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1434 lines (1224 loc) · 49.8 KB
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// Sources flattened with hardhat v2.19.4 https://hardhat.org
// SPDX-License-Identifier: MIT
// File @openzeppelin/contracts/utils/Context.sol@v5.0.1
// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.1) (utils/Context.sol)
pragma solidity ^0.8.20;
/**
* @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;
}
function _contextSuffixLength() internal view virtual returns (uint256) {
return 0;
}
}
// File @openzeppelin/contracts/access/Ownable.sol@v5.0.1
// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (access/Ownable.sol)
pragma solidity ^0.8.20;
/**
* @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.
*
* The initial owner is set to the address provided by the deployer. 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;
/**
* @dev The caller account is not authorized to perform an operation.
*/
error OwnableUnauthorizedAccount(address account);
/**
* @dev The owner is not a valid owner account. (eg. `address(0)`)
*/
error OwnableInvalidOwner(address owner);
event OwnershipTransferred(address indexed previousOwner, address indexed newOwner);
/**
* @dev Initializes the contract setting the address provided by the deployer as the initial owner.
*/
constructor(address initialOwner) {
if (initialOwner == address(0)) {
revert OwnableInvalidOwner(address(0));
}
_transferOwnership(initialOwner);
}
/**
* @dev Throws if called by any account other than the owner.
*/
modifier onlyOwner() {
_checkOwner();
_;
}
/**
* @dev Returns the address of the current owner.
*/
function owner() public view virtual returns (address) {
return _owner;
}
/**
* @dev Throws if the sender is not the owner.
*/
function _checkOwner() internal view virtual {
if (owner() != _msgSender()) {
revert OwnableUnauthorizedAccount(_msgSender());
}
}
/**
* @dev Leaves the contract without owner. It will not be possible to call
* `onlyOwner` functions. Can only be called by the current owner.
*
* NOTE: Renouncing ownership will leave the contract without an owner,
* thereby disabling 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 {
if (newOwner == address(0)) {
revert OwnableInvalidOwner(address(0));
}
_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);
}
}
// File @openzeppelin/contracts/utils/introspection/IERC165.sol@v5.0.1
// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/introspection/IERC165.sol)
pragma solidity ^0.8.20;
/**
* @dev Interface of the ERC165 standard, as defined in the
* https://eips.ethereum.org/EIPS/eip-165[EIP].
*
* Implementers can declare support of contract interfaces, which can then be
* queried by others ({ERC165Checker}).
*
* For an implementation, see {ERC165}.
*/
interface IERC165 {
/**
* @dev Returns true if this contract implements the interface defined by
* `interfaceId`. See the corresponding
* https://eips.ethereum.org/EIPS/eip-165#how-interfaces-are-identified[EIP section]
* to learn more about how these ids are created.
*
* This function call must use less than 30 000 gas.
*/
function supportsInterface(bytes4 interfaceId) external view returns (bool);
}
// File @openzeppelin/contracts/token/ERC1155/IERC1155.sol@v5.0.1
// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.1) (token/ERC1155/IERC1155.sol)
pragma solidity ^0.8.20;
/**
* @dev Required interface of an ERC1155 compliant contract, as defined in the
* https://eips.ethereum.org/EIPS/eip-1155[EIP].
*/
interface IERC1155 is IERC165 {
/**
* @dev Emitted when `value` amount of tokens of type `id` are transferred from `from` to `to` by `operator`.
*/
event TransferSingle(address indexed operator, address indexed from, address indexed to, uint256 id, uint256 value);
/**
* @dev Equivalent to multiple {TransferSingle} events, where `operator`, `from` and `to` are the same for all
* transfers.
*/
event TransferBatch(
address indexed operator,
address indexed from,
address indexed to,
uint256[] ids,
uint256[] values
);
/**
* @dev Emitted when `account` grants or revokes permission to `operator` to transfer their tokens, according to
* `approved`.
*/
event ApprovalForAll(address indexed account, address indexed operator, bool approved);
/**
* @dev Emitted when the URI for token type `id` changes to `value`, if it is a non-programmatic URI.
*
* If an {URI} event was emitted for `id`, the standard
* https://eips.ethereum.org/EIPS/eip-1155#metadata-extensions[guarantees] that `value` will equal the value
* returned by {IERC1155MetadataURI-uri}.
