Contract Source Code:
// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity =0.8.19;
import "solady/src/auth/Ownable.sol";
import "solady/src/utils/SafeTransferLib.sol";
import "weighted-math-lib/WeightedMathLib.sol";
contract Treasury is Ownable {
/// -----------------------------------------------------------------------
/// Dependencies
/// -----------------------------------------------------------------------
using FixedPointMathLib for *;
using SafeTransferLib for address;
/// -----------------------------------------------------------------------
/// Events
/// -----------------------------------------------------------------------
/// @dev Emitted when the fee recipient is updated.
/// @param recipient The new fee recipient address.
/// @param percentage The new fee recipient percentage.
event FeeRecipientUpdated(address recipient, uint256 percentage);
/// -----------------------------------------------------------------------
/// Custom Errors
/// -----------------------------------------------------------------------
/// @dev Error thrown when the input lenght is not same for recipients and percentages.
error InvalidInput();
/// @dev Error thrown when the percentage sum is not 100.
error InvalidPercentageSum();
/// @dev Error thrown when the address is 0x.
error ZeroAddress();
/// -----------------------------------------------------------------------
/// Mutable Storage
/// -----------------------------------------------------------------------
/// @notice Mapping to track fee percentage for each address.
mapping(address => uint256) private feePercents;
/// @notice List of addresses of fee recipients.
address[] private recipients;
/// @notice Address of asset swap fee recipient.
address private assetSwapFeeRecipient;
/// @notice Address of share swap fee recipient.
address private shareSwapFeeRecipient;
/// -----------------------------------------------------------------------
/// Constructor
/// -----------------------------------------------------------------------
/// @param _owner The owner of the factory contract.
constructor(address _owner) {
// Initialize the owner and implementation address.
_initializeOwner(_owner);
// Set the initial recipientes here.
recipients.push(_owner);
feePercents[_owner] = 1 ether;
assetSwapFeeRecipient = _owner;
shareSwapFeeRecipient = _owner;
}
/**
* @notice Update fee recipients and percentages.
* @param _recipients List of addresses to be added as fee recipients.
*/
function updateRecipients(
address[] calldata _recipients,
uint256[] calldata _percentages
)
public
onlyOwner
{
if (_recipients.length != _percentages.length) revert InvalidInput();
delete recipients;
uint256 totalPercentage;
for (uint256 i = 0; i < _recipients.length;) {
if (_recipients[i] == address(0)) revert ZeroAddress();
recipients.push(_recipients[i]);
feePercents[_recipients[i]] = _percentages[i];
totalPercentage += _percentages[i];
emit FeeRecipientUpdated(_recipients[i], _percentages[i]);
unchecked {
++i;
}
}
if (totalPercentage != 1 ether) revert InvalidPercentageSum();
}
function updateAssetSwapFeeRecipient(address _asfr) public onlyOwner {
if (_asfr == address(0)) revert ZeroAddress();
assetSwapFeeRecipient = _asfr;
emit FeeRecipientUpdated(_asfr, 0);
}
function updateShareSwapFeeRecipient(address _ssfr) public onlyOwner {
if (_ssfr == address(0)) revert ZeroAddress();
shareSwapFeeRecipient = _ssfr;
emit FeeRecipientUpdated(_ssfr, 0);
}
/**
* @notice Distriburte the fee to the recipients.
* @param asset Address of the asset that will be distrubuted.
* @param amount Total amount of fees that will be distributed.
*/
function distributeFee(
address asset,
uint256 amount,
uint256 swapFeesAsset,
address share,
uint256 swapFeesShare
)
external
{
for (uint256 i = 0; i < recipients.length;) {
uint256 feeP = feePercents[recipients[i]];
uint256 feeShare = amount.mulWad(feeP);
asset.safeTransfer(recipients[i], feeShare);
unchecked {
++i;
}
}
if (swapFeesShare > 0) {
share.safeTransfer(shareSwapFeeRecipient, swapFeesShare);
}
if (swapFeesAsset > 0) {
asset.safeTransfer(assetSwapFeeRecipient, swapFeesAsset);
}
}
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;
/// @notice Simple single owner authorization mixin.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/auth/Ownable.sol)
///
/// @dev Note:
/// This implementation does NOT auto-initialize the owner to `msg.sender`.
/// You MUST call the `_initializeOwner` in the constructor / initializer.
///
/// While the ownable portion follows
/// [EIP-173](https://eips.ethereum.org/EIPS/eip-173) for compatibility,
/// the nomenclature for the 2-step ownership handover may be unique to this codebase.
abstract contract Ownable {
/*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
/* CUSTOM ERRORS */
/*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
/// @dev The caller is not authorized to call the function.
error Unauthorized();
/// @dev The `newOwner` cannot be the zero address.
error NewOwnerIsZeroAddress();
/// @dev The `pendingOwner` does not have a valid handover request.
error NoHandoverRequest();
/// @dev Cannot double-initialize.
error AlreadyInitialized();
/*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
/* EVENTS */
/*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
/// @dev The ownership is transferred from `oldOwner` to `newOwner`.
/// This event is intentionally kept the same as OpenZeppelin's Ownable to be
/// compatible with indexers and [EIP-173](https://eips.ethereum.org/EIPS/eip-173),
/// despite it not being as lightweight as a single argument event.
event OwnershipTransferred(address indexed oldOwner, address indexed newOwner);
/// @dev An ownership handover to `pendingOwner` has been requested.
event OwnershipHandoverRequested(address indexed pendingOwner);
/// @dev The ownership handover to `pendingOwner` has been canceled.
event OwnershipHandoverCanceled(address indexed pendingOwner);
/// @dev `keccak256(bytes("OwnershipTransferred(address,address)"))`.
uint256 private constant _OWNERSHIP_TRANSFERRED_EVENT_SIGNATURE =
0x8be0079c531659141344cd1fd0a4f28419497f9722a3daafe3b4186f6b6457e0;
/// @dev `keccak256(bytes("OwnershipHandoverRequested(address)"))`.
uint256 private constant _OWNERSHIP_HANDOVER_REQUESTED_EVENT_SIGNATURE =
0xdbf36a107da19e49527a7176a1babf963b4b0ff8cde35ee35d6cd8f1f9ac7e1d;
/// @dev `keccak256(bytes("OwnershipHandoverCanceled(address)"))`.
uint256 private constant _OWNERSHIP_HANDOVER_CANCELED_EVENT_SIGNATURE =
0xfa7b8eab7da67f412cc9575ed43464468f9bfbae89d1675917346ca6d8fe3c92;
/*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
/* STORAGE */
/*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
/// @dev The owner slot is given by:
/// `bytes32(~uint256(uint32(bytes4(keccak256("_OWNER_SLOT_NOT")))))`.
/// It is intentionally chosen to be a high value
/// to avoid collision with lower slots.
/// The choice of manual storage layout is to enable compatibility
/// with both regular and upgradeable contracts.
bytes32 internal constant _OWNER_SLOT =
0xffffffffffffffffffffffffffffffffffffffffffffffffffffffff74873927;
/// The ownership handover slot of `newOwner` is given by:
/// ```
/// mstore(0x00, or(shl(96, user), _HANDOVER_SLOT_SEED))
/// let handoverSlot := keccak256(0x00, 0x20)
/// ```
/// It stores the expiry timestamp of the two-step ownership handover.
uint256 private constant _HANDOVER_SLOT_SEED = 0x389a75e1;
/*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
/* INTERNAL FUNCTIONS */
/*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
/// @dev Override to return true to make `_initializeOwner` prevent double-initialization.
function _guardInitializeOwner() internal pure virtual returns (bool guard) {}
/// @dev Initializes the owner directly without authorization guard.
/// This function must be called upon initialization,
/// regardless of whether the contract is upgradeable or not.
/// This is to enable generalization to both regular and upgradeable contracts,
/// and to save gas in case the initial owner is not the caller.
/// For performance reasons, this function will not check if there
/// is an existing owner.
function _initializeOwner(address newOwner) internal virtual {
if (_guardInitializeOwner()) {
/// @solidity memory-safe-assembly
assembly {
let ownerSlot := _OWNER_SLOT
if sload(ownerSlot) {
mstore(0x00, 0x0dc149f0) // `AlreadyInitialized()`.
revert(0x1c, 0x04)
}
// Clean the upper 96 bits.
newOwner := shr(96, shl(96, newOwner))
// Store the new value.
sstore(ownerSlot, or(newOwner, shl(255, iszero(newOwner))))
// Emit the {OwnershipTransferred} event.
log3(0, 0, _OWNERSHIP_TRANSFERRED_EVENT_SIGNATURE, 0, newOwner)
}
} else {
/// @solidity memory-safe-assembly
assembly {
// Clean the upper 96 bits.
newOwner := shr(96, shl(96, newOwner))
// Store the new value.
sstore(_OWNER_SLOT, newOwner)
// Emit the {OwnershipTransferred} event.
log3(0, 0, _OWNERSHIP_TRANSFERRED_EVENT_SIGNATURE, 0, newOwner)
}
}
}
/// @dev Sets the owner directly without authorization guard.
function _setOwner(address newOwner) internal virtual {
if (_guardInitializeOwner()) {
/// @solidity memory-safe-assembly
assembly {
let ownerSlot := _OWNER_SLOT
// Clean the upper 96 bits.
newOwner := shr(96, shl(96, newOwner))
// Emit the {OwnershipTransferred} event.
log3(0, 0, _OWNERSHIP_TRANSFERRED_EVENT_SIGNATURE, sload(ownerSlot), newOwner)
// Store the new value.
sstore(ownerSlot, or(newOwner, shl(255, iszero(newOwner))))
}
} else {
/// @solidity memory-safe-assembly
assembly {
let ownerSlot := _OWNER_SLOT
// Clean the upper 96 bits.
newOwner := shr(96, shl(96, newOwner))
// Emit the {OwnershipTransferred} event.
log3(0, 0, _OWNERSHIP_TRANSFERRED_EVENT_SIGNATURE, sload(ownerSlot), newOwner)
// Store the new value.
sstore(ownerSlot, newOwner)
}
}
}
/// @dev Throws if the sender is not the owner.
function _checkOwner() internal view virtual {
/// @solidity memory-safe-assembly
assembly {
// If the caller is not the stored owner, revert.
if iszero(eq(caller(), sload(_OWNER_SLOT))) {
mstore(0x00, 0x82b42900) // `Unauthorized()`.
revert(0x1c, 0x04)
}
}
}
/// @dev Returns how long a two-step ownership handover is valid for in seconds.
/// Override to return a different value if needed.
