ERC-20
Overview
Max Total Supply
200 ERC20 ***
Holders
2
Total Transfers
-
Market
Onchain Market Cap
$0.00
Circulating Supply Market Cap
-
Other Info
Token Contract (WITH 18 Decimals)
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# | Exchange | Pair | Price | 24H Volume | % Volume |
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Minimal Proxy Contract for 0x5ed972254112ce134b0ac6816d4fa97c02ac2f3a
Contract Name:
CentaurPool
Compiler Version
v0.6.12+commit.27d51765
Optimization Enabled:
No with 200 runs
Other Settings:
default evmVersion
Contract Source Code (Solidity Standard Json-Input format)
// SPDX-License-Identifier: MIT pragma solidity =0.6.12; pragma experimental ABIEncoderV2; import './CentaurLPToken.sol'; import './libraries/Initializable.sol'; import './libraries/SafeMath.sol'; import './libraries/CentaurMath.sol'; import './interfaces/IERC20.sol'; import './interfaces/ICentaurFactory.sol'; import './interfaces/ICentaurPool.sol'; import './interfaces/ICentaurSettlement.sol'; import './interfaces/IOracle.sol'; contract CentaurPool is Initializable, CentaurLPToken { using SafeMath for uint; bytes4 private constant SELECTOR = bytes4(keccak256(bytes('transfer(address,uint256)'))); address public factory; address public baseToken; uint public baseTokenDecimals; address public oracle; uint public oracleDecimals; uint public baseTokenTargetAmount; uint public baseTokenBalance; uint public liquidityParameter; bool public tradeEnabled; bool public depositEnabled; bool public withdrawEnabled; uint private unlocked; modifier lock() { require(unlocked == 1, 'CentaurSwap: LOCKED'); unlocked = 0; _; unlocked = 1; } modifier tradeAllowed() { require(tradeEnabled, "CentaurSwap: TRADE_NOT_ALLOWED"); _; } modifier depositAllowed() { require(depositEnabled, "CentaurSwap: DEPOSIT_NOT_ALLOWED"); _; } modifier withdrawAllowed() { require(withdrawEnabled, "CentaurSwap: WITHDRAW_NOT_ALLOWED"); _; } modifier onlyRouter() { require(msg.sender == ICentaurFactory(factory).router(), 'CentaurSwap: ONLY_ROUTER_ALLOWED'); _; } modifier onlyFactory() { require(msg.sender == factory, 'CentaurSwap: ONLY_FACTORY_ALLOWED'); _; } event Mint(address indexed sender, uint amount); event Burn(address indexed sender, uint amount, address indexed to); event AmountIn(address indexed sender, uint amount); event AmountOut(address indexed sender, uint amount, address indexed to); event EmergencyWithdraw(uint256 _timestamp, address indexed _token, uint256 _amount, address indexed _to); function init(address _factory, address _baseToken, address _oracle, uint _liquidityParameter) external initializer { factory = _factory; baseToken = _baseToken; baseTokenDecimals = IERC20(baseToken).decimals(); oracle = _oracle; oracleDecimals = IOracle(oracle).decimals(); tradeEnabled = false; depositEnabled = false; withdrawEnabled = false; liquidityParameter = _liquidityParameter; symbol = string(abi.encodePacked("CS-", IERC20(baseToken).symbol())); decimals = baseTokenDecimals; unlocked = 1; } function _safeTransfer(address token, address to, uint value) private { (bool success, bytes memory data) = token.call(abi.encodeWithSelector(SELECTOR, to, value)); require(success && (data.length == 0 || abi.decode(data, (bool))), 'CentaurSwap: TRANSFER_FAILED'); } function mint(address to) external lock onlyRouter depositAllowed returns (uint liquidity) { uint balance = IERC20(baseToken).balanceOf(address(this)); uint amount = balance.sub(baseTokenBalance); if (totalSupply == 0) { liquidity = amount.add(baseTokenTargetAmount); } else { liquidity = amount.mul(totalSupply).div(baseTokenTargetAmount); } require(liquidity > 0, 'CentaurSwap: INSUFFICIENT_LIQUIDITY_MINTED'); _mint(to, liquidity); baseTokenBalance = baseTokenBalance.add(amount); baseTokenTargetAmount = baseTokenTargetAmount.add(amount); emit Mint(msg.sender, amount); } function burn(address to) external lock onlyRouter withdrawAllowed returns (uint amount) { uint liquidity = balanceOf[address(this)]; amount = liquidity.mul(baseTokenTargetAmount).div(totalSupply); require(amount > 0, 'CentaurSwap: INSUFFICIENT_LIQUIDITY_BURNED'); require(baseTokenBalance >= amount, 'CentaurSwap: INSUFFICIENT_LIQUIDITY'); _burn(address(this), liquidity); _safeTransfer(baseToken, to, amount); baseTokenBalance = baseTokenBalance.sub(amount); baseTokenTargetAmount = baseTokenTargetAmount.sub(amount); emit Burn(msg.sender, amount, to); } function swapTo(address _sender, address _fromToken, uint _amountIn, uint _value, address _receiver) external lock onlyRouter tradeAllowed returns (uint maxAmount) { require(_fromToken != baseToken, 'CentaurSwap: INVALID_POOL'); address pool = ICentaurFactory(factory).getPool(_fromToken); require(pool != address(0), 'CentaurSwap: POOL_NOT_FOUND'); // Check if has pendingSettlement address settlement = ICentaurFactory(factory).settlement(); require(!ICentaurSettlement(settlement).hasPendingSettlement(_sender, address(this)), 'CentaurSwap: PENDING_SETTLEMENT'); // maxAmount because amount might be lesser during settlement. (If amount is more, excess is given back to pool) maxAmount = getAmountOutFromValue(_value); ICentaurSettlement.Settlement memory pendingSettlement = ICentaurSettlement.Settlement( pool, _amountIn, ICentaurPool(pool).baseTokenTargetAmount(), (ICentaurPool(pool).baseTokenBalance()).sub(_amountIn), ICentaurPool(pool).liquidityParameter(), address(this), maxAmount, baseTokenTargetAmount, baseTokenBalance, liquidityParameter, _receiver, block.timestamp.add(ICentaurSettlement(settlement).settlementDuration()) ); // Subtract maxAmount from baseTokenBalance first, difference (if any) will be added back during settlement baseTokenBalance = baseTokenBalance.sub(maxAmount); // Add to pending settlement ICentaurSettlement(settlement).addSettlement(_sender, pendingSettlement); // Transfer amount to settlement for escrow _safeTransfer(baseToken, settlement, maxAmount); return maxAmount; } function swapFrom(address _sender) external lock onlyRouter tradeAllowed returns (uint amount, uint value) { uint balance = IERC20(baseToken).balanceOf(address(this)); require(balance > baseTokenBalance, 'CentaurSwap: INSUFFICIENT_SWAP_AMOUNT'); // Check if has pendingSettlement address settlement = ICentaurFactory(factory).settlement(); require(!ICentaurSettlement(settlement).hasPendingSettlement(_sender, address(this)), 'CentaurSwap: PENDING_SETTLEMENT'); amount = balance.sub(baseTokenBalance); value = getValueFromAmountIn(amount); baseTokenBalance = balance; emit AmountIn(_sender, amount); return (amount, value); } function swapSettle(address _sender) external lock returns (uint, address) { address settlement = ICentaurFactory(factory).settlement(); ICentaurSettlement.Settlement memory pendingSettlement = ICentaurSettlement(settlement).getPendingSettlement(_sender, address(this)); require (pendingSettlement.settlementTimestamp != 0, 'CentaurSwap: NO_PENDING_SETTLEMENT'); require (pendingSettlement.tPool == address(this), 'CentaurSwap: WRONG_POOL_SETTLEMENT'); require (block.timestamp >= pendingSettlement.settlementTimestamp, 'CentaurSwap: SETTLEMENT_STILL_PENDING'); uint newfPoolOraclePrice = ICentaurPool(pendingSettlement.fPool).getOraclePrice(); uint newtPoolOraclePrice = getOraclePrice(); uint newValue = CentaurMath.getValueFromAmountIn(pendingSettlement.amountIn, newfPoolOraclePrice, ICentaurPool(pendingSettlement.fPool).baseTokenDecimals(), pendingSettlement.fPoolBaseTokenTargetAmount, pendingSettlement.fPoolBaseTokenBalance, pendingSettlement.fPoolLiquidityParameter); uint newAmount = CentaurMath.getAmountOutFromValue(newValue, newtPoolOraclePrice, baseTokenDecimals, pendingSettlement.tPoolBaseTokenTargetAmount, pendingSettlement.tPoolBaseTokenBalance, pendingSettlement.tPoolLiquidityParameter); uint poolFee = ICentaurFactory(factory).poolFee(); address router = ICentaurFactory(factory).router(); // Remove settlement and receive escrowed amount ICentaurSettlement(settlement).removeSettlement(_sender, pendingSettlement.fPool, pendingSettlement.tPool); if (newAmount > pendingSettlement.maxAmountOut) { uint fee = (pendingSettlement.maxAmountOut).mul(poolFee).div(100 ether); uint amountOut = pendingSettlement.maxAmountOut.sub(fee); if (msg.sender == router) { _safeTransfer(baseToken, router, amountOut); } else { _safeTransfer(baseToken, pendingSettlement.receiver, amountOut); } emit AmountOut(_sender, amountOut, pendingSettlement.receiver); baseTokenBalance = baseTokenBalance.add(fee); baseTokenTargetAmount = baseTokenTargetAmount.add(fee); return (amountOut, pendingSettlement.receiver); } else { uint fee = (newAmount).mul(poolFee).div(100 ether); uint amountOut = newAmount.sub(fee); if (msg.sender == router) { _safeTransfer(baseToken, router, amountOut); } else { _safeTransfer(baseToken, pendingSettlement.receiver, amountOut); } emit AmountOut(_sender, amountOut, pendingSettlement.receiver); // Difference added back to baseTokenBalance uint difference = (pendingSettlement.maxAmountOut).sub(amountOut); baseTokenBalance = baseTokenBalance.add(difference); // TX fee goes back into pool for liquidity providers baseTokenTargetAmount = baseTokenTargetAmount.add(difference); return (amountOut, pendingSettlement.receiver); } } function getOraclePrice() public view returns (uint price) { (, int answer,,,) = IOracle(oracle).latestRoundData(); // Returns price in 18 decimals price = uint(answer).mul(10 ** uint(18).sub(oracleDecimals)); } // Swap Exact Tokens For Tokens (getAmountOut) function getAmountOutFromValue(uint _value) public view returns (uint amount) { amount = CentaurMath.getAmountOutFromValue(_value, getOraclePrice(), baseTokenDecimals, baseTokenTargetAmount, baseTokenBalance, liquidityParameter); require(baseTokenBalance > amount, "CentaurSwap: INSUFFICIENT_LIQUIDITY"); } function getValueFromAmountIn(uint _amount) public view