Address Details
contract
token
0xC2cCCd430E27C7890Be19e7B1475F186d10612c8
- Token
- Continous Token (TOK)
- Creator
- 0xe91286–9209d6 at 0xa3e60c–20bee6
- Balance
- 0 CELO ( )
- Locked CELO Balance
- 0.00 CELO
- Voting CELO Balance
- 0.00 CELO
- Pending Unlocked Gold
- 0.00 CELO
- Tokens
-
Fetching tokens...
- Transactions
- 0 Transactions
- Transfers
- 0 Transfers
- Gas Used
- Fetching gas used...
- Last Balance Update
- 7808190
This contract has been verified via Sourcify.
View contract in Sourcify repository
- Contract name:
- ReputationToken
- Optimization enabled
- true
- Compiler version
- v0.8.0+commit.c7dfd78e
- Optimization runs
- 200
- EVM Version
- istanbul
- Verified at
- 2023-02-06T10:30:14.926230Z
contracts/reputation.sol
// SPDX-License-Identifier: MIT
//Deployed on Ethereum Goerli testnet: 0x97DB500303C219FB11fFded8EADaA8945663D2A5
//Deployed on Near testner: 97db500303c219fb11ffded8eadaa8945663d2a5.factory.goerli.testnet
//Deployed on Aurora testnet: 0x7fc383a117f64b29ab012231ae91dab6dfb95043
pragma solidity ^0.8.0;
import "https://github.com/OpenZeppelin/openzeppelin-contracts/contracts/token/ERC20/ERC20.sol";
import "https://github.com/slim12kg/protofire-continous-token-task/blob/master/contracts/curves/BancorFormula.sol";
contract ReputationToken is BancorFormula, ERC20 {
using SafeMath for uint256;
uint256 public scale = 10**18;
uint256 public reserveBalance = 10 * scale;
uint256 public reserveRatio;
address public reserveTokenAddress;
/**
* @dev Fired when TOK is exchanged for Dai
*/
event ContinuousBurn(
address _address,
uint256 continuousTokenAmount,
uint256 reserveTokenAmount
);
/**
* @dev Fired when Dai us exchanged for TOK
*/
event ContinuousMint(
address _address,
uint256 reserveTokenAmount,
uint256 continuousTokenAmount
);
/**
* @param _reserveRatio(RR) to determine the bonding curve to be used. 50% RR = Linear Bonding Curve, 10% RR = Exponential Bonding Curve
* @param _reserveTokenAddress Contract address of ERC20 Token to use as reserve/exchange of value e.g DAI
*/
constructor(uint256 _reserveRatio, address _reserveTokenAddress)
ERC20("Continous Token", "TOK")
{
reserveRatio = _reserveRatio;
reserveTokenAddress = _reserveTokenAddress;
_mint(msg.sender, 1 * scale);
}
/**
* @dev Mint some TOK token by allowing contract to spend an amount of caller reserve tokens
* @param _amount Number of reserve token approved for this contract to convert to TOK tokens
*/
function mint(uint256 _amount) public returns (uint256 _amountMinted) {
uint256 allowance = IERC20(reserveTokenAddress).allowance(
msg.sender,
address(this)
);
require(allowance > 0, "Must approve DAI to buy tokens.");
require(allowance >= _amount, "Must approve enough DAI.");
bool success = IERC20(reserveTokenAddress).transferFrom(
msg.sender,
address(this),
allowance
);
if (success) {
return _continuousMint(allowance);
} else {
require(allowance > 0, "Failed to transfer Dai tokens");
}
}
/**
* @dev Burn some TOK token and return reserve token based on current curve price
* @param _amount Number of TOK token to convert to reserve tokens
*/
function burn(uint256 _amount) public {
uint256 returnAmount = _continuousBurn(_amount);
IERC20(reserveTokenAddress).transfer(msg.sender, returnAmount);
}
function calculateContinuousMintReturn(uint256 _amount)
public
view
returns (uint256 mintAmount)
{
return
purchaseTargetAmount(
totalSupply(),
reserveBalance,
uint32(reserveRatio),
_amount
);
}
function calculateContinuousBurnReturn(uint256 _amount)
public
view
returns (uint256 burnAmount)
{
return
saleTargetAmount(
totalSupply(),
reserveBalance,
uint32(reserveRatio),
_amount
);
}
function _continuousMint(uint256 _deposit) internal returns (uint256) {
require(_deposit > 0, "Deposit must be non-zero.");
uint256 amount = calculateContinuousMintReturn(_deposit);
_mint(msg.sender, amount);
reserveBalance = reserveBalance.add(_deposit);
emit ContinuousMint(msg.sender, _deposit, amount);
return amount;
}
function _continuousBurn(uint256 _amount) internal returns (uint256) {
require(_amount > 0, "Amount must be non-zero.");
require(
balanceOf(msg.sender) >= _amount,
"Insufficient tokens to burn."
);
uint256 reimburseAmount = calculateContinuousBurnReturn(_amount);
_burn(msg.sender, _amount);
reserveBalance = reserveBalance.sub(reimburseAmount);
emit ContinuousBurn(msg.sender, _amount, reimburseAmount);
return reimburseAmount;
}
}
/_openzeppelin/contracts/utils/math/SafeMath.sol
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
// CAUTION
// This version of SafeMath should only be used with Solidity 0.8 or later,
// because it relies on the compiler's built in overflow checks.
/**
* @dev Wrappers over Solidity's arithmetic operations.
*
* NOTE: `SafeMath` is no longer needed starting with Solidity 0.8. The compiler
* now has built in overflow checking.
*/
library SafeMath {
/**
* @dev Returns the addition of two unsigned integers, with an overflow flag.
*
* _Available since v3.4._
*/
function tryAdd(uint256 a, uint256 b) internal pure returns (bool, uint256) {
unchecked {
uint256 c = a + b;
if (c < a) return (false, 0);
return (true, c);
}
}
/**
* @dev Returns the substraction of two unsigned integers, with an overflow flag.
*
* _Available since v3.4._
*/
function trySub(uint256 a, uint256 b) internal pure returns (bool, uint256) {
unchecked {
if (b > a) return (false, 0);
return (true, a - b);
}
}
/**
* @dev Returns the multiplication of two unsigned integers, with an overflow flag.
*
* _Available since v3.4._
*/
function tryMul(uint256 a, uint256 b) internal pure returns (bool, uint256) {
unchecked {
// Gas optimization: this is cheaper than requiring 'a' not being zero, but the
// benefit is lost if 'b' is also tested.
// See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522
if (a == 0) return (true, 0);
uint256 c = a * b;
if (c / a != b) return (false, 0);
return (true, c);
}
}
/**
* @dev Returns the division of two unsigned integers, with a division by zero flag.
*
* _Available since v3.4._
*/
function tryDiv(uint256 a, uint256 b) internal pure returns (bool, uint256) {
unchecked {
if (b == 0) return (false, 0);
return (true, a / b);
}
}
/**
* @dev Returns the remainder of dividing two unsigned integers, with a division by zero flag.
*
* _Available since v3.4._
*/
function tryMod(uint256 a, uint256 b) internal pure returns (bool, uint256) {
unchecked {
if (b == 0) return (false, 0);
return (true, a % b);
}
}
/**
* @dev Returns the 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) {
return a + b;
}
/**
* @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 a - b;
}
/**
* @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) {
return a * b;
}
/**
* @dev Returns the integer division of two unsigned integers, reverting on
* division by zero. The result is rounded towards zero.
*
* Counterpart to Solidity's `/` operator.
*
* Requirements:
*
* - The divisor cannot be zero.
*/
function div(uint256 a, uint256 b) internal pure returns (uint256) {
return a / b;
}
/**
* @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
* reverting 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 a % b;
}
/**
* @dev Returns the subtraction of two unsigned integers, reverting with custom message on
* overflow (when the result is negative).
*
* CAUTION: This function is deprecated because it requires allocating memory for the error
* message unnecessarily. For custom revert reasons use {trySub}.
*
* Counterpart to Solidity's `-` operator.
*
* Requirements:
*
* - Subtraction cannot overflow.
*/
function sub(
uint256 a,
uint256 b,
string memory errorMessage
) internal pure returns (uint256) {
unchecked {
require(b <= a, errorMessage);
return a - b;
}
}
/**
* @dev Returns the integer division of two unsigned integers, reverting 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) {
unchecked {
require(b > 0, errorMessage);
return a / b;
}
}
/**
* @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
* reverting with custom message when dividing by zero.
*
* CAUTION: This function is deprecated because it requires allocating memory for the error
* message unnecessarily. For custom revert reasons use {tryMod}.
*
* 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) {
unchecked {
require(b > 0, errorMessage);
return a % b;
}
}
}
/https_/github.com/OpenZeppelin/openzeppelin-contracts/contracts/token/ERC20/ERC20.sol
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
import "./IERC20.sol";
import "./extensions/IERC20Metadata.sol";
import "../../utils/Context.sol";
/**
* @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 Contracts guidelines: functions revert
* instead 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, IERC20Metadata {
mapping(address => uint256) private _balances;
mapping(address => mapping(address => uint256)) private _allowances;
uint256 private _totalSupply;
string private _name;
string private _symbol;
/**
* @dev Sets the values for {name} and {symbol}.
*
* The default value of {decimals} is 18. To select a different value for
* {decimals} you should overload it.
*
* All two of these values are immutable: they can only be set once during
* construction.
*/
constructor(string memory name_, string memory symbol_) {
_name = name_;
_symbol = symbol_;
}
/**
* @dev Returns the name of the token.
*/
function name() public view virtual override returns (string memory) {
return _name;
}
/**
* @dev Returns the symbol of the token, usually a shorter version of the
* name.
*/
function symbol() public view virtual override 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 this function is
* overridden;
*
* 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 virtual override returns (uint8) {
return 18;
}
/**
* @dev See {IERC20-totalSupply}.
*/
function totalSupply() public view virtual override returns (uint256) {
return _totalSupply;
}
/**
* @dev See {IERC20-balanceOf}.
*/
function balanceOf(address account) public view virtual 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);
uint256 currentAllowance = _allowances[sender][_msgSender()];
require(currentAllowance >= amount, "ERC20: transfer amount exceeds allowance");
unchecked {
_approve(sender, _msgSender(), currentAllowance - amount);
}
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] + 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) {
uint256 currentAllowance = _allowances[_msgSender()][spender];
require(currentAllowance >= subtractedValue, "ERC20: decreased allowance below zero");
unchecked {
_approve(_msgSender(), spender, currentAllowance - subtractedValue);
}
return true;
}
/**
* @dev Moves `amount` of tokens from `sender` to `recipient`.
*
* This 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);
uint256 senderBalance = _balances[sender];
require(senderBalance >= amount, "ERC20: transfer amount exceeds balance");
unchecked {
_balances[sender] = senderBalance - amount;
}
_balances[recipient] += amount;
emit Transfer(sender, recipient, amount);
_afterTokenTransfer(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:
*
* - `account` 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 += amount;
_balances[account] += amount;
emit Transfer(address(0), account, amount);
_afterTokenTransfer(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);
uint256 accountBalance = _balances[account];
require(accountBalance >= amount, "ERC20: burn amount exceeds balance");
unchecked {
_balances[account] = accountBalance - amount;
}
_totalSupply -= amount;
emit Transfer(account, address(0), amount);
_afterTokenTransfer(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 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 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 {}
/**
* @dev Hook that is called after any transfer of tokens. This includes
* minting and burning.
*
* Calling conditions:
*
* - when `from` and `to` are both non-zero, `amount` of ``from``'s tokens
* has been transferred to `to`.
* - when `from` is zero, `amount` tokens have been minted for `to`.
* - when `to` is zero, `amount` of ``from``'s tokens have been 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 _afterTokenTransfer(
address from,
address to,
uint256 amount
) internal virtual {}
}
/https_/github.com/OpenZeppelin/openzeppelin-contracts/contracts/token/ERC20/IERC20.sol
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
/**
* @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);
}
/https_/github.com/OpenZeppelin/openzeppelin-contracts/contracts/token/ERC20/extensions/IERC20Metadata.sol
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
import "../IERC20.sol";
/**
* @dev Interface for the optional metadata functions from the ERC20 standard.
