ERC-20
Overview
Max Total Supply
769.010640974142134948 ERC20 ***
Holders
53
Market
Onchain Market Cap
$0.00
Circulating Supply Market Cap
-
Other Info
Token Contract (WITH 18 Decimals)
Balance
0.000000883731159985 ERC20 ***Value
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# | Exchange | Pair | Price | 24H Volume | % Volume |
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Contract Name:
Pool
Compiler Version
v0.6.10+commit.00c0fcaf
Contract Source Code (Solidity)
/** *Submitted for verification at Etherscan.io on 2020-10-16 */ // File: @openzeppelin/contracts/GSN/Context.sol pragma solidity ^0.6.0; /* * @dev Provides information about the current execution context, including the * sender of the transaction and its data. While these are generally available * via msg.sender and msg.data, they should not be accessed in such a direct * manner, since when dealing with GSN meta-transactions the account sending and * paying for execution may not be the actual sender (as far as an application * is concerned). * * This contract is only required for intermediate, library-like contracts. */ abstract contract Context { function _msgSender() internal view virtual returns (address payable) { return msg.sender; } function _msgData() internal view virtual returns (bytes memory) { this; // silence state mutability warning without generating bytecode - see https://github.com/ethereum/solidity/issues/2691 return msg.data; } } // File: @openzeppelin/contracts/token/ERC20/IERC20.sol pragma solidity ^0.6.0; /** * @dev Interface of the ERC20 standard as defined in the EIP. */ interface IERC20 { /** * @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); } // File: @openzeppelin/contracts/math/SafeMath.sol pragma solidity ^0.6.0; /** * @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; } } // File: @openzeppelin/contracts/utils/Address.sol pragma solidity ^0.6.2; /** * @dev Collection of functions related to the address type */ library Address { /** * @dev Returns true if `account` is a contract. * * [IMPORTANT] * ==== * It is unsafe to assume that an address for which this function returns * false is an externally-owned account (EOA) and not a contract. * * Among others, `isContract` will return false for the following * types of addresses: * * - an externally-owned account * - a contract in construction * - an address where a contract will be created * - an address where a contract lived, but was destroyed * ==== */ function isContract(address account) internal view returns (bool) { // According to EIP-1052, 0x0 is the value returned for not-yet created accounts // and 0xc5d2460186f7233c927e7db2dcc703c0e500b653ca82273b7bfad8045d85a470 is returned // for accounts without code, i.e. `keccak256('')` bytes32 codehash; bytes32 accountHash = 0xc5d2460186f7233c927e7db2dcc703c0e500b653ca82273b7bfad8045d85a470; // solhint-disable-next-line no-inline-assembly assembly { codehash := extcodehash(account) } return (codehash != accountHash && codehash != 0x0); } /** * @dev Replacement for Solidity's `transfer`: sends `amount` wei to * `recipient`, forwarding all available gas and reverting on errors. * * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost * of certain opcodes, possibly making contracts go over the 2300 gas limit * imposed by `transfer`, making them unable to receive funds via * `transfer`. {sendValue} removes this limitation. * * https://diligence.consensys.net/posts/2019/09/stop-using-soliditys-transfer-now/[Learn more]. * * IMPORTANT: because control is transferred to `recipient`, care must be * taken to not create reentrancy vulnerabilities. Consider using * {ReentrancyGuard} or the * https://solidity.readthedocs.io/en/v0.5.11/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern]. */ function sendValue(address payable recipient, uint256 amount) internal { require(address(this).balance >= amount, "Address: insufficient balance"); // solhint-disable-next-line avoid-low-level-calls, avoid-call-value (bool success, ) = recipient.call{ value: amount }(""); require(success, "Address: unable to send value, recipient may have reverted"); } /** * @dev Performs a Solidity function call using a low level `call`. A * plain`call` is an unsafe replacement for a function call: use this * function instead. * * If `target` reverts with a revert reason, it is bubbled up by this * function (like regular Solidity function calls). * * Returns the raw returned data. To convert to the expected return value, * use https://solidity.readthedocs.io/en/latest/units-and-global-variables.html?highlight=abi.decode#abi-encoding-and-decoding-functions[`abi.decode`]. * * Requirements: * * - `target` must be a contract. * - calling `target` with `data` must not revert. * * _Available since v3.1._ */ function functionCall(address target, bytes memory data) internal returns (bytes memory) { return functionCall(target, data, "Address: low-level call failed"); } /** * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], but with * `errorMessage` as a fallback revert reason when `target` reverts. * * _Available since v3.1._ */ function functionCall(address target, bytes memory data, string memory errorMessage) internal returns (bytes memory) { return _functionCallWithValue(target, data, 0, errorMessage); } /** * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], * but also transferring `value` wei to `target`. * * Requirements: * * - the calling contract must have an ETH balance of at least `value`. * - the called Solidity function must be `payable`. * * _Available since v3.1._ */ function functionCallWithValue(address target, bytes memory data, uint256 value) internal returns (bytes memory) { return functionCallWithValue(target, data, value, "Address: low-level call with value failed"); } /** * @dev Same as {xref-Address-functionCallWithValue-address-bytes-uint256-}[`functionCallWithValue`], but * with `errorMessage` as a fallback revert reason when `target` reverts. * * _Available since v3.1._ */ function functionCallWithValue(address target, bytes memory data, uint256 value, string memory errorMessage) internal returns (bytes memory) { require(address(this).balance >= value, "Address: insufficient balance for call"); return _functionCallWithValue(target, data, value, errorMessage); } function _functionCallWithValue(address target, bytes memory data, uint256 weiValue, string memory errorMessage) private returns (bytes memory) { require(isContract(target), "Address: call to non-contract"); // solhint-disable-next-line avoid-low-level-calls (bool success, bytes memory returndata) = target.call{ value: weiValue }(data); if (success) { return returndata; } else { // Look for revert reason and bubble it up if present if (returndata.length > 0) { // The easiest way to bubble the revert reason is using memory via assembly // solhint-disable-next-line no-inline-assembly assembly { let returndata_size := mload(returndata) revert(add(32, returndata), returndata_size) } } else { revert(errorMessage); } } } } // File: @openzeppelin/contracts/token/ERC20/ERC20.sol pragma solidity ^0.6.0; /** * @dev Implementation of the {IERC20} interface. * * This implementation is agnostic to the way tokens are created. This means * that a supply mechanism has to be added in a derived contract using {_mint}. * For a generic mechanism see {ERC20PresetMinterPauser}. * * TIP: For a detailed writeup see our guide * https://forum.zeppelin.solutions/t/how-to-implement-erc20-supply-mechanisms/226[How * to implement supply mechanisms]. * * We have followed general OpenZeppelin guidelines: functions revert instead * of returning `false` on failure. This behavior is nonetheless conventional * and does not conflict with the expectations of ERC20 applications. * * Additionally, an {Approval} event is emitted on calls to {transferFrom}. * This allows applications to reconstruct the allowance for all accounts just * by listening to said events. Other implementations of the EIP may not emit * these events, as it isn't required by the specification. * * Finally, the non-standard {decreaseAllowance} and {increaseAllowance} * functions have been added to mitigate the well-known issues around setting * allowances. See {IERC20-approve}. */ contract ERC20 is Context, IERC20 { using SafeMath for uint256; using Address for address; mapping (address => uint256) private _balances; mapping (address => mapping (address => uint256)) private _allowances; uint256 private _totalSupply; string private _name; string private _symbol; uint8 private _decimals; /** * @dev Sets the values for {name} and {symbol}, initializes {decimals} with * a default value of 18. * * To select a different value for {decimals}, use {_setupDecimals}. * * All three of these values are immutable: they can only be set once during * construction. */ constructor (string memory name, string memory symbol) public { _name = name; _symbol = symbol; _decimals = 18; } /** * @dev Returns the name of the token. */ function name() public view returns (string memory) { return _name; } /** * @dev Returns the symbol of the token, usually a shorter version of the * name. */ function symbol() public view returns (string memory) { return _symbol; } /** * @dev Returns the number of decimals used to get its user representation. * For example, if `decimals` equals `2`, a balance of `505` tokens should * be displayed to a user as `5,05` (`505 / 10 ** 2`). * * Tokens usually opt for a value of 18, imitating the relationship between * Ether and Wei. This is the value {ERC20} uses, unless {_setupDecimals} is * called. * * NOTE: This information is only used for _display_ purposes: it in * no way affects any of the arithmetic of the contract, including * {IERC20-balanceOf} and {IERC20-transfer}. */ function decimals() public view returns (uint8) { return _decimals; } /** * @dev See {IERC20-totalSupply}. */ function totalSupply() public view override returns (uint256) { return _totalSupply; } /** * @dev See {IERC20-balanceOf}. */ function balanceOf(address account) public view override returns (uint256) { return _balances[account]; } /** * @dev See {IERC20-transfer}. * * Requirements: * * - `recipient` cannot be the zero address. * - the caller must have a balance of at least `amount`. */ function transfer(address recipient, uint256 amount) public virtual override returns (bool) { _transfer(_msgSender(), recipient, amount); return true; } /** * @dev See {IERC20-allowance}. */ function allowance(address owner, address spender) public view virtual override returns (uint256) { return _allowances[owner][spender]; } /** * @dev See {IERC20-approve}. * * Requirements: * * - `spender` cannot be the zero address. */ function approve(address spender, uint256 amount) public virtual override returns (bool) { _approve(_msgSender(), spender, amount); return true; } /** * @dev See {IERC20-transferFrom}. * * Emits an {Approval} event indicating the updated allowance. This is not * required by the EIP. See the note at the beginning of {ERC20}; * * Requirements: * - `sender` and `recipient` cannot be the zero address. * - `sender` must have a balance of at least `amount`. * - the caller must have allowance for ``sender``'s tokens of at least * `amount`. */ function transferFrom(address sender, address recipient, uint256 amount) public virtual override returns (bool) { _transfer(sender, recipient, amount); _approve(sender, _msgSender(), _allowances[sender][_msgSender()].sub(amount, "ERC20: transfer amount exceeds allowance")); return true; } /** * @dev Atomically increases the allowance granted to `spender` by the caller. * * This is an alternative to {approve} that can be used as a mitigation for * problems described in {IERC20-approve}. * * Emits an {Approval} event indicating the updated allowance. * * Requirements: * * - `spender` cannot be the zero address. */ function increaseAllowance(address spender, uint256 addedValue) public virtual returns (bool) { _approve(_msgSender(), spender, _allowances[_msgSender()][spender].add(addedValue)); return true; } /** * @dev Atomically decreases the allowance granted to `spender` by the caller. * * This is an alternative to {approve} that can be used as a mitigation for * problems described in {IERC20-approve}. * * Emits an {Approval} event indicating the updated allowance. * * Requirements: * * - `spender` cannot be the zero address. * - `spender` must have allowance for the caller of at least * `subtractedValue`. */ function decreaseAllowance(address spender, uint256 subtractedValue) public virtual returns (bool) { _approve(_msgSender(), spender, _allowances[_msgSender()][spender].sub(subtractedValue, "ERC20: decreased allowance below zero")); return true; } /** * @dev Moves tokens `amount` from `sender` to `recipient`. * * This is internal function is equivalent to {transfer}, and can be used to * e.g. implement automatic token fees, slashing mechanisms, etc. * * Emits a {Transfer} event. * * Requirements: * * - `sender` cannot be the zero address. * - `recipient` cannot be the zero address. * - `sender` must have a balance of at least `amount`. */ function _transfer(address sender, address recipient, uint256 amount) internal virtual { require(sender != address(0), "ERC20: transfer from the zero address"); require(recipient != address(0), "ERC20: transfer to the zero address"); _beforeTokenTransfer(sender, recipient, amount); _balances[sender] = _balances[sender].sub(amount, "ERC20: transfer amount exceeds balance"); _balances[recipient] = _balances[recipient].add(amount); emit Transfer(sender, recipient, amount); } /** @dev Creates `amount` tokens and assigns them to `account`, increasing * the total supply. * * Emits a {Transfer} event with `from` set to the zero address. * * Requirements * * - `to` cannot be the zero address. */ function _mint(address account, uint256 amount) internal virtual { require(account != address(0), "ERC20: mint to the zero address"); _beforeTokenTransfer(address(0), account, amount); _totalSupply = _totalSupply.add(amount); _balances[account] = _balances[account].add(amount); emit Transfer(address(0), account, amount); } /** * @dev Destroys `amount` tokens from `account`, reducing the * total supply. * * Emits a {Transfer} event with `to` set to the zero address. * * Requirements * * - `account` cannot be the zero address. * - `account` must have at least `amount` tokens. */ function _burn(address account, uint256 amount) internal virtual { require(account != address(0), "ERC20: burn from the zero address"); _beforeTokenTransfer(account, address(0), amount); _balances[account] = _balances[account].sub(amount, "ERC20: burn amount exceeds balance"); _totalSupply = _totalSupply.sub(amount); emit Transfer(account, address(0), amount); } /** * @dev Sets `amount` as the allowance of `spender` over the `owner`s tokens. * * This is internal function is equivalent to `approve`, and can be used to * e.g. set automatic allowances for certain subsystems, etc. * * Emits an {Approval} event. * * Requirements: * * - `owner` cannot be the zero address. * - `spender` cannot be the zero address. */ function _approve(address owner, address spender, uint256 amount) internal virtual { require(owner != address(0), "ERC20: approve from the zero address"); require(spender != address(0), "ERC20: approve to the zero address"); _allowances[owner][spender] = amount; emit Approval(owner, spender, amount); } /** * @dev Sets {decimals} to a value other than the default one of 18. * * WARNING: This function should only be called from the constructor. Most * applications that interact with token contracts will not expect * {decimals} to ever change, and may work incorrectly if it does. */ function _setupDecimals(uint8 decimals_) internal { _decimals = decimals_; } /** * @dev Hook that is called before any transfer of tokens. This includes * minting and burning. * * Calling conditions: * * - when `from` and `to` are both non-zero, `amount` of ``from``'s tokens * will be to transferred to `to`. * - when `from` is zero, `amount` tokens will be minted for `to`. * - when `to` is zero, `amount` of ``from``'s tokens will be burned. * - `from` and `to` are never both zero. * * To learn more about hooks, head to xref:ROOT:extending-contracts.adoc#using-hooks[Using Hooks]. */ function _beforeTokenTransfer(address from, address to, uint256 amount) internal virtual { } } // File: contracts/pool/Math64x64.sol /* * Math 64.64 Smart Contract Library. Copyright © 2019 by Consulting. * Author: Mikhail Vladimirov <[email protected]> */ pragma solidity ^0.6.0; /** * Smart contract library of mathematical functions operating with signed * 64.64-bit fixed point numbers. Signed 64.64-bit fixed point number is * basically a simple fraction whose numerator is signed 128-bit integer and * denominator is 2^64. As long as denominator is always the same, there is no * need to store it, thus in Solidity signed 64.64-bit fixed point numbers are * represented by int128 type holding only the numerator. */ library Math64x64 { /** * @dev Minimum value signed 64.64-bit fixed point number may have. */ int128 private constant MIN_64x64 = -0x80000000000000000000000000000000; /** * @dev Maximum value signed 64.64-bit fixed point number may have. */ int128 private constant MAX_64x64 = 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF; /** * @dev Convert signed 256-bit integer number into signed 64.64-bit fixed point * number. Revert on overflow. * * @param x signed 256-bit integer number * @return signed 64.64-bit fixed point number */ function fromInt (int256 x) internal pure returns (int128) { require (x >= -0x8000000000000000 && x <= 0x7FFFFFFFFFFFFFFF); return int128 (x << 64); } /** * @dev Convert signed 64.64 fixed point number into signed 64-bit integer number * rounding down. * * @param x signed 64.64-bit fixed point number * @return signed 64-bit integer number */ function toInt (int128 x) internal pure returns (int64) { return int64 (x >> 64); } /** * @dev Convert unsigned 256-bit integer number into signed 64.64-bit fixed point * number. Revert on overflow. * * @param x unsigned 256-bit integer number * @return signed 64.64-bit fixed point number */ function fromUInt (uint256 x) internal pure returns (int128) { require (x <= 0x7FFFFFFFFFFFFFFF); return int128 (x << 64); } /** * @dev Convert signed 64.64 fixed point number into unsigned 64-bit integer * number rounding down. Revert on underflow. * * @param x signed 64.64-bit fixed point number * @return unsigned 64-bit integer number */ function toUInt (int128 x) internal pure returns (uint64) { require (x >= 0); return uint64 (x >> 64); } /** * @dev Convert signed 128.128 fixed point number into signed 64.64-bit fixed point * number rounding down. Revert on overflow. * * @param x signed 128.128-bin fixed point number * @return signed 64.64-bit fixed point number */ function from128x128 (int256 x) internal pure returns (int128) { int256 result = x >> 64; require (result >= MIN_64x64 && result <= MAX_64x64); return int128 (result); } /** * @dev Convert signed 64.64 fixed point number into signed 128.128 fixed point * number. * * @param x signed 64.64-bit fixed point number * @return signed 128.128 fixed point number */ function to128x128 (int128 x) internal pure returns (int256) { return int256 (x) << 64; } /** * @dev Calculate x + y. Revert on overflow. * * @param x signed 64.64-bit fixed point number * @param y signed 64.64-bit fixed point number * @return signed 64.64-bit fixed point number */ function add (int128 x, int128 y) internal pure returns (int128) { int256 result = int256(x) + y; require (result >= MIN_64x64 && result <= MAX_64x64); return int128 (result); } /** * @dev Calculate x - y. Revert on overflow. * * @param x signed 64.64-bit fixed point number * @param y signed 64.64-bit fixed point number * @return signed 64.64-bit fixed point number */ function sub (int128 x, int128 y) internal pure returns (int128) { int256 result = int256(x) - y; require (result >= MIN_64x64 && result <= MAX_64x64); return int128 (result); } /** * @dev Calculate x * y rounding down. Revert on overflow. * * @param x signed 64.64-bit fixed point number * @param y signed 64.64-bit fixed point number * @return signed 64.64-bit fixed point number */ function mul (int128 x, int128 y) internal pure returns (int128) { int256 result = int256(x) * y >> 64; require (result >= MIN_64x64 && result <= MAX_64x64); return int128 (result); } /** * @dev Calculate x * y rounding towards zero, where x is signed 64.64 fixed point * number and y is signed 256-bit integer number. Revert on overflow. * * @param x signed 64.64 fixed point number * @param y signed 256-bit integer number * @return signed 256-bit integer number */ function muli (int128 x, int256 y) internal pure returns (int256) { if (x == MIN_64x64) { require (y >= -0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF && y <= 0x1000000000000000000000000000000000000000000000000); return -y << 63; } else { bool negativeResult = false; if (x < 0) { x = -x; negativeResult = true; } if (y < 0) { y = -y; // We rely on overflow behavior here negativeResult = !negativeResult; } uint256 absoluteResult = mulu (x, uint256 (y)); if (negativeResult) { require (absoluteResult <= 0x8000000000000000000000000000000000000000000000000000000000000000); return -int256 (absoluteResult); // We rely on overflow behavior here } else { require (absoluteResult <= 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF); return int256 (absoluteResult); } } } /** * @dev Calculate x * y rounding down, where x is signed 64.64 fixed point number * and y is unsigned 256-bit integer number. Revert on overflow. * * @param x signed 64.64 fixed point number * @param y unsigned 256-bit integer number * @return unsigned 256-bit integer number */ function mulu (int128 x, uint256 y) internal pure returns (uint256) { if (y == 0) return 0; require (x >= 0); uint256 lo = (uint256 (x) * (y & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)) >> 64; uint256 hi = uint256 (x) * (y >> 128); require (hi <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF); hi <<= 64; require (hi <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF - lo); return hi + lo; } /** * @dev Calculate x / y rounding towards zero. Revert on overflow or when y is * zero. * * @param x signed 64.64-bit fixed point number * @param y signed 64.64-bit fixed point number * @return signed 64.64-bit fixed point number */ function div (int128 x, int128 y) internal pure returns (int128) { require (y != 0); int256 result = (int256 (x) << 64) / y; require (result >= MIN_64x64 && result <= MAX_64x64); return int128 (result); } /** * @dev Calculate x / y rounding towards zero, where x and y are signed 256-bit * integer numbers. Revert on overflow or when y is zero. * * @param x signed 256-bit integer number * @param y signed 256-bit integer number * @return signed 64.64-bit fixed point number */ function divi (int256 x, int256 y) internal pure returns (int128) { require (y != 0); bool negativeResult = false; if (x < 0) { x = -x; // We rely on overflow behavior here negativeResult = true; } if (y < 0) { y = -y; // We rely on overflow behavior here negativeResult = !negativeResult; } uint128 absoluteResult = divuu (uint256 (x), uint256 (y)); if (negativeResult) { require (absoluteResult <= 0x80000000000000000000000000000000); return -int128 (absoluteResult); // We rely on overflow behavior here } else { require (absoluteResult <= 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF); return int128 (absoluteResult); // We rely on overflow behavior here } } /** * @dev Calculate x / y rounding towards zero, where x and y are unsigned 256-bit * integer numbers. Revert on overflow or when y is zero. * * @param x unsigned 256-bit integer number * @param y unsigned 256-bit integer number * @return signed 64.64-bit fixed point number */ function divu (uint256 