returns (uint value) { value = CentaurMath.getValueFromAmountIn(_amount, getOraclePrice(), baseTokenDecimals, baseTokenTargetAmount, baseTokenBalance, liquidityParameter); } // Swap Tokens For Exact Tokens (getAmountIn) function getAmountInFromValue(uint _value) public view returns (uint amount) { amount = CentaurMath.getAmountInFromValue(_value, getOraclePrice(), baseTokenDecimals, baseTokenTargetAmount, baseTokenBalance, liquidityParameter); } function getValueFromAmountOut(uint _amount) public view returns (uint value) { require(baseTokenBalance > _amount, "CentaurSwap: INSUFFICIENT_LIQUIDITY"); value = CentaurMath.getValueFromAmountOut(_amount, getOraclePrice(), baseTokenDecimals, baseTokenTargetAmount, baseTokenBalance, liquidityParameter); } // Helper functions function setFactory(address _factory) external onlyFactory { factory = _factory; } function setTradeEnabled(bool _tradeEnabled) external onlyFactory { tradeEnabled = _tradeEnabled; } function setDepositEnabled(bool _depositEnabled) external onlyFactory { depositEnabled = _depositEnabled; } function setWithdrawEnabled(bool _withdrawEnabled) external onlyFactory { withdrawEnabled = _withdrawEnabled; } function setLiquidityParameter(uint _liquidityParameter) external onlyFactory { liquidityParameter = _liquidityParameter; } function emergencyWithdraw(address _token, uint _amount, address _to) external onlyFactory { _safeTransfer(_token, _to, _amount); emit EmergencyWithdraw(block.timestamp, _token, _amount, _to); } }
// SPDX-License-Identifier: MIT pragma solidity =0.6.12; import './libraries/SafeMath.sol'; contract CentaurLPToken { using SafeMath for uint; string public constant name = 'CentaurSwap LP Token'; string public symbol; uint256 public decimals = 18; uint public totalSupply; mapping(address => uint) public balanceOf; mapping(address => mapping(address => uint)) public allowance; event Approval(address indexed owner, address indexed spender, uint value); event Transfer(address indexed from, address indexed to, uint value); function _mint(address to, uint value) internal { totalSupply = totalSupply.add(value); balanceOf[to] = balanceOf[to].add(value); emit Transfer(address(0), to, value); } function _burn(address from, uint value) internal { balanceOf[from] = balanceOf[from].sub(value); totalSupply = totalSupply.sub(value); emit Transfer(from, address(0), value); } function _approve(address owner, address spender, uint value) private { allowance[owner][spender] = value; emit Approval(owner, spender, value); } function _transfer(address from, address to, uint value) private { balanceOf[from] = balanceOf[from].sub(value); balanceOf[to] = balanceOf[to].add(value); emit Transfer(from, to, value); } function approve(address spender, uint value) external returns (bool) { _approve(msg.sender, spender, value); return true; } function transfer(address to, uint value) external returns (bool) { _transfer(msg.sender, to, value); return true; } function transferFrom(address from, address to, uint value) external returns (bool) { if (allowance[from][msg.sender] != uint(-1)) { allowance[from][msg.sender] = allowance[from][msg.sender].sub(value); } _transfer(from, to, value); return true; } }
// SPDX-License-Identifier: MIT // solhint-disable-next-line compiler-version pragma solidity >=0.4.24 <0.8.0; /** * @dev This is a base contract to aid in writing upgradeable contracts, or any kind of contract that will be deployed * behind a proxy. Since a proxied contract can't have a constructor, it's common to move constructor logic to an * external initializer function, usually called `initialize`. It then becomes necessary to protect this initializer * function so it can only be called once. The {initializer} modifier provided by this contract will have this effect. * * TIP: To avoid leaving the proxy in an uninitialized state, the initializer function should be called as early as * possible by providing the encoded function call as the `_data` argument to {UpgradeableProxy-constructor}. * * CAUTION: When used with inheritance, manual care must be taken to not invoke a parent initializer twice, or to ensure * that all initializers are idempotent. This is not verified automatically as constructors are by Solidity. */ abstract contract Initializable { /** * @dev Indicates that the contract has been initialized. */ bool private _initialized; /** * @dev Indicates that the contract is in the process of being initialized. */ bool private _initializing; /** * @dev Modifier to protect an initializer function from being invoked twice. */ modifier initializer() { require(_initializing || _isConstructor() || !_initialized, "Initializable: contract is already initialized"); bool isTopLevelCall = !_initializing; if (isTopLevelCall) { _initializing = true; _initialized = true; } _; if (isTopLevelCall) { _initializing = false; } } /// @dev Returns true if and only if the function is running in the constructor function _isConstructor() private view returns (bool) { // extcodesize checks the size of the code stored in an address, and // address returns the current address. Since the code is still not // deployed when running a constructor, any checks on its code size will // yield zero, making it an effective way to detect if a contract is // under construction or not. address self = address(this); uint256 cs; // solhint-disable-next-line no-inline-assembly assembly { cs := extcodesize(self) } return cs == 0; } }
// SPDX-License-Identifier: MIT pragma solidity >=0.6.0 <0.8.0; /** * @dev Wrappers over Solidity's arithmetic operations with added overflow * checks. * * Arithmetic operations in Solidity wrap on overflow. This can easily result * in bugs, because programmers usually assume that an overflow raises an * error, which is the standard behavior in high level programming languages. * `SafeMath` restores this intuition by reverting the transaction when an * operation overflows. * * Using this library instead of the unchecked operations eliminates an entire * class of bugs, so it's recommended to use it always. */ library SafeMath { /** * @dev Returns the addition of two unsigned integers, reverting on * overflow. * * Counterpart to Solidity's `+` operator. * * Requirements: * * - Addition cannot overflow. */ function add(uint256 a, uint256 b) internal pure returns (uint256) { uint256 c = a + b; require(c >= a, "SafeMath: addition overflow"); return c; } /** * @dev Returns the subtraction of two unsigned integers, reverting on * overflow (when the result is negative). * * Counterpart to Solidity's `-` operator. * * Requirements: * * - Subtraction cannot overflow. */ function sub(uint256 a, uint256 b) internal pure returns (uint256) { return sub(a, b, "SafeMath: subtraction overflow"); } /** * @dev Returns the subtraction of two unsigned integers, reverting with custom message on * overflow (when the result is negative). * * Counterpart to Solidity's `-` operator. * * Requirements: * * - Subtraction cannot overflow. */ function sub(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) { require(b <= a, errorMessage); uint256 c = a - b; return c; } /** * @dev Returns the multiplication of two unsigned integers, reverting on * overflow. * * Counterpart to Solidity's `*` operator. * * Requirements: * * - Multiplication cannot overflow. */ function mul(uint256 a, uint256 b) internal pure returns (uint256) { // 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 0; } uint256 c = a * b; require(c / a == b, "SafeMath: multiplication overflow"); return c; } /** * @dev Returns the integer division of two unsigned integers. Reverts on * division by zero. The result is rounded towards zero. * * Counterpart to Solidity's `/` operator. Note: this function uses a * `revert` opcode (which leaves remaining gas untouched) while Solidity * uses an invalid opcode to revert (consuming all remaining gas). * * Requirements: * * - The divisor cannot be zero. */ function div(uint256 a, uint256 b) internal pure returns (uint256) { return div(a, b, "SafeMath: division by zero"); } /** * @dev Returns the integer division of two unsigned integers. Reverts with custom message on * division by zero. The result is rounded towards zero. * * Counterpart to Solidity's `/` operator. Note: this function uses a * `revert` opcode (which leaves remaining gas untouched) while Solidity * uses an invalid opcode to revert (consuming all remaining gas). * * Requirements: * * - The divisor cannot be zero. */ function div(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) { require(b > 0, errorMessage); uint256 c = a / b; // assert(a == b * c + a % b); // There is no case in which this doesn't hold return c; } /** * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo), * Reverts when dividing by zero. * * Counterpart to Solidity's `%` operator. This function uses a `revert` * opcode (which leaves remaining gas untouched) while Solidity uses an * invalid opcode to revert (consuming all remaining gas). * * Requirements: * * - The divisor cannot be zero. */ function mod(uint256 a, uint256 b) internal pure returns (uint256) { return mod(a, b, "SafeMath: modulo by zero"); } /** * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo), * Reverts with custom message when dividing by zero. * * Counterpart to Solidity's `%` operator. This function uses a `revert` * opcode (which leaves remaining gas untouched) while Solidity uses an * invalid opcode to revert (consuming all remaining gas). * * Requirements: * * - The divisor cannot be zero. */ function mod(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) { require(b != 0, errorMessage); return a % b; } }
