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rayeaster/BptPricing.sol

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Balancer Pool Token pricing
Raw
BptPricing.sol
pragma solidity 0.8.10;
pragma experimental ABIEncoderV2;
/**
* @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;
}
}
/*
* @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) {
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;
}
}
/**
* @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);
}
/**
* @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);
}
}
}
}
/**
* @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 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 { }
}
/**
* @title SafeERC20
* @dev Wrappers around ERC20 operations that throw on failure (when the token
* contract returns false). Tokens that return no value (and instead revert or
* throw on failure) are also supported, non-reverting calls are assumed to be
* successful.
* To use this library you can add a `using SafeERC20 for IERC20;` statement to your contract,
* which allows you to call the safe operations as `token.safeTransfer(...)`, etc.
*/
library SafeERC20 {
using SafeMath for uint256;
using Address for address;
function safeTransfer(IERC20 token, address to, uint256 value) internal {
_callOptionalReturn(token, abi.encodeWithSelector(token.transfer.selector, to, value));
}
function safeTransferFrom(IERC20 token, address from, address to, uint256 value) internal {
_callOptionalReturn(token, abi.encodeWithSelector(token.transferFrom.selector, from, to, value));
}
/**
* @dev Deprecated. This function has issues similar to the ones found in
* {IERC20-approve}, and its usage is discouraged.
*
* Whenever possible, use {safeIncreaseAllowance} and
* {safeDecreaseAllowance} instead.
*/
function safeApprove(IERC20 token, address spender, uint256 value) internal {
// safeApprove should only be called when setting an initial allowance,
// or when resetting it to zero. To increase and decrease it, use
// 'safeIncreaseAllowance' and 'safeDecreaseAllowance'
// solhint-disable-next-line max-line-length
require((value == 0) || (token.allowance(address(this), spender) == 0),
"SafeERC20: approve from non-zero to non-zero allowance"
);
_callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, value));
}
function safeIncreaseAllowance(IERC20 token, address spender, uint256 value) internal {
uint256 newAllowance = token.allowance(address(this), spender).add(value);
_callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, newAllowance));
}
function safeDecreaseAllowance(IERC20 token, address spender, uint256 value) internal {
uint256 newAllowance = token.allowance(address(this), spender).sub(value, "SafeERC20: decreased allowance below zero");
_callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, newAllowance));
}
/**
* @dev Imitates a Solidity high-level call (i.e. a regular function call to a contract), relaxing the requirement
* on the return value: the return value is optional (but if data is returned, it must not be false).
* @param token The token targeted by the call.
* @param data The call data (encoded using abi.encode or one of its variants).
*/
function _callOptionalReturn(IERC20 token, bytes memory data) private {
// We need to perform a low level call here, to bypass Solidity's return data size checking mechanism, since
// we're implementing it ourselves. We use {Address.functionCall} to perform this call, which verifies that
// the target address contains contract code and also asserts for success in the low-level call.
bytes memory returndata = address(token).functionCall(data, "SafeERC20: low-level call failed");
if (returndata.length > 0) { // Return data is optional
// solhint-disable-next-line max-line-length
require(abi.decode(returndata, (bool)), "SafeERC20: ERC20 operation did not succeed");
}
}
}
/**
* @dev Reverts if `condition` is false, with a revert reason containing `errorCode`. Only codes up to 999 are
* supported.
*/
function _require(bool condition, uint256 errorCode) pure {
if (!condition) _revert(errorCode);
}
/**
* @dev Reverts with a revert reason containing `errorCode`. Only codes up to 999 are supported.
*/
function _revert(uint256 errorCode) pure {
// We're going to dynamically create a revert string based on the error code, with the following format:
// 'BAL#{errorCode}'
// where the code is left-padded with zeroes to three digits (so they range from 000 to 999).
//
// We don't have revert strings embedded in the contract to save bytecode size: it takes much less space to store a
// number (8 to 16 bits) than the individual string characters.
//
// The dynamic string creation algorithm that follows could be implemented in Solidity, but assembly allows for a
// much denser implementation, again saving bytecode size. Given this function unconditionally reverts, this is a
// safe place to rely on it without worrying about how its usage might affect e.g. memory contents.
assembly {
// First, we need to compute the ASCII representation of the error code. We assume that it is in the 0-999
// range, so we only need to convert three digits. To convert the digits to ASCII, we add 0x30, the value for
// the '0' character.
let units := add(mod(errorCode, 10), 0x30)
errorCode := div(errorCode, 10)
let tenths := add(mod(errorCode, 10), 0x30)
errorCode := div(errorCode, 10)
let hundreds := add(mod(errorCode, 10), 0x30)
// With the individual characters, we can now construct the full string. The "BAL#" part is a known constant
// (0x42414c23): we simply shift this by 24 (to provide space for the 3 bytes of the error code), and add the
// characters to it, each shifted by a multiple of 8.
