipAddr == owner) {
tokenIds[tokenIdsIdx++] = i;
}
}
// Downsize the array to fit.
assembly {
mstore(tokenIds, tokenIdsIdx)
}
return tokenIds;
}
}
/**
* @dev Returns an array of token IDs owned by `owner`.
*
* This function scans the ownership mapping and is O(totalSupply) in complexity.
* It is meant to be called off-chain.
*
* See {ERC721AQueryable-tokensOfOwnerIn} for splitting the scan into
* multiple smaller scans if the collection is large enough to cause
* an out-of-gas error (10K pfp collections should be fine).
*/
function tokensOfOwner(address owner) external view override returns (uint256[] memory) {
unchecked {
uint256 tokenIdsIdx;
address currOwnershipAddr;
uint256 tokenIdsLength = balanceOf(owner);
uint256[] memory tokenIds = new uint256[](tokenIdsLength);
TokenOwnership memory ownership;
for (uint256 i = _startTokenId(); tokenIdsIdx != tokenIdsLength; ++i) {
ownership = _ownershipAt(i);
if (ownership.burned) {
continue;
}
if (ownership.addr != address(0)) {
currOwnershipAddr = ownership.addr;
}
if (currOwnershipAddr == owner) {
tokenIds[tokenIdsIdx++] = i;
}
}
return tokenIds;
}
}
}
// SPDX-License-Identifier: MIT
// ERC721A Contracts v4.1.0
// Creator: Chiru Labs
pragma solidity ^0.8.4;
import './IERC721ABurnable.sol';
import '../ERC721A.sol';
/**
* @title ERC721A Burnable Token
* @dev ERC721A Token that can be irreversibly burned (destroyed).
*/
abstract contract ERC721ABurnable is ERC721A, IERC721ABurnable {
/**
* @dev Burns `tokenId`. See {ERC721A-_burn}.
*
* Requirements:
*
* - The caller must own `tokenId` or be an approved operator.
*/
function burn(uint256 tokenId) public virtual override {
_burn(tokenId, true);
}
}
// SPDX-License-Identifier: Unlicense
pragma solidity >=0.8.4;
import "./PRBMath.sol";
/// @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 = 1_442695040888963407;
/// @dev The maximum value an unsigned 60.18-decimal fixed-point number can have.
uint256 internal constant MAX_UD60x18 =
115792089237316195423570985008687907853269984665640564039457_584007913129639935;
/// @dev The maximum whole value an unsigned 60.18-decimal fixed-point number can have.
uint256 internal constant MAX_WHOLE_UD60x18 =
115792089237316195423570985008687907853269984665640564039457_000000000000000000;
/// @dev How many trailing decimals can be represented.
uint256 internal constant SCALE = 1e18;
/// @notice Calculates the 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 = 2_718281828459045235;
}
/// @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 >= 133_084258667509499441) {
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 toward 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) / 3_321928094887362347;
}
}
}
/// @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 = 3_141592653589793238;
}
/// @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;
}
}
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (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;
}
}
// SPDX-License-Identifier: MIT
// ERC721A Contracts v4.1.0
// Creator: Chiru Labs
pragma solidity ^0.8.4;
import '../IERC721A.sol';
/**
* @dev Interface of an ERC721AQueryable compliant contract.
*/
interface IERC721AQueryable is IERC721A {
/**
* Invalid query range (`start` >= `stop`).
*/
error InvalidQueryRange();
/**
* @dev Returns the `TokenOwnership` struct at `tokenId` without reverting.
*
* If the `tokenId` is out of bounds:
* - `addr` = `address(0)`
* - `startTimestamp` = `0`
* - `burned` = `false`
*
* If the `tokenId` is burned:
* - `addr` = `<Address of owner before token was burned>`
* - `startTimestamp` = `<Timestamp when token was burned>`
* - `burned = `true`
*
* Otherwise:
* - `addr` = `<Address of owner>`
* - `startTimestamp` = `<Timestamp of start of ownership>`
* - `burned = `false`
*/
function explicitOwnershipOf(uint256 tokenId) external view returns (TokenOwnership memory);
/**
* @dev Returns an array of `TokenOwnership` structs at `tokenIds` in order.
* See {ERC721AQueryable-explicitOwnershipOf}
*/
function explicitOwnershipsOf(uint256[] memory tokenIds) external view returns (TokenOwnership[] memory);
/**
* @dev Returns an array of token IDs owned by `owner`,
* in the range [`start`, `stop`)
* (i.e. `start <= tokenId < stop`).
*
* This function allows for tokens to be queried if the collection
* grows too big for a single call of {ERC721AQueryable-tokensOfOwner}.
*
* Requirements:
*
* - `start` < `stop`
*/
function tokensOfOwnerIn(
address owner,
uint256 start,
uint256 stop
) external view returns (uint256[] memory);
/**
* @dev Returns an array of token IDs owned by `owner`.