// SPDX-License-Identifier: MIT pragma solidity ^0.6.12; import { SafeMath } from "./SafeMath.sol"; import { ABDKMathQuad } from './ABDKMathQuad.sol'; library CentaurMath { using SafeMath for uint256; bytes16 constant ONE_ETHER_QUAD = 0x403ABC16D674EC800000000000000000; // Helper Functions function getAmountOutFromValue(uint _value, uint _P, uint _tokenDecimals, uint _baseTokenTargetAmount, uint _baseTokenBalance, uint _liquidityParameter) external pure returns (uint amount) { bytes16 DECIMAL_QUAD = ABDKMathQuad.fromUInt(10 ** _tokenDecimals); bytes16 value_quad = ABDKMathQuad.div(ABDKMathQuad.fromUInt(_value), ONE_ETHER_QUAD); bytes16 P_quad = ABDKMathQuad.div(ABDKMathQuad.fromUInt(_P), ONE_ETHER_QUAD); bytes16 baseTokenTargetAmount_quad = ABDKMathQuad.div(ABDKMathQuad.fromUInt(_baseTokenTargetAmount), DECIMAL_QUAD); bytes16 baseTokenBalance_quad = ABDKMathQuad.div(ABDKMathQuad.fromUInt(_baseTokenBalance), DECIMAL_QUAD); bytes16 k_quad = ABDKMathQuad.div(ABDKMathQuad.fromUInt(_liquidityParameter), DECIMAL_QUAD); bytes16 X2 = ABDKMathQuad.sub(baseTokenBalance_quad, baseTokenTargetAmount_quad); bytes16 X1 = _solveEquationForAmountOut( value_quad, X2, k_quad, P_quad ); bytes16 amountOut = ABDKMathQuad.sub(X2, X1); amount = ABDKMathQuad.toUInt(ABDKMathQuad.mul(amountOut, DECIMAL_QUAD)); } function getValueFromAmountIn(uint _amount, uint _P, uint _tokenDecimals, uint _baseTokenTargetAmount, uint _baseTokenBalance, uint _liquidityParameter) external pure returns (uint value) { bytes16 DECIMAL_QUAD = ABDKMathQuad.fromUInt(10 ** _tokenDecimals); bytes16 amount_quad = ABDKMathQuad.div(ABDKMathQuad.fromUInt(_amount), DECIMAL_QUAD); bytes16 P_quad = ABDKMathQuad.div(ABDKMathQuad.fromUInt(_P), ONE_ETHER_QUAD); bytes16 baseTokenTargetAmount_quad = ABDKMathQuad.div(ABDKMathQuad.fromUInt(_baseTokenTargetAmount), DECIMAL_QUAD); bytes16 baseTokenBalance_quad = ABDKMathQuad.div(ABDKMathQuad.fromUInt(_baseTokenBalance), DECIMAL_QUAD); bytes16 k_quad = ABDKMathQuad.div(ABDKMathQuad.fromUInt(_liquidityParameter), DECIMAL_QUAD); bytes16 X1 = ABDKMathQuad.sub(baseTokenBalance_quad, baseTokenTargetAmount_quad); bytes16 X2 = ABDKMathQuad.add(X1, amount_quad); value = _solveForIntegral( X1, X2, k_quad, P_quad ); } function getAmountInFromValue(uint _value, uint _P, uint _tokenDecimals, uint _baseTokenTargetAmount, uint _baseTokenBalance, uint _liquidityParameter) external pure returns (uint amount) { bytes16 DECIMAL_QUAD = ABDKMathQuad.fromUInt(10 ** _tokenDecimals); bytes16 value_quad = ABDKMathQuad.div(ABDKMathQuad.fromUInt(_value), ONE_ETHER_QUAD); bytes16 P_quad = ABDKMathQuad.div(ABDKMathQuad.fromUInt(_P), ONE_ETHER_QUAD); bytes16 baseTokenTargetAmount_quad = ABDKMathQuad.div(ABDKMathQuad.fromUInt(_baseTokenTargetAmount), DECIMAL_QUAD); bytes16 baseTokenBalance_quad = ABDKMathQuad.div(ABDKMathQuad.fromUInt(_baseTokenBalance), DECIMAL_QUAD); bytes16 k_quad = ABDKMathQuad.div(ABDKMathQuad.fromUInt(_liquidityParameter), DECIMAL_QUAD); bytes16 X1 = ABDKMathQuad.sub(baseTokenBalance_quad, baseTokenTargetAmount_quad); bytes16 X2 = _solveEquationForAmountIn( value_quad, X1, k_quad, P_quad ); bytes16 amountOut = ABDKMathQuad.sub(X2, X1); amount = ABDKMathQuad.toUInt(ABDKMathQuad.mul(amountOut, DECIMAL_QUAD)); } function getValueFromAmountOut(uint _amount, uint _P, uint _tokenDecimals, uint _baseTokenTargetAmount, uint _baseTokenBalance, uint _liquidityParameter) external pure returns (uint value) { bytes16 DECIMAL_QUAD = ABDKMathQuad.fromUInt(10 ** _tokenDecimals); bytes16 amount_quad = ABDKMathQuad.div(ABDKMathQuad.fromUInt(_amount), DECIMAL_QUAD); bytes16 P_quad = ABDKMathQuad.div(ABDKMathQuad.fromUInt(_P), ONE_ETHER_QUAD); bytes16 baseTokenTargetAmount_quad = ABDKMathQuad.div(ABDKMathQuad.fromUInt(_baseTokenTargetAmount), DECIMAL_QUAD); bytes16 baseTokenBalance_quad = ABDKMathQuad.div(ABDKMathQuad.fromUInt(_baseTokenBalance), DECIMAL_QUAD); bytes16 k_quad = ABDKMathQuad.div(ABDKMathQuad.fromUInt(_liquidityParameter), DECIMAL_QUAD); bytes16 X2 = ABDKMathQuad.sub(baseTokenBalance_quad, baseTokenTargetAmount_quad); bytes16 X1 = ABDKMathQuad.sub(X2, amount_quad); value = _solveForIntegral( X1, X2, k_quad, P_quad ); } // Core Functions // Solve for Delta function _solveForIntegral ( bytes16 X1, bytes16 X2, bytes16 k, bytes16 P ) internal pure returns (uint256) { bytes16 multiplier = ABDKMathQuad.mul(k, P); bytes16 NLog_X2 = ABDKMathQuad.ln(ABDKMathQuad.add(X2, k)); bytes16 NLog_X1 = ABDKMathQuad.ln(ABDKMathQuad.add(X1, k)); bytes16 delta = ABDKMathQuad.mul(multiplier, ABDKMathQuad.sub(NLog_X2, NLog_X1)); return ABDKMathQuad.toUInt(ABDKMathQuad.mul(delta, ONE_ETHER_QUAD)); } // Solve for amountOut // Given X2, solve for X1 function _solveEquationForAmountOut ( bytes16 delta, bytes16 X2, bytes16 k, bytes16 P ) internal pure returns (bytes16 X1) { bytes16 NLog_X2 = ABDKMathQuad.ln(ABDKMathQuad.add(X2, k)); bytes16 deltaOverTotal = ABDKMathQuad.div(delta, ABDKMathQuad.mul(k, P)); bytes16 ePower = ABDKMathQuad.exp(ABDKMathQuad.sub(NLog_X2, deltaOverTotal)); X1 = ABDKMathQuad.sub(ePower, k); } // Solve for amountOut // Given X1, solve for X2 function _solveEquationForAmountIn ( bytes16 delta, bytes16 X1, bytes16 k, bytes16 P ) internal pure returns (bytes16 X2) { bytes16 NLog_X1 = ABDKMathQuad.ln(ABDKMathQuad.add(X1, k)); bytes16 deltaOverTotal = ABDKMathQuad.div(delta, ABDKMathQuad.mul(k, P)); bytes16 ePower = ABDKMathQuad.exp(ABDKMathQuad.add(deltaOverTotal, NLog_X1)); X2 = ABDKMathQuad.sub(ePower, k); } }
// SPDX-License-Identifier: MIT pragma solidity >=0.6.0 <0.8.0; /** * @dev Interface of the ERC20 standard as defined in the EIP. */ interface IERC20 { function symbol() external pure returns (string memory); /** * @dev Returns the token decimal. */ function decimals() external pure returns (uint8); /** * @dev Returns the amount of tokens in existence. */ function totalSupply() external view returns (uint256); /** * @dev Returns the amount of tokens owned by `account`. */ function balanceOf(address account) external view returns (uint256); /** * @dev Moves `amount` tokens from the caller's account to `recipient`. * * Returns a boolean value indicating whether the operation succeeded. * * Emits a {Transfer} event. */ function transfer(address recipient, uint256 amount) 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 `amount` 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 amount) external returns (bool); /** * @dev Moves `amount` tokens from `sender` to `recipient` using the * allowance mechanism. `amount` is then deducted from the caller's * allowance. * * Returns a boolean value indicating whether the operation succeeded. * * Emits a {Transfer} event. */ function transferFrom(address sender, address recipient, uint256 amount) external returns (bool); /** * @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); }
// SPDX-License-Identifier: MIT pragma solidity >=0.5.0; interface ICentaurFactory { event PoolCreated(address indexed token, address pool, uint); function poolFee() external view returns (uint); function poolLogic() external view returns (address); function cloneFactory() external view returns (address); function settlement() external view returns (address); function router() external view returns (address payable); function getPool(address token) external view returns (address pool); function allPools(uint) external view returns (address pool); function allPoolsLength() external view returns (uint); function isValidPool(address pool) external view returns (bool); function createPool(address token, address oracle, uint poolUtilizationPercentage) external returns (address pool); function addPool(address pool) external; function removePool(address pool) external; function setPoolLiquidityParameter(address, uint) external; function setPoolTradeEnabled(address, bool) external; function setPoolDepositEnabled(address, bool) external; function setPoolWithdrawEnabled(address, bool) external; function setAllPoolsTradeEnabled(bool) external; function setAllPoolsDepositEnabled(bool) external; function setAllPoolsWithdrawEnabled(bool) external; function emergencyWithdrawFromPool(address, address, uint, address) external; function setRouterOnlyEOAEnabled(bool) external; function setRouterContractWhitelist(address, bool) external; function setSettlementDuration(uint) external; function setPoolFee(uint) external; function setPoolLogic(address) external; function setCloneFactory(address) external; function setSettlement(address) external; function setRouter(address payable) external; }
// SPDX-License-Identifier: MIT pragma solidity >=0.5.0; interface ICentaurPool { event Approval(address indexed owner, address indexed spender, uint value); event Transfer(address indexed from, address indexed to, uint value); function name() external pure returns (string memory); function symbol() external pure returns (string memory); function decimals() external pure returns (uint8); function totalSupply() external view returns (uint); function balanceOf(address owner) external view returns (uint); function allowance(address owner, address spender) external view returns (uint); function approve(address spender, uint value) external returns (bool); function transfer(address to, uint value) external returns (bool); function transferFrom(address from, address to, uint value) external returns (bool); event Mint(address indexed sender, uint amount); event Burn(address indexed sender, uint amount, address indexed to); event AmountIn(address indexed sender, uint amount); event AmountOut(address indexed sender, uint amount, address indexed to); event EmergencyWithdraw(uint256 _timestamp, address indexed _token, uint256 _amount, address indexed _to); function factory() external view returns (address); function settlement() external view returns (address); function baseToken() external view returns (address); function baseTokenDecimals() external view returns (uint); function oracle() external view returns (address); function oracleDecimals() external view returns (uint); function baseTokenTargetAmount() external view returns (uint); function baseTokenBalance() external view returns (uint); function liquidityParameter() external view returns (uint); function init(address, address, address, uint) external; function mint(address to) external returns (uint liquidity); function burn(address to) external returns (uint amount); function swapTo(address _sender, address _fromToken, uint _amountIn, uint _value, address _receiver) external returns (uint maxAmount); function swapFrom(address _sender) external returns (uint amount, uint value); function swapSettle(address _sender) external returns (uint, address); function getOraclePrice() external view returns (uint price); function getAmountOutFromValue(uint _value) external view returns (uint amount); function getValueFromAmountIn(uint _amount) external view returns (uint value); function getAmountInFromValue(uint _value) external view returns (uint amount); function getValueFromAmountOut(uint _amount) external view returns (uint value); function setFactory(address) external; function setTradeEnabled(bool) external; function setDepositEnabled(bool) external; function setWithdrawEnabled(bool) external; function setLiquidityParameter(uint) external; function emergencyWithdraw(address, uint, address) external; }