// The revert reason is then shifted left by 200 bits (256 minus the length of the string, 7 characters * 8 bits
// per character = 56) to locate it in the most significant part of the 256 slot (the beginning of a byte
// array).
let revertReason := shl(200, add(0x42414c23000000, add(add(units, shl(8, tenths)), shl(16, hundreds))))
// We can now encode the reason in memory, which can be safely overwritten as we're about to revert. The encoded
// message will have the following layout:
// [ revert reason identifier ] [ string location offset ] [ string length ] [ string contents ]
// The Solidity revert reason identifier is 0x08c739a0, the function selector of the Error(string) function. We
// also write zeroes to the next 28 bytes of memory, but those are about to be overwritten.
mstore(0x0, 0x08c379a000000000000000000000000000000000000000000000000000000000)
// Next is the offset to the location of the string, which will be placed immediately after (20 bytes away).
mstore(0x04, 0x0000000000000000000000000000000000000000000000000000000000000020)
// The string length is fixed: 7 characters.
mstore(0x24, 7)
// Finally, the string itself is stored.
mstore(0x44, revertReason)
// Even if the string is only 7 bytes long, we need to return a full 32 byte slot containing it. The length of
// the encoded message is therefore 4 + 32 + 32 + 32 = 100.
revert(0, 100)
}
}
library Errors {
// Math
uint256 internal constant ADD_OVERFLOW = 0;
uint256 internal constant SUB_OVERFLOW = 1;
uint256 internal constant SUB_UNDERFLOW = 2;
uint256 internal constant MUL_OVERFLOW = 3;
uint256 internal constant ZERO_DIVISION = 4;
uint256 internal constant DIV_INTERNAL = 5;
uint256 internal constant X_OUT_OF_BOUNDS = 6;
uint256 internal constant Y_OUT_OF_BOUNDS = 7;
uint256 internal constant PRODUCT_OUT_OF_BOUNDS = 8;
uint256 internal constant INVALID_EXPONENT = 9;
// Input
uint256 internal constant OUT_OF_BOUNDS = 100;
uint256 internal constant UNSORTED_ARRAY = 101;
uint256 internal constant UNSORTED_TOKENS = 102;
uint256 internal constant INPUT_LENGTH_MISMATCH = 103;
uint256 internal constant ZERO_TOKEN = 104;
// Shared pools
uint256 internal constant MIN_TOKENS = 200;
uint256 internal constant MAX_TOKENS = 201;
uint256 internal constant MAX_SWAP_FEE_PERCENTAGE = 202;
uint256 internal constant MIN_SWAP_FEE_PERCENTAGE = 203;
uint256 internal constant MINIMUM_BPT = 204;
uint256 internal constant CALLER_NOT_VAULT = 205;
uint256 internal constant UNINITIALIZED = 206;
uint256 internal constant BPT_IN_MAX_AMOUNT = 207;
uint256 internal constant BPT_OUT_MIN_AMOUNT = 208;
uint256 internal constant EXPIRED_PERMIT = 209;
// Pools
uint256 internal constant MIN_AMP = 300;
uint256 internal constant MAX_AMP = 301;
uint256 internal constant MIN_WEIGHT = 302;
uint256 internal constant MAX_STABLE_TOKENS = 303;
uint256 internal constant MAX_IN_RATIO = 304;
uint256 internal constant MAX_OUT_RATIO = 305;
uint256 internal constant MIN_BPT_IN_FOR_TOKEN_OUT = 306;
uint256 internal constant MAX_OUT_BPT_FOR_TOKEN_IN = 307;
uint256 internal constant NORMALIZED_WEIGHT_INVARIANT = 308;
uint256 internal constant INVALID_TOKEN = 309;
uint256 internal constant UNHANDLED_JOIN_KIND = 310;
uint256 internal constant ZERO_INVARIANT = 311;
uint256 internal constant ORACLE_INVALID_SECONDS_QUERY = 312;
uint256 internal constant ORACLE_NOT_INITIALIZED = 313;
uint256 internal constant ORACLE_QUERY_TOO_OLD = 314;
uint256 internal constant ORACLE_INVALID_INDEX = 315;
uint256 internal constant ORACLE_BAD_SECS = 316;
// Lib
uint256 internal constant REENTRANCY = 400;
uint256 internal constant SENDER_NOT_ALLOWED = 401;
uint256 internal constant PAUSED = 402;
uint256 internal constant PAUSE_WINDOW_EXPIRED = 403;
uint256 internal constant MAX_PAUSE_WINDOW_DURATION = 404;
uint256 internal constant MAX_BUFFER_PERIOD_DURATION = 405;
uint256 internal constant INSUFFICIENT_BALANCE = 406;
uint256 internal constant INSUFFICIENT_ALLOWANCE = 407;
uint256 internal constant ERC20_TRANSFER_FROM_ZERO_ADDRESS = 408;