/// Made internal to conserve bytecode. Wrap it in a public function if needed.
function _ownershipHandoverValidFor() internal view virtual returns (uint64) {
return 48 * 3600;
}
/*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
/* PUBLIC UPDATE FUNCTIONS */
/*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
/// @dev Allows the owner to transfer the ownership to `newOwner`.
function transferOwnership(address newOwner) public payable virtual onlyOwner {
/// @solidity memory-safe-assembly
assembly {
if iszero(shl(96, newOwner)) {
mstore(0x00, 0x7448fbae) // `NewOwnerIsZeroAddress()`.
revert(0x1c, 0x04)
}
}
_setOwner(newOwner);
}
/// @dev Allows the owner to renounce their ownership.
function renounceOwnership() public payable virtual onlyOwner {
_setOwner(address(0));
}
/// @dev Request a two-step ownership handover to the caller.
/// The request will automatically expire in 48 hours (172800 seconds) by default.
function requestOwnershipHandover() public payable virtual {
unchecked {
uint256 expires = block.timestamp + _ownershipHandoverValidFor();
/// @solidity memory-safe-assembly
assembly {
// Compute and set the handover slot to `expires`.
mstore(0x0c, _HANDOVER_SLOT_SEED)
mstore(0x00, caller())
sstore(keccak256(0x0c, 0x20), expires)
// Emit the {OwnershipHandoverRequested} event.
log2(0, 0, _OWNERSHIP_HANDOVER_REQUESTED_EVENT_SIGNATURE, caller())
}
}
}
/// @dev Cancels the two-step ownership handover to the caller, if any.
function cancelOwnershipHandover() public payable virtual {
/// @solidity memory-safe-assembly
assembly {
// Compute and set the handover slot to 0.
mstore(0x0c, _HANDOVER_SLOT_SEED)
mstore(0x00, caller())
sstore(keccak256(0x0c, 0x20), 0)
// Emit the {OwnershipHandoverCanceled} event.
log2(0, 0, _OWNERSHIP_HANDOVER_CANCELED_EVENT_SIGNATURE, caller())
}
}
/// @dev Allows the owner to complete the two-step ownership handover to `pendingOwner`.
/// Reverts if there is no existing ownership handover requested by `pendingOwner`.
function completeOwnershipHandover(address pendingOwner) public payable virtual onlyOwner {
/// @solidity memory-safe-assembly
assembly {
// Compute and set the handover slot to 0.
mstore(0x0c, _HANDOVER_SLOT_SEED)
mstore(0x00, pendingOwner)
let handoverSlot := keccak256(0x0c, 0x20)
// If the handover does not exist, or has expired.
if gt(timestamp(), sload(handoverSlot)) {
mstore(0x00, 0x6f5e8818) // `NoHandoverRequest()`.
revert(0x1c, 0x04)
}
// Set the handover slot to 0.
sstore(handoverSlot, 0)
}
_setOwner(pendingOwner);
}
/*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
/* PUBLIC READ FUNCTIONS */
/*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
/// @dev Returns the owner of the contract.
function owner() public view virtual returns (address result) {
/// @solidity memory-safe-assembly
assembly {
result := sload(_OWNER_SLOT)
}
}
/// @dev Returns the expiry timestamp for the two-step ownership handover to `pendingOwner`.
function ownershipHandoverExpiresAt(address pendingOwner)
public
view
virtual
returns (uint256 result)
{
/// @solidity memory-safe-assembly
assembly {
// Compute the handover slot.
mstore(0x0c, _HANDOVER_SLOT_SEED)
mstore(0x00, pendingOwner)
// Load the handover slot.
result := sload(keccak256(0x0c, 0x20))
}
}
/*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
/* MODIFIERS */
/*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
/// @dev Marks a function as only callable by the owner.
modifier onlyOwner() virtual {
_checkOwner();
_;
}
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;
/// @notice Safe ETH and ERC20 transfer library that gracefully handles missing return values.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/utils/SafeTransferLib.sol)
/// @author Modified from Solmate (https://github.com/transmissions11/solmate/blob/main/src/utils/SafeTransferLib.sol)
///
/// @dev Note:
/// - For ETH transfers, please use `forceSafeTransferETH` for DoS protection.
/// - For ERC20s, this implementation won't check that a token has code,
/// responsibility is delegated to the caller.
library SafeTransferLib {
/*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
/* CUSTOM ERRORS */
/*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
/// @dev The ETH transfer has failed.
error ETHTransferFailed();
/// @dev The ERC20 `transferFrom` has failed.
error TransferFromFailed();
/// @dev The ERC20 `transfer` has failed.
error TransferFailed();
/// @dev The ERC20 `approve` has failed.
error ApproveFailed();
/*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
/* CONSTANTS */
/*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
/// @dev Suggested gas stipend for contract receiving ETH that disallows any storage writes.
uint256 internal constant GAS_STIPEND_NO_STORAGE_WRITES = 2300;
/// @dev Suggested gas stipend for contract receiving ETH to perform a few
/// storage reads and writes, but low enough to prevent griefing.
uint256 internal constant GAS_STIPEND_NO_GRIEF = 100000;
/*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
/* ETH OPERATIONS */
/*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
// If the ETH transfer MUST succeed with a reasonable gas budget, use the force variants.
//
// The regular variants:
// - Forwards all remaining gas to the target.
// - Reverts if the target reverts.
// - Reverts if the current contract has insufficient balance.
//
// The force variants:
// - Forwards with an optional gas stipend
// (defaults to `GAS_STIPEND_NO_GRIEF`, which is sufficient for most cases).
// - If the target reverts, or if the gas stipend is exhausted,
// creates a temporary contract to force send the ETH via `SELFDESTRUCT`.
// Future compatible with `SENDALL`: https://eips.ethereum.org/EIPS/eip-4758.
// - Reverts if the current contract has insufficient balance.
//
// The try variants:
// - Forwards with a mandatory gas stipend.
// - Instead of reverting, returns whether the transfer succeeded.
/// @dev Sends `amount` (in wei) ETH to `to`.
function safeTransferETH(address to, uint256 amount) internal {
/// @solidity memory-safe-assembly
assembly {
if iszero(call(gas(), to, amount, codesize(), 0x00, codesize(), 0x00)) {
mstore(0x00, 0xb12d13eb) // `ETHTransferFailed()`.
revert(0x1c, 0x04)
}
}
}
/// @dev Sends all the ETH in the current contract to `to`.
function safeTransferAllETH(address to) internal {
/// @solidity memory-safe-assembly
assembly {
// Transfer all the ETH and check if it succeeded or not.
if iszero(call(gas(), to, selfbalance(), codesize(), 0x00, codesize(), 0x00)) {
mstore(0x00, 0xb12d13eb) // `ETHTransferFailed()`.
revert(0x1c, 0x04)
}
}
}
/// @dev Force sends `amount` (in wei) ETH to `to`, with a `gasStipend`.
function forceSafeTransferETH(address to, uint256 amount, uint256 gasStipend) internal {
/// @solidity memory-safe-assembly
assembly {
if lt(selfbalance(), amount) {
mstore(0x00, 0xb12d13eb) // `ETHTransferFailed()`.
revert(0x1c, 0x04)
}
if iszero(call(gasStipend, to, amount, codesize(), 0x00, codesize(), 0x00)) {
mstore(0x00, to) // Store the address in scratch space.
mstore8(0x0b, 0x73) // Opcode `PUSH20`.
mstore8(0x20, 0xff) // Opcode `SELFDESTRUCT`.
if iszero(create(amount, 0x0b, 0x16)) { revert(codesize(), codesize()) } // For gas estimation.
}
}
}
/// @dev Force sends all the ETH in the current contract to `to`, with a `gasStipend`.
function forceSafeTransferAllETH(address to, uint256 gasStipend) internal {
/// @solidity memory-safe-assembly
assembly {
if iszero(call(gasStipend, to, selfbalance(), codesize(), 0x00, codesize(), 0x00)) {
mstore(0x00, to) // Store the address in scratch space.
mstore8(0x0b, 0x73) // Opcode `PUSH20`.
mstore8(0x20, 0xff) // Opcode `SELFDESTRUCT`.
if iszero(create(selfbalance(), 0x0b, 0x16)) { revert(codesize(), codesize()) } // For gas estimation.
}
}
}
/// @dev Force sends `amount` (in wei) ETH to `to`, with `GAS_STIPEND_NO_GRIEF`.
function forceSafeTransferETH(address to, uint256 amount) internal {
/// @solidity memory-safe-assembly
assembly {
if lt(selfbalance(), amount) {
mstore(0x00, 0xb12d13eb) // `ETHTransferFailed()`.
revert(0x1c, 0x04)
}
if iszero(call(GAS_STIPEND_NO_GRIEF, to, amount, codesize(), 0x00, codesize(), 0x00)) {
mstore(0x00, to) // Store the address in scratch space.
mstore8(0x0b, 0x73) // Opcode `PUSH20`.
mstore8(0x20, 0xff) // Opcode `SELFDESTRUCT`.
if iszero(create(amount, 0x0b, 0x16)) { revert(codesize(), codesize()) } // For gas estimation.
}
}
}
/// @dev Force sends all the ETH in the current contract to `to`, with `GAS_STIPEND_NO_GRIEF`.
function forceSafeTransferAllETH(address to) internal {
/// @solidity memory-safe-assembly
assembly {
// forgefmt: disable-next-item
if iszero(call(GAS_STIPEND_NO_GRIEF, to, selfbalance(), codesize(), 0x00, codesize(), 0x00)) {
mstore(0x00, to) // Store the address in scratch space.
mstore8(0x0b, 0x73) // Opcode `PUSH20`.
mstore8(0x20, 0xff) // Opcode `SELFDESTRUCT`.
if iszero(create(selfbalance(), 0x0b, 0x16)) { revert(codesize(), codesize()) } // For gas estimation.
}
}
}
/// @dev Sends `amount` (in wei) ETH to `to`, with a `gasStipend`.
function trySafeTransferETH(address to, uint256 amount, uint256 gasStipend)
internal
returns (bool success)
{
/// @solidity memory-safe-assembly
assembly {
success := call(gasStipend, to, amount, codesize(), 0x00, codesize(), 0x00)
}
}
/// @dev Sends all the ETH in the current contract to `to`, with a `gasStipend`.
function trySafeTransferAllETH(address to, uint256 gasStipend)
internal
returns (bool success)
{
/// @solidity memory-safe-assembly
assembly {
success := call(gasStipend, to, selfbalance(), codesize(), 0x00, codesize(), 0x00)
}
}
/*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
/* ERC20 OPERATIONS */
/*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
/// @dev Sends `amount` of ERC20 `token` from `from` to `to`.
/// Reverts upon failure.
///
/// The `from` account must have at least `amount` approved for
/// the current contract to manage.
function safeTransferFrom(address token, address from, address to, uint256 amount) internal {
/// @solidity memory-safe-assembly
assembly {
let m := mload(0x40) // Cache the free memory pointer.
mstore(0x60, amount) // Store the `amount` argument.
mstore(0x40, to) // Store the `to` argument.
mstore(0x2c, shl(96, from)) // Store the `from` argument.
mstore(0x0c, 0x23b872dd000000000000000000000000) // `transferFrom(address,address,uint256)`.