*
* _Available since v4.1._
*/
interface IERC20Metadata is IERC20 {
/**
* @dev Returns the name of the token.
*/
function name() external view returns (string memory);
/**
* @dev Returns the symbol of the token.
*/
function symbol() external view returns (string memory);
/**
* @dev Returns the decimals places of the token.
*/
function decimals() external view returns (uint8);
}
/https_/github.com/OpenZeppelin/openzeppelin-contracts/contracts/utils/Context.sol
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
/**
* @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 meta-transactions the account sending and
* paying for execution may not be the actual sender (as far as an application
* is concerned).
*
* This contract is only required for intermediate, library-like contracts.
*/
abstract contract Context {
function _msgSender() internal view virtual returns (address) {
return msg.sender;
}
function _msgData() internal view virtual returns (bytes calldata) {
return msg.data;
}
}
/https_/github.com/slim12kg/protofire-continous-token-task/blob/master/contracts/curves/BancorFormula.sol
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
import "../interfaces/IBancorFormula.sol";
import "../utils/Power.sol";
contract BancorFormula is IBancorFormula, Power {
using SafeMath for uint256;
uint256 private constant ONE = 1;
uint32 private constant MAX_WEIGHT = 1000000;
uint8 private constant MIN_PRECISION = 32;
uint8 private constant MAX_PRECISION = 127;
// Auto-generated via 'PrintMaxExpArray.py'
uint256[128] private maxExpArray;
/**
* @dev should be executed after construction (too large for the constructor)
*/
function init() public {
initMaxExpArray();
initLambertArray();
}
/**
* @dev given a token supply, reserve balance, weight and a deposit amount (in the reserve token),
* calculates the target amount for a given conversion (in the main token)
*
* Formula:
* return = _supply * ((1 + _amount / _reserveBalance) ^ (_reserveWeight / 1000000) - 1)
*
* @param _supply liquid token supply
* @param _reserveBalance reserve balance
* @param _reserveWeight reserve weight, represented in ppm (1-1000000)
* @param _amount amount of reserve tokens to get the target amount for
*
* @return target
*/
function purchaseTargetAmount(
uint256 _supply,
uint256 _reserveBalance,
uint32 _reserveWeight,
uint256 _amount
) public view override returns (uint256) {
// validate input
require(_supply > 0, "ERR_INVALID_SUPPLY");
require(_reserveBalance > 0, "ERR_INVALID_RESERVE_BALANCE");
require(
_reserveWeight > 0 && _reserveWeight <= MAX_WEIGHT,
"ERR_INVALID_RESERVE_WEIGHT"
);
// special case for 0 deposit amount
if (_amount == 0) return 0;
// special case if the weight = 100%
if (_reserveWeight == MAX_WEIGHT)
return _supply.mul(_amount) / _reserveBalance;
uint256 result;
uint8 precision;
uint256 baseN = _amount.add(_reserveBalance);
(result, precision) = power(
baseN,
_reserveBalance,
_reserveWeight,
MAX_WEIGHT
);
uint256 temp = _supply.mul(result) >> precision;
return temp - _supply;
}
/**
* @dev given a token supply, reserve balance, weight and a sell amount (in the main token),
* calculates the target amount for a given conversion (in the reserve token)
*
* Formula:
* return = _reserveBalance * (1 - (1 - _amount / _supply) ^ (1000000 / _reserveWeight))
*
* @param _supply liquid token supply
* @param _reserveBalance reserve balance
* @param _reserveWeight reserve weight, represented in ppm (1-1000000)
* @param _amount amount of liquid tokens to get the target amount for
*
* @return reserve token amount
*/
function saleTargetAmount(
uint256 _supply,
uint256 _reserveBalance,
uint32 _reserveWeight,
uint256 _amount
) public view override returns (uint256) {
// validate input
require(_supply > 0, "ERR_INVALID_SUPPLY");
require(_reserveBalance > 0, "ERR_INVALID_RESERVE_BALANCE");
require(
_reserveWeight > 0 && _reserveWeight <= MAX_WEIGHT,
"ERR_INVALID_RESERVE_WEIGHT"
);
require(_amount <= _supply, "ERR_INVALID_AMOUNT");
// special case for 0 sell amount
if (_amount == 0) return 0;
// special case for selling the entire supply
if (_amount == _supply) return _reserveBalance;
// special case if the weight = 100%
if (_reserveWeight == MAX_WEIGHT)
return _reserveBalance.mul(_amount) / _supply;
uint256 result;
uint8 precision;
uint256 baseD = _supply - _amount;
(result, precision) = power(_supply, baseD, MAX_WEIGHT, _reserveWeight);
uint256 temp1 = _reserveBalance.mul(result);
uint256 temp2 = _reserveBalance << precision;
return (temp1 - temp2) / result;
}
/**
* @dev given two reserve balances/weights and a sell amount (in the first reserve token),
* calculates the target amount for a conversion from the source reserve token to the target reserve token
*
* Formula:
* return = _targetReserveBalance * (1 - (_sourceReserveBalance / (_sourceReserveBalance + _amount)) ^ (_sourceReserveWeight / _targetReserveWeight))
*
* @param _sourceReserveBalance source reserve balance
* @param _sourceReserveWeight source reserve weight, represented in ppm (1-1000000)
* @param _targetReserveBalance target reserve balance
* @param _targetReserveWeight target reserve weight, represented in ppm (1-1000000)
* @param _amount source reserve amount
*
* @return target reserve amount
*/
function crossReserveTargetAmount(
uint256 _sourceReserveBalance,
uint32 _sourceReserveWeight,
uint256 _targetReserveBalance,
uint32 _targetReserveWeight,
uint256 _amount
) public view override returns (uint256) {
// validate input
require(
_sourceReserveBalance > 0 && _targetReserveBalance > 0,
"ERR_INVALID_RESERVE_BALANCE"
);
require(
_sourceReserveWeight > 0 &&
_sourceReserveWeight <= MAX_WEIGHT &&
_targetReserveWeight > 0 &&
_targetReserveWeight <= MAX_WEIGHT,
"ERR_INVALID_RESERVE_WEIGHT"
);
// special case for equal weights
if (_sourceReserveWeight == _targetReserveWeight)
return
_targetReserveBalance.mul(_amount) /
_sourceReserveBalance.add(_amount);
uint256 result;
uint8 precision;
uint256 baseN = _sourceReserveBalance.add(_amount);
(result, precision) = power(
baseN,
_sourceReserveBalance,
_sourceReserveWeight,
_targetReserveWeight
);
uint256 temp1 = _targetReserveBalance.mul(result);
uint256 temp2 = _targetReserveBalance << precision;
return (temp1 - temp2) / result;
}
/**
* @dev given a pool token supply, reserve balance, reserve ratio and an amount of requested pool tokens,
* calculates the amount of reserve tokens required for purchasing the given amount of pool tokens
*
* Formula:
* return = _reserveBalance * (((_supply + _amount) / _supply) ^ (MAX_WEIGHT / _reserveRatio) - 1)
*
* @param _supply pool token supply
* @param _reserveBalance reserve balance
* @param _reserveRatio reserve ratio, represented in ppm (2-2000000)
* @param _amount requested amount of pool tokens
*
* @return reserve token amount
*/
function fundCost(
uint256 _supply,
uint256 _reserveBalance,
uint32 _reserveRatio,
uint256 _amount
) public view override returns (uint256) {
// validate input
require(_supply > 0, "ERR_INVALID_SUPPLY");
require(_reserveBalance > 0, "ERR_INVALID_RESERVE_BALANCE");
require(
_reserveRatio > 1 && _reserveRatio <= MAX_WEIGHT * 2,
"ERR_INVALID_RESERVE_RATIO"
);
// special case for 0 amount
if (_amount == 0) return 0;
// special case if the reserve ratio = 100%
if (_reserveRatio == MAX_WEIGHT)
return (_amount.mul(_reserveBalance) - 1) / _supply + 1;
uint256 result;
uint8 precision;
uint256 baseN = _supply.add(_amount);
(result, precision) = power(baseN, _supply, MAX_WEIGHT, _reserveRatio);
uint256 temp = ((_reserveBalance.mul(result) - 1) >> precision) + 1;
return temp - _reserveBalance;
}
/**
* @dev given a pool token supply, reserve balance, reserve ratio and an amount of reserve tokens to fund with,
* calculates the amount of pool tokens received for purchasing with the given amount of reserve tokens
*
* Formula:
* return = _supply * ((_amount / _reserveBalance + 1) ^ (_reserveRatio / MAX_WEIGHT) - 1)
*
* @param _supply pool token supply
* @param _reserveBalance reserve balance
* @param _reserveRatio reserve ratio, represented in ppm (2-2000000)
* @param _amount amount of reserve tokens to fund with
*
* @return pool token amount
*/
function fundSupplyAmount(
uint256 _supply,
uint256 _reserveBalance,
uint32 _reserveRatio,
uint256 _amount
) public view override returns (uint256) {
// validate input
require(_supply > 0, "ERR_INVALID_SUPPLY");
require(_reserveBalance > 0, "ERR_INVALID_RESERVE_BALANCE");
require(
_reserveRatio > 1 && _reserveRatio <= MAX_WEIGHT * 2,
"ERR_INVALID_RESERVE_RATIO"
);
// special case for 0 amount
if (_amount == 0) return 0;
// special case if the reserve ratio = 100%
if (_reserveRatio == MAX_WEIGHT)
return _amount.mul(_supply) / _reserveBalance;
uint256 result;
uint8 precision;
uint256 baseN = _reserveBalance.add(_amount);
(result, precision) = power(
baseN,
_reserveBalance,
_reserveRatio,
MAX_WEIGHT
);
uint256 temp = _supply.mul(result) >> precision;
return temp - _supply;
}
/**
* @dev given a pool token supply, reserve balance, reserve ratio and an amount of pool tokens to liquidate,
* calculates the amount of reserve tokens received for selling the given amount of pool tokens
*
* Formula:
* return = _reserveBalance * (1 - ((_supply - _amount) / _supply) ^ (MAX_WEIGHT / _reserveRatio))
*
* @param _supply pool token supply
* @param _reserveBalance reserve balance
* @param _reserveRatio reserve ratio, represented in ppm (2-2000000)
* @param _amount amount of pool tokens to liquidate
*
* @return reserve token amount
*/
function liquidateReserveAmount(
uint256 _supply,
uint256 _reserveBalance,
uint32 _reserveRatio,
uint256 _amount
) public view override returns (uint256) {
// validate input
require(_supply > 0, "ERR_INVALID_SUPPLY");
require(_reserveBalance > 0, "ERR_INVALID_RESERVE_BALANCE");
require(
_reserveRatio > 1 && _reserveRatio <= MAX_WEIGHT * 2,
"ERR_INVALID_RESERVE_RATIO"
);
require(_amount <= _supply, "ERR_INVALID_AMOUNT");
// special case for 0 amount
if (_amount == 0) return 0;
// special case for liquidating the entire supply
if (_amount == _supply) return _reserveBalance;
// special case if the reserve ratio = 100%
if (_reserveRatio == MAX_WEIGHT)
return _amount.mul(_reserveBalance) / _supply;
uint256 result;
uint8 precision;
uint256 baseD = _supply - _amount;
(result, precision) = power(_supply, baseD, MAX_WEIGHT, _reserveRatio);
uint256 temp1 = _reserveBalance.mul(result);
uint256 temp2 = _reserveBalance << precision;
return (temp1 - temp2) / result;
}
/**
* @dev The arbitrage incentive is to convert to the point where the on-chain price is equal to the off-chain price.
* We want this operation to also impact the primary reserve balance becoming equal to the primary reserve staked balance.
* In other words, we want the arbitrager to convert the difference between the reserve balance and the reserve staked balance.