uint256 internal constant ERC20_TRANSFER_TO_ZERO_ADDRESS = 409;
uint256 internal constant ERC20_MINT_TO_ZERO_ADDRESS = 410;
uint256 internal constant ERC20_BURN_FROM_ZERO_ADDRESS = 411;
uint256 internal constant ERC20_APPROVE_FROM_ZERO_ADDRESS = 412;
uint256 internal constant ERC20_APPROVE_TO_ZERO_ADDRESS = 413;
uint256 internal constant ERC20_TRANSFER_EXCEEDS_ALLOWANCE = 414;
uint256 internal constant ERC20_DECREASED_ALLOWANCE_BELOW_ZERO = 415;
uint256 internal constant ERC20_TRANSFER_EXCEEDS_BALANCE = 416;
uint256 internal constant ERC20_BURN_EXCEEDS_ALLOWANCE = 417;
uint256 internal constant SAFE_ERC20_CALL_FAILED = 418;
uint256 internal constant ADDRESS_INSUFFICIENT_BALANCE = 419;
uint256 internal constant ADDRESS_CANNOT_SEND_VALUE = 420;
uint256 internal constant SAFE_CAST_VALUE_CANT_FIT_INT256 = 421;
uint256 internal constant GRANT_SENDER_NOT_ADMIN = 422;
uint256 internal constant REVOKE_SENDER_NOT_ADMIN = 423;
uint256 internal constant RENOUNCE_SENDER_NOT_ALLOWED = 424;
uint256 internal constant BUFFER_PERIOD_EXPIRED = 425;
// Vault
uint256 internal constant INVALID_POOL_ID = 500;
uint256 internal constant CALLER_NOT_POOL = 501;
uint256 internal constant SENDER_NOT_ASSET_MANAGER = 502;
uint256 internal constant USER_DOESNT_ALLOW_RELAYER = 503;
uint256 internal constant INVALID_SIGNATURE = 504;
uint256 internal constant EXIT_BELOW_MIN = 505;
uint256 internal constant JOIN_ABOVE_MAX = 506;
uint256 internal constant SWAP_LIMIT = 507;
uint256 internal constant SWAP_DEADLINE = 508;
uint256 internal constant CANNOT_SWAP_SAME_TOKEN = 509;
uint256 internal constant UNKNOWN_AMOUNT_IN_FIRST_SWAP = 510;
uint256 internal constant MALCONSTRUCTED_MULTIHOP_SWAP = 511;
uint256 internal constant INTERNAL_BALANCE_OVERFLOW = 512;
uint256 internal constant INSUFFICIENT_INTERNAL_BALANCE = 513;
uint256 internal constant INVALID_ETH_INTERNAL_BALANCE = 514;
uint256 internal constant INVALID_POST_LOAN_BALANCE = 515;
uint256 internal constant INSUFFICIENT_ETH = 516;
uint256 internal constant UNALLOCATED_ETH = 517;
uint256 internal constant ETH_TRANSFER = 518;
uint256 internal constant CANNOT_USE_ETH_SENTINEL = 519;
uint256 internal constant TOKENS_MISMATCH = 520;
uint256 internal constant TOKEN_NOT_REGISTERED = 521;
uint256 internal constant TOKEN_ALREADY_REGISTERED = 522;
uint256 internal constant TOKENS_ALREADY_SET = 523;
uint256 internal constant TOKENS_LENGTH_MUST_BE_2 = 524;
uint256 internal constant NONZERO_TOKEN_BALANCE = 525;
uint256 internal constant BALANCE_TOTAL_OVERFLOW = 526;
uint256 internal constant POOL_NO_TOKENS = 527;
uint256 internal constant INSUFFICIENT_FLASH_LOAN_BALANCE = 528;
// Fees
uint256 internal constant SWAP_FEE_PERCENTAGE_TOO_HIGH = 600;
uint256 internal constant FLASH_LOAN_FEE_PERCENTAGE_TOO_HIGH = 601;
uint256 internal constant INSUFFICIENT_FLASH_LOAN_FEE_AMOUNT = 602;
}
library LogExpMath {
// All fixed point multiplications and divisions are inlined. This means we need to divide by ONE when multiplying
// two numbers, and multiply by ONE when dividing them.
// All arguments and return values are 18 decimal fixed point numbers.
int256 constant ONE_18 = 1e18;
// Internally, intermediate values are computed with higher precision as 20 decimal fixed point numbers, and in the
// case of ln36, 36 decimals.
int256 constant ONE_20 = 1e20;
int256 constant ONE_36 = 1e36;
// The domain of natural exponentiation is bound by the word size and number of decimals used.
//
// Because internally the result will be stored using 20 decimals, the largest possible result is
// (2^255 - 1) / 10^20, which makes the largest exponent ln((2^255 - 1) / 10^20) = 130.700829182905140221.
// The smallest possible result is 10^(-18), which makes largest negative argument
// ln(10^(-18)) = -41.446531673892822312.
// We use 130.0 and -41.0 to have some safety margin.
int256 constant MAX_NATURAL_EXPONENT = 130e18;
int256 constant MIN_NATURAL_EXPONENT = -41e18;
// Bounds for ln_36's argument. Both ln(0.9) and ln(1.1) can be represented with 36 decimal places in a fixed point
// 256 bit integer.