// SPDX-License-Identifier: MIT pragma solidity >=0.5.0; pragma experimental ABIEncoderV2; interface ICentaurSettlement { // event SettlementAdded(address indexed sender, address indexed _fromToken, uint _amountIn, address indexed _toToken, uint _amountOut); // event SettlementRemoved(address indexed sender, address indexed _fromToken, address indexed _toToken); struct Settlement { address fPool; uint amountIn; uint fPoolBaseTokenTargetAmount; uint fPoolBaseTokenBalance; uint fPoolLiquidityParameter; address tPool; uint maxAmountOut; uint tPoolBaseTokenTargetAmount; uint tPoolBaseTokenBalance; uint tPoolLiquidityParameter; address receiver; uint settlementTimestamp; } function factory() external pure returns (address); function settlementDuration() external pure returns (uint); function addSettlement( address _sender, Settlement memory _pendingSettlement ) external; function removeSettlement(address _sender, address _fPool, address _tPool) external; function getPendingSettlement(address _sender, address _pool) external view returns (Settlement memory); function hasPendingSettlement(address _sender, address _pool) external view returns (bool); function setSettlementDuration(uint) external; }
// SPDX-License-Identifier: MIT pragma solidity ^0.6.12; interface IOracle { function decimals() external view returns (uint8); function description() external view returns (string memory); function version() external view returns (uint256); // getRoundData and latestRoundData should both raise "No data present" // if they do not have data to report, instead of returning unset values // which could be misinterpreted as actual reported values. function getRoundData(uint80 _roundId) external view returns ( uint80 roundId, int256 answer, uint256 startedAt, uint256 updatedAt, uint80 answeredInRound ); function latestRoundData() external view returns ( uint80 roundId, int256 answer, uint256 startedAt, uint256 updatedAt, uint80 answeredInRound ); }
// SPDX-License-Identifier: BSD-4-Clause /* * ABDK Math Quad Smart Contract Library. Copyright © 2019 by ABDK Consulting. * Author: Mikhail Vladimirov <[email protected]> */ pragma solidity ^0.5.0 || ^0.6.0 || ^0.7.0; /** * Smart contract library of mathematical functions operating with IEEE 754 * quadruple-precision binary floating-point numbers (quadruple precision * numbers). As long as quadruple precision numbers are 16-bytes long, they are * represented by bytes16 type. */ library ABDKMathQuad { /* * 0. */ bytes16 private constant POSITIVE_ZERO = 0x00000000000000000000000000000000; /* * -0. */ bytes16 private constant NEGATIVE_ZERO = 0x80000000000000000000000000000000; /* * +Infinity. */ bytes16 private constant POSITIVE_INFINITY = 0x7FFF0000000000000000000000000000; /* * -Infinity. */ bytes16 private constant NEGATIVE_INFINITY = 0xFFFF0000000000000000000000000000; /* * Canonical NaN value. */ bytes16 private constant NaN = 0x7FFF8000000000000000000000000000; /** * Convert signed 256-bit integer number into quadruple precision number. * * @param x signed 256-bit integer number * @return quadruple precision number */ function fromInt (int256 x) internal pure returns (bytes16) { if (x == 0) return bytes16 (0); else { // We rely on overflow behavior here uint256 result = uint256 (x > 0 ? x : -x); uint256 msb = msb (result); if (msb < 112) result <<= 112 - msb; else if (msb > 112) result >>= msb - 112; result = result & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF | 16383 + msb << 112; if (x < 0) result |= 0x80000000000000000000000000000000; return bytes16 (uint128 (result)); } } /** * Convert quadruple precision number into signed 256-bit integer number * rounding towards zero. Revert on overflow. * * @param x quadruple precision number * @return signed 256-bit integer number */ function toInt (bytes16 x) internal pure returns (int256) { uint256 exponent = uint128 (x) >> 112 & 0x7FFF; require (exponent <= 16638); // Overflow if (exponent < 16383) return 0; // Underflow uint256 result = uint256 (uint128 (x)) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF | 0x10000000000000000000000000000; if (exponent < 16495) result >>= 16495 - exponent; else if (exponent > 16495) result <<= exponent - 16495; if (uint128 (x) >= 0x80000000000000000000000000000000) { // Negative require (result <= 0x8000000000000000000000000000000000000000000000000000000000000000); return -int256 (result); // We rely on overflow behavior here } else { require (result <= 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF); return int256 (result); } } /** * Convert unsigned 256-bit integer number into quadruple precision number. * * @param x unsigned 256-bit integer number * @return quadruple precision number */ function fromUInt (uint256 x) internal pure returns (bytes16) { if (x == 0) return bytes16 (0); else { uint256 result = x; uint256 msb = msb (result); if (msb < 112) result <<= 112 - msb; else if (msb > 112) result >>= msb - 112; result = result & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF | 16383 + msb << 112; return bytes16 (uint128 (result)); } } /** * Convert quadruple precision number into unsigned 256-bit integer number * rounding towards zero. Revert on underflow. Note, that negative floating * point numbers in range (-1.0 .. 0.0) may be converted to unsigned integer * without error, because they are rounded to zero. * * @param x quadruple precision number * @return unsigned 256-bit integer number */ function toUInt (bytes16 x) internal pure returns (uint256) { uint256 exponent = uint128 (x) >> 112 & 0x7FFF; if (exponent < 16383) return 0; // Underflow require (uint128 (x) < 0x80000000000000000000000000000000); // Negative require (exponent <= 16638); // Overflow uint256 result = uint256 (uint128 (x)) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF | 0x10000000000000000000000000000; if (exponent < 16495) result >>= 16495 - exponent; else if (exponent > 16495) result <<= exponent - 16495; return result; } /** * Convert signed 128.128 bit fixed point number into quadruple precision * number. * * @param x signed 128.128 bit fixed point number * @return quadruple precision number */ function from128x128 (int256 x) internal pure returns (bytes16) { if (x == 0) return bytes16 (0); else { // We rely on overflow behavior here uint256 result = uint256 (x > 0 ? x : -x); uint256 msb = msb (result); if (msb < 112) result <<= 112 - msb; else if (msb > 112) result >>= msb - 112; result = result & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF | 16255 + msb << 112; if (x < 0) result |= 0x80000000000000000000000000000000; return bytes16 (uint128 (result)); } } /** * Convert quadruple precision number into signed 128.128 bit fixed point * number. Revert on overflow. * * @param x quadruple precision number * @return signed 128.128 bit fixed point number */ function to128x128 (bytes16 x) internal pure returns (int256) { uint256 exponent = uint128 (x) >> 112 & 0x7FFF; require (exponent <= 16510); // Overflow if (exponent < 16255) return 0; // Underflow uint256 result = uint256 (uint128 (x)) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF | 0x10000000000000000000000000000; if (exponent < 16367) result >>= 16367 - exponent; else if (exponent > 16367) result <<= exponent - 16367; if (uint128 (x) >= 0x80000000000000000000000000000000) { // Negative require (result <= 0x8000000000000000000000000000000000000000000000000000000000000000); return -int256 (result); // We rely on overflow behavior here } else { require (result <= 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF); return int256 (result); } } /** * Convert signed 64.64 bit fixed point number into quadruple precision * number. * * @param x signed 64.64 bit fixed point number * @return quadruple precision number */ function from64x64 (int128 x) internal pure returns (bytes16) { if (x == 0) return bytes16 (0); else { // We rely on overflow behavior here uint256 result = uint128 (x > 0 ? x : -x); uint256 msb = msb (result); if (msb < 112) result <<= 112 - msb; else if (msb > 112) result >>= msb - 112; result = result & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF | 16319 + msb << 112; if (x < 0) result |= 0x80000000000000000000000000000000; return bytes16 (uint128 (result)); } } /** * Convert quadruple precision number into signed 64.64 bit fixed point * number. Revert on overflow. * * @param x quadruple precision number * @return signed 64.64 bit fixed point number */ function to64x64 (bytes16 x) internal pure returns (int128) { uint256 exponent = uint128 (x) >> 112 & 0x7FFF; require (exponent <= 16446); // Overflow if (exponent < 16319) return 0; // Underflow uint256 result = uint256 (uint128 (x)) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF | 0x10000000000000000000000000000; if (exponent < 16431) result >>= 16431 - exponent; else if (exponent > 16431) result <<= exponent - 16431; if (uint128 (x) >= 0x80000000000000000000000000000000) { // Negative require (result <= 0x80000000000000000000000000000000); return -int128 (result); // We rely on overflow behavior here } else { require (result <= 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF); return int128 (result); } } /** * Convert octuple precision number into quadruple precision number. * * @param x octuple precision number * @return quadruple precision number */ function fromOctuple (bytes32 x) internal pure returns (bytes16) { bool negative = x & 0x8000000000000000000000000000000000000000000000000000000000000000 > 0; uint256 exponent = uint256 (x) >> 236 & 0x7FFFF; uint256 significand = uint256 (x) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF; if (exponent == 0x7FFFF) { if (significand > 0) return NaN; else return negative ? NEGATIVE_INFINITY : POSITIVE_INFINITY; } if (exponent > 278526) return negative ? NEGATIVE_INFINITY : POSITIVE_INFINITY; else if (exponent < 245649) return negative ? NEGATIVE_ZERO : POSITIVE_ZERO; else if (exponent < 245761) { significand = (significand | 0x100000000000000000000000000000000000000000000000000000000000) >> 245885 - exponent; exponent = 0; } else { significand >>= 124; exponent -= 245760; } uint128 result = uint128 (significand | exponent << 112); if (negative) result |= 0x80000000000000000000000000000000; return bytes16 (result); } /** * Convert quadruple precision number into octuple precision number. * * @param x quadruple precision number * @return octuple precision number */ function toOctuple (bytes16 x) internal pure returns (bytes32) { uint256 exponent = uint128 (x) >> 112 & 0x7FFF; uint256 result = uint128 (x) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF; if (exponent == 0x7FFF) exponent = 0x7FFFF; // Infinity or NaN else if (exponent == 0) { if (result > 0) { uint256 msb = msb (result); result = result << 236 - msb & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF; exponent = 245649 + msb; } } else { result <<= 124; exponent += 245760; } result |= exponent << 236; if (uint128 (x) >= 0x80000000000000000000000000000000) result |= 0x8000000000000000000000000000000000000000000000000000000000000000; return bytes32 (result); } /** * Convert double precision number into quadruple precision number. * * @param x double precision number * @return quadruple precision number */ function fromDouble (bytes8 x) internal pure returns (bytes16) { uint256 exponent = uint64 (x) >> 52 & 0x7FF; uint256 result = uint64 (x) & 0xFFFFFFFFFFFFF; if (exponent == 0x7FF) exponent = 0x7FFF; // Infinity or NaN else if (exponent == 0) { if (result > 0) { uint256 msb = msb (result); result = result << 112 - msb & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF; exponent = 15309 + msb; } } else { result <<= 60; exponent += 15360; } result |= exponent << 112; if (x & 0x8000000000000000 > 0) result |= 0x80000000000000000000000000000000; return bytes16 (uint128 (result)); } /** * Convert quadruple precision number into double precision number. * * @param x quadruple precision number * @return double precision number */ function toDouble (bytes16 x) internal pure returns (bytes8) { bool negative = uint128 (x) >= 0x80000000000000000000000000000000; uint256 exponent = uint128 (x) >> 112 & 0x7FFF; uint256 significand = uint128 (x) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF; if (exponent == 0x7FFF) { if (significand > 0) return 0x7FF8000000000000; // NaN else return negative ? bytes8 (0xFFF0000000000000) : // -Infinity bytes8 (0x7FF0000000000000); // Infinity } if (exponent > 17406) return negative ? bytes8 (0xFFF0000000000000) : // -Infinity bytes8 (0x7FF0000000000000); // Infinity else if (exponent < 15309) return negative ? bytes8 (0x8000000000000000) : // -0 bytes8 (0x0000000000000000); // 0 else if (exponent < 15361) { significand = (significand | 0x10000000000000000000000000000) >> 15421 - exponent; exponent = 0; } else { significand >>= 60; exponent -= 15360; } uint64 result = uint64 (significand | exponent << 52); if (negative) result |= 0x8000000000000000; return bytes8 (result); } /** * Test whether given quadruple precision number is NaN. * * @param x quadruple precision number * @return true if x is NaN, false otherwise */ function isNaN (bytes16 x) internal pure returns (bool) { return uint128 (x) & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF > 0x7FFF0000000000000000000000000000; } /** * Test whether given quadruple precision number is positive or negative * infinity. * * @param x quadruple precision number * @return true if x is positive or negative infinity, false otherwise */ function isInfinity (bytes16 x) internal pure returns (bool) { return uint128 (x) & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF == 0x7FFF0000000000000000000000000000; } /** * Calculate sign of x, i.e. -1 if x is negative, 0 if x if zero, and 1 if x * is positive. Note that sign (-0) is zero. Revert if x is NaN. * * @param x quadruple precision number * @return sign of x */ function sign (bytes16 x) internal pure returns (int8) { uint128 absoluteX = uint128 (x) & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF; require (absoluteX <= 0x7FFF0000000000000000000000000000); // Not NaN if (absoluteX == 0) return 0; else if (uint128 (x) >= 0x80000000000000000000000000000000) return -1; else return 1; } /** * Calculate sign (x - y). Revert if either argument is NaN, or both * arguments are infinities of the same sign. * * @param x quadruple precision number * @param y quadruple precision number * @return sign (x - y) */ function cmp (bytes16 x, bytes16 y) internal pure returns (int8) { uint128 absoluteX = uint128 (x) & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF; require (absoluteX <= 0x7FFF0000000000000000000000000000); // Not NaN uint128 absoluteY = uint128 (y) & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF; require (absoluteY <= 0x7FFF0000000000000000000000000000); // Not NaN // Not infinities of the same sign require (x != y || absoluteX < 0x7FFF0000000000000000000000000000); if (x == y) return 0; else { bool negativeX = uint128 (x) >= 0x80000000000000000000000000000000; bool negativeY = uint128 (y) >= 0x80000000000000000000000000000000; if (negativeX) { if (negativeY) return absoluteX > absoluteY ? -1 : int8 (1); else return -1; } else { if (negativeY) return 1; else return absoluteX > absoluteY ? int8 (1) : -1; } } } /** * Test whether x equals y. NaN, infinity, and -infinity are not equal to * anything. * * @param x quadruple precision number * @param y quadruple precision number * @return true if x equals to y, false otherwise */ function eq (bytes16 x, bytes16 y) internal pure returns (bool) { if (x == y) { return uint128 (x) & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF < 0x7FFF0000000000000000000000000000; } else return false; } /** * Calculate x + y. Special values behave in the following way: * * NaN + x = NaN for any x. * Infinity + x = Infinity for any finite x. * -Infinity + x = -Infinity for any finite x. * Infinity + Infinity = Infinity. * -Infinity + -Infinity = -Infinity. * Infinity + -Infinity = -Infinity + Infinity = NaN. * * @param x quadruple precision number * @param y quadruple precision number * @return quadruple precision number */ function add (bytes16 x, bytes16 y) internal pure returns (bytes16) { uint256 xExponent = uint128 (x) >> 112 & 0x7FFF; uint256 yExponent = uint128 (y) >> 112 & 0x7FFF; if (xExponent == 0x7FFF) { if (yExponent == 0x7FFF) { if (x == y) return x; else return NaN; } else return x; } else if (yExponent == 0x7FFF) return y; else { bool xSign = uint128 (x) >= 0x80000000000000000000000000000000; uint256 xSignifier = uint128 (x) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF; if (xExponent == 0) xExponent = 1; else xSignifier |= 0x10000000000000000000000000000; bool ySign = uint128 (y) >= 0x80000000000000000000000000000000; uint256 ySignifier = uint128 (y) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF; if (yExponent == 0) yExponent = 1; else ySignifier |= 0x10000000000000000000000000000; if (xSignifier == 0) return y == NEGATIVE_ZERO ? POSITIVE_ZERO : y; else if (ySignifier == 0) return x == NEGATIVE_ZERO ? POSITIVE_ZERO : x; else { int256 delta = int256 (xExponent) - int256 (yExponent); if (xSign == ySign) { if (delta > 112) return x; else if (delta > 0) ySignifier >>= uint256 (delta); else if (delta < -112) return y; else if (delta < 0) { xSignifier >>= uint256 (-delta); xExponent = yExponent; } xSignifier += ySignifier; if (xSignifier >= 0x20000000000000000000000000000) { xSignifier >>= 1; xExponent += 1; } if (xExponent == 0x7FFF) return xSign ? NEGATIVE_INFINITY : POSITIVE_INFINITY; else { if (xSignifier < 0x10000000000000000000000000000) xExponent = 0; else xSignifier &= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF; return bytes16 (uint128 ( (xSign ? 0x80000000000000000000000000000000 : 0) | (xExponent << 112) | xSignifier)); } } else { if (delta > 0) { xSignifier <<= 1; xExponent -= 1; } else if (delta < 0) { ySignifier <<= 1; xExponent = yExponent - 1; } if (delta > 112) ySignifier = 1; else if (delta > 1) ySignifier = (ySignifier - 1 >> uint256 (delta - 1)) + 1; else if (delta < -112) xSignifier = 1; else if (delta < -1) xSignifier = (xSignifier - 1 >> uint256 (-delta - 1)) + 1; if (xSignifier >= ySignifier) xSignifier -= ySignifier; else { xSignifier = ySignifier - xSignifier; xSign = ySign; } if (xSignifier == 0) return POSITIVE_ZERO; uint256 msb = msb (xSignifier); if (msb == 113) { xSignifier = xSignifier >> 1 & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF; xExponent += 1; } else if (msb < 112) { uint256 shift = 112 - msb; if (xExponent > shift) { xSignifier = xSignifier << shift & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF; xExponent -= shift; } else { xSignifier <<= xExponent - 1; xExponent = 0; } } else xSignifier &= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF; if (xExponent == 0x7FFF) return xSign ? NEGATIVE_INFINITY : POSITIVE_INFINITY; else return bytes16 (uint128 ( (xSign ? 