*
* Formula input:
* - let t denote the primary reserve token staked balance
* - let s denote the primary reserve token balance
* - let r denote the secondary reserve token balance
* - let q denote the numerator of the rate between the tokens
* - let p denote the denominator of the rate between the tokens
* Where p primary tokens are equal to q secondary tokens
*
* Formula output:
* - compute x = W(t / r * q / p * log(s / t)) / log(s / t)
* - return x / (1 + x) as the weight of the primary reserve token
* - return 1 / (1 + x) as the weight of the secondary reserve token
* Where W is the Lambert W Function
*
* If the rate-provider provides the rates for a common unit, for example:
* - P = 2 ==> 2 primary reserve tokens = 1 ether
* - Q = 3 ==> 3 secondary reserve tokens = 1 ether
* Then you can simply use p = P and q = Q
*
* If the rate-provider provides the rates for a single unit, for example:
* - P = 2 ==> 1 primary reserve token = 2 ethers
* - Q = 3 ==> 1 secondary reserve token = 3 ethers
* Then you can simply use p = Q and q = P
*
* @param _primaryReserveStakedBalance the primary reserve token staked balance
* @param _primaryReserveBalance the primary reserve token balance
* @param _secondaryReserveBalance the secondary reserve token balance
* @param _reserveRateNumerator the numerator of the rate between the tokens
* @param _reserveRateDenominator the denominator of the rate between the tokens
*
* Note that `numerator / denominator` should represent the amount of secondary tokens equal to one primary token
*
* @return the weight of the primary reserve token and the weight of the secondary reserve token, both in ppm (0-1000000)
*/
function balancedWeights(
uint256 _primaryReserveStakedBalance,
uint256 _primaryReserveBalance,
uint256 _secondaryReserveBalance,
uint256 _reserveRateNumerator,
uint256 _reserveRateDenominator
) public view override returns (uint32, uint32) {
if (_primaryReserveStakedBalance == _primaryReserveBalance)
require(
_primaryReserveStakedBalance > 0 ||
_secondaryReserveBalance > 0,
"ERR_INVALID_RESERVE_BALANCE"
);
else
require(
_primaryReserveStakedBalance > 0 &&
_primaryReserveBalance > 0 &&
_secondaryReserveBalance > 0,
"ERR_INVALID_RESERVE_BALANCE"
);
require(
_reserveRateNumerator > 0 && _reserveRateDenominator > 0,
"ERR_INVALID_RESERVE_RATE"
);
uint256 tq = _primaryReserveStakedBalance.mul(_reserveRateNumerator);
uint256 rp = _secondaryReserveBalance.mul(_reserveRateDenominator);
if (_primaryReserveStakedBalance < _primaryReserveBalance)
return
balancedWeightsByStake(
_primaryReserveBalance,
_primaryReserveStakedBalance,
tq,
rp,
true
);
if (_primaryReserveStakedBalance > _primaryReserveBalance)
return
balancedWeightsByStake(
_primaryReserveStakedBalance,
_primaryReserveBalance,
tq,
rp,
false
);
return normalizedWeights(tq, rp);
}
}
/https_/github.com/slim12kg/protofire-continous-token-task/blob/master/contracts/interfaces/IBancorFormula.sol
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
/*
Bancor Formula interface
*/
interface IBancorFormula {
function purchaseTargetAmount(
uint256 _supply,
uint256 _reserveBalance,
uint32 _reserveWeight,
uint256 _amount
) external view returns (uint256);
function saleTargetAmount(
uint256 _supply,
uint256 _reserveBalance,
uint32 _reserveWeight,
uint256 _amount
) external view returns (uint256);
function crossReserveTargetAmount(
uint256 _sourceReserveBalance,
uint32 _sourceReserveWeight,
uint256 _targetReserveBalance,
uint32 _targetReserveWeight,
uint256 _amount
) external view returns (uint256);
function fundCost(
uint256 _supply,
uint256 _reserveBalance,
uint32 _reserveRatio,
uint256 _amount
) external view returns (uint256);
function fundSupplyAmount(
uint256 _supply,
uint256 _reserveBalance,
uint32 _reserveRatio,
uint256 _amount
) external view returns (uint256);
function liquidateReserveAmount(
uint256 _supply,
uint256 _reserveBalance,
uint32 _reserveRatio,
uint256 _amount
) external view returns (uint256);
function balancedWeights(
uint256 _primaryReserveStakedBalance,
uint256 _primaryReserveBalance,
uint256 _secondaryReserveBalance,
uint256 _reserveRateNumerator,
uint256 _reserveRateDenominator
) external view returns (uint32, uint32);
}
/https_/github.com/slim12kg/protofire-continous-token-task/blob/master/contracts/utils/Power.sol
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
import "@openzeppelin/contracts/utils/math/SafeMath.sol";
contract Power{
using SafeMath for uint256;
uint256 private constant ONE = 1;
uint32 private constant MAX_WEIGHT = 1000000;
uint8 private constant MIN_PRECISION = 32;
uint8 private constant MAX_PRECISION = 127;
// Auto-generated via 'PrintIntScalingFactors.py'
uint256 private constant FIXED_1 = 0x080000000000000000000000000000000;
uint256 private constant FIXED_2 = 0x100000000000000000000000000000000;
uint256 private constant MAX_NUM = 0x200000000000000000000000000000000;
// Auto-generated via 'PrintLn2ScalingFactors.py'
uint256 private constant LN2_NUMERATOR = 0x3f80fe03f80fe03f80fe03f80fe03f8;
uint256 private constant LN2_DENOMINATOR = 0x5b9de1d10bf4103d647b0955897ba80;
// Auto-generated via 'PrintFunctionOptimalLog.py' and 'PrintFunctionOptimalExp.py'
uint256 private constant OPT_LOG_MAX_VAL =
0x15bf0a8b1457695355fb8ac404e7a79e3;
uint256 private constant OPT_EXP_MAX_VAL =
0x800000000000000000000000000000000;
// Auto-generated via 'PrintLambertFactors.py'
uint256 private constant LAMBERT_CONV_RADIUS =
0x002f16ac6c59de6f8d5d6f63c1482a7c86;
uint256 private constant LAMBERT_POS2_SAMPLE =
0x0003060c183060c183060c183060c18306;
uint256 private constant LAMBERT_POS2_MAXVAL =
0x01af16ac6c59de6f8d5d6f63c1482a7c80;
uint256 private constant LAMBERT_POS3_MAXVAL =
0x6b22d43e72c326539cceeef8bb48f255ff;
// Auto-generated via 'PrintWeightFactors.py'
uint256 private constant MAX_UNF_WEIGHT =
0x10c6f7a0b5ed8d36b4c7f34938583621fafc8b0079a2834d26fa3fcc9ea9;
// Auto-generated via 'PrintMaxExpArray.py'
uint256[128] private maxExpArray;
function initMaxExpArray() public {
maxExpArray[32] = 0x1c35fedd14ffffffffffffffffffffffff;
maxExpArray[33] = 0x1b0ce43b323fffffffffffffffffffffff;
maxExpArray[34] = 0x19f0028ec1ffffffffffffffffffffffff;
maxExpArray[35] = 0x18ded91f0e7fffffffffffffffffffffff;
maxExpArray[36] = 0x17d8ec7f0417ffffffffffffffffffffff;
maxExpArray[37] = 0x16ddc6556cdbffffffffffffffffffffff;
maxExpArray[38] = 0x15ecf52776a1ffffffffffffffffffffff;
maxExpArray[39] = 0x15060c256cb2ffffffffffffffffffffff;
maxExpArray[40] = 0x1428a2f98d72ffffffffffffffffffffff;
maxExpArray[41] = 0x13545598e5c23fffffffffffffffffffff;
maxExpArray[42] = 0x1288c4161ce1dfffffffffffffffffffff;
maxExpArray[43] = 0x11c592761c666fffffffffffffffffffff;
maxExpArray[44] = 0x110a688680a757ffffffffffffffffffff;
maxExpArray[45] = 0x1056f1b5bedf77ffffffffffffffffffff;
maxExpArray[46] = 0x0faadceceeff8bffffffffffffffffffff;
maxExpArray[47] = 0x0f05dc6b27edadffffffffffffffffffff;
maxExpArray[48] = 0x0e67a5a25da4107fffffffffffffffffff;
maxExpArray[49] = 0x0dcff115b14eedffffffffffffffffffff;
maxExpArray[50] = 0x0d3e7a392431239fffffffffffffffffff;
maxExpArray[51] = 0x0cb2ff529eb71e4fffffffffffffffffff;
maxExpArray[52] = 0x0c2d415c3db974afffffffffffffffffff;
maxExpArray[53] = 0x0bad03e7d883f69bffffffffffffffffff;
maxExpArray[54] = 0x0b320d03b2c343d5ffffffffffffffffff;
maxExpArray[55] = 0x0abc25204e02828dffffffffffffffffff;
maxExpArray[56] = 0x0a4b16f74ee4bb207fffffffffffffffff;
maxExpArray[57] = 0x09deaf736ac1f569ffffffffffffffffff;
maxExpArray[58] = 0x0976bd9952c7aa957fffffffffffffffff;
maxExpArray[59] = 0x09131271922eaa606fffffffffffffffff;
maxExpArray[60] = 0x08b380f3558668c46fffffffffffffffff;
maxExpArray[61] = 0x0857ddf0117efa215bffffffffffffffff;
maxExpArray[62] = 0x07ffffffffffffffffffffffffffffffff;
maxExpArray[63] = 0x07abbf6f6abb9d087fffffffffffffffff;
maxExpArray[64] = 0x075af62cbac95f7dfa7fffffffffffffff;
maxExpArray[65] = 0x070d7fb7452e187ac13fffffffffffffff;
maxExpArray[66] = 0x06c3390ecc8af379295fffffffffffffff;
maxExpArray[67] = 0x067c00a3b07ffc01fd6fffffffffffffff;
maxExpArray[68] = 0x0637b647c39cbb9d3d27ffffffffffffff;
maxExpArray[69] = 0x05f63b1fc104dbd39587ffffffffffffff;
maxExpArray[70] = 0x05b771955b36e12f7235ffffffffffffff;
maxExpArray[71] = 0x057b3d49dda84556d6f6ffffffffffffff;
maxExpArray[72] = 0x054183095b2c8ececf30ffffffffffffff;
maxExpArray[73] = 0x050a28be635ca2b888f77fffffffffffff;
maxExpArray[74] = 0x04d5156639708c9db33c3fffffffffffff;
maxExpArray[75] = 0x04a23105873875bd52dfdfffffffffffff;
maxExpArray[76] = 0x0471649d87199aa990756fffffffffffff;
maxExpArray[77] = 0x04429a21a029d4c1457cfbffffffffffff;
maxExpArray[78] = 0x0415bc6d6fb7dd71af2cb3ffffffffffff;
maxExpArray[79] = 0x03eab73b3bbfe282243ce1ffffffffffff;
maxExpArray[80] = 0x03c1771ac9fb6b4c18e229ffffffffffff;
maxExpArray[81] = 0x0399e96897690418f785257fffffffffff;
maxExpArray[82] = 0x0373fc456c53bb779bf0ea9fffffffffff;
maxExpArray[83] = 0x034f9e8e490c48e67e6ab8bfffffffffff;
maxExpArray[84] = 0x032cbfd4a7adc790560b3337ffffffffff;
maxExpArray[85] = 0x030b50570f6e5d2acca94613ffffffffff;
maxExpArray[86] = 0x02eb40f9f620fda6b56c2861ffffffffff;
maxExpArray[87] = 0x02cc8340ecb0d0f520a6af58ffffffffff;
maxExpArray[88] = 0x02af09481380a0a35cf1ba02ffffffffff;
maxExpArray[89] = 0x0292c5bdd3b92ec810287b1b3fffffffff;
maxExpArray[90] = 0x0277abdcdab07d5a77ac6d6b9fffffffff;
maxExpArray[91] = 0x025daf6654b1eaa55fd64df5efffffffff;