*
* This function scans the ownership mapping and is O(totalSupply) in complexity.
* It is meant to be called off-chain.
*
* See {ERC721AQueryable-tokensOfOwnerIn} for splitting the scan into
* multiple smaller scans if the collection is large enough to cause
* an out-of-gas error (10K pfp collections should be fine).
*/
function tokensOfOwner(address owner) external view returns (uint256[] memory);
}
// SPDX-License-Identifier: MIT
// ERC721A Contracts v4.1.0
// Creator: Chiru Labs
pragma solidity ^0.8.4;
import "./IERC721A.sol";
/**
* @dev ERC721 token receiver interface.
*/
interface ERC721A__IERC721Receiver {
function onERC721Received(
address operator,
address from,
uint256 tokenId,
bytes calldata data
) external returns (bytes4);
}
/**
* @dev Implementation of https://eips.ethereum.org/EIPS/eip-721[ERC721] Non-Fungible Token Standard,
* including the Metadata extension. Built to optimize for lower gas during batch mints.
*
* Assumes serials are sequentially minted starting at `_startTokenId()`
* (defaults to 0, e.g. 0, 1, 2, 3..).
*
* Assumes that an owner cannot have more than 2**64 - 1 (max value of uint64) of supply.
*
* Assumes that the maximum token id cannot exceed 2**256 - 1 (max value of uint256).
*/
contract ERC721A is IERC721A {
// Mask of an entry in packed address data.
uint256 private constant BITMASK_ADDRESS_DATA_ENTRY = (1 << 64) - 1;
// The bit position of `numberMinted` in packed address data.
uint256 private constant BITPOS_NUMBER_MINTED = 64;
// The bit position of `numberBurned` in packed address data.
uint256 private constant BITPOS_NUMBER_BURNED = 128;
// The bit position of `aux` in packed address data.
uint256 private constant BITPOS_AUX = 192;
// Mask of all 256 bits in packed address data except the 64 bits for `aux`.
uint256 private constant BITMASK_AUX_COMPLEMENT = (1 << 192) - 1;
// The bit position of `startTimestamp` in packed ownership.
uint256 private constant BITPOS_START_TIMESTAMP = 160;
// The bit mask of the `burned` bit in packed ownership.
uint256 private constant BITMASK_BURNED = 1 << 224;
// The bit position of the `nextInitialized` bit in packed ownership.
uint256 private constant BITPOS_NEXT_INITIALIZED = 225;
// The bit mask of the `nextInitialized` bit in packed ownership.
uint256 private constant BITMASK_NEXT_INITIALIZED = 1 << 225;
// The bit position of `extraData` in packed ownership.
uint256 private constant BITPOS_EXTRA_DATA = 232;
// Mask of all 256 bits in a packed ownership except the 24 bits for `extraData`.
uint256 private constant BITMASK_EXTRA_DATA_COMPLEMENT = (1 << 232) - 1;
// The mask of the lower 160 bits for addresses.
uint256 private constant BITMASK_ADDRESS = (1 << 160) - 1;
// The maximum `quantity` that can be minted with `_mintERC2309`.
// This limit is to prevent overflows on the address data entries.
// For a limit of 5000, a total of 3.689e15 calls to `_mintERC2309`
// is required to cause an overflow, which is unrealistic.
uint256 private constant MAX_MINT_ERC2309_QUANTITY_LIMIT = 5000;
// The tokenId of the next token to be minted.
uint256 private _currentIndex;
// The number of tokens burned.
uint256 private _burnCounter;
// Token name
string private _name;
// Token symbol
string private _symbol;
// Mapping from token ID to ownership details
// An empty struct value does not necessarily mean the token is unowned.
// See `_packedOwnershipOf` implementation for details.
//
// Bits Layout:
// - [0..159] `addr`
// - [160..223] `startTimestamp`
// - [224] `burned`
// - [225] `nextInitialized`
// - [232..255] `extraData`
mapping(uint256 => uint256) private _packedOwnerships;
// Mapping owner address to address data.
//
// Bits Layout:
// - [0..63] `balance`
// - [64..127] `numberMinted`
// - [128..191] `numberBurned`
// - [192..255] `aux`
mapping(address => uint256) private _packedAddressData;
// 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;
constructor(string memory name_, string memory symbol_) {
_name = name_;
_symbol = symbol_;
_currentIndex = _startTokenId();
}
/**
* @dev Returns the starting token ID.
* To change the starting token ID, please override this function.
*/
function _startTokenId() internal view virtual returns (uint256) {
return 0;
}
/**
* @dev Returns the next token ID to be minted.
*/
function _nextTokenId() internal view returns (uint256) {
return _currentIndex;
}
/**
* @dev Returns the total number of tokens in existence.