x, uint256 y) internal pure returns (int128) { require (y != 0); uint128 result = divuu (x, y); require (result <= uint128 (MAX_64x64)); return int128 (result); } /** * @dev Calculate -x. Revert on overflow. * * @param x signed 64.64-bit fixed point number * @return signed 64.64-bit fixed point number */ function neg (int128 x) internal pure returns (int128) { require (x != MIN_64x64); return -x; } /** * @dev Calculate |x|. Revert on overflow. * * @param x signed 64.64-bit fixed point number * @return signed 64.64-bit fixed point number */ function abs (int128 x) internal pure returns (int128) { require (x != MIN_64x64); return x < 0 ? -x : x; } /** * @dev Calculate 1 / x rounding towards zero. Revert on overflow or when x is * zero. * * @param x signed 64.64-bit fixed point number * @return signed 64.64-bit fixed point number */ function inv (int128 x) internal pure returns (int128) { require (x != 0); int256 result = int256 (0x100000000000000000000000000000000) / x; require (result >= MIN_64x64 && result <= MAX_64x64); return int128 (result); } /** * @dev Calculate arithmetics average of x and y, i.e. (x + y) / 2 rounding down. * * @param x signed 64.64-bit fixed point number * @param y signed 64.64-bit fixed point number * @return signed 64.64-bit fixed point number */ function avg (int128 x, int128 y) internal pure returns (int128) { return int128 ((int256 (x) + int256 (y)) >> 1); } /** * @dev Calculate geometric average of x and y, i.e. sqrt (x * y) rounding down. * Revert on overflow or in case x * y is negative. * * @param x signed 64.64-bit fixed point number * @param y signed 64.64-bit fixed point number * @return signed 64.64-bit fixed point number */ function gavg (int128 x, int128 y) internal pure returns (int128) { int256 m = int256 (x) * int256 (y); require (m >= 0); require (m < 0x4000000000000000000000000000000000000000000000000000000000000000); return int128 (sqrtu (uint256 (m), uint256 (x) + uint256 (y) >> 1)); } /** * @dev Calculate x^y assuming 0^0 is 1, where x is signed 64.64 fixed point number * and y is unsigned 256-bit integer number. Revert on overflow. * * @param x signed 64.64-bit fixed point number * @param y uint256 value * @return signed 64.64-bit fixed point number */ function pow (int128 x, uint256 y) internal pure returns (int128) { uint256 absoluteResult; bool negativeResult = false; if (x >= 0) { absoluteResult = powu (uint256 (x) << 63, y); } else { // We rely on overflow behavior here absoluteResult = powu (uint256 (uint128 (-x)) << 63, y); negativeResult = y & 1 > 0; } absoluteResult >>= 63; if (negativeResult) { require (absoluteResult <= 0x80000000000000000000000000000000); return -int128 (absoluteResult); // We rely on overflow behavior here } else { require (absoluteResult <= 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF); return int128 (absoluteResult); // We rely on overflow behavior here } } /** * @dev Calculate sqrt (x) rounding down. Revert if x < 0. * * @param x signed 64.64-bit fixed point number * @return signed 64.64-bit fixed point number */ function sqrt (int128 x) internal pure returns (int128) { require (x >= 0); return int128 (sqrtu (uint256 (x) << 64, 0x10000000000000000)); } /** * @dev Calculate binary logarithm of x. Revert if x <= 0. * * @param x signed 64.64-bit fixed point number * @return signed 64.64-bit fixed point number */ function log_2 (int128 x) internal pure returns (int128) { require (x > 0); int256 msb = 0; int256 xc = x; if (xc >= 0x10000000000000000) { xc >>= 64; msb += 64; } if (xc >= 0x100000000) { xc >>= 32; msb += 32; } if (xc >= 0x10000) { xc >>= 16; msb += 16; } if (xc >= 0x100) { xc >>= 8; msb += 8; } if (xc >= 0x10) { xc >>= 4; msb += 4; } if (xc >= 0x4) { xc >>= 2; msb += 2; } if (xc >= 0x2) msb += 1; // No need to shift xc anymore int256 result = msb - 64 << 64; uint256 ux = uint256 (x) << 127 - msb; for (int256 bit = 0x8000000000000000; bit > 0; bit >>= 1) { ux *= ux; uint256 b = ux >> 255; ux >>= 127 + b; result += bit * int256 (b); } return int128 (result); } /** * @dev Calculate natural logarithm of x. Revert if x <= 0. * * @param x signed 64.64-bit fixed point number * @return signed 64.64-bit fixed point number */ function ln (int128 x) internal pure returns (int128) { require (x > 0); return int128 ( uint256 (log_2 (x)) * 0xB17217F7D1CF79ABC9E3B39803F2F6AF >> 128); } /** * @dev Calculate binary exponent of x. Revert on overflow. * * @param x signed 64.64-bit fixed point number * @return signed 64.64-bit fixed point number */ function exp_2 (int128 x) internal pure returns (int128) { require (x < 0x400000000000000000); // Overflow if (x < -0x400000000000000000) return 0; // Underflow uint256 result = 0x80000000000000000000000000000000; if (x & 0x8000000000000000 > 0) result = result * 0x16A09E667F3BCC908B2FB1366EA957D3E >> 128; if (x & 0x4000000000000000 > 0) result = result * 0x1306FE0A31B7152DE8D5A46305C85EDEC >> 128; if (x & 0x2000000000000000 > 0) result = result * 0x1172B83C7D517ADCDF7C8C50EB14A791F >> 128; if (x & 0x1000000000000000 > 0) result = result * 0x10B5586CF9890F6298B92B71842A98363 >> 128; if (x & 0x800000000000000 > 0) result = result * 0x1059B0D31585743AE7C548EB68CA417FD >> 128; if (x & 0x400000000000000 > 0) result = result * 0x102C9A3E778060EE6F7CACA4F7A29BDE8 >> 128; if (x & 0x200000000000000 > 0) result = result * 0x10163DA9FB33356D84A66AE336DCDFA3F >> 128; if (x & 0x100000000000000 > 0) result = result * 0x100B1AFA5ABCBED6129AB13EC11DC9543 >> 128; if (x & 0x80000000000000 > 0) result = result * 0x10058C86DA1C09EA1FF19D294CF2F679B >> 128; if (x & 0x40000000000000 > 0) result = result * 0x1002C605E2E8CEC506D21BFC89A23A00F >> 128; if (x & 0x20000000000000 > 0) result = result * 0x100162F3904051FA128BCA9C55C31E5DF >> 128; if (x & 0x10000000000000 > 0) result = result * 0x1000B175EFFDC76BA38E31671CA939725 >> 128; if (x & 0x8000000000000 > 0) result = result * 0x100058BA01FB9F96D6CACD4B180917C3D >> 128; if (x & 0x4000000000000 > 0) result = result * 0x10002C5CC37DA9491D0985C348C68E7B3 >> 128; if (x & 0x2000000000000 > 0) result = result * 0x1000162E525EE054754457D5995292026 >> 128; if (x & 0x1000000000000 > 0) result = result * 0x10000B17255775C040618BF4A4ADE83FC >> 128; if (x & 0x800000000000 > 0) result = result * 0x1000058B91B5BC9AE2EED81E9B7D4CFAB >> 128; if (x & 0x400000000000 > 0) result = result * 0x100002C5C89D5EC6CA4D7C8ACC017B7C9 >> 128; if (x & 0x200000000000 > 0) result = result * 0x10000162E43F4F831060E02D839A9D16D >> 128; if (x & 0x100000000000 > 0) result = result * 0x100000B1721BCFC99D9F890EA06911763 >> 128; if (x & 0x80000000000 > 0) result = result * 0x10000058B90CF1E6D97F9CA14DBCC1628 >> 128; if (x & 0x40000000000 > 0) result = result * 0x1000002C5C863B73F016468F6BAC5CA2B >> 128; if (x & 0x20000000000 > 0) result = result * 0x100000162E430E5A18F6119E3C02282A5 >> 128; if (x & 0x10000000000 > 0) result = result * 0x1000000B1721835514B86E6D96EFD1BFE >> 128; if (x & 0x8000000000 > 0) result = result * 0x100000058B90C0B48C6BE5DF846C5B2EF >> 128; if (x & 0x4000000000 > 0) result = result * 0x10000002C5C8601CC6B9E94213C72737A >> 128; if (x & 0x2000000000 > 0) result = result * 0x1000000162E42FFF037DF38AA2B219F06 >> 128; if (x & 0x1000000000 > 0) result = result * 0x10000000B17217FBA9C739AA5819F44F9 >> 128; if (x & 0x800000000 > 0) result = result * 0x1000000058B90BFCDEE5ACD3C1CEDC823 >> 128; if (x & 0x400000000 > 0) result = result * 0x100000002C5C85FE31F35A6A30DA1BE50 >> 128; if (x & 0x200000000 > 0) result = result * 0x10000000162E42FF0999CE3541B9FFFCF >> 128; if (x & 0x100000000 > 0) result = result * 0x100000000B17217F80F4EF5AADDA45554 >> 128; if (x & 0x80000000 > 0) result = result * 0x10000000058B90BFBF8479BD5A81B51AD >> 128; if (x & 0x40000000 > 0) result = result * 0x1000000002C5C85FDF84BD62AE30A74CC >> 128; if (x & 0x20000000 > 0) result = result * 0x100000000162E42FEFB2FED257559BDAA >> 128; if (x & 0x10000000 > 0) result = result * 0x1000000000B17217F7D5A7716BBA4A9AE >> 128; if (x & 0x8000000 > 0) result = result * 0x100000000058B90BFBE9DDBAC5E109CCE >> 128; if (x & 0x4000000 > 0) result = result * 0x10000000002C5C85FDF4B15DE6F17EB0D >> 128; if (x & 0x2000000 > 0) result = result * 0x1000000000162E42FEFA494F1478FDE05 >> 128; if (x & 0x1000000 > 0) result = result * 0x10000000000B17217F7D20CF927C8E94C >> 128; if (x & 0x800000 > 0) result = result * 0x1000000000058B90BFBE8F71CB4E4B33D >> 128; if (x & 0x400000 > 0) result = result * 0x100000000002C5C85FDF477B662B26945 >> 128; if (x & 0x200000 > 0) result = result * 0x10000000000162E42FEFA3AE53369388C >> 128; if (x & 0x100000 > 0) result = result * 0x100000000000B17217F7D1D351A389D40 >> 128; if (x & 0x80000 > 0) result = result * 0x10000000000058B90BFBE8E8B2D3D4EDE >> 128; if (x & 0x40000 > 0) result = result * 0x1000000000002C5C85FDF4741BEA6E77E >> 128; if (x & 0x20000 > 0) result = result * 0x100000000000162E42FEFA39FE95583C2 >> 128; if (x & 0x10000 > 0) result = result * 0x1000000000000B17217F7D1CFB72B45E1 >> 128; if (x & 0x8000 > 0) result = result * 0x100000000000058B90BFBE8E7CC35C3F0 >> 128; if (x & 0x4000 > 0) result = result * 0x10000000000002C5C85FDF473E242EA38 >> 128; if (x & 0x2000 > 0) result = result * 0x1000000000000162E42FEFA39F02B772C >> 128; if (x & 0x1000 > 0) result = result * 0x10000000000000B17217F7D1CF7D83C1A >> 128; if (x & 0x800 > 0) result = result * 0x1000000000000058B90BFBE8E7BDCBE2E >> 128; if (x & 0x400 > 0) result = result * 0x100000000000002C5C85FDF473DEA871F >> 128; if (x & 0x200 > 0) result = result * 0x10000000000000162E42FEFA39EF44D91 >> 128; if (x & 0x100 > 0) result = result * 0x100000000000000B17217F7D1CF79E949 >> 128; if (x & 0x80 > 0) result = result * 0x10000000000000058B90BFBE8E7BCE544 >> 128; if (x & 0x40 > 0) result = result * 0x1000000000000002C5C85FDF473DE6ECA >> 128; if (x & 0x20 > 0) result = result * 0x100000000000000162E42FEFA39EF366F >> 128; if (x & 0x10 > 0) result = result * 0x1000000000000000B17217F7D1CF79AFA >> 128; if (x & 0x8 > 0) result = result * 0x100000000000000058B90BFBE8E7BCD6D >> 128; if (x & 0x4 > 0) result = result * 0x10000000000000002C5C85FDF473DE6B2 >> 128; if (x & 0x2 > 0) result = result * 0x1000000000000000162E42FEFA39EF358 >> 128; if (x & 0x1 > 0) result = result * 0x10000000000000000B17217F7D1CF79AB >> 128; result >>= 63 - (x >> 64); require (result <= uint256 (MAX_64x64)); return int128 (result); } /** * @dev Calculate natural exponent of x. Revert on overflow. * * @param x signed 64.64-bit fixed point number * @return signed 64.64-bit fixed point number */ function exp (int128 x) internal pure returns (int128) { require (x < 0x400000000000000000); // Overflow if (x < -0x400000000000000000) return 0; // Underflow return exp_2 ( int128 (int256 (x) * 0x171547652B82FE1777D0FFDA0D23A7D12 >> 128)); } /** * @dev Calculate x / y rounding towards zero, where x and y are unsigned 256-bit * integer numbers. Revert on overflow or when y is zero. * * @param x unsigned 256-bit integer number * @param y unsigned 256-bit integer number * @return unsigned 64.64-bit fixed point number */ function divuu (uint256 x, uint256 y) private pure returns (uint128) { require (y != 0); uint256 result; if (x <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF) result = (x << 64) / y; else { uint256 msb = 192; uint256 xc = x >> 192; if (xc >= 0x100000000) { xc >>= 32; msb += 32; } if (xc >= 0x10000) { xc >>= 16; msb += 16; } if (xc >= 0x100) { xc >>= 8; msb += 8; } if (xc >= 0x10) { xc >>= 4; msb += 4; } if (xc >= 0x4) { xc >>= 2; msb += 2; } if (xc >= 0x2) msb += 1; // No need to shift xc anymore result = (x << 255 - msb) / ((y - 1 >> msb - 191) + 1); require (result <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF); uint256 hi = result * (y >> 128); uint256 lo = result * (y & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF); uint256 xh = x >> 192; uint256 xl = x << 64; if (xl < lo) xh -= 1; xl -= lo; // We rely on overflow behavior here lo = hi << 128; if (xl < lo) xh -= 