maxExpArray[92] = 0x0244c49c648baa98192dce88b7ffffffff;
maxExpArray[93] = 0x022ce03cd5619a311b2471268bffffffff;
maxExpArray[94] = 0x0215f77c045fbe885654a44a0fffffffff;
maxExpArray[95] = 0x01ffffffffffffffffffffffffffffffff;
maxExpArray[96] = 0x01eaefdbdaaee7421fc4d3ede5ffffffff;
maxExpArray[97] = 0x01d6bd8b2eb257df7e8ca57b09bfffffff;
maxExpArray[98] = 0x01c35fedd14b861eb0443f7f133fffffff;
maxExpArray[99] = 0x01b0ce43b322bcde4a56e8ada5afffffff;
maxExpArray[100] = 0x019f0028ec1fff007f5a195a39dfffffff;
maxExpArray[101] = 0x018ded91f0e72ee74f49b15ba527ffffff;
maxExpArray[102] = 0x017d8ec7f04136f4e5615fd41a63ffffff;
maxExpArray[103] = 0x016ddc6556cdb84bdc8d12d22e6fffffff;
maxExpArray[104] = 0x015ecf52776a1155b5bd8395814f7fffff;
maxExpArray[105] = 0x015060c256cb23b3b3cc3754cf40ffffff;
maxExpArray[106] = 0x01428a2f98d728ae223ddab715be3fffff;
maxExpArray[107] = 0x013545598e5c23276ccf0ede68034fffff;
maxExpArray[108] = 0x01288c4161ce1d6f54b7f61081194fffff;
maxExpArray[109] = 0x011c592761c666aa641d5a01a40f17ffff;
maxExpArray[110] = 0x0110a688680a7530515f3e6e6cfdcdffff;
maxExpArray[111] = 0x01056f1b5bedf75c6bcb2ce8aed428ffff;
maxExpArray[112] = 0x00faadceceeff8a0890f3875f008277fff;
maxExpArray[113] = 0x00f05dc6b27edad306388a600f6ba0bfff;
maxExpArray[114] = 0x00e67a5a25da41063de1495d5b18cdbfff;
maxExpArray[115] = 0x00dcff115b14eedde6fc3aa5353f2e4fff;
maxExpArray[116] = 0x00d3e7a3924312399f9aae2e0f868f8fff;
maxExpArray[117] = 0x00cb2ff529eb71e41582cccd5a1ee26fff;
maxExpArray[118] = 0x00c2d415c3db974ab32a51840c0b67edff;
maxExpArray[119] = 0x00bad03e7d883f69ad5b0a186184e06bff;
maxExpArray[120] = 0x00b320d03b2c343d4829abd6075f0cc5ff;
maxExpArray[121] = 0x00abc25204e02828d73c6e80bcdb1a95bf;
maxExpArray[122] = 0x00a4b16f74ee4bb2040a1ec6c15fbbf2df;
maxExpArray[123] = 0x009deaf736ac1f569deb1b5ae3f36c130f;
maxExpArray[124] = 0x00976bd9952c7aa957f5937d790ef65037;
maxExpArray[125] = 0x009131271922eaa6064b73a22d0bd4f2bf;
maxExpArray[126] = 0x008b380f3558668c46c91c49a2f8e967b9;
maxExpArray[127] = 0x00857ddf0117efa215952912839f6473e6;
}
// Auto-generated via 'PrintLambertArray.py'
uint256[128] private lambertArray;
function initLambertArray() public {
lambertArray[0] = 0x60e393c68d20b1bd09deaabc0373b9c5;
lambertArray[1] = 0x5f8f46e4854120989ed94719fb4c2011;
lambertArray[2] = 0x5e479ebb9129fb1b7e72a648f992b606;
lambertArray[3] = 0x5d0bd23fe42dfedde2e9586be12b85fe;
lambertArray[4] = 0x5bdb29ddee979308ddfca81aeeb8095a;
lambertArray[5] = 0x5ab4fd8a260d2c7e2c0d2afcf0009dad;
lambertArray[6] = 0x5998b31359a55d48724c65cf09001221;
lambertArray[7] = 0x5885bcad2b322dfc43e8860f9c018cf5;
lambertArray[8] = 0x577b97aa1fe222bb452fdf111b1f0be2;
lambertArray[9] = 0x5679cb5e3575632e5baa27e2b949f704;
lambertArray[10] = 0x557fe8241b3a31c83c732f1cdff4a1c5;
lambertArray[11] = 0x548d868026504875d6e59bbe95fc2a6b;
lambertArray[12] = 0x53a2465ce347cf34d05a867c17dd3088;
lambertArray[13] = 0x52bdce5dcd4faed59c7f5511cf8f8acc;
lambertArray[14] = 0x51dfcb453c07f8da817606e7885f7c3e;
lambertArray[15] = 0x5107ef6b0a5a2be8f8ff15590daa3cce;
lambertArray[16] = 0x5035f241d6eae0cd7bacba119993de7b;
lambertArray[17] = 0x4f698fe90d5b53d532171e1210164c66;
lambertArray[18] = 0x4ea288ca297a0e6a09a0eee240e16c85;
lambertArray[19] = 0x4de0a13fdcf5d4213fc398ba6e3becde;
lambertArray[20] = 0x4d23a145eef91fec06b06140804c4808;
lambertArray[21] = 0x4c6b5430d4c1ee5526473db4ae0f11de;
lambertArray[22] = 0x4bb7886c240562eba11f4963a53b4240;
lambertArray[23] = 0x4b080f3f1cb491d2d521e0ea4583521e;
lambertArray[24] = 0x4a5cbc96a05589cb4d86be1db3168364;
lambertArray[25] = 0x49b566d40243517658d78c33162d6ece;
lambertArray[26] = 0x4911e6a02e5507a30f947383fd9a3276;
lambertArray[27] = 0x487216c2b31be4adc41db8a8d5cc0c88;
lambertArray[28] = 0x47d5d3fc4a7a1b188cd3d788b5c5e9fc;
lambertArray[29] = 0x473cfce4871a2c40bc4f9e1c32b955d0;
lambertArray[30] = 0x46a771ca578ab878485810e285e31c67;
lambertArray[31] = 0x4615149718aed4c258c373dc676aa72d;
lambertArray[32] = 0x4585c8b3f8fe489c6e1833ca47871384;
lambertArray[33] = 0x44f972f174e41e5efb7e9d63c29ce735;
lambertArray[34] = 0x446ff970ba86d8b00beb05ecebf3c4dc;
lambertArray[35] = 0x43e9438ec88971812d6f198b5ccaad96;
lambertArray[36] = 0x436539d11ff7bea657aeddb394e809ef;
lambertArray[37] = 0x42e3c5d3e5a913401d86f66db5d81c2c;
lambertArray[38] = 0x4264d2395303070ea726cbe98df62174;
lambertArray[39] = 0x41e84a9a593bb7194c3a6349ecae4eea;
lambertArray[40] = 0x416e1b785d13eba07a08f3f18876a5ab;
lambertArray[41] = 0x40f6322ff389d423ba9dd7e7e7b7e809;
lambertArray[42] = 0x40807cec8a466880ecf4184545d240a4;
lambertArray[43] = 0x400cea9ce88a8d3ae668e8ea0d9bf07f;
lambertArray[44] = 0x3f9b6ae8772d4c55091e0ed7dfea0ac1;
lambertArray[45] = 0x3f2bee253fd84594f54bcaafac383a13;
lambertArray[46] = 0x3ebe654e95208bb9210c575c081c5958;
lambertArray[47] = 0x3e52c1fc5665635b78ce1f05ad53c086;
lambertArray[48] = 0x3de8f65ac388101ddf718a6f5c1eff65;
lambertArray[49] = 0x3d80f522d59bd0b328ca012df4cd2d49;
lambertArray[50] = 0x3d1ab193129ea72b23648a161163a85a;
lambertArray[51] = 0x3cb61f68d32576c135b95cfb53f76d75;
lambertArray[52] = 0x3c5332d9f1aae851a3619e77e4cc8473;
lambertArray[53] = 0x3bf1e08edbe2aa109e1525f65759ef73;
lambertArray[54] = 0x3b921d9cff13fa2c197746a3dfc4918f;
lambertArray[55] = 0x3b33df818910bfc1a5aefb8f63ae2ac4;
lambertArray[56] = 0x3ad71c1c77e34fa32a9f184967eccbf6;
lambertArray[57] = 0x3a7bc9abf2c5bb53e2f7384a8a16521a;
lambertArray[58] = 0x3a21dec7e76369783a68a0c6385a1c57;
lambertArray[59] = 0x39c9525de6c9cdf7c1c157ca4a7a6ee3;
lambertArray[60] = 0x39721bad3dc85d1240ff0190e0adaac3;
lambertArray[61] = 0x391c324344d3248f0469eb28dd3d77e0;
lambertArray[62] = 0x38c78df7e3c796279fb4ff84394ab3da;
lambertArray[63] = 0x387426ea4638ae9aae08049d3554c20a;
lambertArray[64] = 0x3821f57dbd2763256c1a99bbd2051378;
lambertArray[65] = 0x37d0f256cb46a8c92ff62fbbef289698;
lambertArray[66] = 0x37811658591ffc7abdd1feaf3cef9b73;
lambertArray[67] = 0x37325aa10e9e82f7df0f380f7997154b;
lambertArray[68] = 0x36e4b888cfb408d873b9a80d439311c6;
lambertArray[69] = 0x3698299e59f4bb9de645fc9b08c64cca;
lambertArray[70] = 0x364ca7a5012cb603023b57dd3ebfd50d;
lambertArray[71] = 0x36022c928915b778ab1b06aaee7e61d4;
lambertArray[72] = 0x35b8b28d1a73dc27500ffe35559cc028;
lambertArray[73] = 0x357033e951fe250ec5eb4e60955132d7;
lambertArray[74] = 0x3528ab2867934e3a21b5412e4c4f8881;
lambertArray[75] = 0x34e212f66c55057f9676c80094a61d59;
lambertArray[76] = 0x349c66289e5b3c4b540c24f42fa4b9bb;
lambertArray[77] = 0x34579fbbd0c733a9c8d6af6b0f7d00f7;
lambertArray[78] = 0x3413bad2e712288b924b5882b5b369bf;
lambertArray[79] = 0x33d0b2b56286510ef730e213f71f12e9;
lambertArray[80] = 0x338e82ce00e2496262c64457535ba1a1;
lambertArray[81] = 0x334d26a96b373bb7c2f8ea1827f27a92;
lambertArray[82] = 0x330c99f4f4211469e00b3e18c31475ea;
lambertArray[83] = 0x32ccd87d6486094999c7d5e6f33237d8;
lambertArray[84] = 0x328dde2dd617b6665a2e8556f250c1af;
lambertArray[85] = 0x324fa70e9adc270f8262755af5a99af9;
lambertArray[86] = 0x32122f443110611ca51040f41fa6e1e3;
lambertArray[87] = 0x31d5730e42c0831482f0f1485c4263d8;
lambertArray[88] = 0x31996ec6b07b4a83421b5ebc4ab4e1f1;
lambertArray[89] = 0x315e1ee0a68ff46bb43ec2b85032e876;
lambertArray[90] = 0x31237fe7bc4deacf6775b9efa1a145f8;
lambertArray[91] = 0x30e98e7f1cc5a356e44627a6972ea2ff;
lambertArray[92] = 0x30b04760b8917ec74205a3002650ec05;
lambertArray[93] = 0x3077a75c803468e9132ce0cf3224241d;
lambertArray[94] = 0x303fab57a6a275c36f19cda9bace667a;
lambertArray[95] = 0x3008504beb8dcbd2cf3bc1f6d5a064f0;
lambertArray[96] = 0x2fd19346ed17dac61219ce0c2c5ac4b0;
lambertArray[97] = 0x2f9b7169808c324b5852fd3d54ba9714;
lambertArray[98] = 0x2f65e7e711cf4b064eea9c08cbdad574;
lambertArray[99] = 0x2f30f405093042ddff8a251b6bf6d103;
lambertArray[100] = 0x2efc931a3750f2e8bfe323edfe037574;
lambertArray[101] = 0x2ec8c28e46dbe56d98685278339400cb;
lambertArray[102] = 0x2e957fd933c3926d8a599b602379b851;
lambertArray[103] = 0x2e62c882c7c9ed4473412702f08ba0e5;
lambertArray[104] = 0x2e309a221c12ba361e3ed695167feee2;
lambertArray[105] = 0x2dfef25d1f865ae18dd07cfea4bcea10;
lambertArray[106] = 0x2dcdcee821cdc80decc02c44344aeb31;
lambertArray[107] = 0x2d9d2d8562b34944d0b201bb87260c83;
lambertArray[108] = 0x2d6d0c04a5b62a2c42636308669b729a;
lambertArray[109] = 0x2d3d6842c9a235517fc5a0332691528f;
lambertArray[110] = 0x2d0e402963fe1ea2834abc408c437c10;
lambertArray[111] = 0x2cdf91ae602647908aff975e4d6a2a8c;
lambertArray[112] = 0x2cb15ad3a1eb65f6d74a75da09a1b6c5;
lambertArray[113] = 0x2c8399a6ab8e9774d6fcff373d210727;
lambertArray[114] = 0x2c564c4046f64edba6883ca06bbc4535;
lambertArray[115] = 0x2c2970c431f952641e05cb493e23eed3;
lambertArray[116] = 0x2bfd0560cd9eb14563bc7c0732856c18;
lambertArray[117] = 0x2bd1084ed0332f7ff4150f9d0ef41a2c;
lambertArray[118] = 0x2ba577d0fa1628b76d040b12a82492fb;
lambertArray[119] = 0x2b7a5233cd21581e855e89dc2f1e8a92;
lambertArray[120] = 0x2b4f95cd46904d05d72bdcde337d9cc7;
lambertArray[121] = 0x2b2540fc9b4d9abba3faca6691914675;
lambertArray[122] = 0x2afb5229f68d0830d8be8adb0a0db70f;
lambertArray[123] = 0x2ad1c7c63a9b294c5bc73a3ba3ab7a2b;
lambertArray[124] = 0x2aa8a04ac3cbe1ee1c9c86361465dbb8;
lambertArray[125] = 0x2a7fda392d725a44a2c8aeb9ab35430d;
lambertArray[126] = 0x2a57741b18cde618717792b4faa216db;
lambertArray[127] = 0x2a2f6c81f5d84dd950a35626d6d5503a;
}
/**
* @dev General Description:
* Determine a value of precision.