// Perform the transfer, reverting upon failure.
if iszero(
and( // The arguments of `and` are evaluated from right to left.
or(eq(mload(0x00), 1), iszero(returndatasize())), // Returned 1 or nothing.
call(gas(), token, 0, 0x1c, 0x64, 0x00, 0x20)
)
) {
mstore(0x00, 0x7939f424) // `TransferFromFailed()`.
revert(0x1c, 0x04)
}
mstore(0x60, 0) // Restore the zero slot to zero.
mstore(0x40, m) // Restore the free memory pointer.
}
}
/// @dev Sends all of ERC20 `token` from `from` to `to`.
/// Reverts upon failure.
///
/// The `from` account must have their entire balance approved for
/// the current contract to manage.
function safeTransferAllFrom(address token, address from, address to)
internal
returns (uint256 amount)
{
/// @solidity memory-safe-assembly
assembly {
let m := mload(0x40) // Cache the free memory pointer.
mstore(0x40, to) // Store the `to` argument.
mstore(0x2c, shl(96, from)) // Store the `from` argument.
mstore(0x0c, 0x70a08231000000000000000000000000) // `balanceOf(address)`.
// Read the balance, reverting upon failure.
if iszero(
and( // The arguments of `and` are evaluated from right to left.
gt(returndatasize(), 0x1f), // At least 32 bytes returned.
staticcall(gas(), token, 0x1c, 0x24, 0x60, 0x20)
)
) {
mstore(0x00, 0x7939f424) // `TransferFromFailed()`.
revert(0x1c, 0x04)
}
mstore(0x00, 0x23b872dd) // `transferFrom(address,address,uint256)`.
amount := mload(0x60) // The `amount` is already at 0x60. We'll need to return it.
// Perform the transfer, reverting upon failure.
if iszero(
and( // The arguments of `and` are evaluated from right to left.
or(eq(mload(0x00), 1), iszero(returndatasize())), // Returned 1 or nothing.
call(gas(), token, 0, 0x1c, 0x64, 0x00, 0x20)
)
) {
mstore(0x00, 0x7939f424) // `TransferFromFailed()`.
revert(0x1c, 0x04)
}
mstore(0x60, 0) // Restore the zero slot to zero.
mstore(0x40, m) // Restore the free memory pointer.
}
}
/// @dev Sends `amount` of ERC20 `token` from the current contract to `to`.
/// Reverts upon failure.
function safeTransfer(address token, address to, uint256 amount) internal {
/// @solidity memory-safe-assembly
assembly {
mstore(0x14, to) // Store the `to` argument.
mstore(0x34, amount) // Store the `amount` argument.
mstore(0x00, 0xa9059cbb000000000000000000000000) // `transfer(address,uint256)`.
// Perform the transfer, reverting upon failure.
if iszero(
and( // The arguments of `and` are evaluated from right to left.
or(eq(mload(0x00), 1), iszero(returndatasize())), // Returned 1 or nothing.
call(gas(), token, 0, 0x10, 0x44, 0x00, 0x20)
)
) {
mstore(0x00, 0x90b8ec18) // `TransferFailed()`.
revert(0x1c, 0x04)
}
mstore(0x34, 0) // Restore the part of the free memory pointer that was overwritten.
}
}
/// @dev Sends all of ERC20 `token` from the current contract to `to`.
/// Reverts upon failure.
function safeTransferAll(address token, address to) internal returns (uint256 amount) {
/// @solidity memory-safe-assembly
assembly {
mstore(0x00, 0x70a08231) // Store the function selector of `balanceOf(address)`.
mstore(0x20, address()) // Store the address of the current contract.
// Read the balance, reverting upon failure.
if iszero(
and( // The arguments of `and` are evaluated from right to left.
gt(returndatasize(), 0x1f), // At least 32 bytes returned.
staticcall(gas(), token, 0x1c, 0x24, 0x34, 0x20)
)
) {
mstore(0x00, 0x90b8ec18) // `TransferFailed()`.
revert(0x1c, 0x04)
}
mstore(0x14, to) // Store the `to` argument.
amount := mload(0x34) // The `amount` is already at 0x34. We'll need to return it.
mstore(0x00, 0xa9059cbb000000000000000000000000) // `transfer(address,uint256)`.
// Perform the transfer, reverting upon failure.
if iszero(
and( // The arguments of `and` are evaluated from right to left.
or(eq(mload(0x00), 1), iszero(returndatasize())), // Returned 1 or nothing.
call(gas(), token, 0, 0x10, 0x44, 0x00, 0x20)
)
) {
mstore(0x00, 0x90b8ec18) // `TransferFailed()`.
revert(0x1c, 0x04)
}
mstore(0x34, 0) // Restore the part of the free memory pointer that was overwritten.
}
}
/// @dev Sets `amount` of ERC20 `token` for `to` to manage on behalf of the current contract.
/// Reverts upon failure.
function safeApprove(address token, address to, uint256 amount) internal {
/// @solidity memory-safe-assembly
assembly {
mstore(0x14, to) // Store the `to` argument.
mstore(0x34, amount) // Store the `amount` argument.
mstore(0x00, 0x095ea7b3000000000000000000000000) // `approve(address,uint256)`.
// Perform the approval, reverting upon failure.
if iszero(
and( // The arguments of `and` are evaluated from right to left.
or(eq(mload(0x00), 1), iszero(returndatasize())), // Returned 1 or nothing.
call(gas(), token, 0, 0x10, 0x44, 0x00, 0x20)
)
) {
mstore(0x00, 0x3e3f8f73) // `ApproveFailed()`.
revert(0x1c, 0x04)
}
mstore(0x34, 0) // Restore the part of the free memory pointer that was overwritten.
}
}
/// @dev Sets `amount` of ERC20 `token` for `to` to manage on behalf of the current contract.
/// If the initial attempt to approve fails, attempts to reset the approved amount to zero,
/// then retries the approval again (some tokens, e.g. USDT, requires this).
/// Reverts upon failure.
function safeApproveWithRetry(address token, address to, uint256 amount) internal {
/// @solidity memory-safe-assembly
assembly {
mstore(0x14, to) // Store the `to` argument.
mstore(0x34, amount) // Store the `amount` argument.
mstore(0x00, 0x095ea7b3000000000000000000000000) // `approve(address,uint256)`.
// Perform the approval, retrying upon failure.
if iszero(
and( // The arguments of `and` are evaluated from right to left.
or(eq(mload(0x00), 1), iszero(returndatasize())), // Returned 1 or nothing.
call(gas(), token, 0, 0x10, 0x44, 0x00, 0x20)
)
) {
mstore(0x34, 0) // Store 0 for the `amount`.
mstore(0x00, 0x095ea7b3000000000000000000000000) // `approve(address,uint256)`.
pop(call(gas(), token, 0, 0x10, 0x44, codesize(), 0x00)) // Reset the approval.
mstore(0x34, amount) // Store back the original `amount`.
// Retry the approval, reverting upon failure.
if iszero(
and(
or(eq(mload(0x00), 1), iszero(returndatasize())), // Returned 1 or nothing.
call(gas(), token, 0, 0x10, 0x44, 0x00, 0x20)
)
) {
mstore(0x00, 0x3e3f8f73) // `ApproveFailed()`.
revert(0x1c, 0x04)
}
}
mstore(0x34, 0) // Restore the part of the free memory pointer that was overwritten.
}
}
/// @dev Returns the amount of ERC20 `token` owned by `account`.
/// Returns zero if the `token` does not exist.
function balanceOf(address token, address account) internal view returns (uint256 amount) {
/// @solidity memory-safe-assembly
assembly {
mstore(0x14, account) // Store the `account` argument.
mstore(0x00, 0x70a08231000000000000000000000000) // `balanceOf(address)`.
amount :=
mul(
mload(0x20),
and( // The arguments of `and` are evaluated from right to left.
gt(returndatasize(), 0x1f), // At least 32 bytes returned.
staticcall(gas(), token, 0x10, 0x24, 0x20, 0x20)
)
)
}
}
}
// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.19;
import "solady/src/utils/FixedPointMathLib.sol";
import "solady/src/utils/SafeCastLib.sol";
library WeightedMathLib {
/// -----------------------------------------------------------------------
/// Dependencies
/// -----------------------------------------------------------------------
using SafeCastLib for *;
using FixedPointMathLib for *;
/// -----------------------------------------------------------------------
/// Errors
/// -----------------------------------------------------------------------
/// @dev Thrown when `amountIn` exceeds `MAX_PERCENTAGE_IN`, which is imposed by balancer.
error AmountInTooLarge();
/// @dev Thrown when `amountOut` exceeds `MAX_PERCENTAGE_OUT`, which is imposed by balancer.
error AmountOutTooLarge();
/// -----------------------------------------------------------------------
/// Constants
/// -----------------------------------------------------------------------
/// @dev Maximum relative error allowed for fixed-point math operations (10^(-14)).
uint256 internal constant MAX_POW_RELATIVE_ERROR = 10000;
/// @dev Maximum percentage of reserveIn allowed to be swapped in when using `getAmountOut` (30%).
uint256 internal constant MAX_PERCENTAGE_IN = 0.3 ether;
/// @dev Maximum percentage of reserveOut allowed to be swapped out when using `getAmountIn` (30%).
uint256 internal constant MAX_PERCENTAGE_OUT = 0.3 ether;
/// -----------------------------------------------------------------------
/// Weighted Arithmetic
/// -----------------------------------------------------------------------
/// @notice Calculate the spot price given reserves and weights of two assets in a pool.
/// @param reserveIn The reserve of the input asset in the pool.
/// @param reserveOut The reserve of the output asset in the pool.
/// @param weightIn The weight of the input asset in the pool.
/// @param weightOut The weight of the output asset in the pool.
function getSpotPrice(
uint256 reserveIn,
uint256 reserveOut,
uint256 weightIn,
uint256 weightOut
) internal pure returns (uint256) {
// -----------------------------------------------------------------------
// (reserveIn / weightIn) / (reserveOut / weightOut)
// -----------------------------------------------------------------------
return reserveIn.divWad(weightIn).divWad(reserveOut.divWad(weightOut));
}
/// @notice Calculate the invariant of a weighted pool given reserves and weights of the assets.
/// @param reserves An array of reserves for all the assets in the pool.
/// @param weights An array of weights for all the assets in the pool.
function getInvariant(uint256[] memory reserves, uint256[] memory weights)
internal
pure
returns (uint256 invariant)
{
// -----------------------------------------------------------------------
// ____
// ⎟⎟ weight
// ⎟⎟ reserve ^ = i
// n = totalAssets
// -----------------------------------------------------------------------
invariant = 1e18;
uint256 n = weights.length;
for (uint256 i; i < n; i = i.rawAdd(1)) {
invariant = invariant.mulWad(int256(reserves[i]).powWad(int256(weights[i])).toUint256());
}
}
/// @notice Calculate the invariant of a weighted pool given two reserves and weights.