1; xl -= lo; // We rely on overflow behavior here assert (xh == hi >> 128); result += xl / y; } require (result <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF); return uint128 (result); } /** * @dev Calculate x^y assuming 0^0 is 1, where x is unsigned 129.127 fixed point * number and y is unsigned 256-bit integer number. Revert on overflow. * * @param x unsigned 129.127-bit fixed point number * @param y uint256 value * @return unsigned 129.127-bit fixed point number */ function powu (uint256 x, uint256 y) private pure returns (uint256) { if (y == 0) return 0x80000000000000000000000000000000; else if (x == 0) return 0; else { int256 msb = 0; uint256 xc = x; if (xc >= 0x100000000000000000000000000000000) { xc >>= 128; msb += 128; } if (xc >= 0x10000000000000000) { xc >>= 64; msb += 64; } if (xc >= 0x100000000) { xc >>= 32; msb += 32; } if (xc >= 0x10000) { xc >>= 16; msb += 16; } if (xc >= 0x100) { xc >>= 8; msb += 8; } if (xc >= 0x10) { xc >>= 4; msb += 4; } if (xc >= 0x4) { xc >>= 2; msb += 2; } if (xc >= 0x2) msb += 1; // No need to shift xc anymore int256 xe = msb - 127; if (xe > 0) x >>= xe; else x <<= -xe; uint256 result = 0x80000000000000000000000000000000; int256 re = 0; while (y > 0) { if (y & 1 > 0) { result = result * x; y -= 1; re += xe; if (result >= 0x8000000000000000000000000000000000000000000000000000000000000000) { result >>= 128; re += 1; } else result >>= 127; if (re < -127) return 0; // Underflow require (re < 128); // Overflow } else { x = x * x; y >>= 1; xe <<= 1; if (x >= 0x8000000000000000000000000000000000000000000000000000000000000000) { x >>= 128; xe += 1; } else x >>= 127; if (xe < -127) return 0; // Underflow require (xe < 128); // Overflow } } if (re > 0) result <<= re; else if (re < 0) result >>= -re; return result; } } /** * @dev Calculate sqrt (x) rounding down, where x is unsigned 256-bit integer * number. * * @param x unsigned 256-bit integer number * @return unsigned 128-bit integer number */ function sqrtu (uint256 x, uint256 r) private pure returns (uint128) { if (x == 0) return 0; else { require (r > 0); while (true) { uint256 rr = x / r; if (r == rr || r + 1 == rr) return uint128 (r); else if (r == rr + 1) return uint128 (rr); r = r + rr + 1 >> 1; } } } } // File: contracts/pool/YieldMath.sol pragma solidity ^0.6.0; /** * Ethereum smart contract library implementing Yield Math model. */ library YieldMath { /** * Calculate the amount of fyDai a user would get for given amount of Dai. * * @param daiReserves Dai reserves amount * @param fyDaiReserves fyDai reserves amount * @param daiAmount Dai amount to be traded * @param timeTillMaturity time till maturity in seconds * @param k time till maturity coefficient, multiplied by 2^64 * @param g fee coefficient, multiplied by 2^64 * @return the amount of fyDai a user would get for given amount of Dai */ function fyDaiOutForDaiIn ( uint128 daiReserves, uint128 fyDaiReserves, uint128 daiAmount, uint128 timeTillMaturity, int128 k, int128 g) internal pure returns (uint128) { // t = k * timeTillMaturity int128 t = Math64x64.mul (k, Math64x64.fromUInt (timeTillMaturity)); // a = (1 - gt) int128 a = Math64x64.sub (0x10000000000000000, Math64x64.mul (g, t)); require (a > 0, "YieldMath: Too far from maturity"); // xdx = daiReserves + daiAmount uint256 xdx = uint256 (daiReserves) + uint256 (daiAmount); require (xdx < 0x100000000000000000000000000000000, "YieldMath: Too much Dai in"); uint256 sum = pow (daiReserves, uint128 (a), 0x10000000000000000) + pow (fyDaiReserves, uint128 (a), 0x10000000000000000) - pow (uint128(xdx), uint128 (a), 0x10000000000000000); require (sum < 0x100000000000000000000000000000000, "YieldMath: Insufficient fyDai reserves"); uint256 result = fyDaiReserves - pow (uint128 (sum), 0x10000000000000000, uint128 (a)); require (result < 0x100000000000000000000000000000000, "YieldMath: Rounding induced error"); result = result > 1e12 ? result - 1e12 : 0; // Substract error guard, flooring the result at zero return uint128 (result); } /** * Calculate the amount of Dai a user would get for certain amount of fyDai. * * @param daiReserves Dai reserves amount * @param fyDaiReserves fyDai reserves amount * @param fyDaiAmount fyDai amount to be traded * @param timeTillMaturity time till maturity in seconds * @param k time till maturity coefficient, multiplied by 2^64 * @param g fee coefficient, multiplied by 2^64 * @return the amount of Dai a user would get for given amount of fyDai */ function daiOutForFYDaiIn ( uint128 daiReserves, uint128 fyDaiReserves, uint128 fyDaiAmount, uint128 timeTillMaturity, int128 k, int128 g) internal pure returns (uint128) { // t = k * timeTillMaturity int128 t = Math64x64.mul (k, Math64x64.fromUInt (timeTillMaturity)); // a = (1 - gt) int128 a = Math64x64.sub (0x10000000000000000, Math64x64.mul (g, t)); require (a > 0, "YieldMath: Too far from maturity"); // ydy = fyDaiReserves + fyDaiAmount; uint256 ydy = uint256 (fyDaiReserves) + uint256 (fyDaiAmount); require (ydy < 0x100000000000000000000000000000000, "YieldMath: Too much fyDai in"); uint256 sum = pow (uint128 (daiReserves), uint128 (a), 0x10000000000000000) - pow (uint128 (ydy), uint128 (a), 0x10000000000000000) + pow (fyDaiReserves, uint128 (a), 0x10000000000000000); require (sum < 0x100000000000000000000000000000000, "YieldMath: Insufficient Dai reserves"); uint256 result = daiReserves - pow (uint128 (sum), 0x10000000000000000, uint128 (a)); require (result < 0x100000000000000000000000000000000, "YieldMath: Rounding induced error"); result = result > 1e12 ? result - 1e12 : 0; // Substract error guard, flooring the result at zero return uint128 (result); } /** * Calculate the amount of fyDai a user could sell for given amount of Dai. * * @param daiReserves Dai reserves amount * @param fyDaiReserves fyDai reserves amount * @param daiAmount Dai amount to be traded * @param timeTillMaturity time till maturity in seconds * @param k time till maturity coefficient, multiplied by 2^64 * @param g fee coefficient, multiplied by 2^64 * @return the amount of fyDai a user could sell for given amount of Dai */ function fyDaiInForDaiOut ( uint128 daiReserves, uint128 fyDaiReserves, uint128 daiAmount, uint128 timeTillMaturity, int128 k, int128 g) internal pure returns (uint128) { // t = k * timeTillMaturity int128 t = Math64x64.mul (k, Math64x64.fromUInt (timeTillMaturity)); // a = (1 - gt) int128 a = Math64x64.sub (0x10000000000000000, Math64x64.mul (g, t)); require (a > 0, "YieldMath: Too far from maturity"); // xdx = daiReserves - daiAmount uint256 xdx = uint256 (daiReserves) - uint256 (daiAmount); require (xdx < 0x100000000000000000000000000000000, "YieldMath: Too much Dai out"); uint256 sum = pow (uint128 (daiReserves), uint128 (a), 0x10000000000000000) + pow (fyDaiReserves, uint128 (a), 0x10000000000000000) - pow (uint128 (xdx), uint128 (a), 0x10000000000000000); require (sum < 0x100000000000000000000000000000000, "YieldMath: Resulting fyDai reserves too high"); uint256 result = pow (uint128 (sum), 0x10000000000000000, uint128 (a)) - fyDaiReserves; require (result < 0x100000000000000000000000000000000, "YieldMath: Rounding induced error"); result = result < type(uint128).max - 1e12 ? result + 1e12 : type(uint128).max; // Add error guard, ceiling the result at max return uint128 (result); } /** * Calculate the amount of Dai a user would have to pay for certain amount of * fyDai. * * @param daiReserves Dai reserves amount * @param fyDaiReserves fyDai reserves amount * @param fyDaiAmount fyDai amount to be traded * @param timeTillMaturity time till maturity in seconds * @param k time till maturity coefficient, multiplied by 2^64 * @param g fee coefficient, multiplied by 2^64 * @return the amount of Dai a user would have to pay for given amount of * fyDai */ function daiInForFYDaiOut ( uint128 daiReserves, uint128 fyDaiReserves, uint128 fyDaiAmount, uint128 timeTillMaturity, int128 k, int128 g) internal pure returns (uint128) { // a = (1 - g * k * timeTillMaturity) int128 a = Math64x64.sub (0x10000000000000000, Math64x64.mul (g, Math64x64.mul (k, Math64x64.fromUInt (timeTillMaturity)))); require (a > 0, "YieldMath: Too far from maturity"); // ydy = fyDaiReserves - fyDaiAmount; uint256 ydy = uint256 (fyDaiReserves) - uint256 (fyDaiAmount); require (ydy < 0x100000000000000000000000000000000, "YieldMath: Too much fyDai out"); uint256 sum = pow (daiReserves, uint128 (a), 0x10000000000000000) + pow (fyDaiReserves, uint128 (a), 0x10000000000000000) - pow (uint128 (ydy), uint128 (a), 0x10000000000000000); require (sum < 0x100000000000000000000000000000000, "YieldMath: Resulting Dai reserves too high"); uint256 result = pow (uint128 (sum), 0x10000000000000000, uint128 (a)) - daiReserves; require (result < 0x100000000000000000000000000000000, "YieldMath: Rounding induced error"); result = result < type(uint128).max - 1e12 ? result + 1e12 : type(uint128).max; // Add error guard, ceiling the result at max return uint128 (result); } /** * Raise given number x into power specified as a simple fraction y/z and then * multiply the result by the normalization factor 2^(128 * (1 - y/z)). * Revert if z is zero, or if both x and y are zeros. * * @param x number to raise into given power y/z * @param y numerator of the power to raise x into * @param z denominator of the power to raise x into * @return x raised into power y/z and then multiplied by 2^(128 * (1 - y/z)) */ function pow (uint128 x, uint128 y, uint128 z) internal pure returns (uint256) { require (z != 0); if (x == 0) { require (y != 0); return 0; } else { uint256 l = uint256 (0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF - log_2 (x)) * y / z; if (l > 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF) return 0; else return uint256 (pow_2 (uint128 (0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF - l))); } } /** * Calculate base 2 logarithm of an unsigned 128-bit integer number. Revert * in case x is zero. * * @param x number to calculate base 2 logarithm of * @return base 2 logarithm of x, multiplied by 2^121 */ function log_2 (uint128 x) internal pure returns (uint128) { require (x != 0); uint b = x; uint l = 0xFE000000000000000000000000000000; if (b < 0x10000000000000000) {l -= 0x80000000000000000000000000000000; b <<= 64;} if (b < 0x1000000000000000000000000) {l -= 0x40000000000000000000000000000000; b <<= 32;} if (b < 0x10000000000000000000000000000) {l -= 0x20000000000000000000000000000000; b <<= 16;} if (b < 0x1000000000000000000000000000000) {l -= 0x10000000000000000000000000000000; b <<= 8;} if (b < 0x10000000000000000000000000000000) {l -= 0x8000000000000000000000000000000; b <<= 4;} if (b < 0x40000000000000000000000000000000) {l -= 0x4000000000000000000000000000000; b <<= 2;} if (b < 0x80000000000000000000000000000000) {l -= 0x2000000000000000000000000000000; b <<= 