* Calculate an integer approximation of (_baseN / _baseD) ^ (_expN / _expD) * 2 ^ precision.
* Return the result along with the precision used.
*
* Detailed Description:
* Instead of calculating "base ^ exp", we calculate "e ^ (log(base) * exp)".
* The value of "log(base)" is represented with an integer slightly smaller than "log(base) * 2 ^ precision".
* The larger "precision" is, the more accurately this value represents the real value.
* However, the larger "precision" is, the more bits are required in order to store this value.
* And the exponentiation function, which takes "x" and calculates "e ^ x", is limited to a maximum exponent (maximum value of "x").
* This maximum exponent depends on the "precision" used, and it is given by "maxExpArray[precision] >> (MAX_PRECISION - precision)".
* Hence we need to determine the highest precision which can be used for the given input, before calling the exponentiation function.
* This allows us to compute "base ^ exp" with maximum accuracy and without exceeding 256 bits in any of the intermediate computations.
* This functions assumes that "_expN < 2 ^ 256 / log(MAX_NUM - 1)", otherwise the multiplication should be replaced with a "safeMul".
* Since we rely on unsigned-integer arithmetic and "base < 1" ==> "log(base) < 0", this function does not support "_baseN < _baseD".
*/
function power(
uint256 _baseN,
uint256 _baseD,
uint32 _expN,
uint32 _expD
) public view returns (uint256, uint8) {
require(_baseN < MAX_NUM);
uint256 baseLog;
uint256 base = (_baseN * FIXED_1) / _baseD;
if (base < OPT_LOG_MAX_VAL) {
baseLog = optimalLog(base);
} else {
baseLog = generalLog(base);
}
uint256 baseLogTimesExp = (baseLog * _expN) / _expD;
if (baseLogTimesExp < OPT_EXP_MAX_VAL) {
return (optimalExp(baseLogTimesExp), MAX_PRECISION);
} else {
uint8 precision = findPositionInMaxExpArray(baseLogTimesExp);
return (
generalExp(
baseLogTimesExp >> (MAX_PRECISION - precision),
precision
),
precision
);
}
}
/**
* @dev computes log(x / FIXED_1) * FIXED_1.
* This functions assumes that "x >= FIXED_1", because the output would be negative otherwise.
*/
function generalLog(uint256 x) internal pure returns (uint256) {
uint256 res = 0;
// If x >= 2, then we compute the integer part of log2(x), which is larger than 0.
if (x >= FIXED_2) {
uint8 count = floorLog2(x / FIXED_1);
x >>= count; // now x < 2
res = count * FIXED_1;
}
// If x > 1, then we compute the fraction part of log2(x), which is larger than 0.
if (x > FIXED_1) {
for (uint8 i = MAX_PRECISION; i > 0; --i) {
x = (x * x) / FIXED_1; // now 1 < x < 4
if (x >= FIXED_2) {
x >>= 1; // now 1 < x < 2
res += ONE << (i - 1);
}
}
}
return (res * LN2_NUMERATOR) / LN2_DENOMINATOR;
}
/**
* @dev computes the largest integer smaller than or equal to the binary logarithm of the input.
*/
function floorLog2(uint256 _n) internal pure returns (uint8) {
uint8 res = 0;
if (_n < 256) {
// At most 8 iterations
while (_n > 1) {
_n >>= 1;
res += 1;
}
} else {
// Exactly 8 iterations
for (uint8 s = 128; s > 0; s >>= 1) {
if (_n >= (ONE << s)) {
_n >>= s;
res |= s;
}
}
}
return res;
}
/**
* @dev the global "maxExpArray" is sorted in descending order, and therefore the following statements are equivalent:
* - This function finds the position of [the smallest value in "maxExpArray" larger than or equal to "x"]
* - This function finds the highest position of [a value in "maxExpArray" larger than or equal to "x"]
*/
function findPositionInMaxExpArray(uint256 _x)
internal
view
returns (uint8 pos)
{
uint8 lo = MIN_PRECISION;
uint8 hi = MAX_PRECISION;
while (lo + 1 < hi) {
uint8 mid = (lo + hi) / 2;
if (maxExpArray[mid] >= _x) lo = mid;
else hi = mid;
}
if (maxExpArray[hi] >= _x) return pos = hi;
if (maxExpArray[lo] >= _x) return pos = lo;
require(false);
}
/**
* @dev this function can be auto-generated by the script 'PrintFunctionGeneralExp.py'.
* it approximates "e ^ x" via maclaurin summation: "(x^0)/0! + (x^1)/1! + ... + (x^n)/n!".
* it returns "e ^ (x / 2 ^ precision) * 2 ^ precision", that is, the result is upshifted for accuracy.
* the global "maxExpArray" maps each "precision" to "((maximumExponent + 1) << (MAX_PRECISION - precision)) - 1".
* the maximum permitted value for "x" is therefore given by "maxExpArray[precision] >> (MAX_PRECISION - precision)".
*/
function generalExp(uint256 _x, uint8 _precision)
internal
pure
returns (uint256)
{
uint256 xi = _x;
uint256 res = 0;
xi = (xi * _x) >> _precision;
res += xi * 0x3442c4e6074a82f1797f72ac0000000; // add x^02 * (33! / 02!)
xi = (xi * _x) >> _precision;
res += xi * 0x116b96f757c380fb287fd0e40000000; // add x^03 * (33! / 03!)
xi = (xi * _x) >> _precision;
res += xi * 0x045ae5bdd5f0e03eca1ff4390000000; // add x^04 * (33! / 04!)
xi = (xi * _x) >> _precision;
res += xi * 0x00defabf91302cd95b9ffda50000000; // add x^05 * (33! / 05!)
xi = (xi * _x) >> _precision;
res += xi * 0x002529ca9832b22439efff9b8000000; // add x^06 * (33! / 06!)
xi = (xi * _x) >> _precision;
res += xi * 0x00054f1cf12bd04e516b6da88000000; // add x^07 * (33! / 07!)
xi = (xi * _x) >> _precision;
res += xi * 0x0000a9e39e257a09ca2d6db51000000; // add x^08 * (33! / 08!)
xi = (xi * _x) >> _precision;
res += xi * 0x000012e066e7b839fa050c309000000; // add x^09 * (33! / 09!)
xi = (xi * _x) >> _precision;
res += xi * 0x000001e33d7d926c329a1ad1a800000; // add x^10 * (33! / 10!)
xi = (xi * _x) >> _precision;
res += xi * 0x0000002bee513bdb4a6b19b5f800000; // add x^11 * (33! / 11!)
xi = (xi * _x) >> _precision;
res += xi * 0x00000003a9316fa79b88eccf2a00000; // add x^12 * (33! / 12!)
xi = (xi * _x) >> _precision;
res += xi * 0x0000000048177ebe1fa812375200000; // add x^13 * (33! / 13!)
xi = (xi * _x) >> _precision;
res += xi * 0x0000000005263fe90242dcbacf00000; // add x^14 * (33! / 14!)
xi = (xi * _x) >> _precision;
res += xi * 0x000000000057e22099c030d94100000; // add x^15 * (33! / 15!)
xi = (xi * _x) >> _precision;
res += xi * 0x0000000000057e22099c030d9410000; // add x^16 * (33! / 16!)
xi = (xi * _x) >> _precision;
res += xi * 0x00000000000052b6b54569976310000; // add x^17 * (33! / 17!)
xi = (xi * _x) >> _precision;
res += xi * 0x00000000000004985f67696bf748000; // add x^18 * (33! / 18!)
xi = (xi * _x) >> _precision;
res += xi * 0x000000000000003dea12ea99e498000; // add x^19 * (33! / 19!)
xi = (xi * _x) >> _precision;
res += xi * 0x00000000000000031880f2214b6e000; // add x^20 * (33! / 20!)
xi = (xi * _x) >> _precision;
res += xi * 0x000000000000000025bcff56eb36000; // add x^21 * (33! / 21!)
xi = (xi * _x) >> _precision;
res += xi * 0x000000000000000001b722e10ab1000; // add x^22 * (33! / 22!)
xi = (xi * _x) >> _precision;
res += xi * 0x0000000000000000001317c70077000; // add x^23 * (33! / 23!)
xi = (xi * _x) >> _precision;
res += xi * 0x00000000000000000000cba84aafa00; // add x^24 * (33! / 24!)
xi = (xi * _x) >> _precision;
res += xi * 0x00000000000000000000082573a0a00; // add x^25 * (33! / 25!)
xi = (xi * _x) >> _precision;
res += xi * 0x00000000000000000000005035ad900; // add x^26 * (33! / 26!)
xi = (xi * _x) >> _precision;
res += xi * 0x000000000000000000000002f881b00; // add x^27 * (33! / 27!)
xi = (xi * _x) >> _precision;
res += xi * 0x0000000000000000000000001b29340; // add x^28 * (33! / 28!)
xi = (xi * _x) >> _precision;
res += xi * 0x00000000000000000000000000efc40; // add x^29 * (33! / 29!)
xi = (xi * _x) >> _precision;
res += xi * 0x0000000000000000000000000007fe0; // add x^30 * (33! / 30!)
xi = (xi * _x) >> _precision;
res += xi * 0x0000000000000000000000000000420; // add x^31 * (33! / 31!)
xi = (xi * _x) >> _precision;
res += xi * 0x0000000000000000000000000000021; // add x^32 * (33! / 32!)
xi = (xi * _x) >> _precision;
res += xi * 0x0000000000000000000000000000001; // add x^33 * (33! / 33!)
return
res / 0x688589cc0e9505e2f2fee5580000000 + _x + (ONE << _precision); // divide by 33! and then add x^1 / 1! + x^0 / 0!