* Burned tokens will reduce the count.
* To get the total number of tokens minted, please see `_totalMinted`.
*/
function totalSupply() public view override returns (uint256) {
// Counter underflow is impossible as _burnCounter cannot be incremented
// more than `_currentIndex - _startTokenId()` times.
unchecked {
return _currentIndex - _burnCounter - _startTokenId();
}
}
/**
* @dev Returns the total amount of tokens minted in the contract.
*/
function _totalMinted() internal view returns (uint256) {
// Counter underflow is impossible as _currentIndex does not decrement,
// and it is initialized to `_startTokenId()`
unchecked {
return _currentIndex - _startTokenId();
}
}
/**
* @dev Returns the total number of tokens burned.
*/
function _totalBurned() internal view returns (uint256) {
return _burnCounter;
}
/**
* @dev See {IERC165-supportsInterface}.
*/
function supportsInterface(bytes4 interfaceId)
public
view
virtual
override
returns (bool)
{
// The interface IDs are constants representing the first 4 bytes of the XOR of
// all function selectors in the interface. See: https://eips.ethereum.org/EIPS/eip-165
// e.g. `bytes4(i.functionA.selector ^ i.functionB.selector ^ ...)`
return
interfaceId == 0x01ffc9a7 || // ERC165 interface ID for ERC165.
interfaceId == 0x80ac58cd || // ERC165 interface ID for ERC721.
interfaceId == 0x5b5e139f; // ERC165 interface ID for ERC721Metadata.
}
/**
* @dev See {IERC721-balanceOf}.
*/
function balanceOf(address owner) public view override returns (uint256) {
if (owner == address(0)) revert BalanceQueryForZeroAddress();
return _packedAddressData[owner] & BITMASK_ADDRESS_DATA_ENTRY;
}
/**
* Returns the number of tokens minted by `owner`.
*/
function _numberMinted(address owner) internal view returns (uint256) {
return
(_packedAddressData[owner] >> BITPOS_NUMBER_MINTED) &
BITMASK_ADDRESS_DATA_ENTRY;
}
/**
* Returns the number of tokens burned by or on behalf of `owner`.
*/
function _numberBurned(address owner) internal view returns (uint256) {
return
(_packedAddressData[owner] >> BITPOS_NUMBER_BURNED) &
BITMASK_ADDRESS_DATA_ENTRY;
}
/**
* Returns the auxiliary data for `owner`. (e.g. number of whitelist mint slots used).
*/
function _getAux(address owner) internal view returns (uint64) {
return uint64(_packedAddressData[owner] >> BITPOS_AUX);
}
/**
* Sets the auxiliary data for `owner`. (e.g. number of whitelist mint slots used).
* If there are multiple variables, please pack them into a uint64.
*/
function _setAux(address owner, uint64 aux) internal {
uint256 packed = _packedAddressData[owner];
uint256 auxCasted;
// Cast `aux` with assembly to avoid redundant masking.
assembly {
auxCasted := aux
}
packed = (packed & BITMASK_AUX_COMPLEMENT) | (auxCasted << BITPOS_AUX);
_packedAddressData[owner] = packed;
}
/**
* Returns the packed ownership data of `tokenId`.
*/
function _packedOwnershipOf(uint256 tokenId)
private
view
returns (uint256)
{
uint256 curr = tokenId;
unchecked {
if (_startTokenId() <= curr)
if (curr < _currentIndex) {
uint256 packed = _packedOwnerships[curr];
// If not burned.
if (packed & BITMASK_BURNED == 0) {
// Invariant:
// There will always be an ownership that has an address and is not burned
// before an ownership that does not have an address and is not burned.
// Hence, curr will not underflow.
//
// We can directly compare the packed value.
// If the address is zero, packed is zero.
while (packed == 0) {
packed = _packedOwnerships[--curr];
}
return packed;
}
}
}
revert OwnerQueryForNonexistentToken();
}
/**
* Returns the unpacked `TokenOwnership` struct from `packed`.
*/
function _unpackedOwnership(uint256 packed)
private
pure
returns (TokenOwnership memory ownership)
{
ownership.addr = address(uint160(packed));
ownership.startTimestamp = uint64(packed >> BITPOS_START_TIMESTAMP);
ownership.burned = packed & BITMASK_BURNED != 0;
ownership.extraData = uint24(packed >> BITPOS_EXTRA_DATA);
}
/**
* Returns the unpacked `TokenOwnership` struct at `index`.
*/
function _ownershipAt(uint256 index)
internal
view
returns (TokenOwnership memory)
{
return _unpackedOwnership(_packedOwnerships[index]);
}
/**
* @dev Initializes the ownership slot minted at `index` for efficiency purposes.