*/
event URI(string value, uint256 indexed id);
/**
* @dev Returns the value of tokens of token type `id` owned by `account`.
*
* Requirements:
*
* - `account` cannot be the zero address.
*/
function balanceOf(address account, uint256 id) external view returns (uint256);
/**
* @dev xref:ROOT:erc1155.adoc#batch-operations[Batched] version of {balanceOf}.
*
* Requirements:
*
* - `accounts` and `ids` must have the same length.
*/
function balanceOfBatch(
address[] calldata accounts,
uint256[] calldata ids
) external view returns (uint256[] memory);
/**
* @dev Grants or revokes permission to `operator` to transfer the caller's tokens, according to `approved`,
*
* Emits an {ApprovalForAll} event.
*
* Requirements:
*
* - `operator` cannot be the caller.
*/
function setApprovalForAll(address operator, bool approved) external;
/**
* @dev Returns true if `operator` is approved to transfer ``account``'s tokens.
*
* See {setApprovalForAll}.
*/
function isApprovedForAll(address account, address operator) external view returns (bool);
/**
* @dev Transfers a `value` amount of tokens of type `id` from `from` to `to`.
*
* WARNING: This function can potentially allow a reentrancy attack when transferring tokens
* to an untrusted contract, when invoking {onERC1155Received} on the receiver.
* Ensure to follow the checks-effects-interactions pattern and consider employing
* reentrancy guards when interacting with untrusted contracts.
*
* Emits a {TransferSingle} event.
*
* Requirements:
*
* - `to` cannot be the zero address.
* - If the caller is not `from`, it must have been approved to spend ``from``'s tokens via {setApprovalForAll}.
* - `from` must have a balance of tokens of type `id` of at least `value` amount.
* - If `to` refers to a smart contract, it must implement {IERC1155Receiver-onERC1155Received} and return the
* acceptance magic value.
*/
function safeTransferFrom(address from, address to, uint256 id, uint256 value, bytes calldata data) external;
/**
* @dev xref:ROOT:erc1155.adoc#batch-operations[Batched] version of {safeTransferFrom}.
*
* WARNING: This function can potentially allow a reentrancy attack when transferring tokens
* to an untrusted contract, when invoking {onERC1155BatchReceived} on the receiver.
* Ensure to follow the checks-effects-interactions pattern and consider employing
* reentrancy guards when interacting with untrusted contracts.
*
* Emits either a {TransferSingle} or a {TransferBatch} event, depending on the length of the array arguments.
*
* Requirements:
*
* - `ids` and `values` must have the same length.
* - If `to` refers to a smart contract, it must implement {IERC1155Receiver-onERC1155BatchReceived} and return the
* acceptance magic value.
*/
function safeBatchTransferFrom(
address from,
address to,
uint256[] calldata ids,
uint256[] calldata values,
bytes calldata data
) external;
}
// File @openzeppelin/contracts/token/ERC1155/IERC1155Receiver.sol@v5.0.1
// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (token/ERC1155/IERC1155Receiver.sol)
pragma solidity ^0.8.20;
/**
* @dev Interface that must be implemented by smart contracts in order to receive
* ERC-1155 token transfers.
*/
interface IERC1155Receiver is IERC165 {
/**
* @dev Handles the receipt of a single ERC1155 token type. This function is
* called at the end of a `safeTransferFrom` after the balance has been updated.
*
* NOTE: To accept the transfer, this must return
* `bytes4(keccak256("onERC1155Received(address,address,uint256,uint256,bytes)"))`
* (i.e. 0xf23a6e61, or its own function selector).
*
* @param operator The address which initiated the transfer (i.e. msg.sender)
* @param from The address which previously owned the token
* @param id The ID of the token being transferred
* @param value The amount of tokens being transferred
* @param data Additional data with no specified format
* @return `bytes4(keccak256("onERC1155Received(address,address,uint256,uint256,bytes)"))` if transfer is allowed
*/
function onERC1155Received(
address operator,
address from,
uint256 id,
uint256 value,
bytes calldata data
) external returns (bytes4);
/**
* @dev Handles the receipt of a multiple ERC1155 token types. This function
* is called at the end of a `safeBatchTransferFrom` after the balances have
* been updated.