0x80000000000000000000000000000000 : 0) | (xExponent << 112) | xSignifier)); } } } } /** * Calculate x - y. Special values behave in the following way: * * NaN - x = NaN for any x. * Infinity - x = Infinity for any finite x. * -Infinity - x = -Infinity for any finite x. * Infinity - -Infinity = Infinity. * -Infinity - Infinity = -Infinity. * Infinity - Infinity = -Infinity - -Infinity = NaN. * * @param x quadruple precision number * @param y quadruple precision number * @return quadruple precision number */ function sub (bytes16 x, bytes16 y) internal pure returns (bytes16) { return add (x, y ^ 0x80000000000000000000000000000000); } /** * Calculate x * y. Special values behave in the following way: * * NaN * x = NaN for any x. * Infinity * x = Infinity for any finite positive x. * Infinity * x = -Infinity for any finite negative x. * -Infinity * x = -Infinity for any finite positive x. * -Infinity * x = Infinity for any finite negative x. * Infinity * 0 = NaN. * -Infinity * 0 = NaN. * Infinity * Infinity = Infinity. * Infinity * -Infinity = -Infinity. * -Infinity * Infinity = -Infinity. * -Infinity * -Infinity = Infinity. * * @param x quadruple precision number * @param y quadruple precision number * @return quadruple precision number */ function mul (bytes16 x, bytes16 y) internal pure returns (bytes16) { uint256 xExponent = uint128 (x) >> 112 & 0x7FFF; uint256 yExponent = uint128 (y) >> 112 & 0x7FFF; if (xExponent == 0x7FFF) { if (yExponent == 0x7FFF) { if (x == y) return x ^ y & 0x80000000000000000000000000000000; else if (x ^ y == 0x80000000000000000000000000000000) return x | y; else return NaN; } else { if (y & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF == 0) return NaN; else return x ^ y & 0x80000000000000000000000000000000; } } else if (yExponent == 0x7FFF) { if (x & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF == 0) return NaN; else return y ^ x & 0x80000000000000000000000000000000; } else { uint256 xSignifier = uint128 (x) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF; if (xExponent == 0) xExponent = 1; else xSignifier |= 0x10000000000000000000000000000; uint256 ySignifier = uint128 (y) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF; if (yExponent == 0) yExponent = 1; else ySignifier |= 0x10000000000000000000000000000; xSignifier *= ySignifier; if (xSignifier == 0) return (x ^ y) & 0x80000000000000000000000000000000 > 0 ? NEGATIVE_ZERO : POSITIVE_ZERO; xExponent += yExponent; uint256 msb = xSignifier >= 0x200000000000000000000000000000000000000000000000000000000 ? 225 : xSignifier >= 0x100000000000000000000000000000000000000000000000000000000 ? 224 : msb (xSignifier); if (xExponent + msb < 16496) { // Underflow xExponent = 0; xSignifier = 0; } else if (xExponent + msb < 16608) { // Subnormal if (xExponent < 16496) xSignifier >>= 16496 - xExponent; else if (xExponent > 16496) xSignifier <<= xExponent - 16496; xExponent = 0; } else if (xExponent + msb > 49373) { xExponent = 0x7FFF; xSignifier = 0; } else { if (msb > 112) xSignifier >>= msb - 112; else if (msb < 112) xSignifier <<= 112 - msb; xSignifier &= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF; xExponent = xExponent + msb - 16607; } return bytes16 (uint128 (uint128 ((x ^ y) & 0x80000000000000000000000000000000) | xExponent << 112 | xSignifier)); } } /** * Calculate x / y. Special values behave in the following way: * * NaN / x = NaN for any x. * x / NaN = NaN for any x. * Infinity / x = Infinity for any finite non-negative x. * Infinity / x = -Infinity for any finite negative x including -0. * -Infinity / x = -Infinity for any finite non-negative x. * -Infinity / x = Infinity for any finite negative x including -0. * x / Infinity = 0 for any finite non-negative x. * x / -Infinity = -0 for any finite non-negative x. * x / Infinity = -0 for any finite non-negative x including -0. * x / -Infinity = 0 for any finite non-negative x including -0. * * Infinity / Infinity = NaN. * Infinity / -Infinity = -NaN. * -Infinity / Infinity = -NaN. * -Infinity / -Infinity = NaN. * * Division by zero behaves in the following way: * * x / 0 = Infinity for any finite positive x. * x / -0 = -Infinity for any finite positive x. * x / 0 = -Infinity for any finite negative x. * x / -0 = Infinity for any finite negative x. * 0 / 0 = NaN. * 0 / -0 = NaN. * -0 / 0 = NaN. * -0 / -0 = NaN. * * @param x quadruple precision number * @param y quadruple precision number * @return quadruple precision number */ function div (bytes16 x, bytes16 y) internal pure returns (bytes16) { uint256 xExponent = uint128 (x) >> 112 & 0x7FFF; uint256 yExponent = uint128 (y) >> 112 & 0x7FFF; if (xExponent == 0x7FFF) { if (yExponent == 0x7FFF) return NaN; else return x ^ y & 0x80000000000000000000000000000000; } else if (yExponent == 0x7FFF) { if (y & 0x0000FFFFFFFFFFFFFFFFFFFFFFFFFFFF != 0) return NaN; else return POSITIVE_ZERO | (x ^ y) & 0x80000000000000000000000000000000; } else if (y & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF == 0) { if (x & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF == 0) return NaN; else return POSITIVE_INFINITY | (x ^ y) & 0x80000000000000000000000000000000; } else { uint256 ySignifier = uint128 (y) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF; if (yExponent == 0) yExponent = 1; else ySignifier |= 0x10000000000000000000000000000; uint256 xSignifier = uint128 (x) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF; if (xExponent == 0) { if (xSignifier != 0) { uint shift = 226 - msb (xSignifier); xSignifier <<= shift; xExponent = 1; yExponent += shift - 114; } } else { xSignifier = (xSignifier | 0x10000000000000000000000000000) << 114; } xSignifier = xSignifier / ySignifier; if (xSignifier == 0) return (x ^ y) & 0x80000000000000000000000000000000 > 0 ? NEGATIVE_ZERO : POSITIVE_ZERO; assert (xSignifier >= 0x1000000000000000000000000000); uint256 msb = xSignifier >= 0x80000000000000000000000000000 ? msb (xSignifier) : xSignifier >= 0x40000000000000000000000000000 ? 114 : xSignifier >= 0x20000000000000000000000000000 ? 113 : 112; if (xExponent + msb > yExponent + 16497) { // Overflow xExponent = 0x7FFF; xSignifier = 0; } else if (xExponent + msb + 16380 < yExponent) { // Underflow xExponent = 0; xSignifier = 0; } else if (xExponent + msb + 16268 < yExponent) { // Subnormal if (xExponent + 16380 > yExponent) xSignifier <<= xExponent + 16380 - yExponent; else if (xExponent + 16380 < yExponent) xSignifier >>= yExponent - xExponent - 16380; xExponent = 0; } else { // Normal if (msb > 112) xSignifier >>= msb - 112; xSignifier &= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF; xExponent = xExponent + msb + 16269 - yExponent; } return bytes16 (uint128 (uint128 ((x ^ y) & 0x80000000000000000000000000000000) | xExponent << 112 | xSignifier)); } } /** * Calculate -x. * * @param x quadruple precision number * @return quadruple precision number */ function neg (bytes16 x) internal pure returns (bytes16) { return x ^ 0x80000000000000000000000000000000; } /** * Calculate |x|. * * @param x quadruple precision number * @return quadruple precision number */ function abs (bytes16 x) internal pure returns (bytes16) { return x & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF; } /** * Calculate square root of x. Return NaN on negative x excluding -0. * * @param x quadruple precision number * @return quadruple precision number */ function sqrt (bytes16 x) internal pure returns (bytes16) { if (uint128 (x) > 0x80000000000000000000000000000000) return NaN; else { uint256 xExponent = uint128 (x) >> 112 & 0x7FFF; if (xExponent == 0x7FFF) return x; else { uint256 xSignifier = uint128 (x) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF; if (xExponent == 0) xExponent = 1; else xSignifier |= 0x10000000000000000000000000000; if (xSignifier == 0) return POSITIVE_ZERO; bool oddExponent = xExponent & 0x1 == 0; xExponent = xExponent + 16383 >> 1; if (oddExponent) { if (xSignifier >= 0x10000000000000000000000000000) xSignifier <<= 113; else { uint256 msb = msb (xSignifier); uint256 shift = (226 - msb) & 0xFE; xSignifier <<= shift; xExponent -= shift - 112 >> 1; } } else { if (xSignifier >= 0x10000000000000000000000000000) xSignifier <<= 112; else { uint256 msb = msb (xSignifier); uint256 shift = (225 - msb) & 0xFE; xSignifier <<= shift; xExponent -= shift - 112 >> 1; } } uint256 r = 0x10000000000000000000000000000; r = (r + xSignifier / r) >> 1; r = (r + xSignifier / r) >> 1; r = (r + xSignifier / r) >> 1; r = (r + xSignifier / r) >> 1; r = (r + xSignifier / r) >> 1; r = (r + xSignifier / r) >> 1; r = (r + xSignifier / r) >> 1; // Seven iterations should be enough uint256 r1 = xSignifier / r; if (r1 < r) r = r1; return bytes16 (uint128 (xExponent << 112 | r & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF)); } } } /** * Calculate binary logarithm of x. Return NaN on negative x excluding -0. * * @param x quadruple precision number * @return quadruple precision number */ function log_2 (bytes16 x) internal pure returns (bytes16) { if (uint128 (x) > 0x80000000000000000000000000000000) return NaN; else if (x == 0x3FFF0000000000000000000000000000) return POSITIVE_ZERO; else { uint256 xExponent = uint128 (x) >> 112 & 0x7FFF; if (xExponent == 0x7FFF) return x; else { uint256 xSignifier = uint128 (x) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF; if (xExponent == 0) xExponent = 1; else xSignifier |= 0x10000000000000000000000000000; if (xSignifier == 0) return NEGATIVE_INFINITY; bool resultNegative; uint256 resultExponent = 16495; uint256 resultSignifier; if (xExponent >= 0x3FFF) { resultNegative = false; resultSignifier = xExponent - 0x3FFF; xSignifier <<= 15; } else { resultNegative = true; if (xSignifier >= 0x10000000000000000000000000000) { resultSignifier = 0x3FFE - xExponent; xSignifier <<= 15; } else { uint256 msb = msb (xSignifier); resultSignifier = 16493 - msb; xSignifier <<= 127 - msb; } } if (xSignifier == 0x80000000000000000000000000000000) { if (resultNegative) resultSignifier += 1; uint256 shift = 112 - msb (resultSignifier); resultSignifier <<= shift; resultExponent -= shift; } else { uint256 bb = resultNegative ? 