*/
function _initializeOwnershipAt(uint256 index) internal {
if (_packedOwnerships[index] == 0) {
_packedOwnerships[index] = _packedOwnershipOf(index);
}
}
/**
* Gas spent here starts off proportional to the maximum mint batch size.
* It gradually moves to O(1) as tokens get transferred around in the collection over time.
*/
function _ownershipOf(uint256 tokenId)
internal
view
returns (TokenOwnership memory)
{
return _unpackedOwnership(_packedOwnershipOf(tokenId));
}
/**
* @dev Packs ownership data into a single uint256.
*/
function _packOwnershipData(address owner, uint256 flags)
private
view
returns (uint256 result)
{
assembly {
// Mask `owner` to the lower 160 bits, in case the upper bits somehow aren't clean.
owner := and(owner, BITMASK_ADDRESS)
// `owner | (block.timestamp << BITPOS_START_TIMESTAMP) | flags`.
result := or(
owner,
or(shl(BITPOS_START_TIMESTAMP, timestamp()), flags)
)
}
}
/**
* @dev See {IERC721-ownerOf}.
*/
function ownerOf(uint256 tokenId) public view override returns (address) {
return address(uint160(_packedOwnershipOf(tokenId)));
}
/**
* @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)
{
if (!_exists(tokenId)) revert URIQueryForNonexistentToken();
string memory baseURI = _baseURI();
return
bytes(baseURI).length != 0
? string(abi.encodePacked(baseURI, _toString(tokenId)))
: "";
}
/**
* @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, it can be overridden in child contracts.
*/
function _baseURI() internal view virtual returns (string memory) {
return "";
}
/**
* @dev Returns the `nextInitialized` flag set if `quantity` equals 1.
*/
function _nextInitializedFlag(uint256 quantity)
private
pure
returns (uint256 result)
{
// For branchless setting of the `nextInitialized` flag.
assembly {
// `(quantity == 1) << BITPOS_NEXT_INITIALIZED`.
result := shl(BITPOS_NEXT_INITIALIZED, eq(quantity, 1))
}
}
/**
* @dev See {IERC721-approve}.
*/
function approve(address to, uint256 tokenId) public override {
address owner = ownerOf(tokenId);
if (_msgSenderERC721A() != owner)
if (!isApprovedForAll(owner, _msgSenderERC721A())) {
revert ApprovalCallerNotOwnerNorApproved();
}
_tokenApprovals[tokenId] = to;
emit Approval(owner, to, tokenId);
}
/**
* @dev See {IERC721-getApproved}.
*/
function getApproved(uint256 tokenId)
public
view
override
returns (address)
{
if (!_exists(tokenId)) revert ApprovalQueryForNonexistentToken();
return _tokenApprovals[tokenId];
}
/**
* @dev See {IERC721-setApprovalForAll}.
*/
function setApprovalForAll(address operator, bool approved)
public
virtual
override
{
if (operator == _msgSenderERC721A()) revert ApproveToCaller();
_operatorApprovals[_msgSenderERC721A()][operator] = approved;
emit ApprovalForAll(_msgSenderERC721A(), 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-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 {
transferFrom(from, to, tokenId);
if (to.code.length != 0)
if (!_checkContractOnERC721Received(from, to, tokenId, _data)) {
revert TransferToNonERC721ReceiverImplementer();
}
}
/**
* @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`),
*/
function _exists(uint256 tokenId) internal view returns (bool) {
return
_startTokenId() <= tokenId &&
tokenId < _currentIndex && // If within bounds,
_packedOwnerships[tokenId] & BITMASK_BURNED == 0; // and not burned.
}
/**
* @dev Equivalent to `_safeMint(to, quantity, '')`.
*/
function _safeMint(address to, uint256 quantity) internal {
_safeMint(to, quantity, "");
}
/**
* @dev Safely mints `quantity` tokens and transfers them to `to`.
*
* Requirements:
*
* - If `to` refers to a smart contract, it must implement
* {IERC721Receiver-onERC721Received}, which is called for each safe transfer.
* - `quantity` must be greater than 0.
*
* See {_mint}.
*
* Emits a {Transfer} event for each mint.
*/
function _safeMint(
address to,
uint256 quantity,
bytes memory _data
) internal {
_mint(to, quantity);
unchecked {
if (to.code.length != 0) {
uint256 end = _currentIndex;
uint256 index = end - quantity;
do {
if (
!_checkContractOnERC721Received(
address(0),
to,
index++,
_data
)
) {
revert TransferToNonERC721ReceiverImplementer();
}
} while (index < end);
// Reentrancy protection.
if (_currentIndex != end) revert();
}
}
}
/**
* @dev Mints `quantity` tokens and transfers them to `to`.
*
* Requirements:
*
* - `to` cannot be the zero address.
* - `quantity` must be greater than 0.
*
* Emits a {Transfer} event for each mint.