int256 constant LN_36_LOWER_BOUND = ONE_18 - 1e17;
int256 constant LN_36_UPPER_BOUND = ONE_18 + 1e17;
uint256 constant MILD_EXPONENT_BOUND = 2**254 / uint256(ONE_20);
// 18 decimal constants
int256 constant x0 = 128000000000000000000; // 2ˆ7
int256 constant a0 = 38877084059945950922200000000000000000000000000000000000; // eˆ(x0) (no decimals)
int256 constant x1 = 64000000000000000000; // 2ˆ6
int256 constant a1 = 6235149080811616882910000000; // eˆ(x1) (no decimals)
// 20 decimal constants
int256 constant x2 = 3200000000000000000000; // 2ˆ5
int256 constant a2 = 7896296018268069516100000000000000; // eˆ(x2)
int256 constant x3 = 1600000000000000000000; // 2ˆ4
int256 constant a3 = 888611052050787263676000000; // eˆ(x3)
int256 constant x4 = 800000000000000000000; // 2ˆ3
int256 constant a4 = 298095798704172827474000; // eˆ(x4)
int256 constant x5 = 400000000000000000000; // 2ˆ2
int256 constant a5 = 5459815003314423907810; // eˆ(x5)
int256 constant x6 = 200000000000000000000; // 2ˆ1
int256 constant a6 = 738905609893065022723; // eˆ(x6)
int256 constant x7 = 100000000000000000000; // 2ˆ0
int256 constant a7 = 271828182845904523536; // eˆ(x7)
int256 constant x8 = 50000000000000000000; // 2ˆ-1
int256 constant a8 = 164872127070012814685; // eˆ(x8)
int256 constant x9 = 25000000000000000000; // 2ˆ-2
int256 constant a9 = 128402541668774148407; // eˆ(x9)
int256 constant x10 = 12500000000000000000; // 2ˆ-3
int256 constant a10 = 113314845306682631683; // eˆ(x10)
int256 constant x11 = 6250000000000000000; // 2ˆ-4
int256 constant a11 = 106449445891785942956; // eˆ(x11)
/**
* @dev Exponentiation (x^y) with unsigned 18 decimal fixed point base and exponent.
*
* Reverts if ln(x) * y is smaller than `MIN_NATURAL_EXPONENT`, or larger than `MAX_NATURAL_EXPONENT`.
*/
function pow(uint256 x, uint256 y) internal pure returns (uint256) {
if (y == 0) {
// We solve the 0^0 indetermination by making it equal one.
return uint256(ONE_18);
}
if (x == 0) {
return 0;
}
// Instead of computing x^y directly, we instead rely on the properties of logarithms and exponentiation to
// arrive at that result. In particular, exp(ln(x)) = x, and ln(x^y) = y * ln(x). This means
// x^y = exp(y * ln(x)).
// The ln function takes a signed value, so we need to make sure x fits in the signed 256 bit range.
_require(x < 2**255, Errors.X_OUT_OF_BOUNDS);
int256 x_int256 = int256(x);
// We will compute y * ln(x) in a single step. Depending on the value of x, we can either use ln or ln_36. In
// both cases, we leave the division by ONE_18 (due to fixed point multiplication) to the end.
// This prevents y * ln(x) from overflowing, and at the same time guarantees y fits in the signed 256 bit range.
_require(y < MILD_EXPONENT_BOUND, Errors.Y_OUT_OF_BOUNDS);
int256 y_int256 = int256(y);
int256 logx_times_y;
if (LN_36_LOWER_BOUND < x_int256 && x_int256 < LN_36_UPPER_BOUND) {
int256 ln_36_x = _ln_36(x_int256);
// ln_36_x has 36 decimal places, so multiplying by y_int256 isn't as straightforward, since we can't just
// bring y_int256 to 36 decimal places, as it might overflow. Instead, we perform two 18 decimal
// multiplications and add the results: one with the first 18 decimals of ln_36_x, and one with the
// (downscaled) last 18 decimals.
logx_times_y = ((ln_36_x / ONE_18) * y_int256 + ((ln_36_x % ONE_18) * y_int256) / ONE_18);
} else {
logx_times_y = _ln(x_int256) * y_int256;
}
logx_times_y /= ONE_18;
// Finally, we compute exp(y * ln(x)) to arrive at x^y
_require(
MIN_NATURAL_EXPONENT <= logx_times_y && logx_times_y <= MAX_NATURAL_EXPONENT,
Errors.PRODUCT_OUT_OF_BOUNDS
);
return uint256(exp(logx_times_y));
}
/**
* @dev Natural exponentiation (e^x) with signed 18 decimal fixed point exponent.
*
* Reverts if `x` is smaller than MIN_NATURAL_EXPONENT, or larger than `MAX_NATURAL_EXPONENT`.
*/
function exp(int256 x) internal pure returns (int256) {
_require(x >= MIN_NATURAL_EXPONENT && x <= MAX_NATURAL_EXPONENT, Errors.INVALID_EXPONENT);
if (x < 0) {
// We only handle positive exponents: e^(-x) is computed as 1 / e^x. We can safely make x positive since it
// fits in the signed 256 bit range (as it is larger than MIN_NATURAL_EXPONENT).
// Fixed point division requires multiplying by ONE_18.
return ((ONE_18 * ONE_18) / exp(-x));
}
// First, we use the fact that e^(x+y) = e^x * e^y to decompose x into a sum of powers of two, which we call x_n,
// where x_n == 2^(7 - n), and e^x_n = a_n has been precomputed. We choose the first x_n, x0, to equal 2^7
// because all larger powers are larger than MAX_NATURAL_EXPONENT, and therefore not present in the
// decomposition.
// At the end of this process we will have the product of all e^x_n = a_n that apply, and the remainder of this
// decomposition, which will be lower than the smallest x_n.
// exp(x) = k_0 * a_0 * k_1 * a_1 * ... + k_n * a_n * exp(remainder), where each k_n equals either 0 or 1.
// We mutate x by subtracting x_n, making it the remainder of the decomposition.
// The first two a_n (e^(2^7) and e^(2^6)) are too large if stored as 18 decimal numbers, and could cause
// intermediate overflows. Instead we store them as plain integers, with 0 decimals.
// Additionally, x0 + x1 is larger than MAX_NATURAL_EXPONENT, which means they will not both be present in the
// decomposition.