/// @dev Optimized for pools that contain exactly two assets.
/// @param reserveIn The reserve of the input asset in the pool.
/// @param reserveOut The reserve of the output asset in the pool.
/// @param weightIn The weight of the input asset in the pool.
/// @param weightOut The weight of the output asset in the pool.
function getInvariant(
uint256 reserveIn,
uint256 reserveOut,
uint256 weightIn,
uint256 weightOut
) internal pure returns (uint256 invariant) {
// -----------------------------------------------------------------------
// ____
// ⎟⎟ weight
// ⎟⎟ reserve ^ = i
// n = 2
// -----------------------------------------------------------------------
invariant = 1e18.mulWad(powWad(reserveIn, weightIn)).mulWad(powWad(reserveOut, weightOut));
}
/// @notice Calculate the amount of input asset required to get a specific amount of output asset from the pool.
/// @param amountOut The desired amount of output asset.
/// @param reserveIn The reserve of the input asset in the pool.
/// @param reserveOut The reserve of the output asset in the pool.
/// @param weightIn The weight of the input asset in the pool.
/// @param weightOut The weight of the output asset in the pool.
function getAmountIn(
uint256 amountOut,
uint256 reserveIn,
uint256 reserveOut,
uint256 weightIn,
uint256 weightOut
) internal pure returns (uint256) {
unchecked {
// -----------------------------------------------------------------------
//
// ⎛ ⎛weightIn ⎞ ⎞
// ⎜ ───────── ⎟
// ⎜ ⎝weightOut⎠ ⎟
// ⎜⎛ reserveOut ⎞ ⎟
// reserveIn ⋅ ───────────────────── - 1
// ⎝⎝reserveOut - amountIn⎠ ⎠
// -----------------------------------------------------------------------
// Assert `amountOut` cannot exceed `MAX_PERCENTAGE_OUT`.
if (amountOut > reserveOut.mulWad(MAX_PERCENTAGE_OUT)) {
revert AmountOutTooLarge();
}
// `MAX_PERCENTAGE_OUT` check ensures `amountOut` is always less than `reserveOut`.
return reserveIn.mulWadUp(
powWadUp(
reserveOut.divWadUp(reserveOut.rawSub(amountOut)), weightOut.divWadUp(weightIn)
) - 1 ether
);
}
}
/// @notice Calculate the amount of output asset received by providing a specific amount of input asset to the pool.
/// @param amountIn The amount of input asset provided.
/// @param reserveIn The reserve of the input asset in the pool.
/// @param reserveOut The reserve of the output asset in the pool.
/// @param weightIn The weight of the input asset in the pool.
/// @param weightOut The weight of the output asset in the pool.
function getAmountOut(
uint256 amountIn,
uint256 reserveIn,
uint256 reserveOut,
uint256 weightIn,
uint256 weightOut
) internal pure returns (uint256) {
// -----------------------------------------------------------------------
//
// ⎛ ⎛weightIn ⎞⎞
// ⎜ ───────── ⎟
// ⎜ ⎝weightOut⎠⎟
// ⎜ ⎛ reserveIn ⎞ ⎟
// reserveOut ⋅ 1 - ────────────────────
// ⎝ ⎝reserveIn + amountIn⎠ ⎠
// -----------------------------------------------------------------------
// Assert `amountIn` cannot exceed `MAX_PERCENTAGE_IN`.
if (amountIn > reserveIn.mulWad(MAX_PERCENTAGE_IN)) {
revert AmountInTooLarge();
}
return reserveOut.mulWad(
1e18.rawSub(
powWadUp(reserveIn.divWadUp(reserveIn + amountIn), weightIn.divWad(weightOut))
)
);
}
function linearInterpolation(uint256 x, uint256 y, uint256 i, uint256 n)
internal
pure
returns (uint256)
{
// -----------------------------------------------------------------------
//
// ⎛ |x - y| ⎞
// x ± i ⋅ ─────────
// ⎝ n ⎠
// -----------------------------------------------------------------------
return x > y
? x.rawSub(x.rawSub(y).mulDiv(i.min(n), n))
: x.rawAdd(y.rawSub(x).mulDiv(i.min(n), n));
}
/// -----------------------------------------------------------------------
/// Fixed-point Arithmetic
/// -----------------------------------------------------------------------
function powWad(uint256 x, uint256 y) internal pure returns (uint256) {
if (y == 1 ether) {
return x;
} else if (y == 2 ether) {
return x.mulWad(x);
} else if (y == 4 ether) {
uint256 square = x.mulWad(x);
return square.mulWad(square);
}
return int256(x).powWad(int256(y)).toUint256();
}
function powWadUp(uint256 x, uint256 y) internal pure returns (uint256) {
if (y == 1 ether) {
return x;
} else if (y == 2 ether) {
return x.mulWadUp(x);
} else if (y == 4 ether) {
uint256 square = x.mulWadUp(x);
return square.mulWadUp(square);
}
uint256 power = int256(x).powWad(int256(y)).toUint256();
return power + power.mulWadUp(MAX_POW_RELATIVE_ERROR) + 1;
}
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;
/// @notice Arithmetic library with operations for fixed-point numbers.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/utils/FixedPointMathLib.sol)
/// @author Modified from Solmate (https://github.com/transmissions11/solmate/blob/main/src/utils/FixedPointMathLib.sol)
library FixedPointMathLib {
/*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
/* CUSTOM ERRORS */
/*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
/// @dev The operation failed, as the output exceeds the maximum value of uint256.
error ExpOverflow();
/// @dev The operation failed, as the output exceeds the maximum value of uint256.
error FactorialOverflow();
/// @dev The operation failed, due to an overflow.
error RPowOverflow();
/// @dev The mantissa is too big to fit.
error MantissaOverflow();
/// @dev The operation failed, due to an multiplication overflow.
error MulWadFailed();
/// @dev The operation failed, due to an multiplication overflow.
error SMulWadFailed();
/// @dev The operation failed, either due to a multiplication overflow, or a division by a zero.
error DivWadFailed();
/// @dev The operation failed, either due to a multiplication overflow, or a division by a zero.
error SDivWadFailed();
/// @dev The operation failed, either due to a multiplication overflow, or a division by a zero.
error MulDivFailed();
/// @dev The division failed, as the denominator is zero.
error DivFailed();
/// @dev The full precision multiply-divide operation failed, either due
/// to the result being larger than 256 bits, or a division by a zero.
error FullMulDivFailed();
/// @dev The output is undefined, as the input is less-than-or-equal to zero.
error LnWadUndefined();
/// @dev The input outside the acceptable domain.
error OutOfDomain();
/*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
/* CONSTANTS */
/*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
/// @dev The scalar of ETH and most ERC20s.
uint256 internal constant WAD = 1e18;
/*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
/* SIMPLIFIED FIXED POINT OPERATIONS */
/*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
/// @dev Equivalent to `(x * y) / WAD` rounded down.
function mulWad(uint256 x, uint256 y) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
// Equivalent to `require(y == 0 || x <= type(uint256).max / y)`.
if mul(y, gt(x, div(not(0), y))) {
mstore(0x00, 0xbac65e5b) // `MulWadFailed()`.
revert(0x1c, 0x04)
}
z := div(mul(x, y), WAD)
}
}
/// @dev Equivalent to `(x * y) / WAD` rounded down.
function sMulWad(int256 x, int256 y) internal pure returns (int256 z) {
/// @solidity memory-safe-assembly
assembly {
z := mul(x, y)
// Equivalent to `require((x == 0 || z / x == y) && !(x == -1 && y == type(int256).min))`.
if iszero(gt(or(iszero(x), eq(sdiv(z, x), y)), lt(not(x), eq(y, shl(255, 1))))) {
mstore(0x00, 0xedcd4dd4) // `SMulWadFailed()`.
revert(0x1c, 0x04)
}
z := sdiv(z, WAD)
}
}
/// @dev Equivalent to `(x * y) / WAD` rounded down, but without overflow checks.
function rawMulWad(uint256 x, uint256 y) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
z := div(mul(x, y), WAD)
}
}
/// @dev Equivalent to `(x * y) / WAD` rounded down, but without overflow checks.
function rawSMulWad(int256 x, int256 y) internal pure returns (int256 z) {
/// @solidity memory-safe-assembly
assembly {
z := sdiv(mul(x, y), WAD)
}
}
/// @dev Equivalent to `(x * y) / WAD` rounded up.
function mulWadUp(uint256 x, uint256 y) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
// Equivalent to `require(y == 0 || x <= type(uint256).max / y)`.
if mul(y, gt(x, div(not(0), y))) {
mstore(0x00, 0xbac65e5b) // `MulWadFailed()`.
revert(0x1c, 0x04)
}
z := add(iszero(iszero(mod(mul(x, y), WAD))), div(mul(x, y), WAD))
}
}
/// @dev Equivalent to `(x * y) / WAD` rounded up, but without overflow checks.
function rawMulWadUp(uint256 x, uint256 y) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
z := add(iszero(iszero(mod(mul(x, y), WAD))), div(mul(x, y), WAD))
}
}
/// @dev Equivalent to `(x * WAD) / y` rounded down.
function divWad(uint256 x, uint256 y) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
// Equivalent to `require(y != 0 && (WAD == 0 || x <= type(uint256).max / WAD))`.
if iszero(mul(y, iszero(mul(WAD, gt(x, div(not(0), WAD)))))) {
mstore(0x00, 0x7c5f487d) // `DivWadFailed()`.
revert(0x1c, 0x04)
}
z := div(mul(x, WAD), y)
}
}
/// @dev Equivalent to `(x * WAD) / y` rounded down.
function sDivWad(int256 x, int256 y) internal pure returns (int256 z) {
/// @solidity memory-safe-assembly
assembly {
z := mul(x, WAD)
// Equivalent to `require(y != 0 && ((x * WAD) / WAD == x))`.
if iszero(and(iszero(iszero(y)), eq(sdiv(z, WAD), x))) {
mstore(0x00, 0x5c43740d) // `SDivWadFailed()`.
revert(0x1c, 0x04)
}
z := sdiv(mul(x, WAD), y)
}
}
/// @dev Equivalent to `(x * WAD) / y` rounded down, but without overflow and divide by zero checks.
function rawDivWad(uint256 x, uint256 y) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
z := div(mul(x, WAD), y)
}
}
/// @dev Equivalent to `(x * WAD) / y` rounded down, but without overflow and divide by zero checks.
function rawSDivWad(int256 x, int256 y) internal pure returns (int256 z) {
/// @solidity memory-safe-assembly
assembly {
z := sdiv(mul(x, WAD), y)
}
}
/// @dev Equivalent to `(x * WAD) / y` rounded up.
function divWadUp(uint256 x, uint256 y) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
// Equivalent to `require(y != 0 && (WAD == 0 || x <= type(uint256).max / WAD))`.
if iszero(mul(y, iszero(mul(WAD, gt(x, div(not(0), WAD)))))) {
mstore(0x00, 0x7c5f487d) // `DivWadFailed()`.
revert(0x1c, 0x04)
}
z := add(iszero(iszero(mod(mul(x, WAD), y))), div(mul(x, WAD), y))
}
}
/// @dev Equivalent to `(x * WAD) / y` rounded up, but without overflow and divide by zero checks.
function rawDivWadUp(uint256 x, uint256 y) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
z := add(iszero(iszero(mod(mul(x, WAD), y))), div(mul(x, WAD), y))
}
}
/// @dev Equivalent to `x` to the power of `y`.