*/
function _mint(address to, uint256 quantity) internal {
uint256 startTokenId = _currentIndex;
if (to == address(0)) revert MintToZeroAddress();
if (quantity == 0) revert MintZeroQuantity();
_beforeTokenTransfers(address(0), to, startTokenId, quantity);
// Overflows are incredibly unrealistic.
// `balance` and `numberMinted` have a maximum limit of 2**64.
// `tokenId` has a maximum limit of 2**256.
unchecked {
// Updates:
// - `balance += quantity`.
// - `numberMinted += quantity`.
//
// We can directly add to the `balance` and `numberMinted`.
_packedAddressData[to] +=
quantity *
((1 << BITPOS_NUMBER_MINTED) | 1);
// Updates:
// - `address` to the owner.
// - `startTimestamp` to the timestamp of minting.
// - `burned` to `false`.
// - `nextInitialized` to `quantity == 1`.
_packedOwnerships[startTokenId] = _packOwnershipData(
to,
_nextInitializedFlag(quantity) |
_nextExtraData(address(0), to, 0)
);
uint256 tokenId = startTokenId;
uint256 end = startTokenId + quantity;
do {
emit Transfer(address(0), to, tokenId++);
} while (tokenId < end);
_currentIndex = end;
}
_afterTokenTransfers(address(0), to, startTokenId, quantity);
}
/**
* @dev Mints `quantity` tokens and transfers them to `to`.
*
* This function is intended for efficient minting only during contract creation.
*
* It emits only one {ConsecutiveTransfer} as defined in
* [ERC2309](https://eips.ethereum.org/EIPS/eip-2309),
* instead of a sequence of {Transfer} event(s).
*
* Calling this function outside of contract creation WILL make your contract
* non-compliant with the ERC721 standard.
* For full ERC721 compliance, substituting ERC721 {Transfer} event(s) with the ERC2309
* {ConsecutiveTransfer} event is only permissible during contract creation.
*
* Requirements:
*
* - `to` cannot be the zero address.
* - `quantity` must be greater than 0.
*
* Emits a {ConsecutiveTransfer} event.
*/
function _mintERC2309(address to, uint256 quantity) internal {
uint256 startTokenId = _currentIndex;
if (to == address(0)) revert MintToZeroAddress();
if (quantity == 0) revert MintZeroQuantity();
if (quantity > MAX_MINT_ERC2309_QUANTITY_LIMIT)
revert MintERC2309QuantityExceedsLimit();
_beforeTokenTransfers(address(0), to, startTokenId, quantity);
// Overflows are unrealistic due to the above check for `quantity` to be below the limit.
unchecked {
// Updates:
// - `balance += quantity`.
// - `numberMinted += quantity`.
//
// We can directly add to the `balance` and `numberMinted`.
_packedAddressData[to] +=
quantity *
((1 << BITPOS_NUMBER_MINTED) | 1);
// Updates:
// - `address` to the owner.
// - `startTimestamp` to the timestamp of minting.
// - `burned` to `false`.
// - `nextInitialized` to `quantity == 1`.
_packedOwnerships[startTokenId] = _packOwnershipData(
to,
_nextInitializedFlag(quantity) |
_nextExtraData(address(0), to, 0)
);
emit ConsecutiveTransfer(
startTokenId,
startTokenId + quantity - 1,
address(0),
to
);
_currentIndex = startTokenId + quantity;
}
_afterTokenTransfers(address(0), to, startTokenId, quantity);
}
/**
* @dev Returns the storage slot and value for the approved address of `tokenId`.
*/
function _getApprovedAddress(uint256 tokenId)
private
view
returns (uint256 approvedAddressSlot, address approvedAddress)
{
mapping(uint256 => address) storage tokenApprovalsPtr = _tokenApprovals;
// The following is equivalent to `approvedAddress = _tokenApprovals[tokenId]`.
assembly {
// Compute the slot.
mstore(0x00, tokenId)
mstore(0x20, tokenApprovalsPtr.slot)
approvedAddressSlot := keccak256(0x00, 0x40)
// Load the slot's value from storage.
approvedAddress := sload(approvedAddressSlot)
}
}
/**
* @dev Returns whether the `approvedAddress` is equals to `from` or `msgSender`.
*/
function _isOwnerOrApproved(
address approvedAddress,
address from,
address msgSender
) private pure returns (bool result) {
assembly {
// Mask `from` to the lower 160 bits, in case the upper bits somehow aren't clean.
from := and(from, BITMASK_ADDRESS)
// Mask `msgSender` to the lower 160 bits, in case the upper bits somehow aren't clean.
msgSender := and(msgSender, BITMASK_ADDRESS)
// `msgSender == from || msgSender == approvedAddress`.
result := or(eq(msgSender, from), eq(msgSender, approvedAddress))
}
}
/**
* @dev Transfers `tokenId` from `from` to `to`.