// For each x_n, we test if that term is present in the decomposition (if x is larger than it), and if so deduct
// it and compute the accumulated product.
int256 firstAN;
if (x >= x0) {
x -= x0;
firstAN = a0;
} else if (x >= x1) {
x -= x1;
firstAN = a1;
} else {
firstAN = 1; // One with no decimal places
}
// We now transform x into a 20 decimal fixed point number, to have enhanced precision when computing the
// smaller terms.
x *= 100;
// `product` is the accumulated product of all a_n (except a0 and a1), which starts at 20 decimal fixed point
// one. Recall that fixed point multiplication requires dividing by ONE_20.
int256 product = ONE_20;
if (x >= x2) {
x -= x2;
product = (product * a2) / ONE_20;
}
if (x >= x3) {
x -= x3;
product = (product * a3) / ONE_20;
}
if (x >= x4) {
x -= x4;
product = (product * a4) / ONE_20;
}
if (x >= x5) {
x -= x5;
product = (product * a5) / ONE_20;
}
if (x >= x6) {
x -= x6;
product = (product * a6) / ONE_20;
}
if (x >= x7) {
x -= x7;
product = (product * a7) / ONE_20;
}
if (x >= x8) {
x -= x8;
product = (product * a8) / ONE_20;
}
if (x >= x9) {
x -= x9;
product = (product * a9) / ONE_20;
}
// x10 and x11 are unnecessary here since we have high enough precision already.
// Now we need to compute e^x, where x is small (in particular, it is smaller than x9). We use the Taylor series
// expansion for e^x: 1 + x + (x^2 / 2!) + (x^3 / 3!) + ... + (x^n / n!).
int256 seriesSum = ONE_20; // The initial one in the sum, with 20 decimal places.
int256 term; // Each term in the sum, where the nth term is (x^n / n!).
// The first term is simply x.
term = x;
seriesSum += term;
// Each term (x^n / n!) equals the previous one times x, divided by n. Since x is a fixed point number,
// multiplying by it requires dividing by ONE_20, but dividing by the non-fixed point n values does not.
term = ((term * x) / ONE_20) / 2;
seriesSum += term;
term = ((term * x) / ONE_20) / 3;
seriesSum += term;
term = ((term * x) / ONE_20) / 4;
seriesSum += term;
term = ((term * x) / ONE_20) / 5;
seriesSum += term;
term = ((term * x) / ONE_20) / 6;
seriesSum += term;
term = ((term * x) / ONE_20) / 7;
seriesSum += term;
term = ((term * x) / ONE_20) / 8;
seriesSum += term;
term = ((term * x) / ONE_20) / 9;
seriesSum += term;
term = ((term * x) / ONE_20) / 10;
seriesSum += term;
term = ((term * x) / ONE_20) / 11;
seriesSum += term;
term = ((term * x) / ONE_20) / 12;
seriesSum += term;
// 12 Taylor terms are sufficient for 18 decimal precision.
// We now have the first a_n (with no decimals), and the product of all other a_n present, and the Taylor
// approximation of the exponentiation of the remainder (both with 20 decimals). All that remains is to multiply
// all three (one 20 decimal fixed point multiplication, dividing by ONE_20, and one integer multiplication),
// and then drop two digits to return an 18 decimal value.
return (((product * seriesSum) / ONE_20) * firstAN) / 100;
}
/**
* @dev Logarithm (log(arg, base), with signed 18 decimal fixed point base and argument.
*/
function log(int256 arg, int256 base) internal pure returns (int256) {
// This performs a simple base change: log(arg, base) = ln(arg) / ln(base).
// Both logBase and logArg are computed as 36 decimal fixed point numbers, either by using ln_36, or by
// upscaling.
int256 logBase;
if (LN_36_LOWER_BOUND < base && base < LN_36_UPPER_BOUND) {
logBase = _ln_36(base);
} else {
logBase = _ln(base) * ONE_18;
}
int256 logArg;
if (LN_36_LOWER_BOUND < arg && arg < LN_36_UPPER_BOUND) {
logArg = _ln_36(arg);
} else {
logArg = _ln(arg) * ONE_18;
}
// When dividing, we multiply by ONE_18 to arrive at a result with 18 decimal places
return (logArg * ONE_18) / logBase;
}
/**
* @dev Natural logarithm (ln(a)) with signed 18 decimal fixed point argument.
*/
function ln(int256 a) internal pure returns (int256) {
// The real natural logarithm is not defined for negative numbers or zero.
_require(a > 0, Errors.OUT_OF_BOUNDS);
if (LN_36_LOWER_BOUND < a && a < LN_36_UPPER_BOUND) {
return _ln_36(a) / ONE_18;
} else {
return _ln(a);
}
}
/**
* @dev Internal natural logarithm (ln(a)) with signed 18 decimal fixed point argument.
*/
function _ln(int256 a) private pure returns (int256) {
if (a < ONE_18) {
// Since ln(a^k) = k * ln(a), we can compute ln(a) as ln(a) = ln((1/a)^(-1)) = - ln((1/a)). If a is less
// than one, 1/a will be greater than one, and this if statement will not be entered in the recursive call.