/// because `x ** y = (e ** ln(x)) ** y = e ** (ln(x) * y)`.
function powWad(int256 x, int256 y) internal pure returns (int256) {
// Using `ln(x)` means `x` must be greater than 0.
return expWad((lnWad(x) * y) / int256(WAD));
}
/// @dev Returns `exp(x)`, denominated in `WAD`.
/// Credit to Remco Bloemen under MIT license: https://2π.com/22/exp-ln
function expWad(int256 x) internal pure returns (int256 r) {
unchecked {
// When the result is less than 0.5 we return zero.
// This happens when `x <= (log(1e-18) * 1e18) ~ -4.15e19`.
if (x <= -41446531673892822313) return r;
/// @solidity memory-safe-assembly
assembly {
// When the result is greater than `(2**255 - 1) / 1e18` we can not represent it as
// an int. This happens when `x >= floor(log((2**255 - 1) / 1e18) * 1e18) ≈ 135`.
if iszero(slt(x, 135305999368893231589)) {
mstore(0x00, 0xa37bfec9) // `ExpOverflow()`.
revert(0x1c, 0x04)
}
}
// `x` is now in the range `(-42, 136) * 1e18`. Convert to `(-42, 136) * 2**96`
// for more intermediate precision and a binary basis. This base conversion
// is a multiplication by 1e18 / 2**96 = 5**18 / 2**78.
x = (x << 78) / 5 ** 18;
// Reduce range of x to (-½ ln 2, ½ ln 2) * 2**96 by factoring out powers
// of two such that exp(x) = exp(x') * 2**k, where k is an integer.
// Solving this gives k = round(x / log(2)) and x' = x - k * log(2).
int256 k = ((x << 96) / 54916777467707473351141471128 + 2 ** 95) >> 96;
x = x - k * 54916777467707473351141471128;
// `k` is in the range `[-61, 195]`.
// Evaluate using a (6, 7)-term rational approximation.
// `p` is made monic, we'll multiply by a scale factor later.
int256 y = x + 1346386616545796478920950773328;
y = ((y * x) >> 96) + 57155421227552351082224309758442;
int256 p = y + x - 94201549194550492254356042504812;
p = ((p * y) >> 96) + 28719021644029726153956944680412240;
p = p * x + (4385272521454847904659076985693276 << 96);
// We leave `p` in `2**192` basis so we don't need to scale it back up for the division.
int256 q = x - 2855989394907223263936484059900;
q = ((q * x) >> 96) + 50020603652535783019961831881945;
q = ((q * x) >> 96) - 533845033583426703283633433725380;
q = ((q * x) >> 96) + 3604857256930695427073651918091429;
q = ((q * x) >> 96) - 14423608567350463180887372962807573;
q = ((q * x) >> 96) + 26449188498355588339934803723976023;
/// @solidity memory-safe-assembly
assembly {
// Div in assembly because solidity adds a zero check despite the unchecked.
// The q polynomial won't have zeros in the domain as all its roots are complex.
// No scaling is necessary because p is already `2**96` too large.
r := sdiv(p, q)
}
// r should be in the range `(0.09, 0.25) * 2**96`.
// We now need to multiply r by:
// - The scale factor `s ≈ 6.031367120`.
// - The `2**k` factor from the range reduction.
// - The `1e18 / 2**96` factor for base conversion.
// We do this all at once, with an intermediate result in `2**213`
// basis, so the final right shift is always by a positive amount.
r = int256(
(uint256(r) * 3822833074963236453042738258902158003155416615667) >> uint256(195 - k)
);
}
}
/// @dev Returns `ln(x)`, denominated in `WAD`.
/// Credit to Remco Bloemen under MIT license: https://2π.com/22/exp-ln
function lnWad(int256 x) internal pure returns (int256 r) {
/// @solidity memory-safe-assembly
assembly {
// We want to convert `x` from `10**18` fixed point to `2**96` fixed point.
// We do this by multiplying by `2**96 / 10**18`. But since
// `ln(x * C) = ln(x) + ln(C)`, we can simply do nothing here
// and add `ln(2**96 / 10**18)` at the end.
// Compute `k = log2(x) - 96`, `r = 159 - k = 255 - log2(x) = 255 ^ log2(x)`.
r := shl(7, lt(0xffffffffffffffffffffffffffffffff, x))
r := or(r, shl(6, lt(0xffffffffffffffff, shr(r, x))))
r := or(r, shl(5, lt(0xffffffff, shr(r, x))))
r := or(r, shl(4, lt(0xffff, shr(r, x))))
r := or(r, shl(3, lt(0xff, shr(r, x))))
// We place the check here for more optimal stack operations.
if iszero(sgt(x, 0)) {
mstore(0x00, 0x1615e638) // `LnWadUndefined()`.
revert(0x1c, 0x04)
}
// forgefmt: disable-next-item
r := xor(r, byte(and(0x1f, shr(shr(r, x), 0x8421084210842108cc6318c6db6d54be)),
0xf8f9f9faf9fdfafbf9fdfcfdfafbfcfef9fafdfafcfcfbfefafafcfbffffffff))
// Reduce range of x to (1, 2) * 2**96
// ln(2^k * x) = k * ln(2) + ln(x)
x := shr(159, shl(r, x))
// Evaluate using a (8, 8)-term rational approximation.
// `p` is made monic, we will multiply by a scale factor later.
// forgefmt: disable-next-item
let p := sub( // This heavily nested expression is to avoid stack-too-deep for via-ir.
sar(96, mul(add(43456485725739037958740375743393,
sar(96, mul(add(24828157081833163892658089445524,
sar(96, mul(add(3273285459638523848632254066296,
x), x))), x))), x)), 11111509109440967052023855526967)
p := sub(sar(96, mul(p, x)), 45023709667254063763336534515857)
p := sub(sar(96, mul(p, x)), 14706773417378608786704636184526)
p := sub(mul(p, x), shl(96, 795164235651350426258249787498))
// We leave `p` in `2**192` basis so we don't need to scale it back up for the division.
// `q` is monic by convention.
let q := add(5573035233440673466300451813936, x)
q := add(71694874799317883764090561454958, sar(96, mul(x, q)))
q := add(283447036172924575727196451306956, sar(96, mul(x, q)))
q := add(401686690394027663651624208769553, sar(96, mul(x, q)))
q := add(204048457590392012362485061816622, sar(96, mul(x, q)))
q := add(31853899698501571402653359427138, sar(96, mul(x, q)))
q := add(909429971244387300277376558375, sar(96, mul(x, q)))
// `p / q` is in the range `(0, 0.125) * 2**96`.
// Finalization, we need to:
// - Multiply by the scale factor `s = 5.549…`.
// - Add `ln(2**96 / 10**18)`.
// - Add `k * ln(2)`.
// - Multiply by `10**18 / 2**96 = 5**18 >> 78`.
// The q polynomial is known not to have zeros in the domain.
// No scaling required because p is already `2**96` too large.
p := sdiv(p, q)
// Multiply by the scaling factor: `s * 5**18 * 2**96`, base is now `5**18 * 2**192`.
p := mul(1677202110996718588342820967067443963516166, p)
// Add `ln(2) * k * 5**18 * 2**192`.
// forgefmt: disable-next-item
p := add(mul(16597577552685614221487285958193947469193820559219878177908093499208371, sub(159, r)), p)
// Add `ln(2**96 / 10**18) * 5**18 * 2**192`.
p := add(600920179829731861736702779321621459595472258049074101567377883020018308, p)
// Base conversion: mul `2**18 / 2**192`.
r := sar(174, p)
}
}
/// @dev Returns `W_0(x)`, denominated in `WAD`.
/// See: https://en.wikipedia.org/wiki/Lambert_W_function
/// a.k.a. Product log function. This is an approximation of the principal branch.
function lambertW0Wad(int256 x) internal pure returns (int256 w) {
// forgefmt: disable-next-item
unchecked {
if ((w = x) <= -367879441171442322) revert OutOfDomain(); // `x` less than `-1/e`.
int256 wad = int256(WAD);
int256 p = x;
uint256 c; // Whether we need to avoid catastrophic cancellation.
uint256 i = 4; // Number of iterations.
if (w <= 0x1ffffffffffff) {
if (-0x4000000000000 <= w) {
i = 1; // Inputs near zero only take one step to converge.
} else if (w <= -0x3ffffffffffffff) {
i = 32; // Inputs near `-1/e` take very long to converge.
}
} else if (w >> 63 == 0) {
/// @solidity memory-safe-assembly
assembly {
// Inline log2 for more performance, since the range is small.
let v := shr(49, w)
let l := shl(3, lt(0xff, v))
l := add(or(l, byte(and(0x1f, shr(shr(l, v), 0x8421084210842108cc6318c6db6d54be)),
0x0706060506020504060203020504030106050205030304010505030400000000)), 49)
w := sdiv(shl(l, 7), byte(sub(l, 31), 0x0303030303030303040506080c13))
c := gt(l, 60)
i := add(2, add(gt(l, 53), c))
}
} else {
int256 ll = lnWad(w = lnWad(w));
/// @solidity memory-safe-assembly
assembly {
// `w = ln(x) - ln(ln(x)) + b * ln(ln(x)) / ln(x)`.
w := add(sdiv(mul(ll, 1023715080943847266), w), sub(w, ll))
i := add(3, iszero(shr(68, x)))
c := iszero(shr(143, x))
}
if (c == 0) {
do { // If `x` is big, use Newton's so that intermediate values won't overflow.
int256 e = expWad(w);
/// @solidity memory-safe-assembly
assembly {
let t := mul(w, div(e, wad))
w := sub(w, sdiv(sub(t, x), div(add(e, t), wad)))
}
if (p <= w) break;
p = w;
} while (--i != 0);
/// @solidity memory-safe-assembly
assembly {
w := sub(w, sgt(w, 2))
}
return w;
}
}
do { // Otherwise, use Halley's for faster convergence.
int256 e = expWad(w);
/// @solidity memory-safe-assembly
assembly {
let t := add(w, wad)
let s := sub(mul(w, e), mul(x, wad))
w := sub(w, sdiv(mul(s, wad), sub(mul(e, t), sdiv(mul(add(t, wad), s), add(t, t)))))
}
if (p <= w) break;
p = w;
} while (--i != c);
/// @solidity memory-safe-assembly
assembly {
w := sub(w, sgt(w, 2))
}
// For certain ranges of `x`, we'll use the quadratic-rate recursive formula of
// R. Iacono and J.P. Boyd for the last iteration, to avoid catastrophic cancellation.
if (c != 0) {
int256 t = w | 1;
/// @solidity memory-safe-assembly
assembly {
x := sdiv(mul(x, wad), t)
}
x = (t * (wad + lnWad(x)));
/// @solidity memory-safe-assembly
assembly {
w := sdiv(x, add(wad, t))
}
}
}
}
/*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
/* GENERAL NUMBER UTILITIES */
/*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
/// @dev Calculates `floor(x * y / d)` with full precision.