1;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x1000000000000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x800000000000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x400000000000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x200000000000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x100000000000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x80000000000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x40000000000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x20000000000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x10000000000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x8000000000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x4000000000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x2000000000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x1000000000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x800000000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x400000000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x200000000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x100000000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x80000000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x40000000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x20000000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x10000000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x8000000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x4000000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x2000000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x1000000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x800000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x400000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x200000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x100000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x80000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x40000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x20000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x10000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x8000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x4000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x2000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x1000000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x800000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x400000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x200000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x100000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x80000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x40000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x20000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x10000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x8000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x4000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x2000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x1000000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x800000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x400000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x200000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x100000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x80000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x40000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x20000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x10000000000000000;} /* Precision reduced to 64 bits b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x8000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x4000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x2000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x1000000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x800000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x400000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x200000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x100000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x80000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x40000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x20000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x10000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x8000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x4000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x2000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x1000000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x800000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x400000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x200000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x100000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x80000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x40000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x20000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x10000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x8000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x4000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x2000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x1000000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x800000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x400000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x200000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x100000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x80000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x40000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x20000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x10000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x8000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x4000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x2000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x1000000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x800000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x400000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x200000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x100000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x80000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x40000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x20000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x10000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x8000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x4000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x2000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x1000;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x800;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x400;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x200;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x100;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x80;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x40;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x20;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x10;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x8;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x4;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) {b >>= 1; l |= 0x2;} b = b * b >> 127; if (b >= 0x100000000000000000000000000000000) l |= 0x1; */ return uint128 (l); } /** * Calculate 2 raised into given power. * * @param x power to raise 2 into, multiplied by 2^121 * @return 2 raised into given power */ function pow_2 (uint128 x) internal pure returns (uint128) { uint r = 0x80000000000000000000000000000000; if (x & 0x1000000000000000000000000000000 > 0) r = r * 0xb504f333f9de6484597d89b3754abe9f >> 127; if (x & 0x800000000000000000000000000000 > 0) r = r * 0x9837f0518db8a96f46ad23182e42f6f6 >> 127; if (x & 0x400000000000000000000000000000 > 0) r = r * 0x8b95c1e3ea8bd6e6fbe4628758a53c90 >> 127; if (x & 0x200000000000000000000000000000 > 0) r = r * 0x85aac367cc487b14c5c95b8c2154c1b2 >> 127; if (x & 0x100000000000000000000000000000 > 0) r = r * 0x82cd8698ac2ba1d73e2a475b46520bff >> 127; if (x & 0x80000000000000000000000000000 > 0) r = r * 0x8164d1f3bc0307737be56527bd14def4 >> 127; if (x & 0x40000000000000000000000000000 > 0) r = r * 0x80b1ed4fd999ab6c25335719b6e6fd20 >> 127; if (x & 0x20000000000000000000000000000 > 0) r = r * 0x8058d7d2d5e5f6b094d589f608ee4aa2 >> 127; if (x & 0x10000000000000000000000000000 > 0) r = r * 0x802c6436d0e04f50ff8ce94a6797b3ce >> 127; if (x & 0x8000000000000000000000000000 > 0) r = r * 0x8016302f174676283690dfe44d11d008 >> 127; if (x & 0x4000000000000000000000000000 > 0) r = r * 0x800b179c82028fd0945e54e2ae18f2f0 >> 127; if (x & 0x2000000000000000000000000000 > 0) r = r * 0x80058baf7fee3b5d1c718b38e549cb93 >> 127; if (x & 0x1000000000000000000000000000 > 0) r = r * 0x8002c5d00fdcfcb6b6566a58c048be1f >> 127; if (x & 0x800000000000000000000000000 > 0) r = r * 0x800162e61bed4a48e84c2e1a463473d9 >> 127; if (x & 0x400000000000000000000000000 > 0) r = r * 0x8000b17292f702a3aa22beacca949013 >> 127; if (x & 0x200000000000000000000000000 > 0) r = r * 0x800058b92abbae02030c5fa5256f41fe >> 127; if (x & 0x100000000000000000000000000 > 0) r = r * 0x80002c5c8dade4d71776c0f4dbea67d6 >> 127; if (x & 0x80000000000000000000000000 > 0) r = r * 0x8000162e44eaf636526be456600bdbe4 >> 127; if (x & 0x40000000000000000000000000 > 0) r = r * 0x80000b1721fa7c188307016c1cd4e8b6 >> 127; if (x & 0x20000000000000000000000000 > 0) r = r * 0x8000058b90de7e4cecfc487503488bb1 >> 127; if (x & 0x10000000000000000000000000 > 0) r = r * 0x800002c5c8678f36cbfce50a6de60b14 >> 127; if (x & 0x8000000000000000000000000 > 0) r = r * 0x80000162e431db9f80b2347b5d62e516 >> 127; if (x & 0x4000000000000000000000000 > 0) r = r * 0x800000b1721872d0c7b08cf1e0114152 >> 127; if (x & 0x2000000000000000000000000 > 0) r = r * 0x80000058b90c1aa8a5c3736cb77e8dff >> 127; if (x & 0x1000000000000000000000000 > 0) r = r * 0x8000002c5c8605a4635f2efc2362d978 >> 127; if (x & 0x800000000000000000000000 > 0) r = r * 0x800000162e4300e635cf4a109e3939bd >> 127; if (x & 0x400000000000000000000000 > 0) r = r * 0x8000000b17217ff81bef9c551590cf83 >> 127; if (x & 0x200000000000000000000000 > 0) r = r * 0x800000058b90bfdd4e39cd52c0cfa27c >> 127; if (x & 0x100000000000000000000000 > 0) r = r * 0x80000002c5c85fe6f72d669e0e76e411 >> 127; if (x & 0x80000000000000000000000 > 0) r = r * 0x8000000162e42ff18f9ad35186d0df28 >> 127; if (x & 0x40000000000000000000000 > 0) r = r * 0x80000000b17217f84cce71aa0dcfffe7 >> 127; if (x & 0x20000000000000000000000 > 0) r = r * 0x8000000058b90bfc07a77ad56ed22aaa >> 127; if (x & 0x10000000000000000000000 > 0) r = r * 0x800000002c5c85fdfc23cdead40da8d6 >> 127; if (x & 0x8000000000000000000000 > 0) r = r * 0x80000000162e42fefc25eb1571853a66 >> 127; if (x & 0x4000000000000000000000 > 0) r = r * 0x800000000b17217f7d97f692baacded5 >> 127; if (x & 0x2000000000000000000000 > 0) r = r * 0x80000000058b90bfbead3b8b5dd254d7 >> 127; if (x & 0x1000000000000000000000 > 0) r = r * 0x8000000002c5c85fdf4eedd62f084e67 >> 127; if (x & 0x800000000000000000000 > 0) r = r * 0x800000000162e42fefa58aef378bf586 >> 127; if (x & 0x400000000000000000000 > 0) r = r * 0x8000000000b17217f7d24a78a3c7ef02 >> 127; if (x & 0x200000000000000000000 > 0) r = r * 0x800000000058b90bfbe9067c93e474a6 >> 127; if (x & 0x100000000000000000000 > 0) r = r * 0x80000000002c5c85fdf47b8e5a72599f >> 127; if (x & 0x80000000000000000000 > 0) r = r * 0x8000000000162e42fefa3bdb315934a2 >> 127; if (x & 0x40000000000000000000 > 0) r = r * 0x80000000000b17217f7d1d7299b49c46 >> 127; if (x & 0x20000000000000000000 > 0) r = r * 0x8000000000058b90bfbe8e9a8d1c4ea0 >> 127; if (x & 0x10000000000000000000 > 0) r = r * 0x800000000002c5c85fdf4745969ea76f >> 127; if (x & 0x8000000000000000000 > 0) r = r * 0x80000000000162e42fefa3a0df5373bf >> 127; if (x & 0x4000000000000000000 > 0) r = r * 0x800000000000b17217f7d1cff4aac1e1 >> 127; if (x & 0x2000000000000000000 > 0) r = r * 0x80000000000058b90bfbe8e7db95a2f1 >> 127; if (x & 0x1000000000000000000 > 0) r = r * 0x8000000000002c5c85fdf473e61ae1f8 >> 127; if (x & 0x800000000000000000 > 0) r = r * 0x800000000000162e42fefa39f121751c >> 127; if (x & 0x400000000000000000 > 0) r = r * 0x8000000000000b17217f7d1cf815bb96 >> 127; if (x & 0x200000000000000000 > 0) r = r * 0x800000000000058b90bfbe8e7bec1e0d >> 127; if (x & 0x100000000000000000 > 0) r = r * 0x80000000000002c5c85fdf473dee5f17 >> 127; if (x & 0x80000000000000000 > 0) r = r * 0x8000000000000162e42fefa39ef5438f >> 127; if (x & 0x40000000000000000 > 0) r = r * 0x80000000000000b17217f7d1cf7a26c8 >> 127; if (x & 0x20000000000000000 > 0) r = r * 0x8000000000000058b90bfbe8e7bcf4a4 >> 127; if (x & 0x10000000000000000 > 0) r = r * 0x800000000000002c5c85fdf473de72a2 >> 127; /* Precision reduced to 64 bits if (x & 0x8000000000000000 > 0) r = r * 0x80000000000000162e42fefa39ef3765 >> 127; if (x & 0x4000000000000000 > 0) r = r * 0x800000000000000b17217f7d1cf79b37 >> 127; if (x & 0x2000000000000000 > 0) r = r * 0x80000000000000058b90bfbe8e7bcd7d >> 127; if (x & 0x1000000000000000 > 0) r = r * 0x8000000000000002c5c85fdf473de6b6 >> 127; if (x & 0x800000000000000 > 0) r = r * 0x800000000000000162e42fefa39ef359 >> 127; if (x & 0x400000000000000 > 0) r = r * 0x8000000000000000b17217f7d1cf79ac >> 127; if (x & 0x200000000000000 > 0) r = r * 0x800000000000000058b90bfbe8e7bcd6 >> 127; if (x & 0x100000000000000 > 0) r = r * 0x80000000000000002c5c85fdf473de6a >> 127; if (x & 0x80000000000000 > 0) r = r * 0x8000000000000000162e42fefa39ef35 >> 127; if (x & 0x40000000000000 > 0) r = r * 0x80000000000000000b17217f7d1cf79a >> 127; if (x & 0x20000000000000 > 0) r = r * 0x8000000000000000058b90bfbe8e7bcd >> 127; if (x & 0x10000000000000 > 0) r = r * 0x800000000000000002c5c85fdf473de6 >> 127; if (x & 0x8000000000000 > 0) r = r * 0x80000000000000000162e42fefa39ef3 >> 127; if (x & 0x4000000000000 > 0) r = r * 0x800000000000000000b17217f7d1cf79 >> 127; if (x & 0x2000000000000 > 0) r = r * 0x80000000000000000058b90bfbe8e7bc >> 127; if (x & 0x1000000000000 > 0) r = r * 0x8000000000000000002c5c85fdf473de >> 127; if (x & 0x800000000000 > 0) r = r * 0x800000000000000000162e42fefa39ef >> 127; if (x & 0x400000000000 > 0) r = r * 0x8000000000000000000b17217f7d1cf7 >> 127; if (x & 0x200000000000 > 0) r = r * 0x800000000000000000058b90bfbe8e7b >> 127; if (x & 0x100000000000 > 0) r = r * 0x80000000000000000002c5c85fdf473d >> 127; if (x & 0x80000000000 > 0) r = r * 0x8000000000000000000162e42fefa39e >> 127; if (x & 0x40000000000 > 0) r = r * 0x80000000000000000000b17217f7d1cf >> 127; if (x & 0x20000000000 > 0) r = r * 0x8000000000000000000058b90bfbe8e7 >> 127; if (x & 0x10000000000 > 0) r = r * 0x800000000000000000002c5c85fdf473 >> 127; if (x & 0x8000000000 > 0) r = r * 0x80000000000000000000162e42fefa39 >> 127; if (x & 0x4000000000 > 0) r = r * 0x800000000000000000000b17217f7d1c >> 127; if (x & 0x2000000000 > 0) r = r * 0x80000000000000000000058b90bfbe8e >> 127; if (x & 0x1000000000 > 0) r = r * 0x8000000000000000000002c5c85fdf47 >> 127; if (x & 0x800000000 > 0) r = r * 0x800000000000000000000162e42fefa3 >> 127; if (x & 0x400000000 > 0) r = r * 0x8000000000000000000000b17217f7d1 >> 127; if (x & 0x200000000 > 0) r = r * 0x800000000000000000000058b90bfbe8 >> 127; if (x & 0x100000000 > 0) r = r * 0x80000000000000000000002c5c85fdf4 >> 127; if (x & 0x80000000 > 0) r = r * 0x8000000000000000000000162e42fefa >> 127; if (x & 0x40000000 > 0) r = r * 0x80000000000000000000000b17217f7d >> 127; if (x & 0x20000000 > 0) r = r * 0x8000000000000000000000058b90bfbe >> 127; if (x & 0x10000000 > 0) r = r * 0x800000000000000000000002c5c85fdf >> 127; if (x & 0x8000000 > 0) r = r * 0x80000000000000000000000162e42fef >> 127; if (x & 0x4000000 > 0) r = r * 0x800000000000000000000000b17217f7 >> 127; if (x & 0x2000000 > 0) r = r * 0x80000000000000000000000058b90bfb >> 127; if (x & 0x1000000 > 0) r = r * 0x8000000000000000000000002c5c85fd >> 127; if (x & 0x800000 > 0) r = r * 0x800000000000000000000000162e42fe >> 127; if (x & 0x400000 > 0) r = r * 0x8000000000000000000000000b17217f >> 127; if (x & 0x200000 > 0) r = r * 0x800000000000000000000000058b90bf >> 127; if (x & 0x100000 > 0) r = r * 0x80000000000000000000000002c5c85f >> 127; if (x & 0x80000 > 0) r = r * 0x8000000000000000000000000162e42f >> 127; if (x & 0x40000 > 0) r = r * 0x80000000000000000000000000b17217 >> 127; if (x & 0x20000 > 0) r = r * 0x8000000000000000000000000058b90b >> 127; if (x & 0x10000 > 0) r = r * 0x800000000000000000000000002c5c85 >> 127; if (x & 0x8000 > 0) r = r * 0x80000000000000000000000000162e42 >> 127; if (x & 0x4000 > 0) r = r * 0x800000000000000000000000000b1721 >> 127; if (x & 0x2000 > 0) r = r * 0x80000000000000000000000000058b90 >> 127; if (x & 0x1000 > 0) r = r * 0x8000000000000000000000000002c5c8 >> 127; if (x & 0x800 > 0) r = r * 0x800000000000000000000000000162e4 >> 127; if (x & 0x400 > 0) r = r * 0x8000000000000000000000000000b172 >> 127; if (x & 0x200 > 0) r = r * 0x800000000000000000000000000058b9 >> 127; if (x & 0x100 > 0) r = r * 0x80000000000000000000000000002c5c >> 127; if (x & 0x80 > 0) r = r * 0x8000000000000000000000000000162e >> 127; if (x & 0x40 > 0) r = r * 0x80000000000000000000000000000b17 >> 127; if (x & 0x20 > 0) r = r * 0x8000000000000000000000000000058b >> 127; if (x & 0x10 > 0) r = r * 0x800000000000000000000000000002c5 >> 127; if (x & 0x8 > 0) r = r * 0x80000000000000000000000000000162 >> 127; if (x & 0x4 > 0) r = r * 0x800000000000000000000000000000b1 >> 127; if (x & 0x2 > 0) r = r * 0x80000000000000000000000000000058 >> 127; if (x & 0x1 > 0) r = r * 0x8000000000000000000000000000002c >> 127; */ r >>= 127 - (x >> 121); return uint128 (r); } } // File: contracts/interfaces/IDelegable.sol pragma solidity ^0.6.10; interface IDelegable { function addDelegate(address) external; function addDelegateBySignature(address, address, uint, uint8, bytes32, bytes32) external; } // File: contracts/helpers/Delegable.sol pragma solidity ^0.6.10; /// @dev Delegable enables users to delegate their account management to other users. /// Delegable implements addDelegateBySignature, to add delegates using a signature instead of a separate transaction. contract Delegable is IDelegable { event Delegate(address indexed user, address indexed delegate, bool enabled); // keccak256("Signature(address user,address delegate,uint256 nonce,uint256 deadline)"); bytes32 public immutable SIGNATURE_TYPEHASH = 0x0d077601844dd17f704bafff948229d27f33b57445915754dfe3d095fda2beb7; bytes32 public immutable DELEGABLE_DOMAIN; mapping(address => uint) public signatureCount; mapping(address => mapping(address => bool)) public delegated; constructor () public { uint256 chainId; assembly { chainId := chainid() } DELEGABLE_DOMAIN = keccak256( abi.encode( keccak256('EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)'), keccak256(bytes('Yield')), keccak256(bytes('1')), chainId, address(this) ) ); } /// @dev Require that msg.sender is the account holder or a delegate modifier onlyHolderOrDelegate(address holder, string memory errorMessage) { require( msg.sender == holder || delegated[holder][msg.sender], errorMessage ); _; } /// @dev Enable a delegate to act on the behalf of caller function addDelegate(address delegate) public override { _addDelegate(msg.sender, delegate); } /// @dev Stop a delegate from acting on the behalf of caller function revokeDelegate(address delegate) public { _revokeDelegate(msg.sender, delegate); } /// @dev Add a delegate through an encoded signature function addDelegateBySignature(address user, address delegate, uint deadline, uint8 v, bytes32 r, bytes32 s) public override { require(deadline >= block.timestamp, 'Delegable: Signature expired'); bytes32 hashStruct = keccak256( abi.encode( SIGNATURE_TYPEHASH, user, delegate, signatureCount[user]++, deadline ) ); bytes32 digest = keccak256( abi.encodePacked( '\x19\x01', DELEGABLE_DOMAIN, hashStruct ) ); address signer = ecrecover(digest, v, r, s); require( signer != address(0) && signer == user, 'Delegable: Invalid signature' ); _addDelegate(user, delegate); } /// @dev Enable a delegate to act on the behalf of an user function _addDelegate(address user, address delegate) internal { require(!delegated[user][delegate], "Delegable: Already delegated"); delegated[user][delegate] = true; emit Delegate(user, delegate, true); } /// @dev Stop a delegate from acting on the behalf of an user function _revokeDelegate(address user, address delegate) internal { require(delegated[user][delegate], "Delegable: Already undelegated"); delegated[user][delegate] = false; emit Delegate(user, delegate, false); } } // File: contracts/interfaces/IERC2612.sol // Code adapted from https://github.com/OpenZeppelin/openzeppelin-contracts/pull/2237/ pragma solidity ^0.6.0; /** * @dev Interface of the ERC2612 standard as defined in the EIP. * * Adds the {permit} method, which can be used to change one's * {IERC20-allowance} without having to send a transaction, by signing a * message. This allows users to spend tokens without having to hold Ether. * * See https://eips.ethereum.org/EIPS/eip-2612. */ interface IERC2612 { /** * @dev Sets `amount` as the allowance of `spender` over `owner`'s tokens, * given `owner`'s signed approval. * * IMPORTANT: The same issues {IERC20-approve} has related to transaction * ordering also apply here. * * Emits an {Approval} event. * * Requirements: * * - `owner` cannot be the zero address. * - `spender` cannot be the zero address. * - `deadline` must be a timestamp in the future. * - `v`, `r` and `s` must be a valid `secp256k1` signature from `owner` * over the EIP712-formatted function arguments. * - the signature must use ``owner``'s current nonce (see {nonces}). * * For more information on the signature format, see the * https://eips.ethereum.org/EIPS/eip-2612#specification[relevant EIP * section]. */ function permit(address owner, address spender, uint256 amount, uint256 deadline, uint8 v, bytes32 r, bytes32 s) external; /** * @dev Returns the current ERC2612 nonce for `owner`. This value must be * included whenever a signature is generated for {permit}. * * Every successful call to {permit} increases ``owner``'s nonce by one. This * prevents a signature from being used multiple times. */ function nonces(address owner) external view returns (uint256); } // File: contracts/helpers/ERC20Permit.sol // Adapted from https://github.com/OpenZeppelin/openzeppelin-contracts/blob/53516bc555a454862470e7860a9b5254db4d00f5/contracts/token/ERC20/ERC20Permit.sol pragma solidity ^0.6.0; /** * @dev Extension of {ERC20} that allows token holders to use their tokens * without sending any transactions by setting {IERC20-allowance} with a * signature using the {permit} method, and then spend them via * {IERC20-transferFrom}. * * The {permit} signature mechanism conforms to the {IERC2612} interface. */ abstract contract ERC20Permit is ERC20, IERC2612 { mapping (address => uint256) public override nonces; bytes32 public immutable PERMIT_TYPEHASH = keccak256("Permit(address owner,address spender,uint256 value,uint256 nonce,uint256 deadline)"); bytes32 public immutable DOMAIN_SEPARATOR; constructor(string memory name_, string memory symbol_) internal ERC20(name_, symbol_) { uint256 chainId; assembly { chainId := chainid() } DOMAIN_SEPARATOR = keccak256( abi.encode( keccak256("EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)"), keccak256(bytes(name_)), keccak256(bytes("1")), chainId, address(this) ) ); } /** * @dev See {IERC2612-permit}. * * In cases where the free option is not a concern, deadline can simply be * set to uint(-1), so it should be seen as an optional parameter */ function permit(address owner, address spender, uint256 amount, uint256 deadline, uint8 v, bytes32 r, bytes32 s) public virtual override { require(deadline >= block.timestamp, "ERC20Permit: expired deadline"); bytes32 hashStruct = keccak256( abi.encode( PERMIT_TYPEHASH, owner, spender, amount, nonces[owner]++, deadline ) ); bytes32 hash = keccak256( abi.encodePacked( '\x19\x01', DOMAIN_SEPARATOR, hashStruct ) ); address signer = ecrecover(hash, v, r, s); require( signer != address(0) && signer == owner, "ERC20Permit: invalid signature" ); _approve(owner, spender, amount); } } // File: contracts/interfaces/IPot.sol pragma solidity ^0.6.10; /// @dev interface for the pot contract from MakerDao /// Taken from https://github.com/makerdao/developerguides/blob/master/dai/dsr-integration-guide/dsr.sol interface IPot { function chi() external view returns (uint256); function pie(address) external view returns (uint256); // Not a function, but a public variable. function rho() external returns (uint256); function drip() external returns (uint256); function join(uint256) external; function exit(uint256) external; } // File: contracts/interfaces/IFYDai.sol pragma solidity ^0.6.10; interface IFYDai is IERC20, IERC2612 { function isMature() external view returns(bool); function maturity() external view returns(uint); function chi0() external view returns(uint); function