// Fixed point division requires multiplying by ONE_18.
return (-_ln((ONE_18 * ONE_18) / a));
}
// First, we use the fact that ln^(a * b) = ln(a) + ln(b) to decompose ln(a) into a sum of powers of two, which
// we call x_n, where x_n == 2^(7 - n), which are the natural logarithm of precomputed quantities a_n (that is,
// ln(a_n) = x_n). We choose the first x_n, x0, to equal 2^7 because the exponential of all larger powers cannot
// be represented as 18 fixed point decimal numbers in 256 bits, and are therefore larger than a.
// At the end of this process we will have the sum of all x_n = ln(a_n) that apply, and the remainder of this
// decomposition, which will be lower than the smallest a_n.
// ln(a) = k_0 * x_0 + k_1 * x_1 + ... + k_n * x_n + ln(remainder), where each k_n equals either 0 or 1.
// We mutate a by subtracting a_n, making it the remainder of the decomposition.
// For reasons related to how `exp` works, the first two a_n (e^(2^7) and e^(2^6)) are not stored as fixed point
// numbers with 18 decimals, but instead as plain integers with 0 decimals, so we need to multiply them by
// ONE_18 to convert them to fixed point.
// For each a_n, we test if that term is present in the decomposition (if a is larger than it), and if so divide
// by it and compute the accumulated sum.
int256 sum = 0;
if (a >= a0 * ONE_18) {
a /= a0; // Integer, not fixed point division
sum += x0;
}
if (a >= a1 * ONE_18) {
a /= a1; // Integer, not fixed point division
sum += x1;
}
// All other a_n and x_n are stored as 20 digit fixed point numbers, so we convert the sum and a to this format.
sum *= 100;
a *= 100;
// Because further a_n are 20 digit fixed point numbers, we multiply by ONE_20 when dividing by them.
if (a >= a2) {
a = (a * ONE_20) / a2;
sum += x2;
}
if (a >= a3) {
a = (a * ONE_20) / a3;
sum += x3;
}
if (a >= a4) {
a = (a * ONE_20) / a4;
sum += x4;
}
if (a >= a5) {
a = (a * ONE_20) / a5;
sum += x5;
}
if (a >= a6) {
a = (a * ONE_20) / a6;
sum += x6;
}
if (a >= a7) {
a = (a * ONE_20) / a7;
sum += x7;
}
if (a >= a8) {
a = (a * ONE_20) / a8;
sum += x8;
}
if (a >= a9) {
a = (a * ONE_20) / a9;
sum += x9;
}
if (a >= a10) {
a = (a * ONE_20) / a10;
sum += x10;
}
if (a >= a11) {
a = (a * ONE_20) / a11;
sum += x11;
}
// a is now a small number (smaller than a_11, which roughly equals 1.06). This means we can use a Taylor series
// that converges rapidly for values of `a` close to one - the same one used in ln_36.
// Let z = (a - 1) / (a + 1).
// ln(a) = 2 * (z + z^3 / 3 + z^5 / 5 + z^7 / 7 + ... + z^(2 * n + 1) / (2 * n + 1))
// Recall that 20 digit fixed point division requires multiplying by ONE_20, and multiplication requires
// division by ONE_20.
int256 z = ((a - ONE_20) * ONE_20) / (a + ONE_20);
int256 z_squared = (z * z) / ONE_20;
// num is the numerator of the series: the z^(2 * n + 1) term
int256 num = z;
// seriesSum holds the accumulated sum of each term in the series, starting with the initial z
int256 seriesSum = num;
// In each step, the numerator is multiplied by z^2
num = (num * z_squared) / ONE_20;
seriesSum += num / 3;
num = (num * z_squared) / ONE_20;
seriesSum += num / 5;
num = (num * z_squared) / ONE_20;
seriesSum += num / 7;
num = (num * z_squared) / ONE_20;
seriesSum += num / 9;
num = (num * z_squared) / ONE_20;
seriesSum += num / 11;
// 6 Taylor terms are sufficient for 36 decimal precision.
// Finally, we multiply by 2 (non fixed point) to compute ln(remainder)
seriesSum *= 2;
// We now have the sum of all x_n present, and the Taylor approximation of the logarithm of the remainder (both
// with 20 decimals). All that remains is to sum these two, and then drop two digits to return a 18 decimal
// value.
return (sum + seriesSum) / 100;
}
/**
* @dev Intrnal high precision (36 decimal places) natural logarithm (ln(x)) with signed 18 decimal fixed point argument,
* for x close to one.
*
* Should only be used if x is between LN_36_LOWER_BOUND and LN_36_UPPER_BOUND.
*/
function _ln_36(int256 x) private pure returns (int256) {
// Since ln(1) = 0, a value of x close to one will yield a very small result, which makes using 36 digits
// worthwhile.
// First, we transform x to a 36 digit fixed point value.
x *= ONE_18;
// We will use the following Taylor expansion, which converges very rapidly. Let z = (x - 1) / (x + 1).