/// Throws if result overflows a uint256 or when `d` is zero.
/// Credit to Remco Bloemen under MIT license: https://2π.com/21/muldiv
function fullMulDiv(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 result) {
/// @solidity memory-safe-assembly
assembly {
for {} 1 {} {
// 512-bit multiply `[p1 p0] = x * y`.
// Compute the product mod `2**256` and mod `2**256 - 1`
// then use the Chinese Remainder Theorem to reconstruct
// the 512 bit result. The result is stored in two 256
// variables such that `product = p1 * 2**256 + p0`.
// Least significant 256 bits of the product.
result := mul(x, y) // Temporarily use `result` as `p0` to save gas.
let mm := mulmod(x, y, not(0))
// Most significant 256 bits of the product.
let p1 := sub(mm, add(result, lt(mm, result)))
// Handle non-overflow cases, 256 by 256 division.
if iszero(p1) {
if iszero(d) {
mstore(0x00, 0xae47f702) // `FullMulDivFailed()`.
revert(0x1c, 0x04)
}
result := div(result, d)
break
}
// Make sure the result is less than `2**256`. Also prevents `d == 0`.
if iszero(gt(d, p1)) {
mstore(0x00, 0xae47f702) // `FullMulDivFailed()`.
revert(0x1c, 0x04)
}
/*------------------- 512 by 256 division --------------------*/
// Make division exact by subtracting the remainder from `[p1 p0]`.
// Compute remainder using mulmod.
let r := mulmod(x, y, d)
// `t` is the least significant bit of `d`.
// Always greater or equal to 1.
let t := and(d, sub(0, d))
// Divide `d` by `t`, which is a power of two.
d := div(d, t)
// Invert `d mod 2**256`
// Now that `d` is an odd number, it has an inverse
// modulo `2**256` such that `d * inv = 1 mod 2**256`.
// Compute the inverse by starting with a seed that is correct
// correct for four bits. That is, `d * inv = 1 mod 2**4`.
let inv := xor(2, mul(3, d))
// Now use 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.
inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**8
inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**16
inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**32
inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**64
inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**128
result :=
mul(
// Divide [p1 p0] by the factors of two.
// Shift in bits from `p1` into `p0`. For this we need
// to flip `t` such that it is `2**256 / t`.
or(
mul(sub(p1, gt(r, result)), add(div(sub(0, t), t), 1)),
div(sub(result, r), t)
),
// inverse mod 2**256
mul(inv, sub(2, mul(d, inv)))
)
break
}
}
}
/// @dev Calculates `floor(x * y / d)` with full precision, rounded up.
/// Throws if result overflows a uint256 or when `d` is zero.
/// Credit to Uniswap-v3-core under MIT license:
/// https://github.com/Uniswap/v3-core/blob/main/contracts/libraries/FullMath.sol
function fullMulDivUp(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 result) {
result = fullMulDiv(x, y, d);
/// @solidity memory-safe-assembly
assembly {
if mulmod(x, y, d) {
result := add(result, 1)
if iszero(result) {
mstore(0x00, 0xae47f702) // `FullMulDivFailed()`.
revert(0x1c, 0x04)
}
}
}
}
/// @dev Returns `floor(x * y / d)`.
/// Reverts if `x * y` overflows, or `d` is zero.
function mulDiv(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
// Equivalent to require(d != 0 && (y == 0 || x <= type(uint256).max / y))
if iszero(mul(d, iszero(mul(y, gt(x, div(not(0), y)))))) {
mstore(0x00, 0xad251c27) // `MulDivFailed()`.
revert(0x1c, 0x04)
}
z := div(mul(x, y), d)
}
}
/// @dev Returns `ceil(x * y / d)`.
/// Reverts if `x * y` overflows, or `d` is zero.
function mulDivUp(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
// Equivalent to require(d != 0 && (y == 0 || x <= type(uint256).max / y))
if iszero(mul(d, iszero(mul(y, gt(x, div(not(0), y)))))) {
mstore(0x00, 0xad251c27) // `MulDivFailed()`.
revert(0x1c, 0x04)
}
z := add(iszero(iszero(mod(mul(x, y), d))), div(mul(x, y), d))
}
}
/// @dev Returns `ceil(x / d)`.
/// Reverts if `d` is zero.
function divUp(uint256 x, uint256 d) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
if iszero(d) {
mstore(0x00, 0x65244e4e) // `DivFailed()`.
revert(0x1c, 0x04)
}
z := add(iszero(iszero(mod(x, d))), div(x, d))
}
}
/// @dev Returns `max(0, x - y)`.
function zeroFloorSub(uint256 x, uint256 y) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
z := mul(gt(x, y), sub(x, y))
}
}
/// @dev Exponentiate `x` to `y` by squaring, denominated in base `b`.
/// Reverts if the computation overflows.
function rpow(uint256 x, uint256 y, uint256 b) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
z := mul(b, iszero(y)) // `0 ** 0 = 1`. Otherwise, `0 ** n = 0`.
if x {
z := xor(b, mul(xor(b, x), and(y, 1))) // `z = isEven(y) ? scale : x`
let half := shr(1, b) // Divide `b` by 2.
// Divide `y` by 2 every iteration.
for { y := shr(1, y) } y { y := shr(1, y) } {
let xx := mul(x, x) // Store x squared.
let xxRound := add(xx, half) // Round to the nearest number.
// Revert if `xx + half` overflowed, or if `x ** 2` overflows.
if or(lt(xxRound, xx), shr(128, x)) {
mstore(0x00, 0x49f7642b) // `RPowOverflow()`.
revert(0x1c, 0x04)
}
x := div(xxRound, b) // Set `x` to scaled `xxRound`.
// If `y` is odd:
if and(y, 1) {
let zx := mul(z, x) // Compute `z * x`.
let zxRound := add(zx, half) // Round to the nearest number.
// If `z * x` overflowed or `zx + half` overflowed:
if or(xor(div(zx, x), z), lt(zxRound, zx)) {
// Revert if `x` is non-zero.
if iszero(iszero(x)) {
mstore(0x00, 0x49f7642b) // `RPowOverflow()`.
revert(0x1c, 0x04)
}
}
z := div(zxRound, b) // Return properly scaled `zxRound`.
}
}
}
}
}
/// @dev Returns the square root of `x`.
function sqrt(uint256 x) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
// `floor(sqrt(2**15)) = 181`. `sqrt(2**15) - 181 = 2.84`.
z := 181 // The "correct" value is 1, but this saves a multiplication later.
// This segment is to get a reasonable initial estimate for the Babylonian method. With a bad
// start, the correct # of bits increases ~linearly each iteration instead of ~quadratically.
// Let `y = x / 2**r`. We check `y >= 2**(k + 8)`
// but shift right by `k` bits to ensure that if `x >= 256`, then `y >= 256`.
let r := shl(7, lt(0xffffffffffffffffffffffffffffffffff, x))
r := or(r, shl(6, lt(0xffffffffffffffffff, shr(r, x))))
r := or(r, shl(5, lt(0xffffffffff, shr(r, x))))
r := or(r, shl(4, lt(0xffffff, shr(r, x))))
z := shl(shr(1, r), z)
// Goal was to get `z*z*y` within a small factor of `x`. More iterations could
// get y in a tighter range. Currently, we will have y in `[256, 256*(2**16))`.
// We ensured `y >= 256` so that the relative difference between `y` and `y+1` is small.
// That's not possible if `x < 256` but we can just verify those cases exhaustively.
// Now, `z*z*y <= x < z*z*(y+1)`, and `y <= 2**(16+8)`, and either `y >= 256`, or `x < 256`.
// Correctness can be checked exhaustively for `x < 256`, so we assume `y >= 256`.
// Then `z*sqrt(y)` is within `sqrt(257)/sqrt(256)` of `sqrt(x)`, or about 20bps.
// For `s` in the range `[1/256, 256]`, the estimate `f(s) = (181/1024) * (s+1)`
// is in the range `(1/2.84 * sqrt(s), 2.84 * sqrt(s))`,
// with largest error when `s = 1` and when `s = 256` or `1/256`.
// Since `y` is in `[256, 256*(2**16))`, let `a = y/65536`, so that `a` is in `[1/256, 256)`.
// Then we can estimate `sqrt(y)` using
// `sqrt(65536) * 181/1024 * (a + 1) = 181/4 * (y + 65536)/65536 = 181 * (y + 65536)/2**18`.
// There is no overflow risk here since `y < 2**136` after the first branch above.
z := shr(18, mul(z, add(shr(r, x), 65536))) // A `mul()` is saved from starting `z` at 181.
// Given the worst case multiplicative error of 2.84 above, 7 iterations should be enough.
z := shr(1, add(z, div(x, z)))
z := shr(1, add(z, div(x, z)))
z := shr(1, add(z, div(x, z)))
z := shr(1, add(z, div(x, z)))
z := shr(1, add(z, div(x, z)))
z := shr(1, add(z, div(x, z)))
z := shr(1, add(z, div(x, z)))
// If `x+1` is a perfect square, the Babylonian method cycles between
// `floor(sqrt(x))` and `ceil(sqrt(x))`. This statement ensures we return floor.
// See: https://en.wikipedia.org/wiki/Integer_square_root#Using_only_integer_division
z := sub(z, lt(div(x, z), z))
}
}
/// @dev Returns the cube root of `x`.