*
* Requirements:
*
* - `to` cannot be the zero address.
* - `tokenId` token must be owned by `from`.
*
* Emits a {Transfer} event.
*/
function transferFrom(
address from,
address to,
uint256 tokenId
) public virtual override {
uint256 prevOwnershipPacked = _packedOwnershipOf(tokenId);
if (address(uint160(prevOwnershipPacked)) != from)
revert TransferFromIncorrectOwner();
(
uint256 approvedAddressSlot,
address approvedAddress
) = _getApprovedAddress(tokenId);
// The nested ifs save around 20+ gas over a compound boolean condition.
if (!_isOwnerOrApproved(approvedAddress, from, _msgSenderERC721A()))
if (!isApprovedForAll(from, _msgSenderERC721A()))
revert TransferCallerNotOwnerNorApproved();
if (to == address(0)) revert TransferToZeroAddress();
_beforeTokenTransfers(from, to, tokenId, 1);
// Clear approvals from the previous owner.
assembly {
if approvedAddress {
// This is equivalent to `delete _tokenApprovals[tokenId]`.
sstore(approvedAddressSlot, 0)
}
}
// Underflow of the sender's balance is impossible because we check for
// ownership above and the recipient's balance can't realistically overflow.
// Counter overflow is incredibly unrealistic as tokenId would have to be 2**256.
unchecked {
// We can directly increment and decrement the balances.
--_packedAddressData[from]; // Updates: `balance -= 1`.
++_packedAddressData[to]; // Updates: `balance += 1`.
// Updates:
// - `address` to the next owner.
// - `startTimestamp` to the timestamp of transfering.
// - `burned` to `false`.
// - `nextInitialized` to `true`.
_packedOwnerships[tokenId] = _packOwnershipData(
to,
BITMASK_NEXT_INITIALIZED |
_nextExtraData(from, to, prevOwnershipPacked)
);
// If the next slot may not have been initialized (i.e. `nextInitialized == false`) .
if (prevOwnershipPacked & BITMASK_NEXT_INITIALIZED == 0) {
uint256 nextTokenId = tokenId + 1;
// If the next slot's address is zero and not burned (i.e. packed value is zero).
if (_packedOwnerships[nextTokenId] == 0) {
// If the next slot is within bounds.
if (nextTokenId != _currentIndex) {
// Initialize the next slot to maintain correctness for `ownerOf(tokenId + 1)`.
_packedOwnerships[nextTokenId] = prevOwnershipPacked;
}
}
}
}
emit Transfer(from, to, tokenId);
_afterTokenTransfers(from, to, tokenId, 1);
}
/**
* @dev Equivalent to `_burn(tokenId, false)`.
*/
function _burn(uint256 tokenId) internal virtual {
_burn(tokenId, false);
}
/**
* @dev Destroys `tokenId`.
* The approval is cleared when the token is burned.
*
* Requirements:
*
* - `tokenId` must exist.
*
* Emits a {Transfer} event.
*/
function _burn(uint256 tokenId, bool approvalCheck) internal virtual {
uint256 prevOwnershipPacked = _packedOwnershipOf(tokenId);
address from = address(uint160(prevOwnershipPacked));
(
uint256 approvedAddressSlot,
address approvedAddress
) = _getApprovedAddress(tokenId);
if (approvalCheck) {
// The nested ifs save around 20+ gas over a compound boolean condition.
if (!_isOwnerOrApproved(approvedAddress, from, _msgSenderERC721A()))
if (!isApprovedForAll(from, _msgSenderERC721A()))
revert TransferCallerNotOwnerNorApproved();
}
_beforeTokenTransfers(from, address(0), tokenId, 1);
// Clear approvals from the previous owner.
assembly {
if approvedAddress {
// This is equivalent to `delete _tokenApprovals[tokenId]`.
sstore(approvedAddressSlot, 0)
}
}
// Underflow of the sender's balance is impossible because we check for
// ownership above and the recipient's balance can't realistically overflow.
// Counter overflow is incredibly unrealistic as `tokenId` would have to be 2**256.
unchecked {
// Updates:
// - `balance -= 1`.
// - `numberBurned += 1`.
//
// We can directly decrement the balance, and increment the number burned.
// This is equivalent to `packed -= 1; packed += 1 << BITPOS_NUMBER_BURNED;`.
_packedAddressData[from] += (1 << BITPOS_NUMBER_BURNED) - 1;
// Updates:
// - `address` to the last owner.
// - `startTimestamp` to the timestamp of burning.
// - `burned` to `true`.
// - `nextInitialized` to `true`.