*
* NOTE: To accept the transfer(s), this must return
* `bytes4(keccak256("onERC1155BatchReceived(address,address,uint256[],uint256[],bytes)"))`
* (i.e. 0xbc197c81, or its own function selector).
*
* @param operator The address which initiated the batch transfer (i.e. msg.sender)
* @param from The address which previously owned the token
* @param ids An array containing ids of each token being transferred (order and length must match values array)
* @param values An array containing amounts of each token being transferred (order and length must match ids array)
* @param data Additional data with no specified format
* @return `bytes4(keccak256("onERC1155BatchReceived(address,address,uint256[],uint256[],bytes)"))` if transfer is allowed
*/
function onERC1155BatchReceived(
address operator,
address from,
uint256[] calldata ids,
uint256[] calldata values,
bytes calldata data
) external returns (bytes4);
}
// File @openzeppelin/contracts/utils/introspection/ERC165.sol@v5.0.1
// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/introspection/ERC165.sol)
pragma solidity ^0.8.20;
/**
* @dev Implementation of the {IERC165} interface.
*
* Contracts that want to implement ERC165 should inherit from this contract and override {supportsInterface} to check
* for the additional interface id that will be supported. For example:
*
* ```solidity
* function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
* return interfaceId == type(MyInterface).interfaceId || super.supportsInterface(interfaceId);
* }
* ```
*/
abstract contract ERC165 is IERC165 {
/**
* @dev See {IERC165-supportsInterface}.
*/
function supportsInterface(bytes4 interfaceId) public view virtual returns (bool) {
return interfaceId == type(IERC165).interfaceId;
}
}
// File @openzeppelin/contracts/token/ERC1155/utils/ERC1155Holder.sol@v5.0.1
// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (token/ERC1155/utils/ERC1155Holder.sol)
pragma solidity ^0.8.20;
/**
* @dev Simple implementation of `IERC1155Receiver` that will allow a contract to hold ERC1155 tokens.
*
* IMPORTANT: When inheriting this contract, you must include a way to use the received tokens, otherwise they will be
* stuck.
*/
abstract contract ERC1155Holder is ERC165, IERC1155Receiver {
/**
* @dev See {IERC165-supportsInterface}.
*/
function supportsInterface(bytes4 interfaceId) public view virtual override(ERC165, IERC165) returns (bool) {
return interfaceId == type(IERC1155Receiver).interfaceId || super.supportsInterface(interfaceId);
}
function onERC1155Received(
address,
address,
uint256,
uint256,
bytes memory
) public virtual override returns (bytes4) {
return this.onERC1155Received.selector;
}
function onERC1155BatchReceived(
address,
address,
uint256[] memory,
uint256[] memory,
bytes memory
) public virtual override returns (bytes4) {
return this.onERC1155BatchReceived.selector;
}
}
// File @openzeppelin/contracts/token/ERC721/IERC721.sol@v5.0.1
// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (token/ERC721/IERC721.sol)
pragma solidity ^0.8.20;
/**
* @dev Required interface of an ERC721 compliant contract.
*/
interface IERC721 is IERC165 {
/**
* @dev Emitted when `tokenId` token is transferred from `from` to `to`.
*/
event Transfer(address indexed from, address indexed to, uint256 indexed tokenId);
/**
* @dev Emitted when `owner` enables `approved` to manage the `tokenId` token.
*/
event Approval(address indexed owner, address indexed approved, uint256 indexed tokenId);
/**
* @dev Emitted when `owner` enables or disables (`approved`) `operator` to manage all of its assets.
*/
event ApprovalForAll(address indexed owner, address indexed operator, bool approved);
/**
* @dev Returns the number of tokens in ``owner``'s account.
*/
function balanceOf(address owner) external view returns (uint256 balance);
/**
* @dev Returns the owner of the `tokenId` token.
*
* Requirements:
*
* - `tokenId` must exist.
*/
function ownerOf(uint256 tokenId) external view returns (address owner);
/**
* @dev Safely transfers `tokenId` token from `from` to `to`.
*
* 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 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: Note that the caller is responsible to confirm that the recipient is capable of receiving ERC721
* or else they may be permanently lost. Usage of {safeTransferFrom} prevents loss, though the caller must
* understand this adds an external call which potentially creates a reentrancy vulnerability.