/// Credit to bout3fiddy and pcaversaccio under AGPLv3 license:
/// https://github.com/pcaversaccio/snekmate/blob/main/src/utils/Math.vy
function cbrt(uint256 x) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
let r := shl(7, lt(0xffffffffffffffffffffffffffffffff, x))
r := or(r, shl(6, lt(0xffffffffffffffff, shr(r, x))))
r := or(r, shl(5, lt(0xffffffff, shr(r, x))))
r := or(r, shl(4, lt(0xffff, shr(r, x))))
r := or(r, shl(3, lt(0xff, shr(r, x))))
z := div(shl(div(r, 3), shl(lt(0xf, shr(r, x)), 0xf)), xor(7, mod(r, 3)))
z := div(add(add(div(x, mul(z, z)), z), z), 3)
z := div(add(add(div(x, mul(z, z)), z), z), 3)
z := div(add(add(div(x, mul(z, z)), z), z), 3)
z := div(add(add(div(x, mul(z, z)), z), z), 3)
z := div(add(add(div(x, mul(z, z)), z), z), 3)
z := div(add(add(div(x, mul(z, z)), z), z), 3)
z := div(add(add(div(x, mul(z, z)), z), z), 3)
z := sub(z, lt(div(x, mul(z, z)), z))
}
}
/// @dev Returns the square root of `x`, denominated in `WAD`.
function sqrtWad(uint256 x) internal pure returns (uint256 z) {
unchecked {
z = 10 ** 9;
if (x <= type(uint256).max / 10 ** 36 - 1) {
x *= 10 ** 18;
z = 1;
}
z *= sqrt(x);
}
}
/// @dev Returns the cube root of `x`, denominated in `WAD`.
function cbrtWad(uint256 x) internal pure returns (uint256 z) {
unchecked {
z = 10 ** 12;
if (x <= (type(uint256).max / 10 ** 36) * 10 ** 18 - 1) {
if (x >= type(uint256).max / 10 ** 36) {
x *= 10 ** 18;
z = 10 ** 6;
} else {
x *= 10 ** 36;
z = 1;
}
}
z *= cbrt(x);
}
}
/// @dev Returns the factorial of `x`.
function factorial(uint256 x) internal pure returns (uint256 result) {
/// @solidity memory-safe-assembly
assembly {
if iszero(lt(x, 58)) {
mstore(0x00, 0xaba0f2a2) // `FactorialOverflow()`.
revert(0x1c, 0x04)
}
for { result := 1 } x { x := sub(x, 1) } { result := mul(result, x) }
}
}
/// @dev Returns the log2 of `x`.
/// Equivalent to computing the index of the most significant bit (MSB) of `x`.
/// Returns 0 if `x` is zero.
function log2(uint256 x) internal pure returns (uint256 r) {
/// @solidity memory-safe-assembly
assembly {
r := shl(7, lt(0xffffffffffffffffffffffffffffffff, x))
r := or(r, shl(6, lt(0xffffffffffffffff, shr(r, x))))
r := or(r, shl(5, lt(0xffffffff, shr(r, x))))
r := or(r, shl(4, lt(0xffff, shr(r, x))))
r := or(r, shl(3, lt(0xff, shr(r, x))))
// forgefmt: disable-next-item
r := or(r, byte(and(0x1f, shr(shr(r, x), 0x8421084210842108cc6318c6db6d54be)),
0x0706060506020504060203020504030106050205030304010505030400000000))
}
}
/// @dev Returns the log2 of `x`, rounded up.
/// Returns 0 if `x` is zero.
function log2Up(uint256 x) internal pure returns (uint256 r) {
r = log2(x);
/// @solidity memory-safe-assembly
assembly {
r := add(r, lt(shl(r, 1), x))
}
}
/// @dev Returns the log10 of `x`.
/// Returns 0 if `x` is zero.
function log10(uint256 x) internal pure returns (uint256 r) {
/// @solidity memory-safe-assembly
assembly {
if iszero(lt(x, 100000000000000000000000000000000000000)) {
x := div(x, 100000000000000000000000000000000000000)
r := 38
}
if iszero(lt(x, 100000000000000000000)) {
x := div(x, 100000000000000000000)
r := add(r, 20)
}
if iszero(lt(x, 10000000000)) {
x := div(x, 10000000000)
r := add(r, 10)
}
if iszero(lt(x, 100000)) {
x := div(x, 100000)
r := add(r, 5)
}
r := add(r, add(gt(x, 9), add(gt(x, 99), add(gt(x, 999), gt(x, 9999)))))
}
}
/// @dev Returns the log10 of `x`, rounded up.
/// Returns 0 if `x` is zero.
function log10Up(uint256 x) internal pure returns (uint256 r) {
r = log10(x);
/// @solidity memory-safe-assembly
assembly {
r := add(r, lt(exp(10, r), x))
}
}
/// @dev Returns the log256 of `x`.
/// Returns 0 if `x` is zero.
function log256(uint256 x) internal pure returns (uint256 r) {
/// @solidity memory-safe-assembly
assembly {
r := shl(7, lt(0xffffffffffffffffffffffffffffffff, x))
r := or(r, shl(6, lt(0xffffffffffffffff, shr(r, x))))
r := or(r, shl(5, lt(0xffffffff, shr(r, x))))
r := or(r, shl(4, lt(0xffff, shr(r, x))))
r := or(shr(3, r), lt(0xff, shr(r, x)))
}
}
/// @dev Returns the log256 of `x`, rounded up.
/// Returns 0 if `x` is zero.
function log256Up(uint256 x) internal pure returns (uint256 r) {
r = log256(x);
/// @solidity memory-safe-assembly
assembly {
r := add(r, lt(shl(shl(3, r), 1), x))
}
}
/// @dev Returns the scientific notation format `mantissa * 10 ** exponent` of `x`.
/// Useful for compressing prices (e.g. using 25 bit mantissa and 7 bit exponent).
function sci(uint256 x) internal pure returns (uint256 mantissa, uint256 exponent) {
/// @solidity memory-safe-assembly
assembly {
mantissa := x
if mantissa {
if iszero(mod(mantissa, 1000000000000000000000000000000000)) {
mantissa := div(mantissa, 1000000000000000000000000000000000)
exponent := 33
}
if iszero(mod(mantissa, 10000000000000000000)) {
mantissa := div(mantissa, 10000000000000000000)
exponent := add(exponent, 19)
}
if iszero(mod(mantissa, 1000000000000)) {
mantissa := div(mantissa, 1000000000000)
exponent := add(exponent, 12)
}
if iszero(mod(mantissa, 1000000)) {
mantissa := div(mantissa, 1000000)
exponent := add(exponent, 6)
}
if iszero(mod(mantissa, 10000)) {
mantissa := div(mantissa, 10000)
exponent := add(exponent, 4)
}
if iszero(mod(mantissa, 100)) {
mantissa := div(mantissa, 100)
exponent := add(exponent, 2)
}
if iszero(mod(mantissa, 10)) {
mantissa := div(mantissa, 10)
exponent := add(exponent, 1)
}
}
}
}
/// @dev Convenience function for packing `x` into a smaller number using `sci`.
/// The `mantissa` will be in bits [7..255] (the upper 249 bits).
/// The `exponent` will be in bits [0..6] (the lower 7 bits).
/// Use `SafeCastLib` to safely ensure that the `packed` number is small
/// enough to fit in the desired unsigned integer type:
/// ```
/// uint32 packed = SafeCastLib.toUint32(FixedPointMathLib.packSci(777 ether));
/// ```
function packSci(uint256 x) internal pure returns (uint256 packed) {
(x, packed) = sci(x); // Reuse for `mantissa` and `exponent`.
/// @solidity memory-safe-assembly
assembly {
if shr(249, x) {
mstore(0x00, 0xce30380c) // `MantissaOverflow()`.
revert(0x1c, 0x04)
}
packed := or(shl(7, x), packed)
}
}
/// @dev Convenience function for unpacking a packed number from `packSci`.
function unpackSci(uint256 packed) internal pure returns (uint256 unpacked) {
unchecked {
unpacked = (packed >> 7) * 10 ** (packed & 0x7f);
}
}
/// @dev Returns the average of `x` and `y`.
function avg(uint256 x, uint256 y) internal pure returns (uint256 z) {
unchecked {
z = (x & y) + ((x ^ y) >> 1);
}
}
/// @dev Returns the average of `x` and `y`.
function avg(int256 x, int256 y) internal pure returns (int256 z) {
unchecked {
z = (x >> 1) + (y >> 1) + (((x & 1) + (y & 1)) >> 1);
}
}
/// @dev Returns the absolute value of `x`.
function abs(int256 x) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
z := xor(sub(0, shr(255, x)), add(sub(0, shr(255, x)), x))
}
}
/// @dev Returns the absolute distance between `x` and `y`.
function dist(int256 x, int256 y) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
z := xor(mul(xor(sub(y, x), sub(x, y)), sgt(x, y)), sub(y, x))
}
}
/// @dev Returns the minimum of `x` and `y`.
function min(uint256 x, uint256 y) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
z := xor(x, mul(xor(x, y), lt(y, x)))
}
}
/// @dev Returns the minimum of `x` and `y`.
function min(int256 x, int256 y) internal pure returns (int256 z) {
/// @solidity memory-safe-assembly
assembly {
z := xor(x, mul(xor(x, y), slt(y, x)))
}
}
/// @dev Returns the maximum of `x` and `y`.
function max(uint256 x, uint256 y) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
z := xor(x, mul(xor(x, y), gt(y, x)))
}
}
/// @dev Returns the maximum of `x` and `y`.
function max(int256 x, int256 y) internal pure returns (int256 z) {
/// @solidity memory-safe-assembly
assembly {
z := xor(x, mul(xor(x, y), sgt(y, x)))
}
}
/// @dev Returns `x`, bounded to `minValue` and `maxValue`.
function clamp(uint256 x, uint256 minValue, uint256 maxValue)
internal
pure
returns (uint256 z)
{
/// @solidity memory-safe-assembly
assembly {
z := xor(x, mul(xor(x, minValue), gt(minValue, x)))
z := xor(z, mul(xor(z, maxValue), lt(maxValue, z)))
}
}
/// @dev Returns `x`, bounded to `minValue` and `maxValue`.
function clamp(int256 x, int256 minValue, int256 maxValue) internal pure returns (int256 z) {
/// @solidity memory-safe-assembly
assembly {
z := xor(x, mul(xor(x, minValue), sgt(minValue, x)))
z := xor(z, mul(xor(z, maxValue), slt(maxValue, z)))
}
}
/// @dev Returns greatest common divisor of `x` and `y`.
function gcd(uint256 x, uint256 y) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
for { z := x } y {} {
let t := y
y := mod(z, y)
z := t
}
}
}
/*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
/* RAW NUMBER OPERATIONS */
/*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
/// @dev Returns `x + y`, without checking for overflow.
function rawAdd(uint256 x, uint256 y) internal pure returns (uint256 z) {
unchecked {
z = x + y;
}
}
/// @dev Returns `x + y`, without checking for overflow.
function rawAdd(int256 x, int256 y) internal pure returns (int256 z) {
unchecked {
z = x + y;
}
}
/// @dev Returns `x - y`, without checking for underflow.
function rawSub(uint256 x, uint256 y) internal pure returns (uint256 z) {
unchecked {
z = x - y;
}
}
/// @dev Returns `x - y`, without checking for underflow.
function rawSub(int256 x, int256 y) internal pure returns (int256 z) {
unchecked {
z = x - y;
}
}
/// @dev Returns `x * y`, without checking for overflow.
function rawMul(uint256 x, uint256 y) internal pure returns (uint256 z) {
unchecked {
z = x * y;
}
}
/// @dev Returns `x * y`, without checking for overflow.