_packedOwnerships[tokenId] = _packOwnershipData(
from,
(BITMASK_BURNED | BITMASK_NEXT_INITIALIZED) |
_nextExtraData(from, address(0), prevOwnershipPacked)
);
// If the next slot may not have been initialized (i.e. `nextInitialized == false`) .
if (prevOwnershipPacked & BITMASK_NEXT_INITIALIZED == 0) {
uint256 nextTokenId = tokenId + 1;
// If the next slot's address is zero and not burned (i.e. packed value is zero).
if (_packedOwnerships[nextTokenId] == 0) {
// If the next slot is within bounds.
if (nextTokenId != _currentIndex) {
// Initialize the next slot to maintain correctness for `ownerOf(tokenId + 1)`.
_packedOwnerships[nextTokenId] = prevOwnershipPacked;
}
}
}
}
emit Transfer(from, address(0), tokenId);
_afterTokenTransfers(from, address(0), tokenId, 1);
// Overflow not possible, as _burnCounter cannot be exceed _currentIndex times.
unchecked {
_burnCounter++;
}
}
/**
* @dev Internal function to invoke {IERC721Receiver-onERC721Received} on a target 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 _checkContractOnERC721Received(
address from,
address to,
uint256 tokenId,
bytes memory _data
) private returns (bool) {
try
ERC721A__IERC721Receiver(to).onERC721Received(
_msgSenderERC721A(),
from,
tokenId,
_data
)
returns (bytes4 retval) {
return
retval ==
ERC721A__IERC721Receiver(to).onERC721Received.selector;
} catch (bytes memory reason) {
if (reason.length == 0) {
revert TransferToNonERC721ReceiverImplementer();
} else {
assembly {
revert(add(32, reason), mload(reason))
}
}
}
}
/**
* @dev Directly sets the extra data for the ownership data `index`.
*/
function _setExtraDataAt(uint256 index, uint24 extraData) internal {
uint256 packed = _packedOwnerships[index];
if (packed == 0) revert OwnershipNotInitializedForExtraData();
uint256 extraDataCasted;
// Cast `extraData` with assembly to avoid redundant masking.
assembly {
extraDataCasted := extraData
}
packed =
(packed & BITMASK_EXTRA_DATA_COMPLEMENT) |
(extraDataCasted << BITPOS_EXTRA_DATA);
_packedOwnerships[index] = packed;
}
/**
* @dev Returns the next extra data for the packed ownership data.
* The returned result is shifted into position.
*/
function _nextExtraData(
address from,
address to,
uint256 prevOwnershipPacked
) private view returns (uint256) {
uint24 extraData = uint24(prevOwnershipPacked >> BITPOS_EXTRA_DATA);
return uint256(_extraData(from, to, extraData)) << BITPOS_EXTRA_DATA;
}
/**
* @dev Called during each token transfer to set the 24bit `extraData` field.
* Intended to be overridden by the cosumer contract.
*
* `previousExtraData` - the value of `extraData` before transfer.
*
* 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, `tokenId` will be burned by `from`.
* - `from` and `to` are never both zero.
*/
function _extraData(
address from,
address to,
uint24 previousExtraData
) internal view virtual returns (uint24) {}
/**
* @dev Hook that is called before a set of serially-ordered token ids are about to be transferred.
* This includes minting.
* And also called before burning one token.
*
* startTokenId - the first token id to be transferred
* quantity - the amount to be transferred
*
* 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, `tokenId` will be burned by `from`.
* - `from` and `to` are never both zero.
*/
function _beforeTokenTransfers(
address from,
address to,
uint256 startTokenId,
uint256 quantity
) internal virtual {}
/**
* @dev Hook that is called after a set of serially-ordered token ids have been transferred.
* This includes minting.
* And also called after one token has been burned.
*
* startTokenId - the first token id to be transferred
* quantity - the amount to be transferred
*
* Calling conditions:
*
* - When `from` and `to` are both non-zero, `from`'s `tokenId` has been
* transferred to `to`.
* - When `from` is zero, `tokenId` has been minted for `to`.
* - When `to` is zero, `tokenId` has been burned by `from`.
* - `from` and `to` are never both zero.
*/
function _afterTokenTransfers(
address from,
address to,
uint256 startTokenId,
uint256 quantity
) internal virtual {}
/**
* @dev Returns the message sender (defaults to `msg.sender`).
*
* If you are writing GSN compatible contracts, you need to override this function.
*/
function _msgSenderERC721A() internal view virtual returns (address) {
return msg.sender;
}
/**
* @dev Converts a `uint256` to its ASCII `string` decimal representation.
*/
function _toString(uint256 value)
internal
pure
returns (string memory ptr)
{
assembly {
// The maximum value of a uint256 contains 78 digits (1 byte per digit),
// but we allocate 128 bytes to keep the free memory pointer 32-byte word aliged.