// ln(x) = 2 * (z + z^3 / 3 + z^5 / 5 + z^7 / 7 + ... + z^(2 * n + 1) / (2 * n + 1))
// Recall that 36 digit fixed point division requires multiplying by ONE_36, and multiplication requires
// division by ONE_36.
int256 z = ((x - ONE_36) * ONE_36) / (x + ONE_36);
int256 z_squared = (z * z) / ONE_36;
// num is the numerator of the series: the z^(2 * n + 1) term
int256 num = z;
// seriesSum holds the accumulated sum of each term in the series, starting with the initial z
int256 seriesSum = num;
// In each step, the numerator is multiplied by z^2
num = (num * z_squared) / ONE_36;
seriesSum += num / 3;
num = (num * z_squared) / ONE_36;
seriesSum += num / 5;
num = (num * z_squared) / ONE_36;
seriesSum += num / 7;
num = (num * z_squared) / ONE_36;
seriesSum += num / 9;
num = (num * z_squared) / ONE_36;
seriesSum += num / 11;
num = (num * z_squared) / ONE_36;
seriesSum += num / 13;
num = (num * z_squared) / ONE_36;
seriesSum += num / 15;
// 8 Taylor terms are sufficient for 36 decimal precision.
// All that remains is multiplying by 2 (non fixed point).
return seriesSum * 2;
}
}
library FixedPoint {
uint256 internal constant ONE = 1e18; // 18 decimal places
uint256 internal constant MAX_POW_RELATIVE_ERROR = 10000; // 10^(-14)
// Minimum base for the power function when the exponent is 'free' (larger than ONE).
uint256 internal constant MIN_POW_BASE_FREE_EXPONENT = 0.7e18;
function add(uint256 a, uint256 b) internal pure returns (uint256) {
// Fixed Point addition is the same as regular checked addition
uint256 c = a + b;
_require(c >= a, Errors.ADD_OVERFLOW);
return c;
}
function sub(uint256 a, uint256 b) internal pure returns (uint256) {
// Fixed Point addition is the same as regular checked addition
_require(b <= a, Errors.SUB_OVERFLOW);
uint256 c = a - b;
return c;
}
function mulDown(uint256 a, uint256 b) internal pure returns (uint256) {
uint256 product = a * b;
_require(a == 0 || product / a == b, Errors.MUL_OVERFLOW);
return product / ONE;
}
function mulUp(uint256 a, uint256 b) internal pure returns (uint256) {
uint256 product = a * b;
_require(a == 0 || product / a == b, Errors.MUL_OVERFLOW);
if (product == 0) {
return 0;
} else {
// The traditional divUp formula is:
// divUp(x, y) := (x + y - 1) / y
// To avoid intermediate overflow in the addition, we distribute the division and get:
// divUp(x, y) := (x - 1) / y + 1
// Note that this requires x != 0, which we already tested for.
return ((product - 1) / ONE) + 1;
}
}
function divDown(uint256 a, uint256 b) internal pure returns (uint256) {
_require(b != 0, Errors.ZERO_DIVISION);
if (a == 0) {
return 0;
} else {
uint256 aInflated = a * ONE;
_require(aInflated / a == ONE, Errors.DIV_INTERNAL); // mul overflow
return aInflated / b;
}
}
function divUp(uint256 a, uint256 b) internal pure returns (uint256) {
_require(b != 0, Errors.ZERO_DIVISION);
if (a == 0) {
return 0;
} else {
uint256 aInflated = a * ONE;
_require(aInflated / a == ONE, Errors.DIV_INTERNAL); // mul overflow
// The traditional divUp formula is:
// divUp(x, y) := (x + y - 1) / y
// To avoid intermediate overflow in the addition, we distribute the division and get:
// divUp(x, y) := (x - 1) / y + 1
// Note that this requires x != 0, which we already tested for.
return ((aInflated - 1) / b) + 1;
}
}
/**
* @dev Returns x^y, assuming both are fixed point numbers, rounding down. The result is guaranteed to not be above
* the true value (that is, the error function expected - actual is always positive).
*/
function powDown(uint256 x, uint256 y) internal pure returns (uint256) {
uint256 raw = LogExpMath.pow(x, y);
uint256 maxError = add(mulUp(raw, MAX_POW_RELATIVE_ERROR), 1);
if (raw < maxError) {
return 0;
} else {
return sub(raw, maxError);
}
}
/**
* @dev Returns x^y, assuming both are fixed point numbers, rounding up. The result is guaranteed to not be below
* the true value (that is, the error function expected - actual is always negative).
*/
function powUp(uint256 x, uint256 y) internal pure returns (uint256) {
uint256 raw = LogExpMath.pow(x, y);
uint256 maxError = add(mulUp(raw, MAX_POW_RELATIVE_ERROR), 1);
return add(raw, maxError);
}
/**
* @dev Returns the complement of a value (1 - x), capped to 0 if x is larger than 1.
*
* Useful when computing the complement for values with some level of relative error, as it strips this error and
* prevents intermediate negative values.