function rawMul(int256 x, int256 y) internal pure returns (int256 z) {
unchecked {
z = x * y;
}
}
/// @dev Returns `x / y`, returning 0 if `y` is zero.
function rawDiv(uint256 x, uint256 y) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
z := div(x, y)
}
}
/// @dev Returns `x / y`, returning 0 if `y` is zero.
function rawSDiv(int256 x, int256 y) internal pure returns (int256 z) {
/// @solidity memory-safe-assembly
assembly {
z := sdiv(x, y)
}
}
/// @dev Returns `x % y`, returning 0 if `y` is zero.
function rawMod(uint256 x, uint256 y) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
z := mod(x, y)
}
}
/// @dev Returns `x % y`, returning 0 if `y` is zero.
function rawSMod(int256 x, int256 y) internal pure returns (int256 z) {
/// @solidity memory-safe-assembly
assembly {
z := smod(x, y)
}
}
/// @dev Returns `(x + y) % d`, return 0 if `d` if zero.
function rawAddMod(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
z := addmod(x, y, d)
}
}
/// @dev Returns `(x * y) % d`, return 0 if `d` if zero.
function rawMulMod(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 z) {
/// @solidity memory-safe-assembly
assembly {
z := mulmod(x, y, d)
}
}
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;
/// @notice Safe integer casting library that reverts on overflow.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/utils/SafeCastLib.sol)
/// @author Modified from OpenZeppelin (https://github.com/OpenZeppelin/openzeppelin-contracts/blob/master/contracts/utils/math/SafeCast.sol)
library SafeCastLib {
/*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
/* CUSTOM ERRORS */
/*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
error Overflow();
/*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
/* UNSIGNED INTEGER SAFE CASTING OPERATIONS */
/*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
function toUint8(uint256 x) internal pure returns (uint8) {
if (x >= 1 << 8) _revertOverflow();
return uint8(x);
}
function toUint16(uint256 x) internal pure returns (uint16) {
if (x >= 1 << 16) _revertOverflow();
return uint16(x);
}
function toUint24(uint256 x) internal pure returns (uint24) {
if (x >= 1 << 24) _revertOverflow();
return uint24(x);
}
function toUint32(uint256 x) internal pure returns (uint32) {
if (x >= 1 << 32) _revertOverflow();
return uint32(x);
}
function toUint40(uint256 x) internal pure returns (uint40) {
if (x >= 1 << 40) _revertOverflow();
return uint40(x);
}
function toUint48(uint256 x) internal pure returns (uint48) {
if (x >= 1 << 48) _revertOverflow();
return uint48(x);
}
function toUint56(uint256 x) internal pure returns (uint56) {
if (x >= 1 << 56) _revertOverflow();
return uint56(x);
}
function toUint64(uint256 x) internal pure returns (uint64) {
if (x >= 1 << 64) _revertOverflow();
return uint64(x);
}
function toUint72(uint256 x) internal pure returns (uint72) {
if (x >= 1 << 72) _revertOverflow();
return uint72(x);
}
function toUint80(uint256 x) internal pure returns (uint80) {
if (x >= 1 << 80) _revertOverflow();
return uint80(x);
}
function toUint88(uint256 x) internal pure returns (uint88) {
if (x >= 1 << 88) _revertOverflow();
return uint88(x);
}
function toUint96(uint256 x) internal pure returns (uint96) {
if (x >= 1 << 96) _revertOverflow();
return uint96(x);
}
function toUint104(uint256 x) internal pure returns (uint104) {
if (x >= 1 << 104) _revertOverflow();
return uint104(x);
}
function toUint112(uint256 x) internal pure returns (uint112) {
if (x >= 1 << 112) _revertOverflow();
return uint112(x);
}
function toUint120(uint256 x) internal pure returns (uint120) {
if (x >= 1 << 120) _revertOverflow();
return uint120(x);
}
function toUint128(uint256 x) internal pure returns (uint128) {
if (x >= 1 << 128) _revertOverflow();
return uint128(x);
}
function toUint136(uint256 x) internal pure returns (uint136) {
if (x >= 1 << 136) _revertOverflow();
return uint136(x);
}
function toUint144(uint256 x) internal pure returns (uint144) {
if (x >= 1 << 144) _revertOverflow();
return uint144(x);
}
function toUint152(uint256 x) internal pure returns (uint152) {
if (x >= 1 << 152) _revertOverflow();
return uint152(x);
}
function toUint160(uint256 x) internal pure returns (uint160) {
if (x >= 1 << 160) _revertOverflow();
return uint160(x);
}
function toUint168(uint256 x) internal pure returns (uint168) {
if (x >= 1 << 168) _revertOverflow();
return uint168(x);
}
function toUint176(uint256 x) internal pure returns (uint176) {
if (x >= 1 << 176) _revertOverflow();
return uint176(x);
}
function toUint184(uint256 x) internal pure returns (uint184) {
if (x >= 1 << 184) _revertOverflow();
return uint184(x);
}
function toUint192(uint256 x) internal pure returns (uint192) {
if (x >= 1 << 192) _revertOverflow();
return uint192(x);
}
function toUint200(uint256 x) internal pure returns (uint200) {
if (x >= 1 << 200) _revertOverflow();
return uint200(x);
}
function toUint208(uint256 x) internal pure returns (uint208) {
if (x >= 1 << 208) _revertOverflow();
return uint208(x);
}
function toUint216(uint256 x) internal pure returns (uint216) {
if (x >= 1 << 216) _revertOverflow();
return uint216(x);
}
function toUint224(uint256 x) internal pure returns (uint224) {
if (x >= 1 << 224) _revertOverflow();
return uint224(x);
}
function toUint232(uint256 x) internal pure returns (uint232) {
if (x >= 1 << 232) _revertOverflow();
return uint232(x);
}
function toUint240(uint256 x) internal pure returns (uint240) {
if (x >= 1 << 240) _revertOverflow();
return uint240(x);
}
function toUint248(uint256 x) internal pure returns (uint248) {
if (x >= 1 << 248) _revertOverflow();
return uint248(x);
}
/*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
/* SIGNED INTEGER SAFE CASTING OPERATIONS */
/*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
function toInt8(int256 x) internal pure returns (int8) {
int8 y = int8(x);
if (x != y) _revertOverflow();
return y;
}
function toInt16(int256 x) internal pure returns (int16) {
int16 y = int16(x);
if (x != y) _revertOverflow();
return y;
}
function toInt24(int256 x) internal pure returns (int24) {
int24 y = int24(x);
if (x != y) _revertOverflow();
return y;
}
function toInt32(int256 x) internal pure returns (int32) {
int32 y = int32(x);
if (x != y) _revertOverflow();
return y;
}
function toInt40(int256 x) internal pure returns (int40) {
int40 y = int40(x);
if (x != y) _revertOverflow();
return y;
}
function toInt48(int256 x) internal pure returns (int48) {
int48 y = int48(x);
if (x != y) _revertOverflow();
return y;
}
function toInt56(int256 x) internal pure returns (int56) {
int56 y = int56(x);
if (x != y) _revertOverflow();
return y;
}
function toInt64(int256 x) internal pure returns (int64) {
int64 y = int64(x);
if (x != y) _revertOverflow();
return y;
}
function toInt72(int256 x) internal pure returns (int72) {
int72 y = int72(x);
if (x != y) _revertOverflow();
return y;
}
function toInt80(int256 x) internal pure returns (int80) {
int80 y = int80(x);
if (x != y) _revertOverflow();
return y;
}
function toInt88(int256 x) internal pure returns (int88) {
int88 y = int88(x);
if (x != y) _revertOverflow();
return y;
}
function toInt96(int256 x) internal pure returns (int96) {
int96 y = int96(x);
if (x != y) _revertOverflow();
return y;
}
function toInt104(int256 x) internal pure returns (int104) {
int104 y = int104(x);
if (x != y) _revertOverflow();
return y;
}
function toInt112(int256 x) internal pure returns (int112) {
int112 y = int112(x);
if (x != y) _revertOverflow();
return y;
}
function toInt120(int256 x) internal pure returns (int120) {
int120 y = int120(x);
if (x != y) _revertOverflow();
return y;
}
function toInt128(int256 x) internal pure returns (int128) {
int128 y = int128(x);
if (x != y) _revertOverflow();
return y;
}
function toInt136(int256 x) internal pure returns (int136) {
int136 y = int136(x);
if (x != y) _revertOverflow();
return y;
}
function toInt144(int256 x) internal pure returns (int144) {
int144 y = int144(x);
if (x != y) _revertOverflow();
return y;
}
function toInt152(int256 x) internal pure returns (int152) {
int152 y = int152(x);
if (x != y) _revertOverflow();
return y;
}
function toInt160(int256 x) internal pure returns (int160) {
int160 y = int160(x);
if (x != y) _revertOverflow();
return y;
}
function toInt168(int256 x) internal pure returns (int168) {
int168 y = int168(x);
if (x != y) _revertOverflow();
return y;
}
function toInt176(int256 x) internal pure returns (int176) {
int176 y = int176(x);
if (x != y) _revertOverflow();
return y;
}
function toInt184(int256 x) internal pure returns (int184) {
int184 y = int184(x);
if (x != y) _revertOverflow();
return y;
}
function toInt192(int256 x) internal pure returns (int192) {
int192 y = int192(x);
if (x != y) _revertOverflow();
return y;
}
function toInt200(int256 x) internal pure returns (int200) {
int200 y = int200(x);
if (x != y) _revertOverflow();
return y;
}
function toInt208(int256 x) internal pure returns (int208) {
int208 y = int208(x);
if (x != y) _revertOverflow();
return y;
}
function toInt216(int256 x) internal pure returns (int216) {
int216 y = int216(x);
if (x != y) _revertOverflow();
return y;
}
function toInt224(int256 x) internal pure returns (int224) {
int224 y = int224(x);
if (x != y) _revertOverflow();
return y;
}
function toInt232(int256 x) internal pure returns (int232) {
int232 y = int232(x);
if (x != y) _revertOverflow();
return y;
}
function toInt240(int256 x) internal pure returns (int240) {
int240 y = int240(x);
if (x != y) _revertOverflow();
return y;
}
function toInt248(int256 x) internal pure returns (int248) {
int248 y = int248(x);
if (x != y) _revertOverflow();
return y;
}
/*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
/* OTHER SAFE CASTING OPERATIONS */
/*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
function toInt256(uint256 x) internal pure returns (int256) {
if (x >= 1 << 255) _revertOverflow();
return int256(x);
}
function toUint256(int256 x) internal pure returns (uint256) {
if (x < 0) _revertOverflow();
return uint256(x);
}
/*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
/* PRIVATE HELPERS */
/*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
function _revertOverflow() private pure {
/// @solidity memory-safe-assembly
assembly {
// Store the function selector of `Overflow()`.
mstore(0x00, 0x35278d12)
// Revert with (offset, size).
revert(0x1c, 0x04)
}
}
}