// We will need 1 32-byte word to store the length,
// and 3 32-byte words to store a maximum of 78 digits. Total: 32 + 3 * 32 = 128.
ptr := add(mload(0x40), 128)
// Update the free memory pointer to allocate.
mstore(0x40, ptr)
// Cache the end of the memory to calculate the length later.
let end := ptr
// We write the string from the rightmost digit to the leftmost digit.
// The following is essentially a do-while loop that also handles the zero case.
// Costs a bit more than early returning for the zero case,
// but cheaper in terms of deployment and overall runtime costs.
for {
// Initialize and perform the first pass without check.
let temp := value
// Move the pointer 1 byte leftwards to point to an empty character slot.
ptr := sub(ptr, 1)
// Write the character to the pointer. 48 is the ASCII index of '0'.
mstore8(ptr, add(48, mod(temp, 10)))
temp := div(temp, 10)
} temp {
// Keep dividing `temp` until zero.
temp := div(temp, 10)
} {
// Body of the for loop.
ptr := sub(ptr, 1)
mstore8(ptr, add(48, mod(temp, 10)))
}
let length := sub(end, ptr)
// Move the pointer 32 bytes leftwards to make room for the length.
ptr := sub(ptr, 32)
// Store the length.
mstore(ptr, length)
}
}
}
// SPDX-License-Identifier: MIT
// ERC721A Contracts v4.1.0
// Creator: Chiru Labs
pragma solidity ^0.8.4;
/**
* @dev Interface of an ERC721A compliant contract.
*/
interface IERC721A {
/**
* The caller must own the token or be an approved operator.
*/
error ApprovalCallerNotOwnerNorApproved();
/**
* The token does not exist.
*/
error ApprovalQueryForNonexistentToken();
/**
* The caller cannot approve to their own address.
*/
error ApproveToCaller();
/**
* Cannot query the balance for the zero address.
*/
error BalanceQueryForZeroAddress();
/**
* Cannot mint to the zero address.
*/
error MintToZeroAddress();
/**
* The quantity of tokens minted must be more than zero.
*/
error MintZeroQuantity();
/**
* The token does not exist.
*/
error OwnerQueryForNonexistentToken();
/**
* The caller must own the token or be an approved operator.
*/
error TransferCallerNotOwnerNorApproved();
/**
* The token must be owned by `from`.
*/
error TransferFromIncorrectOwner();
/**
* Cannot safely transfer to a contract that does not implement the ERC721Receiver interface.
*/
error TransferToNonERC721ReceiverImplementer();
/**
* Cannot transfer to the zero address.
*/
error TransferToZeroAddress();
/**
* The token does not exist.
*/
error URIQueryForNonexistentToken();
/**
* The `quantity` minted with ERC2309 exceeds the safety limit.
*/
error MintERC2309QuantityExceedsLimit();
/**
* The `extraData` cannot be set on an unintialized ownership slot.
*/
error OwnershipNotInitializedForExtraData();
struct TokenOwnership {
// The address of the owner.
address addr;
// Keeps track of the start time of ownership with minimal overhead for tokenomics.
uint64 startTimestamp;
// Whether the token has been burned.
bool burned;
// Arbitrary data similar to `startTimestamp` that can be set through `_extraData`.
uint24 extraData;
}
/**
* @dev Returns the total amount of tokens stored by the contract.
*
* Burned tokens are calculated here, use `_totalMinted()` if you want to count just minted tokens.
*/
function totalSupply() external view returns (uint256);
// ==============================
// 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);
// ==============================
// IERC721
// ==============================
/**
* @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`.
*
* 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;
/**
* @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 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 the account approved for `tokenId` token.
*
* Requirements:
*
* - `tokenId` must exist.
*/
function getApproved(uint256 tokenId) external view returns (address operator);
/**
* @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);
// ==============================
// IERC721Metadata
// ==============================
/**
* @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);
// ==============================
// IERC2309
// ==============================
/**
* @dev Emitted when tokens in `fromTokenId` to `toTokenId` (inclusive) is transferred from `from` to `to`,
* as defined in the ERC2309 standard. See `_mintERC2309` for more details.
*/
event ConsecutiveTransfer(uint256 indexed fromTokenId, uint256 toTokenId, address indexed from, address indexed to);
}
// SPDX-License-Identifier: MIT
// ERC721A Contracts v4.1.0
// Creator: Chiru Labs
pragma solidity ^0.8.4;
import '../IERC721A.sol';
/**
* @dev Interface of an ERC721ABurnable compliant contract.
*/
interface IERC721ABurnable is IERC721A {
/**
* @dev Burns `tokenId`. See {ERC721A-_burn}.
*
* Requirements:
*
* - The caller must own `tokenId` or be an approved operator.
*/
function burn(uint256 tokenId) external;
}
// SPDX-License-Identifier: Unlicense
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 =
78156646155174841979727994598816262306175212592076161876661_508869554232690281;
/// 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 least power of two that is greater than or equal to sqrt(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;
}
}
}