*
* 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 address zero.
*
* 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);
}
// File @openzeppelin/contracts/token/ERC20/IERC20.sol@v5.0.1
// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (token/ERC20/IERC20.sol)
pragma solidity ^0.8.20;
/**
* @dev Interface of the ERC20 standard as defined in the EIP.
*/
interface IERC20 {
/**
* @dev Emitted when `value` tokens are moved from one account (`from`) to
* another (`to`).
*
* Note that `value` may be zero.
*/
event Transfer(address indexed from, address indexed to, uint256 value);
/**
* @dev Emitted when the allowance of a `spender` for an `owner` is set by
* a call to {approve}. `value` is the new allowance.
*/
event Approval(address indexed owner, address indexed spender, uint256 value);
/**
* @dev Returns the value of tokens in existence.
*/
function totalSupply() external view returns (uint256);
/**
* @dev Returns the value of tokens owned by `account`.
*/
function balanceOf(address account) external view returns (uint256);
/**
* @dev Moves a `value` amount of tokens from the caller's account to `to`.
*
* Returns a boolean value indicating whether the operation succeeded.
*
* Emits a {Transfer} event.
*/
function transfer(address to, uint256 value) external returns (bool);
/**
* @dev Returns the remaining number of tokens that `spender` will be
* allowed to spend on behalf of `owner` through {transferFrom}. This is
* zero by default.
*
* This value changes when {approve} or {transferFrom} are called.
*/
function allowance(address owner, address spender) external view returns (uint256);
/**
* @dev Sets a `value` amount of tokens as the allowance of `spender` over the
* caller's tokens.
*
* Returns a boolean value indicating whether the operation succeeded.
*
* IMPORTANT: Beware that changing an allowance with this method brings the risk
* that someone may use both the old and the new allowance by unfortunate
* transaction ordering. One possible solution to mitigate this race
* condition is to first reduce the spender's allowance to 0 and set the
* desired value afterwards:
* https://github.com/ethereum/EIPs/issues/20#issuecomment-263524729
*
* Emits an {Approval} event.
*/
function approve(address spender, uint256 value) external returns (bool);
/**
* @dev Moves a `value` amount of tokens from `from` to `to` using the
* allowance mechanism. `value` is then deducted from the caller's
* allowance.
*
* Returns a boolean value indicating whether the operation succeeded.
*
* Emits a {Transfer} event.
*/
function transferFrom(address from, address to, uint256 value) external returns (bool);
}
// File @openzeppelin/contracts/utils/math/Math.sol@v5.0.1
// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/math/Math.sol)
pragma solidity ^0.8.20;
/**
* @dev Standard math utilities missing in the Solidity language.
*/
library Math {
/**
* @dev Muldiv operation overflow.
*/
error MathOverflowedMulDiv();
enum Rounding {
Floor, // Toward negative infinity
Ceil, // Toward positive infinity
Trunc, // Toward zero
Expand // Away from zero
}
/**
* @dev Returns the addition of two unsigned integers, with an overflow flag.
*/
function tryAdd(uint256 a, uint256 b) internal pure returns (bool, uint256) {
unchecked {
uint256 c = a + b;
if (c < a) return (false, 0);
return (true, c);
}
}
/**
* @dev Returns the subtraction of two unsigned integers, with an overflow flag.
*/
function trySub(uint256 a, uint256 b) internal pure returns (bool, uint256) {
unchecked {
if (b > a) return (false, 0);
return (true, a - b);
}
}
/**
* @dev Returns the multiplication of two unsigned integers, with an overflow flag.
*/
function tryMul(uint256 a, uint256 b) internal pure returns (bool, uint256) {
unchecked {
// Gas optimization: this is cheaper than requiring 'a' not being zero, but the
// benefit is lost if 'b' is also tested.
// See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522
if (a == 0) return (true, 0);
uint256 c = a * b;
if (c / a != b) return (false, 0);
return (true, c);
}
}
/**
* @dev Returns the division of two unsigned integers, with a division by zero flag.
*/
function tryDiv(uint256 a, uint256 b) internal pure returns (bool, uint256) {
unchecked {
if (b == 0) return (false, 0);
return (true, a / b);
}
}
/**
* @dev Returns the remainder of dividing two unsigned integers, with a division by zero flag.