rate0() external view returns(uint); function chiGrowth() external view returns(uint); function rateGrowth() external view returns(uint); function mature() external; function unlocked() external view returns (uint); function mint(address, uint) external; function burn(address, uint) external; function flashMint(uint, bytes calldata) external; function redeem(address, address, uint256) external returns (uint256); // function transfer(address, uint) external returns (bool); // function transferFrom(address, address, uint) external returns (bool); // function approve(address, uint) external returns (bool); } // File: contracts/interfaces/IPool.sol pragma solidity ^0.6.10; interface IPool is IDelegable, IERC20, IERC2612 { function dai() external view returns(IERC20); function fyDai() external view returns(IFYDai); function getDaiReserves() external view returns(uint128); function getFYDaiReserves() external view returns(uint128); function sellDai(address from, address to, uint128 daiIn) external returns(uint128); function buyDai(address from, address to, uint128 daiOut) external returns(uint128); function sellFYDai(address from, address to, uint128 fyDaiIn) external returns(uint128); function buyFYDai(address from, address to, uint128 fyDaiOut) external returns(uint128); function sellDaiPreview(uint128 daiIn) external view returns(uint128); function buyDaiPreview(uint128 daiOut) external view returns(uint128); function sellFYDaiPreview(uint128 fyDaiIn) external view returns(uint128); function buyFYDaiPreview(uint128 fyDaiOut) external view returns(uint128); function mint(address from, address to, uint256 daiOffered) external returns (uint256); function burn(address from, address to, uint256 tokensBurned) external returns (uint256, uint256); } // File: contracts/pool/Pool.sol pragma solidity ^0.6.10; /// @dev The Pool contract exchanges Dai for fyDai at a price defined by a specific formula. contract Pool is IPool, Delegable(), ERC20Permit { event Trade(uint256 maturity, address indexed from, address indexed to, int256 daiTokens, int256 fyDaiTokens); event Liquidity(uint256 maturity, address indexed from, address indexed to, int256 daiTokens, int256 fyDaiTokens, int256 poolTokens); int128 constant public k = int128(uint256((1 << 64)) / 126144000); // 1 / Seconds in 4 years, in 64.64 int128 constant public g1 = int128(uint256((950 << 64)) / 1000); // To be used when selling Dai to the pool. All constants are `ufixed`, to divide them they must be converted to uint256 int128 constant public g2 = int128(uint256((1000 << 64)) / 950); // To be used when selling fyDai to the pool. All constants are `ufixed`, to divide them they must be converted to uint256 uint128 immutable public maturity; IERC20 public override dai; IFYDai public override fyDai; constructor(address dai_, address fyDai_, string memory name_, string memory symbol_) public ERC20Permit(name_, symbol_) { dai = IERC20(dai_); fyDai = IFYDai(fyDai_); maturity = toUint128(fyDai.maturity()); } /// @dev Trading can only be done before maturity modifier beforeMaturity() { require( now < maturity, "Pool: Too late" ); _; } /// @dev Overflow-protected addition, from OpenZeppelin function add(uint128 a, uint128 b) internal pure returns (uint128) { uint128 c = a + b; require(c >= a, "Pool: Dai reserves too high"); return c; } /// @dev Overflow-protected substraction, from OpenZeppelin function sub(uint128 a, uint128 b) internal pure returns (uint128) { require(b <= a, "Pool: fyDai reserves too low"); uint128 c = a - b; return c; } /// @dev Safe casting from uint256 to uint128 function toUint128(uint256 x) internal pure returns(uint128) { require( x <= type(uint128).max, "Pool: Cast overflow" ); return uint128(x); } /// @dev Safe casting from uint256 to int256 function toInt256(uint256 x) internal pure returns(int256) { require( x <= uint256(type(int256).max), "Pool: Cast overflow" ); return int256(x); } /// @dev Mint initial liquidity tokens. /// The liquidity provider needs to have called `dai.approve` /// @param daiIn The initial Dai liquidity to provide. function init(uint256 daiIn) internal beforeMaturity returns (uint256) { require( totalSupply() == 0, "Pool: Already initialized" ); // no fyDai transferred, because initial fyDai deposit is entirely virtual dai.transferFrom(msg.sender, address(this), daiIn); _mint(msg.sender, daiIn); emit Liquidity(maturity, msg.sender, msg.sender, -toInt256(daiIn), 0, toInt256(daiIn)); return daiIn; } /// @dev Mint liquidity tokens in exchange for adding dai and fyDai /// The liquidity provider needs to have called `dai.approve` and `fyDai.approve`. /// @param from Wallet providing the dai and fyDai. Must have approved the operator with `pool.addDelegate(operator)`. /// @param to Wallet receiving the minted liquidity tokens. /// @param daiOffered Amount of `dai` being invested, an appropriate amount of `fyDai` to be invested alongside will be calculated and taken by this function from the caller. /// @return The amount of liquidity tokens minted. function mint(address from, address to, uint256 daiOffered) external override onlyHolderOrDelegate(from, "Pool: Only Holder Or Delegate") returns (uint256) { uint256 supply = totalSupply(); if (supply == 0) return init(daiOffered); uint256 daiReserves = dai.balanceOf(address(this)); // use the actual reserves rather than the virtual reserves uint256 fyDaiReserves = fyDai.balanceOf(address(this)); uint256 tokensMinted = supply.mul(daiOffered).div(daiReserves); uint256 fyDaiRequired = fyDaiReserves.mul(tokensMinted).div(supply); require(daiReserves.add(daiOffered) <= type(uint128).max); // fyDaiReserves can't go over type(uint128).max require(supply.add(fyDaiReserves.add(fyDaiRequired)) <= type(uint128).max); // fyDaiReserves can't go over type(uint128).max require(dai.transferFrom(from, address(this), daiOffered)); require(fyDai.transferFrom(from, address(this), fyDaiRequired)); _mint(to, tokensMinted); emit Liquidity(maturity, from, to, -toInt256(daiOffered), -toInt256(fyDaiRequired), toInt256(tokensMinted)); return tokensMinted; } /// @dev Burn liquidity tokens in exchange for dai and fyDai. /// The liquidity provider needs to have called `pool.approve`. /// @param from Wallet providing the liquidity tokens. Must have approved the operator with `pool.addDelegate(operator)`. /// @param to Wallet receiving the dai and fyDai. /// @param tokensBurned Amount of liquidity tokens being burned. /// @return The amount of reserve tokens returned (daiTokens, fyDaiTokens). function burn(address from, address to, uint256 tokensBurned) external override onlyHolderOrDelegate(from, "Pool: Only Holder Or Delegate") returns (uint256, uint256) { uint256 supply = totalSupply(); uint256 daiReserves = dai.balanceOf(address(this)); // use the actual reserves rather than the virtual reserves uint256 daiReturned; uint256 fyDaiReturned; { // avoiding stack too deep uint256 fyDaiReserves = fyDai.balanceOf(address(this)); daiReturned = tokensBurned.mul(daiReserves).div(supply); fyDaiReturned = tokensBurned.mul(fyDaiReserves).div(supply); } _burn(from, tokensBurned); dai.transfer(to, daiReturned); fyDai.transfer(to, fyDaiReturned); emit Liquidity(maturity, from, to, toInt256(daiReturned), toInt256(fyDaiReturned), -toInt256(tokensBurned)); return (daiReturned, fyDaiReturned); } /// @dev Sell Dai for fyDai /// The trader needs to have called `dai.approve` /// @param from Wallet providing the dai being sold. Must have approved the operator with `pool.addDelegate(operator)`. /// @param to Wallet receiving the fyDai being bought /// @param daiIn Amount of dai being sold that will be taken from the user's wallet /// @return Amount of fyDai that will be deposited on `to` wallet function sellDai(address from, address to, uint128 daiIn) external override onlyHolderOrDelegate(from, "Pool: Only Holder Or Delegate") returns(uint128) { uint128 fyDaiOut = sellDaiPreview(daiIn); dai.transferFrom(from, address(this), daiIn); fyDai.transfer(to, fyDaiOut); emit Trade(maturity, from, to, -toInt256(daiIn), toInt256(fyDaiOut)); return fyDaiOut; } /// @dev Returns how much fyDai would be obtained by selling `daiIn` dai /// @param daiIn Amount of dai hypothetically sold. /// @return Amount of fyDai hypothetically bought. function sellDaiPreview(uint128 daiIn) public view override beforeMaturity returns(uint128) { uint128 daiReserves = getDaiReserves(); uint128 fyDaiReserves = getFYDaiReserves(); uint128 fyDaiOut = YieldMath.fyDaiOutForDaiIn( daiReserves, fyDaiReserves, daiIn, toUint128(maturity - now), // This can't be called after maturity k, g1 ); require( sub(fyDaiReserves, fyDaiOut) >= add(daiReserves, daiIn), "Pool: fyDai reserves too low" ); return fyDaiOut; } /// @dev Buy Dai for fyDai /// The trader needs to have called `fyDai.approve` /// @param from Wallet providing the fyDai being sold. Must have approved the operator with `pool.addDelegate(operator)`. /// @param to Wallet receiving the dai being bought /// @param daiOut Amount of dai being bought that will be deposited in `to` wallet /// @return Amount of fyDai that will be taken from `from` wallet function buyDai(address from, address to, uint128 daiOut) external override onlyHolderOrDelegate(from, "Pool: Only Holder Or Delegate") returns(uint128) { uint128 fyDaiIn = buyDaiPreview(daiOut); fyDai.transferFrom(from, address(this), fyDaiIn); dai.transfer(to, daiOut); emit Trade(maturity, from, to, toInt256(daiOut), -toInt256(fyDaiIn)); return fyDaiIn; } /// @dev Returns how much fyDai would be required to buy `daiOut` dai. /// @param daiOut Amount of dai hypothetically desired. /// @return Amount of fyDai hypothetically required. function buyDaiPreview(uint128 daiOut) public view override beforeMaturity returns(uint128) { return YieldMath.fyDaiInForDaiOut( getDaiReserves(), getFYDaiReserves(), daiOut, toUint128(maturity - now), // This can't be called after maturity k, g2 ); } /// @dev Sell fyDai for Dai /// The trader needs to have called `fyDai.approve` /// @param from Wallet providing the fyDai being sold. Must have approved the operator with `pool.addDelegate(operator)`. /// @param to Wallet receiving the dai being bought /// @param fyDaiIn Amount of fyDai being sold that will be taken from the user's wallet /// @return Amount of dai that will be deposited on `to` wallet function sellFYDai(address from, address to, uint128 fyDaiIn) external override onlyHolderOrDelegate(from, "Pool: Only Holder Or Delegate") returns(uint128) { uint128 daiOut = sellFYDaiPreview(fyDaiIn); fyDai.transferFrom(from, address(this), fyDaiIn); dai.transfer(to, daiOut); emit Trade(maturity, from, to, toInt256(daiOut), -toInt256(fyDaiIn)); return daiOut; } /// @dev Returns how much dai would be obtained by selling `fyDaiIn` fyDai. /// @param fyDaiIn Amount of fyDai hypothetically sold. /// @return Amount of Dai hypothetically bought. function sellFYDaiPreview(uint128 fyDaiIn) public view override beforeMaturity returns(uint128) { return YieldMath.daiOutForFYDaiIn( getDaiReserves(), getFYDaiReserves(), fyDaiIn, toUint128(maturity - now), // This can't be called after maturity k, g2 ); } /// @dev Buy fyDai for dai /// The trader needs to have called `dai.approve` /// @param from Wallet providing the dai being sold. Must have approved the operator with `pool.addDelegate(operator)`. /// @param to Wallet receiving the fyDai being bought /// @param fyDaiOut Amount of fyDai being bought that will be deposited in `to` wallet /// @return Amount of dai that will be taken from `from` wallet function buyFYDai(address from, address to, uint128 fyDaiOut) external override onlyHolderOrDelegate(from, "Pool: Only Holder Or Delegate") returns(uint128) { uint128 daiIn = buyFYDaiPreview(fyDaiOut); dai.transferFrom(from, address(this), daiIn); fyDai.transfer(to, fyDaiOut); emit Trade(maturity, from, to, -toInt256(daiIn), toInt256(fyDaiOut)); return daiIn; } /// @dev Returns how much dai would be required to buy `fyDaiOut` fyDai. /// @param fyDaiOut Amount of fyDai hypothetically desired. /// @return Amount of Dai hypothetically required. function buyFYDaiPreview(uint128 fyDaiOut) public view override beforeMaturity returns(uint128) { uint128 daiReserves = getDaiReserves(); uint128 fyDaiReserves = getFYDaiReserves(); uint128 daiIn = YieldMath.daiInForFYDaiOut( daiReserves, fyDaiReserves, fyDaiOut, toUint128(maturity - now), // This can't be called after maturity k, g1 ); require( sub(fyDaiReserves, fyDaiOut) >= add(daiReserves, daiIn), "Pool: fyDai reserves too low" ); return daiIn; } /// @dev Returns the "virtual" fyDai reserves function getFYDaiReserves() public view override returns(uint128) { return toUint128(fyDai.balanceOf(address(this)).add(totalSupply())); } /// @dev Returns the Dai reserves function getDaiReserves() public view override returns(uint128) { return toUint128(dai.balanceOf(address(this))); } }