1 : 0; while (resultSignifier < 0x10000000000000000000000000000) { resultSignifier <<= 1; resultExponent -= 1; xSignifier *= xSignifier; uint256 b = xSignifier >> 255; resultSignifier += b ^ bb; xSignifier >>= 127 + b; } } return bytes16 (uint128 ((resultNegative ? 0x80000000000000000000000000000000 : 0) | resultExponent << 112 | resultSignifier & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF)); } } } /** * Calculate natural logarithm of x. Return NaN on negative x excluding -0. * * @param x quadruple precision number * @return quadruple precision number */ function ln (bytes16 x) internal pure returns (bytes16) { return mul (log_2 (x), 0x3FFE62E42FEFA39EF35793C7673007E5); } /** * Calculate 2^x. * * @param x quadruple precision number * @return quadruple precision number */ function pow_2 (bytes16 x) internal pure returns (bytes16) { bool xNegative = uint128 (x) > 0x80000000000000000000000000000000; uint256 xExponent = uint128 (x) >> 112 & 0x7FFF; uint256 xSignifier = uint128 (x) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF; if (xExponent == 0x7FFF && xSignifier != 0) return NaN; else if (xExponent > 16397) return xNegative ? POSITIVE_ZERO : POSITIVE_INFINITY; else if (xExponent < 16255) return 0x3FFF0000000000000000000000000000; else { if (xExponent == 0) xExponent = 1; else xSignifier |= 0x10000000000000000000000000000; if (xExponent > 16367) xSignifier <<= xExponent - 16367; else if (xExponent < 16367) xSignifier >>= 16367 - xExponent; if (xNegative && xSignifier > 0x406E00000000000000000000000000000000) return POSITIVE_ZERO; if (!xNegative && xSignifier > 0x3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF) return POSITIVE_INFINITY; uint256 resultExponent = xSignifier >> 128; xSignifier &= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF; if (xNegative && xSignifier != 0) { xSignifier = ~xSignifier; resultExponent += 1; } uint256 resultSignifier = 0x80000000000000000000000000000000; if (xSignifier & 0x80000000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x16A09E667F3BCC908B2FB1366EA957D3E >> 128; if (xSignifier & 0x40000000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x1306FE0A31B7152DE8D5A46305C85EDEC >> 128; if (xSignifier & 0x20000000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x1172B83C7D517ADCDF7C8C50EB14A791F >> 128; if (xSignifier & 0x10000000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x10B5586CF9890F6298B92B71842A98363 >> 128; if (xSignifier & 0x8000000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x1059B0D31585743AE7C548EB68CA417FD >> 128; if (xSignifier & 0x4000000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x102C9A3E778060EE6F7CACA4F7A29BDE8 >> 128; if (xSignifier & 0x2000000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x10163DA9FB33356D84A66AE336DCDFA3F >> 128; if (xSignifier & 0x1000000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x100B1AFA5ABCBED6129AB13EC11DC9543 >> 128; if (xSignifier & 0x800000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x10058C86DA1C09EA1FF19D294CF2F679B >> 128; if (xSignifier & 0x400000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x1002C605E2E8CEC506D21BFC89A23A00F >> 128; if (xSignifier & 0x200000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x100162F3904051FA128BCA9C55C31E5DF >> 128; if (xSignifier & 0x100000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x1000B175EFFDC76BA38E31671CA939725 >> 128; if (xSignifier & 0x80000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x100058BA01FB9F96D6CACD4B180917C3D >> 128; if (xSignifier & 0x40000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x10002C5CC37DA9491D0985C348C68E7B3 >> 128; if (xSignifier & 0x20000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x1000162E525EE054754457D5995292026 >> 128; if (xSignifier & 0x10000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x10000B17255775C040618BF4A4ADE83FC >> 128; if (xSignifier & 0x8000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x1000058B91B5BC9AE2EED81E9B7D4CFAB >> 128; if (xSignifier & 0x4000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x100002C5C89D5EC6CA4D7C8ACC017B7C9 >> 128; if (xSignifier & 0x2000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x10000162E43F4F831060E02D839A9D16D >> 128; if (xSignifier & 0x1000000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x100000B1721BCFC99D9F890EA06911763 >> 128; if (xSignifier & 0x800000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x10000058B90CF1E6D97F9CA14DBCC1628 >> 128; if (xSignifier & 0x400000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x1000002C5C863B73F016468F6BAC5CA2B >> 128; if (xSignifier & 0x200000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x100000162E430E5A18F6119E3C02282A5 >> 128; if (xSignifier & 0x100000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x1000000B1721835514B86E6D96EFD1BFE >> 128; if (xSignifier & 0x80000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x100000058B90C0B48C6BE5DF846C5B2EF >> 128; if (xSignifier & 0x40000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x10000002C5C8601CC6B9E94213C72737A >> 128; if (xSignifier & 0x20000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x1000000162E42FFF037DF38AA2B219F06 >> 128; if (xSignifier & 0x10000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x10000000B17217FBA9C739AA5819F44F9 >> 128; if (xSignifier & 0x8000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x1000000058B90BFCDEE5ACD3C1CEDC823 >> 128; if (xSignifier & 0x4000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x100000002C5C85FE31F35A6A30DA1BE50 >> 128; if (xSignifier & 0x2000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x10000000162E42FF0999CE3541B9FFFCF >> 128; if (xSignifier & 0x1000000000000000000000000 > 0) resultSignifier = resultSignifier * 0x100000000B17217F80F4EF5AADDA45554 >> 128; if (xSignifier & 0x800000000000000000000000 > 0) resultSignifier = resultSignifier * 0x10000000058B90BFBF8479BD5A81B51AD >> 128; if (xSignifier & 0x400000000000000000000000 > 0) resultSignifier = resultSignifier * 0x1000000002C5C85FDF84BD62AE30A74CC >> 128; if (xSignifier & 0x200000000000000000000000 > 0) resultSignifier = resultSignifier * 0x100000000162E42FEFB2FED257559BDAA >> 128; if (xSignifier & 0x100000000000000000000000 > 0) resultSignifier = resultSignifier * 0x1000000000B17217F7D5A7716BBA4A9AE >> 128; if (xSignifier & 0x80000000000000000000000 > 0) resultSignifier = resultSignifier * 0x100000000058B90BFBE9DDBAC5E109CCE >> 128; if (xSignifier & 0x40000000000000000000000 > 0) resultSignifier = resultSignifier * 0x10000000002C5C85FDF4B15DE6F17EB0D >> 128; if (xSignifier & 0x20000000000000000000000 > 0) resultSignifier = resultSignifier * 0x1000000000162E42FEFA494F1478FDE05 >> 128; if (xSignifier & 0x10000000000000000000000 > 0) resultSignifier = resultSignifier * 0x10000000000B17217F7D20CF927C8E94C >> 128; if (xSignifier & 0x8000000000000000000000 > 0) resultSignifier = resultSignifier * 0x1000000000058B90BFBE8F71CB4E4B33D >> 128; if (xSignifier & 0x4000000000000000000000 > 0) resultSignifier = resultSignifier * 0x100000000002C5C85FDF477B662B26945 >> 128; if (xSignifier & 0x2000000000000000000000 > 0) resultSignifier = resultSignifier * 0x10000000000162E42FEFA3AE53369388C >> 128; if (xSignifier & 0x1000000000000000000000 > 0) resultSignifier = resultSignifier * 0x100000000000B17217F7D1D351A389D40 >> 128; if (xSignifier & 0x800000000000000000000 > 0) resultSignifier = resultSignifier * 0x10000000000058B90BFBE8E8B2D3D4EDE >> 128; if (xSignifier & 0x400000000000000000000 > 0) resultSignifier = resultSignifier * 0x1000000000002C5C85FDF4741BEA6E77E >> 128; if (xSignifier & 0x200000000000000000000 > 0) resultSignifier = resultSignifier * 0x100000000000162E42FEFA39FE95583C2 >> 128; if (xSignifier & 0x100000000000000000000 > 0) resultSignifier = resultSignifier * 0x1000000000000B17217F7D1CFB72B45E1 >> 128; if (xSignifier & 0x80000000000000000000 > 0) resultSignifier = resultSignifier * 0x100000000000058B90BFBE8E7CC35C3F0 >> 128; if (xSignifier & 0x40000000000000000000 > 0) resultSignifier = resultSignifier * 0x10000000000002C5C85FDF473E242EA38 >> 128; if (xSignifier & 0x20000000000000000000 > 0) resultSignifier = resultSignifier * 0x1000000000000162E42FEFA39F02B772C >> 128; if (xSignifier & 0x10000000000000000000 > 0) resultSignifier = resultSignifier * 0x10000000000000B17217F7D1CF7D83C1A >> 128; if (xSignifier & 0x8000000000000000000 > 0) resultSignifier = resultSignifier * 0x1000000000000058B90BFBE8E7BDCBE2E >> 128; if (xSignifier & 0x4000000000000000000 > 0) resultSignifier = resultSignifier * 0x100000000000002C5C85FDF473DEA871F >> 128; if (xSignifier & 0x2000000000000000000 > 0) resultSignifier = resultSignifier * 0x10000000000000162E42FEFA39EF44D91 >> 128; if (xSignifier & 0x1000000000000000000 > 0) resultSignifier = resultSignifier * 0x100000000000000B17217F7D1CF79E949 >> 128; if (xSignifier & 0x800000000000000000 > 0) resultSignifier = resultSignifier * 0x10000000000000058B90BFBE8E7BCE544 >> 128; if (xSignifier & 0x400000000000000000 > 0) resultSignifier = resultSignifier * 0x1000000000000002C5C85FDF473DE6ECA >> 128; if (xSignifier & 0x200000000000000000 > 0) resultSignifier = resultSignifier * 0x100000000000000162E42FEFA39EF366F >> 128; if (xSignifier & 0x100000000000000000 > 0) resultSignifier = resultSignifier * 0x1000000000000000B17217F7D1CF79AFA >> 128; if (xSignifier & 0x80000000000000000 > 0) resultSignifier = resultSignifier * 0x100000000000000058B90BFBE8E7BCD6D >> 128; if (xSignifier & 0x40000000000000000 > 0) resultSignifier = resultSignifier * 0x10000000000000002C5C85FDF473DE6B2 >> 128; if (xSignifier & 0x20000000000000000 > 0) resultSignifier = resultSignifier * 0x1000000000000000162E42FEFA39EF358 >> 128; if (xSignifier & 0x10000000000000000 > 0) resultSignifier = resultSignifier * 0x10000000000000000B17217F7D1CF79AB >> 128; if (xSignifier & 0x8000000000000000 > 0) resultSignifier = resultSignifier * 0x1000000000000000058B90BFBE8E7BCD5 >> 128; if (xSignifier & 0x4000000000000000 > 0) resultSignifier = resultSignifier * 0x100000000000000002C5C85FDF473DE6A >> 128; if (xSignifier & 0x2000000000000000 > 0) resultSignifier = resultSignifier * 0x10000000000000000162E42FEFA39EF34 >> 128; if (xSignifier & 0x1000000000000000 > 0) resultSignifier = resultSignifier * 0x100000000000000000B17217F7D1CF799 >> 128; if (xSignifier & 0x800000000000000 > 0) resultSignifier = resultSignifier * 0x10000000000000000058B90BFBE8E7BCC >> 128; if (xSignifier & 0x400000000000000 > 0) resultSignifier = resultSignifier * 0x1000000000000000002C5C85FDF473DE5 >> 128; if (xSignifier & 0x200000000000000 > 0) resultSignifier = resultSignifier * 0x100000000000000000162E42FEFA39EF2 >> 128; if (xSignifier & 0x100000000000000 > 0) resultSignifier = resultSignifier * 0x1000000000000000000B17217F7D1CF78 >> 128; if (xSignifier & 0x80000000000000 > 0) resultSignifier = resultSignifier * 0x100000000000000000058B90BFBE8E7BB >> 128; if (xSignifier & 0x40000000000000 > 0) resultSignifier = resultSignifier * 0x10000000000000000002C5C85FDF473DD >> 128; if (xSignifier & 0x20000000000000 > 0) resultSignifier = resultSignifier * 0x1000000000000000000162E42FEFA39EE >> 128; if (xSignifier & 0x10000000000000 > 0) resultSignifier = resultSignifier * 0x10000000000000000000B17217F7D1CF6 >> 128; if (xSignifier & 0x8000000000000 > 0) resultSignifier = resultSignifier * 0x1000000000000000000058B90BFBE8E7A >> 128; if (xSignifier & 0x4000000000000 > 0) resultSignifier = resultSignifier * 0x100000000000000000002C5C85FDF473C >> 128; if (xSignifier & 0x2000000000000 > 0) resultSignifier = resultSignifier * 0x10000000000000000000162E42FEFA39D >> 128; if (xSignifier & 0x1000000000000 > 0) resultSignifier = resultSignifier * 0x100000000000000000000B17217F7D1CE >> 128; if (xSignifier & 0x800000000000 > 0) resultSignifier = resultSignifier * 0x10000000000000000000058B90BFBE8E6 >> 128; if (xSignifier & 0x400000000000 > 0) resultSignifier = resultSignifier * 0x1000000000000000000002C5C85FDF472 >> 128; if (xSignifier & 0x200000000000 > 0) resultSignifier = resultSignifier * 0x100000000000000000000162E42FEFA38 >> 128; if (xSignifier & 0x100000000000 > 0) resultSignifier = resultSignifier * 0x1000000000000000000000B17217F7D1B >> 128; if (xSignifier & 0x80000000000 > 0) resultSignifier = resultSignifier * 0x100000000000000000000058B90BFBE8D >> 128; if (xSignifier & 0x40000000000 > 0) resultSignifier = resultSignifier * 0x10000000000000000000002C5C85FDF46 >> 128; if (xSignifier & 0x20000000000 > 0) resultSignifier = resultSignifier * 0x1000000000000000000000162E42FEFA2 >> 128; if (xSignifier & 0x10000000000 > 0) resultSignifier = resultSignifier * 0x10000000000000000000000B17217F7D0 >> 128; if (xSignifier & 0x8000000000 > 0) resultSignifier = resultSignifier * 0x1000000000000000000000058B90BFBE7 >> 128; if (xSignifier & 0x4000000000 > 0) resultSignifier = resultSignifier * 0x100000000000000000000002C5C85FDF3 >> 128; if (xSignifier & 0x2000000000 > 0) resultSignifier = resultSignifier * 0x10000000000000000000000162E42FEF9 >> 128; if (xSignifier & 0x1000000000 > 0) resultSignifier = resultSignifier * 0x100000000000000000000000B17217F7C >> 128; if (xSignifier & 0x800000000 > 0) resultSignifier = resultSignifier * 0x10000000000000000000000058B90BFBD >> 128; if (xSignifier & 0x400000000 > 0) resultSignifier = resultSignifier * 0x1000000000000000000000002C5C85FDE >> 128; if (xSignifier & 0x200000000 > 0) resultSignifier = resultSignifier * 0x100000000000000000000000162E42FEE >> 128; if (xSignifier & 0x100000000 > 0) resultSignifier = resultSignifier * 0x1000000000000000000000000B17217F6 >> 128; if (xSignifier & 0x80000000 > 0) resultSignifier = resultSignifier * 0x100000000000000000000000058B90BFA >> 128; if (xSignifier & 0x40000000 > 0) resultSignifier = resultSignifier * 0x10000000000000000000000002C5C85FC >> 128; if (xSignifier & 0x20000000 > 0) resultSignifier = resultSignifier * 0x1000000000000000000000000162E42FD >> 128; if (xSignifier & 0x10000000 > 0) resultSignifier = resultSignifier * 0x10000000000000000000000000B17217E >> 128; if (xSignifier & 0x8000000 > 0) resultSignifier = resultSignifier * 0x1000000000000000000000000058B90BE >> 128; if (xSignifier & 0x4000000 > 0) resultSignifier = resultSignifier * 0x100000000000000000000000002C5C85E >> 128; if (xSignifier & 0x2000000 > 0) resultSignifier = resultSignifier * 0x10000000000000000000000000162E42E >> 128; if (xSignifier & 0x1000000 > 0) resultSignifier = resultSignifier * 0x100000000000000000000000000B17216 >> 128; if (xSignifier & 0x800000 > 0) resultSignifier = resultSignifier * 0x10000000000000000000000000058B90A >> 128; if (xSignifier & 0x400000 > 0) resultSignifier = resultSignifier * 0x1000000000000000000000000002C5C84 >> 128; if (xSignifier & 0x200000 > 0) resultSignifier = resultSignifier * 0x100000000000000000000000000162E41 >> 128; if (xSignifier & 0x100000 > 0) resultSignifier = resultSignifier * 0x1000000000000000000000000000B1720 >> 128; if (xSignifier & 0x80000 > 0) resultSignifier = resultSignifier * 0x100000000000000000000000000058B8F >> 128; if (xSignifier & 0x40000 > 0) resultSignifier = resultSignifier * 0x10000000000000000000000000002C5C7 >> 128; if (xSignifier & 0x20000 > 0) resultSignifier = resultSignifier * 0x1000000000000000000000000000162E3 >> 128; if (xSignifier & 0x10000 > 0) resultSignifier = resultSignifier * 0x10000000000000000000000000000B171 >> 128; if (xSignifier & 0x8000 > 0) resultSignifier = resultSignifier * 0x1000000000000000000000000000058B8 >> 128; if (xSignifier & 0x4000 > 0) resultSignifier = resultSignifier * 0x100000000000000000000000000002C5B >> 128; if (xSignifier & 0x2000 > 0) resultSignifier = resultSignifier * 0x10000000000000000000000000000162D >> 128; if (xSignifier & 0x1000 > 0) resultSignifier = resultSignifier * 0x100000000000000000000000000000B16 >> 128; if (xSignifier & 0x800 > 0) resultSignifier = resultSignifier * 0x10000000000000000000000000000058A >> 128; if (xSignifier & 0x400 > 0) resultSignifier = resultSignifier * 0x1000000000000000000000000000002C4 >> 128; if (xSignifier & 0x200 > 0) resultSignifier = resultSignifier * 0x100000000000000000000000000000161 >> 128; if (xSignifier & 0x100 > 0) resultSignifier = resultSignifier * 0x1000000000000000000000000000000B0 >> 128; if (xSignifier & 0x80 > 0) resultSignifier = resultSignifier * 0x100000000000000000000000000000057 >> 128; if (xSignifier & 0x40 > 0) resultSignifier = resultSignifier * 0x10000000000000000000000000000002B >> 128; if (xSignifier & 0x20 > 0) resultSignifier = resultSignifier * 0x100000000000000000000000000000015 >> 128; if (xSignifier & 0x10 > 0) resultSignifier = resultSignifier * 0x10000000000000000000000000000000A >> 128; if (xSignifier & 0x8 > 0) resultSignifier = resultSignifier * 0x100000000000000000000000000000004 >> 128; if (xSignifier & 0x4 > 0) resultSignifier = resultSignifier * 0x100000000000000000000000000000001 >> 128; if (!xNegative) { resultSignifier = resultSignifier >> 15 & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF; resultExponent += 0x3FFF; } else if (resultExponent <= 0x3FFE) { resultSignifier = resultSignifier >> 15 & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF; resultExponent = 0x3FFF - resultExponent; } else { resultSignifier = resultSignifier >> resultExponent - 16367; resultExponent = 0; } return bytes16 (uint128 (resultExponent << 112 | resultSignifier)); } } /** * Calculate e^x. * * @param x quadruple precision number * @return quadruple precision number */ function exp (bytes16 x) internal pure returns (bytes16) { return pow_2 (mul (x, 0x3FFF71547652B82FE1777D0FFDA0D23A)); } /** * Get index of the most significant non-zero bit in binary representation of * x. Reverts if x is zero. * * @return index of the most significant non-zero bit in binary representation * of x */ function msb (uint256 x) private pure returns (uint256) { require (x > 0); uint256 result = 0; if (x >= 0x100000000000000000000000000000000) { x >>= 128; result += 128; } if (x >= 0x10000000000000000) { x >>= 64; result += 64; } if (x >= 0x100000000) { x >>= 32; result += 32; } if (x >= 0x10000) { x >>= 16; result += 16; } if (x >= 0x100) { x >>= 8; result += 8; } if (x >= 0x10) { x >>= 4; result += 4; } if (x >= 0x4) { x >>= 2; result += 2; } if (x >= 0x2) result += 1; // No need to shift x anymore return result; } }
{ "optimizer": { "enabled": false, "runs": 200 }, "outputSelection": { "*": { "*": [ "evm.bytecode", "evm.deployedBytecode", "abi" ] } }, "libraries": { "contracts/libraries/CentaurMath.sol": { "CentaurMath": "0xfe40675976c6dbecad7b98b07c29f1cd90e70129" } } }
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A token is a representation of an on-chain or off-chain asset. The token page shows information such as price, total supply, holders, transfers and social links. Learn more about this page in our Knowledge Base.