*/
function tryMod(uint256 a, uint256 b) internal pure returns (bool, uint256) {
unchecked {
if (b == 0) return (false, 0);
return (true, a % b);
}
}
/**
* @dev Returns the largest of two numbers.
*/
function max(uint256 a, uint256 b) internal pure returns (uint256) {
return a > b ? a : b;
}
/**
* @dev Returns the smallest of two numbers.
*/
function min(uint256 a, uint256 b) internal pure returns (uint256) {
return a < b ? a : b;
}
/**
* @dev Returns the average of two numbers. The result is rounded towards
* zero.
*/
function average(uint256 a, uint256 b) internal pure returns (uint256) {
// (a + b) / 2 can overflow.
return (a & b) + (a ^ b) / 2;
}
/**
* @dev Returns the ceiling of the division of two numbers.
*
* This differs from standard division with `/` in that it rounds towards infinity instead
* of rounding towards zero.
*/
function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {
if (b == 0) {
// Guarantee the same behavior as in a regular Solidity division.
return a / b;
}
// (a + b - 1) / b can overflow on addition, so we distribute.
return a == 0 ? 0 : (a - 1) / b + 1;
}
/**
* @notice Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or
* denominator == 0.
* @dev Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv) with further edits by
* Uniswap Labs also under MIT license.
*/
function mulDiv(uint256 x, uint256 y, uint256 denominator) internal pure returns (uint256 result) {
unchecked {
// 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use
// use the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
// variables such that product = prod1 * 2^256 + prod0.
uint256 prod0 = x * y; // Least significant 256 bits of the product
uint256 prod1; // Most significant 256 bits of the product
assembly {
let mm := mulmod(x, y, not(0))
prod1 := sub(sub(mm, prod0), lt(mm, prod0))
}
// Handle non-overflow cases, 256 by 256 division.
if (prod1 == 0) {
// Solidity will revert if denominator == 0, unlike the div opcode on its own.
// The surrounding unchecked block does not change this fact.
// See https://docs.soliditylang.org/en/latest/control-structures.html#checked-or-unchecked-arithmetic.
return prod0 / denominator;
}
// Make sure the result is less than 2^256. Also prevents denominator == 0.
if (denominator <= prod1) {
revert MathOverflowedMulDiv();
}
///////////////////////////////////////////////
// 512 by 256 division.
///////////////////////////////////////////////
// Make division exact by subtracting the remainder from [prod1 prod0].
uint256 remainder;
assembly {
// Compute remainder using mulmod.
remainder := mulmod(x, y, denominator)
// Subtract 256 bit number from 512 bit number.
prod1 := sub(prod1, gt(remainder, prod0))
prod0 := sub(prod0, remainder)
}
// Factor powers of two out of denominator and compute largest power of two divisor of denominator.
// Always >= 1. See https://cs.stackexchange.com/q/138556/92363.
uint256 twos = denominator & (0 - denominator);
assembly {
// Divide denominator by twos.
denominator := div(denominator, twos)
// Divide [prod1 prod0] by twos.
prod0 := div(prod0, twos)
// Flip twos such that it is 2^256 / twos. If twos is zero, then it becomes one.
twos := add(div(sub(0, twos), twos), 1)
}
// Shift in bits from prod1 into prod0.
prod0 |= prod1 * twos;
// Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such
// that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for
// four bits. That is, denominator * inv = 1 mod 2^4.
uint256 inverse = (3 * denominator) ^ 2;
// Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also
// works in modular arithmetic, doubling the correct bits in each step.
inverse *= 2 - denominator * inverse; // inverse mod 2^8
inverse *= 2 - denominator * inverse; // inverse mod 2^16
inverse *= 2 - denominator * inverse; // inverse mod 2^32
inverse *= 2 - denominator * inverse; // inverse mod 2^64
inverse *= 2 - denominator * inverse; // inverse mod 2^128
inverse *= 2 - denominator * inverse; // inverse mod 2^256
// Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
// This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is
// less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1
// is no longer required.
result = prod0 * inverse;
return result;
}
}
/**
* @notice Calculates x * y / denominator with full precision, following the selected rounding direction.