}
/**
* @dev computes log(x / FIXED_1) * FIXED_1
* Input range: FIXED_1 <= x <= OPT_LOG_MAX_VAL - 1
* Auto-generated via 'PrintFunctionOptimalLog.py'
* Detailed description:
* - Rewrite the input as a product of natural exponents and a single residual r, such that 1 < r < 2
* - The natural logarithm of each (pre-calculated) exponent is the degree of the exponent
* - The natural logarithm of r is calculated via Taylor series for log(1 + x), where x = r - 1
* - The natural logarithm of the input is calculated by summing up the intermediate results above
* - For example: log(250) = log(e^4 * e^1 * e^0.5 * 1.021692859) = 4 + 1 + 0.5 + log(1 + 0.021692859)
*/
function optimalLog(uint256 x) internal pure returns (uint256) {
uint256 res = 0;
uint256 y;
uint256 z;
uint256 w;
if (x >= 0xd3094c70f034de4b96ff7d5b6f99fcd8) {
res += 0x40000000000000000000000000000000;
x = (x * FIXED_1) / 0xd3094c70f034de4b96ff7d5b6f99fcd8;
} // add 1 / 2^1
if (x >= 0xa45af1e1f40c333b3de1db4dd55f29a7) {
res += 0x20000000000000000000000000000000;
x = (x * FIXED_1) / 0xa45af1e1f40c333b3de1db4dd55f29a7;
} // add 1 / 2^2
if (x >= 0x910b022db7ae67ce76b441c27035c6a1) {
res += 0x10000000000000000000000000000000;
x = (x * FIXED_1) / 0x910b022db7ae67ce76b441c27035c6a1;
} // add 1 / 2^3
if (x >= 0x88415abbe9a76bead8d00cf112e4d4a8) {
res += 0x08000000000000000000000000000000;
x = (x * FIXED_1) / 0x88415abbe9a76bead8d00cf112e4d4a8;
} // add 1 / 2^4
if (x >= 0x84102b00893f64c705e841d5d4064bd3) {
res += 0x04000000000000000000000000000000;
x = (x * FIXED_1) / 0x84102b00893f64c705e841d5d4064bd3;
} // add 1 / 2^5
if (x >= 0x8204055aaef1c8bd5c3259f4822735a2) {
res += 0x02000000000000000000000000000000;
x = (x * FIXED_1) / 0x8204055aaef1c8bd5c3259f4822735a2;
} // add 1 / 2^6
if (x >= 0x810100ab00222d861931c15e39b44e99) {
res += 0x01000000000000000000000000000000;
x = (x * FIXED_1) / 0x810100ab00222d861931c15e39b44e99;
} // add 1 / 2^7
if (x >= 0x808040155aabbbe9451521693554f733) {
res += 0x00800000000000000000000000000000;
x = (x * FIXED_1) / 0x808040155aabbbe9451521693554f733;
} // add 1 / 2^8
z = y = x - FIXED_1;
w = (y * y) / FIXED_1;
res +=
(z * (0x100000000000000000000000000000000 - y)) /
0x100000000000000000000000000000000;
z = (z * w) / FIXED_1; // add y^01 / 01 - y^02 / 02
res +=
(z * (0x0aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa - y)) /
0x200000000000000000000000000000000;
z = (z * w) / FIXED_1; // add y^03 / 03 - y^04 / 04
res +=
(z * (0x099999999999999999999999999999999 - y)) /
0x300000000000000000000000000000000;
z = (z * w) / FIXED_1; // add y^05 / 05 - y^06 / 06
res +=
(z * (0x092492492492492492492492492492492 - y)) /
0x400000000000000000000000000000000;
z = (z * w) / FIXED_1; // add y^07 / 07 - y^08 / 08
res +=
(z * (0x08e38e38e38e38e38e38e38e38e38e38e - y)) /
0x500000000000000000000000000000000;
z = (z * w) / FIXED_1; // add y^09 / 09 - y^10 / 10
res +=
(z * (0x08ba2e8ba2e8ba2e8ba2e8ba2e8ba2e8b - y)) /
0x600000000000000000000000000000000;
z = (z * w) / FIXED_1; // add y^11 / 11 - y^12 / 12
res +=
(z * (0x089d89d89d89d89d89d89d89d89d89d89 - y)) /
0x700000000000000000000000000000000;
z = (z * w) / FIXED_1; // add y^13 / 13 - y^14 / 14
res +=
(z * (0x088888888888888888888888888888888 - y)) /
0x800000000000000000000000000000000; // add y^15 / 15 - y^16 / 16
return res;
}
/**
* @dev computes e ^ (x / FIXED_1) * FIXED_1
* input range: 0 <= x <= OPT_EXP_MAX_VAL - 1
* auto-generated via 'PrintFunctionOptimalExp.py'
* Detailed description:
* - Rewrite the input as a sum of binary exponents and a single residual r, as small as possible
* - The exponentiation of each binary exponent is given (pre-calculated)
* - The exponentiation of r is calculated via Taylor series for e^x, where x = r
* - The exponentiation of the input is calculated by multiplying the intermediate results above
* - For example: e^5.521692859 = e^(4 + 1 + 0.5 + 0.021692859) = e^4 * e^1 * e^0.5 * e^0.021692859
*/
function optimalExp(uint256 x) internal pure returns (uint256) {
uint256 res = 0;
uint256 y;
uint256 z;
z = y = x % 0x10000000000000000000000000000000; // get the input modulo 2^(-3)
z = (z * y) / FIXED_1;
res += z * 0x10e1b3be415a0000; // add y^02 * (20! / 02!)
z = (z * y) / FIXED_1;
res += z * 0x05a0913f6b1e0000; // add y^03 * (20! / 03!)
z = (z * y) / FIXED_1;
res += z * 0x0168244fdac78000; // add y^04 * (20! / 04!)
z = (z * y) / FIXED_1;
res += z * 0x004807432bc18000; // add y^05 * (20! / 05!)
z = (z * y) / FIXED_1;
res += z * 0x000c0135dca04000; // add y^06 * (20! / 06!)
z = (z * y) / FIXED_1;
res += z * 0x0001b707b1cdc000; // add y^07 * (20! / 07!)
z = (z * y) / FIXED_1;
res += z * 0x000036e0f639b800; // add y^08 * (20! / 08!)
z = (z * y) / FIXED_1;
res += z * 0x00000618fee9f800; // add y^09 * (20! / 09!)
z = (z * y) / FIXED_1;
res += z * 0x0000009c197dcc00; // add y^10 * (20! / 10!)
z = (z * y) / FIXED_1;
res += z * 0x0000000e30dce400; // add y^11 * (20! / 11!)
z = (z * y) / FIXED_1;
res += z * 0x000000012ebd1300; // add y^12 * (20! / 12!)
z = (z * y) / FIXED_1;
res += z * 0x0000000017499f00; // add y^13 * (20! / 13!)
z = (z * y) / FIXED_1;
res += z * 0x0000000001a9d480; // add y^14 * (20! / 14!)
z = (z * y) / FIXED_1;
res += z * 0x00000000001c6380; // add y^15 * (20! / 15!)
z = (z * y) / FIXED_1;
res += z * 0x000000000001c638; // add y^16 * (20! / 16!)
z = (z * y) / FIXED_1;
res += z * 0x0000000000001ab8; // add y^17 * (20! / 17!)
z = (z * y) / FIXED_1;
res += z * 0x000000000000017c; // add y^18 * (20! / 18!)
z = (z * y) / FIXED_1;
res += z * 0x0000000000000014; // add y^19 * (20! / 19!)
z = (z * y) / FIXED_1;
res += z * 0x0000000000000001; // add y^20 * (20! / 20!)
res = res / 0x21c3677c82b40000 + y + FIXED_1; // divide by 20! and then add y^1 / 1! + y^0 / 0!
if ((x & 0x010000000000000000000000000000000) != 0)
res =
(res * 0x1c3d6a24ed82218787d624d3e5eba95f9) /
0x18ebef9eac820ae8682b9793ac6d1e776; // multiply by e^2^(-3)
if ((x & 0x020000000000000000000000000000000) != 0)
res =
(res * 0x18ebef9eac820ae8682b9793ac6d1e778) /
0x1368b2fc6f9609fe7aceb46aa619baed4; // multiply by e^2^(-2)
if ((x & 0x040000000000000000000000000000000) != 0)
res =
(res * 0x1368b2fc6f9609fe7aceb46aa619baed5) /
0x0bc5ab1b16779be3575bd8f0520a9f21f; // multiply by e^2^(-1)
if ((x & 0x080000000000000000000000000000000) != 0)
res =
(res * 0x0bc5ab1b16779be3575bd8f0520a9f21e) /
0x0454aaa8efe072e7f6ddbab84b40a55c9; // multiply by e^2^(+0)
if ((x & 0x100000000000000000000000000000000) != 0)
res =
(res * 0x0454aaa8efe072e7f6ddbab84b40a55c5) /
0x00960aadc109e7a3bf4578099615711ea; // multiply by e^2^(+1)
if ((x & 0x200000000000000000000000000000000) != 0)
res =
(res * 0x00960aadc109e7a3bf4578099615711d7) /
0x0002bf84208204f5977f9a8cf01fdce3d; // multiply by e^2^(+2)
if ((x & 0x400000000000000000000000000000000) != 0)
res =
(res * 0x0002bf84208204f5977f9a8cf01fdc307) /
0x0000003c6ab775dd0b95b4cbee7e65d11; // multiply by e^2^(+3)
return res;
}
/**
* @dev computes W(x / FIXED_1) / (x / FIXED_1) * FIXED_1
*/
function lowerStake(uint256 _x) internal view returns (uint256 pos) {
if (_x <= LAMBERT_CONV_RADIUS) return pos = lambertPos1(_x);
if (_x <= LAMBERT_POS2_MAXVAL) return pos = lambertPos2(_x);
if (_x <= LAMBERT_POS3_MAXVAL) return pos = lambertPos3(_x);
require(false);
}
/**
* @dev computes W(-x / FIXED_1) / (-x / FIXED_1) * FIXED_1
*/
function higherStake(uint256 _x) internal pure returns (uint256) {
if (_x <= LAMBERT_CONV_RADIUS) return lambertNeg1(_x);
return (FIXED_1 * FIXED_1) / _x;
}
/**
* @dev computes W(x / FIXED_1) / (x / FIXED_1) * FIXED_1
* input range: 1 <= x <= 1 / e * FIXED_1
* auto-generated via 'PrintFunctionLambertPos1.py'
*/
function lambertPos1(uint256 _x) internal pure returns (uint256) {
uint256 xi = _x;
uint256 res = (FIXED_1 - _x) * 0xde1bc4d19efcac82445da75b00000000; // x^(1-1) * (34! * 1^(1-1) / 1!) - x^(2-1) * (34! * 2^(2-1) / 2!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x00000000014d29a73a6e7b02c3668c7b0880000000; // add x^(03-1) * (34! * 03^(03-1) / 03!)
xi = (xi * _x) / FIXED_1;
res -= xi * 0x0000000002504a0cd9a7f7215b60f9be4800000000; // sub x^(04-1) * (34! * 04^(04-1) / 04!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x000000000484d0a1191c0ead267967c7a4a0000000; // add x^(05-1) * (34! * 05^(05-1) / 05!)
xi = (xi * _x) / FIXED_1;
res -= xi * 0x00000000095ec580d7e8427a4baf26a90a00000000; // sub x^(06-1) * (34! * 06^(06-1) / 06!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x000000001440b0be1615a47dba6e5b3b1f10000000; // add x^(07-1) * (34! * 07^(07-1) / 07!)
xi = (xi * _x) / FIXED_1;
res -= xi * 0x000000002d207601f46a99b4112418400000000000; // sub x^(08-1) * (34! * 08^(08-1) / 08!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x0000000066ebaac4c37c622dd8288a7eb1b2000000; // add x^(09-1) * (34! * 09^(09-1) / 09!)
xi = (xi * _x) / FIXED_1;
res -= xi * 0x00000000ef17240135f7dbd43a1ba10cf200000000; // sub x^(10-1) * (34! * 10^(10-1) / 10!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x0000000233c33c676a5eb2416094a87b3657000000; // add x^(11-1) * (34! * 11^(11-1) / 11!)