Contract Security Audit
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[{"inputs":[{"internalType":"address","name":"dai_","type":"address"},{"internalType":"address","name":"fyDai_","type":"address"},{"internalType":"string","name":"name_","type":"string"},{"internalType":"string","name":"symbol_","type":"string"}],"stateMutability":"nonpayable","type":"constructor"},{"anonymous":false,"inputs":[{"indexed":true,"internalType":"address","name":"owner","type":"address"},{"indexed":true,"internalType":"address","name":"spender","type":"address"},{"indexed":false,"internalType":"uint256","name":"value","type":"uint256"}],"name":"Approval","type":"event"},{"anonymous":false,"inputs":[{"indexed":true,"internalType":"address","name":"user","type":"address"},{"indexed":true,"internalType":"address","name":"delegate","type":"address"},{"indexed":false,"internalType":"bool","name":"enabled","type":"bool"}],"name":"Delegate","type":"event"},{"anonymous":false,"inputs":[{"indexed":false,"internalType":"uint256","name":"maturity","type":"uint256"},{"indexed":true,"internalType":"address","name":"from","type":"address"},{"indexed":true,"internalType":"address","name":"to","type":"address"},{"indexed":false,"internalType":"int256","name":"daiTokens","type":"int256"},{"indexed":false,"internalType":"int256","name":"fyDaiTokens","type":"int256"},{"indexed":false,"internalType":"int256","name":"poolTokens","type":"int256"}],"name":"Liquidity","type":"event"},{"anonymous":false,"inputs":[{"indexed":false,"internalType":"uint256","name":"maturity","type":"uint256"},{"indexed":true,"internalType":"address","name":"from","type":"address"},{"indexed":true,"internalType":"address","name":"to","type":"address"},{"indexed":false,"internalType":"int256","name":"daiTokens","type":"int256"},{"indexed":false,"internalType":"int256","name":"fyDaiTokens","type":"int256"}],"name":"Trade","type":"event"},{"anonymous":false,"inputs":[{"indexed":true,"internalType":"address","name":"from","type":"address"},{"indexed":true,"internalType":"address","name":"to","type":"address"},{"indexed":false,"internalType":"uint256","name":"value","type":"uint256"}],"name":"Transfer","type":"event"},{"inputs":[],"name":"DELEGABLE_DOMAIN","outputs":[{"internalType":"bytes32","name":"","type":"bytes32"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"DOMAIN_SEPARATOR","outputs":[{"internalType":"bytes32","name":"","type":"bytes32"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"PERMIT_TYPEHASH","outputs":[{"internalType":"bytes32","name":"","type":"bytes32"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"SIGNATURE_TYPEHASH","outputs":[{"internalType":"bytes32","name":"","type":"bytes32"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"delegate","type":"address"}],"name":"addDelegate","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"address","name":"user","type":"address"},{"internalType":"address","name":"delegate","type":"address"},{"internalType":"uint256","name":"deadline","type":"uint256"},{"internalType":"uint8","name":"v","type":"uint8"},{"internalType":"bytes32","name":"r","type":"bytes32"},{"internalType":"bytes32","name":"s","type":"bytes32"}],"name":"addDelegateBySignature","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"address","name":"owner","type":"address"},{"internalType":"address","name":"spender","type":"address"}],"name":"allowance","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"spender","type":"address"},{"internalType":"uint256","name":"amount","type":"uint256"}],"name":"approve","outputs":[{"internalType":"bool","name":"","type":"bool"}],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"address","name":"account","type":"address"}],"name":"balanceOf","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"from","type":"address"},{"internalType":"address","name":"to","type":"address"},{"internalType":"uint256","name":"tokensBurned","type":"uint256"}],"name":"burn","outputs":[{"internalType":"uint256","name":"","type":"uint256"},{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"address","name":"from","type":"address"},{"internalType":"address","name":"to","type":"address"},{"internalType":"uint128","name":"daiOut","type":"uint128"}],"name":"buyDai","outputs":[{"internalType":"uint128","name":"","type":"uint128"}],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"uint128","name":"daiOut","type":"uint128"}],"name":"buyDaiPreview","outputs":[{"internalType":"uint128","name":"","type":"uint128"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"from","type":"address"},{"internalType":"address","name":"to","type":"address"},{"internalType":"uint128","name":"fyDaiOut","type":"uint128"}],"name":"buyFYDai","outputs":[{"internalType":"uint128","name":"","type":"uint128"}],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"uint128","name":"fyDaiOut","type":"uint128"}],"name":"buyFYDaiPreview","outputs":[{"internalType":"uint128","name":"","type":"uint128"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"dai","outputs":[{"internalType":"contract IERC20","name":"","type":"address"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"decimals","outputs":[{"internalType":"uint8","name":"","type":"uint8"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"spender","type":"address"},{"internalType":"uint256","name":"subtractedValue","type":"uint256"}],"name":"decreaseAllowance","outputs":[{"internalType":"bool","name":"","type":"bool"}],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"address","name":"","type":"address"},{"internalType":"address","name":"","type":"address"}],"name":"delegated","outputs":[{"internalType":"bool","name":"","type":"bool"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"fyDai","outputs":[{"internalType":"contract IFYDai","name":"","type":"address"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"g1","outputs":[{"internalType":"int128","name":"","type":"int128"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"g2","outputs":[{"internalType":"int128","name":"","type":"int128"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"getDaiReserves","outputs":[{"internalType":"uint128","name":"","type":"uint128"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"getFYDaiReserves","outputs":[{"internalType":"uint128","name":"","type":"uint128"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"spender","type":"address"},{"internalType":"uint256","name":"addedValue","type":"uint256"}],"name":"increaseAllowance","outputs":[{"internalType":"bool","name":"","type":"bool"}],"stateMutability":"nonpayable","type":"function"},{"inputs":[],"name":"k","outputs":[{"internalType":"int128","name":"","type":"int128"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"maturity","outputs":[{"internalType":"uint128","name":"","type":"uint128"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"from","type":"address"},{"internalType":"address","name":"to","type":"address"},{"internalType":"uint256","name":"daiOffered","type":"uint256"}],"name":"mint","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"nonpayable","type":"function"},{"inputs":[],"name":"name","outputs":[{"internalType":"string","name":"","type":"string"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"","type":"address"}],"name":"nonces","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"owner","type":"address"},{"internalType":"address","name":"spender","type":"address"},{"internalType":"uint256","name":"amount","type":"uint256"},{"internalType":"uint256","name":"deadline","type":"uint256"},{"internalType":"uint8","name":"v","type":"uint8"},{"internalType":"bytes32","name":"r","type":"bytes32"},{"internalType":"bytes32","name":"s","type":"bytes32"}],"name":"permit","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"address","name":"delegate","type":"address"}],"name":"revokeDelegate","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"address","name":"from","type":"address"},{"internalType":"address","name":"to","type":"address"},{"internalType":"uint128","name":"daiIn","type":"uint128"}],"name":"sellDai","outputs":[{"internalType":"uint128","name":"","type":"uint128"}],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"uint128","name":"daiIn","type":"uint128"}],"name":"sellDaiPreview","outputs":[{"internalType":"uint128","name":"","type":"uint128"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"from","type":"address"},{"internalType":"address","name":"to","type":"address"},{"internalType":"uint128","name":"fyDaiIn","type":"uint128"}],"name":"sellFYDai","outputs":[{"internalType":"uint128","name":"","type":"uint128"}],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"uint128","name":"fyDaiIn","type":"uint128"}],"name":"sellFYDaiPreview","outputs":[{"internalType":"uint128","name":"","type":"uint128"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"","type":"address"}],"name":"signatureCount","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"symbol","outputs":[{"internalType":"string","name":"","type":"string"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"totalSupply","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"recipient","type":"address"},{"internalType":"uint256","name":"amount","type":"uint256"}],"name":"transfer","outputs":[{"internalType":"bool","name":"","type":"bool"}],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"address","name":"sender","type":"address"},{"internalType":"address","name":"recipient","type":"address"},{"internalType":"uint256","name":"amount","type":"uint256"}],"name":"transferFrom","outputs":[{"internalType":"bool","name":"","type":"bool"}],"stateMutability":"nonpayable","type":"function"}]
Contract Creation Code
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Constructor Arguments (ABI-Encoded and is the last bytes of the Contract Creation Code above)
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
-----Decoded View---------------
Arg [0] : dai_ (address): 0x6B175474E89094C44Da98b954EedeAC495271d0F
Arg [1] : fyDai_ (address): 0x92c25C17C0C908E52b16627F353F1004543f8A32
Arg [2] : name_ (string): Yield Dai - 2020-10-31-Pool
Arg [3] : symbol_ (string): fyDaiLP20Oct
-----Encoded View---------------
8 Constructor Arguments found :
Arg [0] : 0000000000000000000000006b175474e89094c44da98b954eedeac495271d0f
Arg [1] : 00000000000000000000000092c25c17c0c908e52b16627f353f1004543f8a32
Arg [2] : 0000000000000000000000000000000000000000000000000000000000000080
Arg [3] : 00000000000000000000000000000000000000000000000000000000000000c0
Arg [4] : 000000000000000000000000000000000000000000000000000000000000001b
Arg [5] : 5969656c6420446169202d20323032302d31302d33312d506f6f6c0000000000
Arg [6] : 000000000000000000000000000000000000000000000000000000000000000c
Arg [7] : 66794461694c5032304f63740000000000000000000000000000000000000000
Deployed Bytecode Sourcemap
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Swarm Source
ipfs://dfcf38324d56249e8a26c32edabb5f6f86fc1ce3ab9e6844ae333018550aedef
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