*/
function mulDiv(uint256 x, uint256 y, uint256 denominator, Rounding rounding) internal pure returns (uint256) {
uint256 result = mulDiv(x, y, denominator);
if (unsignedRoundsUp(rounding) && mulmod(x, y, denominator) > 0) {
result += 1;
}
return result;
}
/**
* @dev Returns the square root of a number. If the number is not a perfect square, the value is rounded
* towards zero.
*
* Inspired by Henry S. Warren, Jr.'s "Hacker's Delight" (Chapter 11).
*/
function sqrt(uint256 a) internal pure returns (uint256) {
if (a == 0) {
return 0;
}
// For our first guess, we get the biggest power of 2 which is smaller than the square root of the target.
//
// We know that the "msb" (most significant bit) of our target number `a` is a power of 2 such that we have
// `msb(a) <= a < 2*msb(a)`. This value can be written `msb(a)=2**k` with `k=log2(a)`.
//
// This can be rewritten `2**log2(a) <= a < 2**(log2(a) + 1)`
// → `sqrt(2**k) <= sqrt(a) < sqrt(2**(k+1))`
// → `2**(k/2) <= sqrt(a) < 2**((k+1)/2) <= 2**(k/2 + 1)`
//
// Consequently, `2**(log2(a) / 2)` is a good first approximation of `sqrt(a)` with at least 1 correct bit.
uint256 result = 1 << (log2(a) >> 1);
// At this point `result` is an estimation with one bit of precision. We know the true value is a uint128,
// since it is the square root of a uint256. Newton's method converges quadratically (precision doubles at
// every iteration). We thus need at most 7 iteration to turn our partial result with one bit of precision
// into the expected uint128 result.
unchecked {
result = (result + a / result) >> 1;
result = (result + a / result) >> 1;
result = (result + a / result) >> 1;
result = (result + a / result) >> 1;
result = (result + a / result) >> 1;
result = (result + a / result) >> 1;
result = (result + a / result) >> 1;
return min(result, a / result);
}
}
/**
* @notice Calculates sqrt(a), following the selected rounding direction.
*/
function sqrt(uint256 a, Rounding rounding) internal pure returns (uint256) {
unchecked {
uint256 result = sqrt(a);
return result + (unsignedRoundsUp(rounding) && result * result < a ? 1 : 0);
}
}
/**
* @dev Return the log in base 2 of a positive value rounded towards zero.
* Returns 0 if given 0.
*/
function log2(uint256 value) internal pure returns (uint256) {
uint256 result = 0;
unchecked {
if (value >> 128 > 0) {
value >>= 128;
result += 128;
}
if (value >> 64 > 0) {
value >>= 64;
result += 64;
}
if (value >> 32 > 0) {
value >>= 32;
result += 32;
}
if (value >> 16 > 0) {
value >>= 16;
result += 16;
}
if (value >> 8 > 0) {
value >>= 8;
result += 8;
}
if (value >> 4 > 0) {
value >>= 4;
result += 4;
}
if (value >> 2 > 0) {
value >>= 2;
result += 2;
}
if (value >> 1 > 0) {
result += 1;
}
}
return result;
}
/**
* @dev Return the log in base 2, following the selected rounding direction, of a positive value.
* Returns 0 if given 0.
*/
function log2(uint256 value, Rounding rounding) internal pure returns (uint256) {
unchecked {
uint256 result = log2(value);
return result + (unsignedRoundsUp(rounding) && 1 << result < value ? 1 : 0);
}
}
/**
* @dev Return the log in base 10 of a positive value rounded towards zero.
* Returns 0 if given 0.
*/
function log10(uint256 value) internal pure returns (uint256) {
uint256 result = 0;
unchecked {
if (value >= 10 ** 64) {
value /= 10 ** 64;
result += 64;
}
if (value >= 10 ** 32) {
value /= 10 ** 32;
result += 32;
}
if (value >= 10 ** 16) {
value /= 10 ** 16;
result += 16;
}
if (value >= 10 ** 8) {
value /= 10 ** 8;
result += 8;
}
if (value >= 10 ** 4) {
value /= 10 ** 4;
result += 4;
}
if (value >= 10 ** 2) {
value /= 10 ** 2;
result += 2;
}
if (value >= 10 ** 1) {