xi = (xi * _x) / FIXED_1;
res -= xi * 0x0000000541cde48bc0254bed49a9f8700000000000; // sub x^(12-1) * (34! * 12^(12-1) / 12!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x0000000cae1fad2cdd4d4cb8d73abca0d19a400000; // add x^(13-1) * (34! * 13^(13-1) / 13!)
xi = (xi * _x) / FIXED_1;
res -= xi * 0x0000001edb2aa2f760d15c41ceedba956400000000; // sub x^(14-1) * (34! * 14^(14-1) / 14!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x0000004ba8d20d2dabd386c9529659841a2e200000; // add x^(15-1) * (34! * 15^(15-1) / 15!)
xi = (xi * _x) / FIXED_1;
res -= xi * 0x000000bac08546b867cdaa20000000000000000000; // sub x^(16-1) * (34! * 16^(16-1) / 16!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x000001cfa8e70c03625b9db76c8ebf5bbf24820000; // add x^(17-1) * (34! * 17^(17-1) / 17!)
xi = (xi * _x) / FIXED_1;
res -= xi * 0x000004851d99f82060df265f3309b26f8200000000; // sub x^(18-1) * (34! * 18^(18-1) / 18!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x00000b550d19b129d270c44f6f55f027723cbb0000; // add x^(19-1) * (34! * 19^(19-1) / 19!)
xi = (xi * _x) / FIXED_1;
res -= xi * 0x00001c877dadc761dc272deb65d4b0000000000000; // sub x^(20-1) * (34! * 20^(20-1) / 20!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x000048178ece97479f33a77f2ad22a81b64406c000; // add x^(21-1) * (34! * 21^(21-1) / 21!)
xi = (xi * _x) / FIXED_1;
res -= xi * 0x0000b6ca8268b9d810fedf6695ef2f8a6c00000000; // sub x^(22-1) * (34! * 22^(22-1) / 22!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x0001d0e76631a5b05d007b8cb72a7c7f11ec36e000; // add x^(23-1) * (34! * 23^(23-1) / 23!)
xi = (xi * _x) / FIXED_1;
res -= xi * 0x0004a1c37bd9f85fd9c6c780000000000000000000; // sub x^(24-1) * (34! * 24^(24-1) / 24!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x000bd8369f1b702bf491e2ebfcee08250313b65400; // add x^(25-1) * (34! * 25^(25-1) / 25!)
xi = (xi * _x) / FIXED_1;
res -= xi * 0x001e5c7c32a9f6c70ab2cb59d9225764d400000000; // sub x^(26-1) * (34! * 26^(26-1) / 26!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x004dff5820e165e910f95120a708e742496221e600; // add x^(27-1) * (34! * 27^(27-1) / 27!)
xi = (xi * _x) / FIXED_1;
res -= xi * 0x00c8c8f66db1fced378ee50e536000000000000000; // sub x^(28-1) * (34! * 28^(28-1) / 28!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x0205db8dffff45bfa2938f128f599dbf16eb11d880; // add x^(29-1) * (34! * 29^(29-1) / 29!)
xi = (xi * _x) / FIXED_1;
res -= xi * 0x053a044ebd984351493e1786af38d39a0800000000; // sub x^(30-1) * (34! * 30^(30-1) / 30!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x0d86dae2a4cc0f47633a544479735869b487b59c40; // add x^(31-1) * (34! * 31^(31-1) / 31!)
xi = (xi * _x) / FIXED_1;
res -= xi * 0x231000000000000000000000000000000000000000; // sub x^(32-1) * (34! * 32^(32-1) / 32!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x5b0485a76f6646c2039db1507cdd51b08649680822; // add x^(33-1) * (34! * 33^(33-1) / 33!)
xi = (xi * _x) / FIXED_1;
res -= xi * 0xec983c46c49545bc17efa6b5b0055e242200000000; // sub x^(34-1) * (34! * 34^(34-1) / 34!)
return res / 0xde1bc4d19efcac82445da75b00000000; // divide by 34!
}
/**
* @dev computes W(x / FIXED_1) / (x / FIXED_1) * FIXED_1
* input range: LAMBERT_CONV_RADIUS + 1 <= x <= LAMBERT_POS2_MAXVAL
*/
function lambertPos2(uint256 _x) internal view returns (uint256) {
uint256 x = _x - LAMBERT_CONV_RADIUS - 1;
uint256 i = x / LAMBERT_POS2_SAMPLE;
uint256 a = LAMBERT_POS2_SAMPLE * i;
uint256 b = LAMBERT_POS2_SAMPLE * (i + 1);
uint256 c = lambertArray[i];
uint256 d = lambertArray[i + 1];
return (c * (b - x) + d * (x - a)) / LAMBERT_POS2_SAMPLE;
}
/**
* @dev computes W(x / FIXED_1) / (x / FIXED_1) * FIXED_1
* input range: LAMBERT_POS2_MAXVAL + 1 <= x <= LAMBERT_POS3_MAXVAL
*/
function lambertPos3(uint256 _x) internal pure returns (uint256) {
uint256 l1 = _x < OPT_LOG_MAX_VAL ? optimalLog(_x) : generalLog(_x);
uint256 l2 = l1 < OPT_LOG_MAX_VAL ? optimalLog(l1) : generalLog(l1);
return ((l1 - l2 + (l2 * FIXED_1) / l1) * FIXED_1) / _x;
}
/**
* @dev computes W(-x / FIXED_1) / (-x / FIXED_1) * FIXED_1
* input range: 1 <= x <= 1 / e * FIXED_1
* auto-generated via 'PrintFunctionLambertNeg1.py'
*/
function lambertNeg1(uint256 _x) internal pure returns (uint256) {
uint256 xi = _x;
uint256 res = 0;
xi = (xi * _x) / FIXED_1;
res += xi * 0x00000000014d29a73a6e7b02c3668c7b0880000000; // add x^(03-1) * (34! * 03^(03-1) / 03!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x0000000002504a0cd9a7f7215b60f9be4800000000; // add x^(04-1) * (34! * 04^(04-1) / 04!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x000000000484d0a1191c0ead267967c7a4a0000000; // add x^(05-1) * (34! * 05^(05-1) / 05!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x00000000095ec580d7e8427a4baf26a90a00000000; // add x^(06-1) * (34! * 06^(06-1) / 06!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x000000001440b0be1615a47dba6e5b3b1f10000000; // add x^(07-1) * (34! * 07^(07-1) / 07!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x000000002d207601f46a99b4112418400000000000; // add x^(08-1) * (34! * 08^(08-1) / 08!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x0000000066ebaac4c37c622dd8288a7eb1b2000000; // add x^(09-1) * (34! * 09^(09-1) / 09!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x00000000ef17240135f7dbd43a1ba10cf200000000; // add x^(10-1) * (34! * 10^(10-1) / 10!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x0000000233c33c676a5eb2416094a87b3657000000; // add x^(11-1) * (34! * 11^(11-1) / 11!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x0000000541cde48bc0254bed49a9f8700000000000; // add x^(12-1) * (34! * 12^(12-1) / 12!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x0000000cae1fad2cdd4d4cb8d73abca0d19a400000; // add x^(13-1) * (34! * 13^(13-1) / 13!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x0000001edb2aa2f760d15c41ceedba956400000000; // add x^(14-1) * (34! * 14^(14-1) / 14!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x0000004ba8d20d2dabd386c9529659841a2e200000; // add x^(15-1) * (34! * 15^(15-1) / 15!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x000000bac08546b867cdaa20000000000000000000; // add x^(16-1) * (34! * 16^(16-1) / 16!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x000001cfa8e70c03625b9db76c8ebf5bbf24820000; // add x^(17-1) * (34! * 17^(17-1) / 17!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x000004851d99f82060df265f3309b26f8200000000; // add x^(18-1) * (34! * 18^(18-1) / 18!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x00000b550d19b129d270c44f6f55f027723cbb0000; // add x^(19-1) * (34! * 19^(19-1) / 19!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x00001c877dadc761dc272deb65d4b0000000000000; // add x^(20-1) * (34! * 20^(20-1) / 20!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x000048178ece97479f33a77f2ad22a81b64406c000; // add x^(21-1) * (34! * 21^(21-1) / 21!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x0000b6ca8268b9d810fedf6695ef2f8a6c00000000; // add x^(22-1) * (34! * 22^(22-1) / 22!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x0001d0e76631a5b05d007b8cb72a7c7f11ec36e000; // add x^(23-1) * (34! * 23^(23-1) / 23!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x0004a1c37bd9f85fd9c6c780000000000000000000; // add x^(24-1) * (34! * 24^(24-1) / 24!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x000bd8369f1b702bf491e2ebfcee08250313b65400; // add x^(25-1) * (34! * 25^(25-1) / 25!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x001e5c7c32a9f6c70ab2cb59d9225764d400000000; // add x^(26-1) * (34! * 26^(26-1) / 26!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x004dff5820e165e910f95120a708e742496221e600; // add x^(27-1) * (34! * 27^(27-1) / 27!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x00c8c8f66db1fced378ee50e536000000000000000; // add x^(28-1) * (34! * 28^(28-1) / 28!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x0205db8dffff45bfa2938f128f599dbf16eb11d880; // add x^(29-1) * (34! * 29^(29-1) / 29!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x053a044ebd984351493e1786af38d39a0800000000; // add x^(30-1) * (34! * 30^(30-1) / 30!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x0d86dae2a4cc0f47633a544479735869b487b59c40; // add x^(31-1) * (34! * 31^(31-1) / 31!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x231000000000000000000000000000000000000000; // add x^(32-1) * (34! * 32^(32-1) / 32!)
xi = (xi * _x) / FIXED_1;
res += xi * 0x5b0485a76f6646c2039db1507cdd51b08649680822; // add x^(33-1) * (34! * 33^(33-1) / 33!)
xi = (xi * _x) / FIXED_1;
res += xi * 0xec983c46c49545bc17efa6b5b0055e242200000000; // add x^(34-1) * (34! * 34^(34-1) / 34!)
return res / 0xde1bc4d19efcac82445da75b00000000 + _x + FIXED_1; // divide by 34! and then add x^(2-1) * (34! * 2^(2-1) / 2!) + x^(1-1) * (34! * 1^(1-1) / 1!)
}
/**
* @dev computes the weights based on "W(log(hi / lo) * tq / rp) * tq / rp", where "W" is a variation of the Lambert W function.
*/
function balancedWeightsByStake(
uint256 _hi,
uint256 _lo,
uint256 _tq,
uint256 _rp,
bool _lowerStake
) public view returns (uint32, uint32) {
(_tq, _rp) = safeFactors(_tq, _rp);
uint256 f = _hi.mul(FIXED_1) / _lo;
uint256 g = f < OPT_LOG_MAX_VAL ? optimalLog(f) : generalLog(f);
uint256 x = g.mul(_tq) / _rp;
uint256 y = _lowerStake ? lowerStake(x) : higherStake(x);
return normalizedWeights(y.mul(_tq), _rp.mul(FIXED_1));
}
/**
* @dev reduces "a" and "b" while maintaining their ratio.
*/
function safeFactors(uint256 _a, uint256 _b)
public
pure
returns (uint256, uint256)
{
if (_a <= FIXED_2 && _b <= FIXED_2) return (_a, _b);
if (_a < FIXED_2) return ((_a * FIXED_2) / _b, FIXED_2);
if (_b < FIXED_2) return (FIXED_2, (_b * FIXED_2) / _a);
uint256 c = _a > _b ? _a : _b;
uint256 n = floorLog2(c / FIXED_1);
return (_a >> n, _b >> n);
}
/**
* @dev computes "MAX_WEIGHT * a / (a + b)" and "MAX_WEIGHT * b / (a + b)".