*/
function complement(uint256 x) internal pure returns (uint256) {
return (x < ONE) ? (ONE - x) : 0;
}
}
enum SwapKind { GIVEN_IN, GIVEN_OUT }
struct SingleSwap {
bytes32 poolId;
SwapKind kind;
address assetIn;
address assetOut;
uint256 amount;
bytes userData;
}
struct FundManagement {
address sender;
bool fromInternalBalance;
address recipient;
bool toInternalBalance;
}
interface IBalancerV2Vault {
function swap(SingleSwap calldata singleSwap, FundManagement calldata funds, uint256 limit, uint256 deadline) external returns (uint256 amountCalculatedInOut);
function getPoolTokens(bytes32 poolId) external view returns (address[] memory tokens, uint256[] memory balances, uint256 lastChangeBlock);
}
interface IBalancerV2Pool {
function getInvariant() external view returns (uint256);
}
interface AggregatorV3Interface {
function latestRoundData() external view returns (uint80 roundId, int256 answer, uint256 startedAt, uint256 updatedAt, uint80 answeredInRound);
}
contract BptPricing {
using SafeERC20 for IERC20;
using Address for address;
using FixedPoint for uint256;
address public owner;
// constant address - Ethereum
bytes32 public constant balETHPoolId = 0x5c6ee304399dbdb9c8ef030ab642b10820db8f56000200000000000000000014;
address public constant balETHPool = 0x5c6Ee304399DBdB9C8Ef030aB642B10820DB8F56;
address public constant balancerVault = 0xBA12222222228d8Ba445958a75a0704d566BF2C8;
address public constant balETHChainlinkFeed = 0xC1438AA3823A6Ba0C159CfA8D98dF5A994bA120b;
address public constant wrappedNativeToken = 0xC02aaA39b223FE8D0A0e5C4F27eAD9083C756Cc2;//wETH
address public constant balToken = 0xba100000625a3754423978a60c9317c58a424e3D;//BAL
uint256 public constant balPoolWeight = 800000000000000000;
uint256 public constant ethPoolWeight = 200000000000000000;
constructor() {
// for swap
IERC20(wrappedNativeToken).approve(balancerVault, type(uint256).max);
IERC20(balToken).approve(balancerVault, type(uint256).max);
}
function swapInBpt() external{
SingleSwap memory singleSwap = SingleSwap(balETHPoolId, SwapKind.GIVEN_IN, wrappedNativeToken, balToken, IERC20(wrappedNativeToken).balanceOf(address(this)), "");
FundManagement memory funds = FundManagement(address(this), false, address(this), false);
IBalancerV2Vault(balancerVault).swap(singleSwap, funds, 0, block.timestamp);
}
function calculateBpt(bool _beforeSwap) public view returns(uint256, uint256, uint256, uint256){
uint256 _V = IBalancerV2Pool(balETHPool).getInvariant();
(,int price,,,) = AggregatorV3Interface(balETHChainlinkFeed).latestRoundData();
if (_beforeSwap){
(,uint256[] memory _bals,) = IBalancerV2Vault(balancerVault).getPoolTokens(balETHPoolId);
(uint256 _p,,) = calcBptPrice(uint256(price), _V, IERC20(balETHPool).totalSupply(), balPoolWeight, ethPoolWeight);
return (_p, _bals[0], _bals[1], _V);
}else{
(uint256 _p, uint256 _fairBal1, uint256 _fairBal2) = calcBptPrice(uint256(price), _V, IERC20(balETHPool).totalSupply(), balPoolWeight, ethPoolWeight);
return (_p, _fairBal1, _fairBal2, _V);
}
}
function calcBptPrice(uint256 relativeFairPrice, uint256 invariant, uint256 totalSupply, uint256 weight1, uint256 weight2) public pure returns(uint256, uint256, uint256){
require(weight1.add(weight2) == 1e18, '!weights');
uint256 _fairBal1 = invariant.mulDown(weight1.powDown(weight2).divDown(weight2.powDown(weight2))).divDown(relativeFairPrice.powDown(weight2));
uint256 _fairBal2 = invariant.mulDown(weight2.powDown(weight1).divDown(weight1.powDown(weight1))).mulDown(relativeFairPrice.powDown(weight1));
uint256 _fairBptPrice = _fairBal2.add(_fairBal1.mulDown(relativeFairPrice)).divDown(totalSupply);
return (_fairBptPrice, _fairBal1, _fairBal2);
}
}
Raw
test_bpt_pricing.py
import brownie
from brownie import *
import pytest
"""
test BPT pricing
@pytest.fixture
def bptpricing():
return BptPricing.deploy({"from": a[0]})
"""
def test_bpt_pricing_bal_eth(weth_whale, weth, bptpricing):
(_p, _bal1, _bal2, _V) = bptpricing.calculateBpt(True)
print('Before swap: bptPriceInETH=' + str(_p) + ', fairBal1=' + str(_bal1) + ', fairBal2=' + str(_bal2) + ', invariant=' + str(_V))
## check bpt pricing against swap manipulation, e.g., swap WETH for BAL to push BAL price much higher
## balancer got some limit in one swap: https://dev.balancer.fi/references/error-codes#pools
## bal-eth pool: https://etherscan.io/address/0x5c6ee304399dbdb9c8ef030ab642b10820db8f56#code#F6#L36
sugar_amount = _bal2 * 0.299
weth.transfer(bptpricing.address, sugar_amount, {'from': weth_whale})
bptpricing.swapInBpt()
(_pAfter, _bal1After, _bal2After, _VAfter) = bptpricing.calculateBpt(False)
print('After swap: bptPriceInETH=' + str(_pAfter) + ', fairBal1=' + str(_bal1After) + ', fairBal2=' + str(_bal2After) + ', invariant=' + str(_VAfter))
# check if any serious change after swap
diff = 0
if(_pAfter > _p):
diff = _pAfter - _p
else:
diff = _p - _pAfter
assert (diff / _p) <= 0.001
@rayeaster
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rayeaster commented Jun 20, 2022 •
edited
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https://hackmd.io/@re73/SJHmQaCFq

another analysis using spot-price derivation https://hackmd.io/@shuklaayush/BkAtKbCY9

image

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