*/
function normalizedWeights(uint256 _a, uint256 _b)
public
pure
returns (uint32, uint32)
{
if (_a <= _b) return accurateWeights(_a, _b);
(uint32 y, uint32 x) = accurateWeights(_b, _a);
return (x, y);
}
/**
* @dev computes "MAX_WEIGHT * a / (a + b)" and "MAX_WEIGHT * b / (a + b)", assuming that "a <= b".
*/
function accurateWeights(uint256 _a, uint256 _b)
public
pure
returns (uint32, uint32)
{
if (_a > MAX_UNF_WEIGHT) {
uint256 c = _a / (MAX_UNF_WEIGHT + 1) + 1;
_a /= c;
_b /= c;
}
uint256 x = roundDiv(_a * MAX_WEIGHT, _a.add(_b));
uint256 y = MAX_WEIGHT - x;
return (uint32(x), uint32(y));
}
/**
* @dev computes the nearest integer to a given quotient without overflowing or underflowing.
*/
function roundDiv(uint256 _n, uint256 _d) internal pure returns (uint256) {
return _n / _d + (_n % _d) / (_d - _d / 2);
}
}
Contract ABI
[{"type":"constructor","stateMutability":"nonpayable","inputs":[{"type":"uint256","name":"_reserveRatio","internalType":"uint256"},{"type":"address","name":"_reserveTokenAddress","internalType":"address"}]},{"type":"event","name":"Approval","inputs":[{"type":"address","name":"owner","internalType":"address","indexed":true},{"type":"address","name":"spender","internalType":"address","indexed":true},{"type":"uint256","name":"value","internalType":"uint256","indexed":false}],"anonymous":false},{"type":"event","name":"ContinuousBurn","inputs":[{"type":"address","name":"_address","internalType":"address","indexed":false},{"type":"uint256","name":"continuousTokenAmount","internalType":"uint256","indexed":false},{"type":"uint256","name":"reserveTokenAmount","internalType":"uint256","indexed":false}],"anonymous":false},{"type":"event","name":"ContinuousMint","inputs":[{"type":"address","name":"_address","internalType":"address","indexed":false},{"type":"uint256","name":"reserveTokenAmount","internalType":"uint256","indexed":false},{"type":"uint256","name":"continuousTokenAmount","internalType":"uint256","indexed":false}],"anonymous":false},{"type":"event","name":"Transfer","inputs":[{"type":"address","name":"from","internalType":"address","indexed":true},{"type":"address","name":"to","internalType":"address","indexed":true},{"type":"uint256","name":"value","internalType":"uint256","indexed":false}],"anonymous":false},{"type":"function","stateMutability":"pure","outputs":[{"type":"uint32","name":"","internalType":"uint32"},{"type":"uint32","name":"","internalType":"uint32"}],"name":"accurateWeights","inputs":[{"type":"uint256","name":"_a","internalType":"uint256"},{"type":"uint256","name":"_b","internalType":"uint256"}]},{"type":"function","stateMutability":"view","outputs":[{"type":"uint256","name":"","internalType":"uint256"}],"name":"allowance","inputs":[{"type":"address","name":"owner","internalType":"address"},{"type":"address","name":"spender","internalType":"address"}]},{"type":"function","stateMutability":"nonpayable","outputs":[{"type":"bool","name":"","internalType":"bool"}],"name":"approve","inputs":[{"type":"address","name":"spender","internalType":"address"},{"type":"uint256","name":"amount","internalType":"uint256"}]},{"type":"function","stateMutability":"view","outputs":[{"type":"uint256","name":"","internalType":"uint256"}],"name":"balanceOf","inputs":[{"type":"address","name":"account","internalType":"address"}]},{"type":"function","stateMutability":"view","outputs":[{"type":"uint32","name":"","internalType":"uint32"},{"type":"uint32","name":"","internalType":"uint32"}],"name":"balancedWeights","inputs":[{"type":"uint256","name":"_primaryReserveStakedBalance","internalType":"uint256"},{"type":"uint256","name":"_primaryReserveBalance","internalType":"uint256"},{"type":"uint256","name":"_secondaryReserveBalance","internalType":"uint256"},{"type":"uint256","name":"_reserveRateNumerator","internalType":"uint256"},{"type":"uint256","name":"_reserveRateDenominator","internalType":"uint256"}]},{"type":"function","stateMutability":"view","outputs":[{"type":"uint32","name":"","internalType":"uint32"},{"type":"uint32","name":"","internalType":"uint32"}],"name":"balancedWeightsByStake","inputs":[{"type":"uint256","name":"_hi","internalType":"uint256"},{"type":"uint256","name":"_lo","internalType":"uint256"},{"type":"uint256","name":"_tq","internalType":"uint256"},{"type":"uint256","name":"_rp","internalType":"uint256"},{"type":"bool","name":"_lowerStake","internalType":"bool"}]},{"type":"function","stateMutability":"nonpayable","outputs":[],"name":"burn","inputs":[{"type":"uint256","name":"_amount","internalType":"uint256"}]},{"type":"function","stateMutability":"view","outputs":[{"type":"uint256","name":"burnAmount","internalType":"uint256"}],"name":"calculateContinuousBurnReturn","inputs":[{"type":"uint256","name":"_amount","internalType":"uint256"}]},{"type":"function","stateMutability":"view","outputs":[{"type":"uint256","name":"mintAmount","internalType":"uint256"}],"name":"calculateContinuousMintReturn","inputs":[{"type":"uint256","name":"_amount","internalType":"uint256"}]},{"type":"function","stateMutability":"view","outputs":[{"type":"uint256","name":"","internalType":"uint256"}],"name":"crossReserveTargetAmount","inputs":[{"type":"uint256","name":"_sourceReserveBalance","internalType":"uint256"},{"type":"uint32","name":"_sourceReserveWeight","internalType":"uint32"},{"type":"uint256","name":"_targetReserveBalance","internalType":"uint256"},{"type":"uint32","name":"_targetReserveWeight","internalType":"uint32"},{"type":"uint256","name":"_amount","internalType":"uint256"}]},{"type":"function","stateMutability":"view","outputs":[{"type":"uint8","name":"","internalType":"uint8"}],"name":"decimals","inputs":[]},{"type":"function","stateMutability":"nonpayable","outputs":[{"type":"bool","name":"","internalType":"bool"}],"name":"decreaseAllowance","inputs":[{"type":"address","name":"spender","internalType":"address"},{"type":"uint256","name":"subtractedValue","internalType":"uint256"}]},{"type":"function","stateMutability":"view","outputs":[{"type":"uint256","name":"","internalType":"uint256"}],"name":"fundCost","inputs":[{"type":"uint256","name":"_supply","internalType":"uint256"},{"type":"uint256","name":"_reserveBalance","internalType":"uint256"},{"type":"uint32","name":"_reserveRatio","internalType":"uint32"},{"type":"uint256","name":"_amount","internalType":"uint256"}]},{"type":"function","stateMutability":"view","outputs":[{"type":"uint256","name":"","internalType":"uint256"}],"name":"fundSupplyAmount","inputs":[{"type":"uint256","name":"_supply","internalType":"uint256"},{"type":"uint256","name":"_reserveBalance","internalType":"uint256"},{"type":"uint32","name":"_reserveRatio","internalType":"uint32"},{"type":"uint256","name":"_amount","internalType":"uint256"}]},{"type":"function","stateMutability":"nonpayable","outputs":[{"type":"bool","name":"","internalType":"bool"}],"name":"increaseAllowance","inputs":[{"type":"address","name":"spender","internalType":"address"},{"type":"uint256","name":"addedValue","internalType":"uint256"}]},{"type":"function","stateMutability":"nonpayable","outputs":[],"name":"init","inputs":[]},{"type":"function","stateMutability":"nonpayable","outputs":[],"name":"initLambertArray","inputs":[]},{"type":"function","stateMutability":"nonpayable","outputs":[],"name":"initMaxExpArray","inputs":[]},{"type":"function","stateMutability":"view","outputs":[{"type":"uint256","name":"","internalType":"uint256"}],"name":"liquidateReserveAmount","inputs":[{"type":"uint256","name":"_supply","internalType":"uint256"},{"type":"uint256","name":"_reserveBalance","internalType":"uint256"},{"type":"uint32","name":"_reserveRatio","internalType":"uint32"},{"type":"uint256","name":"_amount","internalType":"uint256"}]},{"type":"function","stateMutability":"nonpayable","outputs":[{"type":"uint256","name":"_amountMinted","internalType":"uint256"}],"name":"mint","inputs":[{"type":"uint256","name":"_amount","internalType":"uint256"}]},{"type":"function","stateMutability":"view","outputs":[{"type":"string","name":"","internalType":"string"}],"name":"name","inputs":[]},{"type":"function","stateMutability":"pure","outputs":[{"type":"uint32","name":"","internalType":"uint32"},{"type":"uint32","name":"","internalType":"uint32"}],"name":"normalizedWeights","inputs":[{"type":"uint256","name":"_a","internalType":"uint256"},{"type":"uint256","name":"_b","internalType":"uint256"}]},{"type":"function","stateMutability":"view","outputs":[{"type":"uint256","name":"","internalType":"uint256"},{"type":"uint8","name":"","internalType":"uint8"}],"name":"power","inputs":[{"type":"uint256","name":"_baseN","internalType":"uint256"},{"type":"uint256","name":"_baseD","internalType":"uint256"},{"type":"uint32","name":"_expN","internalType":"uint32"},{"type":"uint32","name":"_expD","internalType":"uint32"}]},{"type":"function","stateMutability":"view","outputs":[{"type":"uint256","name":"","internalType":"uint256"}],"name":"purchaseTargetAmount","inputs":[{"type":"uint256","name":"_supply","internalType":"uint256"},{"type":"uint256","name":"_reserveBalance","internalType":"uint256"},{"type":"uint32","name":"_reserveWeight","internalType":"uint32"},{"type":"uint256","name":"_amount","internalType":"uint256"}]},{"type":"function","stateMutability":"view","outputs":[{"type":"uint256","name":"","internalType":"uint256"}],"name":"reserveBalance","inputs":[]},{"type":"function","stateMutability":"view","outputs":[{"type":"uint256","name":"","internalType":"uint256"}],"name":"reserveRatio","inputs":[]},{"type":"function","stateMutability":"view","outputs":[{"type":"address","name":"","internalType":"address"}],"name":"reserveTokenAddress","inputs":[]},{"type":"function","stateMutability":"pure","outputs":[{"type":"uint256","name":"","internalType":"uint256"},{"type":"uint256","name":"","internalType":"uint256"}],"name":"safeFactors","inputs":[{"type":"uint256","name":"_a","internalType":"uint256"},{"type":"uint256","name":"_b","internalType":"uint256"}]},{"type":"function","stateMutability":"view","outputs":[{"type":"uint256","name":"","internalType":"uint256"}],"name":"saleTargetAmount","inputs":[{"type":"uint256","name":"_supply","internalType":"uint256"},{"type":"uint256","name":"_reserveBalance","internalType":"uint256"},{"type":"uint32","name":"_reserveWeight","internalType":"uint32"},{"type":"uint256","name":"_amount","internalType":"uint256"}]},{"type":"function","stateMutability":"view","outputs":[{"type":"uint256","name":"","internalType":"uint256"}],"name":"scale","inputs":[]},{"type":"function","stateMutability":"view","outputs":[{"type":"string","name":"","internalType":"string"}],"name":"symbol","inputs":[]},{"type":"function","stateMutability":"view","outputs":[{"type":"uint256","name":"","internalType":"uint256"}],"name":"totalSupply","inputs":[]},{"type":"function","stateMutability":"nonpayable","outputs":[{"type":"bool","name":"","internalType":"bool"}],"name":"transfer","inputs":[{"type":"address","name":"recipient","internalType":"address"},{"type":"uint256","name":"amount","internalType":"uint256"}]},{"type":"function","stateMutability":"nonpayable","outputs":[{"type":"bool","name":"","internalType":"bool"}],"name":"transferFrom","inputs":[{"type":"address","name":"sender","internalType":"address"},{"type":"address","name":"recipient","internalType":"address"},{"type":"uint256","name":"amount","internalType":"uint256"}]}]
Contract Creation Code
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